LMFDB - Embedded newform 196.2.j.a.111.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [196,2,Mod(27,196)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("196.27"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(196, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([7, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	196.j (of order $14$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.56506787962$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			111.24
Character	$\chi$	$=$	196.111
Dual form			196.2.j.a.83.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.32010 + 0.507284i) q^{2} +(-1.45168 - 1.82035i) q^{3} +(1.48533 + 1.33933i) q^{4} +(1.13412 - 0.904431i) q^{5} +(-0.992928 - 3.13945i) q^{6} +(-0.147062 - 2.64166i) q^{7} +(1.28136 + 2.52153i) q^{8} +(-0.538730 + 2.36033i) q^{9} +(1.95596 - 0.618618i) q^{10} +(-0.655703 + 0.149660i) q^{11} +(0.281829 - 4.64809i) q^{12} +(1.04204 - 0.237840i) q^{13} +(1.14594 - 3.56186i) q^{14} +(-3.29276 - 0.751550i) q^{15} +(0.412390 + 3.97869i) q^{16} +(-0.527427 + 1.09521i) q^{17} +(-1.90853 + 2.84258i) q^{18} +3.97680 q^{19} +(2.89587 + 0.175587i) q^{20} +(-4.59525 + 4.10254i) q^{21} +(-0.941513 - 0.135061i) q^{22} +(2.80013 + 5.81454i) q^{23} +(2.72994 - 5.99297i) q^{24} +(-0.644370 + 2.82317i) q^{25} +(1.49625 + 0.214640i) q^{26} +(-1.21452 + 0.584884i) q^{27} +(3.31962 - 4.12069i) q^{28} +(-7.01088 - 3.37626i) q^{29} +(-3.96552 - 2.66248i) q^{30} -9.48293 q^{31} +(-1.47393 + 5.46146i) q^{32} +(1.22430 + 0.976349i) q^{33} +(-1.25184 + 1.17823i) q^{34} +(-2.55599 - 2.86296i) q^{35} +(-3.96145 + 2.78432i) q^{36} +(3.82889 + 1.84390i) q^{37} +(5.24978 + 2.01737i) q^{38} +(-1.94566 - 1.55161i) q^{39} +(3.73377 + 1.70082i) q^{40} +(-0.0397106 + 0.0316681i) q^{41} +(-8.14735 + 3.08467i) q^{42} +(1.03558 + 0.825848i) q^{43} +(-1.17438 - 0.655909i) q^{44} +(1.52377 + 3.16414i) q^{45} +(0.746836 + 9.09624i) q^{46} +(2.66423 + 11.6727i) q^{47} +(6.64393 - 6.52646i) q^{48} +(-6.95675 + 0.776975i) q^{49} +(-2.28278 + 3.39999i) q^{50} +(2.75932 - 0.629797i) q^{51} +(1.86632 + 1.04237i) q^{52} +(12.3270 - 5.93639i) q^{53} +(-1.90000 + 0.155997i) q^{54} +(-0.608289 + 0.762771i) q^{55} +(6.47259 - 3.75574i) q^{56} +(-5.77304 - 7.23916i) q^{57} +(-7.54234 - 8.01351i) q^{58} +(0.840007 - 1.05334i) q^{59} +(-3.88424 - 5.52639i) q^{60} +(3.30426 - 6.86136i) q^{61} +(-12.5184 - 4.81053i) q^{62} +(6.31442 + 1.07603i) q^{63} +(-4.71624 + 6.46197i) q^{64} +(0.966693 - 1.21220i) q^{65} +(1.12092 + 1.90995i) q^{66} -9.72058i q^{67} +(-2.25025 + 0.920350i) q^{68} +(6.51958 - 13.5381i) q^{69} +(-1.92183 - 5.07600i) q^{70} +(1.46244 + 3.03678i) q^{71} +(-6.64195 + 1.66601i) q^{72} +(-1.66705 - 0.380492i) q^{73} +(4.11914 + 4.37646i) q^{74} +(6.07457 - 2.92536i) q^{75} +(5.90685 + 5.32625i) q^{76} +(0.491780 + 1.71014i) q^{77} +(-1.78136 - 3.03529i) q^{78} -11.0108i q^{79} +(4.06615 + 4.13933i) q^{80} +(9.37161 + 4.51313i) q^{81} +(-0.0684866 + 0.0216605i) q^{82} +(0.0444993 - 0.194964i) q^{83} +(-12.3201 - 0.0609416i) q^{84} +(0.392379 + 1.71912i) q^{85} +(0.948130 + 1.61553i) q^{86} +(4.03158 + 17.6635i) q^{87} +(-1.21756 - 1.46161i) q^{88} +(-14.2293 - 3.24775i) q^{89} +(0.406412 + 4.94997i) q^{90} +(-0.781536 - 2.71775i) q^{91} +(-3.62847 + 12.3868i) q^{92} +(13.7662 + 17.2622i) q^{93} +(-2.40435 + 16.7607i) q^{94} +(4.51018 - 3.59674i) q^{95} +(12.0814 - 5.24522i) q^{96} -14.5971i q^{97} +(-9.57774 - 2.50336i) q^{98} -1.62830i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 11 q^{8} - 32 q^{9} - 7 q^{10} - 42 q^{12} - 14 q^{13} + 21 q^{14} - 13 q^{16} - 14 q^{17} - 12 q^{18} - 7 q^{20} - 14 q^{21} + 3 q^{22} + 35 q^{24} - 7 q^{26}+ \cdots + 105 q^{98}+O(q^{100}) $ 156 * q - 5 * q^2 - 5 * q^4 - 14 * q^5 - 7 * q^6 - 11 * q^8 - 32 * q^9 - 7 * q^10 - 42 * q^12 - 14 * q^13 + 21 * q^14 - 13 * q^16 - 14 * q^17 - 12 * q^18 - 7 * q^20 - 14 * q^21 + 3 * q^22 + 35 * q^24 - 7 * q^26 + 42 * q^28 - 30 * q^29 - 4 * q^30 - 5 * q^32 - 14 * q^33 + 77 * q^34 - 11 * q^36 + 10 * q^37 - 21 * q^38 - 63 * q^40 - 14 * q^41 - 7 * q^42 - 55 * q^44 - 14 * q^45 - 19 * q^46 - 132 * q^50 - 7 * q^52 - 2 * q^53 + 14 * q^54 - 70 * q^56 - 64 * q^57 - 3 * q^58 - 107 * q^60 + 14 * q^61 - 21 * q^62 - 11 * q^64 - 22 * q^65 + 161 * q^66 - 70 * q^69 - 77 * q^70 + 114 * q^72 - 14 * q^73 + 5 * q^74 + 70 * q^76 - 42 * q^77 + 61 * q^78 + 92 * q^81 - 42 * q^82 + 70 * q^84 - 6 * q^85 + 47 * q^86 + 65 * q^88 - 14 * q^89 + 112 * q^90 - 70 * q^92 - 48 * q^93 - 28 * q^94 + 238 * q^96 + 105 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$e\left(\frac{11}{14}\right)$

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 $

$2$	1.32010	+	0.507284i	0.933451	+	0.358704i
$2$	1.32010	+	0.507284i	0.933451	+	0.358704i
$3$	−1.45168	−	1.82035i	−0.838127	−	1.05098i	−0.997961	−	0.0638337i	$-0.979667\pi$
$3$	−1.45168	−	1.82035i	−0.838127	−	1.05098i	0.159834	−	0.987144i	$-0.448904\pi$
$4$	1.48533	+	1.33933i	0.742663	+	0.669665i
$5$	1.13412	−	0.904431i	0.507194	−	0.404474i	−0.336182	−	0.941797i	$-0.609136\pi$
$5$	1.13412	−	0.904431i	0.507194	−	0.404474i	0.843377	+	0.537323i	$0.180564\pi$
$6$	−0.992928	−	3.13945i	−0.405361	−	1.28168i
$7$	−0.147062	−	2.64166i	−0.0555841	−	0.998454i
$7$	−0.147062	−	2.64166i	−0.0555841	−	0.998454i
$8$	1.28136	+	2.52153i	0.453029	+	0.891496i
$9$	−0.538730	+	2.36033i	−0.179577	+	0.786777i
$10$	1.95596	−	0.618618i	0.618528	−	0.195624i
$11$	−0.655703	+	0.149660i	−0.197702	+	0.0451242i	−0.320225	−	0.947341i	$-0.603759\pi$
$11$	−0.655703	+	0.149660i	−0.197702	+	0.0451242i	0.122523	+	0.992466i	$0.460901\pi$
$12$	0.281829	−	4.64809i	0.0813571	−	1.34179i
$13$	1.04204	−	0.237840i	0.289011	−	0.0659648i	−0.0755576	−	0.997141i	$-0.524074\pi$
$13$	1.04204	−	0.237840i	0.289011	−	0.0659648i	0.364568	+	0.931177i	$0.381217\pi$
$14$	1.14594	−	3.56186i	0.306264	−	0.951947i
$15$	−3.29276	−	0.751550i	−0.850186	−	0.194049i
$16$	0.412390	+	3.97869i	0.103097	+	0.994671i
$17$	−0.527427	+	1.09521i	−0.127920	+	0.265628i	−0.955086	−	0.296330i	$-0.904237\pi$
$17$	−0.527427	+	1.09521i	−0.127920	+	0.265628i	0.827166	+	0.561958i	$0.189952\pi$
$18$	−1.90853	+	2.84258i	−0.449846	+	0.670003i
$19$	3.97680			0.912341			0.456171	−	0.889892i	$-0.349221\pi$
$19$	3.97680			0.912341			0.456171	+	0.889892i	$0.349221\pi$
$20$	2.89587	+	0.175587i	0.647537	+	0.0392623i
$21$	−4.59525	+	4.10254i	−1.00277	+	0.895249i
$22$	−0.941513	−	0.135061i	−0.200731	−	0.0287952i
$23$	2.80013	+	5.81454i	0.583868	+	1.21242i	0.958460	+	0.285226i	$0.0920685\pi$
$23$	2.80013	+	5.81454i	0.583868	+	1.21242i	−0.374592	+	0.927190i	$0.622217\pi$
$24$	2.72994	−	5.99297i	0.557247	−	1.22331i
$25$	−0.644370	+	2.82317i	−0.128874	+	0.564634i
$26$	1.49625	+	0.214640i	0.293439	+	0.0420943i
$27$	−1.21452	+	0.584884i	−0.233735	+	0.112561i
$28$	3.31962	−	4.12069i	0.627349	−	0.778738i
$29$	−7.01088	−	3.37626i	−1.30189	−	0.626956i	−0.350967	−	0.936388i	$-0.614147\pi$
$29$	−7.01088	−	3.37626i	−1.30189	−	0.626956i	−0.950922	+	0.309431i	$0.899861\pi$
$30$	−3.96552	−	2.66248i	−0.724001	−	0.486101i
$31$	−9.48293			−1.70318			−0.851592	−	0.524205i	$-0.824363\pi$
$31$	−9.48293			−1.70318			−0.851592	+	0.524205i	$0.824363\pi$
$32$	−1.47393	+	5.46146i	−0.260556	+	0.965459i
$33$	1.22430	+	0.976349i	0.213124	+	0.169961i
$34$	−1.25184	+	1.17823i	−0.214689	+	0.202066i
$35$	−2.55599	−	2.86296i	−0.432041	−	0.483928i
$36$	−3.96145	+	2.78432i	−0.660242	+	0.464054i
$37$	3.82889	+	1.84390i	0.629465	+	0.303135i	0.721282	−	0.692641i	$-0.243553\pi$
$37$	3.82889	+	1.84390i	0.629465	+	0.303135i	−0.0918168	+	0.995776i	$0.529267\pi$
$38$	5.24978	+	2.01737i	0.851626	+	0.327260i
$39$	−1.94566	−	1.55161i	−0.311555	−	0.248457i
$40$	3.73377	+	1.70082i	0.590360	+	0.268923i
$41$	−0.0397106	+	0.0316681i	−0.00620175	+	0.00494573i	−0.626586	−	0.779352i	$-0.715548\pi$
$41$	−0.0397106	+	0.0316681i	−0.00620175	+	0.00494573i	0.620384	+	0.784298i	$0.286977\pi$
$42$	−8.14735	+	3.08467i	−1.25716	+	0.475975i
$43$	1.03558	+	0.825848i	0.157925	+	0.125941i	0.699264	−	0.714863i	$-0.253511\pi$
$43$	1.03558	+	0.825848i	0.157925	+	0.125941i	−0.541339	+	0.840804i	$0.682083\pi$
$44$	−1.17438	−	0.655909i	−0.177044	−	0.0988820i
$45$	1.52377	+	3.16414i	0.227150	+	0.471683i
$46$	0.746836	+	9.09624i	0.110115	+	1.34117i
$47$	2.66423	+	11.6727i	0.388617	+	1.70264i	0.669425	+	0.742880i	$0.266541\pi$
$47$	2.66423	+	11.6727i	0.388617	+	1.70264i	−0.280808	+	0.959764i	$0.590602\pi$
$48$	6.64393	−	6.52646i	0.958969	−	0.942014i
$49$	−6.95675	+	0.776975i	−0.993821	+	0.110996i
$50$	−2.28278	+	3.39999i	−0.322834	+	0.480831i
$51$	2.75932	−	0.629797i	0.386382	−	0.0881892i
$52$	1.86632	+	1.04237i	0.258812	+	0.144551i
$53$	12.3270	−	5.93639i	1.69325	−	0.815426i	0.698215	−	0.715888i	$-0.253978\pi$
$53$	12.3270	−	5.93639i	1.69325	−	0.815426i	0.995034	−	0.0995380i	$-0.0317365\pi$
$54$	−1.90000	+	0.155997i	−0.258557	+	0.0212285i
$55$	−0.608289	+	0.762771i	−0.0820217	+	0.102852i
$56$	6.47259	−	3.75574i	0.864936	−	0.501881i
$57$	−5.77304	−	7.23916i	−0.764657	−	0.958850i
$58$	−7.54234	−	8.01351i	−0.990358	−	1.05223i
$59$	0.840007	−	1.05334i	0.109360	−	0.137133i	−0.724139	−	0.689654i	$-0.757763\pi$
$59$	0.840007	−	1.05334i	0.109360	−	0.137133i	0.833499	+	0.552521i	$0.186334\pi$
$60$	−3.88424	−	5.52639i	−0.501454	−	0.713453i
$61$	3.30426	−	6.86136i	0.423067	−	0.878507i	−0.575106	−	0.818079i	$-0.695039\pi$
$61$	3.30426	−	6.86136i	0.423067	−	0.878507i	0.998173	−	0.0604280i	$-0.0192466\pi$
$62$	−12.5184	−	4.81053i	−1.58984	−	0.610939i
$63$	6.31442	+	1.07603i	0.795542	+	0.135567i
$64$	−4.71624	+	6.46197i	−0.589530	+	0.807747i
$65$	0.966693	−	1.21220i	0.119904	−	0.150354i
$66$	1.12092	+	1.90995i	0.137975	+	0.235098i
$67$		−	9.72058i		−	1.18756i	−0.804628	−	0.593779i	$-0.797635\pi$
$67$		−	9.72058i		−	1.18756i	0.804628	−	0.593779i	$-0.202365\pi$
$68$	−2.25025	+	0.920350i	−0.272883	+	0.111609i
$69$	6.51958	−	13.5381i	0.784866	−	1.62979i
$70$	−1.92183	−	5.07600i	−0.229702	−	0.606698i
$71$	1.46244	+	3.03678i	0.173559	+	0.360400i	0.969544	−	0.244917i	$-0.0787607\pi$
$71$	1.46244	+	3.03678i	0.173559	+	0.360400i	−0.795985	+	0.605317i	$0.793046\pi$
$72$	−6.64195	+	1.66601i	−0.782762	+	0.196341i
$73$	−1.66705	−	0.380492i	−0.195113	−	0.0445333i	0.123848	−	0.992301i	$-0.460477\pi$
$73$	−1.66705	−	0.380492i	−0.195113	−	0.0445333i	−0.318961	+	0.947768i	$0.603334\pi$
$74$	4.11914	+	4.37646i	0.478840	+	0.508753i
$75$	6.07457	−	2.92536i	0.701431	−	0.337791i
$76$	5.90685	+	5.32625i	0.677562	+	0.610963i
$77$	0.491780	+	1.71014i	0.0560435	+	0.194888i
$78$	−1.78136	−	3.03529i	−0.201699	−	0.343679i
$79$		−	11.0108i		−	1.23881i	−0.785072	−	0.619404i	$-0.787374\pi$
$79$		−	11.0108i		−	1.23881i	0.785072	−	0.619404i	$-0.212626\pi$
$80$	4.06615	+	4.13933i	0.454609	+	0.462791i
$81$	9.37161	+	4.51313i	1.04129	+	0.501459i
$82$	−0.0684866	+	0.0216605i	−0.00756308	+	0.00239201i
$83$	0.0444993	−	0.194964i	0.00488444	−	0.0214001i	−0.972427	−	0.233208i	$-0.925078\pi$
$83$	0.0444993	−	0.194964i	0.00488444	−	0.0214001i	0.977311	+	0.211807i	$0.0679350\pi$
$84$	−12.3201	−	0.0609416i	−1.34423	−	0.00664928i
$85$	0.392379	+	1.71912i	0.0425595	+	0.186465i
$86$	0.948130	+	1.61553i	0.102240	+	0.174208i
$87$	4.03158	+	17.6635i	0.432230	+	1.89372i
$88$	−1.21756	−	1.46161i	−0.129793	−	0.155808i
$89$	−14.2293	−	3.24775i	−1.50831	−	0.344261i	−0.613133	−	0.789979i	$-0.710091\pi$
$89$	−14.2293	−	3.24775i	−1.50831	−	0.344261i	−0.895173	+	0.445718i	$0.852948\pi$
$90$	0.406412	+	4.94997i	0.0428395	+	0.521773i
$91$	−0.781536	−	2.71775i	−0.0819273	−	0.284897i
$92$	−3.62847	+	12.3868i	−0.378295	+	1.29141i
$93$	13.7662	+	17.2622i	1.42748	+	1.79001i
$94$	−2.40435	+	16.7607i	−0.247989	+	1.72873i
$95$	4.51018	−	3.59674i	0.462734	−	0.369018i
$96$	12.0814	−	5.24522i	1.23305	−	0.535338i
$97$		−	14.5971i		−	1.48211i	−0.671444	−	0.741056i	$-0.734326\pi$
$97$		−	14.5971i		−	1.48211i	0.671444	−	0.741056i	$-0.265674\pi$
$98$	−9.57774	−	2.50336i	−0.967498	−	0.252878i
$99$		−	1.62830i		−	0.163651i
$100$	−4.73826	+	3.33031i	−0.473826	+	0.333031i
$101$	−7.46988	+	5.95703i	−0.743281	+	0.592747i	−0.920186	−	0.391481i	$-0.871963\pi$
$101$	−7.46988	+	5.95703i	−0.743281	+	0.592747i	0.176905	+	0.984228i	$0.443391\pi$
$102$	3.96206	+	0.568364i	0.392303	+	0.0562764i
$103$	5.85519	+	7.34217i	0.576929	+	0.723446i	0.981586	−	0.191023i	$-0.0611805\pi$
$103$	5.85519	+	7.34217i	0.576929	+	0.723446i	−0.404657	+	0.914469i	$0.632609\pi$
$104$	1.93495	+	2.32279i	0.189738	+	0.227768i
$105$	−1.50110	+	8.80887i	−0.146493	+	0.859658i
$106$	19.2844	−	1.58332i	1.87306	−	0.153786i
$107$	−1.58578	−	0.361943i	−0.153303	−	0.0349904i	0.145181	−	0.989405i	$-0.453624\pi$
$107$	−1.58578	−	0.361943i	−0.153303	−	0.0349904i	−0.298484	+	0.954415i	$0.596481\pi$
$108$	−2.58732	−	0.757905i	−0.248965	−	0.0729295i
$109$	−1.75220	−	7.67689i	−0.167830	−	0.735313i	−0.986862	−	0.161565i	$-0.948346\pi$
$109$	−1.75220	−	7.67689i	−0.167830	−	0.735313i	0.819032	−	0.573748i	$-0.194511\pi$
$110$	−1.18994	+	0.698358i	−0.113457	+	0.0665858i
$111$	−2.20178	−	9.64665i	−0.208984	−	0.915619i
$112$	10.4497	−	1.67451i	0.987403	−	0.158226i
$113$	−2.41363	+	10.5748i	−0.227055	+	0.994793i	0.724972	+	0.688779i	$0.241853\pi$
$113$	−2.41363	+	10.5748i	−0.227055	+	0.994793i	−0.952027	+	0.306015i	$0.901004\pi$
$114$	−3.94868	−	12.4850i	−0.369828	−	1.16933i
$115$	8.43454	+	4.06186i	0.786525	+	0.378771i
$116$	−5.89152	−	14.4047i	−0.547014	−	1.33745i
$117$			2.58770i			0.239233i
$118$	1.64323	−	0.964386i	0.151272	−	0.0887790i
$119$	2.97074	+	1.23222i	0.272328	+	0.112957i
$120$	−2.32415	−	9.26579i	−0.212164	−	0.845847i
$121$	−9.50311	+	4.57646i	−0.863919	+	0.416041i
$122$	7.84260	−	7.38148i	0.710036	−	0.668288i
$123$	0.115294	+	0.0263151i	0.0103957	+	0.00237275i
$124$	−14.0852	−	12.7008i	−1.26489	−	1.14056i
$125$	4.96952	+	10.3193i	0.444487	+	0.922987i
$126$	7.78981	+	4.62367i	0.693972	+	0.411909i
$127$	7.90715	−	16.4194i	0.701646	−	1.45698i	−0.179313	−	0.983792i	$-0.557388\pi$
$127$	7.90715	−	16.4194i	0.701646	−	1.45698i	0.880960	−	0.473192i	$-0.156898\pi$
$128$	−9.50396	+	6.13798i	−0.840039	+	0.542526i
$129$		−	3.08398i		−	0.271529i
$130$	1.89106	−	1.10983i	0.165857	−	0.0973386i
$131$	−4.50176	+	5.64503i	−0.393321	+	0.493209i	−0.938581	−	0.345058i	$-0.887859\pi$
$131$	−4.50176	+	5.64503i	−0.393321	+	0.493209i	0.545261	+	0.838267i	$0.316431\pi$
$132$	0.510836	+	3.08994i	0.0444626	+	0.268945i
$133$	−0.584836	−	10.5054i	−0.0507117	−	0.910931i
$134$	4.93109	−	12.8321i	0.425981	−	1.10853i
$135$	−0.848430	+	1.76178i	−0.0730212	+	0.151630i
$136$	−3.43744	+	0.0734377i	−0.294758	+	0.00629723i
$137$	−2.76229	+	3.46380i	−0.235998	+	0.295933i	−0.885701	−	0.464256i	$-0.846322\pi$
$137$	−2.76229	+	3.46380i	−0.235998	+	0.295933i	0.649703	+	0.760188i	$0.274893\pi$
$138$	15.4741	−	14.5643i	1.31725	−	1.23980i
$139$	−2.00893	−	2.51912i	−0.170395	−	0.213669i	0.689300	−	0.724476i	$-0.257918\pi$
$139$	−2.00893	−	2.51912i	−0.170395	−	0.213669i	−0.859695	+	0.510807i	$0.829347\pi$
$140$	0.0379681	−	7.67573i	0.00320889	−	0.648718i
$141$	17.3808	−	21.7949i	1.46373	−	1.83546i
$142$	0.390053	+	4.75073i	0.0327325	+	0.398672i
$143$	−0.647676	+	0.311904i	−0.0541614	+	0.0260827i
$144$	−9.61318	−	1.17006i	−0.801098	−	0.0975051i
$145$	−11.0048	+	2.51177i	−0.913898	+	0.208591i
$146$	−2.00765	−	1.34795i	−0.166154	−	0.111557i
$147$	11.5133	+	11.5358i	0.949602	+	0.951454i
$148$	3.21756	+	7.86693i	0.264482	+	0.646658i
$149$	−0.268808	−	1.17772i	−0.0220216	−	0.0964829i	0.962723	−	0.270490i	$-0.0871856\pi$
$149$	−0.268808	−	1.17772i	−0.0220216	−	0.0964829i	−0.984744	+	0.174007i	$0.944328\pi$
$150$	9.50302	−	0.780235i	0.775919	−	0.0637059i
$151$	6.83128	+	14.1853i	0.555922	+	1.15438i	0.969766	+	0.244036i	$0.0784714\pi$
$151$	6.83128	+	14.1853i	0.555922	+	1.15438i	−0.413844	+	0.910348i	$0.635814\pi$
$152$	5.09571	+	10.0276i	0.413317	+	0.813348i
$153$	−2.30092	−	1.83492i	−0.186019	−	0.148345i
$154$	−0.218326	+	2.50702i	−0.0175932	+	0.202022i
$155$	−10.7548	+	8.57666i	−0.863845	+	0.688894i
$156$	−0.811820	−	4.91054i	−0.0649976	−	0.393158i
$157$	−16.2069	−	12.9246i	−1.29346	−	1.03150i	−0.997075	−	0.0764261i	$-0.975649\pi$
$157$	−16.2069	−	12.9246i	−1.29346	−	1.03150i	−0.296380	−	0.955070i	$-0.595780\pi$
$158$	5.58558	−	14.5353i	0.444365	−	1.15637i
$159$	−28.7012	−	13.8218i	−2.27615	−	1.09614i
$160$	3.26790	+	7.52702i	0.258350	+	0.595063i
$161$	14.9483	−	8.25210i	1.17809	−	0.650357i
$162$	10.0820	+	10.7118i	0.792119	+	0.841602i
$163$	−12.1633	−	9.69992i	−0.952705	−	0.759757i	0.0180483	−	0.999837i	$-0.494255\pi$
$163$	−12.1633	−	9.69992i	−0.952705	−	0.759757i	−0.970753	+	0.240080i	$0.922826\pi$
$164$	−0.101397	−	0.00614806i	−0.00791779	−	0.000480083i
$165$	2.27155			0.176840
$166$	0.157646	−	0.234799i	0.0122357	−	0.0182239i
$167$	−2.91840	−	1.40543i	−0.225832	−	0.108755i	0.317547	−	0.948243i	$-0.397141\pi$
$167$	−2.91840	−	1.40543i	−0.225832	−	0.108755i	−0.543379	+	0.839488i	$0.682855\pi$
$168$	−16.2329	−	6.33024i	−1.25239	−	0.488389i
$169$	−10.6833	+	5.14481i	−0.821793	+	0.395755i
$170$	−0.354104	+	2.46846i	−0.0271586	+	0.189322i
$171$	−2.14242	+	9.38657i	−0.163835	+	0.717809i
$172$	0.432092	+	2.61364i	0.0329467	+	0.199288i
$173$	8.07860	+	16.7754i	0.614205	+	1.27541i	0.943559	+	0.331203i	$0.107455\pi$
$173$	8.07860	+	16.7754i	0.614205	+	1.27541i	−0.329354	+	0.944206i	$0.606831\pi$
$174$	−3.63832	+	25.3627i	−0.275820	+	1.92274i
$175$	7.55262	+	1.28703i	0.570925	+	0.0972901i
$176$	−0.865855	−	2.54712i	−0.0652663	−	0.191996i
$177$	−3.13686			−0.235781
$178$	−17.1366	−	11.5057i	−1.28444	−	0.862386i
$179$	2.69466	−	5.59551i	0.201408	−	0.418228i	−0.775661	−	0.631149i	$-0.782584\pi$
$179$	2.69466	−	5.59551i	0.201408	−	0.418228i	0.977069	+	0.212921i	$0.0682978\pi$
$180$	−1.97454	+	6.74062i	−0.147173	+	0.502416i
$181$	6.49366	+	1.48214i	0.482670	+	0.110166i	0.456931	−	0.889502i	$-0.348949\pi$
$181$	6.49366	+	1.48214i	0.482670	+	0.110166i	0.0257395	+	0.999669i	$0.491806\pi$
$182$	0.346963	−	3.98416i	0.0257186	−	0.295325i
$183$	−17.2868	+	3.94559i	−1.27787	+	0.291667i
$184$	−11.0736	+	14.5111i	−0.816354	+	1.06978i
$185$	6.01010	−	1.37177i	0.441871	−	0.100854i
$186$	9.41586	+	29.7712i	0.690404	+	2.18293i
$187$	0.181926	−	0.797069i	0.0133037	−	0.0582875i
$188$	−11.6764	+	20.9061i	−0.851589	+	1.52473i
$189$	1.72368	+	3.12235i	0.125379	+	0.227117i
$190$	7.77845	−	2.46012i	0.564308	−	0.178476i
$191$	8.83454	−	7.04531i	0.639245	−	0.509781i	−0.249386	−	0.968404i	$-0.580229\pi$
$191$	8.83454	−	7.04531i	0.639245	−	0.509781i	0.888631	+	0.458623i	$0.151657\pi$
$192$	18.6095	−	0.795513i	1.34302	−	0.0574112i
$193$	8.81519	+	11.0539i	0.634531	+	0.795677i	0.990307	−	0.138894i	$-0.0443549\pi$
$193$	8.81519	+	11.0539i	0.634531	+	0.795677i	−0.355776	+	0.934571i	$0.615783\pi$
$194$	7.40487	−	19.2696i	0.531639	−	1.38348i
$195$	−3.60994			−0.258513
$196$	−11.3737	−	8.16332i	−0.812405	−	0.583094i
$197$	11.1258			0.792682			0.396341	−	0.918103i	$-0.370280\pi$
$197$	11.1258			0.792682			0.396341	+	0.918103i	$0.370280\pi$
$198$	0.826011	−	2.14952i	0.0587021	−	0.152760i
$199$	−11.1219	−	13.9464i	−0.788412	−	0.988637i	−0.999937	−	0.0112645i	$-0.996414\pi$
$199$	−11.1219	−	13.9464i	−0.788412	−	0.988637i	0.211525	−	0.977373i	$-0.432157\pi$
$200$	−7.94438	+	1.99270i	−0.561753	+	0.140905i
$201$	−17.6948	+	14.1112i	−1.24810	+	0.995324i
$202$	−12.8829	+	4.07453i	−0.906437	+	0.286683i
$203$	−7.88791	+	19.0169i	−0.553623	+	1.33472i
$204$	4.94200	+	2.76019i	0.346009	+	0.193252i
$205$	−0.0163949	+	0.0718309i	−0.00114507	+	0.00501689i
$206$	4.00487	+	12.6626i	0.279032	+	0.882248i
$207$	−15.2328	+	3.47678i	−1.05875	+	0.241653i
$208$	1.37602	+	4.04788i	0.0954096	+	0.280670i
$209$	−2.60760	+	0.595168i	−0.180372	+	0.0411686i
$210$	−6.45020	+	10.8671i	−0.445106	+	0.749901i
$211$	−16.8062	−	3.83592i	−1.15699	−	0.264075i	−0.399381	−	0.916785i	$-0.630775\pi$
$211$	−16.8062	−	3.83592i	−1.15699	−	0.264075i	−0.757608	+	0.652710i	$0.773632\pi$
$212$	26.2605	+	7.69250i	1.80358	+	0.528323i
$213$	3.40501	−	7.07057i	0.233307	−	0.484468i
$214$	−1.90978	−	1.28224i	−0.130550	−	0.0876522i
$215$	1.92140			0.131038
$216$	−3.03105	−	2.31302i	−0.206237	−	0.157381i
$217$	1.39458	+	25.0507i	0.0946700	+	1.70055i
$218$	1.58128	−	11.0231i	0.107098	−	0.746580i
$219$	1.72739	+	3.58695i	0.116726	+	0.242384i
$220$	−1.92511	+	0.318263i	−0.129791	+	0.0214573i
$221$	−0.289116	+	1.26670i	−0.0194481	+	0.0852076i
$222$	1.98701	−	13.8515i	0.133359	−	0.929649i
$223$	4.57700	−	2.20417i	0.306499	−	0.147602i	−0.274312	−	0.961641i	$-0.588450\pi$
$223$	4.57700	−	2.20417i	0.306499	−	0.147602i	0.580811	+	0.814039i	$0.302736\pi$
$224$	14.6441	+	3.09044i	0.978449	+	0.206489i
$225$	−6.31648	−	3.04185i	−0.421098	−	0.202790i
$226$	−8.55065	+	12.7354i	−0.568781	+	0.847146i
$227$	5.50386			0.365304			0.182652	−	0.983178i	$-0.441532\pi$
$227$	5.50386			0.365304			0.182652	+	0.983178i	$0.441532\pi$
$228$	1.12078	−	18.4845i	0.0742254	−	1.22417i
$229$	3.37834	+	2.69414i	0.223247	+	0.178034i	0.728726	−	0.684805i	$-0.240113\pi$
$229$	3.37834	+	2.69414i	0.223247	+	0.178034i	−0.505479	+	0.862839i	$0.668684\pi$
$230$	9.07392	+	9.64077i	0.598317	+	0.635693i
$231$	2.39913	−	3.37778i	0.157851	−	0.222241i
$232$	−0.470103	−	22.0044i	−0.0308638	−	1.44466i
$233$	−14.0199	−	6.75163i	−0.918475	−	0.442314i	−0.0859484	−	0.996300i	$-0.527392\pi$
$233$	−14.0199	−	6.75163i	−0.918475	−	0.442314i	−0.832526	+	0.553985i	$0.813106\pi$
$234$	−1.31270	+	3.41602i	−0.0858137	+	0.223312i
$235$	13.5787	+	10.8287i	0.885779	+	0.706386i
$236$	2.65845	−	0.439501i	0.173050	−	0.0286091i
$237$	−20.0434	+	15.9841i	−1.30196	+	1.03828i
$238$	3.29660	+	3.13366i	0.213687	+	0.203125i
$239$	−4.05644	−	3.23490i	−0.262389	−	0.209248i	0.483454	−	0.875370i	$-0.339382\pi$
$239$	−4.05644	−	3.23490i	−0.262389	−	0.209248i	−0.745844	+	0.666121i	$0.767953\pi$
$240$	1.63228	−	13.4108i	0.105363	−	0.865662i
$241$	−8.86995	−	18.4186i	−0.571363	−	1.18645i	−0.963789	−	0.266665i	$-0.914078\pi$
$241$	−8.86995	−	18.4186i	−0.571363	−	1.18645i	0.392426	−	0.919784i	$-0.371636\pi$
$242$	−14.8666	+	1.22061i	−0.955662	+	0.0784635i
$243$	−4.48921	−	19.6685i	−0.287983	−	1.26174i
$244$	14.0975	−	5.76587i	0.902502	−	0.369122i
$245$	−7.18707	+	7.17308i	−0.459165	+	0.458271i
$246$	0.138850	+	0.0932252i	0.00885277	+	0.00594382i
$247$	4.14400	−	0.945841i	0.263676	−	0.0601824i
$248$	−12.1510	−	23.9115i	−0.771591	−	1.51838i
$249$	−0.419501	+	0.202021i	−0.0265848	+	0.0128026i
$250$	1.32544	+	16.1435i	0.0838283	+	1.02100i
$251$	−11.9828	+	15.0259i	−0.756345	+	0.948427i	−0.999769	−	0.0214932i	$-0.993158\pi$
$251$	−11.9828	+	15.0259i	−0.756345	+	0.948427i	0.243424	+	0.969920i	$0.421729\pi$
$252$	7.93782	+	10.0553i	0.500036	+	0.633427i
$253$	−2.70626	−	3.39354i	−0.170141	−	0.213350i
$254$	18.7675	−	17.6640i	1.17758	−	1.10834i
$255$	2.55979	−	3.20988i	0.160301	−	0.201011i
$256$	−15.6599	+	3.28154i	−0.978742	+	0.205096i
$257$	7.94565	−	16.4993i	0.495636	−	1.02920i	−0.491731	−	0.870747i	$-0.663635\pi$
$257$	7.94565	−	16.4993i	0.495636	−	1.02920i	0.987367	−	0.158452i	$-0.0506502\pi$
$258$	1.56445	−	4.07116i	0.0973986	−	0.253459i
$259$	4.30786	−	10.3858i	0.267678	−	0.645342i
$260$	3.05938	−	0.505784i	0.189735	−	0.0313674i
$261$	11.7461	−	14.7291i	0.727064	−	0.911709i
$262$	−8.80641	+	5.16834i	−0.544062	+	0.319301i
$263$		−	23.7258i		−	1.46300i	−0.681844	−	0.731498i	$-0.738822\pi$
$263$		−	23.7258i		−	1.46300i	0.681844	−	0.731498i	$-0.261178\pi$
$264$	−0.893123	+	4.33817i	−0.0549679	+	0.266996i
$265$	8.61130	−	17.8815i	0.528988	−	1.09845i
$266$	4.55716	−	14.1648i	0.279417	−	0.868500i
$267$	14.7444	+	30.6170i	0.902341	+	1.87373i
$268$	13.0191	−	14.4382i	0.795266	−	0.881956i
$269$	16.2373	+	3.70605i	0.990003	+	0.225962i	0.686707	−	0.726934i	$-0.259056\pi$
$269$	16.2373	+	3.70605i	0.990003	+	0.225962i	0.303296	+	0.952896i	$0.401913\pi$
$270$	−2.01374	+	1.89533i	−0.122552	+	0.115346i
$271$	18.5855	−	8.95030i	1.12899	−	0.543692i	0.226330	−	0.974051i	$-0.427327\pi$
$271$	18.5855	−	8.95030i	1.12899	−	0.543692i	0.902658	+	0.430359i	$0.141613\pi$
$272$	−4.57501	−	1.64681i	−0.277401	−	0.0998525i
$273$	−3.81270	+	5.36796i	−0.230755	+	0.324884i
$274$	−5.40363	+	3.17130i	−0.326445	+	0.191585i
$275$		−	1.94760i		−	0.117445i
$276$	27.8156	−	11.3766i	1.67430	−	0.684788i
$277$	−4.38586	−	2.11212i	−0.263521	−	0.126905i	0.297459	−	0.954735i	$-0.403861\pi$
$277$	−4.38586	−	2.11212i	−0.263521	−	0.126905i	−0.560979	+	0.827830i	$0.689575\pi$
$278$	−1.37408	−	4.34458i	−0.0824118	−	0.260571i
$279$	5.10874	−	22.3828i	0.305852	−	1.34003i
$280$	3.94390	−	10.1135i	0.235693	−	0.604396i
$281$	5.03736	+	22.0701i	0.300504	+	1.31659i	0.869370	+	0.494162i	$0.164525\pi$
$281$	5.03736	+	22.0701i	0.300504	+	1.31659i	−0.568866	+	0.822430i	$0.692618\pi$
$282$	34.0006	−	19.9544i	2.02471	−	1.18827i
$283$	−3.96856	−	17.3874i	−0.235906	−	1.03357i	−0.944643	−	0.328100i	$-0.893592\pi$
$283$	−3.96856	−	17.3874i	−0.235906	−	1.03357i	0.708737	−	0.705473i	$-0.249265\pi$
$284$	−1.89506	+	6.46930i	−0.112451	+	0.383882i
$285$	−13.0946	−	2.98877i	−0.775660	−	0.177039i
$286$	−1.01322	+	0.0831893i	−0.0599130	+	0.00491909i
$287$	0.0894963	+	0.100245i	0.00528280	+	0.00591725i
$288$	−12.0968	−	6.42121i	−0.712811	−	0.378373i
$289$	9.67801	+	12.1358i	0.569295	+	0.713873i
$290$	−15.8016	−	2.26676i	−0.927902	−	0.133109i
$291$	−26.5718	+	21.1903i	−1.55767	+	1.24220i
$292$	−1.96650	−	2.79788i	−0.115081	−	0.163734i
$293$			9.38809i			0.548458i	0.961664	+	0.274229i	$0.0884227\pi$
$293$			9.38809i			0.548458i	−0.961664	+	0.274229i	$0.911577\pi$
$294$	9.34682	+	21.0689i	0.545118	+	1.22876i
$295$		−	1.95434i		−	0.113786i
$296$	0.256740	+	12.0174i	0.0149227	+	0.698494i
$297$	0.708834	−	0.565276i	0.0411307	−	0.0328006i
$298$	0.242587	−	1.69107i	0.0140527	−	0.0979613i
$299$	4.30079	+	5.39302i	0.248721	+	0.311886i
$300$	12.9407	+	3.79074i	0.747134	+	0.218859i
$301$	2.02932	−	2.85710i	0.116968	−	0.164681i
$302$	1.82200	+	22.1914i	0.104844	+	1.27697i
$303$	21.6877	+	4.95008i	1.24593	+	0.284375i
$304$	1.63999	+	15.8224i	0.0940600	+	0.907480i
$305$	−2.45820	−	10.7701i	−0.140756	−	0.616693i
$306$	−2.10662	−	3.58950i	−0.120427	−	0.205198i
$307$	3.71593	+	16.2806i	0.212079	+	0.929180i	0.963151	+	0.268960i	$0.0866799\pi$
$307$	3.71593	+	16.2806i	0.212079	+	0.929180i	−0.751072	+	0.660220i	$0.770463\pi$
$308$	−1.55998	+	3.19877i	−0.0888883	+	0.182267i
$309$	4.86545	−	21.3169i	0.276786	−	1.21268i
$310$	−18.5482	+	5.86631i	−1.05347	+	0.333184i
$311$	14.6943	+	7.07640i	0.833237	+	0.401266i	0.801328	−	0.598225i	$-0.204127\pi$
$311$	14.6943	+	7.07640i	0.833237	+	0.401266i	0.0319090	+	0.999491i	$0.489841\pi$
$312$	1.41935	−	6.89422i	0.0803549	−	0.390308i
$313$			27.7256i			1.56714i	0.621303	+	0.783571i	$0.286604\pi$
$313$			27.7256i			1.56714i	−0.621303	+	0.783571i	$0.713396\pi$
$314$	−14.8383	−	25.2833i	−0.837376	−	1.42682i
$315$	8.13451	−	4.49061i	0.458328	−	0.253017i
$316$	14.7470	−	16.3546i	0.829586	−	0.920017i
$317$	−4.49018	+	2.16235i	−0.252193	+	0.121450i	−0.555710	−	0.831376i	$-0.687554\pi$
$317$	−4.49018	+	2.16235i	−0.252193	+	0.121450i	0.303517	+	0.952826i	$0.401839\pi$
$318$	−30.8769	−	32.8057i	−1.73149	−	1.83965i
$319$	5.10235	+	1.16458i	0.285677	+	0.0652039i
$320$	0.495624	+	11.5942i	0.0277062	+	0.648134i
$321$	1.64318	+	3.41209i	0.0917132	+	0.190444i
$322$	23.9193	−	3.31060i	1.33297	−	0.184492i
$323$	−2.09747	+	4.35544i	−0.116706	+	0.242343i
$324$	7.87533	+	19.2552i	0.437518	+	1.06973i
$325$			3.09512i			0.171687i
$326$	−11.1362	−	18.9751i	−0.616776	−	1.05093i
$327$	−11.4310	+	14.3340i	−0.632134	+	0.792671i
$328$	−0.130736	−	0.0595532i	−0.00721867	−	0.00328827i
$329$	30.4436	−	8.75460i	1.67841	−	0.482656i
$330$	2.99867	+	1.15232i	0.165071	+	0.0634331i
$331$	−0.0629372	+	0.130690i	−0.00345934	+	0.00718340i	−0.902691	−	0.430289i	$-0.858412\pi$
$331$	−0.0629372	+	0.130690i	−0.00345934	+	0.00718340i	0.899232	+	0.437472i	$0.144126\pi$
$332$	0.327218	−	0.229986i	0.0179584	−	0.0126221i
$333$	−6.41494	+	8.04408i	−0.351536	+	0.440813i
$334$	−3.13963	−	3.33576i	−0.171793	−	0.182525i
$335$	−8.79160	−	11.0243i	−0.480336	−	0.602322i
$336$	−18.2178	−	16.5912i	−0.993861	−	0.905125i
$337$	2.94573	−	3.69383i	0.160464	−	0.201216i	−0.695099	−	0.718914i	$-0.744640\pi$
$337$	2.94573	−	3.69383i	0.160464	−	0.201216i	0.855563	+	0.517698i	$0.173211\pi$
$338$	−16.7129	+	1.37219i	−0.909063	+	0.0746375i
$339$	22.7536	−	10.9576i	1.23581	−	0.595133i
$340$	−1.71966	+	3.07899i	−0.0932619	+	0.166981i
$341$	6.21798	−	1.41921i	0.336723	−	0.0768548i
$342$	−7.58987	+	11.3044i	−0.410413	+	0.611271i
$343$	3.07558	+	18.2631i	0.166065	+	0.986115i
$344$	−0.755451	+	3.66946i	−0.0407312	+	0.197844i
$345$	−4.85024	−	21.2503i	−0.261128	−	1.14408i
$346$	2.15468	+	26.2433i	0.115836	+	1.41085i
$347$	−7.81835	−	16.2350i	−0.419711	−	0.871539i	−0.998430	−	0.0560119i	$-0.982162\pi$
$347$	−7.81835	−	16.2350i	−0.419711	−	0.871539i	0.578719	−	0.815527i	$-0.303553\pi$
$348$	−17.6690	+	31.6357i	−0.947160	+	1.69585i
$349$	10.7938	+	8.60775i	0.577778	+	0.460762i	0.868254	−	0.496120i	$-0.165242\pi$
$349$	10.7938	+	8.60775i	0.577778	+	0.460762i	−0.290476	+	0.956882i	$0.593814\pi$
$350$	9.31733	+	5.53033i	0.498032	+	0.295608i
$351$	−1.12648	+	0.898337i	−0.0601270	+	0.0479497i
$352$	0.149096	−	3.80168i	0.00794686	−	0.202630i
$353$	−7.29578	−	5.81819i	−0.388315	−	0.309671i	0.409801	−	0.912175i	$-0.365598\pi$
$353$	−7.29578	−	5.81819i	−0.388315	−	0.309671i	−0.798116	+	0.602504i	$0.794170\pi$
$354$	−4.14096	−	1.59128i	−0.220090	−	0.0845754i
$355$	4.40514	+	2.12140i	0.233801	+	0.112592i
$356$	−16.7854	−	23.8818i	−0.889624	−	1.26573i
$357$	−2.06950	−	7.19657i	−0.109530	−	0.380883i
$358$	6.39573	−	6.01968i	0.338025	−	0.318150i
$359$	8.70135	+	6.93910i	0.459240	+	0.366231i	0.825613	−	0.564236i	$-0.190829\pi$
$359$	8.70135	+	6.93910i	0.459240	+	0.366231i	−0.366374	+	0.930468i	$0.619401\pi$
$360$	−6.02599	+	7.89664i	−0.317598	+	0.416190i
$361$	−3.18504			−0.167634
$362$	7.82042	+	5.25070i	0.411032	+	0.275970i
$363$	22.1262	+	10.6554i	1.16132	+	0.559264i
$364$	2.47912	−	5.08348i	0.129941	−	0.266447i
$365$	−2.23476	+	1.07620i	−0.116973	+	0.0563311i
$366$	−24.8218	−	3.56072i	−1.29746	−	0.186122i
$367$	−2.82592	+	12.3812i	−0.147512	+	0.646291i	0.846060	+	0.533088i	$0.178968\pi$
$367$	−2.82592	+	12.3812i	−0.147512	+	0.646291i	−0.993572	+	0.113204i	$0.963889\pi$
$368$	−21.9795	+	13.5387i	−1.14576	+	0.705754i
$369$	−0.0533539	−	0.110791i	−0.00277749	−	0.00576753i
$370$	8.62980	+	1.23796i	0.448642	+	0.0643583i
$371$	−17.4948	−	31.6908i	−0.908283	−	1.64531i
$372$	−2.67257	+	44.0775i	−0.138566	+	2.28531i
$373$	8.79325			0.455297			0.227649	−	0.973743i	$-0.426896\pi$
$373$	8.79325			0.455297			0.227649	+	0.973743i	$0.426896\pi$
$374$	0.644500	−	0.959922i	0.0333263	−	0.0496364i
$375$	11.5706	−	24.0266i	0.597502	−	1.24073i
$376$	−26.0193	+	21.6749i	−1.34185	+	1.11780i
$377$	−8.10865	−	1.85075i	−0.417617	−	0.0953183i
$378$	0.691508	+	4.99620i	0.0355673	+	0.256977i
$379$	30.2229	−	6.89818i	1.55245	−	0.354336i	0.641586	−	0.767051i	$-0.278277\pi$
$379$	30.2229	−	6.89818i	1.55245	−	0.354336i	0.910860	+	0.412715i	$0.135420\pi$
$380$	11.5163	+	0.698273i	0.590774	+	0.0358207i
$381$	−41.3676	+	9.44188i	−2.11933	+	0.483722i
$382$	15.2364	−	4.81889i	0.779564	−	0.246556i
$383$	−3.83674	+	16.8099i	−0.196048	+	0.858944i	0.777212	+	0.629239i	$0.216633\pi$
$383$	−3.83674	+	16.8099i	−0.196048	+	0.858944i	−0.973260	+	0.229705i	$0.926224\pi$
$384$	24.9699	+	8.39013i	1.27424	+	0.428157i
$385$	2.10444	+	1.49472i	0.107252	+	0.0761780i
$386$	6.02947	+	19.0640i	0.306892	+	0.970334i
$387$	−2.50717	+	1.99940i	−0.127447	+	0.101635i
$388$	19.5503	−	21.6815i	0.992518	−	1.10071i
$389$	−23.3361	−	29.2626i	−1.18319	−	1.48367i	−0.838456	−	0.544969i	$-0.816541\pi$
$389$	−23.3361	−	29.2626i	−1.18319	−	1.48367i	−0.344732	−	0.938701i	$-0.612030\pi$
$390$	−4.76548	−	1.83127i	−0.241310	−	0.0927297i
$391$	−7.84502			−0.396740
$392$	−10.8733	−	16.5461i	−0.549182	−	0.835703i
$393$	16.8110			0.848004
$394$	14.6872	+	5.64395i	0.739930	+	0.284338i
$395$	−9.95848	−	12.4875i	−0.501065	−	0.628316i
$396$	2.18083	−	2.41856i	0.109591	−	0.121537i
$397$	13.7729	−	10.9835i	0.691241	−	0.551247i	−0.213639	−	0.976913i	$-0.568532\pi$
$397$	13.7729	−	10.9835i	0.691241	−	0.551247i	0.904880	+	0.425666i	$0.139960\pi$
$398$	−7.60724	−	24.0527i	−0.381316	−	1.20565i
$399$	−18.2744	+	16.3150i	−0.914865	+	0.816772i
$400$	−11.4982	−	1.39950i	−0.574912	−	0.0699750i
$401$	5.92553	−	25.9614i	0.295907	−	1.29645i	−0.580255	−	0.814435i	$-0.697047\pi$
$401$	5.92553	−	25.9614i	0.295907	−	1.29645i	0.876162	−	0.482017i	$-0.160096\pi$
$402$	−30.5173	+	9.65183i	−1.52206	+	0.481390i
$403$	−9.88162	+	2.25542i	−0.492239	+	0.112350i
$404$	−19.0736	−	1.15650i	−0.948949	−	0.0575380i
$405$	14.7104	−	3.35754i	0.730963	−	0.166838i
$406$	−20.0598	+	21.1028i	−0.995551	+	1.04731i
$407$	−2.78657	−	0.636017i	−0.138125	−	0.0315262i
$408$	5.12373	+	6.15072i	0.253663	+	0.304506i
$409$	4.17880	−	8.67737i	0.206628	−	0.429068i	−0.771740	−	0.635938i	$-0.780613\pi$
$409$	4.17880	−	8.67737i	0.206628	−	0.429068i	0.978368	+	0.206870i	$0.0663276\pi$
$410$	−0.0580816	+	0.0865071i	−0.00286845	+	0.00427228i
$411$	10.3153			0.508815
$412$	−1.13673	+	18.7475i	−0.0560026	+	0.923625i
$413$	−2.90609	−	2.06411i	−0.142999	−	0.101568i
$414$	−21.8725	−	3.13764i	−1.07497	−	0.154206i
$415$	−0.125864	−	0.261360i	−0.00617843	−	0.0128296i
$416$	−0.236944	+	6.04163i	−0.0116171	+	0.296216i
$417$	−1.66935	+	7.31390i	−0.0817484	+	0.358163i
$418$	−3.74421	−	0.537113i	−0.183135	−	0.0262710i
$419$	19.1868	−	9.23986i	0.937335	−	0.451397i	0.0981065	−	0.995176i	$-0.468721\pi$
$419$	19.1868	−	9.23986i	0.937335	−	0.451397i	0.839228	+	0.543779i	$0.183007\pi$
$420$	−14.0276	+	11.0736i	−0.684477	+	0.540335i
$421$	8.17196	+	3.93541i	0.398277	+	0.191800i	0.622291	−	0.782786i	$-0.286202\pi$
$421$	8.17196	+	3.93541i	0.398277	+	0.191800i	−0.224014	+	0.974586i	$0.571916\pi$
$422$	−20.2400	−	13.5893i	−0.985269	−	0.661518i
$423$	−28.9868			−1.40939
$424$	30.7642	+	23.4764i	1.49404	+	1.14011i
$425$	−2.75211	−	2.19474i	−0.133497	−	0.106460i
$426$	8.08174	−	7.60656i	0.391562	−	0.368539i
$427$	−18.6113	−	7.71968i	−0.900665	−	0.373582i
$428$	−1.87064	−	2.66148i	−0.0904206	−	0.128648i
$429$	1.50799	+	0.726210i	0.0728065	+	0.0350618i
$430$	2.53643	+	0.974693i	0.122318	+	0.0470039i
$431$	18.7802	+	14.9767i	0.904610	+	0.721402i	0.960866	−	0.277014i	$-0.0893449\pi$
$431$	18.7802	+	14.9767i	0.904610	+	0.721402i	−0.0562561	+	0.998416i	$0.517916\pi$
$432$	−2.82793	−	4.59101i	−0.136059	−	0.220885i
$433$	−1.17210	+	0.934722i	−0.0563278	+	0.0449199i	−0.651249	−	0.758864i	$-0.725755\pi$
$433$	−1.17210	+	0.934722i	−0.0563278	+	0.0449199i	0.594921	+	0.803784i	$0.297183\pi$
$434$	−10.8668	+	33.7768i	−0.521624	+	1.62134i
$435$	20.5477	+	16.3862i	0.985187	+	0.785660i
$436$	7.67930	−	13.7495i	0.367772	−	0.658480i
$437$	11.1356	+	23.1233i	0.532687	+	1.10614i
$438$	0.460719	+	5.61141i	0.0220140	+	0.268124i
$439$	4.63096	+	20.2896i	0.221024	+	0.968368i	0.956709	+	0.291045i	$0.0940029\pi$
$439$	4.63096	+	20.2896i	0.221024	+	0.968368i	−0.735686	+	0.677323i	$0.763140\pi$
$440$	−2.70279	−	0.556438i	−0.128850	−	0.0265271i
$441$	1.91389	−	16.8388i	0.0911376	−	0.801848i
$442$	−1.02424	+	1.52551i	−0.0487181	+	0.0725610i
$443$	−23.9884	+	5.47520i	−1.13972	+	0.260134i	−0.750411	−	0.660972i	$-0.770144\pi$
$443$	−23.9884	+	5.47520i	−1.13972	+	0.260134i	−0.389312	+	0.921106i	$0.627287\pi$
$444$	9.64967	−	17.2773i	0.457953	−	0.819946i
$445$	−19.0752	+	9.18611i	−0.904249	+	0.435463i
$446$	7.16024	−	0.587883i	0.339047	−	0.0278371i
$447$	−1.75364	+	2.19900i	−0.0829444	+	0.104009i
$448$	17.7639	+	11.5084i	0.839266	+	0.543721i
$449$	−11.5227	−	14.4490i	−0.543791	−	0.681892i	0.431679	−	0.902027i	$-0.357921\pi$
$449$	−11.5227	−	14.4490i	−0.543791	−	0.681892i	−0.975469	+	0.220136i	$0.929350\pi$
$450$	−6.79529	−	7.21980i	−0.320333	−	0.340344i
$451$	0.0212989	−	0.0267080i	0.00100293	−	0.00125763i
$452$	−17.7482	+	12.4744i	−0.834804	+	0.586745i
$453$	15.9053	−	33.0278i	0.747298	−	1.55178i
$454$	7.26564	+	2.79202i	0.340994	+	0.131036i
$455$	−3.34437	−	2.37541i	−0.156787	−	0.111361i
$456$	10.8564	−	23.8329i	0.508399	−	1.11608i
$457$	4.98346	−	6.24907i	0.233117	−	0.292319i	−0.651490	−	0.758657i	$-0.725856\pi$
$457$	4.98346	−	6.24907i	0.233117	−	0.292319i	0.884606	+	0.466338i	$0.154427\pi$
$458$	3.09306	+	5.27031i	0.144529	+	0.246265i
$459$		−	1.63865i		−	0.0764854i
$460$	7.08788	+	17.3298i	0.330474	+	0.808007i
$461$	−14.7228	+	30.5722i	−0.685708	+	1.42389i	0.209306	+	0.977850i	$0.432880\pi$
$461$	−14.7228	+	30.5722i	−0.685708	+	1.42389i	−0.895014	+	0.446038i	$0.852835\pi$
$462$	4.88059	−	3.24196i	0.227065	−	0.150830i
$463$	10.2534	+	21.2913i	0.476514	+	0.989491i	0.991232	+	0.132132i	$0.0421822\pi$
$463$	10.2534	+	21.2913i	0.476514	+	0.989491i	−0.514718	+	0.857359i	$0.672103\pi$
$464$	10.5419	−	29.2864i	0.489394	−	1.35959i
$465$	31.2250	+	7.12690i	1.44802	+	0.330502i
$466$	−15.0827	−	16.0249i	−0.698692	−	0.742339i
$467$	12.4325	−	5.98717i	0.575307	−	0.277053i	−0.123522	−	0.992342i	$-0.539419\pi$
$467$	12.4325	−	5.98717i	0.575307	−	0.277053i	0.698829	+	0.715289i	$0.253705\pi$
$468$	−3.46578	+	3.84358i	−0.160206	+	0.177669i
$469$	−25.6785	+	1.42953i	−1.18572	+	0.0660094i
$470$	12.4321	+	21.1832i	0.573449	+	0.977109i
$471$			48.2646i			2.22392i
$472$	3.73237	+	0.768404i	0.171796	+	0.0353686i
$473$	−0.802630	−	0.386526i	−0.0369049	−	0.0177725i
$474$	−34.5678	+	10.9329i	−1.58775	+	0.502164i
$475$	−2.56253	+	11.2272i	−0.117577	+	0.515139i
$476$	2.76218	+	5.80905i	0.126604	+	0.266258i
$477$	7.37089	+	32.2940i	0.337490	+	1.47864i
$478$	−3.71389	−	6.32816i	−0.169869	−	0.289443i
$479$	−0.771082	−	3.37833i	−0.0352316	−	0.154360i	0.954252	−	0.299003i	$-0.0966539\pi$
$479$	−0.771082	−	3.37833i	−0.0352316	−	0.154360i	−0.989484	+	0.144643i	$0.953797\pi$
$480$	8.95784	−	16.8755i	0.408868	−	0.770259i
$481$	4.42842	+	1.01076i	0.201918	+	0.0460866i
$482$	−2.36574	−	28.8140i	−0.107757	−	1.31244i
$483$	−36.7217	−	15.2316i	−1.67090	−	0.693062i
$484$	−20.2446	−	5.93027i	−0.920209	−	0.269558i
$485$	−13.2021	−	16.5549i	−0.599475	−	0.751718i
$486$	4.05131	−	28.2417i	0.183771	−	1.28107i
$487$	−2.18816	+	1.74500i	−0.0991551	+	0.0790736i	−0.671813	−	0.740721i	$-0.734484\pi$
$487$	−2.18816	+	1.74500i	−0.0991551	+	0.0790736i	0.572657	+	0.819795i	$0.305913\pi$
$488$	21.5351	−	0.460077i	0.974847	−	0.0208267i
$489$			36.2226i			1.63804i
$490$	−13.1264	+	5.82330i	−0.592992	+	0.263070i
$491$		−	41.1929i		−	1.85901i	−0.368808	−	0.929506i	$-0.620234\pi$
$491$		−	41.1929i		−	1.85901i	0.368808	−	0.929506i	$-0.379766\pi$
$492$	0.136004	+	0.193503i	0.00613156	+	0.00872379i
$493$	7.39545	−	5.89768i	0.333074	−	0.265618i
$494$	5.95030	+	0.853579i	0.267717	+	0.0384044i
$495$	−1.47269	−	1.84669i	−0.0661924	−	0.0830026i
$496$	−3.91066	−	37.7296i	−0.175594	−	1.69411i
$497$	7.80708	−	4.30986i	0.350196	−	0.193324i
$498$	−0.656266	+	0.0538819i	−0.0294080	+	0.00241451i
$499$	−18.8862	−	4.31066i	−0.845463	−	0.192971i	−0.222217	−	0.974997i	$-0.571329\pi$
$499$	−18.8862	−	4.31066i	−0.845463	−	0.192971i	−0.623246	+	0.782026i	$0.714187\pi$
$500$	−6.43961	+	21.9834i	−0.287988	+	0.983126i
$501$	1.67821	+	7.35272i	0.0749769	+	0.328495i
$502$	−23.4408	+	13.7570i	−1.04622	+	0.614007i
$503$	3.94933	+	17.3031i	0.176092	+	0.771508i	0.983411	+	0.181393i	$0.0580606\pi$
$503$	3.94933	+	17.3031i	0.176092	+	0.771508i	−0.807319	+	0.590115i	$0.799082\pi$
$504$	5.37780	+	17.3008i	0.239546	+	0.770638i
$505$	−3.08402	+	13.5120i	−0.137237	+	0.601275i
$506$	−1.85104	−	5.85266i	−0.0822890	−	0.260182i
$507$	24.8741	+	11.9787i	1.10470	+	0.531994i
$508$	33.7357	−	13.7978i	1.49678	−	0.612180i
$509$		−	9.09369i		−	0.403071i	−0.979481	−	0.201535i	$-0.935407\pi$
$509$		−	9.09369i		−	0.403071i	0.979481	−	0.201535i	$-0.0645931\pi$
$510$	5.00750	−	2.93882i	0.221736	−	0.130133i
$511$	−0.759973	+	4.45973i	−0.0336192	+	0.197287i
$512$	−22.3373	−	3.61204i	−0.987177	−	0.159631i
$513$	−4.82992	+	2.32597i	−0.213246	+	0.102694i
$514$	18.8589	−	17.7500i	0.831830	−	0.782921i
$515$	13.2810	+	3.03130i	0.585230	+	0.133575i
$516$	4.13047	−	4.58072i	0.181834	−	0.201655i
$517$	−3.49388	−	7.25512i	−0.153661	−	0.319080i
$518$	10.9554	−	11.5250i	0.481350	−	0.506378i
$519$	18.8095	−	39.0583i	0.825646	−	1.71447i
$520$	4.29527	+	0.884291i	0.188360	+	0.0387787i
$521$			17.6440i			0.772996i	0.922290	+	0.386498i	$0.126315\pi$
$521$			17.6440i			0.772996i	−0.922290	+	0.386498i	$0.873685\pi$
$522$	22.9778	−	13.4853i	1.00571	−	0.590236i
$523$	0.600243	−	0.752681i	0.0262468	−	0.0329125i	−0.768535	−	0.639808i	$-0.779014\pi$
$523$	0.600243	−	0.752681i	0.0262468	−	0.0329125i	0.794782	+	0.606895i	$0.207585\pi$
$524$	−14.2472	+	2.35537i	−0.622390	+	0.102895i
$525$	−8.62114	−	15.6167i	−0.376257	−	0.681571i
$526$	12.0357	−	31.3204i	0.524782	−	1.36564i
$527$	5.00155	−	10.3858i	0.217871	−	0.452414i
$528$	−3.37969	+	5.27375i	−0.147082	+	0.229511i
$529$	−11.6279	+	14.5809i	−0.505559	+	0.633951i
$530$	20.4388	−	19.2370i	0.887804	−	0.835604i
$531$	2.03368	+	2.55016i	0.0882544	+	0.110667i
$532$	13.2015	−	16.3872i	0.572357	−	0.710475i
$533$	−0.0338482	+	0.0424443i	−0.00146613	+	0.00183847i
$534$	3.93254	+	47.8971i	0.170177	+	2.07271i
$535$	−2.12582	+	1.02374i	−0.0919071	+	0.0442601i
$536$	24.5107	−	12.4556i	1.05870	−	0.537998i
$537$	−14.0975	+	3.21767i	−0.608354	+	0.138853i
$538$	19.5548	+	13.1293i	0.843067	+	0.566042i
$539$	4.44528	−	1.55061i	0.191472	−	0.0667895i
$540$	−3.61980	+	1.48050i	−0.155772	+	0.0637104i
$541$	2.44608	+	10.7170i	0.105165	+	0.460759i	0.999900	+	0.0141603i	$0.00450752\pi$
$541$	2.44608	+	10.7170i	0.105165	+	0.460759i	−0.894735	+	0.446598i	$0.852635\pi$
$542$	29.0750	−	2.38717i	1.24888	−	0.102538i
$543$	−6.72870	−	13.9723i	−0.288756	−	0.599609i
$544$	−5.20407	−	4.49478i	−0.223123	−	0.192712i
$545$	−8.93043	−	7.12178i	−0.382538	−	0.305064i
$546$	−7.75623	+	5.15212i	−0.331936	+	0.220490i
$547$	8.84560	−	7.05413i	0.378211	−	0.301613i	−0.415872	−	0.909423i	$-0.636523\pi$
$547$	8.84560	−	7.05413i	0.378211	−	0.301613i	0.794082	+	0.607811i	$0.207952\pi$
$548$	−8.74208	+	1.44526i	−0.373443	+	0.0617384i
$549$	14.4150	+	11.4956i	0.615216	+	0.490618i
$550$	0.987985	−	2.57102i	0.0421278	−	0.109629i
$551$	−27.8809	−	13.4267i	−1.18777	−	0.571998i
$552$	42.4906	−	0.907772i	1.80852	−	0.0386373i
$553$	−29.0867	+	1.61926i	−1.23689	+	0.0688580i
$554$	−4.71833	−	5.01308i	−0.200463	−	0.212985i
$555$	−11.2218	−	8.94910i	−0.476340	−	0.379868i
$556$	0.390014	−	6.43233i	0.0165403	−	0.272792i
$557$	0.364405			0.0154403			0.00772016	−	0.999970i	$-0.497543\pi$
$557$	0.364405			0.0154403			0.00772016	+	0.999970i	$0.497543\pi$
$558$	18.0985	−	26.9560i	0.766170	−	1.14114i
$559$	1.27554	+	0.614267i	0.0539495	+	0.0259807i
$560$	10.3367	−	11.3501i	0.436807	−	0.479630i
$561$	−1.71504	+	0.825919i	−0.0724090	+	0.0348703i
$562$	−4.54599	+	31.6901i	−0.191761	+	1.33677i
$563$	0.154902	−	0.678672i	0.00652836	−	0.0286026i	−0.971559	−	0.236798i	$-0.923902\pi$
$563$	0.154902	−	0.678672i	0.00652836	−	0.0286026i	0.978087	+	0.208196i	$0.0667591\pi$
$564$	55.0067	−	9.09383i	2.31620	−	0.382919i
$565$	6.82683	+	14.1761i	0.287207	+	0.596391i
$566$	3.58145	−	24.9663i	0.150539	−	1.04941i
$567$	10.5440	−	25.4203i	0.442804	−	1.06755i
$568$	−5.78344	+	7.57879i	−0.242668	+	0.317999i
$569$	−13.7463			−0.576276			−0.288138	−	0.957589i	$-0.593036\pi$
$569$	−13.7463			−0.576276			−0.288138	+	0.957589i	$0.593036\pi$
$570$	−15.7701	−	10.5882i	−0.660536	−	0.443490i
$571$	−13.4199	+	27.8667i	−0.561605	+	1.16618i	0.406037	+	0.913857i	$0.366910\pi$
$571$	−13.4199	+	27.8667i	−0.561605	+	1.16618i	−0.967642	+	0.252328i	$0.918804\pi$
$572$	−1.37975	−	0.404172i	−0.0576904	−	0.0168993i
$573$	−25.6498	−	5.85440i	−1.07154	−	0.244571i
$574$	0.0672916	+	0.177733i	0.00280870	+	0.00741843i
$575$	−18.2198	+	4.15854i	−0.759817	+	0.173423i
$576$	−12.7116	−	14.6131i	−0.529650	−	0.608881i
$577$	25.5066	−	5.82170i	1.06185	−	0.242361i	0.344296	−	0.938861i	$-0.388118\pi$
$577$	25.5066	−	5.82170i	1.06185	−	0.242361i	0.717556	+	0.696501i	$0.245261\pi$
$578$	6.61963	+	20.9300i	0.275340	+	0.870574i
$579$	7.32511	−	32.0934i	0.304421	−	1.33376i
$580$	−19.7098	−	11.0082i	−0.818405	−	0.457092i
$581$	−0.521574	−	0.0888804i	−0.0216385	−	0.00368738i
$582$	−45.8269	+	14.4939i	−1.89959	+	0.600790i
$583$	−7.19444	+	5.73737i	−0.297963	+	0.237618i
$584$	−1.17666	−	4.69106i	−0.0486906	−	0.194117i
$585$	2.34039	+	2.93476i	0.0967634	+	0.121337i
$586$	−4.76243	+	12.3932i	−0.196734	+	0.511959i
$587$	−31.3599			−1.29436			−0.647180	−	0.762337i	$-0.724052\pi$
$587$	−31.3599			−1.29436			−0.647180	+	0.762337i	$0.724052\pi$
$588$	1.65083	+	32.5545i	0.0680791	+	1.34253i
$589$	−37.7117			−1.55389
$590$	0.991404	−	2.57992i	0.0408155	−	0.106214i
$591$	−16.1511	−	20.2529i	−0.664368	−	0.833091i
$592$	−5.75728	+	15.9943i	−0.236623	+	0.657363i
$593$	34.8534	−	27.7947i	1.43126	−	1.14139i	0.464539	−	0.885553i	$-0.346220\pi$
$593$	34.8534	−	27.7947i	1.43126	−	1.14139i	0.966720	−	0.255838i	$-0.0823514\pi$
$594$	1.22249	−	0.386641i	0.0501592	−	0.0158641i
$595$	4.48364	−	1.28935i	0.183811	−	0.0528582i
$596$	1.17809	−	2.10933i	0.0482566	−	0.0864014i
$597$	−9.24192	+	40.4915i	−0.378247	+	1.65721i
$598$	2.94168	+	9.30104i	0.120294	+	0.380348i
$599$	9.17324	−	2.09373i	0.374809	−	0.0855476i	−0.0309669	−	0.999520i	$-0.509859\pi$
$599$	9.17324	−	2.09373i	0.374809	−	0.0855476i	0.405775	+	0.913973i	$0.367002\pi$
$600$	15.1601	+	11.5688i	0.618908	+	0.472293i
$601$	38.1074	−	8.69777i	1.55443	−	0.354790i	0.642879	−	0.765967i	$-0.277740\pi$
$601$	38.1074	−	8.69777i	1.55443	−	0.354790i	0.911555	+	0.411178i	$0.134883\pi$
$602$	4.12826	−	2.74222i	0.168255	−	0.111765i
$603$	22.9438	+	5.23677i	0.934343	+	0.213258i
$604$	−8.85212	+	30.2191i	−0.360188	+	1.22960i
$605$	−6.63858	+	13.7852i	−0.269897	+	0.560447i
$606$	26.1189	+	17.5364i	1.06101	+	0.712368i
$607$	−6.89261			−0.279762			−0.139881	−	0.990168i	$-0.544672\pi$
$607$	−6.89261			−0.279762			−0.139881	+	0.990168i	$0.544672\pi$
$608$	−5.86152	+	21.7191i	−0.237716	+	0.880828i
$609$	46.0681	−	13.2477i	1.86677	−	0.536823i
$610$	2.21842	−	15.4646i	0.0898211	−	0.626143i
$611$	5.55248	+	11.5298i	0.224629	+	0.466447i
$612$	−0.960052	−	5.80716i	−0.0388078	−	0.234740i
$613$	4.61876	−	20.2361i	0.186550	−	0.817329i	−0.791868	−	0.610693i	$-0.790891\pi$
$613$	4.61876	−	20.2361i	0.186550	−	0.817329i	0.978418	−	0.206636i	$-0.0662517\pi$
$614$	−3.35346	+	23.3770i	−0.135335	+	0.943418i
$615$	0.154557	−	0.0744309i	0.00623235	−	0.00300134i
$616$	−3.68202	+	3.43134i	−0.148353	+	0.138252i
$617$	13.1767	+	6.34558i	0.530475	+	0.255463i	0.679894	−	0.733311i	$-0.262026\pi$
$617$	13.1767	+	6.34558i	0.530475	+	0.255463i	−0.149419	+	0.988774i	$0.547740\pi$
$618$	17.2366	−	25.6723i	0.693358	−	1.03269i
$619$	−30.9095			−1.24236			−0.621179	−	0.783669i	$-0.713346\pi$
$619$	−30.9095			−1.24236			−0.621179	+	0.783669i	$0.713346\pi$
$620$	−27.4613	−	1.66507i	−1.10287	−	0.0668710i
$621$	−6.80167	−	5.42415i	−0.272941	−	0.217664i
$622$	15.8082	+	16.7957i	0.633851	+	0.673448i
$623$	−6.48687	+	38.0667i	−0.259891	+	1.52511i
$624$	5.37101	−	8.38104i	0.215012	−	0.335510i
$625$	1.92413	+	0.926611i	0.0769651	+	0.0370644i
$626$	−14.0647	+	36.6005i	−0.562140	+	1.46285i
$627$	4.86881	+	3.88275i	0.194442	+	0.155062i
$628$	−6.76229	−	40.9037i	−0.269845	−	1.63224i
$629$	−4.03891	+	3.22093i	−0.161042	+	0.128427i
$630$	13.0164	−	1.80155i	0.518585	−	0.0717756i
$631$	−11.8306	−	9.43462i	−0.470970	−	0.375586i	0.359051	−	0.933318i	$-0.383100\pi$
$631$	−11.8306	−	9.43462i	−0.470970	−	0.375586i	−0.830021	+	0.557732i	$0.811672\pi$
$632$	27.7640	−	14.1087i	1.10439	−	0.561216i
$633$	17.4146	+	36.1617i	0.692167	+	1.43730i
$634$	−7.02441	+	0.576731i	−0.278975	+	0.0229049i
$635$	−5.88253	−	25.7730i	−0.233441	−	1.02277i
$636$	−24.1187	−	58.9702i	−0.956370	−	2.33832i
$637$	−7.06443	+	2.46423i	−0.279903	+	0.0976364i
$638$	6.14484	+	4.12570i	0.243277	+	0.163338i
$639$	−7.95567	+	1.81583i	−0.314721	+	0.0718331i
$640$	−5.22726	+	15.5569i	−0.206626	+	0.614940i
$641$	−30.7552	+	14.8109i	−1.21476	+	0.584996i	−0.927847	−	0.372962i	$-0.878342\pi$
$641$	−30.7552	+	14.8109i	−1.21476	+	0.584996i	−0.286910	+	0.957958i	$0.592628\pi$
$642$	0.438259	+	5.33786i	0.0172967	+	0.210668i
$643$	−8.05520	+	10.1009i	−0.317666	+	0.398340i	−0.914870	−	0.403749i	$-0.867707\pi$
$643$	−8.05520	+	10.1009i	−0.317666	+	0.398340i	0.597204	+	0.802089i	$0.296278\pi$
$644$	33.2553	+	7.76357i	1.31044	+	0.305928i
$645$	−2.78925	−	3.49761i	−0.109827	−	0.137718i
$646$	−4.97832	+	4.68561i	−0.195869	+	0.184353i
$647$	7.56190	−	9.48232i	0.297289	−	0.372788i	−0.610643	−	0.791906i	$-0.709089\pi$
$647$	7.56190	−	9.48232i	0.297289	−	0.372788i	0.907932	+	0.419118i	$0.137660\pi$
$648$	0.628398	+	29.4137i	0.0246858	+	1.15548i
$649$	−0.393153	+	0.816391i	−0.0154326	+	0.0320462i
$650$	−1.57011	+	4.08587i	−0.0615846	+	0.160261i
$651$	43.5764	−	38.9041i	1.70790	−	1.52477i
$652$	−5.07510	−	30.6983i	−0.198756	−	1.20224i
$653$	−1.66896	+	2.09281i	−0.0653115	+	0.0818981i	−0.813414	−	0.581685i	$-0.802394\pi$
$653$	−1.66896	+	2.09281i	−0.0653115	+	0.0818981i	0.748103	+	0.663583i	$0.230965\pi$
$654$	−22.3614	+	13.1235i	−0.874401	+	0.513171i
$655$			10.4737i			0.409241i
$656$	−0.142374	−	0.144936i	−0.00555876	−	0.00565881i
$657$	1.79618	−	3.72980i	0.0700755	−	0.145513i
$658$	44.6297	+	3.88661i	1.73985	+	0.151516i
$659$	−5.98152	−	12.4208i	−0.233007	−	0.483844i	0.751378	−	0.659872i	$-0.229389\pi$
$659$	−5.98152	−	12.4208i	−0.233007	−	0.483844i	−0.984385	+	0.176028i	$0.943675\pi$
$660$	3.37399	+	3.04235i	0.131332	+	0.118423i
$661$	5.19826	+	1.18647i	0.202189	+	0.0461482i	0.322416	−	0.946598i	$-0.395505\pi$
$661$	5.19826	+	1.18647i	0.202189	+	0.0461482i	−0.120227	+	0.992746i	$0.538362\pi$
$662$	−0.149381	+	0.140597i	−0.00580584	+	0.00546447i
$663$	2.72554	−	1.31255i	0.105851	−	0.0509753i
$664$	0.548628	−	0.137613i	0.0212909	−	0.00534041i
$665$	−10.1647	−	11.3854i	−0.394168	−	0.441507i
$666$	−12.5490	+	7.36479i	−0.486263	+	0.285380i
$667$		−	50.2191i		−	1.94449i
$668$	−2.45244	−	5.99622i	−0.0948879	−	0.232001i
$669$	−10.6567	−	5.13199i	−0.412011	−	0.198414i
$670$	−6.01333	−	19.0130i	−0.232315	−	0.734537i
$671$	−1.13974	+	4.99353i	−0.0439992	+	0.192773i
$672$	−15.6328	−	31.1436i	−0.603049	−	1.20139i
$673$	4.47406	+	19.6021i	0.172462	+	0.755606i	0.984980	+	0.172670i	$0.0552393\pi$
$673$	4.47406	+	19.6021i	0.172462	+	0.755606i	−0.812518	+	0.582937i	$0.801904\pi$
$674$	5.76248	−	3.38190i	0.221963	−	0.130266i
$675$	−0.868625	−	3.80569i	−0.0334334	−	0.146481i
$676$	−22.7588	−	6.66675i	−0.875339	−	0.256414i
$677$	35.8373	+	8.17963i	1.37734	+	0.314369i	0.846177	−	0.532902i	$-0.178899\pi$
$677$	35.8373	+	8.17963i	1.37734	+	0.314369i	0.531162	+	0.847270i	$0.321756\pi$
$678$	35.5956	−	2.92254i	1.36704	−	0.112239i
$679$	−38.5606	+	2.14668i	−1.47982	+	0.0823818i
$680$	−3.83205	+	3.19221i	−0.146952	+	0.122416i
$681$	−7.98983	−	10.0189i	−0.306171	−	0.383926i
$682$	8.92830	+	1.28078i	0.341882	+	0.0490435i
$683$	−7.87807	+	6.28255i	−0.301446	+	0.240395i	−0.762517	−	0.646968i	$-0.776037\pi$
$683$	−7.87807	+	6.28255i	−0.301446	+	0.240395i	0.461071	+	0.887363i	$0.347465\pi$
$684$	−15.7539	+	11.0727i	−0.602366	+	0.423376i
$685$			6.42667i			0.245551i
$686$	−5.20451	+	25.6693i	−0.198709	+	0.980059i
$687$		−	10.0608i		−	0.383843i
$688$	−2.85873	+	4.46082i	−0.108988	+	0.170067i
$689$	11.4334	−	9.11783i	0.435578	−	0.347362i
$690$	4.37713	−	30.5130i	0.166634	−	1.16161i
$691$	−4.28751	−	5.37636i	−0.163104	−	0.204526i	0.693562	−	0.720397i	$-0.256040\pi$
$691$	−4.28751	−	5.37636i	−0.163104	−	0.204526i	−0.856667	+	0.515870i	$0.827469\pi$
$692$	−10.4684	+	35.7369i	−0.397950	+	1.35851i
$693$	−4.30142	+	0.239461i	−0.163398	+	0.00909637i
$694$	−2.08527	−	25.3979i	−0.0791556	−	0.964091i
$695$	−4.55674	−	1.04005i	−0.172847	−	0.0394512i
$696$	−39.3731	+	32.7990i	−1.49243	+	1.24324i
$697$	−0.0137389	−	0.0601941i	−0.000520398	−	0.00228001i
$698$	9.88229	+	16.8386i	0.374050	+	0.637350i
$699$	8.06208	+	35.3223i	0.304936	+	1.33601i
$700$	9.49436	+	12.0271i	0.358853	+	0.454582i
$701$	−7.50652	+	32.8882i	−0.283517	+	1.24217i	0.609732	+	0.792608i	$0.291277\pi$
$701$	−7.50652	+	32.8882i	−0.283517	+	1.24217i	−0.893249	+	0.449562i	$0.851580\pi$
$702$	−1.94278	+	0.614450i	−0.0733253	+	0.0231909i
$703$	15.2267	+	7.33281i	0.574287	+	0.276562i
$704$	2.12535	−	4.94297i	0.0801023	−	0.186295i
$705$		−	40.4378i		−	1.52297i
$706$	−6.67968	−	11.3816i	−0.251393	−	0.428353i
$707$	16.8350	+	18.8568i	0.633145	+	0.709184i
$708$	−4.65926	−	4.20129i	−0.175106	−	0.157894i
$709$	−6.52530	+	3.14242i	−0.245063	+	0.118016i	−0.552384	−	0.833590i	$-0.686282\pi$
$709$	−6.52530	+	3.14242i	−0.245063	+	0.118016i	0.307321	+	0.951606i	$0.400567\pi$
$710$	4.73907	+	5.03512i	0.177854	+	0.188965i
$711$	25.9890	+	5.93183i	0.974665	+	0.222461i
$712$	−10.0436	−	40.0413i	−0.376399	−	1.50061i
$713$	−26.5535	−	55.1389i	−0.994436	−	2.06497i
$714$	0.918756	−	10.5500i	0.0343836	−	0.394824i
$715$	−0.452447	+	0.939515i	−0.0169205	+	0.0351359i
$716$	11.4967	−	4.70213i	0.429651	−	0.175727i
$717$			12.0802i			0.451142i
$718$	7.96656	+	13.5744i	0.297309	+	0.506590i
$719$	−1.61864	+	2.02972i	−0.0603652	+	0.0756956i	−0.811097	−	0.584911i	$-0.801129\pi$
$719$	−1.61864	+	2.02972i	−0.0603652	+	0.0756956i	0.750732	+	0.660607i	$0.229701\pi$
$720$	−11.9607	+	7.36747i	−0.445751	+	0.274569i
$721$	18.5345	−	16.5472i	0.690259	−	0.616249i
$722$	−4.20457	−	1.61572i	−0.156478	−	0.0601308i
$723$	−20.6520	+	42.8843i	−0.768056	+	1.59488i
$724$	7.66014	+	10.8986i	0.284687	+	0.405044i
$725$	14.0494	−	17.6174i	0.521781	−	0.654292i
$726$	23.8035	+	25.2905i	0.883429	+	0.938617i
$727$	−7.04878	−	8.83890i	−0.261425	−	0.327816i	0.633745	−	0.773542i	$-0.281517\pi$
$727$	−7.04878	−	8.83890i	−0.261425	−	0.327816i	−0.895169	+	0.445726i	$0.852946\pi$
$728$	5.85146	−	5.45308i	0.216869	−	0.202105i
$729$	−9.83057	+	12.3271i	−0.364095	+	0.456561i
$730$	−3.49605	+	0.287039i	−0.129395	+	0.0106238i
$731$	−1.45067	+	0.698607i	−0.0536550	+	0.0258389i
$732$	−30.9609	−	17.2922i	−1.14435	−	0.639138i
$733$	30.7234	−	7.01242i	1.13480	−	0.259010i	0.386445	−	0.922313i	$-0.373703\pi$
$733$	30.7234	−	7.01242i	1.13480	−	0.259010i	0.748351	+	0.663303i	$0.230846\pi$
$734$	−10.0113	+	14.9108i	−0.369522	+	0.550368i
$735$	23.4908	+	2.66995i	0.866471	+	0.0984828i
$736$	−35.8831	+	6.72262i	−1.32267	+	0.247799i
$737$	1.45478	+	6.37381i	0.0535876	+	0.234782i
$738$	−0.0142303	−	0.173320i	−0.000523823	−	0.00638000i
$739$	12.5159	+	25.9895i	0.460405	+	0.956040i	0.993905	+	0.110240i	$0.0351621\pi$
$739$	12.5159	+	25.9895i	0.460405	+	0.956040i	−0.533500	+	0.845800i	$0.679124\pi$
$740$	10.7642	+	6.01199i	0.395700	+	0.221005i
$741$	−7.73751	−	6.17046i	−0.284245	−	0.226678i
$742$	−7.01859	−	50.7099i	−0.257660	−	1.86162i
$743$	−18.6036	+	14.8359i	−0.682500	+	0.544275i	−0.902214	−	0.431289i	$-0.858059\pi$
$743$	−18.6036	+	14.8359i	−0.682500	+	0.544275i	0.219714	+	0.975564i	$0.429488\pi$
$744$	−25.8878	+	56.8309i	−0.949094	+	2.08352i
$745$	−1.37003	−	1.09256i	−0.0501940	−	0.0400284i
$746$	11.6080	+	4.46067i	0.424998	+	0.163317i
$747$	0.436207	+	0.210066i	0.0159600	+	0.00768592i
$748$	1.33776	−	0.940249i	0.0489133	−	0.0343789i
$749$	−0.722925	+	4.24232i	−0.0264151	+	0.155011i
$750$	27.4626	−	25.8479i	1.00279	−	0.943831i
$751$	18.7888	+	14.9835i	0.685611	+	0.546757i	0.903166	−	0.429291i	$-0.141237\pi$
$751$	18.7888	+	14.9835i	0.685611	+	0.546757i	−0.217555	+	0.976048i	$0.569808\pi$
$752$	−45.3434	+	15.4138i	−1.65351	+	0.562085i
$753$	44.7475			1.63069
$754$	−9.76538	−	6.55656i	−0.355634	−	0.238776i
$755$	20.5771	+	9.90942i	0.748878	+	0.360641i
$756$	−1.62163	+	6.94628i	−0.0589782	+	0.252634i
$757$	26.1432	−	12.5899i	0.950191	−	0.457588i	0.106438	−	0.994319i	$-0.466055\pi$
$757$	26.1432	−	12.5899i	0.950191	−	0.457588i	0.843753	+	0.536731i	$0.180341\pi$
$758$	43.3966	+	6.22530i	1.57623	+	0.226113i
$759$	−2.24881	+	9.85267i	−0.0816265	+	0.357629i
$760$	14.8485	+	6.76383i	0.538610	+	0.245350i
$761$	0.615243	+	1.27756i	0.0223025	+	0.0463117i	0.911823	−	0.410585i	$-0.134675\pi$
$761$	0.615243	+	1.27756i	0.0223025	+	0.0463117i	−0.889520	+	0.456896i	$0.848961\pi$
$762$	−59.3991	−	8.52088i	−2.15180	−	0.308679i
$763$	−20.0221	+	5.75770i	−0.724848	+	0.208443i
$764$	22.5582	+	1.36778i	0.816126	+	0.0494845i
$765$	−4.26909			−0.154349
$766$	−13.5923	+	20.2444i	−0.491108	+	0.731459i
$767$	0.624799	−	1.29741i	0.0225602	−	0.0468467i
$768$	28.7066	+	23.7427i	1.03586	+	0.856739i
$769$	−20.5291	−	4.68563i	−0.740298	−	0.168968i	−0.164290	−	0.986412i	$-0.552533\pi$
$769$	−20.5291	−	4.68563i	−0.740298	−	0.168968i	−0.576008	+	0.817444i	$0.695390\pi$
$770$	2.01982	+	3.04073i	0.0727893	+	0.109580i
$771$	−41.5690	+	9.48785i	−1.49707	+	0.341697i
$772$	−1.71138	+	28.2251i	−0.0615940	+	1.01584i
$773$	−6.89037	+	1.57268i	−0.247829	+	0.0565654i	−0.344631	−	0.938738i	$-0.611996\pi$
$773$	−6.89037	+	1.57268i	−0.247829	+	0.0565654i	0.0968015	+	0.995304i	$0.469139\pi$
$774$	−4.32398	+	1.36756i	−0.155422	+	0.0491561i
$775$	6.11052	−	26.7719i	0.219496	−	0.961676i
$776$	36.8070	−	18.7041i	1.32130	−	0.671439i
$777$	−25.1594	+	7.23502i	−0.902587	+	0.259555i
$778$	−15.9616	−	50.4675i	−0.572250	−	1.80935i
$779$	−0.157921	+	0.125938i	−0.00565811	+	0.00451219i
$780$	−5.36194	−	4.83491i	−0.191988	−	0.173117i
$781$	−1.41341	−	1.77236i	−0.0505758	−	0.0634200i
$782$	−10.3562	−	3.97965i	−0.370337	−	0.142312i
$783$	10.4896			0.374868
$784$	−5.96023	−	27.3583i	−0.212865	−	0.977082i
$785$	−30.0701			−1.07325
$786$	22.1922	+	8.52796i	0.791571	+	0.304182i
$787$	25.9535	+	32.5447i	0.925143	+	1.16009i	0.986792	+	0.161995i	$0.0517927\pi$
$787$	25.9535	+	32.5447i	0.925143	+	1.16009i	−0.0616488	+	0.998098i	$0.519636\pi$
$788$	16.5255	+	14.9012i	0.588696	+	0.530832i
$789$	−43.1892	+	34.4422i	−1.53758	+	1.22618i
$790$	−6.81146	−	21.5366i	−0.242341	−	0.766237i
$791$	28.2900	+	4.82084i	1.00588	+	0.171409i
$792$	4.10581	−	2.08644i	0.145894	−	0.0741384i
$793$	1.81128	−	7.93572i	0.0643203	−	0.281806i
$794$	23.7533	−	7.51257i	0.842974	−	0.266611i
$795$	−45.0514	+	10.2827i	−1.59781	+	0.364690i
$796$	2.15921	−	35.6109i	0.0765313	−	1.26220i
$797$	−23.6882	+	5.40668i	−0.839080	+	0.191515i	−0.620404	−	0.784283i	$-0.713031\pi$
$797$	−23.6882	+	5.40668i	−0.839080	+	0.191515i	−0.218677	+	0.975797i	$0.570174\pi$
$798$	−32.4004	+	12.2671i	−1.14696	+	0.434252i
$799$	−14.1893	−	3.23862i	−0.501982	−	0.114574i
$800$	−14.4689	−	7.68035i	−0.511552	−	0.271541i
$801$	15.3315	−	31.8363i	0.541713	−	1.12488i
$802$	20.9921	−	31.2657i	0.741256	−	1.10403i
$803$	1.15003			0.0405837
$804$	−45.1821	−	2.73954i	−1.59345	−	0.0966162i
$805$	9.48966	−	22.8785i	0.334467	−	0.806363i
$806$	−14.1889	−	2.03541i	−0.499781	−	0.0716943i
$807$	−16.8250	−	34.9374i	−0.592267	−	1.22986i
$808$	−24.5924	−	11.2024i	−0.865159	−	0.394100i
$809$	3.40216	−	14.9058i	0.119613	−	0.524061i	−0.879248	−	0.476364i	$-0.841955\pi$
$809$	3.40216	−	14.9058i	0.119613	−	0.524061i	0.998862	−	0.0476972i	$-0.0151882\pi$
$810$	21.1224	+	3.03003i	0.742164	+	0.106464i
$811$	17.6239	−	8.48724i	0.618860	−	0.298027i	−0.0980622	−	0.995180i	$-0.531264\pi$
$811$	17.6239	−	8.48724i	0.618860	−	0.298027i	0.716922	+	0.697153i	$0.245550\pi$
$812$	−37.1860	+	17.6818i	−1.30497	+	0.620509i
$813$	−43.2728	−	20.8391i	−1.51764	−	0.730858i
$814$	−3.35591	−	2.25319i	−0.117625	−	0.0789742i
$815$	−22.5676			−0.790508
$816$	3.64368	+	10.7187i	0.127554	+	0.375231i
$817$	4.11830	+	3.28423i	0.144081	+	0.114901i
$818$	9.91832	−	9.33516i	0.346786	−	0.326396i
$819$	6.83582	−	0.380551i	0.238863	−	0.0132975i
$820$	−0.120557	+	0.0847341i	−0.00421004	+	0.00295904i
$821$	−13.4244	−	6.46485i	−0.468514	−	0.225625i	0.184704	−	0.982794i	$-0.440867\pi$
$821$	−13.4244	−	6.46485i	−0.468514	−	0.225625i	−0.653218	+	0.757170i	$0.726582\pi$
$822$	13.6172	+	5.23277i	0.474954	+	0.182514i
$823$	17.3688	+	13.8512i	0.605440	+	0.482822i	0.877577	−	0.479436i	$-0.159159\pi$
$823$	17.3688	+	13.8512i	0.605440	+	0.482822i	−0.272137	+	0.962259i	$0.587730\pi$
$824$	−11.0109	+	24.1720i	−0.383584	+	0.842071i
$825$	−3.54530	+	2.82729i	−0.123432	+	0.0984335i
$826$	−2.78924	−	4.19904i	−0.0970500	−	0.146103i
$827$	35.4147	+	28.2423i	1.23149	+	0.982081i	0.999957	+	0.00925449i	$0.00294584\pi$
$827$	35.4147	+	28.2423i	1.23149	+	0.982081i	0.231534	+	0.972827i	$0.425626\pi$
$828$	−27.2822	−	15.2375i	−0.948121	−	0.529541i
$829$	−11.5134	−	23.9077i	−0.399876	−	0.830350i	−0.999547	−	0.0301039i	$-0.990416\pi$
$829$	−11.5134	−	23.9077i	−0.399876	−	0.830350i	0.599671	−	0.800247i	$-0.295298\pi$
$830$	−0.0335698	−	0.408870i	−0.00116522	−	0.0141921i
$831$	2.52207	+	11.0499i	0.0874896	+	0.383317i
$832$	−3.37761	+	7.85536i	−0.117098	+	0.272336i
$833$	2.81822	−	8.02891i	0.0976455	−	0.278185i
$834$	−5.91393	+	8.80824i	−0.204783	+	0.305004i
$835$	−4.58093	+	1.04557i	−0.158530	+	0.0361833i
$836$	−4.67027	−	2.60842i	−0.161525	−	0.0902141i
$837$	11.5172	−	5.54641i	0.398094	−	0.191712i
$838$	30.0157	−	2.46440i	1.03687	−	0.0851314i
$839$	25.0606	−	31.4250i	0.865188	−	1.08491i	−0.130435	−	0.991457i	$-0.541637\pi$
$839$	25.0606	−	31.4250i	0.865188	−	1.08491i	0.995623	−	0.0934552i	$-0.0297912\pi$
$840$	−24.1353	+	7.50225i	−0.832747	+	0.258852i
$841$	19.6721	+	24.6681i	0.678349	+	0.850623i
$842$	8.79144	+	9.34064i	0.302973	+	0.321900i
$843$	32.8626	−	41.2084i	1.13185	−	1.41929i
$844$	−19.8252	−	28.2067i	−0.682412	−	0.970914i
$845$	−7.46304	+	15.4972i	−0.256736	+	0.533118i
$846$	−38.2655	−	14.7045i	−1.31559	−	0.505552i
$847$	13.4870	+	24.4310i	0.463418	+	0.839458i
$848$	28.7026	+	46.5973i	0.985650	+	1.60016i
$849$	−25.8900	+	32.4650i	−0.888543	+	1.11420i
$850$	−2.51971	−	4.29338i	−0.0864254	−	0.147262i
$851$			27.4264i			0.940164i
$852$	14.5274	−	5.94168i	0.497700	−	0.203559i
$853$	−1.99245	+	4.13737i	−0.0682203	+	0.141661i	−0.932291	−	0.361710i	$-0.882193\pi$
$853$	−1.99245	+	4.13737i	−0.0682203	+	0.141661i	0.864070	+	0.503371i	$0.167907\pi$
$854$	−20.6527	−	19.6320i	−0.706722	−	0.671792i
$855$	6.05974	+	12.5832i	0.207239	+	0.430336i
$856$	−1.11930	−	4.46237i	−0.0382568	−	0.152521i
$857$	9.75284	+	2.22602i	0.333151	+	0.0760395i	0.385824	−	0.922572i	$-0.373917\pi$
$857$	9.75284	+	2.22602i	0.333151	+	0.0760395i	−0.0526735	+	0.998612i	$0.516774\pi$
$858$	1.62230	+	1.72365i	0.0553845	+	0.0588444i
$859$	−12.0508	+	5.80338i	−0.411169	+	0.198009i	−0.628022	−	0.778196i	$-0.716135\pi$
$859$	−12.0508	+	5.80338i	−0.411169	+	0.198009i	0.216853	+	0.976204i	$0.430421\pi$
$860$	2.85390	+	2.57338i	0.0973172	+	0.0877516i
$861$	0.0525602	−	0.308437i	0.00179125	−	0.0105115i
$862$	17.1943	+	29.2976i	0.585640	+	0.997881i
$863$		−	20.3797i		−	0.693733i	−0.937915	−	0.346866i	$-0.887246\pi$
$863$		−	20.3797i		−	0.693733i	0.937915	−	0.346866i	$-0.112754\pi$
$864$	−1.40420	−	7.49515i	−0.0477719	−	0.254990i
$865$	24.3343	+	11.7188i	0.827391	+	0.398451i
$866$	−2.02146	+	0.639337i	−0.0686922	+	0.0217256i
$867$	8.04209	−	35.2347i	0.273124	−	1.19663i
$868$	−31.4797	+	39.0762i	−1.06849	+	1.32633i
$869$	1.64787	+	7.21979i	0.0559002	+	0.244915i
$870$	18.8125	+	32.0550i	0.637805	+	1.08677i
$871$	−2.31194	−	10.1293i	−0.0783370	−	0.343217i
$872$	17.1123	−	14.2551i	0.579497	−	0.482738i
$873$	34.4540	+	7.86390i	1.16609	+	0.266153i
$874$	2.97002	+	36.1739i	0.100462	+	1.22360i
$875$	26.5293	−	14.6454i	0.896854	−	0.495103i
$876$	−2.23838	+	7.64134i	−0.0756280	+	0.258177i
$877$	−15.8102	−	19.8254i	−0.533874	−	0.669457i	0.439616	−	0.898186i	$-0.355114\pi$
$877$	−15.8102	−	19.8254i	−0.533874	−	0.669457i	−0.973490	+	0.228729i	$0.926543\pi$
$878$	−4.17923	+	29.1334i	−0.141042	+	0.983206i
$879$	17.0896	−	13.6285i	0.576417	−	0.459678i
$880$	−3.28568	−	2.10563i	−0.110760	−	0.0709809i
$881$			38.8961i			1.31044i	0.755437	+	0.655222i	$0.227425\pi$
$881$			38.8961i			1.31044i	−0.755437	+	0.655222i	$0.772575\pi$
$882$	11.0686	−	21.2580i	0.372698	−	0.715794i
$883$			40.1661i			1.35170i	0.737040	+	0.675849i	$0.236223\pi$
$883$			40.1661i			1.35170i	−0.737040	+	0.675849i	$0.763777\pi$
$884$	−2.12596	+	1.49424i	−0.0715039	+	0.0502568i
$885$	−3.55757	+	2.83707i	−0.119587	+	0.0953671i
$886$	−34.4446	−	4.94112i	−1.15719	−	0.166000i
$887$	22.6974	+	28.4617i	0.762105	+	0.955649i	0.999877	−	0.0156715i	$-0.00498861\pi$
$887$	22.6974	+	28.4617i	0.762105	+	0.955649i	−0.237772	+	0.971321i	$0.576417\pi$
$888$	21.5030	−	17.9127i	0.721595	−	0.601110i
$889$	−44.5373	−	18.4734i	−1.49373	−	0.619576i
$890$	−29.8411	+	2.45007i	−1.00028	+	0.0821264i
$891$	−6.82043	−	1.55672i	−0.228493	−	0.0521520i
$892$	9.75046	+	2.85621i	0.326469	+	0.0956329i
$893$	10.5951	+	46.4202i	0.354552	+	1.55339i
$894$	−3.43050	+	2.01330i	−0.114733	+	0.0673349i
$895$	−2.00469	−	8.78311i	−0.0670094	−	0.293587i
$896$	17.6121	+	24.2036i	0.588380	+	0.808585i
$897$	3.57380	−	15.6579i	0.119326	−	0.522801i
$898$	−7.88138	−	24.9194i	−0.263005	−	0.831573i
$899$	66.4837	+	32.0169i	2.21736	+	1.06782i
$900$	−5.30798	−	12.9780i	−0.176933	−	0.432600i
$901$			16.6317i			0.554084i
$902$	0.0416652	−	0.0244526i	0.00138730	−	0.000814182i
$903$	−8.14683	+	0.453536i	−0.271110	+	0.0150927i
$904$	−29.7574	+	7.46407i	−0.989716	+	0.248251i
$905$	8.70509	−	4.19215i	0.289367	−	0.139352i
$906$	37.7511	−	35.5315i	1.25420	−	1.18045i
$907$	−37.9905	−	8.67107i	−1.26145	−	0.287918i	−0.461046	−	0.887376i	$-0.652526\pi$
$907$	−37.9905	−	8.67107i	−1.26145	−	0.287918i	−0.800406	+	0.599458i	$0.795383\pi$
$908$	8.17503	+	7.37148i	0.271298	+	0.244631i
$909$	−10.0363	−	20.8406i	−0.332883	−	0.691239i
$910$	−3.20990	−	4.83232i	−0.106407	−	0.160190i
$911$	9.20738	−	19.1193i	0.305054	−	0.633452i	−0.690936	−	0.722916i	$-0.742801\pi$
$911$	9.20738	−	19.1193i	0.305054	−	0.633452i	0.995990	+	0.0894645i	$0.0285156\pi$
$912$	26.4216	−	25.9545i	0.874906	−	0.859438i
$913$			0.134498i			0.00445125i
$914$	9.74872	−	5.72136i	0.322459	−	0.189246i
$915$	−16.0368	+	20.1095i	−0.530159	+	0.664799i
$916$	1.40960	+	8.52639i	0.0465745	+	0.281720i
$917$	15.5743	+	11.0620i	0.514309	+	0.365298i
$918$	0.831258	−	2.16318i	0.0274356	−	0.0713955i
$919$	2.89323	−	6.00785i	0.0954388	−	0.198181i	−0.847784	−	0.530342i	$-0.822064\pi$
$919$	2.89323	−	6.00785i	0.0954388	−	0.198181i	0.943223	+	0.332161i	$0.107778\pi$
$920$	0.565564	+	26.4727i	0.0186461	+	0.872778i
$921$	24.2419	−	30.3984i	0.798798	−	1.00166i
$922$	−34.9443	+	32.8897i	−1.15083	+	1.08316i
$923$	2.24619	+	2.81663i	0.0739343	+	0.0927106i
$924$	8.08746	−	1.80387i	0.266058	−	0.0593429i
$925$	−7.67285	+	9.62145i	−0.252282	+	0.316351i
$926$	2.73472	+	33.3080i	0.0898684	+	1.09457i
$927$	−20.4843	+	9.86473i	−0.672793	+	0.324000i
$928$	28.7729	−	33.3133i	0.944515	−	1.09356i
$929$	9.71183	−	2.21666i	0.318635	−	0.0727263i	−0.0602122	−	0.998186i	$-0.519178\pi$
$929$	9.71183	−	2.21666i	0.318635	−	0.0727263i	0.378847	+	0.925459i	$0.376321\pi$
$930$	37.6047	+	25.2481i	1.23311	+	0.827919i
$931$	−27.6656	+	3.08988i	−0.906704	+	0.101267i
$932$	−11.7815	−	28.8057i	−0.385915	−	0.943561i
$933$	−8.44989	−	37.0214i	−0.276637	−	1.21203i
$934$	19.4493	−	1.59686i	0.636401	−	0.0522510i
$935$	−0.514568	−	1.06851i	−0.0168282	−	0.0349441i
$936$	−6.52496	+	3.31577i	−0.213275	+	0.108379i
$937$	30.1877	+	24.0739i	0.986189	+	0.786459i	0.976944	−	0.213498i	$-0.0684857\pi$
$937$	30.1877	+	24.0739i	0.986189	+	0.786459i	0.00924530	+	0.999957i	$0.497057\pi$
$938$	−34.6233	−	11.1392i	−1.13049	−	0.363706i
$939$	50.4701	−	40.2486i	1.64703	−	1.31346i
$940$	5.66568	+	34.2706i	0.184794	+	1.11778i
$941$	−9.42057	−	7.51266i	−0.307102	−	0.244906i	0.457796	−	0.889057i	$-0.348639\pi$
$941$	−9.42057	−	7.51266i	−0.307102	−	0.244906i	−0.764898	+	0.644152i	$0.777210\pi$
$942$	−24.4839	+	63.7141i	−0.797727	+	2.07592i
$943$	−0.295330	−	0.142224i	−0.00961728	−	0.00463144i
$944$	4.53730	+	2.90774i	0.147677	+	0.0946389i
$945$	4.77881	+	1.98217i	0.155455	+	0.0644801i
$946$	−0.863473	−	0.917414i	−0.0280739	−	0.0298277i
$947$	−15.5722	−	12.4184i	−0.506029	−	0.403544i	0.336924	−	0.941532i	$-0.390613\pi$
$947$	−15.5722	−	12.4184i	−0.506029	−	0.403544i	−0.842953	+	0.537987i	$0.819185\pi$
$948$	−51.1790	−	3.10316i	−1.66222	−	0.100786i
$949$	−1.82763			−0.0593274
$950$	−9.07817	+	13.5211i	−0.294535	+	0.438682i
$951$	10.4545	+	5.03463i	0.339011	+	0.163259i
$952$	0.699513	+	9.06974i	0.0226713	+	0.293952i
$953$	40.4520	−	19.4806i	1.31037	−	0.631040i	0.357355	−	0.933969i	$-0.383679\pi$
$953$	40.4520	−	19.4806i	1.31037	−	0.631040i	0.953013	+	0.302929i	$0.0979645\pi$
$954$	−6.65190	+	46.3704i	−0.215363	+	1.50130i
$955$	3.64744	−	15.9805i	0.118028	−	0.517116i
$956$	−1.69253	−	10.2378i	−0.0547405	−	0.331114i
$957$	−5.28703	−	10.9786i	−0.170906	−	0.354889i
$958$	0.695867	−	4.85089i	0.0224824	−	0.156725i
$959$	9.55642	+	6.78764i	0.308593	+	0.219184i
$960$	20.3859	−	17.7332i	0.657953	−	0.572337i
$961$	58.9259			1.90084
$962$	5.33321	+	3.58076i	0.171950	+	0.115448i
$963$	1.70861	−	3.54797i	0.0550593	−	0.114332i
$964$	11.4939	−	39.2375i	0.370192	−	1.26375i
$965$	19.9950	+	4.56372i	0.643661	+	0.146911i
$966$	−40.7496	−	38.7356i	−1.31110	−	1.24630i
$967$	−41.6938	+	9.51635i	−1.34078	+	0.306025i	−0.831955	−	0.554843i	$-0.812778\pi$
$967$	−41.6938	+	9.51635i	−1.34078	+	0.306025i	−0.508828	+	0.860868i	$0.669921\pi$
$968$	−23.7166	−	18.0983i	−0.762279	−	0.581702i
$969$	10.9733	−	2.50458i	0.352512	−	0.0804586i
$970$	−9.03003	−	28.5513i	−0.289937	−	0.916726i
$971$	3.70172	−	16.2183i	0.118794	−	0.520469i	−0.880158	−	0.474682i	$-0.842563\pi$
$971$	3.70172	−	16.2183i	0.118794	−	0.520469i	0.998951	−	0.0457874i	$-0.0145797\pi$
$972$	19.6747	−	35.2267i	0.631066	−	1.12990i
$973$	−6.35922	+	5.67738i	−0.203867	+	0.182008i
$974$	−3.77380	+	1.19356i	−0.120920	+	0.0382440i
$975$	5.63420	−	4.49312i	0.180439	−	0.143895i
$976$	28.6618	+	10.3170i	0.917443	+	0.330240i
$977$	−7.77489	−	9.74940i	−0.248741	−	0.311911i	0.641749	−	0.766915i	$-0.278209\pi$
$977$	−7.77489	−	9.74940i	−0.248741	−	0.311911i	−0.890489	+	0.455004i	$0.849638\pi$
$978$	−18.3751	+	47.8175i	−0.587572	+	1.52903i
$979$	9.81628			0.313730
$980$	−20.2823	+	1.02851i	−0.647893	+	0.0328545i
$981$	19.0640			0.608666
$982$	20.8965	−	54.3788i	0.666834	−	1.73530i
$983$	−20.0724	−	25.1699i	−0.640209	−	0.802797i	0.350820	−	0.936443i	$-0.385903\pi$
$983$	−20.0724	−	25.1699i	−0.640209	−	0.802797i	−0.991029	+	0.133646i	$0.957331\pi$
$984$	0.0813785	+	0.324436i	0.00259425	+	0.0103426i
$985$	12.6180	−	10.0625i	0.402044	−	0.320619i
$986$	12.7545	−	4.03393i	0.406187	−	0.128466i
$987$	−60.1307	−	42.7091i	−1.91398	−	1.35944i
$988$	7.42199	+	4.14530i	0.236125	+	0.131880i
$989$	−1.90216	+	8.33391i	−0.0604852	+	0.265003i
$990$	−1.00730	−	3.18489i	−0.0320140	−	0.101222i
$991$	8.38553	−	1.91394i	0.266375	−	0.0607984i	−0.0872471	−	0.996187i	$-0.527807\pi$
$991$	8.38553	−	1.91394i	0.266375	−	0.0607984i	0.353622	+	0.935388i	$0.384950\pi$
$992$	13.9771	−	51.7906i	0.443775	−	1.64435i
$993$	0.329266	−	0.0751529i	0.0104490	−	0.00238491i
$994$	12.4924	−	1.72904i	0.396236	−	0.0548418i
$995$	−25.2272	−	5.75794i	−0.799756	−	0.182539i
$996$	−0.893670	−	0.261783i	−0.0283170	−	0.00829492i
$997$	22.8551	−	47.4591i	0.723828	−	1.50304i	−0.135035	−	0.990841i	$-0.543115\pi$
$997$	22.8551	−	47.4591i	0.723828	−	1.50304i	0.858864	−	0.512204i	$-0.171171\pi$
$998$	−22.7450	−	15.2712i	−0.719979	−	0.483400i
$999$	−5.72874			−0.181249

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.2.j.a.111.24	yes	156
4.3	odd	2	inner	196.2.j.a.111.7	yes	156
49.34	odd	14	inner	196.2.j.a.83.7	✓	156
196.83	even	14	inner	196.2.j.a.83.24	yes	156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
196.2.j.a.83.7	✓	156	49.34	odd	14	inner
196.2.j.a.83.24	yes	156	196.83	even	14	inner
196.2.j.a.111.7	yes	156	4.3	odd	2	inner
196.2.j.a.111.24	yes	156	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	196.j (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.32010 + 0.507284i) q^{2} +(-1.45168 - 1.82035i) q^{3} +(1.48533 + 1.33933i) q^{4} +(1.13412 - 0.904431i) q^{5} +(-0.992928 - 3.13945i) q^{6} +(-0.147062 - 2.64166i) q^{7} +(1.28136 + 2.52153i) q^{8} +(-0.538730 + 2.36033i) q^{9} +(1.95596 - 0.618618i) q^{10} +(-0.655703 + 0.149660i) q^{11} +(0.281829 - 4.64809i) q^{12} +(1.04204 - 0.237840i) q^{13} +(1.14594 - 3.56186i) q^{14} +(-3.29276 - 0.751550i) q^{15} +(0.412390 + 3.97869i) q^{16} +(-0.527427 + 1.09521i) q^{17} +(-1.90853 + 2.84258i) q^{18} +3.97680 q^{19} +(2.89587 + 0.175587i) q^{20} +(-4.59525 + 4.10254i) q^{21} +(-0.941513 - 0.135061i) q^{22} +(2.80013 + 5.81454i) q^{23} +(2.72994 - 5.99297i) q^{24} +(-0.644370 + 2.82317i) q^{25} +(1.49625 + 0.214640i) q^{26} +(-1.21452 + 0.584884i) q^{27} +(3.31962 - 4.12069i) q^{28} +(-7.01088 - 3.37626i) q^{29} +(-3.96552 - 2.66248i) q^{30} -9.48293 q^{31} +(-1.47393 + 5.46146i) q^{32} +(1.22430 + 0.976349i) q^{33} +(-1.25184 + 1.17823i) q^{34} +(-2.55599 - 2.86296i) q^{35} +(-3.96145 + 2.78432i) q^{36} +(3.82889 + 1.84390i) q^{37} +(5.24978 + 2.01737i) q^{38} +(-1.94566 - 1.55161i) q^{39} +(3.73377 + 1.70082i) q^{40} +(-0.0397106 + 0.0316681i) q^{41} +(-8.14735 + 3.08467i) q^{42} +(1.03558 + 0.825848i) q^{43} +(-1.17438 - 0.655909i) q^{44} +(1.52377 + 3.16414i) q^{45} +(0.746836 + 9.09624i) q^{46} +(2.66423 + 11.6727i) q^{47} +(6.64393 - 6.52646i) q^{48} +(-6.95675 + 0.776975i) q^{49} +(-2.28278 + 3.39999i) q^{50} +(2.75932 - 0.629797i) q^{51} +(1.86632 + 1.04237i) q^{52} +(12.3270 - 5.93639i) q^{53} +(-1.90000 + 0.155997i) q^{54} +(-0.608289 + 0.762771i) q^{55} +(6.47259 - 3.75574i) q^{56} +(-5.77304 - 7.23916i) q^{57} +(-7.54234 - 8.01351i) q^{58} +(0.840007 - 1.05334i) q^{59} +(-3.88424 - 5.52639i) q^{60} +(3.30426 - 6.86136i) q^{61} +(-12.5184 - 4.81053i) q^{62} +(6.31442 + 1.07603i) q^{63} +(-4.71624 + 6.46197i) q^{64} +(0.966693 - 1.21220i) q^{65} +(1.12092 + 1.90995i) q^{66} -9.72058i q^{67} +(-2.25025 + 0.920350i) q^{68} +(6.51958 - 13.5381i) q^{69} +(-1.92183 - 5.07600i) q^{70} +(1.46244 + 3.03678i) q^{71} +(-6.64195 + 1.66601i) q^{72} +(-1.66705 - 0.380492i) q^{73} +(4.11914 + 4.37646i) q^{74} +(6.07457 - 2.92536i) q^{75} +(5.90685 + 5.32625i) q^{76} +(0.491780 + 1.71014i) q^{77} +(-1.78136 - 3.03529i) q^{78} -11.0108i q^{79} +(4.06615 + 4.13933i) q^{80} +(9.37161 + 4.51313i) q^{81} +(-0.0684866 + 0.0216605i) q^{82} +(0.0444993 - 0.194964i) q^{83} +(-12.3201 - 0.0609416i) q^{84} +(0.392379 + 1.71912i) q^{85} +(0.948130 + 1.61553i) q^{86} +(4.03158 + 17.6635i) q^{87} +(-1.21756 - 1.46161i) q^{88} +(-14.2293 - 3.24775i) q^{89} +(0.406412 + 4.94997i) q^{90} +(-0.781536 - 2.71775i) q^{91} +(-3.62847 + 12.3868i) q^{92} +(13.7662 + 17.2622i) q^{93} +(-2.40435 + 16.7607i) q^{94} +(4.51018 - 3.59674i) q^{95} +(12.0814 - 5.24522i) q^{96} -14.5971i q^{97} +(-9.57774 - 2.50336i) q^{98} -1.62830i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 11 q^{8} - 32 q^{9} - 7 q^{10} - 42 q^{12} - 14 q^{13} + 21 q^{14} - 13 q^{16} - 14 q^{17} - 12 q^{18} - 7 q^{20} - 14 q^{21} + 3 q^{22} + 35 q^{24} - 7 q^{26}+ \cdots + 105 q^{98}+O(q^{100}) \) 156 * q - 5 * q^2 - 5 * q^4 - 14 * q^5 - 7 * q^6 - 11 * q^8 - 32 * q^9 - 7 * q^10 - 42 * q^12 - 14 * q^13 + 21 * q^14 - 13 * q^16 - 14 * q^17 - 12 * q^18 - 7 * q^20 - 14 * q^21 + 3 * q^22 + 35 * q^24 - 7 * q^26 + 42 * q^28 - 30 * q^29 - 4 * q^30 - 5 * q^32 - 14 * q^33 + 77 * q^34 - 11 * q^36 + 10 * q^37 - 21 * q^38 - 63 * q^40 - 14 * q^41 - 7 * q^42 - 55 * q^44 - 14 * q^45 - 19 * q^46 - 132 * q^50 - 7 * q^52 - 2 * q^53 + 14 * q^54 - 70 * q^56 - 64 * q^57 - 3 * q^58 - 107 * q^60 + 14 * q^61 - 21 * q^62 - 11 * q^64 - 22 * q^65 + 161 * q^66 - 70 * q^69 - 77 * q^70 + 114 * q^72 - 14 * q^73 + 5 * q^74 + 70 * q^76 - 42 * q^77 + 61 * q^78 + 92 * q^81 - 42 * q^82 + 70 * q^84 - 6 * q^85 + 47 * q^86 + 65 * q^88 - 14 * q^89 + 112 * q^90 - 70 * q^92 - 48 * q^93 - 28 * q^94 + 238 * q^96 + 105 * q^98

Introduction

L-functions

Modular forms

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Database

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