LMFDB - Embedded newform 23.25.b.c.22.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [23,25,Mod(22,23)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(23, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 25, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("23.22"); S:= CuspForms(chi, 25); N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 25 $
Character orbit:	$[\chi]$	$=$	23.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [44] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$83.9424450193$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			22.10
Character	$\chi$	$=$	23.22
Dual form			23.25.b.c.22.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-4898.68 q^{2} -558886. q^{3} +7.21988e6 q^{4} +3.44673e8i q^{5} +2.73780e9 q^{6} +1.10267e10i q^{7} +4.68184e10 q^{8} +2.99237e10 q^{9} -1.68844e12i q^{10} +3.20119e12i q^{11} -4.03509e12 q^{12} +2.99647e13 q^{13} -5.40165e13i q^{14} -1.92633e14i q^{15} -3.50478e14 q^{16} -8.68847e14i q^{17} -1.46587e14 q^{18} +4.61494e14i q^{19} +2.48850e15i q^{20} -6.16269e15i q^{21} -1.56816e16i q^{22} +(1.41046e16 + 1.67723e16i) q^{23} -2.61661e16 q^{24} -5.91949e16 q^{25} -1.46788e17 q^{26} +1.41122e17 q^{27} +7.96117e16i q^{28} +4.83522e17 q^{29} +9.43647e17i q^{30} -1.01314e18 q^{31} +9.31398e17 q^{32} -1.78910e18i q^{33} +4.25620e18i q^{34} -3.80062e18 q^{35} +2.16046e17 q^{36} +4.31926e18i q^{37} -2.26071e18i q^{38} -1.67469e19 q^{39} +1.61370e19i q^{40} -4.06252e19 q^{41} +3.01891e19i q^{42} +1.34334e18i q^{43} +2.31122e19i q^{44} +1.03139e19i q^{45} +(-6.90940e19 - 8.21623e19i) q^{46} -3.48139e19 q^{47} +1.95877e20 q^{48} +6.99922e19 q^{49} +2.89977e20 q^{50} +4.85586e20i q^{51} +2.16342e20 q^{52} -1.18991e20i q^{53} -6.91311e20 q^{54} -1.10336e21 q^{55} +5.16254e20i q^{56} -2.57923e20i q^{57} -2.36862e21 q^{58} -1.83985e21 q^{59} -1.39079e21i q^{60} +2.94336e21i q^{61} +4.96307e21 q^{62} +3.29961e20i q^{63} +1.31742e21 q^{64} +1.03280e22i q^{65} +8.76422e21i q^{66} -1.48528e22i q^{67} -6.27297e21i q^{68} +(-7.88287e21 - 9.37381e21i) q^{69} +1.86180e22 q^{70} -6.39534e21 q^{71} +1.40098e21 q^{72} +4.93273e21 q^{73} -2.11587e22i q^{74} +3.30832e22 q^{75} +3.33193e21i q^{76} -3.52986e22 q^{77} +8.20376e22 q^{78} -7.06115e22i q^{79} -1.20800e23i q^{80} -8.73224e22 q^{81} +1.99010e23 q^{82} -1.88596e23i q^{83} -4.44939e22i q^{84} +2.99468e23 q^{85} -6.58060e21i q^{86} -2.70234e23 q^{87} +1.49874e23i q^{88} -5.32504e22i q^{89} -5.05245e22i q^{90} +3.30413e23i q^{91} +(1.01834e23 + 1.21094e23i) q^{92} +5.66232e23 q^{93} +1.70542e23 q^{94} -1.59065e23 q^{95} -5.20545e23 q^{96} -6.10526e23i q^{97} -3.42870e23 q^{98} +9.57914e22i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 4232 q^{2} - 434562 q^{3} + 317760360 q^{4} - 8460029520 q^{6} - 198307023760 q^{8} + 4220041988298 q^{9} - 67439597688792 q^{12} + 5771152551358 q^{13} + 18\!\cdots\!92 q^{16} + 18\!\cdots\!68 q^{18}+ \cdots - 20\!\cdots\!92 q^{98}+O(q^{100}) $ 44 * q - 4232 * q^2 - 434562 * q^3 + 317760360 * q^4 - 8460029520 * q^6 - 198307023760 * q^8 + 4220041988298 * q^9 - 67439597688792 * q^12 + 5771152551358 * q^13 + 1801550792530192 * q^16 + 1842830558165568 * q^18 - 117204213263210644 * q^23 - 186493005437450784 * q^24 - 689533084157602612 * q^25 - 548650296251047576 * q^26 + 824037505793640630 * q^27 - 1583078054945709602 * q^29 - 77249813729122274 * q^31 - 2838716832733708512 * q^32 + 3418569899175948192 * q^35 + 71181245116739335248 * q^36 + 47106572467817156310 * q^39 - 9150679195666184738 * q^41 - 153049487518536134480 * q^46 + 22735751396127769438 * q^47 - 1317482931964495330032 * q^48 - 1842110772006482246836 * q^49 + 284936617115007894520 * q^50 + 207129175371045152568 * q^52 - 381774025126375304544 * q^54 - 5430040696094013021792 * q^55 - 2168901871328366220760 * q^58 + 16048018791948427185304 * q^59 + 14054450375064171442400 * q^62 + 20310379126091866412192 * q^64 + 24476879859710435470878 * q^69 - 118028399895318845638416 * q^70 - 68204988047209908888578 * q^71 - 106777935582637627887744 * q^72 - 7319375899831086678722 * q^73 + 12913295383070041819998 * q^75 + 111116199573084838704480 * q^77 - 422583593213386075404144 * q^78 - 331350288185757013618680 * q^81 + 1000764218021118649437320 * q^82 - 113385735487939722862944 * q^85 - 248828610584854760185290 * q^87 - 4238455111972177116774696 * q^92 + 4492289396741153284965270 * q^93 - 1602622056539190351258592 * q^94 - 1668692394291208047471936 * q^95 - 12092663288748189077973504 * q^96 - 2067304853876486831513192 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/23\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$-1$

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 $

$2$	−4898.68			−1.19597			−0.597984	−	0.801508i	$-0.704031\pi$
$2$	−4898.68			−1.19597			−0.597984	+	0.801508i	$0.704031\pi$
$3$	−558886.			−1.05164			−0.525821	−	0.850595i	$-0.676242\pi$
$3$	−558886.			−1.05164			−0.525821	+	0.850595i	$0.676242\pi$
$4$	7.21988e6			0.430338
$5$			3.44673e8i			1.41178i	0.708321	+	0.705890i	$0.249453\pi$
$5$			3.44673e8i			1.41178i	−0.708321	+	0.705890i	$0.750547\pi$
$6$	2.73780e9			1.25773
$7$			1.10267e10i			0.796656i	0.917243	+	0.398328i	$0.130409\pi$
$7$			1.10267e10i			0.796656i	−0.917243	+	0.398328i	$0.869591\pi$
$8$	4.68184e10			0.681297
$9$	2.99237e10			0.105951
$10$		−	1.68844e12i		−	1.68844i
$11$			3.20119e12i			1.02000i	0.860175	+	0.509998i	$0.170354\pi$
$11$			3.20119e12i			1.02000i	−0.860175	+	0.509998i	$0.829646\pi$
$12$	−4.03509e12			−0.452562
$13$	2.99647e13			1.28615			0.643073	−	0.765805i	$-0.277659\pi$
$13$	2.99647e13			1.28615			0.643073	+	0.765805i	$0.277659\pi$
$14$		−	5.40165e13i		−	0.952774i
$15$		−	1.92633e14i		−	1.48469i
$16$	−3.50478e14			−1.24515
$17$		−	8.68847e14i		−	1.49127i	−0.666355	−	0.745635i	$-0.732146\pi$
$17$		−	8.68847e14i		−	1.49127i	0.666355	−	0.745635i	$-0.267854\pi$
$18$	−1.46587e14			−0.126714
$19$			4.61494e14i			0.208508i	0.994551	+	0.104254i	$0.0332455\pi$
$19$			4.61494e14i			0.208508i	−0.994551	+	0.104254i	$0.966754\pi$
$20$			2.48850e15i			0.607543i
$21$		−	6.16269e15i		−	0.837797i
$22$		−	1.56816e16i		−	1.21988i
$23$	1.41046e16	+	1.67723e16i	0.643617	+	0.765348i
$23$	1.41046e16	+	1.67723e16i	0.643617	+	0.765348i
$24$	−2.61661e16			−0.716480
$25$	−5.91949e16			−0.993125
$26$	−1.46788e17			−1.53819
$27$	1.41122e17			0.940219
$28$			7.96117e16i			0.342831i
$29$	4.83522e17			1.36660			0.683299	−	0.730139i	$-0.260545\pi$
$29$	4.83522e17			1.36660			0.683299	+	0.730139i	$0.260545\pi$
$30$			9.43647e17i			1.77564i
$31$	−1.01314e18			−1.28627			−0.643133	−	0.765755i	$-0.722366\pi$
$31$	−1.01314e18			−1.28627			−0.643133	+	0.765755i	$0.722366\pi$
$32$	9.31398e17			0.807859
$33$		−	1.78910e18i		−	1.07267i
$34$			4.25620e18i			1.78351i
$35$	−3.80062e18			−1.12470
$36$	2.16046e17			0.0455948
$37$			4.31926e18i			0.656129i	0.944655	+	0.328064i	$0.106396\pi$
$37$			4.31926e18i			0.656129i	−0.944655	+	0.328064i	$0.893604\pi$
$38$		−	2.26071e18i		−	0.249369i
$39$	−1.67469e19			−1.35257
$40$			1.61370e19i			0.961842i
$41$	−4.06252e19			−1.80048			−0.900242	−	0.435389i	$-0.856611\pi$
$41$	−4.06252e19			−1.80048			−0.900242	+	0.435389i	$0.856611\pi$
$42$			3.01891e19i			1.00198i
$43$			1.34334e18i			0.0336174i	0.999859	+	0.0168087i	$0.00535063\pi$
$43$			1.34334e18i			0.0336174i	−0.999859	+	0.0168087i	$0.994649\pi$
$44$			2.31122e19i			0.438944i
$45$			1.03139e19i			0.149580i
$46$	−6.90940e19	−	8.21623e19i	−0.769745	−	0.915331i
$47$	−3.48139e19			−0.299625			−0.149813	−	0.988714i	$-0.547867\pi$
$47$	−3.48139e19			−0.299625			−0.149813	+	0.988714i	$0.547867\pi$
$48$	1.95877e20			1.30945
$49$	6.99922e19			0.365340
$50$	2.89977e20			1.18775
$51$			4.85586e20i			1.56828i
$52$	2.16342e20			0.553478
$53$		−	1.18991e20i		−	0.242217i	−0.992639	−	0.121108i	$-0.961355\pi$
$53$		−	1.18991e20i		−	0.242217i	0.992639	−	0.121108i	$-0.0386449\pi$
$54$	−6.91311e20			−1.12447
$55$	−1.10336e21			−1.44001
$56$			5.16254e20i			0.542759i
$57$		−	2.57923e20i		−	0.219276i
$58$	−2.36862e21			−1.63441
$59$	−1.83985e21			−1.03409			−0.517046	−	0.855958i	$-0.672968\pi$
$59$	−1.83985e21			−1.03409			−0.517046	+	0.855958i	$0.672968\pi$
$60$		−	1.39079e21i		−	0.638918i
$61$			2.94336e21i			1.10888i	0.832223	+	0.554441i	$0.187068\pi$
$61$			2.94336e21i			1.10888i	−0.832223	+	0.554441i	$0.812932\pi$
$62$	4.96307e21			1.53833
$63$			3.29961e20i			0.0844066i
$64$	1.31742e21			0.278974
$65$			1.03280e22i			1.81576i
$66$			8.76422e21i			1.28288i
$67$		−	1.48528e22i		−	1.81514i	−0.419903	−	0.907569i	$-0.637936\pi$
$67$		−	1.48528e22i		−	1.81514i	0.419903	−	0.907569i	$-0.362064\pi$
$68$		−	6.27297e21i		−	0.641750i
$69$	−7.88287e21	−	9.37381e21i	−0.676854	−	0.804872i
$70$	1.86180e22			1.34511
$71$	−6.39534e21			−0.389730			−0.194865	−	0.980830i	$-0.562427\pi$
$71$	−6.39534e21			−0.389730			−0.194865	+	0.980830i	$0.562427\pi$
$72$	1.40098e21			0.0721842
$73$	4.93273e21			0.215384			0.107692	−	0.994184i	$-0.465654\pi$
$73$	4.93273e21			0.215384			0.107692	+	0.994184i	$0.465654\pi$
$74$		−	2.11587e22i		−	0.784708i
$75$	3.30832e22			1.04441
$76$			3.33193e21i			0.0897291i
$77$	−3.52986e22			−0.812586
$78$	8.20376e22			1.61762
$79$		−	7.06115e22i		−	1.19495i	−0.801887	−	0.597476i	$-0.796170\pi$
$79$		−	7.06115e22i		−	1.19495i	0.801887	−	0.597476i	$-0.203830\pi$
$80$		−	1.20800e23i		−	1.75787i
$81$	−8.73224e22			−1.09473
$82$	1.99010e23			2.15332
$83$		−	1.88596e23i		−	1.76439i	−0.470881	−	0.882197i	$-0.656064\pi$
$83$		−	1.88596e23i		−	1.76439i	0.470881	−	0.882197i	$-0.343936\pi$
$84$		−	4.44939e22i		−	0.360536i
$85$	2.99468e23			2.10535
$86$		−	6.58060e21i		−	0.0402054i
$87$	−2.70234e23			−1.43717
$88$			1.49874e23i			0.694920i
$89$		−	5.32504e22i		−	0.215597i	−0.994173	−	0.107799i	$-0.965620\pi$
$89$		−	5.32504e22i		−	0.215597i	0.994173	−	0.107799i	$-0.0343801\pi$
$90$		−	5.05245e22i		−	0.178893i
$91$			3.30413e23i			1.02462i
$92$	1.01834e23	+	1.21094e23i	0.276973	+	0.329359i
$93$	5.66232e23			1.35269
$94$	1.70542e23			0.358342
$95$	−1.59065e23			−0.294368
$96$	−5.20545e23			−0.849578
$97$		−	6.10526e23i		−	0.879921i	−0.898017	−	0.439960i	$-0.854993\pi$
$97$		−	6.10526e23i		−	0.879921i	0.898017	−	0.439960i	$-0.145007\pi$
$98$	−3.42870e23			−0.436934
$99$			9.57914e22i			0.108070i
$100$	−4.27380e23			−0.427380
$101$	−1.20912e24			−1.07304			−0.536518	−	0.843889i	$-0.680260\pi$
$101$	−1.20912e24			−1.07304			−0.536518	+	0.843889i	$0.680260\pi$
$102$		−	2.37873e24i		−	1.87561i
$103$			2.03061e24i			1.42423i	0.702063	+	0.712115i	$0.252262\pi$
$103$			2.03061e24i			1.42423i	−0.702063	+	0.712115i	$0.747738\pi$
$104$	1.40290e24			0.876247
$105$	2.12411e24			1.18279
$106$			5.82900e23i			0.289684i
$107$		−	2.20342e24i		−	0.978345i	−0.872187	−	0.489172i	$-0.837299\pi$
$107$		−	2.20342e24i		−	0.978345i	0.872187	−	0.489172i	$-0.162701\pi$
$108$	1.01888e24			0.404612
$109$		−	1.39261e24i		−	0.495122i	−0.968872	−	0.247561i	$-0.920371\pi$
$109$		−	1.39261e24i		−	0.495122i	0.968872	−	0.247561i	$-0.0796291\pi$
$110$	5.40502e24			1.72221
$111$		−	2.41397e24i		−	0.690012i
$112$		−	3.86463e24i		−	0.991954i
$113$		−	5.84039e24i		−	1.34741i	−0.738999	−	0.673707i	$-0.764701\pi$
$113$		−	5.84039e24i		−	1.34741i	0.738999	−	0.673707i	$-0.235299\pi$
$114$			1.26348e24i			0.262247i
$115$	−5.78096e24	+	4.86148e24i	−1.08050	+	0.908646i
$116$	3.49097e24			0.588099
$117$	8.96657e23			0.136269
$118$	9.01285e24			1.23674
$119$	9.58055e24			1.18803
$120$		−	9.01875e24i		−	1.01151i
$121$	−3.97861e23			−0.0403930
$122$		−	1.44186e25i		−	1.32619i
$123$	2.27049e25			1.89347
$124$	−7.31477e24			−0.553529
$125$			1.41241e23i			0.00970603i
$126$		−	1.61638e24i		−	0.100948i
$127$	−1.10569e25			−0.628045			−0.314022	−	0.949416i	$-0.601677\pi$
$127$	−1.10569e25			−0.628045			−0.314022	+	0.949416i	$0.601677\pi$
$128$	−2.20799e25			−1.14150
$129$		−	7.50774e23i		−	0.0353535i
$130$		−	5.05938e25i		−	2.17159i
$131$	1.57347e24			0.0616033			0.0308017	−	0.999526i	$-0.490194\pi$
$131$	1.57347e24			0.0616033			0.0308017	+	0.999526i	$0.490194\pi$
$132$		−	1.29171e25i		−	0.461612i
$133$	−5.08878e24			−0.166109
$134$			7.27590e25i			2.17085i
$135$			4.86409e25i			1.32738i
$136$		−	4.06780e25i		−	1.01600i
$137$			5.74668e25i			1.31453i	0.753660	+	0.657264i	$0.228286\pi$
$137$			5.74668e25i			1.31453i	−0.753660	+	0.657264i	$0.771714\pi$
$138$	3.86157e25	+	4.59193e25i	0.809496	+	0.962601i
$139$	−1.00297e26			−1.92802			−0.964008	−	0.265872i	$-0.914340\pi$
$139$	−1.00297e26			−1.92802			−0.964008	+	0.265872i	$0.914340\pi$
$140$	−2.74400e25			−0.484003
$141$	1.94570e25			0.315098
$142$	3.13287e25			0.466104
$143$			9.59227e25i			1.31186i
$144$	−1.04876e25			−0.131925
$145$			1.66657e26i			1.92934i
$146$	−2.41639e25			−0.257592
$147$	−3.91177e25			−0.384207
$148$			3.11846e25i			0.282357i
$149$		−	1.64753e26i		−	1.37594i	−0.725741	−	0.687968i	$-0.758503\pi$
$149$		−	1.64753e26i		−	1.37594i	0.725741	−	0.687968i	$-0.241497\pi$
$150$	−1.62064e26			−1.24908
$151$	−1.91291e26			−1.36136			−0.680678	−	0.732583i	$-0.738315\pi$
$151$	−1.91291e26			−1.36136			−0.680678	+	0.732583i	$0.738315\pi$
$152$			2.16064e25i			0.142056i
$153$		−	2.59991e25i		−	0.158002i
$154$	1.72917e26			0.971827
$155$		−	3.49203e26i		−	1.81593i
$156$	−1.20910e26			−0.582061
$157$		−	1.42229e26i		−	0.634149i	−0.948401	−	0.317074i	$-0.897300\pi$
$157$		−	1.42229e26i		−	0.634149i	0.948401	−	0.317074i	$-0.102700\pi$
$158$			3.45903e26i			1.42912i
$159$			6.65025e25i			0.254726i
$160$			3.21028e26i			1.14052i
$161$	−1.84944e26	+	1.55528e26i	−0.609719	+	0.512741i
$162$	4.27765e26			1.30926
$163$	−1.41885e26			−0.403353			−0.201676	−	0.979452i	$-0.564639\pi$
$163$	−1.41885e26			−0.403353			−0.201676	+	0.979452i	$0.564639\pi$
$164$	−2.93309e26			−0.774818
$165$	6.16654e26			1.51438
$166$			9.23872e26i			2.11016i
$167$	−2.34417e26			−0.498185			−0.249093	−	0.968480i	$-0.580132\pi$
$167$	−2.34417e26			−0.498185			−0.249093	+	0.968480i	$0.580132\pi$
$168$		−	2.88527e26i		−	0.570788i
$169$	3.55085e26			0.654172
$170$	−1.46700e27			−2.51792
$171$			1.38096e25i			0.0220917i
$172$			9.69876e24i			0.0144669i
$173$	−4.43019e26			−0.616409			−0.308205	−	0.951320i	$-0.599728\pi$
$173$	−4.43019e26			−0.616409			−0.308205	+	0.951320i	$0.599728\pi$
$174$	1.32379e27			1.71881
$175$		−	6.52726e26i		−	0.791179i
$176$		−	1.12194e27i		−	1.27005i
$177$	1.02827e27			1.08749
$178$			2.60857e26i			0.257847i
$179$	6.31877e26			0.583978			0.291989	−	0.956422i	$-0.405683\pi$
$179$	6.31877e26			0.583978			0.291989	+	0.956422i	$0.405683\pi$
$180$			7.44651e25i			0.0643699i
$181$		−	5.84915e25i		−	0.0473097i	−0.999720	−	0.0236548i	$-0.992470\pi$
$181$		−	5.84915e25i		−	0.0473097i	0.999720	−	0.0236548i	$-0.00753027\pi$
$182$		−	1.61859e27i		−	1.22541i
$183$		−	1.64500e27i		−	1.16615i
$184$	6.60355e26	+	7.85252e26i	0.438494	+	0.521429i
$185$	−1.48873e27			−0.926310
$186$	−2.77379e27			−1.61777
$187$	2.78134e27			1.52109
$188$	−2.51352e26			−0.128940
$189$			1.55611e27i			0.749031i
$190$	7.79207e26			0.352054
$191$		−	1.74910e27i		−	0.742018i	−0.928629	−	0.371009i	$-0.879012\pi$
$191$		−	1.74910e27i		−	0.742018i	0.928629	−	0.371009i	$-0.120988\pi$
$192$	−7.36287e26			−0.293381
$193$	2.08176e27			0.779368			0.389684	−	0.920949i	$-0.372584\pi$
$193$	2.08176e27			0.779368			0.389684	+	0.920949i	$0.372584\pi$
$194$			2.99077e27i			1.05236i
$195$		−	5.77219e27i		−	1.90953i
$196$	5.05335e26			0.157220
$197$	3.59501e27			1.05222			0.526108	−	0.850418i	$-0.323651\pi$
$197$	3.59501e27			1.05222			0.526108	+	0.850418i	$0.323651\pi$
$198$		−	4.69252e26i		−	0.129248i
$199$			1.71314e27i			0.444177i	0.975027	+	0.222088i	$0.0712874\pi$
$199$			1.71314e27i			0.444177i	−0.975027	+	0.222088i	$0.928713\pi$
$200$	−2.77141e27			−0.676613
$201$			8.30100e27i			1.90888i
$202$	5.92311e27			1.28332
$203$			5.33167e27i			1.08871i
$204$			3.50587e27i			0.674892i
$205$		−	1.40024e28i		−	2.54189i
$206$		−	9.94732e27i		−	1.70333i
$207$	4.22063e26	+	5.01890e26i	0.0681919	+	0.0810895i
$208$	−1.05020e28			−1.60144
$209$	−1.47733e27			−0.212678
$210$	−1.04054e28			−1.41457
$211$	1.02156e28			1.31182			0.655909	−	0.754840i	$-0.272285\pi$
$211$	1.02156e28			1.31182			0.655909	+	0.754840i	$0.272285\pi$
$212$		−	8.59102e26i		−	0.104235i
$213$	3.57426e27			0.409856
$214$			1.07939e28i			1.17007i
$215$	−4.63013e26			−0.0474605
$216$	6.60710e27			0.640569
$217$		−	1.11717e28i		−	1.02471i
$218$			6.82197e27i			0.592150i
$219$	−2.75683e27			−0.226507
$220$	−7.96614e27			−0.619692
$221$		−	2.60348e28i		−	1.91799i
$222$			1.18253e28i			0.825232i
$223$	9.26098e27			0.612349			0.306174	−	0.951975i	$-0.400951\pi$
$223$	9.26098e27			0.612349			0.306174	+	0.951975i	$0.400951\pi$
$224$			1.02703e28i			0.643585i
$225$	−1.77133e27			−0.105223
$226$			2.86102e28i			1.61146i
$227$		−	1.29950e28i		−	0.694168i	−0.937834	−	0.347084i	$-0.887172\pi$
$227$		−	1.29950e28i		−	0.694168i	0.937834	−	0.347084i	$-0.112828\pi$
$228$		−	1.86217e27i		−	0.0943629i
$229$		−	3.07988e28i		−	1.48084i	−0.672145	−	0.740420i	$-0.734627\pi$
$229$		−	3.07988e28i		−	1.48084i	0.672145	−	0.740420i	$-0.265373\pi$
$230$	2.83191e28	−	2.38149e28i	1.29225	−	1.08671i
$231$	1.97279e28			0.854550
$232$	2.26377e28			0.931058
$233$	5.14940e27			0.201134			0.100567	−	0.994930i	$-0.467934\pi$
$233$	5.14940e27			0.201134			0.100567	+	0.994930i	$0.467934\pi$
$234$	−4.39244e27			−0.162973
$235$		−	1.19994e28i		−	0.423005i
$236$	−1.32835e28			−0.445009
$237$			3.94637e28i			1.25666i
$238$	−4.69321e28			−1.42084
$239$	−1.52770e28			−0.439807			−0.219904	−	0.975522i	$-0.570574\pi$
$239$	−1.52770e28			−0.439807			−0.219904	+	0.975522i	$0.570574\pi$
$240$			6.75135e28i			1.84866i
$241$		−	4.55873e28i		−	1.18752i	−0.804644	−	0.593758i	$-0.797644\pi$
$241$		−	4.55873e28i		−	1.18752i	0.804644	−	0.593758i	$-0.202356\pi$
$242$	1.94899e27			0.0483088
$243$	8.94623e27			0.211040
$244$			2.12507e28i			0.477195i
$245$			2.41244e28i			0.515780i
$246$	−1.11224e29			−2.26452
$247$			1.38286e28i			0.268172i
$248$	−4.74337e28			−0.876329
$249$			1.05404e29i			1.85551i
$250$		−	6.91896e26i		−	0.0116081i
$251$			2.40649e28i			0.384856i	0.981311	+	0.192428i	$0.0616362\pi$
$251$			2.40649e28i			0.384856i	−0.981311	+	0.192428i	$0.938364\pi$
$252$			2.38228e27i			0.0363234i
$253$	−5.36913e28	+	4.51515e28i	−0.780652	+	0.656487i
$254$	5.41645e28			0.751121
$255$	−1.67368e29			−2.21407
$256$	8.60597e28			1.08623
$257$	−7.13777e28			−0.859736			−0.429868	−	0.902892i	$-0.641440\pi$
$257$	−7.13777e28			−0.859736			−0.429868	+	0.902892i	$0.641440\pi$
$258$			3.67780e27i			0.0422817i
$259$	−4.76274e28			−0.522708
$260$			7.45672e28i			0.781390i
$261$	1.44688e28			0.144793
$262$	−7.70795e27			−0.0736756
$263$			1.94537e29i			1.77637i	0.459491	+	0.888183i	$0.348032\pi$
$263$			1.94537e29i			1.77637i	−0.459491	+	0.888183i	$0.651968\pi$
$264$		−	8.37626e28i		−	0.730808i
$265$	4.10131e28			0.341957
$266$	2.49283e28			0.198661
$267$			2.97609e28i			0.226731i
$268$		−	1.07235e29i		−	0.781124i
$269$	1.23899e29			0.863056			0.431528	−	0.902099i	$-0.357975\pi$
$269$	1.23899e29			0.863056			0.431528	+	0.902099i	$0.357975\pi$
$270$		−	2.38276e29i		−	1.58751i
$271$	1.71744e29			1.09459			0.547293	−	0.836941i	$-0.315658\pi$
$271$	1.71744e29			1.09459			0.547293	+	0.836941i	$0.315658\pi$
$272$			3.04511e29i			1.85685i
$273$		−	1.84663e29i		−	1.07753i
$274$		−	2.81512e29i		−	1.57213i
$275$		−	1.89494e29i		−	1.01298i
$276$	−5.69134e28	−	6.76778e28i	−0.291276	−	0.346367i
$277$	3.29395e29			1.61421			0.807104	−	0.590410i	$-0.201034\pi$
$277$	3.29395e29			1.61421			0.807104	+	0.590410i	$0.201034\pi$
$278$	4.91324e29			2.30585
$279$	−3.03170e28			−0.136281
$280$	−1.77939e29			−0.766257
$281$			1.88960e29i			0.779638i	0.920891	+	0.389819i	$0.127462\pi$
$281$			1.88960e29i			0.779638i	−0.920891	+	0.389819i	$0.872538\pi$
$282$	−9.53136e28			−0.376847
$283$		−	2.13934e28i		−	0.0810666i	−0.999178	−	0.0405333i	$-0.987094\pi$
$283$		−	2.13934e28i		−	0.0810666i	0.999178	−	0.0405333i	$-0.0129057\pi$
$284$	−4.61736e28			−0.167716
$285$	8.88990e28			0.309570
$286$		−	4.69895e29i		−	1.56895i
$287$		−	4.47964e29i		−	1.43437i
$288$	2.78709e28			0.0855936
$289$	−4.15446e29			−1.22388
$290$		−	8.16400e29i		−	2.30742i
$291$			3.41214e29i			0.925362i
$292$	3.56137e28			0.0926880
$293$		−	1.35561e29i		−	0.338629i	−0.985562	−	0.169314i	$-0.945845\pi$
$293$		−	1.35561e29i		−	0.338629i	0.985562	−	0.169314i	$-0.0541553\pi$
$294$	1.91625e29			0.459499
$295$		−	6.34147e29i		−	1.45991i
$296$			2.02221e29i			0.447018i
$297$			4.51757e29i			0.959021i
$298$			8.07073e29i			1.64557i
$299$	4.22641e29	+	5.02578e29i	0.827785	+	0.984350i
$300$	2.38856e29			0.449451
$301$	−1.48127e28			−0.0267815
$302$	9.37075e29			1.62814
$303$	6.75762e29			1.12845
$304$		−	1.61744e29i		−	0.259623i
$305$	−1.01450e30			−1.56550
$306$			1.27362e29i			0.188965i
$307$	4.25550e29			0.607142			0.303571	−	0.952809i	$-0.401821\pi$
$307$	4.25550e29			0.607142			0.303571	+	0.952809i	$0.401821\pi$
$308$	−2.54852e29			−0.349687
$309$		−	1.13488e30i		−	1.49778i
$310$			1.71064e30i			2.17179i
$311$	−6.75335e29			−0.824887			−0.412443	−	0.910983i	$-0.635325\pi$
$311$	−6.75335e29			−0.824887			−0.412443	+	0.910983i	$0.635325\pi$
$312$	−7.84061e29			−0.921499
$313$		−	1.34263e30i		−	1.51854i	−0.650778	−	0.759268i	$-0.725557\pi$
$313$		−	1.34263e30i		−	1.51854i	0.650778	−	0.759268i	$-0.274443\pi$
$314$			6.96733e29i			0.758421i
$315$	−1.13729e29			−0.119164
$316$		−	5.09806e29i		−	0.514233i
$317$	−1.40672e30			−1.36614			−0.683070	−	0.730353i	$-0.739356\pi$
$317$	−1.40672e30			−1.36614			−0.683070	+	0.730353i	$0.739356\pi$
$318$		−	3.25775e29i		−	0.304644i
$319$			1.54784e30i			1.39392i
$320$			4.54079e29i			0.393851i
$321$			1.23146e30i			1.02887i
$322$	9.05982e29	−	7.61882e29i	0.729204	−	0.613221i
$323$	4.00968e29			0.310942
$324$	−6.30457e29			−0.471102
$325$	−1.77376e30			−1.27730
$326$	6.95050e29			0.482397
$327$			7.78312e29i			0.520692i
$328$	−1.90201e30			−1.22666
$329$		−	3.83884e29i		−	0.238698i
$330$	−3.02079e30			−1.81115
$331$	8.53886e29			0.493701			0.246850	−	0.969054i	$-0.420604\pi$
$331$	8.53886e29			0.493701			0.246850	+	0.969054i	$0.420604\pi$
$332$		−	1.36164e30i		−	0.759286i
$333$			1.29248e29i			0.0695176i
$334$	1.14833e30			0.595813
$335$	5.11935e30			2.56258
$336$			2.15989e30i			1.04318i
$337$		−	1.85086e30i		−	0.862609i	−0.902206	−	0.431305i	$-0.858053\pi$
$337$		−	1.85086e30i		−	0.862609i	0.902206	−	0.431305i	$-0.141947\pi$
$338$	−1.73945e30			−0.782369
$339$			3.26411e30i			1.41700i
$340$	2.16212e30			0.906011
$341$		−	3.24326e30i		−	1.31199i
$342$		−	6.76490e28i		−	0.0264209i
$343$			2.88430e30i			1.08771i
$344$			6.28930e28i			0.0229035i
$345$	3.23090e30	−	2.71701e30i	1.13630	−	0.955570i
$346$	2.17021e30			0.737206
$347$	−4.80947e30			−1.57813			−0.789066	−	0.614309i	$-0.789435\pi$
$347$	−4.80947e30			−1.57813			−0.789066	+	0.614309i	$0.789435\pi$
$348$	−1.95105e30			−0.618470
$349$	1.60875e30			0.492701			0.246350	−	0.969181i	$-0.420769\pi$
$349$	1.60875e30			0.492701			0.246350	+	0.969181i	$0.420769\pi$
$350$			3.19750e30i			0.946224i
$351$	4.22868e30			1.20926
$352$			2.98158e30i			0.824013i
$353$	−4.50147e30			−1.20243			−0.601213	−	0.799089i	$-0.705316\pi$
$353$	−4.50147e30			−1.20243			−0.601213	+	0.799089i	$0.705316\pi$
$354$	−5.03715e30			−1.30061
$355$		−	2.20430e30i		−	0.550213i
$356$		−	3.84462e29i		−	0.0927797i
$357$	−5.35443e30			−1.24938
$358$	−3.09537e30			−0.698419
$359$		−	3.08580e30i		−	0.673340i	−0.941623	−	0.336670i	$-0.890699\pi$
$359$		−	3.08580e30i		−	0.673340i	0.941623	−	0.336670i	$-0.109301\pi$
$360$			4.82880e29i			0.101908i
$361$	4.68579e30			0.956524
$362$			2.86531e29i			0.0565808i
$363$	2.22359e29			0.0424790
$364$			2.38555e30i			0.440931i
$365$			1.70018e30i			0.304075i
$366$			8.05835e30i			1.39467i
$367$			1.97613e30i			0.330995i	0.986210	+	0.165498i	$0.0529231\pi$
$367$			1.97613e30i			0.330995i	−0.986210	+	0.165498i	$0.947077\pi$
$368$	−4.94336e30	−	5.87832e30i	−0.801398	−	0.952971i
$369$	−1.21566e30			−0.190763
$370$	7.29283e30			1.10784
$371$	1.31209e30			0.192964
$372$	4.08812e30			0.582115
$373$		−	1.09084e31i		−	1.50402i	−0.659150	−	0.752012i	$-0.729084\pi$
$373$		−	1.09084e31i		−	1.50402i	0.659150	−	0.752012i	$-0.270916\pi$
$374$	−1.36249e31			−1.81917
$375$		−	7.89378e28i		−	0.0102073i
$376$	−1.62993e30			−0.204134
$377$	1.44886e31			1.75764
$378$		−	7.62291e30i		−	0.895817i
$379$		−	3.60912e30i		−	0.410895i	−0.978668	−	0.205447i	$-0.934135\pi$
$379$		−	3.60912e30i		−	0.410895i	0.978668	−	0.205447i	$-0.0658649\pi$
$380$	−1.14843e30			−0.126678
$381$	6.17957e30			0.660478
$382$			8.56829e30i			0.887429i
$383$			7.38277e30i			0.741027i	0.928827	+	0.370514i	$0.120818\pi$
$383$			7.38277e30i			0.741027i	−0.928827	+	0.370514i	$0.879182\pi$
$384$	1.23401e31			1.20045
$385$		−	1.21665e31i		−	1.14719i
$386$	−1.01979e31			−0.932099
$387$			4.01978e28i			0.00356181i
$388$		−	4.40793e30i		−	0.378664i
$389$			1.15521e31i			0.962198i	0.876666	+	0.481099i	$0.159762\pi$
$389$			1.15521e31i			0.962198i	−0.876666	+	0.481099i	$0.840238\pi$
$390$			2.82761e31i			2.28373i
$391$	1.45726e31	−	1.22547e31i	1.14134	−	0.959806i
$392$	3.27692e30			0.248905
$393$	−8.79393e29			−0.0647847
$394$	−1.76108e31			−1.25842
$395$	2.43379e31			1.68701
$396$			6.91603e29i			0.0465066i
$397$	−1.45245e31			−0.947575			−0.473788	−	0.880639i	$-0.657114\pi$
$397$	−1.45245e31			−0.947575			−0.473788	+	0.880639i	$0.657114\pi$
$398$		−	8.39213e30i		−	0.531221i
$399$	2.84405e30			0.174687
$400$	2.07465e31			1.23659
$401$		−	1.15179e31i		−	0.666257i	−0.942881	−	0.333129i	$-0.891896\pi$
$401$		−	1.15179e31i		−	0.666257i	0.942881	−	0.333129i	$-0.108104\pi$
$402$		−	4.06640e31i		−	2.28295i
$403$	−3.03586e31			−1.65433
$404$	−8.72972e30			−0.461768
$405$		−	3.00977e31i		−	1.54551i
$406$		−	2.61182e31i		−	1.30206i
$407$	−1.38268e31			−0.669249
$408$			2.27343e31i			1.06847i
$409$	−1.67201e31			−0.763062			−0.381531	−	0.924356i	$-0.624603\pi$
$409$	−1.67201e31			−0.763062			−0.381531	+	0.924356i	$0.624603\pi$
$410$			6.85934e31i			3.04002i
$411$		−	3.21174e31i		−	1.38241i
$412$			1.46608e31i			0.612900i
$413$		−	2.02876e31i		−	0.823814i
$414$	−2.06755e30	−	2.45860e30i	−0.0815553	−	0.0969804i
$415$	6.50040e31			2.49094
$416$	2.79091e31			1.03902
$417$	5.60546e31			2.02758
$418$	7.23697e30			0.254356
$419$			1.51229e31i			0.516495i	0.966079	+	0.258248i	$0.0831451\pi$
$419$			1.51229e31i			0.516495i	−0.966079	+	0.258248i	$0.916855\pi$
$420$	1.53358e31			0.508998
$421$		−	2.92647e31i		−	0.943972i	−0.881606	−	0.471986i	$-0.843537\pi$
$421$		−	2.92647e31i		−	0.943972i	0.881606	−	0.471986i	$-0.156463\pi$
$422$	−5.00429e31			−1.56889
$423$	−1.04176e30			−0.0317456
$424$		−	5.57098e30i		−	0.165022i
$425$			5.14313e31i			1.48102i
$426$	−1.75092e31			−0.490175
$427$	−3.24557e31			−0.883398
$428$		−	1.59084e31i		−	0.421019i
$429$		−	5.36098e31i		−	1.37961i
$430$	2.26816e30			0.0567612
$431$			3.70986e31i			0.902882i	0.892301	+	0.451441i	$0.149090\pi$
$431$			3.70986e31i			0.902882i	−0.892301	+	0.451441i	$0.850910\pi$
$432$	−4.94601e31			−1.17071
$433$			5.48239e31i			1.26216i	0.775717	+	0.631081i	$0.217388\pi$
$433$			5.48239e31i			1.26216i	−0.775717	+	0.631081i	$0.782612\pi$
$434$			5.47265e31i			1.22552i
$435$		−	9.31423e31i		−	2.02897i
$436$		−	1.00545e31i		−	0.213070i
$437$	−7.74033e30	+	6.50920e30i	−0.159581	+	0.134199i
$438$	1.35049e31			0.270895
$439$	3.64373e31			0.711168			0.355584	−	0.934644i	$-0.384282\pi$
$439$	3.64373e31			0.711168			0.355584	+	0.934644i	$0.384282\pi$
$440$	−5.16576e31			−0.981075
$441$	2.09443e30			0.0387082
$442$			1.27536e32i			2.29385i
$443$	−2.21298e31			−0.387376			−0.193688	−	0.981063i	$-0.562045\pi$
$443$	−2.21298e31			−0.387376			−0.193688	+	0.981063i	$0.562045\pi$
$444$		−	1.74286e31i		−	0.296939i
$445$	1.83540e31			0.304376
$446$	−4.53666e31			−0.732349
$447$			9.20781e31i			1.44699i
$448$			1.45268e31i			0.222247i
$449$	2.29892e31			0.342427			0.171213	−	0.985234i	$-0.445231\pi$
$449$	2.29892e31			0.342427			0.171213	+	0.985234i	$0.445231\pi$
$450$	8.67719e30			0.125843
$451$		−	1.30049e32i		−	1.83649i
$452$		−	4.21669e31i		−	0.579844i
$453$	1.06910e32			1.43166
$454$			6.36582e31i			0.830202i
$455$	−1.13885e32			−1.44653
$456$		−	1.20755e31i		−	0.149392i
$457$		−	8.38802e31i		−	1.01080i	−0.862885	−	0.505400i	$-0.831345\pi$
$457$		−	8.38802e31i		−	1.01080i	0.862885	−	0.505400i	$-0.168655\pi$
$458$			1.50874e32i			1.77104i
$459$		−	1.22613e32i		−	1.40212i
$460$	−4.17379e31	+	3.50993e31i	−0.464982	+	0.391025i
$461$	2.07184e31			0.224877			0.112438	−	0.993659i	$-0.464134\pi$
$461$	2.07184e31			0.224877			0.112438	+	0.993659i	$0.464134\pi$
$462$	−9.66408e31			−1.02201
$463$	−1.35648e32			−1.39779			−0.698894	−	0.715225i	$-0.746324\pi$
$463$	−1.35648e32			−1.39779			−0.698894	+	0.715225i	$0.746324\pi$
$464$	−1.69464e32			−1.70161
$465$			1.95165e32i			1.90970i
$466$	−2.52253e31			−0.240550
$467$			1.71200e32i			1.59112i	0.605876	+	0.795559i	$0.292823\pi$
$467$			1.71200e32i			1.59112i	−0.605876	+	0.795559i	$0.707177\pi$
$468$	6.47376e30			0.0586416
$469$	1.63778e32			1.44604
$470$			5.87813e31i			0.505900i
$471$			7.94895e31i			0.666897i
$472$	−8.61389e31			−0.704523
$473$	−4.30028e30			−0.0342897
$474$		−	1.93320e32i		−	1.50293i
$475$		−	2.73181e31i		−	0.207075i
$476$	6.91704e31			0.511254
$477$		−	3.56066e30i		−	0.0256632i
$478$	7.48371e31			0.525995
$479$			6.81488e31i			0.467124i	0.972342	+	0.233562i	$0.0750381\pi$
$479$			6.81488e31i			0.467124i	−0.972342	+	0.233562i	$0.924962\pi$
$480$		−	1.79418e32i		−	1.19942i
$481$			1.29426e32i			0.843877i
$482$			2.23318e32i			1.42023i
$483$	1.03363e32	−	8.69224e31i	0.641206	−	0.539220i
$484$	−2.87251e30			−0.0173827
$485$	2.10432e32			1.24226
$486$	−4.38247e31			−0.252397
$487$	7.76729e31			0.436437			0.218219	−	0.975900i	$-0.429975\pi$
$487$	7.76729e31			0.436437			0.218219	+	0.975900i	$0.429975\pi$
$488$			1.37803e32i			0.755478i
$489$	7.92975e31			0.424183
$490$		−	1.18178e32i		−	0.616856i
$491$	−3.07491e32			−1.56623			−0.783114	−	0.621878i	$-0.786370\pi$
$491$	−3.07491e32			−1.56623			−0.783114	+	0.621878i	$0.786370\pi$
$492$	1.63926e32			0.814831
$493$		−	4.20107e32i		−	2.03796i
$494$		−	6.77417e31i		−	0.320725i
$495$	−3.30167e31			−0.152571
$496$	3.55084e32			1.60159
$497$		−	7.05198e31i		−	0.310480i
$498$		−	5.16339e32i		−	2.21913i
$499$	−1.86709e32			−0.783357			−0.391679	−	0.920102i	$-0.628105\pi$
$499$	−1.86709e32			−0.783357			−0.391679	+	0.920102i	$0.628105\pi$
$500$			1.01975e30i			0.00417688i
$501$	1.31012e32			0.523912
$502$		−	1.17886e32i		−	0.460276i
$503$		−	3.74767e32i		−	1.42871i	−0.699782	−	0.714357i	$-0.746720\pi$
$503$		−	3.74767e32i		−	1.42871i	0.699782	−	0.714357i	$-0.253280\pi$
$504$			1.54482e31i			0.0575059i
$505$		−	4.16752e32i		−	1.51489i
$506$	2.63017e32	−	2.21183e32i	0.933635	−	0.785137i
$507$	−1.98452e32			−0.687955
$508$	−7.98298e31			−0.270272
$509$	1.69375e32			0.560062			0.280031	−	0.959991i	$-0.409655\pi$
$509$	1.69375e32			0.560062			0.280031	+	0.959991i	$0.409655\pi$
$510$	8.19885e32			2.64796
$511$			5.43920e31i			0.171587i
$512$	−5.11403e31			−0.157588
$513$			6.51270e31i			0.196043i
$514$	3.49657e32			1.02822
$515$	−6.99897e32			−2.01070
$516$		−	5.42050e30i		−	0.0152140i
$517$		−	1.11446e32i		−	0.305617i
$518$	2.33311e32			0.625142
$519$	2.47597e32			0.648242
$520$			4.83542e32i			1.23707i
$521$			2.24702e31i			0.0561765i	0.999605	+	0.0280882i	$0.00894194\pi$
$521$			2.24702e31i			0.0561765i	−0.999605	+	0.0280882i	$0.991058\pi$
$522$	−7.08780e31			−0.173167
$523$			5.14923e32i			1.22948i	0.788729	+	0.614741i	$0.210739\pi$
$523$			5.14923e32i			1.22948i	−0.788729	+	0.614741i	$0.789261\pi$
$524$	1.13603e31			0.0265103
$525$			3.64799e32i			0.832037i
$526$		−	9.52973e32i		−	2.12447i
$527$			8.80266e32i			1.91817i
$528$			6.27039e32i			1.33563i
$529$	−8.23703e31	+	4.73134e32i	−0.171515	+	0.985181i
$530$	−2.00910e32			−0.408970
$531$	−5.50552e31			−0.109563
$532$	−3.67404e31			−0.0714832
$533$	−1.21732e33			−2.31569
$534$		−	1.45789e32i		−	0.271163i
$535$	7.59459e32			1.38121
$536$		−	6.95382e32i		−	1.23665i
$537$	−3.53147e32			−0.614136
$538$	−6.06940e32			−1.03219
$539$			2.24058e32i			0.372645i
$540$			3.51181e32i			0.571224i
$541$	−2.41100e31			−0.0383556			−0.0191778	−	0.999816i	$-0.506105\pi$
$541$	−2.41100e31			−0.0383556			−0.0191778	+	0.999816i	$0.506105\pi$
$542$	−8.41319e32			−1.30909
$543$			3.26901e31i			0.0497528i
$544$		−	8.09242e32i		−	1.20473i
$545$	4.79996e32			0.699004
$546$			9.04607e32i			1.28869i
$547$	−1.82567e32			−0.254433			−0.127216	−	0.991875i	$-0.540604\pi$
$547$	−1.82567e32			−0.254433			−0.127216	+	0.991875i	$0.540604\pi$
$548$			4.14903e32i			0.565692i
$549$			8.80764e31i			0.117487i
$550$			9.28270e32i			1.21150i
$551$			2.23143e32i			0.284947i
$552$	−3.69063e32	−	4.38866e32i	−0.461139	−	0.548357i
$553$	7.78614e32			0.951965
$554$	−1.61360e33			−1.93054
$555$	8.32032e32			0.974146
$556$	−7.24133e32			−0.829699
$557$		−	8.49114e32i		−	0.952146i	−0.879406	−	0.476073i	$-0.842060\pi$
$557$		−	8.49114e32i		−	0.952146i	0.879406	−	0.476073i	$-0.157940\pi$
$558$	1.48514e32			0.162988
$559$			4.02529e31i			0.0432369i
$560$	1.33203e33			1.40042
$561$	−1.55445e33			−1.59964
$562$		−	9.25653e32i		−	0.932422i
$563$			1.15356e33i			1.13747i	0.822520	+	0.568737i	$0.192568\pi$
$563$			1.15356e33i			1.13747i	−0.822520	+	0.568737i	$0.807432\pi$
$564$	1.40477e32			0.135599
$565$	2.01303e33			1.90225
$566$			1.04799e32i			0.0969531i
$567$		−	9.62881e32i		−	0.872119i
$568$	−2.99419e32			−0.265522
$569$		−	1.87491e33i		−	1.62792i	−0.580923	−	0.813959i	$-0.697308\pi$
$569$		−	1.87491e33i		−	1.62792i	0.580923	−	0.813959i	$-0.302692\pi$
$570$	−4.35488e32			−0.370235
$571$		−	1.61732e32i		−	0.134636i	−0.997732	−	0.0673181i	$-0.978556\pi$
$571$		−	1.61732e32i		−	0.134636i	0.997732	−	0.0673181i	$-0.0214442\pi$
$572$			6.92550e32i			0.564546i
$573$			9.77548e32i			0.780337i
$574$			2.19443e33i			1.71546i
$575$	−8.34921e32	−	9.92835e32i	−0.639192	−	0.760086i
$576$	3.94221e31			0.0295577
$577$	9.50928e31			0.0698294			0.0349147	−	0.999390i	$-0.488884\pi$
$577$	9.50928e31			0.0698294			0.0349147	+	0.999390i	$0.488884\pi$
$578$	2.03514e33			1.46373
$579$	−1.16346e33			−0.819616
$580$			1.20324e33i			0.830267i
$581$	2.07960e33			1.40561
$582$		−	1.67150e33i		−	1.10670i
$583$	3.80913e32			0.247060
$584$	2.30943e32			0.146740
$585$			3.09054e32i			0.192381i
$586$			6.64071e32i			0.404989i
$587$	3.09527e32			0.184944			0.0924722	−	0.995715i	$-0.470523\pi$
$587$	3.09527e32			0.184944			0.0924722	+	0.995715i	$0.470523\pi$
$588$	−2.82425e32			−0.165339
$589$		−	4.67560e32i		−	0.268197i
$590$			3.10649e33i			1.74600i
$591$	−2.00920e33			−1.10655
$592$		−	1.51381e33i		−	0.816977i
$593$	1.65481e33			0.875169			0.437584	−	0.899177i	$-0.355834\pi$
$593$	1.65481e33			0.875169			0.437584	+	0.899177i	$0.355834\pi$
$594$		−	2.21302e33i		−	1.14696i
$595$			3.30216e33i			1.67724i
$596$		−	1.18950e33i		−	0.592118i
$597$		−	9.57450e32i		−	0.467115i
$598$	−2.07039e33	−	2.46197e33i	−0.990004	−	1.17725i
$599$	−5.91810e32			−0.277371			−0.138685	−	0.990337i	$-0.544288\pi$
$599$	−5.91810e32			−0.277371			−0.138685	+	0.990337i	$0.544288\pi$
$600$	1.54890e33			0.711555
$601$	−3.18189e33			−1.43282			−0.716410	−	0.697680i	$-0.754216\pi$
$601$	−3.18189e33			−1.43282			−0.716410	+	0.697680i	$0.754216\pi$
$602$	7.25626e31			0.0320298
$603$		−	4.44450e32i		−	0.192316i
$604$	−1.38110e33			−0.585844
$605$		−	1.37132e32i		−	0.0570261i
$606$	−3.31034e33			−1.34959
$607$	−9.58330e32			−0.383046			−0.191523	−	0.981488i	$-0.561343\pi$
$607$	−9.58330e32			−0.383046			−0.191523	+	0.981488i	$0.561343\pi$
$608$			4.29835e32i			0.168445i
$609$		−	2.97980e33i		−	1.14493i
$610$	4.96970e33			1.87229
$611$	−1.04319e33			−0.385362
$612$		−	1.87711e32i		−	0.0679942i
$613$		−	1.96209e33i		−	0.696937i	−0.937320	−	0.348469i	$-0.886702\pi$
$613$		−	1.96209e33i		−	0.696937i	0.937320	−	0.348469i	$-0.113298\pi$
$614$	−2.08464e33			−0.726122
$615$			7.82575e33i			2.67316i
$616$	−1.65262e33			−0.553612
$617$			3.67411e33i			1.20706i	0.797339	+	0.603531i	$0.206240\pi$
$617$			3.67411e33i			1.20706i	−0.797339	+	0.603531i	$0.793760\pi$
$618$			5.55941e33i			1.79130i
$619$		−	4.94029e33i		−	1.56122i	−0.625018	−	0.780610i	$-0.714908\pi$
$619$		−	4.94029e33i		−	1.56122i	0.625018	−	0.780610i	$-0.285092\pi$
$620$		−	2.52121e33i		−	0.781462i
$621$	1.99047e33	+	2.36694e33i	0.605141	+	0.719595i
$622$	3.30825e33			0.986538
$623$	5.87178e32			0.171757
$624$	5.86941e33			1.68414
$625$	−3.57697e33			−1.00683
$626$			6.57713e33i			1.81612i
$627$	8.25658e32			0.223661
$628$		−	1.02687e33i		−	0.272898i
$629$	3.75278e33			0.978464
$630$	5.57121e32			0.142516
$631$			1.87085e33i			0.469555i	0.972049	+	0.234777i	$0.0754361\pi$
$631$			1.87085e33i			0.469555i	−0.972049	+	0.234777i	$0.924564\pi$
$632$		−	3.30591e33i		−	0.814117i
$633$	−5.70934e33			−1.37956
$634$	6.89105e33			1.63386
$635$		−	3.81103e33i		−	0.886661i
$636$			4.80140e32i			0.109618i
$637$	2.09730e33			0.469880
$638$		−	7.58240e33i		−	1.66709i
$639$	−1.91372e32			−0.0412923
$640$		−	7.61034e33i		−	1.61155i
$641$		−	6.05639e33i		−	1.25869i	−0.777127	−	0.629343i	$-0.783324\pi$
$641$		−	6.05639e33i		−	1.25869i	0.777127	−	0.629343i	$-0.216676\pi$
$642$		−	6.03253e33i		−	1.23049i
$643$		−	2.38142e33i		−	0.476765i	−0.971171	−	0.238382i	$-0.923383\pi$
$643$		−	2.38142e33i		−	0.476765i	0.971171	−	0.238382i	$-0.0766171\pi$
$644$	−1.33527e33	+	1.12289e33i	−0.262385	+	0.220652i
$645$	2.58772e32			0.0499114
$646$	−1.96421e33			−0.371876
$647$	3.94305e33			0.732792			0.366396	−	0.930459i	$-0.380592\pi$
$647$	3.94305e33			0.732792			0.366396	+	0.930459i	$0.380592\pi$
$648$	−4.08829e33			−0.745833
$649$		−	5.88971e33i		−	1.05477i
$650$	8.68908e33			1.52761
$651$			6.24369e33i			1.07763i
$652$	−1.02439e33			−0.173578
$653$	−9.53515e33			−1.58624			−0.793121	−	0.609064i	$-0.791545\pi$
$653$	−9.53515e33			−1.58624			−0.793121	+	0.609064i	$0.791545\pi$
$654$		−	3.81270e33i		−	0.622730i
$655$			5.42334e32i			0.0869704i
$656$	1.42382e34			2.24187
$657$	1.47606e32			0.0228202
$658$			1.88052e33i			0.285475i
$659$			7.94767e33i			1.18472i	0.805674	+	0.592359i	$0.201803\pi$
$659$			7.94767e33i			1.18472i	−0.805674	+	0.592359i	$0.798197\pi$
$660$	4.45216e33			0.651694
$661$		−	4.04531e33i		−	0.581480i	−0.956802	−	0.290740i	$-0.906099\pi$
$661$		−	4.04531e33i		−	0.581480i	0.956802	−	0.290740i	$-0.0939014\pi$
$662$	−4.18292e33			−0.590450
$663$			1.45505e34i			2.01704i
$664$		−	8.82976e33i		−	1.20208i
$665$		−	1.75396e33i		−	0.234510i
$666$		−	6.33147e32i		−	0.0831408i
$667$	6.81990e33	+	8.10979e33i	0.879565	+	1.04592i
$668$	−1.69246e33			−0.214388
$669$	−5.17583e33			−0.643972
$670$	−2.50781e34			−3.06476
$671$	−9.42225e33			−1.13106
$672$		−	5.73991e33i		−	0.676821i
$673$	1.57655e34			1.82611			0.913056	−	0.407834i	$-0.133716\pi$
$673$	1.57655e34			1.82611			0.913056	+	0.407834i	$0.133716\pi$
$674$			9.06676e33i			1.03165i
$675$	−8.35369e33			−0.933755
$676$	2.56367e33			0.281515
$677$			1.61422e33i			0.174140i	0.996202	+	0.0870698i	$0.0277503\pi$
$677$			1.61422e33i			0.174140i	−0.996202	+	0.0870698i	$0.972250\pi$
$678$		−	1.59899e34i		−	1.69468i
$679$	6.73211e33			0.700994
$680$	1.40206e34			1.43437
$681$			7.26270e33i			0.730016i
$682$			1.58877e34i			1.56909i
$683$	1.25325e34			1.21616			0.608079	−	0.793876i	$-0.291940\pi$
$683$	1.25325e34			1.21616			0.608079	+	0.793876i	$0.291940\pi$
$684$			9.97039e31i			0.00950690i
$685$	−1.98073e34			−1.85583
$686$		−	1.41293e34i		−	1.30086i
$687$			1.72130e34i			1.55731i
$688$		−	4.70811e32i		−	0.0418587i
$689$		−	3.56554e33i		−	0.311526i
$690$	−1.58271e34	+	1.33098e34i	−1.35898	+	1.14283i
$691$	−2.54129e33			−0.214446			−0.107223	−	0.994235i	$-0.534196\pi$
$691$	−2.54129e33			−0.214446			−0.107223	+	0.994235i	$0.534196\pi$
$692$	−3.19854e33			−0.265265
$693$	−1.05627e33			−0.0860944
$694$	2.35601e34			1.88739
$695$		−	3.45697e34i		−	2.72194i
$696$	−1.26519e34			−0.979140
$697$			3.52971e34i			2.68501i
$698$	−7.88075e33			−0.589254
$699$	−2.87793e33			−0.211521
$700$		−	4.71261e33i		−	0.340474i
$701$			1.95400e34i			1.38774i	0.720099	+	0.693872i	$0.244096\pi$
$701$			1.95400e34i			1.38774i	−0.720099	+	0.693872i	$0.755904\pi$
$702$	−2.07150e34			−1.44624
$703$	−1.99332e33			−0.136808
$704$			4.21730e33i			0.284553i
$705$			6.70630e33i			0.444850i
$706$	2.20513e34			1.43806
$707$		−	1.33327e34i		−	0.854840i
$708$	7.42396e33			0.467990
$709$			1.00172e34i			0.620859i	0.950596	+	0.310429i	$0.100473\pi$
$709$			1.00172e34i			0.620859i	−0.950596	+	0.310429i	$0.899527\pi$
$710$			1.07982e34i			0.658037i
$711$		−	2.11296e33i		−	0.126606i
$712$		−	2.49310e33i		−	0.146886i
$713$	−1.42900e34	−	1.69928e34i	−0.827862	−	0.984441i
$714$	2.62297e34			1.49422
$715$	−3.30620e34			−1.85207
$716$	4.56208e33			0.251308
$717$	8.53808e33			0.462520
$718$			1.51164e34i			0.805292i
$719$	−2.44640e34			−1.28168			−0.640841	−	0.767674i	$-0.721414\pi$
$719$	−2.44640e34			−1.28168			−0.640841	+	0.767674i	$0.721414\pi$
$720$		−	3.61479e33i		−	0.186249i
$721$	−2.23910e34			−1.13462
$722$	−2.29542e34			−1.14397
$723$			2.54781e34i			1.24884i
$724$		−	4.22302e32i		−	0.0203592i
$725$	−2.86220e34			−1.35720
$726$	−1.08926e33			−0.0508035
$727$			1.39350e33i			0.0639282i	0.999489	+	0.0319641i	$0.0101762\pi$
$727$			1.39350e33i			0.0639282i	−0.999489	+	0.0319641i	$0.989824\pi$
$728$			1.54694e34i			0.698067i
$729$	1.96625e34			0.872787
$730$		−	8.32864e33i		−	0.363664i
$731$	1.16716e33			0.0501327
$732$		−	1.18767e34i		−	0.501838i
$733$		−	1.49456e34i		−	0.621249i	−0.950533	−	0.310625i	$-0.899462\pi$
$733$		−	1.49456e34i		−	0.621249i	0.950533	−	0.310625i	$-0.100538\pi$
$734$		−	9.68042e33i		−	0.395860i
$735$		−	1.34828e34i		−	0.542416i
$736$	1.31370e34	+	1.56217e34i	0.519951	+	0.618293i
$737$	4.75465e34			1.85143
$738$	5.95512e33			0.228147
$739$	2.27194e34			0.856373			0.428187	−	0.903690i	$-0.359153\pi$
$739$	2.27194e34			0.856373			0.428187	+	0.903690i	$0.359153\pi$
$740$	−1.07485e34			−0.398627
$741$		−	7.72859e33i		−	0.282021i
$742$	−6.42749e33			−0.230778
$743$		−	4.62470e34i		−	1.63387i	−0.576728	−	0.816936i	$-0.695671\pi$
$743$		−	4.62470e34i		−	1.63387i	0.576728	−	0.816936i	$-0.304329\pi$
$744$	2.65100e34			0.921584
$745$	5.67859e34			1.94252
$746$			5.34367e34i			1.79876i
$747$		−	5.64350e33i		−	0.186940i
$748$	2.00809e34			0.654583
$749$	2.42965e34			0.779404
$750$			3.86691e32i			0.0122076i
$751$		−	1.16235e34i		−	0.361126i	−0.983563	−	0.180563i	$-0.942208\pi$
$751$		−	1.16235e34i		−	0.361126i	0.983563	−	0.180563i	$-0.0577920\pi$
$752$	1.22015e34			0.373077
$753$		−	1.34495e34i		−	0.404731i
$754$	−7.09752e34			−2.10209
$755$		−	6.59329e34i		−	1.92194i
$756$			1.12350e34i			0.322337i
$757$		−	8.00591e33i		−	0.226079i	−0.993590	−	0.113040i	$-0.963941\pi$
$757$		−	8.00591e33i		−	0.226079i	0.993590	−	0.113040i	$-0.0360587\pi$
$758$			1.76799e34i			0.491417i
$759$	3.00073e34	−	2.52345e34i	0.820967	−	0.690389i
$760$	−7.44715e33			−0.200552
$761$	1.12708e34			0.298771			0.149385	−	0.988779i	$-0.452270\pi$
$761$	1.12708e34			0.298771			0.149385	+	0.988779i	$0.452270\pi$
$762$	−3.02718e34			−0.789910
$763$	1.53560e34			0.394442
$764$		−	1.26283e34i		−	0.319319i
$765$	8.96120e33			0.223064
$766$		−	3.61659e34i		−	0.886244i
$767$	−5.51307e34			−1.32999
$768$	−4.80975e34			−1.14232
$769$		−	6.45411e34i		−	1.50911i	−0.656238	−	0.754554i	$-0.727853\pi$
$769$		−	6.45411e34i		−	1.50911i	0.656238	−	0.754554i	$-0.272147\pi$
$770$			5.95998e34i			1.37201i
$771$	3.98920e34			0.904134
$772$	1.50300e34			0.335392
$773$			6.98520e34i			1.53471i	0.641225	+	0.767353i	$0.278427\pi$
$773$			6.98520e34i			1.53471i	−0.641225	+	0.767353i	$0.721573\pi$
$774$		−	1.96916e32i		−	0.00425980i
$775$	5.99729e34			1.27742
$776$		−	2.85838e34i		−	0.599487i
$777$	2.66183e34			0.549702
$778$		−	5.65899e34i		−	1.15076i
$779$		−	1.87483e34i		−	0.375416i
$780$		−	4.16745e34i		−	0.821742i
$781$		−	2.04727e34i		−	0.397523i
$782$	−7.13864e34	+	6.00321e34i	−1.36501	+	1.14790i
$783$	6.82356e34			1.28490
$784$	−2.45307e34			−0.454902
$785$	4.90224e34			0.895279
$786$	4.30787e33			0.0774803
$787$		−	3.08130e34i		−	0.545805i	−0.962042	−	0.272903i	$-0.912016\pi$
$787$		−	3.08130e34i		−	0.545805i	0.962042	−	0.272903i	$-0.0879837\pi$
$788$	2.59555e34			0.452809
$789$		−	1.08724e35i		−	1.86810i
$790$	−1.19224e35			−2.01761
$791$	6.44005e34			1.07342
$792$			4.48480e33i			0.0736276i
$793$			8.81971e34i			1.42619i
$794$	7.11507e34			1.13327
$795$	−2.29216e34			−0.359617
$796$			1.23687e34i			0.191146i
$797$			3.62352e34i			0.551608i	0.961214	+	0.275804i	$0.0889441\pi$
$797$			3.62352e34i			0.551608i	−0.961214	+	0.275804i	$0.911056\pi$
$798$	−1.39321e34			−0.208921
$799$			3.02479e34i			0.446822i
$800$	−5.51340e34			−0.802305
$801$		−	1.59345e33i		−	0.0228428i
$802$			5.64227e34i			0.796822i
$803$			1.57906e34i			0.219691i
$804$			5.99322e34i			0.821462i
$805$	−5.36063e34	−	6.37452e34i	−0.723878	−	0.860789i
$806$	1.48717e35			1.97852
$807$	−6.92452e34			−0.907626
$808$	−5.66092e34			−0.731055
$809$	−1.03164e35			−1.31264			−0.656319	−	0.754483i	$-0.727888\pi$
$809$	−1.03164e35			−1.31264			−0.656319	+	0.754483i	$0.727888\pi$
$810$			1.47439e35i			1.84838i
$811$	1.13149e35			1.39766			0.698831	−	0.715287i	$-0.253704\pi$
$811$	1.13149e35			1.39766			0.698831	+	0.715287i	$0.253704\pi$
$812$			3.84940e34i			0.468513i
$813$	−9.59853e34			−1.15111
$814$	6.77329e34			0.800400
$815$		−	4.89039e34i		−	0.569446i
$816$		−	1.70187e35i		−	1.95274i
$817$	−6.19944e32			−0.00700951
$818$	8.19066e34			0.912597
$819$			9.88720e33i			0.108559i
$820$		−	1.01096e35i		−	1.09387i
$821$	−3.93906e34			−0.420024			−0.210012	−	0.977699i	$-0.567350\pi$
$821$	−3.93906e34			−0.420024			−0.210012	+	0.977699i	$0.567350\pi$
$822$			1.57333e35i			1.65332i
$823$	1.69461e34			0.175498			0.0877490	−	0.996143i	$-0.472033\pi$
$823$	1.69461e34			0.175498			0.0877490	+	0.996143i	$0.472033\pi$
$824$			9.50699e34i			0.970323i
$825$			1.05905e35i			1.06530i
$826$			9.93824e34i			0.985255i
$827$			1.51125e35i			1.47662i	0.674460	+	0.738312i	$0.264377\pi$
$827$			1.51125e35i			1.47662i	−0.674460	+	0.738312i	$0.735623\pi$
$828$	3.04724e33	+	3.62359e33i	0.0293456	+	0.0348959i
$829$	9.70828e34			0.921485			0.460742	−	0.887534i	$-0.347583\pi$
$829$	9.70828e34			0.921485			0.460742	+	0.887534i	$0.347583\pi$
$830$	−3.18434e35			−2.97908
$831$	−1.84094e35			−1.69757
$832$	3.94761e34			0.358802
$833$		−	6.08125e34i		−	0.544820i
$834$	−2.74594e35			−2.42492
$835$		−	8.07971e34i		−	0.703328i
$836$	−1.06661e34			−0.0915233
$837$	−1.42977e35			−1.20937
$838$		−	7.40822e34i		−	0.617712i
$839$		−	4.32420e34i		−	0.355437i	−0.984081	−	0.177718i	$-0.943128\pi$
$839$		−	4.32420e34i		−	0.355437i	0.984081	−	0.177718i	$-0.0568716\pi$
$840$	9.94475e34			0.805828
$841$	1.08609e35			0.867588
$842$			1.43359e35i			1.12896i
$843$		−	1.05607e35i		−	0.819900i
$844$	7.37553e34			0.564526
$845$			1.22388e35i			0.923548i
$846$	5.10326e33			0.0379667
$847$		−	4.38711e33i		−	0.0321793i
$848$			4.17038e34i			0.301596i
$849$			1.19565e34i			0.0852531i
$850$		−	2.51945e35i		−	1.77125i
$851$	−7.24440e34	+	6.09215e34i	−0.502167	+	0.422295i
$852$	2.58058e34			0.176377
$853$	1.01128e35			0.681527			0.340764	−	0.940149i	$-0.389314\pi$
$853$	1.01128e35			0.681527			0.340764	+	0.940149i	$0.389314\pi$
$854$	1.58990e35			1.05651
$855$	−4.75981e33			−0.0311886
$856$		−	1.03160e35i		−	0.666543i
$857$	−2.87828e35			−1.83385			−0.916924	−	0.399061i	$-0.869336\pi$
$857$	−2.87828e35			−1.83385			−0.916924	+	0.399061i	$0.869336\pi$
$858$			2.62618e35i			1.64997i
$859$	1.39068e35			0.861608			0.430804	−	0.902446i	$-0.358230\pi$
$859$	1.39068e35			0.861608			0.430804	+	0.902446i	$0.358230\pi$
$860$	−3.34290e33			−0.0204241
$861$			2.50361e35i			1.50844i
$862$		−	1.81735e35i		−	1.07982i
$863$	1.46272e35			0.857099			0.428549	−	0.903518i	$-0.359025\pi$
$863$	1.46272e35			0.857099			0.428549	+	0.903518i	$0.359025\pi$
$864$	1.31441e35			0.759565
$865$		−	1.52697e35i		−	0.870235i
$866$		−	2.68565e35i		−	1.50950i
$867$	2.32187e35			1.28709
$868$		−	8.06581e34i		−	0.440972i
$869$	2.26040e35			1.21885
$870$			4.56275e35i			2.42658i
$871$		−	4.45059e35i		−	2.33453i
$872$		−	6.51999e34i		−	0.337325i
$873$		−	1.82692e34i		−	0.0932286i
$874$	3.79174e34	−	3.18865e34i	0.190854	−	0.160498i
$875$	−1.55743e33			−0.00773236
$876$	−1.99040e34			−0.0974746
$877$	−7.54154e34			−0.364305			−0.182152	−	0.983270i	$-0.558306\pi$
$877$	−7.54154e34			−0.364305			−0.182152	+	0.983270i	$0.558306\pi$
$878$	−1.78495e35			−0.850534
$879$			7.57632e34i			0.356116i
$880$	3.86704e35			1.79303
$881$			3.20670e35i			1.46672i	0.679839	+	0.733361i	$0.262050\pi$
$881$			3.20670e35i			1.46672i	−0.679839	+	0.733361i	$0.737950\pi$
$882$	−1.02599e34			−0.0462937
$883$	4.25303e34			0.189308			0.0946542	−	0.995510i	$-0.469825\pi$
$883$	4.25303e34			0.189308			0.0946542	+	0.995510i	$0.469825\pi$
$884$		−	1.87968e35i		−	0.825385i
$885$			3.54416e35i			1.53530i
$886$	1.08407e35			0.463289
$887$	−3.55528e35			−1.49896			−0.749481	−	0.662026i	$-0.769697\pi$
$887$	−3.55528e35			−1.49896			−0.749481	+	0.662026i	$0.769697\pi$
$888$		−	1.13018e35i		−	0.470103i
$889$		−	1.21922e35i		−	0.500335i
$890$	−8.99103e34			−0.364024
$891$		−	2.79535e35i		−	1.11662i
$892$	6.68632e34			0.263517
$893$		−	1.60664e34i		−	0.0624743i
$894$		−	4.51062e35i		−	1.73056i
$895$			2.17791e35i			0.824449i
$896$		−	2.43469e35i		−	0.909385i
$897$	−2.36208e35	−	2.80884e35i	−0.870534	−	1.03518i
$898$	−1.12617e35			−0.409531
$899$	−4.89878e35			−1.75781
$900$	−1.27888e34			−0.0452814
$901$	−1.03385e35			−0.361211
$902$			6.37068e35i			2.19638i
$903$	8.27859e33			0.0281646
$904$		−	2.73438e35i		−	0.917989i
$905$	2.01604e34			0.0667909
$906$	−5.23718e35			−1.71222
$907$			4.63541e35i			1.49555i	0.663952	+	0.747775i	$0.268878\pi$
$907$			4.63541e35i			1.49555i	−0.663952	+	0.747775i	$0.731122\pi$
$908$		−	9.38220e34i		−	0.298727i
$909$	−3.61815e34			−0.113689
$910$	5.57885e35			1.73001
$911$		−	5.22560e35i		−	1.59925i	−0.600501	−	0.799624i	$-0.705032\pi$
$911$		−	5.22560e35i		−	1.59925i	0.600501	−	0.799624i	$-0.294968\pi$
$912$			9.03961e34i			0.273031i
$913$	6.03731e35			1.79968
$914$			4.10902e35i			1.20888i
$915$	5.66988e35			1.64634
$916$		−	2.22364e35i		−	0.637262i
$917$			1.73503e34i			0.0490766i
$918$			6.00644e35i			1.67689i
$919$			4.54530e35i			1.25250i	0.779623	+	0.626249i	$0.215410\pi$
$919$			4.54530e35i			1.25250i	−0.779623	+	0.626249i	$0.784590\pi$
$920$	−2.70655e35	+	2.27607e35i	−0.736144	+	0.619057i
$921$	−2.37834e35			−0.638496
$922$	−1.01493e35			−0.268945
$923$	−1.91635e35			−0.501249
$924$	1.42433e35			0.367745
$925$		−	2.55678e35i		−	0.651618i
$926$	6.64496e35			1.67171
$927$			6.07635e34i			0.150899i
$928$	4.50352e35			1.10402
$929$	−3.53672e35			−0.855878			−0.427939	−	0.903808i	$-0.640760\pi$
$929$	−3.53672e35			−0.855878			−0.427939	+	0.903808i	$0.640760\pi$
$930$		−	9.56050e35i		−	2.28394i
$931$			3.23010e34i			0.0761763i
$932$	3.71781e34			0.0865557
$933$	3.77435e35			0.867486
$934$		−	8.38657e35i		−	1.90293i
$935$			9.58653e35i			2.14744i
$936$	4.19800e34			0.0928394
$937$			7.54184e34i			0.164665i	0.996605	+	0.0823327i	$0.0262370\pi$
$937$			7.54184e34i			0.164665i	−0.996605	+	0.0823327i	$0.973763\pi$
$938$	−8.02295e35			−1.72942
$939$			7.50378e35i			1.59696i
$940$		−	8.66343e34i		−	0.182035i
$941$		−	4.59074e35i		−	0.952374i	−0.879344	−	0.476187i	$-0.842019\pi$
$941$		−	4.59074e35i		−	0.952374i	0.879344	−	0.476187i	$-0.157981\pi$
$942$		−	3.89394e35i		−	0.797588i
$943$	−5.73003e35	−	6.81379e35i	−1.15882	−	1.37800i
$944$	6.44827e35			1.28760
$945$	−5.36351e35			−1.05747
$946$	2.10657e34			0.0410093
$947$	−2.04328e35			−0.392762			−0.196381	−	0.980528i	$-0.562919\pi$
$947$	−2.04328e35			−0.392762			−0.196381	+	0.980528i	$0.562919\pi$
$948$			2.84923e35i			0.540789i
$949$	1.47808e35			0.277015
$950$			1.33823e35i			0.247655i
$951$	7.86193e35			1.43669
$952$	4.48545e35			0.809400
$953$			3.60033e35i			0.641545i	0.947156	+	0.320772i	$0.103942\pi$
$953$			3.60033e35i			0.641545i	−0.947156	+	0.320772i	$0.896058\pi$
$954$			1.74426e34i			0.0306923i
$955$	6.02868e35			1.04757
$956$	−1.10298e35			−0.189266
$957$		−	8.65068e35i		−	1.46591i
$958$		−	3.33839e35i		−	0.558665i
$959$	−6.33671e35			−1.04723
$960$		−	2.53778e35i		−	0.414190i
$961$	4.06047e35			0.654480
$962$		−	6.34015e35i		−	1.00925i
$963$		−	6.59345e34i		−	0.103657i
$964$		−	3.29135e35i		−	0.511034i
$965$			7.17526e35i			1.10030i
$966$	−5.06340e35	+	4.25805e35i	−0.766862	+	0.644889i
$967$	2.25322e35			0.337043			0.168521	−	0.985698i	$-0.446101\pi$
$967$	2.25322e35			0.337043			0.168521	+	0.985698i	$0.446101\pi$
$968$	−1.86272e34			−0.0275197
$969$	−2.24095e35			−0.327000
$970$	−1.03084e36			−1.48570
$971$			5.90223e35i			0.840205i	0.907477	+	0.420103i	$0.138006\pi$
$971$			5.90223e35i			0.840205i	−0.907477	+	0.420103i	$0.861994\pi$
$972$	6.45907e34			0.0908186
$973$		−	1.10595e36i		−	1.53597i
$974$	−3.80495e35			−0.521965
$975$	9.91329e35			1.34327
$976$		−	1.03158e36i		−	1.38072i
$977$			5.69697e34i			0.0753198i	0.999291	+	0.0376599i	$0.0119904\pi$
$977$			5.69697e34i			0.0753198i	−0.999291	+	0.0376599i	$0.988010\pi$
$978$	−3.88453e35			−0.507309
$979$	1.70464e35			0.219908
$980$			1.74176e35i			0.221960i
$981$		−	4.16722e34i		−	0.0524588i
$982$	1.50630e36			1.87316
$983$		−	1.00687e36i		−	1.23689i	−0.785826	−	0.618447i	$-0.787762\pi$
$983$		−	1.00687e36i		−	1.23689i	0.785826	−	0.618447i	$-0.212238\pi$
$984$	1.06300e36			1.29001
$985$			1.23910e36i			1.48550i
$986$			2.05797e36i			2.43734i
$987$			2.14547e35i			0.251025i
$988$			9.98405e34i			0.115405i
$989$	−2.25309e34	+	1.89473e34i	−0.0257290	+	0.0216367i
$990$	1.61738e35			0.182470
$991$	−1.09414e36			−1.21952			−0.609759	−	0.792587i	$-0.708734\pi$
$991$	−1.09414e36			−1.21952			−0.609759	+	0.792587i	$0.708734\pi$
$992$	−9.43640e35			−1.03912
$993$	−4.77225e35			−0.519197
$994$			3.45454e35i			0.371324i
$995$	−5.90473e35			−0.627080
$996$			7.61002e35i			0.798497i
$997$	−2.54053e35			−0.263379			−0.131690	−	0.991291i	$-0.542040\pi$
$997$	−2.54053e35			−0.263379			−0.131690	+	0.991291i	$0.542040\pi$
$998$	9.14631e35			0.936870
$999$			6.09542e35i			0.616905i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.25.b.c.22.10	yes	44
23.22	odd	2	inner	23.25.b.c.22.9	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.25.b.c.22.9	✓	44	23.22	odd	2	inner
23.25.b.c.22.10	yes	44	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 25 \)
Character orbit:	\([\chi]\)	\(=\)	23.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4898.68 q^{2} -558886. q^{3} +7.21988e6 q^{4} +3.44673e8i q^{5} +2.73780e9 q^{6} +1.10267e10i q^{7} +4.68184e10 q^{8} +2.99237e10 q^{9} -1.68844e12i q^{10} +3.20119e12i q^{11} -4.03509e12 q^{12} +2.99647e13 q^{13} -5.40165e13i q^{14} -1.92633e14i q^{15} -3.50478e14 q^{16} -8.68847e14i q^{17} -1.46587e14 q^{18} +4.61494e14i q^{19} +2.48850e15i q^{20} -6.16269e15i q^{21} -1.56816e16i q^{22} +(1.41046e16 + 1.67723e16i) q^{23} -2.61661e16 q^{24} -5.91949e16 q^{25} -1.46788e17 q^{26} +1.41122e17 q^{27} +7.96117e16i q^{28} +4.83522e17 q^{29} +9.43647e17i q^{30} -1.01314e18 q^{31} +9.31398e17 q^{32} -1.78910e18i q^{33} +4.25620e18i q^{34} -3.80062e18 q^{35} +2.16046e17 q^{36} +4.31926e18i q^{37} -2.26071e18i q^{38} -1.67469e19 q^{39} +1.61370e19i q^{40} -4.06252e19 q^{41} +3.01891e19i q^{42} +1.34334e18i q^{43} +2.31122e19i q^{44} +1.03139e19i q^{45} +(-6.90940e19 - 8.21623e19i) q^{46} -3.48139e19 q^{47} +1.95877e20 q^{48} +6.99922e19 q^{49} +2.89977e20 q^{50} +4.85586e20i q^{51} +2.16342e20 q^{52} -1.18991e20i q^{53} -6.91311e20 q^{54} -1.10336e21 q^{55} +5.16254e20i q^{56} -2.57923e20i q^{57} -2.36862e21 q^{58} -1.83985e21 q^{59} -1.39079e21i q^{60} +2.94336e21i q^{61} +4.96307e21 q^{62} +3.29961e20i q^{63} +1.31742e21 q^{64} +1.03280e22i q^{65} +8.76422e21i q^{66} -1.48528e22i q^{67} -6.27297e21i q^{68} +(-7.88287e21 - 9.37381e21i) q^{69} +1.86180e22 q^{70} -6.39534e21 q^{71} +1.40098e21 q^{72} +4.93273e21 q^{73} -2.11587e22i q^{74} +3.30832e22 q^{75} +3.33193e21i q^{76} -3.52986e22 q^{77} +8.20376e22 q^{78} -7.06115e22i q^{79} -1.20800e23i q^{80} -8.73224e22 q^{81} +1.99010e23 q^{82} -1.88596e23i q^{83} -4.44939e22i q^{84} +2.99468e23 q^{85} -6.58060e21i q^{86} -2.70234e23 q^{87} +1.49874e23i q^{88} -5.32504e22i q^{89} -5.05245e22i q^{90} +3.30413e23i q^{91} +(1.01834e23 + 1.21094e23i) q^{92} +5.66232e23 q^{93} +1.70542e23 q^{94} -1.59065e23 q^{95} -5.20545e23 q^{96} -6.10526e23i q^{97} -3.42870e23 q^{98} +9.57914e22i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 4232 q^{2} - 434562 q^{3} + 317760360 q^{4} - 8460029520 q^{6} - 198307023760 q^{8} + 4220041988298 q^{9} - 67439597688792 q^{12} + 5771152551358 q^{13} + 18\!\cdots\!92 q^{16} + 18\!\cdots\!68 q^{18}+ \cdots - 20\!\cdots\!92 q^{98}+O(q^{100}) \) 44 * q - 4232 * q^2 - 434562 * q^3 + 317760360 * q^4 - 8460029520 * q^6 - 198307023760 * q^8 + 4220041988298 * q^9 - 67439597688792 * q^12 + 5771152551358 * q^13 + 1801550792530192 * q^16 + 1842830558165568 * q^18 - 117204213263210644 * q^23 - 186493005437450784 * q^24 - 689533084157602612 * q^25 - 548650296251047576 * q^26 + 824037505793640630 * q^27 - 1583078054945709602 * q^29 - 77249813729122274 * q^31 - 2838716832733708512 * q^32 + 3418569899175948192 * q^35 + 71181245116739335248 * q^36 + 47106572467817156310 * q^39 - 9150679195666184738 * q^41 - 153049487518536134480 * q^46 + 22735751396127769438 * q^47 - 1317482931964495330032 * q^48 - 1842110772006482246836 * q^49 + 284936617115007894520 * q^50 + 207129175371045152568 * q^52 - 381774025126375304544 * q^54 - 5430040696094013021792 * q^55 - 2168901871328366220760 * q^58 + 16048018791948427185304 * q^59 + 14054450375064171442400 * q^62 + 20310379126091866412192 * q^64 + 24476879859710435470878 * q^69 - 118028399895318845638416 * q^70 - 68204988047209908888578 * q^71 - 106777935582637627887744 * q^72 - 7319375899831086678722 * q^73 + 12913295383070041819998 * q^75 + 111116199573084838704480 * q^77 - 422583593213386075404144 * q^78 - 331350288185757013618680 * q^81 + 1000764218021118649437320 * q^82 - 113385735487939722862944 * q^85 - 248828610584854760185290 * q^87 - 4238455111972177116774696 * q^92 + 4492289396741153284965270 * q^93 - 1602622056539190351258592 * q^94 - 1668692394291208047471936 * q^95 - 12092663288748189077973504 * q^96 - 2067304853876486831513192 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more