LMFDB - Embedded newform 98.13.d.a.19.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,13,Mod(19,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("98.19");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	98.d (of order $6$, degree $2$, not 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:	$89.5713940931$
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} - 8 x^{15} - 2204556 x^{14} - 87623088 x^{13} + 1948666431190 x^{12} + 195028079162640 x^{11} + \cdots + 24\!\cdots\!25 $ x^16 - 8x^15 - 2204556x^14 - 87623088x^13 + 1948666431190x^12 + 195028079162640x^11 - 880028445307457796x^10 - 151849761581608663584x^9 + 211028190361269390536623x^8 + 54528516937299786222168960x^7 - 23832744423106572444860463196x^6 - 9141197551096679767843476458896x^5 + 523508549551073444838291611810734x^4 + 566732587460008152706924066069468392x^3 + 73514373627956541910802883627148139944x^2 + 2445664577552004486793879639585121170640*x + 24120197826518417347025654428599335187025
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{48}\cdot 3^{8}\cdot 7^{8} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.4
Root			$-496.819 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	98.19
Dual form			98.13.d.a.31.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-22.6274 + 39.1918i) q^{2} +(745.979 - 430.691i) q^{3} +(-1024.00 - 1773.62i) q^{4} +(7532.28 + 4348.76i) q^{5} +38981.7i q^{6} +92681.9 q^{8} +(105269. - 182331. i) q^{9} +O(q^{10})$	\(q+(-22.6274 + 39.1918i) q^{2} +(745.979 - 430.691i) q^{3} +(-1024.00 - 1773.62i) q^{4} +(7532.28 + 4348.76i) q^{5} +38981.7i q^{6} +92681.9 q^{8} +(105269. - 182331. i) q^{9} +(-340872. + 196803. i) q^{10} +(257922. + 446735. i) q^{11} +(-1.52776e6 - 882055. i) q^{12} -2.74786e6i q^{13} +7.49190e6 q^{15} +(-2.09715e6 + 3.63237e6i) q^{16} +(-5.50579e6 + 3.17877e6i) q^{17} +(4.76393e6 + 8.25138e6i) q^{18} +(-6.71736e7 - 3.87827e7i) q^{19} -1.78125e7i q^{20} -2.33445e7 q^{22} +(5.20289e7 - 9.01168e7i) q^{23} +(6.91387e7 - 3.99173e7i) q^{24} +(-8.42468e7 - 1.45920e8i) q^{25} +(1.07694e8 + 6.21770e7i) q^{26} +2.76420e8i q^{27} -1.41564e8 q^{29} +(-1.69522e8 + 2.93621e8i) q^{30} +(6.99677e8 - 4.03959e8i) q^{31} +(-9.49063e7 - 1.64382e8i) q^{32} +(3.84809e8 + 2.22170e8i) q^{33} -2.87709e8i q^{34} -4.31182e8 q^{36} +(1.86759e9 - 3.23475e9i) q^{37} +(3.03993e9 - 1.75510e9i) q^{38} +(-1.18348e9 - 2.04985e9i) q^{39} +(6.98106e8 + 4.03052e8i) q^{40} +4.75235e9i q^{41} +8.94118e9 q^{43} +(5.28225e8 - 9.14913e8i) q^{44} +(1.58583e9 - 9.15581e8i) q^{45} +(2.35456e9 + 4.07822e9i) q^{46} +(-1.79163e10 - 1.03440e10i) q^{47} +3.61290e9i q^{48} +7.62515e9 q^{50} +(-2.73814e9 + 4.74259e9i) q^{51} +(-4.87367e9 + 2.81381e9i) q^{52} +(-1.17271e10 - 2.03119e10i) q^{53} +(-1.08334e10 - 6.25467e9i) q^{54} +4.48657e9i q^{55} -6.68134e10 q^{57} +(3.20324e9 - 5.54817e9i) q^{58} +(1.83475e9 - 1.05929e9i) q^{59} +(-7.67170e9 - 1.32878e10i) q^{60} +(7.28376e9 + 4.20528e9i) q^{61} +3.65622e10i q^{62} +8.58993e9 q^{64} +(1.19498e10 - 2.06977e10i) q^{65} +(-1.74145e10 + 1.00543e10i) q^{66} +(3.27239e10 + 5.66794e10i) q^{67} +(1.12759e10 + 6.51012e9i) q^{68} -8.96336e10i q^{69} -2.46780e11 q^{71} +(9.75654e9 - 1.68988e10i) q^{72} +(-8.87210e10 + 5.12231e10i) q^{73} +(8.45173e10 + 1.46388e11i) q^{74} +(-1.25693e11 - 7.25687e10i) q^{75} +1.58854e11i q^{76} +1.07116e11 q^{78} +(1.38548e11 - 2.39973e11i) q^{79} +(-3.15927e10 + 1.82400e10i) q^{80} +(1.74996e11 + 3.03102e11i) q^{81} +(-1.86253e11 - 1.07533e11i) q^{82} -8.18271e10i q^{83} -5.52949e10 q^{85} +(-2.02316e11 + 3.50421e11i) q^{86} +(-1.05604e11 + 6.09705e10i) q^{87} +(2.39047e10 + 4.14042e10i) q^{88} +(4.69496e10 + 2.71064e10i) q^{89} +8.28689e10i q^{90} -2.13111e11 q^{92} +(3.47963e11 - 6.02689e11i) q^{93} +(8.10797e11 - 4.68114e11i) q^{94} +(-3.37314e11 - 5.84244e11i) q^{95} +(-1.41596e11 - 8.17506e10i) q^{96} -3.42738e11i q^{97} +1.08605e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16384 q^{4} - 18144 q^{5} + 2362248 q^{9}+O(q^{10}) $ 16 * q - 16384 * q^4 - 18144 * q^5 + 2362248 * q^9	\( 16 q - 16384 q^{4} - 18144 q^{5} + 2362248 q^{9} + 2290176 q^{10} + 2072088 q^{11} - 27163728 q^{15} - 33554432 q^{16} + 101561040 q^{17} - 4592640 q^{18} - 174931848 q^{19} + 62776320 q^{22} + 25630560 q^{23} - 242221056 q^{24} + 521205808 q^{25} + 1434682368 q^{26} + 532360944 q^{29} - 2151917568 q^{30} - 4583818344 q^{31} - 6054957720 q^{33} - 9675767808 q^{36} + 5764524040 q^{37} + 149506560 q^{38} + 10526083272 q^{39} - 4690280448 q^{40} - 66929432000 q^{43} + 4243636224 q^{44} - 57253352184 q^{45} + 7203213312 q^{46} - 18116171640 q^{47} - 99248080896 q^{50} - 23299256376 q^{51} - 8269578240 q^{52} + 39134161800 q^{53} - 105152205312 q^{54} - 328243960080 q^{57} + 29637396480 q^{58} - 201845459088 q^{59} + 27815657472 q^{60} - 336780254328 q^{61} + 137438953472 q^{64} + 158322703896 q^{65} - 268884080640 q^{66} + 107767119920 q^{67} - 207997009920 q^{68} - 1150259029344 q^{71} - 9405726720 q^{72} + 738414283320 q^{73} + 4902778368 q^{74} - 1537028640000 q^{75} - 786088888320 q^{78} + 227632064768 q^{79} + 76101451776 q^{80} - 391984178400 q^{81} + 302578053120 q^{82} + 710209696080 q^{85} - 38105192448 q^{86} - 1957017683880 q^{87} - 64282951680 q^{88} + 2485007442792 q^{89} - 104982773760 q^{92} - 458668768680 q^{93} + 2021298693120 q^{94} - 186503862960 q^{95} + 496068722688 q^{96} + 3921180354576 q^{99}+O(q^{100}) \) 16 * q - 16384 * q^4 - 18144 * q^5 + 2362248 * q^9 + 2290176 * q^10 + 2072088 * q^11 - 27163728 * q^15 - 33554432 * q^16 + 101561040 * q^17 - 4592640 * q^18 - 174931848 * q^19 + 62776320 * q^22 + 25630560 * q^23 - 242221056 * q^24 + 521205808 * q^25 + 1434682368 * q^26 + 532360944 * q^29 - 2151917568 * q^30 - 4583818344 * q^31 - 6054957720 * q^33 - 9675767808 * q^36 + 5764524040 * q^37 + 149506560 * q^38 + 10526083272 * q^39 - 4690280448 * q^40 - 66929432000 * q^43 + 4243636224 * q^44 - 57253352184 * q^45 + 7203213312 * q^46 - 18116171640 * q^47 - 99248080896 * q^50 - 23299256376 * q^51 - 8269578240 * q^52 + 39134161800 * q^53 - 105152205312 * q^54 - 328243960080 * q^57 + 29637396480 * q^58 - 201845459088 * q^59 + 27815657472 * q^60 - 336780254328 * q^61 + 137438953472 * q^64 + 158322703896 * q^65 - 268884080640 * q^66 + 107767119920 * q^67 - 207997009920 * q^68 - 1150259029344 * q^71 - 9405726720 * q^72 + 738414283320 * q^73 + 4902778368 * q^74 - 1537028640000 * q^75 - 786088888320 * q^78 + 227632064768 * q^79 + 76101451776 * q^80 - 391984178400 * q^81 + 302578053120 * q^82 + 710209696080 * q^85 - 38105192448 * q^86 - 1957017683880 * q^87 - 64282951680 * q^88 + 2485007442792 * q^89 - 104982773760 * q^92 - 458668768680 * q^93 + 2021298693120 * q^94 - 186503862960 * q^95 + 496068722688 * q^96 + 3921180354576 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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
$3$	745.979	−	430.691i	1.02329	−	0.590797i	0.108235	−	0.994125i	$-0.465480\pi$
$3$	745.979	−	430.691i	1.02329	−	0.590797i	0.915055	+	0.403328i	$0.132147\pi$
$4$	−1024.00	−	1773.62i	−0.250000	−	0.433013i
$5$	7532.28	+	4348.76i	0.482066	+	0.278321i	0.721277	−	0.692647i	$-0.243555\pi$
$5$	7532.28	+	4348.76i	0.482066	+	0.278321i	−0.239211	+	0.970968i	$0.576889\pi$
$6$			38981.7i			0.835513i
$7$		0			0
$7$		0			0
$8$	92681.9			0.353553
$9$	105269.	−	182331.i	0.198082	−	0.343089i
$10$	−340872.	+	196803.i	−0.340872	+	0.196803i
$11$	257922.	+	446735.i	0.145590	+	0.252170i	0.929593	−	0.368587i	$-0.120158\pi$
$11$	257922.	+	446735.i	0.145590	+	0.252170i	−0.784003	+	0.620758i	$0.786825\pi$
$12$	−1.52776e6	−	882055.i	−0.511645	−	0.295399i
$13$		−	2.74786e6i		−	0.569292i	−0.958633	−	0.284646i	$-0.908124\pi$
$13$		−	2.74786e6i		−	0.569292i	0.958633	−	0.284646i	$-0.0918760\pi$
$14$		0			0
$15$	7.49190e6			0.657725
$16$	−2.09715e6	+	3.63237e6i	−0.125000	+	0.216506i
$17$	−5.50579e6	+	3.17877e6i	−0.228100	+	0.131694i	−0.609695	−	0.792636i	$-0.708708\pi$
$17$	−5.50579e6	+	3.17877e6i	−0.228100	+	0.131694i	0.381595	+	0.924330i	$0.375375\pi$
$18$	4.76393e6	+	8.25138e6i	0.140065	+	0.242600i
$19$	−6.71736e7	−	3.87827e7i	−1.42783	−	0.824359i	−0.430882	−	0.902408i	$-0.641797\pi$
$19$	−6.71736e7	−	3.87827e7i	−1.42783	−	0.824359i	−0.996949	+	0.0780497i	$0.975131\pi$
$20$		−	1.78125e7i		−	0.278321i
$21$		0			0
$22$	−2.33445e7			−0.205896
$23$	5.20289e7	−	9.01168e7i	0.351462	−	0.608750i	−0.635044	−	0.772476i	$-0.719018\pi$
$23$	5.20289e7	−	9.01168e7i	0.351462	−	0.608750i	0.986506	+	0.163726i	$0.0523514\pi$
$24$	6.91387e7	−	3.99173e7i	0.361788	−	0.208878i
$25$	−8.42468e7	−	1.45920e8i	−0.345075	−	0.597687i
$26$	1.07694e8	+	6.21770e7i	0.348619	+	0.201275i
$27$			2.76420e8i			0.713488i
$28$		0			0
$29$	−1.41564e8			−0.237994			−0.118997	−	0.992895i	$-0.537968\pi$
$29$	−1.41564e8			−0.237994			−0.118997	+	0.992895i	$0.537968\pi$
$30$	−1.69522e8	+	2.93621e8i	−0.232541	+	0.402772i
$31$	6.99677e8	−	4.03959e8i	0.788365	−	0.455163i	−0.0510215	−	0.998698i	$-0.516248\pi$
$31$	6.99677e8	−	4.03959e8i	0.788365	−	0.455163i	0.839387	+	0.543535i	$0.182914\pi$
$32$	−9.49063e7	−	1.64382e8i	−0.0883883	−	0.153093i
$33$	3.84809e8	+	2.22170e8i	0.297963	+	0.172029i
$34$		−	2.87709e8i		−	0.186243i
$35$		0			0
$36$	−4.31182e8			−0.198082
$37$	1.86759e9	−	3.23475e9i	0.727898	−	1.26076i	−0.229873	−	0.973221i	$-0.573831\pi$
$37$	1.86759e9	−	3.23475e9i	0.727898	−	1.26076i	0.957770	−	0.287535i	$-0.0928357\pi$
$38$	3.03993e9	−	1.75510e9i	1.00963	−	0.582910i
$39$	−1.18348e9	−	2.04985e9i	−0.336336	−	0.582551i
$40$	6.98106e8	+	4.03052e8i	0.170436	+	0.0984013i
$41$			4.75235e9i			1.00047i	0.865889	+	0.500236i	$0.166754\pi$
$41$			4.75235e9i			1.00047i	−0.865889	+	0.500236i	$0.833246\pi$
$42$		0			0
$43$	8.94118e9			1.41444			0.707219	−	0.706994i	$-0.249949\pi$
$43$	8.94118e9			1.41444			0.707219	+	0.706994i	$0.249949\pi$
$44$	5.28225e8	−	9.14913e8i	0.0727952	−	0.126085i
$45$	1.58583e9	−	9.15581e8i	0.190977	−	0.110261i
$46$	2.35456e9	+	4.07822e9i	0.248521	+	0.430451i
$47$	−1.79163e10	−	1.03440e10i	−1.66211	−	0.959621i	−0.971705	−	0.236199i	$-0.924098\pi$
$47$	−1.79163e10	−	1.03440e10i	−1.66211	−	0.959621i	−0.690407	−	0.723421i	$-0.742568\pi$
$48$			3.61290e9i			0.295399i
$49$		0			0
$50$	7.62515e9			0.488010
$51$	−2.73814e9	+	4.74259e9i	−0.155609	+	0.269522i
$52$	−4.87367e9	+	2.81381e9i	−0.246511	+	0.142323i
$53$	−1.17271e10	−	2.03119e10i	−0.529097	−	0.916423i	−0.999424	−	0.0339308i	$-0.989197\pi$
$53$	−1.17271e10	−	2.03119e10i	−0.529097	−	0.916423i	0.470327	−	0.882492i	$-0.344136\pi$
$54$	−1.08334e10	−	6.25467e9i	−0.436921	−	0.252256i
$55$			4.48657e9i			0.162083i
$56$		0			0
$57$	−6.68134e10			−1.94811
$58$	3.20324e9	−	5.54817e9i	0.0841436	−	0.145741i
$59$	1.83475e9	−	1.05929e9i	0.0434976	−	0.0251133i	−0.478094	−	0.878309i	$-0.658672\pi$
$59$	1.83475e9	−	1.05929e9i	0.0434976	−	0.0251133i	0.521591	+	0.853196i	$0.325339\pi$
$60$	−7.67170e9	−	1.32878e10i	−0.164431	−	0.284803i
$61$	7.28376e9	+	4.20528e9i	0.141376	+	0.0816237i	0.569020	−	0.822324i	$-0.307323\pi$
$61$	7.28376e9	+	4.20528e9i	0.141376	+	0.0816237i	−0.427643	+	0.903947i	$0.640656\pi$
$62$			3.65622e10i			0.643697i
$63$		0			0
$64$	8.58993e9			0.125000
$65$	1.19498e10	−	2.06977e10i	0.158446	−	0.274436i
$66$	−1.74145e10	+	1.00543e10i	−0.210691	+	0.121643i
$67$	3.27239e10	+	5.66794e10i	0.361756	+	0.626580i	0.988250	−	0.152846i	$-0.0488439\pi$
$67$	3.27239e10	+	5.66794e10i	0.361756	+	0.626580i	−0.626494	+	0.779426i	$0.715511\pi$
$68$	1.12759e10	+	6.51012e9i	0.114050	+	0.0658469i
$69$		−	8.96336e10i		−	0.830570i
$70$		0			0
$71$	−2.46780e11			−1.92646			−0.963229	−	0.268683i	$-0.913411\pi$
$71$	−2.46780e11			−1.92646			−0.963229	+	0.268683i	$0.913411\pi$
$72$	9.75654e9	−	1.68988e10i	0.0700327	−	0.121300i
$73$	−8.87210e10	+	5.12231e10i	−0.586259	+	0.338477i	−0.763617	−	0.645670i	$-0.776578\pi$
$73$	−8.87210e10	+	5.12231e10i	−0.586259	+	0.338477i	0.177358	+	0.984146i	$0.443245\pi$
$74$	8.45173e10	+	1.46388e11i	0.514701	+	0.891489i
$75$	−1.25693e11	−	7.25687e10i	−0.706224	−	0.407738i
$76$			1.58854e11i			0.824359i
$77$		0			0
$78$	1.07116e11			0.475651
$79$	1.38548e11	−	2.39973e11i	0.569952	−	0.987187i	−0.426618	−	0.904432i	$-0.640295\pi$
$79$	1.38548e11	−	2.39973e11i	0.569952	−	0.987187i	0.996570	−	0.0827544i	$-0.0263717\pi$
$80$	−3.15927e10	+	1.82400e10i	−0.120516	+	0.0695802i
$81$	1.74996e11	+	3.03102e11i	0.619609	+	1.07319i
$82$	−1.86253e11	−	1.07533e11i	−0.612662	−	0.353720i
$83$		−	8.18271e10i		−	0.250281i	−0.992139	−	0.125141i	$-0.960062\pi$
$83$		−	8.18271e10i		−	0.250281i	0.992139	−	0.125141i	$-0.0399382\pi$
$84$		0			0
$85$	−5.52949e10			−0.146613
$86$	−2.02316e11	+	3.50421e11i	−0.500080	+	0.866163i
$87$	−1.05604e11	+	6.09705e10i	−0.243537	+	0.140606i
$88$	2.39047e10	+	4.14042e10i	0.0514740	+	0.0891556i
$89$	4.69496e10	+	2.71064e10i	0.0944695	+	0.0545420i	0.546491	−	0.837465i	$-0.315963\pi$
$89$	4.69496e10	+	2.71064e10i	0.0944695	+	0.0545420i	−0.452021	+	0.892007i	$0.649297\pi$
$90$			8.28689e10i			0.155932i
$91$		0			0
$92$	−2.13111e11			−0.351462
$93$	3.47963e11	−	6.02689e11i	0.537818	−	0.931528i
$94$	8.10797e11	−	4.68114e11i	1.17529	−	0.678554i
$95$	−3.37314e11	−	5.84244e11i	−0.458873	−	0.794791i
$96$	−1.41596e11	−	8.17506e10i	−0.180894	−	0.104439i
$97$		−	3.42738e11i		−	0.411465i	−0.978608	−	0.205732i	$-0.934042\pi$
$97$		−	3.42738e11i		−	0.411465i	0.978608	−	0.205732i	$-0.0659576\pi$
$98$		0			0
$99$	1.08605e11			0.115356
$100$	−1.72537e11	+	2.98844e11i	−0.172537	+	0.298844i
$101$	1.47590e12	−	8.52112e11i	1.39037	−	0.802728i	0.397010	−	0.917814i	$-0.370048\pi$
$101$	1.47590e12	−	8.52112e11i	1.39037	−	0.802728i	0.993356	+	0.115086i	$0.0367144\pi$
$102$	−1.23914e11	−	2.14625e11i	−0.110032	−	0.190581i
$103$	−1.13530e12	−	6.55464e11i	−0.950793	−	0.548941i	−0.0574658	−	0.998347i	$-0.518302\pi$
$103$	−1.13530e12	−	6.55464e11i	−0.950793	−	0.548941i	−0.893327	+	0.449407i	$0.851635\pi$
$104$		−	2.54677e11i		−	0.201275i
$105$		0			0
$106$	1.06142e12			0.748256
$107$	1.01708e12	−	1.76164e12i	0.677727	−	1.17386i	−0.297937	−	0.954585i	$-0.596299\pi$
$107$	1.01708e12	−	1.76164e12i	0.677727	−	1.17386i	0.975664	−	0.219271i	$-0.0703680\pi$
$108$	4.90264e11	−	2.83054e11i	0.308950	−	0.178372i
$109$	−1.09731e12	−	1.90060e12i	−0.654290	−	1.13326i	−0.982071	−	0.188510i	$-0.939634\pi$
$109$	−1.09731e12	−	1.90060e12i	−0.654290	−	1.13326i	0.327781	−	0.944754i	$-0.393699\pi$
$110$	−1.75837e11	−	1.01520e11i	−0.0992555	−	0.0573052i
$111$		−	3.21741e12i		−	1.72016i
$112$		0			0
$113$	−2.33384e11			−0.112098			−0.0560492	−	0.998428i	$-0.517850\pi$
$113$	−2.33384e11			−0.112098			−0.0560492	+	0.998428i	$0.517850\pi$
$114$	1.51182e12	−	2.61854e12i	0.688763	−	1.19297i
$115$	7.83793e11	−	4.52523e11i	0.338855	−	0.195638i
$116$	1.44962e11	+	2.51081e11i	0.0594985	+	0.103054i
$117$	−5.01022e11	−	2.89265e11i	−0.195318	−	0.112767i
$118$			9.58763e10i			0.0355156i
$119$		0			0
$120$	6.94363e11			0.232541
$121$	1.43617e12	−	2.48751e12i	0.457607	−	0.792598i
$122$	−3.29625e11	+	1.90309e11i	−0.0999682	+	0.0577166i
$123$	2.04679e12	+	3.54515e12i	0.591076	+	1.02377i
$124$	−1.43294e12	−	8.27307e11i	−0.394183	−	0.227581i
$125$		−	3.58890e12i		−	0.940808i
$126$		0			0
$127$	5.43716e12			1.29583			0.647917	−	0.761711i	$-0.275640\pi$
$127$	5.43716e12			1.29583			0.647917	+	0.761711i	$0.275640\pi$
$128$	−1.94368e11	+	3.36655e11i	−0.0441942	+	0.0765466i
$129$	6.66993e12	−	3.85089e12i	1.44738	−	0.835646i
$130$	5.40787e11	+	9.36670e11i	0.112038	+	0.194056i
$131$	−7.18347e12	−	4.14738e12i	−1.42137	−	0.820627i	−0.424953	−	0.905216i	$-0.639709\pi$
$131$	−7.18347e12	−	4.14738e12i	−1.42137	−	0.820627i	−0.996416	+	0.0845881i	$0.973043\pi$
$132$		−	9.10007e11i		−	0.172029i
$133$		0			0
$134$	−2.96183e12			−0.511601
$135$	−1.20209e12	+	2.08207e12i	−0.198579	+	0.343948i
$136$	−5.10287e11	+	2.94614e11i	−0.0806457	+	0.0465608i
$137$	−1.43911e12	−	2.49260e12i	−0.217655	−	0.376990i	0.736435	−	0.676508i	$-0.236508\pi$
$137$	−1.43911e12	−	2.49260e12i	−0.217655	−	0.376990i	−0.954091	+	0.299518i	$0.903174\pi$
$138$	3.51291e12	+	2.02818e12i	0.508618	+	0.293651i
$139$			7.39529e12i			1.02534i	0.858587	+	0.512669i	$0.171343\pi$
$139$			7.39529e12i			1.02534i	−0.858587	+	0.512669i	$0.828657\pi$
$140$		0			0
$141$	−1.78202e13			−2.26776
$142$	5.58399e12	−	9.67175e12i	0.681105	−	1.17971i
$143$	1.22757e12	−	7.08735e11i	0.143558	−	0.0828835i
$144$	4.41530e11	+	7.64753e11i	0.0495206	+	0.0857722i
$145$	−1.06630e12	−	6.15630e11i	−0.114729	−	0.0662387i
$146$		−	4.63619e12i		−	0.478678i
$147$		0			0
$148$	−7.64963e12			−0.727898
$149$	−9.78126e11	+	1.69416e12i	−0.0893876	+	0.154824i	−0.907252	−	0.420587i	$-0.861824\pi$
$149$	−9.78126e11	+	1.69416e12i	−0.0893876	+	0.154824i	0.817865	+	0.575410i	$0.195158\pi$
$150$	5.68820e12	−	3.28408e12i	0.499376	−	0.288315i
$151$	7.20437e12	+	1.24783e13i	0.607763	+	1.05268i	0.991608	+	0.129279i	$0.0412662\pi$
$151$	7.20437e12	+	1.24783e13i	0.607763	+	1.05268i	−0.383845	+	0.923397i	$0.625400\pi$
$152$	−6.22577e12	−	3.59445e12i	−0.504815	−	0.291455i
$153$			1.33850e12i			0.104345i
$154$		0			0
$155$	7.02689e12			0.506725
$156$	−2.42377e12	+	4.19809e12i	−0.168168	+	0.291276i
$157$	−1.59678e13	+	9.21899e12i	−1.06622	+	0.615582i	−0.927146	−	0.374701i	$-0.877745\pi$
$157$	−1.59678e13	+	9.21899e12i	−1.06622	+	0.615582i	−0.139073	+	0.990282i	$0.544412\pi$
$158$	6.26998e12	+	1.08599e13i	0.403017	+	0.698046i
$159$	−1.74963e13	−	1.01015e13i	−1.08284	−	0.625178i
$160$		−	1.65090e12i		−	0.0984013i
$161$		0			0
$162$	−1.58388e13			−0.876260
$163$	1.38586e13	−	2.40039e13i	0.738916	−	1.27984i	−0.214069	−	0.976819i	$-0.568672\pi$
$163$	1.38586e13	−	2.40039e13i	0.738916	−	1.27984i	0.952984	−	0.303021i	$-0.0979951\pi$
$164$	8.42886e12	−	4.86641e12i	0.433217	−	0.250118i
$165$	1.93233e12	+	3.34689e12i	0.0957584	+	0.165858i
$166$	3.20695e12	+	1.85154e12i	0.153265	+	0.0884879i
$167$		−	1.19940e12i		−	0.0552923i	−0.999618	−	0.0276461i	$-0.991199\pi$
$167$		−	1.19940e12i		−	0.0552923i	0.999618	−	0.0276461i	$-0.00880116\pi$
$168$		0			0
$169$	1.57473e13			0.675907
$170$	1.25118e12	−	2.16711e12i	0.0518354	−	0.0897815i
$171$	−1.41426e13	+	8.16523e12i	−0.565656	+	0.326582i
$172$	−9.15577e12	−	1.58583e13i	−0.353610	−	0.612470i
$173$	−3.84029e12	−	2.21719e12i	−0.143248	−	0.0827041i	0.426663	−	0.904411i	$-0.359689\pi$
$173$	−3.84029e12	−	2.21719e12i	−0.143248	−	0.0827041i	−0.569911	+	0.821706i	$0.693022\pi$
$174$		−	5.51842e12i		−	0.198847i
$175$		0			0
$176$	−2.16361e12			−0.0727952
$177$	9.12456e11	−	1.58042e12i	0.0296738	−	0.0513964i
$178$	−2.12470e12	+	1.22669e12i	−0.0668001	+	0.0385670i
$179$	−2.21016e13	−	3.82811e13i	−0.671902	−	1.16377i	−0.977364	−	0.211564i	$-0.932144\pi$
$179$	−2.21016e13	−	3.82811e13i	−0.671902	−	1.16377i	0.305462	−	0.952204i	$-0.401189\pi$
$180$	−3.24778e12	−	1.87511e12i	−0.0954887	−	0.0551305i
$181$		−	1.41993e12i		−	0.0403828i	−0.999796	−	0.0201914i	$-0.993572\pi$
$181$		−	1.41993e12i		−	0.0403828i	0.999796	−	0.0201914i	$-0.00642756\pi$
$182$		0			0
$183$	7.24471e12			0.192892
$184$	4.82214e12	−	8.35219e12i	0.124260	−	0.215225i
$185$	2.81344e13	−	1.62434e13i	0.701789	−	0.405178i
$186$	1.57470e13	+	2.72746e13i	0.380295	+	0.658690i
$187$	−2.84013e12	−	1.63975e12i	−0.0664185	−	0.0383467i
$188$			4.23688e13i			0.959621i
$189$		0			0
$190$	3.05301e13			0.648944
$191$	−2.94428e13	+	5.09965e13i	−0.606428	+	1.05036i	0.385396	+	0.922751i	$0.374065\pi$
$191$	−2.94428e13	+	5.09965e13i	−0.606428	+	1.05036i	−0.991824	+	0.127613i	$0.959268\pi$
$192$	6.40791e12	−	3.69961e12i	0.127911	−	0.0738496i
$193$	−2.84219e13	−	4.92282e13i	−0.549933	−	0.952512i	−0.998279	−	0.0586517i	$-0.981320\pi$
$193$	−2.84219e13	−	4.92282e13i	−0.549933	−	0.952512i	0.448345	−	0.893860i	$-0.352013\pi$
$194$	1.34325e13	+	7.75529e12i	0.251970	+	0.145475i
$195$		−	2.05867e13i		−	0.374437i
$196$		0			0
$197$	−5.01766e13			−0.858428			−0.429214	−	0.903203i	$-0.641209\pi$
$197$	−5.01766e13			−0.858428			−0.429214	+	0.903203i	$0.641209\pi$
$198$	−2.45745e12	+	4.25643e12i	−0.0407844	+	0.0706406i
$199$	2.71256e13	−	1.56610e13i	0.436778	−	0.252174i	−0.265452	−	0.964124i	$-0.585521\pi$
$199$	2.71256e13	−	1.56610e13i	0.436778	−	0.252174i	0.702230	+	0.711950i	$0.252188\pi$
$200$	−7.80815e12	−	1.35241e13i	−0.122002	−	0.211314i
$201$	4.88226e13	+	2.81878e13i	0.740363	+	0.427449i
$202$			7.71244e13i			1.13523i
$203$		0			0
$204$	1.12154e13			0.155609
$205$	−2.06668e13	+	3.57960e13i	−0.278452	+	0.482294i
$206$	5.13777e13	−	2.96629e13i	0.672312	−	0.388160i
$207$	−1.09541e13	−	1.89730e13i	−0.139237	−	0.241165i
$208$	9.98127e12	+	5.76269e12i	0.123255	+	0.0711615i
$209$		−	4.00117e13i		−	0.480075i
$210$		0			0
$211$	1.26653e14			1.43523			0.717616	−	0.696438i	$-0.245233\pi$
$211$	1.26653e14			1.43523			0.717616	+	0.696438i	$0.245233\pi$
$212$	−2.40171e13	+	4.15988e13i	−0.264549	+	0.458211i
$213$	−1.84092e14	+	1.06286e14i	−1.97133	+	1.13815i
$214$	4.60280e13	+	7.97228e13i	0.479225	+	0.830042i
$215$	6.73475e13	+	3.88831e13i	0.681853	+	0.393668i
$216$			2.56191e13i			0.252256i
$217$		0			0
$218$	9.93172e13			0.925306
$219$	−4.41227e13	+	7.64227e13i	−0.399942	+	0.692720i
$220$	7.95748e12	−	4.59425e12i	0.0701842	−	0.0405209i
$221$	8.73482e12	+	1.51292e13i	0.0749723	+	0.129856i
$222$	1.26096e14	+	7.28017e13i	1.05338	+	0.608168i
$223$		−	8.65375e13i		−	0.703680i	−0.936060	−	0.351840i	$-0.885556\pi$
$223$		−	8.65375e13i		−	0.703680i	0.936060	−	0.351840i	$-0.114444\pi$
$224$		0			0
$225$	−3.54743e13			−0.273413
$226$	5.28087e12	−	9.14673e12i	0.0396328	−	0.0686460i
$227$	−1.42952e14	+	8.25335e13i	−1.04481	+	0.603220i	−0.921191	−	0.389111i	$-0.872782\pi$
$227$	−1.42952e14	+	8.25335e13i	−1.04481	+	0.603220i	−0.123616	+	0.992330i	$0.539449\pi$
$228$	6.84169e13	+	1.18502e14i	0.487029	+	0.843558i
$229$	8.41450e13	+	4.85811e13i	0.583466	+	0.336864i	0.762510	−	0.646977i	$-0.223967\pi$
$229$	8.41450e13	+	4.85811e13i	0.583466	+	0.336864i	−0.179044	+	0.983841i	$0.557300\pi$
$230$			4.09577e13i			0.276674i
$231$		0			0
$232$	−1.31205e13			−0.0841436
$233$	−2.12110e13	+	3.67385e13i	−0.132564	+	0.229607i	−0.924664	−	0.380784i	$-0.875654\pi$
$233$	−2.12110e13	+	3.67385e13i	−0.132564	+	0.229607i	0.792100	+	0.610391i	$0.208988\pi$
$234$	2.26737e13	−	1.30906e13i	0.138110	−	0.0797381i
$235$	−8.99669e13	−	1.55827e14i	−0.534165	−	0.925201i
$236$	−3.75757e12	−	2.16943e12i	−0.0217488	−	0.0125567i
$237$		−	2.38686e14i		−	1.34690i
$238$		0			0
$239$	−5.49165e13			−0.294656			−0.147328	−	0.989088i	$-0.547067\pi$
$239$	−5.49165e13			−0.294656			−0.147328	+	0.989088i	$0.547067\pi$
$240$	−1.57116e13	+	2.72134e13i	−0.0822156	+	0.142402i
$241$	−2.63730e14	+	1.52264e14i	−1.34604	+	0.777134i	−0.987685	−	0.156453i	$-0.949994\pi$
$241$	−2.63730e14	+	1.52264e14i	−1.34604	+	0.777134i	−0.358351	+	0.933587i	$0.616661\pi$
$242$	6.49935e13	+	1.12572e14i	0.323577	+	0.560452i
$243$	1.33867e14	+	7.72879e13i	0.650181	+	0.375382i
$244$		−	1.72248e13i		−	0.0816237i
$245$		0			0
$246$	−1.85255e14			−0.835908
$247$	−1.06570e14	+	1.84584e14i	−0.469301	+	0.812853i
$248$	6.48474e13	−	3.74397e13i	0.278729	−	0.160924i
$249$	−3.52422e13	−	6.10413e13i	−0.147866	−	0.256111i
$250$	1.40656e14	+	8.12075e13i	0.576125	+	0.332626i
$251$			3.75080e14i			1.49996i	0.661458	+	0.749982i	$0.269938\pi$
$251$			3.75080e14i			1.49996i	−0.661458	+	0.749982i	$0.730062\pi$
$252$		0			0
$253$	5.36777e13			0.204678
$254$	−1.23029e14	+	2.13092e14i	−0.458147	+	0.793534i
$255$	−4.12488e13	+	2.38150e13i	−0.150027	+	0.0866183i
$256$	−8.79609e12	−	1.52353e13i	−0.0312500	−	0.0541266i
$257$	−2.15923e14	−	1.24663e14i	−0.749378	−	0.432653i	0.0760913	−	0.997101i	$-0.475756\pi$
$257$	−2.15923e14	−	1.24663e14i	−0.749378	−	0.432653i	−0.825469	+	0.564447i	$0.809089\pi$
$258$			3.48542e14i			1.18178i
$259$		0			0
$260$	−4.89464e13			−0.158446
$261$	−1.49023e13	+	2.58116e13i	−0.0471424	+	0.0816530i
$262$	3.25087e14	−	1.87689e14i	1.00506	−	0.580271i
$263$	−2.94573e14	−	5.10216e14i	−0.890141	−	1.54177i	−0.839705	−	0.543042i	$-0.817272\pi$
$263$	−2.94573e14	−	5.10216e14i	−0.890141	−	1.54177i	−0.0504357	−	0.998727i	$-0.516061\pi$
$264$	3.56649e13	+	2.05911e13i	0.105346	+	0.0608214i
$265$		−	2.03994e14i		−	0.589035i
$266$		0			0
$267$	4.66979e13			0.128893
$268$	6.70185e13	−	1.16079e14i	0.180878	−	0.313290i
$269$	−2.77909e14	+	1.60451e14i	−0.733482	+	0.423476i	−0.819694	−	0.572801i	$-0.805857\pi$
$269$	−2.77909e14	+	1.60451e14i	−0.733482	+	0.423476i	0.0862129	+	0.996277i	$0.472523\pi$
$270$	−5.44002e13	−	9.42239e13i	−0.140416	−	0.243208i
$271$	−8.39461e13	−	4.84663e13i	−0.211926	−	0.122356i	0.390280	−	0.920696i	$-0.372378\pi$
$271$	−8.39461e13	−	4.84663e13i	−0.211926	−	0.122356i	−0.602206	+	0.798340i	$0.705712\pi$
$272$		−	2.66655e13i		−	0.0658469i
$273$		0			0
$274$	1.30253e14			0.307811
$275$	4.34583e13	−	7.52719e13i	0.100479	−	0.174035i
$276$	−1.58976e14	+	9.17848e13i	−0.359647	+	0.207643i
$277$	2.88703e14	+	5.00048e14i	0.639106	+	1.10696i	0.985629	+	0.168923i	$0.0540288\pi$
$277$	2.88703e14	+	5.00048e14i	0.639106	+	1.10696i	−0.346523	+	0.938041i	$0.612638\pi$
$278$	−2.89835e14	−	1.67336e14i	−0.627888	−	0.362511i
$279$		−	1.70097e14i		−	0.360639i
$280$		0			0
$281$	5.01179e14			1.01802			0.509009	−	0.860761i	$-0.330012\pi$
$281$	5.01179e14			1.01802			0.509009	+	0.860761i	$0.330012\pi$
$282$	4.03225e14	−	6.98406e14i	0.801776	−	1.38872i
$283$	7.28775e14	−	4.20758e14i	1.41865	−	0.819057i	0.422468	−	0.906378i	$-0.361164\pi$
$283$	7.28775e14	−	4.20758e14i	1.41865	−	0.819057i	0.996180	+	0.0873212i	$0.0278306\pi$
$284$	2.52702e14	+	4.37693e14i	0.481614	+	0.834180i
$285$	−5.03257e14	−	2.90556e14i	−0.939120	−	0.542201i
$286$			6.41474e13i			0.117215i
$287$		0			0
$288$	−3.99628e13			−0.0700327
$289$	−2.71102e14	+	4.69562e14i	−0.465313	+	0.805947i
$290$	4.82553e13	−	2.78602e13i	0.0811255	−	0.0468378i
$291$	−1.47614e14	−	2.55676e14i	−0.243092	−	0.421048i
$292$	1.81701e14	+	1.04905e14i	0.293129	+	0.169238i
$293$			9.39106e14i			1.48426i	0.670258	+	0.742128i	$0.266183\pi$
$293$			9.39106e14i			1.48426i	−0.670258	+	0.742128i	$0.733817\pi$
$294$		0			0
$295$	1.84265e13			0.0279583
$296$	1.73091e14	−	2.99803e14i	0.257351	−	0.445744i
$297$	−1.23486e14	+	7.12949e13i	−0.179920	+	0.103877i
$298$	−4.42649e13	−	7.66691e13i	−0.0632066	−	0.109477i
$299$	−2.47629e14	−	1.42968e14i	−0.346556	−	0.200084i
$300$			2.97241e14i			0.407738i
$301$		0			0
$302$	−6.52065e14			−0.859506
$303$	7.33994e14	−	1.27131e15i	0.948499	−	1.64285i
$304$	2.81746e14	−	1.62666e14i	0.356958	−	0.206090i
$305$	3.65756e13	+	6.33507e13i	0.0454351	+	0.0786960i
$306$	−5.24584e13	−	3.02869e13i	−0.0638979	−	0.0368915i
$307$		−	6.66830e14i		−	0.796498i	−0.917277	−	0.398249i	$-0.869618\pi$
$307$		−	6.66830e14i		−	0.796498i	0.917277	−	0.398249i	$-0.130382\pi$
$308$		0			0
$309$	−1.12921e15			−1.29725
$310$	−1.59000e14	+	2.75397e14i	−0.179154	+	0.310305i
$311$	2.70814e14	−	1.56355e14i	0.299302	−	0.172802i	−0.342827	−	0.939398i	$-0.611385\pi$
$311$	2.70814e14	−	1.56355e14i	0.299302	−	0.172802i	0.642129	+	0.766596i	$0.278051\pi$
$312$	−1.09687e14	−	1.89984e14i	−0.118913	−	0.205963i
$313$	2.09440e14	+	1.20920e14i	0.222738	+	0.128598i	0.607217	−	0.794536i	$-0.292286\pi$
$313$	2.09440e14	+	1.20920e14i	0.222738	+	0.128598i	−0.384479	+	0.923134i	$0.625619\pi$
$314$		−	8.34408e14i		−	0.870564i
$315$		0			0
$316$	−5.67494e14			−0.569952
$317$	6.62099e13	−	1.14679e14i	0.0652480	−	0.113013i	−0.831556	−	0.555441i	$-0.812549\pi$
$317$	6.62099e13	−	1.14679e14i	0.0652480	−	0.113013i	0.896804	+	0.442428i	$0.145883\pi$
$318$	7.91794e14	−	4.57142e14i	0.765684	−	0.442068i
$319$	−3.65126e13	−	6.32417e13i	−0.0346497	−	0.0600150i
$320$	6.47018e13	+	3.73556e13i	0.0602582	+	0.0347901i
$321$		−	1.75220e15i		−	1.60160i
$322$		0			0
$323$	4.93125e14			0.434252
$324$	3.58392e14	−	6.20753e14i	0.309805	−	0.536597i
$325$	−4.00968e14	+	2.31499e14i	−0.340259	+	0.196448i
$326$	6.27170e14	+	1.08629e15i	0.522492	+	0.904983i
$327$	−1.63714e15	−	9.45203e14i	−1.33906	−	0.773106i
$328$			4.40457e14i			0.353720i
$329$		0			0
$330$	−1.74894e14			−0.135423
$331$	−4.14852e14	+	7.18544e14i	−0.315446	+	0.546368i	−0.979532	−	0.201288i	$-0.935487\pi$
$331$	−4.14852e14	+	7.18544e14i	−0.315446	+	0.546368i	0.664086	+	0.747656i	$0.268821\pi$
$332$	−1.45130e14	+	8.37910e13i	−0.108375	+	0.0625704i
$333$	−3.93198e14	−	6.81039e14i	−0.288367	−	0.499467i
$334$	4.70066e13	+	2.71393e13i	0.0338595	+	0.0195488i
$335$			5.69234e14i			0.402737i
$336$		0			0
$337$	−2.75664e14			−0.188192			−0.0940958	−	0.995563i	$-0.529996\pi$
$337$	−2.75664e14			−0.188192			−0.0940958	+	0.995563i	$0.529996\pi$
$338$	−3.56321e14	+	6.17167e14i	−0.238969	+	0.413907i
$339$	−1.74099e14	+	1.00516e14i	−0.114709	+	0.0662274i
$340$	5.66220e13	+	9.80721e13i	0.0366532	+	0.0634851i
$341$	3.60925e14	+	2.08380e14i	0.229557	+	0.132535i
$342$		−	7.39033e14i		−	0.461856i
$343$		0			0
$344$	8.28685e14			0.500080
$345$	3.89795e14	−	6.75146e14i	0.231165	−	0.400390i
$346$	1.73792e14	−	1.00339e14i	0.101291	−	0.0584806i
$347$	−6.45392e12	−	1.11785e13i	−0.00369698	−	0.00640335i	0.864171	−	0.503198i	$-0.167843\pi$
$347$	−6.45392e12	−	1.11785e13i	−0.00369698	−	0.00640335i	−0.867868	+	0.496795i	$0.834510\pi$
$348$	2.16277e14	+	1.24868e14i	0.121768	+	0.0703031i
$349$		−	7.51191e14i		−	0.415717i	−0.978159	−	0.207858i	$-0.933351\pi$
$349$		−	7.51191e14i		−	0.415717i	0.978159	−	0.207858i	$-0.0666493\pi$
$350$		0			0
$351$	7.59564e14			0.406183
$352$	4.89569e13	−	8.47958e13i	0.0257370	−	0.0445778i
$353$	−9.28243e14	+	5.35921e14i	−0.479748	+	0.276983i	−0.720312	−	0.693651i	$-0.756001\pi$
$353$	−9.28243e14	+	5.35921e14i	−0.479748	+	0.276983i	0.240563	+	0.970633i	$0.422668\pi$
$354$	4.12931e13	+	7.15217e13i	0.0209825	+	0.0363428i
$355$	−1.85881e15	−	1.07319e15i	−0.928679	−	0.536173i
$356$		−	1.11028e14i		−	0.0545420i
$357$		0			0
$358$	2.00041e15			0.950213
$359$	9.15290e14	−	1.58533e15i	0.427555	−	0.740547i	−0.569100	−	0.822268i	$-0.692708\pi$
$359$	9.15290e14	−	1.58533e15i	0.427555	−	0.740547i	0.996655	+	0.0817210i	$0.0260416\pi$
$360$	1.46978e14	−	8.48578e13i	0.0675207	−	0.0389831i
$361$	1.90154e15	+	3.29356e15i	0.859135	+	1.48806i
$362$	5.56498e13	+	3.21294e13i	0.0247293	+	0.0142775i
$363$		−	2.47418e15i		−	1.08141i
$364$		0			0
$365$	−8.91029e14			−0.376821
$366$	−1.63929e14	+	2.83933e14i	−0.0681976	+	0.118122i
$367$	1.74439e15	−	1.00713e15i	0.713917	−	0.412180i	−0.0985926	−	0.995128i	$-0.531434\pi$
$367$	1.74439e15	−	1.00713e15i	0.713917	−	0.412180i	0.812510	+	0.582948i	$0.198101\pi$
$368$	2.18225e14	+	3.77977e14i	0.0878654	+	0.152187i
$369$	8.66502e14	+	5.00275e14i	0.343251	+	0.198176i
$370$			1.47018e15i			0.573009i
$371$		0			0
$372$	−1.42526e15			−0.537818
$373$	9.67420e14	−	1.67562e15i	0.359221	−	0.622189i	−0.628610	−	0.777721i	$-0.716376\pi$
$373$	9.67420e14	−	1.67562e15i	0.359221	−	0.622189i	0.987831	+	0.155531i	$0.0497090\pi$
$374$	1.28530e14	−	7.42067e13i	0.0469650	−	0.0271152i
$375$	−1.54571e15	−	2.67724e15i	−0.555827	−	0.962720i
$376$	−1.66051e15	−	9.58698e14i	−0.587645	−	0.339277i
$377$			3.89000e14i			0.135488i
$378$		0			0
$379$	2.16588e15			0.730802			0.365401	−	0.930850i	$-0.380932\pi$
$379$	2.16588e15			0.730802			0.365401	+	0.930850i	$0.380932\pi$
$380$	−6.90818e14	+	1.19653e15i	−0.229436	+	0.397395i
$381$	4.05600e15	−	2.34174e15i	1.32602	−	0.765575i
$382$	−1.33243e15	−	2.30784e15i	−0.428809	−	0.742720i
$383$	4.61537e15	+	2.66469e15i	1.46222	+	0.844215i	0.999114	−	0.0420855i	$-0.0134002\pi$
$383$	4.61537e15	+	2.66469e15i	1.46222	+	0.844215i	0.463110	+	0.886301i	$0.346734\pi$
$384$			3.34850e14i			0.104439i
$385$		0			0
$386$	2.57246e15			0.777723
$387$	9.41230e14	−	1.63026e15i	0.280175	−	0.485278i
$388$	−6.07888e14	+	3.50964e14i	−0.178169	+	0.102866i
$389$	−1.08260e15	−	1.87512e15i	−0.312444	−	0.541168i	0.666447	−	0.745552i	$-0.267814\pi$
$389$	−1.08260e15	−	1.87512e15i	−0.312444	−	0.541168i	−0.978891	+	0.204384i	$0.934481\pi$
$390$	8.06831e14	+	4.65824e14i	0.229295	+	0.132384i
$391$			6.61552e14i			0.185141i
$392$		0			0
$393$	−7.14496e15			−1.93930
$394$	1.13537e15	−	1.96651e15i	0.303500	−	0.525678i
$395$	2.08717e15	−	1.20503e15i	0.549509	−	0.317259i
$396$	−1.11212e14	−	1.92624e14i	−0.0288389	−	0.0499504i
$397$	7.75072e14	+	4.47488e14i	0.197970	+	0.114298i	0.595708	−	0.803201i	$-0.296872\pi$
$397$	7.75072e14	+	4.47488e14i	0.197970	+	0.114298i	−0.397738	+	0.917499i	$0.630205\pi$
$398$			1.41747e15i			0.356628i
$399$		0			0
$400$	7.06713e14			0.172537
$401$	−3.82791e15	+	6.63014e15i	−0.920653	+	1.59462i	−0.122245	+	0.992500i	$0.539009\pi$
$401$	−3.82791e15	+	6.63014e15i	−0.920653	+	1.59462i	−0.798408	+	0.602117i	$0.794324\pi$
$402$	−2.20946e15	+	1.27563e15i	−0.523516	+	0.302252i
$403$	−1.11002e15	−	1.92262e15i	−0.259121	−	0.448810i
$404$	−3.02265e15	−	1.74513e15i	−0.695183	−	0.401364i
$405$			3.04406e15i			0.689801i
$406$		0			0
$407$	1.92677e15			0.423900
$408$	−2.53776e14	+	4.39552e14i	−0.0550160	+	0.0952905i
$409$	−3.13235e15	+	1.80846e15i	−0.669160	+	0.386340i	−0.795758	−	0.605614i	$-0.792927\pi$
$409$	−3.13235e15	+	1.80846e15i	−0.669160	+	0.386340i	0.126598	+	0.991954i	$0.459594\pi$
$410$	−9.35275e14	−	1.61994e15i	−0.196896	−	0.341033i
$411$	−2.14708e15	−	1.23962e15i	−0.445449	−	0.257180i
$412$			2.68478e15i			0.548941i
$413$		0			0
$414$	9.91450e14			0.196910
$415$	3.55847e14	−	6.16345e14i	0.0696586	−	0.120652i
$416$	−4.51701e14	+	2.60789e14i	−0.0871547	+	0.0503188i
$417$	3.18509e15	+	5.51673e15i	0.605766	+	1.04922i
$418$	1.56813e15	+	9.05361e14i	0.293985	+	0.169732i
$419$			3.64888e15i			0.674335i	0.941445	+	0.337168i	$0.109469\pi$
$419$			3.64888e15i			0.674335i	−0.941445	+	0.337168i	$0.890531\pi$
$420$		0			0
$421$	3.29475e15			0.591739			0.295870	−	0.955228i	$-0.404391\pi$
$421$	3.29475e15			0.591739			0.295870	+	0.955228i	$0.404391\pi$
$422$	−2.86584e15	+	4.96378e15i	−0.507431	+	0.878897i
$423$	−3.77206e15	+	2.17780e15i	−0.658470	+	0.380168i
$424$	−1.08689e15	−	1.88255e15i	−0.187064	−	0.324004i
$425$	9.27691e14	+	5.35602e14i	0.157423	+	0.0908885i
$426$		−	9.61989e15i		−	1.60958i
$427$		0			0
$428$	−4.16598e15			−0.677727
$429$	6.10492e14	−	1.05740e15i	0.0979346	−	0.169628i
$430$	−3.04780e15	+	1.75965e15i	−0.482143	+	0.278365i
$431$	4.72907e15	+	8.19099e15i	0.737755	+	1.27783i	0.953504	+	0.301381i	$0.0974475\pi$
$431$	4.72907e15	+	8.19099e15i	0.737755	+	1.27783i	−0.215749	+	0.976449i	$0.569219\pi$
$432$	−1.00406e15	−	5.79695e14i	−0.154475	−	0.0891860i
$433$			9.38135e15i			1.42344i	0.702465	+	0.711718i	$0.252083\pi$
$433$			9.38135e15i			1.42344i	−0.702465	+	0.711718i	$0.747917\pi$
$434$		0			0
$435$	−1.06059e15			−0.156535
$436$	−2.24729e15	+	3.89242e15i	−0.327145	+	0.566632i
$437$	−6.98994e15	+	4.03564e15i	−1.00366	+	0.579461i
$438$	−1.99676e15	−	3.45850e15i	−0.282802	−	0.489827i
$439$	3.10191e14	+	1.79089e14i	0.0433353	+	0.0250196i	0.521511	−	0.853244i	$-0.325369\pi$
$439$	3.10191e14	+	1.79089e14i	0.0433353	+	0.0250196i	−0.478176	+	0.878264i	$0.658702\pi$
$440$			4.15824e14i			0.0573052i
$441$		0			0
$442$	−7.90586e14			−0.106027
$443$	−1.44826e15	+	2.50846e15i	−0.191613	+	0.331883i	−0.945785	−	0.324794i	$-0.894705\pi$
$443$	−1.44826e15	+	2.50846e15i	−0.191613	+	0.331883i	0.754172	+	0.656677i	$0.228038\pi$
$444$	−5.70646e15	+	3.29463e15i	−0.744851	+	0.430040i
$445$	2.35758e14	+	4.08345e14i	0.0303604	+	0.0525857i
$446$	3.39156e15	+	1.95812e15i	0.430914	+	0.248788i
$447$			1.68508e15i			0.211240i
$448$		0			0
$449$	5.51822e15			0.673474			0.336737	−	0.941599i	$-0.390677\pi$
$449$	5.51822e15			0.673474			0.336737	+	0.941599i	$0.390677\pi$
$450$	8.02692e14	−	1.39030e15i	0.0966661	−	0.167431i
$451$	−2.12304e15	+	1.22574e15i	−0.252289	+	0.145659i
$452$	2.38985e14	+	4.13934e14i	0.0280246	+	0.0485401i
$453$	1.07486e16	+	6.20571e15i	1.24384	+	0.718129i
$454$		−	7.47008e15i		−	0.853081i
$455$		0			0
$456$	−6.19239e15			−0.688763
$457$	−3.58011e15	+	6.20094e15i	−0.393006	+	0.680707i	−0.992845	−	0.119414i	$-0.961898\pi$
$457$	−3.58011e15	+	6.20094e15i	−0.393006	+	0.680707i	0.599838	+	0.800121i	$0.295232\pi$
$458$	−3.80797e15	+	2.19853e15i	−0.412573	+	0.238199i
$459$	−8.78676e14	−	1.52191e15i	−0.0939620	−	0.162747i
$460$	−1.60521e15	−	9.26768e14i	−0.169428	−	0.0978191i
$461$			7.56470e15i			0.788108i	0.919087	+	0.394054i	$0.128928\pi$
$461$			7.56470e15i			0.788108i	−0.919087	+	0.394054i	$0.871072\pi$
$462$		0			0
$463$	−4.69921e15			−0.477022			−0.238511	−	0.971140i	$-0.576659\pi$
$463$	−4.69921e15			−0.477022			−0.238511	+	0.971140i	$0.576659\pi$
$464$	2.96882e14	−	5.14215e14i	0.0297492	−	0.0515272i
$465$	5.24191e15	−	3.02642e15i	0.518527	−	0.299372i
$466$	−9.59898e14	−	1.66259e15i	−0.0937367	−	0.162357i
$467$	1.24885e16	+	7.21026e15i	1.20395	+	0.695103i	0.961432	−	0.275043i	$-0.0886919\pi$
$467$	1.24885e16	+	7.21026e15i	1.20395	+	0.695103i	0.242522	+	0.970146i	$0.422025\pi$
$468$			1.18483e15i			0.112767i
$469$		0			0
$470$	8.14287e15			0.755423
$471$	−7.94108e15	+	1.37543e16i	−0.727368	+	1.25984i
$472$	1.70048e14	−	9.81773e13i	0.0153787	−	0.00887890i
$473$	2.30613e15	+	3.99433e15i	0.205929	+	0.356679i
$474$	9.35454e15	+	5.40085e15i	0.824807	+	0.476203i
$475$			1.30693e16i			1.13786i
$476$		0			0
$477$	−4.93800e15			−0.419219
$478$	1.24262e15	−	2.15228e15i	0.104177	−	0.180439i
$479$	8.75512e15	−	5.05477e15i	0.724851	−	0.418493i	−0.0916844	−	0.995788i	$-0.529225\pi$
$479$	8.75512e15	−	5.05477e15i	0.724851	−	0.418493i	0.816536	+	0.577295i	$0.195892\pi$
$480$	−7.11028e14	−	1.23154e15i	−0.0581352	−	0.100693i
$481$	−8.88866e15	−	5.13187e15i	−0.717738	−	0.414386i
$482$		−	1.37814e16i		−	1.09903i
$483$		0			0
$484$	−5.88254e15			−0.457607
$485$	1.49049e15	−	2.58160e15i	0.114519	−	0.198353i
$486$	−6.05811e15	+	3.49765e15i	−0.459748	+	0.265435i
$487$	3.21346e15	+	5.56587e15i	0.240879	+	0.417215i	0.960965	−	0.276670i	$-0.0892310\pi$
$487$	3.21346e15	+	5.56587e15i	0.240879	+	0.417215i	−0.720086	+	0.693885i	$0.755898\pi$
$488$	6.75073e14	+	3.89753e14i	0.0499841	+	0.0288583i
$489$		−	2.38752e16i		−	1.74620i
$490$		0			0
$491$	1.05122e16			0.750244			0.375122	−	0.926975i	$-0.377601\pi$
$491$	1.05122e16			0.750244			0.375122	+	0.926975i	$0.377601\pi$
$492$	4.19183e15	−	7.26047e15i	0.295538	−	0.511887i
$493$	7.79424e14	−	4.50000e14i	0.0542865	−	0.0313423i
$494$	−4.82279e15	−	8.35331e15i	−0.331846	−	0.574774i
$495$	8.18043e14	+	4.72298e14i	0.0556090	+	0.0321059i
$496$			3.38865e15i			0.227581i
$497$		0			0
$498$	3.18976e15			0.209113
$499$	1.95068e14	−	3.37868e14i	0.0126352	−	0.0218849i	−0.859639	−	0.510903i	$-0.829311\pi$
$499$	1.95068e14	−	3.37868e14i	0.0126352	−	0.0218849i	0.872274	+	0.489018i	$0.162645\pi$
$500$	−6.36534e15	+	3.67503e15i	−0.407382	+	0.235202i
$501$	−5.16570e14	−	8.94725e14i	−0.0326665	−	0.0565800i
$502$	−1.47001e16	−	8.48708e15i	−0.918537	−	0.530318i
$503$			1.10468e16i			0.682070i	0.940051	+	0.341035i	$0.110777\pi$
$503$			1.10468e16i			0.682070i	−0.940051	+	0.341035i	$0.889223\pi$
$504$		0			0
$505$	1.48225e16			0.893664
$506$	−1.21459e15	+	2.10373e15i	−0.0723646	+	0.125339i
$507$	1.17472e16	−	6.78224e15i	0.691649	−	0.399324i
$508$	−5.56765e15	−	9.64345e15i	−0.323959	−	0.561113i
$509$	−1.97600e15	−	1.14085e15i	−0.113627	−	0.0656024i	0.442110	−	0.896961i	$-0.354230\pi$
$509$	−1.97600e15	−	1.14085e15i	−0.113627	−	0.0656024i	−0.555736	+	0.831359i	$0.687564\pi$
$510$		−	2.15549e15i		−	0.122497i
$511$		0			0
$512$	7.96131e14			0.0441942
$513$	1.07203e16	−	1.85681e16i	0.588170	−	1.01874i
$514$	9.77157e15	−	5.64162e15i	0.529890	−	0.305932i
$515$	−5.70091e15	−	9.87427e15i	−0.305563	−	0.529251i
$516$	−1.36600e16	−	7.88661e15i	−0.723691	−	0.417823i
$517$		−	1.06718e16i		−	0.558846i
$518$		0			0
$519$	−3.81970e15			−0.195445
$520$	1.10753e15	−	1.91830e15i	0.0560191	−	0.0970279i
$521$	2.36143e16	−	1.36337e16i	1.18073	−	0.681693i	0.224544	−	0.974464i	$-0.427911\pi$
$521$	2.36143e16	−	1.36337e16i	1.18073	−	0.681693i	0.956183	+	0.292771i	$0.0945773\pi$
$522$	−6.74403e14	−	1.16810e15i	−0.0333347	−	0.0577374i
$523$	8.67291e15	+	5.00731e15i	0.423794	+	0.244678i	0.696699	−	0.717363i	$-0.254651\pi$
$523$	8.67291e15	+	5.00731e15i	0.423794	+	0.244678i	−0.272905	+	0.962041i	$0.587985\pi$
$524$			1.69877e16i			0.820627i
$525$		0			0
$526$	2.66617e16			1.25885
$527$	−2.56818e15	+	4.44822e15i	−0.119884	+	0.207646i
$528$	−1.61401e15	+	9.31847e14i	−0.0744907	+	0.0430072i
$529$	5.54329e15	+	9.60126e15i	0.252949	+	0.438121i
$530$	7.99488e15	+	4.61585e15i	0.360709	+	0.208255i
$531$		−	4.46043e14i		−	0.0198980i
$532$		0			0
$533$	1.30588e16			0.569561
$534$	−1.05665e15	+	1.83018e15i	−0.0455706	+	0.0789306i
$535$	1.53219e16	−	8.84612e15i	0.653418	−	0.377251i
$536$	3.03291e15	+	5.25316e15i	0.127900	+	0.221530i
$537$	−3.29747e16	−	1.90379e16i	−1.37510	−	0.793915i
$538$		−	1.45224e16i		−	0.598885i
$539$		0			0
$540$	4.92374e15			0.198579
$541$	2.03051e16	−	3.51694e16i	0.809880	−	1.40275i	−0.103067	−	0.994674i	$-0.532866\pi$
$541$	2.03051e16	−	3.51694e16i	0.809880	−	1.40275i	0.912947	−	0.408079i	$-0.133801\pi$
$542$	3.79897e15	−	2.19334e15i	0.149855	−	0.0865186i
$543$	−6.11553e14	−	1.05924e15i	−0.0238580	−	0.0413233i
$544$	1.04507e15	+	6.03370e14i	0.0403228	+	0.0232804i
$545$		−	1.90878e16i		−	0.728411i
$546$		0			0
$547$	−3.98211e16			−1.48658			−0.743291	−	0.668968i	$-0.766736\pi$
$547$	−3.98211e16			−1.48658			−0.743291	+	0.668968i	$0.766736\pi$
$548$	−2.94729e15	+	5.10485e15i	−0.108828	+	0.188495i
$549$	1.53351e15	−	8.85372e14i	0.0560083	−	0.0323364i
$550$	1.96670e15	+	3.40642e15i	0.0710495	+	0.123061i
$551$	9.50938e15	+	5.49025e15i	0.339815	+	0.196192i
$552$		−	8.30741e15i		−	0.293651i
$553$		0			0
$554$	−2.61304e16			−0.903832
$555$	1.39918e16	−	2.42344e16i	0.478756	−	0.829230i
$556$	1.31164e16	−	7.57278e15i	0.443984	−	0.256334i
$557$	−1.37991e16	−	2.39007e16i	−0.462081	−	0.800348i	0.536983	−	0.843593i	$-0.319564\pi$
$557$	−1.37991e16	−	2.39007e16i	−0.462081	−	0.800348i	−0.999065	+	0.0432447i	$0.986230\pi$
$558$	6.66643e15	+	3.84887e15i	0.220845	+	0.127505i
$559$		−	2.45691e16i		−	0.805228i
$560$		0			0
$561$	−2.82491e15			−0.0906206
$562$	−1.13404e16	+	1.96421e16i	−0.359924	+	0.623406i
$563$	−5.01324e16	+	2.89439e16i	−1.57423	+	0.908882i	−0.578587	+	0.815620i	$0.696396\pi$
$563$	−5.01324e16	+	2.89439e16i	−1.57423	+	0.908882i	−0.995642	+	0.0932613i	$0.970271\pi$
$564$	1.82479e16	+	3.16063e16i	0.566941	+	0.981971i
$565$	−1.75791e15	−	1.01493e15i	−0.0540389	−	0.0311993i
$566$			3.80827e16i			1.15832i
$567$		0			0
$568$	−2.28720e16			−0.681105
$569$	2.77987e15	−	4.81487e15i	0.0819125	−	0.141877i	−0.822159	−	0.569258i	$-0.807231\pi$
$569$	2.77987e15	−	4.81487e15i	0.0819125	−	0.141877i	0.904071	+	0.427381i	$0.140564\pi$
$570$	2.27748e16	−	1.31491e16i	0.664058	−	0.383394i
$571$	1.02171e16	+	1.76965e16i	0.294788	+	0.510588i	0.974936	−	0.222487i	$-0.0714176\pi$
$571$	1.02171e16	+	1.76965e16i	0.294788	+	0.510588i	−0.680147	+	0.733075i	$0.738084\pi$
$572$	−2.51405e15	−	1.45149e15i	−0.0717792	−	0.0414417i
$573$			5.07231e16i			1.43310i
$574$		0			0
$575$	−1.75331e16			−0.485122
$576$	9.04254e14	−	1.56621e15i	0.0247603	−	0.0428861i
$577$	−3.56461e14	+	2.05803e14i	−0.00965956	+	0.00557695i	−0.504822	−	0.863223i	$-0.668442\pi$
$577$	−3.56461e14	+	2.05803e14i	−0.00965956	+	0.00557695i	0.495162	+	0.868800i	$0.335109\pi$
$578$	−1.22687e16	−	2.12500e16i	−0.329026	−	0.569890i
$579$	−4.24043e16	−	2.44822e16i	−1.12548	−	0.649798i
$580$			2.52162e15i			0.0662387i
$581$		0			0
$582$	1.33605e16			0.343784
$583$	6.04936e15	−	1.04778e16i	0.154063	−	0.266845i
$584$	−8.22283e15	+	4.74746e15i	−0.207274	+	0.119670i
$585$	−2.51589e15	−	4.35765e15i	−0.0627706	−	0.108722i
$586$	−3.68053e16	−	2.12495e16i	−0.908918	−	0.524764i
$587$		−	4.40809e16i		−	1.07751i	−0.842462	−	0.538756i	$-0.818894\pi$
$587$		−	4.40809e16i		−	1.07751i	0.842462	−	0.538756i	$-0.181106\pi$
$588$		0			0
$589$	−6.26664e16			−1.50087
$590$	−4.16943e14	+	7.22167e14i	−0.00988474	+	0.0171209i
$591$	−3.74307e16	+	2.16106e16i	−0.878421	+	0.507157i
$592$	7.83322e15	+	1.35675e16i	0.181974	+	0.315189i
$593$	−3.84620e16	−	2.22061e16i	−0.884513	−	0.510674i	−0.0123689	−	0.999924i	$-0.503937\pi$
$593$	−3.84620e16	−	2.22061e16i	−0.884513	−	0.510674i	−0.872144	+	0.489250i	$0.837271\pi$
$594$		−	6.45288e15i		−	0.146904i
$595$		0			0
$596$	4.00640e15			0.0893876
$597$	1.34901e16	−	2.33655e16i	0.297967	−	0.516095i
$598$	1.12064e16	−	6.47001e15i	0.245052	−	0.141481i
$599$	4.03286e16	+	6.98511e16i	0.873075	+	1.51221i	0.858799	+	0.512313i	$0.171211\pi$
$599$	4.03286e16	+	6.98511e16i	0.873075	+	1.51221i	0.0142767	+	0.999898i	$0.495455\pi$
$600$	−1.16494e16	−	6.72580e15i	−0.249688	−	0.144157i
$601$		−	5.23496e16i		−	1.11088i	−0.831557	−	0.555439i	$-0.812550\pi$
$601$		−	5.23496e16i		−	1.11088i	0.831557	−	0.555439i	$-0.187450\pi$
$602$		0			0
$603$	1.37792e16			0.286630
$604$	1.47545e16	−	2.55556e16i	0.303881	−	0.526338i
$605$	2.16352e16	−	1.24911e16i	0.441193	−	0.254723i
$606$	3.32168e16	+	5.75331e16i	0.670690	+	1.16167i
$607$	−1.93747e16	−	1.11860e16i	−0.387350	−	0.223636i	0.293662	−	0.955909i	$-0.405126\pi$
$607$	−1.93747e16	−	1.11860e16i	−0.387350	−	0.223636i	−0.681011	+	0.732273i	$0.738459\pi$
$608$			1.47229e16i			0.291455i
$609$		0			0
$610$	−3.31044e15			−0.0642550
$611$	−2.84238e16	+	4.92314e16i	−0.546304	+	0.946227i
$612$	2.37400e15	−	1.37063e15i	0.0451827	−	0.0260862i
$613$	−2.91851e16	−	5.05500e16i	−0.550045	−	0.952705i	−0.998271	−	0.0587849i	$-0.981277\pi$
$613$	−2.91851e16	−	5.05500e16i	−0.550045	−	0.952705i	0.448226	−	0.893920i	$-0.352056\pi$
$614$	2.61343e16	+	1.50886e16i	0.487754	+	0.281605i
$615$			3.56041e16i			0.658036i
$616$		0			0
$617$	−1.98026e16			−0.358931			−0.179466	−	0.983764i	$-0.557437\pi$
$617$	−1.98026e16			−0.358931			−0.179466	+	0.983764i	$0.557437\pi$
$618$	2.55511e16	−	4.42558e16i	0.458647	−	0.794400i
$619$	−1.60595e16	+	9.27195e15i	−0.285488	+	0.164827i	−0.635905	−	0.771767i	$-0.719373\pi$
$619$	−1.60595e16	+	9.27195e15i	−0.285488	+	0.164827i	0.350417	+	0.936594i	$0.386040\pi$
$620$	−7.19553e15	−	1.24630e16i	−0.126681	−	0.219419i
$621$	2.49101e16	+	1.43818e16i	0.434336	+	0.250764i
$622$			1.41516e16i			0.244379i
$623$		0			0
$624$	9.92775e15			0.168168
$625$	−4.96079e15	+	8.59235e15i	−0.0832283	+	0.144156i
$626$	−9.47819e15	+	5.47224e15i	−0.157500	+	0.0909324i
$627$	−1.72327e16	−	2.98479e16i	−0.283627	−	0.491256i
$628$	3.27020e16	+	1.88805e16i	0.533109	+	0.307791i
$629$			2.37465e16i			0.383439i
$630$		0			0
$631$	1.12464e16			0.178171			0.0890855	−	0.996024i	$-0.471606\pi$
$631$	1.12464e16			0.178171			0.0890855	+	0.996024i	$0.471606\pi$
$632$	1.28409e16	−	2.22411e16i	0.201509	−	0.349023i
$633$	9.44808e16	−	5.45485e16i	1.46866	−	0.847931i
$634$	2.99632e15	+	5.18978e15i	0.0461373	+	0.0799122i
$635$	4.09542e16	+	2.36449e16i	0.624678	+	0.360658i
$636$			4.13758e16i			0.625178i
$637$		0			0
$638$	3.30474e15			0.0490020
$639$	−2.59783e16	+	4.49957e16i	−0.381597	+	0.660946i
$640$	−2.92807e15	+	1.69052e15i	−0.0426090	+	0.0246003i
$641$	−2.17347e16	−	3.76457e16i	−0.313333	−	0.542709i	0.665749	−	0.746176i	$-0.268112\pi$
$641$	−2.17347e16	−	3.76457e16i	−0.313333	−	0.542709i	−0.979082	+	0.203467i	$0.934779\pi$
$642$	6.86718e16	+	3.96477e16i	0.980773	+	0.566249i
$643$		−	3.56902e16i		−	0.504990i	−0.967598	−	0.252495i	$-0.918749\pi$
$643$		−	3.56902e16i		−	0.504990i	0.967598	−	0.252495i	$-0.0812512\pi$
$644$		0			0
$645$	6.69864e16			0.930311
$646$	−1.11581e16	+	1.93265e16i	−0.153531	+	0.265924i
$647$	−8.83324e16	+	5.09987e16i	−1.20419	+	0.695238i	−0.961484	−	0.274862i	$-0.911368\pi$
$647$	−8.83324e16	+	5.09987e16i	−1.20419	+	0.695238i	−0.242704	+	0.970100i	$0.578034\pi$
$648$	1.62190e16	+	2.80921e16i	0.219065	+	0.379432i
$649$	9.46446e14	+	5.46431e14i	0.0126657	+	0.00731252i
$650$		−	2.09529e16i		−	0.277820i
$651$		0			0
$652$	−5.67650e16			−0.738916
$653$	−1.37945e16	+	2.38927e16i	−0.177921	+	0.308168i	−0.941168	−	0.337939i	$-0.890270\pi$
$653$	−1.37945e16	+	2.38927e16i	−0.177921	+	0.308168i	0.763247	+	0.646106i	$0.223604\pi$
$654$	7.40885e16	−	4.27750e16i	0.946857	−	0.546668i
$655$	−3.60720e16	−	6.24785e16i	−0.456796	−	0.791193i
$656$	−1.72623e16	−	9.96640e15i	−0.216609	−	0.125059i
$657$			2.15688e16i			0.268185i
$658$		0			0
$659$	8.60974e16			1.05118			0.525590	−	0.850738i	$-0.323844\pi$
$659$	8.60974e16			1.05118			0.525590	+	0.850738i	$0.323844\pi$
$660$	3.95741e15	−	6.85443e15i	0.0478792	−	0.0829292i
$661$	−1.10364e16	+	6.37188e15i	−0.132318	+	0.0763939i	−0.564698	−	0.825298i	$-0.691007\pi$
$661$	−1.10364e16	+	6.37188e15i	−0.132318	+	0.0763939i	0.432380	+	0.901692i	$0.357674\pi$
$662$	−1.87740e16	−	3.25176e16i	−0.223054	−	0.386341i
$663$	1.30320e16	+	7.52402e15i	0.153437	+	0.0885868i
$664$		−	7.58389e15i		−	0.0884879i
$665$		0			0
$666$	3.55882e16			0.407813
$667$	−7.36544e15	+	1.27573e16i	−0.0836458	+	0.144879i
$668$	−2.12728e15	+	1.22818e15i	−0.0239423	+	0.0138231i
$669$	−3.72709e16	−	6.45551e16i	−0.415732	−	0.720069i
$670$	−2.23093e16	−	1.28803e16i	−0.246625	−	0.142389i
$671$			4.33854e15i			0.0475345i
$672$		0			0
$673$	1.37493e17			1.47976			0.739879	−	0.672740i	$-0.234883\pi$
$673$	1.37493e17			1.47976			0.739879	+	0.672740i	$0.234883\pi$
$674$	6.23756e15	−	1.08038e16i	0.0665358	−	0.115243i
$675$	4.03351e16	−	2.32875e16i	0.426443	−	0.246207i
$676$	−1.61253e16	−	2.79298e16i	−0.168977	−	0.292676i
$677$	2.86231e16	+	1.65256e16i	0.297293	+	0.171642i	0.641226	−	0.767352i	$-0.278426\pi$
$677$	2.86231e16	+	1.65256e16i	0.297293	+	0.171642i	−0.343933	+	0.938994i	$0.611759\pi$
$678$		−	9.09769e15i		−	0.0936597i
$679$		0			0
$680$	−5.12483e15			−0.0518354
$681$	−7.10929e16	+	1.23137e17i	−0.712761	+	1.23454i
$682$	−1.63336e16	+	9.43020e15i	−0.162321	+	0.0937162i
$683$	1.98041e16	+	3.43017e16i	0.195088	+	0.337903i	0.946929	−	0.321441i	$-0.104167\pi$
$683$	1.98041e16	+	3.43017e16i	0.195088	+	0.337903i	−0.751841	+	0.659344i	$0.770834\pi$
$684$	2.89640e16	+	1.67224e16i	0.282828	+	0.163291i
$685$		−	2.50333e16i		−	0.242312i
$686$		0			0
$687$	8.36938e16			0.796073
$688$	−1.87510e16	+	3.24777e16i	−0.176805	+	0.306235i
$689$	−5.58144e16	+	3.22245e16i	−0.521712	+	0.301211i
$690$	1.76401e16	+	3.05536e16i	0.163458	+	0.283118i
$691$	6.34564e16	+	3.66366e16i	0.582918	+	0.336548i	0.762292	−	0.647233i	$-0.224074\pi$
$691$	6.34564e16	+	3.66366e16i	0.582918	+	0.336548i	−0.179374	+	0.983781i	$0.557407\pi$
$692$			9.08162e15i			0.0827041i
$693$		0			0
$694$	5.84142e14			0.00522831
$695$	−3.21604e16	+	5.57034e16i	−0.285373	+	0.494280i
$696$	−9.78758e15	+	5.65086e15i	−0.0861033	+	0.0497118i
$697$	−1.51066e16	−	2.61654e16i	−0.131756	−	0.228208i
$698$	2.94405e16	+	1.69975e16i	0.254574	+	0.146978i
$699$			3.65415e16i			0.313273i
$700$		0			0
$701$	−2.17411e16			−0.183220			−0.0916101	−	0.995795i	$-0.529201\pi$
$701$	−2.17411e16			−0.183220			−0.0916101	+	0.995795i	$0.529201\pi$
$702$	−1.71870e16	+	2.97687e16i	−0.143607	+	0.248735i
$703$	−2.50905e17	+	1.44860e17i	−2.07863	+	1.20010i
$704$	2.21554e15	+	3.83742e15i	0.0181988	+	0.0315213i
$705$	−1.34227e17	−	7.74958e16i	−1.09321	−	0.631166i
$706$		−	4.85060e16i		−	0.391713i
$707$		0			0
$708$	−3.73742e15			−0.0296738
$709$	1.03734e17	−	1.79673e17i	0.816665	−	1.41450i	−0.0914619	−	0.995809i	$-0.529154\pi$
$709$	1.03734e17	−	1.79673e17i	0.816665	−	1.41450i	0.908126	−	0.418696i	$-0.137513\pi$
$710$	8.41203e16	−	4.85669e16i	0.656676	−	0.379132i
$711$	−2.91697e16	−	5.05234e16i	−0.225795	−	0.391088i
$712$	4.35138e15	+	2.51227e15i	0.0334000	+	0.0192835i
$713$		−	8.40702e16i		−	0.639889i
$714$		0			0
$715$	1.23285e16			0.0922728
$716$	−4.52641e16	+	7.83998e16i	−0.335951	+	0.581884i
$717$	−4.09665e16	+	2.36520e16i	−0.301519	+	0.174082i
$718$	4.14213e16	+	7.17438e16i	0.302327	+	0.523646i
$719$	2.07457e17	+	1.19775e17i	1.50160	+	0.866950i	0.999998	+	0.00185138i	$0.000589312\pi$
$719$	2.07457e17	+	1.19775e17i	1.50160	+	0.866950i	0.501602	+	0.865098i	$0.332744\pi$
$720$			7.68045e15i			0.0551305i
$721$		0			0
$722$	−1.72107e17			−1.21500
$723$	−1.31158e17	+	2.27172e17i	−0.918257	+	1.59047i
$724$	−2.51842e15	+	1.45401e15i	−0.0174863	+	0.0100957i
$725$	1.19263e16	+	2.06570e16i	0.0821257	+	0.142246i
$726$	9.69675e16	+	5.59842e16i	0.662226	+	0.382337i
$727$		−	5.15434e16i		−	0.349113i	−0.984647	−	0.174557i	$-0.944151\pi$
$727$		−	5.15434e16i		−	0.349113i	0.984647	−	0.174557i	$-0.0558492\pi$
$728$		0			0
$729$	−5.28512e16			−0.352119
$730$	2.01617e16	−	3.49211e16i	0.133226	−	0.230755i
$731$	−4.92283e16	+	2.84220e16i	−0.322634	+	0.186273i
$732$	−7.41858e15	−	1.28494e16i	−0.0482230	−	0.0835247i
$733$	1.01615e17	+	5.86675e16i	0.655140	+	0.378245i	0.790423	−	0.612562i	$-0.209861\pi$
$733$	1.01615e17	+	5.86675e16i	0.655140	+	0.378245i	−0.135283	+	0.990807i	$0.543194\pi$
$734$			9.11546e16i			0.582911i
$735$		0			0
$736$	−1.97515e16			−0.124260
$737$	−1.68804e16	+	2.92378e16i	−0.105337	+	0.182448i
$738$	−3.92134e16	+	2.26399e16i	−0.242715	+	0.140132i
$739$	−5.17864e15	−	8.96968e15i	−0.0317943	−	0.0550694i	0.849690	−	0.527282i	$-0.176789\pi$
$739$	−5.17864e15	−	8.96968e15i	−0.0317943	−	0.0550694i	−0.881485	+	0.472213i	$0.843455\pi$
$740$	−5.76192e16	−	3.32664e16i	−0.350895	−	0.202589i
$741$			1.83594e17i			1.10905i
$742$		0			0
$743$	−2.76902e17			−1.64586			−0.822929	−	0.568144i	$-0.807662\pi$
$743$	−2.76902e17			−1.64586			−0.822929	+	0.568144i	$0.807662\pi$
$744$	3.22499e16	−	5.58584e16i	0.190147	−	0.329345i
$745$	−1.47350e16	+	8.50728e15i	−0.0861814	+	0.0497569i
$746$	4.37804e16	+	7.58299e16i	0.254008	+	0.439954i
$747$	−1.49196e16	−	8.61386e15i	−0.0858687	−	0.0495763i
$748$			6.71642e15i			0.0383467i
$749$		0			0
$750$	1.39901e17			0.786058
$751$	−2.83851e15	+	4.91644e15i	−0.0158216	+	0.0274038i	−0.873828	−	0.486236i	$-0.838370\pi$
$751$	−2.83851e15	+	4.91644e15i	−0.0158216	+	0.0274038i	0.858006	+	0.513639i	$0.171703\pi$
$752$	7.51462e16	−	4.33857e16i	0.415528	−	0.239905i
$753$	1.61543e17	+	2.79801e17i	0.886175	+	1.53490i
$754$	−1.52456e16	−	8.80205e15i	−0.0829691	−	0.0479023i
$755$			1.25320e17i			0.676612i
$756$		0			0
$757$	5.87044e16			0.311957			0.155979	−	0.987760i	$-0.450147\pi$
$757$	5.87044e16			0.311957			0.155979	+	0.987760i	$0.450147\pi$
$758$	−4.90083e16	+	8.48849e16i	−0.258378	+	0.447523i
$759$	4.00424e16	−	2.31185e16i	0.209445	−	0.120923i
$760$	−3.12629e16	−	5.41489e16i	−0.162236	−	0.281001i
$761$	1.47143e17	+	8.49529e16i	0.757585	+	0.437392i	0.828428	−	0.560096i	$-0.189236\pi$
$761$	1.47143e17	+	8.49529e16i	0.757585	+	0.437392i	−0.0708433	+	0.997487i	$0.522569\pi$
$762$			2.11950e17i			1.08269i
$763$		0			0
$764$	1.20598e17			0.606428
$765$	−5.82084e15	+	1.00820e16i	−0.0290414	+	0.0503011i
$766$	−2.08868e17	+	1.20590e17i	−1.03395	+	0.596950i
$767$	−2.91079e15	−	5.04164e15i	−0.0142968	−	0.0247628i
$768$	−1.31234e16	−	7.57680e15i	−0.0639557	−	0.0369248i
$769$		−	1.95491e17i		−	0.945298i	−0.881251	−	0.472649i	$-0.843298\pi$
$769$		−	1.95491e17i		−	0.945298i	0.881251	−	0.472649i	$-0.156702\pi$
$770$		0			0
$771$	−2.14766e17			−1.02244
$772$	−5.82081e16	+	1.00819e17i	−0.274967	+	0.476256i
$773$	1.12824e17	−	6.51389e16i	0.528840	−	0.305326i	−0.211704	−	0.977334i	$-0.567901\pi$
$773$	1.12824e17	−	6.51389e16i	0.528840	−	0.305326i	0.740544	+	0.672008i	$0.234568\pi$
$774$	4.25952e16	+	7.37770e16i	0.198114	+	0.343143i
$775$	−1.17891e17	−	6.80645e16i	−0.544090	−	0.314131i
$776$		−	3.17657e16i		−	0.145475i
$777$		0			0
$778$	9.79860e16			0.441862
$779$	1.84309e17	−	3.19232e17i	0.824748	−	1.42851i
$780$	−3.65130e16	+	2.10808e16i	−0.162136	+	0.0936093i
$781$	−6.36500e16	−	1.10245e17i	−0.280474	−	0.485795i
$782$	−2.59274e16	−	1.49692e16i	−0.113375	−	0.0654574i
$783$		−	3.91312e16i		−	0.169806i
$784$		0			0
$785$	−1.60365e17			−0.685317
$786$	1.61672e17	−	2.80024e17i	0.685645	−	1.18757i
$787$	1.17760e17	−	6.79890e16i	0.495622	−	0.286148i	−0.231282	−	0.972887i	$-0.574292\pi$
$787$	1.17760e17	−	6.79890e16i	0.495622	−	0.286148i	0.726904	+	0.686739i	$0.240959\pi$
$788$	5.13809e16	+	8.89942e16i	0.214607	+	0.371710i
$789$	−4.39491e17	−	2.53740e17i	−1.82175	−	1.05179i
$790$			1.09067e17i			0.448673i
$791$		0			0
$792$	1.00657e16			0.0407844
$793$	1.15555e16	−	2.00148e16i	0.0464677	−	0.0804844i
$794$	−3.50757e16	+	2.02510e16i	−0.139986	+	0.0808208i
$795$	−8.78582e16	−	1.52175e17i	−0.348000	−	0.602754i
$796$	−5.55533e16	−	3.20737e16i	−0.218389	−	0.126087i
$797$		−	7.42818e16i		−	0.289823i	−0.989445	−	0.144911i	$-0.953710\pi$
$797$		−	7.42818e16i		−	0.289823i	0.989445	−	0.144911i	$-0.0462897\pi$
$798$		0			0
$799$	1.31524e17			0.505505
$800$	−1.59911e16	+	2.76974e16i	−0.0610012	+	0.105657i
$801$	9.88468e15	−	5.70692e15i	0.0374255	−	0.0216076i
$802$	−1.73232e17	−	3.00046e17i	−0.651000	−	1.12756i
$803$	−4.57663e16	−	2.64232e16i	−0.170707	−	0.0985580i
$804$		−	1.15457e17i		−	0.427449i
$805$		0			0
$806$	1.00468e17			0.366452
$807$	−1.38210e17	+	2.39386e17i	−0.500376	+	0.866677i
$808$	1.36789e17	−	7.89754e16i	0.491569	−	0.283807i
$809$	8.62235e16	+	1.49343e17i	0.307563	+	0.532715i	0.977829	−	0.209406i	$-0.0671531\pi$
$809$	8.62235e16	+	1.49343e17i	0.307563	+	0.532715i	−0.670265	+	0.742121i	$0.733820\pi$
$810$	−1.19302e17	−	6.88793e16i	−0.422415	−	0.243881i
$811$			9.05781e16i			0.318345i	0.987251	+	0.159172i	$0.0508826\pi$
$811$			9.05781e16i			0.318345i	−0.987251	+	0.159172i	$0.949117\pi$
$812$		0			0
$813$	−8.34960e16			−0.289150
$814$	−4.35978e16	+	7.55136e16i	−0.149871	+	0.259585i
$815$	2.08774e17	−	1.20536e17i	0.712412	−	0.411311i
$816$	−1.14846e16	−	1.98919e16i	−0.0389022	−	0.0673805i
$817$	−6.00611e17	−	3.46763e17i	−2.01958	−	1.16600i
$818$		−	1.63683e17i		−	0.546367i
$819$		0			0
$820$	8.46514e16			0.278452
$821$	2.90373e17	−	5.02941e17i	0.948195	−	1.64232i	0.198971	−	0.980005i	$-0.436240\pi$
$821$	2.90373e17	−	5.02941e17i	0.948195	−	1.64232i	0.749224	−	0.662316i	$-0.230426\pi$
$822$	9.71660e16	−	5.60988e16i	0.314980	−	0.181854i
$823$	−9.00951e16	−	1.56049e17i	−0.289936	−	0.502184i	0.683858	−	0.729615i	$-0.260301\pi$
$823$	−9.00951e16	−	1.56049e17i	−0.289936	−	0.502184i	−0.973794	+	0.227431i	$0.926967\pi$
$824$	−1.05221e17	−	6.07496e16i	−0.336156	−	0.194080i
$825$		−	7.48684e16i		−	0.237451i
$826$		0			0
$827$	3.77617e17			1.18037			0.590185	−	0.807268i	$-0.299055\pi$
$827$	3.77617e17			1.18037			0.590185	+	0.807268i	$0.299055\pi$
$828$	−2.24339e16	+	3.88567e16i	−0.0696183	+	0.120583i
$829$	5.20459e16	−	3.00487e16i	0.160346	−	0.0925760i	−0.417680	−	0.908594i	$-0.637157\pi$
$829$	5.20459e16	−	3.00487e16i	0.160346	−	0.0925760i	0.578026	+	0.816018i	$0.303823\pi$
$830$	1.61038e16	+	2.78926e16i	0.0492560	+	0.0853140i
$831$	4.30733e17	+	2.48684e17i	1.30798	+	0.755164i
$832$		−	2.36040e16i		−	0.0711615i
$833$		0			0
$834$	−2.88281e17			−0.856683
$835$	5.21590e15	−	9.03420e15i	0.0153890	−	0.0266545i
$836$	−7.09655e16	+	4.09720e16i	−0.207879	+	0.120019i
$837$	1.11662e17	+	1.93405e17i	0.324753	+	0.562489i
$838$	−1.43006e17	−	8.25648e16i	−0.412944	−	0.238414i
$839$			2.04585e17i			0.586546i	0.956029	+	0.293273i	$0.0947444\pi$
$839$			2.04585e17i			0.586546i	−0.956029	+	0.293273i	$0.905256\pi$
$840$		0			0
$841$	−3.33774e17			−0.943359
$842$	−7.45518e16	+	1.29127e17i	−0.209211	+	0.362365i
$843$	3.73869e17	−	2.15853e17i	1.04173	−	0.601442i
$844$	−1.29693e17	−	2.24635e17i	−0.358808	−	0.621474i
$845$	1.18613e17	+	6.84814e16i	0.325832	+	0.188119i
$846$		−	1.97112e17i		−	0.537638i
$847$		0			0
$848$	9.83740e16			0.264549
$849$	3.62434e17	−	6.27753e17i	0.967793	−	1.67627i
$850$	−4.19825e16	+	2.42386e16i	−0.111315	+	0.0642679i
$851$	−1.94337e17	−	3.36602e17i	−0.511656	−	0.886215i
$852$	3.77021e17	+	2.17673e17i	0.985663	+	0.569073i
$853$		−	5.22323e17i		−	1.35595i	−0.735083	−	0.677977i	$-0.762857\pi$
$853$		−	5.22323e17i		−	1.35595i	0.735083	−	0.677977i	$-0.237143\pi$
$854$		0			0
$855$	−1.42035e17			−0.363578
$856$	9.42653e16	−	1.63272e17i	0.239613	−	0.415021i
$857$	2.73203e17	−	1.57734e17i	0.689605	−	0.398144i	−0.113859	−	0.993497i	$-0.536321\pi$
$857$	2.73203e17	−	1.57734e17i	0.689605	−	0.398144i	0.803464	+	0.595353i	$0.202988\pi$
$858$	2.76277e16	+	4.78526e16i	0.0692502	+	0.119945i
$859$	4.29262e17	+	2.47835e17i	1.06847	+	0.616883i	0.927764	−	0.373168i	$-0.121728\pi$
$859$	4.29262e17	+	2.47835e17i	1.06847	+	0.616883i	0.140709	+	0.990051i	$0.455062\pi$
$860$		−	1.59265e17i		−	0.393668i
$861$		0			0
$862$	−4.28027e17			−1.04334
$863$	1.43524e17	−	2.48591e17i	0.347424	−	0.601755i	−0.638367	−	0.769732i	$-0.720390\pi$
$863$	1.43524e17	−	2.48591e17i	0.347424	−	0.601755i	0.985791	+	0.167976i	$0.0537233\pi$
$864$	4.54386e16	−	2.62340e16i	0.109230	−	0.0630641i
$865$	−1.92841e16	−	3.34010e16i	−0.0460366	−	0.0797377i
$866$	−3.67672e17	−	2.12276e17i	−0.871673	−	0.503261i
$867$			4.67045e17i			1.09962i
$868$		0			0
$869$	1.42939e17			0.331919
$870$	2.39983e16	−	4.15663e16i	0.0553433	−	0.0958574i
$871$	1.55747e17	−	8.99208e16i	0.356707	−	0.205945i
$872$	−1.01701e17	−	1.76151e17i	−0.231327	−	0.400669i
$873$	−6.24920e16	−	3.60798e16i	−0.141169	−	0.0815039i
$874$		−	3.65265e17i		−	0.819482i
$875$		0			0
$876$	1.80726e17			0.399942
$877$	−1.90465e17	+	3.29896e17i	−0.418619	+	0.725069i	−0.995801	−	0.0915468i	$-0.970819\pi$
$877$	−1.90465e17	+	3.29896e17i	−0.418619	+	0.725069i	0.577182	+	0.816615i	$0.304152\pi$
$878$	−1.40376e16	+	8.10463e15i	−0.0306427	+	0.0176916i
$879$	4.04465e17	+	7.00553e17i	0.876894	+	1.51883i
$880$	−1.62969e16	−	9.40903e15i	−0.0350921	−	0.0202604i
$881$			4.35093e17i			0.930522i	0.885174	+	0.465261i	$0.154039\pi$
$881$			4.35093e17i			0.930522i	−0.885174	+	0.465261i	$0.845961\pi$
$882$		0			0
$883$	7.33662e17			1.54786			0.773931	−	0.633270i	$-0.218288\pi$
$883$	7.33662e17			1.54786			0.773931	+	0.633270i	$0.218288\pi$
$884$	1.78889e16	−	3.09845e16i	0.0374861	−	0.0649279i
$885$	1.37458e16	−	7.93612e15i	0.0286094	−	0.0165177i
$886$	−6.55408e16	−	1.13520e17i	−0.135491	−	0.234677i
$887$	−5.12834e17	−	2.96085e17i	−1.05302	−	0.607959i	−0.129524	−	0.991576i	$-0.541345\pi$
$887$	−5.12834e17	−	2.96085e17i	−1.05302	−	0.607959i	−0.923492	+	0.383617i	$0.874678\pi$
$888$		−	2.98196e17i		−	0.608168i
$889$		0			0
$890$	−2.13384e16			−0.0429360
$891$	−9.02707e16	+	1.56353e17i	−0.180418	+	0.312494i
$892$	−1.53485e17	+	8.86144e16i	−0.304702	+	0.175920i
$893$	8.02333e17	+	1.38968e18i	1.58214	+	2.74035i
$894$	−6.60414e16	−	3.81290e16i	−0.129357	−	0.0746845i
$895$		−	3.84459e17i		−	0.748018i
$896$		0			0
$897$	−2.46301e17			−0.472837
$898$	−1.24863e17	+	2.16269e17i	−0.238109	+	0.412417i
$899$	−9.90493e16	+	5.71862e16i	−0.187626	+	0.108326i
$900$	3.63257e16	+	6.29180e16i	0.0683532	+	0.118391i
$901$	1.29134e17	+	7.45555e16i	0.241375	+	0.139358i
$902$		−	1.10941e17i		−	0.205993i
$903$		0			0
$904$	−2.16304e16			−0.0396328
$905$	6.17496e15	−	1.06953e16i	0.0112394	−	0.0194672i
$906$	−4.86427e17	+	2.80838e17i	−0.879525	+	0.507794i
$907$	1.30494e16	+	2.26022e16i	0.0234394	+	0.0405982i	0.877507	−	0.479564i	$-0.159205\pi$
$907$	1.30494e16	+	2.26022e16i	0.0234394	+	0.0405982i	−0.854068	+	0.520162i	$0.825872\pi$
$908$	2.92766e17	+	1.69029e17i	0.522403	+	0.301610i
$909$		−	3.58804e17i		−	0.636025i
$910$		0			0
$911$	3.22736e17			0.564595			0.282297	−	0.959327i	$-0.408904\pi$
$911$	3.22736e17			0.564595			0.282297	+	0.959327i	$0.408904\pi$
$912$	1.40118e17	−	2.42691e17i	0.243514	−	0.421779i
$913$	3.65550e16	−	2.11050e16i	0.0631135	−	0.0364386i
$914$	−1.62017e17	−	2.80622e17i	−0.277898	−	0.481333i
$915$	5.45692e16	+	3.15055e16i	0.0929867	+	0.0536859i
$916$		−	1.98988e17i		−	0.336864i
$917$		0			0
$918$	7.95286e16			0.132882
$919$	−3.47547e17	+	6.01969e17i	−0.576926	+	0.999266i	0.418903	+	0.908031i	$0.362415\pi$
$919$	−3.47547e17	+	6.01969e17i	−0.576926	+	0.999266i	−0.995829	+	0.0912348i	$0.970919\pi$
$920$	7.26435e16	−	4.19407e16i	0.119804	−	0.0691686i
$921$	−2.87198e17	−	4.97441e17i	−0.470569	−	0.815049i
$922$	−2.96474e17	−	1.71170e17i	−0.482616	−	0.278638i
$923$			6.78117e17i			1.09672i
$924$		0			0
$925$	−6.29353e17			−1.00472
$926$	1.06331e17	−	1.84171e17i	0.168653	−	0.292115i
$927$	−2.39023e17	+	1.38000e17i	−0.376671	+	0.217471i
$928$	1.34353e16	+	2.32707e16i	0.0210359	+	0.0364352i
$929$	2.55576e17	+	1.47557e17i	0.397581	+	0.229544i	0.685440	−	0.728129i	$-0.259610\pi$
$929$	2.55576e17	+	1.47557e17i	0.397581	+	0.229544i	−0.287858	+	0.957673i	$0.592943\pi$
$930$			2.73920e17i			0.423376i
$931$		0			0
$932$	8.68801e16			0.132564
$933$	1.34681e17	−	2.33275e17i	0.204182	−	0.353653i
$934$	−5.65166e17	+	3.26299e17i	−0.851324	+	0.491512i
$935$	−1.42618e16	−	2.47021e16i	−0.0213454	−	0.0369713i
$936$	−4.64356e16	−	2.68096e16i	−0.0690552	−	0.0398690i
$937$			6.78231e17i			1.00217i	0.865399	+	0.501083i	$0.167065\pi$
$937$			6.78231e17i			1.00217i	−0.865399	+	0.501083i	$0.832935\pi$
$938$		0			0
$939$	2.08317e17			0.303901
$940$	−1.84252e17	+	3.19134e17i	−0.267082	+	0.462600i
$941$	8.12976e17	−	4.69372e17i	1.17095	−	0.676051i	0.217050	−	0.976160i	$-0.430356\pi$
$941$	8.12976e17	−	4.69372e17i	1.17095	−	0.676051i	0.953905	+	0.300109i	$0.0970232\pi$
$942$	−3.59372e17	−	6.22451e17i	−0.514326	−	0.890840i
$943$	4.28266e17	+	2.47260e17i	0.609037	+	0.351628i
$944$			8.88600e15i			0.0125567i
$945$		0			0
$946$	−2.08727e17			−0.291227
$947$	−4.28673e17	+	7.42484e17i	−0.594328	+	1.02941i	0.399313	+	0.916815i	$0.369249\pi$
$947$	−4.28673e17	+	7.42484e17i	−0.594328	+	1.02941i	−0.993641	+	0.112592i	$0.964085\pi$
$948$	−4.23338e17	+	2.44414e17i	−0.583227	+	0.336726i
$949$	1.40754e17	+	2.43793e17i	0.192692	+	0.333752i
$950$	−5.12209e17	−	2.95724e17i	−0.696795	−	0.402295i
$951$		−	1.14064e17i		−	0.154193i
$952$		0			0
$953$	−8.08071e17			−1.07868			−0.539339	−	0.842088i	$-0.681326\pi$
$953$	−8.08071e17			−1.07868			−0.539339	+	0.842088i	$0.681326\pi$
$954$	1.11734e17	−	1.93529e17i	0.148216	−	0.256718i
$955$	−4.43543e17	+	2.56080e17i	−0.584677	+	0.337563i
$956$	5.62345e16	+	9.74010e16i	0.0736640	+	0.127590i
$957$	−5.44753e16	−	3.14513e16i	−0.0709133	−	0.0409418i
$958$			4.57505e17i			0.591838i
$959$		0			0
$960$	6.43549e16			0.0822156
$961$	−6.74661e16	+	1.16855e17i	−0.0856536	+	0.148356i
$962$	4.02255e17	−	2.32242e17i	0.507517	−	0.293015i
$963$	−2.14135e17	−	3.70893e17i	−0.268491	−	0.465041i
$964$	5.40118e17	+	3.11837e17i	0.673018	+	0.388567i
$965$		−	4.94401e17i		−	0.612232i
$966$		0			0
$967$	4.31160e17			0.527326			0.263663	−	0.964615i	$-0.415069\pi$
$967$	4.31160e17			0.527326			0.263663	+	0.964615i	$0.415069\pi$
$968$	1.33107e17	−	2.30547e17i	0.161788	−	0.280226i
$969$	3.67861e17	−	2.12384e17i	0.444366	−	0.256555i
$970$	6.74518e16	+	1.16830e17i	0.0809773	+	0.140257i
$971$	2.24945e17	+	1.29872e17i	0.268387	+	0.154953i	0.628154	−	0.778089i	$-0.283811\pi$
$971$	2.24945e17	+	1.29872e17i	0.268387	+	0.154953i	−0.359767	+	0.933042i	$0.617144\pi$
$972$		−	3.16571e17i		−	0.375382i
$973$		0			0
$974$	−2.90849e17			−0.340654
$975$	−1.99409e17	+	3.45386e17i	−0.232122	+	0.402047i
$976$	−3.05503e16	+	1.76382e16i	−0.0353441	+	0.0204059i
$977$	−6.71442e17	−	1.16297e18i	−0.772042	−	1.33722i	−0.936442	−	0.350822i	$-0.885902\pi$
$977$	−6.71442e17	−	1.16297e18i	−0.772042	−	1.33722i	0.164400	−	0.986394i	$-0.447431\pi$
$978$	9.35711e17	+	5.40233e17i	1.06932	+	0.617374i
$979$			2.79654e16i			0.0317632i
$980$		0			0
$981$	−4.62051e17			−0.518413
$982$	−2.37863e17	+	4.11991e17i	−0.265251	+	0.459429i
$983$	−6.08952e17	+	3.51578e17i	−0.674935	+	0.389674i	−0.797944	−	0.602732i	$-0.794079\pi$
$983$	−6.08952e17	+	3.51578e17i	−0.674935	+	0.389674i	0.123009	+	0.992406i	$0.460746\pi$
$984$	1.89701e17	+	3.28571e17i	0.208977	+	0.361959i
$985$	−3.77944e17	−	2.18206e17i	−0.413819	−	0.238919i
$986$			4.07294e16i			0.0443248i
$987$		0			0
$988$	4.36509e17			0.469301
$989$	4.65200e17	−	8.05750e17i	0.497121	−	0.861039i
$990$	−3.70204e16	+	2.13737e16i	−0.0393215	+	0.0227023i
$991$	−4.22531e17	−	7.31845e17i	−0.446084	−	0.772640i	0.552043	−	0.833815i	$-0.313848\pi$
$991$	−4.22531e17	−	7.31845e17i	−0.446084	−	0.772640i	−0.998127	+	0.0611757i	$0.980515\pi$
$992$	−1.32807e17	−	7.66764e16i	−0.139365	−	0.0804622i
$993$			7.14692e17i			0.745458i
$994$		0			0
$995$	2.72424e17			0.280741
$996$	−7.21760e16	+	1.25013e17i	−0.0739328	+	0.128055i
$997$	−1.30531e18	+	7.53621e17i	−1.32905	+	0.767330i	−0.985153	−	0.171676i	$-0.945082\pi$
$997$	−1.30531e18	+	7.53621e17i	−1.32905	+	0.767330i	−0.343901	+	0.939006i	$0.611748\pi$
$998$	8.82778e15	+	1.52902e16i	0.00893446	+	0.0154749i
$999$	8.94151e17	+	5.16238e17i	0.899534	+	0.519346i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.13.d.a.19.4		16
7.2	even	3		98.13.b.c.97.15		16
7.3	odd	6	inner	98.13.d.a.31.4		16
7.4	even	3		14.13.d.a.3.1	✓	16
7.5	odd	6		98.13.b.c.97.10		16
7.6	odd	2		14.13.d.a.5.1	yes	16
21.11	odd	6		126.13.n.a.73.7		16
21.20	even	2		126.13.n.a.19.7		16
28.11	odd	6		112.13.s.c.17.7		16
28.27	even	2		112.13.s.c.33.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.13.d.a.3.1	✓	16	7.4	even	3
14.13.d.a.5.1	yes	16	7.6	odd	2
98.13.b.c.97.10		16	7.5	odd	6
98.13.b.c.97.15		16	7.2	even	3
98.13.d.a.19.4		16	1.1	even	1	trivial
98.13.d.a.31.4		16	7.3	odd	6	inner
112.13.s.c.17.7		16	28.11	odd	6
112.13.s.c.33.7		16	28.27	even	2
126.13.n.a.19.7		16	21.20	even	2
126.13.n.a.73.7		16	21.11	odd	6

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	98.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-22.6274 + 39.1918i) q^{2} +(745.979 - 430.691i) q^{3} +(-1024.00 - 1773.62i) q^{4} +(7532.28 + 4348.76i) q^{5} +38981.7i q^{6} +92681.9 q^{8} +(105269. - 182331. i) q^{9} +O(q^{10})\)	\(q+(-22.6274 + 39.1918i) q^{2} +(745.979 - 430.691i) q^{3} +(-1024.00 - 1773.62i) q^{4} +(7532.28 + 4348.76i) q^{5} +38981.7i q^{6} +92681.9 q^{8} +(105269. - 182331. i) q^{9} +(-340872. + 196803. i) q^{10} +(257922. + 446735. i) q^{11} +(-1.52776e6 - 882055. i) q^{12} -2.74786e6i q^{13} +7.49190e6 q^{15} +(-2.09715e6 + 3.63237e6i) q^{16} +(-5.50579e6 + 3.17877e6i) q^{17} +(4.76393e6 + 8.25138e6i) q^{18} +(-6.71736e7 - 3.87827e7i) q^{19} -1.78125e7i q^{20} -2.33445e7 q^{22} +(5.20289e7 - 9.01168e7i) q^{23} +(6.91387e7 - 3.99173e7i) q^{24} +(-8.42468e7 - 1.45920e8i) q^{25} +(1.07694e8 + 6.21770e7i) q^{26} +2.76420e8i q^{27} -1.41564e8 q^{29} +(-1.69522e8 + 2.93621e8i) q^{30} +(6.99677e8 - 4.03959e8i) q^{31} +(-9.49063e7 - 1.64382e8i) q^{32} +(3.84809e8 + 2.22170e8i) q^{33} -2.87709e8i q^{34} -4.31182e8 q^{36} +(1.86759e9 - 3.23475e9i) q^{37} +(3.03993e9 - 1.75510e9i) q^{38} +(-1.18348e9 - 2.04985e9i) q^{39} +(6.98106e8 + 4.03052e8i) q^{40} +4.75235e9i q^{41} +8.94118e9 q^{43} +(5.28225e8 - 9.14913e8i) q^{44} +(1.58583e9 - 9.15581e8i) q^{45} +(2.35456e9 + 4.07822e9i) q^{46} +(-1.79163e10 - 1.03440e10i) q^{47} +3.61290e9i q^{48} +7.62515e9 q^{50} +(-2.73814e9 + 4.74259e9i) q^{51} +(-4.87367e9 + 2.81381e9i) q^{52} +(-1.17271e10 - 2.03119e10i) q^{53} +(-1.08334e10 - 6.25467e9i) q^{54} +4.48657e9i q^{55} -6.68134e10 q^{57} +(3.20324e9 - 5.54817e9i) q^{58} +(1.83475e9 - 1.05929e9i) q^{59} +(-7.67170e9 - 1.32878e10i) q^{60} +(7.28376e9 + 4.20528e9i) q^{61} +3.65622e10i q^{62} +8.58993e9 q^{64} +(1.19498e10 - 2.06977e10i) q^{65} +(-1.74145e10 + 1.00543e10i) q^{66} +(3.27239e10 + 5.66794e10i) q^{67} +(1.12759e10 + 6.51012e9i) q^{68} -8.96336e10i q^{69} -2.46780e11 q^{71} +(9.75654e9 - 1.68988e10i) q^{72} +(-8.87210e10 + 5.12231e10i) q^{73} +(8.45173e10 + 1.46388e11i) q^{74} +(-1.25693e11 - 7.25687e10i) q^{75} +1.58854e11i q^{76} +1.07116e11 q^{78} +(1.38548e11 - 2.39973e11i) q^{79} +(-3.15927e10 + 1.82400e10i) q^{80} +(1.74996e11 + 3.03102e11i) q^{81} +(-1.86253e11 - 1.07533e11i) q^{82} -8.18271e10i q^{83} -5.52949e10 q^{85} +(-2.02316e11 + 3.50421e11i) q^{86} +(-1.05604e11 + 6.09705e10i) q^{87} +(2.39047e10 + 4.14042e10i) q^{88} +(4.69496e10 + 2.71064e10i) q^{89} +8.28689e10i q^{90} -2.13111e11 q^{92} +(3.47963e11 - 6.02689e11i) q^{93} +(8.10797e11 - 4.68114e11i) q^{94} +(-3.37314e11 - 5.84244e11i) q^{95} +(-1.41596e11 - 8.17506e10i) q^{96} -3.42738e11i q^{97} +1.08605e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16384 q^{4} - 18144 q^{5} + 2362248 q^{9}+O(q^{10}) \) 16 * q - 16384 * q^4 - 18144 * q^5 + 2362248 * q^9	\( 16 q - 16384 q^{4} - 18144 q^{5} + 2362248 q^{9} + 2290176 q^{10} + 2072088 q^{11} - 27163728 q^{15} - 33554432 q^{16} + 101561040 q^{17} - 4592640 q^{18} - 174931848 q^{19} + 62776320 q^{22} + 25630560 q^{23} - 242221056 q^{24} + 521205808 q^{25} + 1434682368 q^{26} + 532360944 q^{29} - 2151917568 q^{30} - 4583818344 q^{31} - 6054957720 q^{33} - 9675767808 q^{36} + 5764524040 q^{37} + 149506560 q^{38} + 10526083272 q^{39} - 4690280448 q^{40} - 66929432000 q^{43} + 4243636224 q^{44} - 57253352184 q^{45} + 7203213312 q^{46} - 18116171640 q^{47} - 99248080896 q^{50} - 23299256376 q^{51} - 8269578240 q^{52} + 39134161800 q^{53} - 105152205312 q^{54} - 328243960080 q^{57} + 29637396480 q^{58} - 201845459088 q^{59} + 27815657472 q^{60} - 336780254328 q^{61} + 137438953472 q^{64} + 158322703896 q^{65} - 268884080640 q^{66} + 107767119920 q^{67} - 207997009920 q^{68} - 1150259029344 q^{71} - 9405726720 q^{72} + 738414283320 q^{73} + 4902778368 q^{74} - 1537028640000 q^{75} - 786088888320 q^{78} + 227632064768 q^{79} + 76101451776 q^{80} - 391984178400 q^{81} + 302578053120 q^{82} + 710209696080 q^{85} - 38105192448 q^{86} - 1957017683880 q^{87} - 64282951680 q^{88} + 2485007442792 q^{89} - 104982773760 q^{92} - 458668768680 q^{93} + 2021298693120 q^{94} - 186503862960 q^{95} + 496068722688 q^{96} + 3921180354576 q^{99}+O(q^{100}) \) 16 * q - 16384 * q^4 - 18144 * q^5 + 2362248 * q^9 + 2290176 * q^10 + 2072088 * q^11 - 27163728 * q^15 - 33554432 * q^16 + 101561040 * q^17 - 4592640 * q^18 - 174931848 * q^19 + 62776320 * q^22 + 25630560 * q^23 - 242221056 * q^24 + 521205808 * q^25 + 1434682368 * q^26 + 532360944 * q^29 - 2151917568 * q^30 - 4583818344 * q^31 - 6054957720 * q^33 - 9675767808 * q^36 + 5764524040 * q^37 + 149506560 * q^38 + 10526083272 * q^39 - 4690280448 * q^40 - 66929432000 * q^43 + 4243636224 * q^44 - 57253352184 * q^45 + 7203213312 * q^46 - 18116171640 * q^47 - 99248080896 * q^50 - 23299256376 * q^51 - 8269578240 * q^52 + 39134161800 * q^53 - 105152205312 * q^54 - 328243960080 * q^57 + 29637396480 * q^58 - 201845459088 * q^59 + 27815657472 * q^60 - 336780254328 * q^61 + 137438953472 * q^64 + 158322703896 * q^65 - 268884080640 * q^66 + 107767119920 * q^67 - 207997009920 * q^68 - 1150259029344 * q^71 - 9405726720 * q^72 + 738414283320 * q^73 + 4902778368 * q^74 - 1537028640000 * q^75 - 786088888320 * q^78 + 227632064768 * q^79 + 76101451776 * q^80 - 391984178400 * q^81 + 302578053120 * q^82 + 710209696080 * q^85 - 38105192448 * q^86 - 1957017683880 * q^87 - 64282951680 * q^88 + 2485007442792 * q^89 - 104982773760 * q^92 - 458668768680 * q^93 + 2021298693120 * q^94 - 186503862960 * q^95 + 496068722688 * q^96 + 3921180354576 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more