LMFDB - Embedded newform 16.8.e.a.5.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,8,Mod(5,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("16.5");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	16.e (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:	$4.99816040775$
Analytic rank:	$0$
Dimension:	$26$
Relative dimension:	$13$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			5.6
Character	$\chi$	$=$	16.5
Dual form			16.8.e.a.13.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.66996 - 10.9941i) q^{2} +(-21.1050 + 21.1050i) q^{3} +(-113.743 + 58.7079i) q^{4} +(328.807 + 328.807i) q^{5} +(288.382 + 175.682i) q^{6} -874.718i q^{7} +(949.131 + 1093.76i) q^{8} +1296.15i q^{9} +O(q^{10})$	\(q+(-2.66996 - 10.9941i) q^{2} +(-21.1050 + 21.1050i) q^{3} +(-113.743 + 58.7079i) q^{4} +(328.807 + 328.807i) q^{5} +(288.382 + 175.682i) q^{6} -874.718i q^{7} +(949.131 + 1093.76i) q^{8} +1296.15i q^{9} +(2737.06 - 4492.86i) q^{10} +(4822.03 + 4822.03i) q^{11} +(1161.51 - 3639.58i) q^{12} +(-7512.32 + 7512.32i) q^{13} +(-9616.78 + 2335.46i) q^{14} -13879.0 q^{15} +(9490.77 - 13355.2i) q^{16} -7422.40 q^{17} +(14250.1 - 3460.68i) q^{18} +(3622.90 - 3622.90i) q^{19} +(-56703.0 - 18095.8i) q^{20} +(18461.0 + 18461.0i) q^{21} +(40139.5 - 65888.8i) q^{22} -18558.7i q^{23} +(-43115.2 - 3052.31i) q^{24} +138104. i q^{25} +(102649. + 62533.9i) q^{26} +(-73512.1 - 73512.1i) q^{27} +(51352.8 + 99492.7i) q^{28} +(81907.6 - 81907.6i) q^{29} +(37056.4 + 152588. i) q^{30} +106899. q^{31} +(-172169. - 68685.2i) q^{32} -203538. q^{33} +(19817.5 + 81603.0i) q^{34} +(287614. - 287614. i) q^{35} +(-76094.4 - 147428. i) q^{36} +(168013. + 168013. i) q^{37} +(-49503.7 - 30157.7i) q^{38} -317096. i q^{39} +(-47553.6 + 671716. i) q^{40} -80786.4i q^{41} +(153673. - 252253. i) q^{42} +(-471268. - 471268. i) q^{43} +(-831562. - 265379. i) q^{44} +(-426185. + 426185. i) q^{45} +(-204037. + 49550.9i) q^{46} -124705. q^{47} +(81558.4 + 482165. i) q^{48} +58411.9 q^{49} +(1.51833e6 - 368731. i) q^{50} +(156650. - 156650. i) q^{51} +(413439. - 1.29550e6i) q^{52} +(533570. + 533570. i) q^{53} +(-611929. + 1.00448e6i) q^{54} +3.17104e6i q^{55} +(956728. - 830222. i) q^{56} +152923. i q^{57} +(-1.11919e6 - 681814. i) q^{58} +(-76070.0 - 76070.0i) q^{59} +(1.57863e6 - 814806. i) q^{60} +(2.46668e6 - 2.46668e6i) q^{61} +(-285417. - 1.17527e6i) q^{62} +1.13377e6 q^{63} +(-295452. + 2.07624e6i) q^{64} -4.94021e6 q^{65} +(543439. + 2.23773e6i) q^{66} +(-903040. + 903040. i) q^{67} +(844244. - 435753. i) q^{68} +(391682. + 391682. i) q^{69} +(-3.92998e6 - 2.39415e6i) q^{70} +2.53069e6i q^{71} +(-1.41768e6 + 1.23022e6i) q^{72} +478985. i q^{73} +(1.39857e6 - 2.29575e6i) q^{74} +(-2.91468e6 - 2.91468e6i) q^{75} +(-199385. + 624770. i) q^{76} +(4.21792e6 - 4.21792e6i) q^{77} +(-3.48620e6 + 846632. i) q^{78} -2.01354e6 q^{79} +(7.51192e6 - 1.27064e6i) q^{80} +268265. q^{81} +(-888177. + 215696. i) q^{82} +(5.67496e6 - 5.67496e6i) q^{83} +(-3.18360e6 - 1.01599e6i) q^{84} +(-2.44054e6 - 2.44054e6i) q^{85} +(-3.92292e6 + 6.43946e6i) q^{86} +3.45733e6i q^{87} +(-697384. + 9.85087e6i) q^{88} -8.04261e6i q^{89} +(5.82344e6 + 3.54765e6i) q^{90} +(6.57116e6 + 6.57116e6i) q^{91} +(1.08954e6 + 2.11091e6i) q^{92} +(-2.25612e6 + 2.25612e6i) q^{93} +(332958. + 1.37103e6i) q^{94} +2.38247e6 q^{95} +(5.08323e6 - 2.18403e6i) q^{96} +1.06700e6 q^{97} +(-155957. - 642189. i) q^{98} +(-6.25009e6 + 6.25009e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 2 q^{2} - 2 q^{3} - 184 q^{4} - 2 q^{5} - 176 q^{6} - 1004 q^{8}+O(q^{10}) $ 26 * q - 2 * q^2 - 2 * q^3 - 184 * q^4 - 2 * q^5 - 176 * q^6 - 1004 * q^8	\( 26 q - 2 q^{2} - 2 q^{3} - 184 q^{4} - 2 q^{5} - 176 q^{6} - 1004 q^{8} + 12972 q^{10} + 1202 q^{11} - 27356 q^{12} - 2 q^{13} + 22268 q^{14} - 27004 q^{15} + 13336 q^{16} - 4 q^{17} - 29346 q^{18} + 60582 q^{19} + 46204 q^{20} + 4372 q^{21} - 44348 q^{22} - 59216 q^{24} - 35960 q^{26} - 233672 q^{27} + 220312 q^{28} - 51690 q^{29} + 27636 q^{30} + 357488 q^{31} - 248632 q^{32} - 4 q^{33} + 924660 q^{34} - 252004 q^{35} - 1015508 q^{36} + 415574 q^{37} - 5472 q^{38} - 1121976 q^{40} + 124600 q^{42} + 569754 q^{43} - 758620 q^{44} + 151874 q^{45} + 2335660 q^{46} - 2076464 q^{47} + 4141288 q^{48} - 1647090 q^{49} - 787194 q^{50} + 2609508 q^{51} + 410324 q^{52} + 907814 q^{53} - 7404512 q^{54} - 4093160 q^{56} - 1860712 q^{58} - 4865142 q^{59} + 5147328 q^{60} + 2279886 q^{61} + 6274096 q^{62} + 8295108 q^{63} + 10452224 q^{64} - 1426892 q^{65} + 10937812 q^{66} - 5564458 q^{67} - 7403760 q^{68} - 4786076 q^{69} - 22140800 q^{70} - 25293948 q^{72} - 13177044 q^{74} + 6212566 q^{75} + 17814260 q^{76} + 7604308 q^{77} + 37993916 q^{78} - 9598912 q^{79} + 40047272 q^{80} - 5314414 q^{81} + 22858240 q^{82} + 4531198 q^{83} - 30159704 q^{84} + 7377748 q^{85} - 54129468 q^{86} - 59216392 q^{88} - 33515304 q^{90} + 2587652 q^{91} + 21810936 q^{92} - 14504144 q^{93} + 77196112 q^{94} - 4900620 q^{95} + 116940464 q^{96} - 4 q^{97} + 21823866 q^{98} + 18815006 q^{99}+O(q^{100}) \) 26 * q - 2 * q^2 - 2 * q^3 - 184 * q^4 - 2 * q^5 - 176 * q^6 - 1004 * q^8 + 12972 * q^10 + 1202 * q^11 - 27356 * q^12 - 2 * q^13 + 22268 * q^14 - 27004 * q^15 + 13336 * q^16 - 4 * q^17 - 29346 * q^18 + 60582 * q^19 + 46204 * q^20 + 4372 * q^21 - 44348 * q^22 - 59216 * q^24 - 35960 * q^26 - 233672 * q^27 + 220312 * q^28 - 51690 * q^29 + 27636 * q^30 + 357488 * q^31 - 248632 * q^32 - 4 * q^33 + 924660 * q^34 - 252004 * q^35 - 1015508 * q^36 + 415574 * q^37 - 5472 * q^38 - 1121976 * q^40 + 124600 * q^42 + 569754 * q^43 - 758620 * q^44 + 151874 * q^45 + 2335660 * q^46 - 2076464 * q^47 + 4141288 * q^48 - 1647090 * q^49 - 787194 * q^50 + 2609508 * q^51 + 410324 * q^52 + 907814 * q^53 - 7404512 * q^54 - 4093160 * q^56 - 1860712 * q^58 - 4865142 * q^59 + 5147328 * q^60 + 2279886 * q^61 + 6274096 * q^62 + 8295108 * q^63 + 10452224 * q^64 - 1426892 * q^65 + 10937812 * q^66 - 5564458 * q^67 - 7403760 * q^68 - 4786076 * q^69 - 22140800 * q^70 - 25293948 * q^72 - 13177044 * q^74 + 6212566 * q^75 + 17814260 * q^76 + 7604308 * q^77 + 37993916 * q^78 - 9598912 * q^79 + 40047272 * q^80 - 5314414 * q^81 + 22858240 * q^82 + 4531198 * q^83 - 30159704 * q^84 + 7377748 * q^85 - 54129468 * q^86 - 59216392 * q^88 - 33515304 * q^90 + 2587652 * q^91 + 21810936 * q^92 - 14504144 * q^93 + 77196112 * q^94 - 4900620 * q^95 + 116940464 * q^96 - 4 * q^97 + 21823866 * q^98 + 18815006 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−2.66996	−	10.9941i	−0.235993	−	0.971755i
$2$	−2.66996	−	10.9941i	−0.235993	−	0.971755i
$3$	−21.1050	+	21.1050i	−0.451296	+	0.451296i	−0.895785	−	0.444488i	$-0.853386\pi$
$3$	−21.1050	+	21.1050i	−0.451296	+	0.451296i	0.444488	+	0.895785i	$0.353386\pi$
$4$	−113.743	+	58.7079i	−0.888614	+	0.458655i
$5$	328.807	+	328.807i	1.17638	+	1.17638i	0.980660	+	0.195717i	$0.0627033\pi$
$5$	328.807	+	328.807i	1.17638	+	1.17638i	0.195717	+	0.980660i	$0.437297\pi$
$6$	288.382	+	175.682i	0.545052	+	0.332047i
$7$		−	874.718i		−	0.963884i	−0.876203	−	0.481942i	$-0.839932\pi$
$7$		−	874.718i		−	0.963884i	0.876203	−	0.481942i	$-0.160068\pi$
$8$	949.131	+	1093.76i	0.655407	+	0.755276i
$9$			1296.15i			0.592663i
$10$	2737.06	−	4492.86i	0.865533	−	1.42077i
$11$	4822.03	+	4822.03i	1.09233	+	1.09233i	0.995279	+	0.0970555i	$0.0309424\pi$
$11$	4822.03	+	4822.03i	1.09233	+	1.09233i	0.0970555	+	0.995279i	$0.469058\pi$
$12$	1161.51	−	3639.58i	0.194039	−	0.608018i
$13$	−7512.32	+	7512.32i	−0.948358	+	0.948358i	−0.998730	−	0.0503729i	$-0.983959\pi$
$13$	−7512.32	+	7512.32i	−0.948358	+	0.948358i	0.0503729	+	0.998730i	$0.483959\pi$
$14$	−9616.78	+	2335.46i	−0.936659	+	0.227470i
$15$	−13879.0			−1.06179
$16$	9490.77	−	13355.2i	0.579271	−	0.815135i
$17$	−7422.40			−0.366415			−0.183208	−	0.983074i	$-0.558648\pi$
$17$	−7422.40			−0.366415			−0.183208	+	0.983074i	$0.558648\pi$
$18$	14250.1	−	3460.68i	0.575923	−	0.139864i
$19$	3622.90	−	3622.90i	0.121176	−	0.121176i	−0.643918	−	0.765094i	$-0.722692\pi$
$19$	3622.90	−	3622.90i	0.121176	−	0.121176i	0.765094	+	0.643918i	$0.222692\pi$
$20$	−56703.0	−	18095.8i	−1.58490	−	0.505794i
$21$	18461.0	+	18461.0i	0.434997	+	0.434997i
$22$	40139.5	−	65888.8i	0.803697	−	1.31926i
$23$		−	18558.7i		−	0.318053i	−0.987274	−	0.159027i	$-0.949164\pi$
$23$		−	18558.7i		−	0.318053i	0.987274	−	0.159027i	$-0.0508355\pi$
$24$	−43115.2	−	3052.31i	−0.636636	−	0.0450702i
$25$			138104.i			1.76773i
$26$	102649.	+	62533.9i	1.14538	+	0.697765i
$27$	−73512.1	−	73512.1i	−0.718763	−	0.718763i
$28$	51352.8	+	99492.7i	0.442090	+	0.856521i
$29$	81907.6	−	81907.6i	0.623636	−	0.623636i	−0.322823	−	0.946459i	$-0.604632\pi$
$29$	81907.6	−	81907.6i	0.623636	−	0.623636i	0.946459	+	0.322823i	$0.104632\pi$
$30$	37056.4	+	152588.i	0.250575	+	1.03180i
$31$	106899.			0.644480			0.322240	−	0.946658i	$-0.395564\pi$
$31$	106899.			0.644480			0.322240	+	0.946658i	$0.395564\pi$
$32$	−172169.	−	68685.2i	−0.928815	−	0.370543i
$33$	−203538.			−0.985933
$34$	19817.5	+	81603.0i	0.0864715	+	0.356066i
$35$	287614.	−	287614.i	1.13389	−	1.13389i
$36$	−76094.4	−	147428.i	−0.271828	−	0.526649i
$37$	168013.	+	168013.i	0.545301	+	0.545301i	0.925078	−	0.379777i	$-0.123999\pi$
$37$	168013.	+	168013.i	0.545301	+	0.545301i	−0.379777	+	0.925078i	$0.623999\pi$
$38$	−49503.7	−	30157.7i	−0.146351	−	0.0891570i
$39$		−	317096.i		−	0.855981i
$40$	−47553.6	+	671716.i	−0.117483	+	1.65950i
$41$		−	80786.4i		−	0.183060i	−0.995802	−	0.0915302i	$-0.970824\pi$
$41$		−	80786.4i		−	0.183060i	0.995802	−	0.0915302i	$-0.0291758\pi$
$42$	153673.	−	252253.i	0.320054	−	0.525367i
$43$	−471268.	−	471268.i	−0.903917	−	0.903917i	0.0918558	−	0.995772i	$-0.470720\pi$
$43$	−471268.	−	471268.i	−0.903917	−	0.903917i	−0.995772	+	0.0918558i	$0.970720\pi$
$44$	−831562.	−	265379.i	−1.47167	−	0.469659i
$45$	−426185.	+	426185.i	−0.697195	+	0.697195i
$46$	−204037.	+	49550.9i	−0.309070	+	0.0750584i
$47$	−124705.			−0.175204			−0.0876018	−	0.996156i	$-0.527920\pi$
$47$	−124705.			−0.175204			−0.0876018	+	0.996156i	$0.527920\pi$
$48$	81558.4	+	482165.i	0.106445	+	0.629290i
$49$	58411.9			0.0709276
$50$	1.51833e6	−	368731.i	1.71780	−	0.417172i
$51$	156650.	−	156650.i	0.165362	−	0.165362i
$52$	413439.	−	1.29550e6i	0.407755	−	1.27769i
$53$	533570.	+	533570.i	0.492296	+	0.492296i	0.909029	−	0.416733i	$-0.136825\pi$
$53$	533570.	+	533570.i	0.492296	+	0.492296i	−0.416733	+	0.909029i	$0.636825\pi$
$54$	−611929.	+	1.00448e6i	−0.528838	+	0.868085i
$55$			3.17104e6i			2.56999i
$56$	956728.	−	830222.i	0.727998	−	0.631737i
$57$			152923.i			0.109373i
$58$	−1.11919e6	−	681814.i	−0.753195	−	0.458847i
$59$	−76070.0	−	76070.0i	−0.0482205	−	0.0482205i	0.682585	−	0.730806i	$-0.260856\pi$
$59$	−76070.0	−	76070.0i	−0.0482205	−	0.0482205i	−0.730806	+	0.682585i	$0.760856\pi$
$60$	1.57863e6	−	814806.i	0.943522	−	0.486995i
$61$	2.46668e6	−	2.46668e6i	1.39142	−	1.39142i	0.569276	−	0.822147i	$-0.307224\pi$
$61$	2.46668e6	−	2.46668e6i	1.39142	−	1.39142i	0.822147	−	0.569276i	$-0.192776\pi$
$62$	−285417.	−	1.17527e6i	−0.152093	−	0.626276i
$63$	1.13377e6			0.571258
$64$	−295452.	+	2.07624e6i	−0.140882	+	0.990026i
$65$	−4.94021e6			−2.23125
$66$	543439.	+	2.23773e6i	0.232674	+	0.958085i
$67$	−903040.	+	903040.i	−0.366813	+	0.366813i	−0.866314	−	0.499500i	$-0.833517\pi$
$67$	−903040.	+	903040.i	−0.366813	+	0.366813i	0.499500	+	0.866314i	$0.333517\pi$
$68$	844244.	−	435753.i	0.325602	−	0.168058i
$69$	391682.	+	391682.i	0.143536	+	0.143536i
$70$	−3.92998e6	−	2.39415e6i	−1.36945	−	0.834273i
$71$			2.53069e6i			0.839142i	0.907723	+	0.419571i	$0.137819\pi$
$71$			2.53069e6i			0.839142i	−0.907723	+	0.419571i	$0.862181\pi$
$72$	−1.41768e6	+	1.23022e6i	−0.447624	+	0.388436i
$73$			478985.i			0.144109i	0.997401	+	0.0720546i	$0.0229556\pi$
$73$			478985.i			0.144109i	−0.997401	+	0.0720546i	$0.977044\pi$
$74$	1.39857e6	−	2.29575e6i	0.401212	−	0.658587i
$75$	−2.91468e6	−	2.91468e6i	−0.797769	−	0.797769i
$76$	−199385.	+	624770.i	−0.0521009	+	0.163257i
$77$	4.21792e6	−	4.21792e6i	1.05288	−	1.05288i
$78$	−3.48620e6	+	846632.i	−0.831803	+	0.202006i
$79$	−2.01354e6			−0.459479			−0.229739	−	0.973252i	$-0.573787\pi$
$79$	−2.01354e6			−0.459479			−0.229739	+	0.973252i	$0.573787\pi$
$80$	7.51192e6	−	1.27064e6i	1.64035	−	0.277465i
$81$	268265.			0.0560876
$82$	−888177.	+	215696.i	−0.177890	+	0.0432010i
$83$	5.67496e6	−	5.67496e6i	1.08940	−	1.08940i	0.0938150	−	0.995590i	$-0.470094\pi$
$83$	5.67496e6	−	5.67496e6i	1.08940	−	1.08940i	0.995590	−	0.0938150i	$-0.0299062\pi$
$84$	−3.18360e6	−	1.01599e6i	−0.586059	−	0.187031i
$85$	−2.44054e6	−	2.44054e6i	−0.431042	−	0.431042i
$86$	−3.92292e6	+	6.43946e6i	−0.665067	+	1.09170i
$87$			3.45733e6i			0.562889i
$88$	−697384.	+	9.85087e6i	−0.109089	+	1.54094i
$89$		−	8.04261e6i		−	1.20929i	−0.796493	−	0.604647i	$-0.793314\pi$
$89$		−	8.04261e6i		−	1.20929i	0.796493	−	0.604647i	$-0.206686\pi$
$90$	5.82344e6	+	3.54765e6i	0.842036	+	0.512969i
$91$	6.57116e6	+	6.57116e6i	0.914107	+	0.914107i
$92$	1.08954e6	+	2.11091e6i	0.145877	+	0.282626i
$93$	−2.25612e6	+	2.25612e6i	−0.290851	+	0.290851i
$94$	332958.	+	1.37103e6i	0.0413469	+	0.170255i
$95$	2.38247e6			0.285099
$96$	5.08323e6	−	2.18403e6i	0.586396	−	0.251947i
$97$	1.06700e6			0.118703			0.0593515	−	0.998237i	$-0.481097\pi$
$97$	1.06700e6			0.118703			0.0593515	+	0.998237i	$0.481097\pi$
$98$	−155957.	−	642189.i	−0.0167384	−	0.0689242i
$99$	−6.25009e6	+	6.25009e6i	−0.647386	+	0.647386i
$100$	−8.10777e6	−	1.57083e7i	−0.810777	−	1.57083i
$101$	1.08063e7	+	1.08063e7i	1.04365	+	1.04365i	0.999003	+	0.0446440i	$0.0142154\pi$
$101$	1.08063e7	+	1.08063e7i	1.04365	+	1.04365i	0.0446440	+	0.999003i	$0.485785\pi$
$102$	−2.14048e6	−	1.30399e6i	−0.199715	−	0.121667i
$103$		−	1.05134e7i		−	0.948013i	−0.880521	−	0.474006i	$-0.842807\pi$
$103$		−	1.05134e7i		−	0.948013i	0.880521	−	0.474006i	$-0.157193\pi$
$104$	−1.53468e7	−	1.08647e6i	−1.33783	−	0.0947108i
$105$			1.21402e7i			1.02344i
$106$	4.44154e6	−	7.29076e6i	0.362212	−	0.594569i
$107$	−1.46376e7	−	1.46376e7i	−1.15512	−	1.15512i	−0.985513	−	0.169602i	$-0.945752\pi$
$107$	−1.46376e7	−	1.46376e7i	−1.15512	−	1.15512i	−0.169602	−	0.985513i	$-0.554248\pi$
$108$	1.26772e7	+	4.04572e6i	0.968368	+	0.309039i
$109$	−6.54748e6	+	6.54748e6i	−0.484263	+	0.484263i	−0.906490	−	0.422227i	$-0.861249\pi$
$109$	−6.54748e6	+	6.54748e6i	−0.484263	+	0.484263i	0.422227	+	0.906490i	$0.361249\pi$
$110$	3.48629e7	−	8.46655e6i	2.49740	−	0.606502i
$111$	−7.09184e6			−0.492185
$112$	−1.16820e7	−	8.30175e6i	−0.785696	−	0.558350i
$113$	−3.94399e6			−0.257135			−0.128568	−	0.991701i	$-0.541038\pi$
$113$	−3.94399e6			−0.257135			−0.128568	+	0.991701i	$0.541038\pi$
$114$	1.68126e6	−	408298.i	0.106284	−	0.0258113i
$115$	6.10223e6	−	6.10223e6i	0.374150	−	0.374150i
$116$	−4.50776e6	+	1.41250e7i	−0.268138	+	0.840205i
$117$	−9.73712e6	−	9.73712e6i	−0.562056	−	0.562056i
$118$	−633221.	+	1.03943e6i	−0.0354788	+	0.0582382i
$119$			6.49251e6i			0.353182i
$120$	−1.31730e7	−	1.51802e7i	−0.695905	−	0.801944i
$121$			2.70168e7i			1.38639i
$122$	−3.37050e7	−	2.05331e7i	−1.68049	−	1.02375i
$123$	1.70500e6	+	1.70500e6i	0.0826145	+	0.0826145i
$124$	−1.21590e7	+	6.27583e6i	−0.572694	+	0.295594i
$125$	−1.97214e7	+	1.97214e7i	−0.903137	+	0.903137i
$126$	−3.02712e6	−	1.24648e7i	−0.134813	−	0.555123i
$127$	3.96790e7			1.71889			0.859445	−	0.511229i	$-0.170810\pi$
$127$	3.96790e7			1.71889			0.859445	+	0.511229i	$0.170810\pi$
$128$	2.36153e7	−	2.29523e6i	0.995310	−	0.0967365i
$129$	1.98923e7			0.815869
$130$	1.31902e7	+	5.43134e7i	0.526561	+	2.16823i
$131$	−8.97855e6	+	8.97855e6i	−0.348945	+	0.348945i	−0.859716	−	0.510772i	$-0.829360\pi$
$131$	−8.97855e6	+	8.97855e6i	−0.348945	+	0.348945i	0.510772	+	0.859716i	$0.329360\pi$
$132$	2.31510e7	−	1.19493e7i	0.876115	−	0.452203i
$133$	−3.16901e6	−	3.16901e6i	−0.116800	−	0.116800i
$134$	1.23392e7	+	7.51707e6i	0.443018	+	0.269887i
$135$		−	4.83427e7i		−	1.69107i
$136$	−7.04483e6	−	8.11830e6i	−0.240151	−	0.276744i
$137$		−	4.54483e7i		−	1.51006i	−0.655687	−	0.755032i	$-0.727621\pi$
$137$		−	4.54483e7i		−	1.51006i	0.655687	−	0.755032i	$-0.272379\pi$
$138$	3.26043e6	−	5.35198e6i	0.105608	−	0.173356i
$139$	3.25749e7	+	3.25749e7i	1.02880	+	1.02880i	0.999573	+	0.0292279i	$0.00930485\pi$
$139$	3.25749e7	+	3.25749e7i	1.02880	+	1.02880i	0.0292279	+	0.999573i	$0.490695\pi$
$140$	−1.58288e7	+	4.95991e7i	−0.487527	+	1.52766i
$141$	2.63191e6	−	2.63191e6i	0.0790687	−	0.0790687i
$142$	2.78228e7	−	6.75685e6i	0.815440	−	0.198032i
$143$	−7.24492e7			−2.07185
$144$	1.73104e7	+	1.23015e7i	0.483100	+	0.343312i
$145$	5.38636e7			1.46726
$146$	5.26603e6	−	1.27887e6i	0.140039	−	0.0340088i
$147$	−1.23279e6	+	1.23279e6i	−0.0320094	+	0.0320094i
$148$	−2.89739e7	−	9.24655e6i	−0.734668	−	0.234457i
$149$	−5.36259e6	−	5.36259e6i	−0.132807	−	0.132807i	0.637578	−	0.770386i	$-0.279936\pi$
$149$	−5.36259e6	−	5.36259e6i	−0.132807	−	0.132807i	−0.770386	+	0.637578i	$0.779936\pi$
$150$	−2.42624e7	+	3.98266e7i	−0.586968	+	0.963504i
$151$		−	4.47760e7i		−	1.05834i	−0.848515	−	0.529171i	$-0.822503\pi$
$151$		−	4.47760e7i		−	1.05834i	0.848515	−	0.529171i	$-0.177497\pi$
$152$	7.40117e6	+	523960.i	0.170942	+	0.0121017i
$153$		−	9.62058e6i		−	0.217161i
$154$	−5.76341e7	−	3.51107e7i	−1.27162	−	0.774671i
$155$	3.51493e7	+	3.51493e7i	0.758151	+	0.758151i
$156$	1.86160e7	+	3.60673e7i	0.392600	+	0.760637i
$157$	2.30314e6	−	2.30314e6i	0.0474977	−	0.0474977i	−0.682959	−	0.730457i	$-0.739307\pi$
$157$	2.30314e6	−	2.30314e6i	0.0474977	−	0.0474977i	0.730457	+	0.682959i	$0.239307\pi$
$158$	5.37607e6	+	2.21372e7i	0.108434	+	0.446501i
$159$	−2.25220e7			−0.444343
$160$	−3.40262e7	−	7.91946e7i	−0.656739	−	1.52854i
$161$	−1.62336e7			−0.306566
$162$	−716257.	−	2.94935e6i	−0.0132363	−	0.0545034i
$163$	−2.99834e7	+	2.99834e7i	−0.542282	+	0.542282i	−0.924197	−	0.381916i	$-0.875265\pi$
$163$	−2.99834e7	+	2.99834e7i	−0.542282	+	0.542282i	0.381916	+	0.924197i	$0.375265\pi$
$164$	4.74280e6	+	9.18885e6i	0.0839616	+	0.162670i
$165$	−6.69249e7	−	6.69249e7i	−1.15983	−	1.15983i
$166$	−7.75432e7	−	4.72394e7i	−1.31573	−	0.801542i
$167$			3.93802e7i			0.654289i	0.944974	+	0.327145i	$0.106086\pi$
$167$			3.93802e7i			0.654289i	−0.944974	+	0.327145i	$0.893914\pi$
$168$	−2.66991e6	+	3.77137e7i	−0.0434424	+	0.613644i
$169$		−	5.01213e7i		−	0.798764i
$170$	−2.03155e7	+	3.33478e7i	−0.317144	+	0.520590i
$171$	4.69583e6	+	4.69583e6i	0.0718168	+	0.0718168i
$172$	8.12704e7	+	2.59361e7i	1.21782	+	0.388647i
$173$	3.43712e7	−	3.43712e7i	0.504700	−	0.504700i	−0.408195	−	0.912895i	$-0.633842\pi$
$173$	3.43712e7	−	3.43712e7i	0.504700	−	0.504700i	0.912895	+	0.408195i	$0.133842\pi$
$174$	3.80104e7	−	9.23092e6i	0.546990	−	0.132838i
$175$	1.20802e8			1.70388
$176$	1.10164e8	−	1.86343e7i	1.52316	−	0.257643i
$177$	3.21092e6			0.0435235
$178$	−8.84217e7	+	2.14734e7i	−1.17514	+	0.285385i
$179$	−6.30231e7	+	6.30231e7i	−0.821323	+	0.821323i	−0.986298	−	0.164975i	$-0.947246\pi$
$179$	−6.30231e7	+	6.30231e7i	−0.821323	+	0.821323i	0.164975	+	0.986298i	$0.447246\pi$
$180$	2.34550e7	−	7.34958e7i	0.299765	−	0.939310i
$181$	3.05870e7	+	3.05870e7i	0.383409	+	0.383409i	0.872329	−	0.488920i	$-0.162609\pi$
$181$	3.05870e7	+	3.05870e7i	0.383409	+	0.383409i	−0.488920	+	0.872329i	$0.662609\pi$
$182$	5.46995e7	−	8.97890e7i	0.672564	−	1.10401i
$183$			1.04119e8i			1.25589i
$184$	2.02987e7	−	1.76146e7i	0.240218	−	0.208454i
$185$			1.10488e8i			1.28296i
$186$	3.08278e7	+	1.87803e7i	0.351275	+	0.213997i
$187$	−3.57911e7	−	3.57911e7i	−0.400248	−	0.400248i
$188$	1.41843e7	−	7.32119e6i	0.155688	−	0.0803580i
$189$	−6.43024e7	+	6.43024e7i	−0.692804	+	0.692804i
$190$	−6.36110e6	−	2.61932e7i	−0.0672813	−	0.277046i
$191$	−6.32071e7			−0.656370			−0.328185	−	0.944613i	$-0.606437\pi$
$191$	−6.32071e7			−0.656370			−0.328185	+	0.944613i	$0.606437\pi$
$192$	−3.75835e7	−	5.00546e7i	−0.383216	−	0.510375i
$193$	−4.36893e7			−0.437447			−0.218723	−	0.975787i	$-0.570189\pi$
$193$	−4.36893e7			−0.437447			−0.218723	+	0.975787i	$0.570189\pi$
$194$	−2.84884e6	−	1.17307e7i	−0.0280131	−	0.115350i
$195$	1.04263e8	−	1.04263e8i	1.00696	−	1.00696i
$196$	−6.64392e6	+	3.42924e6i	−0.0630272	+	0.0325313i
$197$	8.39344e7	+	8.39344e7i	0.782183	+	0.782183i	0.980199	−	0.198016i	$-0.0634497\pi$
$197$	8.39344e7	+	8.39344e7i	0.782183	+	0.782183i	−0.198016	+	0.980199i	$0.563450\pi$
$198$	8.54020e7	+	5.20270e7i	0.781879	+	0.476322i
$199$			1.05173e8i			0.946062i	0.881046	+	0.473031i	$0.156840\pi$
$199$			1.05173e8i			0.946062i	−0.881046	+	0.473031i	$0.843160\pi$
$200$	−1.51052e8	+	1.31079e8i	−1.33512	+	1.15858i
$201$		−	3.81174e7i		−	0.331083i
$202$	8.99540e7	−	1.47659e8i	0.767875	−	1.26046i
$203$	−7.16460e7	−	7.16460e7i	−0.601113	−	0.601113i
$204$	−8.62120e6	+	2.70144e7i	−0.0710988	+	0.222787i
$205$	2.65632e7	−	2.65632e7i	0.215348	−	0.215348i
$206$	−1.15586e8	+	2.80704e7i	−0.921236	+	0.223725i
$207$	2.40549e7			0.188498
$208$	2.90306e7	+	1.71626e8i	0.223684	+	1.32240i
$209$	3.49394e7			0.264730
$210$	1.33471e8	−	3.24138e7i	0.994535	−	0.241526i
$211$	−1.82125e7	+	1.82125e7i	−0.133469	+	0.133469i	−0.770685	−	0.637216i	$-0.780086\pi$
$211$	−1.82125e7	+	1.82125e7i	−0.133469	+	0.133469i	0.637216	+	0.770685i	$0.280086\pi$
$212$	−9.20144e7	−	2.93649e7i	−0.663255	−	0.211667i
$213$	−5.34104e7	−	5.34104e7i	−0.378702	−	0.378702i
$214$	−1.21846e8	+	2.00009e8i	−0.849889	+	1.39509i
$215$		−	3.09913e8i		−	2.12669i
$216$	1.06317e7	−	1.50177e8i	0.0717816	−	1.01395i
$217$		−	9.35068e7i		−	0.621204i
$218$	8.94655e7	+	5.45025e7i	0.584868	+	0.356302i
$219$	−1.01090e7	−	1.01090e7i	−0.0650360	−	0.0650360i
$220$	−1.86165e8	−	3.60682e8i	−1.17874	−	2.28373i
$221$	5.57594e7	−	5.57594e7i	0.347492	−	0.347492i
$222$	1.89349e7	+	7.79687e7i	0.116152	+	0.478283i
$223$	−6.74789e7			−0.407475			−0.203738	−	0.979026i	$-0.565309\pi$
$223$	−6.74789e7			−0.407475			−0.203738	+	0.979026i	$0.565309\pi$
$224$	−6.00802e7	+	1.50599e8i	−0.357160	+	0.895270i
$225$	−1.79004e8			−1.04767
$226$	1.05303e7	+	4.33608e7i	0.0606821	+	0.249872i
$227$	1.37027e8	−	1.37027e8i	0.777530	−	0.777530i	−0.201880	−	0.979410i	$-0.564705\pi$
$227$	1.37027e8	−	1.37027e8i	0.777530	−	0.777530i	0.979410	+	0.201880i	$0.0647052\pi$
$228$	−8.97777e6	−	1.73938e7i	−0.0501645	−	0.0971904i
$229$	1.57724e8	+	1.57724e8i	0.867906	+	0.867906i	0.992240	−	0.124334i	$-0.0396795\pi$
$229$	1.57724e8	+	1.57724e8i	0.867906	+	0.867906i	−0.124334	+	0.992240i	$0.539679\pi$
$230$	−8.33815e7	−	5.07961e7i	−0.451879	−	0.275285i
$231$			1.78039e8i			0.950325i
$232$	1.67328e8	+	1.18458e7i	0.879752	+	0.0622814i
$233$			1.31577e8i			0.681451i	0.940163	+	0.340725i	$0.110673\pi$
$233$			1.31577e8i			0.681451i	−0.940163	+	0.340725i	$0.889327\pi$
$234$	−8.10536e7	+	1.33049e8i	−0.413539	+	0.678823i
$235$	−4.10041e7	−	4.10041e7i	−0.206105	−	0.206105i
$236$	1.31183e7	+	4.18650e6i	0.0649660	+	0.0207328i
$237$	4.24959e7	−	4.24959e7i	0.207361	−	0.207361i
$238$	7.13796e7	−	1.73347e7i	0.343206	−	0.0833485i
$239$	8.42285e7			0.399086			0.199543	−	0.979889i	$-0.436054\pi$
$239$	8.42285e7			0.399086			0.199543	+	0.979889i	$0.436054\pi$
$240$	−1.31722e8	+	1.85356e8i	−0.615064	+	0.865502i
$241$	−2.42588e8			−1.11637			−0.558186	−	0.829716i	$-0.688503\pi$
$241$	−2.42588e8			−1.11637			−0.558186	+	0.829716i	$0.688503\pi$
$242$	2.97027e8	−	7.21338e7i	1.34723	−	0.327179i
$243$	1.55109e8	−	1.55109e8i	0.693451	−	0.693451i
$244$	−1.35753e8	+	4.25381e8i	−0.598255	+	1.87462i
$245$	1.92063e7	+	1.92063e7i	0.0834376	+	0.0834376i
$246$	1.41927e7	−	2.32973e7i	0.0607846	−	0.0997775i
$247$			5.44327e7i			0.229837i
$248$	1.01462e8	+	1.16922e8i	0.422397	+	0.486760i
$249$			2.39540e8i			0.983289i
$250$	2.69476e8	+	1.64165e8i	1.09076	+	0.664493i
$251$	−2.89321e8	−	2.89321e8i	−1.15484	−	1.15484i	−0.985570	−	0.169270i	$-0.945859\pi$
$251$	−2.89321e8	−	2.89321e8i	−1.15484	−	1.15484i	−0.169270	−	0.985570i	$-0.554141\pi$
$252$	−1.28958e8	+	6.65611e7i	−0.507628	+	0.262011i
$253$	8.94905e7	−	8.94905e7i	0.347420	−	0.347420i
$254$	−1.05941e8	−	4.36237e8i	−0.405646	−	1.67034i
$255$	1.03015e8			0.389056
$256$	−8.82859e7	−	2.53502e8i	−0.328891	−	0.944368i
$257$	1.76826e8			0.649801			0.324901	−	0.945748i	$-0.394669\pi$
$257$	1.76826e8			0.649801			0.324901	+	0.945748i	$0.394669\pi$
$258$	−5.31115e7	−	2.18699e8i	−0.192540	−	0.792824i
$259$	1.46964e8	−	1.46964e8i	0.525607	−	0.525607i
$260$	5.61913e8	−	2.90029e8i	1.98272	−	1.02338i
$261$	1.06165e8	+	1.06165e8i	0.369606	+	0.369606i
$262$	1.22684e8	+	7.47392e7i	0.421437	+	0.256740i
$263$			2.79422e8i			0.947142i	0.880756	+	0.473571i	$0.157035\pi$
$263$			2.79422e8i			0.947142i	−0.880756	+	0.473571i	$0.842965\pi$
$264$	−1.93185e8	−	2.22621e8i	−0.646188	−	0.744651i
$265$			3.50884e8i			1.15825i
$266$	−2.63795e7	+	4.33017e7i	−0.0859370	+	0.141065i
$267$	1.69740e8	+	1.69740e8i	0.545750	+	0.545750i
$268$	4.96986e7	−	1.55730e8i	0.157715	−	0.494196i
$269$	1.33075e8	−	1.33075e8i	0.416833	−	0.416833i	−0.467277	−	0.884111i	$-0.654765\pi$
$269$	1.33075e8	−	1.33075e8i	0.416833	−	0.416833i	0.884111	+	0.467277i	$0.154765\pi$
$270$	−5.31487e8	+	1.29073e8i	−1.64331	+	0.399082i
$271$	−6.61549e7			−0.201916			−0.100958	−	0.994891i	$-0.532191\pi$
$271$	−6.61549e7			−0.201916			−0.100958	+	0.994891i	$0.532191\pi$
$272$	−7.04443e7	+	9.91275e7i	−0.212254	+	0.298678i
$273$	−2.77369e8			−0.825066
$274$	−4.99665e8	+	1.21345e8i	−1.46741	+	0.356365i
$275$	−6.65940e8	+	6.65940e8i	−1.93095	+	1.93095i
$276$	−6.75457e7	−	2.15561e7i	−0.193382	−	0.0617147i
$277$	−3.04666e8	−	3.04666e8i	−0.861281	−	0.861281i	0.130206	−	0.991487i	$-0.458436\pi$
$277$	−3.04666e8	−	3.04666e8i	−0.861281	−	0.861281i	−0.991487	+	0.130206i	$0.958436\pi$
$278$	2.71160e8	−	4.45107e8i	0.756952	−	1.24253i
$279$			1.38558e8i			0.381959i
$280$	5.87562e8	+	4.15960e7i	1.59956	+	0.113240i
$281$		−	6.46004e8i		−	1.73685i	−0.495817	−	0.868427i	$-0.665131\pi$
$281$		−	6.46004e8i		−	1.73685i	0.495817	−	0.868427i	$-0.334869\pi$
$282$	−3.59628e7	−	2.19085e7i	−0.0954951	−	0.0581757i
$283$	2.23351e8	+	2.23351e8i	0.585782	+	0.585782i	0.936486	−	0.350704i	$-0.114058\pi$
$283$	2.23351e8	+	2.23351e8i	0.585782	+	0.585782i	−0.350704	+	0.936486i	$0.614058\pi$
$284$	−1.48572e8	−	2.87848e8i	−0.384877	−	0.745674i
$285$	−5.02822e7	+	5.02822e7i	−0.128664	+	0.128664i
$286$	1.93437e8	+	7.96518e8i	0.488942	+	2.01333i
$287$	−7.06653e7			−0.176449
$288$	8.90266e7	−	2.23157e8i	0.219607	−	0.550475i
$289$	−3.55247e8			−0.865740
$290$	−1.43814e8	−	5.92185e8i	−0.346264	−	1.42582i
$291$	−2.25190e7	+	2.25190e7i	−0.0535702	+	0.0535702i
$292$	−2.81202e7	−	5.44810e7i	−0.0660965	−	0.128058i
$293$	6.98803e6	+	6.98803e6i	0.0162300	+	0.0162300i	0.715175	−	0.698945i	$-0.246347\pi$
$293$	6.98803e6	+	6.98803e6i	0.0162300	+	0.0162300i	−0.698945	+	0.715175i	$0.746347\pi$
$294$	1.68449e7	+	1.02619e7i	0.0386592	+	0.0235512i
$295$		−	5.00248e7i		−	0.113451i
$296$	−2.42988e7	+	3.43231e8i	−0.0544582	+	0.769247i
$297$		−	7.08956e8i		−	1.57026i
$298$	−4.46392e7	+	7.32750e7i	−0.0977146	+	0.160398i
$299$	1.39419e8	+	1.39419e8i	0.301628	+	0.301628i
$300$	5.02639e8	+	1.60409e8i	1.07481	+	0.343008i
$301$	−4.12226e8	+	4.12226e8i	−0.871271	+	0.871271i
$302$	−4.92274e8	+	1.19550e8i	−1.02845	+	0.249762i
$303$	−4.56136e8			−0.941988
$304$	−1.40003e7	−	8.27685e7i	−0.0285812	−	0.168969i
$305$	1.62213e9			3.27368
$306$	−1.05770e8	+	2.56865e7i	−0.211027	+	0.0512485i
$307$	1.76246e8	−	1.76246e8i	0.347645	−	0.347645i	−0.511587	−	0.859232i	$-0.670942\pi$
$307$	1.76246e8	−	1.76246e8i	0.347645	−	0.347645i	0.859232	+	0.511587i	$0.170942\pi$
$308$	−2.32132e8	+	7.27382e8i	−0.452697	+	1.41852i
$309$	2.21886e8	+	2.21886e8i	0.427835	+	0.427835i
$310$	2.92589e8	−	4.80284e8i	0.557818	−	0.915656i
$311$		−	3.84417e8i		−	0.724672i	−0.932048	−	0.362336i	$-0.881979\pi$
$311$		−	3.84417e8i		−	0.724672i	0.932048	−	0.362336i	$-0.118021\pi$
$312$	3.46825e8	−	3.00965e8i	0.646501	−	0.561016i
$313$			4.33191e7i			0.0798500i	0.999203	+	0.0399250i	$0.0127119\pi$
$313$			4.33191e7i			0.0798500i	−0.999203	+	0.0399250i	$0.987288\pi$
$314$	−3.14704e7	−	1.91718e7i	−0.0573652	−	0.0349469i
$315$	3.72792e8	+	3.72792e8i	0.672015	+	0.672015i
$316$	2.29025e8	−	1.18211e8i	0.408299	−	0.210742i
$317$	3.57477e7	−	3.57477e7i	0.0630291	−	0.0630291i	−0.674890	−	0.737919i	$-0.735809\pi$
$317$	3.57477e7	−	3.57477e7i	0.0630291	−	0.0630291i	0.737919	+	0.674890i	$0.235809\pi$
$318$	6.01329e7	+	2.47611e8i	0.104862	+	0.431792i
$319$	7.89922e8			1.36244
$320$	−7.79828e8	+	5.85535e8i	−1.33038	+	0.998914i
$321$	6.17852e8			1.04260
$322$	4.33431e7	+	1.78475e8i	0.0723476	+	0.297907i
$323$	−2.68906e7	+	2.68906e7i	−0.0444009	+	0.0444009i
$324$	−3.05132e7	+	1.57493e7i	−0.0498402	+	0.0257249i
$325$	−1.03748e9	−	1.03748e9i	−1.67644	−	1.67644i
$326$	4.09697e8	+	2.49588e8i	0.654940	+	0.398990i
$327$		−	2.76370e8i		−	0.437093i
$328$	8.83606e7	−	7.66769e7i	0.138261	−	0.119979i
$329$			1.09082e8i			0.168876i
$330$	−5.57096e8	+	9.14470e8i	−0.853358	+	1.40078i
$331$	−6.23727e8	−	6.23727e8i	−0.945358	−	0.945358i	0.0532242	−	0.998583i	$-0.483050\pi$
$331$	−6.23727e8	−	6.23727e8i	−0.945358	−	0.945358i	−0.998583	+	0.0532242i	$0.983050\pi$
$332$	−3.12320e8	+	9.78649e8i	−0.468399	+	1.46772i
$333$	−2.17771e8	+	2.17771e8i	−0.323180	+	0.323180i
$334$	4.32951e8	−	1.05143e8i	0.635809	−	0.154408i
$335$	−5.93852e8			−0.863022
$336$	4.21758e8	−	7.13406e7i	0.606563	−	0.102600i
$337$	−9.97818e8			−1.42019			−0.710095	−	0.704106i	$-0.751348\pi$
$337$	−9.97818e8			−1.42019			−0.710095	+	0.704106i	$0.751348\pi$
$338$	−5.51041e8	+	1.33822e8i	−0.776203	+	0.188503i
$339$	8.32381e7	−	8.32381e7i	0.116044	−	0.116044i
$340$	4.20873e8	+	1.34315e8i	0.580730	+	0.185331i
$341$	5.15472e8	+	5.15472e8i	0.703987	+	0.703987i
$342$	3.90890e7	−	6.41644e7i	0.0528400	−	0.0867366i
$343$		−	7.71462e8i		−	1.03225i
$344$	6.81569e7	−	9.62747e8i	0.0902725	−	1.27514i
$345$			2.57576e8i			0.337705i
$346$	−4.69651e8	−	2.86112e8i	−0.609550	−	0.371338i
$347$	7.58877e8	+	7.58877e8i	0.975031	+	0.975031i	0.999696	−	0.0246648i	$-0.00785184\pi$
$347$	7.58877e8	+	7.58877e8i	0.975031	+	0.975031i	−0.0246648	+	0.999696i	$0.507852\pi$
$348$	−2.02972e8	−	3.93245e8i	−0.258172	−	0.500191i
$349$	2.29847e8	−	2.29847e8i	0.289434	−	0.289434i	−0.547422	−	0.836856i	$-0.684391\pi$
$349$	2.29847e8	−	2.29847e8i	0.289434	−	0.289434i	0.836856	+	0.547422i	$0.184391\pi$
$350$	−3.22536e8	−	1.32811e9i	−0.402105	−	1.65576i
$351$	1.10449e9			1.36329
$352$	−4.99001e8	−	1.16141e9i	−0.609821	−	1.41933i
$353$	−4.19353e8			−0.507421			−0.253710	−	0.967280i	$-0.581651\pi$
$353$	−4.19353e8			−0.507421			−0.253710	+	0.967280i	$0.581651\pi$
$354$	−8.57303e6	−	3.53014e7i	−0.0102712	−	0.0422941i
$355$	−8.32111e8	+	8.32111e8i	−0.987148	+	0.987148i
$356$	4.72164e8	+	9.14788e8i	0.554649	+	1.07460i
$357$	−1.37025e8	−	1.37025e8i	−0.159390	−	0.159390i
$358$	8.61154e8	+	5.24616e8i	0.991951	+	0.604298i
$359$		−	2.81117e8i		−	0.320669i	−0.987063	−	0.160334i	$-0.948743\pi$
$359$		−	2.81117e8i		−	0.320669i	0.987063	−	0.160334i	$-0.0512573\pi$
$360$	−8.70648e8	−	6.16368e7i	−0.983521	−	0.0696276i
$361$			8.67621e8i			0.970633i
$362$	2.54612e8	−	4.17944e8i	0.282097	−	0.463061i
$363$	−5.70191e8	−	5.70191e8i	−0.625672	−	0.625672i
$364$	−1.13320e9	−	3.61642e8i	−1.23155	−	0.393029i
$365$	−1.57494e8	+	1.57494e8i	−0.169527	+	0.169527i
$366$	1.14470e9	−	2.77993e8i	1.22042	−	0.296381i
$367$	−9.69500e8			−1.02380			−0.511902	−	0.859044i	$-0.671059\pi$
$367$	−9.69500e8			−1.02380			−0.511902	+	0.859044i	$0.671059\pi$
$368$	−2.47854e8	−	1.76136e8i	−0.259256	−	0.184239i
$369$	1.04712e8			0.108493
$370$	1.21472e9	−	2.94998e8i	1.24672	−	0.302770i
$371$	4.66723e8	−	4.66723e8i	0.474516	−	0.474516i
$372$	1.24165e8	−	3.89068e8i	0.125054	−	0.391855i
$373$	−2.48348e7	−	2.48348e7i	−0.0247787	−	0.0247787i	0.694609	−	0.719388i	$-0.255577\pi$
$373$	−2.48348e7	−	2.48348e7i	−0.0247787	−	0.0247787i	−0.719388	+	0.694609i	$0.755577\pi$
$374$	−2.97932e8	+	4.89053e8i	−0.294487	+	0.483398i
$375$		−	8.32444e8i		−	0.815165i
$376$	−1.18362e8	−	1.36397e8i	−0.114830	−	0.132327i
$377$			1.23063e9i			1.18286i
$378$	8.78634e8	+	5.35265e8i	0.836733	+	0.509739i
$379$	9.37224e8	+	9.37224e8i	0.884313	+	0.884313i	0.993970	−	0.109657i	$-0.0349751\pi$
$379$	9.37224e8	+	9.37224e8i	0.884313	+	0.884313i	−0.109657	+	0.993970i	$0.534975\pi$
$380$	−2.70988e8	+	1.39870e8i	−0.253343	+	0.130762i
$381$	−8.37428e8	+	8.37428e8i	−0.775729	+	0.775729i
$382$	1.68760e8	+	6.94908e8i	0.154899	+	0.637831i
$383$	−1.61232e9			−1.46641			−0.733205	−	0.680008i	$-0.761976\pi$
$383$	−1.61232e9			−1.46641			−0.733205	+	0.680008i	$0.761976\pi$
$384$	−4.49961e8	+	5.46843e8i	−0.405523	+	0.492837i
$385$	2.77376e9			2.47718
$386$	1.16649e8	+	4.80327e8i	0.103234	+	0.425091i
$387$	6.10836e8	−	6.10836e8i	0.535718	−	0.535718i
$388$	−1.21363e8	+	6.26411e7i	−0.105481	+	0.0544438i
$389$	1.14411e9	+	1.14411e9i	0.985474	+	0.985474i	0.999896	−	0.0144220i	$-0.00459082\pi$
$389$	1.14411e9	+	1.14411e9i	0.985474	+	0.985474i	−0.0144220	+	0.999896i	$0.504591\pi$
$390$	−1.42467e9	−	8.67908e8i	−1.21615	−	0.740880i
$391$			1.37750e8i			0.116539i
$392$	5.54406e7	+	6.38883e7i	0.0464864	+	0.0535698i
$393$		−	3.78986e8i		−	0.314955i
$394$	6.98686e8	−	1.14689e9i	0.575500	−	0.944680i
$395$	−6.62067e8	−	6.62067e8i	−0.540520	−	0.540520i
$396$	3.43973e8	−	1.07783e9i	0.278350	−	0.872204i
$397$	−4.68621e8	+	4.68621e8i	−0.375885	+	0.375885i	−0.869615	−	0.493730i	$-0.835633\pi$
$397$	−4.68621e8	+	4.68621e8i	−0.375885	+	0.375885i	0.493730	+	0.869615i	$0.335633\pi$
$398$	1.15629e9	−	2.80808e8i	0.919341	−	0.223264i
$399$	1.33764e8			0.105423
$400$	1.84440e9	+	1.31071e9i	1.44094	+	1.02399i
$401$	−2.03389e9			−1.57515			−0.787576	−	0.616218i	$-0.788664\pi$
$401$	−2.03389e9			−1.57515			−0.787576	+	0.616218i	$0.788664\pi$
$402$	−4.19068e8	+	1.01772e8i	−0.321732	+	0.0781334i
$403$	−8.03062e8	+	8.03062e8i	−0.611197	+	0.611197i
$404$	−1.86356e9	−	5.94724e8i	−1.40607	−	0.448726i
$405$	8.82076e7	+	8.82076e7i	0.0659802	+	0.0659802i
$406$	−5.96395e8	+	9.78979e8i	−0.442275	+	0.725992i
$407$			1.62033e9i			1.19130i
$408$	3.20019e8	+	2.26555e7i	0.233273	+	0.0165144i
$409$		−	1.81320e9i		−	1.31043i	−0.755441	−	0.655216i	$-0.772577\pi$
$409$		−	1.81320e9i		−	1.31043i	0.755441	−	0.655216i	$-0.227423\pi$
$410$	−3.62962e8	−	2.21117e8i	−0.260086	−	0.158445i
$411$	9.59188e8	+	9.59188e8i	0.681487	+	0.681487i
$412$	6.17221e8	+	1.19583e9i	0.434811	+	0.842418i
$413$	−6.65398e7	+	6.65398e7i	−0.0464789	+	0.0464789i
$414$	−6.42256e7	−	2.64463e8i	−0.0444843	−	0.183174i
$415$	3.73194e9			2.56310
$416$	1.80937e9	−	7.77401e8i	1.23226	−	0.529442i
$417$	−1.37499e9			−0.928588
$418$	−9.32869e7	−	3.84129e8i	−0.0624746	−	0.257253i
$419$	1.81244e9	−	1.81244e9i	1.20369	−	1.20369i	0.230656	−	0.973035i	$-0.425913\pi$
$419$	1.81244e9	−	1.81244e9i	1.20369	−	1.20369i	0.973035	−	0.230656i	$-0.0740871\pi$
$420$	−7.12725e8	−	1.38086e9i	−0.469407	−	0.909445i
$421$	−1.30545e9	−	1.30545e9i	−0.852656	−	0.852656i	0.137804	−	0.990460i	$-0.455996\pi$
$421$	−1.30545e9	−	1.30545e9i	−0.852656	−	0.852656i	−0.990460	+	0.137804i	$0.955996\pi$
$422$	2.48858e8	+	1.51604e8i	0.161197	+	0.0982015i
$423$		−	1.61637e8i		−	0.103837i
$424$	−7.71674e7	+	1.09002e9i	−0.0491647	+	0.694473i
$425$		−	1.02506e9i		−	0.647722i
$426$	−4.44599e8	+	7.29806e8i	−0.278634	+	0.457376i
$427$	−2.15765e9	−	2.15765e9i	−1.34117	−	1.34117i
$428$	2.52425e9	+	8.05574e8i	1.55625	+	0.496652i
$429$	1.52904e9	−	1.52904e9i	0.935017	−	0.935017i
$430$	−3.40723e9	+	8.27455e8i	−2.06662	+	0.501885i
$431$	−1.91525e9			−1.15227			−0.576136	−	0.817354i	$-0.695440\pi$
$431$	−1.91525e9			−1.15227			−0.576136	+	0.817354i	$0.695440\pi$
$432$	−1.67945e9	+	2.84080e8i	−1.00225	+	0.169531i
$433$	−3.14194e8			−0.185990			−0.0929952	−	0.995667i	$-0.529644\pi$
$433$	−3.14194e8			−0.185990			−0.0929952	+	0.995667i	$0.529644\pi$
$434$	−1.02803e9	+	2.49659e8i	−0.603658	+	0.146600i
$435$	−1.13679e9	+	1.13679e9i	−0.662170	+	0.662170i
$436$	3.60339e8	−	1.12912e9i	0.208213	−	0.652433i
$437$	−6.72362e7	−	6.72362e7i	−0.0385405	−	0.0385405i
$438$	−8.41493e7	+	1.38131e8i	−0.0478510	+	0.0785471i
$439$			5.20606e8i			0.293686i	0.989160	+	0.146843i	$0.0469112\pi$
$439$			5.20606e8i			0.293686i	−0.989160	+	0.146843i	$0.953089\pi$
$440$	−3.46834e9	+	3.00973e9i	−1.94105	+	1.68439i
$441$			7.57108e7i			0.0420361i
$442$	−7.61903e8	−	4.64152e8i	−0.419683	−	0.255672i
$443$	−1.62324e9	−	1.62324e9i	−0.887096	−	0.887096i	0.107147	−	0.994243i	$-0.465828\pi$
$443$	−1.62324e9	−	1.62324e9i	−0.887096	−	0.887096i	−0.994243	+	0.107147i	$0.965828\pi$
$444$	8.06644e8	−	4.16347e8i	0.437363	−	0.225743i
$445$	2.64447e9	−	2.64447e9i	1.42259	−	1.42259i
$446$	1.80166e8	+	7.41873e8i	0.0961614	+	0.395966i
$447$	2.26355e8			0.119871
$448$	1.81612e9	+	2.58437e8i	0.954271	+	0.135794i
$449$	4.54823e7			0.0237127			0.0118563	−	0.999930i	$-0.496226\pi$
$449$	4.54823e7			0.0237127			0.0118563	+	0.999930i	$0.496226\pi$
$450$	4.77932e8	+	1.96799e9i	0.247242	+	1.01807i
$451$	3.89554e8	−	3.89554e8i	0.199963	−	0.199963i
$452$	4.48600e8	−	2.31543e8i	0.228494	−	0.117936i
$453$	9.45000e8	+	9.45000e8i	0.477626	+	0.477626i
$454$	−1.87236e9	−	1.14064e9i	−0.939060	−	0.572076i
$455$			4.32129e9i			2.15067i
$456$	−1.67260e8	+	1.45144e8i	−0.0826068	+	0.0716839i
$457$			3.25037e9i			1.59304i	0.604615	+	0.796518i	$0.293327\pi$
$457$			3.25037e9i			1.59304i	−0.604615	+	0.796518i	$0.706673\pi$
$458$	1.31292e9	−	2.15515e9i	0.638572	−	1.04821i
$459$	5.45637e8	+	5.45637e8i	0.263366	+	0.263366i
$460$	−3.35835e8	+	1.05233e9i	−0.160869	+	0.504081i
$461$	1.19125e9	−	1.19125e9i	0.566302	−	0.566302i	−0.364788	−	0.931091i	$-0.618859\pi$
$461$	1.19125e9	−	1.19125e9i	0.566302	−	0.566302i	0.931091	+	0.364788i	$0.118859\pi$
$462$	1.95738e9	−	4.75356e8i	0.923483	−	0.224270i
$463$	8.96248e8			0.419657			0.209829	−	0.977738i	$-0.432709\pi$
$463$	8.96248e8			0.419657			0.209829	+	0.977738i	$0.432709\pi$
$464$	−3.16524e8	−	1.87126e9i	−0.147093	−	0.869601i
$465$	−1.48366e9			−0.684302
$466$	1.44658e9	−	3.51305e8i	0.662203	−	0.160818i
$467$	−1.23605e8	+	1.23605e8i	−0.0561598	+	0.0561598i	−0.734629	−	0.678469i	$-0.762644\pi$
$467$	−1.23605e8	+	1.23605e8i	−0.0561598	+	0.0561598i	0.678469	+	0.734629i	$0.262644\pi$
$468$	1.67917e9	+	5.35880e8i	0.757241	+	0.241661i
$469$	7.89905e8	+	7.89905e8i	0.353565	+	0.353565i
$470$	−3.41326e8	+	5.60284e8i	−0.151644	+	0.248923i
$471$			9.72159e7i			0.0428710i
$472$	1.10016e7	−	1.55402e8i	0.00481569	−	0.0680238i
$473$		−	4.54494e9i		−	1.97476i
$474$	−5.80668e8	−	3.53744e8i	−0.250440	−	0.152568i
$475$	5.00335e8	+	5.00335e8i	0.214207	+	0.214207i
$476$	−3.81161e8	−	7.38475e8i	−0.161989	−	0.313842i
$477$	−6.91589e8	+	6.91589e8i	−0.291765	+	0.291765i
$478$	−2.24887e8	−	9.26020e8i	−0.0941816	−	0.387813i
$479$	9.97188e8			0.414575			0.207287	−	0.978280i	$-0.433536\pi$
$479$	9.97188e8			0.414575			0.207287	+	0.978280i	$0.433536\pi$
$480$	2.38953e9	+	9.53281e8i	0.986207	+	0.393438i
$481$	−2.52433e9			−1.03428
$482$	6.47699e8	+	2.66704e9i	0.263456	+	1.08484i
$483$	3.42611e8	−	3.42611e8i	0.138352	−	0.138352i
$484$	−1.58610e9	−	3.07296e9i	−0.635875	−	1.23197i
$485$	3.50836e8	+	3.50836e8i	0.139640	+	0.139640i
$486$	−2.11943e9	−	1.29116e9i	−0.837514	−	0.510214i
$487$			3.71858e9i			1.45890i	0.684033	+	0.729451i	$0.260224\pi$
$487$			3.71858e9i			1.45890i	−0.684033	+	0.729451i	$0.739776\pi$
$488$	5.03916e9	+	3.56743e8i	1.96286	+	0.138959i
$489$		−	1.26560e9i		−	0.489460i
$490$	1.59877e8	−	2.62436e8i	0.0613901	−	0.100772i
$491$	1.54159e9	+	1.54159e9i	0.587736	+	0.587736i	0.937018	−	0.349282i	$-0.113574\pi$
$491$	1.54159e9	+	1.54159e9i	0.587736	+	0.587736i	−0.349282	+	0.937018i	$0.613574\pi$
$492$	−2.94028e8	−	9.38343e7i	−0.111304	−	0.0355209i
$493$	−6.07951e8	+	6.07951e8i	−0.228510	+	0.228510i
$494$	5.98441e8	−	1.45333e8i	0.223345	−	0.0542401i
$495$	−4.11016e9			−1.52314
$496$	1.01456e9	−	1.42766e9i	0.373328	−	0.525338i
$497$	2.21364e9			0.808836
$498$	2.63354e9	−	6.39563e8i	0.955516	−	0.232050i
$499$	−2.42561e9	+	2.42561e9i	−0.873914	+	0.873914i	−0.992896	−	0.118983i	$-0.962037\pi$
$499$	−2.42561e9	+	2.42561e9i	−0.873914	+	0.873914i	0.118983	+	0.992896i	$0.462037\pi$
$500$	1.08536e9	−	3.40097e9i	0.388312	−	1.21677i
$501$	−8.31120e8	−	8.31120e8i	−0.295278	−	0.295278i
$502$	−2.40836e9	+	3.95331e9i	−0.849687	+	1.39476i
$503$		−	4.69480e9i		−	1.64486i	−0.568866	−	0.822430i	$-0.692618\pi$
$503$		−	4.69480e9i		−	1.64486i	0.568866	−	0.822430i	$-0.307382\pi$
$504$	1.07610e9	+	1.24007e9i	0.374407	+	0.431458i
$505$			7.10641e9i			2.45545i
$506$	−1.22281e9	−	7.44936e8i	−0.419596	−	0.255618i
$507$	1.05781e9	+	1.05781e9i	0.360479	+	0.360479i
$508$	−4.51320e9	+	2.32947e9i	−1.52743	+	0.788378i
$509$	−1.37717e9	+	1.37717e9i	−0.462887	+	0.462887i	−0.899601	−	0.436713i	$-0.856142\pi$
$509$	−1.37717e9	+	1.37717e9i	−0.462887	+	0.462887i	0.436713	+	0.899601i	$0.356142\pi$
$510$	−2.75047e8	−	1.13257e9i	−0.0918146	−	0.378067i
$511$	4.18977e8			0.138905
$512$	−2.55132e9	+	1.64747e9i	−0.840078	+	0.542466i
$513$	−5.32654e8			−0.174194
$514$	−4.72119e8	−	1.94405e9i	−0.153349	−	0.631447i
$515$	3.45689e9	−	3.45689e9i	1.11522	−	1.11522i
$516$	−2.26260e9	+	1.16783e9i	−0.724993	+	0.374202i
$517$	−6.01333e8	−	6.01333e8i	−0.191381	−	0.191381i
$518$	−2.00813e9	−	1.22335e9i	−0.634801	−	0.386721i
$519$			1.45081e9i			0.455538i
$520$	−4.68891e9	−	5.40338e9i	−1.46238	−	1.68521i
$521$		−	4.46346e7i		−	0.0138274i	−0.999976	−	0.00691368i	$-0.997799\pi$
$521$		−	4.46346e7i		−	0.0138274i	0.999976	−	0.00691368i	$-0.00220071\pi$
$522$	8.83736e8	−	1.45065e9i	0.271942	−	0.446391i
$523$	−2.04652e9	−	2.04652e9i	−0.625547	−	0.625547i	0.321397	−	0.946945i	$-0.395848\pi$
$523$	−2.04652e9	−	2.04652e9i	−0.625547	−	0.625547i	−0.946945	+	0.321397i	$0.895848\pi$
$524$	4.94133e8	−	1.54836e9i	0.150032	−	0.470123i
$525$	−2.54953e9	+	2.54953e9i	−0.768957	+	0.768957i
$526$	3.07200e9	−	7.46045e8i	0.920390	−	0.223519i
$527$	−7.93450e8			−0.236147
$528$	−1.93174e9	+	2.71829e9i	−0.571122	+	0.803669i
$529$	3.06040e9			0.898842
$530$	3.85767e9	−	9.36845e8i	1.12554	−	0.273339i
$531$	9.85985e7	−	9.85985e7i	0.0285785	−	0.0285785i
$532$	5.46498e8	+	1.74406e8i	0.157361	+	0.0502193i
$533$	6.06893e8	+	6.06893e8i	0.173607	+	0.173607i
$534$	1.41295e9	−	2.31934e9i	0.401542	−	0.659129i
$535$		−	9.62587e9i		−	2.71770i
$536$	−1.84481e9	−	1.30602e8i	−0.517457	−	0.0366330i
$537$		−	2.66021e9i		−	0.741321i
$538$	−1.81835e9	−	1.10774e9i	−0.503430	−	0.306690i
$539$	2.81664e8	+	2.81664e8i	0.0774766	+	0.0774766i
$540$	2.83810e9	+	5.49862e9i	0.775620	+	1.50271i
$541$	2.15624e9	−	2.15624e9i	0.585474	−	0.585474i	−0.350928	−	0.936402i	$-0.614134\pi$
$541$	2.15624e9	−	2.15624e9i	0.585474	−	0.585474i	0.936402	+	0.350928i	$0.114134\pi$
$542$	1.76631e8	+	7.27317e8i	0.0476507	+	0.196212i
$543$	−1.29108e9			−0.346062
$544$	1.27791e9	+	5.09809e8i	0.340332	+	0.135772i
$545$	−4.30572e9			−1.13935
$546$	7.40564e8	+	3.04944e9i	0.194710	+	0.801762i
$547$	2.49968e9	−	2.49968e9i	0.653024	−	0.653024i	−0.300696	−	0.953720i	$-0.597219\pi$
$547$	2.49968e9	−	2.49968e9i	0.653024	−	0.653024i	0.953720	+	0.300696i	$0.0972189\pi$
$548$	2.66817e9	+	5.16941e9i	0.692599	+	1.34187i
$549$	3.19720e9	+	3.19720e9i	0.824645	+	0.824645i
$550$	9.09948e9	+	5.54341e9i	2.33210	+	1.42072i
$551$		−	5.93485e8i		−	0.151140i
$552$	−5.66468e7	+	8.00162e8i	−0.0143347	+	0.202484i
$553$			1.76128e9i			0.442884i
$554$	−2.53610e9	+	4.16299e9i	−0.633697	+	1.04021i
$555$	−2.33185e9	−	2.33185e9i	−0.578995	−	0.578995i
$556$	−5.61756e9	−	1.79275e9i	−1.38607	−	0.442342i
$557$	−1.89867e9	+	1.89867e9i	−0.465539	+	0.465539i	−0.900466	−	0.434927i	$-0.856774\pi$
$557$	−1.89867e9	+	1.89867e9i	−0.465539	+	0.465539i	0.434927	+	0.900466i	$0.356774\pi$
$558$	1.52333e9	−	3.69944e8i	0.371171	−	0.0901398i
$559$	7.08063e9			1.71447
$560$	−1.11145e9	−	6.57081e9i	−0.267445	−	1.58110i
$561$	1.51074e9			0.361261
$562$	−7.10227e9	+	1.72481e9i	−1.68780	+	0.409886i
$563$	−4.96629e9	+	4.96629e9i	−1.17288	+	1.17288i	−0.191357	+	0.981520i	$0.561289\pi$
$563$	−4.96629e9	+	4.96629e9i	−1.17288	+	1.17288i	−0.981520	+	0.191357i	$0.938711\pi$
$564$	−1.44847e8	+	4.53875e8i	−0.0339963	+	0.106527i
$565$	−1.29681e9	−	1.29681e9i	−0.302488	−	0.302488i
$566$	1.85922e9	−	3.05190e9i	0.430996	−	0.707477i
$567$		−	2.34656e8i		−	0.0540619i
$568$	−2.76796e9	+	2.40196e9i	−0.633783	+	0.549980i
$569$			2.96284e9i			0.674242i	0.941461	+	0.337121i	$0.109453\pi$
$569$			2.96284e9i			0.674242i	−0.941461	+	0.337121i	$0.890547\pi$
$570$	6.87061e8	+	4.18558e8i	0.155394	+	0.0946660i
$571$	1.52183e9	+	1.52183e9i	0.342089	+	0.342089i	0.857152	−	0.515063i	$-0.172232\pi$
$571$	1.52183e9	+	1.52183e9i	0.342089	+	0.342089i	−0.515063	+	0.857152i	$0.672232\pi$
$572$	8.24057e9	−	4.25334e9i	1.84107	−	0.950264i
$573$	1.33399e9	−	1.33399e9i	0.296218	−	0.296218i
$574$	1.88673e8	+	7.76904e8i	0.0416408	+	0.171465i
$575$	2.56302e9			0.562231
$576$	−2.69112e9	−	3.82951e8i	−0.586752	−	0.0834958i
$577$	7.57727e9			1.64209			0.821046	−	0.570861i	$-0.193391\pi$
$577$	7.57727e9			1.64209			0.821046	+	0.570861i	$0.193391\pi$
$578$	9.48494e8	+	3.90563e9i	0.204309	+	0.841287i
$579$	9.22066e8	−	9.22066e8i	0.197418	−	0.197418i
$580$	−6.12659e9	+	3.16222e9i	−1.30383	+	0.672967i
$581$	−4.96399e9	−	4.96399e9i	−1.05006	−	1.05006i
$582$	3.07702e8	+	1.87452e8i	0.0646994	+	0.0394149i
$583$			5.14578e9i			1.07550i
$584$	−5.23893e8	+	4.54620e8i	−0.108842	+	0.0944503i
$585$		−	6.40327e9i		−	1.32238i
$586$	5.81697e7	−	9.54852e7i	0.0119414	−	0.0196017i
$587$	1.47270e9	+	1.47270e9i	0.300525	+	0.300525i	0.841219	−	0.540694i	$-0.181838\pi$
$587$	1.47270e9	+	1.47270e9i	0.300525	+	0.300525i	−0.540694	+	0.841219i	$0.681838\pi$
$588$	6.78461e7	−	2.12595e8i	0.0137627	−	0.0431252i
$589$	3.87285e8	−	3.87285e8i	0.0780958	−	0.0780958i
$590$	−5.49980e8	+	1.33564e8i	−0.110246	+	0.0267737i
$591$	−3.54288e9			−0.705993
$592$	3.83841e9	−	6.49269e8i	0.760371	−	0.128617i
$593$	4.77735e9			0.940796			0.470398	−	0.882454i	$-0.344110\pi$
$593$	4.77735e9			0.940796			0.470398	+	0.882454i	$0.344110\pi$
$594$	−7.79436e9	+	1.89288e9i	−1.52591	+	0.370571i
$595$	−2.13478e9	+	2.13478e9i	−0.415475	+	0.415475i
$596$	9.24781e8	+	2.95129e8i	0.178927	+	0.0571018i
$597$	−2.21969e9	−	2.21969e9i	−0.426955	−	0.426955i
$598$	1.16055e9	−	1.90503e9i	0.221926	−	0.364291i
$599$		−	9.22147e9i		−	1.75310i	−0.481313	−	0.876549i	$-0.659840\pi$
$599$		−	9.22147e9i		−	1.75310i	0.481313	−	0.876549i	$-0.340160\pi$
$600$	4.21535e8	−	5.95437e9i	0.0796717	−	1.12540i
$601$			4.34031e8i			0.0815568i	0.999168	+	0.0407784i	$0.0129838\pi$
$601$			4.34031e8i			0.0815568i	−0.999168	+	0.0407784i	$0.987016\pi$
$602$	5.63271e9	+	3.43145e9i	1.05228	+	0.641047i
$603$	−1.17048e9	−	1.17048e9i	−0.217397	−	0.217397i
$604$	2.62870e9	+	5.09294e9i	0.485414	+	0.940458i
$605$	−8.88333e9	+	8.88333e9i	−1.63092	+	1.63092i
$606$	1.21787e9	+	5.01483e9i	0.222303	+	0.915382i
$607$	−8.30934e8			−0.150802			−0.0754008	−	0.997153i	$-0.524024\pi$
$607$	−8.30934e8			−0.150802			−0.0754008	+	0.997153i	$0.524024\pi$
$608$	−8.72589e8	+	3.74910e8i	−0.157452	+	0.0676495i
$609$	3.02418e9			0.542560
$610$	−4.33102e9	−	1.78339e10i	−0.772565	−	3.18121i
$611$	9.36827e8	−	9.36827e8i	0.166156	−	0.166156i
$612$	5.64803e8	+	1.09427e9i	0.0996018	+	0.192972i
$613$	1.25167e9	+	1.25167e9i	0.219472	+	0.219472i	0.808276	−	0.588804i	$-0.200401\pi$
$613$	1.25167e9	+	1.25167e9i	0.219472	+	0.219472i	−0.588804	+	0.808276i	$0.700401\pi$
$614$	−2.40825e9	−	1.46711e9i	−0.419867	−	0.255784i
$615$			1.12123e9i			0.194372i
$616$	8.61673e9	+	6.10014e8i	1.48529	+	0.105150i
$617$		−	2.31008e9i		−	0.395940i	−0.980208	−	0.197970i	$-0.936565\pi$
$617$		−	2.31008e9i		−	0.395940i	0.980208	−	0.197970i	$-0.0634348\pi$
$618$	1.84702e9	−	3.03188e9i	0.314784	−	0.516717i
$619$	7.17315e8	+	7.17315e8i	0.121561	+	0.121561i	0.765270	−	0.643709i	$-0.222605\pi$
$619$	7.17315e8	+	7.17315e8i	0.121561	+	0.121561i	−0.643709	+	0.765270i	$0.722605\pi$
$620$	−6.06152e9	−	1.93443e9i	−1.02143	−	0.325974i
$621$	−1.36429e9	+	1.36429e9i	−0.228605	+	0.228605i
$622$	−4.22634e9	+	1.02638e9i	−0.704203	+	0.171018i
$623$	−7.03501e9			−1.16562
$624$	−4.23487e9	−	3.00948e9i	−0.697740	−	0.495845i
$625$	−2.17976e9			−0.357132
$626$	4.76257e8	−	1.15660e8i	0.0775946	−	0.0188441i
$627$	−7.37399e8	+	7.37399e8i	−0.119472	+	0.119472i
$628$	−1.26753e8	+	3.97178e8i	−0.0204220	+	0.0639921i
$629$	−1.24706e9	−	1.24706e9i	−0.199807	−	0.199807i
$630$	3.10319e9	−	5.09387e9i	0.494443	−	0.811625i
$631$			3.33466e9i			0.528382i	0.964470	+	0.264191i	$0.0851050\pi$
$631$			3.33466e9i			0.528382i	−0.964470	+	0.264191i	$0.914895\pi$
$632$	−1.91111e9	−	2.20232e9i	−0.301146	−	0.347033i
$633$		−	7.68752e8i		−	0.120468i
$634$	−4.88461e8	−	2.97571e8i	−0.0761232	−	0.0463744i
$635$	1.30468e10	+	1.30468e10i	2.02206	+	2.02206i
$636$	2.56172e9	−	1.32222e9i	0.394849	−	0.203800i
$637$	−4.38809e8	+	4.38809e8i	−0.0672647	+	0.0672647i
$638$	−2.10906e9	−	8.68452e9i	−0.321526	−	1.32396i
$639$	−3.28017e9			−0.497328
$640$	8.51957e9	+	7.01020e9i	1.28466	+	1.05706i
$641$	−6.68726e9			−1.00287			−0.501435	−	0.865195i	$-0.667194\pi$
$641$	−6.68726e9			−1.00287			−0.501435	+	0.865195i	$0.667194\pi$
$642$	−1.64964e9	−	6.79276e9i	−0.246046	−	1.01315i
$643$	−8.09348e9	+	8.09348e9i	−1.20060	+	1.20060i	−0.226610	+	0.973986i	$0.572764\pi$
$643$	−8.09348e9	+	8.09348e9i	−1.20060	+	1.20060i	−0.973986	+	0.226610i	$0.927236\pi$
$644$	1.84645e9	−	9.53040e8i	0.272419	−	0.140608i
$645$	6.54073e9	+	6.54073e9i	0.959769	+	0.959769i
$646$	3.67436e8	+	2.23842e8i	0.0536251	+	0.0326685i
$647$		−	1.19294e9i		−	0.173162i	−0.996245	−	0.0865812i	$-0.972406\pi$
$647$		−	1.19294e9i		−	0.173162i	0.996245	−	0.0865812i	$-0.0275942\pi$
$648$	2.54619e8	+	2.93417e8i	0.0367602	+	0.0423616i
$649$		−	7.33624e8i		−	0.105346i
$650$	−8.63617e9	+	1.41762e10i	−1.23346	+	2.02471i
$651$	1.97346e9	+	1.97346e9i	0.280347	+	0.280347i
$652$	1.65013e9	−	5.17066e9i	0.233159	−	0.730600i
$653$	6.88630e9	−	6.88630e9i	0.967809	−	0.967809i	−0.0316889	−	0.999498i	$-0.510089\pi$
$653$	6.88630e9	−	6.88630e9i	0.967809	−	0.967809i	0.999498	+	0.0316889i	$0.0100886\pi$
$654$	−3.03845e9	+	7.37896e8i	−0.424747	+	0.103151i
$655$	−5.90443e9			−0.820982
$656$	−1.07892e9	−	7.66725e8i	−0.149219	−	0.106042i
$657$	−6.20838e8			−0.0854082
$658$	1.19926e9	−	2.91245e8i	0.164106	−	0.0398536i
$659$	−2.94934e9	+	2.94934e9i	−0.401445	+	0.401445i	−0.878742	−	0.477297i	$-0.841617\pi$
$659$	−2.94934e9	+	2.94934e9i	−0.401445	+	0.401445i	0.477297	+	0.878742i	$0.341617\pi$
$660$	1.15412e10	+	3.68320e9i	1.56260	+	0.498679i
$661$	−6.26888e9	−	6.26888e9i	−0.844277	−	0.844277i	0.145135	−	0.989412i	$-0.453638\pi$
$661$	−6.26888e9	−	6.26888e9i	−0.844277	−	0.844277i	−0.989412	+	0.145135i	$0.953638\pi$
$662$	−5.19202e9	+	8.52267e9i	−0.695558	+	1.14175i
$663$			2.35361e9i			0.313644i
$664$	1.15933e10	+	8.20738e8i	1.53680	+	0.108797i
$665$		−	2.08399e9i		−	0.274802i
$666$	2.97564e9	+	1.81276e9i	0.390320	+	0.237783i
$667$	−1.52010e9	−	1.52010e9i	−0.198349	−	0.198349i
$668$	−2.31193e9	−	4.47920e9i	−0.300093	−	0.581411i
$669$	1.42415e9	−	1.42415e9i	0.183892	−	0.183892i
$670$	1.58556e9	+	6.52890e9i	0.203667	+	0.838645i
$671$	2.37888e10			3.03980
$672$	−1.91041e9	−	4.44640e9i	−0.242847	−	0.565217i
$673$	5.36484e9			0.678428			0.339214	−	0.940709i	$-0.389839\pi$
$673$	5.36484e9			0.678428			0.339214	+	0.940709i	$0.389839\pi$
$674$	2.66413e9	+	1.09702e10i	0.335155	+	1.38008i
$675$	1.01523e10	−	1.01523e10i	1.27058	−	1.27058i
$676$	2.94251e9	+	5.70092e9i	0.366357	+	0.709793i
$677$	−5.35602e9	−	5.35602e9i	−0.663410	−	0.663410i	0.292772	−	0.956182i	$-0.405422\pi$
$677$	−5.35602e9	−	5.35602e9i	−0.663410	−	0.663410i	−0.956182	+	0.292772i	$0.905422\pi$
$678$	−1.13737e9	−	6.92890e8i	−0.140152	−	0.0853808i
$679$		−	9.33320e8i		−	0.114416i
$680$	3.52962e8	−	4.98575e9i	0.0430474	−	0.608064i
$681$			5.78394e9i			0.701793i
$682$	4.29089e9	−	7.04347e9i	0.517967	−	0.850239i
$683$	−6.43495e9	−	6.43495e9i	−0.772810	−	0.772810i	0.205787	−	0.978597i	$-0.434025\pi$
$683$	−6.43495e9	−	6.43495e9i	−0.772810	−	0.772810i	−0.978597	+	0.205787i	$0.934025\pi$
$684$	−8.09798e8	−	2.58434e8i	−0.0967566	−	0.0308783i
$685$	1.49437e10	−	1.49437e10i	1.77641	−	1.77641i
$686$	−8.48156e9	+	2.05977e9i	−1.00309	+	0.243604i
$687$	−6.65753e9			−0.783366
$688$	−1.07666e10	+	1.82117e9i	−1.26043	+	0.213202i
$689$	−8.01669e9			−0.933744
$690$	2.83183e9	−	6.87717e8i	0.328167	−	0.0796962i
$691$	−3.16619e9	+	3.16619e9i	−0.365060	+	0.365060i	−0.865672	−	0.500612i	$-0.833108\pi$
$691$	−3.16619e9	+	3.16619e9i	−0.365060	+	0.365060i	0.500612	+	0.865672i	$0.333108\pi$
$692$	−1.89161e9	+	5.92732e9i	−0.217000	+	0.679966i
$693$	5.46707e9	+	5.46707e9i	0.624005	+	0.624005i
$694$	6.31704e9	−	1.03694e10i	0.717390	−	1.17759i
$695$			2.14217e10i			2.42052i
$696$	−3.78147e9	+	3.28146e9i	−0.425136	+	0.368922i
$697$			5.99629e8i			0.0670761i
$698$	−3.14065e9	−	1.91329e9i	−0.349563	−	0.212954i
$699$	−2.77694e9	−	2.77694e9i	−0.307536	−	0.307536i
$700$	−1.37403e10	+	7.09201e9i	−1.51410	+	0.781495i
$701$	−3.43730e9	+	3.43730e9i	−0.376881	+	0.376881i	−0.869976	−	0.493095i	$-0.835866\pi$
$701$	−3.43730e9	+	3.43730e9i	−0.376881	+	0.376881i	0.493095	+	0.869976i	$0.335866\pi$
$702$	−2.94895e9	−	1.21430e10i	−0.321727	−	1.32478i
$703$	1.21739e9			0.132155
$704$	−1.14364e10	+	8.58700e9i	−1.23533	+	0.927549i
$705$	1.73079e9			0.186029
$706$	1.11966e9	+	4.61043e9i	0.119748	+	0.493088i
$707$	9.45249e9	−	9.45249e9i	1.00595	−	1.00595i
$708$	−3.65219e8	+	1.88506e8i	−0.0386756	+	0.0199623i
$709$	−1.13849e9	−	1.13849e9i	−0.119969	−	0.119969i	0.644574	−	0.764542i	$-0.277035\pi$
$709$	−1.13849e9	−	1.13849e9i	−0.119969	−	0.119969i	−0.764542	+	0.644574i	$0.777035\pi$
$710$	1.13701e10	+	6.92665e9i	1.19223	+	0.726305i
$711$		−	2.60986e9i		−	0.272316i
$712$	8.79665e9	−	7.63349e9i	0.913350	−	0.792580i
$713$		−	1.98391e9i		−	0.204979i
$714$	−1.14062e9	+	1.87232e9i	−0.117273	+	0.192502i
$715$	−2.38219e10	−	2.38219e10i	−2.43727	−	2.43727i
$716$	3.46846e9	−	1.08684e10i	0.353135	−	1.10654i
$717$	−1.77765e9	+	1.77765e9i	−0.180106	+	0.180106i
$718$	−3.09064e9	+	7.50571e8i	−0.311611	+	0.0756757i
$719$	−9.17848e9			−0.920915			−0.460458	−	0.887682i	$-0.652315\pi$
$719$	−9.17848e9			−0.920915			−0.460458	+	0.887682i	$0.652315\pi$
$720$	1.64695e9	+	9.73660e9i	0.164444	+	0.972173i
$721$	−9.19628e9			−0.913774
$722$	9.53875e9	−	2.31651e9i	0.943217	−	0.229063i
$723$	5.11982e9	−	5.11982e9i	0.503815	−	0.503815i
$724$	−5.27475e9	−	1.68335e9i	−0.516555	−	0.164850i
$725$	1.13117e10	+	1.13117e10i	1.10242	+	1.10242i
$726$	−4.74638e9	+	7.79115e9i	−0.460346	+	0.755655i
$727$		−	1.58959e10i		−	1.53432i	−0.641456	−	0.767159i	$-0.721669\pi$
$727$		−	1.58959e10i		−	1.53432i	0.641456	−	0.767159i	$-0.278331\pi$
$728$	−9.50351e8	+	1.34241e10i	−0.0912902	+	1.28951i
$729$			7.13387e9i			0.681992i
$730$	2.15201e9	+	1.31101e9i	0.204746	+	0.124731i
$731$	3.49794e9	+	3.49794e9i	0.331209	+	0.331209i
$732$	−6.11260e9	−	1.18428e10i	−0.576020	−	1.11600i
$733$	1.42015e9	−	1.42015e9i	0.133190	−	0.133190i	−0.637369	−	0.770559i	$-0.719977\pi$
$733$	1.42015e9	−	1.42015e9i	0.133190	−	0.133190i	0.770559	+	0.637369i	$0.219977\pi$
$734$	2.58853e9	+	1.06588e10i	0.241611	+	0.994886i
$735$	−8.10698e8			−0.0753102
$736$	−1.27471e9	+	3.19522e9i	−0.117852	+	0.295413i
$737$	−8.70897e9			−0.801366
$738$	−2.79576e8	−	1.15121e9i	−0.0256037	−	0.105429i
$739$	−8.41877e9	+	8.41877e9i	−0.767349	+	0.767349i	−0.977639	−	0.210290i	$-0.932559\pi$
$739$	−8.41877e9	+	8.41877e9i	−0.767349	+	0.767349i	0.210290	+	0.977639i	$0.432559\pi$
$740$	−6.48650e9	−	1.25672e10i	−0.588436	−	1.14006i
$741$	−1.14880e9	−	1.14880e9i	−0.103725	−	0.103725i
$742$	−6.37736e9	−	3.88509e9i	−0.573096	−	0.349130i
$743$		−	2.24065e9i		−	0.200407i	−0.994967	−	0.100204i	$-0.968051\pi$
$743$		−	2.24065e9i		−	0.200407i	0.994967	−	0.100204i	$-0.0319495\pi$
$744$	−4.60899e9	−	3.26290e8i	−0.410299	−	0.0290468i
$745$		−	3.52652e9i		−	0.312463i
$746$	−2.06729e8	+	3.39345e8i	−0.0182312	+	0.0299265i
$747$	7.35562e9	+	7.35562e9i	0.645650	+	0.645650i
$748$	6.17219e9	+	1.96975e9i	0.539242	+	0.172090i
$749$	−1.28037e10	+	1.28037e10i	−1.11340	+	1.11340i
$750$	−9.15201e9	+	2.22259e9i	−0.792140	+	0.192373i
$751$	1.91051e10			1.64592			0.822960	−	0.568099i	$-0.192321\pi$
$751$	1.91051e10			1.64592			0.822960	+	0.568099i	$0.192321\pi$
$752$	−1.18355e9	+	1.66546e9i	−0.101490	+	0.142815i
$753$	1.22123e10			1.04235
$754$	1.35297e10	−	3.28573e9i	1.14945	−	0.279147i
$755$	1.47227e10	−	1.47227e10i	1.24501	−	1.24501i
$756$	3.53887e9	−	1.10890e10i	0.297878	−	0.933394i
$757$	2.83456e9	+	2.83456e9i	0.237492	+	0.237492i	0.815811	−	0.578319i	$-0.196291\pi$
$757$	2.83456e9	+	2.83456e9i	0.237492	+	0.237492i	−0.578319	+	0.815811i	$0.696291\pi$
$758$	7.80163e9	−	1.28063e10i	0.650643	−	1.06803i
$759$			3.77740e9i			0.313579i
$760$	2.26128e9	+	2.60584e9i	0.186856	+	0.215328i
$761$		−	9.27899e9i		−	0.763228i	−0.924322	−	0.381614i	$-0.875368\pi$
$761$		−	9.27899e9i		−	0.763228i	0.924322	−	0.381614i	$-0.124632\pi$
$762$	1.14427e10	+	6.97091e9i	0.936885	+	0.570751i
$763$	5.72720e9	+	5.72720e9i	0.466774	+	0.466774i
$764$	7.18934e9	−	3.71075e9i	0.583260	−	0.301048i
$765$	3.16332e9	−	3.16332e9i	0.255463	−	0.255463i
$766$	4.30483e9	+	1.77261e10i	0.346063	+	1.42499i
$767$	1.14292e9			0.0914605
$768$	7.21345e9	+	3.48689e9i	0.574617	+	0.277763i
$769$	−1.95077e10			−1.54691			−0.773454	−	0.633853i	$-0.781473\pi$
$769$	−1.95077e10			−1.54691			−0.773454	+	0.633853i	$0.781473\pi$
$770$	−7.40584e9	−	3.04952e10i	−0.584597	−	2.40721i
$771$	−3.73192e9	+	3.73192e9i	−0.293253	+	0.293253i
$772$	4.96934e9	−	2.56491e9i	0.388721	−	0.200637i
$773$	1.50803e10	+	1.50803e10i	1.17431	+	1.17431i	0.981171	+	0.193139i	$0.0618669\pi$
$773$	1.50803e10	+	1.50803e10i	1.17431	+	1.17431i	0.193139	+	0.981171i	$0.438133\pi$
$774$	−8.34653e9	−	5.08471e9i	−0.647012	−	0.394161i
$775$			1.47632e10i			1.13926i
$776$	1.01272e9	+	1.16703e9i	0.0777988	+	0.0896535i
$777$			6.20336e9i			0.474409i
$778$	9.52381e9	−	1.56333e10i	0.725074	−	1.19020i
$779$	−2.92681e8	−	2.92681e8i	−0.0221826	−	0.0221826i
$780$	−5.73811e9	+	1.79803e10i	−0.432950	+	1.35664i
$781$	−1.22031e10	+	1.22031e10i	−0.916624	+	0.916624i
$782$	1.51444e9	−	3.67787e8i	0.113248	−	0.0275025i
$783$	−1.20424e10			−0.896493
$784$	5.54374e8	−	7.80101e8i	0.0410863	−	0.0578155i
$785$	1.51458e9			0.111750
$786$	−4.16662e9	+	1.01188e9i	−0.306059	+	0.0743273i
$787$	4.72870e9	−	4.72870e9i	0.345804	−	0.345804i	−0.512740	−	0.858544i	$-0.671370\pi$
$787$	4.72870e9	−	4.72870e9i	0.345804	−	0.345804i	0.858544	+	0.512740i	$0.171370\pi$
$788$	−1.44745e10	−	4.61931e9i	−1.05381	−	0.336307i
$789$	−5.89721e9	−	5.89721e9i	−0.427442	−	0.427442i
$790$	−5.51117e9	+	9.04656e9i	−0.397694	+	0.652813i
$791$			3.44988e9i			0.247848i
$792$	−1.27682e10	−	9.03917e8i	−0.913257	−	0.0646533i
$793$			3.70610e10i			2.63913i
$794$	6.40329e9	+	3.90089e9i	0.453975	+	0.276562i
$795$	−7.40542e9	−	7.40542e9i	−0.522714	−	0.522714i
$796$	−6.17450e9	−	1.19627e10i	−0.433916	−	0.840685i
$797$	1.23529e10	−	1.23529e10i	0.864298	−	0.864298i	−0.127536	−	0.991834i	$-0.540707\pi$
$797$	1.23529e10	−	1.23529e10i	0.864298	−	0.864298i	0.991834	+	0.127536i	$0.0407068\pi$
$798$	−3.57145e8	−	1.47062e9i	−0.0248791	−	0.102445i
$799$	9.25614e8			0.0641972
$800$	9.48568e9	−	2.37771e10i	0.655018	−	1.64189i
$801$	1.04245e10			0.716704
$802$	5.43041e9	+	2.23609e10i	0.371725	+	1.53066i
$803$	−2.30968e9	+	2.30968e9i	−0.157416	+	0.157416i
$804$	2.23779e9	+	4.33557e9i	0.151853	+	0.294205i
$805$	−5.33773e9	−	5.33773e9i	−0.360638	−	0.360638i
$806$	1.09731e10	+	6.68484e9i	0.738172	+	0.449695i
$807$			5.61710e9i			0.376231i
$808$	−1.56286e9	+	2.20761e10i	−0.104227	+	1.47225i
$809$		−	4.52949e9i		−	0.300767i	−0.988628	−	0.150383i	$-0.951949\pi$
$809$		−	4.52949e9i		−	0.300767i	0.988628	−	0.150383i	$-0.0480508\pi$
$810$	7.34257e8	−	1.20528e9i	0.0485457	−	0.0796874i
$811$	−1.02238e10	−	1.02238e10i	−0.673037	−	0.673037i	0.285378	−	0.958415i	$-0.407881\pi$
$811$	−1.02238e10	−	1.02238e10i	−0.673037	−	0.673037i	−0.958415	+	0.285378i	$0.907881\pi$
$812$	1.23554e10	+	3.94302e9i	0.809861	+	0.258454i
$813$	1.39620e9	−	1.39620e9i	0.0911238	−	0.0911238i
$814$	1.78141e10	−	4.32621e9i	1.15765	−	0.281139i
$815$	−1.97176e10			−1.27586
$816$	−6.05359e8	−	3.57882e9i	−0.0390030	−	0.230581i
$817$	−3.41471e9			−0.219067
$818$	−1.99346e10	+	4.84118e9i	−1.27342	+	0.309253i
$819$	−8.51723e9	+	8.51723e9i	−0.541757	+	0.541757i
$820$	−1.46190e9	+	4.58083e9i	−0.0925909	+	0.290132i
$821$	2.66230e9	+	2.66230e9i	0.167902	+	0.167902i	0.786056	−	0.618155i	$-0.212119\pi$
$821$	2.66230e9	+	2.66230e9i	0.167902	+	0.167902i	−0.618155	+	0.786056i	$0.712119\pi$
$822$	7.98447e9	−	1.31065e10i	0.501412	−	0.823064i
$823$		−	1.15718e10i		−	0.723605i	−0.932255	−	0.361803i	$-0.882161\pi$
$823$		−	1.15718e10i		−	0.723605i	0.932255	−	0.361803i	$-0.117839\pi$
$824$	1.14991e10	−	9.97862e9i	0.716011	−	0.621334i
$825$		−	2.81094e10i		−	1.74286i
$826$	9.09207e8	+	5.53890e8i	0.0561349	+	0.0341974i
$827$	−4.51747e9	−	4.51747e9i	−0.277732	−	0.277732i	0.554471	−	0.832203i	$-0.312921\pi$
$827$	−4.51747e9	−	4.51747e9i	−0.277732	−	0.277732i	−0.832203	+	0.554471i	$0.812921\pi$
$828$	−2.73607e9	+	1.41221e9i	−0.167502	+	0.0864557i
$829$	7.88195e9	−	7.88195e9i	0.480499	−	0.480499i	−0.424792	−	0.905291i	$-0.639653\pi$
$829$	7.88195e9	−	7.88195e9i	0.480499	−	0.480499i	0.905291	+	0.424792i	$0.139653\pi$
$830$	−9.96412e9	−	4.10295e10i	−0.604875	−	2.49071i
$831$	1.28600e10			0.777386
$832$	−1.33778e10	−	1.78169e10i	−0.805292	−	1.07251i
$833$	−4.33557e8			−0.0259889
$834$	3.67117e9	+	1.51168e10i	0.219141	+	0.902360i
$835$	−1.29485e10	+	1.29485e10i	−0.769691	+	0.769691i
$836$	−3.97410e9	+	2.05122e9i	−0.235243	+	0.121420i
$837$	−7.85840e9	−	7.85840e9i	−0.463228	−	0.463228i
$838$	−2.47654e10	−	1.50871e10i	−1.45376	−	0.885629i
$839$			1.06263e9i			0.0621175i	0.999518	+	0.0310587i	$0.00988789\pi$
$839$			1.06263e9i			0.0621175i	−0.999518	+	0.0310587i	$0.990112\pi$
$840$	−1.32784e10	+	1.15226e10i	−0.772981	+	0.670772i
$841$			3.83218e9i			0.222157i
$842$	−1.08668e10	+	1.78378e10i	−0.627351	+	1.02979i
$843$	1.36340e10	+	1.36340e10i	0.783836	+	0.783836i
$844$	1.00232e9	−	3.14076e9i	0.0573863	−	0.179819i
$845$	1.64802e10	−	1.64802e10i	0.939648	−	0.939648i
$846$	−1.77707e9	+	4.31565e8i	−0.100904	+	0.0245048i
$847$	2.36321e10			1.33632
$848$	1.21899e10	−	2.06193e9i	0.686460	−	0.116115i
$849$	−9.42769e9			−0.528723
$850$	−1.12697e10	+	2.73687e9i	−0.629427	+	0.152858i
$851$	3.11810e9	−	3.11810e9i	0.173435	−	0.173435i
$852$	9.21065e9	+	2.93943e9i	0.510213	+	0.162826i
$853$	−1.44847e10	−	1.44847e10i	−0.799078	−	0.799078i	0.183872	−	0.982950i	$-0.441137\pi$
$853$	−1.44847e10	−	1.44847e10i	−0.799078	−	0.799078i	−0.982950	+	0.183872i	$0.941137\pi$
$854$	−1.79607e10	+	2.94824e10i	−0.986781	+	1.61980i
$855$			3.08805e9i			0.168967i
$856$	2.11695e9	−	2.99029e10i	0.115359	−	1.62950i
$857$		−	1.43909e10i		−	0.781006i	−0.920602	−	0.390503i	$-0.872301\pi$
$857$		−	1.43909e10i		−	0.781006i	0.920602	−	0.390503i	$-0.127699\pi$
$858$	−2.08930e10	−	1.27281e10i	−1.12927	−	0.687950i
$859$	1.38425e10	+	1.38425e10i	0.745142	+	0.745142i	0.973563	−	0.228421i	$-0.0733561\pi$
$859$	1.38425e10	+	1.38425e10i	0.745142	+	0.745142i	−0.228421	+	0.973563i	$0.573356\pi$
$860$	1.81943e10	+	3.52503e10i	0.975419	+	1.88981i
$861$	1.49139e9	−	1.49139e9i	0.0796308	−	0.0796308i
$862$	5.11364e9	+	2.10565e10i	0.271928	+	1.11973i
$863$	−1.18417e10			−0.627158			−0.313579	−	0.949562i	$-0.601528\pi$
$863$	−1.18417e10			−0.627158			−0.313579	+	0.949562i	$0.601528\pi$
$864$	7.60730e9	+	1.77057e10i	0.401266	+	0.933931i
$865$	2.26030e10			1.18743
$866$	8.38885e8	+	3.45430e9i	0.0438925	+	0.180737i
$867$	7.49750e9	−	7.49750e9i	0.390705	−	0.390705i
$868$	5.48958e9	+	1.06357e10i	0.284918	+	0.552010i
$869$	−9.70935e9	−	9.70935e9i	−0.501905	−	0.501905i
$870$	1.55333e10	+	9.46289e9i	0.799735	+	0.487199i
$871$		−	1.35678e10i		−	0.695740i
$872$	−1.33758e10	−	9.46927e8i	−0.683142	−	0.0483625i
$873$			1.38299e9i			0.0703509i
$874$	−5.59687e8	+	9.18722e8i	−0.0283566	+	0.0465473i
$875$	1.72507e10	+	1.72507e10i	0.870519	+	0.870519i
$876$	1.74330e9	+	5.56347e8i	0.0876210	+	0.0279628i
$877$	−1.54420e10	+	1.54420e10i	−0.773046	+	0.773046i	−0.978638	−	0.205591i	$-0.934088\pi$
$877$	−1.54420e10	+	1.54420e10i	−0.773046	+	0.773046i	0.205591	+	0.978638i	$0.434088\pi$
$878$	5.72362e9	−	1.39000e9i	0.285391	−	0.0693080i
$879$	−2.94965e8			−0.0146491
$880$	4.23498e10	+	3.00956e10i	2.09489	+	1.48872i
$881$	4.22278e9			0.208057			0.104028	−	0.994574i	$-0.466827\pi$
$881$	4.22278e9			0.208057			0.104028	+	0.994574i	$0.466827\pi$
$882$	8.32376e8	−	2.02145e8i	0.0408488	−	0.00992025i
$883$	−4.90850e9	+	4.90850e9i	−0.239931	+	0.239931i	−0.816822	−	0.576890i	$-0.804266\pi$
$883$	−4.90850e9	+	4.90850e9i	−0.239931	+	0.239931i	0.576890	+	0.816822i	$0.304266\pi$
$884$	−3.06871e9	+	9.61574e9i	−0.149408	+	0.468166i
$885$	1.05578e9	+	1.05578e9i	0.0512000	+	0.0512000i
$886$	−1.35122e10	+	2.21802e10i	−0.652691	+	1.07139i
$887$		−	4.53602e9i		−	0.218244i	−0.994028	−	0.109122i	$-0.965196\pi$
$887$		−	4.53602e9i		−	0.218244i	0.994028	−	0.109122i	$-0.0348039\pi$
$888$	−6.73109e9	−	7.75674e9i	−0.322582	−	0.371735i
$889$		−	3.47079e10i		−	1.65681i
$890$	−3.61343e10	−	2.20131e10i	−1.71813	−	1.04668i
$891$	1.29358e9	+	1.29358e9i	0.0612664	+	0.0612664i
$892$	7.67523e9	−	3.96154e9i	0.362088	−	0.186891i
$893$	−4.51795e8	+	4.51795e8i	−0.0212305	+	0.0212305i
$894$	−6.04359e8	−	2.48858e9i	−0.0282888	−	0.116485i
$895$	−4.14449e10			−1.93237
$896$	−2.00767e9	−	2.06567e10i	−0.0932428	−	0.959363i
$897$	−5.88487e9			−0.272247
$898$	−1.21436e8	−	5.00040e8i	−0.00559603	−	0.0230429i
$899$	8.75587e9	−	8.75587e9i	0.401921	−	0.401921i
$900$	2.03603e10	−	1.05089e10i	0.930971	−	0.480518i
$901$	−3.96037e9	−	3.96037e9i	−0.180384	−	0.180384i
$902$	−5.32291e9	−	3.24272e9i	−0.241505	−	0.147125i
$903$		−	1.74001e10i		−	0.786403i
$904$	−3.74336e9	−	4.31376e9i	−0.168528	−	0.194208i
$905$			2.01145e10i			0.902067i
$906$	7.86636e9	−	1.29126e10i	0.351419	−	0.576852i
$907$	2.66719e10	+	2.66719e10i	1.18694	+	1.18694i	0.977910	+	0.209028i	$0.0670301\pi$
$907$	2.66719e10	+	2.66719e10i	1.18694	+	1.18694i	0.209028	+	0.977910i	$0.432970\pi$
$908$	−7.54127e9	+	2.36305e10i	−0.334306	+	1.04754i
$909$	−1.40067e10	+	1.40067e10i	−0.618531	+	0.618531i
$910$	4.75089e10	−	1.15377e10i	2.08992	−	0.507543i
$911$	2.25426e10			0.987846			0.493923	−	0.869506i	$-0.335562\pi$
$911$	2.25426e10			0.987846			0.493923	+	0.869506i	$0.335562\pi$
$912$	2.04231e9	+	1.45136e9i	0.0891538	+	0.0633566i
$913$	5.47296e10			2.37999
$914$	3.57350e10	−	8.67834e9i	1.54804	−	0.375946i
$915$	−3.42351e10	+	3.42351e10i	−1.47740	+	1.47740i
$916$	−2.71995e10	−	8.68029e9i	−1.16930	−	0.373164i
$917$	7.85370e9	+	7.85370e9i	0.336342	+	0.336342i
$918$	4.54198e9	−	7.45564e9i	0.193774	−	0.318079i
$919$		−	7.07727e9i		−	0.300789i	−0.988626	−	0.150394i	$-0.951946\pi$
$919$		−	7.07727e9i		−	0.300789i	0.988626	−	0.150394i	$-0.0480544\pi$
$920$	1.24662e10	+	8.82533e8i	0.527808	+	0.0373657i
$921$			7.43937e9i			0.313782i
$922$	−1.62773e10	−	9.91616e9i	−0.683950	−	0.416663i
$923$	−1.90114e10	−	1.90114e10i	−0.795807	−	0.795807i
$924$	−1.04523e10	−	2.02506e10i	−0.435872	−	0.844473i
$925$	−2.32032e10	+	2.32032e10i	−0.963944	+	0.963944i
$926$	−2.39295e9	−	9.85349e9i	−0.0990363	−	0.407804i
$927$	1.36270e10			0.561852
$928$	−1.97278e10	+	8.47609e9i	−0.810326	+	0.348159i
$929$	3.28443e10			1.34402			0.672009	−	0.740543i	$-0.265432\pi$
$929$	3.28443e10			1.34402			0.672009	+	0.740543i	$0.265432\pi$
$930$	3.96130e9	+	1.63115e10i	0.161491	+	0.664974i
$931$	2.11620e8	−	2.11620e8i	0.00859475	−	0.00859475i
$932$	−7.72461e9	−	1.49659e10i	−0.312551	−	0.605547i
$933$	8.11314e9	+	8.11314e9i	0.327042	+	0.327042i
$934$	1.68895e9	+	1.02891e9i	0.0678269	+	0.0413202i
$935$		−	2.35367e10i		−	0.941685i
$936$	1.40823e9	−	1.98918e10i	0.0561316	−	0.792883i
$937$		−	4.56150e9i		−	0.181142i	−0.995890	−	0.0905710i	$-0.971131\pi$
$937$		−	4.56150e9i		−	0.181142i	0.995890	−	0.0905710i	$-0.0288692\pi$
$938$	6.57532e9	−	1.07933e10i	0.260140	−	0.427018i
$939$	−9.14253e8	−	9.14253e8i	−0.0360360	−	0.0360360i
$940$	7.07117e9	+	2.25665e9i	0.277680	+	0.0886169i
$941$	−1.44557e10	+	1.44557e10i	−0.565556	+	0.565556i	−0.930880	−	0.365325i	$-0.880958\pi$
$941$	−1.44557e10	+	1.44557e10i	−0.565556	+	0.565556i	0.365325	+	0.930880i	$0.380958\pi$
$942$	1.06881e9	−	2.59562e8i	0.0416601	−	0.0101173i
$943$	−1.49929e9			−0.0582229
$944$	−1.73789e9	+	2.93965e8i	−0.0672389	+	0.0113735i
$945$	−4.22862e10			−1.63000
$946$	−4.99677e10	+	1.21348e10i	−1.91898	+	0.466030i
$947$	−1.88943e10	+	1.88943e10i	−0.722946	+	0.722946i	−0.969204	−	0.246258i	$-0.920799\pi$
$947$	−1.88943e10	+	1.88943e10i	−0.722946	+	0.722946i	0.246258	+	0.969204i	$0.420799\pi$
$948$	−2.33875e9	+	7.32843e9i	−0.0891568	+	0.279371i
$949$	−3.59829e9	−	3.59829e9i	−0.136667	−	0.136667i
$950$	4.16489e9	−	6.83664e9i	0.157605	−	0.258708i
$951$			1.50891e9i			0.0568896i
$952$	−7.10122e9	+	6.16224e9i	−0.266749	+	0.231478i
$953$		−	1.95228e10i		−	0.730662i	−0.930878	−	0.365331i	$-0.880956\pi$
$953$		−	1.95228e10i		−	0.730662i	0.930878	−	0.365331i	$-0.119044\pi$
$954$	9.44995e9	+	5.75692e9i	0.352379	+	0.214670i
$955$	−2.07830e10	−	2.07830e10i	−0.772139	−	0.772139i
$956$	−9.58037e9	+	4.94487e9i	−0.354633	+	0.183043i
$957$	−1.66713e10	+	1.66713e10i	−0.614863	+	0.614863i
$958$	−2.66245e9	−	1.09632e10i	−0.0978369	−	0.402865i
$959$	−3.97544e10			−1.45553
$960$	4.10057e9	−	2.88161e10i	0.149587	−	1.05120i
$961$	−1.60851e10			−0.584646
$962$	6.73986e9	+	2.77529e10i	0.244083	+	1.00507i
$963$	1.89725e10	−	1.89725e10i	0.684594	−	0.684594i
$964$	2.75926e10	−	1.42418e10i	0.992024	−	0.512030i
$965$	−1.43654e10	−	1.43654e10i	−0.514602	−	0.514602i
$966$	−4.68147e9	−	2.85196e9i	−0.167095	−	0.101794i
$967$			5.14640e10i			1.83025i	0.403169	+	0.915126i	$0.367909\pi$
$967$			5.14640e10i			1.83025i	−0.403169	+	0.915126i	$0.632091\pi$
$968$	−2.95498e10	+	2.56425e10i	−1.04711	+	0.908650i
$969$		−	1.13505e9i		−	0.0400759i
$970$	2.92043e9	−	4.79386e9i	0.102741	−	0.168649i
$971$	6.37399e9	+	6.37399e9i	0.223431	+	0.223431i	0.809942	−	0.586510i	$-0.199499\pi$
$971$	6.37399e9	+	6.37399e9i	0.223431	+	0.223431i	−0.586510	+	0.809942i	$0.699499\pi$
$972$	−8.53640e9	+	2.67487e10i	−0.298156	+	0.934265i
$973$	2.84938e10	−	2.84938e10i	0.991645	−	0.991645i
$974$	4.08826e10	−	9.92846e9i	1.41769	−	0.344291i
$975$	4.37921e10			1.51314
$976$	−9.53226e9	−	5.63537e10i	−0.328187	−	1.94021i
$977$	−2.71276e9			−0.0930637			−0.0465319	−	0.998917i	$-0.514817\pi$
$977$	−2.71276e9			−0.0930637			−0.0465319	+	0.998917i	$0.514817\pi$
$978$	−1.39142e10	+	3.37911e9i	−0.475635	+	0.115509i
$979$	3.87817e10	−	3.87817e10i	1.32095	−	1.32095i
$980$	−3.31213e9	−	1.05701e9i	−0.112413	−	0.0358747i
$981$	−8.48654e9	−	8.48654e9i	−0.287005	−	0.287005i
$982$	1.28325e10	−	2.10644e10i	0.432434	−	0.709837i
$983$			1.70442e10i			0.572320i	0.958182	+	0.286160i	$0.0923789\pi$
$983$			1.70442e10i			0.572320i	−0.958182	+	0.286160i	$0.907621\pi$
$984$	−2.46585e8	+	3.48312e9i	−0.00825056	+	0.116543i
$985$			5.51965e10i			1.84028i
$986$	8.30711e9	+	5.06070e9i	0.275982	+	0.168128i
$987$	−2.30218e9	−	2.30218e9i	−0.0762131	−	0.0762131i
$988$	−3.19563e9	−	6.19132e9i	−0.105416	−	0.204237i
$989$	−8.74611e9	+	8.74611e9i	−0.287493	+	0.287493i
$990$	1.09739e10	+	4.51877e10i	0.359451	+	1.48012i
$991$	1.18441e10			0.386583			0.193291	−	0.981141i	$-0.438084\pi$
$991$	1.18441e10			0.386583			0.193291	+	0.981141i	$0.438084\pi$
$992$	−1.84047e10	−	7.34240e9i	−0.598603	−	0.238807i
$993$	2.63276e10			0.853274
$994$	−5.91034e9	−	2.43371e10i	−0.190880	−	0.785990i
$995$	−3.45818e10	+	3.45818e10i	−1.11293	+	1.11293i
$996$	−1.40629e10	−	2.72460e10i	−0.450991	−	0.873765i
$997$	1.85596e10	+	1.85596e10i	0.593109	+	0.593109i	0.938470	−	0.345361i	$-0.112244\pi$
$997$	1.85596e10	+	1.85596e10i	0.593109	+	0.593109i	−0.345361	+	0.938470i	$0.612244\pi$
$998$	3.31438e10	+	2.01912e10i	1.05547	+	0.642992i
$999$		−	2.47020e10i		−	0.783885i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.8.e.a.5.6	✓	26
4.3	odd	2		64.8.e.a.49.9		26
8.3	odd	2		128.8.e.a.97.5		26
8.5	even	2		128.8.e.b.97.9		26
16.3	odd	4		64.8.e.a.17.9		26
16.5	even	4		128.8.e.b.33.9		26
16.11	odd	4		128.8.e.a.33.5		26
16.13	even	4	inner	16.8.e.a.13.6	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.8.e.a.5.6	✓	26	1.1	even	1	trivial
16.8.e.a.13.6	yes	26	16.13	even	4	inner
64.8.e.a.17.9		26	16.3	odd	4
64.8.e.a.49.9		26	4.3	odd	2
128.8.e.a.33.5		26	16.11	odd	4
128.8.e.a.97.5		26	8.3	odd	2
128.8.e.b.33.9		26	16.5	even	4
128.8.e.b.97.9		26	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	16.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.66996 - 10.9941i) q^{2} +(-21.1050 + 21.1050i) q^{3} +(-113.743 + 58.7079i) q^{4} +(328.807 + 328.807i) q^{5} +(288.382 + 175.682i) q^{6} -874.718i q^{7} +(949.131 + 1093.76i) q^{8} +1296.15i q^{9} +O(q^{10})\)	\(q+(-2.66996 - 10.9941i) q^{2} +(-21.1050 + 21.1050i) q^{3} +(-113.743 + 58.7079i) q^{4} +(328.807 + 328.807i) q^{5} +(288.382 + 175.682i) q^{6} -874.718i q^{7} +(949.131 + 1093.76i) q^{8} +1296.15i q^{9} +(2737.06 - 4492.86i) q^{10} +(4822.03 + 4822.03i) q^{11} +(1161.51 - 3639.58i) q^{12} +(-7512.32 + 7512.32i) q^{13} +(-9616.78 + 2335.46i) q^{14} -13879.0 q^{15} +(9490.77 - 13355.2i) q^{16} -7422.40 q^{17} +(14250.1 - 3460.68i) q^{18} +(3622.90 - 3622.90i) q^{19} +(-56703.0 - 18095.8i) q^{20} +(18461.0 + 18461.0i) q^{21} +(40139.5 - 65888.8i) q^{22} -18558.7i q^{23} +(-43115.2 - 3052.31i) q^{24} +138104. i q^{25} +(102649. + 62533.9i) q^{26} +(-73512.1 - 73512.1i) q^{27} +(51352.8 + 99492.7i) q^{28} +(81907.6 - 81907.6i) q^{29} +(37056.4 + 152588. i) q^{30} +106899. q^{31} +(-172169. - 68685.2i) q^{32} -203538. q^{33} +(19817.5 + 81603.0i) q^{34} +(287614. - 287614. i) q^{35} +(-76094.4 - 147428. i) q^{36} +(168013. + 168013. i) q^{37} +(-49503.7 - 30157.7i) q^{38} -317096. i q^{39} +(-47553.6 + 671716. i) q^{40} -80786.4i q^{41} +(153673. - 252253. i) q^{42} +(-471268. - 471268. i) q^{43} +(-831562. - 265379. i) q^{44} +(-426185. + 426185. i) q^{45} +(-204037. + 49550.9i) q^{46} -124705. q^{47} +(81558.4 + 482165. i) q^{48} +58411.9 q^{49} +(1.51833e6 - 368731. i) q^{50} +(156650. - 156650. i) q^{51} +(413439. - 1.29550e6i) q^{52} +(533570. + 533570. i) q^{53} +(-611929. + 1.00448e6i) q^{54} +3.17104e6i q^{55} +(956728. - 830222. i) q^{56} +152923. i q^{57} +(-1.11919e6 - 681814. i) q^{58} +(-76070.0 - 76070.0i) q^{59} +(1.57863e6 - 814806. i) q^{60} +(2.46668e6 - 2.46668e6i) q^{61} +(-285417. - 1.17527e6i) q^{62} +1.13377e6 q^{63} +(-295452. + 2.07624e6i) q^{64} -4.94021e6 q^{65} +(543439. + 2.23773e6i) q^{66} +(-903040. + 903040. i) q^{67} +(844244. - 435753. i) q^{68} +(391682. + 391682. i) q^{69} +(-3.92998e6 - 2.39415e6i) q^{70} +2.53069e6i q^{71} +(-1.41768e6 + 1.23022e6i) q^{72} +478985. i q^{73} +(1.39857e6 - 2.29575e6i) q^{74} +(-2.91468e6 - 2.91468e6i) q^{75} +(-199385. + 624770. i) q^{76} +(4.21792e6 - 4.21792e6i) q^{77} +(-3.48620e6 + 846632. i) q^{78} -2.01354e6 q^{79} +(7.51192e6 - 1.27064e6i) q^{80} +268265. q^{81} +(-888177. + 215696. i) q^{82} +(5.67496e6 - 5.67496e6i) q^{83} +(-3.18360e6 - 1.01599e6i) q^{84} +(-2.44054e6 - 2.44054e6i) q^{85} +(-3.92292e6 + 6.43946e6i) q^{86} +3.45733e6i q^{87} +(-697384. + 9.85087e6i) q^{88} -8.04261e6i q^{89} +(5.82344e6 + 3.54765e6i) q^{90} +(6.57116e6 + 6.57116e6i) q^{91} +(1.08954e6 + 2.11091e6i) q^{92} +(-2.25612e6 + 2.25612e6i) q^{93} +(332958. + 1.37103e6i) q^{94} +2.38247e6 q^{95} +(5.08323e6 - 2.18403e6i) q^{96} +1.06700e6 q^{97} +(-155957. - 642189. i) q^{98} +(-6.25009e6 + 6.25009e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 2 q^{2} - 2 q^{3} - 184 q^{4} - 2 q^{5} - 176 q^{6} - 1004 q^{8}+O(q^{10}) \) 26 * q - 2 * q^2 - 2 * q^3 - 184 * q^4 - 2 * q^5 - 176 * q^6 - 1004 * q^8	\( 26 q - 2 q^{2} - 2 q^{3} - 184 q^{4} - 2 q^{5} - 176 q^{6} - 1004 q^{8} + 12972 q^{10} + 1202 q^{11} - 27356 q^{12} - 2 q^{13} + 22268 q^{14} - 27004 q^{15} + 13336 q^{16} - 4 q^{17} - 29346 q^{18} + 60582 q^{19} + 46204 q^{20} + 4372 q^{21} - 44348 q^{22} - 59216 q^{24} - 35960 q^{26} - 233672 q^{27} + 220312 q^{28} - 51690 q^{29} + 27636 q^{30} + 357488 q^{31} - 248632 q^{32} - 4 q^{33} + 924660 q^{34} - 252004 q^{35} - 1015508 q^{36} + 415574 q^{37} - 5472 q^{38} - 1121976 q^{40} + 124600 q^{42} + 569754 q^{43} - 758620 q^{44} + 151874 q^{45} + 2335660 q^{46} - 2076464 q^{47} + 4141288 q^{48} - 1647090 q^{49} - 787194 q^{50} + 2609508 q^{51} + 410324 q^{52} + 907814 q^{53} - 7404512 q^{54} - 4093160 q^{56} - 1860712 q^{58} - 4865142 q^{59} + 5147328 q^{60} + 2279886 q^{61} + 6274096 q^{62} + 8295108 q^{63} + 10452224 q^{64} - 1426892 q^{65} + 10937812 q^{66} - 5564458 q^{67} - 7403760 q^{68} - 4786076 q^{69} - 22140800 q^{70} - 25293948 q^{72} - 13177044 q^{74} + 6212566 q^{75} + 17814260 q^{76} + 7604308 q^{77} + 37993916 q^{78} - 9598912 q^{79} + 40047272 q^{80} - 5314414 q^{81} + 22858240 q^{82} + 4531198 q^{83} - 30159704 q^{84} + 7377748 q^{85} - 54129468 q^{86} - 59216392 q^{88} - 33515304 q^{90} + 2587652 q^{91} + 21810936 q^{92} - 14504144 q^{93} + 77196112 q^{94} - 4900620 q^{95} + 116940464 q^{96} - 4 q^{97} + 21823866 q^{98} + 18815006 q^{99}+O(q^{100}) \) 26 * q - 2 * q^2 - 2 * q^3 - 184 * q^4 - 2 * q^5 - 176 * q^6 - 1004 * q^8 + 12972 * q^10 + 1202 * q^11 - 27356 * q^12 - 2 * q^13 + 22268 * q^14 - 27004 * q^15 + 13336 * q^16 - 4 * q^17 - 29346 * q^18 + 60582 * q^19 + 46204 * q^20 + 4372 * q^21 - 44348 * q^22 - 59216 * q^24 - 35960 * q^26 - 233672 * q^27 + 220312 * q^28 - 51690 * q^29 + 27636 * q^30 + 357488 * q^31 - 248632 * q^32 - 4 * q^33 + 924660 * q^34 - 252004 * q^35 - 1015508 * q^36 + 415574 * q^37 - 5472 * q^38 - 1121976 * q^40 + 124600 * q^42 + 569754 * q^43 - 758620 * q^44 + 151874 * q^45 + 2335660 * q^46 - 2076464 * q^47 + 4141288 * q^48 - 1647090 * q^49 - 787194 * q^50 + 2609508 * q^51 + 410324 * q^52 + 907814 * q^53 - 7404512 * q^54 - 4093160 * q^56 - 1860712 * q^58 - 4865142 * q^59 + 5147328 * q^60 + 2279886 * q^61 + 6274096 * q^62 + 8295108 * q^63 + 10452224 * q^64 - 1426892 * q^65 + 10937812 * q^66 - 5564458 * q^67 - 7403760 * q^68 - 4786076 * q^69 - 22140800 * q^70 - 25293948 * q^72 - 13177044 * q^74 + 6212566 * q^75 + 17814260 * q^76 + 7604308 * q^77 + 37993916 * q^78 - 9598912 * q^79 + 40047272 * q^80 - 5314414 * q^81 + 22858240 * q^82 + 4531198 * q^83 - 30159704 * q^84 + 7377748 * q^85 - 54129468 * q^86 - 59216392 * q^88 - 33515304 * q^90 + 2587652 * q^91 + 21810936 * q^92 - 14504144 * q^93 + 77196112 * q^94 - 4900620 * q^95 + 116940464 * q^96 - 4 * q^97 + 21823866 * q^98 + 18815006 * q^99

Introduction

L-functions

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