LMFDB - Embedded newform 345.2.t.a.259.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [345,2,Mod(4,345)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(345, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 11, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("345.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 345 = 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	345.t (of order $22$, degree $10$, 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:	$2.75483886973$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			259.3
Character	$\chi$	$=$	345.259
Dual form			345.2.t.a.4.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.19367 - 1.00182i) q^{2} +(-0.281733 + 0.959493i) q^{3} +(2.49885 + 2.88382i) q^{4} +(-2.20845 - 0.350356i) q^{5} +(1.57927 - 1.82257i) q^{6} +(-1.24858 - 0.179518i) q^{7} +(-1.23374 - 4.20172i) q^{8} +(-0.841254 - 0.540641i) q^{9} +(4.49363 + 2.98103i) q^{10} +(-1.16248 - 2.54548i) q^{11} +(-3.47102 + 1.58516i) q^{12} +(0.533062 - 0.0766428i) q^{13} +(2.55913 + 1.64465i) q^{14} +(0.958357 - 2.02029i) q^{15} +(-0.416839 + 2.89918i) q^{16} +(1.94840 + 1.68830i) q^{17} +(1.30381 + 2.02877i) q^{18} +(3.08801 + 3.56376i) q^{19} +(-4.50821 - 7.24427i) q^{20} +(0.524011 - 1.14742i) q^{21} +6.74854i q^{22} +(4.16486 + 2.37780i) q^{23} +4.37911 q^{24} +(4.75450 + 1.54749i) q^{25} +(-1.24615 - 0.365902i) q^{26} +(0.755750 - 0.654861i) q^{27} +(-2.60230 - 4.04926i) q^{28} +(2.84344 - 3.28151i) q^{29} +(-4.12628 + 3.47175i) q^{30} +(4.04542 - 1.18784i) q^{31} +(-0.916192 + 1.42562i) q^{32} +(2.76988 - 0.398248i) q^{33} +(-2.58279 - 5.65552i) q^{34} +(2.69452 + 0.833904i) q^{35} +(-0.543052 - 3.77701i) q^{36} +(0.902873 - 1.40490i) q^{37} +(-3.20386 - 10.9113i) q^{38} +(-0.0766428 + 0.533062i) q^{39} +(1.25255 + 9.71154i) q^{40} +(4.05048 - 2.60309i) q^{41} +(-2.29902 + 1.99211i) q^{42} +(3.06670 - 10.4442i) q^{43} +(4.43585 - 9.71315i) q^{44} +(1.66845 + 1.48872i) q^{45} +(-6.75423 - 9.38855i) q^{46} +3.67888i q^{47} +(-2.66430 - 1.21675i) q^{48} +(-5.18973 - 1.52384i) q^{49} +(-8.87953 - 8.15783i) q^{50} +(-2.16884 + 1.39383i) q^{51} +(1.55307 + 1.34574i) q^{52} +(11.8737 + 1.70719i) q^{53} +(-2.31392 + 0.679428i) q^{54} +(1.67546 + 6.02884i) q^{55} +(0.786129 + 5.46765i) q^{56} +(-4.28939 + 1.95890i) q^{57} +(-9.52506 + 4.34995i) q^{58} +(-0.487328 - 3.38944i) q^{59} +(8.22094 - 2.28465i) q^{60} +(0.324953 - 0.0954149i) q^{61} +(-10.0643 - 1.44703i) q^{62} +(0.953315 + 0.826052i) q^{63} +(8.36609 - 5.37656i) q^{64} +(-1.20409 - 0.0175000i) q^{65} +(-6.47518 - 1.90128i) q^{66} +(4.42300 + 2.01992i) q^{67} +9.83765i q^{68} +(-3.45486 + 3.32625i) q^{69} +(-5.07549 - 4.52873i) q^{70} +(-5.19432 + 11.3740i) q^{71} +(-1.23374 + 4.20172i) q^{72} +(0.141332 - 0.122465i) q^{73} +(-3.38806 + 2.17738i) q^{74} +(-2.82430 + 4.12593i) q^{75} +(-2.56077 + 17.8106i) q^{76} +(0.994486 + 3.38691i) q^{77} +(0.702161 - 1.09258i) q^{78} +(1.76858 + 12.3008i) q^{79} +(1.93631 - 6.25665i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-11.4933 + 1.65248i) q^{82} +(0.470360 - 0.731895i) q^{83} +(4.61839 - 1.35608i) q^{84} +(-3.71144 - 4.41116i) q^{85} +(-17.1906 + 19.8390i) q^{86} +(2.34749 + 3.65277i) q^{87} +(-9.26119 + 8.02487i) q^{88} +(-3.16343 - 0.928865i) q^{89} +(-2.16861 - 4.93724i) q^{90} -0.679328 q^{91} +(3.55020 + 17.9525i) q^{92} +4.21621i q^{93} +(3.68557 - 8.07026i) q^{94} +(-5.57114 - 8.95228i) q^{95} +(-1.10975 - 1.28072i) q^{96} +(-9.96989 - 15.5135i) q^{97} +(9.85797 + 8.54198i) q^{98} +(-0.398248 + 2.76988i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 28 q^{4} - 4 q^{5} - 4 q^{6} + 24 q^{9} + 8 q^{14} + 4 q^{15} - 36 q^{16} - 8 q^{19} - 92 q^{20} + 8 q^{21} + 12 q^{24} - 44 q^{25} + 32 q^{26} - 12 q^{29} + 8 q^{30} - 20 q^{31} - 54 q^{34} + 36 q^{35}+ \cdots + 44 q^{99}+O(q^{100}) $ 240 * q + 28 * q^4 - 4 * q^5 - 4 * q^6 + 24 * q^9 + 8 * q^14 + 4 * q^15 - 36 * q^16 - 8 * q^19 - 92 * q^20 + 8 * q^21 + 12 * q^24 - 44 * q^25 + 32 * q^26 - 12 * q^29 + 8 * q^30 - 20 * q^31 - 54 * q^34 + 36 * q^35 - 28 * q^36 - 36 * q^39 - 24 * q^40 - 28 * q^41 - 224 * q^44 + 4 * q^45 - 8 * q^46 + 52 * q^49 - 48 * q^50 - 18 * q^54 - 22 * q^55 - 56 * q^59 - 36 * q^60 + 44 * q^61 + 12 * q^64 - 16 * q^65 + 8 * q^66 + 8 * q^69 - 152 * q^70 + 4 * q^71 + 88 * q^74 - 8 * q^75 - 100 * q^76 - 84 * q^79 + 122 * q^80 - 24 * q^81 - 56 * q^84 + 186 * q^85 - 392 * q^86 + 48 * q^89 - 304 * q^91 + 80 * q^94 + 190 * q^95 + 16 * q^96 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/345\mathbb{Z}\right)^\times$.

$n$	$116$	$166$	$277$
$\chi(n)$	$1$	$e\left(\frac{9}{11}\right)$	$-1$

Coefficient data

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

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

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

$2$	−2.19367	−	1.00182i	−1.55116	−	0.708392i	−0.558522	−	0.829490i	$-0.688631\pi$
$2$	−2.19367	−	1.00182i	−1.55116	−	0.708392i	−0.992641	+	0.121098i	$0.961358\pi$
$3$	−0.281733	+	0.959493i	−0.162658	+	0.553964i
$3$	−0.281733	+	0.959493i	−0.162658	+	0.553964i
$4$	2.49885	+	2.88382i	1.24942	+	1.44191i
$5$	−2.20845	−	0.350356i	−0.987649	−	0.156684i
$5$	−2.20845	−	0.350356i	−0.987649	−	0.156684i
$6$	1.57927	−	1.82257i	0.644733	−	0.744061i
$7$	−1.24858	−	0.179518i	−0.471918	−	0.0678515i	−0.0977468	−	0.995211i	$-0.531164\pi$
$7$	−1.24858	−	0.179518i	−0.471918	−	0.0678515i	−0.374171	+	0.927360i	$0.622073\pi$
$8$	−1.23374	−	4.20172i	−0.436192	−	1.48553i
$9$	−0.841254	−	0.540641i	−0.280418	−	0.180214i
$10$	4.49363	+	2.98103i	1.42101	+	0.942685i
$11$	−1.16248	−	2.54548i	−0.350501	−	0.767490i	−0.999975	−	0.00710625i	$-0.997738\pi$
$11$	−1.16248	−	2.54548i	−0.350501	−	0.767490i	0.649474	−	0.760384i	$-0.274989\pi$
$12$	−3.47102	+	1.58516i	−1.00200	+	0.457596i
$13$	0.533062	−	0.0766428i	0.147845	−	0.0212569i	−0.0679950	−	0.997686i	$-0.521660\pi$
$13$	0.533062	−	0.0766428i	0.147845	−	0.0212569i	0.215840	+	0.976429i	$0.430751\pi$
$14$	2.55913	+	1.64465i	0.683955	+	0.439551i
$15$	0.958357	−	2.02029i	0.247447	−	0.521635i
$16$	−0.416839	+	2.89918i	−0.104210	+	0.724794i
$17$	1.94840	+	1.68830i	0.472557	+	0.409473i	0.858312	−	0.513129i	$-0.171514\pi$
$17$	1.94840	+	1.68830i	0.472557	+	0.409473i	−0.385755	+	0.922601i	$0.626059\pi$
$18$	1.30381	+	2.02877i	0.307312	+	0.478186i
$19$	3.08801	+	3.56376i	0.708439	+	0.817582i	0.989867	−	0.142001i	$-0.0453535\pi$
$19$	3.08801	+	3.56376i	0.708439	+	0.817582i	−0.281428	+	0.959582i	$0.590808\pi$
$20$	−4.50821	−	7.24427i	−1.00807	−	1.61987i
$21$	0.524011	−	1.14742i	0.114349	−	0.250389i
$22$			6.74854i			1.43879i
$23$	4.16486	+	2.37780i	0.868434	+	0.495805i
$23$	4.16486	+	2.37780i	0.868434	+	0.495805i
$24$	4.37911			0.893881
$25$	4.75450	+	1.54749i	0.950900	+	0.309498i
$26$	−1.24615	−	0.365902i	−0.244390	−	0.0717593i
$27$	0.755750	−	0.654861i	0.145444	−	0.126028i
$28$	−2.60230	−	4.04926i	−0.491789	−	0.765239i
$29$	2.84344	−	3.28151i	0.528014	−	0.609361i	−0.427605	−	0.903966i	$-0.640643\pi$
$29$	2.84344	−	3.28151i	0.528014	−	0.609361i	0.955619	+	0.294605i	$0.0951880\pi$
$30$	−4.12628	+	3.47175i	−0.753352	+	0.633852i
$31$	4.04542	−	1.18784i	0.726580	−	0.213343i	0.102532	−	0.994730i	$-0.467305\pi$
$31$	4.04542	−	1.18784i	0.726580	−	0.213343i	0.624047	+	0.781387i	$0.285487\pi$
$32$	−0.916192	+	1.42562i	−0.161961	+	0.252017i
$33$	2.76988	−	0.398248i	0.482174	−	0.0693261i
$34$	−2.58279	−	5.65552i	−0.442945	−	0.969914i
$35$	2.69452	+	0.833904i	0.455458	+	0.140955i
$36$	−0.543052	−	3.77701i	−0.0905086	−	0.629501i
$37$	0.902873	−	1.40490i	0.148431	−	0.230964i	−0.759074	−	0.651005i	$-0.774348\pi$
$37$	0.902873	−	1.40490i	0.148431	−	0.230964i	0.907505	+	0.420041i	$0.137984\pi$
$38$	−3.20386	−	10.9113i	−0.519735	−	1.77005i
$39$	−0.0766428	+	0.533062i	−0.0122727	+	0.0853583i
$40$	1.25255	+	9.71154i	0.198045	+	1.53553i
$41$	4.05048	−	2.60309i	0.632579	−	0.406534i	−0.184684	−	0.982798i	$-0.559126\pi$
$41$	4.05048	−	2.60309i	0.632579	−	0.406534i	0.817264	+	0.576264i	$0.195490\pi$
$42$	−2.29902	+	1.99211i	−0.354746	+	0.307390i
$43$	3.06670	−	10.4442i	0.467668	−	1.59273i	−0.301357	−	0.953512i	$-0.597439\pi$
$43$	3.06670	−	10.4442i	0.467668	−	1.59273i	0.769024	−	0.639219i	$-0.220742\pi$
$44$	4.43585	−	9.71315i	0.668729	−	1.46431i
$45$	1.66845	+	1.48872i	0.248718	+	0.221925i
$46$	−6.75423	−	9.38855i	−0.995857	−	1.38427i
$47$			3.67888i			0.536620i	0.963333	+	0.268310i	$0.0864651\pi$
$47$			3.67888i			0.536620i	−0.963333	+	0.268310i	$0.913535\pi$
$48$	−2.66430	−	1.21675i	−0.384559	−	0.175622i
$49$	−5.18973	−	1.52384i	−0.741391	−	0.217692i
$50$	−8.87953	−	8.15783i	−1.25575	−	1.15369i
$51$	−2.16884	+	1.39383i	−0.303698	+	0.195175i
$52$	1.55307	+	1.34574i	0.215372	+	0.186620i
$53$	11.8737	+	1.70719i	1.63098	+	0.234500i	0.896151	−	0.443749i	$-0.146352\pi$
$53$	11.8737	+	1.70719i	1.63098	+	0.234500i	0.734832	+	0.678249i	$0.237261\pi$
$54$	−2.31392	+	0.679428i	−0.314885	+	0.0924585i
$55$	1.67546	+	6.02884i	0.225918	+	0.812929i
$56$	0.786129	+	5.46765i	0.105051	+	0.730646i
$57$	−4.28939	+	1.95890i	−0.568144	+	0.259463i
$58$	−9.52506	+	4.34995i	−1.25070	+	0.571176i
$59$	−0.487328	−	3.38944i	−0.0634446	−	0.441267i	−0.996641	−	0.0818993i	$-0.973901\pi$
$59$	−0.487328	−	3.38944i	−0.0634446	−	0.441267i	0.933196	−	0.359368i	$-0.117008\pi$
$60$	8.22094	−	2.28465i	1.06132	−	0.294948i
$61$	0.324953	−	0.0954149i	0.0416060	−	0.0122166i	−0.260863	−	0.965376i	$-0.584007\pi$
$61$	0.324953	−	0.0954149i	0.0416060	−	0.0122166i	0.302469	+	0.953159i	$0.402189\pi$
$62$	−10.0643	−	1.44703i	−1.27817	−	0.183774i
$63$	0.953315	+	0.826052i	0.120106	+	0.104073i
$64$	8.36609	−	5.37656i	1.04576	−	0.672070i
$65$	−1.20409	−	0.0175000i	−0.149349	−	0.00217061i
$66$	−6.47518	−	1.90128i	−0.797039	−	0.234032i
$67$	4.42300	+	2.01992i	0.540356	+	0.246772i	0.666846	−	0.745196i	$-0.267644\pi$
$67$	4.42300	+	2.01992i	0.540356	+	0.246772i	−0.126490	+	0.991968i	$0.540371\pi$
$68$			9.83765i			1.19299i
$69$	−3.45486	+	3.32625i	−0.415916	+	0.400434i
$70$	−5.07549	−	4.52873i	−0.606637	−	0.541287i
$71$	−5.19432	+	11.3740i	−0.616452	+	1.34984i	0.301620	+	0.953428i	$0.402473\pi$
$71$	−5.19432	+	11.3740i	−0.616452	+	1.34984i	−0.918072	+	0.396414i	$0.870255\pi$
$72$	−1.23374	+	4.20172i	−0.145397	+	0.495178i
$73$	0.141332	−	0.122465i	0.0165416	−	0.0143334i	−0.646551	−	0.762871i	$-0.723789\pi$
$73$	0.141332	−	0.122465i	0.0165416	−	0.0143334i	0.663092	+	0.748538i	$0.269244\pi$
$74$	−3.38806	+	2.17738i	−0.393854	+	0.253115i
$75$	−2.82430	+	4.12593i	−0.326122	+	0.476422i
$76$	−2.56077	+	17.8106i	−0.293741	+	2.04301i
$77$	0.994486	+	3.38691i	0.113332	+	0.385974i
$78$	0.702161	−	1.09258i	0.0795040	−	0.123711i
$79$	1.76858	+	12.3008i	0.198981	+	1.38394i	0.807248	+	0.590212i	$0.200956\pi$
$79$	1.76858	+	12.3008i	0.198981	+	1.38394i	−0.608267	+	0.793732i	$0.708135\pi$
$80$	1.93631	−	6.25665i	0.216486	−	0.699514i
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$	−11.4933	+	1.65248i	−1.26922	+	0.182486i
$83$	0.470360	−	0.731895i	0.0516288	−	0.0803359i	−0.814480	−	0.580192i	$-0.802977\pi$
$83$	0.470360	−	0.731895i	0.0516288	−	0.0803359i	0.866108	+	0.499856i	$0.166614\pi$
$84$	4.61839	−	1.35608i	0.503908	−	0.147961i
$85$	−3.71144	−	4.41116i	−0.402562	−	0.478457i
$86$	−17.1906	+	19.8390i	−1.85371	+	2.13929i
$87$	2.34749	+	3.65277i	0.251678	+	0.391618i
$88$	−9.26119	+	8.02487i	−0.987247	+	0.855454i
$89$	−3.16343	−	0.928865i	−0.335322	−	0.0984595i	0.109737	−	0.993961i	$-0.464999\pi$
$89$	−3.16343	−	0.928865i	−0.335322	−	0.0984595i	−0.445059	+	0.895501i	$0.646817\pi$
$90$	−2.16861	−	4.93724i	−0.228592	−	0.520431i
$91$	−0.679328			−0.0712129
$92$	3.55020	+	17.9525i	0.370134	+	1.87168i
$93$			4.21621i			0.437201i
$94$	3.68557	−	8.07026i	0.380137	−	0.832384i
$95$	−5.57114	−	8.95228i	−0.571586	−	0.918485i
$96$	−1.10975	−	1.28072i	−0.113264	−	0.130713i
$97$	−9.96989	−	15.5135i	−1.01229	−	1.57515i	−0.801832	−	0.597549i	$-0.796141\pi$
$97$	−9.96989	−	15.5135i	−1.01229	−	1.57515i	−0.210457	−	0.977603i	$-0.567495\pi$
$98$	9.85797	+	8.54198i	0.995806	+	0.862871i
$99$	−0.398248	+	2.76988i	−0.0400254	+	0.278383i
$100$	7.41809	+	17.5781i	0.741809	+	1.75781i
$101$	15.9864	+	10.2738i	1.59070	+	1.02228i	0.971497	+	0.237052i	$0.0761812\pi$
$101$	15.9864	+	10.2738i	1.59070	+	1.02228i	0.619205	+	0.785230i	$0.287455\pi$
$102$	6.15409	−	0.884824i	0.609346	−	0.0876107i
$103$	−10.7075	+	4.88995i	−1.05504	+	0.481821i	−0.865946	−	0.500137i	$-0.833283\pi$
$103$	−10.7075	+	4.88995i	−1.05504	+	0.481821i	−0.189096	+	0.981959i	$0.560556\pi$
$104$	−0.979690	−	2.14522i	−0.0960666	−	0.210356i
$105$	−1.55926	+	2.35044i	−0.152168	+	0.229379i
$106$	−24.3368	−	15.6403i	−2.36380	−	1.51912i
$107$	−4.03123	−	13.7291i	−0.389714	−	1.32724i	−0.887845	−	0.460142i	$-0.847798\pi$
$107$	−4.03123	−	13.7291i	−0.389714	−	1.32724i	0.498131	−	0.867102i	$-0.334020\pi$
$108$	3.77701	+	0.543052i	0.363443	+	0.0522552i
$109$	7.67896	−	8.86199i	0.735511	−	0.848824i	−0.257570	−	0.966260i	$-0.582922\pi$
$109$	7.67896	−	8.86199i	0.735511	−	0.848824i	0.993081	+	0.117435i	$0.0374672\pi$
$110$	2.36439	−	14.9038i	0.225436	−	1.42102i
$111$	1.09362	+	1.26211i	0.103802	+	0.119794i
$112$	1.04091	−	3.54502i	0.0983568	−	0.334972i
$113$	8.29542	+	3.78839i	0.780367	+	0.356382i	0.765440	−	0.643507i	$-0.222521\pi$
$113$	8.29542	+	3.78839i	0.780367	+	0.356382i	0.0149268	+	0.999889i	$0.495248\pi$
$114$	11.3720			1.06508
$115$	−8.36481	−	6.71043i	−0.780023	−	0.625751i
$116$	16.5686			1.53836
$117$	−0.489877	−	0.223719i	−0.0452891	−	0.0206828i
$118$	−2.32656	+	7.92354i	−0.214177	+	0.729421i
$119$	−2.12965	−	2.45774i	−0.195224	−	0.225301i
$120$	−9.67104	−	1.53425i	−0.882841	−	0.140057i
$121$	2.07537	−	2.39511i	0.188670	−	0.217737i
$122$	−0.808430	−	0.116235i	−0.0731918	−	0.0105234i
$123$	1.35649	+	4.61979i	0.122311	+	0.416552i
$124$	13.5344	+	8.69805i	1.21543	+	0.781108i
$125$	−9.95790	−	5.08332i	−0.890662	−	0.454666i
$126$	−1.26371	−	2.76714i	−0.112580	−	0.246516i
$127$	−4.76710	+	2.17706i	−0.423012	+	0.193183i	−0.615535	−	0.788109i	$-0.711060\pi$
$127$	−4.76710	+	2.17706i	−0.423012	+	0.193183i	0.192523	+	0.981292i	$0.438333\pi$
$128$	−20.3840	+	2.93078i	−1.80171	+	0.259047i
$129$	9.15718	+	5.88496i	0.806245	+	0.518142i
$130$	2.62386	+	1.24467i	0.230128	+	0.109165i
$131$	−2.77030	+	19.2678i	−0.242042	+	1.68344i	0.399801	+	0.916602i	$0.369079\pi$
$131$	−2.77030	+	19.2678i	−0.242042	+	1.68344i	−0.641843	+	0.766836i	$0.721830\pi$
$132$	8.06998	+	6.99268i	0.702401	+	0.608634i
$133$	−3.21586	−	5.00398i	−0.278851	−	0.433900i
$134$	−7.67904	−	8.86208i	−0.663368	−	0.765567i
$135$	−1.89847	+	1.18145i	−0.163394	+	0.101683i
$136$	4.68995	−	10.2696i	0.402160	−	0.880607i
$137$		−	18.2863i		−	1.56231i	−0.624339	−	0.781154i	$-0.714632\pi$
$137$		−	18.2863i		−	1.56231i	0.624339	−	0.781154i	$-0.285368\pi$
$138$	10.9111	−	3.83558i	0.928817	−	0.326506i
$139$	17.0438			1.44564			0.722819	−	0.691038i	$-0.242846\pi$
$139$	17.0438			1.44564			0.722819	+	0.691038i	$0.242846\pi$
$140$	4.32837	+	9.85433i	0.365814	+	0.832843i
$141$	−3.52986	−	1.03646i	−0.297268	−	0.0872857i
$142$	22.7893	−	19.7470i	1.91243	−	1.65713i
$143$	−0.814767	−	1.26780i	−0.0681342	−	0.106019i
$144$	1.91808	−	2.21358i	0.159840	−	0.184465i
$145$	−7.42930	+	6.25083i	−0.616970	+	0.519103i
$146$	−0.432724	+	0.127059i	−0.0358125	+	0.0105155i
$147$	2.92423	−	4.55020i	0.241187	−	0.375294i
$148$	6.30762	−	0.906899i	0.518483	−	0.0745467i
$149$	−7.95590	−	17.4210i	−0.651773	−	1.42718i	−0.889994	−	0.455972i	$-0.849292\pi$
$149$	−7.95590	−	17.4210i	−0.651773	−	1.42718i	0.238221	−	0.971211i	$-0.423436\pi$
$150$	10.3290	−	6.22152i	0.843362	−	0.507985i
$151$	−2.11689	−	14.7233i	−0.172270	−	1.19816i	−0.874073	−	0.485794i	$-0.838531\pi$
$151$	−2.11689	−	14.7233i	−0.172270	−	1.19816i	0.701803	−	0.712371i	$-0.252379\pi$
$152$	11.1641	−	17.3717i	0.905530	−	1.40903i
$153$	−0.726336	−	2.47367i	−0.0587208	−	0.199985i
$154$	1.21149	−	8.42607i	0.0976243	−	0.678992i
$155$	−9.35029	+	1.20595i	−0.751033	+	0.0968645i
$156$	−1.72878	+	1.11102i	−0.138413	+	0.0889526i
$157$	−8.11840	+	7.03463i	−0.647919	+	0.561425i	−0.915604	−	0.402082i	$-0.868287\pi$
$157$	−8.11840	+	7.03463i	−0.647919	+	0.561425i	0.267685	+	0.963506i	$0.413741\pi$
$158$	8.44343	−	28.7557i	0.671723	−	2.28768i
$159$	−4.98325	+	10.9118i	−0.395198	+	0.865362i
$160$	2.52284	−	2.82742i	0.199448	−	0.223527i
$161$	−4.77329	−	3.71653i	−0.376188	−	0.292904i
$162$		−	2.41161i		−	0.189474i
$163$	12.2524	+	5.59546i	0.959679	+	0.438271i	0.832755	−	0.553642i	$-0.186762\pi$
$163$	12.2524	+	5.59546i	0.959679	+	0.438271i	0.126924	+	0.991912i	$0.459490\pi$
$164$	17.6284	+	5.17616i	1.37655	+	0.404190i
$165$	−6.25666	−	0.0909327i	−0.487080	−	0.00707910i
$166$	−1.76504	+	1.13432i	−0.136994	+	0.0880406i
$167$	15.4179	+	13.3597i	1.19307	+	1.03380i	0.998600	+	0.0528954i	$0.0168450\pi$
$167$	15.4179	+	13.3597i	1.19307	+	1.03380i	0.194473	+	0.980908i	$0.437700\pi$
$168$	−5.46765	−	0.786129i	−0.421838	−	0.0606512i
$169$	−12.1951	+	3.58081i	−0.938087	+	0.275447i
$170$	3.72251	+	13.3948i	0.285504	+	1.02734i
$171$	−0.671089	−	4.66753i	−0.0513195	−	0.356935i
$172$	37.7826	−	17.2547i	2.88089	−	1.31566i
$173$	2.32067	−	1.05981i	0.176437	−	0.0805761i	−0.325238	−	0.945632i	$-0.605444\pi$
$173$	2.32067	−	1.05981i	0.176437	−	0.0805761i	0.501675	+	0.865056i	$0.332717\pi$
$174$	−1.49023	−	10.3648i	−0.112974	−	0.785750i
$175$	−5.65856	−	2.78568i	−0.427747	−	0.210577i
$176$	7.86436	−	2.30918i	0.592798	−	0.174061i
$177$	3.38944	+	0.487328i	0.254766	+	0.0366298i
$178$	6.00897	+	5.20680i	0.450391	+	0.390266i
$179$	−6.77432	+	4.35359i	−0.506337	+	0.325403i	−0.768746	−	0.639554i	$-0.779119\pi$
$179$	−6.77432	+	4.35359i	−0.506337	+	0.325403i	0.262410	+	0.964957i	$0.415483\pi$
$180$	−0.123996	+	8.53159i	−0.00924212	+	0.635907i
$181$	14.4429	+	4.24082i	1.07353	+	0.315218i	0.770289	−	0.637695i	$-0.220112\pi$
$181$	14.4429	+	4.24082i	1.07353	+	0.315218i	0.303244	+	0.952913i	$0.401930\pi$
$182$	1.49022	+	0.680563i	0.110463	+	0.0504467i
$183$			0.338672i			0.0250353i
$184$	4.85250	−	20.4332i	0.357731	−	1.50635i
$185$	−2.48617	+	2.78632i	−0.182787	+	0.204854i
$186$	4.22387	−	9.24899i	0.309709	−	0.678169i
$187$	2.03255	−	6.92223i	0.148635	−	0.506203i
$188$	−10.6092	+	9.19296i	−0.773758	+	0.670466i
$189$	−1.06117	+	0.681973i	−0.0771888	+	0.0496062i
$190$	3.25271	+	25.2197i	0.235976	+	1.82963i
$191$	1.31751	−	9.16347i	0.0953316	−	0.663046i	−0.884986	−	0.465618i	$-0.845832\pi$
$191$	1.31751	−	9.16347i	0.0953316	−	0.663046i	0.980317	−	0.197428i	$-0.0632588\pi$
$192$	2.80177	+	9.54195i	0.202200	+	0.688631i
$193$	4.43900	−	6.90721i	0.319526	−	0.497192i	−0.643921	−	0.765092i	$-0.722693\pi$
$193$	4.43900	−	6.90721i	0.319526	−	0.497192i	0.963447	+	0.267900i	$0.0863297\pi$
$194$	6.32905	+	44.0195i	0.454399	+	3.16041i
$195$	0.356023	−	1.15039i	0.0254954	−	0.0823811i
$196$	−8.57386	−	18.7741i	−0.612419	−	1.34101i
$197$	−9.17382	+	1.31900i	−0.653607	+	0.0939746i	−0.461138	−	0.887328i	$-0.652559\pi$
$197$	−9.17382	+	1.31900i	−0.653607	+	0.0939746i	−0.192469	+	0.981303i	$0.561650\pi$
$198$	3.64854	−	5.67724i	0.259290	−	0.403464i
$199$	−19.4465	+	5.71000i	−1.37852	+	0.404771i	−0.885255	−	0.465106i	$-0.846016\pi$
$199$	−19.4465	+	5.71000i	−1.37852	+	0.404771i	−0.493269	+	0.869877i	$0.664198\pi$
$200$	0.636314	−	21.8863i	0.0449942	−	1.54759i
$201$	−3.18420	+	3.67476i	−0.224596	+	0.259198i
$202$	−24.7764	−	38.5528i	−1.74326	−	2.71256i
$203$	−4.13935	+	3.58677i	−0.290525	+	0.251742i
$204$	−9.43915	−	2.77159i	−0.660873	−	0.194050i
$205$	−9.85730	+	4.32968i	−0.688464	+	0.302398i
$206$	28.3876			1.97786
$207$	−2.21817	−	4.25203i	−0.154173	−	0.295536i
$208$			1.57739i			0.109372i
$209$	5.48171	−	12.0033i	0.379178	−	0.830283i
$210$	5.77522	−	3.59400i	0.398528	−	0.248010i
$211$	14.6772	+	16.9384i	1.01042	+	1.16609i	0.986061	+	0.166382i	$0.0532086\pi$
$211$	14.6772	+	16.9384i	1.01042	+	1.16609i	0.0243577	+	0.999703i	$0.492246\pi$
$212$	24.7474	+	38.5078i	1.69966	+	2.64472i
$213$	−9.44984	−	8.18833i	−0.647492	−	0.561055i
$214$	−4.91086	+	34.1558i	−0.335699	+	2.33484i
$215$	−10.4319	+	21.9911i	−0.711447	+	1.49978i
$216$	−3.68394	−	2.36752i	−0.250660	−	0.161090i
$217$	−5.26426	+	0.756887i	−0.357361	+	0.0513808i
$218$	−25.7232	+	11.7474i	−1.74220	+	0.795635i
$219$	0.0776863	+	0.170109i	0.00524955	+	0.0114949i
$220$	−13.1994	+	19.8969i	−0.889904	+	1.34145i
$221$	1.16801	+	0.750638i	0.0785692	+	0.0504934i
$222$	−1.13465	−	3.86426i	−0.0761527	−	0.259352i
$223$	23.1463	+	3.32793i	1.54999	+	0.222855i	0.863524	−	0.504308i	$-0.168252\pi$
$223$	23.1463	+	3.32793i	1.54999	+	0.222855i	0.686465	+	0.727163i	$0.259161\pi$
$224$	1.39986	−	1.61553i	0.0935321	−	0.107942i
$225$	−3.16311	−	3.87231i	−0.210874	−	0.258154i
$226$	−14.4022	−	16.6210i	−0.958018	−	1.10561i
$227$	−0.476313	+	1.62217i	−0.0316140	+	0.107667i	−0.973789	−	0.227455i	$-0.926960\pi$
$227$	−0.476313	+	1.62217i	−0.0316140	+	0.107667i	0.942175	+	0.335122i	$0.108778\pi$
$228$	−16.3677	−	7.47486i	−1.08398	−	0.495035i
$229$	−10.6859			−0.706141			−0.353071	−	0.935597i	$-0.614862\pi$
$229$	−10.6859			−0.706141			−0.353071	+	0.935597i	$0.614862\pi$
$230$	11.6270	+	23.1005i	0.766665	+	1.52320i
$231$	−3.52990			−0.232250
$232$	−17.2961	−	7.89884i	−1.13554	−	0.518584i
$233$	−2.17194	+	7.39696i	−0.142289	+	0.484591i	−0.999541	−	0.0303064i	$-0.990352\pi$
$233$	−2.17194	+	7.39696i	−0.142289	+	0.484591i	0.857252	+	0.514897i	$0.172170\pi$
$234$	0.850504	+	0.981534i	0.0555992	+	0.0641649i
$235$	1.28892	−	8.12462i	0.0840798	−	0.529992i
$236$	8.55678	−	9.87506i	0.556999	−	0.642811i
$237$	−12.3008	−	1.76858i	−0.799021	−	0.114882i
$238$	2.20954	+	7.52501i	0.143223	+	0.487774i
$239$	10.3541	+	6.65416i	0.669749	+	0.430422i	0.830835	−	0.556519i	$-0.187863\pi$
$239$	10.3541	+	6.65416i	0.669749	+	0.430422i	−0.161086	+	0.986940i	$0.551500\pi$
$240$	5.45769	+	3.62058i	0.352292	+	0.233707i
$241$	−2.94214	−	6.44238i	−0.189520	−	0.414990i	0.790890	−	0.611958i	$-0.209618\pi$
$241$	−2.94214	−	6.44238i	−0.189520	−	0.414990i	−0.980410	+	0.196968i	$0.936891\pi$
$242$	−6.95216	+	3.17494i	−0.446902	+	0.204093i
$243$	−0.989821	+	0.142315i	−0.0634971	+	0.00912950i
$244$	1.08717	+	0.698681i	0.0695989	+	0.0447285i
$245$	10.9274	+	5.18359i	0.698125	+	0.331167i
$246$	1.65248	−	11.4933i	0.105358	−	0.732784i
$247$	1.91924	+	1.66303i	0.122118	+	0.105816i
$248$	−9.98198	−	15.5323i	−0.633856	−	0.986300i
$249$	0.569732	+	0.657506i	0.0361053	+	0.0416678i
$250$	16.7518	+	21.1272i	1.05948	+	1.33620i
$251$	2.54721	−	5.57762i	0.160779	−	0.352056i	−0.812048	−	0.583591i	$-0.801647\pi$
$251$	2.54721	−	5.57762i	0.160779	−	0.352056i	0.972827	+	0.231534i	$0.0743745\pi$
$252$			4.81337i			0.303214i
$253$	1.21106	−	13.3657i	0.0761387	−	0.840295i
$254$	12.6385			0.793009
$255$	5.27811	−	2.31833i	0.330528	−	0.145180i
$256$	28.5681	+	8.38835i	1.78551	+	0.524272i
$257$	6.91603	−	5.99278i	0.431410	−	0.373819i	−0.411915	−	0.911222i	$-0.635140\pi$
$257$	6.91603	−	5.99278i	0.431410	−	0.373819i	0.843326	+	0.537403i	$0.180595\pi$
$258$	−14.1922	−	22.0835i	−0.883569	−	1.37486i
$259$	−1.37951	+	1.59204i	−0.0857187	+	0.0989246i
$260$	−2.95838	−	3.51612i	−0.183471	−	0.218061i
$261$	−4.16617	+	1.22330i	−0.257880	+	0.0757203i
$262$	25.3800	−	39.4920i	1.56798	−	2.43983i
$263$	9.31336	−	1.33906i	0.574286	−	0.0825699i	0.150948	−	0.988542i	$-0.451767\pi$
$263$	9.31336	−	1.33906i	0.574286	−	0.0825699i	0.423338	+	0.905972i	$0.360858\pi$
$264$	−5.09063	−	11.1469i	−0.313306	−	0.686045i
$265$	−25.6244	−	7.93027i	−1.57410	−	0.487153i
$266$	2.04148	+	14.1988i	0.125171	+	0.870584i
$267$	1.78248	−	2.77359i	0.109086	−	0.169741i
$268$	5.22732	+	17.8026i	0.319310	+	1.08747i
$269$	3.65299	−	25.4071i	0.222727	−	1.54910i	−0.504931	−	0.863160i	$-0.668482\pi$
$269$	3.65299	−	25.4071i	0.222727	−	1.54910i	0.727658	−	0.685940i	$-0.240609\pi$
$270$	5.34822	−	0.689786i	0.325482	−	0.0419791i
$271$	0.643794	−	0.413741i	0.0391077	−	0.0251330i	−0.520941	−	0.853593i	$-0.674419\pi$
$271$	0.643794	−	0.413741i	0.0391077	−	0.0251330i	0.560049	+	0.828460i	$0.310782\pi$
$272$	−5.70685	+	4.94501i	−0.346028	+	0.299835i
$273$	0.191389	−	0.651810i	0.0115834	−	0.0394494i
$274$	−18.3196	+	40.1143i	−1.10673	+	2.42339i
$275$	−1.58792	−	13.9014i	−0.0957550	−	0.838286i
$276$	−18.2255	−	1.65140i	−1.09705	−	0.0994028i
$277$			7.85288i			0.471834i	0.971773	+	0.235917i	$0.0758094\pi$
$277$			7.85288i			0.471834i	−0.971773	+	0.235917i	$0.924191\pi$
$278$	−37.3886	−	17.0748i	−2.24242	−	1.02408i
$279$	−4.04542	−	1.18784i	−0.242193	−	0.0711143i
$280$	0.179498	−	12.3505i	0.0107271	−	0.738081i
$281$	8.32255	−	5.34858i	0.496482	−	0.319069i	−0.268326	−	0.963328i	$-0.586470\pi$
$281$	8.32255	−	5.34858i	0.496482	−	0.319069i	0.764808	+	0.644259i	$0.222834\pi$
$282$	6.70502	+	5.80993i	0.399278	+	0.345976i
$283$	18.0490	+	2.59505i	1.07290	+	0.154260i	0.656052	−	0.754716i	$-0.272225\pi$
$283$	18.0490	+	2.59505i	1.07290	+	0.154260i	0.416849	+	0.908976i	$0.363134\pi$
$284$	−45.7804	+	13.4423i	−2.71656	+	0.797655i
$285$	10.1592	−	2.82332i	0.601780	−	0.167239i
$286$	0.517227	+	3.59739i	0.0305843	+	0.212718i
$287$	−5.52464	+	2.52302i	−0.326109	+	0.148929i
$288$	1.54150	−	0.703979i	0.0908337	−	0.0414824i
$289$	−1.47344	−	10.2480i	−0.0866729	−	0.602823i
$290$	22.5597	−	6.26948i	1.32475	−	0.368157i
$291$	17.6939	−	5.19540i	1.03723	−	0.304559i
$292$	0.706334	+	0.101555i	0.0413351	+	0.00594308i
$293$	2.74420	+	2.37787i	0.160318	+	0.138916i	0.731326	−	0.682028i	$-0.238902\pi$
$293$	2.74420	+	2.37787i	0.160318	+	0.138916i	−0.571008	+	0.820945i	$0.693447\pi$
$294$	−10.9733	+	7.05210i	−0.639975	+	0.411287i
$295$	−0.111272	+	7.65614i	−0.00647853	+	0.445758i
$296$	−7.01690	−	2.06035i	−0.407849	−	0.119755i
$297$	−2.54548	−	1.16248i	−0.147704	−	0.0674540i
$298$			46.1863i			2.67550i
$299$	2.40237	+	0.948308i	0.138933	+	0.0548421i
$300$	−18.9560	+	2.16529i	−1.09442	+	0.125013i
$301$	−5.70394	+	12.4899i	−0.328770	+	0.719906i
$302$	−10.1063	+	34.4189i	−0.581552	+	1.98058i
$303$	−14.3615	+	12.4443i	−0.825048	+	0.714908i
$304$	−11.6192	+	7.46719i	−0.666405	+	0.428272i
$305$	−0.751072	+	0.0968696i	−0.0430063	+	0.00554674i
$306$	−0.884824	+	6.15409i	−0.0505820	+	0.351806i
$307$	0.767294	+	2.61316i	0.0437918	+	0.149141i	0.978487	−	0.206310i	$-0.0661455\pi$
$307$	0.767294	+	2.61316i	0.0437918	+	0.149141i	−0.934695	+	0.355451i	$0.884327\pi$
$308$	−7.28218	+	11.3313i	−0.414941	+	0.645661i
$309$	−1.67522	−	11.6514i	−0.0953001	−	0.662827i
$310$	21.7196	+	6.72181i	1.23359	+	0.381773i
$311$	6.07317	+	13.2984i	0.344378	+	0.754083i	0.999999	−	0.00100692i	$-0.000320511\pi$
$311$	6.07317	+	13.2984i	0.344378	+	0.754083i	−0.655621	+	0.755090i	$0.727593\pi$
$312$	2.33434	−	0.335627i	0.132156	−	0.0190011i
$313$	−12.4382	+	19.3543i	−0.703051	+	1.09397i	0.287627	+	0.957743i	$0.407134\pi$
$313$	−12.4382	+	19.3543i	−0.703051	+	1.09397i	−0.990678	+	0.136226i	$0.956503\pi$
$314$	24.8565	−	7.29854i	1.40274	−	0.411880i
$315$	−1.81593	−	2.15829i	−0.102316	−	0.121606i
$316$	−31.0538	+	35.8380i	−1.74691	+	2.01605i
$317$	−0.331105	−	0.515209i	−0.0185967	−	0.0289370i	0.831831	−	0.555029i	$-0.187293\pi$
$317$	−0.331105	−	0.515209i	−0.0185967	−	0.0289370i	−0.850427	+	0.526092i	$0.823657\pi$
$318$	21.8633	−	18.9446i	1.22603	−	1.06236i
$319$	−11.6585	−	3.42323i	−0.652748	−	0.191664i
$320$	−20.3598	+	8.94275i	−1.13815	+	0.499915i
$321$	14.3087			0.798635
$322$	6.74776	+	12.9348i	0.376038	+	0.720830i
$323$			12.1571i			0.676440i
$324$	−1.58516	+	3.47102i	−0.0880644	+	0.192834i
$325$	2.65305	+	0.460510i	0.147165	+	0.0255445i
$326$	−21.2720	−	24.5493i	−1.17815	−	1.35966i
$327$	6.33960	+	9.86461i	0.350581	+	0.545514i
$328$	−15.9347	−	13.8075i	−0.879846	−	0.762391i
$329$	0.660426	−	4.59336i	0.0364105	−	0.253240i
$330$	13.6340	+	6.46751i	0.750526	+	0.356025i
$331$	−0.108288	−	0.0695926i	−0.00595206	−	0.00382516i	0.537661	−	0.843161i	$-0.319308\pi$
$331$	−0.108288	−	0.0695926i	−0.00595206	−	0.00382516i	−0.543613	+	0.839336i	$0.682944\pi$
$332$	3.28602	−	0.472458i	0.180344	−	0.0259295i
$333$	−1.51909	+	0.693746i	−0.0832457	+	0.0380170i
$334$	−20.4379	−	44.7527i	−1.11831	−	2.44876i
$335$	−9.06029	−	6.01051i	−0.495016	−	0.328389i
$336$	3.10816	+	1.99749i	0.169564	+	0.108972i
$337$	1.58080	+	5.38370i	0.0861115	+	0.293269i	0.991278	−	0.131789i	$-0.0420720\pi$
$337$	1.58080	+	5.38370i	0.0861115	+	0.293269i	−0.905166	+	0.425058i	$0.860254\pi$
$338$	30.3395	+	4.36216i	1.65025	+	0.237270i
$339$	−5.97202	+	6.89208i	−0.324356	+	0.374326i
$340$	3.44668	−	21.7260i	0.186923	−	1.17826i
$341$	−7.72636	−	8.91669i	−0.418406	−	0.482866i
$342$	−3.20386	+	10.9113i	−0.173245	+	0.590018i
$343$	14.2382	+	6.50236i	0.768790	+	0.351095i
$344$	−47.6673			−2.57005
$345$	8.79525	−	6.13543i	0.473521	−	0.330320i
$346$	−6.15253			−0.330762
$347$	7.35346	+	3.35821i	0.394755	+	0.180278i	0.602895	−	0.797821i	$-0.294014\pi$
$347$	7.35346	+	3.35821i	0.394755	+	0.180278i	−0.208140	+	0.978099i	$0.566741\pi$
$348$	−4.66792	+	15.8975i	−0.250227	+	0.852194i
$349$	9.66532	+	11.1544i	0.517373	+	0.597080i	0.952971	−	0.303061i	$-0.0980086\pi$
$349$	9.66532	+	11.1544i	0.517373	+	0.597080i	−0.435598	+	0.900141i	$0.643463\pi$
$350$	9.62229	+	11.7797i	0.514333	+	0.629652i
$351$	0.352671	−	0.407004i	0.0188242	−	0.0217243i
$352$	4.69395	+	0.674887i	0.250188	+	0.0359716i
$353$	−6.71937	−	22.8841i	−0.357636	−	1.21800i	−0.920268	−	0.391288i	$-0.872030\pi$
$353$	−6.71937	−	22.8841i	−0.357636	−	1.21800i	0.562632	−	0.826707i	$-0.309789\pi$
$354$	−6.94711	−	4.46464i	−0.369235	−	0.237293i
$355$	15.4563	−	23.2990i	0.820337	−	1.23658i
$356$	−5.22623	−	11.4439i	−0.276990	−	0.606523i
$357$	2.95818	−	1.35096i	0.156563	−	0.0715001i
$358$	19.2222	−	2.76373i	1.01592	−	0.146068i
$359$	−14.3071	−	9.19465i	−0.755102	−	0.485275i	0.105584	−	0.994410i	$-0.466329\pi$
$359$	−14.3071	−	9.19465i	−0.755102	−	0.485275i	−0.860686	+	0.509136i	$0.829965\pi$
$360$	4.19675	−	8.84705i	0.221188	−	0.466280i
$361$	−0.460557	+	3.20324i	−0.0242398	+	0.168592i
$362$	−27.4345	−	23.7721i	−1.44193	−	1.24944i
$363$	1.71339	+	2.66609i	0.0899296	+	0.139933i
$364$	−1.69754	−	1.95906i	−0.0889751	−	0.102683i
$365$	−0.355031	+	0.220941i	−0.0185832	+	0.0115646i
$366$	0.339288	−	0.742936i	0.0177348	−	0.0388339i
$367$			12.4098i			0.647789i	0.946093	+	0.323894i	$0.104992\pi$
$367$			12.4098i			0.647789i	−0.946093	+	0.323894i	$0.895008\pi$
$368$	−8.62974	+	11.0835i	−0.449856	+	0.577768i
$369$	−4.81482			−0.250649
$370$	8.24522	−	3.62160i	0.428649	−	0.188278i
$371$	−14.5188	−	4.26310i	−0.753779	−	0.221329i
$372$	−12.1588	+	10.5357i	−0.630405	+	0.546249i
$373$	4.43248	+	6.89708i	0.229505	+	0.357117i	0.936838	−	0.349764i	$-0.113738\pi$
$373$	4.43248	+	6.89708i	0.229505	+	0.357117i	−0.707333	+	0.706881i	$0.750102\pi$
$374$	−11.3936	+	13.1489i	−0.589147	+	0.679912i
$375$	7.68288	−	8.12240i	0.396742	−	0.419439i
$376$	15.4576	−	4.53877i	0.797166	−	0.234069i
$377$	1.26423	−	1.96718i	0.0651111	−	0.101315i
$378$	3.01108	−	0.432927i	0.154873	−	0.0222674i
$379$	−1.84971	−	4.05031i	−0.0950134	−	0.208050i	0.856158	−	0.516715i	$-0.172845\pi$
$379$	−1.84971	−	4.05031i	−0.0950134	−	0.208050i	−0.951171	+	0.308665i	$0.900118\pi$
$380$	11.8954	−	38.4366i	0.610220	−	1.97175i
$381$	−0.745828	−	5.18735i	−0.0382099	−	0.265756i
$382$	−12.0703	+	18.7818i	−0.617571	+	0.960959i
$383$	−2.07015	−	7.05029i	−0.105780	−	0.360253i	0.889544	−	0.456850i	$-0.151022\pi$
$383$	−2.07015	−	7.05029i	−0.105780	−	0.360253i	−0.995324	+	0.0965970i	$0.969204\pi$
$384$	2.93078	−	20.3840i	0.149561	−	1.04022i
$385$	−1.00965	−	7.82825i	−0.0514564	−	0.398964i
$386$	−16.6575	+	10.7051i	−0.847844	+	0.544876i
$387$	−8.22646	+	7.12826i	−0.418174	+	0.362350i
$388$	19.8248	−	67.5172i	1.00645	−	3.42767i
$389$	11.0585	−	24.2147i	0.560687	−	1.22773i	−0.390922	−	0.920424i	$-0.627844\pi$
$389$	11.0585	−	24.2147i	0.560687	−	1.22773i	0.951609	−	0.307310i	$-0.0994290\pi$
$390$	−1.93348	+	2.16691i	−0.0979055	+	0.109726i
$391$	4.10039	+	11.6644i	0.207365	+	0.589896i
$392$			23.6858i			1.19632i
$393$	−17.7069	−	8.08646i	−0.893193	−	0.407908i
$394$	21.4458	+	6.29704i	1.08042	+	0.317240i
$395$	0.403824	−	27.7853i	0.0203186	−	1.39803i
$396$	−8.98300	+	5.77302i	−0.451413	+	0.290105i
$397$	−10.3756	−	8.99049i	−0.520735	−	0.451220i	0.354403	−	0.935093i	$-0.384684\pi$
$397$	−10.3756	−	8.99049i	−0.520735	−	0.451220i	−0.875138	+	0.483873i	$0.839230\pi$
$398$	48.3796	+	6.95594i	2.42505	+	0.348670i
$399$	5.70729	−	1.67581i	0.285722	−	0.0838956i
$400$	−6.46831	+	13.1391i	−0.323415	+	0.656955i
$401$	−1.60714	−	11.1779i	−0.0802568	−	0.558198i	−0.989786	−	0.142559i	$-0.954467\pi$
$401$	−1.60714	−	11.1779i	−0.0802568	−	0.558198i	0.909529	−	0.415639i	$-0.136442\pi$
$402$	10.6665	−	4.87125i	0.531999	−	0.242956i
$403$	2.06542	−	0.943247i	0.102886	−	0.0469865i
$404$	10.3196	+	71.7745i	0.513420	+	3.57092i
$405$	−0.598728	−	2.15442i	−0.0297510	−	0.107054i
$406$	12.6737	−	3.72132i	0.628983	−	0.184686i
$407$	−4.62571	−	0.665077i	−0.229288	−	0.0329666i
$408$	8.53226	+	7.39324i	0.422410	+	0.366020i
$409$	−5.46518	+	3.51225i	−0.270236	+	0.173670i	−0.668740	−	0.743497i	$-0.733166\pi$
$409$	−5.46518	+	3.51225i	−0.270236	+	0.173670i	0.398504	+	0.917167i	$0.369529\pi$
$410$	25.9612	+	0.377314i	1.28213	+	0.0186342i
$411$	17.5456	+	5.15186i	0.865461	+	0.254122i
$412$	−40.8582	−	18.6593i	−2.01294	−	0.919278i
$413$			4.31946i			0.212547i
$414$	0.606189	+	11.5498i	0.0297926	+	0.567640i
$415$	−1.29519	+	1.45156i	−0.0635785	+	0.0712543i
$416$	−0.379124	+	0.830165i	−0.0185881	+	0.0407022i
$417$	−4.80180	+	16.3534i	−0.235145	+	0.800830i
$418$	−24.0502	+	20.8396i	−1.17633	+	1.01930i
$419$	27.2883	−	17.5371i	1.33312	−	0.856744i	0.336726	−	0.941603i	$-0.390680\pi$
$419$	27.2883	−	17.5371i	1.33312	−	0.856744i	0.996393	+	0.0848589i	$0.0270440\pi$
$420$	−10.6746	+	1.37676i	−0.520867	+	0.0671789i
$421$	−1.06599	+	7.41414i	−0.0519533	+	0.361343i	0.947216	+	0.320595i	$0.103883\pi$
$421$	−1.06599	+	7.41414i	−0.0519533	+	0.361343i	−0.999169	+	0.0407474i	$0.987026\pi$
$422$	−15.2278	−	51.8611i	−0.741278	−	2.52456i
$423$	1.98895	−	3.09487i	0.0967062	−	0.150478i
$424$	−7.47595	−	51.9964i	−0.363064	−	2.52517i
$425$	6.65105	+	11.0421i	0.322623	+	0.535623i
$426$	12.5267	+	27.4295i	0.606918	+	1.32897i
$427$	−0.422858	+	0.0607978i	−0.0204635	+	0.00294221i
$428$	29.5189	−	45.9323i	1.42685	−	2.22022i
$429$	1.44599	−	0.424582i	0.0698132	−	0.0204990i
$430$	44.9152	−	37.7906i	2.16600	−	1.82242i
$431$	−15.9268	+	18.3806i	−0.767169	+	0.885360i	−0.996113	−	0.0880793i	$-0.971927\pi$
$431$	−15.9268	+	18.3806i	−0.767169	+	0.885360i	0.228945	+	0.973439i	$0.426473\pi$
$432$	1.58353	+	2.46402i	0.0761877	+	0.118550i
$433$	11.9964	−	10.3949i	0.576510	−	0.499549i	−0.317101	−	0.948392i	$-0.602709\pi$
$433$	11.9964	−	10.3949i	0.576510	−	0.499549i	0.893611	+	0.448843i	$0.148164\pi$
$434$	12.3063	+	3.61347i	0.590723	+	0.173452i
$435$	−3.90455	−	8.88942i	−0.187209	−	0.426215i
$436$	44.7450			2.14289
$437$	4.38725	+	22.1852i	0.209871	+	1.06126i
$438$		−	0.450992i		−	0.0215492i
$439$	−11.3056	+	24.7557i	−0.539585	+	1.18153i	0.421894	+	0.906645i	$0.361366\pi$
$439$	−11.3056	+	24.7557i	−0.539585	+	1.18153i	−0.961478	+	0.274881i	$0.911362\pi$
$440$	23.2644	−	14.4778i	1.10909	−	0.690202i
$441$	3.54203	+	4.08772i	0.168668	+	0.194653i
$442$	−1.81024	−	2.81679i	−0.0861045	−	0.133981i
$443$	−29.2018	−	25.3035i	−1.38742	−	1.20220i	−0.953552	−	0.301227i	$-0.902604\pi$
$443$	−29.2018	−	25.3035i	−1.38742	−	1.20220i	−0.433866	−	0.900978i	$-0.642851\pi$
$444$	−0.906899	+	6.30762i	−0.0430395	+	0.299347i
$445$	6.66083	+	3.15968i	0.315754	+	0.149783i
$446$	−47.4414	−	30.4887i	−2.24642	−	1.44368i
$447$	18.9568	−	2.72557i	0.896624	−	0.128915i
$448$	−11.4109	+	5.21118i	−0.539114	+	0.246205i
$449$	6.97882	+	15.2815i	0.329351	+	0.721178i	0.999784	−	0.0207920i	$-0.00661879\pi$
$449$	6.97882	+	15.2815i	0.329351	+	0.721178i	−0.670433	+	0.741970i	$0.733892\pi$
$450$	3.05948	+	11.6634i	0.144225	+	0.549820i
$451$	−11.3347	−	7.28438i	−0.533731	−	0.343008i
$452$	9.80393	+	33.3891i	0.461138	+	1.57049i
$453$	14.7233	+	2.11689i	0.691761	+	0.0994602i
$454$	2.67000	−	3.08134i	0.125309	−	0.144614i
$455$	1.50026	+	0.238007i	0.0703333	+	0.0111579i
$456$	13.5227	+	15.6061i	0.633260	+	0.730821i
$457$	−7.45893	+	25.4028i	−0.348914	+	1.18829i	0.578946	+	0.815366i	$0.303464\pi$
$457$	−7.45893	+	25.4028i	−0.348914	+	1.18829i	−0.927861	+	0.372927i	$0.878354\pi$
$458$	23.4413	+	10.7053i	1.09534	+	0.500225i
$459$	2.57810			0.120336
$460$	−1.55068	−	40.8910i	−0.0723009	−	1.90655i
$461$	35.2109			1.63994			0.819968	−	0.572409i	$-0.193991\pi$
$461$	35.2109			1.63994			0.819968	+	0.572409i	$0.193991\pi$
$462$	7.74344	+	3.53631i	0.360258	+	0.164524i
$463$	−8.82647	+	30.0602i	−0.410201	+	1.39702i	0.452709	+	0.891658i	$0.350458\pi$
$463$	−8.82647	+	30.0602i	−0.410201	+	1.39702i	−0.862910	+	0.505358i	$0.831360\pi$
$464$	8.32842	+	9.61151i	0.386637	+	0.446203i
$465$	1.47718	−	9.31129i	0.0685024	−	0.431801i
$466$	12.1749	−	14.0506i	0.563993	−	0.650883i
$467$	−14.0382	−	2.01838i	−0.649609	−	0.0933996i	−0.190370	−	0.981712i	$-0.560969\pi$
$467$	−14.0382	−	2.01838i	−0.649609	−	0.0933996i	−0.459239	+	0.888313i	$0.651878\pi$
$468$	−0.578961	−	1.97176i	−0.0267625	−	0.0911446i
$469$	−5.15984	−	3.31603i	−0.238260	−	0.153120i
$470$	−10.9669	+	16.5315i	−0.505863	+	0.762542i
$471$	−4.46246	−	9.77143i	−0.205619	−	0.450244i
$472$	−13.6402	+	6.22929i	−0.627843	+	0.286726i
$473$	−30.1505	+	4.33499i	−1.38632	+	0.199323i
$474$	25.2121	+	16.2028i	1.15803	+	0.744220i
$475$	9.16709	+	21.7225i	0.420615	+	0.996699i
$476$	1.76604	−	12.2831i	0.0809462	−	0.562993i
$477$	−9.06585	−	7.85560i	−0.415097	−	0.359683i
$478$	−16.0472	−	24.9699i	−0.733982	−	1.14210i
$479$	10.7652	+	12.4237i	0.491876	+	0.567655i	0.946366	−	0.323097i	$-0.104724\pi$
$479$	10.7652	+	12.4237i	0.491876	+	0.567655i	−0.454490	+	0.890752i	$0.650179\pi$
$480$	2.00213	+	3.21722i	0.0913841	+	0.146846i
$481$	0.373612	−	0.818097i	0.0170353	−	0.0373020i
$482$			17.0800i			0.777971i
$483$	4.91078	−	3.53287i	0.223448	−	0.160751i
$484$	12.0931			0.549687
$485$	16.5828	+	37.7537i	0.752985	+	1.71431i
$486$	2.31392	+	0.679428i	0.104962	+	0.0308195i
$487$	−25.0607	+	21.7152i	−1.13561	+	0.984009i	−0.999977	−	0.00675074i	$-0.997851\pi$
$487$	−25.0607	+	21.7152i	−1.13561	+	0.984009i	−0.135630	+	0.990760i	$0.543306\pi$
$488$	−0.801814	−	1.24765i	−0.0362964	−	0.0564783i
$489$	−8.82070	+	10.1796i	−0.398886	+	0.460339i
$490$	−18.7781	−	22.3183i	−0.848308	−	1.00824i
$491$	12.2327	−	3.59186i	0.552056	−	0.162098i	0.00620548	−	0.999981i	$-0.498025\pi$
$491$	12.2327	−	3.59186i	0.552056	−	0.162098i	0.545851	+	0.837882i	$0.316207\pi$
$492$	−9.93298	+	15.4560i	−0.447813	+	0.696811i
$493$	11.0803	−	1.59311i	0.499033	−	0.0717501i
$494$	−2.54413	−	5.57088i	−0.114466	−	0.250646i
$495$	1.84995	−	5.97760i	0.0831493	−	0.268673i
$496$	1.75748	+	12.2235i	0.0789132	+	0.548853i
$497$	8.52734	−	13.2688i	0.382504	−	0.595187i
$498$	−0.591106	−	2.01312i	−0.0264881	−	0.0902102i
$499$	2.66276	−	18.5199i	0.119201	−	0.829064i	−0.839237	−	0.543765i	$-0.816998\pi$
$499$	2.66276	−	18.5199i	0.119201	−	0.829064i	0.958439	−	0.285299i	$-0.0920928\pi$
$500$	−10.2239	−	41.4193i	−0.457226	−	1.85233i
$501$	−17.1622	+	11.0295i	−0.766753	+	0.492762i
$502$	−11.1755	+	9.68364i	−0.498788	+	0.432202i
$503$	−0.854811	+	2.91122i	−0.0381141	+	0.129805i	−0.976352	−	0.216185i	$-0.930639\pi$
$503$	−0.854811	+	2.91122i	−0.0381141	+	0.129805i	0.938238	+	0.345990i	$0.112457\pi$
$504$	2.29470	−	5.02469i	0.102214	−	0.223818i
$505$	−31.7056	−	28.2901i	−1.41088	−	1.25889i
$506$	−16.0467	+	28.1067i	−0.713362	+	1.24950i
$507$		−	12.7100i		−	0.564470i
$508$	−18.1905	−	8.30734i	−0.807074	−	0.368578i
$509$	−29.0726	−	8.53649i	−1.28862	−	0.378373i	−0.435548	−	0.900166i	$-0.643445\pi$
$509$	−29.0726	−	8.53649i	−1.28862	−	0.378373i	−0.853072	+	0.521792i	$0.825264\pi$
$510$	−13.9010	−	0.202034i	−0.615547	−	0.00894620i
$511$	−0.198448	+	0.127535i	−0.00877884	+	0.00564182i
$512$	−23.1383	−	20.0494i	−1.02258	−	0.886068i
$513$	4.66753	+	0.671089i	0.206076	+	0.0296293i
$514$	−21.1752	+	6.21760i	−0.933998	+	0.274246i
$515$	25.3602	−	7.04777i	1.11750	−	0.310562i
$516$	5.91120	+	41.1133i	0.260226	+	1.80991i
$517$	9.36450	−	4.27663i	0.411850	−	0.188086i
$518$	4.62113	−	2.11040i	0.203041	−	0.0927257i
$519$	0.363076	+	2.52525i	0.0159373	+	0.110846i
$520$	1.41200	+	5.08086i	0.0619205	+	0.222810i
$521$	−2.90755	+	0.853733i	−0.127382	+	0.0374027i	−0.344802	−	0.938675i	$-0.612054\pi$
$521$	−2.90755	+	0.853733i	−0.127382	+	0.0374027i	0.217420	+	0.976078i	$0.430236\pi$
$522$	10.3648	+	1.49023i	0.453653	+	0.0652254i
$523$	−32.6523	−	28.2934i	−1.42779	−	1.23718i	−0.928803	−	0.370573i	$-0.879161\pi$
$523$	−32.6523	−	28.2934i	−1.42779	−	1.23718i	−0.498984	−	0.866611i	$-0.666293\pi$
$524$	−62.4876	+	40.1583i	−2.72978	+	1.75433i
$525$	4.26704	−	4.64453i	0.186229	−	0.202704i
$526$	−21.7720	−	6.39283i	−0.949303	−	0.278741i
$527$	9.88754	+	4.51549i	0.430708	+	0.196698i
$528$			8.19637i			0.356701i
$529$	11.6922	+	19.8064i	0.508354	+	0.861148i
$530$	48.2670	+	43.0674i	2.09658	+	1.87073i
$531$	−1.42250	+	3.11485i	−0.0617313	+	0.135173i
$532$	6.39464	−	21.7782i	0.277243	−	0.944203i
$533$	1.95965	−	1.69805i	0.0848820	−	0.0735506i
$534$	−6.68881	+	4.29864i	−0.289453	+	0.186020i
$535$	4.09269	+	31.7324i	0.176943	+	1.37191i
$536$	3.03031	−	21.0763i	0.130889	−	0.910356i
$537$	−2.26869	−	7.72647i	−0.0979014	−	0.333422i
$538$	−33.4668	+	52.0753i	−1.44286	+	2.24513i
$539$	2.15406	+	14.9818i	0.0927818	+	0.645311i
$540$	−8.15107	−	2.52260i	−0.350766	−	0.108555i
$541$	7.99129	+	17.4985i	0.343572	+	0.752319i	0.999998	−	0.00207231i	$-0.000659638\pi$
$541$	7.99129	+	17.4985i	0.343572	+	0.752319i	−0.656425	+	0.754391i	$0.727932\pi$
$542$	−1.82677	+	0.262650i	−0.0784664	+	0.0112818i
$543$	−8.13807	+	12.6631i	−0.349238	+	0.543425i
$544$	−4.19199	+	1.23088i	−0.179730	+	0.0527735i
$545$	−20.0634	+	16.8809i	−0.859423	+	0.723098i
$546$	−1.07284	+	1.23812i	−0.0459133	+	0.0529868i
$547$	5.72317	+	8.90543i	0.244705	+	0.380769i	0.941780	−	0.336230i	$-0.109152\pi$
$547$	5.72317	+	8.90543i	0.244705	+	0.380769i	−0.697075	+	0.716998i	$0.745515\pi$
$548$	52.7346	−	45.6948i	2.25271	−	1.95198i
$549$	−0.324953	−	0.0954149i	−0.0138687	−	0.00407221i
$550$	−10.4433	+	32.0860i	−0.445304	+	1.36815i
$551$	20.4751			0.872268
$552$	18.2384	+	10.4126i	0.776277	+	0.443191i
$553$		−	15.6759i		−	0.666609i
$554$	7.86716	−	17.2267i	0.334244	−	0.731891i
$555$	−1.97302	−	3.17046i	−0.0837501	−	0.134578i
$556$	42.5899	+	49.1514i	1.80621	+	2.08448i
$557$	4.74234	+	7.37922i	0.200939	+	0.312668i	0.927069	−	0.374890i	$-0.122319\pi$
$557$	4.74234	+	7.37922i	0.200939	+	0.312668i	−0.726130	+	0.687557i	$0.758683\pi$
$558$	7.68434	+	6.65852i	0.325304	+	0.281878i
$559$	0.834269	−	5.80247i	0.0352858	−	0.245418i
$560$	−3.54082	+	7.46430i	−0.149627	+	0.315424i
$561$	6.06919	+	3.90043i	0.256241	+	0.164676i
$562$	−23.6153	+	3.39536i	−0.996150	+	0.143225i
$563$	−2.19508	+	1.00246i	−0.0925117	+	0.0422487i	−0.461133	−	0.887331i	$-0.652557\pi$
$563$	−2.19508	+	1.00246i	−0.0925117	+	0.0422487i	0.368622	+	0.929579i	$0.379830\pi$
$564$	−5.83161	−	12.7694i	−0.245555	−	0.537691i
$565$	−16.9927	−	11.2728i	−0.714889	−	0.474251i
$566$	−36.9938	−	23.7745i	−1.55497	−	0.999316i
$567$	−0.355382	−	1.21032i	−0.0149246	−	0.0508287i
$568$	54.1987	+	7.79260i	2.27413	+	0.326970i
$569$	28.3075	−	32.6686i	1.18671	−	1.36954i	0.273594	−	0.961845i	$-0.411788\pi$
$569$	28.3075	−	32.6686i	1.18671	−	1.36954i	0.913119	−	0.407694i	$-0.133667\pi$
$570$	−25.1145	−	3.98425i	−1.05193	−	0.166882i
$571$	−2.63989	−	3.04659i	−0.110476	−	0.127496i	0.697818	−	0.716275i	$-0.254154\pi$
$571$	−2.63989	−	3.04659i	−0.110476	−	0.127496i	−0.808294	+	0.588779i	$0.799609\pi$
$572$	1.62014	−	5.51769i	0.0677415	−	0.230706i
$573$	8.42110	+	3.84579i	0.351797	+	0.160660i
$574$	14.6469			0.611348
$575$	16.1222	+	17.7503i	0.672343	+	0.740240i
$576$	−9.94479			−0.414366
$577$	14.7489	+	6.73558i	0.614003	+	0.280406i	0.698042	−	0.716057i	$-0.254055\pi$
$577$	14.7489	+	6.73558i	0.614003	+	0.280406i	−0.0840390	+	0.996462i	$0.526782\pi$
$578$	−7.03438	+	23.9569i	−0.292592	+	0.996475i
$579$	5.37681	+	6.20517i	0.223453	+	0.257878i
$580$	−36.5910	−	5.80492i	−1.51936	−	0.241036i
$581$	−0.718670	+	0.829389i	−0.0298154	+	0.0344088i
$582$	−44.0195	−	6.32905i	−1.82467	−	0.262347i
$583$	−9.45739	−	32.2089i	−0.391685	−	1.33396i
$584$	−0.688929	−	0.442748i	−0.0285081	−	0.0183210i
$585$	1.00349	+	0.665704i	0.0414891	+	0.0275235i
$586$	−3.63770	−	7.96546i	−0.150272	−	0.329050i
$587$	4.83801	−	2.20944i	0.199686	−	0.0911935i	−0.313062	−	0.949733i	$-0.601355\pi$
$587$	4.83801	−	2.20944i	0.199686	−	0.0911935i	0.512748	+	0.858539i	$0.328628\pi$
$588$	20.4292	−	2.93727i	0.842485	−	0.121131i
$589$	16.7255	+	10.7488i	0.689163	+	0.442898i
$590$	7.91415	−	16.6836i	0.325820	−	0.686853i
$591$	1.31900	−	9.17382i	0.0542562	−	0.377360i
$592$	3.69670	+	3.20321i	0.151933	+	0.131651i
$593$	21.3594	+	33.2359i	0.877125	+	1.36483i	0.930513	+	0.366260i	$0.119362\pi$
$593$	21.3594	+	33.2359i	0.877125	+	1.36483i	−0.0533871	+	0.998574i	$0.517002\pi$
$594$	4.41936	+	5.10021i	0.181328	+	0.209264i
$595$	3.84213	+	6.17394i	0.157512	+	0.253107i
$596$	30.3585	−	66.4758i	1.24353	−	2.72296i
$597$		−	20.2675i		−	0.829492i
$598$	−4.31999	−	4.48702i	−0.176658	−	0.183488i
$599$	−30.1036			−1.23000			−0.615001	−	0.788526i	$-0.710844\pi$
$599$	−30.1036			−1.23000			−0.615001	+	0.788526i	$0.710844\pi$
$600$	20.8205	+	6.77662i	0.849992	+	0.276654i
$601$	−17.4770	−	5.13171i	−0.712902	−	0.209327i	−0.0948809	−	0.995489i	$-0.530247\pi$
$601$	−17.4770	−	5.13171i	−0.712902	−	0.209327i	−0.618021	+	0.786162i	$0.712065\pi$
$602$	25.0252	−	21.6845i	1.01995	−	0.883792i
$603$	−2.62882	−	4.09052i	−0.107054	−	0.166579i
$604$	37.1696	−	42.8960i	1.51241	−	1.74541i
$605$	−5.42250	+	4.56236i	−0.220456	+	0.185486i
$606$	43.9714	−	12.9112i	1.78622	−	0.524481i
$607$	23.8918	−	37.1763i	0.969737	−	1.50894i	0.112737	−	0.993625i	$-0.464038\pi$
$607$	23.8918	−	37.1763i	0.969737	−	1.50894i	0.857000	−	0.515316i	$-0.172325\pi$
$608$	−7.90978	+	1.13726i	−0.320784	+	0.0461218i
$609$	−2.27529	−	4.98218i	−0.0921993	−	0.201888i
$610$	1.74465	+	0.539937i	0.0706390	+	0.0218614i
$611$	0.281960	+	1.96107i	0.0114069	+	0.0793365i
$612$	5.31863	−	8.27596i	0.214993	−	0.334536i
$613$	1.48445	+	5.05556i	0.0599563	+	0.204192i	0.984024	−	0.178037i	$-0.0569747\pi$
$613$	1.48445	+	5.05556i	0.0599563	+	0.204192i	−0.924068	+	0.382229i	$0.875156\pi$
$614$	0.934719	−	6.50112i	0.0377222	−	0.262364i
$615$	−1.37717	−	10.6778i	−0.0555329	−	0.430571i
$616$	13.0039	−	8.35711i	0.523943	−	0.336718i
$617$	−24.0439	+	20.8342i	−0.967973	+	0.838753i	−0.986944	−	0.161067i	$-0.948507\pi$
$617$	−24.0439	+	20.8342i	−0.967973	+	0.838753i	0.0189707	+	0.999820i	$0.493961\pi$
$618$	−7.99772	+	27.2377i	−0.321715	+	1.09566i
$619$	−15.7708	+	34.5332i	−0.633880	+	1.38800i	0.271100	+	0.962551i	$0.412613\pi$
$619$	−15.7708	+	34.5332i	−0.633880	+	1.38800i	−0.904980	+	0.425453i	$0.860115\pi$
$620$	−26.8427	−	23.9511i	−1.07803	−	0.961899i
$621$	4.70472	−	0.930384i	0.188794	−	0.0373350i
$622$		−	35.2566i		−	1.41366i
$623$	3.78303	+	1.72765i	0.151564	+	0.0692169i
$624$	−1.51349	−	0.444402i	−0.0605883	−	0.0177903i
$625$	20.2106	+	14.7151i	0.808422	+	0.588603i
$626$	46.6749	−	29.9961i	1.86550	−	1.19889i
$627$	9.97267	+	8.64137i	0.398270	+	0.345103i
$628$	−40.5733	−	5.83356i	−1.61905	−	0.232784i
$629$	4.13105	−	1.21299i	0.164716	−	0.0483649i
$630$	1.82135	+	6.55383i	0.0725645	+	0.261111i
$631$	−1.80754	−	12.5717i	−0.0719570	−	0.500472i	−0.993647	−	0.112544i	$-0.964100\pi$
$631$	−1.80754	−	12.5717i	−0.0719570	−	0.500472i	0.921690	−	0.387928i	$-0.126809\pi$
$632$	49.5024	−	22.6070i	1.96910	−	0.899259i
$633$	−20.3873	+	9.31056i	−0.810322	+	0.370062i
$634$	0.210190	+	1.46191i	0.00834773	+	0.0580597i
$635$	11.2907	−	3.13775i	0.448056	−	0.124518i
$636$	−43.9201	+	12.8961i	−1.74155	+	0.511364i
$637$	−2.88324	−	0.414548i	−0.114238	−	0.0164250i
$638$	22.1454	+	19.1891i	0.876745	+	0.759704i
$639$	10.5190	−	6.76013i	0.416124	−	0.267427i
$640$	46.0439	+	0.669191i	1.82005	+	0.0264521i
$641$	−31.3190	−	9.19607i	−1.23702	−	0.363223i	−0.403128	−	0.915144i	$-0.632077\pi$
$641$	−31.3190	−	9.19607i	−1.23702	−	0.363223i	−0.833897	+	0.551921i	$0.813895\pi$
$642$	−31.3887	−	14.3347i	−1.23881	−	0.565747i
$643$		−	5.98717i		−	0.236111i	−0.993007	−	0.118055i	$-0.962334\pi$
$643$		−	5.98717i		−	0.236111i	0.993007	−	0.118055i	$-0.0376661\pi$
$644$	−1.20990	−	23.0524i	−0.0476769	−	0.908391i
$645$	−18.1613	−	16.2049i	−0.715102	−	0.638068i
$646$	12.1792	−	26.6688i	0.479185	−	1.04927i
$647$	6.53751	−	22.2647i	0.257016	−	0.875316i	−0.725355	−	0.688375i	$-0.758324\pi$
$647$	6.53751	−	22.2647i	0.257016	−	0.875316i	0.982371	−	0.186941i	$-0.0598575\pi$
$648$	3.30951	−	2.86771i	0.130010	−	0.112654i
$649$	−8.06123	+	5.18064i	−0.316431	+	0.203358i
$650$	−5.35858	−	3.66808i	−0.210181	−	0.143874i
$651$	0.756887	−	5.26426i	0.0296647	−	0.206323i
$652$	14.4804	+	49.3159i	0.567098	+	1.93136i
$653$	10.2424	−	15.9375i	0.400816	−	0.623683i	−0.580913	−	0.813966i	$-0.697304\pi$
$653$	10.2424	−	15.9375i	0.400816	−	0.623683i	0.981729	+	0.190283i	$0.0609406\pi$
$654$	−4.02448	−	27.9909i	−0.157370	−	1.09453i
$655$	12.8687	−	41.5815i	0.502820	−	1.62472i
$656$	5.85842	+	12.8281i	0.228733	+	0.500855i
$657$	−0.185105	+	0.0266141i	−0.00722165	+	0.00103832i
$658$	−6.05047	+	9.41472i	−0.235872	+	0.367024i
$659$	−19.3305	+	5.67594i	−0.753008	+	0.221103i	−0.635640	−	0.771985i	$-0.719264\pi$
$659$	−19.3305	+	5.67594i	−0.753008	+	0.221103i	−0.117368	+	0.993089i	$0.537446\pi$
$660$	−15.3722	−	18.2703i	−0.598363	−	0.711172i
$661$	16.3032	−	18.8149i	0.634122	−	0.731816i	−0.344202	−	0.938896i	$-0.611851\pi$
$661$	16.3032	−	18.8149i	0.634122	−	0.731816i	0.978324	+	0.207080i	$0.0663960\pi$
$662$	0.167830	+	0.261149i	0.00652290	+	0.0101498i
$663$	−1.04930	+	0.909223i	−0.0407514	+	0.0353113i
$664$	−3.65552	−	1.07336i	−0.141862	−	0.0416544i
$665$	5.34889	+	12.1777i	0.207421	+	0.472232i
$666$	4.02740			0.156058
$667$	19.6453	−	6.90590i	0.760670	−	0.267397i
$668$			77.8463i			3.01196i
$669$	−9.71419	+	21.2711i	−0.375572	+	0.822388i
$670$	13.8539	+	22.2619i	0.535222	+	0.860051i
$671$	−0.620628	−	0.716243i	−0.0239591	−	0.0276503i
$672$	1.15570	+	1.79830i	0.0445821	+	0.0693710i
$673$	−24.9296	−	21.6016i	−0.960966	−	0.832682i	0.0249902	−	0.999688i	$-0.492045\pi$
$673$	−24.9296	−	21.6016i	−0.960966	−	0.832682i	−0.985956	+	0.167006i	$0.946590\pi$
$674$	1.92573	−	13.3938i	0.0741764	−	0.515908i
$675$	4.60660	−	1.94402i	0.177308	−	0.0748254i
$676$	−40.8002	−	26.2207i	−1.56924	−	1.00849i
$677$	−16.7309	+	2.40555i	−0.643023	+	0.0924527i	−0.456109	−	0.889924i	$-0.650757\pi$
$677$	−16.7309	+	2.40555i	−0.643023	+	0.0924527i	−0.186913	+	0.982376i	$0.559848\pi$
$678$	20.0053	−	9.13611i	0.768298	−	0.350870i
$679$	9.66322	+	21.1595i	0.370841	+	0.812028i
$680$	−13.9555	+	21.0366i	−0.535170	+	0.806719i
$681$	−1.42227	−	0.914038i	−0.0545015	−	0.0350260i
$682$	8.01621	+	27.3007i	0.306957	+	1.04540i
$683$	−42.4959	−	6.10998i	−1.62606	−	0.233792i	−0.731858	−	0.681457i	$-0.761347\pi$
$683$	−42.4959	−	6.10998i	−1.62606	−	0.233792i	−0.894201	+	0.447665i	$0.852256\pi$
$684$	11.7834	−	13.5987i	0.450549	−	0.519961i
$685$	−6.40673	+	40.3845i	−0.244789	+	1.54301i
$686$	−24.7198	−	28.5281i	−0.943805	−	1.08921i
$687$	3.01055	−	10.2530i	0.114860	−	0.391177i
$688$	29.0014	+	13.2445i	1.10567	+	0.504941i
$689$	6.46029			0.246117
$690$	−25.4405	+	4.64790i	−0.968504	+	0.176942i
$691$	21.5268			0.818917			0.409459	−	0.912329i	$-0.365718\pi$
$691$	21.5268			0.818917			0.409459	+	0.912329i	$0.365718\pi$
$692$	8.85531	+	4.04408i	0.336628	+	0.153733i
$693$	0.994486	−	3.38691i	0.0377774	−	0.128658i
$694$	−12.7668	−	14.7337i	−0.484621	−	0.559282i
$695$	−37.6404	−	5.97141i	−1.42778	−	0.226508i
$696$	12.4517	−	14.3701i	0.471982	−	0.544696i
$697$	12.2868	+	1.76657i	0.465394	+	0.0669136i
$698$	−10.0279	−	34.1520i	−0.379562	−	1.29267i
$699$	−6.48542	−	4.16793i	−0.245301	−	0.157645i
$700$	−6.10647	−	23.2793i	−0.230803	−	0.879874i
$701$	−7.44598	−	16.3044i	−0.281231	−	0.615810i	0.715320	−	0.698797i	$-0.246281\pi$
$701$	−7.44598	−	16.3044i	−0.281231	−	0.615810i	−0.996551	+	0.0829877i	$0.973554\pi$
$702$	−1.18139	+	0.539523i	−0.0445887	+	0.0203630i
$703$	7.79480	−	1.12072i	0.293986	−	0.0422689i
$704$	−23.4113	−	15.0455i	−0.882347	−	0.567050i
$705$	7.43239	+	3.52568i	0.279920	+	0.132785i
$706$	−8.18555	+	56.9318i	−0.308067	+	2.14265i
$707$	−18.1158	−	15.6975i	−0.681317	−	0.590364i
$708$	7.06432	+	10.9923i	0.265493	+	0.413116i
$709$	−12.7551	−	14.7202i	−0.479027	−	0.552827i	0.463873	−	0.885902i	$-0.346459\pi$
$709$	−12.7551	−	14.7202i	−0.479027	−	0.552827i	−0.942900	+	0.333075i	$0.891914\pi$
$710$	−57.2475	+	35.6260i	−2.14846	+	1.33702i
$711$	5.16247	−	11.3042i	0.193608	−	0.423942i
$712$			14.4378i			0.541080i
$713$	19.6731	+	4.67200i	0.736763	+	0.174968i
$714$	−7.84269			−0.293505
$715$	1.35519	+	3.08534i	0.0506812	+	0.115385i
$716$	−29.4830	−	8.65699i	−1.10183	−	0.323527i
$717$	−9.30169	+	8.05996i	−0.347378	+	0.301005i
$718$	22.1739	+	34.5032i	0.827521	+	1.28765i
$719$	−25.3177	+	29.2181i	−0.944189	+	1.08965i	0.0516628	+	0.998665i	$0.483548\pi$
$719$	−25.3177	+	29.2181i	−0.944189	+	1.08965i	−0.995852	+	0.0909878i	$0.970998\pi$
$720$	−5.01153	+	4.21658i	−0.186769	+	0.157143i
$721$	14.2470	−	4.18329i	0.530585	−	0.155794i
$722$	4.21938	−	6.56548i	0.157029	−	0.244342i
$723$	7.01031	−	1.00793i	0.260716	−	0.0374853i
$724$	23.8608	+	52.2480i	0.886781	+	1.94178i
$725$	18.5973	−	11.2017i	0.690685	−	0.416022i
$726$	−1.08769	−	7.56503i	−0.0403679	−	0.280765i
$727$	−13.1348	+	20.4382i	−0.487144	+	0.758011i	−0.994613	−	0.103659i	$-0.966945\pi$
$727$	−13.1348	+	20.4382i	−0.487144	+	0.758011i	0.507469	+	0.861670i	$0.330581\pi$
$728$	0.838112	+	2.85435i	0.0310625	+	0.105789i
$729$	0.142315	−	0.989821i	0.00527092	−	0.0366601i
$730$	1.00016	−	0.128996i	0.0370177	−	0.00477436i
$731$	23.6082	−	15.1720i	0.873179	−	0.561158i
$732$	−0.976670	+	0.846290i	−0.0360988	+	0.0312798i
$733$	8.11056	−	27.6220i	0.299570	−	1.02024i	−0.662866	−	0.748738i	$-0.730660\pi$
$733$	8.11056	−	27.6220i	0.299570	−	1.02024i	0.962437	−	0.271506i	$-0.0875216\pi$
$734$	12.4324	−	27.2232i	0.458888	−	1.00483i
$735$	−8.05221	+	9.02436i	−0.297010	+	0.332868i
$736$	−7.20566	+	3.75900i	−0.265604	+	0.138559i
$737$		−	13.6068i		−	0.501212i
$738$	10.5621	+	4.82357i	0.388798	+	0.177558i
$739$	1.28749	+	0.378042i	0.0473612	+	0.0139065i	0.305327	−	0.952247i	$-0.401234\pi$
$739$	1.28749	+	0.378042i	0.0473612	+	0.0139065i	−0.257966	+	0.966154i	$0.583052\pi$
$740$	−14.2478	−	0.207074i	−0.523760	−	0.00761219i
$741$	−2.13638	+	1.37297i	−0.0784818	+	0.0504372i
$742$	27.5787	+	23.8971i	1.01244	+	0.877288i
$743$	−19.8002	−	2.84684i	−0.726398	−	0.104440i	−0.230811	−	0.972999i	$-0.574138\pi$
$743$	−19.8002	−	2.84684i	−0.726398	−	0.104440i	−0.495587	+	0.868558i	$0.665047\pi$
$744$	17.7153	−	5.20170i	0.649476	−	0.190703i
$745$	11.4667	+	41.2608i	0.420106	+	1.51168i
$746$	−2.81381	−	19.5705i	−0.103021	−	0.716526i
$747$	−0.791385	+	0.361413i	−0.0289553	+	0.0132234i
$748$	25.0415	−	11.4361i	0.915608	−	0.418144i
$749$	2.56868	+	17.8655i	0.0938574	+	0.652792i
$750$	−24.9909	+	10.1211i	−0.912538	+	0.369569i
$751$	−39.9561	+	11.7322i	−1.45802	+	0.428113i	−0.912185	−	0.409780i	$-0.865606\pi$
$751$	−39.9561	+	11.7322i	−1.45802	+	0.428113i	−0.545835	+	0.837893i	$0.683787\pi$
$752$	−10.6657	−	1.53350i	−0.388939	−	0.0559210i
$753$	4.63406	+	4.01543i	0.168874	+	0.146330i
$754$	−4.74406	+	3.04882i	−0.172768	+	0.111032i
$755$	−0.483354	+	33.2573i	−0.0175910	+	1.21036i
$756$	−4.61839	−	1.35608i	−0.167969	−	0.0493203i
$757$	18.9848	+	8.67006i	0.690013	+	0.315119i	0.729382	−	0.684106i	$-0.239808\pi$
$757$	18.9848	+	8.67006i	0.690013	+	0.315119i	−0.0393690	+	0.999225i	$0.512535\pi$
$758$			10.7381i			0.390026i
$759$	12.4831	+	4.92756i	0.453108	+	0.178859i
$760$	−30.7417	+	34.4531i	−1.11512	+	1.24975i
$761$	−8.60393	+	18.8400i	−0.311892	+	0.682948i	−0.999051	−	0.0435589i	$-0.986130\pi$
$761$	−8.60393	+	18.8400i	−0.311892	+	0.682948i	0.687159	+	0.726507i	$0.258858\pi$
$762$	−3.56067	+	12.1265i	−0.128990	+	0.439298i
$763$	−11.1787	+	9.68636i	−0.404694	+	0.350670i
$764$	29.7181	−	19.0987i	1.07516	−	0.690966i
$765$	0.737409	+	5.71746i	0.0266611	+	0.206715i
$766$	−2.52186	+	17.5400i	−0.0911187	+	0.633744i
$767$	−0.519552	−	1.76943i	−0.0187599	−	0.0638905i
$768$	−16.0971	+	25.0476i	−0.580855	+	0.903828i
$769$	−7.85405	−	54.6261i	−0.283224	−	1.96987i	−0.239848	−	0.970810i	$-0.577098\pi$
$769$	−7.85405	−	54.6261i	−0.283224	−	1.96987i	−0.0433766	−	0.999059i	$-0.513812\pi$
$770$	−5.62763	+	18.1841i	−0.202806	+	0.655310i
$771$	3.80156	+	8.32424i	0.136910	+	0.299790i
$772$	31.0116	−	4.45879i	1.11613	−	0.160475i
$773$	−10.2283	+	15.9155i	−0.367885	+	0.572440i	−0.975009	−	0.222167i	$-0.928687\pi$
$773$	−10.2283	+	15.9155i	−0.367885	+	0.572440i	0.607124	+	0.794607i	$0.292323\pi$
$774$	25.1874	−	7.39568i	0.905342	−	0.265832i
$775$	21.0721	+	0.612644i	0.756934	+	0.0220068i
$776$	−52.8830	+	61.0302i	−1.89839	+	2.19086i
$777$	−1.13890	−	1.77216i	−0.0408578	−	0.0635759i
$778$	−48.5174	+	42.0406i	−1.73943	+	1.50723i
$779$	21.7847	+	6.39657i	0.780518	+	0.229181i
$780$	4.20717	−	1.84794i	0.150641	−	0.0661668i
$781$	34.9905			1.25206
$782$	2.69072	−	29.6958i	0.0962201	−	1.06192i
$783$		−	4.34206i		−	0.155173i
$784$	6.58118	−	14.4108i	0.235042	−	0.514670i
$785$	20.3937	−	12.6913i	0.727883	−	0.452972i
$786$	30.7420	+	35.4781i	1.09653	+	1.26546i
$787$	−15.3830	−	23.9365i	−0.548346	−	0.853244i	0.450879	−	0.892585i	$-0.351110\pi$
$787$	−15.3830	−	23.9365i	−0.548346	−	0.853244i	−0.999226	+	0.0393412i	$0.987474\pi$
$788$	−26.7277	−	23.1597i	−0.952136	−	0.825030i
$789$	−1.33906	+	9.31336i	−0.0476718	+	0.331564i
$790$	−28.7216	+	60.5473i	−1.02187	+	2.15418i
$791$	−9.67738	−	6.21927i	−0.344088	−	0.221132i
$792$	12.1296	−	1.74397i	0.431006	−	0.0619693i
$793$	0.165908	−	0.0757674i	0.00589155	−	0.00269058i
$794$	13.7538	+	30.1166i	0.488104	+	1.06880i
$795$	14.8283	−	22.3522i	0.525905	−	0.792752i
$796$	−65.0604	−	41.8118i	−2.30601	−	1.48198i
$797$	5.85244	+	19.9316i	0.207304	+	0.706013i	0.995848	+	0.0910343i	$0.0290173\pi$
$797$	5.85244	+	19.9316i	0.207304	+	0.706013i	−0.788544	+	0.614979i	$0.789165\pi$
$798$	−14.1988	−	2.04148i	−0.502632	−	0.0722676i
$799$	−6.21105	+	7.16793i	−0.219731	+	0.253583i
$800$	−6.56217	+	5.36033i	−0.232008	+	0.189516i
$801$	2.15906	+	2.49169i	0.0762866	+	0.0880395i
$802$	−7.67269	+	26.1308i	−0.270932	+	0.922710i
$803$	−0.476027	−	0.217394i	−0.0167986	−	0.00767168i
$804$	−18.5542			−0.654356
$805$	9.23946	+	9.88013i	0.325648	+	0.348229i
$806$	−5.47583			−0.192878
$807$	23.3488	+	10.6630i	0.821916	+	0.375357i
$808$	23.4447	−	79.8454i	0.824782	−	2.80895i
$809$	−23.0708	−	26.6251i	−0.811126	−	0.936089i	0.187810	−	0.982205i	$-0.439861\pi$
$809$	−23.0708	−	26.6251i	−0.811126	−	0.936089i	−0.998936	+	0.0461160i	$0.985316\pi$
$810$	−0.844922	+	5.32591i	−0.0296875	+	0.187133i
$811$	−8.50865	+	9.81950i	−0.298779	+	0.344809i	−0.885212	−	0.465189i	$-0.845986\pi$
$811$	−8.50865	+	9.81950i	−0.298779	+	0.344809i	0.586433	+	0.809998i	$0.300532\pi$
$812$	−20.6872	−	2.97437i	−0.725978	−	0.104380i
$813$	0.215604	+	0.734281i	0.00756157	+	0.0257523i
$814$	9.48102	+	6.09308i	0.332309	+	0.213562i
$815$	−25.0983	−	16.6500i	−0.879155	−	0.583224i
$816$	−3.13690	−	6.86885i	−0.109813	−	0.240458i
$817$	46.6907	−	21.3229i	1.63350	−	0.745995i
$818$	15.5075	−	2.22964i	0.542205	−	0.0779574i
$819$	0.571487	+	0.367272i	0.0199694	+	0.0128335i
$820$	−37.1179	−	17.6075i	−1.29621	−	0.614881i
$821$	−6.94200	+	48.2827i	−0.242278	+	1.68508i	0.398356	+	0.917231i	$0.369581\pi$
$821$	−6.94200	+	48.2827i	−0.242278	+	1.68508i	−0.640634	+	0.767847i	$0.721328\pi$
$822$	−33.3281	−	28.8790i	−1.16245	−	1.00727i
$823$	−1.59367	−	2.47980i	−0.0555520	−	0.0864405i	0.812367	−	0.583147i	$-0.198179\pi$
$823$	−1.59367	−	2.47980i	−0.0555520	−	0.0864405i	−0.867919	+	0.496707i	$0.834543\pi$
$824$	33.7565	+	38.9570i	1.17596	+	1.35713i
$825$	13.7857	+	2.39288i	0.479955	+	0.0833094i
$826$	4.32731	−	9.47548i	0.150566	−	0.329694i
$827$		−	32.5190i		−	1.13080i	−0.824818	−	0.565399i	$-0.808722\pi$
$827$		−	32.5190i		−	1.13080i	0.824818	−	0.565399i	$-0.191278\pi$
$828$	6.71923	−	17.0220i	0.233509	−	0.591555i
$829$	−18.7910			−0.652637			−0.326319	−	0.945260i	$-0.605808\pi$
$829$	−18.7910			−0.652637			−0.326319	+	0.945260i	$0.605808\pi$
$830$	4.29543	−	1.88670i	0.149096	−	0.0654885i
$831$	−7.53479	−	2.21241i	−0.261379	−	0.0767478i
$832$	4.04757	−	3.50724i	0.140324	−	0.121592i
$833$	−7.53898	−	11.7309i	−0.261210	−	0.406451i
$834$	26.9167	−	31.0635i	0.932050	−	1.07564i
$835$	−29.3690	−	34.9059i	−1.01636	−	1.20797i
$836$	48.3133	−	14.1861i	1.67095	−	0.490635i
$837$	2.27946	−	3.54690i	0.0787895	−	0.122599i
$838$	−77.4306	+	11.1328i	−2.67479	+	0.384577i
$839$	17.7447	+	38.8554i	0.612615	+	1.34144i	0.920771	+	0.390103i	$0.127561\pi$
$839$	17.7447	+	38.8554i	0.612615	+	1.34144i	−0.308157	+	0.951336i	$0.599712\pi$
$840$	11.7996	+	3.65175i	0.407125	+	0.125997i
$841$	1.44400	+	10.0433i	0.0497932	+	0.346319i
$842$	9.76605	−	15.1963i	0.336560	−	0.523698i
$843$	2.78719	+	9.49230i	0.0959959	+	0.326932i
$844$	−12.1712	+	84.6528i	−0.418951	+	2.91387i
$845$	28.1869	−	3.63540i	0.969658	−	0.125062i
$846$	−7.46361	+	4.79657i	−0.256604	+	0.164909i
$847$	−3.02123	+	2.61791i	−0.103811	+	0.0899524i
$848$	−9.89887	+	33.7125i	−0.339929	+	1.15769i
$849$	−7.57492	+	16.5868i	−0.259971	+	0.569256i
$850$	−3.52802	−	30.8860i	−0.121010	−	1.05938i
$851$	7.10091	−	3.70436i	0.243416	−	0.126984i
$852$		−	47.7131i		−	1.63462i
$853$	−19.1351	−	8.73870i	−0.655173	−	0.299207i	0.0599550	−	0.998201i	$-0.480904\pi$
$853$	−19.1351	−	8.73870i	−0.655173	−	0.299207i	−0.715128	+	0.698994i	$0.753632\pi$
$854$	0.988521	+	0.290256i	0.0338265	+	0.00993235i
$855$	−0.153231	+	10.5431i	−0.00524039	+	0.360567i
$856$	−52.7125	+	33.8762i	−1.80167	+	1.15787i
$857$	35.2226	+	30.5206i	1.20318	+	1.04256i	0.997960	+	0.0638485i	$0.0203375\pi$
$857$	35.2226	+	30.5206i	1.20318	+	1.04256i	0.205223	+	0.978715i	$0.434208\pi$
$858$	−3.59739	−	0.517227i	−0.122813	−	0.0176578i
$859$	33.4154	−	9.81165i	1.14012	−	0.334769i	0.343441	−	0.939174i	$-0.388407\pi$
$859$	33.4154	−	9.81165i	1.14012	−	0.334769i	0.796677	+	0.604405i	$0.206589\pi$
$860$	−89.4862	+	24.8688i	−3.05145	+	0.848020i
$861$	−0.864348	−	6.01167i	−0.0294569	−	0.204877i
$862$	53.3523	−	24.3652i	1.81719	−	0.829881i
$863$	−40.3097	+	18.4088i	−1.37216	+	0.626643i	−0.958841	−	0.283944i	$-0.908357\pi$
$863$	−40.3097	+	18.4088i	−1.37216	+	0.626643i	−0.413316	+	0.910587i	$0.635630\pi$
$864$	0.241173	+	1.67739i	0.00820486	+	0.0570660i
$865$	−5.49639	+	1.52748i	−0.186883	+	0.0519360i
$866$	−36.7300	+	10.7849i	−1.24814	+	0.366486i
$867$	10.2480	+	1.47344i	0.348040	+	0.0500406i
$868$	−15.3373	−	13.2899i	−0.520582	−	0.451087i
$869$	29.2554	−	18.8013i	0.992421	−	0.637790i
$870$	−0.340266	+	23.4121i	−0.0115361	+	0.793746i
$871$	2.51255	+	0.737751i	0.0851344	+	0.0249977i
$872$	−46.7094	−	21.3315i	−1.58178	−	0.722375i
$873$			18.4409i			0.624129i
$874$	12.6013	−	53.0624i	0.426247	−	1.79486i
$875$	11.5207	+	8.13454i	0.389469	+	0.274998i
$876$	−0.296439	+	0.649111i	−0.0100157	+	0.0219314i
$877$	2.70626	−	9.21667i	0.0913838	−	0.311225i	−0.901098	−	0.433615i	$-0.857238\pi$
$877$	2.70626	−	9.21667i	0.0913838	−	0.311225i	0.992482	+	0.122390i	$0.0390560\pi$
$878$	49.6014	−	42.9799i	1.67397	−	1.45050i
$879$	−3.05468	+	1.96312i	−0.103032	+	0.0662145i
$880$	−18.1771	+	2.34439i	−0.612749	+	0.0790294i
$881$	−7.80983	+	54.3186i	−0.263120	+	1.83004i	0.245913	+	0.969292i	$0.420912\pi$
$881$	−7.80983	+	54.3186i	−0.263120	+	1.83004i	−0.509033	+	0.860747i	$0.669997\pi$
$882$	−3.67491	−	12.5156i	−0.123741	−	0.421422i
$883$	5.50320	−	8.56314i	0.185197	−	0.288173i	−0.736224	−	0.676738i	$-0.763393\pi$
$883$	5.50320	−	8.56314i	0.185197	−	0.288173i	0.921421	+	0.388566i	$0.127029\pi$
$884$	0.753985	+	5.24408i	0.0253593	+	0.176377i
$885$	−7.31466	−	2.26375i	−0.245880	−	0.0760951i
$886$	38.7097	+	84.7625i	1.30048	+	2.84765i
$887$	−18.5998	+	2.67425i	−0.624521	+	0.0897925i	−0.447308	−	0.894380i	$-0.647617\pi$
$887$	−18.5998	+	2.67425i	−0.624521	+	0.0897925i	−0.177213	+	0.984173i	$0.556708\pi$
$888$	3.95378	−	6.15220i	0.132680	−	0.206454i
$889$	6.34291	−	1.86245i	0.212735	−	0.0624645i
$890$	−11.4463	−	13.6042i	−0.383680	−	0.456015i
$891$	1.83254	−	2.11486i	0.0613923	−	0.0708504i
$892$	48.2419	+	75.0658i	1.61526	+	2.51339i
$893$	−13.1106	+	11.3604i	−0.438730	+	0.380162i
$894$	−44.3155	−	13.0122i	−1.48213	−	0.435193i
$895$	16.4861	−	7.24127i	0.551068	−	0.242049i
$896$	25.9771			0.867835
$897$	−1.58672	+	2.03789i	−0.0529791	+	0.0680432i
$898$		−	40.5141i		−	1.35197i
$899$	7.60502	−	16.6527i	0.253641	−	0.555397i
$900$	3.26294	−	18.7981i	0.108765	−	0.626605i
$901$	20.2526	+	23.3727i	0.674711	+	0.778658i
$902$	17.5670	+	27.3349i	0.584919	+	0.910151i
$903$	−10.3770	−	8.99171i	−0.345324	−	0.299225i
$904$	5.68340	−	39.5289i	0.189027	−	1.31471i
$905$	−30.4106	−	14.4258i	−1.01088	−	0.479530i
$906$	−30.1774	−	19.3938i	−1.00258	−	0.644317i
$907$	−19.2193	+	2.76332i	−0.638167	+	0.0917545i	−0.453801	−	0.891103i	$-0.649932\pi$
$907$	−19.2193	+	2.76332i	−0.638167	+	0.0917545i	−0.184366	+	0.982858i	$0.559023\pi$
$908$	−5.86829	+	2.67996i	−0.194746	+	0.0889376i
$909$	−7.89414	−	17.2857i	−0.261832	−	0.573332i
$910$	−3.05265	−	2.02510i	−0.101194	−	0.0671313i
$911$	−38.2932	−	24.6096i	−1.26871	−	0.815351i	−0.279259	−	0.960216i	$-0.590089\pi$
$911$	−38.2932	−	24.6096i	−1.26871	−	0.815351i	−0.989451	+	0.144865i	$0.953725\pi$
$912$	−3.89121	−	13.2523i	−0.128851	−	0.438826i
$913$	−2.40981	−	0.346478i	−0.0797530	−	0.0114667i
$914$	41.8114	−	48.2530i	1.38300	−	1.59607i
$915$	0.118656	−	0.747940i	0.00392264	−	0.0247261i
$916$	−26.7023	−	30.8161i	−0.882270	−	1.01819i
$917$	6.91785	−	23.5600i	0.228448	−	0.778021i
$918$	−5.65552	−	2.58279i	−0.186660	−	0.0852448i
$919$	47.8360			1.57796			0.788982	−	0.614416i	$-0.210608\pi$
$919$	47.8360			1.57796			0.788982	+	0.614416i	$0.210608\pi$
$920$	−17.8754	+	43.4255i	−0.589335	+	1.43170i
$921$	−2.72348			−0.0897418
$922$	−77.2413	−	35.2749i	−2.54381	−	1.16172i
$923$	−1.89716	+	6.46114i	−0.0624459	+	0.212671i
$924$	−8.82067	−	10.1796i	−0.290179	−	0.334884i
$925$	6.46678	−	5.28240i	0.212626	−	0.173684i
$926$	49.4773	−	57.0998i	1.62592	−	1.87642i
$927$	11.6514	+	1.67522i	0.382683	+	0.0550215i
$928$	2.07305	+	7.06017i	0.0680513	+	0.231761i
$929$	40.4305	+	25.9831i	1.32648	+	0.852478i	0.995826	−	0.0912735i	$-0.0290937\pi$
$929$	40.4305	+	25.9831i	1.32648	+	0.852478i	0.330656	+	0.943751i	$0.392730\pi$
$930$	−12.5687	+	18.9461i	−0.412142	+	0.621266i
$931$	−10.5954	−	23.2006i	−0.347249	−	0.760369i
$932$	−26.7589	+	12.2204i	−0.876516	+	0.400291i
$933$	−14.4707	+	2.08058i	−0.473750	+	0.0681150i
$934$	28.7731	+	18.4914i	0.941485	+	0.605056i
$935$	−6.91403	+	14.5753i	−0.226113	+	0.476662i
$936$	−0.335627	+	2.33434i	−0.0109703	+	0.0763002i
$937$	11.3389	+	9.82519i	0.370425	+	0.320975i	0.820103	−	0.572216i	$-0.193916\pi$
$937$	11.3389	+	9.82519i	0.370425	+	0.320975i	−0.449678	+	0.893191i	$0.648461\pi$
$938$	7.99696	+	12.4435i	0.261110	+	0.406295i
$939$	−15.0660	−	17.3871i	−0.491662	−	0.567408i
$940$	26.6508	−	16.5852i	0.869253	−	0.540949i
$941$	−2.46775	+	5.40363i	−0.0804465	+	0.176153i	−0.945581	−	0.325386i	$-0.894506\pi$
$941$	−2.46775	+	5.40363i	−0.0804465	+	0.176153i	0.865135	+	0.501540i	$0.167233\pi$
$942$			25.9059i			0.844060i
$943$	23.0593	−	1.21027i	0.750915	−	0.0394117i
$944$	10.0297			0.326440
$945$	2.58248	−	1.13432i	0.0840079	−	0.0368993i
$946$	70.4834	+	20.6958i	2.29161	+	0.672878i
$947$	22.8327	−	19.7847i	0.741965	−	0.642916i	−0.199550	−	0.979888i	$-0.563948\pi$
$947$	22.8327	−	19.7847i	0.741965	−	0.642916i	0.941515	+	0.336972i	$0.109403\pi$
$948$	−25.6375	−	39.8927i	−0.832666	−	1.29565i
$949$	0.0659527	−	0.0761134i	0.00214091	−	0.00247075i
$950$	1.65243	−	56.8359i	0.0536118	−	1.84400i
$951$	0.587622	−	0.172541i	0.0190550	−	0.00559504i
$952$	−7.69933	+	11.9804i	−0.249537	+	0.388287i
$953$	−18.3972	+	2.64512i	−0.595943	+	0.0856837i	−0.433685	−	0.901065i	$-0.642787\pi$
$953$	−18.3972	+	2.64512i	−0.595943	+	0.0856837i	−0.162258	+	0.986748i	$0.551878\pi$
$954$	12.0176	+	26.3150i	0.389086	+	0.851978i
$955$	−6.12013	+	19.7755i	−0.198043	+	0.639919i
$956$	6.68383	+	46.4870i	0.216170	+	1.50350i
$957$	6.56913	−	10.2218i	0.212350	−	0.330423i
$958$	−11.1691	−	38.0384i	−0.360857	−	1.22897i
$959$	−3.28273	+	22.8319i	−0.106005	+	0.737280i
$960$	−2.84449	−	22.0545i	−0.0918054	−	0.711807i
$961$	−11.1244	+	7.14920i	−0.358851	+	0.230619i
$962$	−1.63917	+	1.42035i	−0.0528489	+	0.0457938i
$963$	−4.03123	+	13.7291i	−0.129905	+	0.442415i
$964$	11.2267	−	24.5831i	0.361589	−	0.791769i
$965$	−12.2233	+	13.6990i	−0.393482	+	0.440987i
$966$	−14.3119	+	2.83027i	−0.460479	+	0.0910623i
$967$			17.6623i			0.567980i	0.958827	+	0.283990i	$0.0916582\pi$
$967$			17.6623i			0.567980i	−0.958827	+	0.283990i	$0.908342\pi$
$968$	−12.6240	−	5.76521i	−0.405752	−	0.185301i
$969$	−11.6647	−	3.42505i	−0.374723	−	0.110029i
$970$	1.44512	−	99.4322i	0.0464001	−	3.19258i
$971$	−29.3901	+	18.8879i	−0.943174	+	0.606141i	−0.919293	−	0.393574i	$-0.871239\pi$
$971$	−29.3901	+	18.8879i	−0.943174	+	0.606141i	−0.0238811	+	0.999715i	$0.507602\pi$
$972$	−2.88382	−	2.49885i	−0.0924987	−	0.0801506i
$973$	−21.2805	−	3.05967i	−0.682222	−	0.0980886i
$974$	76.7296	−	22.5298i	2.45857	−	0.721903i
$975$	−1.18931	+	2.41584i	−0.0380883	+	0.0773688i
$976$	0.141172	+	0.981870i	0.00451879	+	0.0314289i
$977$	47.9504	−	21.8982i	1.53407	−	0.700586i	0.543731	−	0.839260i	$-0.317011\pi$
$977$	47.9504	−	21.8982i	1.53407	−	0.700586i	0.990338	+	0.138674i	$0.0442841\pi$
$978$	29.5479	−	13.4941i	0.944836	−	0.431492i
$979$	1.31301	+	9.13222i	0.0419641	+	0.291867i
$980$	12.3573	+	44.4656i	0.394740	+	1.42040i
$981$	−11.2511	+	3.30362i	−0.359220	+	0.105477i
$982$	−30.4331	−	4.37561i	−0.971158	−	0.139631i
$983$	9.82485	+	8.51328i	0.313364	+	0.271532i	0.797315	−	0.603564i	$-0.206253\pi$
$983$	9.82485	+	8.51328i	0.313364	+	0.271532i	−0.483951	+	0.875095i	$0.660799\pi$
$984$	17.7375	−	11.3992i	0.565451	−	0.363393i
$985$	20.7220	+	0.301169i	0.660259	+	0.00959604i
$986$	−25.9027	−	7.60571i	−0.824909	−	0.242215i
$987$	4.22124	+	1.92777i	0.134363	+	0.0613617i
$988$			9.69041i			0.308293i
$989$	37.6067	−	36.2068i	1.19582	−	1.15131i
$990$	−10.0467	+	11.2596i	−0.319304	+	0.357854i
$991$	16.3382	−	35.7757i	0.519000	−	1.13645i	−0.450817	−	0.892616i	$-0.648867\pi$
$991$	16.3382	−	35.7757i	0.519000	−	1.13645i	0.969817	−	0.243835i	$-0.0784054\pi$
$992$	−2.01297	+	6.85554i	−0.0639118	+	0.217664i
$993$	0.0972820	−	0.0842953i	0.00308715	−	0.00267503i
$994$	−31.9991	+	20.5646i	−1.01495	+	0.652269i
$995$	44.9471	−	5.79705i	1.42492	−	0.183779i
$996$	−0.472458	+	3.28602i	−0.0149704	+	0.104121i
$997$	−9.60524	−	32.7125i	−0.304201	−	1.03601i	−0.959749	−	0.280860i	$-0.909380\pi$
$997$	−9.60524	−	32.7125i	−0.304201	−	1.03601i	0.655548	−	0.755154i	$-0.272438\pi$
$998$	−24.3948	+	37.9590i	−0.772203	+	1.20157i
$999$	−0.237667	−	1.65301i	−0.00751944	−	0.0522989i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	345.2.t.a.259.3	yes	240
5.4	even	2	inner	345.2.t.a.259.22	yes	240
23.4	even	11	inner	345.2.t.a.4.22	yes	240
115.4	even	22	inner	345.2.t.a.4.3	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.t.a.4.3	✓	240	115.4	even	22	inner
345.2.t.a.4.22	yes	240	23.4	even	11	inner
345.2.t.a.259.3	yes	240	1.1	even	1	trivial
345.2.t.a.259.22	yes	240	5.4	even	2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 345 = 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	345.t (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.19367 - 1.00182i) q^{2} +(-0.281733 + 0.959493i) q^{3} +(2.49885 + 2.88382i) q^{4} +(-2.20845 - 0.350356i) q^{5} +(1.57927 - 1.82257i) q^{6} +(-1.24858 - 0.179518i) q^{7} +(-1.23374 - 4.20172i) q^{8} +(-0.841254 - 0.540641i) q^{9} +(4.49363 + 2.98103i) q^{10} +(-1.16248 - 2.54548i) q^{11} +(-3.47102 + 1.58516i) q^{12} +(0.533062 - 0.0766428i) q^{13} +(2.55913 + 1.64465i) q^{14} +(0.958357 - 2.02029i) q^{15} +(-0.416839 + 2.89918i) q^{16} +(1.94840 + 1.68830i) q^{17} +(1.30381 + 2.02877i) q^{18} +(3.08801 + 3.56376i) q^{19} +(-4.50821 - 7.24427i) q^{20} +(0.524011 - 1.14742i) q^{21} +6.74854i q^{22} +(4.16486 + 2.37780i) q^{23} +4.37911 q^{24} +(4.75450 + 1.54749i) q^{25} +(-1.24615 - 0.365902i) q^{26} +(0.755750 - 0.654861i) q^{27} +(-2.60230 - 4.04926i) q^{28} +(2.84344 - 3.28151i) q^{29} +(-4.12628 + 3.47175i) q^{30} +(4.04542 - 1.18784i) q^{31} +(-0.916192 + 1.42562i) q^{32} +(2.76988 - 0.398248i) q^{33} +(-2.58279 - 5.65552i) q^{34} +(2.69452 + 0.833904i) q^{35} +(-0.543052 - 3.77701i) q^{36} +(0.902873 - 1.40490i) q^{37} +(-3.20386 - 10.9113i) q^{38} +(-0.0766428 + 0.533062i) q^{39} +(1.25255 + 9.71154i) q^{40} +(4.05048 - 2.60309i) q^{41} +(-2.29902 + 1.99211i) q^{42} +(3.06670 - 10.4442i) q^{43} +(4.43585 - 9.71315i) q^{44} +(1.66845 + 1.48872i) q^{45} +(-6.75423 - 9.38855i) q^{46} +3.67888i q^{47} +(-2.66430 - 1.21675i) q^{48} +(-5.18973 - 1.52384i) q^{49} +(-8.87953 - 8.15783i) q^{50} +(-2.16884 + 1.39383i) q^{51} +(1.55307 + 1.34574i) q^{52} +(11.8737 + 1.70719i) q^{53} +(-2.31392 + 0.679428i) q^{54} +(1.67546 + 6.02884i) q^{55} +(0.786129 + 5.46765i) q^{56} +(-4.28939 + 1.95890i) q^{57} +(-9.52506 + 4.34995i) q^{58} +(-0.487328 - 3.38944i) q^{59} +(8.22094 - 2.28465i) q^{60} +(0.324953 - 0.0954149i) q^{61} +(-10.0643 - 1.44703i) q^{62} +(0.953315 + 0.826052i) q^{63} +(8.36609 - 5.37656i) q^{64} +(-1.20409 - 0.0175000i) q^{65} +(-6.47518 - 1.90128i) q^{66} +(4.42300 + 2.01992i) q^{67} +9.83765i q^{68} +(-3.45486 + 3.32625i) q^{69} +(-5.07549 - 4.52873i) q^{70} +(-5.19432 + 11.3740i) q^{71} +(-1.23374 + 4.20172i) q^{72} +(0.141332 - 0.122465i) q^{73} +(-3.38806 + 2.17738i) q^{74} +(-2.82430 + 4.12593i) q^{75} +(-2.56077 + 17.8106i) q^{76} +(0.994486 + 3.38691i) q^{77} +(0.702161 - 1.09258i) q^{78} +(1.76858 + 12.3008i) q^{79} +(1.93631 - 6.25665i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-11.4933 + 1.65248i) q^{82} +(0.470360 - 0.731895i) q^{83} +(4.61839 - 1.35608i) q^{84} +(-3.71144 - 4.41116i) q^{85} +(-17.1906 + 19.8390i) q^{86} +(2.34749 + 3.65277i) q^{87} +(-9.26119 + 8.02487i) q^{88} +(-3.16343 - 0.928865i) q^{89} +(-2.16861 - 4.93724i) q^{90} -0.679328 q^{91} +(3.55020 + 17.9525i) q^{92} +4.21621i q^{93} +(3.68557 - 8.07026i) q^{94} +(-5.57114 - 8.95228i) q^{95} +(-1.10975 - 1.28072i) q^{96} +(-9.96989 - 15.5135i) q^{97} +(9.85797 + 8.54198i) q^{98} +(-0.398248 + 2.76988i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 28 q^{4} - 4 q^{5} - 4 q^{6} + 24 q^{9} + 8 q^{14} + 4 q^{15} - 36 q^{16} - 8 q^{19} - 92 q^{20} + 8 q^{21} + 12 q^{24} - 44 q^{25} + 32 q^{26} - 12 q^{29} + 8 q^{30} - 20 q^{31} - 54 q^{34} + 36 q^{35}+ \cdots + 44 q^{99}+O(q^{100}) \) 240 * q + 28 * q^4 - 4 * q^5 - 4 * q^6 + 24 * q^9 + 8 * q^14 + 4 * q^15 - 36 * q^16 - 8 * q^19 - 92 * q^20 + 8 * q^21 + 12 * q^24 - 44 * q^25 + 32 * q^26 - 12 * q^29 + 8 * q^30 - 20 * q^31 - 54 * q^34 + 36 * q^35 - 28 * q^36 - 36 * q^39 - 24 * q^40 - 28 * q^41 - 224 * q^44 + 4 * q^45 - 8 * q^46 + 52 * q^49 - 48 * q^50 - 18 * q^54 - 22 * q^55 - 56 * q^59 - 36 * q^60 + 44 * q^61 + 12 * q^64 - 16 * q^65 + 8 * q^66 + 8 * q^69 - 152 * q^70 + 4 * q^71 + 88 * q^74 - 8 * q^75 - 100 * q^76 - 84 * q^79 + 122 * q^80 - 24 * q^81 - 56 * q^84 + 186 * q^85 - 392 * q^86 + 48 * q^89 - 304 * q^91 + 80 * q^94 + 190 * q^95 + 16 * q^96 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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