LMFDB - Embedded newform 197.2.g.a.16.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,2,Mod(16,197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(197, base_ring=CyclotomicField(98))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("197.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	197.g (of order $49$, degree $42$, 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:	$1.57305291982$
Analytic rank:	$0$
Dimension:	$630$
Relative dimension:	$15$ over $\Q(\zeta_{49})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{49}]$

Embedding invariants

Embedding label			16.1
Character	$\chi$	$=$	197.16
Dual form			197.2.g.a.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.48397 - 0.159476i) q^{2} +(-1.29377 + 1.85472i) q^{3} +(4.16109 + 0.536513i) q^{4} +(-0.977512 + 0.636290i) q^{5} +(3.50947 - 4.40074i) q^{6} +(5.00407 - 0.321272i) q^{7} +(-5.36410 - 1.04466i) q^{8} +(-0.730042 - 1.98376i) q^{9} +(2.52958 - 1.42464i) q^{10} +(-0.0220780 + 0.0743880i) q^{11} +(-6.37859 + 7.02353i) q^{12} +(-0.0995861 + 3.10546i) q^{13} -12.4812 q^{14} +(0.0845386 - 2.63622i) q^{15} +(5.04102 + 1.32191i) q^{16} +(1.85730 + 1.79869i) q^{17} +(1.49704 + 5.04403i) q^{18} +(-3.68983 - 1.77693i) q^{19} +(-4.40890 + 2.12321i) q^{20} +(-5.87826 + 9.69680i) q^{21} +(0.0667041 - 0.181257i) q^{22} +(1.29633 + 8.01827i) q^{23} +(8.87747 - 8.59735i) q^{24} +(-1.47325 + 3.32810i) q^{25} +(0.742616 - 7.69799i) q^{26} +(-1.93843 - 0.508316i) q^{27} +(20.9948 + 1.34791i) q^{28} +(6.35929 - 7.00229i) q^{29} +(-0.630406 + 6.53482i) q^{30} +(-5.96511 + 2.41501i) q^{31} +(-1.93798 - 0.643453i) q^{32} +(-0.109405 - 0.137190i) q^{33} +(-4.32662 - 4.76409i) q^{34} +(-4.68712 + 3.49809i) q^{35} +(-1.97346 - 8.64629i) q^{36} +(-6.07522 + 1.59311i) q^{37} +(8.88206 + 5.00228i) q^{38} +(-5.63092 - 4.20246i) q^{39} +(5.90818 - 2.39196i) q^{40} +(-1.69143 - 1.63806i) q^{41} +(16.1478 - 23.1491i) q^{42} +(1.12698 - 3.79717i) q^{43} +(-0.131779 + 0.297690i) q^{44} +(1.97587 + 1.47463i) q^{45} +(-1.94133 - 20.1239i) q^{46} +(1.19445 + 2.28954i) q^{47} +(-8.97370 + 7.63942i) q^{48} +(17.9950 - 2.32020i) q^{49} +(4.19026 - 8.03195i) q^{50} +(-5.73899 + 1.11767i) q^{51} +(-2.08051 + 12.8687i) q^{52} +(0.0834526 + 0.865073i) q^{53} +(4.73393 + 1.57177i) q^{54} +(-0.0257509 - 0.0867632i) q^{55} +(-27.1780 - 3.50421i) q^{56} +(8.06951 - 4.54466i) q^{57} +(-16.9130 + 16.3793i) q^{58} +(-6.37625 - 3.59104i) q^{59} +(1.76614 - 10.9242i) q^{60} +(4.07740 + 5.84527i) q^{61} +(15.2023 - 5.04751i) q^{62} +(-4.29051 - 9.69234i) q^{63} +(-4.94992 - 2.00400i) q^{64} +(-1.87863 - 3.09899i) q^{65} +(0.249880 + 0.358222i) q^{66} +(3.93794 + 7.54829i) q^{67} +(6.76337 + 8.48099i) q^{68} +(-16.5488 - 7.96948i) q^{69} +(12.2005 - 7.94166i) q^{70} +(3.39590 + 9.22776i) q^{71} +(1.84367 + 11.4037i) q^{72} +(4.12498 - 1.08170i) q^{73} +(15.3447 - 2.98838i) q^{74} +(-4.26664 - 7.03827i) q^{75} +(-14.4004 - 9.37362i) q^{76} +(-0.0865810 + 0.379336i) q^{77} +(13.3168 + 11.3368i) q^{78} +(6.37498 + 4.14965i) q^{79} +(-5.76878 + 1.91537i) q^{80} +(8.27937 - 7.04833i) q^{81} +(3.94023 + 4.33863i) q^{82} +(-10.3001 + 4.96024i) q^{83} +(-29.6624 + 37.1955i) q^{84} +(-2.96002 - 0.576464i) q^{85} +(-3.40495 + 9.25234i) q^{86} +(4.75980 + 20.8541i) q^{87} +(0.196139 - 0.375961i) q^{88} +(4.26513 + 1.72676i) q^{89} +(-4.67284 - 3.97805i) q^{90} +(0.499362 + 15.5719i) q^{91} +(1.09225 + 34.0603i) q^{92} +(3.23833 - 14.1881i) q^{93} +(-2.60185 - 5.87762i) q^{94} +(4.73750 - 0.610833i) q^{95} +(3.70073 - 2.76192i) q^{96} +(4.08029 - 6.73087i) q^{97} +(-45.0690 + 2.89353i) q^{98} +(0.163686 - 0.0105090i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 630 q - 42 q^{2} - 42 q^{3} - 28 q^{4} - 42 q^{5} - 21 q^{6} - 28 q^{7} - 28 q^{8} - 42 q^{9} - 28 q^{10} - 28 q^{11} - 28 q^{12} - 42 q^{13} - 28 q^{14} - 154 q^{15} - 42 q^{17} - 21 q^{18} - 7 q^{19}+ \cdots - 161 q^{99}+O(q^{100}) $ 630 * q - 42 * q^2 - 42 * q^3 - 28 * q^4 - 42 * q^5 - 21 * q^6 - 28 * q^7 - 28 * q^8 - 42 * q^9 - 28 * q^10 - 28 * q^11 - 28 * q^12 - 42 * q^13 - 28 * q^14 - 154 * q^15 - 42 * q^17 - 21 * q^18 - 7 * q^19 - 35 * q^20 - 42 * q^21 - 42 * q^23 + 28 * q^24 - 42 * q^25 - 7 * q^26 + 42 * q^27 - 49 * q^28 - 182 * q^29 + 77 * q^30 - 14 * q^31 - 28 * q^32 + 35 * q^33 - 14 * q^34 - 42 * q^35 + 84 * q^36 + 14 * q^37 - 28 * q^38 - 21 * q^39 + 28 * q^40 - 28 * q^41 - 112 * q^42 - 56 * q^43 - 210 * q^44 + 49 * q^45 - 7 * q^47 + 42 * q^48 + 42 * q^49 + 98 * q^50 - 14 * q^51 + 49 * q^52 - 42 * q^53 + 63 * q^54 - 161 * q^56 - 175 * q^57 - 42 * q^58 + 42 * q^59 + 126 * q^60 - 14 * q^61 + 42 * q^62 + 49 * q^63 + 98 * q^64 + 56 * q^65 + 175 * q^66 + 28 * q^67 + 273 * q^68 - 7 * q^69 - 252 * q^70 - 77 * q^71 - 364 * q^72 - 28 * q^73 + 35 * q^74 + 7 * q^75 + 133 * q^76 + 21 * q^77 + 210 * q^78 + 42 * q^79 - 14 * q^80 - 14 * q^81 - 42 * q^82 + 161 * q^83 - 245 * q^84 - 266 * q^85 - 147 * q^86 - 35 * q^87 + 77 * q^88 + 28 * q^89 + 315 * q^90 + 154 * q^91 + 84 * q^92 - 7 * q^93 + 182 * q^94 + 126 * q^95 + 245 * q^96 + 42 * q^97 - 308 * q^98 - 161 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/197\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{49}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.48397	−	0.159476i	−1.75643	−	0.112767i	−0.847787	−	0.530337i	$-0.822065\pi$
$2$	−2.48397	−	0.159476i	−1.75643	−	0.112767i	−0.908645	+	0.417570i	$0.862882\pi$
$3$	−1.29377	+	1.85472i	−0.746959	+	1.07082i	0.247823	+	0.968805i	$0.420285\pi$
$3$	−1.29377	+	1.85472i	−0.746959	+	1.07082i	−0.994783	+	0.102017i	$0.967470\pi$
$4$	4.16109	+	0.536513i	2.08055	+	0.268257i
$5$	−0.977512	+	0.636290i	−0.437157	+	0.284558i	−0.745233	−	0.666804i	$-0.767662\pi$
$5$	−0.977512	+	0.636290i	−0.437157	+	0.284558i	0.308076	+	0.951362i	$0.400315\pi$
$6$	3.50947	−	4.40074i	1.43274	−	1.79659i
$7$	5.00407	−	0.321272i	1.89136	−	0.121429i	0.925218	−	0.379436i	$-0.123882\pi$
$7$	5.00407	−	0.321272i	1.89136	−	0.121429i	0.966143	+	0.258007i	$0.0830658\pi$
$8$	−5.36410	−	1.04466i	−1.89650	−	0.369342i
$9$	−0.730042	−	1.98376i	−0.243347	−	0.661254i
$10$	2.52958	−	1.42464i	0.799925	−	0.450509i
$11$	−0.0220780	+	0.0743880i	−0.00665676	+	0.0224288i	−0.961931	−	0.273294i	$-0.911887\pi$
$11$	−0.0220780	+	0.0743880i	−0.00665676	+	0.0224288i	0.955274	+	0.295723i	$0.0955604\pi$
$12$	−6.37859	+	7.02353i	−1.84134	+	2.02752i
$13$	−0.0995861	+	3.10546i	−0.0276202	+	0.861300i	0.888140	+	0.459574i	$0.151998\pi$
$13$	−0.0995861	+	3.10546i	−0.0276202	+	0.861300i	−0.915760	+	0.401726i	$0.868410\pi$
$14$	−12.4812			−3.33574
$15$	0.0845386	−	2.63622i	0.0218278	−	0.680670i
$16$	5.04102	+	1.32191i	1.26025	+	0.330478i
$17$	1.85730	+	1.79869i	0.450461	+	0.436247i	0.885834	−	0.464003i	$-0.153587\pi$
$17$	1.85730	+	1.79869i	0.450461	+	0.436247i	−0.435372	+	0.900250i	$0.643383\pi$
$18$	1.49704	+	5.04403i	0.352856	+	1.18889i
$19$	−3.68983	−	1.77693i	−0.846506	−	0.407656i	−0.0402264	−	0.999191i	$-0.512808\pi$
$19$	−3.68983	−	1.77693i	−0.846506	−	0.407656i	−0.806279	+	0.591535i	$0.798522\pi$
$20$	−4.40890	+	2.12321i	−0.985859	+	0.474765i
$21$	−5.87826	+	9.69680i	−1.28274	+	2.11601i
$22$	0.0667041	−	0.181257i	0.0142214	−	0.0386441i
$23$	1.29633	+	8.01827i	0.270304	+	1.67193i	0.660218	+	0.751074i	$0.270464\pi$
$23$	1.29633	+	8.01827i	0.270304	+	1.67193i	−0.389914	+	0.920851i	$0.627495\pi$
$24$	8.87747	−	8.59735i	1.81211	−	1.75493i
$25$	−1.47325	+	3.32810i	−0.294650	+	0.665620i
$26$	0.742616	−	7.69799i	0.145639	−	1.50970i
$27$	−1.93843	−	0.508316i	−0.373051	−	0.0978254i
$28$	20.9948	+	1.34791i	3.96764	+	0.254731i
$29$	6.35929	−	7.00229i	1.18089	−	1.30029i	0.236437	−	0.971647i	$-0.424020\pi$
$29$	6.35929	−	7.00229i	1.18089	−	1.30029i	0.944453	−	0.328645i	$-0.106592\pi$
$30$	−0.630406	+	6.53482i	−0.115096	+	1.19309i
$31$	−5.96511	+	2.41501i	−1.07137	+	0.433748i	−0.841936	−	0.539578i	$-0.818584\pi$
$31$	−5.96511	+	2.41501i	−1.07137	+	0.433748i	−0.229429	+	0.973325i	$0.573686\pi$
$32$	−1.93798	−	0.643453i	−0.342589	−	0.113747i
$33$	−0.109405	−	0.137190i	−0.0190450	−	0.0238816i
$34$	−4.32662	−	4.76409i	−0.742010	−	0.817035i
$35$	−4.68712	+	3.49809i	−0.792268	+	0.591285i
$36$	−1.97346	−	8.64629i	−0.328910	−	1.44105i
$37$	−6.07522	+	1.59311i	−0.998760	+	0.261906i	−0.716617	−	0.697467i	$-0.754310\pi$
$37$	−6.07522	+	1.59311i	−0.998760	+	0.261906i	−0.282143	+	0.959372i	$0.591045\pi$
$38$	8.88206	+	5.00228i	1.44086	+	0.811477i
$39$	−5.63092	−	4.20246i	−0.901668	−	0.672932i
$40$	5.90818	−	2.39196i	0.934165	−	0.378202i
$41$	−1.69143	−	1.63806i	−0.264157	−	0.255822i	0.551744	−	0.834014i	$-0.313963\pi$
$41$	−1.69143	−	1.63806i	−0.264157	−	0.255822i	−0.815901	+	0.578192i	$0.803758\pi$
$42$	16.1478	−	23.1491i	2.49166	−	3.57199i
$43$	1.12698	−	3.79717i	0.171863	−	0.579064i	−0.827970	−	0.560773i	$-0.810504\pi$
$43$	1.12698	−	3.79717i	0.171863	−	0.579064i	0.999833	−	0.0182908i	$-0.00582246\pi$
$44$	−0.131779	+	0.297690i	−0.0198664	+	0.0448785i
$45$	1.97587	+	1.47463i	0.294546	+	0.219825i
$46$	−1.94133	−	20.1239i	−0.286233	−	2.96710i
$47$	1.19445	+	2.28954i	0.174228	+	0.333963i	0.957847	−	0.287279i	$-0.0927507\pi$
$47$	1.19445	+	2.28954i	0.174228	+	0.333963i	−0.783619	+	0.621242i	$0.786628\pi$
$48$	−8.97370	+	7.63942i	−1.29524	+	1.10266i
$49$	17.9950	−	2.32020i	2.57071	−	0.331456i
$50$	4.19026	−	8.03195i	0.592593	−	1.13589i
$51$	−5.73899	+	1.11767i	−0.803619	+	0.156505i
$52$	−2.08051	+	12.8687i	−0.288515	+	1.78456i
$53$	0.0834526	+	0.865073i	0.0114631	+	0.118827i	0.999336	−	0.0364383i	$-0.0116013\pi$
$53$	0.0834526	+	0.865073i	0.0114631	+	0.118827i	−0.987873	+	0.155265i	$0.950377\pi$
$54$	4.73393	+	1.57177i	0.644207	+	0.213891i
$55$	−0.0257509	−	0.0867632i	−0.00347225	−	0.0116991i
$56$	−27.1780	−	3.50421i	−3.63181	−	0.468270i
$57$	8.06951	−	4.54466i	1.06883	−	0.601955i
$58$	−16.9130	+	16.3793i	−2.22078	+	2.15071i
$59$	−6.37625	−	3.59104i	−0.830117	−	0.467513i	0.0164061	−	0.999865i	$-0.494778\pi$
$59$	−6.37625	−	3.59104i	−0.830117	−	0.467513i	−0.846523	+	0.532352i	$0.821308\pi$
$60$	1.76614	−	10.9242i	0.228008	−	1.41031i
$61$	4.07740	+	5.84527i	0.522058	+	0.748410i	0.990860	−	0.134894i	$-0.0430693\pi$
$61$	4.07740	+	5.84527i	0.522058	+	0.748410i	−0.468802	+	0.883303i	$0.655314\pi$
$62$	15.2023	−	5.04751i	1.93069	−	0.641034i
$63$	−4.29051	−	9.69234i	−0.540554	−	1.22112i
$64$	−4.94992	−	2.00400i	−0.618740	−	0.250500i
$65$	−1.87863	−	3.09899i	−0.233015	−	0.384383i
$66$	0.249880	+	0.358222i	0.0307581	+	0.0440941i
$67$	3.93794	+	7.54829i	0.481096	+	0.922171i	0.997818	+	0.0660177i	$0.0210294\pi$
$67$	3.93794	+	7.54829i	0.481096	+	0.922171i	−0.516723	+	0.856153i	$0.672848\pi$
$68$	6.76337	+	8.48099i	0.820179	+	1.02847i
$69$	−16.5488	−	7.96948i	−1.99224	−	0.959413i
$70$	12.2005	−	7.94166i	1.45824	−	0.949210i
$71$	3.39590	+	9.22776i	0.403019	+	1.09513i	0.963673	+	0.267083i	$0.0860599\pi$
$71$	3.39590	+	9.22776i	0.403019	+	1.09513i	−0.560654	+	0.828050i	$0.689450\pi$
$72$	1.84367	+	11.4037i	0.217278	+	1.34394i
$73$	4.12498	−	1.08170i	0.482792	−	0.126603i	−0.00423301	−	0.999991i	$-0.501347\pi$
$73$	4.12498	−	1.08170i	0.482792	−	0.126603i	0.487025	+	0.873388i	$0.338082\pi$
$74$	15.3447	−	2.98838i	1.78379	−	0.347393i
$75$	−4.26664	−	7.03827i	−0.492669	−	0.812709i
$76$	−14.4004	−	9.37362i	−1.65184	−	1.07523i
$77$	−0.0865810	+	0.379336i	−0.00986682	+	0.0432293i
$78$	13.3168	+	11.3368i	1.50783	+	1.28364i
$79$	6.37498	+	4.14965i	0.717242	+	0.466873i	0.851689	−	0.524048i	$-0.175579\pi$
$79$	6.37498	+	4.14965i	0.717242	+	0.466873i	−0.134447	+	0.990921i	$0.542926\pi$
$80$	−5.76878	+	1.91537i	−0.644969	+	0.214144i
$81$	8.27937	−	7.04833i	0.919930	−	0.783147i
$82$	3.94023	+	4.33863i	0.435125	+	0.479121i
$83$	−10.3001	+	4.96024i	−1.13058	+	0.544457i	−0.903145	−	0.429336i	$-0.858748\pi$
$83$	−10.3001	+	4.96024i	−1.13058	+	0.544457i	−0.227433	+	0.973794i	$0.573033\pi$
$84$	−29.6624	+	37.1955i	−3.23644	+	4.05836i
$85$	−2.96002	−	0.576464i	−0.321060	−	0.0625263i
$86$	−3.40495	+	9.25234i	−0.367165	+	0.997705i
$87$	4.75980	+	20.8541i	0.510304	+	2.23579i
$88$	0.196139	−	0.375961i	0.0209084	−	0.0400776i
$89$	4.26513	+	1.72676i	0.452103	+	0.183036i	0.589988	−	0.807412i	$-0.299132\pi$
$89$	4.26513	+	1.72676i	0.452103	+	0.183036i	−0.137885	+	0.990448i	$0.544030\pi$
$90$	−4.67284	−	3.97805i	−0.492560	−	0.419323i
$91$	0.499362	+	15.5719i	0.0523473	+	1.63238i
$92$	1.09225	+	34.0603i	0.113875	+	3.55103i
$93$	3.23833	−	14.1881i	0.335800	−	1.47123i
$94$	−2.60185	−	5.87762i	−0.268360	−	0.606231i
$95$	4.73750	−	0.610833i	0.486057	−	0.0626702i
$96$	3.70073	−	2.76192i	0.377704	−	0.281888i
$97$	4.08029	−	6.73087i	0.414291	−	0.683416i	−0.576758	−	0.816915i	$-0.695682\pi$
$97$	4.08029	−	6.73087i	0.414291	−	0.683416i	0.991049	+	0.133499i	$0.0426212\pi$
$98$	−45.0690	+	2.89353i	−4.55266	+	0.292290i
$99$	0.163686	−	0.0105090i	0.0164511	−	0.00105619i
$100$	−7.91591	+	13.0581i	−0.791591	+	1.30581i
$101$	1.87547	−	1.39970i	0.186616	−	0.139275i	−0.500735	−	0.865601i	$-0.666937\pi$
$101$	1.87547	−	1.39970i	0.186616	−	0.139275i	0.687351	+	0.726326i	$0.258774\pi$
$102$	14.4337	−	1.86102i	1.42915	−	0.184269i
$103$	−7.62235	−	17.2190i	−0.751052	−	1.69664i	−0.716852	−	0.697225i	$-0.754418\pi$
$103$	−7.62235	−	17.2190i	−0.751052	−	1.69664i	−0.0342005	−	0.999415i	$-0.510888\pi$
$104$	3.77834	−	16.5540i	0.370496	−	1.62325i
$105$	−0.423908	−	13.2190i	−0.0413692	−	1.29004i
$106$	−0.0693351	−	2.16212i	−0.00673442	−	0.210004i
$107$	5.62050	+	4.78480i	0.543355	+	0.462565i	0.877242	−	0.480048i	$-0.159381\pi$
$107$	5.62050	+	4.78480i	0.543355	+	0.462565i	−0.333887	+	0.942613i	$0.608361\pi$
$108$	−7.79326	−	3.15514i	−0.749907	−	0.303604i
$109$	1.52176	−	2.91693i	0.145758	−	0.279391i	−0.802646	−	0.596456i	$-0.796575\pi$
$109$	1.52176	−	2.91693i	0.145758	−	0.279391i	0.948404	+	0.317065i	$0.102697\pi$
$110$	0.0501277	+	0.219624i	0.00477949	+	0.0209403i
$111$	4.90517	−	13.3289i	0.465579	−	1.26513i
$112$	25.6503	+	4.99540i	2.42373	+	0.472021i
$113$	4.84266	−	6.07251i	0.455559	−	0.571253i	−0.500010	−	0.866020i	$-0.666670\pi$
$113$	4.84266	−	6.07251i	0.455559	−	0.571253i	0.955569	+	0.294766i	$0.0952418\pi$
$114$	−20.7692	+	10.0019i	−1.94521	+	0.936765i
$115$	−6.36913	−	7.01312i	−0.593924	−	0.653976i
$116$	30.2184	−	25.7253i	2.80571	−	2.38854i
$117$	6.23319	−	2.06956i	0.576259	−	0.191331i
$118$	15.2657	+	9.93688i	1.40532	+	0.914764i
$119$	9.87192	+	8.40409i	0.904958	+	0.770402i
$120$	−3.20743	+	14.0527i	−0.292797	+	1.28283i
$121$	9.21392	+	5.99760i	0.837629	+	0.545236i
$122$	−9.19597	−	15.1697i	−0.832564	−	1.37340i
$123$	5.22646	−	1.01785i	0.471254	−	0.0917767i
$124$	−26.1171	+	6.84870i	−2.34538	+	0.615031i
$125$	−1.60827	−	9.94772i	−0.143848	−	0.889751i
$126$	9.11180	+	24.7597i	0.811744	+	2.20577i
$127$	−6.47415	+	4.21421i	−0.574488	+	0.373950i	−0.799737	−	0.600351i	$-0.795028\pi$
$127$	−6.47415	+	4.21421i	−0.574488	+	0.373950i	0.225248	+	0.974301i	$0.427681\pi$
$128$	15.6554	+	7.53925i	1.38376	+	0.666382i
$129$	5.58464	+	7.00291i	0.491700	+	0.616572i
$130$	4.17224	+	7.99740i	0.365929	+	0.701418i
$131$	−8.75577	−	12.5520i	−0.764995	−	1.09668i	−0.992421	−	0.122882i	$-0.960786\pi$
$131$	−8.75577	−	12.5520i	−0.764995	−	1.09668i	0.227427	−	0.973795i	$-0.426969\pi$
$132$	−0.381640	−	0.629556i	−0.0332175	−	0.0547958i
$133$	−19.0351	−	7.70644i	−1.65055	−	0.668233i
$134$	−8.57795	−	19.3777i	−0.741022	−	1.67398i
$135$	2.21827	−	0.736518i	0.190919	−	0.0633894i
$136$	−8.08371	−	11.5886i	−0.693173	−	0.993715i
$137$	3.42287	−	21.1717i	0.292436	−	1.80882i	−0.249473	−	0.968382i	$-0.580257\pi$
$137$	3.42287	−	21.1717i	0.292436	−	1.80882i	0.541909	−	0.840437i	$-0.317702\pi$
$138$	39.8358	+	22.4351i	3.39105	+	1.90980i
$139$	−0.653474	+	0.632855i	−0.0554270	+	0.0536780i	−0.722878	−	0.690976i	$-0.757181\pi$
$139$	−0.653474	+	0.632855i	−0.0554270	+	0.0536780i	0.667451	+	0.744654i	$0.267385\pi$
$140$	−21.3803	+	12.0412i	−1.80697	+	1.01766i
$141$	−5.79179	−	0.746769i	−0.487757	−	0.0628893i
$142$	−6.96370	−	23.4630i	−0.584381	−	1.96897i
$143$	−0.228810	−	0.0759703i	−0.0191341	−	0.00635296i
$144$	−1.05780	−	10.9652i	−0.0881502	−	0.913769i
$145$	−1.76080	+	10.8912i	−0.146227	+	0.904463i
$146$	−10.4188	+	2.02906i	−0.862267	+	0.167927i
$147$	−18.9781	+	36.3774i	−1.56529	+	3.00036i
$148$	−26.1343	+	3.36964i	−2.14822	+	0.276983i
$149$	−5.40561	+	4.60186i	−0.442845	+	0.376999i	−0.841638	−	0.540041i	$-0.818409\pi$
$149$	−5.40561	+	4.60186i	−0.442845	+	0.376999i	0.398794	+	0.917041i	$0.369429\pi$
$150$	9.47577	+	18.1633i	0.773693	+	1.48303i
$151$	−0.985890	−	10.2198i	−0.0802306	−	0.831674i	−0.944471	−	0.328595i	$-0.893425\pi$
$151$	−0.985890	−	10.2198i	−0.0802306	−	0.831674i	0.864240	−	0.503079i	$-0.167800\pi$
$152$	17.9363	+	13.3862i	1.45483	+	1.08577i
$153$	2.21227	−	4.99756i	0.178852	−	0.404029i
$154$	0.275560	−	0.928451i	0.0222052	−	0.0748167i
$155$	4.29432	−	6.15624i	0.344928	−	0.494481i
$156$	−21.1761	−	20.5079i	−1.69544	−	1.64195i
$157$	7.28753	−	2.95039i	0.581608	−	0.235467i	−0.0655162	−	0.997852i	$-0.520869\pi$
$157$	7.28753	−	2.95039i	0.581608	−	0.235467i	0.647124	+	0.762384i	$0.275971\pi$
$158$	−15.1735	−	11.3243i	−1.20714	−	0.900911i
$159$	−1.71244	−	0.964426i	−0.135805	−	0.0764840i
$160$	2.30382	−	0.604133i	0.182133	−	0.0477609i
$161$	9.06298	+	39.7075i	0.714263	+	3.12939i
$162$	−21.6897	+	16.1875i	−1.70411	+	1.27181i
$163$	4.01219	+	4.41787i	0.314259	+	0.346034i	0.876905	−	0.480664i	$-0.159604\pi$
$163$	4.01219	+	4.41787i	0.314259	+	0.346034i	−0.562646	+	0.826698i	$0.690216\pi$
$164$	−6.15935	−	7.72358i	−0.480964	−	0.603110i
$165$	0.194237	+	0.0644912i	0.0151213	+	0.00502063i
$166$	26.3761	−	10.6785i	2.04718	−	0.828811i
$167$	0.763032	−	7.90962i	0.0590452	−	0.612065i	−0.917644	−	0.397404i	$-0.869911\pi$
$167$	0.763032	−	7.90962i	0.0590452	−	0.612065i	0.976689	−	0.214660i	$-0.0688645\pi$
$168$	41.6614	−	45.8738i	3.21425	−	3.53924i
$169$	3.33932	+	0.214391i	0.256871	+	0.0164916i
$170$	7.26067	+	1.90397i	0.556868	+	0.146028i
$171$	−0.831270	+	8.61698i	−0.0635688	+	0.658957i
$172$	6.72671	−	15.1958i	0.512907	−	1.15867i
$173$	−2.25861	+	2.18734i	−0.171719	+	0.166300i	−0.776555	−	0.630050i	$-0.783035\pi$
$173$	−2.25861	+	2.18734i	−0.171719	+	0.166300i	0.604836	+	0.796350i	$0.293239\pi$
$174$	−8.49748	−	52.5599i	−0.644192	−	3.98456i
$175$	−6.30303	+	17.1274i	−0.476464	+	1.29471i
$176$	−0.209630	+	0.345806i	−0.0158014	+	0.0260661i
$177$	14.9098	−	7.18017i	1.12069	−	0.539694i
$178$	−10.3191	−	4.96941i	−0.773448	−	0.372473i
$179$	−1.24157	−	4.18325i	−0.0927991	−	0.312671i	0.899435	−	0.437054i	$-0.143978\pi$
$179$	−1.24157	−	4.18325i	−0.0927991	−	0.312671i	−0.992234	+	0.124383i	$0.960305\pi$
$180$	7.43063	+	7.19616i	0.553846	+	0.536370i
$181$	25.3505	+	6.64768i	1.88429	+	0.494118i	0.999610	+	0.0279100i	$0.00888517\pi$
$181$	25.3505	+	6.64768i	1.88429	+	0.494118i	0.884675	+	0.466208i	$0.154380\pi$
$182$	1.24295	−	38.7599i	0.0921338	−	2.87307i
$183$	−16.1166			−1.19137
$184$	1.42270	−	44.3650i	0.104883	−	3.27063i
$185$	4.92492	−	5.42288i	0.362087	−	0.398698i
$186$	−10.3066	+	34.7263i	−0.755715	+	2.54626i
$187$	−0.174807	+	0.0984493i	−0.0127831	+	0.00719932i
$188$	3.74185	+	10.1678i	0.272902	+	0.741564i
$189$	−9.86334	−	1.92089i	−0.717453	−	0.139724i
$190$	−11.8652	+	0.761772i	−0.860794	+	0.0552648i
$191$	−0.865314	+	1.08507i	−0.0626120	+	0.0785129i	−0.812151	−	0.583447i	$-0.801704\pi$
$191$	−0.865314	+	1.08507i	−0.0626120	+	0.0785129i	0.749539	+	0.661960i	$0.230275\pi$
$192$	10.1209	−	6.58799i	0.730414	−	0.475447i
$193$	−18.2625	−	2.35469i	−1.31456	−	0.169494i	−0.561519	−	0.827464i	$-0.689783\pi$
$193$	−18.2625	−	2.35469i	−1.31456	−	0.169494i	−0.753044	+	0.657970i	$0.771416\pi$
$194$	−11.2087	+	16.0686i	−0.804740	+	1.15366i
$195$	8.17827	+	0.525063i	0.585658	+	0.0376005i
$196$	76.1236			5.43740
$197$	13.9127	+	1.85394i	0.991238	+	0.132088i
$197$	13.9127	+	1.85394i	0.991238	+	0.132088i
$198$	−0.408267			−0.0290143
$199$	−4.30150	−	0.276165i	−0.304925	−	0.0195768i	−0.0891445	−	0.996019i	$-0.528413\pi$
$199$	−4.30150	−	0.276165i	−0.304925	−	0.0195768i	−0.215781	+	0.976442i	$0.569230\pi$
$200$	11.3794	−	16.3132i	0.804645	−	1.15352i
$201$	−19.0948	−	2.46200i	−1.34684	−	0.173656i
$202$	−4.88182	+	3.17771i	−0.343484	+	0.223583i
$203$	29.5727	−	37.0830i	2.07560	−	2.60272i
$204$	−24.4801	+	1.57168i	−1.71395	+	0.110039i
$205$	2.69567	+	0.524982i	0.188274	+	0.0366663i
$206$	16.1877	+	43.9871i	1.12785	+	3.06473i
$207$	14.9600	−	8.42529i	1.03979	−	0.585598i
$208$	−4.60716	+	15.5230i	−0.319449	+	1.07633i
$209$	0.213646	−	0.235248i	0.0147782	−	0.0162725i
$210$	−1.05514	+	32.9032i	−0.0728118	+	2.27054i
$211$	17.5288			1.20673			0.603367	−	0.797463i	$-0.293825\pi$
$211$	17.5288			1.20673			0.603367	+	0.797463i	$0.293825\pi$
$212$	−0.116870	+	3.64442i	−0.00802663	+	0.250300i
$213$	−21.5084	−	5.64017i	−1.47373	−	0.386458i
$214$	−13.1981	−	12.7816i	−0.902203	−	0.873735i
$215$	1.31447	+	4.42887i	0.0896458	+	0.302047i
$216$	9.86691	+	4.75165i	0.671358	+	0.323309i
$217$	−29.0740	+	14.0013i	−1.97367	+	0.950469i
$218$	−4.24519	+	7.00288i	−0.287520	+	0.474295i
$219$	−3.33053	+	9.05014i	−0.225057	+	0.611552i
$220$	−0.0606021	−	0.374845i	−0.00408579	−	0.0252721i
$221$	−5.77073	+	5.58864i	−0.388181	+	0.375933i
$222$	−14.3100	+	32.3264i	−0.960421	+	2.16961i
$223$	1.11341	−	11.5417i	0.0745596	−	0.772888i	−0.880021	−	0.474935i	$-0.842472\pi$
$223$	1.11341	−	11.5417i	0.0745596	−	0.772888i	0.954580	−	0.297953i	$-0.0963040\pi$
$224$	−9.90450	−	2.59727i	−0.661772	−	0.173537i
$225$	7.67769	+	0.492924i	0.511846	+	0.0328616i
$226$	−12.9974	+	14.3116i	−0.864577	+	0.951995i
$227$	−1.39061	+	14.4151i	−0.0922980	+	0.956765i	0.826737	+	0.562589i	$0.190195\pi$
$227$	−1.39061	+	14.4151i	−0.0922980	+	0.956765i	−0.919035	+	0.394176i	$0.871030\pi$
$228$	36.0162	−	14.5814i	2.38523	−	0.965674i
$229$	1.15076	+	0.382080i	0.0760446	+	0.0252486i	0.352878	−	0.935670i	$-0.385203\pi$
$229$	1.15076	+	0.382080i	0.0760446	+	0.0252486i	−0.276833	+	0.960918i	$0.589285\pi$
$230$	14.7023	+	18.4361i	0.969440	+	1.21564i
$231$	−0.591546	−	0.651358i	−0.0389208	−	0.0428562i
$232$	−41.4269	+	30.9177i	−2.71981	+	2.02984i
$233$	6.16588	+	27.0145i	0.403940	+	1.76978i	0.611184	+	0.791488i	$0.290693\pi$
$233$	6.16588	+	27.0145i	0.403940	+	1.76978i	−0.207244	+	0.978289i	$0.566449\pi$
$234$	−15.8131	+	4.14669i	−1.03374	+	0.271077i
$235$	−2.62440	−	1.47803i	−0.171197	−	0.0964163i
$236$	−24.6055	−	18.3636i	−1.60168	−	1.19537i
$237$	−15.9442	+	6.45510i	−1.03569	+	0.419304i
$238$	−23.1813	−	22.4498i	−1.50262	−	1.45521i
$239$	15.6680	−	22.4612i	1.01348	−	1.45289i	0.126006	−	0.992030i	$-0.459784\pi$
$239$	15.6680	−	22.4612i	1.01348	−	1.45289i	0.887470	−	0.460865i	$-0.152461\pi$
$240$	3.91101	−	13.1775i	0.252455	−	0.850604i
$241$	6.37479	−	14.4008i	0.410637	−	0.927635i	−0.582732	−	0.812664i	$-0.698016\pi$
$241$	6.37479	−	14.4008i	0.410637	−	0.927635i	0.993369	−	0.114971i	$-0.0366775\pi$
$242$	−21.9306	−	16.3673i	−1.40975	−	1.05213i
$243$	1.78378	+	18.4907i	0.114429	+	1.18618i
$244$	13.8304	+	26.5103i	0.885400	+	1.69715i
$245$	−16.1140	+	13.7180i	−1.02949	+	0.876414i
$246$	−13.1447	+	1.69482i	−0.838074	+	0.108058i
$247$	5.88564	−	11.2817i	0.374495	−	0.717836i
$248$	34.5203	−	6.72283i	2.19204	−	0.426900i
$249$	4.12606	−	25.5211i	0.261478	−	1.61734i
$250$	2.40847	+	24.9663i	0.152325	+	1.57901i
$251$	17.9161	+	5.94855i	1.13085	+	0.375469i	0.818506	−	0.574499i	$-0.194803\pi$
$251$	17.9161	+	5.94855i	1.13085	+	0.375469i	0.312348	+	0.949968i	$0.398885\pi$
$252$	−12.6531	−	42.6326i	−0.797073	−	2.68560i
$253$	−0.625084	−	0.0805956i	−0.0392987	−	0.00506700i
$254$	16.7537	−	9.43549i	1.05122	−	0.592035i
$255$	4.89877	−	4.74420i	0.306773	−	0.297093i
$256$	−28.3792	−	15.9829i	−1.77370	−	0.998930i
$257$	−2.32763	+	14.3972i	−0.145193	+	0.898073i	0.806547	+	0.591170i	$0.201334\pi$
$257$	−2.32763	+	14.3972i	−0.145193	+	0.898073i	−0.951741	+	0.306903i	$0.900707\pi$
$258$	−12.7553	−	18.2856i	−0.794108	−	1.13841i
$259$	−29.8890	+	9.92383i	−1.85721	+	0.616637i
$260$	−6.15449	−	13.9031i	−0.381685	−	0.862234i
$261$	−18.5334	−	7.50335i	−1.14719	−	0.464446i
$262$	19.7473	+	32.5752i	1.21999	+	2.01251i
$263$	−0.399848	−	0.573212i	−0.0246557	−	0.0353458i	0.807654	−	0.589657i	$-0.200737\pi$
$263$	−0.399848	−	0.573212i	−0.0246557	−	0.0353458i	−0.832310	+	0.554311i	$0.812982\pi$
$264$	0.443543	+	0.850189i	0.0272982	+	0.0523255i
$265$	−0.632013	−	0.792520i	−0.0388243	−	0.0486841i
$266$	46.0535	+	22.1782i	2.82372	+	1.35983i
$267$	−8.72077	+	5.67659i	−0.533702	+	0.347402i
$268$	12.3364	+	33.5219i	0.753564	+	2.04768i
$269$	0.493511	+	3.05254i	0.0300899	+	0.186117i	0.997831	−	0.0658308i	$-0.0209698\pi$
$269$	0.493511	+	3.05254i	0.0300899	+	0.186117i	−0.967741	+	0.251948i	$0.918929\pi$
$270$	−5.62758	+	1.47573i	−0.342484	+	0.0898098i
$271$	−3.18184	+	0.619664i	−0.193283	+	0.0376419i	−0.286871	−	0.957969i	$-0.592615\pi$
$271$	−3.18184	+	0.619664i	−0.193283	+	0.0376419i	0.0935882	+	0.995611i	$0.470166\pi$
$272$	6.98496	+	11.5224i	0.423526	+	0.698650i
$273$	−29.5276	−	19.2204i	−1.78709	−	1.16327i
$274$	−11.8787	+	52.0439i	−0.717618	+	3.14409i
$275$	−0.215044	−	0.183070i	−0.0129677	−	0.0110395i
$276$	−64.5853	−	42.0404i	−3.88758	−	2.53053i
$277$	7.62171	−	2.53058i	0.457944	−	0.152048i	−0.0768278	−	0.997044i	$-0.524479\pi$
$277$	7.62171	−	2.53058i	0.457944	−	0.152048i	0.534772	+	0.844996i	$0.320398\pi$
$278$	1.72414	−	1.46778i	0.103407	−	0.0880315i
$279$	9.14558	+	10.0703i	0.547531	+	0.602893i
$280$	28.7965	−	13.8677i	1.72092	−	0.828751i
$281$	7.60791	−	9.54001i	0.453850	−	0.569109i	−0.501285	−	0.865282i	$-0.667139\pi$
$281$	7.60791	−	9.54001i	0.453850	−	0.569109i	0.955134	+	0.296173i	$0.0957105\pi$
$282$	14.2675	+	2.77860i	0.849620	+	0.165463i
$283$	0.345633	−	0.939196i	0.0205457	−	0.0558294i	−0.927780	−	0.373127i	$-0.878286\pi$
$283$	0.345633	−	0.939196i	0.0205457	−	0.0558294i	0.948326	+	0.317298i	$0.102775\pi$
$284$	9.17984	+	40.2195i	0.544723	+	2.38659i
$285$	−4.99632	+	9.57701i	−0.295956	+	0.567293i
$286$	0.556243	+	0.225198i	0.0328913	+	0.0133162i
$287$	−8.99029	−	7.65354i	−0.530680	−	0.451774i
$288$	0.138349	+	4.31423i	0.00815230	+	0.254219i
$289$	−0.330617	−	10.3098i	−0.0194480	−	0.606461i
$290$	6.11066	−	26.7725i	0.358830	−	1.57214i
$291$	7.20491	+	16.2760i	0.422359	+	0.954117i
$292$	17.7447	−	2.28793i	1.03843	−	0.133891i
$293$	6.43813	−	4.80490i	0.376119	−	0.280705i	−0.393350	−	0.919389i	$-0.628684\pi$
$293$	6.43813	−	4.80490i	0.376119	−	0.280705i	0.769469	+	0.638684i	$0.220521\pi$
$294$	52.9423	−	87.3339i	3.08766	−	5.09341i
$295$	8.51780	−	0.546861i	0.495926	−	0.0318395i
$296$	34.2523	−	2.19907i	1.99088	−	0.127818i
$297$	0.0806092	−	0.132973i	0.00467742	−	0.00771589i
$298$	14.1613	−	10.5688i	0.820339	−	0.612235i
$299$	−25.0295	+	3.22720i	−1.44749	+	0.186634i
$300$	−13.9778	−	31.5760i	−0.807006	−	1.82304i
$301$	4.41957	−	19.3634i	0.254740	−	1.11609i
$302$	0.819109	+	25.5428i	0.0471344	+	1.46983i
$303$	0.169619	+	5.28935i	0.00974437	+	0.303865i
$304$	−16.2516	−	13.8352i	−0.932092	−	0.793501i
$305$	−7.70500	−	3.11941i	−0.441187	−	0.178617i
$306$	−6.29220	+	12.0610i	−0.359701	+	0.689480i
$307$	−1.07378	−	4.70455i	−0.0612841	−	0.268503i	0.934998	−	0.354653i	$-0.115401\pi$
$307$	−1.07378	−	4.70455i	−0.0612841	−	0.268503i	−0.996282	+	0.0861495i	$0.972544\pi$
$308$	−0.563790	+	1.53200i	−0.0321249	+	0.0872938i
$309$	41.7980	+	8.14016i	2.37781	+	0.463078i
$310$	−11.6487	+	14.6071i	−0.661604	+	0.829625i
$311$	−23.7629	+	11.4436i	−1.34747	+	0.648909i	−0.961807	−	0.273730i	$-0.911743\pi$
$311$	−23.7629	+	11.4436i	−1.34747	+	0.648909i	−0.385666	+	0.922638i	$0.626028\pi$
$312$	25.8147	+	28.4248i	1.46147	+	1.60924i
$313$	−8.99493	+	7.65749i	−0.508423	+	0.432827i	−0.865248	−	0.501344i	$-0.832839\pi$
$313$	−8.99493	+	7.65749i	−0.508423	+	0.432827i	0.356825	+	0.934171i	$0.383859\pi$
$314$	−18.5725	+	6.16650i	−1.04811	+	0.347996i
$315$	10.3612	+	6.74437i	0.583785	+	0.380002i
$316$	24.3005	+	20.6874i	1.36701	+	1.16375i
$317$	3.89657	−	17.0720i	0.218853	−	0.958859i	−0.739474	−	0.673186i	$-0.764926\pi$
$317$	3.89657	−	17.0720i	0.218853	−	0.958859i	0.958327	−	0.285674i	$-0.0922173\pi$
$318$	4.09984	+	2.66870i	0.229907	+	0.149653i
$319$	0.380486	+	0.627651i	0.0213031	+	0.0351417i
$320$	6.11373	−	1.19065i	0.341768	−	0.0665593i
$321$	−16.1461	+	4.23401i	−0.901188	+	0.236319i
$322$	−16.1798	−	100.078i	−0.901663	−	5.57711i
$323$	−3.65697	−	9.93717i	−0.203479	−	0.552919i
$324$	38.2327	−	24.8867i	2.12404	−	1.38260i
$325$	−10.1886	−	4.90656i	−0.565160	−	0.272167i
$326$	−9.26162	−	11.6137i	−0.512954	−	0.643224i
$327$	3.44127	+	6.59628i	0.190303	+	0.364775i
$328$	7.36178	+	10.5537i	0.406486	+	0.582729i
$329$	6.71267	+	11.0733i	0.370082	+	0.610488i
$330$	−0.472194	−	0.191170i	−0.0259934	−	0.0105236i
$331$	−10.3811	−	23.4511i	−0.570596	−	1.28899i	−0.933973	−	0.357344i	$-0.883682\pi$
$331$	−10.3811	−	23.4511i	−0.570596	−	1.28899i	0.363377	−	0.931642i	$-0.381624\pi$
$332$	−45.5207	+	15.1139i	−2.49827	+	0.829484i
$333$	7.59552	+	10.8887i	0.416232	+	0.596699i
$334$	−3.15674	+	19.5256i	−0.172729	+	1.06839i
$335$	−8.65229	−	4.87288i	−0.472725	−	0.266234i
$336$	−42.4507	+	41.1112i	−2.31588	+	2.24280i
$337$	−6.24936	+	3.51957i	−0.340424	+	0.191723i	−0.651475	−	0.758670i	$-0.725850\pi$
$337$	−6.24936	+	3.51957i	−0.340424	+	0.191723i	0.311051	+	0.950393i	$0.399319\pi$
$338$	−8.26058	−	1.06508i	−0.449316	−	0.0579329i
$339$	4.99749	+	16.8382i	0.271427	+	0.914526i
$340$	−12.0076	−	3.98681i	−0.651206	−	0.216215i
$341$	−0.0479499	−	0.497051i	−0.00259663	−	0.0269168i
$342$	3.43905	−	21.2718i	0.185963	−	1.15024i
$343$	54.8494	−	10.6819i	2.96159	−	0.576769i
$344$	−10.0120	+	19.1911i	−0.539810	+	1.03472i
$345$	21.2476	−	2.73957i	1.14393	−	0.147493i
$346$	5.95914	−	5.07309i	0.320365	−	0.272731i
$347$	1.42592	+	2.73323i	0.0765476	+	0.146727i	0.921833	−	0.387588i	$-0.126692\pi$
$347$	1.42592	+	2.73323i	0.0765476	+	0.146727i	−0.845285	+	0.534316i	$0.820569\pi$
$348$	8.61750	+	89.3294i	0.461946	+	4.78856i
$349$	−0.476560	−	0.355666i	−0.0255097	−	0.0190384i	0.585280	−	0.810831i	$-0.300985\pi$
$349$	−0.476560	−	0.355666i	−0.0255097	−	0.0190384i	−0.610790	+	0.791793i	$0.709148\pi$
$350$	18.3879	−	41.5387i	0.982877	−	2.22034i
$351$	1.77160	−	5.96909i	0.0945608	−	0.318607i
$352$	0.0906518	−	0.129956i	0.00483176	−	0.00692669i
$353$	−2.89977	−	2.80828i	−0.154339	−	0.149469i	0.614487	−	0.788927i	$-0.289363\pi$
$353$	−2.89977	−	2.80828i	−0.154339	−	0.149469i	−0.768826	+	0.639458i	$0.779159\pi$
$354$	−38.1805	+	15.4576i	−2.02927	+	0.821560i
$355$	−9.19106	−	6.85947i	−0.487811	−	0.364063i
$356$	16.8212	+	9.47351i	0.891521	+	0.502095i
$357$	−28.3592	+	7.43667i	−1.50093	+	0.393590i
$358$	2.41689	+	10.5891i	0.127736	+	0.559650i
$359$	4.53928	−	3.38775i	0.239574	−	0.178799i	−0.471605	−	0.881810i	$-0.656325\pi$
$359$	4.53928	−	3.38775i	0.239574	−	0.178799i	0.711178	+	0.703012i	$0.248162\pi$
$360$	−9.05829	−	9.97419i	−0.477414	−	0.525686i
$361$	−1.38892	−	1.74165i	−0.0731008	−	0.0916656i
$362$	−61.9097	−	20.5554i	−3.25390	−	1.08037i
$363$	−23.0446	+	9.32971i	−1.20953	+	0.489683i
$364$	−6.27666	+	65.0642i	−0.328987	+	3.41029i
$365$	−3.34394	+	3.68205i	−0.175030	+	0.192727i
$366$	40.0330	+	2.57021i	2.09256	+	0.134347i
$367$	5.72271	+	1.50067i	0.298723	+	0.0783344i	0.399974	−	0.916527i	$-0.369019\pi$
$367$	5.72271	+	1.50067i	0.298723	+	0.0783344i	−0.101251	+	0.994861i	$0.532284\pi$
$368$	−4.06461	+	42.1339i	−0.211882	+	2.19638i
$369$	−2.01470	+	4.55124i	−0.104881	+	0.236928i
$370$	−13.0982	+	12.6849i	−0.680942	+	0.659455i
$371$	0.695526	+	4.30208i	0.0361099	+	0.223353i
$372$	21.0871	−	57.3004i	1.09331	−	2.97089i
$373$	−3.86888	+	6.38212i	−0.200323	+	0.330454i	−0.939190	−	0.343397i	$-0.888422\pi$
$373$	−3.86888	+	6.38212i	−0.200323	+	0.330454i	0.738867	+	0.673851i	$0.235361\pi$
$374$	0.449915	−	0.216667i	0.0232645	−	0.0112036i
$375$	20.5310	+	9.88719i	1.06021	+	0.510572i
$376$	−4.01536	−	13.5291i	−0.207077	−	0.697710i
$377$	21.1120	+	20.4459i	1.08732	+	1.05302i
$378$	24.1939	+	6.34439i	1.24440	+	0.326320i
$379$	−0.310962	+	9.69693i	−0.0159730	+	0.498098i	0.959974	+	0.280089i	$0.0903641\pi$
$379$	−0.310962	+	9.69693i	−0.0159730	+	0.498098i	−0.975947	+	0.218008i	$0.930044\pi$
$380$	20.0409			1.02808
$381$	0.559907	−	17.4600i	0.0286849	−	0.894501i
$382$	2.32246	−	2.55728i	0.118827	−	0.130842i
$383$	1.32407	−	4.46121i	0.0676566	−	0.227957i	−0.918040	−	0.396488i	$-0.870229\pi$
$383$	1.32407	−	4.46121i	0.0676566	−	0.227957i	0.985696	+	0.168531i	$0.0539022\pi$
$384$	−34.2377	+	19.2823i	−1.74719	+	0.983997i
$385$	−0.156734	−	0.425896i	−0.00798789	−	0.0217057i
$386$	44.9880	+	8.76141i	2.28983	+	0.445944i
$387$	−8.35543	+	0.536437i	−0.424730	+	0.0272686i
$388$	20.5897	−	25.8186i	1.04528	−	1.31074i
$389$	11.9129	−	7.75445i	0.604009	−	0.393166i	−0.206880	−	0.978366i	$-0.566331\pi$
$389$	11.9129	−	7.75445i	0.604009	−	0.393166i	0.810889	+	0.585200i	$0.198984\pi$
$390$	−20.2309	−	2.60848i	−1.02443	−	0.132085i
$391$	−12.0147	+	17.2240i	−0.607611	+	0.871056i
$392$	−98.9507	−	6.35284i	−4.99776	−	0.320867i
$393$	34.6085			1.74577
$394$	−34.2630	−	6.82388i	−1.72615	−	0.343782i
$395$	−8.87201			−0.446399
$396$	0.686750	+	0.0440908i	0.0345105	+	0.00221565i
$397$	14.3708	−	20.6017i	0.721251	−	1.03397i	−0.276093	−	0.961131i	$-0.589040\pi$
$397$	14.3708	−	20.6017i	0.721251	−	1.03397i	0.997344	−	0.0728363i	$-0.0232051\pi$
$398$	10.6407	+	1.37197i	0.533373	+	0.0687708i
$399$	38.9203	−	25.3343i	1.94845	−	1.26830i
$400$	−11.8261	+	14.8295i	−0.591307	+	0.741475i
$401$	−10.3209	+	0.662621i	−0.515399	+	0.0330897i	−0.319597	−	0.947554i	$-0.603547\pi$
$401$	−10.3209	+	0.662621i	−0.515399	+	0.0330897i	−0.195802	+	0.980643i	$0.562731\pi$
$402$	47.0382	+	9.16068i	2.34605	+	0.456893i
$403$	−6.90566	−	18.7649i	−0.343996	−	0.934747i
$404$	8.55494	−	4.81805i	0.425624	−	0.239707i
$405$	−3.60840	+	12.1579i	−0.179303	+	0.604131i
$406$	−79.3716	+	87.3969i	−3.93914	+	4.33744i
$407$	0.0156202	−	0.487096i	0.000774266	−	0.0241445i
$408$	31.9521			1.58186
$409$	−0.988198	+	30.8157i	−0.0488633	+	1.52374i	0.622507	+	0.782614i	$0.286114\pi$
$409$	−0.988198	+	30.8157i	−0.0488633	+	1.52374i	−0.671370	+	0.741122i	$0.734294\pi$
$410$	−6.61224	−	1.73393i	−0.326555	−	0.0856329i
$411$	34.8391	+	33.7398i	1.71849	+	1.66426i
$412$	−22.4791	−	75.7394i	−1.10746	−	3.73141i
$413$	−33.0609	−	15.9213i	−1.62682	−	0.783435i
$414$	−38.5037	+	18.5424i	−1.89235	+	0.911310i
$415$	6.91227	−	11.4025i	0.339310	−	0.559728i
$416$	2.19121	−	5.95424i	0.107433	−	0.291930i
$417$	−0.328321	−	2.03078i	−0.0160779	−	0.0994478i
$418$	−0.568208	+	0.550278i	−0.0277919	+	0.0269150i
$419$	3.43035	−	7.74923i	0.167584	−	0.378575i	−0.810815	−	0.585303i	$-0.800976\pi$
$419$	3.43035	−	7.74923i	0.167584	−	0.378575i	0.978398	+	0.206728i	$0.0662817\pi$
$420$	5.32826	−	55.2330i	0.259992	−	2.69509i
$421$	15.6988	+	4.11670i	0.765111	+	0.200636i	0.615530	−	0.788114i	$-0.288942\pi$
$421$	15.6988	+	4.11670i	0.765111	+	0.200636i	0.149582	+	0.988749i	$0.452207\pi$
$422$	−43.5411	−	2.79543i	−2.11955	−	0.136079i
$423$	3.66989	−	4.04096i	0.178436	−	0.196478i
$424$	0.456058	−	4.72752i	0.0221481	−	0.229589i
$425$	−8.72250	+	3.53135i	−0.423103	+	0.171296i
$426$	52.5268	+	17.4401i	2.54493	+	0.844975i
$427$	22.2815	+	27.9402i	1.07828	+	1.35212i
$428$	20.8203	+	22.9255i	1.00639	+	1.10815i
$429$	0.436932	−	0.326091i	0.0210953	−	0.0157438i
$430$	−2.55879	−	11.2108i	−0.123396	−	0.540633i
$431$	5.06830	−	1.32907i	0.244132	−	0.0640188i	−0.129561	−	0.991571i	$-0.541357\pi$
$431$	5.06830	−	1.32907i	0.244132	−	0.0640188i	0.373693	+	0.927553i	$0.378091\pi$
$432$	−9.09971	−	5.12486i	−0.437810	−	0.246570i
$433$	14.9678	+	11.1707i	0.719306	+	0.536832i	0.894152	−	0.447764i	$-0.147780\pi$
$433$	14.9678	+	11.1707i	0.719306	+	0.536832i	−0.174846	+	0.984596i	$0.555943\pi$
$434$	74.4517	−	30.1421i	3.57380	−	1.44687i
$435$	−17.9220	−	17.3565i	−0.859294	−	0.832180i
$436$	7.89715	−	11.3212i	0.378205	−	0.542185i
$437$	9.46466	−	31.8896i	0.452756	−	1.52549i
$438$	9.71623	−	21.9491i	0.464259	−	1.04877i
$439$	−21.9365	−	16.3717i	−1.04697	−	0.781376i	−0.0706082	−	0.997504i	$-0.522494\pi$
$439$	−21.9365	−	16.3717i	−1.04697	−	0.781376i	−0.976365	+	0.216128i	$0.930657\pi$
$440$	0.0474923	+	0.492307i	0.00226411	+	0.0234698i
$441$	−17.7398	−	34.0039i	−0.844753	−	1.61923i
$442$	15.2256	−	12.9617i	0.724207	−	0.616526i
$443$	−4.01876	+	0.518162i	−0.190937	+	0.0246186i	−0.222752	−	0.974875i	$-0.571504\pi$
$443$	−4.01876	+	0.518162i	−0.190937	+	0.0246186i	0.0318148	+	0.999494i	$0.489871\pi$
$444$	27.5620	−	52.8313i	1.30804	−	2.50726i
$445$	−5.26794	+	1.02593i	−0.249724	+	0.0486338i
$446$	−4.60631	+	28.4916i	−0.218115	+	1.34912i
$447$	−1.54154	−	15.9796i	−0.0729122	−	0.755811i
$448$	−25.4136	−	8.43788i	−1.20068	−	0.398652i
$449$	−4.55204	−	15.3373i	−0.214824	−	0.723814i	−0.995144	−	0.0984329i	$-0.968617\pi$
$449$	−4.55204	−	15.3373i	−0.214824	−	0.723814i	0.780319	−	0.625381i	$-0.215056\pi$
$450$	−18.9925	−	2.44882i	−0.895317	−	0.115438i
$451$	0.159195	−	0.0896570i	0.00749621	−	0.00422178i
$452$	23.4087	−	22.6701i	1.10105	−	1.06631i
$453$	20.2303	+	11.3935i	0.950504	+	0.535314i
$454$	5.75310	−	35.5849i	0.270006	−	1.67008i
$455$	−10.3964	−	14.9040i	−0.487391	−	0.698711i
$456$	−48.0333	+	15.9481i	−2.24936	+	0.746840i
$457$	−5.31895	−	12.0156i	−0.248810	−	0.562066i	0.745751	−	0.666225i	$-0.232091\pi$
$457$	−5.31895	−	12.0156i	−0.248810	−	0.562066i	−0.994561	+	0.104159i	$0.966785\pi$
$458$	−2.79753	−	1.13259i	−0.130720	−	0.0529227i
$459$	−2.68594	−	4.43073i	−0.125369	−	0.206809i
$460$	−22.7399	−	32.5993i	−1.06025	−	1.51995i
$461$	4.44426	+	8.51881i	0.206990	+	0.396761i	0.967615	−	0.252431i	$-0.0812299\pi$
$461$	4.44426	+	8.51881i	0.206990	+	0.396761i	−0.760625	+	0.649191i	$0.775107\pi$
$462$	1.36551	+	1.71229i	0.0635291	+	0.0796629i
$463$	−5.27286	−	2.53927i	−0.245050	−	0.118010i	0.307328	−	0.951604i	$-0.400565\pi$
$463$	−5.27286	−	2.53927i	−0.245050	−	0.118010i	−0.552378	+	0.833594i	$0.686280\pi$
$464$	41.3137	−	26.8922i	1.91794	−	1.24844i
$465$	5.86221	+	15.9295i	0.271854	+	0.738714i
$466$	−11.0077	−	68.0865i	−0.509921	−	3.15404i
$467$	−25.5306	+	6.69491i	−1.18142	+	0.309804i	−0.791571	−	0.611077i	$-0.790737\pi$
$467$	−25.5306	+	6.69491i	−1.18142	+	0.309804i	−0.389844	+	0.920881i	$0.627471\pi$
$468$	27.0472	−	5.26745i	1.25026	−	0.243488i
$469$	22.1308	+	36.5070i	1.02190	+	1.68574i
$470$	6.28321	+	4.08992i	0.289823	+	0.188654i
$471$	−3.95625	+	17.3335i	−0.182294	+	0.798684i
$472$	30.4514	+	25.9237i	1.40164	+	1.19323i
$473$	0.257583	+	0.167668i	0.0118437	+	0.00770938i
$474$	40.6344	−	13.4915i	1.86640	−	0.619687i
$475$	11.3499	−	9.66227i	0.520767	−	0.443335i
$476$	36.5691	+	40.2666i	1.67614	+	1.84562i
$477$	1.65517	−	0.797090i	0.0757852	−	0.0364962i
$478$	−42.5008	+	53.2943i	−1.94394	+	2.43762i
$479$	−9.39788	−	1.83024i	−0.429400	−	0.0836256i	−0.0281703	−	0.999603i	$-0.508968\pi$
$479$	−9.39788	−	1.83024i	−0.429400	−	0.0836256i	−0.401230	+	0.915978i	$0.631417\pi$
$480$	−1.86012	+	5.05455i	−0.0849025	+	0.230708i
$481$	−4.34233	−	19.0250i	−0.197993	−	0.867465i
$482$	−18.1314	+	34.7545i	−0.825861	+	1.58302i
$483$	−85.3717	−	34.5632i	−3.88455	−	1.57268i
$484$	35.1222	+	29.9000i	1.59646	+	1.35909i
$485$	0.294249	+	9.17576i	0.0133611	+	0.416650i
$486$	−1.48202	−	46.2148i	−0.0672257	−	2.09635i
$487$	−9.63769	+	42.2255i	−0.436725	+	1.91342i	−0.0307698	+	0.999526i	$0.509796\pi$
$487$	−9.63769	+	42.2255i	−0.436725	+	1.91342i	−0.405956	+	0.913893i	$0.633061\pi$
$488$	−15.7653	−	35.6141i	−0.713662	−	1.61217i
$489$	−13.3848	+	1.72578i	−0.605280	+	0.0780423i
$490$	42.2144	−	31.5054i	1.90705	−	1.42327i
$491$	−4.40543	+	7.26721i	−0.198814	+	0.327965i	−0.938680	−	0.344790i	$-0.887950\pi$
$491$	−4.40543	+	7.26721i	−0.198814	+	0.327965i	0.739866	+	0.672754i	$0.234889\pi$
$492$	22.2939	−	1.43131i	1.00508	−	0.0645286i
$493$	24.4061	−	1.56692i	1.09919	−	0.0705706i
$494$	−16.4189	+	27.0847i	−0.738722	+	1.21860i
$495$	−0.153318	+	0.114424i	−0.00689114	+	0.00514299i
$496$	−33.2626	+	4.28874i	−1.49354	+	0.192570i
$497$	19.9579	+	45.0853i	0.895236	+	2.02235i
$498$	−14.3190	+	62.7357i	−0.641650	+	2.81125i
$499$	−0.000636469	−	0.0198475i	−2.84923e−5	−	0.000888494i	0.999472	−	0.0324958i	$-0.0103456\pi$
$499$	−0.000636469	−	0.0198475i	−2.84923e−5	−	0.000888494i	−0.999500	+	0.0316073i	$0.989937\pi$
$500$	−1.35508	−	42.2562i	−0.0606008	−	1.88976i
$501$	13.6829	+	11.6485i	0.611309	+	0.520415i
$502$	−43.5544	−	17.6332i	−1.94393	−	0.787009i
$503$	12.1550	−	23.2988i	0.541963	−	1.03884i	−0.447531	−	0.894268i	$-0.647697\pi$
$503$	12.1550	−	23.2988i	0.541963	−	1.03884i	0.989494	−	0.144573i	$-0.0461808\pi$
$504$	12.8895	+	56.4728i	0.574146	+	2.51550i
$505$	−0.942678	+	2.56156i	−0.0419486	+	0.113988i
$506$	1.53984	+	0.299883i	0.0684541	+	0.0133314i
$507$	−4.71795	+	5.91613i	−0.209532	+	0.262744i
$508$	−29.2005	+	14.0622i	−1.29556	+	0.623911i
$509$	0.699540	+	0.770271i	0.0310066	+	0.0341417i	0.755584	−	0.655051i	$-0.227353\pi$
$509$	0.699540	+	0.770271i	0.0310066	+	0.0341417i	−0.724578	+	0.689193i	$0.757965\pi$
$510$	−12.9250	+	11.0032i	−0.572328	+	0.487230i
$511$	20.2941	−	6.73812i	0.897760	−	0.298077i
$512$	38.8187	+	25.2682i	1.71556	+	1.11671i
$513$	6.24924	+	5.32005i	0.275911	+	0.234886i
$514$	8.07777	−	35.3910i	0.356295	−	1.56103i
$515$	18.4072	+	11.9818i	0.811120	+	0.527980i
$516$	19.4810	+	32.1360i	0.857604	+	1.41471i
$517$	−0.196685	+	0.0383044i	−0.00865020	+	0.00168463i
$518$	75.8260	−	19.8839i	3.33160	−	0.873649i
$519$	−1.13478	−	7.01900i	−0.0498112	−	0.308100i
$520$	6.83976	+	18.5858i	0.299943	+	0.815042i
$521$	−12.8184	+	8.34388i	−0.561586	+	0.365552i	−0.794798	−	0.606874i	$-0.792423\pi$
$521$	−12.8184	+	8.34388i	−0.561586	+	0.365552i	0.233212	+	0.972426i	$0.425076\pi$
$522$	44.8398	+	21.5937i	1.96259	+	0.945132i
$523$	17.0123	+	21.3327i	0.743895	+	0.932815i	0.999422	−	0.0339871i	$-0.0108205\pi$
$523$	17.0123	+	21.3327i	0.743895	+	0.932815i	−0.255527	+	0.966802i	$0.582249\pi$
$524$	−29.6992	−	56.9278i	−1.29742	−	2.48690i
$525$	−23.6118	−	33.8492i	−1.03050	−	1.47730i
$526$	0.901797	+	1.48761i	0.0393202	+	0.0648628i
$527$	−15.4228	−	6.24402i	−0.671830	−	0.271994i
$528$	−0.370160	−	0.836199i	−0.0161092	−	0.0363909i
$529$	−40.7839	+	13.5412i	−1.77321	+	0.588748i
$530$	1.44351	+	2.06939i	0.0627022	+	0.0898884i
$531$	−2.46883	+	15.2706i	−0.107138	+	0.662686i
$532$	−75.0720	−	42.2798i	−3.25479	−	1.83306i
$533$	5.25536	−	5.08954i	0.227635	−	0.220452i
$534$	22.5674	−	12.7097i	0.976587	−	0.550003i
$535$	−8.53864	−	1.10094i	−0.369157	−	0.0475976i
$536$	−13.2381	−	44.6036i	−0.571799	−	1.92658i
$537$	9.36506	+	3.10941i	0.404132	+	0.134181i
$538$	−0.739060	−	7.66113i	−0.0318631	−	0.330295i
$539$	−0.224698	+	1.38984i	−0.00967842	+	0.0598645i
$540$	9.62560	−	1.87458i	0.414220	−	0.0806693i
$541$	9.36199	−	17.9452i	0.402503	−	0.771524i	−0.597025	−	0.802222i	$-0.703651\pi$
$541$	9.36199	−	17.9452i	0.402503	−	0.771524i	0.999529	+	0.0306988i	$0.00977325\pi$
$542$	8.00243	−	1.03180i	0.343734	−	0.0443195i
$543$	−45.1273	+	38.4174i	−1.93660	+	1.64865i
$544$	−2.44203	−	4.68091i	−0.104701	−	0.200692i
$545$	0.368474	+	3.81961i	0.0157837	+	0.163614i
$546$	70.2806	+	52.4517i	3.00773	+	2.24473i
$547$	−7.75533	+	17.5194i	−0.331594	+	0.749076i	0.668392	+	0.743809i	$0.266983\pi$
$547$	−7.75533	+	17.5194i	−0.331594	+	0.749076i	−0.999986	+	0.00526743i	$0.998323\pi$
$548$	25.6018	−	86.2609i	1.09365	−	3.68488i
$549$	8.61893	−	12.3559i	0.367847	−	0.527336i
$550$	0.504969	+	0.489035i	0.0215319	+	0.0208525i
$551$	−35.9073	+	14.5373i	−1.52970	+	0.619308i
$552$	80.4440	+	60.0369i	3.42392	+	2.55534i
$553$	33.2340	+	18.7171i	1.41325	+	0.795930i
$554$	−19.3357	+	5.07041i	−0.821494	+	0.215421i
$555$	3.68620	+	16.1503i	0.156471	+	0.685543i
$556$	−3.05870	+	2.28277i	−0.129718	+	0.0968110i
$557$	−18.8204	−	20.7233i	−0.797445	−	0.878076i	0.197312	−	0.980341i	$-0.436779\pi$
$557$	−18.8204	−	20.7233i	−0.797445	−	0.878076i	−0.994757	+	0.102265i	$0.967391\pi$
$558$	−21.1114	−	26.4728i	−0.893715	−	1.12068i
$559$	11.6797	+	3.87794i	0.494001	+	0.164020i
$560$	−28.2520	+	11.4380i	−1.19387	+	0.483342i
$561$	0.0435642	−	0.451588i	0.00183928	−	0.0190661i
$562$	−20.4192	+	22.4838i	−0.861332	+	0.948423i
$563$	−28.6174	−	1.83730i	−1.20608	−	0.0774329i	−0.551991	−	0.833850i	$-0.686132\pi$
$563$	−28.6174	−	1.83730i	−1.20608	−	0.0774329i	−0.654089	+	0.756417i	$0.726948\pi$
$564$	−23.6995	−	6.21475i	−0.997930	−	0.261688i
$565$	−0.869887	+	9.01729i	−0.0365964	+	0.379360i
$566$	−1.00832	+	2.27781i	−0.0423829	+	0.0957437i
$567$	39.1661	−	37.9303i	1.64482	−	1.59292i
$568$	−8.57609	−	53.0462i	−0.359845	−	2.22577i
$569$	−3.61697	+	9.82847i	−0.151631	+	0.412031i	−0.991392	−	0.130925i	$-0.958205\pi$
$569$	−3.61697	+	9.82847i	−0.151631	+	0.412031i	0.839761	+	0.542956i	$0.182695\pi$
$570$	13.9380	−	22.9922i	0.583799	−	0.963038i
$571$	14.6861	−	7.07246i	0.614595	−	0.295973i	−0.100569	−	0.994930i	$-0.532066\pi$
$571$	14.6861	−	7.07246i	0.614595	−	0.295973i	0.715164	+	0.698957i	$0.246352\pi$
$572$	−0.911342	−	0.438879i	−0.0381051	−	0.0183505i
$573$	−0.892981	−	3.00875i	−0.0373048	−	0.125692i
$574$	21.1110	+	20.4449i	0.881158	+	0.853354i
$575$	−28.5954	−	7.49861i	−1.19251	−	0.312714i
$576$	−0.361806	+	11.2825i	−0.0150753	+	0.470102i
$577$	−31.7061			−1.31994			−0.659972	−	0.751290i	$-0.729432\pi$
$577$	−31.7061			−1.31994			−0.659972	+	0.751290i	$0.729432\pi$
$578$	−0.822933	+	25.6621i	−0.0342295	+	1.06740i
$579$	27.9948	−	30.8254i	1.16342	−	1.28106i
$580$	−13.1701	+	44.3745i	−0.546859	+	1.84255i
$581$	−49.9486	+	28.1305i	−2.07222	+	1.16705i
$582$	−15.3011	−	41.5781i	−0.634252	−	1.72347i
$583$	−0.0661936	−	0.0128912i	−0.00274146	−	0.000533899i
$584$	−23.2568	+	1.49313i	−0.962372	+	0.0617864i
$585$	−4.77618	+	5.98914i	−0.197471	+	0.247621i
$586$	−16.7584	+	10.9085i	−0.692282	+	0.450626i
$587$	2.19287	+	0.282739i	0.0905093	+	0.0116699i	0.172999	−	0.984922i	$-0.444654\pi$
$587$	2.19287	+	0.282739i	0.0905093	+	0.0116699i	−0.0824893	+	0.996592i	$0.526287\pi$
$588$	−98.4865	+	141.188i	−4.06152	+	5.82249i
$589$	26.3016	+	1.68862i	1.08374	+	0.0695782i
$590$	−21.2452			−0.874650
$591$	−21.4384	+	23.4055i	−0.881857	+	0.962776i
$592$	−32.7312			−1.34525
$593$	−19.1620	−	1.23024i	−0.786887	−	0.0505198i	−0.334563	−	0.942373i	$-0.608589\pi$
$593$	−19.1620	−	1.23024i	−0.786887	−	0.0505198i	−0.452324	+	0.891854i	$0.649405\pi$
$594$	−0.221437	+	0.317446i	−0.00908567	+	0.0130250i
$595$	−14.9974	−	1.93370i	−0.614832	−	0.0792738i
$596$	−24.9622	+	16.2486i	−1.02249	+	0.665568i
$597$	6.07737	−	7.62078i	0.248730	−	0.311898i
$598$	62.6872	−	4.02465i	2.56347	−	0.164580i
$599$	−29.3096	−	5.70805i	−1.19756	−	0.233225i	−0.447309	−	0.894379i	$-0.647618\pi$
$599$	−29.3096	−	5.70805i	−1.19756	−	0.233225i	−0.750250	+	0.661155i	$0.770067\pi$
$600$	15.5341	+	42.2112i	0.634177	+	1.72326i
$601$	12.3201	−	6.93854i	0.502547	−	0.283029i	−0.218596	−	0.975815i	$-0.570148\pi$
$601$	12.3201	−	6.93854i	0.502547	−	0.283029i	0.721143	+	0.692786i	$0.243617\pi$
$602$	−14.0661	+	47.3933i	−0.573290	+	1.93161i
$603$	12.0991	−	13.3225i	0.492715	−	0.542534i
$604$	1.38067	−	43.0544i	0.0561787	−	1.75186i
$605$	−12.8229			−0.521326
$606$	0.422196	−	13.1656i	0.0171506	−	0.534817i
$607$	−18.8218	−	4.93566i	−0.763954	−	0.200332i	−0.148938	−	0.988847i	$-0.547585\pi$
$607$	−18.8218	−	4.93566i	−0.763954	−	0.200332i	−0.615017	+	0.788514i	$0.710851\pi$
$608$	6.00744	+	5.81789i	0.243634	+	0.235946i
$609$	30.5182	+	102.826i	1.23666	+	4.16672i
$610$	18.6415	+	8.97728i	0.754773	+	0.363479i
$611$	−7.22902	+	3.48131i	−0.292455	+	0.140839i
$612$	11.8867	−	19.6084i	0.480492	−	0.792622i
$613$	−2.76114	+	7.50292i	−0.111522	+	0.303040i	−0.981917	−	0.189314i	$-0.939374\pi$
$613$	−2.76114	+	7.50292i	−0.111522	+	0.303040i	0.870395	+	0.492354i	$0.163863\pi$
$614$	1.91698	+	11.8572i	0.0773631	+	0.478518i
$615$	−4.46128	+	4.32051i	−0.179896	+	0.174220i
$616$	0.860705	−	1.94435i	0.0346788	−	0.0783400i
$617$	−1.93394	+	20.0473i	−0.0778576	+	0.807075i	0.870982	+	0.491315i	$0.163484\pi$
$617$	−1.93394	+	20.0473i	−0.0778576	+	0.807075i	−0.948839	+	0.315760i	$0.897741\pi$
$618$	−102.527	−	26.8857i	−4.12424	−	1.08150i
$619$	11.1292	+	0.714516i	0.447319	+	0.0287188i	0.286100	−	0.958200i	$-0.407641\pi$
$619$	11.1292	+	0.714516i	0.447319	+	0.0287188i	0.161219	+	0.986919i	$0.448457\pi$
$620$	21.1720	−	23.3127i	0.850287	−	0.936261i
$621$	1.56297	−	16.2018i	0.0627197	−	0.650156i
$622$	60.8514	−	24.6360i	2.43992	−	0.987814i
$623$	21.8978	+	7.27057i	0.877316	+	0.291289i
$624$	−22.8303	−	28.6283i	−0.913942	−	1.14605i
$625$	−4.33281	−	4.77090i	−0.173312	−	0.190836i
$626$	23.5643	−	17.5865i	0.941819	−	0.702898i
$627$	0.159910	+	0.700612i	0.00638619	+	0.0279797i
$628$	31.9070	−	8.36700i	1.27323	−	0.333880i
$629$	−14.1490	−	7.96857i	−0.564158	−	0.317728i
$630$	−24.6613	−	18.4052i	−0.982528	−	0.733280i
$631$	28.3544	−	11.4794i	1.12877	−	0.456989i	0.266702	−	0.963779i	$-0.414066\pi$
$631$	28.3544	−	11.4794i	1.12877	−	0.456989i	0.862069	+	0.506790i	$0.169168\pi$
$632$	−29.8611	−	28.9188i	−1.18781	−	1.15033i
$633$	−22.6783	+	32.5111i	−0.901382	+	1.29220i
$634$	−12.4015	+	41.7849i	−0.492528	+	1.65949i
$635$	3.64711	−	8.23888i	0.144731	−	0.326950i
$636$	−6.60818	−	4.93181i	−0.262031	−	0.195559i
$637$	5.41323	+	56.1138i	0.214480	+	2.22331i
$638$	−0.845020	−	1.61975i	−0.0334547	−	0.0641263i
$639$	15.8265	−	13.4733i	0.626087	−	0.532996i
$640$	−20.1005	+	2.59167i	−0.794543	+	0.102445i
$641$	18.4891	−	35.4401i	0.730276	−	1.39980i	−0.179102	−	0.983830i	$-0.557319\pi$
$641$	18.4891	−	35.4401i	0.730276	−	1.39980i	0.909378	−	0.415971i	$-0.136558\pi$
$642$	40.7817	−	7.94223i	1.60952	−	0.313455i
$643$	5.20330	−	32.1843i	0.205198	−	1.26922i	−0.653573	−	0.756864i	$-0.726731\pi$
$643$	5.20330	−	32.1843i	0.205198	−	1.26922i	0.858771	−	0.512360i	$-0.171229\pi$
$644$	16.4083	+	170.089i	0.646577	+	6.70245i
$645$	−9.91493	−	3.29198i	−0.390400	−	0.129622i
$646$	7.49906	+	25.2668i	0.295047	+	0.994110i
$647$	−0.986683	−	0.127219i	−0.0387905	−	0.00500148i	0.108457	−	0.994101i	$-0.465409\pi$
$647$	−0.986683	−	0.127219i	−0.0387905	−	0.00500148i	−0.147248	+	0.989100i	$0.547042\pi$
$648$	−51.7744	+	29.1588i	−2.03389	+	1.14547i
$649$	0.407905	−	0.395034i	0.0160117	−	0.0155064i
$650$	24.5256	+	13.8126i	0.961974	+	0.541774i
$651$	11.6466	−	72.0385i	0.456467	−	2.82341i
$652$	14.3249	+	20.5358i	0.561005	+	0.804243i
$653$	28.5101	−	9.46601i	1.11569	−	0.370434i	0.302916	−	0.953017i	$-0.402040\pi$
$653$	28.5101	−	9.46601i	1.11569	−	0.370434i	0.812771	+	0.582583i	$0.197958\pi$
$654$	−7.49607	−	16.9338i	−0.293120	−	0.662162i
$655$	16.5456	+	6.69858i	0.646491	+	0.261735i
$656$	−6.36116	−	10.4934i	−0.248361	−	0.409698i
$657$	−5.15723	−	7.39328i	−0.201203	−	0.288439i
$658$	−14.9082	−	28.5761i	−0.581180	−	1.11401i
$659$	3.46240	+	4.34171i	0.134876	+	0.169129i	0.844683	−	0.535268i	$-0.179789\pi$
$659$	3.46240	+	4.34171i	0.134876	+	0.169129i	−0.709807	+	0.704396i	$0.751218\pi$
$660$	0.773638	+	0.372565i	0.0301138	+	0.0145021i
$661$	−0.453215	+	0.295011i	−0.0176280	+	0.0114746i	−0.554319	−	0.832304i	$-0.687021\pi$
$661$	−0.453215	+	0.295011i	−0.0176280	+	0.0114746i	0.536691	+	0.843779i	$0.319674\pi$
$662$	22.0464	+	59.9072i	0.856858	+	2.32836i
$663$	−2.89935	−	17.9335i	−0.112601	−	0.696480i
$664$	60.4323	−	15.8472i	2.34523	−	0.614991i
$665$	23.5105	−	4.57868i	0.911700	−	0.177554i
$666$	−17.1305	−	28.2586i	−0.663795	−	1.09500i
$667$	64.3900	+	41.9132i	2.49319	+	1.62289i
$668$	7.41866	−	32.5033i	0.287037	−	1.25759i
$669$	19.9661	+	16.9974i	0.771933	+	0.657156i
$670$	20.7149	+	13.4839i	0.800287	+	0.520929i
$671$	−0.524839	+	0.174258i	−0.0202612	+	0.00672717i
$672$	17.6314	−	15.0098i	0.680145	−	0.579016i
$673$	2.40419	+	2.64728i	0.0926745	+	0.102045i	0.784855	−	0.619680i	$-0.212737\pi$
$673$	2.40419	+	2.64728i	0.0926745	+	0.102045i	−0.692180	+	0.721725i	$0.743350\pi$
$674$	16.0845	−	7.74589i	0.619552	−	0.298360i
$675$	4.54752	−	5.70241i	0.175034	−	0.219486i
$676$	13.7802	+	2.68369i	0.530007	+	0.103219i
$677$	5.77624	−	15.6959i	0.221999	−	0.603243i	−0.777678	−	0.628663i	$-0.783603\pi$
$677$	5.77624	−	15.6959i	0.221999	−	0.603243i	0.999677	+	0.0254200i	$0.00809230\pi$
$678$	−9.72833	−	42.6226i	−0.373614	−	1.63691i
$679$	18.2556	−	34.9926i	0.700587	−	1.34289i
$680$	15.2756	+	6.18442i	0.585794	+	0.237162i
$681$	−24.9369	−	21.2291i	−0.955583	−	0.813499i
$682$	0.0398384	+	1.24231i	0.00152549	+	0.0475704i
$683$	0.990817	+	30.8973i	0.0379126	+	1.18225i	0.824898	+	0.565282i	$0.191233\pi$
$683$	0.990817	+	30.8973i	0.0379126	+	1.18225i	−0.786985	+	0.616972i	$0.788359\pi$
$684$	−8.08212	+	35.4101i	−0.309027	+	1.35394i
$685$	10.1254	+	22.8735i	0.386873	+	0.873952i
$686$	−137.948	+	17.7864i	−5.26687	+	0.679087i
$687$	−2.19748	+	1.64002i	−0.0838390	+	0.0625706i
$688$	10.7007	−	17.6519i	0.407959	−	0.672971i
$689$	−2.69476	+	0.173009i	−0.102662	+	0.00659114i
$690$	−53.2152	+	3.41653i	−2.02587	+	0.130065i
$691$	19.7630	−	32.6012i	0.751821	−	1.24021i	−0.212936	−	0.977066i	$-0.568303\pi$
$691$	19.7630	−	32.6012i	0.751821	−	1.24021i	0.964757	−	0.263141i	$-0.0847585\pi$
$692$	−10.5718	+	7.88995i	−0.401880	+	0.299931i
$693$	0.815720	−	0.105175i	0.0309866	−	0.00399528i
$694$	−3.10606	−	7.01665i	−0.117905	−	0.266349i
$695$	0.236100	−	1.03442i	0.00895579	−	0.0392379i
$696$	−3.74669	−	116.836i	−0.142018	−	4.42864i
$697$	−0.195125	−	6.08472i	−0.00739089	−	0.230475i
$698$	1.12704	+	0.959464i	0.0426591	+	0.0363162i
$699$	−58.0815	−	23.5146i	−2.19684	−	0.889404i
$700$	−35.4165	+	67.8869i	−1.33862	+	2.56588i
$701$	−4.47352	−	19.5998i	−0.168963	−	0.740274i	−0.986414	−	0.164276i	$-0.947471\pi$
$701$	−4.47352	−	19.5998i	−0.168963	−	0.740274i	0.817452	−	0.575997i	$-0.195386\pi$
$702$	−5.35252	+	14.5445i	−0.202018	+	0.548948i
$703$	25.2474	+	4.91693i	0.952223	+	0.185445i
$704$	0.258358	−	0.323970i	0.00973722	−	0.0122101i
$705$	6.13671	−	2.95528i	0.231122	−	0.111302i
$706$	6.75510	+	7.43812i	0.254232	+	0.279937i
$707$	8.93528	−	7.60671i	0.336046	−	0.286080i
$708$	65.8932	−	21.8780i	2.47642	−	0.822227i
$709$	−37.5008	−	24.4103i	−1.40837	−	0.916748i	−0.999992	−	0.00393561i	$-0.998747\pi$
$709$	−37.5008	−	24.4103i	−1.40837	−	0.916748i	−0.408379	−	0.912812i	$-0.633906\pi$
$710$	21.7364	+	18.5045i	0.815752	+	0.694460i
$711$	3.57791	−	15.6759i	0.134182	−	0.587891i
$712$	−21.0747	−	13.7181i	−0.789809	−	0.514109i
$713$	−27.0969	−	44.6992i	−1.01479	−	1.67400i
$714$	71.6295	−	13.9498i	2.68067	−	0.522059i
$715$	0.272004	−	0.0713279i	0.0101724	−	0.00266751i
$716$	−2.92190	−	18.0730i	−0.109197	−	0.675420i
$717$	21.3885	+	58.1193i	0.798766	+	2.17051i
$718$	−11.8157	+	7.69116i	−0.440958	+	0.287032i
$719$	−8.84020	−	4.25722i	−0.329684	−	0.158767i	0.261718	−	0.965144i	$-0.415711\pi$
$719$	−8.84020	−	4.25722i	−0.329684	−	0.158767i	−0.591402	+	0.806377i	$0.701425\pi$
$720$	8.01108	+	10.0456i	0.298555	+	0.374376i
$721$	−43.6748	−	83.7163i	−1.62653	−	3.11776i
$722$	3.17227	+	4.54769i	0.118060	+	0.169248i
$723$	18.4619	+	30.4548i	0.686604	+	1.13262i
$724$	101.919	+	41.2625i	3.78779	+	1.53351i
$725$	13.9355	+	31.4805i	0.517551	+	1.16916i
$726$	58.7299	−	19.4997i	2.17967	−	0.723701i
$727$	22.1661	+	31.7768i	0.822097	+	1.17854i	0.981526	+	0.191328i	$0.0612795\pi$
$727$	22.1661	+	31.7768i	0.822097	+	1.17854i	−0.159429	+	0.987209i	$0.550965\pi$
$728$	13.5887	−	84.0511i	0.503632	−	3.11514i
$729$	−8.18074	−	4.60731i	−0.302990	−	0.170641i
$730$	8.89345	−	8.61283i	0.329161	−	0.318775i
$731$	8.92309	−	5.02539i	0.330033	−	0.185871i
$732$	−67.0625	−	8.64675i	−2.47870	−	0.319593i
$733$	−2.26644	−	7.63638i	−0.0837128	−	0.282056i	0.906381	−	0.422460i	$-0.138833\pi$
$733$	−2.26644	−	7.63638i	−0.0837128	−	0.282056i	−0.990094	+	0.140404i	$0.955160\pi$
$734$	−13.9757	−	4.64026i	−0.515853	−	0.171275i
$735$	−4.59529	−	47.6349i	−0.169500	−	1.75704i
$736$	2.64712	−	16.3734i	0.0975741	−	0.603530i
$737$	−0.648444	+	0.126285i	−0.0238858	+	0.00465175i
$738$	5.73027	−	10.9838i	0.210934	−	0.404321i
$739$	−29.5078	+	3.80461i	−1.08546	+	0.139955i	−0.649763	−	0.760137i	$-0.725132\pi$
$739$	−29.5078	+	3.80461i	−1.08546	+	0.139955i	−0.435700	+	0.900092i	$0.643499\pi$
$740$	23.4025	−	19.9228i	0.860293	−	0.732378i
$741$	13.3097	+	25.5121i	0.488943	+	0.937211i
$742$	−1.04159	−	10.7971i	−0.0382379	−	0.396376i
$743$	14.6732	+	10.9509i	0.538309	+	0.401751i	0.832524	−	0.553989i	$-0.186895\pi$
$743$	14.6732	+	10.9509i	0.538309	+	0.401751i	−0.294215	+	0.955739i	$0.595058\pi$
$744$	−32.1924	+	72.7233i	−1.18023	+	2.66616i
$745$	2.35593	−	7.93791i	0.0863146	−	0.290823i
$746$	10.6280	−	15.2360i	0.389118	−	0.557830i
$747$	17.3594	+	16.8117i	0.635148	+	0.615106i
$748$	−0.780206	+	0.315870i	−0.0285272	+	0.0115494i
$749$	29.6626	+	22.1378i	1.08385	+	0.808897i
$750$	−49.4215	−	27.8337i	−1.80462	−	1.01634i
$751$	32.8756	−	8.62099i	1.19965	−	0.314584i	0.400826	−	0.916154i	$-0.368723\pi$
$751$	32.8756	−	8.62099i	1.19965	−	0.314584i	0.798820	+	0.601570i	$0.205458\pi$
$752$	2.99468	+	13.1205i	0.109205	+	0.478457i
$753$	−34.2122	+	25.5332i	−1.24676	+	0.930483i
$754$	−49.1810	−	54.1538i	−1.79107	−	1.97216i
$755$	7.46646	+	9.36265i	0.271732	+	0.340742i
$756$	−40.0117	−	13.2848i	−1.45521	−	0.483163i
$757$	−45.2296	+	18.3114i	−1.64390	+	0.665540i	−0.995412	−	0.0956862i	$-0.969495\pi$
$757$	−45.2296	+	18.3114i	−1.64390	+	0.665540i	−0.648486	+	0.761227i	$0.724598\pi$
$758$	2.31885	−	24.0373i	0.0842243	−	0.873073i
$759$	0.958198	−	1.05508i	0.0347804	−	0.0382971i
$760$	−26.0505	−	1.67250i	−0.944952	−	0.0606679i
$761$	34.7560	+	9.11409i	1.25990	+	0.330385i	0.822440	−	0.568851i	$-0.192612\pi$
$761$	34.7560	+	9.11409i	1.25990	+	0.330385i	0.437462	+	0.899237i	$0.355877\pi$
$762$	−4.17524	+	43.2807i	−0.151253	+	1.56790i
$763$	6.67787	−	15.0854i	0.241755	−	0.546129i
$764$	−4.18281	+	4.05082i	−0.151329	+	0.146554i
$765$	1.01737	+	6.29282i	0.0367833	+	0.227517i
$766$	−4.00039	+	10.8704i	−0.144540	+	0.392762i
$767$	11.7868	−	19.4436i	0.425597	−	0.702067i
$768$	66.3600	−	31.9573i	2.39456	−	1.15316i
$769$	−42.6466	−	20.5375i	−1.53788	−	0.740602i	−0.542814	−	0.839853i	$-0.682641\pi$
$769$	−42.6466	−	20.5375i	−1.53788	−	0.740602i	−0.995062	+	0.0992507i	$0.968355\pi$
$770$	0.321402	+	1.08291i	0.0115825	+	0.0390253i
$771$	−23.6914	−	22.9438i	−0.853223	−	0.826301i
$772$	−74.7286	−	19.5962i	−2.68954	−	0.705281i
$773$	0.542116	−	16.9052i	0.0194986	−	0.608037i	−0.942377	−	0.334551i	$-0.891415\pi$
$773$	0.542116	−	16.9052i	0.0194986	−	0.608037i	0.961876	−	0.273486i	$-0.0881766\pi$
$774$	20.8402			0.749085
$775$	0.750726	−	23.4104i	0.0269669	−	0.840926i
$776$	−28.9186	+	31.8425i	−1.03812	+	1.14308i
$777$	20.2636	−	68.2749i	0.726953	−	2.44935i
$778$	−30.8280	+	17.3620i	−1.10524	+	0.622457i
$779$	3.33038	+	9.04971i	0.119323	+	0.324239i
$780$	33.7489	+	6.57259i	1.20840	+	0.235336i
$781$	−0.761409	+	0.0488841i	−0.0272454	+	0.00174921i
$782$	32.5911	−	40.8679i	1.16545	−	1.46143i
$783$	−15.8864	+	10.3409i	−0.567734	+	0.369554i
$784$	93.7801	+	12.0916i	3.34929	+	0.431843i
$785$	−5.24634	+	7.52103i	−0.187250	+	0.268437i
$786$	−85.9664	−	5.51923i	−3.06632	−	0.196864i
$787$	−5.82568			−0.207663			−0.103832	−	0.994595i	$-0.533110\pi$
$787$	−5.82568			−0.207663			−0.103832	+	0.994595i	$0.533110\pi$
$788$	56.8973	+	15.1788i	2.02688	+	0.540722i
$789$	1.58046			0.0562659
$790$	22.0378	+	1.41487i	0.784070	+	0.0503389i
$791$	22.2821	−	31.9431i	0.792260	−	1.13576i
$792$	−0.889006	−	0.114625i	−0.0315895	−	0.00407301i
$793$	−18.5583	+	12.0801i	−0.659025	+	0.428977i
$794$	−38.9821	+	48.8821i	−1.38342	+	1.73476i
$795$	2.28758	−	0.146868i	0.0811322	−	0.00520886i
$796$	−17.7508	−	3.45696i	−0.629159	−	0.122529i
$797$	18.3334	+	49.8178i	0.649402	+	1.76464i	0.644449	+	0.764648i	$0.277087\pi$
$797$	18.3334	+	49.8178i	0.649402	+	1.76464i	0.00495352	+	0.999988i	$0.498423\pi$
$798$	−100.717	+	56.7228i	−3.56535	+	2.00797i
$799$	−1.89972	+	6.40080i	−0.0672074	+	0.226444i
$800$	4.99660	−	5.50182i	0.176657	−	0.194519i
$801$	0.311753	−	9.72162i	0.0110153	−	0.343496i
$802$	25.7424			0.908995
$803$	−0.0106059	+	0.330730i	−0.000374273	+	0.0116712i
$804$	−78.1341	−	20.4892i	−2.75558	−	0.722598i
$805$	−34.1247	−	33.0479i	−1.20274	−	1.16479i
$806$	14.1609	+	47.7128i	0.498796	+	1.68061i
$807$	−6.30010	−	3.03397i	−0.221774	−	0.106801i
$808$	−11.5224	+	5.54889i	−0.405356	+	0.195209i
$809$	15.7621	−	26.0012i	0.554164	−	0.914152i	−0.445656	−	0.895204i	$-0.647030\pi$
$809$	15.7621	−	26.0012i	0.554164	−	0.914152i	0.999820	−	0.0189480i	$-0.00603169\pi$
$810$	10.9021	−	29.6244i	0.383059	−	1.04090i
$811$	6.63307	+	41.0279i	0.232918	+	1.44068i	0.791467	+	0.611211i	$0.209317\pi$
$811$	6.63307	+	41.0279i	0.232918	+	1.44068i	−0.558549	+	0.829471i	$0.688642\pi$
$812$	142.950	−	138.440i	5.01657	−	4.85828i
$813$	2.96728	−	6.70313i	0.104067	−	0.235089i
$814$	−0.116480	+	1.20744i	−0.00408263	+	0.0423208i
$815$	−6.73302	−	1.76560i	−0.235847	−	0.0618464i
$816$	−30.4078	−	1.95225i	−1.06449	−	0.0683423i
$817$	−10.9057	+	12.0084i	−0.381542	+	0.420120i
$818$	7.36902	−	76.3876i	0.257652	−	2.67083i
$819$	30.5265	−	12.3588i	1.06668	−	0.431851i
$820$	10.9353	+	3.63076i	0.381876	+	0.126792i
$821$	18.8780	+	23.6723i	0.658848	+	0.826170i	0.993217	−	0.116272i	$-0.0370946\pi$
$821$	18.8780	+	23.6723i	0.658848	+	0.826170i	−0.334369	+	0.942442i	$0.608523\pi$
$822$	−81.1586	−	89.3646i	−2.83073	−	3.11695i
$823$	44.5597	−	33.2557i	1.55325	−	1.15922i	0.629021	−	0.777389i	$-0.283456\pi$
$823$	44.5597	−	33.2557i	1.55325	−	1.15922i	0.924231	−	0.381833i	$-0.124707\pi$
$824$	22.8990	+	100.327i	0.797726	+	3.49507i
$825$	0.617762	−	0.161996i	0.0215077	−	0.00563998i
$826$	79.5832	+	44.8204i	2.76905	+	1.55950i
$827$	−27.8897	−	20.8146i	−0.969819	−	0.723794i	−0.00870908	−	0.999962i	$-0.502772\pi$
$827$	−27.8897	−	20.8146i	−0.969819	−	0.723794i	−0.961109	+	0.276168i	$0.910935\pi$
$828$	66.7700	−	27.0322i	2.32042	−	0.939434i
$829$	26.7267	+	25.8834i	0.928257	+	0.898967i	0.995108	−	0.0987962i	$-0.0314992\pi$
$829$	26.7267	+	25.8834i	0.928257	+	0.898967i	−0.0668507	+	0.997763i	$0.521295\pi$
$830$	−18.9883	+	27.2212i	−0.659094	+	0.944861i
$831$	−5.16723	+	17.4101i	−0.179249	+	0.603951i
$832$	6.71628	−	15.1722i	0.232845	−	0.526001i
$833$	37.5954	+	28.0581i	1.30260	+	0.972157i
$834$	0.491678	+	5.09676i	0.0170254	+	0.176486i
$835$	4.28694	+	8.21726i	0.148356	+	0.284370i
$836$	1.01522	−	0.864266i	0.0351120	−	0.0298913i
$837$	12.7905	−	1.64916i	0.442105	−	0.0570032i
$838$	−9.75671	+	18.7018i	−0.337040	+	0.646043i
$839$	−14.7659	+	2.87566i	−0.509776	+	0.0992789i	−0.439489	−	0.898248i	$-0.644840\pi$
$839$	−14.7659	+	2.87566i	−0.509776	+	0.0992789i	−0.0702869	+	0.997527i	$0.522391\pi$
$840$	−11.5355	+	71.3509i	−0.398011	+	2.46184i
$841$	−5.80676	−	60.1932i	−0.200233	−	2.07563i
$842$	−38.3388	−	12.7293i	−1.32124	−	0.438682i
$843$	7.85115	+	26.4531i	0.270408	+	0.911094i
$844$	72.9391	+	9.40445i	2.51067	+	0.323715i
$845$	−3.40064	+	1.91521i	−0.116986	+	0.0658851i
$846$	−9.76034	+	9.45236i	−0.335567	+	0.324979i
$847$	48.0340	+	27.0522i	1.65047	+	0.929526i
$848$	−0.722864	+	4.47117i	−0.0248232	+	0.153540i
$849$	1.29477	+	1.85616i	0.0444366	+	0.0637031i
$850$	22.2296	−	7.38073i	0.762469	−	0.253157i
$851$	−20.6495	−	46.6475i	−0.707855	−	1.59906i
$852$	−86.4725	−	35.0088i	−2.96250	−	1.19938i
$853$	9.03331	+	14.9014i	0.309295	+	0.510214i	0.970852	−	0.239681i	$-0.0770428\pi$
$853$	9.03331	+	14.9014i	0.309295	+	0.510214i	−0.661557	+	0.749895i	$0.730104\pi$
$854$	−50.8909	−	72.9559i	−1.74145	−	2.49650i
$855$	−4.67032	−	8.95213i	−0.159722	−	0.306157i
$856$	−25.1505	−	31.5377i	−0.859625	−	1.07794i
$857$	−6.38263	−	3.07371i	−0.218026	−	0.104996i	0.321683	−	0.946847i	$-0.395752\pi$
$857$	−6.38263	−	3.07371i	−0.218026	−	0.104996i	−0.539709	+	0.841852i	$0.681466\pi$
$858$	−1.13733	+	0.740320i	−0.0388278	+	0.0252741i
$859$	9.21496	+	25.0400i	0.314410	+	0.854355i	0.992814	+	0.119665i	$0.0381822\pi$
$859$	9.21496	+	25.0400i	0.314410	+	0.854355i	−0.678404	+	0.734689i	$0.737328\pi$
$860$	3.09346	+	19.1342i	0.105486	+	0.652470i
$861$	25.8266	−	6.77252i	0.880167	−	0.230807i
$862$	−12.8015	+	2.49309i	−0.436020	+	0.0849148i
$863$	2.75484	+	4.54439i	0.0937758	+	0.154693i	0.898526	−	0.438921i	$-0.144639\pi$
$863$	2.75484	+	4.54439i	0.0937758	+	0.154693i	−0.804750	+	0.593614i	$0.797701\pi$
$864$	3.42955	+	2.23239i	0.116676	+	0.0759475i
$865$	0.816034	−	3.57528i	0.0277460	−	0.121563i
$866$	−35.3981	−	30.1348i	−1.20287	−	1.02402i
$867$	19.5496	+	12.7254i	0.663940	+	0.432177i
$868$	−128.491	+	42.6620i	−4.36128	+	1.44804i
$869$	−0.449431	+	0.382606i	−0.0152459	+	0.0129790i
$870$	41.7497	+	45.9711i	1.41545	+	1.55857i
$871$	−23.8331	+	11.4774i	−0.807553	+	0.388897i
$872$	−11.2101	+	14.0570i	−0.379621	+	0.476029i
$873$	−16.3312	−	3.18051i	−0.552728	−	0.107644i
$874$	−28.5956	+	77.7034i	−0.967259	+	2.62836i
$875$	−11.2438	−	49.2624i	−0.380111	−	1.66537i
$876$	−18.7142	+	35.8716i	−0.632294	+	1.21199i
$877$	−28.6882	−	11.6146i	−0.968733	−	0.392196i	−0.164412	−	0.986392i	$-0.552573\pi$
$877$	−28.6882	−	11.6146i	−0.968733	−	0.392196i	−0.804321	+	0.594195i	$0.797471\pi$
$878$	51.8788	+	44.1650i	1.75082	+	1.49050i
$879$	0.582271	+	18.1574i	0.0196395	+	0.612432i
$880$	−0.0151174	−	0.471415i	−0.000509606	−	0.0158914i
$881$	−3.30430	+	14.4771i	−0.111325	+	0.487745i	0.888271	+	0.459319i	$0.151907\pi$
$881$	−3.30430	+	14.4771i	−0.111325	+	0.487745i	−0.999596	+	0.0284257i	$0.990951\pi$
$882$	38.6423	+	87.2937i	1.30116	+	2.93933i
$883$	−17.0781	+	2.20197i	−0.574723	+	0.0741024i	−0.409754	−	0.912196i	$-0.634385\pi$
$883$	−17.0781	+	2.20197i	−0.574723	+	0.0741024i	−0.164970	+	0.986299i	$0.552753\pi$
$884$	−27.0109	+	20.1588i	−0.908476	+	0.678013i
$885$	−10.0058	+	16.5056i	−0.336342	+	0.554831i
$886$	10.0651	−	0.646202i	0.338144	−	0.0217096i
$887$	29.6580	−	1.90411i	0.995818	−	0.0639336i	0.442383	−	0.896826i	$-0.354133\pi$
$887$	29.6580	−	1.90411i	0.995818	−	0.0639336i	0.553435	+	0.832893i	$0.313317\pi$
$888$	−40.2360	+	66.3735i	−1.35023	+	2.22735i
$889$	−31.0432	+	23.1682i	−1.04116	+	0.777035i
$890$	13.2490	−	1.70827i	0.444108	−	0.0572614i
$891$	0.341519	+	0.771498i	0.0114413	+	0.0258462i
$892$	10.8253	−	47.4287i	0.362457	−	1.58803i
$893$	−0.338974	−	10.5705i	−0.0113433	−	0.353727i
$894$	1.28076	+	39.9388i	0.0428350	+	1.33575i
$895$	3.87541	+	3.29918i	0.129541	+	0.110280i
$896$	80.7630	+	32.6973i	2.69810	+	1.09234i
$897$	26.3969	−	50.5980i	0.881368	−	1.68942i
$898$	8.86120	+	38.8234i	0.295702	+	1.29555i
$899$	−21.0233	+	57.1271i	−0.701167	+	1.90530i
$900$	31.6831	+	6.17029i	1.05610	+	0.205676i
$901$	−1.40101	+	1.75680i	−0.0466742	+	0.0585277i
$902$	−0.409734	+	0.197318i	−0.0136427	+	0.00656995i
$903$	30.1957	+	33.2489i	1.00485	+	1.10645i
$904$	−32.3202	+	27.5146i	−1.07495	+	0.915122i
$905$	−29.0102	+	9.63207i	−0.964333	+	0.320181i
$906$	−48.4345	−	31.5274i	−1.60913	−	1.04743i
$907$	−3.76120	−	3.20196i	−0.124889	−	0.106319i	0.583601	−	0.812041i	$-0.301643\pi$
$907$	−3.76120	−	3.20196i	−0.124889	−	0.106319i	−0.708489	+	0.705722i	$0.750623\pi$
$908$	−13.5204	+	59.2366i	−0.448689	+	1.96583i
$909$	−4.14583	−	2.69864i	−0.137509	−	0.0895082i
$910$	23.4475	+	38.6791i	0.777277	+	1.28220i
$911$	−17.5445	+	3.41679i	−0.581275	+	0.113203i	−0.473224	−	0.880942i	$-0.656910\pi$
$911$	−17.5445	+	3.41679i	−0.581275	+	0.113203i	−0.108051	+	0.994145i	$0.534461\pi$
$912$	46.6862	−	12.2426i	1.54593	−	0.405392i
$913$	−0.141578	−	0.875713i	−0.00468556	−	0.0289819i
$914$	11.2959	+	30.6946i	0.373636	+	1.01529i
$915$	15.7541	−	10.2548i	0.520816	−	0.339013i
$916$	4.58344	+	2.20727i	0.151441	+	0.0729303i
$917$	−47.8471	−	59.9983i	−1.58005	−	1.98132i
$918$	5.96519	+	11.4341i	0.196881	+	0.377383i
$919$	9.55379	+	13.6961i	0.315151	+	0.451792i	0.946025	−	0.324093i	$-0.105059\pi$
$919$	9.55379	+	13.6961i	0.315151	+	0.451792i	−0.630875	+	0.775885i	$0.717304\pi$
$920$	26.8383	+	44.2726i	0.884833	+	1.45962i
$921$	10.1149	+	4.09505i	0.333296	+	0.134937i
$922$	−9.68086	−	21.8692i	−0.318822	−	0.720225i
$923$	−28.9946	+	9.62688i	−0.954370	+	0.316873i
$924$	−2.11201	−	3.02773i	−0.0694802	−	0.0996050i
$925$	3.64829	−	22.5660i	0.119955	−	0.741965i
$926$	12.6927	+	7.14837i	0.417107	+	0.234910i
$927$	−28.5938	+	27.6915i	−0.939143	+	0.909509i
$928$	−16.8298	+	9.47837i	−0.552466	+	0.311143i
$929$	11.7358	+	1.51317i	0.385040	+	0.0496454i	0.317965	−	0.948103i	$-0.397001\pi$
$929$	11.7358	+	1.51317i	0.385040	+	0.0496454i	0.0670751	+	0.997748i	$0.478633\pi$
$930$	−12.0212	−	40.5034i	−0.394190	−	1.32816i
$931$	−70.5213	−	23.4147i	−2.31124	−	0.767385i
$932$	11.1632	+	115.718i	0.365661	+	3.79046i
$933$	9.51910	−	58.8790i	0.311641	−	1.92761i
$934$	64.4849	−	12.5584i	2.11001	−	0.410925i
$935$	0.108233	−	0.207463i	0.00353961	−	0.00678477i
$936$	−35.5975	+	4.58978i	−1.16354	+	0.150022i
$937$	−18.3527	+	15.6239i	−0.599557	+	0.510410i	−0.895656	−	0.444747i	$-0.853294\pi$
$937$	−18.3527	+	15.6239i	−0.599557	+	0.510410i	0.296099	+	0.955157i	$0.404314\pi$
$938$	−49.1502	−	94.2117i	−1.60481	−	3.07612i
$939$	−2.56512	−	26.5901i	−0.0837094	−	0.867735i
$940$	−10.1274	−	7.55826i	−0.330319	−	0.246523i
$941$	−12.4978	+	28.2328i	−0.407418	+	0.920363i	0.586470	+	0.809971i	$0.300517\pi$
$941$	−12.4978	+	28.2328i	−0.407418	+	0.920363i	−0.993888	+	0.110393i	$0.964789\pi$
$942$	12.5915	−	42.4249i	0.410252	−	1.38228i
$943$	10.9417	−	15.6858i	0.356312	−	0.510800i
$944$	−27.3958	−	26.5313i	−0.891656	−	0.863521i
$945$	10.8638	−	4.39826i	0.353399	−	0.143075i
$946$	−0.613089	−	0.457560i	−0.0199332	−	0.0148766i
$947$	8.97561	+	5.05497i	0.291668	+	0.164264i	0.629630	−	0.776896i	$-0.283207\pi$
$947$	8.97561	+	5.05497i	0.291668	+	0.164264i	−0.337961	+	0.941160i	$0.609737\pi$
$948$	−69.8086	+	18.3060i	−2.26728	+	0.594550i
$949$	2.94837	+	12.9177i	0.0957083	+	0.419325i
$950$	−29.7336	+	22.1908i	−0.964685	+	0.719963i
$951$	26.6225	+	29.3143i	0.863293	+	0.950582i
$952$	−44.1746	−	55.3932i	−1.43171	−	1.79530i
$953$	6.28077	+	2.08536i	0.203454	+	0.0675514i	0.415020	−	0.909812i	$-0.363775\pi$
$953$	6.28077	+	2.08536i	0.203454	+	0.0675514i	−0.211566	+	0.977364i	$0.567856\pi$
$954$	−4.23852	+	1.71599i	−0.137227	+	0.0555571i
$955$	0.155436	−	1.61126i	0.00502980	−	0.0521392i
$956$	77.2466	−	85.0570i	2.49833	−	2.75094i
$957$	−1.65638	−	0.106343i	−0.0535431	−	0.00343758i
$958$	23.0522	+	6.04499i	0.744781	+	0.195305i
$959$	10.3264	−	107.044i	0.333458	−	3.45664i
$960$	−5.70145	+	12.8797i	−0.184014	+	0.415690i
$961$	7.48145	−	7.24538i	0.241337	−	0.233722i
$962$	7.75219	+	47.9500i	0.249941	+	1.54597i
$963$	5.38870	−	14.6428i	0.173649	−	0.471859i
$964$	34.2523	−	56.5028i	1.10319	−	1.81983i
$965$	19.3501	−	9.31851i	0.622901	−	0.299973i
$966$	206.549	+	99.4686i	6.64560	+	3.20035i
$967$	−12.4202	−	41.8477i	−0.399406	−	1.34573i	−0.882562	−	0.470196i	$-0.844183\pi$
$967$	−12.4202	−	41.8477i	−0.399406	−	1.34573i	0.483156	−	0.875534i	$-0.339490\pi$
$968$	−43.1590	−	41.7971i	−1.38718	−	1.34341i
$969$	23.1619	+	6.07378i	0.744069	+	0.195118i
$970$	0.732410	−	22.8392i	0.0235163	−	0.733324i
$971$	19.9119			0.639002			0.319501	−	0.947586i	$-0.396485\pi$
$971$	19.9119			0.639002			0.319501	+	0.947586i	$0.396485\pi$
$972$	−2.49805	+	77.8985i	−0.0801251	+	2.49860i
$973$	−3.06671	+	3.37679i	−0.0983143	+	0.108255i
$974$	30.6737	−	103.350i	0.982848	−	3.31154i
$975$	22.2820	−	12.5490i	0.713594	−	0.401889i
$976$	12.8274	+	34.8561i	0.410594	+	1.11572i
$977$	6.18209	+	1.20396i	0.197782	+	0.0385181i	0.289077	−	0.957306i	$-0.406652\pi$
$977$	6.18209	+	1.20396i	0.197782	+	0.0385181i	−0.0912948	+	0.995824i	$0.529101\pi$
$978$	33.5226	−	2.15222i	1.07193	−	0.0688205i
$979$	−0.222616	+	0.279152i	−0.00711483	+	0.00892172i
$980$	−74.4117	+	48.4367i	−2.37700	+	1.54725i
$981$	−6.89744	−	0.889326i	−0.220218	−	0.0283940i
$982$	12.1019	−	17.3490i	0.386187	−	0.553628i
$983$	46.5159	+	2.98642i	1.48363	+	0.0952520i	0.784671	−	0.619912i	$-0.212832\pi$
$983$	46.5159	+	2.98642i	1.48363	+	0.0952520i	0.698956	+	0.715164i	$0.253648\pi$
$984$	−29.0985			−0.927628
$985$	−14.7795	+	7.04025i	−0.470913	+	0.224321i
$986$	−60.8738			−1.93862
$987$	−29.2224	−	1.87614i	−0.930161	−	0.0597183i
$988$	30.5435	−	43.7864i	0.971717	−	1.39303i
$989$	31.9077	+	4.11405i	1.01461	+	0.130819i
$990$	0.399086	−	0.259776i	0.0126838	−	0.00825623i
$991$	15.5189	−	19.4601i	0.492975	−	0.618171i	−0.471654	−	0.881784i	$-0.656343\pi$
$991$	15.5189	−	19.4601i	0.492975	−	0.618171i	0.964629	+	0.263613i	$0.0849141\pi$
$992$	13.1142	−	0.841959i	0.416376	−	0.0267322i
$993$	56.9259	+	11.0863i	1.80649	+	0.351814i
$994$	−42.3849	−	115.173i	−1.34437	−	3.65308i
$995$	4.38049	−	2.46705i	0.138871	−	0.0782106i
$996$	30.8613	−	103.982i	0.977879	−	3.29480i
$997$	−6.81262	+	7.50145i	−0.215758	+	0.237573i	−0.838564	−	0.544803i	$-0.816605\pi$
$997$	−6.81262	+	7.50145i	−0.215758	+	0.237573i	0.622807	+	0.782376i	$0.285992\pi$
$998$	−0.00158423	+	0.0494020i	−5.01478e−5	+	0.00156379i
$999$	12.5862			0.398209

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.2.g.a.16.1	✓	630
197.37	even	49	inner	197.2.g.a.37.1	yes	630

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.2.g.a.16.1	✓	630	1.1	even	1	trivial
197.2.g.a.37.1	yes	630	197.37	even	49	inner

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:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	197.g (of order \(49\), degree \(42\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.48397 - 0.159476i) q^{2} +(-1.29377 + 1.85472i) q^{3} +(4.16109 + 0.536513i) q^{4} +(-0.977512 + 0.636290i) q^{5} +(3.50947 - 4.40074i) q^{6} +(5.00407 - 0.321272i) q^{7} +(-5.36410 - 1.04466i) q^{8} +(-0.730042 - 1.98376i) q^{9} +(2.52958 - 1.42464i) q^{10} +(-0.0220780 + 0.0743880i) q^{11} +(-6.37859 + 7.02353i) q^{12} +(-0.0995861 + 3.10546i) q^{13} -12.4812 q^{14} +(0.0845386 - 2.63622i) q^{15} +(5.04102 + 1.32191i) q^{16} +(1.85730 + 1.79869i) q^{17} +(1.49704 + 5.04403i) q^{18} +(-3.68983 - 1.77693i) q^{19} +(-4.40890 + 2.12321i) q^{20} +(-5.87826 + 9.69680i) q^{21} +(0.0667041 - 0.181257i) q^{22} +(1.29633 + 8.01827i) q^{23} +(8.87747 - 8.59735i) q^{24} +(-1.47325 + 3.32810i) q^{25} +(0.742616 - 7.69799i) q^{26} +(-1.93843 - 0.508316i) q^{27} +(20.9948 + 1.34791i) q^{28} +(6.35929 - 7.00229i) q^{29} +(-0.630406 + 6.53482i) q^{30} +(-5.96511 + 2.41501i) q^{31} +(-1.93798 - 0.643453i) q^{32} +(-0.109405 - 0.137190i) q^{33} +(-4.32662 - 4.76409i) q^{34} +(-4.68712 + 3.49809i) q^{35} +(-1.97346 - 8.64629i) q^{36} +(-6.07522 + 1.59311i) q^{37} +(8.88206 + 5.00228i) q^{38} +(-5.63092 - 4.20246i) q^{39} +(5.90818 - 2.39196i) q^{40} +(-1.69143 - 1.63806i) q^{41} +(16.1478 - 23.1491i) q^{42} +(1.12698 - 3.79717i) q^{43} +(-0.131779 + 0.297690i) q^{44} +(1.97587 + 1.47463i) q^{45} +(-1.94133 - 20.1239i) q^{46} +(1.19445 + 2.28954i) q^{47} +(-8.97370 + 7.63942i) q^{48} +(17.9950 - 2.32020i) q^{49} +(4.19026 - 8.03195i) q^{50} +(-5.73899 + 1.11767i) q^{51} +(-2.08051 + 12.8687i) q^{52} +(0.0834526 + 0.865073i) q^{53} +(4.73393 + 1.57177i) q^{54} +(-0.0257509 - 0.0867632i) q^{55} +(-27.1780 - 3.50421i) q^{56} +(8.06951 - 4.54466i) q^{57} +(-16.9130 + 16.3793i) q^{58} +(-6.37625 - 3.59104i) q^{59} +(1.76614 - 10.9242i) q^{60} +(4.07740 + 5.84527i) q^{61} +(15.2023 - 5.04751i) q^{62} +(-4.29051 - 9.69234i) q^{63} +(-4.94992 - 2.00400i) q^{64} +(-1.87863 - 3.09899i) q^{65} +(0.249880 + 0.358222i) q^{66} +(3.93794 + 7.54829i) q^{67} +(6.76337 + 8.48099i) q^{68} +(-16.5488 - 7.96948i) q^{69} +(12.2005 - 7.94166i) q^{70} +(3.39590 + 9.22776i) q^{71} +(1.84367 + 11.4037i) q^{72} +(4.12498 - 1.08170i) q^{73} +(15.3447 - 2.98838i) q^{74} +(-4.26664 - 7.03827i) q^{75} +(-14.4004 - 9.37362i) q^{76} +(-0.0865810 + 0.379336i) q^{77} +(13.3168 + 11.3368i) q^{78} +(6.37498 + 4.14965i) q^{79} +(-5.76878 + 1.91537i) q^{80} +(8.27937 - 7.04833i) q^{81} +(3.94023 + 4.33863i) q^{82} +(-10.3001 + 4.96024i) q^{83} +(-29.6624 + 37.1955i) q^{84} +(-2.96002 - 0.576464i) q^{85} +(-3.40495 + 9.25234i) q^{86} +(4.75980 + 20.8541i) q^{87} +(0.196139 - 0.375961i) q^{88} +(4.26513 + 1.72676i) q^{89} +(-4.67284 - 3.97805i) q^{90} +(0.499362 + 15.5719i) q^{91} +(1.09225 + 34.0603i) q^{92} +(3.23833 - 14.1881i) q^{93} +(-2.60185 - 5.87762i) q^{94} +(4.73750 - 0.610833i) q^{95} +(3.70073 - 2.76192i) q^{96} +(4.08029 - 6.73087i) q^{97} +(-45.0690 + 2.89353i) q^{98} +(0.163686 - 0.0105090i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 630 q - 42 q^{2} - 42 q^{3} - 28 q^{4} - 42 q^{5} - 21 q^{6} - 28 q^{7} - 28 q^{8} - 42 q^{9} - 28 q^{10} - 28 q^{11} - 28 q^{12} - 42 q^{13} - 28 q^{14} - 154 q^{15} - 42 q^{17} - 21 q^{18} - 7 q^{19}+ \cdots - 161 q^{99}+O(q^{100}) \) 630 * q - 42 * q^2 - 42 * q^3 - 28 * q^4 - 42 * q^5 - 21 * q^6 - 28 * q^7 - 28 * q^8 - 42 * q^9 - 28 * q^10 - 28 * q^11 - 28 * q^12 - 42 * q^13 - 28 * q^14 - 154 * q^15 - 42 * q^17 - 21 * q^18 - 7 * q^19 - 35 * q^20 - 42 * q^21 - 42 * q^23 + 28 * q^24 - 42 * q^25 - 7 * q^26 + 42 * q^27 - 49 * q^28 - 182 * q^29 + 77 * q^30 - 14 * q^31 - 28 * q^32 + 35 * q^33 - 14 * q^34 - 42 * q^35 + 84 * q^36 + 14 * q^37 - 28 * q^38 - 21 * q^39 + 28 * q^40 - 28 * q^41 - 112 * q^42 - 56 * q^43 - 210 * q^44 + 49 * q^45 - 7 * q^47 + 42 * q^48 + 42 * q^49 + 98 * q^50 - 14 * q^51 + 49 * q^52 - 42 * q^53 + 63 * q^54 - 161 * q^56 - 175 * q^57 - 42 * q^58 + 42 * q^59 + 126 * q^60 - 14 * q^61 + 42 * q^62 + 49 * q^63 + 98 * q^64 + 56 * q^65 + 175 * q^66 + 28 * q^67 + 273 * q^68 - 7 * q^69 - 252 * q^70 - 77 * q^71 - 364 * q^72 - 28 * q^73 + 35 * q^74 + 7 * q^75 + 133 * q^76 + 21 * q^77 + 210 * q^78 + 42 * q^79 - 14 * q^80 - 14 * q^81 - 42 * q^82 + 161 * q^83 - 245 * q^84 - 266 * q^85 - 147 * q^86 - 35 * q^87 + 77 * q^88 + 28 * q^89 + 315 * q^90 + 154 * q^91 + 84 * q^92 - 7 * q^93 + 182 * q^94 + 126 * q^95 + 245 * q^96 + 42 * q^97 - 308 * q^98 - 161 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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