LMFDB - Embedded newform 14.13.d.a.3.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [14,13,Mod(3,14)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(14, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 13, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("14.3");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	14.d (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.7959134419$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 527434 x^{14} - 31307480 x^{13} + 193554267483 x^{12} - 12267558721140 x^{11} + \cdots + 73\!\cdots\!36 $ x^16 + 527434x^14 - 31307480x^13 + 193554267483x^12 - 12267558721140x^11 + 36740634631350658x^10 - 2684653740993140180x^9 + 5051027688394458110177x^8 - 329042050982173184619740x^7 + 328571000441888143595366884x^6 - 20799163177686535050419379920x^5 + 15169931128056380497155715556632x^4 - 685746033739471361446313307383040x^3 + 159607415711477686151635843287775328x^2 + 6015487435743293961505549572273215360x + 735121207672317095821497912841120438336
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{48}\cdot 3^{8}\cdot 7^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			3.3
Root			$127.460 + 220.767i$ of defining polynomial
Character	$\chi$	$=$	14.3
Dual form			14.13.d.a.5.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-22.6274 - 39.1918i) q^{2} +(702.607 + 405.650i) q^{3} +(-1024.00 + 1773.62i) q^{4} +(-18305.2 + 10568.5i) q^{5} -36715.3i q^{6} +(-9080.55 - 117298. i) q^{7} +92681.9 q^{8} +(63384.0 + 109784. i) q^{9} +O(q^{10})$	\(q+(-22.6274 - 39.1918i) q^{2} +(702.607 + 405.650i) q^{3} +(-1024.00 + 1773.62i) q^{4} +(-18305.2 + 10568.5i) q^{5} -36715.3i q^{6} +(-9080.55 - 117298. i) q^{7} +92681.9 q^{8} +(63384.0 + 109784. i) q^{9} +(828399. + 478276. i) q^{10} +(651539. - 1.12850e6i) q^{11} +(-1.43894e6 + 830772. i) q^{12} -7.09849e6i q^{13} +(-4.39166e6 + 3.01003e6i) q^{14} -1.71485e7 q^{15} +(-2.09715e6 - 3.63237e6i) q^{16} +(-2.79240e7 - 1.61219e7i) q^{17} +(2.86843e6 - 4.96827e6i) q^{18} +(-2.32303e7 + 1.34120e7i) q^{19} -4.32886e7i q^{20} +(4.12019e7 - 8.60980e7i) q^{21} -5.89706e7 q^{22} +(6.22412e7 + 1.07805e8i) q^{23} +(6.51190e7 + 3.75965e7i) q^{24} +(1.01317e8 - 1.75486e8i) q^{25} +(-2.78203e8 + 1.60621e8i) q^{26} -3.28312e8i q^{27} +(2.17341e8 + 1.04008e8i) q^{28} -7.52793e8 q^{29} +(3.88026e8 + 6.72081e8i) q^{30} +(9.46508e8 + 5.46467e8i) q^{31} +(-9.49063e7 + 1.64382e8i) q^{32} +(9.15552e8 - 5.28594e8i) q^{33} +1.45919e9i q^{34} +(1.40589e9 + 2.05120e9i) q^{35} -2.59621e8 q^{36} +(-1.93585e9 - 3.35299e9i) q^{37} +(1.05129e9 + 6.06960e8i) q^{38} +(2.87951e9 - 4.98745e9i) q^{39} +(-1.69656e9 + 9.79510e8i) q^{40} +2.55800e9i q^{41} +(-4.30663e9 + 3.33395e8i) q^{42} -4.36133e9 q^{43} +(1.33435e9 + 2.31116e9i) q^{44} +(-2.32051e9 - 1.33975e9i) q^{45} +(2.81672e9 - 4.87869e9i) q^{46} +(8.04169e9 - 4.64287e9i) q^{47} -3.40284e9i q^{48} +(-1.36764e10 + 2.13026e9i) q^{49} -9.17013e9 q^{50} +(-1.30797e10 - 2.26548e10i) q^{51} +(1.25900e10 + 7.26886e9i) q^{52} +(-1.09179e8 + 1.89104e8i) q^{53} +(-1.28671e10 + 7.42884e9i) q^{54} +2.75432e10i q^{55} +(-8.41602e8 - 1.08714e10i) q^{56} -2.17624e10 q^{57} +(1.70338e10 + 2.95033e10i) q^{58} +(5.45224e10 + 3.14785e10i) q^{59} +(1.75600e10 - 3.04149e10i) q^{60} +(4.19753e10 - 2.42344e10i) q^{61} -4.94605e10i q^{62} +(1.23019e10 - 8.43172e9i) q^{63} +8.58993e9 q^{64} +(7.50205e10 + 1.29939e11i) q^{65} +(-4.14331e10 - 2.39214e10i) q^{66} +(-5.49220e10 + 9.51277e10i) q^{67} +(5.71884e10 - 3.30177e10i) q^{68} +1.00993e11i q^{69} +(4.85786e10 - 1.01513e11i) q^{70} -7.43754e10 q^{71} +(5.87455e9 + 1.01750e10i) q^{72} +(-2.26320e11 - 1.30666e11i) q^{73} +(-8.76065e10 + 1.51739e11i) q^{74} +(1.42372e11 - 8.21982e10i) q^{75} -5.49357e10i q^{76} +(-1.38287e11 - 6.61769e10i) q^{77} -2.60623e11 q^{78} +(-1.20639e11 - 2.08953e11i) q^{79} +(7.67776e10 + 4.43276e10i) q^{80} +(1.66865e11 - 2.89018e11i) q^{81} +(1.00253e11 - 5.78810e10i) q^{82} +2.09983e11i q^{83} +(1.10514e11 + 1.61241e11i) q^{84} +6.81540e11 q^{85} +(9.86855e10 + 1.70928e11i) q^{86} +(-5.28918e11 - 3.05371e11i) q^{87} +(6.03859e10 - 1.04591e11i) q^{88} +(1.79050e10 - 1.03374e10i) q^{89} +1.21260e11i q^{90} +(-8.32640e11 + 6.44582e10i) q^{91} -2.54940e11 q^{92} +(4.43349e11 + 7.67903e11i) q^{93} +(-3.63926e11 - 2.10113e11i) q^{94} +(2.83491e11 - 4.91020e11i) q^{95} +(-1.33364e11 + 7.69975e10i) q^{96} -4.74911e11i q^{97} +(3.92950e11 + 4.87800e11i) q^{98} +1.65189e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16384 q^{4} + 18144 q^{5} - 469720 q^{7} + 2362248 q^{9}+O(q^{10}) $ 16 * q - 16384 * q^4 + 18144 * q^5 - 469720 * q^7 + 2362248 * q^9	\( 16 q - 16384 q^{4} + 18144 q^{5} - 469720 q^{7} + 2362248 q^{9} - 2290176 q^{10} + 2072088 q^{11} - 11501568 q^{14} - 27163728 q^{15} - 33554432 q^{16} - 101561040 q^{17} - 4592640 q^{18} + 174931848 q^{19} - 323731368 q^{21} + 62776320 q^{22} + 25630560 q^{23} + 242221056 q^{24} + 521205808 q^{25} - 1434682368 q^{26} + 350863360 q^{28} + 532360944 q^{29} - 2151917568 q^{30} + 4583818344 q^{31} + 6054957720 q^{33} - 1612540440 q^{35} - 9675767808 q^{36} + 5764524040 q^{37} - 149506560 q^{38} + 10526083272 q^{39} + 4690280448 q^{40} - 12685086720 q^{42} - 66929432000 q^{43} + 4243636224 q^{44} + 57253352184 q^{45} + 7203213312 q^{46} + 18116171640 q^{47} - 9977452064 q^{49} - 99248080896 q^{50} - 23299256376 q^{51} + 8269578240 q^{52} + 39134161800 q^{53} + 105152205312 q^{54} + 3623878656 q^{56} - 328243960080 q^{57} + 29637396480 q^{58} + 201845459088 q^{59} + 27815657472 q^{60} + 336780254328 q^{61} - 389095094520 q^{63} + 137438953472 q^{64} + 158322703896 q^{65} + 268884080640 q^{66} + 107767119920 q^{67} + 207997009920 q^{68} - 6077815296 q^{70} - 1150259029344 q^{71} - 9405726720 q^{72} - 738414283320 q^{73} + 4902778368 q^{74} + 1537028640000 q^{75} - 321203352960 q^{77} - 786088888320 q^{78} + 227632064768 q^{79} - 76101451776 q^{80} - 391984178400 q^{81} - 302578053120 q^{82} - 32685686784 q^{84} + 710209696080 q^{85} - 38105192448 q^{86} + 1957017683880 q^{87} - 64282951680 q^{88} - 2485007442792 q^{89} + 1803248333904 q^{91} - 104982773760 q^{92} - 458668768680 q^{93} - 2021298693120 q^{94} - 186503862960 q^{95} - 496068722688 q^{96} - 356371660800 q^{98} + 3921180354576 q^{99}+O(q^{100}) \) 16 * q - 16384 * q^4 + 18144 * q^5 - 469720 * q^7 + 2362248 * q^9 - 2290176 * q^10 + 2072088 * q^11 - 11501568 * q^14 - 27163728 * q^15 - 33554432 * q^16 - 101561040 * q^17 - 4592640 * q^18 + 174931848 * q^19 - 323731368 * q^21 + 62776320 * q^22 + 25630560 * q^23 + 242221056 * q^24 + 521205808 * q^25 - 1434682368 * q^26 + 350863360 * q^28 + 532360944 * q^29 - 2151917568 * q^30 + 4583818344 * q^31 + 6054957720 * q^33 - 1612540440 * q^35 - 9675767808 * q^36 + 5764524040 * q^37 - 149506560 * q^38 + 10526083272 * q^39 + 4690280448 * q^40 - 12685086720 * q^42 - 66929432000 * q^43 + 4243636224 * q^44 + 57253352184 * q^45 + 7203213312 * q^46 + 18116171640 * q^47 - 9977452064 * q^49 - 99248080896 * q^50 - 23299256376 * q^51 + 8269578240 * q^52 + 39134161800 * q^53 + 105152205312 * q^54 + 3623878656 * q^56 - 328243960080 * q^57 + 29637396480 * q^58 + 201845459088 * q^59 + 27815657472 * q^60 + 336780254328 * q^61 - 389095094520 * q^63 + 137438953472 * q^64 + 158322703896 * q^65 + 268884080640 * q^66 + 107767119920 * q^67 + 207997009920 * q^68 - 6077815296 * q^70 - 1150259029344 * q^71 - 9405726720 * q^72 - 738414283320 * q^73 + 4902778368 * q^74 + 1537028640000 * q^75 - 321203352960 * q^77 - 786088888320 * q^78 + 227632064768 * q^79 - 76101451776 * q^80 - 391984178400 * q^81 - 302578053120 * q^82 - 32685686784 * q^84 + 710209696080 * q^85 - 38105192448 * q^86 + 1957017683880 * q^87 - 64282951680 * q^88 - 2485007442792 * q^89 + 1803248333904 * q^91 - 104982773760 * q^92 - 458668768680 * q^93 - 2021298693120 * q^94 - 186503862960 * q^95 - 496068722688 * q^96 - 356371660800 * q^98 + 3921180354576 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−22.6274	−	39.1918i	−0.353553	−	0.612372i
$2$	−22.6274	−	39.1918i	−0.353553	−	0.612372i
$3$	702.607	+	405.650i	0.963796	+	0.556448i	0.897339	−	0.441342i	$-0.145497\pi$
$3$	702.607	+	405.650i	0.963796	+	0.556448i	0.0664566	+	0.997789i	$0.478831\pi$
$4$	−1024.00	+	1773.62i	−0.250000	+	0.433013i
$5$	−18305.2	+	10568.5i	−1.17153	+	0.676385i	−0.954041	−	0.299677i	$-0.903121\pi$
$5$	−18305.2	+	10568.5i	−1.17153	+	0.676385i	−0.217492	+	0.976062i	$0.569788\pi$
$6$		−	36715.3i		−	0.786936i
$7$	−9080.55	−	117298.i	−0.0771834	−	0.997017i
$7$	−9080.55	−	117298.i	−0.0771834	−	0.997017i
$8$	92681.9			0.353553
$9$	63384.0	+	109784.i	0.119268	+	0.206579i
$10$	828399.	+	478276.i	0.828399	+	0.478276i
$11$	651539.	−	1.12850e6i	0.367777	−	0.637008i	−0.621441	−	0.783461i	$-0.713452\pi$
$11$	651539.	−	1.12850e6i	0.367777	−	0.637008i	0.989218	+	0.146453i	$0.0467857\pi$
$12$	−1.43894e6	+	830772.i	−0.481898	+	0.278224i
$13$		−	7.09849e6i		−	1.47064i	−0.677720	−	0.735320i	$-0.737032\pi$
$13$		−	7.09849e6i		−	1.47064i	0.677720	−	0.735320i	$-0.262968\pi$
$14$	−4.39166e6	+	3.01003e6i	−0.583257	+	0.399764i
$15$	−1.71485e7			−1.50549
$16$	−2.09715e6	−	3.63237e6i	−0.125000	−	0.216506i
$17$	−2.79240e7	−	1.61219e7i	−1.15687	−	0.667919i	−0.206318	−	0.978485i	$-0.566148\pi$
$17$	−2.79240e7	−	1.61219e7i	−1.15687	−	0.667919i	−0.950552	+	0.310566i	$0.899481\pi$
$18$	2.86843e6	−	4.96827e6i	0.0843353	−	0.146073i
$19$	−2.32303e7	+	1.34120e7i	−0.493780	+	0.285084i	−0.726141	−	0.687545i	$-0.758688\pi$
$19$	−2.32303e7	+	1.34120e7i	−0.493780	+	0.285084i	0.232361	+	0.972630i	$0.425355\pi$
$20$		−	4.32886e7i		−	0.676385i
$21$	4.12019e7	−	8.60980e7i	0.480399	−	1.00387i
$22$	−5.89706e7			−0.520115
$23$	6.22412e7	+	1.07805e8i	0.420447	+	0.728235i	0.995983	−	0.0895411i	$-0.0285400\pi$
$23$	6.22412e7	+	1.07805e8i	0.420447	+	0.728235i	−0.575536	+	0.817776i	$0.695207\pi$
$24$	6.51190e7	+	3.75965e7i	0.340753	+	0.196734i
$25$	1.01317e8	−	1.75486e8i	0.414993	−	0.718789i
$26$	−2.78203e8	+	1.60621e8i	−0.900579	+	0.519950i
$27$		−	3.28312e8i		−	0.847429i
$28$	2.17341e8	+	1.04008e8i	0.451017	+	0.215833i
$29$	−7.52793e8			−1.26557			−0.632787	−	0.774326i	$-0.718089\pi$
$29$	−7.52793e8			−1.26557			−0.632787	+	0.774326i	$0.718089\pi$
$30$	3.88026e8	+	6.72081e8i	0.532272	+	0.921921i
$31$	9.46508e8	+	5.46467e8i	1.06648	+	0.615735i	0.927219	−	0.374520i	$-0.122193\pi$
$31$	9.46508e8	+	5.46467e8i	1.06648	+	0.615735i	0.139265	+	0.990255i	$0.455526\pi$
$32$	−9.49063e7	+	1.64382e8i	−0.0883883	+	0.153093i
$33$	9.15552e8	−	5.28594e8i	0.708923	−	0.409297i
$34$			1.45919e9i			0.944580i
$35$	1.40589e9	+	2.05120e9i	0.764790	+	1.11583i
$36$	−2.59621e8			−0.119268
$37$	−1.93585e9	−	3.35299e9i	−0.754503	−	1.30684i	−0.945621	−	0.325271i	$-0.894544\pi$
$37$	−1.93585e9	−	3.35299e9i	−0.754503	−	1.30684i	0.191117	−	0.981567i	$-0.438789\pi$
$38$	1.05129e9	+	6.06960e8i	0.349156	+	0.201585i
$39$	2.87951e9	−	4.98745e9i	0.818334	−	1.41740i
$40$	−1.69656e9	+	9.79510e8i	−0.414199	+	0.239138i
$41$			2.55800e9i			0.538516i	0.963068	+	0.269258i	$0.0867784\pi$
$41$			2.55800e9i			0.538516i	−0.963068	+	0.269258i	$0.913222\pi$
$42$	−4.30663e9	+	3.33395e8i	−0.784588	+	0.0607384i
$43$	−4.36133e9			−0.689934			−0.344967	−	0.938615i	$-0.612110\pi$
$43$	−4.36133e9			−0.689934			−0.344967	+	0.938615i	$0.612110\pi$
$44$	1.33435e9	+	2.31116e9i	0.183888	+	0.318504i
$45$	−2.32051e9	−	1.33975e9i	−0.279453	−	0.161342i
$46$	2.81672e9	−	4.87869e9i	0.297301	−	0.514940i
$47$	8.04169e9	−	4.64287e9i	0.746037	−	0.430725i	−0.0782231	−	0.996936i	$-0.524925\pi$
$47$	8.04169e9	−	4.64287e9i	0.746037	−	0.430725i	0.824260	+	0.566211i	$0.191591\pi$
$48$		−	3.40284e9i		−	0.278224i
$49$	−1.36764e10	+	2.13026e9i	−0.988085	+	0.153906i
$50$	−9.17013e9			−0.586888
$51$	−1.30797e10	−	2.26548e10i	−0.743324	−	1.28747i
$52$	1.25900e10	+	7.26886e9i	0.636805	+	0.367660i
$53$	−1.09179e8	+	1.89104e8i	−0.00492590	+	0.00853191i	−0.868478	−	0.495728i	$-0.834901\pi$
$53$	−1.09179e8	+	1.89104e8i	−0.00492590	+	0.00853191i	0.863552	+	0.504260i	$0.168235\pi$
$54$	−1.28671e10	+	7.42884e9i	−0.518942	+	0.299612i
$55$			2.75432e10i			0.995034i
$56$	−8.41602e8	−	1.08714e10i	−0.0272884	−	0.352499i
$57$	−2.17624e10			−0.634538
$58$	1.70338e10	+	2.95033e10i	0.447448	+	0.775003i
$59$	5.45224e10	+	3.14785e10i	1.29260	+	0.746280i	0.979114	−	0.203314i	$-0.0651712\pi$
$59$	5.45224e10	+	3.14785e10i	1.29260	+	0.746280i	0.313482	+	0.949594i	$0.398505\pi$
$60$	1.75600e10	−	3.04149e10i	0.376373	−	0.651897i
$61$	4.19753e10	−	2.42344e10i	0.814732	−	0.470386i	−0.0338645	−	0.999426i	$-0.510781\pi$
$61$	4.19753e10	−	2.42344e10i	0.814732	−	0.470386i	0.848596	+	0.529041i	$0.177448\pi$
$62$		−	4.94605e10i		−	0.870780i
$63$	1.23019e10	−	8.43172e9i	0.196757	−	0.134857i
$64$	8.58993e9			0.125000
$65$	7.50205e10	+	1.29939e11i	0.994718	+	1.72290i
$66$	−4.14331e10	−	2.39214e10i	−0.501284	−	0.289417i
$67$	−5.49220e10	+	9.51277e10i	−0.607152	+	1.05162i	0.384556	+	0.923102i	$0.374355\pi$
$67$	−5.49220e10	+	9.51277e10i	−0.607152	+	1.05162i	−0.991707	+	0.128516i	$0.958979\pi$
$68$	5.71884e10	−	3.30177e10i	0.578435	−	0.333959i
$69$			1.00993e11i			0.935826i
$70$	4.85786e10	−	1.01513e11i	0.412911	−	0.862843i
$71$	−7.43754e10			−0.580603			−0.290302	−	0.956935i	$-0.593756\pi$
$71$	−7.43754e10			−0.580603			−0.290302	+	0.956935i	$0.593756\pi$
$72$	5.87455e9	+	1.01750e10i	0.0421677	+	0.0730366i
$73$	−2.26320e11	−	1.30666e11i	−1.49550	−	0.863427i	−0.495512	−	0.868601i	$-0.665020\pi$
$73$	−2.26320e11	−	1.30666e11i	−1.49550	−	0.863427i	−0.999987	+	0.00517437i	$0.998353\pi$
$74$	−8.76065e10	+	1.51739e11i	−0.533514	+	0.924074i
$75$	1.42372e11	−	8.21982e10i	0.799937	−	0.461844i
$76$		−	5.49357e10i		−	0.285084i
$77$	−1.38287e11	−	6.61769e10i	−0.663494	−	0.317513i
$78$	−2.60623e11			−1.15730
$79$	−1.20639e11	−	2.08953e11i	−0.496279	−	0.859580i	0.503712	−	0.863871i	$-0.331967\pi$
$79$	−1.20639e11	−	2.08953e11i	−0.496279	−	0.859580i	−0.999991	+	0.00429190i	$0.998634\pi$
$80$	7.67776e10	+	4.43276e10i	0.292883	+	0.169096i
$81$	1.66865e11	−	2.89018e11i	0.590818	−	1.02333i
$82$	1.00253e11	−	5.78810e10i	0.329772	−	0.190394i
$83$			2.09983e11i			0.642268i	0.947034	+	0.321134i	$0.104064\pi$
$83$			2.09983e11i			0.642268i	−0.947034	+	0.321134i	$0.895936\pi$
$84$	1.10514e11	+	1.61241e11i	0.314588	+	0.458986i
$85$	6.81540e11			1.80708
$86$	9.86855e10	+	1.70928e11i	0.243929	+	0.422497i
$87$	−5.28918e11	−	3.05371e11i	−1.21975	−	0.704226i
$88$	6.03859e10	−	1.04591e11i	0.130029	−	0.225216i
$89$	1.79050e10	−	1.03374e10i	0.0360275	−	0.0208005i	−0.481878	−	0.876238i	$-0.660045\pi$
$89$	1.79050e10	−	1.03374e10i	0.0360275	−	0.0208005i	0.517906	+	0.855438i	$0.326712\pi$
$90$			1.21260e11i			0.228173i
$91$	−8.32640e11	+	6.44582e10i	−1.46625	+	0.113509i
$92$	−2.54940e11			−0.420447
$93$	4.43349e11	+	7.67903e11i	0.685248	+	1.18689i
$94$	−3.63926e11	−	2.10113e11i	−0.527528	−	0.304568i
$95$	2.83491e11	−	4.91020e11i	0.385653	−	0.667971i
$96$	−1.33364e11	+	7.69975e10i	−0.170377	+	0.0983670i
$97$		−	4.74911e11i		−	0.570140i	−0.958507	−	0.285070i	$-0.907983\pi$
$97$		−	4.74911e11i		−	0.570140i	0.958507	−	0.285070i	$-0.0920169\pi$
$98$	3.92950e11	+	4.87800e11i	0.443589	+	0.550662i
$99$	1.65189e11			0.175456
$100$	2.07496e11	+	3.59394e11i	0.207496	+	0.359394i
$101$	9.97000e11	+	5.75618e11i	0.939219	+	0.542259i	0.889715	−	0.456515i	$-0.150903\pi$
$101$	9.97000e11	+	5.75618e11i	0.939219	+	0.542259i	0.0495038	+	0.998774i	$0.484236\pi$
$102$	−5.91921e11	+	1.02524e12i	−0.525609	+	0.910382i
$103$	8.21363e11	−	4.74214e11i	0.687878	−	0.397147i	−0.114938	−	0.993373i	$-0.536667\pi$
$103$	8.21363e11	−	4.74214e11i	0.687878	−	0.397147i	0.802817	+	0.596226i	$0.203334\pi$
$104$		−	6.57902e11i		−	0.519950i
$105$	1.55718e11	+	2.01148e12i	0.116199	+	1.50100i
$106$	9.88179e9			0.00696628
$107$	1.66978e11	+	2.89214e11i	0.111264	+	0.192715i	0.916280	−	0.400538i	$-0.131177\pi$
$107$	1.66978e11	+	2.89214e11i	0.111264	+	0.192715i	−0.805016	+	0.593253i	$0.797843\pi$
$108$	5.82300e11	+	3.36191e11i	0.366948	+	0.211857i
$109$	3.67785e11	−	6.37022e11i	0.219298	−	0.379835i	−0.735295	−	0.677747i	$-0.762957\pi$
$109$	3.67785e11	−	6.37022e11i	0.219298	−	0.379835i	0.954594	+	0.297911i	$0.0962899\pi$
$110$	1.07947e12	−	6.23231e11i	0.609332	−	0.351798i
$111$		−	3.14111e12i		−	1.67937i
$112$	−4.07027e11	+	2.78976e11i	−0.206213	+	0.141338i
$113$	−2.66369e12			−1.27942			−0.639709	−	0.768617i	$-0.720945\pi$
$113$	−2.66369e12			−1.27942			−0.639709	+	0.768617i	$0.720945\pi$
$114$	4.92427e11	+	8.52908e11i	0.224343	+	0.388574i
$115$	−2.27868e12	−	1.31559e12i	−0.985134	−	0.568768i
$116$	7.70860e11	−	1.33517e12i	0.316394	−	0.548010i
$117$	7.79303e11	−	4.49931e11i	0.303803	−	0.175400i
$118$		−	2.84911e12i		−	1.05540i
$119$	−1.63751e12	+	3.42183e12i	−0.576635	+	1.20497i
$120$	−1.58935e12			−0.532272
$121$	7.20208e11	+	1.24744e12i	0.229481	+	0.397472i
$122$	−1.89958e12	−	1.09673e12i	−0.576102	−	0.332613i
$123$	−1.03766e12	+	1.79727e12i	−0.299656	+	0.519019i
$124$	−1.93845e12	+	1.11916e12i	−0.533242	+	0.307867i
$125$		−	8.77343e11i		−	0.229990i
$126$	−6.08815e11	−	2.91347e11i	−0.152147	−	0.0728094i
$127$	−2.69168e11			−0.0641506			−0.0320753	−	0.999485i	$-0.510212\pi$
$127$	−2.69168e11			−0.0641506			−0.0320753	+	0.999485i	$0.510212\pi$
$128$	−1.94368e11	−	3.36655e11i	−0.0441942	−	0.0765466i
$129$	−3.06430e12	−	1.76917e12i	−0.664956	−	0.383912i
$130$	3.39504e12	−	5.88038e12i	0.703372	−	1.21828i
$131$	4.16356e12	−	2.40383e12i	0.823829	−	0.475638i	−0.0279059	−	0.999611i	$-0.508884\pi$
$131$	4.16356e12	−	2.40383e12i	0.823829	−	0.475638i	0.851735	+	0.523972i	$0.175551\pi$
$132$			2.16512e12i			0.409297i
$133$	1.78415e12	+	2.60308e12i	0.322345	+	0.470304i
$134$	4.97097e12			0.858642
$135$	3.46976e12	+	6.00981e12i	0.573188	+	0.992791i
$136$	−2.58805e12	−	1.49421e12i	−0.409015	−	0.236145i
$137$	−5.08937e12	+	8.81505e12i	−0.769734	+	1.33322i	0.167973	+	0.985792i	$0.446278\pi$
$137$	−5.08937e12	+	8.81505e12i	−0.769734	+	1.33322i	−0.937707	+	0.347427i	$0.887056\pi$
$138$	3.95809e12	−	2.28520e12i	0.573074	−	0.330865i
$139$			3.81539e11i			0.0528994i	0.999650	+	0.0264497i	$0.00842018\pi$
$139$			3.81539e11i			0.0528994i	−0.999650	+	0.0264497i	$0.991580\pi$
$140$	−5.07767e12	+	3.93084e11i	−0.674367	+	0.0522057i
$141$	7.53354e12			0.958703
$142$	1.68292e12	+	2.91491e12i	0.205274	+	0.355545i
$143$	−8.01064e12	−	4.62495e12i	−0.936809	−	0.540867i
$144$	2.65852e11	−	4.60469e11i	0.0298170	−	0.0516446i
$145$	1.37800e13	−	7.95590e12i	1.48266	−	0.856015i
$146$			1.18265e13i			1.22107i
$147$	−1.04733e13	−	4.05109e12i	−1.03795	−	0.401484i
$148$	7.92924e12			0.754503
$149$	1.01352e13	+	1.75546e13i	0.926218	+	1.60426i	0.789591	+	0.613634i	$0.210293\pi$
$149$	1.01352e13	+	1.75546e13i	0.926218	+	1.60426i	0.136627	+	0.990623i	$0.456374\pi$
$150$	−6.44300e12	−	3.71987e12i	−0.565641	−	0.326573i
$151$	9.98191e12	−	1.72892e13i	0.842077	−	1.45852i	−0.0460585	−	0.998939i	$-0.514666\pi$
$151$	9.98191e12	−	1.72892e13i	0.842077	−	1.45852i	0.888136	−	0.459582i	$-0.152001\pi$
$152$	−2.15303e12	+	1.24305e12i	−0.174578	+	0.100793i
$153$		−	4.08749e12i		−	0.318646i
$154$	5.35485e11	+	6.91713e12i	0.0401442	+	0.518563i
$155$	−2.31014e13			−1.66589
$156$	5.89723e12	+	1.02143e13i	0.409167	+	0.708698i
$157$	6.85383e12	+	3.95706e12i	0.457652	+	0.264226i	0.711057	−	0.703135i	$-0.248217\pi$
$157$	6.85383e12	+	3.95706e12i	0.457652	+	0.264226i	−0.253404	+	0.967360i	$0.581550\pi$
$158$	−5.45950e12	+	9.45613e12i	−0.350922	+	0.607815i
$159$	−1.53420e11	+	8.85774e10i	−0.00949512	+	0.00548201i
$160$		−	4.01207e12i		−	0.239138i
$161$	1.20801e13	−	8.27970e12i	0.693611	−	0.475400i
$162$	−1.51029e13			−0.835543
$163$	−1.22758e13	−	2.12623e13i	−0.654521	−	1.13366i	−0.982014	−	0.188810i	$-0.939537\pi$
$163$	−1.22758e13	−	2.12623e13i	−0.654521	−	1.13366i	0.327493	−	0.944854i	$-0.393796\pi$
$164$	−4.53693e12	−	2.61940e12i	−0.233184	−	0.134629i
$165$	−1.11729e13	+	1.93520e13i	−0.553685	+	0.959010i
$166$	8.22964e12	−	4.75138e12i	0.393307	−	0.227076i
$167$		−	2.03607e13i		−	0.938629i	−0.883031	−	0.469315i	$-0.844501\pi$
$167$		−	2.03607e13i		−	0.938629i	0.883031	−	0.469315i	$-0.155499\pi$
$168$	3.81867e12	−	7.97972e12i	0.169847	−	0.354921i
$169$	−2.70905e13			−1.16278
$170$	−1.54215e13	−	2.67108e13i	−0.638899	−	1.10661i
$171$	−2.94486e12	−	1.70022e12i	−0.117785	−	0.0680030i
$172$	4.46600e12	−	7.73533e12i	0.172484	−	0.298750i
$173$	1.88719e13	−	1.08957e13i	0.703945	−	0.406423i	−0.104870	−	0.994486i	$-0.533443\pi$
$173$	1.88719e13	−	1.08957e13i	0.703945	−	0.406423i	0.808815	+	0.588063i	$0.200109\pi$
$174$			2.76390e13i			0.995926i
$175$	−2.15041e13	−	1.02907e13i	−0.748675	−	0.358276i
$176$	−5.46550e12			−0.183888
$177$	2.55385e13	+	4.42340e13i	0.830532	+	1.43852i
$178$	−8.10287e11	−	4.67819e11i	−0.0254753	−	0.0147081i
$179$	−5.29449e12	+	9.17033e12i	−0.160956	+	0.278783i	−0.935212	−	0.354089i	$-0.884791\pi$
$179$	−5.29449e12	+	9.17033e12i	−0.160956	+	0.278783i	0.774256	+	0.632872i	$0.218124\pi$
$180$	4.75241e12	−	2.74381e12i	0.139727	−	0.0806712i
$181$		−	5.35655e13i		−	1.52340i	−0.647930	−	0.761700i	$-0.724365\pi$
$181$		−	5.35655e13i		−	1.52340i	0.647930	−	0.761700i	$-0.275635\pi$
$182$	2.13667e13	+	3.11742e13i	0.587908	+	0.857761i
$183$	3.93229e13			1.04698
$184$	5.76863e12	+	9.99156e12i	0.148650	+	0.257470i
$185$	7.08722e13	+	4.09181e13i	1.76785	+	1.02067i
$186$	2.00637e13	−	3.47513e13i	0.484544	−	0.839255i
$187$	−3.63872e13	+	2.10081e13i	−0.850939	+	0.491290i
$188$			1.90172e13i			0.430725i
$189$	−3.85103e13	+	2.98125e12i	−0.844901	+	0.0654075i
$190$	−2.56586e13			−0.545396
$191$	−3.11402e13	−	5.39365e13i	−0.641390	−	1.11092i	−0.985123	−	0.171852i	$-0.945025\pi$
$191$	−3.11402e13	−	5.39365e13i	−0.641390	−	1.11092i	0.343733	−	0.939067i	$-0.388308\pi$
$192$	6.03535e12	+	3.48451e12i	0.120474	+	0.0695560i
$193$	1.97810e13	−	3.42617e13i	0.382740	−	0.662926i	−0.608713	−	0.793391i	$-0.708314\pi$
$193$	1.97810e13	−	3.42617e13i	0.382740	−	0.662926i	0.991453	+	0.130465i	$0.0416471\pi$
$194$	−1.86126e13	+	1.07460e13i	−0.349138	+	0.201575i
$195$			1.21728e14i			2.21403i
$196$	1.02263e13	−	2.64381e13i	0.180378	−	0.466330i
$197$	2.98938e12			0.0511427			0.0255713	−	0.999673i	$-0.491860\pi$
$197$	2.98938e12			0.0511427			0.0255713	+	0.999673i	$0.491860\pi$
$198$	−3.73779e12	−	6.47404e12i	−0.0620332	−	0.107445i
$199$	5.16217e13	+	2.98038e13i	0.831216	+	0.479903i	0.854269	−	0.519831i	$-0.174005\pi$
$199$	5.16217e13	+	2.98038e13i	0.831216	+	0.479903i	−0.0230526	+	0.999734i	$0.507339\pi$
$200$	9.39022e12	−	1.62643e13i	0.146722	−	0.254130i
$201$	−7.71771e13	+	4.45582e13i	−1.17034	+	0.675697i
$202$		−	5.20990e13i		−	0.766869i
$203$	6.83577e12	+	8.83011e13i	0.0976813	+	1.26180i
$204$	5.35746e13			0.743324
$205$	−2.70343e13	−	4.68248e13i	−0.364244	−	0.630889i
$206$	−3.71706e13	−	2.14605e13i	−0.486403	−	0.280825i
$207$	−7.89019e12	+	1.36662e13i	−0.100292	+	0.173711i
$208$	−2.57844e13	+	1.48866e13i	−0.318403	+	0.183830i
$209$			3.49539e13i			0.419389i
$210$	7.53103e13	−	5.16175e13i	0.878089	−	0.601841i
$211$	1.29666e14			1.46937			0.734684	−	0.678409i	$-0.237330\pi$
$211$	1.29666e14			1.46937			0.734684	+	0.678409i	$0.237330\pi$
$212$	−2.23599e11	−	3.87286e11i	−0.00246295	−	0.00426595i
$213$	−5.22567e13	−	3.01704e13i	−0.559583	−	0.323075i
$214$	7.55654e12	−	1.30883e13i	0.0786756	−	0.136270i
$215$	7.98349e13	−	4.60927e13i	0.808281	−	0.466661i
$216$		−	3.04285e13i		−	0.299612i
$217$	5.55047e13	−	1.15986e14i	0.531583	−	1.11083i
$218$	−3.32881e13			−0.310134
$219$	−1.06009e14	−	1.83614e14i	−0.960904	−	1.66433i
$220$	−4.88512e13	−	2.82042e13i	−0.430863	−	0.248759i
$221$	−1.14441e14	+	1.98218e14i	−0.982268	+	1.70134i
$222$	−1.23106e14	+	7.10753e13i	−1.02840	+	0.593746i
$223$		−	1.05020e14i		−	0.853972i	−0.904258	−	0.426986i	$-0.859575\pi$
$223$		−	1.05020e14i		−	0.853972i	0.904258	−	0.426986i	$-0.140425\pi$
$224$	2.01435e13	+	9.63964e12i	0.159459	+	0.0763084i
$225$	2.56874e13			0.197982
$226$	6.02724e13	+	1.04395e14i	0.452343	+	0.783481i
$227$	6.69859e13	+	3.86743e13i	0.489585	+	0.282662i	0.724402	−	0.689378i	$-0.242116\pi$
$227$	6.69859e13	+	3.86743e13i	0.489585	+	0.282662i	−0.234817	+	0.972040i	$0.575449\pi$
$228$	2.22847e13	−	3.85982e13i	0.158635	−	0.274763i
$229$	−1.53002e14	+	8.83360e13i	−1.06093	+	0.612526i	−0.925688	−	0.378287i	$-0.876513\pi$
$229$	−1.53002e14	+	8.83360e13i	−1.06093	+	0.612526i	−0.135238	+	0.990813i	$0.543180\pi$
$230$			1.19074e14i			0.804359i
$231$	−7.03168e13	−	1.02593e14i	−0.462793	−	0.675218i
$232$	−6.97703e13			−0.447448
$233$	−1.16414e14	−	2.01635e14i	−0.727562	−	1.26017i	−0.957911	−	0.287066i	$-0.907320\pi$
$233$	−1.16414e14	−	2.01635e14i	−0.727562	−	1.26017i	0.230349	−	0.973108i	$-0.426013\pi$
$234$	−3.52672e13	−	2.03616e13i	−0.214821	−	0.124027i
$235$	−9.81366e13	+	1.69977e14i	−0.582671	+	1.00922i
$236$	−1.11662e14	+	6.44680e13i	−0.646298	+	0.373140i
$237$		−	1.95749e14i		−	1.10461i
$238$	1.71160e14	−	1.32503e13i	0.941762	−	0.0729058i
$239$	1.20020e14			0.643971			0.321986	−	0.946745i	$-0.395650\pi$
$239$	1.20020e14			0.643971			0.321986	+	0.946745i	$0.395650\pi$
$240$	3.59630e13	+	6.22897e13i	0.188186	+	0.325948i
$241$	4.44336e13	+	2.56537e13i	0.226782	+	0.130933i	0.609087	−	0.793104i	$-0.291536\pi$
$241$	4.44336e13	+	2.56537e13i	0.226782	+	0.130933i	−0.382305	+	0.924036i	$0.624869\pi$
$242$	3.25929e13	−	5.64526e13i	0.162267	−	0.281055i
$243$	8.33779e13	−	4.81383e13i	0.404961	−	0.233804i
$244$			9.92643e13i			0.470386i
$245$	2.27835e14	−	1.83534e14i	1.05347	−	0.848632i
$246$	9.39179e13			0.423777
$247$	9.52053e13	+	1.64900e14i	0.419256	+	0.726173i
$248$	8.77242e13	+	5.06476e13i	0.377059	+	0.217695i
$249$	−8.51799e13	+	1.47536e14i	−0.357389	+	0.619016i
$250$	−3.43847e13	+	1.98520e13i	−0.140840	+	0.0813138i
$251$			1.04293e14i			0.417073i	0.978015	+	0.208537i	$0.0668700\pi$
$251$			1.04293e14i			0.417073i	−0.978015	+	0.208537i	$0.933130\pi$
$252$	2.35750e12	+	3.04530e13i	0.00920552	+	0.118912i
$253$	1.62210e14			0.618522
$254$	6.09057e12	+	1.05492e13i	0.0226807	+	0.0392841i
$255$	4.78855e14	+	2.76467e14i	1.74166	+	1.00555i
$256$	−8.79609e12	+	1.52353e13i	−0.0312500	+	0.0541266i
$257$	2.30306e14	−	1.32967e14i	0.799295	−	0.461473i	−0.0439295	−	0.999035i	$-0.513988\pi$
$257$	2.30306e14	−	1.32967e14i	0.799295	−	0.461473i	0.843225	+	0.537561i	$0.180654\pi$
$258$			1.60127e14i			0.542934i
$259$	−3.75721e14	+	2.57518e14i	−1.24470	+	0.853119i
$260$	−3.07284e14			−0.994718
$261$	−4.77150e13	−	8.26449e13i	−0.150943	−	0.261440i
$262$	−1.88421e14	−	1.08785e14i	−0.582535	−	0.336327i
$263$	1.98352e14	−	3.43556e14i	0.599380	−	1.03816i	−0.393533	−	0.919311i	$-0.628747\pi$
$263$	1.98352e14	−	3.43556e14i	0.599380	−	1.03816i	0.992913	−	0.118846i	$-0.0379195\pi$
$264$	8.48551e13	−	4.89911e13i	0.250642	−	0.144708i
$265$		−	4.61546e12i		−	0.0133272i
$266$	6.16489e13	−	1.28825e14i	0.174035	−	0.363673i
$267$	1.67735e13			0.0462975
$268$	−1.12480e14	−	1.94821e14i	−0.303576	−	0.525809i
$269$	−5.98003e13	−	3.45257e13i	−0.157830	−	0.0911232i	0.419005	−	0.907984i	$-0.362379\pi$
$269$	−5.98003e13	−	3.45257e13i	−0.157830	−	0.0911232i	−0.576835	+	0.816861i	$0.695712\pi$
$270$	1.57024e14	−	2.71973e14i	0.405305	−	0.702010i
$271$	−6.55851e14	+	3.78656e14i	−1.65573	+	0.955936i	−0.681078	+	0.732211i	$0.738489\pi$
$271$	−6.55851e14	+	3.78656e14i	−1.65573	+	0.955936i	−0.974652	+	0.223726i	$0.928178\pi$
$272$			1.35241e14i			0.333959i
$273$	−6.11166e14	−	2.92472e14i	−1.47633	−	0.706493i
$274$	4.60637e14			1.08857
$275$	−1.32023e14	−	2.28671e14i	−0.305249	−	0.528707i
$276$	−1.79123e14	−	1.03416e14i	−0.405225	−	0.233957i
$277$	−1.16361e14	+	2.01543e14i	−0.257590	+	0.446159i	−0.965596	−	0.260047i	$-0.916262\pi$
$277$	−1.16361e14	+	2.01543e14i	−0.257590	+	0.446159i	0.708006	+	0.706207i	$0.249595\pi$
$278$	1.49532e13	−	8.63325e12i	0.0323941	−	0.0187028i
$279$			1.38549e14i			0.293750i
$280$	1.30300e14	+	1.90109e14i	0.270394	+	0.394506i
$281$	−7.05866e14			−1.43379			−0.716893	−	0.697183i	$-0.754436\pi$
$281$	−7.05866e14			−1.43379			−0.716893	+	0.697183i	$0.754436\pi$
$282$	−1.70464e14	−	2.95253e14i	−0.338953	−	0.587083i
$283$	6.72043e14	+	3.88004e14i	1.30821	+	0.755297i	0.981798	−	0.189930i	$-0.0608262\pi$
$283$	6.72043e14	+	3.88004e14i	1.30821	+	0.755297i	0.326414	+	0.945227i	$0.394159\pi$
$284$	7.61604e13	−	1.31914e14i	0.145151	−	0.251409i
$285$	3.98365e14	−	2.29996e14i	0.743382	−	0.429192i
$286$			4.18602e14i			0.764901i
$287$	3.00049e14	−	2.32281e13i	0.536909	−	0.0415644i
$288$	−2.40622e13			−0.0421677
$289$	2.28522e14	+	3.95813e14i	0.392231	+	0.679364i
$290$	−6.23613e14	−	3.60043e14i	−1.04840	−	0.605294i
$291$	1.92648e14	−	3.33676e14i	0.317253	−	0.549499i
$292$	4.63504e14	−	2.67604e14i	0.747749	−	0.431713i
$293$		−	6.68824e14i		−	1.05708i	−0.848910	−	0.528538i	$-0.822740\pi$
$293$		−	6.68824e14i		−	1.05708i	0.848910	−	0.528538i	$-0.177260\pi$
$294$	7.82131e13	+	5.02132e14i	0.121114	+	0.777560i
$295$	−1.33072e15			−2.01909
$296$	−1.79418e14	−	3.10761e14i	−0.266757	−	0.462037i
$297$	−3.70499e14	−	2.13908e14i	−0.539819	−	0.311665i
$298$	4.58665e14	−	7.94431e14i	0.654935	−	1.13438i
$299$	7.65253e14	−	4.41819e14i	1.07097	−	0.618325i
$300$			3.36684e14i			0.461844i
$301$	3.96032e13	+	5.11575e14i	0.0532515	+	0.687876i
$302$	−9.03459e14			−1.19088
$303$	4.67000e14	+	8.08867e14i	0.603477	+	1.04525i
$304$	9.74351e13	+	5.62542e13i	0.123445	+	0.0712711i
$305$	−5.12244e14	+	8.87233e14i	−0.636323	+	1.10214i
$306$	−1.60196e14	+	9.24894e13i	−0.195130	+	0.112658i
$307$		−	7.37934e14i		−	0.881429i	−0.897647	−	0.440714i	$-0.854725\pi$
$307$		−	7.37934e14i		−	0.881429i	0.897647	−	0.440714i	$-0.145275\pi$
$308$	2.58978e14	−	1.77503e14i	0.303361	−	0.207923i
$309$	7.69460e14			0.883965
$310$	5.22724e14	+	9.05385e14i	0.588983	+	1.02015i
$311$	4.21657e14	+	2.43444e14i	0.466012	+	0.269052i	0.714569	−	0.699565i	$-0.246623\pi$
$311$	4.21657e14	+	2.43444e14i	0.466012	+	0.269052i	−0.248557	+	0.968617i	$0.579956\pi$
$312$	2.66878e14	−	4.62247e14i	0.289325	−	0.501125i
$313$	2.88228e14	−	1.66408e14i	0.306528	−	0.176974i	−0.338844	−	0.940843i	$-0.610036\pi$
$313$	2.88228e14	−	1.66408e14i	0.306528	−	0.176974i	0.645372	+	0.763869i	$0.276703\pi$
$314$		−	3.58152e14i		−	0.373671i
$315$	−1.36078e14	+	2.84357e14i	−0.139292	+	0.291073i
$316$	4.94138e14			0.496279
$317$	7.44042e14	+	1.28872e15i	0.733233	+	1.27000i	0.955494	+	0.295010i	$0.0953229\pi$
$317$	7.44042e14	+	1.28872e15i	0.733233	+	1.27000i	−0.222261	+	0.974987i	$0.571344\pi$
$318$	6.94302e12	+	4.00855e12i	0.00671407	+	0.00387637i
$319$	−4.90474e14	+	8.49526e14i	−0.465449	+	0.806181i
$320$	−1.57240e14	+	9.07828e13i	−0.146442	+	0.0845481i
$321$			2.70938e14i			0.247651i
$322$	−5.97839e14	−	2.86094e14i	−0.536350	−	0.256669i
$323$	8.64912e14			0.761653
$324$	3.41739e14	+	5.91909e14i	0.295409	+	0.511664i
$325$	−1.24568e15	−	7.19195e14i	−1.05708	−	0.610305i
$326$	−5.55538e14	+	9.62221e14i	−0.462816	+	0.801621i
$327$	5.16817e14	−	2.98384e14i	0.422717	−	0.244056i
$328$			2.37081e14i			0.190394i
$329$	−6.17623e14	−	9.01115e14i	−0.487021	−	0.710567i
$330$	1.01126e15			0.783028
$331$	−1.12300e14	−	1.94510e14i	−0.0853912	−	0.147902i	0.820167	−	0.572125i	$-0.193881\pi$
$331$	−1.12300e14	−	1.94510e14i	−0.0853912	−	0.147902i	−0.905558	+	0.424223i	$0.860547\pi$
$332$	−3.72431e14	−	2.15023e14i	−0.278110	−	0.160567i
$333$	2.45404e14	−	4.25052e14i	0.179977	−	0.311728i
$334$	−7.97974e14	+	4.60710e14i	−0.574791	+	0.331856i
$335$		−	2.32177e15i		−	1.64267i
$336$	−3.99147e14	+	3.08997e13i	−0.277394	+	0.0214743i
$337$	1.02994e15			0.703124			0.351562	−	0.936165i	$-0.385651\pi$
$337$	1.02994e15			0.703124			0.351562	+	0.936165i	$0.385651\pi$
$338$	6.12989e14	+	1.06173e15i	0.411105	+	0.712054i
$339$	−1.87153e15	−	1.08053e15i	−1.23310	−	0.711930i
$340$	−6.97896e14	+	1.20879e15i	−0.451770	+	0.782489i
$341$	1.23337e15	−	7.12089e14i	0.784456	−	0.452906i
$342$			1.53886e14i			0.0961707i
$343$	3.74064e14	+	1.58487e15i	0.229711	+	0.973259i
$344$	−4.04216e14			−0.243929
$345$	−1.06734e15	−	1.84869e15i	−0.632979	−	1.09635i
$346$	−8.54044e14	−	4.93083e14i	−0.497764	−	0.287384i
$347$	4.36316e14	−	7.55722e14i	0.249934	−	0.432898i	−0.713574	−	0.700580i	$-0.752925\pi$
$347$	4.36316e14	−	7.55722e14i	0.249934	−	0.432898i	0.963507	+	0.267683i	$0.0862579\pi$
$348$	1.08322e15	−	6.25399e14i	0.609877	−	0.352113i
$349$		−	2.50531e14i		−	0.138647i	−0.997594	−	0.0693233i	$-0.977916\pi$
$349$		−	2.50531e14i		−	0.138647i	0.997594	−	0.0693233i	$-0.0220840\pi$
$350$	8.32698e13	+	1.07564e15i	0.0452980	+	0.585138i
$351$	−2.33052e15			−1.24626
$352$	1.23670e14	+	2.14203e14i	0.0650144	+	0.112608i
$353$	−2.45457e14	−	1.41714e14i	−0.126861	−	0.0732430i	0.435227	−	0.900321i	$-0.356668\pi$
$353$	−2.45457e14	−	1.41714e14i	−0.126861	−	0.0732430i	−0.562087	+	0.827078i	$0.690002\pi$
$354$	1.15574e15	−	2.00180e15i	0.587275	−	1.01719i
$355$	1.36146e15	−	7.86038e14i	0.680196	−	0.392711i
$356$			4.23422e13i			0.0208005i
$357$	−2.53859e15	+	1.73995e15i	−1.22626	+	0.840478i
$358$	4.79203e14			0.227626
$359$	−2.96270e14	−	5.13154e14i	−0.138395	−	0.239707i	0.788494	−	0.615042i	$-0.210861\pi$
$359$	−2.96270e14	−	5.13154e14i	−0.138395	−	0.239707i	−0.926889	+	0.375335i	$0.877528\pi$
$360$	−2.15070e14	−	1.24171e14i	−0.0988016	−	0.0570431i
$361$	−7.46892e14	+	1.29365e15i	−0.337454	+	0.584487i
$362$	−2.09933e15	+	1.21205e15i	−0.932888	+	0.538603i
$363$			1.16861e15i			0.510776i
$364$	7.38299e14	−	1.54279e15i	0.317412	−	0.663283i
$365$	5.52378e15			2.33603
$366$	−8.89775e14	−	1.54113e15i	−0.370163	−	0.641142i
$367$	−4.05423e14	−	2.34071e14i	−0.165925	−	0.0957969i	0.414738	−	0.909941i	$-0.363873\pi$
$367$	−4.05423e14	−	2.34071e14i	−0.165925	−	0.0957969i	−0.580663	+	0.814144i	$0.697207\pi$
$368$	2.61059e14	−	4.52167e14i	0.105112	−	0.182059i
$369$	−2.80829e14	+	1.62137e14i	−0.111246	+	0.0642278i
$370$		−	3.70348e15i		−	1.44344i
$371$	2.31730e13	+	1.10894e13i	0.00888666	+	0.00425268i
$372$	−1.81596e15			−0.685248
$373$	1.17094e15	+	2.02812e15i	0.434791	+	0.753081i	0.997279	−	0.0737253i	$-0.0234888\pi$
$373$	1.17094e15	+	2.02812e15i	0.434791	+	0.753081i	−0.562487	+	0.826806i	$0.690155\pi$
$374$	1.64669e15	+	9.50720e14i	0.601705	+	0.347394i
$375$	3.55895e14	−	6.16428e14i	0.127978	−	0.221664i
$376$	7.45320e14	−	4.30310e14i	0.263764	−	0.152284i
$377$			5.34370e15i			1.86120i
$378$	9.88229e14	+	1.44183e15i	0.338772	+	0.494269i
$379$	−4.89878e15			−1.65292			−0.826461	−	0.562994i	$-0.809649\pi$
$379$	−4.89878e15			−1.65292			−0.826461	+	0.562994i	$0.809649\pi$
$380$	5.80589e14	+	1.00561e15i	0.192827	+	0.333986i
$381$	−1.89119e14	−	1.09188e14i	−0.0618281	−	0.0356965i
$382$	−1.40925e15	+	2.44089e15i	−0.453531	+	0.785539i
$383$	−4.07029e15	+	2.34998e15i	−1.28953	+	0.744513i	−0.978571	−	0.205909i	$-0.933985\pi$
$383$	−4.07029e15	+	2.34998e15i	−1.28953	+	0.744513i	−0.310963	+	0.950422i	$0.600652\pi$
$384$		−	3.15382e14i		−	0.0983670i
$385$	3.23076e15	−	2.50107e14i	0.992066	−	0.0768001i
$386$	−1.79037e15			−0.541276
$387$	−2.76438e14	−	4.78805e14i	−0.0822872	−	0.142526i
$388$	8.42311e14	+	4.86309e14i	0.246878	+	0.142535i
$389$	1.04054e15	−	1.80226e15i	0.300303	−	0.520140i	−0.675901	−	0.736992i	$-0.736246\pi$
$389$	1.04054e15	−	1.80226e15i	0.300303	−	0.520140i	0.976205	+	0.216852i	$0.0695788\pi$
$390$	4.77076e15	−	2.75440e15i	1.35581	−	0.782779i
$391$		−	4.01379e15i		−	1.12330i
$392$	−1.26755e15	+	1.97437e14i	−0.349341	+	0.0544141i
$393$	3.90046e15			1.05867
$394$	−6.76419e13	−	1.17159e14i	−0.0180817	−	0.0313184i
$395$	4.41665e15	+	2.54995e15i	1.16281	+	0.671350i
$396$	−1.69153e14	+	2.92982e14i	−0.0438641	+	0.0759748i
$397$	5.98851e14	−	3.45747e14i	0.152959	−	0.0883110i	−0.421567	−	0.906797i	$-0.638520\pi$
$397$	5.98851e14	−	3.45747e14i	0.152959	−	0.0883110i	0.574526	+	0.818486i	$0.305186\pi$
$398$		−	2.69753e15i		−	0.678685i
$399$	1.97614e14	+	2.55269e15i	0.0489758	+	0.632645i
$400$	−8.49905e14			−0.207496
$401$	2.13958e15	+	3.70586e15i	0.514592	+	0.891299i	0.999857	+	0.0169316i	$0.00538977\pi$
$401$	2.13958e15	+	3.70586e15i	0.514592	+	0.891299i	−0.485265	+	0.874367i	$0.661277\pi$
$402$	3.49264e15	+	2.01648e15i	0.827556	+	0.477790i
$403$	3.87909e15	−	6.71878e15i	0.905524	−	1.56841i
$404$	−2.04186e15	+	1.17887e15i	−0.469610	+	0.271129i
$405$			7.05404e15i			1.59848i
$406$	3.30601e15	−	2.26593e15i	0.738155	−	0.505931i
$407$	−5.04512e15			−1.10996
$408$	−1.21226e15	−	2.09969e15i	−0.262805	−	0.455191i
$409$	−5.93554e13	−	3.42689e13i	−0.0126800	−	0.00732082i	0.493647	−	0.869663i	$-0.335664\pi$
$409$	−5.93554e13	−	3.42689e13i	−0.0126800	−	0.00732082i	−0.506327	+	0.862342i	$0.668997\pi$
$410$	−1.22343e15	+	2.11905e15i	−0.257559	+	0.446106i
$411$	−7.15166e15	+	4.12901e15i	−1.48373	+	0.856633i
$412$			1.94238e15i			0.397147i
$413$	3.19727e15	−	6.68121e15i	0.644287	−	1.34634i
$414$	7.14139e14			0.141834
$415$	−2.21921e15	−	3.84379e15i	−0.434421	−	0.752439i
$416$	1.16687e15	+	6.73692e14i	0.225145	+	0.129987i
$417$	−1.54772e14	+	2.68072e14i	−0.0294357	+	0.0509842i
$418$	1.36991e15	−	7.90916e14i	0.256823	−	0.148277i
$419$		−	2.03797e15i		−	0.376628i	−0.982109	−	0.188314i	$-0.939698\pi$
$419$		−	2.03797e15i		−	0.376628i	0.982109	−	0.188314i	$-0.0603023\pi$
$420$	−3.72706e15	−	1.78358e15i	−0.679002	−	0.324934i
$421$	−7.75234e15			−1.39232			−0.696162	−	0.717885i	$-0.745110\pi$
$421$	−7.75234e15			−1.39232			−0.696162	+	0.717885i	$0.745110\pi$
$422$	−2.93400e15	−	5.08184e15i	−0.519500	−	0.899801i
$423$	1.01943e15	+	5.88568e14i	0.177957	+	0.102744i
$424$	−1.01190e13	+	1.75265e13i	−0.00174157	+	0.00301649i
$425$	−5.65833e15	+	3.26684e15i	−0.960185	+	0.554363i
$426$			2.73071e15i			0.456897i
$427$	−3.22381e15	−	4.70356e15i	−0.531866	−	0.775996i
$428$	−6.83940e14			−0.111264
$429$	−3.75222e15	−	6.49904e15i	−0.601928	−	1.04257i
$430$	−3.61292e15	−	2.08592e15i	−0.571541	−	0.329979i
$431$	−3.20180e13	+	5.54569e13i	−0.00499495	+	0.00865151i	−0.868512	−	0.495668i	$-0.834923\pi$
$431$	−3.20180e13	+	5.54569e13i	−0.00499495	+	0.00865151i	0.863517	+	0.504320i	$0.168257\pi$
$432$	−1.19255e15	+	6.88519e14i	−0.183474	+	0.105929i
$433$		−	3.93012e14i		−	0.0596319i	−0.999555	−	0.0298159i	$-0.990508\pi$
$433$		−	3.93012e14i		−	0.0596319i	0.999555	−	0.0298159i	$-0.00949211\pi$
$434$	−5.80162e15	+	4.49129e14i	−0.868183	+	0.0672098i
$435$	1.29093e16			1.90531
$436$	7.53223e14	+	1.30462e15i	0.109649	+	0.189918i
$437$	−2.89177e15	−	1.66956e15i	−0.415217	−	0.239725i
$438$	−4.79744e15	+	8.30941e15i	−0.679461	+	1.17686i
$439$	6.94942e15	−	4.01225e15i	0.970871	−	0.560533i	0.0713694	−	0.997450i	$-0.477263\pi$
$439$	6.94942e15	−	4.01225e15i	0.970871	−	0.560533i	0.899502	+	0.436917i	$0.143930\pi$
$440$			2.55276e15i			0.351798i
$441$	−1.10073e15	−	1.36643e15i	−0.149641	−	0.185761i
$442$	1.03581e16			1.38914
$443$	−7.81118e14	−	1.35294e15i	−0.103346	−	0.179001i	0.809715	−	0.586823i	$-0.199622\pi$
$443$	−7.81118e14	−	1.35294e15i	−0.103346	−	0.179001i	−0.913061	+	0.407822i	$0.866288\pi$
$444$	5.57114e15	+	3.21650e15i	0.727187	+	0.419842i
$445$	−2.18503e14	+	3.78458e14i	−0.0281382	+	0.0487369i
$446$	−4.11593e15	+	2.37633e15i	−0.522949	+	0.301925i
$447$			1.64453e16i			2.06157i
$448$	−7.80013e13	−	1.00758e15i	−0.00964792	−	0.124627i
$449$	−2.29552e15			−0.280158			−0.140079	−	0.990140i	$-0.544736\pi$
$449$	−2.29552e15			−0.280158			−0.140079	+	0.990140i	$0.544736\pi$
$450$	−5.81240e14	−	1.00674e15i	−0.0699971	−	0.121239i
$451$	2.88670e15	+	1.66664e15i	0.343039	+	0.198053i
$452$	2.72762e15	−	4.72437e15i	0.319855	−	0.554005i
$453$	1.40267e16	−	8.09833e15i	1.62318	−	0.937144i
$454$		−	3.50040e15i		−	0.399744i
$455$	1.45604e16	−	9.97968e15i	1.64099	−	1.12473i
$456$	−2.01698e15			−0.224343
$457$	−3.78307e15	−	6.55247e15i	−0.415286	−	0.719296i	0.580173	−	0.814493i	$-0.302985\pi$
$457$	−3.78307e15	−	6.55247e15i	−0.415286	−	0.719296i	−0.995458	+	0.0951976i	$0.969652\pi$
$458$	6.92410e15	+	3.99763e15i	0.750188	+	0.433121i
$459$	−5.29302e15	+	9.16777e15i	−0.566014	+	0.980365i
$460$	4.66673e15	−	2.69434e15i	0.492567	−	0.284384i
$461$		−	3.83644e15i		−	0.399690i	−0.979828	−	0.199845i	$-0.935956\pi$
$461$		−	3.83644e15i		−	0.399690i	0.979828	−	0.199845i	$-0.0640439\pi$
$462$	−2.42970e15	+	5.07725e15i	−0.249863	+	0.522127i
$463$	4.62714e15			0.469707			0.234853	−	0.972031i	$-0.424539\pi$
$463$	4.62714e15			0.469707			0.234853	+	0.972031i	$0.424539\pi$
$464$	1.57872e15	+	2.73443e15i	0.158197	+	0.274005i
$465$	−1.62312e16	−	9.37108e15i	−1.60558	−	0.926983i
$466$	−5.26830e15	+	9.12496e15i	−0.514464	+	0.891078i
$467$	−1.22742e16	+	7.08650e15i	−1.18329	+	0.683173i	−0.956773	−	0.290834i	$-0.906067\pi$
$467$	−1.22742e16	+	7.08650e15i	−1.18329	+	0.683173i	−0.226517	+	0.974007i	$0.572734\pi$
$468$			1.84292e15i			0.175400i
$469$	1.16570e16	+	5.57843e15i	1.09534	+	0.524173i
$470$	8.88231e15			0.824022
$471$	3.21037e15	+	5.56052e15i	0.294056	+	0.509319i
$472$	5.05324e15	+	2.91749e15i	0.457001	+	0.263850i
$473$	−2.84157e15	+	4.92175e15i	−0.253742	+	0.439494i
$474$	−7.67177e15	+	4.42930e15i	−0.676434	+	0.390539i
$475$			5.43545e15i			0.473232i
$476$	−4.39222e15	−	6.40827e15i	−0.377609	−	0.550933i
$477$	−2.76809e13			−0.00235001
$478$	−2.71575e15	−	4.70381e15i	−0.227678	−	0.394350i
$479$	3.20508e15	+	1.85045e15i	0.265354	+	0.153202i	0.626774	−	0.779201i	$-0.284375\pi$
$479$	3.20508e15	+	1.85045e15i	0.265354	+	0.153202i	−0.361421	+	0.932403i	$0.617708\pi$
$480$	1.62750e15	−	2.81891e15i	0.133068	−	0.230480i
$481$	−2.38012e16	+	1.37416e16i	−1.92189	+	1.10960i
$482$		−	2.32191e15i		−	0.185167i
$483$	1.18462e16	−	9.17069e14i	0.933035	−	0.0722302i
$484$	−2.94997e15			−0.229481
$485$	5.01910e15	+	8.69334e15i	0.385634	+	0.667938i
$486$	−3.77325e15	−	2.17849e15i	−0.286351	−	0.165325i
$487$	8.57581e15	−	1.48537e16i	0.642838	−	1.11343i	−0.341959	−	0.939715i	$-0.611090\pi$
$487$	8.57581e15	−	1.48537e16i	0.642838	−	1.11343i	0.984796	−	0.173713i	$-0.0555764\pi$
$488$	3.89035e15	−	2.24609e15i	0.288051	−	0.166306i
$489$		−	1.99187e16i		−	1.45683i
$490$	−1.23483e16	−	4.77638e15i	−0.892139	−	0.345082i
$491$	−1.18747e16			−0.847487			−0.423744	−	0.905782i	$-0.639284\pi$
$491$	−1.18747e16			−0.847487			−0.423744	+	0.905782i	$0.639284\pi$
$492$	−2.12512e15	−	3.68081e15i	−0.149828	−	0.259510i
$493$	2.10210e16	+	1.21365e16i	1.46410	+	0.845301i
$494$	4.30850e15	−	7.46254e15i	0.296459	−	0.513482i
$495$	−3.02381e15	+	1.74580e15i	−0.205553	+	0.118676i
$496$		−	4.58410e15i		−	0.307867i
$497$	6.75369e14	+	8.72409e15i	0.0448129	+	0.578871i
$498$	7.70960e15			0.505424
$499$	1.47725e15	+	2.55868e15i	0.0956868	+	0.165734i	0.909895	−	0.414839i	$-0.136162\pi$
$499$	1.47725e15	+	2.55868e15i	0.0956868	+	0.165734i	−0.814208	+	0.580573i	$0.802829\pi$
$500$	1.55607e15	+	8.98399e14i	0.0995887	+	0.0574976i
$501$	8.25933e15	−	1.43056e16i	0.522298	−	0.904647i
$502$	4.08743e15	−	2.35988e15i	0.255404	−	0.147458i
$503$			3.88753e15i			0.240030i	0.992772	+	0.120015i	$0.0382943\pi$
$503$			3.88753e15i			0.240030i	−0.992772	+	0.120015i	$0.961706\pi$
$504$	1.14017e15	−	7.81468e14i	0.0695640	−	0.0476791i
$505$	−2.43337e16			−1.46710
$506$	−3.67040e15	−	6.35732e15i	−0.218681	−	0.378766i
$507$	−1.90340e16	−	1.09893e16i	−1.12068	−	0.647026i
$508$	2.75628e14	−	4.77402e14i	0.0160377	−	0.0277780i
$509$	−2.28834e15	+	1.32117e15i	−0.131587	+	0.0759719i	−0.564349	−	0.825537i	$-0.690873\pi$
$509$	−2.28834e15	+	1.32117e15i	−0.131587	+	0.0759719i	0.432761	+	0.901509i	$0.357539\pi$
$510$		−	2.50229e16i		−	1.42206i
$511$	−1.32718e16	+	2.77334e16i	−0.745423	+	1.55768i
$512$	7.96131e14			0.0441942
$513$	4.40333e15	+	7.62679e15i	0.241589	+	0.418444i
$514$	−1.04225e16	−	6.01742e15i	−0.565187	−	0.326311i
$515$	−1.00235e16	+	1.73612e16i	−0.537248	+	0.930541i
$516$	6.27568e15	−	3.62327e15i	0.332478	−	0.191956i
$517$		−	1.21001e16i		−	0.633642i
$518$	1.85942e16	+	8.89820e15i	0.962496	+	0.460600i
$519$	1.76794e16			0.904613
$520$	6.95305e15	+	1.20430e16i	0.351686	+	0.609138i
$521$	−8.74947e15	−	5.05151e15i	−0.437477	−	0.252578i	0.265050	−	0.964235i	$-0.414612\pi$
$521$	−8.74947e15	−	5.05151e15i	−0.437477	−	0.252578i	−0.702527	+	0.711657i	$0.747945\pi$
$522$	−2.15934e15	+	3.74008e15i	−0.106733	+	0.184866i
$523$	2.00319e16	−	1.15654e16i	0.978843	−	0.565135i	0.0769222	−	0.997037i	$-0.475491\pi$
$523$	2.00319e16	−	1.15654e16i	0.978843	−	0.565135i	0.901921	+	0.431902i	$0.142157\pi$
$524$			9.84610e15i			0.475638i
$525$	−1.09345e16	−	1.59535e16i	−0.522208	−	0.761904i
$526$	−1.79528e16			−0.847651
$527$	−1.76202e16	−	3.05191e16i	−0.822522	−	1.42465i
$528$	−3.84010e15	−	2.21708e15i	−0.177231	−	0.102324i
$529$	3.20938e15	−	5.55881e15i	0.146449	−	0.253657i
$530$	−1.80888e14	+	1.04436e14i	−0.00816122	+	0.00471188i
$531$			7.98093e15i			0.356030i
$532$	−6.44385e15	+	4.98846e14i	−0.284234	+	0.0220038i
$533$	1.81580e16			0.791962
$534$	−3.79542e14	−	6.57386e14i	−0.0163686	−	0.0283513i
$535$	−6.11311e15	−	3.52941e15i	−0.260699	−	0.150515i
$536$	−5.09027e15	+	8.81661e15i	−0.214661	+	0.371803i
$537$	−7.43989e15	+	4.29542e15i	−0.310257	+	0.179127i
$538$			3.12491e15i			0.128868i
$539$	−6.50669e15	+	1.68217e16i	−0.265355	+	0.686021i
$540$	−1.42122e16			−0.573188
$541$	1.20154e16	+	2.08113e16i	0.479243	+	0.830073i	0.999717	−	0.0238046i	$-0.00757796\pi$
$541$	1.20154e16	+	2.08113e16i	0.479243	+	0.830073i	−0.520474	+	0.853878i	$0.674245\pi$
$542$	2.96804e16	+	1.71360e16i	1.17078	+	0.675949i
$543$	2.17289e16	−	3.76355e16i	0.847692	−	1.46825i
$544$	5.30033e15	−	3.06015e15i	0.204508	−	0.118072i
$545$			1.55478e16i			0.593320i
$546$	2.36660e15	+	3.05706e16i	0.0893242	+	1.15385i
$547$	2.61473e16			0.976119			0.488060	−	0.872810i	$-0.337705\pi$
$547$	2.61473e16			0.976119			0.488060	+	0.872810i	$0.337705\pi$
$548$	−1.04230e16	−	1.80532e16i	−0.384867	−	0.666609i
$549$	5.32112e15	+	3.07215e15i	0.194343	+	0.112204i
$550$	−5.97470e15	+	1.03485e16i	−0.215844	+	0.373853i
$551$	1.74876e16	−	1.00965e16i	0.624916	−	0.360795i
$552$			9.36019e15i			0.330865i
$553$	−2.34143e16	+	1.60481e16i	−0.818711	+	0.561143i
$554$	1.05318e16			0.364288
$555$	3.31969e16	+	5.74987e16i	1.13590	+	1.96743i
$556$	−6.76706e14	−	3.90696e14i	−0.0229061	−	0.0132248i
$557$	9.52588e15	−	1.64993e16i	0.318988	−	0.552503i	−0.661289	−	0.750131i	$-0.729990\pi$
$557$	9.52588e15	−	1.64993e16i	0.318988	−	0.552503i	0.980277	+	0.197628i	$0.0633238\pi$
$558$	5.42999e15	−	3.13501e15i	0.179885	−	0.103856i
$559$			3.09588e16i			1.01464i
$560$	4.50235e15	−	9.40838e15i	0.145986	−	0.305061i
$561$	−3.40878e16			−1.09351
$562$	1.59719e16	+	2.76642e16i	0.506920	+	0.878011i
$563$	−1.49006e16	−	8.60286e15i	−0.467900	−	0.270142i	0.247460	−	0.968898i	$-0.420404\pi$
$563$	−1.49006e16	−	8.60286e15i	−0.467900	−	0.270142i	−0.715360	+	0.698756i	$0.753737\pi$
$564$	−7.71434e15	+	1.33616e16i	−0.239676	+	0.415131i
$565$	4.87593e16	−	2.81512e16i	1.49888	−	0.865379i
$566$		−	3.51181e16i		−	1.06815i
$567$	−3.54165e16	−	1.69484e16i	−1.06588	−	0.510072i
$568$	−6.89326e15			−0.205274
$569$	−1.64180e16	−	2.84368e16i	−0.483779	−	0.837930i	0.516048	−	0.856560i	$-0.327403\pi$
$569$	−1.64180e16	−	2.84368e16i	−0.483779	−	0.837930i	−0.999826	+	0.0186304i	$0.994069\pi$
$570$	−1.80279e16	−	1.04084e16i	−0.525651	−	0.303484i
$571$	−2.21946e16	+	3.84422e16i	−0.640369	+	1.10915i	0.344981	+	0.938610i	$0.387885\pi$
$571$	−2.21946e16	+	3.84422e16i	−0.640369	+	1.10915i	−0.985350	+	0.170543i	$0.945448\pi$
$572$	1.64058e16	−	9.47189e15i	0.468404	−	0.270433i
$573$		−	5.05282e16i		−	1.42760i
$574$	−7.69968e15	−	1.12339e16i	−0.215279	−	0.314093i
$575$	2.52243e16			0.697929
$576$	5.44464e14	+	9.43040e14i	0.0149085	+	0.0258223i
$577$	−1.53625e16	−	8.86954e15i	−0.416300	−	0.240351i	0.277193	−	0.960814i	$-0.410596\pi$
$577$	−1.53625e16	−	8.86954e15i	−0.416300	−	0.240351i	−0.693493	+	0.720463i	$0.743929\pi$
$578$	1.03417e16	−	1.79124e16i	0.277349	−	0.480383i
$579$	2.77965e16	−	1.60483e16i	0.737767	−	0.425950i
$580$			3.25874e16i			0.856015i
$581$	2.46307e16	−	1.90676e15i	0.640352	−	0.0495724i
$582$	−1.74365e16			−0.448664
$583$	1.42269e14	+	2.46418e14i	0.00362326	+	0.00627568i
$584$	−2.09758e16	−	1.21104e16i	−0.528739	−	0.305267i
$585$	−9.51020e15	+	1.64722e16i	−0.237276	+	0.410975i
$586$	−2.62124e16	+	1.51338e16i	−0.647324	+	0.373733i
$587$		−	1.42997e16i		−	0.349542i	−0.984609	−	0.174771i	$-0.944081\pi$
$587$		−	1.42997e16i		−	0.349542i	0.984609	−	0.174771i	$-0.0559185\pi$
$588$	1.79097e16	−	1.44273e16i	0.433336	−	0.349076i
$589$	−2.93169e16			−0.702145
$590$	3.01108e16	+	5.21535e16i	0.713856	+	1.23644i
$591$	2.10036e15	+	1.21264e15i	0.0492911	+	0.0284582i
$592$	−8.11954e15	+	1.40635e16i	−0.188626	+	0.326710i
$593$	6.69933e15	−	3.86786e15i	0.154065	−	0.0889493i	−0.420986	−	0.907067i	$-0.638316\pi$
$593$	6.69933e15	−	3.86786e15i	0.154065	−	0.0889493i	0.575050	+	0.818118i	$0.304982\pi$
$594$			1.93607e16i			0.440761i
$595$	−6.18875e15	−	7.99433e16i	−0.139477	−	1.80169i
$596$	−4.15136e16			−0.926218
$597$	2.41799e16	+	4.18807e16i	0.534082	+	0.925057i
$598$	−3.46314e16	−	1.99944e16i	−0.757291	−	0.437222i
$599$	−1.42448e16	+	2.46727e16i	−0.308387	+	0.534141i	−0.978010	−	0.208560i	$-0.933122\pi$
$599$	−1.42448e16	+	2.46727e16i	−0.308387	+	0.534141i	0.669623	+	0.742701i	$0.266456\pi$
$600$	1.31953e16	−	7.61829e15i	0.282820	−	0.163286i
$601$		−	1.25771e16i		−	0.266892i	−0.991056	−	0.133446i	$-0.957396\pi$
$601$		−	1.25771e16i		−	0.266892i	0.991056	−	0.133446i	$-0.0426042\pi$
$602$	1.91534e16	−	1.31277e16i	0.402409	−	0.275811i
$603$	−1.39247e16			−0.289656
$604$	2.04429e16	+	3.54082e16i	0.421039	+	0.729260i
$605$	−2.63671e16	−	1.52231e16i	−0.537688	−	0.310434i
$606$	2.11340e16	−	3.66051e16i	0.426723	−	0.739105i
$607$	−3.41643e16	+	1.97248e16i	−0.683030	+	0.394348i	−0.800996	−	0.598670i	$-0.795696\pi$
$607$	−3.41643e16	+	1.97248e16i	−0.683030	+	0.394348i	0.117965	+	0.993018i	$0.462363\pi$
$608$		−	5.09155e15i		−	0.100793i
$609$	−3.10165e16	+	6.48139e16i	−0.607980	+	1.27047i
$610$	4.63630e16			0.899897
$611$	−3.29574e16	−	5.70839e16i	−0.633441	−	1.09715i
$612$	7.24966e15	+	4.18559e15i	0.137978	+	0.0796615i
$613$	1.23442e16	−	2.13807e16i	0.232648	−	0.402958i	−0.725939	−	0.687759i	$-0.758594\pi$
$613$	1.23442e16	−	2.13807e16i	0.232648	−	0.402958i	0.958586	+	0.284802i	$0.0919277\pi$
$614$	−2.89210e16	+	1.66975e16i	−0.539763	+	0.311632i
$615$		−	4.38659e16i		−	0.810730i
$616$	−1.28167e16	−	6.13340e15i	−0.234581	−	0.112258i
$617$	−4.97598e16			−0.901919			−0.450959	−	0.892545i	$-0.648918\pi$
$617$	−4.97598e16			−0.901919			−0.450959	+	0.892545i	$0.648918\pi$
$618$	−1.74109e16	−	3.01566e16i	−0.312529	−	0.541316i
$619$	−1.68034e16	−	9.70147e15i	−0.298713	−	0.172462i	0.343152	−	0.939280i	$-0.388506\pi$
$619$	−1.68034e16	−	9.70147e15i	−0.298713	−	0.172462i	−0.641865	+	0.766818i	$0.721839\pi$
$620$	2.36558e16	−	4.09730e16i	0.416474	−	0.721353i
$621$	3.53936e16	−	2.04345e16i	0.617128	−	0.356299i
$622$		−	2.20340e16i		−	0.380497i
$623$	−1.37515e15	−	2.00635e15i	−0.0235191	−	0.0343145i
$624$	−2.41551e16			−0.409167
$625$	3.40077e16	+	5.89031e16i	0.570555	+	0.988230i
$626$	−1.30437e16	−	7.53079e15i	−0.216748	−	0.125139i
$627$	−1.41791e16	+	2.45588e16i	−0.233368	+	0.404206i
$628$	−1.40366e16	+	8.10406e15i	−0.228826	+	0.132113i
$629$			1.24839e17i			2.01579i
$630$	1.42236e16	−	1.10111e15i	0.227492	−	0.0176111i
$631$	1.89698e16			0.300530			0.150265	−	0.988646i	$-0.451987\pi$
$631$	1.89698e16			0.300530			0.150265	+	0.988646i	$0.451987\pi$
$632$	−1.11811e16	−	1.93662e16i	−0.175461	−	0.303907i
$633$	9.11041e16	+	5.25990e16i	1.41617	+	0.817627i
$634$	3.36715e16	−	5.83208e16i	0.518474	−	0.898024i
$635$	4.92717e15	−	2.84470e15i	0.0751546	−	0.0433905i
$636$		−	3.62813e14i		−	0.00548201i
$637$	1.51216e16	+	9.70817e16i	0.226341	+	1.45312i
$638$	4.43926e16			0.658244
$639$	−4.71421e15	−	8.16526e15i	−0.0692475	−	0.119940i
$640$	7.11589e15	+	4.10836e15i	0.103550	+	0.0597845i
$641$	−2.80509e16	+	4.85856e16i	−0.404389	+	0.700422i	−0.994250	−	0.107083i	$-0.965849\pi$
$641$	−2.80509e16	+	4.85856e16i	−0.404389	+	0.700422i	0.589861	+	0.807505i	$0.299182\pi$
$642$	1.06186e16	−	6.13063e15i	0.151655	−	0.0875578i
$643$			3.11805e15i			0.0441182i	0.999757	+	0.0220591i	$0.00702220\pi$
$643$			3.11805e15i			0.0441182i	−0.999757	+	0.0220591i	$0.992978\pi$
$644$	2.31499e15	+	2.99040e16i	0.0324515	+	0.419192i
$645$	7.47901e16			1.03869
$646$	−1.95707e16	−	3.38975e16i	−0.269285	−	0.466415i
$647$	6.91898e16	+	3.99467e16i	0.943227	+	0.544572i	0.890970	−	0.454061i	$-0.150025\pi$
$647$	6.91898e16	+	3.99467e16i	0.943227	+	0.544572i	0.0522565	+	0.998634i	$0.483359\pi$
$648$	1.54653e16	−	2.67867e16i	0.208886	−	0.361801i
$649$	7.10469e16	−	4.10189e16i	0.950773	−	0.548929i
$650$			6.50941e16i			0.863101i
$651$	8.60477e16	−	5.89769e16i	1.13045	−	0.774812i
$652$	5.02816e16			0.654521
$653$	−6.87264e16	−	1.19038e17i	−0.886430	−	1.53534i	−0.844066	−	0.536240i	$-0.819844\pi$
$653$	−6.87264e16	−	1.19038e17i	−0.886430	−	1.53534i	−0.0423648	−	0.999102i	$-0.513489\pi$
$654$	−2.33884e16	−	1.35033e16i	−0.298906	−	0.172574i
$655$	−5.08099e16	+	8.80053e16i	−0.643429	+	1.11445i
$656$	9.29163e15	−	5.36453e15i	0.116592	−	0.0673144i
$657$		−	3.31285e16i		−	0.411917i
$658$	−2.13411e16	+	4.45957e16i	−0.262943	+	0.549462i
$659$	−2.77636e15			−0.0338972			−0.0169486	−	0.999856i	$-0.505395\pi$
$659$	−2.77636e15			−0.0338972			−0.0169486	+	0.999856i	$0.505395\pi$
$660$	−2.28821e16	−	3.96330e16i	−0.276842	−	0.479505i
$661$	1.34435e17	+	7.76164e16i	1.61178	+	0.930560i	0.988958	+	0.148195i	$0.0473463\pi$
$661$	1.34435e17	+	7.76164e16i	1.61178	+	0.930560i	0.622820	+	0.782365i	$0.285987\pi$
$662$	−5.08213e15	+	8.80251e15i	−0.0603807	+	0.104582i
$663$	−1.60815e17	+	9.28465e16i	−1.89341	+	1.09316i
$664$			1.94617e16i			0.227076i
$665$	−6.01700e16	−	2.87942e16i	−0.695745	−	0.332947i
$666$	−2.22114e16			−0.254525
$667$	−4.68547e16	−	8.11548e16i	−0.532106	−	0.921635i
$668$	3.61122e16	+	2.08494e16i	0.406438	+	0.234657i
$669$	4.26015e16	−	7.37879e16i	0.475191	−	0.823054i
$670$	−9.09946e16	+	5.25358e16i	−1.00593	+	0.580773i
$671$		−	6.31587e16i		−	0.691988i
$672$	1.02427e16	+	1.49441e16i	0.111224	+	0.162276i
$673$	4.53293e15			0.0487852			0.0243926	−	0.999702i	$-0.492235\pi$
$673$	4.53293e15			0.0487852			0.0243926	+	0.999702i	$0.492235\pi$
$674$	−2.33048e16	−	4.03652e16i	−0.248592	−	0.430574i
$675$	−5.76139e16	−	3.32634e16i	−0.609123	−	0.351677i
$676$	2.77407e16	−	4.80483e16i	0.290695	−	0.503498i
$677$	−8.53907e16	+	4.93003e16i	−0.886908	+	0.512057i	−0.872930	−	0.487846i	$-0.837783\pi$
$677$	−8.53907e16	+	4.93003e16i	−0.886908	+	0.512057i	−0.0139781	+	0.999902i	$0.504450\pi$
$678$			9.77981e16i			1.00682i
$679$	−5.57061e16	+	4.31245e15i	−0.568439	+	0.0440053i
$680$	6.31664e16			0.638899
$681$	3.13765e16	+	5.43457e16i	0.314573	+	0.544857i
$682$	−5.58161e16	−	3.22255e16i	−0.554694	−	0.320253i
$683$	−3.01263e16	+	5.21802e16i	−0.296771	+	0.514022i	−0.975395	−	0.220463i	$-0.929243\pi$
$683$	−3.01263e16	+	5.21802e16i	−0.296771	+	0.514022i	0.678625	+	0.734485i	$0.262576\pi$
$684$	6.03108e15	−	3.48205e15i	0.0588923	−	0.0340015i
$685$		−	2.15148e17i		−	2.08255i
$686$	5.36498e16	−	5.05217e16i	0.514782	−	0.484768i
$687$	−1.43334e17			−1.36336
$688$	9.14636e15	+	1.58420e16i	0.0862418	+	0.149375i
$689$	1.34236e15	+	7.75010e14i	0.0125474	+	0.00724422i
$690$	−4.83024e16	+	8.36622e16i	−0.447584	+	0.775238i
$691$	1.24730e15	−	7.20129e14i	0.0114578	−	0.00661518i	−0.494260	−	0.869314i	$-0.664561\pi$
$691$	1.24730e15	−	7.20129e14i	0.0114578	−	0.00661518i	0.505718	+	0.862699i	$0.331228\pi$
$692$			4.46288e16i			0.406423i
$693$	−1.50000e15	−	1.93763e16i	−0.0135423	−	0.174933i
$694$	−3.94909e16			−0.353460
$695$	−4.03230e15	−	6.98415e15i	−0.0357803	−	0.0619733i
$696$	−4.90211e16	−	2.83023e16i	−0.431248	−	0.248981i
$697$	4.12400e16	−	7.14298e16i	0.359685	−	0.622992i
$698$	−9.81877e15	+	5.66887e15i	−0.0849033	+	0.0490190i
$699$		−	1.88894e17i		−	1.61940i
$700$	4.02721e16	−	2.76024e16i	0.342307	−	0.234617i
$701$	1.76004e17			1.48325			0.741623	−	0.670817i	$-0.234056\pi$
$701$	1.76004e17			1.48325			0.741623	+	0.670817i	$0.234056\pi$
$702$	5.27336e16	+	9.13373e16i	0.440621	+	0.763177i
$703$	8.99409e16	+	5.19274e16i	0.745118	+	0.430194i
$704$	5.59668e15	−	9.69373e15i	0.0459721	−	0.0796260i
$705$	−1.37903e17	+	7.96183e16i	−1.12315	+	0.648452i
$706$			1.28265e16i			0.103581i
$707$	5.84656e16	−	1.22173e17i	0.468149	−	0.978271i
$708$	−1.04606e17			−0.830532
$709$	−7.39721e16	−	1.28123e17i	−0.582358	−	1.00867i	−0.995199	−	0.0978712i	$-0.968797\pi$
$709$	−7.39721e16	−	1.28123e17i	−0.582358	−	1.00867i	0.412841	−	0.910803i	$-0.364537\pi$
$710$	−6.16125e16	−	3.55720e16i	−0.480971	−	0.277689i
$711$	1.52932e16	−	2.64886e16i	0.118380	−	0.205041i
$712$	1.65947e15	−	9.58094e14i	0.0127376	−	0.00735407i
$713$			1.36051e17i			1.03553i
$714$	1.25633e17	+	6.01215e16i	0.948235	+	0.453775i
$715$	1.95515e17			1.46334
$716$	−1.08431e16	−	1.87808e16i	−0.0804778	−	0.139392i
$717$	8.43270e16	+	4.86862e16i	0.620657	+	0.358336i
$718$	−1.34076e16	+	2.32227e16i	−0.0978601	+	0.169499i
$719$	−1.77523e16	+	1.02493e16i	−0.128493	+	0.0741857i	−0.562869	−	0.826546i	$-0.690302\pi$
$719$	−1.77523e16	+	1.02493e16i	−0.128493	+	0.0741857i	0.434375	+	0.900732i	$0.356969\pi$
$720$			1.12386e16i			0.0806712i
$721$	−6.30828e16	−	9.20381e16i	−0.449055	−	0.655173i
$722$	6.76009e16			0.477232
$723$	2.08129e16	+	3.60490e16i	0.145714	+	0.252385i
$724$	9.50049e16	+	5.48511e16i	0.659651	+	0.380850i
$725$	−7.62704e16	+	1.32104e17i	−0.525204	+	0.909680i
$726$	4.58000e16	−	2.64427e16i	0.312785	−	0.180586i
$727$			9.52642e15i			0.0645243i	0.999479	+	0.0322621i	$0.0102711\pi$
$727$			9.52642e15i			0.0645243i	−0.999479	+	0.0322621i	$0.989729\pi$
$728$	−7.71706e16	+	5.97411e15i	−0.518398	+	0.0401315i
$729$	−9.92481e16			−0.661237
$730$	−1.24989e17	−	2.16487e17i	−0.825913	−	1.43052i
$731$	1.21786e17	+	7.03130e16i	0.798164	+	0.460820i
$732$	−4.02666e16	+	6.97438e16i	−0.261745	+	0.453356i
$733$	8.31903e16	−	4.80299e16i	0.536351	−	0.309662i	−0.207248	−	0.978288i	$-0.566451\pi$
$733$	8.31903e16	−	4.80299e16i	0.536351	−	0.309662i	0.743599	+	0.668626i	$0.233117\pi$
$734$			2.11857e16i			0.135477i
$735$	2.34529e17	−	3.65307e16i	1.48755	−	0.231704i
$736$	−2.36283e16			−0.148650
$737$	7.15676e16	+	1.23959e17i	0.446593	+	0.773521i
$738$	1.27089e16	+	7.33747e15i	0.0786626	+	0.0454159i
$739$	−1.14442e17	+	1.98220e17i	−0.702618	+	1.21697i	0.264926	+	0.964269i	$0.414653\pi$
$739$	−1.14442e17	+	1.98220e17i	−0.702618	+	1.21697i	−0.967544	+	0.252702i	$0.918681\pi$
$740$	−1.45146e17	+	8.38003e16i	−0.883926	+	0.510335i
$741$			1.54480e17i			0.933177i
$742$	−8.97321e13	−	1.15912e15i	−0.000537681	−	0.00694549i
$743$	−1.73334e17			−1.03027			−0.515136	−	0.857109i	$-0.672258\pi$
$743$	−1.73334e17			−1.03027			−0.515136	+	0.857109i	$0.672258\pi$
$744$	4.10904e16	+	7.11707e16i	0.242272	+	0.419627i
$745$	−3.71052e17	−	2.14227e17i	−2.17019	−	1.25296i
$746$	5.29906e16	−	9.17824e16i	0.307444	−	0.532508i
$747$	−2.30529e16	+	1.33096e16i	−0.132679	+	0.0766022i
$748$		−	8.60493e16i		−	0.491290i
$749$	3.24079e16	−	2.22124e16i	0.183553	−	0.125807i
$750$	−3.22119e16			−0.180988
$751$	−5.91242e16	−	1.02406e17i	−0.329553	−	0.570803i	0.652870	−	0.757470i	$-0.273565\pi$
$751$	−5.91242e16	−	1.02406e17i	−0.329553	−	0.570803i	−0.982423	+	0.186667i	$0.940231\pi$
$752$	−3.37293e16	−	1.94736e16i	−0.186509	−	0.107681i
$753$	−4.23064e16	+	7.32769e16i	−0.232079	+	0.401973i
$754$	2.09429e17	−	1.20914e17i	1.13975	−	0.658035i
$755$			4.21976e17i			2.27827i
$756$	3.41469e16	−	7.13554e16i	0.182903	−	0.382205i
$757$	2.23980e17			1.19024			0.595118	−	0.803638i	$-0.297105\pi$
$757$	2.23980e17			1.19024			0.595118	+	0.803638i	$0.297105\pi$
$758$	1.10847e17	+	1.91992e17i	0.584396	+	1.01220i
$759$	1.13970e17	+	6.58007e16i	0.596129	+	0.344175i
$760$	2.62745e16	−	4.55087e16i	0.136349	−	0.236163i
$761$	7.69944e16	−	4.44527e16i	0.396416	−	0.228871i	−0.288521	−	0.957474i	$-0.593163\pi$
$761$	7.69944e16	−	4.44527e16i	0.396416	−	0.228871i	0.684936	+	0.728603i	$0.259830\pi$
$762$			9.88258e15i			0.0504824i
$763$	−7.80611e16	−	3.73559e16i	−0.395629	−	0.189327i
$764$	1.27550e17			0.641390
$765$	4.31987e16	+	7.48224e16i	0.215527	+	0.373304i
$766$	1.84200e17	+	1.06348e17i	0.911839	+	0.526450i
$767$	2.23450e17	−	3.87027e17i	1.09751	−	1.90094i
$768$	−1.23604e16	+	7.13628e15i	−0.0602372	+	0.0347780i
$769$			6.79519e16i			0.328582i	0.986412	+	0.164291i	$0.0525336\pi$
$769$			6.79519e16i			0.328582i	−0.986412	+	0.164291i	$0.947466\pi$
$770$	−8.29060e16	−	1.20960e17i	−0.397779	−	0.580361i
$771$	2.15753e17			1.02714
$772$	4.05115e16	+	7.01679e16i	0.191370	+	0.331463i
$773$	−1.75550e17	−	1.01354e17i	−0.822856	−	0.475076i	0.0285441	−	0.999593i	$-0.490913\pi$
$773$	−1.75550e17	−	1.01354e17i	−0.822856	−	0.475076i	−0.851400	+	0.524516i	$0.824246\pi$
$774$	−1.25102e16	+	2.16682e16i	−0.0581859	+	0.100781i
$775$	1.91794e17	−	1.10732e17i	0.885166	−	0.511051i
$776$		−	4.40156e16i		−	0.201575i
$777$	−3.68446e17	+	2.85230e16i	−1.67436	+	0.129619i
$778$	−9.41786e16			−0.424693
$779$	−3.43081e16	−	5.94233e16i	−0.153522	−	0.265908i
$780$	−2.15900e17	−	1.24650e17i	−0.958705	−	0.553509i
$781$	−4.84585e16	+	8.39326e16i	−0.213532	+	0.369849i
$782$	−1.57308e17	+	9.08218e16i	−0.687876	+	0.397145i
$783$			2.47151e17i			1.07248i
$784$	3.64193e16	+	4.52102e16i	0.156832	+	0.194688i
$785$	−1.67281e17			−0.714873
$786$	−8.82574e16	−	1.52866e17i	−0.374297	−	0.648301i
$787$	5.94097e15	+	3.43002e15i	0.0250040	+	0.0144361i	0.512450	−	0.858717i	$-0.328738\pi$
$787$	5.94097e15	+	3.43002e15i	0.0250040	+	0.0144361i	−0.487446	+	0.873153i	$0.662071\pi$
$788$	−3.06112e15	+	5.30202e15i	−0.0127857	+	0.0221454i
$789$	2.78727e17	−	1.60923e17i	1.15536	−	0.667047i
$790$		−	2.30795e17i		−	0.949433i
$791$	2.41877e16	+	3.12445e17i	0.0987498	+	1.27560i
$792$	1.53100e16			0.0620332
$793$	−1.72028e17	−	2.97961e17i	−0.691768	−	1.19818i
$794$	−2.71009e16	−	1.56467e16i	−0.108158	−	0.0624453i
$795$	1.87226e15	−	3.24285e15i	0.00741590	−	0.0128447i
$796$	−1.05721e17	+	6.10382e16i	−0.415608	+	0.239951i
$797$		−	3.49871e17i		−	1.36508i	−0.730848	−	0.682540i	$-0.760875\pi$
$797$		−	3.49871e17i		−	1.36508i	0.730848	−	0.682540i	$-0.239125\pi$
$798$	9.55730e16	−	6.55056e16i	0.370099	−	0.253665i
$799$	−2.99408e17			−1.15076
$800$	1.92312e16	+	3.33093e16i	0.0733611	+	0.127065i
$801$	2.26978e15	+	1.31046e15i	0.00859386	+	0.00496167i
$802$	9.68264e16	−	1.67708e17i	0.363871	−	0.630243i
$803$	−2.94913e17	+	1.70268e17i	−1.10002	+	0.635096i
$804$		−	1.82511e17i		−	0.675697i
$805$	−1.33625e17	+	2.79230e17i	−0.491035	+	1.02609i
$806$	−3.51095e17			−1.28060
$807$	−2.80107e16	−	4.85160e16i	−0.101411	−	0.175648i
$808$	9.24039e16	+	5.33494e16i	0.332064	+	0.191717i
$809$	2.06423e17	−	3.57535e17i	0.736320	−	1.27534i	−0.217822	−	0.975989i	$-0.569895\pi$
$809$	2.06423e17	−	3.57535e17i	0.736320	−	1.27534i	0.954142	−	0.299355i	$-0.0967714\pi$
$810$	2.76461e17	−	1.59615e17i	0.978867	−	0.565149i
$811$			1.30953e17i			0.460246i	0.973162	+	0.230123i	$0.0739129\pi$
$811$			1.30953e17i			0.460246i	−0.973162	+	0.230123i	$0.926087\pi$
$812$	−1.63613e17	−	7.82963e16i	−0.570795	−	0.273152i
$813$	−6.14408e17			−2.12771
$814$	1.14158e17	+	1.97728e17i	0.392428	+	0.679706i
$815$	4.49421e17	+	2.59473e17i	1.53359	+	0.885416i
$816$	−5.48604e16	+	9.50210e16i	−0.185831	+	0.321869i
$817$	1.01315e17	−	5.84943e16i	0.340676	−	0.196689i
$818$			3.10166e15i			0.0103532i
$819$	−5.98525e16	−	8.73251e16i	−0.198326	−	0.289358i
$820$	1.10733e17			0.364244
$821$	2.28661e17	+	3.96053e17i	0.746679	+	1.29329i	0.949406	+	0.314050i	$0.101686\pi$
$821$	2.28661e17	+	3.96053e17i	0.746679	+	1.29329i	−0.202728	+	0.979235i	$0.564981\pi$
$822$	3.23647e17	+	1.86858e17i	1.04916	+	0.605731i
$823$	−1.34881e17	+	2.33620e17i	−0.434061	+	0.751816i	−0.997218	−	0.0745339i	$-0.976253\pi$
$823$	−1.34881e17	+	2.33620e17i	−0.434061	+	0.751816i	0.563157	+	0.826350i	$0.309586\pi$
$824$	7.61254e16	−	4.39510e16i	0.243202	−	0.140413i
$825$		−	2.14221e17i		−	0.679421i
$826$	−3.34195e17	+	2.58715e16i	−1.05225	+	0.0814593i
$827$	3.09486e17			0.967403			0.483702	−	0.875233i	$-0.339292\pi$
$827$	3.09486e17			0.967403			0.483702	+	0.875233i	$0.339292\pi$
$828$	−1.61591e16	−	2.79884e16i	−0.0501459	−	0.0868553i
$829$	−3.48271e17	−	2.01074e17i	−1.07298	−	0.619482i	−0.143982	−	0.989580i	$-0.545991\pi$
$829$	−3.48271e17	−	2.01074e17i	−1.07298	−	0.619482i	−0.928993	+	0.370098i	$0.879324\pi$
$830$	−1.00430e17	+	1.73950e17i	−0.307182	+	0.532054i
$831$	−1.63512e17	+	9.44039e16i	−0.496529	+	0.286671i
$832$		−	6.09756e16i		−	0.183830i
$833$	4.16243e17	+	1.61004e17i	1.24588	+	0.481911i
$834$	1.40083e16			0.0416284
$835$	2.15182e17	+	3.72707e17i	0.634875	+	1.09964i
$836$	−6.19949e16	−	3.57928e16i	−0.181601	−	0.104847i
$837$	1.79411e17	−	3.10750e17i	0.521792	−	0.903770i
$838$	−7.98716e16	+	4.61139e16i	−0.230637	+	0.133158i
$839$		−	6.07001e17i		−	1.74027i	−0.492810	−	0.870137i	$-0.664030\pi$
$839$		−	6.07001e17i		−	1.74027i	0.492810	−	0.870137i	$-0.335970\pi$
$840$	1.44322e16	+	1.86428e17i	0.0410825	+	0.530684i
$841$	2.12882e17			0.601678
$842$	1.75415e17	+	3.03828e17i	0.492261	+	0.852620i
$843$	−4.95947e17	−	2.86335e17i	−1.38188	−	0.797827i
$844$	−1.32778e17	+	2.29978e17i	−0.367342	+	0.636255i
$845$	4.95898e17	−	2.86307e17i	1.36223	−	0.786487i
$846$		−	5.32711e16i		−	0.145301i
$847$	1.39782e17	−	9.58064e16i	0.378574	−	0.259474i
$848$	9.15863e14			0.00246295
$849$	3.14788e17	+	5.45229e17i	0.840566	+	1.45590i
$850$	2.56067e17	+	1.47840e17i	0.678953	+	0.391994i
$851$	2.40979e17	−	4.17388e17i	0.634457	−	1.09891i
$852$	1.07022e17	−	6.17890e16i	0.279791	−	0.161538i
$853$			9.20133e16i			0.238867i	0.992842	+	0.119434i	$0.0381078\pi$
$853$			9.20133e16i			0.238867i	−0.992842	+	0.119434i	$0.961892\pi$
$854$	−1.11395e17	+	2.32776e17i	−0.287155	+	0.600056i
$855$	7.18751e16			0.183985
$856$	1.54758e16	+	2.68049e16i	0.0393378	+	0.0681351i
$857$	−4.68450e17	−	2.70460e17i	−1.18244	−	0.682681i	−0.225860	−	0.974160i	$-0.572519\pi$
$857$	−4.68450e17	−	2.70460e17i	−1.18244	−	0.682681i	−0.956577	+	0.291479i	$0.905853\pi$
$858$	−1.69806e17	+	2.94113e17i	−0.425628	+	0.737209i
$859$	−1.73078e16	+	9.99268e15i	−0.0430808	+	0.0248727i	−0.521386	−	0.853321i	$-0.674585\pi$
$859$	−1.73078e16	+	9.99268e15i	−0.0430808	+	0.0248727i	0.478305	+	0.878194i	$0.341251\pi$
$860$			1.88796e17i			0.466661i
$861$	2.20239e17	+	1.05395e17i	0.540599	+	0.258702i
$862$	2.89794e15			0.00706393
$863$	−2.56860e17	−	4.44894e17i	−0.621772	−	1.07694i	−0.989156	−	0.146871i	$-0.953080\pi$
$863$	−2.56860e17	−	4.44894e17i	−0.621772	−	1.07694i	0.367384	−	0.930069i	$-0.380254\pi$
$864$	5.39687e16	+	3.11588e16i	0.129736	+	0.0749029i
$865$	−2.30303e17	+	3.98896e17i	−0.549797	+	0.952276i
$866$	−1.54029e16	+	8.89285e15i	−0.0365169	+	0.0210831i
$867$			3.70801e17i			0.873024i
$868$	1.48878e17	+	2.17214e17i	0.348106	+	0.507889i
$869$	−3.14404e17			−0.730079
$870$	−2.92103e17	−	5.05938e17i	−0.673629	−	1.16676i
$871$	6.75263e17	+	3.89863e17i	1.54655	+	0.892901i
$872$	3.40870e16	−	5.90404e16i	0.0775336	−	0.134292i
$873$	5.21378e16	−	3.01017e16i	0.117779	−	0.0679996i
$874$			1.51112e17i			0.339023i
$875$	−1.02911e17	+	7.96676e15i	−0.229304	+	0.0177514i
$876$	4.34215e17			0.960904
$877$	2.23428e17	+	3.86989e17i	0.491066	+	0.850551i	0.999947	−	0.0102854i	$-0.00327400\pi$
$877$	2.23428e17	+	3.86989e17i	0.491066	+	0.850551i	−0.508881	+	0.860837i	$0.669941\pi$
$878$	−3.14495e17	−	1.81574e17i	−0.686510	−	0.396356i
$879$	2.71309e17	−	4.69920e17i	0.588207	−	1.01880i
$880$	1.00047e17	−	5.77623e16i	0.215431	−	0.124379i
$881$		−	1.15011e17i		−	0.245971i	−0.992408	−	0.122985i	$-0.960753\pi$
$881$		−	1.15011e17i		−	0.245971i	0.992408	−	0.122985i	$-0.0392469\pi$
$882$	−2.86460e16	+	7.40584e16i	−0.0608490	+	0.157312i
$883$	2.25816e16			0.0476421			0.0238210	−	0.999716i	$-0.492417\pi$
$883$	2.25816e16			0.0476421			0.0238210	+	0.999716i	$0.492417\pi$
$884$	−2.34376e17	−	4.05951e17i	−0.491134	−	0.850669i
$885$	−9.34976e17	−	5.39809e17i	−1.94599	−	1.12352i
$886$	−3.53494e16	+	6.12269e16i	−0.0730767	+	0.126573i
$887$	−3.28689e17	+	1.89769e17i	−0.674907	+	0.389658i	−0.797933	−	0.602746i	$-0.794073\pi$
$887$	−3.28689e17	+	1.89769e17i	−0.674907	+	0.389658i	0.123026	+	0.992403i	$0.460740\pi$
$888$		−	2.91124e17i		−	0.593746i
$889$	2.44419e15	+	3.15729e16i	0.00495136	+	0.0639593i
$890$	1.97766e16			0.0397935
$891$	−2.17438e17	−	3.76613e17i	−0.434579	−	0.752712i
$892$	1.86266e17	+	1.07541e17i	0.369781	+	0.213493i
$893$	−1.24541e17	+	2.15711e17i	−0.245586	+	0.425367i
$894$	6.44523e17	−	3.72115e17i	1.26245	−	0.728874i
$895$		−	2.23820e17i		−	0.435472i
$896$	−3.77240e16	+	2.58560e16i	−0.0729072	+	0.0499705i
$897$	7.16896e17			1.37626
$898$	5.19417e16	+	8.99656e16i	0.0990508	+	0.171561i
$899$	−7.12525e17	−	4.11376e17i	−1.34971	−	0.779258i
$900$	−2.63039e16	+	4.55597e16i	−0.0494954	+	0.0857286i
$901$	6.09746e15	−	3.52037e15i	0.0113972	−	0.00658020i
$902$		−	1.50847e17i		−	0.280090i
$903$	−1.79695e17	+	3.75501e17i	−0.331444	+	0.692604i
$904$	−2.46876e17			−0.452343
$905$	5.66108e17	+	9.80527e17i	1.03040	+	1.78471i
$906$	−6.34777e17	−	3.66489e17i	−1.14776	−	0.662661i
$907$	−2.02438e17	+	3.50632e17i	−0.363620	+	0.629808i	−0.988554	−	0.150870i	$-0.951793\pi$
$907$	−2.02438e17	+	3.50632e17i	−0.363620	+	0.629808i	0.624934	+	0.780678i	$0.285126\pi$
$908$	−1.37187e17	+	7.92050e16i	−0.244792	+	0.141331i
$909$			1.45940e17i			0.258697i
$910$	−7.20586e17	−	3.44835e17i	−1.26893	−	0.607243i
$911$	1.61744e17			0.282956			0.141478	−	0.989941i	$-0.454815\pi$
$911$	1.61744e17			0.282956			0.141478	+	0.989941i	$0.454815\pi$
$912$	4.56391e16	+	7.90492e16i	0.0793173	+	0.137382i
$913$	2.36966e17	+	1.36812e17i	0.409130	+	0.236211i
$914$	−1.71202e17	+	2.96531e17i	−0.293651	+	0.508619i
$915$	−7.19813e17	+	4.15584e17i	−1.22657	+	0.708161i
$916$		−	3.61824e17i		−	0.612526i
$917$	−3.19772e17	−	4.66550e17i	−0.537805	−	0.784660i
$918$	4.79069e17			0.800465
$919$	−2.48909e17	−	4.31123e17i	−0.413188	−	0.715662i	0.582049	−	0.813154i	$-0.302251\pi$
$919$	−2.48909e17	−	4.31123e17i	−0.413188	−	0.715662i	−0.995236	+	0.0974921i	$0.968918\pi$
$920$	−2.11192e17	−	1.21932e17i	−0.348298	−	0.201090i
$921$	2.99343e17	−	5.18478e17i	0.490469	−	0.849517i
$922$	−1.50357e17	+	8.68088e16i	−0.244759	+	0.141312i
$923$			5.27954e17i			0.853858i
$924$	2.53964e17	−	1.96605e16i	0.408076	−	0.0315909i
$925$	−7.84535e17			−1.25245
$926$	−1.04700e17	−	1.81346e17i	−0.166066	−	0.287636i
$927$	1.04122e17	+	6.01151e16i	0.164084	+	0.0947339i
$928$	7.14448e16	−	1.23746e17i	0.111862	−	0.193751i
$929$	2.35012e17	−	1.35684e17i	0.365591	−	0.211074i	−0.305939	−	0.952051i	$-0.598970\pi$
$929$	2.35012e17	−	1.35684e17i	0.365591	−	0.211074i	0.671531	+	0.740977i	$0.265637\pi$
$930$			8.48173e17i			1.31095i
$931$	2.89136e17	−	2.32915e17i	0.444021	−	0.357684i
$932$	4.76832e17			0.727562
$933$	1.97506e17	+	3.42091e17i	0.299427	+	0.518623i
$934$	5.55466e17	+	3.20699e17i	0.836713	+	0.483076i
$935$	4.44050e17	−	7.69116e17i	0.664602	−	1.15112i
$936$	7.22273e16	−	4.17005e16i	0.107410	−	0.0620134i
$937$		−	1.19374e18i		−	1.76389i	−0.471356	−	0.881943i	$-0.656235\pi$
$937$		−	1.19374e18i		−	1.76389i	0.471356	−	0.881943i	$-0.343765\pi$
$938$	−4.51391e16	−	5.83085e17i	−0.0662729	−	0.856081i
$939$	2.70015e17			0.393907
$940$	−2.00984e17	−	3.48114e17i	−0.291336	−	0.504608i
$941$	−2.05289e17	−	1.18523e17i	−0.295684	−	0.170713i	0.344819	−	0.938669i	$-0.387940\pi$
$941$	−2.05289e17	−	1.18523e17i	−0.295684	−	0.170713i	−0.640502	+	0.767956i	$0.721274\pi$
$942$	1.45285e17	−	2.51640e17i	0.207929	−	0.360143i
$943$	−2.75766e17	+	1.59213e17i	−0.392166	+	0.226417i
$944$		−	2.64061e17i		−	0.373140i
$945$	6.73431e17	−	4.61569e17i	0.945589	−	0.648106i
$946$	2.57190e17			0.358845
$947$	−1.20199e17	−	2.08191e17i	−0.166648	−	0.288643i	0.770591	−	0.637330i	$-0.219961\pi$
$947$	−1.20199e17	−	2.08191e17i	−0.166648	−	0.288643i	−0.937239	+	0.348687i	$0.886628\pi$
$948$	3.47185e17	+	2.00447e17i	0.478311	+	0.276153i
$949$	−9.27532e17	+	1.60653e18i	−1.26979	+	2.19934i
$950$	2.13025e17	−	1.22990e17i	0.289794	−	0.167313i
$951$			1.20728e18i			1.63202i
$952$	−1.51767e17	+	3.17142e17i	−0.203871	+	0.426021i
$953$	1.51022e17			0.201596			0.100798	−	0.994907i	$-0.467860\pi$
$953$	1.51022e17			0.201596			0.100798	+	0.994907i	$0.467860\pi$
$954$	6.26348e14	+	1.08487e15i	0.000830855	+	0.00143908i
$955$	1.14006e18	+	6.58212e17i	1.50282	+	0.867652i
$956$	−1.22901e17	+	2.12870e17i	−0.160993	+	0.278848i
$957$	−6.89221e17	+	3.97922e17i	−0.897195	+	0.517996i
$958$		−	1.67484e17i		−	0.216660i
$959$	1.08020e18	+	5.16928e17i	1.38865	+	0.664535i
$960$	−1.47304e17			−0.188186
$961$	2.03421e17	+	3.52335e17i	0.258259	+	0.447317i
$962$	1.07712e18	+	6.21875e17i	1.35898	+	0.784607i
$963$	−2.11674e16	+	3.66630e16i	−0.0265406	+	0.0459696i
$964$	−9.09999e16	+	5.25388e16i	−0.113391	+	0.0654664i
$965$			8.36223e17i			1.03552i
$966$	−3.03991e17	−	4.43525e17i	−0.374109	−	0.545828i
$967$	−1.07464e18			−1.31433			−0.657166	−	0.753746i	$-0.728245\pi$
$967$	−1.07464e18			−1.31433			−0.657166	+	0.753746i	$0.728245\pi$
$968$	6.67503e16	+	1.15615e17i	0.0811336	+	0.140528i
$969$	6.07694e17	+	3.50852e17i	0.734078	+	0.423820i
$970$	2.27139e17	−	3.93416e17i	0.272685	−	0.472303i
$971$	1.29510e18	−	7.47725e17i	1.54521	−	0.892127i	0.546712	−	0.837320i	$-0.315879\pi$
$971$	1.29510e18	−	7.47725e17i	1.54521	−	0.892127i	0.998497	−	0.0548066i	$-0.0174542\pi$
$972$			1.97174e17i			0.233804i
$973$	4.47538e16	−	3.46459e15i	0.0527416	−	0.00408295i
$974$	−7.76194e17			−0.909110
$975$	−5.83484e17	−	1.01062e18i	−0.679205	−	1.17642i
$976$	−1.76057e17	−	1.01647e17i	−0.203683	−	0.117596i
$977$	−4.73033e16	+	8.19317e16i	−0.0543906	+	0.0942073i	−0.891939	−	0.452156i	$-0.850655\pi$
$977$	−4.73033e16	+	8.19317e16i	−0.0543906	+	0.0942073i	0.837548	+	0.546364i	$0.183988\pi$
$978$	−7.80650e17	+	4.50709e17i	−0.892120	+	0.515066i
$979$		−	2.69410e16i		−	0.0305997i
$980$	9.22161e16	+	5.92031e17i	0.104100	+	0.668326i
$981$	9.32467e16			0.104621
$982$	2.68693e17	+	4.65391e17i	0.299632	+	0.518978i
$983$	−1.78182e17	−	1.02873e17i	−0.197488	−	0.114020i	0.397995	−	0.917388i	$-0.369706\pi$
$983$	−1.78182e17	−	1.02873e17i	−0.197488	−	0.114020i	−0.595483	+	0.803368i	$0.703039\pi$
$984$	−9.61719e16	+	1.66575e17i	−0.105944	+	0.183501i
$985$	−5.47212e16	+	3.15933e16i	−0.0599153	+	0.0345921i
$986$		−	1.09847e18i		−	1.19544i
$987$	−6.84086e16	−	8.83669e17i	−0.0739959	−	0.955843i
$988$	−3.89961e17			−0.419256
$989$	−2.71454e17	−	4.70172e17i	−0.290081	−	0.502434i
$990$	1.36842e17	+	7.90058e16i	0.145348	+	0.0839166i
$991$	−4.00321e16	+	6.93377e16i	−0.0422636	+	0.0732027i	−0.886383	−	0.462952i	$-0.846790\pi$
$991$	−4.00321e16	+	6.93377e16i	−0.0422636	+	0.0732027i	0.844120	+	0.536155i	$0.180124\pi$
$992$	−1.79659e17	+	1.03726e17i	−0.188529	+	0.108848i
$993$		−	1.82219e17i		−	0.190063i
$994$	3.26631e17	−	2.23873e17i	0.338641	−	0.232104i
$995$	−1.25993e18			−1.29840
$996$	−1.74448e17	−	3.02153e17i	−0.178694	−	0.309508i
$997$	9.46237e17	+	5.46310e17i	0.963449	+	0.556248i	0.897233	−	0.441558i	$-0.145574\pi$
$997$	9.46237e17	+	5.46310e17i	0.963449	+	0.556248i	0.0662163	+	0.997805i	$0.478907\pi$
$998$	6.68529e16	−	1.15793e17i	0.0676608	−	0.117192i
$999$	−1.10083e18	+	6.35562e17i	−1.10745	+	0.639388i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.13.d.a.3.3	✓	16
3.2	odd	2		126.13.n.a.73.8		16
4.3	odd	2		112.13.s.c.17.3		16
7.2	even	3		98.13.d.a.19.2		16
7.3	odd	6		98.13.b.c.97.14		16
7.4	even	3		98.13.b.c.97.11		16
7.5	odd	6	inner	14.13.d.a.5.3	yes	16
7.6	odd	2		98.13.d.a.31.2		16
21.5	even	6		126.13.n.a.19.8		16
28.19	even	6		112.13.s.c.33.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.13.d.a.3.3	✓	16	1.1	even	1	trivial
14.13.d.a.5.3	yes	16	7.5	odd	6	inner
98.13.b.c.97.11		16	7.4	even	3
98.13.b.c.97.14		16	7.3	odd	6
98.13.d.a.19.2		16	7.2	even	3
98.13.d.a.31.2		16	7.6	odd	2
112.13.s.c.17.3		16	4.3	odd	2
112.13.s.c.33.3		16	28.19	even	6
126.13.n.a.19.8		16	21.5	even	6
126.13.n.a.73.8		16	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	14.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-22.6274 - 39.1918i) q^{2} +(702.607 + 405.650i) q^{3} +(-1024.00 + 1773.62i) q^{4} +(-18305.2 + 10568.5i) q^{5} -36715.3i q^{6} +(-9080.55 - 117298. i) q^{7} +92681.9 q^{8} +(63384.0 + 109784. i) q^{9} +O(q^{10})\)	\(q+(-22.6274 - 39.1918i) q^{2} +(702.607 + 405.650i) q^{3} +(-1024.00 + 1773.62i) q^{4} +(-18305.2 + 10568.5i) q^{5} -36715.3i q^{6} +(-9080.55 - 117298. i) q^{7} +92681.9 q^{8} +(63384.0 + 109784. i) q^{9} +(828399. + 478276. i) q^{10} +(651539. - 1.12850e6i) q^{11} +(-1.43894e6 + 830772. i) q^{12} -7.09849e6i q^{13} +(-4.39166e6 + 3.01003e6i) q^{14} -1.71485e7 q^{15} +(-2.09715e6 - 3.63237e6i) q^{16} +(-2.79240e7 - 1.61219e7i) q^{17} +(2.86843e6 - 4.96827e6i) q^{18} +(-2.32303e7 + 1.34120e7i) q^{19} -4.32886e7i q^{20} +(4.12019e7 - 8.60980e7i) q^{21} -5.89706e7 q^{22} +(6.22412e7 + 1.07805e8i) q^{23} +(6.51190e7 + 3.75965e7i) q^{24} +(1.01317e8 - 1.75486e8i) q^{25} +(-2.78203e8 + 1.60621e8i) q^{26} -3.28312e8i q^{27} +(2.17341e8 + 1.04008e8i) q^{28} -7.52793e8 q^{29} +(3.88026e8 + 6.72081e8i) q^{30} +(9.46508e8 + 5.46467e8i) q^{31} +(-9.49063e7 + 1.64382e8i) q^{32} +(9.15552e8 - 5.28594e8i) q^{33} +1.45919e9i q^{34} +(1.40589e9 + 2.05120e9i) q^{35} -2.59621e8 q^{36} +(-1.93585e9 - 3.35299e9i) q^{37} +(1.05129e9 + 6.06960e8i) q^{38} +(2.87951e9 - 4.98745e9i) q^{39} +(-1.69656e9 + 9.79510e8i) q^{40} +2.55800e9i q^{41} +(-4.30663e9 + 3.33395e8i) q^{42} -4.36133e9 q^{43} +(1.33435e9 + 2.31116e9i) q^{44} +(-2.32051e9 - 1.33975e9i) q^{45} +(2.81672e9 - 4.87869e9i) q^{46} +(8.04169e9 - 4.64287e9i) q^{47} -3.40284e9i q^{48} +(-1.36764e10 + 2.13026e9i) q^{49} -9.17013e9 q^{50} +(-1.30797e10 - 2.26548e10i) q^{51} +(1.25900e10 + 7.26886e9i) q^{52} +(-1.09179e8 + 1.89104e8i) q^{53} +(-1.28671e10 + 7.42884e9i) q^{54} +2.75432e10i q^{55} +(-8.41602e8 - 1.08714e10i) q^{56} -2.17624e10 q^{57} +(1.70338e10 + 2.95033e10i) q^{58} +(5.45224e10 + 3.14785e10i) q^{59} +(1.75600e10 - 3.04149e10i) q^{60} +(4.19753e10 - 2.42344e10i) q^{61} -4.94605e10i q^{62} +(1.23019e10 - 8.43172e9i) q^{63} +8.58993e9 q^{64} +(7.50205e10 + 1.29939e11i) q^{65} +(-4.14331e10 - 2.39214e10i) q^{66} +(-5.49220e10 + 9.51277e10i) q^{67} +(5.71884e10 - 3.30177e10i) q^{68} +1.00993e11i q^{69} +(4.85786e10 - 1.01513e11i) q^{70} -7.43754e10 q^{71} +(5.87455e9 + 1.01750e10i) q^{72} +(-2.26320e11 - 1.30666e11i) q^{73} +(-8.76065e10 + 1.51739e11i) q^{74} +(1.42372e11 - 8.21982e10i) q^{75} -5.49357e10i q^{76} +(-1.38287e11 - 6.61769e10i) q^{77} -2.60623e11 q^{78} +(-1.20639e11 - 2.08953e11i) q^{79} +(7.67776e10 + 4.43276e10i) q^{80} +(1.66865e11 - 2.89018e11i) q^{81} +(1.00253e11 - 5.78810e10i) q^{82} +2.09983e11i q^{83} +(1.10514e11 + 1.61241e11i) q^{84} +6.81540e11 q^{85} +(9.86855e10 + 1.70928e11i) q^{86} +(-5.28918e11 - 3.05371e11i) q^{87} +(6.03859e10 - 1.04591e11i) q^{88} +(1.79050e10 - 1.03374e10i) q^{89} +1.21260e11i q^{90} +(-8.32640e11 + 6.44582e10i) q^{91} -2.54940e11 q^{92} +(4.43349e11 + 7.67903e11i) q^{93} +(-3.63926e11 - 2.10113e11i) q^{94} +(2.83491e11 - 4.91020e11i) q^{95} +(-1.33364e11 + 7.69975e10i) q^{96} -4.74911e11i q^{97} +(3.92950e11 + 4.87800e11i) q^{98} +1.65189e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16384 q^{4} + 18144 q^{5} - 469720 q^{7} + 2362248 q^{9}+O(q^{10}) \) 16 * q - 16384 * q^4 + 18144 * q^5 - 469720 * q^7 + 2362248 * q^9	\( 16 q - 16384 q^{4} + 18144 q^{5} - 469720 q^{7} + 2362248 q^{9} - 2290176 q^{10} + 2072088 q^{11} - 11501568 q^{14} - 27163728 q^{15} - 33554432 q^{16} - 101561040 q^{17} - 4592640 q^{18} + 174931848 q^{19} - 323731368 q^{21} + 62776320 q^{22} + 25630560 q^{23} + 242221056 q^{24} + 521205808 q^{25} - 1434682368 q^{26} + 350863360 q^{28} + 532360944 q^{29} - 2151917568 q^{30} + 4583818344 q^{31} + 6054957720 q^{33} - 1612540440 q^{35} - 9675767808 q^{36} + 5764524040 q^{37} - 149506560 q^{38} + 10526083272 q^{39} + 4690280448 q^{40} - 12685086720 q^{42} - 66929432000 q^{43} + 4243636224 q^{44} + 57253352184 q^{45} + 7203213312 q^{46} + 18116171640 q^{47} - 9977452064 q^{49} - 99248080896 q^{50} - 23299256376 q^{51} + 8269578240 q^{52} + 39134161800 q^{53} + 105152205312 q^{54} + 3623878656 q^{56} - 328243960080 q^{57} + 29637396480 q^{58} + 201845459088 q^{59} + 27815657472 q^{60} + 336780254328 q^{61} - 389095094520 q^{63} + 137438953472 q^{64} + 158322703896 q^{65} + 268884080640 q^{66} + 107767119920 q^{67} + 207997009920 q^{68} - 6077815296 q^{70} - 1150259029344 q^{71} - 9405726720 q^{72} - 738414283320 q^{73} + 4902778368 q^{74} + 1537028640000 q^{75} - 321203352960 q^{77} - 786088888320 q^{78} + 227632064768 q^{79} - 76101451776 q^{80} - 391984178400 q^{81} - 302578053120 q^{82} - 32685686784 q^{84} + 710209696080 q^{85} - 38105192448 q^{86} + 1957017683880 q^{87} - 64282951680 q^{88} - 2485007442792 q^{89} + 1803248333904 q^{91} - 104982773760 q^{92} - 458668768680 q^{93} - 2021298693120 q^{94} - 186503862960 q^{95} - 496068722688 q^{96} - 356371660800 q^{98} + 3921180354576 q^{99}+O(q^{100}) \) 16 * q - 16384 * q^4 + 18144 * q^5 - 469720 * q^7 + 2362248 * q^9 - 2290176 * q^10 + 2072088 * q^11 - 11501568 * q^14 - 27163728 * q^15 - 33554432 * q^16 - 101561040 * q^17 - 4592640 * q^18 + 174931848 * q^19 - 323731368 * q^21 + 62776320 * q^22 + 25630560 * q^23 + 242221056 * q^24 + 521205808 * q^25 - 1434682368 * q^26 + 350863360 * q^28 + 532360944 * q^29 - 2151917568 * q^30 + 4583818344 * q^31 + 6054957720 * q^33 - 1612540440 * q^35 - 9675767808 * q^36 + 5764524040 * q^37 - 149506560 * q^38 + 10526083272 * q^39 + 4690280448 * q^40 - 12685086720 * q^42 - 66929432000 * q^43 + 4243636224 * q^44 + 57253352184 * q^45 + 7203213312 * q^46 + 18116171640 * q^47 - 9977452064 * q^49 - 99248080896 * q^50 - 23299256376 * q^51 + 8269578240 * q^52 + 39134161800 * q^53 + 105152205312 * q^54 + 3623878656 * q^56 - 328243960080 * q^57 + 29637396480 * q^58 + 201845459088 * q^59 + 27815657472 * q^60 + 336780254328 * q^61 - 389095094520 * q^63 + 137438953472 * q^64 + 158322703896 * q^65 + 268884080640 * q^66 + 107767119920 * q^67 + 207997009920 * q^68 - 6077815296 * q^70 - 1150259029344 * q^71 - 9405726720 * q^72 - 738414283320 * q^73 + 4902778368 * q^74 + 1537028640000 * q^75 - 321203352960 * q^77 - 786088888320 * q^78 + 227632064768 * q^79 - 76101451776 * q^80 - 391984178400 * q^81 - 302578053120 * q^82 - 32685686784 * q^84 + 710209696080 * q^85 - 38105192448 * q^86 + 1957017683880 * q^87 - 64282951680 * q^88 - 2485007442792 * q^89 + 1803248333904 * q^91 - 104982773760 * q^92 - 458668768680 * q^93 - 2021298693120 * q^94 - 186503862960 * q^95 - 496068722688 * q^96 - 356371660800 * q^98 + 3921180354576 * q^99

Introduction

L-functions

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