LMFDB - Embedded newform 10.13.c.b.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,13,Mod(3,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

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

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

chi := DirichletCharacter("10.3");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	10.c (of order $4$, 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:	$9.13993817276$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 43009x^{4} + 461169144x^{2} + 392422062096 $ x^6 + 43009x^4 + 461169144x^2 + 392422062096
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{5}\cdot 5^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.1
Root			$-159.940i$ of defining polynomial
Character	$\chi$	$=$	10.3
Dual form			10.13.c.b.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(32.0000 - 32.0000i) q^{2} +(-748.698 - 748.698i) q^{3} -2048.00i q^{4} +(11268.2 - 10824.4i) q^{5} -47916.6 q^{6} +(-121018. + 121018. i) q^{7} +(-65536.0 - 65536.0i) q^{8} +589655. i q^{9} +O(q^{10})$	\(q+(32.0000 - 32.0000i) q^{2} +(-748.698 - 748.698i) q^{3} -2048.00i q^{4} +(11268.2 - 10824.4i) q^{5} -47916.6 q^{6} +(-121018. + 121018. i) q^{7} +(-65536.0 - 65536.0i) q^{8} +589655. i q^{9} +(14201.0 - 706964. i) q^{10} -855152. q^{11} +(-1.53333e6 + 1.53333e6i) q^{12} +(563543. + 563543. i) q^{13} +7.74518e6i q^{14} +(-1.65407e7 - 332259. i) q^{15} -4.19430e6 q^{16} +(-1.33894e7 + 1.33894e7i) q^{17} +(1.88690e7 + 1.88690e7i) q^{18} -9.07626e7i q^{19} +(-2.21684e7 - 2.30773e7i) q^{20} +1.81212e8 q^{21} +(-2.73649e7 + 2.73649e7i) q^{22} +(6.22062e7 + 6.22062e7i) q^{23} +9.81333e7i q^{24} +(9.80431e6 - 2.43944e8i) q^{25} +3.60667e7 q^{26} +(4.35847e7 - 4.35847e7i) q^{27} +(2.47846e8 + 2.47846e8i) q^{28} -9.61877e8i q^{29} +(-5.39935e8 + 5.18670e8i) q^{30} -1.55856e9 q^{31} +(-1.34218e8 + 1.34218e8i) q^{32} +(6.40250e8 + 6.40250e8i) q^{33} +8.56919e8i q^{34} +(-5.37058e7 + 2.67361e9i) q^{35} +1.20761e9 q^{36} +(7.41446e8 - 7.41446e8i) q^{37} +(-2.90440e9 - 2.90440e9i) q^{38} -8.43846e8i q^{39} +(-1.44786e9 - 2.90837e7i) q^{40} +9.28740e8 q^{41} +(5.79880e9 - 5.79880e9i) q^{42} +(-2.23346e9 - 2.23346e9i) q^{43} +1.75135e9i q^{44} +(6.38268e9 + 6.64435e9i) q^{45} +3.98120e9 q^{46} +(-7.22768e9 + 7.22768e9i) q^{47} +(3.14027e9 + 3.14027e9i) q^{48} -1.54496e10i q^{49} +(-7.49246e9 - 8.11994e9i) q^{50} +2.00492e10 q^{51} +(1.15414e9 - 1.15414e9i) q^{52} +(-9.05683e8 - 9.05683e8i) q^{53} -2.78942e9i q^{54} +(-9.63603e9 + 9.25652e9i) q^{55} +1.58621e10 q^{56} +(-6.79538e10 + 6.79538e10i) q^{57} +(-3.07801e10 - 3.07801e10i) q^{58} -1.35545e10i q^{59} +(-6.80466e8 + 3.38753e10i) q^{60} +6.94051e10 q^{61} +(-4.98740e10 + 4.98740e10i) q^{62} +(-7.13591e10 - 7.13591e10i) q^{63} +8.58993e9i q^{64} +(1.24501e10 + 2.50090e8i) q^{65} +4.09760e10 q^{66} +(1.13753e11 - 1.13753e11i) q^{67} +(2.74214e10 + 2.74214e10i) q^{68} -9.31472e10i q^{69} +(8.38371e10 + 8.72743e10i) q^{70} +1.09453e11 q^{71} +(3.86436e10 - 3.86436e10i) q^{72} +(-8.58305e9 - 8.58305e9i) q^{73} -4.74526e10i q^{74} +(-1.89980e11 + 1.75300e11i) q^{75} -1.85882e11 q^{76} +(1.03489e11 - 1.03489e11i) q^{77} +(-2.70031e10 - 2.70031e10i) q^{78} +1.74264e11i q^{79} +(-4.72623e10 + 4.54009e10i) q^{80} +2.48103e11 q^{81} +(2.97197e10 - 2.97197e10i) q^{82} +(-2.87263e11 - 2.87263e11i) q^{83} -3.71123e11i q^{84} +(-5.94196e9 + 2.95806e11i) q^{85} -1.42941e11 q^{86} +(-7.20155e11 + 7.20155e11i) q^{87} +(5.60432e10 + 5.60432e10i) q^{88} -2.51008e11i q^{89} +(4.16865e11 + 8.37371e9i) q^{90} -1.36398e11 q^{91} +(1.27398e11 - 1.27398e11i) q^{92} +(1.16689e12 + 1.16689e12i) q^{93} +4.62572e11i q^{94} +(-9.82453e11 - 1.02273e12i) q^{95} +2.00977e11 q^{96} +(2.97289e11 - 2.97289e11i) q^{97} +(-4.94388e11 - 4.94388e11i) q^{98} -5.04244e11i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 192 q^{2} + 296 q^{3} + 14460 q^{5} + 18944 q^{6} - 322104 q^{7} - 393216 q^{8}+O(q^{10}) $ 6 * q + 192 * q^2 + 296 * q^3 + 14460 * q^5 + 18944 * q^6 - 322104 * q^7 - 393216 * q^8	\( 6 q + 192 q^{2} + 296 q^{3} + 14460 q^{5} + 18944 q^{6} - 322104 q^{7} - 393216 q^{8} - 18240 q^{10} + 1652712 q^{11} + 606208 q^{12} - 4646814 q^{13} - 41776360 q^{15} - 25165824 q^{16} + 51200226 q^{17} + 36525632 q^{18} - 30781440 q^{20} + 117123272 q^{21} + 52886784 q^{22} + 105826896 q^{23} - 161517150 q^{25} - 297396096 q^{26} + 627050120 q^{27} + 659668992 q^{28} - 699452160 q^{30} - 2667117168 q^{31} - 805306368 q^{32} + 4381479992 q^{33} - 7758629520 q^{35} + 2337640448 q^{36} + 1747956246 q^{37} - 2125152000 q^{38} - 1932656640 q^{40} + 22722098232 q^{41} + 3747944704 q^{42} - 15890524824 q^{43} - 8103444470 q^{45} + 6772921344 q^{46} - 18495531264 q^{47} - 1241513984 q^{48} + 8149569600 q^{50} + 114152506432 q^{51} - 9516675072 q^{52} - 88020413514 q^{53} + 37466287320 q^{55} + 42218815488 q^{56} - 174270786400 q^{57} - 107861859840 q^{58} + 40793047040 q^{60} + 291794891352 q^{61} - 85347749376 q^{62} - 297541783984 q^{63} + 26961608790 q^{65} + 280414719488 q^{66} - 3887251464 q^{67} - 104858062848 q^{68} - 110954853120 q^{70} + 929135015472 q^{71} + 74804494336 q^{72} + 12678070086 q^{73} - 928285655600 q^{75} - 136009728000 q^{76} - 436526954808 q^{77} - 80105703936 q^{78} - 60649635840 q^{80} + 833935849906 q^{81} + 727107143424 q^{82} + 68676615456 q^{83} + 142549278930 q^{85} - 1016993588736 q^{86} - 943420476880 q^{87} - 108312133632 q^{88} + 717302271680 q^{90} - 1619146872048 q^{91} + 216733483008 q^{92} + 2320495891112 q^{93} - 1510780128600 q^{95} - 79456894976 q^{96} + 675735777846 q^{97} - 1327663144512 q^{98}+O(q^{100}) \) 6 * q + 192 * q^2 + 296 * q^3 + 14460 * q^5 + 18944 * q^6 - 322104 * q^7 - 393216 * q^8 - 18240 * q^10 + 1652712 * q^11 + 606208 * q^12 - 4646814 * q^13 - 41776360 * q^15 - 25165824 * q^16 + 51200226 * q^17 + 36525632 * q^18 - 30781440 * q^20 + 117123272 * q^21 + 52886784 * q^22 + 105826896 * q^23 - 161517150 * q^25 - 297396096 * q^26 + 627050120 * q^27 + 659668992 * q^28 - 699452160 * q^30 - 2667117168 * q^31 - 805306368 * q^32 + 4381479992 * q^33 - 7758629520 * q^35 + 2337640448 * q^36 + 1747956246 * q^37 - 2125152000 * q^38 - 1932656640 * q^40 + 22722098232 * q^41 + 3747944704 * q^42 - 15890524824 * q^43 - 8103444470 * q^45 + 6772921344 * q^46 - 18495531264 * q^47 - 1241513984 * q^48 + 8149569600 * q^50 + 114152506432 * q^51 - 9516675072 * q^52 - 88020413514 * q^53 + 37466287320 * q^55 + 42218815488 * q^56 - 174270786400 * q^57 - 107861859840 * q^58 + 40793047040 * q^60 + 291794891352 * q^61 - 85347749376 * q^62 - 297541783984 * q^63 + 26961608790 * q^65 + 280414719488 * q^66 - 3887251464 * q^67 - 104858062848 * q^68 - 110954853120 * q^70 + 929135015472 * q^71 + 74804494336 * q^72 + 12678070086 * q^73 - 928285655600 * q^75 - 136009728000 * q^76 - 436526954808 * q^77 - 80105703936 * q^78 - 60649635840 * q^80 + 833935849906 * q^81 + 727107143424 * q^82 + 68676615456 * q^83 + 142549278930 * q^85 - 1016993588736 * q^86 - 943420476880 * q^87 - 108312133632 * q^88 + 717302271680 * q^90 - 1619146872048 * q^91 + 216733483008 * q^92 + 2320495891112 * q^93 - 1510780128600 * q^95 - 79456894976 * q^96 + 675735777846 * q^97 - 1327663144512 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/10\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	32.0000	−	32.0000i	0.500000	−	0.500000i
$2$	32.0000	−	32.0000i	0.500000	−	0.500000i
$3$	−748.698	−	748.698i	−1.02702	−	1.02702i	−0.999625	−	0.0273952i	$-0.991279\pi$
$3$	−748.698	−	748.698i	−1.02702	−	1.02702i	−0.0273952	−	0.999625i	$-0.508721\pi$
$4$		−	2048.00i		−	0.500000i
$5$	11268.2	−	10824.4i	0.721165	−	0.692763i
$5$	11268.2	−	10824.4i	0.721165	−	0.692763i
$6$	−47916.6			−1.02702
$7$	−121018.	+	121018.i	−1.02864	+	1.02864i	−0.0290619	+	0.999578i	$0.509252\pi$
$7$	−121018.	+	121018.i	−1.02864	+	1.02864i	−0.999578	+	0.0290619i	$0.990748\pi$
$8$	−65536.0	−	65536.0i	−0.250000	−	0.250000i
$9$			589655.i			1.10954i
$10$	14201.0	−	706964.i	0.0142010	−	0.706964i
$11$	−855152.			−0.482711			−0.241355	−	0.970437i	$-0.577592\pi$
$11$	−855152.			−0.482711			−0.241355	+	0.970437i	$0.577592\pi$
$12$	−1.53333e6	+	1.53333e6i	−0.513510	+	0.513510i
$13$	563543.	+	563543.i	0.116753	+	0.116753i	0.763069	−	0.646317i	$-0.223691\pi$
$13$	563543.	+	563543.i	0.116753	+	0.116753i	−0.646317	+	0.763069i	$0.723691\pi$
$14$			7.74518e6i			1.02864i
$15$	−1.65407e7	−	332259.i	−1.45213	−	0.0291695i
$16$	−4.19430e6			−0.250000
$17$	−1.33894e7	+	1.33894e7i	−0.554710	+	0.554710i	−0.927797	−	0.373086i	$-0.878300\pi$
$17$	−1.33894e7	+	1.33894e7i	−0.554710	+	0.554710i	0.373086	+	0.927797i	$0.378300\pi$
$18$	1.88690e7	+	1.88690e7i	0.554770	+	0.554770i
$19$		−	9.07626e7i		−	1.92924i	−0.263650	−	0.964618i	$-0.584926\pi$
$19$		−	9.07626e7i		−	1.92924i	0.263650	−	0.964618i	$-0.415074\pi$
$20$	−2.21684e7	−	2.30773e7i	−0.346382	−	0.360583i
$21$	1.81212e8			2.11287
$22$	−2.73649e7	+	2.73649e7i	−0.241355	+	0.241355i
$23$	6.22062e7	+	6.22062e7i	0.420210	+	0.420210i	0.885276	−	0.465066i	$-0.153969\pi$
$23$	6.22062e7	+	6.22062e7i	0.420210	+	0.420210i	−0.465066	+	0.885276i	$0.653969\pi$
$24$			9.81333e7i			0.513510i
$25$	9.80431e6	−	2.43944e8i	0.0401585	−	0.999193i
$26$	3.60667e7			0.116753
$27$	4.35847e7	−	4.35847e7i	0.112500	−	0.112500i
$28$	2.47846e8	+	2.47846e8i	0.514320	+	0.514320i
$29$		−	9.61877e8i		−	1.61708i	−0.588441	−	0.808540i	$-0.700258\pi$
$29$		−	9.61877e8i		−	1.61708i	0.588441	−	0.808540i	$-0.299742\pi$
$30$	−5.39935e8	+	5.18670e8i	−0.740651	+	0.711482i
$31$	−1.55856e9			−1.75612			−0.878060	−	0.478551i	$-0.841162\pi$
$31$	−1.55856e9			−1.75612			−0.878060	+	0.478551i	$0.841162\pi$
$32$	−1.34218e8	+	1.34218e8i	−0.125000	+	0.125000i
$33$	6.40250e8	+	6.40250e8i	0.495754	+	0.495754i
$34$			8.56919e8i			0.554710i
$35$	−5.37058e7	+	2.67361e9i	−0.0292155	+	1.45442i
$36$	1.20761e9			0.554770
$37$	7.41446e8	−	7.41446e8i	0.288981	−	0.288981i	−0.547696	−	0.836677i	$-0.684495\pi$
$37$	7.41446e8	−	7.41446e8i	0.288981	−	0.288981i	0.836677	+	0.547696i	$0.184495\pi$
$38$	−2.90440e9	−	2.90440e9i	−0.964618	−	0.964618i
$39$		−	8.43846e8i		−	0.239815i
$40$	−1.44786e9	−	2.90837e7i	−0.353482	−	0.00710051i
$41$	9.28740e8			0.195520			0.0977600	−	0.995210i	$-0.468832\pi$
$41$	9.28740e8			0.195520			0.0977600	+	0.995210i	$0.468832\pi$
$42$	5.79880e9	−	5.79880e9i	1.05643	−	1.05643i
$43$	−2.23346e9	−	2.23346e9i	−0.353319	−	0.353319i	0.508024	−	0.861343i	$-0.330376\pi$
$43$	−2.23346e9	−	2.23346e9i	−0.353319	−	0.353319i	−0.861343	+	0.508024i	$0.830376\pi$
$44$			1.75135e9i			0.241355i
$45$	6.38268e9	+	6.64435e9i	0.768648	+	0.800162i
$46$	3.98120e9			0.420210
$47$	−7.22768e9	+	7.22768e9i	−0.670520	+	0.670520i	−0.957836	−	0.287316i	$-0.907237\pi$
$47$	−7.22768e9	+	7.22768e9i	−0.670520	+	0.670520i	0.287316	+	0.957836i	$0.407237\pi$
$48$	3.14027e9	+	3.14027e9i	0.256755	+	0.256755i
$49$		−	1.54496e10i		−	1.11620i
$50$	−7.49246e9	−	8.11994e9i	−0.479517	−	0.519676i
$51$	2.00492e10			1.13940
$52$	1.15414e9	−	1.15414e9i	0.0583763	−	0.0583763i
$53$	−9.05683e8	−	9.05683e8i	−0.0408621	−	0.0408621i	0.686380	−	0.727243i	$-0.259198\pi$
$53$	−9.05683e8	−	9.05683e8i	−0.0408621	−	0.0408621i	−0.727243	+	0.686380i	$0.759198\pi$
$54$		−	2.78942e9i		−	0.112500i
$55$	−9.63603e9	+	9.25652e9i	−0.348114	+	0.334404i
$56$	1.58621e10			0.514320
$57$	−6.79538e10	+	6.79538e10i	−1.98136	+	1.98136i
$58$	−3.07801e10	−	3.07801e10i	−0.808540	−	0.808540i
$59$		−	1.35545e10i		−	0.321346i	−0.987008	−	0.160673i	$-0.948634\pi$
$59$		−	1.35545e10i		−	0.321346i	0.987008	−	0.160673i	$-0.0513665\pi$
$60$	−6.80466e8	+	3.38753e10i	−0.0145847	+	0.726066i
$61$	6.94051e10			1.34714			0.673570	−	0.739124i	$-0.264760\pi$
$61$	6.94051e10			1.34714			0.673570	+	0.739124i	$0.264760\pi$
$62$	−4.98740e10	+	4.98740e10i	−0.878060	+	0.878060i
$63$	−7.13591e10	−	7.13591e10i	−1.14132	−	1.14132i
$64$			8.58993e9i			0.125000i
$65$	1.24501e10	+	2.50090e8i	0.165080	+	0.00331602i
$66$	4.09760e10			0.495754
$67$	1.13753e11	−	1.13753e11i	1.25752	−	1.25752i	0.305243	−	0.952275i	$-0.401262\pi$
$67$	1.13753e11	−	1.13753e11i	1.25752	−	1.25752i	0.952275	−	0.305243i	$-0.0987376\pi$
$68$	2.74214e10	+	2.74214e10i	0.277355	+	0.277355i
$69$		−	9.31472e10i		−	0.863128i
$70$	8.38371e10	+	8.72743e10i	0.712604	+	0.741819i
$71$	1.09453e11			0.854434			0.427217	−	0.904149i	$-0.359494\pi$
$71$	1.09453e11			0.854434			0.427217	+	0.904149i	$0.359494\pi$
$72$	3.86436e10	−	3.86436e10i	0.277385	−	0.277385i
$73$	−8.58305e9	−	8.58305e9i	−0.0567158	−	0.0567158i	0.678180	−	0.734896i	$-0.262769\pi$
$73$	−8.58305e9	−	8.58305e9i	−0.0567158	−	0.0567158i	−0.734896	+	0.678180i	$0.762769\pi$
$74$		−	4.74526e10i		−	0.288981i
$75$	−1.89980e11	+	1.75300e11i	−1.06744	+	0.984948i
$76$	−1.85882e11			−0.964618
$77$	1.03489e11	−	1.03489e11i	0.496535	−	0.496535i
$78$	−2.70031e10	−	2.70031e10i	−0.119907	−	0.119907i
$79$			1.74264e11i			0.716880i	0.933553	+	0.358440i	$0.116691\pi$
$79$			1.74264e11i			0.716880i	−0.933553	+	0.358440i	$0.883309\pi$
$80$	−4.72623e10	+	4.54009e10i	−0.180291	+	0.173191i
$81$	2.48103e11			0.878461
$82$	2.97197e10	−	2.97197e10i	0.0977600	−	0.0977600i
$83$	−2.87263e11	−	2.87263e11i	−0.878639	−	0.878639i	0.114754	−	0.993394i	$-0.463392\pi$
$83$	−2.87263e11	−	2.87263e11i	−0.878639	−	0.878639i	−0.993394	+	0.114754i	$0.963392\pi$
$84$		−	3.71123e11i		−	1.05643i
$85$	−5.94196e9	+	2.95806e11i	−0.0157549	+	0.784321i
$86$	−1.42941e11			−0.353319
$87$	−7.20155e11	+	7.20155e11i	−1.66077	+	1.66077i
$88$	5.60432e10	+	5.60432e10i	0.120678	+	0.120678i
$89$		−	2.51008e11i		−	0.505066i	−0.967588	−	0.252533i	$-0.918736\pi$
$89$		−	2.51008e11i		−	0.505066i	0.967588	−	0.252533i	$-0.0812636\pi$
$90$	4.16865e11	+	8.37371e9i	0.784405	+	0.0157566i
$91$	−1.36398e11			−0.240193
$92$	1.27398e11	−	1.27398e11i	0.210105	−	0.210105i
$93$	1.16689e12	+	1.16689e12i	1.80357	+	1.80357i
$94$			4.62572e11i			0.670520i
$95$	−9.82453e11	−	1.02273e12i	−1.33650	−	1.39130i
$96$	2.00977e11			0.256755
$97$	2.97289e11	−	2.97289e11i	0.356901	−	0.356901i	−0.505768	−	0.862669i	$-0.668791\pi$
$97$	2.97289e11	−	2.97289e11i	0.356901	−	0.356901i	0.862669	+	0.505768i	$0.168791\pi$
$98$	−4.94388e11	−	4.94388e11i	−0.558099	−	0.558099i
$99$		−	5.04244e11i		−	0.535587i
$100$	−4.99597e11	−	2.00792e10i	−0.499597	−	0.0200792i
$101$	5.97476e10			0.0562850			0.0281425	−	0.999604i	$-0.491041\pi$
$101$	5.97476e10			0.0562850			0.0281425	+	0.999604i	$0.491041\pi$
$102$	6.41573e11	−	6.41573e11i	0.569699	−	0.569699i
$103$	4.83171e11	+	4.83171e11i	0.404648	+	0.404648i	0.879867	−	0.475219i	$-0.157631\pi$
$103$	4.83171e11	+	4.83171e11i	0.404648	+	0.404648i	−0.475219	+	0.879867i	$0.657631\pi$
$104$		−	7.38647e10i		−	0.0583763i
$105$	2.04194e12	−	1.96152e12i	1.52373	−	1.46372i
$106$	−5.79637e10			−0.0408621
$107$	−4.37350e11	+	4.37350e11i	−0.291425	+	0.291425i	−0.837643	−	0.546218i	$-0.816067\pi$
$107$	−4.37350e11	+	4.37350e11i	−0.291425	+	0.291425i	0.546218	+	0.837643i	$0.316067\pi$
$108$	−8.92614e10	−	8.92614e10i	−0.0562498	−	0.0562498i
$109$			1.92444e12i			1.14748i	0.819037	+	0.573741i	$0.194508\pi$
$109$			1.92444e12i			1.14748i	−0.819037	+	0.573741i	$0.805492\pi$
$110$	−1.21440e10	+	6.04562e11i	−0.00685499	+	0.341259i
$111$	−1.11024e12			−0.593579
$112$	5.07588e11	−	5.07588e11i	0.257160	−	0.257160i
$113$	−9.05644e11	−	9.05644e11i	−0.434997	−	0.434997i	0.455327	−	0.890324i	$-0.349522\pi$
$113$	−9.05644e11	−	9.05644e11i	−0.434997	−	0.434997i	−0.890324	+	0.455327i	$0.849522\pi$
$114$			4.34904e12i			1.98136i
$115$	1.37430e12	+	2.76060e10i	0.594147	+	0.0119348i
$116$	−1.96992e12			−0.808540
$117$	−3.32296e11	+	3.32296e11i	−0.129542	+	0.129542i
$118$	−4.33746e11	−	4.33746e11i	−0.160673	−	0.160673i
$119$		−	3.24072e12i		−	1.14119i
$120$	1.06224e12	+	1.10579e12i	0.355741	+	0.370326i
$121$	−2.40714e12			−0.766990
$122$	2.22096e12	−	2.22096e12i	0.673570	−	0.673570i
$123$	−6.95345e11	−	6.95345e11i	−0.200803	−	0.200803i
$124$			3.19194e12i			0.878060i
$125$	−2.53007e12	−	2.85493e12i	−0.663243	−	0.748404i
$126$	−4.56698e12			−1.14132
$127$	−1.67708e12	+	1.67708e12i	−0.399697	+	0.399697i	−0.878126	−	0.478429i	$-0.841206\pi$
$127$	−1.67708e12	+	1.67708e12i	−0.399697	+	0.399697i	0.478429	+	0.878126i	$0.341206\pi$
$128$	2.74878e11	+	2.74878e11i	0.0625000	+	0.0625000i
$129$			3.34437e12i			0.725731i
$130$	4.06408e11	−	3.90402e11i	0.0841980	−	0.0808820i
$131$	−7.97530e11			−0.157805			−0.0789023	−	0.996882i	$-0.525142\pi$
$131$	−7.97530e11			−0.157805			−0.0789023	+	0.996882i	$0.525142\pi$
$132$	1.31123e12	−	1.31123e12i	0.247877	−	0.247877i
$133$	1.09840e13	+	1.09840e13i	1.98449	+	1.98449i
$134$		−	7.28019e12i		−	1.25752i
$135$	1.93421e10	−	9.62900e11i	0.00319522	−	0.159066i
$136$	1.75497e12			0.277355
$137$	2.43459e12	−	2.43459e12i	0.368216	−	0.368216i	−0.498610	−	0.866826i	$-0.666156\pi$
$137$	2.43459e12	−	2.43459e12i	0.368216	−	0.368216i	0.866826	+	0.498610i	$0.166156\pi$
$138$	−2.98071e12	−	2.98071e12i	−0.431564	−	0.431564i
$139$		−	5.33949e12i		−	0.740305i	−0.928971	−	0.370153i	$-0.879305\pi$
$139$		−	5.33949e12i		−	0.740305i	0.928971	−	0.370153i	$-0.120695\pi$
$140$	5.47556e12	+	1.09989e11i	0.727211	+	0.0146077i
$141$	1.08227e13			1.37728
$142$	3.50250e12	−	3.50250e12i	0.427217	−	0.427217i
$143$	−4.81915e11	−	4.81915e11i	−0.0563578	−	0.0563578i
$144$		−	2.47319e12i		−	0.277385i
$145$	−1.04118e13	−	1.08386e13i	−1.12025	−	1.16618i
$146$	−5.49315e11			−0.0567158
$147$	−1.15671e13	+	1.15671e13i	−1.14636	+	1.14636i
$148$	−1.51848e12	−	1.51848e12i	−0.144491	−	0.144491i
$149$			5.11787e12i			0.467705i	0.972272	+	0.233852i	$0.0751333\pi$
$149$			5.11787e12i			0.467705i	−0.972272	+	0.233852i	$0.924867\pi$
$150$	−4.69790e11	+	1.16890e13i	−0.0412435	+	1.02619i
$151$	1.53338e13			1.29356			0.646781	−	0.762676i	$-0.276115\pi$
$151$	1.53338e13			1.29356			0.646781	+	0.762676i	$0.276115\pi$
$152$	−5.94822e12	+	5.94822e12i	−0.482309	+	0.482309i
$153$	−7.89510e12	−	7.89510e12i	−0.615473	−	0.615473i
$154$		−	6.62330e12i		−	0.496535i
$155$	−1.75622e13	+	1.68705e13i	−1.26645	+	1.21657i
$156$	−1.72820e12			−0.119907
$157$	−1.80237e12	+	1.80237e12i	−0.120350	+	0.120350i	−0.764717	−	0.644367i	$-0.777121\pi$
$157$	−1.80237e12	+	1.80237e12i	−0.120350	+	0.120350i	0.644367	+	0.764717i	$0.277121\pi$
$158$	5.57646e12	+	5.57646e12i	0.358440	+	0.358440i
$159$			1.35617e12i			0.0839324i
$160$	−5.95634e10	+	2.96522e12i	−0.00355026	+	0.176741i
$161$	−1.50562e13			−0.864490
$162$	7.93931e12	−	7.93931e12i	0.439231	−	0.439231i
$163$	−3.11771e12	−	3.11771e12i	−0.166230	−	0.166230i	0.619090	−	0.785320i	$-0.287502\pi$
$163$	−3.11771e12	−	3.11771e12i	−0.166230	−	0.166230i	−0.785320	+	0.619090i	$0.787502\pi$
$164$		−	1.90206e12i		−	0.0977600i
$165$	1.41448e13	+	2.84131e11i	0.700960	+	0.0140804i
$166$	−1.83848e13			−0.878639
$167$	9.05825e12	−	9.05825e12i	0.417586	−	0.417586i	−0.466785	−	0.884371i	$-0.654588\pi$
$167$	9.05825e12	−	9.05825e12i	0.417586	−	0.417586i	0.884371	+	0.466785i	$0.154588\pi$
$168$	−1.18759e13	−	1.18759e13i	−0.528217	−	0.528217i
$169$		−	2.26629e13i		−	0.972738i
$170$	9.27565e12	+	9.65594e12i	0.384283	+	0.400038i
$171$	5.35186e13			2.14057
$172$	−4.57412e12	+	4.57412e12i	−0.176659	+	0.176659i
$173$	−1.08460e13	−	1.08460e13i	−0.404568	−	0.404568i	0.475272	−	0.879839i	$-0.342350\pi$
$173$	−1.08460e13	−	1.08460e13i	−0.404568	−	0.404568i	−0.879839	+	0.475272i	$0.842350\pi$
$174$			4.60899e13i			1.66077i
$175$	2.83352e13	+	3.07082e13i	0.986501	+	1.06912i
$176$	3.58677e12			0.120678
$177$	−1.01483e13	+	1.01483e13i	−0.330029	+	0.330029i
$178$	−8.03226e12	−	8.03226e12i	−0.252533	−	0.252533i
$179$		−	3.24354e13i		−	0.986055i	−0.870014	−	0.493028i	$-0.835890\pi$
$179$		−	3.24354e13i		−	0.986055i	0.870014	−	0.493028i	$-0.164110\pi$
$180$	1.36076e13	−	1.30717e13i	0.400081	−	0.384324i
$181$	−3.61575e13			−1.02832			−0.514158	−	0.857695i	$-0.671896\pi$
$181$	−3.61575e13			−1.02832			−0.514158	+	0.857695i	$0.671896\pi$
$182$	−4.36474e12	+	4.36474e12i	−0.120096	+	0.120096i
$183$	−5.19634e13	−	5.19634e13i	−1.38354	−	1.38354i
$184$		−	8.15349e12i		−	0.210105i
$185$	3.29041e11	−	1.63805e13i	0.00820765	−	0.408598i
$186$	7.46811e13			1.80357
$187$	1.14499e13	−	1.14499e13i	0.267765	−	0.267765i
$188$	1.48023e13	+	1.48023e13i	0.335260	+	0.335260i
$189$			1.05491e13i			0.231443i
$190$	−6.41659e13	−	1.28892e12i	−1.36390	−	0.0273971i
$191$	7.85798e13			1.61849			0.809246	−	0.587470i	$-0.199876\pi$
$191$	7.85798e13			1.61849			0.809246	+	0.587470i	$0.199876\pi$
$192$	6.43126e12	−	6.43126e12i	0.128377	−	0.128377i
$193$	4.88933e13	+	4.88933e13i	0.946031	+	0.946031i	0.998616	−	0.0525853i	$-0.0167461\pi$
$193$	4.88933e13	+	4.88933e13i	0.946031	+	0.946031i	−0.0525853	+	0.998616i	$0.516746\pi$
$194$		−	1.90265e13i		−	0.356901i
$195$	−9.13415e12	−	9.50864e12i	−0.166135	−	0.172946i
$196$	−3.16408e13			−0.558099
$197$	−5.71062e13	+	5.71062e13i	−0.976981	+	0.976981i	−0.999741	−	0.0227601i	$-0.992755\pi$
$197$	−5.71062e13	+	5.71062e13i	−0.976981	+	0.976981i	0.0227601	+	0.999741i	$0.492755\pi$
$198$	−1.61358e13	−	1.61358e13i	−0.267793	−	0.267793i
$199$			1.89668e13i			0.305404i	0.988272	+	0.152702i	$0.0487975\pi$
$199$			1.89668e13i			0.305404i	−0.988272	+	0.152702i	$0.951202\pi$
$200$	−1.66296e13	+	1.53446e13i	−0.259838	+	0.239759i
$201$	−1.70333e14			−2.58299
$202$	1.91192e12	−	1.91192e12i	0.0281425	−	0.0281425i
$203$	1.16405e14	+	1.16405e14i	1.66339	+	1.66339i
$204$		−	4.10607e13i		−	0.569699i
$205$	1.04652e13	−	1.00531e13i	0.141002	−	0.135449i
$206$	3.09229e13			0.404648
$207$	−3.66802e13	+	3.66802e13i	−0.466240	+	0.466240i
$208$	−2.36367e12	−	2.36367e12i	−0.0291882	−	0.0291882i
$209$			7.76158e13i			0.931264i
$210$	2.57340e12	−	1.28111e14i	0.0300049	−	1.49372i
$211$	−4.49925e13			−0.509854			−0.254927	−	0.966960i	$-0.582051\pi$
$211$	−4.49925e13			−0.509854			−0.254927	+	0.966960i	$0.582051\pi$
$212$	−1.85484e12	+	1.85484e12i	−0.0204311	+	0.0204311i
$213$	−8.19474e13	−	8.19474e13i	−0.877521	−	0.877521i
$214$			2.79904e13i			0.291425i
$215$	−4.93429e13	−	9.91168e11i	−0.499567	−	0.0100350i
$216$	−5.71273e12			−0.0562498
$217$	1.88615e14	−	1.88615e14i	1.80641	−	1.80641i
$218$	6.15821e13	+	6.15821e13i	0.573741	+	0.573741i
$219$			1.28522e13i			0.116497i
$220$	1.89574e13	+	1.97346e13i	0.167202	+	0.174057i
$221$	−1.50910e13			−0.129528
$222$	−3.55276e13	+	3.55276e13i	−0.296789	+	0.296789i
$223$	−2.61788e13	−	2.61788e13i	−0.212873	−	0.212873i	0.592614	−	0.805487i	$-0.298096\pi$
$223$	−2.61788e13	−	2.61788e13i	−0.212873	−	0.212873i	−0.805487	+	0.592614i	$0.798096\pi$
$224$		−	3.24856e13i		−	0.257160i
$225$	1.43843e14	+	5.78116e12i	1.10864	+	0.0445574i
$226$	−5.79612e13			−0.434997
$227$	1.30078e14	−	1.30078e14i	0.950711	−	0.950711i	−0.0481299	−	0.998841i	$-0.515326\pi$
$227$	1.30078e14	−	1.30078e14i	0.950711	−	0.950711i	0.998841	+	0.0481299i	$0.0153262\pi$
$228$	1.39169e14	+	1.39169e14i	0.990682	+	0.990682i
$229$		−	1.72785e13i		−	0.119810i	−0.998204	−	0.0599051i	$-0.980920\pi$
$229$		−	1.72785e13i		−	0.119810i	0.998204	−	0.0599051i	$-0.0190798\pi$
$230$	4.48609e13	−	4.30942e13i	0.303041	−	0.291106i
$231$	−1.54964e14			−1.01990
$232$	−6.30376e13	+	6.30376e13i	−0.404270	+	0.404270i
$233$	9.01182e13	+	9.01182e13i	0.563218	+	0.563218i	0.930220	−	0.367002i	$-0.119616\pi$
$233$	9.01182e13	+	9.01182e13i	0.563218	+	0.563218i	−0.367002	+	0.930220i	$0.619616\pi$
$234$			2.12669e13i			0.129542i
$235$	−3.20752e12	+	1.59679e14i	−0.0190442	+	0.948068i
$236$	−2.77597e13			−0.160673
$237$	1.30471e14	−	1.30471e14i	0.736250	−	0.736250i
$238$	−1.03703e14	−	1.03703e14i	−0.570597	−	0.570597i
$239$			5.48888e13i			0.294508i	0.989099	+	0.147254i	$0.0470434\pi$
$239$			5.48888e13i			0.294508i	−0.989099	+	0.147254i	$0.952957\pi$
$240$	6.93767e13	+	1.39359e12i	0.363033	+	0.00729237i
$241$	9.29129e13			0.474213			0.237107	−	0.971484i	$-0.423801\pi$
$241$	9.29129e13			0.474213			0.237107	+	0.971484i	$0.423801\pi$
$242$	−7.70286e13	+	7.70286e13i	−0.383495	+	0.383495i
$243$	−2.08917e14	−	2.08917e14i	−1.01470	−	1.01470i
$244$		−	1.42142e14i		−	0.673570i
$245$	−1.67233e14	−	1.74090e14i	−0.773261	−	0.804964i
$246$	−4.45021e13			−0.200803
$247$	5.11486e13	−	5.11486e13i	0.225244	−	0.225244i
$248$	1.02142e14	+	1.02142e14i	0.439030	+	0.439030i
$249$			4.30146e14i			1.80476i
$250$	−1.72320e14	−	1.03955e13i	−0.705824	−	0.0425802i
$251$	−4.19707e14			−1.67843			−0.839216	−	0.543798i	$-0.816986\pi$
$251$	−4.19707e14			−1.67843			−0.839216	+	0.543798i	$0.816986\pi$
$252$	−1.46143e14	+	1.46143e14i	−0.570658	+	0.570658i
$253$	−5.31957e13	−	5.31957e13i	−0.202840	−	0.202840i
$254$			1.07333e14i			0.399697i
$255$	2.25918e14	−	2.17021e14i	0.821694	−	0.789332i
$256$	1.75922e13			0.0625000
$257$	−2.85003e14	+	2.85003e14i	−0.989123	+	0.989123i	−0.999941	−	0.0108183i	$-0.996556\pi$
$257$	−2.85003e14	+	2.85003e14i	−0.989123	+	0.989123i	0.0108183	+	0.999941i	$0.496556\pi$
$258$	1.07020e14	+	1.07020e14i	0.362865	+	0.362865i
$259$			1.79457e14i			0.594515i
$260$	5.12185e11	−	2.54979e13i	0.00165801	−	0.0825400i
$261$	5.67176e14			1.79421
$262$	−2.55210e13	+	2.55210e13i	−0.0789023	+	0.0789023i
$263$	−6.06586e13	−	6.06586e13i	−0.183298	−	0.183298i	0.609493	−	0.792791i	$-0.291373\pi$
$263$	−6.06586e13	−	6.06586e13i	−0.183298	−	0.183298i	−0.792791	+	0.609493i	$0.791373\pi$
$264$		−	8.39188e13i		−	0.247877i
$265$	−2.00089e13	−	4.01926e11i	−0.0577761	−	0.00116057i
$266$	7.02973e14			1.98449
$267$	−1.87929e14	+	1.87929e14i	−0.518713	+	0.518713i
$268$	−2.32966e14	−	2.32966e14i	−0.628759	−	0.628759i
$269$		−	5.47959e14i		−	1.44622i	−0.690733	−	0.723110i	$-0.742712\pi$
$269$		−	5.47959e14i		−	1.44622i	0.690733	−	0.723110i	$-0.257288\pi$
$270$	−3.01938e13	−	3.14317e13i	−0.0779356	−	0.0811308i
$271$	2.37596e14			0.599822			0.299911	−	0.953967i	$-0.403043\pi$
$271$	2.37596e14			0.599822			0.299911	+	0.953967i	$0.403043\pi$
$272$	5.61590e13	−	5.61590e13i	0.138678	−	0.138678i
$273$	1.02121e14	+	1.02121e14i	0.246683	+	0.246683i
$274$		−	1.55814e14i		−	0.368216i
$275$	−8.38418e12	+	2.08609e14i	−0.0193849	+	0.482321i
$276$	−1.90766e14			−0.431564
$277$	1.41768e13	−	1.41768e13i	0.0313834	−	0.0313834i	−0.691241	−	0.722624i	$-0.742936\pi$
$277$	1.41768e13	−	1.41768e13i	0.0313834	−	0.0313834i	0.722624	+	0.691241i	$0.242936\pi$
$278$	−1.70864e14	−	1.70864e14i	−0.370153	−	0.370153i
$279$		−	9.19014e14i		−	1.94848i
$280$	1.78738e14	−	1.71698e14i	0.370910	−	0.356302i
$281$	2.37323e14			0.482061			0.241030	−	0.970518i	$-0.422515\pi$
$281$	2.37323e14			0.482061			0.241030	+	0.970518i	$0.422515\pi$
$282$	3.46326e14	−	3.46326e14i	0.688638	−	0.688638i
$283$	4.23007e14	+	4.23007e14i	0.823435	+	0.823435i	0.986599	−	0.163164i	$-0.0521700\pi$
$283$	4.23007e14	+	4.23007e14i	0.823435	+	0.823435i	−0.163164	+	0.986599i	$0.552170\pi$
$284$		−	2.24160e14i		−	0.427217i
$285$	−3.01567e13	+	1.50128e15i	−0.0562748	+	2.80151i
$286$	−3.08425e13			−0.0563578
$287$	−1.12395e14	+	1.12395e14i	−0.201120	+	0.201120i
$288$	−7.91422e13	−	7.91422e13i	−0.138692	−	0.138692i
$289$			2.24072e14i			0.384593i
$290$	−6.80013e14	−	1.36596e13i	−1.14322	−	0.0229642i
$291$	−4.45159e14			−0.733089
$292$	−1.75781e13	+	1.75781e13i	−0.0283579	+	0.0283579i
$293$	−7.05611e14	−	7.05611e14i	−1.11522	−	1.11522i	−0.992433	−	0.122784i	$-0.960818\pi$
$293$	−7.05611e14	−	7.05611e14i	−1.11522	−	1.11522i	−0.122784	−	0.992433i	$-0.539182\pi$
$294$			7.40294e14i			1.14636i
$295$	−1.46720e14	−	1.52735e14i	−0.222617	−	0.231744i
$296$	−9.71828e13			−0.144491
$297$	−3.72715e13	+	3.72715e13i	−0.0543048	+	0.0543048i
$298$	1.63772e14	+	1.63772e14i	0.233852	+	0.233852i
$299$			7.01117e13i			0.0981213i
$300$	3.59014e14	+	3.89080e14i	0.492474	+	0.533718i
$301$	5.40579e14			0.726875
$302$	4.90681e14	−	4.90681e14i	0.646781	−	0.646781i
$303$	−4.47329e13	−	4.47329e13i	−0.0578058	−	0.0578058i
$304$			3.80686e14i			0.482309i
$305$	7.82071e14	−	7.51270e14i	0.971510	−	0.933248i
$306$	−5.05287e14			−0.615473
$307$	−3.72483e13	+	3.72483e13i	−0.0444914	+	0.0444914i	−0.729002	−	0.684511i	$-0.760016\pi$
$307$	−3.72483e13	+	3.72483e13i	−0.0444914	+	0.0444914i	0.684511	+	0.729002i	$0.260016\pi$
$308$	−2.11946e14	−	2.11946e14i	−0.248268	−	0.248268i
$309$		−	7.23498e14i		−	0.831163i
$310$	−2.21332e13	+	1.10185e15i	−0.0249387	+	1.24151i
$311$	−7.13323e14			−0.788358			−0.394179	−	0.919034i	$-0.628971\pi$
$311$	−7.13323e14			−0.788358			−0.394179	+	0.919034i	$0.628971\pi$
$312$	−5.53023e13	+	5.53023e13i	−0.0599537	+	0.0599537i
$313$	−3.18840e14	−	3.18840e14i	−0.339084	−	0.339084i	0.516939	−	0.856023i	$-0.327072\pi$
$313$	−3.18840e14	−	3.18840e14i	−0.339084	−	0.339084i	−0.856023	+	0.516939i	$0.827072\pi$
$314$			1.15352e14i			0.120350i
$315$	−1.57651e15	−	3.16679e13i	−1.61374	−	0.0324157i
$316$	3.56894e14			0.358440
$317$	−5.96896e14	+	5.96896e14i	−0.588224	+	0.588224i	−0.937150	−	0.348926i	$-0.886546\pi$
$317$	−5.96896e14	+	5.96896e14i	−0.588224	+	0.588224i	0.348926	+	0.937150i	$0.386546\pi$
$318$	4.33973e13	+	4.33973e13i	0.0419662	+	0.0419662i
$319$			8.22551e14i			0.780582i
$320$	9.29811e13	+	9.67932e13i	0.0865954	+	0.0901456i
$321$	6.54886e14			0.598598
$322$	−4.81798e14	+	4.81798e14i	−0.432245	+	0.432245i
$323$	1.21525e15	+	1.21525e15i	1.07017	+	1.07017i
$324$		−	5.08116e14i		−	0.439231i
$325$	1.42998e14	−	1.31948e14i	0.121347	−	0.111970i
$326$	−1.99534e14			−0.166230
$327$	1.44082e15	−	1.44082e15i	1.17849	−	1.17849i
$328$	−6.08659e13	−	6.08659e13i	−0.0488800	−	0.0488800i
$329$		−	1.74937e15i		−	1.37945i
$330$	4.61726e14	−	4.43542e14i	0.357520	−	0.343440i
$331$	1.16106e15			0.882850			0.441425	−	0.897298i	$-0.354473\pi$
$331$	1.16106e15			0.882850			0.441425	+	0.897298i	$0.354473\pi$
$332$	−5.88314e14	+	5.88314e14i	−0.439320	+	0.439320i
$333$	4.37197e14	+	4.37197e14i	0.320636	+	0.320636i
$334$		−	5.79728e14i		−	0.417586i
$335$	5.04815e13	−	2.51310e15i	0.0357161	−	1.77804i
$336$	−7.60060e14			−0.528217
$337$	−4.47217e14	+	4.47217e14i	−0.305308	+	0.305308i	−0.843086	−	0.537778i	$-0.819264\pi$
$337$	−4.47217e14	+	4.47217e14i	−0.305308	+	0.305308i	0.537778	+	0.843086i	$0.319264\pi$
$338$	−7.25214e14	−	7.25214e14i	−0.486369	−	0.486369i
$339$			1.35611e15i			0.893502i
$340$	6.05811e14	+	1.21691e13i	0.392160	+	0.00787746i
$341$	1.33281e15			0.847698
$342$	1.71260e15	−	1.71260e15i	1.07028	−	1.07028i
$343$	1.94638e14	+	1.94638e14i	0.119526	+	0.119526i
$344$			2.92744e14i			0.176659i
$345$	−1.00827e15	−	1.04960e15i	−0.597944	−	0.622458i
$346$	−6.94141e14			−0.404568
$347$	−1.67027e15	+	1.67027e15i	−0.956776	+	0.956776i	−0.999104	−	0.0423279i	$-0.986523\pi$
$347$	−1.67027e15	+	1.67027e15i	−0.956776	+	0.956776i	0.0423279	+	0.999104i	$0.486523\pi$
$348$	1.47488e15	+	1.47488e15i	0.830387	+	0.830387i
$349$			2.71867e15i			1.50454i	0.658853	+	0.752272i	$0.271042\pi$
$349$			2.71867e15i			1.50454i	−0.658853	+	0.752272i	$0.728958\pi$
$350$	1.88939e15	+	7.59362e13i	1.02781	+	0.0413086i
$351$	4.91237e13			0.0262693
$352$	1.14777e14	−	1.14777e14i	0.0603389	−	0.0603389i
$353$	−4.34561e14	−	4.34561e14i	−0.224596	−	0.224596i	0.585835	−	0.810431i	$-0.300767\pi$
$353$	−4.34561e14	−	4.34561e14i	−0.224596	−	0.224596i	−0.810431	+	0.585835i	$0.800767\pi$
$354$			6.49489e14i			0.330029i
$355$	1.23334e15	−	1.18477e15i	0.616188	−	0.591920i
$356$	−5.14065e14			−0.252533
$357$	−2.42632e15	+	2.42632e15i	−1.17203	+	1.17203i
$358$	−1.03793e15	−	1.03793e15i	−0.493028	−	0.493028i
$359$			4.03664e14i			0.188562i	0.995546	+	0.0942808i	$0.0300552\pi$
$359$			4.03664e14i			0.188562i	−0.995546	+	0.0942808i	$0.969945\pi$
$360$	1.71494e13	−	8.53739e14i	0.00787830	−	0.392202i
$361$	−6.02454e15			−2.72195
$362$	−1.15704e15	+	1.15704e15i	−0.514158	+	0.514158i
$363$	1.80222e15	+	1.80222e15i	0.787714	+	0.787714i
$364$			2.79343e14i			0.120096i
$365$	−1.89622e14	−	3.80900e12i	−0.0801921	−	0.00161085i
$366$	−3.32566e15			−1.38354
$367$	3.14067e15	−	3.14067e15i	1.28536	−	1.28536i	0.347789	−	0.937573i	$-0.386933\pi$
$367$	3.14067e15	−	3.14067e15i	1.28536	−	1.28536i	0.937573	−	0.347789i	$-0.113067\pi$
$368$	−2.60912e14	−	2.60912e14i	−0.105053	−	0.105053i
$369$			5.47636e14i			0.216937i
$370$	−5.13647e14	−	5.34705e14i	−0.200195	−	0.208403i
$371$	2.19209e14			0.0840648
$372$	2.38979e15	−	2.38979e15i	0.901785	−	0.901785i
$373$	−2.88499e15	−	2.88499e15i	−1.07125	−	1.07125i	−0.997259	−	0.0739924i	$-0.976426\pi$
$373$	−2.88499e15	−	2.88499e15i	−1.07125	−	1.07125i	−0.0739924	−	0.997259i	$-0.523574\pi$
$374$		−	7.32796e14i		−	0.267765i
$375$	−2.43223e14	+	4.03174e15i	−0.0874614	+	1.44979i
$376$	9.47347e14			0.335260
$377$	5.42059e14	−	5.42059e14i	0.188798	−	0.188798i
$378$	3.37571e14	+	3.37571e14i	0.115722	+	0.115722i
$379$			9.94190e14i			0.335455i	0.985833	+	0.167727i	$0.0536428\pi$
$379$			9.94190e14i			0.335455i	−0.985833	+	0.167727i	$0.946357\pi$
$380$	−2.09456e15	+	2.01206e15i	−0.695649	+	0.668252i
$381$	2.51125e15			0.820993
$382$	2.51455e15	−	2.51455e15i	0.809246	−	0.809246i
$383$	3.15021e15	+	3.15021e15i	0.998037	+	0.998037i	0.999998	−	0.00196149i	$-0.000624361\pi$
$383$	3.15021e15	+	3.15021e15i	0.998037	+	0.998037i	−0.00196149	+	0.999998i	$0.500624\pi$
$384$		−	4.11601e14i		−	0.128377i
$385$	4.59266e13	−	2.28635e15i	0.0141026	−	0.702066i
$386$	3.12917e15			0.946031
$387$	1.31697e15	−	1.31697e15i	0.392021	−	0.392021i
$388$	−6.08847e14	−	6.08847e14i	−0.178451	−	0.178451i
$389$			2.91921e15i			0.842497i	0.906945	+	0.421248i	$0.138408\pi$
$389$			2.91921e15i			0.842497i	−0.906945	+	0.421248i	$0.861592\pi$
$390$	−5.96569e14	−	1.19835e13i	−0.169540	−	0.00340561i
$391$	−1.66580e15			−0.466190
$392$	−1.01251e15	+	1.01251e15i	−0.279050	+	0.279050i
$393$	5.97109e14	+	5.97109e14i	0.162068	+	0.162068i
$394$			3.65480e15i			0.976981i
$395$	1.88631e15	+	1.96365e15i	0.496628	+	0.516989i
$396$	−1.03269e15			−0.267793
$397$	2.06257e15	−	2.06257e15i	0.526825	−	0.526825i	−0.392799	−	0.919624i	$-0.628493\pi$
$397$	2.06257e15	−	2.06257e15i	0.526825	−	0.526825i	0.919624	+	0.392799i	$0.128493\pi$
$398$	6.06937e14	+	6.06937e14i	0.152702	+	0.152702i
$399$		−	1.64473e16i		−	4.07622i
$400$	−4.11223e13	+	1.02317e15i	−0.0100396	+	0.249798i
$401$	1.15805e14			0.0278523			0.0139262	−	0.999903i	$-0.495567\pi$
$401$	1.15805e14			0.0278523			0.0139262	+	0.999903i	$0.495567\pi$
$402$	−5.45066e15	+	5.45066e15i	−1.29150	+	1.29150i
$403$	−8.78317e14	−	8.78317e14i	−0.205032	−	0.205032i
$404$		−	1.22363e14i		−	0.0281425i
$405$	2.79568e15	−	2.68558e15i	0.633516	−	0.608566i
$406$	7.44991e15			1.66339
$407$	−6.34049e14	+	6.34049e14i	−0.139494	+	0.139494i
$408$	−1.31394e15	−	1.31394e15i	−0.284849	−	0.284849i
$409$		−	1.65778e15i		−	0.354149i	−0.984197	−	0.177074i	$-0.943337\pi$
$409$		−	1.65778e15i		−	0.354149i	0.984197	−	0.177074i	$-0.0566633\pi$
$410$	1.31891e13	−	6.56586e14i	0.00277658	−	0.138226i
$411$	−3.64554e15			−0.756330
$412$	9.89534e14	−	9.89534e14i	0.202324	−	0.202324i
$413$	1.64035e15	+	1.64035e15i	0.330549	+	0.330549i
$414$			2.34753e15i			0.466240i
$415$	−6.34639e15	−	1.27482e14i	−1.24233	−	0.0249552i
$416$	−1.51275e14			−0.0291882
$417$	−3.99766e15	+	3.99766e15i	−0.760308	+	0.760308i
$418$	2.48371e15	+	2.48371e15i	0.465632	+	0.465632i
$419$			5.93151e15i			1.09618i	0.836420	+	0.548089i	$0.184645\pi$
$419$			5.93151e15i			1.09618i	−0.836420	+	0.548089i	$0.815355\pi$
$420$	−4.01719e15	−	4.18189e15i	−0.731858	−	0.761863i
$421$	4.46283e15			0.801526			0.400763	−	0.916182i	$-0.368745\pi$
$421$	4.46283e15			0.801526			0.400763	+	0.916182i	$0.368745\pi$
$422$	−1.43976e15	+	1.43976e15i	−0.254927	+	0.254927i
$423$	−4.26184e15	−	4.26184e15i	−0.743969	−	0.743969i
$424$			1.18710e14i			0.0204311i
$425$	3.13498e15	+	3.39752e15i	0.531987	+	0.576539i
$426$	−5.24463e15			−0.877521
$427$	−8.39930e15	+	8.39930e15i	−1.38572	+	1.38572i
$428$	8.95693e14	+	8.95693e14i	0.145712	+	0.145712i
$429$			7.21617e14i			0.115761i
$430$	−1.61069e15	+	1.54726e15i	−0.254801	+	0.244766i
$431$	6.40433e15			0.999103			0.499552	−	0.866284i	$-0.333498\pi$
$431$	6.40433e15			0.999103			0.499552	+	0.866284i	$0.333498\pi$
$432$	−1.82807e14	+	1.82807e14i	−0.0281249	+	0.0281249i
$433$	−2.32112e15	−	2.32112e15i	−0.352185	−	0.352185i	0.508737	−	0.860922i	$-0.330113\pi$
$433$	−2.32112e15	−	2.32112e15i	−0.352185	−	0.352185i	−0.860922	+	0.508737i	$0.830113\pi$
$434$		−	1.20713e16i		−	1.80641i
$435$	−3.19592e14	+	1.59101e16i	−0.0471694	+	2.34821i
$436$	3.94125e15			0.573741
$437$	5.64600e15	−	5.64600e15i	0.810685	−	0.810685i
$438$	4.11271e14	+	4.11271e14i	0.0582483	+	0.0582483i
$439$		−	2.58953e15i		−	0.361771i	−0.983504	−	0.180885i	$-0.942104\pi$
$439$		−	2.58953e15i		−	0.361771i	0.983504	−	0.180885i	$-0.0578963\pi$
$440$	1.23814e15	+	2.48710e13i	0.170630	+	0.00342749i
$441$	9.10995e15			1.23847
$442$	−4.82911e14	+	4.82911e14i	−0.0647639	+	0.0647639i
$443$	−3.47542e15	−	3.47542e15i	−0.459817	−	0.459817i	0.438778	−	0.898595i	$-0.355411\pi$
$443$	−3.47542e15	−	3.47542e15i	−0.459817	−	0.459817i	−0.898595	+	0.438778i	$0.855411\pi$
$444$			2.27377e15i			0.296789i
$445$	−2.71702e15	−	2.82841e15i	−0.349891	−	0.364236i
$446$	−1.67544e15			−0.212873
$447$	3.83174e15	−	3.83174e15i	0.480342	−	0.480342i
$448$	−1.03954e15	−	1.03954e15i	−0.128580	−	0.128580i
$449$			9.29319e15i			1.13419i	0.823652	+	0.567096i	$0.191933\pi$
$449$			9.29319e15i			1.13419i	−0.823652	+	0.567096i	$0.808067\pi$
$450$	4.78796e15	−	4.41797e15i	0.576601	−	0.532044i
$451$	−7.94214e14			−0.0943796
$452$	−1.85476e15	+	1.85476e15i	−0.217499	+	0.217499i
$453$	−1.14804e16	−	1.14804e16i	−1.32851	−	1.32851i
$454$		−	8.32499e15i		−	0.950711i
$455$	−1.53696e15	+	1.47643e15i	−0.173219	+	0.166397i
$456$	8.90684e15			0.990682
$457$	4.17939e15	−	4.17939e15i	0.458792	−	0.458792i	−0.439467	−	0.898259i	$-0.644833\pi$
$457$	4.17939e15	−	4.17939e15i	0.458792	−	0.458792i	0.898259	+	0.439467i	$0.144833\pi$
$458$	−5.52913e14	−	5.52913e14i	−0.0599051	−	0.0599051i
$459$			1.16714e15i			0.124809i
$460$	5.65371e13	−	2.81456e15i	0.00596742	−	0.297074i
$461$	−1.61867e16			−1.68637			−0.843183	−	0.537627i	$-0.819321\pi$
$461$	−1.61867e16			−1.68637			−0.843183	+	0.537627i	$0.819321\pi$
$462$	−4.95885e15	+	4.95885e15i	−0.509952	+	0.509952i
$463$	−1.00417e15	−	1.00417e15i	−0.101934	−	0.101934i	0.654300	−	0.756235i	$-0.272963\pi$
$463$	−1.00417e15	−	1.00417e15i	−0.101934	−	0.101934i	−0.756235	+	0.654300i	$0.772963\pi$
$464$			4.03440e15i			0.404270i
$465$	2.57797e16	+	5.17846e14i	2.55012	+	0.0512251i
$466$	5.76756e15			0.563218
$467$	8.83224e15	−	8.83224e15i	0.851471	−	0.851471i	−0.138843	−	0.990314i	$-0.544338\pi$
$467$	8.83224e15	−	8.83224e15i	0.851471	−	0.851471i	0.990314	+	0.138843i	$0.0443385\pi$
$468$	6.80542e14	+	6.80542e14i	0.0647709	+	0.0647709i
$469$			2.75324e16i			2.58706i
$470$	5.00707e15	+	5.21235e15i	0.464512	+	0.483556i
$471$	2.69886e15			0.247204
$472$	−8.88311e14	+	8.88311e14i	−0.0803365	+	0.0803365i
$473$	1.90994e15	+	1.90994e15i	0.170551	+	0.170551i
$474$		−	8.35017e15i		−	0.736250i
$475$	−2.21410e16	−	8.89865e14i	−1.92768	−	0.0774752i
$476$	−6.63699e15			−0.570597
$477$	5.34040e14	−	5.34040e14i	0.0453382	−	0.0453382i
$478$	1.75644e15	+	1.75644e15i	0.147254	+	0.147254i
$479$		−	1.93454e16i		−	1.60164i	−0.598903	−	0.800821i	$-0.704397\pi$
$479$		−	1.93454e16i		−	1.60164i	0.598903	−	0.800821i	$-0.295603\pi$
$480$	2.26465e15	−	2.17546e15i	0.185163	−	0.177870i
$481$	8.35674e14			0.0674786
$482$	2.97321e15	−	2.97321e15i	0.237107	−	0.237107i
$483$	1.12725e16	+	1.12725e16i	0.887848	+	0.887848i
$484$			4.92983e15i			0.383495i
$485$	1.31931e14	−	6.56789e15i	0.0101367	−	0.504633i
$486$	−1.33707e16			−1.01470
$487$	1.18030e16	−	1.18030e16i	0.884744	−	0.884744i	−0.109268	−	0.994012i	$-0.534851\pi$
$487$	1.18030e16	−	1.18030e16i	0.884744	−	0.884744i	0.994012	+	0.109268i	$0.0348508\pi$
$488$	−4.54853e15	−	4.54853e15i	−0.336785	−	0.336785i
$489$			4.66845e15i			0.341444i
$490$	−1.09223e16	−	2.19401e14i	−0.789112	−	0.0158512i
$491$	−1.58301e16			−1.12978			−0.564890	−	0.825166i	$-0.691081\pi$
$491$	−1.58301e16			−1.12978			−0.564890	+	0.825166i	$0.691081\pi$
$492$	−1.42407e15	+	1.42407e15i	−0.100401	+	0.100401i
$493$	1.28789e16	+	1.28789e16i	0.897011	+	0.897011i
$494$		−	3.27351e15i		−	0.225244i
$495$	−5.45816e15	−	5.68193e15i	−0.371035	−	0.386247i
$496$	6.53708e15			0.439030
$497$	−1.32459e16	+	1.32459e16i	−0.878904	+	0.878904i
$498$	1.37647e16	+	1.37647e16i	0.902380	+	0.902380i
$499$		−	3.75944e15i		−	0.243512i	−0.992560	−	0.121756i	$-0.961147\pi$
$499$		−	3.75944e15i		−	0.243512i	0.992560	−	0.121756i	$-0.0388525\pi$
$500$	−5.84690e15	+	5.18159e15i	−0.374202	+	0.331622i
$501$	−1.35638e16			−0.857738
$502$	−1.34306e16	+	1.34306e16i	−0.839216	+	0.839216i
$503$	−3.05571e15	−	3.05571e15i	−0.188671	−	0.188671i	0.606451	−	0.795121i	$-0.292593\pi$
$503$	−3.05571e15	−	3.05571e15i	−0.188671	−	0.188671i	−0.795121	+	0.606451i	$0.792593\pi$
$504$			9.35318e15i			0.570658i
$505$	6.73249e14	−	6.46734e14i	0.0405908	−	0.0389922i
$506$	−3.40453e15			−0.202840
$507$	−1.69677e16	+	1.69677e16i	−0.999021	+	0.999021i
$508$	3.43465e15	+	3.43465e15i	0.199848	+	0.199848i
$509$		−	3.31917e16i		−	1.90863i	−0.298796	−	0.954317i	$-0.596585\pi$
$509$		−	3.31917e16i		−	1.90863i	0.298796	−	0.954317i	$-0.403415\pi$
$510$	2.84719e14	−	1.41740e16i	0.0161806	−	0.805513i
$511$	2.07741e15			0.116680
$512$	5.62950e14	−	5.62950e14i	0.0312500	−	0.0312500i
$513$	−3.95586e15	−	3.95586e15i	−0.217038	−	0.217038i
$514$			1.82402e16i			0.989123i
$515$	1.06745e16	+	2.14423e14i	0.572143	+	0.0114928i
$516$	6.84926e15			0.362865
$517$	6.18077e15	−	6.18077e15i	0.323667	−	0.323667i
$518$	5.74263e15	+	5.74263e15i	0.297257	+	0.297257i
$519$			1.62407e16i			0.830998i
$520$	−7.99543e14	−	8.32323e14i	−0.0404410	−	0.0420990i
$521$	5.90021e15			0.295013			0.147506	−	0.989061i	$-0.452875\pi$
$521$	5.90021e15			0.295013			0.147506	+	0.989061i	$0.452875\pi$
$522$	1.81496e16	−	1.81496e16i	0.897107	−	0.897107i
$523$	1.06234e16	+	1.06234e16i	0.519104	+	0.519104i	0.917300	−	0.398196i	$-0.130364\pi$
$523$	1.06234e16	+	1.06234e16i	0.519104	+	0.519104i	−0.398196	+	0.917300i	$0.630364\pi$
$524$			1.63334e15i			0.0789023i
$525$	1.77666e15	−	4.42056e16i	0.0848495	−	2.11116i
$526$	−3.88215e15			−0.183298
$527$	2.08682e16	−	2.08682e16i	0.974138	−	0.974138i
$528$	−2.68540e15	−	2.68540e15i	−0.123938	−	0.123938i
$529$		−	1.41754e16i		−	0.646847i
$530$	−6.53147e14	+	6.27424e14i	−0.0294683	+	0.0283078i
$531$	7.99251e15			0.356546
$532$	2.24951e16	−	2.24951e16i	0.992245	−	0.992245i
$533$	5.23385e14	+	5.23385e14i	0.0228275	+	0.0228275i
$534$			1.20275e16i			0.518713i
$535$	−1.94088e14	+	9.66222e15i	−0.00827707	+	0.412054i
$536$	−1.49098e16			−0.628759
$537$	−2.42843e16	+	2.42843e16i	−1.01270	+	1.01270i
$538$	−1.75347e16	−	1.75347e16i	−0.723110	−	0.723110i
$539$			1.32118e16i			0.538801i
$540$	−1.97202e15	−	3.96126e13i	−0.0795332	−	0.00159761i
$541$	3.33454e16			1.33000			0.665001	−	0.746843i	$-0.268431\pi$
$541$	3.33454e16			1.33000			0.665001	+	0.746843i	$0.268431\pi$
$542$	7.60306e15	−	7.60306e15i	0.299911	−	0.299911i
$543$	2.70710e16	+	2.70710e16i	1.05610	+	1.05610i
$544$		−	3.59418e15i		−	0.138678i
$545$	2.08310e16	+	2.16850e16i	0.794933	+	0.827523i
$546$	6.53574e15			0.246683
$547$	2.55655e16	−	2.55655e16i	0.954399	−	0.954399i	−0.0446060	−	0.999005i	$-0.514203\pi$
$547$	2.55655e16	−	2.55655e16i	0.954399	−	0.954399i	0.999005	+	0.0446060i	$0.0142032\pi$
$548$	−4.98604e15	−	4.98604e15i	−0.184108	−	0.184108i
$549$			4.09251e16i			1.49470i
$550$	6.40719e15	+	6.94378e15i	0.231468	+	0.250853i
$551$	−8.73025e16			−3.11973
$552$	−6.10450e15	+	6.10450e15i	−0.215782	+	0.215782i
$553$	−2.10892e16	−	2.10892e16i	−0.737411	−	0.737411i
$554$		−	9.07317e14i		−	0.0313834i
$555$	−1.25104e16	+	1.20177e16i	−0.428068	+	0.411209i
$556$	−1.09353e16			−0.370153
$557$	−1.86183e16	+	1.86183e16i	−0.623462	+	0.623462i	−0.946415	−	0.322953i	$-0.895324\pi$
$557$	−1.86183e16	+	1.86183e16i	−0.623462	+	0.623462i	0.322953	+	0.946415i	$0.395324\pi$
$558$	−2.94085e16	−	2.94085e16i	−0.974242	−	0.974242i
$559$		−	2.51730e15i		−	0.0825018i
$560$	2.25258e14	−	1.12140e16i	0.00730387	−	0.363606i
$561$	−1.71451e16			−0.549999
$562$	7.59434e15	−	7.59434e15i	0.241030	−	0.241030i
$563$	2.80927e16	+	2.80927e16i	0.882152	+	0.882152i	0.993753	−	0.111601i	$-0.0355980\pi$
$563$	2.80927e16	+	2.80927e16i	0.882152	+	0.882152i	−0.111601	+	0.993753i	$0.535598\pi$
$564$		−	2.21649e16i		−	0.688638i
$565$	−2.00081e16	−	4.01908e14i	−0.615055	−	0.0123548i
$566$	2.70725e16			0.823435
$567$	−3.00251e16	+	3.00251e16i	−0.903620	+	0.903620i
$568$	−7.17313e15	−	7.17313e15i	−0.213608	−	0.213608i
$569$		−	2.18381e16i		−	0.643490i	−0.946826	−	0.321745i	$-0.895731\pi$
$569$		−	2.18381e16i		−	0.643490i	0.946826	−	0.321745i	$-0.104269\pi$
$570$	4.70759e16	+	4.90059e16i	1.37262	+	1.42889i
$571$	4.28319e16			1.23581			0.617903	−	0.786254i	$-0.287982\pi$
$571$	4.28319e16			1.23581			0.617903	+	0.786254i	$0.287982\pi$
$572$	−9.86961e14	+	9.86961e14i	−0.0281789	+	0.0281789i
$573$	−5.88325e16	−	5.88325e16i	−1.66222	−	1.66222i
$574$			7.19326e15i			0.201120i
$575$	1.57847e16	−	1.45649e16i	0.436746	−	0.402996i
$576$	−5.06510e15			−0.138692
$577$	−2.40074e16	+	2.40074e16i	−0.650565	+	0.650565i	−0.953129	−	0.302564i	$-0.902157\pi$
$577$	−2.40074e16	+	2.40074e16i	−0.650565	+	0.650565i	0.302564	+	0.953129i	$0.402157\pi$
$578$	7.17032e15	+	7.17032e15i	0.192296	+	0.192296i
$579$		−	7.32126e16i		−	1.94319i
$580$	−2.21975e16	+	2.13233e16i	−0.583091	+	0.560127i
$581$	6.95281e16			1.80761
$582$	−1.42451e16	+	1.42451e16i	−0.366545	+	0.366545i
$583$	7.74496e14	+	7.74496e14i	0.0197246	+	0.0197246i
$584$			1.12500e15i			0.0283579i
$585$	−1.47467e14	+	7.34129e15i	−0.00367925	+	0.183163i
$586$	−4.51591e16			−1.11522
$587$	−1.53437e16	+	1.53437e16i	−0.375060	+	0.375060i	−0.869316	−	0.494256i	$-0.835441\pi$
$587$	−1.53437e16	+	1.53437e16i	−0.375060	+	0.375060i	0.494256	+	0.869316i	$0.335441\pi$
$588$	2.36894e16	+	2.36894e16i	0.573179	+	0.573179i
$589$			1.41459e17i			3.38797i
$590$	−9.58258e15	−	1.92489e14i	−0.227180	−	0.00456344i
$591$	8.55106e16			2.00676
$592$	−3.10985e15	+	3.10985e15i	−0.0722453	+	0.0722453i
$593$	−5.21562e16	−	5.21562e16i	−1.19944	−	1.19944i	−0.974335	−	0.225103i	$-0.927728\pi$
$593$	−5.21562e16	−	5.21562e16i	−1.19944	−	1.19944i	−0.225103	−	0.974335i	$-0.572272\pi$
$594$			2.38538e15i			0.0543048i
$595$	−3.50789e16	−	3.65171e16i	−0.790577	−	0.822989i
$596$	1.04814e16			0.233852
$597$	1.42004e16	−	1.42004e16i	0.313656	−	0.313656i
$598$	2.24357e15	+	2.24357e15i	0.0490607	+	0.0490607i
$599$		−	4.12581e16i		−	0.893199i	−0.894734	−	0.446600i	$-0.852635\pi$
$599$		−	4.12581e16i		−	0.893199i	0.894734	−	0.446600i	$-0.147365\pi$
$600$	2.39390e16	+	9.62129e14i	0.513096	+	0.0206218i
$601$	3.84045e16			0.814959			0.407479	−	0.913214i	$-0.366408\pi$
$601$	3.84045e16			0.814959			0.407479	+	0.913214i	$0.366408\pi$
$602$	1.72985e16	−	1.72985e16i	0.363438	−	0.363438i
$603$	6.70750e16	+	6.70750e16i	1.39527	+	1.39527i
$604$		−	3.14036e16i		−	0.646781i
$605$	−2.71242e16	+	2.60559e16i	−0.553127	+	0.531343i
$606$	−2.86291e15			−0.0578058
$607$	3.27763e16	−	3.27763e16i	0.655281	−	0.655281i	−0.298979	−	0.954260i	$-0.596646\pi$
$607$	3.27763e16	−	3.27763e16i	0.655281	−	0.655281i	0.954260	+	0.298979i	$0.0966460\pi$
$608$	1.21820e16	+	1.21820e16i	0.241155	+	0.241155i
$609$		−	1.74304e17i		−	3.41667i
$610$	9.85624e14	−	4.90669e16i	0.0191308	−	0.952379i
$611$	−8.14622e15			−0.156570
$612$	−1.61692e16	+	1.61692e16i	−0.307737	+	0.307737i
$613$	−1.03368e16	−	1.03368e16i	−0.194816	−	0.194816i	0.602958	−	0.797773i	$-0.293989\pi$
$613$	−1.03368e16	−	1.03368e16i	−0.194816	−	0.194816i	−0.797773	+	0.602958i	$0.793989\pi$
$614$			2.38389e15i			0.0444914i
$615$	−1.53620e16	−	3.08582e14i	−0.283921	−	0.00570321i
$616$	−1.35645e16			−0.248268
$617$	−4.21087e16	+	4.21087e16i	−0.763240	+	0.763240i	−0.976907	−	0.213667i	$-0.931459\pi$
$617$	−4.21087e16	+	4.21087e16i	−0.763240	+	0.763240i	0.213667	+	0.976907i	$0.431459\pi$
$618$	−2.31519e16	−	2.31519e16i	−0.415582	−	0.415582i
$619$		−	5.48244e15i		−	0.0974608i	−0.998812	−	0.0487304i	$-0.984482\pi$
$619$		−	5.48244e15i		−	0.0974608i	0.998812	−	0.0487304i	$-0.0155175\pi$
$620$	3.45509e16	+	3.59674e16i	0.608287	+	0.633226i
$621$	5.42247e15			0.0945470
$622$	−2.28263e16	+	2.28263e16i	−0.394179	+	0.394179i
$623$	3.03766e16	+	3.03766e16i	0.519531	+	0.519531i
$624$			3.53935e15i			0.0599537i
$625$	−5.94124e16	−	4.78340e15i	−0.996775	−	0.0802521i
$626$	−2.04058e16			−0.339084
$627$	5.81108e16	−	5.81108e16i	0.956426	−	0.956426i
$628$	3.69125e15	+	3.69125e15i	0.0601750	+	0.0601750i
$629$			1.98550e16i			0.320601i
$630$	−5.14617e16	+	4.94350e16i	−0.823078	+	0.790662i
$631$	2.86138e16			0.453314			0.226657	−	0.973975i	$-0.427220\pi$
$631$	2.86138e16			0.453314			0.226657	+	0.973975i	$0.427220\pi$
$632$	1.14206e16	−	1.14206e16i	0.179220	−	0.179220i
$633$	3.36858e16	+	3.36858e16i	0.523630	+	0.523630i
$634$			3.82013e16i			0.588224i
$635$	−7.44257e14	+	3.70510e16i	−0.0113522	+	0.565143i
$636$	2.77743e15			0.0419662
$637$	8.70653e15	−	8.70653e15i	0.130319	−	0.130319i
$638$	2.63216e16	+	2.63216e16i	0.390291	+	0.390291i
$639$			6.45396e16i			0.948028i
$640$	6.07278e15	+	1.21986e14i	0.0883705	+	0.00177513i
$641$	3.53007e16			0.508903			0.254451	−	0.967086i	$-0.418105\pi$
$641$	3.53007e16			0.508903			0.254451	+	0.967086i	$0.418105\pi$
$642$	2.09564e16	−	2.09564e16i	0.299299	−	0.299299i
$643$	−8.33444e16	−	8.33444e16i	−1.17926	−	1.17926i	−0.979932	−	0.199330i	$-0.936123\pi$
$643$	−8.33444e16	−	8.33444e16i	−1.17926	−	1.17926i	−0.199330	−	0.979932i	$-0.563877\pi$
$644$			3.08351e16i			0.432245i
$645$	3.62008e16	+	3.76850e16i	0.502760	+	0.523372i
$646$	7.77762e16			1.07017
$647$	−7.64041e16	+	7.64041e16i	−1.04158	+	1.04158i	−0.0424790	+	0.999097i	$0.513526\pi$
$647$	−7.64041e16	+	7.64041e16i	−1.04158	+	1.04158i	−0.999097	+	0.0424790i	$0.986474\pi$
$648$	−1.62597e16	−	1.62597e16i	−0.219615	−	0.219615i
$649$			1.15912e16i			0.155117i
$650$	3.53610e14	−	8.79826e15i	0.00468861	−	0.116659i
$651$	−2.82431e17			−3.71045
$652$	−6.38507e15	+	6.38507e15i	−0.0831152	+	0.0831152i
$653$	−3.17563e16	−	3.17563e16i	−0.409591	−	0.409591i	0.472005	−	0.881596i	$-0.343530\pi$
$653$	−3.17563e16	−	3.17563e16i	−0.409591	−	0.409591i	−0.881596	+	0.472005i	$0.843530\pi$
$654$		−	9.22127e16i		−	1.17849i
$655$	−8.98674e15	+	8.63281e15i	−0.113803	+	0.109321i
$656$	−3.89542e15			−0.0488800
$657$	5.06104e15	−	5.06104e15i	0.0629285	−	0.0629285i
$658$	−5.59797e16	−	5.59797e16i	−0.689724	−	0.689724i
$659$			4.91804e16i			0.600453i	0.953868	+	0.300227i	$0.0970623\pi$
$659$			4.91804e16i			0.600453i	−0.953868	+	0.300227i	$0.902938\pi$
$660$	5.81901e14	−	2.89686e16i	0.00704021	−	0.350480i
$661$	7.37994e15			0.0884798			0.0442399	−	0.999021i	$-0.485913\pi$
$661$	7.37994e15			0.0884798			0.0442399	+	0.999021i	$0.485913\pi$
$662$	3.71539e16	−	3.71539e16i	0.441425	−	0.441425i
$663$	1.12986e16	+	1.12986e16i	0.133028	+	0.133028i
$664$			3.76521e16i			0.439320i
$665$	2.42664e17	+	4.87448e15i	2.80593	+	0.0563636i
$666$	2.79806e16			0.320636
$667$	5.98347e16	−	5.98347e16i	0.679514	−	0.679514i
$668$	−1.85513e16	−	1.85513e16i	−0.208793	−	0.208793i
$669$			3.92000e16i			0.437249i
$670$	−7.88039e16	−	8.20347e16i	−0.871162	−	0.906878i
$671$	−5.93519e16			−0.650279
$672$	−2.43219e16	+	2.43219e16i	−0.264108	+	0.264108i
$673$	1.01038e17	+	1.01038e17i	1.08741	+	1.08741i	0.995794	+	0.0916177i	$0.0292038\pi$
$673$	1.01038e17	+	1.01038e17i	1.08741	+	1.08741i	0.0916177	+	0.995794i	$0.470796\pi$
$674$			2.86219e16i			0.305308i
$675$	−1.02049e16	−	1.10595e16i	−0.107891	−	0.116927i
$676$	−4.64137e16			−0.486369
$677$	5.28834e16	−	5.28834e16i	0.549272	−	0.549272i	−0.376958	−	0.926230i	$-0.623030\pi$
$677$	5.28834e16	−	5.28834e16i	0.549272	−	0.549272i	0.926230	+	0.376958i	$0.123030\pi$
$678$	4.33954e16	+	4.33954e16i	0.446751	+	0.446751i
$679$			7.19548e16i			0.734245i
$680$	1.97754e16	−	1.89965e16i	0.200019	−	0.192141i
$681$	−1.94778e17			−1.95280
$682$	4.26498e16	−	4.26498e16i	0.423849	−	0.423849i
$683$	2.14631e16	+	2.14631e16i	0.211430	+	0.211430i	0.804875	−	0.593444i	$-0.202232\pi$
$683$	2.14631e16	+	2.14631e16i	0.211430	+	0.211430i	−0.593444	+	0.804875i	$0.702232\pi$
$684$		−	1.09606e17i		−	1.07028i
$685$	1.08043e15	−	5.37865e16i	0.0104581	−	0.520631i
$686$	1.24569e16			0.119526
$687$	−1.29364e16	+	1.29364e16i	−0.123048	+	0.123048i
$688$	9.36779e15	+	9.36779e15i	0.0883297	+	0.0883297i
$689$		−	1.02078e15i		−	0.00954153i
$690$	−6.58518e16	−	1.32279e15i	−0.610201	−	0.0122573i
$691$	1.37238e17			1.26068			0.630341	−	0.776318i	$-0.282915\pi$
$691$	1.37238e17			1.26068			0.630341	+	0.776318i	$0.282915\pi$
$692$	−2.22125e16	+	2.22125e16i	−0.202284	+	0.202284i
$693$	6.10229e16	+	6.10229e16i	0.550926	+	0.550926i
$694$			1.06897e17i			0.956776i
$695$	−5.77969e16	−	6.01665e16i	−0.512856	−	0.533882i
$696$	9.43921e16			0.830387
$697$	−1.24352e16	+	1.24352e16i	−0.108457	+	0.108457i
$698$	8.69976e16	+	8.69976e16i	0.752272	+	0.752272i
$699$		−	1.34943e17i		−	1.15687i
$700$	6.28904e16	−	5.80304e16i	0.534559	−	0.493251i
$701$	1.99406e17			1.68046			0.840232	−	0.542227i	$-0.182419\pi$
$701$	1.99406e17			1.68046			0.840232	+	0.542227i	$0.182419\pi$
$702$	1.57196e15	−	1.57196e15i	0.0131346	−	0.0131346i
$703$	−6.72956e16	−	6.72956e16i	−0.557513	−	0.557513i
$704$		−	7.34570e15i		−	0.0603389i
$705$	1.21952e17	−	1.17149e17i	0.993243	−	0.954126i
$706$	−2.78119e16			−0.224596
$707$	−7.23056e15	+	7.23056e15i	−0.0578970	+	0.0578970i
$708$	2.07836e16	+	2.07836e16i	0.165014	+	0.165014i
$709$			2.16689e16i			0.170592i	0.996356	+	0.0852962i	$0.0271837\pi$
$709$			2.16689e16i			0.170592i	−0.996356	+	0.0852962i	$0.972816\pi$
$710$	1.55435e15	−	7.73795e16i	0.0121338	−	0.604054i
$711$	−1.02756e17			−0.795407
$712$	−1.64501e16	+	1.64501e16i	−0.126266	+	0.126266i
$713$	−9.69522e16	−	9.69522e16i	−0.737939	−	0.737939i
$714$			1.55284e17i			1.17203i
$715$	−1.06468e16	−	2.13865e14i	−0.0796859	−	0.00160068i
$716$	−6.64277e16			−0.493028
$717$	4.10951e16	−	4.10951e16i	0.302465	−	0.302465i
$718$	1.29173e16	+	1.29173e16i	0.0942808	+	0.0942808i
$719$			7.26842e16i			0.526098i	0.964783	+	0.263049i	$0.0847281\pi$
$719$			7.26842e16i			0.526098i	−0.964783	+	0.263049i	$0.915272\pi$
$720$	−2.67709e16	−	2.78684e16i	−0.192162	−	0.200040i
$721$	−1.16945e17			−0.832474
$722$	−1.92785e17	+	1.92785e17i	−1.36098	+	1.36098i
$723$	−6.95637e16	−	6.95637e16i	−0.487027	−	0.487027i
$724$			7.40505e16i			0.514158i
$725$	−2.34644e17	−	9.43054e15i	−1.61578	−	0.0649395i
$726$	1.15342e17			0.787714
$727$	3.35546e16	−	3.35546e16i	0.227272	−	0.227272i	−0.584280	−	0.811552i	$-0.698623\pi$
$727$	3.35546e16	−	3.35546e16i	0.227272	−	0.227272i	0.811552	+	0.584280i	$0.198623\pi$
$728$	8.93899e15	+	8.93899e15i	0.0600482	+	0.0600482i
$729$			1.80979e17i			1.20577i
$730$	−6.18980e15	+	5.94602e15i	−0.0409015	+	0.0392906i
$731$	5.98091e16			0.391979
$732$	−1.06421e17	+	1.06421e17i	−0.691769	+	0.691769i
$733$	−4.31922e16	−	4.31922e16i	−0.278472	−	0.278472i	0.554027	−	0.832499i	$-0.313090\pi$
$733$	−4.31922e16	−	4.31922e16i	−0.278472	−	0.278472i	−0.832499	+	0.554027i	$0.813090\pi$
$734$		−	2.01003e17i		−	1.28536i
$735$	−5.13327e15	+	2.55548e17i	−0.0325589	+	1.62087i
$736$	−1.66983e16			−0.105053
$737$	−9.72761e16	+	9.72761e16i	−0.607017	+	0.607017i
$738$	1.75244e16	+	1.75244e16i	0.108469	+	0.108469i
$739$		−	1.04593e17i		−	0.642148i	−0.947054	−	0.321074i	$-0.895956\pi$
$739$		−	1.04593e17i		−	0.642148i	0.947054	−	0.321074i	$-0.104044\pi$
$740$	−3.35473e16	−	6.73875e14i	−0.204299	−	0.00410383i
$741$	−7.65897e16			−0.462659
$742$	7.01468e15	−	7.01468e15i	0.0420324	−	0.0420324i
$743$	7.60382e16	+	7.60382e16i	0.451959	+	0.451959i	0.896004	−	0.444045i	$-0.146457\pi$
$743$	7.60382e16	+	7.60382e16i	0.451959	+	0.451959i	−0.444045	+	0.896004i	$0.646457\pi$
$744$		−	1.52947e17i		−	0.901785i
$745$	5.53980e16	+	5.76693e16i	0.324009	+	0.337293i
$746$	−1.84639e17			−1.07125
$747$	1.69386e17	−	1.69386e17i	0.974885	−	0.974885i
$748$	−2.34495e16	−	2.34495e16i	−0.133882	−	0.133882i
$749$		−	1.05855e17i		−	0.599542i
$750$	1.21233e17	+	1.36799e17i	0.681164	+	0.768626i
$751$	−6.59827e16			−0.367782			−0.183891	−	0.982947i	$-0.558869\pi$
$751$	−6.59827e16			−0.367782			−0.183891	+	0.982947i	$0.558869\pi$
$752$	3.03151e16	−	3.03151e16i	0.167630	−	0.167630i
$753$	3.14233e17	+	3.14233e17i	1.72378	+	1.72378i
$754$		−	3.46918e16i		−	0.188798i
$755$	1.72784e17	−	1.65979e17i	0.932872	−	0.896132i
$756$	2.16045e16			0.115722
$757$	2.16222e17	−	2.16222e17i	1.14901	−	1.14901i	0.162262	−	0.986748i	$-0.448121\pi$
$757$	2.16222e17	−	2.16222e17i	1.14901	−	1.14901i	0.986748	−	0.162262i	$-0.0518790\pi$
$758$	3.18141e16	+	3.18141e16i	0.167727	+	0.167727i
$759$			7.96550e16i			0.416641i
$760$	−2.63971e15	+	1.31412e17i	−0.0136986	+	0.681951i
$761$	−2.00671e17			−1.03318			−0.516592	−	0.856232i	$-0.672799\pi$
$761$	−2.00671e17			−1.03318			−0.516592	+	0.856232i	$0.672799\pi$
$762$	8.03599e16	−	8.03599e16i	0.410496	−	0.410496i
$763$	−2.32893e17	−	2.32893e17i	−1.18034	−	1.18034i
$764$		−	1.60931e17i		−	0.809246i
$765$	−1.74424e17	−	3.50370e15i	−0.870235	−	0.0174807i
$766$	2.01613e17			0.998037
$767$	7.63857e15	−	7.63857e15i	0.0375180	−	0.0375180i
$768$	−1.31712e16	−	1.31712e16i	−0.0641887	−	0.0641887i
$769$			1.35328e17i			0.654379i	0.944959	+	0.327189i	$0.106102\pi$
$769$			1.35328e17i			0.654379i	−0.944959	+	0.327189i	$0.893898\pi$
$770$	−7.16934e16	−	7.46327e16i	−0.343981	−	0.358084i
$771$	4.26762e17			2.03170
$772$	1.00133e17	−	1.00133e17i	0.473016	−	0.473016i
$773$	−2.13648e17	−	2.13648e17i	−1.00143	−	1.00143i	−0.999999	−	0.00143473i	$-0.999543\pi$
$773$	−2.13648e17	−	2.13648e17i	−1.00143	−	1.00143i	−0.00143473	−	0.999999i	$-0.500457\pi$
$774$		−	8.42860e16i		−	0.392021i
$775$	−1.52806e16	+	3.80201e17i	−0.0705231	+	1.75470i
$776$	−3.89662e16			−0.178451
$777$	1.34359e17	−	1.34359e17i	0.610578	−	0.610578i
$778$	9.34148e16	+	9.34148e16i	0.421248	+	0.421248i
$779$		−	8.42949e16i		−	0.377204i
$780$	−1.94737e16	+	1.87067e16i	−0.0864730	+	0.0830674i
$781$	−9.35991e16			−0.412444
$782$	−5.33057e16	+	5.33057e16i	−0.233095	+	0.233095i
$783$	−4.19231e16	−	4.19231e16i	−0.181921	−	0.181921i
$784$			6.48004e16i			0.279050i
$785$	−7.99860e14	+	3.98191e16i	−0.00341819	+	0.170166i
$786$	3.82150e16			0.162068
$787$	−2.72581e17	+	2.72581e17i	−1.14722	+	1.14722i	−0.160125	+	0.987097i	$0.551190\pi$
$787$	−2.72581e17	+	2.72581e17i	−1.14722	+	1.14722i	−0.987097	+	0.160125i	$0.948810\pi$
$788$	1.16954e17	+	1.16954e17i	0.488490	+	0.488490i
$789$			9.08299e16i			0.376502i
$790$	1.23199e17	+	2.47473e15i	0.506808	+	0.0101804i
$791$	2.19199e17			0.894911
$792$	−3.30462e16	+	3.30462e16i	−0.133897	+	0.133897i
$793$	3.91128e16	+	3.91128e16i	0.157282	+	0.157282i
$794$		−	1.32005e17i		−	0.526825i
$795$	1.46797e16	+	1.52815e16i	0.0581453	+	0.0605291i
$796$	3.88440e16			0.152702
$797$	−9.95129e15	+	9.95129e15i	−0.0388266	+	0.0388266i	−0.726254	−	0.687427i	$-0.758740\pi$
$797$	−9.95129e15	+	9.95129e15i	−0.0388266	+	0.0388266i	0.687427	+	0.726254i	$0.258740\pi$
$798$	−5.26314e17	−	5.26314e17i	−2.03811	−	2.03811i
$799$		−	1.93548e17i		−	0.743889i
$800$	3.14257e16	+	3.40575e16i	0.119879	+	0.129919i
$801$	1.48008e17			0.560391
$802$	3.70576e15	−	3.70576e15i	0.0139262	−	0.0139262i
$803$	7.33981e15	+	7.33981e15i	0.0273774	+	0.0273774i
$804$			3.48842e17i			1.29150i
$805$	−1.69656e17	+	1.62975e17i	−0.623440	+	0.598887i
$806$	−5.62123e16			−0.205032
$807$	−4.10256e17	+	4.10256e17i	−1.48530	+	1.48530i
$808$	−3.91562e15	−	3.91562e15i	−0.0140712	−	0.0140712i
$809$		−	4.20362e17i		−	1.49945i	−0.661749	−	0.749726i	$-0.730185\pi$
$809$		−	4.20362e17i		−	1.49945i	0.661749	−	0.749726i	$-0.269815\pi$
$810$	3.52332e15	−	1.75400e17i	0.0124751	−	0.621041i
$811$	2.82759e17			0.993782			0.496891	−	0.867813i	$-0.334475\pi$
$811$	2.82759e17			0.993782			0.496891	+	0.867813i	$0.334475\pi$
$812$	2.38397e17	−	2.38397e17i	0.831696	−	0.831696i
$813$	−1.77887e17	−	1.77887e17i	−0.616030	−	0.616030i
$814$			4.05791e16i			0.139494i
$815$	−6.88785e16	−	1.38358e15i	−0.235038	−	0.00472128i
$816$	−8.40923e16			−0.284849
$817$	−2.02714e17	+	2.02714e17i	−0.681636	+	0.681636i
$818$	−5.30488e16	−	5.30488e16i	−0.177074	−	0.177074i
$819$		−	8.04278e16i		−	0.266504i
$820$	−2.05887e16	−	2.14328e16i	−0.0677245	−	0.0705011i
$821$	2.52092e17			0.823190			0.411595	−	0.911367i	$-0.364972\pi$
$821$	2.52092e17			0.823190			0.411595	+	0.911367i	$0.364972\pi$
$822$	−1.16657e17	+	1.16657e17i	−0.378165	+	0.378165i
$823$	2.88876e17	+	2.88876e17i	0.929636	+	0.929636i	0.997682	−	0.0680459i	$-0.0216764\pi$
$823$	2.88876e17	+	2.88876e17i	0.929636	+	0.929636i	−0.0680459	+	0.997682i	$0.521676\pi$
$824$		−	6.33302e16i		−	0.202324i
$825$	1.62462e17	−	1.49908e17i	0.515262	−	0.475445i
$826$	1.04982e17			0.330549
$827$	−3.11943e17	+	3.11943e17i	−0.975086	+	0.975086i	−0.999697	−	0.0246114i	$-0.992165\pi$
$827$	−3.11943e17	+	3.11943e17i	−0.975086	+	0.975086i	0.0246114	+	0.999697i	$0.492165\pi$
$828$	7.51210e16	+	7.51210e16i	0.233120	+	0.233120i
$829$			3.36774e17i			1.03756i	0.854909	+	0.518778i	$0.173613\pi$
$829$			3.36774e17i			1.03756i	−0.854909	+	0.518778i	$0.826387\pi$
$830$	−2.07164e17	+	1.99005e17i	−0.633644	+	0.608689i
$831$	−2.12283e16			−0.0644628
$832$	−4.84080e15	+	4.84080e15i	−0.0145941	+	0.0145941i
$833$	2.06861e17	+	2.06861e17i	0.619167	+	0.619167i
$834$			2.55850e17i			0.760308i
$835$	4.01989e15	−	2.00121e17i	0.0118603	−	0.590436i
$836$	1.58957e17			0.465632
$837$	−6.79294e16	+	6.79294e16i	−0.197563	+	0.197563i
$838$	1.89808e17	+	1.89808e17i	0.548089	+	0.548089i
$839$			1.34274e17i			0.384965i	0.981300	+	0.192482i	$0.0616538\pi$
$839$			1.34274e17i			0.384965i	−0.981300	+	0.192482i	$0.938346\pi$
$840$	−2.62371e17	−	5.27033e15i	−0.746860	−	0.0150024i
$841$	−5.71392e17			−1.61495
$842$	1.42811e17	−	1.42811e17i	0.400763	−	0.400763i
$843$	−1.77683e17	−	1.77683e17i	−0.495086	−	0.495086i
$844$			9.21446e16i			0.254927i
$845$	−2.45313e17	−	2.55370e17i	−0.673877	−	0.701505i
$846$	−2.72758e17			−0.743969
$847$	2.91309e17	−	2.91309e17i	0.788956	−	0.788956i
$848$	3.79871e15	+	3.79871e15i	0.0102155	+	0.0102155i
$849$		−	6.33409e17i		−	1.69137i
$850$	2.09040e17	+	8.40150e15i	0.554263	+	0.0222763i
$851$	9.22451e16			0.242866
$852$	−1.67828e17	+	1.67828e17i	−0.438760	+	0.438760i
$853$	−1.62154e16	−	1.62154e16i	−0.0420953	−	0.0420953i	0.685746	−	0.727841i	$-0.259476\pi$
$853$	−1.62154e16	−	1.62154e16i	−0.0420953	−	0.0420953i	−0.727841	+	0.685746i	$0.759476\pi$
$854$			5.37555e17i			1.38572i
$855$	6.03059e17	−	5.79309e17i	1.54370	−	1.48290i
$856$	5.73244e16			0.145712
$857$	2.45382e17	−	2.45382e17i	0.619382	−	0.619382i	−0.325991	−	0.945373i	$-0.605698\pi$
$857$	2.45382e17	−	2.45382e17i	0.619382	−	0.619382i	0.945373	+	0.325991i	$0.105698\pi$
$858$	2.30917e16	+	2.30917e16i	0.0578806	+	0.0578806i
$859$		−	4.32544e17i		−	1.07664i	−0.842740	−	0.538322i	$-0.819059\pi$
$859$		−	4.32544e17i		−	1.07664i	0.842740	−	0.538322i	$-0.180941\pi$
$860$	−2.02991e15	+	1.01054e17i	−0.00501749	+	0.249784i
$861$	1.68299e17			0.413108
$862$	2.04939e17	−	2.04939e17i	0.499552	−	0.499552i
$863$	−8.55095e16	−	8.55095e16i	−0.206990	−	0.206990i	0.595997	−	0.802987i	$-0.296757\pi$
$863$	−8.55095e16	−	8.55095e16i	−0.206990	−	0.206990i	−0.802987	+	0.595997i	$0.796757\pi$
$864$			1.16997e16i			0.0281249i
$865$	−2.39616e17	−	4.81324e15i	−0.572030	−	0.0114906i
$866$	−1.48552e17			−0.352185
$867$	1.67762e17	−	1.67762e17i	0.394985	−	0.394985i
$868$	−3.86283e17	−	3.86283e17i	−0.903207	−	0.903207i
$869$		−	1.49023e17i		−	0.346046i
$870$	4.98897e17	+	5.19351e17i	1.15052	+	1.19769i
$871$	1.28209e17			0.293637
$872$	1.26120e17	−	1.26120e17i	0.286870	−	0.286870i
$873$	1.75298e17	+	1.75298e17i	0.395996	+	0.395996i
$874$		−	3.61344e17i		−	0.810685i
$875$	6.51685e17	+	3.93142e16i	1.45208	+	0.0875993i
$876$	2.63213e16			0.0582483
$877$	−2.87016e17	+	2.87016e17i	−0.630825	+	0.630825i	−0.948275	−	0.317450i	$-0.897173\pi$
$877$	−2.87016e17	+	2.87016e17i	−0.630825	+	0.630825i	0.317450	+	0.948275i	$0.397173\pi$
$878$	−8.28648e16	−	8.28648e16i	−0.180885	−	0.180885i
$879$			1.05658e18i			2.29070i
$880$	4.04164e16	−	3.88247e16i	0.0870286	−	0.0836011i
$881$	−6.23644e17			−1.33377			−0.666886	−	0.745160i	$-0.732373\pi$
$881$	−6.23644e17			−1.33377			−0.666886	+	0.745160i	$0.732373\pi$
$882$	2.91518e17	−	2.91518e17i	0.619233	−	0.619233i
$883$	1.06372e17	+	1.06372e17i	0.224420	+	0.224420i	0.810357	−	0.585937i	$-0.199273\pi$
$883$	1.06372e17	+	1.06372e17i	0.224420	+	0.224420i	−0.585937	+	0.810357i	$0.699273\pi$
$884$			3.09063e16i			0.0647639i
$885$	−4.50362e15	+	2.24202e17i	−0.00937350	+	0.466637i
$886$	−2.22427e17			−0.459817
$887$	6.98501e16	−	6.98501e16i	0.143425	−	0.143425i	−0.631748	−	0.775173i	$-0.717662\pi$
$887$	6.98501e16	−	6.98501e16i	0.143425	−	0.143425i	0.775173	+	0.631748i	$0.217662\pi$
$888$	7.27606e16	+	7.27606e16i	0.148395	+	0.148395i
$889$		−	4.05914e17i		−	0.822288i
$890$	−1.77454e17	−	3.56457e15i	−0.357063	−	0.00717245i
$891$	−2.12166e17			−0.424043
$892$	−5.36142e16	+	5.36142e16i	−0.106436	+	0.106436i
$893$	6.56004e17	+	6.56004e17i	1.29359	+	1.29359i
$894$		−	2.45231e17i		−	0.480342i
$895$	−3.51095e17	−	3.65489e17i	−0.683103	−	0.711109i
$896$	−6.65306e16			−0.128580
$897$	5.24925e16	−	5.24925e16i	0.100773	−	0.100773i
$898$	2.97382e17	+	2.97382e17i	0.567096	+	0.567096i
$899$			1.49915e18i			2.83979i
$900$	1.18398e16	−	2.94590e17i	0.0222787	−	0.554322i
$901$	2.42530e16			0.0453333
$902$	−2.54148e16	+	2.54148e16i	−0.0471898	+	0.0471898i
$903$	−4.04730e17	−	4.04730e17i	−0.746515	−	0.746515i
$904$			1.18705e17i			0.217499i
$905$	−4.07430e17	+	3.91384e17i	−0.741586	+	0.712380i
$906$	−7.34743e17			−1.32851
$907$	6.48283e17	−	6.48283e17i	1.16445	−	1.16445i	0.180960	−	0.983490i	$-0.442080\pi$
$907$	6.48283e17	−	6.48283e17i	1.16445	−	1.16445i	0.983490	−	0.180960i	$-0.0579204\pi$
$908$	−2.66400e17	−	2.66400e17i	−0.475356	−	0.475356i
$909$			3.52305e16i			0.0624504i
$910$	−1.93699e15	+	9.64286e16i	−0.00341099	+	0.169808i
$911$	−2.62366e17			−0.458983			−0.229491	−	0.973311i	$-0.573706\pi$
$911$	−2.62366e17			−0.458983			−0.229491	+	0.973311i	$0.573706\pi$
$912$	2.85019e17	−	2.85019e17i	0.495341	−	0.495341i
$913$	2.45653e17	+	2.45653e17i	0.424129	+	0.424129i
$914$		−	2.67481e17i		−	0.458792i
$915$	−1.14801e18	−	2.30604e16i	−1.95622	−	0.0392953i
$916$	−3.53864e16			−0.0599051
$917$	9.65159e16	−	9.65159e16i	0.162324	−	0.162324i
$918$	3.73485e16	+	3.73485e16i	0.0624047	+	0.0624047i
$919$		−	1.04985e18i		−	1.74275i	−0.490621	−	0.871373i	$-0.663230\pi$
$919$		−	1.04985e18i		−	1.74275i	0.490621	−	0.871373i	$-0.336770\pi$
$920$	−8.82568e16	−	9.18752e16i	−0.145553	−	0.151520i
$921$	5.57754e16			0.0913871
$922$	−5.17973e17	+	5.17973e17i	−0.843183	+	0.843183i
$923$	6.16816e16	+	6.16816e16i	0.0997574	+	0.0997574i
$924$			3.17366e17i			0.509952i
$925$	−1.73602e17	−	1.88140e17i	−0.277143	−	0.300353i
$926$	−6.42667e16			−0.101934
$927$	−2.84904e17	+	2.84904e17i	−0.448973	+	0.448973i
$928$	1.29101e17	+	1.29101e17i	0.202135	+	0.202135i
$929$			3.83066e17i			0.595909i	0.954580	+	0.297954i	$0.0963044\pi$
$929$			3.83066e17i			0.595909i	−0.954580	+	0.297954i	$0.903696\pi$
$930$	8.41522e17	−	8.08380e17i	1.30067	−	1.24945i
$931$	−1.40225e18			−2.15341
$932$	1.84562e17	−	1.84562e17i	0.281609	−	0.281609i
$933$	5.34063e17	+	5.34063e17i	0.809660	+	0.809660i
$934$		−	5.65264e17i		−	0.851471i
$935$	5.08128e15	−	2.52959e17i	0.00760507	−	0.378600i
$936$	4.35547e16			0.0647709
$937$	−7.09184e17	+	7.09184e17i	−1.04790	+	1.04790i	−0.0491098	+	0.998793i	$0.515638\pi$
$937$	−7.09184e17	+	7.09184e17i	−1.04790	+	1.04790i	−0.998793	+	0.0491098i	$0.984362\pi$
$938$	8.81037e17	+	8.81037e17i	1.29353	+	1.29353i
$939$			4.77430e17i			0.696492i
$940$	3.27022e17	+	6.56899e15i	0.474034	+	0.00952208i
$941$	1.20839e18			1.74049			0.870244	−	0.492621i	$-0.163961\pi$
$941$	1.20839e18			1.74049			0.870244	+	0.492621i	$0.163961\pi$
$942$	8.63635e16	−	8.63635e16i	0.123602	−	0.123602i
$943$	5.77734e16	+	5.77734e16i	0.0821595	+	0.0821595i
$944$			5.68519e16i			0.0803365i
$945$	1.14188e17	+	1.18869e17i	0.160335	+	0.166909i
$946$	1.22236e17			0.170551
$947$	−3.32493e17	+	3.32493e17i	−0.460980	+	0.460980i	−0.898977	−	0.437996i	$-0.855688\pi$
$947$	−3.32493e17	+	3.32493e17i	−0.460980	+	0.460980i	0.437996	+	0.898977i	$0.355688\pi$
$948$	−2.67205e17	−	2.67205e17i	−0.368125	−	0.368125i
$949$		−	9.67383e15i		−	0.0132435i
$950$	−7.36987e17	+	6.80035e17i	−1.00258	+	0.925103i
$951$	8.93789e17			1.20824
$952$	−2.12384e17	+	2.12384e17i	−0.285298	+	0.285298i
$953$	−9.36824e17	−	9.36824e17i	−1.25055	−	1.25055i	−0.955474	−	0.295074i	$-0.904656\pi$
$953$	−9.36824e17	−	9.36824e17i	−1.25055	−	1.25055i	−0.295074	−	0.955474i	$-0.595344\pi$
$954$		−	3.41786e16i		−	0.0453382i
$955$	8.85453e17	−	8.50581e17i	1.16720	−	1.12123i
$956$	1.12412e17			0.147254
$957$	6.15842e17	−	6.15842e17i	0.801673	−	0.801673i
$958$	−6.19054e17	−	6.19054e17i	−0.800821	−	0.800821i
$959$			5.89260e17i			0.757523i
$960$	2.85408e15	−	1.42084e17i	0.00364618	−	0.181517i
$961$	1.64145e18			2.08396
$962$	2.67416e16	−	2.67416e16i	0.0337393	−	0.0337393i
$963$	−2.57886e17	−	2.57886e17i	−0.323348	−	0.323348i
$964$		−	1.90286e17i		−	0.237107i
$965$	1.08018e18	+	2.16980e16i	1.33762	+	0.0268692i
$966$	7.21442e17			0.887848
$967$	−2.43094e17	+	2.43094e17i	−0.297314	+	0.297314i	−0.839961	−	0.542647i	$-0.817422\pi$
$967$	−2.43094e17	+	2.43094e17i	−0.297314	+	0.297314i	0.542647	+	0.839961i	$0.317422\pi$
$968$	1.57755e17	+	1.57755e17i	0.191748	+	0.191748i
$969$		−	1.81971e18i		−	2.19817i
$970$	−2.05951e17	−	2.14394e17i	−0.247248	−	0.257385i
$971$	4.97139e16			0.0593147			0.0296573	−	0.999560i	$-0.490558\pi$
$971$	4.97139e16			0.0593147			0.0296573	+	0.999560i	$0.490558\pi$
$972$	−4.27862e17	+	4.27862e17i	−0.507348	+	0.507348i
$973$	6.46176e17	+	6.46176e17i	0.761507	+	0.761507i
$974$		−	7.55390e17i		−	0.884744i
$975$	−2.05851e17	−	8.27333e15i	−0.239621	−	0.00963059i
$976$	−2.91106e17			−0.336785
$977$	9.75153e17	−	9.75153e17i	1.12126	−	1.12126i	0.129705	−	0.991553i	$-0.458597\pi$
$977$	9.75153e17	−	9.75153e17i	1.12126	−	1.12126i	0.991553	−	0.129705i	$-0.0414030\pi$
$978$	1.49390e17	+	1.49390e17i	0.170722	+	0.170722i
$979$			2.14650e17i			0.243801i
$980$	−3.56535e17	+	3.42494e17i	−0.402482	+	0.386631i
$981$	−1.13476e18			−1.27318
$982$	−5.06562e17	+	5.06562e17i	−0.564890	+	0.564890i
$983$	−7.61743e17	−	7.61743e17i	−0.844282	−	0.844282i	0.145131	−	0.989412i	$-0.453640\pi$
$983$	−7.61743e17	−	7.61743e17i	−0.844282	−	0.844282i	−0.989412	+	0.145131i	$0.953640\pi$
$984$			9.11403e16i			0.100401i
$985$	−2.53427e16	+	1.26163e18i	−0.0277483	+	1.38138i
$986$	8.24251e17			0.897011
$987$	−1.30975e18	+	1.30975e18i	−1.41672	+	1.41672i
$988$	−1.04752e17	−	1.04752e17i	−0.112622	−	0.112622i
$989$		−	2.77870e17i		−	0.296936i
$990$	−3.56483e17	−	7.16079e15i	−0.378641	−	0.00760588i
$991$	−1.12196e18			−1.18450			−0.592252	−	0.805753i	$-0.701761\pi$
$991$	−1.12196e18			−1.18450			−0.592252	+	0.805753i	$0.701761\pi$
$992$	2.09187e17	−	2.09187e17i	0.219515	−	0.219515i
$993$	−8.69283e17	−	8.69283e17i	−0.906704	−	0.906704i
$994$			8.47735e17i			0.878904i
$995$	2.05304e17	+	2.13722e17i	0.211573	+	0.220247i
$996$	8.80938e17			0.902380
$997$	1.03110e18	−	1.03110e18i	1.04985	−	1.04985i	0.0511616	−	0.998690i	$-0.483708\pi$
$997$	1.03110e18	−	1.03110e18i	1.04985	−	1.04985i	0.998690	−	0.0511616i	$-0.0162923\pi$
$998$	−1.20302e17	−	1.20302e17i	−0.121756	−	0.121756i
$999$		−	6.46314e16i		−	0.0650205i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.13.c.b.3.1	✓	6
3.2	odd	2		90.13.g.a.73.1		6
4.3	odd	2		80.13.p.a.33.3		6
5.2	odd	4	inner	10.13.c.b.7.1	yes	6
5.3	odd	4		50.13.c.c.7.3		6
5.4	even	2		50.13.c.c.43.3		6
15.2	even	4		90.13.g.a.37.1		6
20.7	even	4		80.13.p.a.17.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.13.c.b.3.1	✓	6	1.1	even	1	trivial
10.13.c.b.7.1	yes	6	5.2	odd	4	inner
50.13.c.c.7.3		6	5.3	odd	4
50.13.c.c.43.3		6	5.4	even	2
80.13.p.a.17.3		6	20.7	even	4
80.13.p.a.33.3		6	4.3	odd	2
90.13.g.a.37.1		6	15.2	even	4
90.13.g.a.73.1		6	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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	10.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(32.0000 - 32.0000i) q^{2} +(-748.698 - 748.698i) q^{3} -2048.00i q^{4} +(11268.2 - 10824.4i) q^{5} -47916.6 q^{6} +(-121018. + 121018. i) q^{7} +(-65536.0 - 65536.0i) q^{8} +589655. i q^{9} +O(q^{10})\)	\(q+(32.0000 - 32.0000i) q^{2} +(-748.698 - 748.698i) q^{3} -2048.00i q^{4} +(11268.2 - 10824.4i) q^{5} -47916.6 q^{6} +(-121018. + 121018. i) q^{7} +(-65536.0 - 65536.0i) q^{8} +589655. i q^{9} +(14201.0 - 706964. i) q^{10} -855152. q^{11} +(-1.53333e6 + 1.53333e6i) q^{12} +(563543. + 563543. i) q^{13} +7.74518e6i q^{14} +(-1.65407e7 - 332259. i) q^{15} -4.19430e6 q^{16} +(-1.33894e7 + 1.33894e7i) q^{17} +(1.88690e7 + 1.88690e7i) q^{18} -9.07626e7i q^{19} +(-2.21684e7 - 2.30773e7i) q^{20} +1.81212e8 q^{21} +(-2.73649e7 + 2.73649e7i) q^{22} +(6.22062e7 + 6.22062e7i) q^{23} +9.81333e7i q^{24} +(9.80431e6 - 2.43944e8i) q^{25} +3.60667e7 q^{26} +(4.35847e7 - 4.35847e7i) q^{27} +(2.47846e8 + 2.47846e8i) q^{28} -9.61877e8i q^{29} +(-5.39935e8 + 5.18670e8i) q^{30} -1.55856e9 q^{31} +(-1.34218e8 + 1.34218e8i) q^{32} +(6.40250e8 + 6.40250e8i) q^{33} +8.56919e8i q^{34} +(-5.37058e7 + 2.67361e9i) q^{35} +1.20761e9 q^{36} +(7.41446e8 - 7.41446e8i) q^{37} +(-2.90440e9 - 2.90440e9i) q^{38} -8.43846e8i q^{39} +(-1.44786e9 - 2.90837e7i) q^{40} +9.28740e8 q^{41} +(5.79880e9 - 5.79880e9i) q^{42} +(-2.23346e9 - 2.23346e9i) q^{43} +1.75135e9i q^{44} +(6.38268e9 + 6.64435e9i) q^{45} +3.98120e9 q^{46} +(-7.22768e9 + 7.22768e9i) q^{47} +(3.14027e9 + 3.14027e9i) q^{48} -1.54496e10i q^{49} +(-7.49246e9 - 8.11994e9i) q^{50} +2.00492e10 q^{51} +(1.15414e9 - 1.15414e9i) q^{52} +(-9.05683e8 - 9.05683e8i) q^{53} -2.78942e9i q^{54} +(-9.63603e9 + 9.25652e9i) q^{55} +1.58621e10 q^{56} +(-6.79538e10 + 6.79538e10i) q^{57} +(-3.07801e10 - 3.07801e10i) q^{58} -1.35545e10i q^{59} +(-6.80466e8 + 3.38753e10i) q^{60} +6.94051e10 q^{61} +(-4.98740e10 + 4.98740e10i) q^{62} +(-7.13591e10 - 7.13591e10i) q^{63} +8.58993e9i q^{64} +(1.24501e10 + 2.50090e8i) q^{65} +4.09760e10 q^{66} +(1.13753e11 - 1.13753e11i) q^{67} +(2.74214e10 + 2.74214e10i) q^{68} -9.31472e10i q^{69} +(8.38371e10 + 8.72743e10i) q^{70} +1.09453e11 q^{71} +(3.86436e10 - 3.86436e10i) q^{72} +(-8.58305e9 - 8.58305e9i) q^{73} -4.74526e10i q^{74} +(-1.89980e11 + 1.75300e11i) q^{75} -1.85882e11 q^{76} +(1.03489e11 - 1.03489e11i) q^{77} +(-2.70031e10 - 2.70031e10i) q^{78} +1.74264e11i q^{79} +(-4.72623e10 + 4.54009e10i) q^{80} +2.48103e11 q^{81} +(2.97197e10 - 2.97197e10i) q^{82} +(-2.87263e11 - 2.87263e11i) q^{83} -3.71123e11i q^{84} +(-5.94196e9 + 2.95806e11i) q^{85} -1.42941e11 q^{86} +(-7.20155e11 + 7.20155e11i) q^{87} +(5.60432e10 + 5.60432e10i) q^{88} -2.51008e11i q^{89} +(4.16865e11 + 8.37371e9i) q^{90} -1.36398e11 q^{91} +(1.27398e11 - 1.27398e11i) q^{92} +(1.16689e12 + 1.16689e12i) q^{93} +4.62572e11i q^{94} +(-9.82453e11 - 1.02273e12i) q^{95} +2.00977e11 q^{96} +(2.97289e11 - 2.97289e11i) q^{97} +(-4.94388e11 - 4.94388e11i) q^{98} -5.04244e11i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 192 q^{2} + 296 q^{3} + 14460 q^{5} + 18944 q^{6} - 322104 q^{7} - 393216 q^{8}+O(q^{10}) \) 6 * q + 192 * q^2 + 296 * q^3 + 14460 * q^5 + 18944 * q^6 - 322104 * q^7 - 393216 * q^8	\( 6 q + 192 q^{2} + 296 q^{3} + 14460 q^{5} + 18944 q^{6} - 322104 q^{7} - 393216 q^{8} - 18240 q^{10} + 1652712 q^{11} + 606208 q^{12} - 4646814 q^{13} - 41776360 q^{15} - 25165824 q^{16} + 51200226 q^{17} + 36525632 q^{18} - 30781440 q^{20} + 117123272 q^{21} + 52886784 q^{22} + 105826896 q^{23} - 161517150 q^{25} - 297396096 q^{26} + 627050120 q^{27} + 659668992 q^{28} - 699452160 q^{30} - 2667117168 q^{31} - 805306368 q^{32} + 4381479992 q^{33} - 7758629520 q^{35} + 2337640448 q^{36} + 1747956246 q^{37} - 2125152000 q^{38} - 1932656640 q^{40} + 22722098232 q^{41} + 3747944704 q^{42} - 15890524824 q^{43} - 8103444470 q^{45} + 6772921344 q^{46} - 18495531264 q^{47} - 1241513984 q^{48} + 8149569600 q^{50} + 114152506432 q^{51} - 9516675072 q^{52} - 88020413514 q^{53} + 37466287320 q^{55} + 42218815488 q^{56} - 174270786400 q^{57} - 107861859840 q^{58} + 40793047040 q^{60} + 291794891352 q^{61} - 85347749376 q^{62} - 297541783984 q^{63} + 26961608790 q^{65} + 280414719488 q^{66} - 3887251464 q^{67} - 104858062848 q^{68} - 110954853120 q^{70} + 929135015472 q^{71} + 74804494336 q^{72} + 12678070086 q^{73} - 928285655600 q^{75} - 136009728000 q^{76} - 436526954808 q^{77} - 80105703936 q^{78} - 60649635840 q^{80} + 833935849906 q^{81} + 727107143424 q^{82} + 68676615456 q^{83} + 142549278930 q^{85} - 1016993588736 q^{86} - 943420476880 q^{87} - 108312133632 q^{88} + 717302271680 q^{90} - 1619146872048 q^{91} + 216733483008 q^{92} + 2320495891112 q^{93} - 1510780128600 q^{95} - 79456894976 q^{96} + 675735777846 q^{97} - 1327663144512 q^{98}+O(q^{100}) \) 6 * q + 192 * q^2 + 296 * q^3 + 14460 * q^5 + 18944 * q^6 - 322104 * q^7 - 393216 * q^8 - 18240 * q^10 + 1652712 * q^11 + 606208 * q^12 - 4646814 * q^13 - 41776360 * q^15 - 25165824 * q^16 + 51200226 * q^17 + 36525632 * q^18 - 30781440 * q^20 + 117123272 * q^21 + 52886784 * q^22 + 105826896 * q^23 - 161517150 * q^25 - 297396096 * q^26 + 627050120 * q^27 + 659668992 * q^28 - 699452160 * q^30 - 2667117168 * q^31 - 805306368 * q^32 + 4381479992 * q^33 - 7758629520 * q^35 + 2337640448 * q^36 + 1747956246 * q^37 - 2125152000 * q^38 - 1932656640 * q^40 + 22722098232 * q^41 + 3747944704 * q^42 - 15890524824 * q^43 - 8103444470 * q^45 + 6772921344 * q^46 - 18495531264 * q^47 - 1241513984 * q^48 + 8149569600 * q^50 + 114152506432 * q^51 - 9516675072 * q^52 - 88020413514 * q^53 + 37466287320 * q^55 + 42218815488 * q^56 - 174270786400 * q^57 - 107861859840 * q^58 + 40793047040 * q^60 + 291794891352 * q^61 - 85347749376 * q^62 - 297541783984 * q^63 + 26961608790 * q^65 + 280414719488 * q^66 - 3887251464 * q^67 - 104858062848 * q^68 - 110954853120 * q^70 + 929135015472 * q^71 + 74804494336 * q^72 + 12678070086 * q^73 - 928285655600 * q^75 - 136009728000 * q^76 - 436526954808 * q^77 - 80105703936 * q^78 - 60649635840 * q^80 + 833935849906 * q^81 + 727107143424 * q^82 + 68676615456 * q^83 + 142549278930 * q^85 - 1016993588736 * q^86 - 943420476880 * q^87 - 108312133632 * q^88 + 717302271680 * q^90 - 1619146872048 * q^91 + 216733483008 * q^92 + 2320495891112 * q^93 - 1510780128600 * q^95 - 79456894976 * q^96 + 675735777846 * q^97 - 1327663144512 * q^98

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