LMFDB - Embedded newform 10.17.c.a.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,17,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, 17, names="a")

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

chi := DirichletCharacter("10.3");

S:= CuspForms(chi, 17);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 17 $
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:	$16.2324543857$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 7213550 x^{5} + 3043721913 x^{4} - 386278388950 x^{3} + 26017651801250 x^{2} + \cdots + 77\!\cdots\!36 $ x^8 - 7213550x^5 + 3043721913x^4 - 386278388950x^3 + 26017651801250x^2 - 635609377818800*x + 7763945882921536
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{8}\cdot 5^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.2
Root			$15.9615 - 15.9615i$ of defining polynomial
Character	$\chi$	$=$	10.7
Dual form			10.17.c.a.3.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-128.000 - 128.000i) q^{2} +(-1354.68 + 1354.68i) q^{3} +32768.0i q^{4} +(-371534. + 120625. i) q^{5} +346799. q^{6} +(232276. + 232276. i) q^{7} +(4.19430e6 - 4.19430e6i) q^{8} +3.93764e7i q^{9} +O(q^{10})$	\(q+(-128.000 - 128.000i) q^{2} +(-1354.68 + 1354.68i) q^{3} +32768.0i q^{4} +(-371534. + 120625. i) q^{5} +346799. q^{6} +(232276. + 232276. i) q^{7} +(4.19430e6 - 4.19430e6i) q^{8} +3.93764e7i q^{9} +(6.29964e7 + 3.21163e7i) q^{10} +2.70321e7 q^{11} +(-4.43903e7 - 4.43903e7i) q^{12} +(3.12551e8 - 3.12551e8i) q^{13} -5.94626e7i q^{14} +(3.39902e8 - 6.66720e8i) q^{15} -1.07374e9 q^{16} +(-4.95457e9 - 4.95457e9i) q^{17} +(5.04018e9 - 5.04018e9i) q^{18} -2.77790e10i q^{19} +(-3.95264e9 - 1.21744e10i) q^{20} -6.29320e8 q^{21} +(-3.46011e9 - 3.46011e9i) q^{22} +(4.85746e10 - 4.85746e10i) q^{23} +1.13639e10i q^{24} +(1.23487e11 - 8.96326e10i) q^{25} -8.00131e10 q^{26} +(-1.11657e11 - 1.11657e11i) q^{27} +(-7.61121e9 + 7.61121e9i) q^{28} +1.69301e11i q^{29} +(-1.28848e11 + 4.18326e10i) q^{30} -8.83369e10 q^{31} +(1.37439e11 + 1.37439e11i) q^{32} +(-3.66200e10 + 3.66200e10i) q^{33} +1.26837e12i q^{34} +(-1.14317e11 - 5.82800e10i) q^{35} -1.29029e12 q^{36} +(3.82867e12 + 3.82867e12i) q^{37} +(-3.55572e12 + 3.55572e12i) q^{38} +8.46815e11i q^{39} +(-1.05239e12 + 2.06426e12i) q^{40} +1.29691e12 q^{41} +(8.05529e10 + 8.05529e10i) q^{42} +(1.34076e13 - 1.34076e13i) q^{43} +8.85789e11i q^{44} +(-4.74978e12 - 1.46297e13i) q^{45} -1.24351e13 q^{46} +(-5.93778e12 - 5.93778e12i) q^{47} +(1.45458e12 - 1.45458e12i) q^{48} -3.31250e13i q^{49} +(-2.72793e13 - 4.33338e12i) q^{50} +1.34238e13 q^{51} +(1.02417e13 + 1.02417e13i) q^{52} +(4.58521e13 - 4.58521e13i) q^{53} +2.85842e13i q^{54} +(-1.00434e13 + 3.26075e12i) q^{55} +1.94847e12 q^{56} +(3.76318e13 + 3.76318e13i) q^{57} +(2.16705e13 - 2.16705e13i) q^{58} +2.43196e14i q^{59} +(2.18471e13 + 1.11379e13i) q^{60} -2.08301e14 q^{61} +(1.13071e13 + 1.13071e13i) q^{62} +(-9.14618e12 + 9.14618e12i) q^{63} -3.51844e13i q^{64} +(-7.84219e13 + 1.53825e14i) q^{65} +9.37472e12 q^{66} +(3.69388e13 + 3.69388e13i) q^{67} +(1.62351e14 - 1.62351e14i) q^{68} +1.31606e14i q^{69} +(7.17267e12 + 2.20924e13i) q^{70} -4.12269e14 q^{71} +(1.65157e14 + 1.65157e14i) q^{72} +(1.10105e14 - 1.10105e14i) q^{73} -9.80140e14i q^{74} +(-4.58622e13 + 2.88710e14i) q^{75} +9.10263e14 q^{76} +(6.27891e12 + 6.27891e12i) q^{77} +(1.08392e14 - 1.08392e14i) q^{78} -2.00631e15i q^{79} +(3.98932e14 - 1.29520e14i) q^{80} -1.39250e15 q^{81} +(-1.66005e14 - 1.66005e14i) q^{82} +(1.15652e13 - 1.15652e13i) q^{83} -2.06216e13i q^{84} +(2.43844e15 + 1.24315e15i) q^{85} -3.43235e15 q^{86} +(-2.29349e14 - 2.29349e14i) q^{87} +(1.13381e14 - 1.13381e14i) q^{88} -2.86189e15i q^{89} +(-1.26463e15 + 2.48057e15i) q^{90} +1.45196e14 q^{91} +(1.59169e15 + 1.59169e15i) q^{92} +(1.19668e14 - 1.19668e14i) q^{93} +1.52007e15i q^{94} +(3.35085e15 + 1.03209e16i) q^{95} -3.72372e14 q^{96} +(3.85105e15 + 3.85105e15i) q^{97} +(-4.24000e15 + 4.24000e15i) q^{98} +1.06443e15i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 1024 q^{2} - 5382 q^{3} + 184830 q^{5} + 1377792 q^{6} - 1586702 q^{7} + 33554432 q^{8}+O(q^{10}) $ 8 * q - 1024 * q^2 - 5382 * q^3 + 184830 * q^5 + 1377792 * q^6 - 1586702 * q^7 + 33554432 * q^8	\( 8 q - 1024 q^{2} - 5382 q^{3} + 184830 q^{5} + 1377792 q^{6} - 1586702 q^{7} + 33554432 q^{8} - 179537920 q^{10} + 307957276 q^{11} - 176357376 q^{12} + 202095228 q^{13} - 4140218430 q^{15} - 8589934592 q^{16} - 10825054172 q^{17} - 19318270464 q^{18} + 39905198080 q^{20} - 279317583684 q^{21} - 39418531328 q^{22} - 58166716742 q^{23} + 48765928900 q^{25} - 51736378368 q^{26} - 433782808920 q^{27} + 51993051136 q^{28} + 881686264320 q^{30} - 1503757815484 q^{31} + 1099511627776 q^{32} + 3563163295596 q^{33} + 1361150225890 q^{35} + 4945477238784 q^{36} + 5719558248048 q^{37} + 10471905756160 q^{38} - 4332632145920 q^{40} - 21624661426724 q^{41} + 35752650711552 q^{42} + 694778360778 q^{43} - 125868018043710 q^{45} + 14890679485952 q^{46} + 17454156046938 q^{47} + 5778878496768 q^{48} - 38811694553600 q^{50} - 282689731949724 q^{51} + 6622256431104 q^{52} + 315933715243808 q^{53} - 170380752243540 q^{55} - 13310221090816 q^{56} + 218915538682320 q^{57} + 231112067379200 q^{58} - 90045006151680 q^{60} - 260671832048484 q^{61} + 192481000381952 q^{62} + 12\!\cdots\!78 q^{63}+ \cdots + 18\!\cdots\!04 q^{98}+O(q^{100}) \) 8 * q - 1024 * q^2 - 5382 * q^3 + 184830 * q^5 + 1377792 * q^6 - 1586702 * q^7 + 33554432 * q^8 - 179537920 * q^10 + 307957276 * q^11 - 176357376 * q^12 + 202095228 * q^13 - 4140218430 * q^15 - 8589934592 * q^16 - 10825054172 * q^17 - 19318270464 * q^18 + 39905198080 * q^20 - 279317583684 * q^21 - 39418531328 * q^22 - 58166716742 * q^23 + 48765928900 * q^25 - 51736378368 * q^26 - 433782808920 * q^27 + 51993051136 * q^28 + 881686264320 * q^30 - 1503757815484 * q^31 + 1099511627776 * q^32 + 3563163295596 * q^33 + 1361150225890 * q^35 + 4945477238784 * q^36 + 5719558248048 * q^37 + 10471905756160 * q^38 - 4332632145920 * q^40 - 21624661426724 * q^41 + 35752650711552 * q^42 + 694778360778 * q^43 - 125868018043710 * q^45 + 14890679485952 * q^46 + 17454156046938 * q^47 + 5778878496768 * q^48 - 38811694553600 * q^50 - 282689731949724 * q^51 + 6622256431104 * q^52 + 315933715243808 * q^53 - 170380752243540 * q^55 - 13310221090816 * q^56 + 218915538682320 * q^57 + 231112067379200 * q^58 - 90045006151680 * q^60 - 260671832048484 * q^61 + 192481000381952 * q^62 + 1279595714205978 * q^63 + 442440687522120 * q^65 - 912169803672576 * q^66 + 635885550643738 * q^67 + 354715375108096 * q^68 - 971840253967360 * q^70 - 1149989311263004 * q^71 - 633021086564352 * q^72 + 256748998181048 * q^73 + 1497316176176850 * q^75 - 2680807873576960 * q^76 + 1436195093152556 * q^77 - 1970051682083328 * q^78 - 198459701329920 * q^80 - 8745265883258892 * q^81 + 2767956662620672 * q^82 - 4115160605935662 * q^83 + 5650805123574940 * q^85 - 177863260359168 * q^86 + 3883634567812800 * q^87 + 1291666434555904 * q^88 + 14849617970903040 * q^90 - 28753310620553964 * q^91 - 1906006974201856 * q^92 + 26332871866839036 * q^93 + 40684157497310600 * q^95 - 1479392895172608 * q^96 - 17859102248834952 * q^97 + 18395730493909504 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$7$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−128.000	−	128.000i	−0.500000	−	0.500000i
$2$	−128.000	−	128.000i	−0.500000	−	0.500000i
$3$	−1354.68	+	1354.68i	−0.206475	+	0.206475i	−0.802767	−	0.596292i	$-0.796640\pi$
$3$	−1354.68	+	1354.68i	−0.206475	+	0.206475i	0.596292	+	0.802767i	$0.296640\pi$
$4$			32768.0i			0.500000i
$5$	−371534.	+	120625.i	−0.951127	+	0.308800i
$5$	−371534.	+	120625.i	−0.951127	+	0.308800i
$6$	346799.			0.206475
$7$	232276.	+	232276.i	0.0402920	+	0.0402920i	0.726966	−	0.686674i	$-0.240930\pi$
$7$	232276.	+	232276.i	0.0402920	+	0.0402920i	−0.686674	+	0.726966i	$0.740930\pi$
$8$	4.19430e6	−	4.19430e6i	0.250000	−	0.250000i
$9$			3.93764e7i			0.914736i
$10$	6.29964e7	+	3.21163e7i	0.629964	+	0.321163i
$11$	2.70321e7			0.126107			0.0630535	−	0.998010i	$-0.479916\pi$
$11$	2.70321e7			0.126107			0.0630535	+	0.998010i	$0.479916\pi$
$12$	−4.43903e7	−	4.43903e7i	−0.103238	−	0.103238i
$13$	3.12551e8	−	3.12551e8i	0.383155	−	0.383155i	−0.489083	−	0.872237i	$-0.662668\pi$
$13$	3.12551e8	−	3.12551e8i	0.383155	−	0.383155i	0.872237	+	0.489083i	$0.162668\pi$
$14$		−	5.94626e7i		−	0.0402920i
$15$	3.39902e8	−	6.66720e8i	0.132625	−	0.260144i
$16$	−1.07374e9			−0.250000
$17$	−4.95457e9	−	4.95457e9i	−0.710256	−	0.710256i	0.256333	−	0.966589i	$-0.417486\pi$
$17$	−4.95457e9	−	4.95457e9i	−0.710256	−	0.710256i	−0.966589	+	0.256333i	$0.917486\pi$
$18$	5.04018e9	−	5.04018e9i	0.457368	−	0.457368i
$19$		−	2.77790e10i		−	1.63564i	−0.575472	−	0.817821i	$-0.695182\pi$
$19$		−	2.77790e10i		−	1.63564i	0.575472	−	0.817821i	$-0.304818\pi$
$20$	−3.95264e9	−	1.21744e10i	−0.154400	−	0.475563i
$21$	−6.29320e8			−0.0166386
$22$	−3.46011e9	−	3.46011e9i	−0.0630535	−	0.0630535i
$23$	4.85746e10	−	4.85746e10i	0.620278	−	0.620278i	−0.325325	−	0.945602i	$-0.605474\pi$
$23$	4.85746e10	−	4.85746e10i	0.620278	−	0.620278i	0.945602	+	0.325325i	$0.105474\pi$
$24$			1.13639e10i			0.103238i
$25$	1.23487e11	−	8.96326e10i	0.809285	−	0.587416i
$26$	−8.00131e10			−0.383155
$27$	−1.11657e11	−	1.11657e11i	−0.395345	−	0.395345i
$28$	−7.61121e9	+	7.61121e9i	−0.0201460	+	0.0201460i
$29$			1.69301e11i			0.338435i	0.985579	+	0.169218i	$0.0541241\pi$
$29$			1.69301e11i			0.338435i	−0.985579	+	0.169218i	$0.945876\pi$
$30$	−1.28848e11	+	4.18326e10i	−0.196384	+	0.0637595i
$31$	−8.83369e10			−0.103573			−0.0517867	−	0.998658i	$-0.516492\pi$
$31$	−8.83369e10			−0.103573			−0.0517867	+	0.998658i	$0.516492\pi$
$32$	1.37439e11	+	1.37439e11i	0.125000	+	0.125000i
$33$	−3.66200e10	+	3.66200e10i	−0.0260379	+	0.0260379i
$34$			1.26837e12i			0.710256i
$35$	−1.14317e11	−	5.82800e10i	−0.0507650	−	0.0258807i
$36$	−1.29029e12			−0.457368
$37$	3.82867e12	+	3.82867e12i	1.09002	+	1.09002i	0.995525	+	0.0944949i	$0.0301236\pi$
$37$	3.82867e12	+	3.82867e12i	1.09002	+	1.09002i	0.0944949	+	0.995525i	$0.469876\pi$
$38$	−3.55572e12	+	3.55572e12i	−0.817821	+	0.817821i
$39$			8.46815e11i			0.158224i
$40$	−1.05239e12	+	2.06426e12i	−0.160582	+	0.314982i
$41$	1.29691e12			0.162420			0.0812099	−	0.996697i	$-0.474122\pi$
$41$	1.29691e12			0.162420			0.0812099	+	0.996697i	$0.474122\pi$
$42$	8.05529e10	+	8.05529e10i	0.00831931	+	0.00831931i
$43$	1.34076e13	−	1.34076e13i	1.14711	−	1.14711i	0.159987	−	0.987119i	$-0.448855\pi$
$43$	1.34076e13	−	1.34076e13i	1.14711	−	1.14711i	0.987119	−	0.159987i	$-0.0511452\pi$
$44$			8.85789e11i			0.0630535i
$45$	−4.74978e12	−	1.46297e13i	−0.282471	−	0.870030i
$46$	−1.24351e13			−0.620278
$47$	−5.93778e12	−	5.93778e12i	−0.249368	−	0.249368i	0.571343	−	0.820711i	$-0.306423\pi$
$47$	−5.93778e12	−	5.93778e12i	−0.249368	−	0.249368i	−0.820711	+	0.571343i	$0.806423\pi$
$48$	1.45458e12	−	1.45458e12i	0.0516188	−	0.0516188i
$49$		−	3.31250e13i		−	0.996753i
$50$	−2.72793e13	−	4.33338e12i	−0.698351	−	0.110935i
$51$	1.34238e13			0.293300
$52$	1.02417e13	+	1.02417e13i	0.191577	+	0.191577i
$53$	4.58521e13	−	4.58521e13i	0.736466	−	0.736466i	−0.235426	−	0.971892i	$-0.575649\pi$
$53$	4.58521e13	−	4.58521e13i	0.736466	−	0.736466i	0.971892	+	0.235426i	$0.0756487\pi$
$54$			2.85842e13i			0.395345i
$55$	−1.00434e13	+	3.26075e12i	−0.119944	+	0.0389418i
$56$	1.94847e12			0.0201460
$57$	3.76318e13	+	3.76318e13i	0.337719	+	0.337719i
$58$	2.16705e13	−	2.16705e13i	0.169218	−	0.169218i
$59$			2.43196e14i			1.65631i	0.560501	+	0.828154i	$0.310609\pi$
$59$			2.43196e14i			1.65631i	−0.560501	+	0.828154i	$0.689391\pi$
$60$	2.18471e13	+	1.11379e13i	0.130072	+	0.0663123i
$61$	−2.08301e14			−1.08656			−0.543280	−	0.839552i	$-0.682818\pi$
$61$	−2.08301e14			−1.08656			−0.543280	+	0.839552i	$0.682818\pi$
$62$	1.13071e13	+	1.13071e13i	0.0517867	+	0.0517867i
$63$	−9.14618e12	+	9.14618e12i	−0.0368566	+	0.0368566i
$64$		−	3.51844e13i		−	0.125000i
$65$	−7.84219e13	+	1.53825e14i	−0.246111	+	0.482747i
$66$	9.37472e12			0.0260379
$67$	3.69388e13	+	3.69388e13i	0.0909672	+	0.0909672i	0.751126	−	0.660159i	$-0.229511\pi$
$67$	3.69388e13	+	3.69388e13i	0.0909672	+	0.0909672i	−0.660159	+	0.751126i	$0.729511\pi$
$68$	1.62351e14	−	1.62351e14i	0.355128	−	0.355128i
$69$			1.31606e14i			0.256144i
$70$	7.17267e12	+	2.20924e13i	0.0124422	+	0.0383229i
$71$	−4.12269e14			−0.638431			−0.319215	−	0.947682i	$-0.603419\pi$
$71$	−4.12269e14			−0.638431			−0.319215	+	0.947682i	$0.603419\pi$
$72$	1.65157e14	+	1.65157e14i	0.228684	+	0.228684i
$73$	1.10105e14	−	1.10105e14i	0.136529	−	0.136529i	−0.635540	−	0.772068i	$-0.719222\pi$
$73$	1.10105e14	−	1.10105e14i	0.136529	−	0.136529i	0.772068	+	0.635540i	$0.219222\pi$
$74$		−	9.80140e14i		−	1.09002i
$75$	−4.58622e13	+	2.88710e14i	−0.0458104	+	0.288384i
$76$	9.10263e14			0.817821
$77$	6.27891e12	+	6.27891e12i	0.00508111	+	0.00508111i
$78$	1.08392e14	−	1.08392e14i	0.0791119	−	0.0791119i
$79$		−	2.00631e15i		−	1.32246i	−0.750184	−	0.661230i	$-0.770035\pi$
$79$		−	2.00631e15i		−	1.32246i	0.750184	−	0.661230i	$-0.229965\pi$
$80$	3.98932e14	−	1.29520e14i	0.237782	−	0.0772000i
$81$	−1.39250e15			−0.751478
$82$	−1.66005e14	−	1.66005e14i	−0.0812099	−	0.0812099i
$83$	1.15652e13	−	1.15652e13i	0.00513487	−	0.00513487i	−0.704535	−	0.709670i	$-0.748844\pi$
$83$	1.15652e13	−	1.15652e13i	0.00513487	−	0.00513487i	0.709670	+	0.704535i	$0.248844\pi$
$84$		−	2.06216e13i		−	0.00831931i
$85$	2.43844e15	+	1.24315e15i	0.894871	+	0.456217i
$86$	−3.43235e15			−1.14711
$87$	−2.29349e14	−	2.29349e14i	−0.0698785	−	0.0698785i
$88$	1.13381e14	−	1.13381e14i	0.0315267	−	0.0315267i
$89$		−	2.86189e15i		−	0.726997i	−0.931595	−	0.363499i	$-0.881582\pi$
$89$		−	2.86189e15i		−	0.726997i	0.931595	−	0.363499i	$-0.118418\pi$
$90$	−1.26463e15	+	2.48057e15i	−0.293780	+	0.576250i
$91$	1.45196e14			0.0308762
$92$	1.59169e15	+	1.59169e15i	0.310139	+	0.310139i
$93$	1.19668e14	−	1.19668e14i	0.0213853	−	0.0213853i
$94$			1.52007e15i			0.249368i
$95$	3.35085e15	+	1.03209e16i	0.505086	+	1.55570i
$96$	−3.72372e14			−0.0516188
$97$	3.85105e15	+	3.85105e15i	0.491366	+	0.491366i	0.908736	−	0.417371i	$-0.137048\pi$
$97$	3.85105e15	+	3.85105e15i	0.491366	+	0.491366i	−0.417371	+	0.908736i	$0.637048\pi$
$98$	−4.24000e15	+	4.24000e15i	−0.498377	+	0.498377i
$99$			1.06443e15i			0.115355i
$100$	2.93708e15	+	4.04643e15i	0.293708	+	0.404643i
$101$	−1.27584e16			−1.17822			−0.589111	−	0.808052i	$-0.700522\pi$
$101$	−1.27584e16			−1.17822			−0.589111	+	0.808052i	$0.700522\pi$
$102$	−1.71824e15	−	1.71824e15i	−0.146650	−	0.146650i
$103$	1.67059e16	−	1.67059e16i	1.31878	−	1.31878i	0.404040	−	0.914741i	$-0.367606\pi$
$103$	1.67059e16	−	1.67059e16i	1.31878	−	1.31878i	0.914741	−	0.404040i	$-0.132394\pi$
$104$		−	2.62187e15i		−	0.191577i
$105$	2.33814e14	−	7.59117e13i	0.0158254	−	0.00513800i
$106$	−1.17381e16			−0.736466
$107$	−1.73529e15	−	1.73529e15i	−0.100995	−	0.100995i	0.654804	−	0.755799i	$-0.272751\pi$
$107$	−1.73529e15	−	1.73529e15i	−0.100995	−	0.100995i	−0.755799	+	0.654804i	$0.772751\pi$
$108$	3.65878e15	−	3.65878e15i	0.197673	−	0.197673i
$109$		−	3.03259e16i		−	1.52196i	−0.648778	−	0.760978i	$-0.724720\pi$
$109$		−	3.03259e16i		−	1.52196i	0.648778	−	0.760978i	$-0.275280\pi$
$110$	1.70293e15	+	8.68174e14i	0.0794428	+	0.0405009i
$111$	−1.03733e16			−0.450124
$112$	−2.49404e14	−	2.49404e14i	−0.0100730	−	0.0100730i
$113$	1.46505e16	−	1.46505e16i	0.551094	−	0.551094i	−0.375663	−	0.926756i	$-0.622585\pi$
$113$	1.46505e16	−	1.46505e16i	0.551094	−	0.551094i	0.926756	+	0.375663i	$0.122585\pi$
$114$		−	9.63374e15i		−	0.337719i
$115$	−1.21878e16	+	2.39064e16i	−0.398421	+	0.781505i
$116$	−5.54766e15			−0.169218
$117$	1.23071e16	+	1.23071e16i	0.350485	+	0.350485i
$118$	3.11291e16	−	3.11291e16i	0.828154	−	0.828154i
$119$		−	2.30165e15i		−	0.0572353i
$120$	−1.37077e15	−	4.22208e15i	−0.0318798	−	0.0981920i
$121$	−4.52190e16			−0.984097
$122$	2.66626e16	+	2.66626e16i	0.543280	+	0.543280i
$123$	−1.75690e15	+	1.75690e15i	−0.0335357	+	0.0335357i
$124$		−	2.89462e15i		−	0.0517867i
$125$	−3.50677e16	+	4.81972e16i	−0.588339	+	0.808615i
$126$	2.34142e15			0.0368566
$127$	6.73668e16	+	6.73668e16i	0.995443	+	0.995443i	0.999990	−	0.00454714i	$-0.00144740\pi$
$127$	6.73668e16	+	6.73668e16i	0.995443	+	0.995443i	−0.00454714	+	0.999990i	$0.501447\pi$
$128$	−4.50360e15	+	4.50360e15i	−0.0625000	+	0.0625000i
$129$			3.63261e16i			0.473698i
$130$	2.97276e16	−	9.65158e15i	0.364429	−	0.118318i
$131$	−8.74864e16			−1.00872			−0.504359	−	0.863494i	$-0.668271\pi$
$131$	−8.74864e16			−1.00872			−0.504359	+	0.863494i	$0.668271\pi$
$132$	−1.19996e15	−	1.19996e15i	−0.0130190	−	0.0130190i
$133$	6.45239e15	−	6.45239e15i	0.0659034	−	0.0659034i
$134$		−	9.45634e15i		−	0.0909672i
$135$	5.49531e16	+	2.80158e16i	0.498106	+	0.253941i
$136$	−4.15620e16			−0.355128
$137$	−1.11665e17	−	1.11665e17i	−0.899816	−	0.899816i	0.0956031	−	0.995420i	$-0.469522\pi$
$137$	−1.11665e17	−	1.11665e17i	−0.899816	−	0.899816i	−0.995420	+	0.0956031i	$0.969522\pi$
$138$	1.68456e16	−	1.68456e16i	0.128072	−	0.128072i
$139$			9.45135e16i			0.678227i	0.940745	+	0.339114i	$0.110127\pi$
$139$			9.45135e16i			0.678227i	−0.940745	+	0.339114i	$0.889873\pi$
$140$	1.90972e15	−	3.74592e15i	0.0129403	−	0.0253825i
$141$	1.60876e16			0.102977
$142$	5.27704e16	+	5.27704e16i	0.319215	+	0.319215i
$143$	8.44892e15	−	8.44892e15i	0.0483185	−	0.0483185i
$144$		−	4.22801e16i		−	0.228684i
$145$	−2.04219e16	−	6.29011e16i	−0.104509	−	0.321895i
$146$	−2.81869e16			−0.136529
$147$	4.48739e16	+	4.48739e16i	0.205805	+	0.205805i
$148$	−1.25458e17	+	1.25458e17i	−0.545010	+	0.545010i
$149$		−	3.09214e17i		−	1.27283i	−0.771349	−	0.636413i	$-0.780418\pi$
$149$		−	3.09214e17i		−	1.27283i	0.771349	−	0.636413i	$-0.219582\pi$
$150$	4.28252e16	−	3.10845e16i	0.167097	−	0.121287i
$151$	5.31351e17			1.96592			0.982960	−	0.183819i	$-0.0588462\pi$
$151$	5.31351e17			1.96592			0.982960	+	0.183819i	$0.0588462\pi$
$152$	−1.16514e17	−	1.16514e17i	−0.408911	−	0.408911i
$153$	1.95093e17	−	1.95093e17i	0.649697	−	0.649697i
$154$		−	1.60740e15i		−	0.00508111i
$155$	3.28202e16	−	1.06556e16i	0.0985115	−	0.0319835i
$156$	−2.77484e16			−0.0791119
$157$	−4.59200e17	−	4.59200e17i	−1.24396	−	1.24396i	−0.958346	−	0.285610i	$-0.907804\pi$
$157$	−4.59200e17	−	4.59200e17i	−1.24396	−	1.24396i	−0.285610	−	0.958346i	$-0.592196\pi$
$158$	−2.56808e17	+	2.56808e17i	−0.661230	+	0.661230i
$159$			1.24230e17i			0.304124i
$160$	−6.76418e16	−	3.44847e16i	−0.157491	−	0.0802909i
$161$	2.25654e16			0.0499845
$162$	1.78241e17	+	1.78241e17i	0.375739	+	0.375739i
$163$	−3.09128e17	+	3.09128e17i	−0.620351	+	0.620351i	−0.945621	−	0.325270i	$-0.894545\pi$
$163$	−3.09128e17	+	3.09128e17i	−0.620351	+	0.620351i	0.325270	+	0.945621i	$0.394545\pi$
$164$			4.24972e16i			0.0812099i
$165$	9.18828e15	−	1.80229e16i	0.0167249	−	0.0328059i
$166$	−2.96070e15			−0.00513487
$167$	−5.24550e16	−	5.24550e16i	−0.0867072	−	0.0867072i	0.662423	−	0.749130i	$-0.269528\pi$
$167$	−5.24550e16	−	5.24550e16i	−0.0867072	−	0.0867072i	−0.749130	+	0.662423i	$0.769528\pi$
$168$	−2.63956e15	+	2.63956e15i	−0.00415965	+	0.00415965i
$169$			4.70040e17i			0.706385i
$170$	−1.52997e17	−	4.71243e17i	−0.219327	−	0.675544i
$171$	1.09384e18			1.49618
$172$	4.39340e17	+	4.39340e17i	0.573553	+	0.573553i
$173$	−7.17636e17	+	7.17636e17i	−0.894407	+	0.894407i	−0.994934	−	0.100527i	$-0.967947\pi$
$173$	−7.17636e17	+	7.17636e17i	−0.894407	+	0.894407i	0.100527	+	0.994934i	$0.467947\pi$
$174$			5.87134e16i			0.0698785i
$175$	4.95025e16	+	7.86358e15i	0.0562759	+	0.00893956i
$176$	−2.90255e16			−0.0315267
$177$	−3.29454e17	−	3.29454e17i	−0.341986	−	0.341986i
$178$	−3.66322e17	+	3.66322e17i	−0.363499	+	0.363499i
$179$			1.72973e18i			1.64117i	0.571522	+	0.820587i	$0.306353\pi$
$179$			1.72973e18i			1.64117i	−0.571522	+	0.820587i	$0.693647\pi$
$180$	4.79385e17	−	1.55641e17i	0.435015	−	0.141235i
$181$	8.26166e17			0.717197			0.358599	−	0.933492i	$-0.383255\pi$
$181$	8.26166e17			0.717197			0.358599	+	0.933492i	$0.383255\pi$
$182$	−1.85851e16	−	1.85851e16i	−0.0154381	−	0.0154381i
$183$	2.82182e17	−	2.82182e17i	0.224348	−	0.224348i
$184$		−	4.07473e17i		−	0.310139i
$185$	−1.88432e18	−	9.60649e17i	−1.37335	−	0.700149i
$186$	−3.06351e16			−0.0213853
$187$	−1.33933e17	−	1.33933e17i	−0.0895682	−	0.0895682i
$188$	1.94569e17	−	1.94569e17i	0.124684	−	0.124684i
$189$		−	5.18705e16i		−	0.0318585i
$190$	8.92161e17	−	1.74998e18i	0.525309	−	1.03040i
$191$	−7.16133e17			−0.404322			−0.202161	−	0.979352i	$-0.564796\pi$
$191$	−7.16133e17			−0.404322			−0.202161	+	0.979352i	$0.564796\pi$
$192$	4.76637e16	+	4.76637e16i	0.0258094	+	0.0258094i
$193$	1.19980e18	−	1.19980e18i	0.623233	−	0.623233i	−0.323123	−	0.946357i	$-0.604733\pi$
$193$	1.19980e18	−	1.19980e18i	0.623233	−	0.623233i	0.946357	+	0.323123i	$0.104733\pi$
$194$		−	9.85868e17i		−	0.491366i
$195$	−1.02147e17	−	3.14621e17i	−0.0488595	−	0.150491i
$196$	1.08544e18			0.498377
$197$	−2.63818e18	−	2.63818e18i	−1.16299	−	1.16299i	−0.983819	−	0.179167i	$-0.942660\pi$
$197$	−2.63818e18	−	2.63818e18i	−1.16299	−	1.16299i	−0.179167	−	0.983819i	$-0.557340\pi$
$198$	1.36247e17	−	1.36247e17i	0.0576773	−	0.0576773i
$199$			1.72936e18i			0.703171i	0.936156	+	0.351586i	$0.114357\pi$
$199$			1.72936e18i			0.703171i	−0.936156	+	0.351586i	$0.885643\pi$
$200$	1.41996e17	−	8.93889e17i	0.0554673	−	0.349175i
$201$	−1.00081e17			−0.0375649
$202$	1.63308e18	+	1.63308e18i	0.589111	+	0.589111i
$203$	−3.93245e16	+	3.93245e16i	−0.0136363	+	0.0136363i
$204$			4.39870e17i			0.146650i
$205$	−4.81846e17	+	1.56440e17i	−0.154482	+	0.0501553i
$206$	−4.27672e18			−1.31878
$207$	1.91269e18	+	1.91269e18i	0.567391	+	0.567391i
$208$	−3.35599e17	+	3.35599e17i	−0.0957887	+	0.0957887i
$209$		−	7.50927e17i		−	0.206266i
$210$	−3.96449e16	−	2.02115e16i	−0.0104817	−	0.00534371i
$211$	7.18729e18			1.82939			0.914693	−	0.404148i	$-0.132432\pi$
$211$	7.18729e18			1.82939			0.914693	+	0.404148i	$0.132432\pi$
$212$	1.50248e18	+	1.50248e18i	0.368233	+	0.368233i
$213$	5.58494e17	−	5.58494e17i	0.131820	−	0.131820i
$214$			4.44233e17i			0.100995i
$215$	−3.36409e18	+	6.59867e18i	−0.736817	+	1.44527i
$216$	−9.36649e17			−0.197673
$217$	−2.05185e16	−	2.05185e16i	−0.00417319	−	0.00417319i
$218$	−3.88172e18	+	3.88172e18i	−0.760978	+	0.760978i
$219$			2.98315e17i			0.0563796i
$220$	−1.06848e17	−	3.29101e17i	−0.0194709	−	0.0599718i
$221$	−3.09711e18			−0.544276
$222$	1.32778e18	+	1.32778e18i	0.225062	+	0.225062i
$223$	2.52554e18	−	2.52554e18i	0.412967	−	0.412967i	−0.469804	−	0.882771i	$-0.655675\pi$
$223$	2.52554e18	−	2.52554e18i	0.412967	−	0.412967i	0.882771	+	0.469804i	$0.155675\pi$
$224$			6.38474e16i			0.0100730i
$225$	3.52941e18	+	4.86248e18i	0.537331	+	0.740282i
$226$	−3.75053e18			−0.551094
$227$	−6.53398e18	−	6.53398e18i	−0.926768	−	0.926768i	0.0707276	−	0.997496i	$-0.477468\pi$
$227$	−6.53398e18	−	6.53398e18i	−0.926768	−	0.926768i	−0.997496	+	0.0707276i	$0.977468\pi$
$228$	−1.23312e18	+	1.23312e18i	−0.168860	+	0.168860i
$229$		−	5.12668e18i		−	0.677880i	−0.940808	−	0.338940i	$-0.889932\pi$
$229$		−	5.12668e18i		−	0.677880i	0.940808	−	0.338940i	$-0.110068\pi$
$230$	4.62006e18	−	1.49998e18i	0.589963	−	0.191542i
$231$	−1.70119e16			−0.00209824
$232$	7.10100e17	+	7.10100e17i	0.0846088	+	0.0846088i
$233$	4.64327e18	−	4.64327e18i	0.534536	−	0.534536i	−0.387383	−	0.921919i	$-0.626621\pi$
$233$	4.64327e18	−	4.64327e18i	0.534536	−	0.534536i	0.921919	+	0.387383i	$0.126621\pi$
$234$		−	3.15063e18i		−	0.350485i
$235$	2.92233e18	+	1.48984e18i	0.314186	+	0.160176i
$236$	−7.96906e18			−0.828154
$237$	2.71792e18	+	2.71792e18i	0.273055	+	0.273055i
$238$	−2.94612e17	+	2.94612e17i	−0.0286177	+	0.0286177i
$239$		−	7.37163e18i		−	0.692437i	−0.938154	−	0.346219i	$-0.887466\pi$
$239$		−	7.37163e18i		−	0.692437i	0.938154	−	0.346219i	$-0.112534\pi$
$240$	−3.64967e17	+	7.15885e17i	−0.0331561	+	0.0650359i
$241$	−2.52890e18			−0.222226			−0.111113	−	0.993808i	$-0.535442\pi$
$241$	−2.52890e18			−0.222226			−0.111113	+	0.993808i	$0.535442\pi$
$242$	5.78803e18	+	5.78803e18i	0.492049	+	0.492049i
$243$	6.69288e18	−	6.69288e18i	0.550507	−	0.550507i
$244$		−	6.82562e18i		−	0.543280i
$245$	3.99571e18	+	1.23071e19i	0.307797	+	0.948039i
$246$	4.49767e17			0.0335357
$247$	−8.68237e18	−	8.68237e18i	−0.626704	−	0.626704i
$248$	−3.70512e17	+	3.70512e17i	−0.0258934	+	0.0258934i
$249$			3.13344e16i			0.00212045i
$250$	1.06579e19	−	1.68057e18i	0.698477	−	0.110138i
$251$	−1.41412e19			−0.897625			−0.448813	−	0.893626i	$-0.648153\pi$
$251$	−1.41412e19			−0.897625			−0.448813	+	0.893626i	$0.648153\pi$
$252$	−2.99702e17	−	2.99702e17i	−0.0184283	−	0.0184283i
$253$	1.31307e18	−	1.31307e18i	0.0782213	−	0.0782213i
$254$		−	1.72459e19i		−	0.995443i
$255$	−4.98738e18	+	1.61924e18i	−0.278966	+	0.0905712i
$256$	1.15292e18			0.0625000
$257$	5.94981e18	+	5.94981e18i	0.312635	+	0.312635i	0.845930	−	0.533294i	$-0.179046\pi$
$257$	5.94981e18	+	5.94981e18i	0.312635	+	0.312635i	−0.533294	+	0.845930i	$0.679046\pi$
$258$	4.64974e18	−	4.64974e18i	0.236849	−	0.236849i
$259$			1.77862e18i			0.0878383i
$260$	−5.04053e18	−	2.56973e18i	−0.241373	−	0.123055i
$261$	−6.66646e18			−0.309579
$262$	1.11983e19	+	1.11983e19i	0.504359	+	0.504359i
$263$	−3.83686e18	+	3.83686e18i	−0.167622	+	0.167622i	−0.785933	−	0.618311i	$-0.787817\pi$
$263$	−3.83686e18	+	3.83686e18i	−0.167622	+	0.167622i	0.618311	+	0.785933i	$0.287817\pi$
$264$			3.07191e17i			0.0130190i
$265$	−1.15047e19	+	2.25665e19i	−0.473052	+	0.927893i
$266$	−1.65181e18			−0.0659034
$267$	3.87695e18	+	3.87695e18i	0.150107	+	0.150107i
$268$	−1.21041e18	+	1.21041e18i	−0.0454836	+	0.0454836i
$269$			3.18679e19i			1.16234i	0.813781	+	0.581172i	$0.197406\pi$
$269$			3.18679e19i			1.16234i	−0.813781	+	0.581172i	$0.802594\pi$
$270$	−3.44797e18	−	1.06200e19i	−0.122083	−	0.376024i
$271$	−1.78334e19			−0.613028			−0.306514	−	0.951866i	$-0.599163\pi$
$271$	−1.78334e19			−0.613028			−0.306514	+	0.951866i	$0.599163\pi$
$272$	5.31993e18	+	5.31993e18i	0.177564	+	0.177564i
$273$	−1.96695e17	+	1.96695e17i	−0.00637516	+	0.00637516i
$274$			2.85863e19i			0.899816i
$275$	3.33812e18	−	2.42296e18i	0.102056	−	0.0740772i
$276$	−4.31248e18			−0.128072
$277$	4.93172e17	+	4.93172e17i	0.0142285	+	0.0142285i	0.714185	−	0.699957i	$-0.246797\pi$
$277$	4.93172e17	+	4.93172e17i	0.0142285	+	0.0142285i	−0.699957	+	0.714185i	$0.746797\pi$
$278$	1.20977e19	−	1.20977e19i	0.339114	−	0.339114i
$279$		−	3.47839e18i		−	0.0947424i
$280$	−7.23923e17	+	2.35034e17i	−0.0191614	+	0.00622109i
$281$	5.65921e19			1.45581			0.727906	−	0.685677i	$-0.240494\pi$
$281$	5.65921e19			1.45581			0.727906	+	0.685677i	$0.240494\pi$
$282$	−2.05921e18	−	2.05921e18i	−0.0514883	−	0.0514883i
$283$	−9.52383e18	+	9.52383e18i	−0.231484	+	0.231484i	−0.813312	−	0.581828i	$-0.802338\pi$
$283$	−9.52383e18	+	9.52383e18i	−0.231484	+	0.231484i	0.581828	+	0.813312i	$0.302338\pi$
$284$		−	1.35092e19i		−	0.319215i
$285$	−1.85208e19	−	9.44216e18i	−0.425502	−	0.216926i
$286$	−2.16292e18			−0.0483185
$287$	3.01241e17	+	3.01241e17i	0.00654423	+	0.00654423i
$288$	−5.41185e18	+	5.41185e18i	−0.114342	+	0.114342i
$289$			4.34393e17i			0.00892689i
$290$	−5.43733e18	+	1.06653e19i	−0.108693	+	0.213202i
$291$	−1.04339e19			−0.202910
$292$	3.60792e18	+	3.60792e18i	0.0682644	+	0.0682644i
$293$	5.13529e19	−	5.13529e19i	0.945419	−	0.945419i	−0.0531670	−	0.998586i	$-0.516932\pi$
$293$	5.13529e19	−	5.13529e19i	0.945419	−	0.945419i	0.998586	+	0.0531670i	$0.0169316\pi$
$294$		−	1.14877e19i		−	0.205805i
$295$	−2.93356e19	−	9.03557e19i	−0.511468	−	1.57536i
$296$	3.21172e19			0.545010
$297$	−3.01833e18	−	3.01833e18i	−0.0498558	−	0.0498558i
$298$	−3.95794e19	+	3.95794e19i	−0.636413	+	0.636413i
$299$		−	3.03641e19i		−	0.475325i
$300$	−9.46044e18	−	1.50281e18i	−0.144192	−	0.0229052i
$301$	6.22852e18			0.0924385
$302$	−6.80129e19	−	6.80129e19i	−0.982960	−	0.982960i
$303$	1.72837e19	−	1.72837e19i	0.243273	−	0.243273i
$304$			2.98275e19i			0.408911i
$305$	7.73911e19	−	2.51264e19i	1.03346	−	0.335530i
$306$	−4.99439e19			−0.649697
$307$	−7.49346e19	−	7.49346e19i	−0.949676	−	0.949676i	0.0491167	−	0.998793i	$-0.484359\pi$
$307$	−7.49346e19	−	7.49346e19i	−0.949676	−	0.949676i	−0.998793	+	0.0491167i	$0.984359\pi$
$308$	−2.05747e17	+	2.05747e17i	−0.00254055	+	0.00254055i
$309$			4.52625e19i			0.544591i
$310$	−5.56490e18	−	2.83706e18i	−0.0652475	−	0.0332640i
$311$	1.31750e20			1.50546			0.752728	−	0.658331i	$-0.228737\pi$
$311$	1.31750e20			1.50546			0.752728	+	0.658331i	$0.228737\pi$
$312$	3.55180e18	+	3.55180e18i	0.0395560	+	0.0395560i
$313$	−1.01705e20	+	1.01705e20i	−1.10405	+	1.10405i	−0.110133	+	0.993917i	$0.535128\pi$
$313$	−1.01705e20	+	1.01705e20i	−1.10405	+	1.10405i	−0.993917	+	0.110133i	$0.964872\pi$
$314$			1.17555e20i			1.24396i
$315$	2.29486e18	−	4.50137e18i	0.0236740	−	0.0464366i
$316$	6.57429e19			0.661230
$317$	9.24668e19	+	9.24668e19i	0.906801	+	0.906801i	0.996013	−	0.0892118i	$-0.0284348\pi$
$317$	9.24668e19	+	9.24668e19i	0.906801	+	0.906801i	−0.0892118	+	0.996013i	$0.528435\pi$
$318$	1.59015e19	−	1.59015e19i	0.152062	−	0.152062i
$319$			4.57657e18i			0.0426790i
$320$	4.24412e18	+	1.30722e19i	0.0386000	+	0.118891i
$321$	4.70153e18			0.0417060
$322$	−2.88837e18	−	2.88837e18i	−0.0249923	−	0.0249923i
$323$	−1.37633e20	+	1.37633e20i	−1.16172	+	1.16172i
$324$		−	4.56296e19i		−	0.375739i
$325$	1.05813e19	−	6.66108e19i	0.0850102	−	0.535153i
$326$	7.91367e19			0.620351
$327$	4.10820e19	+	4.10820e19i	0.314246	+	0.314246i
$328$	5.43964e18	−	5.43964e18i	0.0406050	−	0.0406050i
$329$		−	2.75840e18i		−	0.0200951i
$330$	−3.48303e18	+	1.13083e18i	−0.0247654	+	0.00804052i
$331$	−3.69873e19			−0.256701			−0.128351	−	0.991729i	$-0.540968\pi$
$331$	−3.69873e19			−0.256701			−0.128351	+	0.991729i	$0.540968\pi$
$332$	3.78969e17	+	3.78969e17i	0.00256743	+	0.00256743i
$333$	−1.50759e20	+	1.50759e20i	−0.997081	+	0.997081i
$334$			1.34285e19i			0.0867072i
$335$	−1.81798e19	−	9.26829e18i	−0.114612	−	0.0584307i
$336$	6.75727e17			0.00415965
$337$	−2.77882e19	−	2.77882e19i	−0.167040	−	0.167040i	0.618637	−	0.785677i	$-0.287685\pi$
$337$	−2.77882e19	−	2.77882e19i	−0.167040	−	0.167040i	−0.785677	+	0.618637i	$0.787685\pi$
$338$	6.01652e19	−	6.01652e19i	0.353192	−	0.353192i
$339$			3.96936e19i			0.227574i
$340$	−4.07354e19	+	7.99027e19i	−0.228108	+	0.447435i
$341$	−2.38793e18			−0.0130613
$342$	−1.40011e20	−	1.40011e20i	−0.748091	−	0.748091i
$343$	1.54133e19	−	1.54133e19i	0.0804533	−	0.0804533i
$344$		−	1.12471e20i		−	0.573553i
$345$	−1.58750e19	−	4.88962e19i	−0.0790972	−	0.243625i
$346$	1.83715e20			0.894407
$347$	1.52720e19	+	1.52720e19i	0.0726540	+	0.0726540i	0.742500	−	0.669846i	$-0.233640\pi$
$347$	1.52720e19	+	1.52720e19i	0.0726540	+	0.0726540i	−0.669846	+	0.742500i	$0.733640\pi$
$348$	7.51532e18	−	7.51532e18i	0.0349392	−	0.0349392i
$349$		−	3.11930e20i		−	1.41727i	−0.705574	−	0.708636i	$-0.749311\pi$
$349$		−	3.11930e20i		−	1.41727i	0.705574	−	0.708636i	$-0.250689\pi$
$350$	−5.32978e18	−	7.34286e18i	−0.0236682	−	0.0326078i
$351$	−6.97972e19			−0.302957
$352$	3.71527e18	+	3.71527e18i	0.0157634	+	0.0157634i
$353$	1.52339e20	−	1.52339e20i	0.631847	−	0.631847i	−0.316684	−	0.948531i	$-0.602569\pi$
$353$	1.52339e20	−	1.52339e20i	0.631847	−	0.631847i	0.948531	+	0.316684i	$0.102569\pi$
$354$			8.43402e19i			0.341986i
$355$	1.53172e20	−	4.97299e19i	0.607229	−	0.197147i
$356$	9.37784e19			0.363499
$357$	3.11801e18	+	3.11801e18i	0.0118177	+	0.0118177i
$358$	2.21406e20	−	2.21406e20i	0.820587	−	0.820587i
$359$			2.22424e20i			0.806168i	0.915163	+	0.403084i	$0.132062\pi$
$359$			2.22424e20i			0.806168i	−0.915163	+	0.403084i	$0.867938\pi$
$360$	−8.12833e19	−	4.14393e19i	−0.288125	−	0.146890i
$361$	−4.83233e20			−1.67533
$362$	−1.05749e20	−	1.05749e20i	−0.358599	−	0.358599i
$363$	6.12574e19	−	6.12574e19i	0.203192	−	0.203192i
$364$			4.75778e18i			0.0154381i
$365$	−2.76263e19	+	5.41892e19i	−0.0876962	+	0.172016i
$366$	−7.22387e19			−0.224348
$367$	2.14509e20	+	2.14509e20i	0.651804	+	0.651804i	0.953427	−	0.301623i	$-0.0975284\pi$
$367$	2.14509e20	+	2.14509e20i	0.651804	+	0.651804i	−0.301623	+	0.953427i	$0.597528\pi$
$368$	−5.21565e19	+	5.21565e19i	−0.155069	+	0.155069i
$369$			5.10676e19i			0.148571i
$370$	1.18229e20	+	3.64155e20i	0.336598	+	1.03675i
$371$	2.13007e19			0.0593474
$372$	3.92130e18	+	3.92130e18i	0.0106927	+	0.0106927i
$373$	1.17809e20	−	1.17809e20i	0.314418	−	0.314418i	−0.532201	−	0.846618i	$-0.678635\pi$
$373$	1.17809e20	−	1.17809e20i	0.314418	−	0.314418i	0.846618	+	0.532201i	$0.178635\pi$
$374$			3.42868e19i			0.0895682i
$375$	−1.77863e19	−	1.12798e20i	−0.0454815	−	0.288436i
$376$	−4.98097e19			−0.124684
$377$	5.29152e19	+	5.29152e19i	0.129673	+	0.129673i
$378$	−6.63942e18	+	6.63942e18i	−0.0159293	+	0.0159293i
$379$		−	2.34228e20i		−	0.550205i	−0.961415	−	0.275103i	$-0.911288\pi$
$379$		−	2.34228e20i		−	0.550205i	0.961415	−	0.275103i	$-0.0887118\pi$
$380$	−3.38194e20	+	1.09801e20i	−0.777852	+	0.252543i
$381$	−1.82521e20			−0.411068
$382$	9.16651e19	+	9.16651e19i	0.202161	+	0.202161i
$383$	1.84981e20	−	1.84981e20i	0.399519	−	0.399519i	−0.478544	−	0.878063i	$-0.658835\pi$
$383$	1.84981e20	−	1.84981e20i	0.399519	−	0.399519i	0.878063	+	0.478544i	$0.158835\pi$
$384$		−	1.22019e19i		−	0.0258094i
$385$	−3.09022e18	−	1.57543e18i	−0.00640182	−	0.00326373i
$386$	−3.07149e20			−0.623233
$387$	5.27943e20	+	5.27943e20i	1.04930	+	1.04930i
$388$	−1.26191e20	+	1.26191e20i	−0.245683	+	0.245683i
$389$		−	7.93216e19i		−	0.151285i	−0.997135	−	0.0756423i	$-0.975899\pi$
$389$		−	7.93216e19i		−	0.151285i	0.997135	−	0.0756423i	$-0.0241007\pi$
$390$	−2.71966e19	+	5.33463e19i	−0.0508157	+	0.0996752i
$391$	−4.81333e20			−0.881112
$392$	−1.38936e20	−	1.38936e20i	−0.249188	−	0.249188i
$393$	1.18516e20	−	1.18516e20i	0.208275	−	0.208275i
$394$			6.75374e20i			1.16299i
$395$	2.42012e20	+	7.45414e20i	0.408375	+	1.25783i
$396$	−3.48792e19			−0.0576773
$397$	−1.03072e20	−	1.03072e20i	−0.167039	−	0.167039i	0.618637	−	0.785677i	$-0.287685\pi$
$397$	−1.03072e20	−	1.03072e20i	−0.167039	−	0.167039i	−0.785677	+	0.618637i	$0.787685\pi$
$398$	2.21358e20	−	2.21358e20i	0.351586	−	0.351586i
$399$			1.74819e19i			0.0272148i
$400$	−1.32593e20	+	9.62422e19i	−0.202321	+	0.146854i
$401$	−2.22499e20			−0.332792			−0.166396	−	0.986059i	$-0.553213\pi$
$401$	−2.22499e20			−0.332792			−0.166396	+	0.986059i	$0.553213\pi$
$402$	1.28104e19	+	1.28104e19i	0.0187825	+	0.0187825i
$403$	−2.76098e19	+	2.76098e19i	−0.0396847	+	0.0396847i
$404$		−	4.18069e20i		−	0.589111i
$405$	5.17363e20	−	1.67971e20i	0.714751	−	0.232056i
$406$	1.00671e19			0.0136363
$407$	1.03497e20	+	1.03497e20i	0.137459	+	0.137459i
$408$	5.63033e19	−	5.63033e19i	0.0733251	−	0.0733251i
$409$		−	1.10470e21i		−	1.41077i	−0.708823	−	0.705386i	$-0.750774\pi$
$409$		−	1.10470e21i		−	1.41077i	0.708823	−	0.705386i	$-0.249226\pi$
$410$	8.17006e19	+	4.16520e19i	0.102319	+	0.0521633i
$411$	3.02542e20			0.371579
$412$	5.47420e20	+	5.47420e20i	0.659391	+	0.659391i
$413$	−5.64886e19	+	5.64886e19i	−0.0667360	+	0.0667360i
$414$		−	4.89649e20i		−	0.567391i
$415$	−2.90182e18	+	5.69193e18i	−0.00329826	+	0.00646956i
$416$	8.59134e19			0.0957887
$417$	−1.28036e20	−	1.28036e20i	−0.140037	−	0.140037i
$418$	−9.61186e19	+	9.61186e19i	−0.103133	+	0.103133i
$419$		−	3.89473e20i		−	0.409983i	−0.978764	−	0.204991i	$-0.934283\pi$
$419$		−	3.89473e20i		−	0.409983i	0.978764	−	0.204991i	$-0.0657166\pi$
$420$	2.48747e18	+	7.66161e18i	0.00256900	+	0.00791272i
$421$	−3.02146e20			−0.306168			−0.153084	−	0.988213i	$-0.548920\pi$
$421$	−3.02146e20			−0.306168			−0.153084	+	0.988213i	$0.548920\pi$
$422$	−9.19973e20	−	9.19973e20i	−0.914693	−	0.914693i
$423$	2.33808e20	−	2.33808e20i	0.228106	−	0.228106i
$424$		−	3.84636e20i		−	0.368233i
$425$	−1.05592e21	−	1.67735e20i	−0.992015	−	0.157584i
$426$	−1.42974e20			−0.131820
$427$	−4.83834e19	−	4.83834e19i	−0.0437797	−	0.0437797i
$428$	5.68619e19	−	5.68619e19i	0.0504976	−	0.0504976i
$429$			2.28912e19i			0.0199531i
$430$	1.27523e21	−	4.14027e20i	1.09104	−	0.354226i
$431$	−5.88414e19			−0.0494157			−0.0247079	−	0.999695i	$-0.507866\pi$
$431$	−5.88414e19			−0.0494157			−0.0247079	+	0.999695i	$0.507866\pi$
$432$	1.19891e20	+	1.19891e20i	0.0988363	+	0.0988363i
$433$	−3.43128e20	+	3.43128e20i	−0.277685	+	0.277685i	−0.832184	−	0.554499i	$-0.812910\pi$
$433$	−3.43128e20	+	3.43128e20i	−0.277685	+	0.277685i	0.554499	+	0.832184i	$0.312910\pi$
$434$			5.25274e18i			0.00417319i
$435$	1.12876e20	+	5.75458e19i	0.0880418	+	0.0448848i
$436$	9.93720e20			0.760978
$437$	−1.34935e21	−	1.34935e21i	−1.01455	−	1.01455i
$438$	3.81843e19	−	3.81843e19i	0.0281898	−	0.0281898i
$439$			8.49015e20i			0.615459i	0.951474	+	0.307729i	$0.0995692\pi$
$439$			8.49015e20i			0.615459i	−0.951474	+	0.307729i	$0.900431\pi$
$440$	−2.84483e19	+	5.58015e19i	−0.0202505	+	0.0397214i
$441$	1.30434e21			0.911766
$442$	3.96431e20	+	3.96431e20i	0.272138	+	0.272138i
$443$	−1.42170e21	+	1.42170e21i	−0.958471	+	0.958471i	−0.999171	−	0.0407006i	$-0.987041\pi$
$443$	−1.42170e21	+	1.42170e21i	−0.958471	+	0.958471i	0.0407006	+	0.999171i	$0.487041\pi$
$444$		−	3.39912e20i		−	0.225062i
$445$	3.45215e20	+	1.06329e21i	0.224497	+	0.691467i
$446$	−6.46539e20			−0.412967
$447$	4.18887e20	+	4.18887e20i	0.262807	+	0.262807i
$448$	8.17247e18	−	8.17247e18i	0.00503651	−	0.00503651i
$449$			2.72118e21i			1.64735i	0.567060	+	0.823677i	$0.308081\pi$
$449$			2.72118e21i			1.64735i	−0.567060	+	0.823677i	$0.691919\pi$
$450$	1.70633e20	−	1.07416e21i	0.101476	−	0.638806i
$451$	3.50583e19			0.0204823
$452$	4.80068e20	+	4.80068e20i	0.275547	+	0.275547i
$453$	−7.19812e20	+	7.19812e20i	−0.405914	+	0.405914i
$454$			1.67270e21i			0.926768i
$455$	−5.39452e19	+	1.75143e19i	−0.0293672	+	0.00953456i
$456$	3.15678e20			0.168860
$457$	−3.54744e19	−	3.54744e19i	−0.0186460	−	0.0186460i	0.697722	−	0.716368i	$-0.254197\pi$
$457$	−3.54744e19	−	3.54744e19i	−0.0186460	−	0.0186460i	−0.716368	+	0.697722i	$0.754197\pi$
$458$	−6.56215e20	+	6.56215e20i	−0.338940	+	0.338940i
$459$			1.10643e21i			0.561593i
$460$	−7.83365e20	−	3.99370e20i	−0.390752	−	0.199211i
$461$	2.46688e21			1.20932			0.604659	−	0.796484i	$-0.293309\pi$
$461$	2.46688e21			1.20932			0.604659	+	0.796484i	$0.293309\pi$
$462$	2.17752e18	+	2.17752e18i	0.00104912	+	0.00104912i
$463$	1.54920e21	−	1.54920e21i	0.733601	−	0.733601i	−0.237730	−	0.971331i	$-0.576403\pi$
$463$	1.54920e21	−	1.54920e21i	0.733601	−	0.733601i	0.971331	+	0.237730i	$0.0764033\pi$
$464$		−	1.81786e20i		−	0.0846088i
$465$	−3.00259e19	+	5.88959e19i	−0.0137364	+	0.0269440i
$466$	−1.18868e21			−0.534536
$467$	−2.63646e21	−	2.63646e21i	−1.16543	−	1.16543i	−0.983269	−	0.182160i	$-0.941691\pi$
$467$	−2.63646e21	−	2.63646e21i	−1.16543	−	1.16543i	−0.182160	−	0.983269i	$-0.558309\pi$
$468$	−4.03280e20	+	4.03280e20i	−0.175243	+	0.175243i
$469$			1.71600e19i			0.00733051i
$470$	−1.83359e20	−	5.64758e20i	−0.0770049	−	0.237181i
$471$	1.24414e21			0.513692
$472$	1.02004e21	+	1.02004e21i	0.414077	+	0.414077i
$473$	3.62436e20	−	3.62436e20i	0.144658	−	0.144658i
$474$		−	6.95788e20i		−	0.273055i
$475$	−2.48991e21	−	3.43035e21i	−0.960803	−	1.32370i
$476$	7.54206e19			0.0286177
$477$	1.80549e21	+	1.80549e21i	0.673672	+	0.673672i
$478$	−9.43569e20	+	9.43569e20i	−0.346219	+	0.346219i
$479$		−	1.92281e21i		−	0.693828i	−0.937897	−	0.346914i	$-0.887230\pi$
$479$		−	1.92281e21i		−	0.693828i	0.937897	−	0.346914i	$-0.112770\pi$
$480$	1.38349e20	−	4.49174e19i	0.0490960	−	0.0159399i
$481$	2.39331e21			0.835293
$482$	3.23699e20	+	3.23699e20i	0.111113	+	0.111113i
$483$	−3.05689e19	+	3.05689e19i	−0.0103206	+	0.0103206i
$484$		−	1.48174e21i		−	0.492049i
$485$	−1.89533e21	−	9.66262e20i	−0.619085	−	0.315617i
$486$	−1.71338e21			−0.550507
$487$	−2.05301e21	−	2.05301e21i	−0.648874	−	0.648874i	0.303847	−	0.952721i	$-0.401729\pi$
$487$	−2.05301e21	−	2.05301e21i	−0.648874	−	0.648874i	−0.952721	+	0.303847i	$0.901729\pi$
$488$	−8.73680e20	+	8.73680e20i	−0.271640	+	0.271640i
$489$		−	8.37541e20i		−	0.256174i
$490$	1.06385e21	−	2.08676e21i	0.320121	−	0.627918i
$491$	1.23148e21			0.364565			0.182283	−	0.983246i	$-0.441651\pi$
$491$	1.23148e21			0.364565			0.182283	+	0.983246i	$0.441651\pi$
$492$	−5.75702e19	−	5.75702e19i	−0.0167678	−	0.0167678i
$493$	8.38814e20	−	8.38814e20i	0.240376	−	0.240376i
$494$			2.22269e21i			0.626704i
$495$	−1.28397e20	−	3.95471e20i	−0.0356215	−	0.109717i
$496$	9.48510e19			0.0258934
$497$	−9.57600e19	−	9.57600e19i	−0.0257237	−	0.0257237i
$498$	4.01081e18	−	4.01081e18i	0.00106022	−	0.00106022i
$499$			2.83177e21i			0.736636i	0.929700	+	0.368318i	$0.120066\pi$
$499$			2.83177e21i			0.736636i	−0.929700	+	0.368318i	$0.879934\pi$
$500$	−1.57933e21	−	1.14910e21i	−0.404307	−	0.294169i
$501$	1.42120e20			0.0358058
$502$	1.81007e21	+	1.81007e21i	0.448813	+	0.448813i
$503$	5.59006e21	−	5.59006e21i	1.36418	−	1.36418i	0.495674	−	0.868508i	$-0.334921\pi$
$503$	5.59006e21	−	5.59006e21i	1.36418	−	1.36418i	0.868508	−	0.495674i	$-0.165079\pi$
$504$			7.67237e19i			0.0184283i
$505$	4.74020e21	−	1.53899e21i	1.12064	−	0.363835i
$506$	−3.36147e20			−0.0782213
$507$	−6.36756e20	−	6.36756e20i	−0.145851	−	0.145851i
$508$	−2.20748e21	+	2.20748e21i	−0.497721	+	0.497721i
$509$			5.71760e21i			1.26903i	0.772911	+	0.634514i	$0.218800\pi$
$509$			5.71760e21i			1.26903i	−0.772911	+	0.634514i	$0.781200\pi$
$510$	8.45647e20	+	4.31122e20i	0.184769	+	0.0941974i
$511$	5.11494e19			0.0110021
$512$	−1.47574e20	−	1.47574e20i	−0.0312500	−	0.0312500i
$513$	−3.10173e21	+	3.10173e21i	−0.646644	+	0.646644i
$514$		−	1.52315e21i		−	0.312635i
$515$	−4.19167e21	+	8.22197e21i	−0.847089	+	1.66157i
$516$	−1.19033e21			−0.236849
$517$	−1.60511e20	−	1.60511e20i	−0.0314470	−	0.0314470i
$518$	2.27663e20	−	2.27663e20i	0.0439191	−	0.0439191i
$519$		−	1.94434e21i		−	0.369346i
$520$	3.16263e20	+	9.74113e20i	0.0591591	+	0.182214i
$521$	9.49465e20			0.174895			0.0874475	−	0.996169i	$-0.472129\pi$
$521$	9.49465e20			0.174895			0.0874475	+	0.996169i	$0.472129\pi$
$522$	8.53307e20	+	8.53307e20i	0.154789	+	0.154789i
$523$	−3.95890e21	+	3.95890e21i	−0.707230	+	0.707230i	−0.965952	−	0.258722i	$-0.916699\pi$
$523$	−3.95890e21	+	3.95890e21i	−0.707230	+	0.707230i	0.258722	+	0.965952i	$0.416699\pi$
$524$		−	2.86675e21i		−	0.504359i
$525$	−7.77129e19	+	5.64076e19i	−0.0134654	+	0.00977379i
$526$	9.82237e20			0.167622
$527$	4.37672e20	+	4.37672e20i	0.0735637	+	0.0735637i
$528$	3.93204e19	−	3.93204e19i	0.00650949	−	0.00650949i
$529$			1.41363e21i			0.230511i
$530$	4.36112e21	−	1.41591e21i	0.700472	−	0.227421i
$531$	−9.57619e21			−1.51508
$532$	2.11432e20	+	2.11432e20i	0.0329517	+	0.0329517i
$533$	4.05351e20	−	4.05351e20i	0.0622319	−	0.0622319i
$534$		−	9.92500e20i		−	0.150107i
$535$	8.54037e20	+	4.35399e20i	0.127247	+	0.0648720i
$536$	3.09866e20			0.0454836
$537$	−2.34324e21	−	2.34324e21i	−0.338861	−	0.338861i
$538$	4.07909e21	−	4.07909e21i	0.581172	−	0.581172i
$539$		−	8.95440e20i		−	0.125697i
$540$	−9.18022e20	+	1.80070e21i	−0.126970	+	0.249053i
$541$	−2.29350e21			−0.312551			−0.156276	−	0.987713i	$-0.549949\pi$
$541$	−2.29350e21			−0.312551			−0.156276	+	0.987713i	$0.549949\pi$
$542$	2.28268e21	+	2.28268e21i	0.306514	+	0.306514i
$543$	−1.11919e21	+	1.11919e21i	−0.148083	+	0.148083i
$544$		−	1.36190e21i		−	0.177564i
$545$	3.65806e21	+	1.12671e22i	0.469980	+	1.44757i
$546$	5.03538e19			0.00637516
$547$	7.10589e20	+	7.10589e20i	0.0886583	+	0.0886583i	0.750045	−	0.661387i	$-0.230032\pi$
$547$	7.10589e20	+	7.10589e20i	0.0886583	+	0.0886583i	−0.661387	+	0.750045i	$0.730032\pi$
$548$	3.65905e21	−	3.65905e21i	0.449908	−	0.449908i
$549$		−	8.20216e21i		−	0.993915i
$550$	−7.37418e20	−	1.17141e20i	−0.0880668	−	0.0139896i
$551$	4.70302e21			0.553559
$552$	5.51997e20	+	5.51997e20i	0.0640360	+	0.0640360i
$553$	4.66018e20	−	4.66018e20i	0.0532846	−	0.0532846i
$554$		−	1.26252e20i		−	0.0142285i
$555$	3.85403e21	−	1.25128e21i	0.428125	−	0.138998i
$556$	−3.09702e21			−0.339114
$557$	1.81267e20	+	1.81267e20i	0.0195649	+	0.0195649i	0.716822	−	0.697257i	$-0.245596\pi$
$557$	1.81267e20	+	1.81267e20i	0.0195649	+	0.0195649i	−0.697257	+	0.716822i	$0.745596\pi$
$558$	−4.45234e20	+	4.45234e20i	−0.0473712	+	0.0473712i
$559$		−	8.38112e21i		−	0.879038i
$560$	1.22746e20	+	6.25777e19i	0.0126913	+	0.00647017i
$561$	3.62873e20			0.0369872
$562$	−7.24379e21	−	7.24379e21i	−0.727906	−	0.727906i
$563$	7.57299e21	−	7.57299e21i	0.750240	−	0.750240i	−0.224284	−	0.974524i	$-0.572004\pi$
$563$	7.57299e21	−	7.57299e21i	0.750240	−	0.750240i	0.974524	+	0.224284i	$0.0720043\pi$
$564$			5.27159e20i			0.0514883i
$565$	−3.67595e21	+	7.21038e21i	−0.353982	+	0.694338i
$566$	2.43810e21			0.231484
$567$	−3.23445e20	−	3.23445e20i	−0.0302786	−	0.0302786i
$568$	−1.72918e21	+	1.72918e21i	−0.159608	+	0.159608i
$569$		−	1.23825e22i		−	1.12697i	−0.826128	−	0.563483i	$-0.809461\pi$
$569$		−	1.23825e22i		−	1.12697i	0.826128	−	0.563483i	$-0.190539\pi$
$570$	1.16207e21	+	3.57926e21i	0.104288	+	0.321214i
$571$	−1.70415e22			−1.50806			−0.754030	−	0.656840i	$-0.771893\pi$
$571$	−1.70415e22			−1.50806			−0.754030	+	0.656840i	$0.771893\pi$
$572$	2.76854e20	+	2.76854e20i	0.0241592	+	0.0241592i
$573$	9.70134e20	−	9.70134e20i	0.0834823	−	0.0834823i
$574$		−	7.71176e19i		−	0.00654423i
$575$	1.64447e21	−	1.03522e22i	0.137620	−	0.866343i
$576$	1.38543e21			0.114342
$577$	4.72839e21	+	4.72839e21i	0.384864	+	0.384864i	0.872851	−	0.487987i	$-0.162269\pi$
$577$	4.72839e21	+	4.72839e21i	0.384864	+	0.384864i	−0.487987	+	0.872851i	$0.662269\pi$
$578$	5.56023e19	−	5.56023e19i	0.00446344	−	0.00446344i
$579$			3.25070e21i			0.257364i
$580$	2.06114e21	−	6.69186e20i	0.160947	−	0.0522544i
$581$	5.37264e18			0.000413789
$582$	1.33554e21	+	1.33554e21i	0.101455	+	0.101455i
$583$	1.23948e21	−	1.23948e21i	0.0928734	−	0.0928734i
$584$		−	9.23628e20i		−	0.0682644i
$585$	−6.05707e21	−	3.08797e21i	−0.441586	−	0.225126i
$586$	−1.31463e22			−0.945419
$587$	1.58949e22	+	1.58949e22i	1.12760	+	1.12760i	0.990567	+	0.137031i	$0.0437561\pi$
$587$	1.58949e22	+	1.58949e22i	1.12760	+	1.12760i	0.137031	+	0.990567i	$0.456244\pi$
$588$	−1.47043e21	+	1.47043e21i	−0.102902	+	0.102902i
$589$			2.45391e21i			0.169409i
$590$	−7.81058e21	+	1.53205e22i	−0.531945	+	1.04341i
$591$	7.14779e21			0.480255
$592$	−4.11101e21	−	4.11101e21i	−0.272505	−	0.272505i
$593$	2.68529e21	−	2.68529e21i	0.175612	−	0.175612i	−0.613828	−	0.789440i	$-0.710371\pi$
$593$	2.68529e21	−	2.68529e21i	0.175612	−	0.175612i	0.789440	+	0.613828i	$0.210371\pi$
$594$			7.72693e20i			0.0498558i
$595$	2.77637e20	+	8.55142e20i	0.0176743	+	0.0544381i
$596$	1.01323e22			0.636413
$597$	−2.34274e21	−	2.34274e21i	−0.145187	−	0.145187i
$598$	−3.88660e21	+	3.88660e21i	−0.237662	+	0.237662i
$599$			5.74587e21i			0.346690i	0.984861	+	0.173345i	$0.0554576\pi$
$599$			5.74587e21i			0.346690i	−0.984861	+	0.173345i	$0.944542\pi$
$600$	1.01858e21	+	1.40330e21i	0.0606434	+	0.0835486i
$601$	−1.30571e22			−0.767099			−0.383549	−	0.923520i	$-0.625298\pi$
$601$	−1.30571e22			−0.767099			−0.383549	+	0.923520i	$0.625298\pi$
$602$	−7.97251e20	−	7.97251e20i	−0.0462192	−	0.0462192i
$603$	−1.45452e21	+	1.45452e21i	−0.0832110	+	0.0832110i
$604$			1.74113e22i			0.982960i
$605$	1.68004e22	−	5.45454e21i	0.936001	−	0.303889i
$606$	−4.42462e21			−0.243273
$607$	1.73180e22	+	1.73180e22i	0.939697	+	0.939697i	0.998282	−	0.0585852i	$-0.0186589\pi$
$607$	1.73180e22	+	1.73180e22i	0.939697	+	0.939697i	−0.0585852	+	0.998282i	$0.518659\pi$
$608$	3.81792e21	−	3.81792e21i	0.204455	−	0.204455i
$609$		−	1.06545e20i		−	0.00563109i
$610$	−1.31222e22	−	6.68988e21i	−0.684493	−	0.348963i
$611$	−3.71172e21			−0.191093
$612$	6.39281e21	+	6.39281e21i	0.324848	+	0.324848i
$613$	−5.27143e21	+	5.27143e21i	−0.264390	+	0.264390i	−0.826835	−	0.562445i	$-0.809861\pi$
$613$	−5.27143e21	+	5.27143e21i	−0.264390	+	0.264390i	0.562445	+	0.826835i	$0.309861\pi$
$614$			1.91833e22i			0.949676i
$615$	4.40823e20	−	8.64675e20i	0.0215409	−	0.0422525i
$616$	5.26713e19			0.00254055
$617$	−1.29171e22	−	1.29171e22i	−0.615010	−	0.615010i	0.329237	−	0.944247i	$-0.393208\pi$
$617$	−1.29171e22	−	1.29171e22i	−0.615010	−	0.615010i	−0.944247	+	0.329237i	$0.893208\pi$
$618$	5.79360e21	−	5.79360e21i	0.272296	−	0.272296i
$619$			3.88895e22i			1.80429i	0.431431	+	0.902146i	$0.358009\pi$
$619$			3.88895e22i			1.80429i	−0.431431	+	0.902146i	$0.641991\pi$
$620$	3.49164e20	+	1.07545e21i	0.0159917	+	0.0492558i
$621$	−1.08474e22			−0.490448
$622$	−1.68640e22	−	1.68640e22i	−0.752728	−	0.752728i
$623$	6.64747e20	−	6.64747e20i	0.0292922	−	0.0292922i
$624$		−	9.09261e20i		−	0.0395560i
$625$	7.21507e21	−	2.21369e22i	0.309885	−	0.950774i
$626$	2.60366e22			1.10405
$627$	1.01727e21	+	1.01727e21i	0.0425888	+	0.0425888i
$628$	1.50471e22	−	1.50471e22i	0.621978	−	0.621978i
$629$		−	3.79389e22i		−	1.54839i
$630$	−8.69917e20	+	2.82434e20i	−0.0350553	+	0.0113813i
$631$	3.54785e22			1.41166			0.705831	−	0.708380i	$-0.250574\pi$
$631$	3.54785e22			1.41166			0.705831	+	0.708380i	$0.250574\pi$
$632$	−8.41509e21	−	8.41509e21i	−0.330615	−	0.330615i
$633$	−9.73650e21	+	9.73650e21i	−0.377723	+	0.377723i
$634$		−	2.36715e22i		−	0.906801i
$635$	−3.31552e22	−	1.69029e22i	−1.25418	−	0.639400i
$636$	−4.07078e21			−0.152062
$637$	−1.03533e22	−	1.03533e22i	−0.381911	−	0.381911i
$638$	5.85801e20	−	5.85801e20i	0.0213395	−	0.0213395i
$639$		−	1.62337e22i		−	0.583995i
$640$	1.12999e21	−	2.21649e21i	0.0401454	−	0.0787454i
$641$	−3.70351e21			−0.129942			−0.0649709	−	0.997887i	$-0.520695\pi$
$641$	−3.70351e21			−0.129942			−0.0649709	+	0.997887i	$0.520695\pi$
$642$	−6.01796e20	−	6.01796e20i	−0.0208530	−	0.0208530i
$643$	−5.07412e21	+	5.07412e21i	−0.173649	+	0.173649i	−0.788581	−	0.614931i	$-0.789184\pi$
$643$	−5.07412e21	+	5.07412e21i	−0.173649	+	0.173649i	0.614931	+	0.788581i	$0.289184\pi$
$644$			7.39422e20i			0.0249923i
$645$	−4.38184e21	−	1.34964e22i	−0.146278	−	0.450547i
$646$	3.52341e22			1.16172
$647$	−6.32454e21	−	6.32454e21i	−0.205966	−	0.205966i	0.596585	−	0.802550i	$-0.296524\pi$
$647$	−6.32454e21	−	6.32454e21i	−0.205966	−	0.205966i	−0.802550	+	0.596585i	$0.796524\pi$
$648$	−5.84059e21	+	5.84059e21i	−0.187870	+	0.187870i
$649$			6.57412e21i			0.208872i
$650$	−9.88058e21	+	7.17178e21i	−0.310081	+	0.225071i
$651$	5.55922e19			0.00172332
$652$	−1.01295e22	−	1.01295e22i	−0.310175	−	0.310175i
$653$	−3.64390e22	+	3.64390e22i	−1.10220	+	1.10220i	−0.108056	+	0.994145i	$0.534463\pi$
$653$	−3.64390e22	+	3.64390e22i	−1.10220	+	1.10220i	−0.994145	+	0.108056i	$0.965537\pi$
$654$		−	1.05170e22i		−	0.314246i
$655$	3.25042e22	−	1.05530e22i	0.959419	−	0.311492i
$656$	−1.39255e21			−0.0406050
$657$	4.33554e21	+	4.33554e21i	0.124888	+	0.124888i
$658$	−3.53075e20	+	3.53075e20i	−0.0100476	+	0.0100476i
$659$			4.98022e22i			1.40012i	0.714084	+	0.700060i	$0.246843\pi$
$659$			4.98022e22i			1.40012i	−0.714084	+	0.700060i	$0.753157\pi$
$660$	5.90573e20	+	3.01082e20i	0.0164030	+	0.00836244i
$661$	2.50492e22			0.687357			0.343678	−	0.939087i	$-0.388327\pi$
$661$	2.50492e22			0.687357			0.343678	+	0.939087i	$0.388327\pi$
$662$	4.73437e21	+	4.73437e21i	0.128351	+	0.128351i
$663$	4.19561e21	−	4.19561e21i	0.112379	−	0.112379i
$664$		−	9.70161e19i		−	0.00256743i
$665$	−1.61896e21	+	3.17560e21i	−0.0423315	+	0.0830335i
$666$	3.85944e22			0.997081
$667$	8.22373e21	+	8.22373e21i	0.209924	+	0.209924i
$668$	1.71885e21	−	1.71885e21i	0.0433536	−	0.0433536i
$669$			6.84262e21i			0.170535i
$670$	1.14067e21	+	3.51335e21i	0.0280907	+	0.0865214i
$671$	−5.63083e21			−0.137023
$672$	−8.64931e19	−	8.64931e19i	−0.00207983	−	0.00207983i
$673$	−2.03524e22	+	2.03524e22i	−0.483610	+	0.483610i	−0.906283	−	0.422672i	$-0.861092\pi$
$673$	−2.03524e22	+	2.03524e22i	−0.483610	+	0.483610i	0.422672	+	0.906283i	$0.361092\pi$
$674$			7.11377e21i			0.167040i
$675$	−2.37963e22	−	3.78010e21i	−0.552179	−	0.0877149i
$676$	−1.54023e22			−0.353192
$677$	−6.22465e21	−	6.22465e21i	−0.141061	−	0.141061i	0.633050	−	0.774111i	$-0.281803\pi$
$677$	−6.22465e21	−	6.22465e21i	−0.141061	−	0.141061i	−0.774111	+	0.633050i	$0.781803\pi$
$678$	5.08078e21	−	5.08078e21i	0.113787	−	0.113787i
$679$			1.78901e21i			0.0395963i
$680$	1.54417e22	−	5.01341e21i	0.337772	−	0.109664i
$681$	1.77030e22			0.382709
$682$	3.05656e20	+	3.05656e20i	0.00653067	+	0.00653067i
$683$	−4.89308e22	+	4.89308e22i	−1.03328	+	1.03328i	−0.0338506	+	0.999427i	$0.510777\pi$
$683$	−4.89308e22	+	4.89308e22i	−1.03328	+	1.03328i	−0.999427	+	0.0338506i	$0.989223\pi$
$684$			3.58429e22i			0.748091i
$685$	5.49571e22	+	2.80178e22i	1.13370	+	0.577976i
$686$	−3.94581e21			−0.0804533
$687$	6.94503e21	+	6.94503e21i	0.139965	+	0.139965i
$688$	−1.43963e22	+	1.43963e22i	−0.286777	+	0.286777i
$689$		−	2.86623e22i		−	0.564361i
$690$	−4.22671e21	+	8.29072e21i	−0.0822641	+	0.161361i
$691$	−4.15508e22			−0.799383			−0.399692	−	0.916650i	$-0.630883\pi$
$691$	−4.15508e22			−0.799383			−0.399692	+	0.916650i	$0.630883\pi$
$692$	−2.35155e22	−	2.35155e22i	−0.447204	−	0.447204i
$693$	−2.47241e20	+	2.47241e20i	−0.00464787	+	0.00464787i
$694$		−	3.90963e21i		−	0.0726540i
$695$	−1.14007e22	−	3.51150e22i	−0.209437	−	0.645080i
$696$	−1.92392e21			−0.0349392
$697$	−6.42564e21	−	6.42564e21i	−0.115360	−	0.115360i
$698$	−3.99270e22	+	3.99270e22i	−0.708636	+	0.708636i
$699$			1.25803e22i			0.220737i
$700$	−2.57674e20	+	1.62210e21i	−0.00446978	+	0.0281380i
$701$	1.05419e22			0.180790			0.0903952	−	0.995906i	$-0.471187\pi$
$701$	1.05419e22			0.180790			0.0903952	+	0.995906i	$0.471187\pi$
$702$	8.93404e21	+	8.93404e21i	0.151478	+	0.151478i
$703$	1.06357e23	−	1.06357e23i	1.78288	−	1.78288i
$704$		−	9.51109e20i		−	0.0157634i
$705$	−5.97709e21	+	1.94057e21i	−0.0979438	+	0.0317992i
$706$	−3.89987e22			−0.631847
$707$	−2.96348e21	−	2.96348e21i	−0.0474729	−	0.0474729i
$708$	1.07955e22	−	1.07955e22i	0.170993	−	0.170993i
$709$		−	1.57415e22i		−	0.246534i	−0.992374	−	0.123267i	$-0.960663\pi$
$709$		−	1.57415e22i		−	0.246534i	0.992374	−	0.123267i	$-0.0393371\pi$
$710$	−2.59714e22	−	1.32406e22i	−0.402188	−	0.205041i
$711$	7.90014e22			1.20970
$712$	−1.20036e22	−	1.20036e22i	−0.181749	−	0.181749i
$713$	−4.29093e21	+	4.29093e21i	−0.0642443	+	0.0642443i
$714$		−	7.98211e20i		−	0.0118177i
$715$	−2.11991e21	+	4.15821e21i	−0.0310362	+	0.0608777i
$716$	−5.66798e22			−0.820587
$717$	9.98623e21	+	9.98623e21i	0.142971	+	0.142971i
$718$	2.84702e22	−	2.84702e22i	0.403084	−	0.403084i
$719$		−	8.32157e22i		−	1.16513i	−0.812784	−	0.582565i	$-0.802049\pi$
$719$		−	8.32157e22i		−	1.16513i	0.812784	−	0.582565i	$-0.197951\pi$
$720$	5.10003e21	+	1.57085e22i	0.0706176	+	0.217508i
$721$	7.76076e21			0.106273
$722$	6.18539e22	+	6.18539e22i	0.837663	+	0.837663i
$723$	3.42585e21	−	3.42585e21i	0.0458841	−	0.0458841i
$724$			2.70718e22i			0.358599i
$725$	1.51749e22	+	2.09065e22i	0.198802	+	0.273891i
$726$	−1.56819e22			−0.203192
$727$	−1.32708e22	−	1.32708e22i	−0.170068	−	0.170068i	0.616941	−	0.787009i	$-0.288372\pi$
$727$	−1.32708e22	−	1.32708e22i	−0.170068	−	0.170068i	−0.787009	+	0.616941i	$0.788372\pi$
$728$	6.08996e20	−	6.08996e20i	0.00771904	−	0.00771904i
$729$		−	4.18093e22i		−	0.524146i
$730$	1.04724e22	−	3.40004e21i	0.129856	−	0.0421601i
$731$	−1.32858e23			−1.62948
$732$	9.24656e21	+	9.24656e21i	0.112174	+	0.112174i
$733$	2.51170e22	−	2.51170e22i	0.301396	−	0.301396i	−0.540164	−	0.841560i	$-0.681638\pi$
$733$	2.51170e22	−	2.51170e22i	0.301396	−	0.301396i	0.841560	+	0.540164i	$0.181638\pi$
$734$		−	5.49143e22i		−	0.651804i
$735$	−2.20851e22	−	1.12593e22i	−0.259299	−	0.132194i
$736$	1.33521e22			0.155069
$737$	9.98536e20	+	9.98536e20i	0.0114716	+	0.0114716i
$738$	6.53666e21	−	6.53666e21i	0.0742856	−	0.0742856i
$739$			7.41502e22i			0.833599i	0.908999	+	0.416799i	$0.136848\pi$
$739$			7.41502e22i			0.833599i	−0.908999	+	0.416799i	$0.863152\pi$
$740$	3.14785e22	−	6.17453e22i	0.350075	−	0.686673i
$741$	2.35237e22			0.258798
$742$	−2.72648e21	−	2.72648e21i	−0.0296737	−	0.0296737i
$743$	1.12603e23	−	1.12603e23i	1.21239	−	1.21239i	0.242146	−	0.970240i	$-0.422149\pi$
$743$	1.12603e23	−	1.12603e23i	1.21239	−	1.21239i	0.970240	−	0.242146i	$-0.0778513\pi$
$744$		−	1.00385e21i		−	0.0106927i
$745$	3.72989e22	+	1.14883e23i	0.393048	+	1.21062i
$746$	−3.01591e22			−0.314418
$747$	4.55397e20	+	4.55397e20i	0.00469705	+	0.00469705i
$748$	4.38871e21	−	4.38871e21i	0.0447841	−	0.0447841i
$749$		−	8.06130e20i		−	0.00813861i
$750$	−1.21614e22	+	1.67147e22i	−0.121477	+	0.166959i
$751$	−1.01699e23			−1.00508			−0.502538	−	0.864555i	$-0.667600\pi$
$751$	−1.01699e23			−1.00508			−0.502538	+	0.864555i	$0.667600\pi$
$752$	6.37564e21	+	6.37564e21i	0.0623420	+	0.0623420i
$753$	1.91568e22	−	1.91568e22i	0.185337	−	0.185337i
$754$		−	1.35463e22i		−	0.129673i
$755$	−1.97415e23	+	6.40942e22i	−1.86984	+	0.607076i
$756$	1.69969e21			0.0159293
$757$	7.69905e21	+	7.69905e21i	0.0713953	+	0.0713953i	0.741903	−	0.670507i	$-0.233924\pi$
$757$	7.69905e21	+	7.69905e21i	0.0713953	+	0.0713953i	−0.670507	+	0.741903i	$0.733924\pi$
$758$	−2.99812e22	+	2.99812e22i	−0.275103	+	0.275103i
$759$			3.55760e21i			0.0323015i
$760$	5.73433e22	+	2.92343e22i	0.515198	+	0.262654i
$761$	1.12172e22			0.0997258			0.0498629	−	0.998756i	$-0.484122\pi$
$761$	1.12172e22			0.0997258			0.0498629	+	0.998756i	$0.484122\pi$
$762$	2.33627e22	+	2.33627e22i	0.205534	+	0.205534i
$763$	7.04397e21	−	7.04397e21i	0.0613227	−	0.0613227i
$764$		−	2.34663e22i		−	0.202161i
$765$	−4.89506e22	+	9.60169e22i	−0.417318	+	0.818570i
$766$	−4.73552e22			−0.399519
$767$	7.60113e22	+	7.60113e22i	0.634622	+	0.634622i
$768$	−1.56184e21	+	1.56184e21i	−0.0129047	+	0.0129047i
$769$			1.39097e23i			1.13739i	0.822549	+	0.568694i	$0.192551\pi$
$769$			1.39097e23i			1.13739i	−0.822549	+	0.568694i	$0.807449\pi$
$770$	1.93893e20	+	5.97204e20i	0.00156905	+	0.00483278i
$771$	−1.61202e22			−0.129103
$772$	3.93151e22	+	3.93151e22i	0.311617	+	0.311617i
$773$	−6.93443e22	+	6.93443e22i	−0.543970	+	0.543970i	−0.924690	−	0.380720i	$-0.875676\pi$
$773$	−6.93443e22	+	6.93443e22i	−0.543970	+	0.543970i	0.380720	+	0.924690i	$0.375676\pi$
$774$		−	1.35153e23i		−	1.04930i
$775$	−1.09085e22	+	7.91786e21i	−0.0838205	+	0.0608407i
$776$	3.23049e22			0.245683
$777$	−2.40946e21	−	2.40946e21i	−0.0181364	−	0.0181364i
$778$	−1.01532e22	+	1.01532e22i	−0.0756423	+	0.0756423i
$779$		−	3.60269e22i		−	0.265661i
$780$	1.03095e22	−	3.34716e21i	0.0752455	−	0.0244298i
$781$	−1.11445e22			−0.0805105
$782$	6.16106e22	+	6.16106e22i	0.440556	+	0.440556i
$783$	1.89037e22	−	1.89037e22i	0.133799	−	0.133799i
$784$			3.55677e22i			0.249188i
$785$	2.26000e23	+	1.15217e23i	1.56729	+	0.799026i
$786$	−3.03402e22			−0.208275
$787$	−1.14978e23	−	1.14978e23i	−0.781300	−	0.781300i	0.198750	−	0.980050i	$-0.436312\pi$
$787$	−1.14978e23	−	1.14978e23i	−0.781300	−	0.781300i	−0.980050	+	0.198750i	$0.936312\pi$
$788$	8.64478e22	−	8.64478e22i	0.581493	−	0.581493i
$789$		−	1.03955e22i		−	0.0692195i
$790$	6.44355e22	−	1.26390e23i	0.424726	−	0.833101i
$791$	6.80592e21			0.0444094
$792$	4.46453e21	+	4.46453e21i	0.0288386	+	0.0288386i
$793$	−6.51048e22	+	6.51048e22i	−0.416320	+	0.416320i
$794$			2.63865e22i			0.167039i
$795$	−1.49853e22	−	4.61557e22i	−0.0939134	−	0.289260i
$796$	−5.66677e22			−0.351586
$797$	−3.97373e22	−	3.97373e22i	−0.244080	−	0.244080i	0.574456	−	0.818536i	$-0.305214\pi$
$797$	−3.97373e22	−	3.97373e22i	−0.244080	−	0.244080i	−0.818536	+	0.574456i	$0.805214\pi$
$798$	2.23768e21	−	2.23768e21i	0.0136074	−	0.0136074i
$799$			5.88383e22i			0.354230i
$800$	2.92909e22	+	4.65293e21i	0.174588	+	0.0277336i
$801$	1.12691e23			0.665011
$802$	2.84799e22	+	2.84799e22i	0.166396	+	0.166396i
$803$	2.97638e21	−	2.97638e21i	0.0172172	−	0.0172172i
$804$		−	3.27945e21i		−	0.0187825i
$805$	−8.38380e21	+	2.72195e21i	−0.0475416	+	0.0154352i
$806$	7.06811e21			0.0396847
$807$	−4.31709e22	−	4.31709e22i	−0.239995	−	0.239995i
$808$	−5.35128e22	+	5.35128e22i	−0.294555	+	0.294555i
$809$		−	2.17726e23i		−	1.18665i	−0.804964	−	0.593323i	$-0.797816\pi$
$809$		−	2.17726e23i		−	1.18665i	0.804964	−	0.593323i	$-0.202184\pi$
$810$	−8.77227e22	−	4.47221e22i	−0.473404	−	0.241347i
$811$	−1.47243e23			−0.786808			−0.393404	−	0.919366i	$-0.628703\pi$
$811$	−1.47243e23			−0.786808			−0.393404	+	0.919366i	$0.628703\pi$
$812$	−1.28859e21	−	1.28859e21i	−0.00681813	−	0.00681813i
$813$	2.41586e22	−	2.41586e22i	0.126575	−	0.126575i
$814$		−	2.64953e22i		−	0.137459i
$815$	7.75629e22	−	1.52140e23i	0.398468	−	0.781597i
$816$	−1.44136e22			−0.0733251
$817$	−3.72450e23	−	3.72450e23i	−1.87626	−	1.87626i
$818$	−1.41401e23	+	1.41401e23i	−0.705386	+	0.705386i
$819$			5.71729e21i			0.0282435i
$820$	−5.12622e21	−	1.57891e22i	−0.0250776	−	0.0772410i
$821$	2.98995e23			1.44850			0.724249	−	0.689538i	$-0.242186\pi$
$821$	2.98995e23			1.44850			0.724249	+	0.689538i	$0.242186\pi$
$822$	−3.87254e22	−	3.87254e22i	−0.185790	−	0.185790i
$823$	2.41203e23	−	2.41203e23i	1.14600	−	1.14600i	0.158666	−	0.987332i	$-0.449281\pi$
$823$	2.41203e23	−	2.41203e23i	1.14600	−	1.14600i	0.987332	−	0.158666i	$-0.0507192\pi$
$824$		−	1.40139e23i		−	0.659391i
$825$	−1.23975e21	+	7.80444e21i	−0.00577701	+	0.0363672i
$826$	1.44611e22			0.0667360
$827$	2.38986e23	+	2.38986e23i	1.09227	+	1.09227i	0.995286	+	0.0969807i	$0.0309185\pi$
$827$	2.38986e23	+	2.38986e23i	1.09227	+	1.09227i	0.0969807	+	0.995286i	$0.469082\pi$
$828$	−6.26751e22	+	6.26751e22i	−0.283695	+	0.283695i
$829$		−	8.76080e22i		−	0.392742i	−0.980530	−	0.196371i	$-0.937084\pi$
$829$		−	8.76080e22i		−	0.392742i	0.980530	−	0.196371i	$-0.0629157\pi$
$830$	1.10000e21	−	3.57134e20i	0.00488391	−	0.00158565i
$831$	−1.33618e21			−0.00587568
$832$	−1.09969e22	−	1.09969e22i	−0.0478943	−	0.0478943i
$833$	−1.64120e23	+	1.64120e23i	−0.707950	+	0.707950i
$834$			3.27772e22i			0.140037i
$835$	2.58162e22	+	1.31614e22i	0.109245	+	0.0556944i
$836$	2.46064e22			0.103133
$837$	9.86345e21	+	9.86345e21i	0.0409473	+	0.0409473i
$838$	−4.98526e22	+	4.98526e22i	−0.204991	+	0.204991i
$839$			1.96412e23i			0.799966i	0.916522	+	0.399983i	$0.130984\pi$
$839$			1.96412e23i			0.799966i	−0.916522	+	0.399983i	$0.869016\pi$
$840$	6.62289e20	−	1.29908e21i	0.00267186	−	0.00524086i
$841$	2.21584e23			0.885462
$842$	3.86746e22	+	3.86746e22i	0.153084	+	0.153084i
$843$	−7.66644e22	+	7.66644e22i	−0.300589	+	0.300589i
$844$			2.35513e23i			0.914693i
$845$	−5.66986e22	−	1.74636e23i	−0.218132	−	0.671862i
$846$	−5.98549e22			−0.228106
$847$	−1.05033e22	−	1.05033e22i	−0.0396513	−	0.0396513i
$848$	−4.92333e22	+	4.92333e22i	−0.184116	+	0.184116i
$849$		−	2.58036e22i		−	0.0955912i
$850$	1.13687e23	+	1.56627e23i	0.417216	+	0.574800i
$851$	3.71952e23			1.35223
$852$	1.83007e22	+	1.83007e22i	0.0659100	+	0.0659100i
$853$	−2.61350e23	+	2.61350e23i	−0.932459	+	0.932459i	−0.997859	−	0.0654005i	$-0.979167\pi$
$853$	−2.61350e23	+	2.61350e23i	−0.932459	+	0.932459i	0.0654005	+	0.997859i	$0.479167\pi$
$854$			1.23861e22i			0.0437797i
$855$	−4.06398e23	+	1.31944e23i	−1.42306	+	0.462021i
$856$	−1.45566e22			−0.0504976
$857$	2.43300e23	+	2.43300e23i	0.836171	+	0.836171i	0.988353	−	0.152182i	$-0.0486298\pi$
$857$	2.43300e23	+	2.43300e23i	0.836171	+	0.836171i	−0.152182	+	0.988353i	$0.548630\pi$
$858$	2.93008e21	−	2.93008e21i	0.00997656	−	0.00997656i
$859$			4.77046e23i			1.60922i	0.593806	+	0.804608i	$0.297625\pi$
$859$			4.77046e23i			1.60922i	−0.593806	+	0.804608i	$0.702375\pi$
$860$	−2.16225e23	−	1.10234e23i	−0.722635	−	0.368409i
$861$	−8.16171e20			−0.00270244
$862$	7.53170e21	+	7.53170e21i	0.0247079	+	0.0247079i
$863$	1.12597e23	−	1.12597e23i	0.365966	−	0.365966i	−0.500038	−	0.866004i	$-0.666681\pi$
$863$	1.12597e23	−	1.12597e23i	0.365966	−	0.365966i	0.866004	+	0.500038i	$0.166681\pi$
$864$		−	3.06921e22i		−	0.0988363i
$865$	1.80061e23	−	3.53191e23i	0.574502	−	1.12689i
$866$	8.78407e22			0.277685
$867$	−5.88465e20	−	5.88465e20i	−0.00184318	−	0.00184318i
$868$	6.72350e20	−	6.72350e20i	0.00208659	−	0.00208659i
$869$		−	5.42350e22i		−	0.166771i
$870$	−7.08231e21	−	2.18140e22i	−0.0215785	−	0.0664633i
$871$	2.30906e22			0.0697090
$872$	−1.27196e23	−	1.27196e23i	−0.380489	−	0.380489i
$873$	−1.51640e23	+	1.51640e23i	−0.449470	+	0.449470i
$874$			3.45435e23i			1.01455i
$875$	−1.93404e22	+	3.04965e21i	−0.0562861	+	0.00887536i
$876$	−9.77518e21			−0.0281898
$877$	−3.77690e23	−	3.77690e23i	−1.07929	−	1.07929i	−0.996573	−	0.0827187i	$-0.973640\pi$
$877$	−3.77690e23	−	3.77690e23i	−1.07929	−	1.07929i	−0.0827187	−	0.996573i	$-0.526360\pi$
$878$	1.08674e23	−	1.08674e23i	0.307729	−	0.307729i
$879$			1.39134e23i			0.390411i
$880$	1.07840e22	−	3.50121e21i	0.0299859	−	0.00973545i
$881$	−2.43841e23			−0.671891			−0.335946	−	0.941881i	$-0.609056\pi$
$881$	−2.43841e23			−0.671891			−0.335946	+	0.941881i	$0.609056\pi$
$882$	−1.66956e23	−	1.66956e23i	−0.455883	−	0.455883i
$883$	2.63886e23	−	2.63886e23i	0.714053	−	0.714053i	−0.253328	−	0.967380i	$-0.581525\pi$
$883$	2.63886e23	−	2.63886e23i	0.714053	−	0.714053i	0.967380	+	0.253328i	$0.0815252\pi$
$884$		−	1.01486e23i		−	0.272138i
$885$	1.62144e23	+	8.26630e22i	0.430878	+	0.219667i
$886$	3.63956e23			0.958471
$887$	1.74037e23	+	1.74037e23i	0.454207	+	0.454207i	0.896748	−	0.442541i	$-0.145923\pi$
$887$	1.74037e23	+	1.74037e23i	0.454207	+	0.454207i	−0.442541	+	0.896748i	$0.645923\pi$
$888$	−4.35087e22	+	4.35087e22i	−0.112531	+	0.112531i
$889$			3.12953e22i			0.0802168i
$890$	9.19134e22	−	1.80289e23i	0.233485	−	0.457982i
$891$	−3.76424e22			−0.0947666
$892$	8.27569e22	+	8.27569e22i	0.206484	+	0.206484i
$893$	−1.64946e23	+	1.64946e23i	−0.407877	+	0.407877i
$894$		−	1.07235e23i		−	0.262807i
$895$	−2.08649e23	−	6.42654e23i	−0.506794	−	1.56096i
$896$	−2.09215e21			−0.00503651
$897$	4.11337e22	+	4.11337e22i	0.0981427	+	0.0981427i
$898$	3.48311e23	−	3.48311e23i	0.823677	−	0.823677i
$899$		−	1.49555e22i		−	0.0350529i
$900$	−1.59334e23	+	1.15652e23i	−0.370141	+	0.268665i
$901$	−4.54355e23			−1.04616
$902$	−4.48746e21	−	4.48746e21i	−0.0102411	−	0.0102411i
$903$	−8.43767e21	+	8.43767e21i	−0.0190862	+	0.0190862i
$904$		−	1.22897e23i		−	0.275547i
$905$	−3.06949e23	+	9.96563e22i	−0.682146	+	0.221471i
$906$	1.84272e23			0.405914
$907$	−2.65885e20	−	2.65885e20i	−0.000580544	−	0.000580544i	0.706816	−	0.707397i	$-0.250131\pi$
$907$	−2.65885e20	−	2.65885e20i	−0.000580544	−	0.000580544i	−0.707397	+	0.706816i	$0.750131\pi$
$908$	2.14106e23	−	2.14106e23i	0.463384	−	0.463384i
$909$		−	5.02382e23i		−	1.07776i
$910$	9.14682e21	+	4.66316e21i	0.0194509	+	0.00991630i
$911$	2.17453e23			0.458372			0.229186	−	0.973383i	$-0.426394\pi$
$911$	2.17453e23			0.458372			0.229186	+	0.973383i	$0.426394\pi$
$912$	−4.04068e22	−	4.04068e22i	−0.0844299	−	0.0844299i
$913$	3.12633e20	−	3.12633e20i	0.000647542	−	0.000647542i
$914$			9.08143e21i			0.0186460i
$915$	−7.08021e22	+	1.38879e23i	−0.144104	+	0.282662i
$916$	1.67991e23			0.338940
$917$	−2.03209e22	−	2.03209e22i	−0.0406433	−	0.0406433i
$918$	1.41623e23	−	1.41623e23i	0.280796	−	0.280796i
$919$			4.76502e23i			0.936570i	0.883577	+	0.468285i	$0.155128\pi$
$919$			4.76502e23i			0.936570i	−0.883577	+	0.468285i	$0.844872\pi$
$920$	4.91514e22	+	1.51390e23i	0.0957709	+	0.294982i
$921$	2.03025e23			0.392169
$922$	−3.15761e23	−	3.15761e23i	−0.604659	−	0.604659i
$923$	−1.28855e23	+	1.28855e23i	−0.244618	+	0.244618i
$924$		−	5.57445e20i		−	0.00104912i
$925$	8.15966e23	+	1.29618e23i	1.52243	+	0.241842i
$926$	−3.96596e23			−0.733601
$927$	6.57819e23	+	6.57819e23i	1.20634	+	1.20634i
$928$	−2.32686e22	+	2.32686e22i	−0.0423044	+	0.0423044i
$929$		−	5.56419e23i		−	1.00294i	−0.865174	−	0.501471i	$-0.832792\pi$
$929$		−	5.56419e23i		−	1.00294i	0.865174	−	0.501471i	$-0.167208\pi$
$930$	1.13820e22	−	3.69536e21i	0.0203402	−	0.00660379i
$931$	−9.20181e23			−1.63033
$932$	1.52151e23	+	1.52151e23i	0.267268	+	0.267268i
$933$	−1.78480e23	+	1.78480e23i	−0.310839	+	0.310839i
$934$			6.74933e23i			1.16543i
$935$	6.59162e22	+	3.36049e22i	0.112849	+	0.0575321i
$936$	1.03240e23			0.175243
$937$	−2.97700e23	−	2.97700e23i	−0.501028	−	0.501028i	0.410729	−	0.911757i	$-0.365274\pi$
$937$	−2.97700e23	−	2.97700e23i	−0.501028	−	0.501028i	−0.911757	+	0.410729i	$0.865274\pi$
$938$	2.19648e21	−	2.19648e21i	0.00366526	−	0.00366526i
$939$		−	2.75557e23i		−	0.455918i
$940$	−4.88191e22	+	9.57589e22i	−0.0800879	+	0.157093i
$941$	5.05290e22			0.0821909			0.0410955	−	0.999155i	$-0.486915\pi$
$941$	5.05290e22			0.0821909			0.0410955	+	0.999155i	$0.486915\pi$
$942$	−1.59250e23	−	1.59250e23i	−0.256846	−	0.256846i
$943$	6.29969e22	−	6.29969e22i	0.100745	−	0.100745i
$944$		−	2.61130e23i		−	0.414077i
$945$	6.25688e21	+	1.92717e22i	0.00983792	+	0.0303015i
$946$	−9.27837e22			−0.144658
$947$	5.41607e23	+	5.41607e23i	0.837307	+	0.837307i	0.988504	−	0.151197i	$-0.0483127\pi$
$947$	5.41607e23	+	5.41607e23i	0.837307	+	0.837307i	−0.151197	+	0.988504i	$0.548313\pi$
$948$	−8.90608e22	+	8.90608e22i	−0.136527	+	0.136527i
$949$		−	6.88269e22i		−	0.104623i
$950$	−1.20377e23	+	7.57793e23i	−0.181449	+	1.14225i
$951$	−2.50527e23			−0.374464
$952$	−9.65383e21	−	9.65383e21i	−0.0143088	−	0.0143088i
$953$	−3.09567e22	+	3.09567e22i	−0.0455000	+	0.0455000i	−0.729491	−	0.683991i	$-0.760243\pi$
$953$	−3.09567e22	+	3.09567e22i	−0.0455000	+	0.0455000i	0.683991	+	0.729491i	$0.260243\pi$
$954$		−	4.62206e23i		−	0.673672i
$955$	2.66068e23	−	8.63836e22i	0.384561	−	0.124855i
$956$	2.41554e23			0.346219
$957$	−6.19980e21	−	6.19980e21i	−0.00881216	−	0.00881216i
$958$	−2.46120e23	+	2.46120e23i	−0.346914	+	0.346914i
$959$		−	5.18743e22i		−	0.0725109i
$960$	−2.34581e22	−	1.19592e22i	−0.0325179	−	0.0165781i
$961$	−7.19620e23			−0.989273
$962$	−3.06344e23	−	3.06344e23i	−0.417646	−	0.417646i
$963$	6.83293e22	−	6.83293e22i	0.0923840	−	0.0923840i
$964$		−	8.28669e22i		−	0.111113i
$965$	−3.01041e23	+	5.90493e23i	−0.400320	+	0.785229i
$966$	7.82565e21			0.0103206
$967$	6.02694e23	+	6.02694e23i	0.788289	+	0.788289i	0.981214	−	0.192925i	$-0.0617974\pi$
$967$	6.02694e23	+	6.02694e23i	0.788289	+	0.788289i	−0.192925	+	0.981214i	$0.561797\pi$
$968$	−1.89662e23	+	1.89662e23i	−0.246024	+	0.246024i
$969$		−	3.72899e23i		−	0.479734i
$970$	1.18920e23	+	3.66283e23i	0.151734	+	0.467351i
$971$	−5.63725e23			−0.713367			−0.356684	−	0.934225i	$-0.616093\pi$
$971$	−5.63725e23			−0.713367			−0.356684	+	0.934225i	$0.616093\pi$
$972$	2.19312e23	+	2.19312e23i	0.275253	+	0.275253i
$973$	−2.19532e22	+	2.19532e22i	−0.0273272	+	0.0273272i
$974$			5.25572e23i			0.648874i
$975$	7.59022e22	+	1.04571e23i	0.0929432	+	0.128048i
$976$	2.23662e23			0.271640
$977$	−2.40635e23	−	2.40635e23i	−0.289870	−	0.289870i	0.547159	−	0.837029i	$-0.315709\pi$
$977$	−2.40635e23	−	2.40635e23i	−0.289870	−	0.289870i	−0.837029	+	0.547159i	$0.815709\pi$
$978$	−1.07205e23	+	1.07205e23i	−0.128087	+	0.128087i
$979$		−	7.73630e22i		−	0.0916794i
$980$	−4.03278e23	+	1.30931e23i	−0.474019	+	0.153899i
$981$	1.19413e24			1.39219
$982$	−1.57629e23	−	1.57629e23i	−0.182283	−	0.182283i
$983$	2.91880e23	−	2.91880e23i	0.334793	−	0.334793i	−0.519611	−	0.854403i	$-0.673923\pi$
$983$	2.91880e23	−	2.91880e23i	0.334793	−	0.334793i	0.854403	+	0.519611i	$0.173923\pi$
$984$			1.47380e22i			0.0167678i
$985$	1.29840e24	+	6.61943e23i	1.46528	+	0.747017i
$986$	−2.14736e23			−0.240376
$987$	3.73676e21	+	3.73676e21i	0.00414914	+	0.00414914i
$988$	2.84504e23	−	2.84504e23i	0.313352	−	0.313352i
$989$		−	1.30254e24i		−	1.42305i
$990$	−3.41855e22	+	6.70551e22i	−0.0370477	+	0.0726692i
$991$	−3.32140e23			−0.357052			−0.178526	−	0.983935i	$-0.557133\pi$
$991$	−3.32140e23			−0.357052			−0.178526	+	0.983935i	$0.557133\pi$
$992$	−1.21409e22	−	1.21409e22i	−0.0129467	−	0.0129467i
$993$	5.01060e22	−	5.01060e22i	0.0530024	−	0.0530024i
$994$			2.45146e22i			0.0257237i
$995$	−2.08604e23	−	6.42516e23i	−0.217139	−	0.668805i
$996$	−1.02677e21			−0.00106022
$997$	1.08741e23	+	1.08741e23i	0.111387	+	0.111387i	0.760603	−	0.649217i	$-0.224903\pi$
$997$	1.08741e23	+	1.08741e23i	0.111387	+	0.111387i	−0.649217	+	0.760603i	$0.724903\pi$
$998$	3.62466e23	−	3.62466e23i	0.368318	−	0.368318i
$999$		−	8.54998e23i		−	0.861869i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.17.c.a.7.2	yes	8
3.2	odd	2		90.17.g.b.37.4		8
4.3	odd	2		80.17.p.a.17.3		8
5.2	odd	4		50.17.c.d.43.3		8
5.3	odd	4	inner	10.17.c.a.3.2	✓	8
5.4	even	2		50.17.c.d.7.3		8
15.8	even	4		90.17.g.b.73.4		8
20.3	even	4		80.17.p.a.33.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.17.c.a.3.2	✓	8	5.3	odd	4	inner
10.17.c.a.7.2	yes	8	1.1	even	1	trivial
50.17.c.d.7.3		8	5.4	even	2
50.17.c.d.43.3		8	5.2	odd	4
80.17.p.a.17.3		8	4.3	odd	2
80.17.p.a.33.3		8	20.3	even	4
90.17.g.b.37.4		8	3.2	odd	2
90.17.g.b.73.4		8	15.8	even	4

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:	\( k \)	\(=\)	\( 17 \)
Character orbit:	\([\chi]\)	\(=\)	10.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-128.000 - 128.000i) q^{2} +(-1354.68 + 1354.68i) q^{3} +32768.0i q^{4} +(-371534. + 120625. i) q^{5} +346799. q^{6} +(232276. + 232276. i) q^{7} +(4.19430e6 - 4.19430e6i) q^{8} +3.93764e7i q^{9} +O(q^{10})\)	\(q+(-128.000 - 128.000i) q^{2} +(-1354.68 + 1354.68i) q^{3} +32768.0i q^{4} +(-371534. + 120625. i) q^{5} +346799. q^{6} +(232276. + 232276. i) q^{7} +(4.19430e6 - 4.19430e6i) q^{8} +3.93764e7i q^{9} +(6.29964e7 + 3.21163e7i) q^{10} +2.70321e7 q^{11} +(-4.43903e7 - 4.43903e7i) q^{12} +(3.12551e8 - 3.12551e8i) q^{13} -5.94626e7i q^{14} +(3.39902e8 - 6.66720e8i) q^{15} -1.07374e9 q^{16} +(-4.95457e9 - 4.95457e9i) q^{17} +(5.04018e9 - 5.04018e9i) q^{18} -2.77790e10i q^{19} +(-3.95264e9 - 1.21744e10i) q^{20} -6.29320e8 q^{21} +(-3.46011e9 - 3.46011e9i) q^{22} +(4.85746e10 - 4.85746e10i) q^{23} +1.13639e10i q^{24} +(1.23487e11 - 8.96326e10i) q^{25} -8.00131e10 q^{26} +(-1.11657e11 - 1.11657e11i) q^{27} +(-7.61121e9 + 7.61121e9i) q^{28} +1.69301e11i q^{29} +(-1.28848e11 + 4.18326e10i) q^{30} -8.83369e10 q^{31} +(1.37439e11 + 1.37439e11i) q^{32} +(-3.66200e10 + 3.66200e10i) q^{33} +1.26837e12i q^{34} +(-1.14317e11 - 5.82800e10i) q^{35} -1.29029e12 q^{36} +(3.82867e12 + 3.82867e12i) q^{37} +(-3.55572e12 + 3.55572e12i) q^{38} +8.46815e11i q^{39} +(-1.05239e12 + 2.06426e12i) q^{40} +1.29691e12 q^{41} +(8.05529e10 + 8.05529e10i) q^{42} +(1.34076e13 - 1.34076e13i) q^{43} +8.85789e11i q^{44} +(-4.74978e12 - 1.46297e13i) q^{45} -1.24351e13 q^{46} +(-5.93778e12 - 5.93778e12i) q^{47} +(1.45458e12 - 1.45458e12i) q^{48} -3.31250e13i q^{49} +(-2.72793e13 - 4.33338e12i) q^{50} +1.34238e13 q^{51} +(1.02417e13 + 1.02417e13i) q^{52} +(4.58521e13 - 4.58521e13i) q^{53} +2.85842e13i q^{54} +(-1.00434e13 + 3.26075e12i) q^{55} +1.94847e12 q^{56} +(3.76318e13 + 3.76318e13i) q^{57} +(2.16705e13 - 2.16705e13i) q^{58} +2.43196e14i q^{59} +(2.18471e13 + 1.11379e13i) q^{60} -2.08301e14 q^{61} +(1.13071e13 + 1.13071e13i) q^{62} +(-9.14618e12 + 9.14618e12i) q^{63} -3.51844e13i q^{64} +(-7.84219e13 + 1.53825e14i) q^{65} +9.37472e12 q^{66} +(3.69388e13 + 3.69388e13i) q^{67} +(1.62351e14 - 1.62351e14i) q^{68} +1.31606e14i q^{69} +(7.17267e12 + 2.20924e13i) q^{70} -4.12269e14 q^{71} +(1.65157e14 + 1.65157e14i) q^{72} +(1.10105e14 - 1.10105e14i) q^{73} -9.80140e14i q^{74} +(-4.58622e13 + 2.88710e14i) q^{75} +9.10263e14 q^{76} +(6.27891e12 + 6.27891e12i) q^{77} +(1.08392e14 - 1.08392e14i) q^{78} -2.00631e15i q^{79} +(3.98932e14 - 1.29520e14i) q^{80} -1.39250e15 q^{81} +(-1.66005e14 - 1.66005e14i) q^{82} +(1.15652e13 - 1.15652e13i) q^{83} -2.06216e13i q^{84} +(2.43844e15 + 1.24315e15i) q^{85} -3.43235e15 q^{86} +(-2.29349e14 - 2.29349e14i) q^{87} +(1.13381e14 - 1.13381e14i) q^{88} -2.86189e15i q^{89} +(-1.26463e15 + 2.48057e15i) q^{90} +1.45196e14 q^{91} +(1.59169e15 + 1.59169e15i) q^{92} +(1.19668e14 - 1.19668e14i) q^{93} +1.52007e15i q^{94} +(3.35085e15 + 1.03209e16i) q^{95} -3.72372e14 q^{96} +(3.85105e15 + 3.85105e15i) q^{97} +(-4.24000e15 + 4.24000e15i) q^{98} +1.06443e15i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 1024 q^{2} - 5382 q^{3} + 184830 q^{5} + 1377792 q^{6} - 1586702 q^{7} + 33554432 q^{8}+O(q^{10}) \) 8 * q - 1024 * q^2 - 5382 * q^3 + 184830 * q^5 + 1377792 * q^6 - 1586702 * q^7 + 33554432 * q^8	\( 8 q - 1024 q^{2} - 5382 q^{3} + 184830 q^{5} + 1377792 q^{6} - 1586702 q^{7} + 33554432 q^{8} - 179537920 q^{10} + 307957276 q^{11} - 176357376 q^{12} + 202095228 q^{13} - 4140218430 q^{15} - 8589934592 q^{16} - 10825054172 q^{17} - 19318270464 q^{18} + 39905198080 q^{20} - 279317583684 q^{21} - 39418531328 q^{22} - 58166716742 q^{23} + 48765928900 q^{25} - 51736378368 q^{26} - 433782808920 q^{27} + 51993051136 q^{28} + 881686264320 q^{30} - 1503757815484 q^{31} + 1099511627776 q^{32} + 3563163295596 q^{33} + 1361150225890 q^{35} + 4945477238784 q^{36} + 5719558248048 q^{37} + 10471905756160 q^{38} - 4332632145920 q^{40} - 21624661426724 q^{41} + 35752650711552 q^{42} + 694778360778 q^{43} - 125868018043710 q^{45} + 14890679485952 q^{46} + 17454156046938 q^{47} + 5778878496768 q^{48} - 38811694553600 q^{50} - 282689731949724 q^{51} + 6622256431104 q^{52} + 315933715243808 q^{53} - 170380752243540 q^{55} - 13310221090816 q^{56} + 218915538682320 q^{57} + 231112067379200 q^{58} - 90045006151680 q^{60} - 260671832048484 q^{61} + 192481000381952 q^{62} + 12\!\cdots\!78 q^{63}+ \cdots + 18\!\cdots\!04 q^{98}+O(q^{100}) \) 8 * q - 1024 * q^2 - 5382 * q^3 + 184830 * q^5 + 1377792 * q^6 - 1586702 * q^7 + 33554432 * q^8 - 179537920 * q^10 + 307957276 * q^11 - 176357376 * q^12 + 202095228 * q^13 - 4140218430 * q^15 - 8589934592 * q^16 - 10825054172 * q^17 - 19318270464 * q^18 + 39905198080 * q^20 - 279317583684 * q^21 - 39418531328 * q^22 - 58166716742 * q^23 + 48765928900 * q^25 - 51736378368 * q^26 - 433782808920 * q^27 + 51993051136 * q^28 + 881686264320 * q^30 - 1503757815484 * q^31 + 1099511627776 * q^32 + 3563163295596 * q^33 + 1361150225890 * q^35 + 4945477238784 * q^36 + 5719558248048 * q^37 + 10471905756160 * q^38 - 4332632145920 * q^40 - 21624661426724 * q^41 + 35752650711552 * q^42 + 694778360778 * q^43 - 125868018043710 * q^45 + 14890679485952 * q^46 + 17454156046938 * q^47 + 5778878496768 * q^48 - 38811694553600 * q^50 - 282689731949724 * q^51 + 6622256431104 * q^52 + 315933715243808 * q^53 - 170380752243540 * q^55 - 13310221090816 * q^56 + 218915538682320 * q^57 + 231112067379200 * q^58 - 90045006151680 * q^60 - 260671832048484 * q^61 + 192481000381952 * q^62 + 1279595714205978 * q^63 + 442440687522120 * q^65 - 912169803672576 * q^66 + 635885550643738 * q^67 + 354715375108096 * q^68 - 971840253967360 * q^70 - 1149989311263004 * q^71 - 633021086564352 * q^72 + 256748998181048 * q^73 + 1497316176176850 * q^75 - 2680807873576960 * q^76 + 1436195093152556 * q^77 - 1970051682083328 * q^78 - 198459701329920 * q^80 - 8745265883258892 * q^81 + 2767956662620672 * q^82 - 4115160605935662 * q^83 + 5650805123574940 * q^85 - 177863260359168 * q^86 + 3883634567812800 * q^87 + 1291666434555904 * q^88 + 14849617970903040 * q^90 - 28753310620553964 * q^91 - 1906006974201856 * q^92 + 26332871866839036 * q^93 + 40684157497310600 * q^95 - 1479392895172608 * q^96 - 17859102248834952 * q^97 + 18395730493909504 * q^98

Introduction

L-functions

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