LMFDB - Embedded newform 345.2.t.a.4.3

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			4.3
Character	$\chi$	$=$	345.4
Dual form			345.2.t.a.259.3

$q$-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 $\left(\mathbb{Z}/345\mathbb{Z}\right)^\times$.

$n$	$116$	$166$	$277$
$\chi(n)$	$1$	$e\left(\frac{2}{11}\right)$	$-1$

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	−0.992641	−	0.121098i	$-0.961358\pi$
$2$	−2.19367	+	1.00182i	−1.55116	+	0.708392i	−0.558522	+	0.829490i	$0.688631\pi$
$3$	−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	−0.374171	−	0.927360i	$-0.622073\pi$
$7$	−1.24858	+	0.179518i	−0.471918	+	0.0678515i	−0.0977468	+	0.995211i	$0.531164\pi$
$8$	−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	0.649474	+	0.760384i	$0.274989\pi$
$11$	−1.16248	+	2.54548i	−0.350501	+	0.767490i	−0.999975	+	0.00710625i	$0.997738\pi$
$12$	−3.47102	−	1.58516i	−1.00200	−	0.457596i
$13$	0.533062	+	0.0766428i	0.147845	+	0.0212569i	0.215840	−	0.976429i	$-0.430751\pi$
$13$	0.533062	+	0.0766428i	0.147845	+	0.0212569i	−0.0679950	+	0.997686i	$0.521660\pi$
$14$	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	−0.385755	−	0.922601i	$-0.626059\pi$
$17$	1.94840	−	1.68830i	0.472557	−	0.409473i	0.858312	+	0.513129i	$0.171514\pi$
$18$	1.30381	−	2.02877i	0.307312	−	0.478186i
$19$	3.08801	−	3.56376i	0.708439	−	0.817582i	−0.281428	−	0.959582i	$-0.590808\pi$
$19$	3.08801	−	3.56376i	0.708439	−	0.817582i	0.989867	+	0.142001i	$0.0453535\pi$
$20$	−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	0.955619	−	0.294605i	$-0.0951880\pi$
$29$	2.84344	+	3.28151i	0.528014	+	0.609361i	−0.427605	+	0.903966i	$0.640643\pi$
$30$	−4.12628	−	3.47175i	−0.753352	−	0.633852i
$31$	4.04542	+	1.18784i	0.726580	+	0.213343i	0.624047	−	0.781387i	$-0.285487\pi$
$31$	4.04542	+	1.18784i	0.726580	+	0.213343i	0.102532	+	0.994730i	$0.467305\pi$
$32$	−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	0.907505	−	0.420041i	$-0.137984\pi$
$37$	0.902873	+	1.40490i	0.148431	+	0.230964i	−0.759074	+	0.651005i	$0.774348\pi$
$38$	−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	0.817264	−	0.576264i	$-0.195490\pi$
$41$	4.05048	+	2.60309i	0.632579	+	0.406534i	−0.184684	+	0.982798i	$0.559126\pi$
$42$	−2.29902	−	1.99211i	−0.354746	−	0.307390i
$43$	3.06670	+	10.4442i	0.467668	+	1.59273i	0.769024	+	0.639219i	$0.220742\pi$
$43$	3.06670	+	10.4442i	0.467668	+	1.59273i	−0.301357	+	0.953512i	$0.597439\pi$
$44$	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	$-0.913535\pi$
$47$		−	3.67888i		−	0.536620i	0.963333	−	0.268310i	$-0.0864651\pi$
$48$	−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	0.734832	−	0.678249i	$-0.237261\pi$
$53$	11.8737	−	1.70719i	1.63098	−	0.234500i	0.896151	+	0.443749i	$0.146352\pi$
$54$	−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	0.933196	+	0.359368i	$0.117008\pi$
$59$	−0.487328	+	3.38944i	−0.0634446	+	0.441267i	−0.996641	+	0.0818993i	$0.973901\pi$
$60$	8.22094	+	2.28465i	1.06132	+	0.294948i
$61$	0.324953	+	0.0954149i	0.0416060	+	0.0122166i	0.302469	−	0.953159i	$-0.402189\pi$
$61$	0.324953	+	0.0954149i	0.0416060	+	0.0122166i	−0.260863	+	0.965376i	$0.584007\pi$
$62$	−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	−0.126490	−	0.991968i	$-0.540371\pi$
$67$	4.42300	−	2.01992i	0.540356	−	0.246772i	0.666846	+	0.745196i	$0.267644\pi$
$68$		−	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	−0.918072	−	0.396414i	$-0.870255\pi$
$71$	−5.19432	−	11.3740i	−0.616452	−	1.34984i	0.301620	−	0.953428i	$-0.402473\pi$
$72$	−1.23374	−	4.20172i	−0.145397	−	0.495178i
$73$	0.141332	+	0.122465i	0.0165416	+	0.0143334i	0.663092	−	0.748538i	$-0.269244\pi$
$73$	0.141332	+	0.122465i	0.0165416	+	0.0143334i	−0.646551	+	0.762871i	$0.723789\pi$
$74$	−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	−0.608267	−	0.793732i	$-0.708135\pi$
$79$	1.76858	−	12.3008i	0.198981	−	1.38394i	0.807248	−	0.590212i	$-0.200956\pi$
$80$	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	0.866108	−	0.499856i	$-0.166614\pi$
$83$	0.470360	+	0.731895i	0.0516288	+	0.0803359i	−0.814480	+	0.580192i	$0.802977\pi$
$84$	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	−0.445059	−	0.895501i	$-0.646817\pi$
$89$	−3.16343	+	0.928865i	−0.335322	+	0.0984595i	0.109737	+	0.993961i	$0.464999\pi$
$90$	−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	−0.210457	+	0.977603i	$0.567495\pi$
$97$	−9.96989	+	15.5135i	−1.01229	+	1.57515i	−0.801832	+	0.597549i	$0.796141\pi$
$98$	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	0.619205	−	0.785230i	$-0.287455\pi$
$101$	15.9864	−	10.2738i	1.59070	−	1.02228i	0.971497	−	0.237052i	$-0.0761812\pi$
$102$	6.15409	+	0.884824i	0.609346	+	0.0876107i
$103$	−10.7075	−	4.88995i	−1.05504	−	0.481821i	−0.189096	−	0.981959i	$-0.560556\pi$
$103$	−10.7075	−	4.88995i	−1.05504	−	0.481821i	−0.865946	+	0.500137i	$0.833283\pi$
$104$	−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	0.498131	+	0.867102i	$0.334020\pi$
$107$	−4.03123	+	13.7291i	−0.389714	+	1.32724i	−0.887845	+	0.460142i	$0.847798\pi$
$108$	3.77701	−	0.543052i	0.363443	−	0.0522552i
$109$	7.67896	+	8.86199i	0.735511	+	0.848824i	0.993081	−	0.117435i	$-0.0374672\pi$
$109$	7.67896	+	8.86199i	0.735511	+	0.848824i	−0.257570	+	0.966260i	$0.582922\pi$
$110$	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	0.0149268	−	0.999889i	$-0.495248\pi$
$113$	8.29542	−	3.78839i	0.780367	−	0.356382i	0.765440	+	0.643507i	$0.222521\pi$
$114$	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	0.192523	−	0.981292i	$-0.438333\pi$
$127$	−4.76710	−	2.17706i	−0.423012	−	0.193183i	−0.615535	+	0.788109i	$0.711060\pi$
$128$	−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	−0.641843	−	0.766836i	$-0.721830\pi$
$131$	−2.77030	−	19.2678i	−0.242042	−	1.68344i	0.399801	−	0.916602i	$-0.369079\pi$
$132$	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	$0.285368\pi$
$137$			18.2863i			1.56231i	−0.624339	+	0.781154i	$0.714632\pi$
$138$	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	0.238221	+	0.971211i	$0.423436\pi$
$149$	−7.95590	+	17.4210i	−0.651773	+	1.42718i	−0.889994	+	0.455972i	$0.849292\pi$
$150$	10.3290	+	6.22152i	0.843362	+	0.507985i
$151$	−2.11689	+	14.7233i	−0.172270	+	1.19816i	0.701803	+	0.712371i	$0.252379\pi$
$151$	−2.11689	+	14.7233i	−0.172270	+	1.19816i	−0.874073	+	0.485794i	$0.838531\pi$
$152$	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	0.267685	−	0.963506i	$-0.413741\pi$
$157$	−8.11840	−	7.03463i	−0.647919	−	0.561425i	−0.915604	+	0.402082i	$0.868287\pi$
$158$	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	0.126924	−	0.991912i	$-0.459490\pi$
$163$	12.2524	−	5.59546i	0.959679	−	0.438271i	0.832755	+	0.553642i	$0.186762\pi$
$164$	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	0.194473	−	0.980908i	$-0.437700\pi$
$167$	15.4179	−	13.3597i	1.19307	−	1.03380i	0.998600	−	0.0528954i	$-0.0168450\pi$
$168$	−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	0.501675	−	0.865056i	$-0.332717\pi$
$173$	2.32067	+	1.05981i	0.176437	+	0.0805761i	−0.325238	+	0.945632i	$0.605444\pi$
$174$	−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	0.262410	−	0.964957i	$-0.415483\pi$
$179$	−6.77432	−	4.35359i	−0.506337	−	0.325403i	−0.768746	+	0.639554i	$0.779119\pi$
$180$	−0.123996	−	8.53159i	−0.00924212	−	0.635907i
$181$	14.4429	−	4.24082i	1.07353	−	0.315218i	0.303244	−	0.952913i	$-0.401930\pi$
$181$	14.4429	−	4.24082i	1.07353	−	0.315218i	0.770289	+	0.637695i	$0.220112\pi$
$182$	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	0.980317	+	0.197428i	$0.0632588\pi$
$191$	1.31751	+	9.16347i	0.0953316	+	0.663046i	−0.884986	+	0.465618i	$0.845832\pi$
$192$	2.80177	−	9.54195i	0.202200	−	0.688631i
$193$	4.43900	+	6.90721i	0.319526	+	0.497192i	0.963447	−	0.267900i	$-0.0863297\pi$
$193$	4.43900	+	6.90721i	0.319526	+	0.497192i	−0.643921	+	0.765092i	$0.722693\pi$
$194$	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	−0.192469	−	0.981303i	$-0.561650\pi$
$197$	−9.17382	−	1.31900i	−0.653607	−	0.0939746i	−0.461138	+	0.887328i	$0.652559\pi$
$198$	3.64854	+	5.67724i	0.259290	+	0.403464i
$199$	−19.4465	−	5.71000i	−1.37852	−	0.404771i	−0.493269	−	0.869877i	$-0.664198\pi$
$199$	−19.4465	−	5.71000i	−1.37852	−	0.404771i	−0.885255	+	0.465106i	$0.846016\pi$
$200$	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	0.0243577	−	0.999703i	$-0.492246\pi$
$211$	14.6772	−	16.9384i	1.01042	−	1.16609i	0.986061	−	0.166382i	$-0.0532086\pi$
$212$	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	0.686465	−	0.727163i	$-0.259161\pi$
$223$	23.1463	−	3.32793i	1.54999	−	0.222855i	0.863524	+	0.504308i	$0.168252\pi$
$224$	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	0.942175	−	0.335122i	$-0.108778\pi$
$227$	−0.476313	−	1.62217i	−0.0316140	−	0.107667i	−0.973789	+	0.227455i	$0.926960\pi$
$228$	−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	0.857252	−	0.514897i	$-0.172170\pi$
$233$	−2.17194	−	7.39696i	−0.142289	−	0.484591i	−0.999541	+	0.0303064i	$0.990352\pi$
$234$	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	−0.161086	−	0.986940i	$-0.551500\pi$
$239$	10.3541	−	6.65416i	0.669749	−	0.430422i	0.830835	+	0.556519i	$0.187863\pi$
$240$	5.45769	−	3.62058i	0.352292	−	0.233707i
$241$	−2.94214	+	6.44238i	−0.189520	+	0.414990i	−0.980410	−	0.196968i	$-0.936891\pi$
$241$	−2.94214	+	6.44238i	−0.189520	+	0.414990i	0.790890	+	0.611958i	$0.209618\pi$
$242$	−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	0.972827	−	0.231534i	$-0.0743745\pi$
$251$	2.54721	+	5.57762i	0.160779	+	0.352056i	−0.812048	+	0.583591i	$0.801647\pi$
$252$		−	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	0.843326	−	0.537403i	$-0.180595\pi$
$257$	6.91603	+	5.99278i	0.431410	+	0.373819i	−0.411915	+	0.911222i	$0.635140\pi$
$258$	−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	0.423338	−	0.905972i	$-0.360858\pi$
$263$	9.31336	+	1.33906i	0.574286	+	0.0825699i	0.150948	+	0.988542i	$0.451767\pi$
$264$	−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	0.727658	+	0.685940i	$0.240609\pi$
$269$	3.65299	+	25.4071i	0.222727	+	1.54910i	−0.504931	+	0.863160i	$0.668482\pi$
$270$	5.34822	+	0.689786i	0.325482	+	0.0419791i
$271$	0.643794	+	0.413741i	0.0391077	+	0.0251330i	0.560049	−	0.828460i	$-0.310782\pi$
$271$	0.643794	+	0.413741i	0.0391077	+	0.0251330i	−0.520941	+	0.853593i	$0.674419\pi$
$272$	−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	$-0.924191\pi$
$277$		−	7.85288i		−	0.471834i	0.971773	−	0.235917i	$-0.0758094\pi$
$278$	−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	0.764808	−	0.644259i	$-0.222834\pi$
$281$	8.32255	+	5.34858i	0.496482	+	0.319069i	−0.268326	+	0.963328i	$0.586470\pi$
$282$	6.70502	−	5.80993i	0.399278	−	0.345976i
$283$	18.0490	−	2.59505i	1.07290	−	0.154260i	0.416849	−	0.908976i	$-0.363134\pi$
$283$	18.0490	−	2.59505i	1.07290	−	0.154260i	0.656052	+	0.754716i	$0.272225\pi$
$284$	−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	−0.571008	−	0.820945i	$-0.693447\pi$
$293$	2.74420	−	2.37787i	0.160318	−	0.138916i	0.731326	+	0.682028i	$0.238902\pi$
$294$	−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	−0.934695	−	0.355451i	$-0.884327\pi$
$307$	0.767294	−	2.61316i	0.0437918	−	0.149141i	0.978487	+	0.206310i	$0.0661455\pi$
$308$	−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	−0.655621	−	0.755090i	$-0.727593\pi$
$311$	6.07317	−	13.2984i	0.344378	−	0.754083i	0.999999	+	0.00100692i	$0.000320511\pi$
$312$	2.33434	+	0.335627i	0.132156	+	0.0190011i
$313$	−12.4382	−	19.3543i	−0.703051	−	1.09397i	−0.990678	−	0.136226i	$-0.956503\pi$
$313$	−12.4382	−	19.3543i	−0.703051	−	1.09397i	0.287627	−	0.957743i	$-0.407134\pi$
$314$	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	−0.850427	−	0.526092i	$-0.823657\pi$
$317$	−0.331105	+	0.515209i	−0.0185967	+	0.0289370i	0.831831	+	0.555029i	$0.187293\pi$
$318$	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	−0.543613	−	0.839336i	$-0.682944\pi$
$331$	−0.108288	+	0.0695926i	−0.00595206	+	0.00382516i	0.537661	+	0.843161i	$0.319308\pi$
$332$	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	−0.905166	−	0.425058i	$-0.860254\pi$
$337$	1.58080	−	5.38370i	0.0861115	−	0.293269i	0.991278	+	0.131789i	$0.0420720\pi$
$338$	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	−0.208140	−	0.978099i	$-0.566741\pi$
$347$	7.35346	−	3.35821i	0.394755	−	0.180278i	0.602895	+	0.797821i	$0.294014\pi$
$348$	−4.66792	−	15.8975i	−0.250227	−	0.852194i
$349$	9.66532	−	11.1544i	0.517373	−	0.597080i	−0.435598	−	0.900141i	$-0.643463\pi$
$349$	9.66532	−	11.1544i	0.517373	−	0.597080i	0.952971	+	0.303061i	$0.0980086\pi$
$350$	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	0.562632	+	0.826707i	$0.309789\pi$
$353$	−6.71937	+	22.8841i	−0.357636	+	1.21800i	−0.920268	+	0.391288i	$0.872030\pi$
$354$	−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	−0.860686	−	0.509136i	$-0.829965\pi$
$359$	−14.3071	+	9.19465i	−0.755102	+	0.485275i	0.105584	+	0.994410i	$0.466329\pi$
$360$	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	$-0.895008\pi$
$367$		−	12.4098i		−	0.647789i	0.946093	−	0.323894i	$-0.104992\pi$
$368$	−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	−0.707333	−	0.706881i	$-0.750102\pi$
$373$	4.43248	−	6.89708i	0.229505	−	0.357117i	0.936838	+	0.349764i	$0.113738\pi$
$374$	−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	−0.951171	−	0.308665i	$-0.900118\pi$
$379$	−1.84971	+	4.05031i	−0.0950134	+	0.208050i	0.856158	+	0.516715i	$0.172845\pi$
$380$	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	−0.995324	−	0.0965970i	$-0.969204\pi$
$383$	−2.07015	+	7.05029i	−0.105780	+	0.360253i	0.889544	+	0.456850i	$0.151022\pi$
$384$	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	0.951609	+	0.307310i	$0.0994290\pi$
$389$	11.0585	+	24.2147i	0.560687	+	1.22773i	−0.390922	+	0.920424i	$0.627844\pi$
$390$	−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	−0.875138	−	0.483873i	$-0.839230\pi$
$397$	−10.3756	+	8.99049i	−0.520735	+	0.451220i	0.354403	+	0.935093i	$0.384684\pi$
$398$	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	0.909529	+	0.415639i	$0.136442\pi$
$401$	−1.60714	+	11.1779i	−0.0802568	+	0.558198i	−0.989786	+	0.142559i	$0.954467\pi$
$402$	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	0.398504	−	0.917167i	$-0.369529\pi$
$409$	−5.46518	−	3.51225i	−0.270236	−	0.173670i	−0.668740	+	0.743497i	$0.733166\pi$
$410$	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	0.996393	−	0.0848589i	$-0.0270440\pi$
$419$	27.2883	+	17.5371i	1.33312	+	0.856744i	0.336726	+	0.941603i	$0.390680\pi$
$420$	−10.6746	−	1.37676i	−0.520867	−	0.0671789i
$421$	−1.06599	−	7.41414i	−0.0519533	−	0.361343i	−0.999169	−	0.0407474i	$-0.987026\pi$
$421$	−1.06599	−	7.41414i	−0.0519533	−	0.361343i	0.947216	−	0.320595i	$-0.103883\pi$
$422$	−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	0.228945	−	0.973439i	$-0.426473\pi$
$431$	−15.9268	−	18.3806i	−0.767169	−	0.885360i	−0.996113	+	0.0880793i	$0.971927\pi$
$432$	1.58353	−	2.46402i	0.0761877	−	0.118550i
$433$	11.9964	+	10.3949i	0.576510	+	0.499549i	0.893611	−	0.448843i	$-0.148164\pi$
$433$	11.9964	+	10.3949i	0.576510	+	0.499549i	−0.317101	+	0.948392i	$0.602709\pi$
$434$	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	−0.961478	−	0.274881i	$-0.911362\pi$
$439$	−11.3056	−	24.7557i	−0.539585	−	1.18153i	0.421894	−	0.906645i	$-0.361366\pi$
$440$	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	−0.433866	+	0.900978i	$0.642851\pi$
$443$	−29.2018	+	25.3035i	−1.38742	+	1.20220i	−0.953552	+	0.301227i	$0.902604\pi$
$444$	−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	−0.670433	−	0.741970i	$-0.733892\pi$
$449$	6.97882	−	15.2815i	0.329351	−	0.721178i	0.999784	+	0.0207920i	$0.00661879\pi$
$450$	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	−0.927861	−	0.372927i	$-0.878354\pi$
$457$	−7.45893	−	25.4028i	−0.348914	−	1.18829i	0.578946	−	0.815366i	$-0.303464\pi$
$458$	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	−0.862910	−	0.505358i	$-0.831360\pi$
$463$	−8.82647	−	30.0602i	−0.410201	−	1.39702i	0.452709	−	0.891658i	$-0.350458\pi$
$464$	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	−0.459239	−	0.888313i	$-0.651878\pi$
$467$	−14.0382	+	2.01838i	−0.649609	+	0.0933996i	−0.190370	+	0.981712i	$0.560969\pi$
$468$	−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	−0.454490	−	0.890752i	$-0.650179\pi$
$479$	10.7652	−	12.4237i	0.491876	−	0.567655i	0.946366	+	0.323097i	$0.104724\pi$
$480$	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	−0.135630	−	0.990760i	$-0.543306\pi$
$487$	−25.0607	−	21.7152i	−1.13561	−	0.984009i	−0.999977	+	0.00675074i	$0.997851\pi$
$488$	−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	0.545851	−	0.837882i	$-0.316207\pi$
$491$	12.2327	+	3.59186i	0.552056	+	0.162098i	0.00620548	+	0.999981i	$0.498025\pi$
$492$	−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	0.958439	+	0.285299i	$0.0920928\pi$
$499$	2.66276	+	18.5199i	0.119201	+	0.829064i	−0.839237	+	0.543765i	$0.816998\pi$
$500$	−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	0.938238	−	0.345990i	$-0.112457\pi$
$503$	−0.854811	−	2.91122i	−0.0381141	−	0.129805i	−0.976352	+	0.216185i	$0.930639\pi$
$504$	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	−0.853072	−	0.521792i	$-0.825264\pi$
$509$	−29.0726	+	8.53649i	−1.28862	+	0.378373i	−0.435548	+	0.900166i	$0.643445\pi$
$510$	−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	0.217420	−	0.976078i	$-0.430236\pi$
$521$	−2.90755	−	0.853733i	−0.127382	−	0.0374027i	−0.344802	+	0.938675i	$0.612054\pi$
$522$	10.3648	−	1.49023i	0.453653	−	0.0652254i
$523$	−32.6523	+	28.2934i	−1.42779	+	1.23718i	−0.498984	+	0.866611i	$0.666293\pi$
$523$	−32.6523	+	28.2934i	−1.42779	+	1.23718i	−0.928803	+	0.370573i	$0.879161\pi$
$524$	−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	−0.656425	−	0.754391i	$-0.727932\pi$
$541$	7.99129	−	17.4985i	0.343572	−	0.752319i	0.999998	+	0.00207231i	$0.000659638\pi$
$542$	−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	−0.697075	−	0.716998i	$-0.745515\pi$
$547$	5.72317	−	8.90543i	0.244705	−	0.380769i	0.941780	+	0.336230i	$0.109152\pi$
$548$	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	−0.726130	−	0.687557i	$-0.758683\pi$
$557$	4.74234	−	7.37922i	0.200939	−	0.312668i	0.927069	+	0.374890i	$0.122319\pi$
$558$	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	0.368622	−	0.929579i	$-0.379830\pi$
$563$	−2.19508	−	1.00246i	−0.0925117	−	0.0422487i	−0.461133	+	0.887331i	$0.652557\pi$
$564$	−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	0.913119	+	0.407694i	$0.133667\pi$
$569$	28.3075	+	32.6686i	1.18671	+	1.36954i	0.273594	+	0.961845i	$0.411788\pi$
$570$	−25.1145	+	3.98425i	−1.05193	+	0.166882i
$571$	−2.63989	+	3.04659i	−0.110476	+	0.127496i	−0.808294	−	0.588779i	$-0.799609\pi$
$571$	−2.63989	+	3.04659i	−0.110476	+	0.127496i	0.697818	+	0.716275i	$0.254154\pi$
$572$	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	−0.0840390	−	0.996462i	$-0.526782\pi$
$577$	14.7489	−	6.73558i	0.614003	−	0.280406i	0.698042	+	0.716057i	$0.254055\pi$
$578$	−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	0.512748	−	0.858539i	$-0.328628\pi$
$587$	4.83801	+	2.20944i	0.199686	+	0.0911935i	−0.313062	+	0.949733i	$0.601355\pi$
$588$	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	−0.0533871	−	0.998574i	$-0.517002\pi$
$593$	21.3594	−	33.2359i	0.877125	−	1.36483i	0.930513	−	0.366260i	$-0.119362\pi$
$594$	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	−0.618021	−	0.786162i	$-0.712065\pi$
$601$	−17.4770	+	5.13171i	−0.712902	+	0.209327i	−0.0948809	+	0.995489i	$0.530247\pi$
$602$	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	0.857000	+	0.515316i	$0.172325\pi$
$607$	23.8918	+	37.1763i	0.969737	+	1.50894i	0.112737	+	0.993625i	$0.464038\pi$
$608$	−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	−0.924068	−	0.382229i	$-0.875156\pi$
$613$	1.48445	−	5.05556i	0.0599563	−	0.204192i	0.984024	+	0.178037i	$0.0569747\pi$
$614$	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	0.0189707	−	0.999820i	$-0.493961\pi$
$617$	−24.0439	−	20.8342i	−0.967973	−	0.838753i	−0.986944	+	0.161067i	$0.948507\pi$
$618$	−7.99772	−	27.2377i	−0.321715	−	1.09566i
$619$	−15.7708	−	34.5332i	−0.633880	−	1.38800i	−0.904980	−	0.425453i	$-0.860115\pi$
$619$	−15.7708	−	34.5332i	−0.633880	−	1.38800i	0.271100	−	0.962551i	$-0.412613\pi$
$620$	−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	0.921690	+	0.387928i	$0.126809\pi$
$631$	−1.80754	+	12.5717i	−0.0719570	+	0.500472i	−0.993647	+	0.112544i	$0.964100\pi$
$632$	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	−0.833897	−	0.551921i	$-0.813895\pi$
$641$	−31.3190	+	9.19607i	−1.23702	+	0.363223i	−0.403128	+	0.915144i	$0.632077\pi$
$642$	−31.3887	+	14.3347i	−1.23881	+	0.565747i
$643$			5.98717i			0.236111i	0.993007	+	0.118055i	$0.0376661\pi$
$643$			5.98717i			0.236111i	−0.993007	+	0.118055i	$0.962334\pi$
$644$	−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	0.982371	+	0.186941i	$0.0598575\pi$
$647$	6.53751	+	22.2647i	0.257016	+	0.875316i	−0.725355	+	0.688375i	$0.758324\pi$
$648$	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	0.981729	−	0.190283i	$-0.0609406\pi$
$653$	10.2424	+	15.9375i	0.400816	+	0.623683i	−0.580913	+	0.813966i	$0.697304\pi$
$654$	−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	−0.117368	−	0.993089i	$-0.537446\pi$
$659$	−19.3305	−	5.67594i	−0.753008	−	0.221103i	−0.635640	+	0.771985i	$0.719264\pi$
$660$	−15.3722	+	18.2703i	−0.598363	+	0.711172i
$661$	16.3032	+	18.8149i	0.634122	+	0.731816i	0.978324	−	0.207080i	$-0.0663960\pi$
$661$	16.3032	+	18.8149i	0.634122	+	0.731816i	−0.344202	+	0.938896i	$0.611851\pi$
$662$	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	−0.985956	−	0.167006i	$-0.946590\pi$
$673$	−24.9296	+	21.6016i	−0.960966	+	0.832682i	0.0249902	+	0.999688i	$0.492045\pi$
$674$	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	−0.186913	−	0.982376i	$-0.559848\pi$
$677$	−16.7309	−	2.40555i	−0.643023	−	0.0924527i	−0.456109	+	0.889924i	$0.650757\pi$
$678$	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	−0.894201	−	0.447665i	$-0.852256\pi$
$683$	−42.4959	+	6.10998i	−1.62606	+	0.233792i	−0.731858	+	0.681457i	$0.761347\pi$
$684$	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	−0.996551	−	0.0829877i	$-0.973554\pi$
$701$	−7.44598	+	16.3044i	−0.281231	+	0.615810i	0.715320	+	0.698797i	$0.246281\pi$
$702$	−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	−0.942900	−	0.333075i	$-0.891914\pi$
$709$	−12.7551	+	14.7202i	−0.479027	+	0.552827i	0.463873	+	0.885902i	$0.346459\pi$
$710$	−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	−0.995852	−	0.0909878i	$-0.970998\pi$
$719$	−25.3177	−	29.2181i	−0.944189	−	1.08965i	0.0516628	−	0.998665i	$-0.483548\pi$
$720$	−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	0.507469	−	0.861670i	$-0.330581\pi$
$727$	−13.1348	−	20.4382i	−0.487144	−	0.758011i	−0.994613	+	0.103659i	$0.966945\pi$
$728$	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	0.962437	+	0.271506i	$0.0875216\pi$
$733$	8.11056	+	27.6220i	0.299570	+	1.02024i	−0.662866	+	0.748738i	$0.730660\pi$
$734$	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	−0.257966	−	0.966154i	$-0.583052\pi$
$739$	1.28749	−	0.378042i	0.0473612	−	0.0139065i	0.305327	+	0.952247i	$0.401234\pi$
$740$	−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	−0.495587	−	0.868558i	$-0.665047\pi$
$743$	−19.8002	+	2.84684i	−0.726398	+	0.104440i	−0.230811	+	0.972999i	$0.574138\pi$
$744$	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	−0.545835	−	0.837893i	$-0.683787\pi$
$751$	−39.9561	−	11.7322i	−1.45802	−	0.428113i	−0.912185	+	0.409780i	$0.865606\pi$
$752$	−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	−0.0393690	−	0.999225i	$-0.512535\pi$
$757$	18.9848	−	8.67006i	0.690013	−	0.315119i	0.729382	+	0.684106i	$0.239808\pi$
$758$		−	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	0.687159	−	0.726507i	$-0.258858\pi$
$761$	−8.60393	−	18.8400i	−0.311892	−	0.682948i	−0.999051	+	0.0435589i	$0.986130\pi$
$762$	−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	−0.0433766	+	0.999059i	$0.513812\pi$
$769$	−7.85405	+	54.6261i	−0.283224	+	1.96987i	−0.239848	+	0.970810i	$0.577098\pi$
$770$	−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	0.607124	−	0.794607i	$-0.292323\pi$
$773$	−10.2283	−	15.9155i	−0.367885	−	0.572440i	−0.975009	+	0.222167i	$0.928687\pi$
$774$	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	−0.999226	−	0.0393412i	$-0.987474\pi$
$787$	−15.3830	+	23.9365i	−0.548346	+	0.853244i	0.450879	+	0.892585i	$0.351110\pi$
$788$	−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	−0.788544	−	0.614979i	$-0.789165\pi$
$797$	5.85244	−	19.9316i	0.207304	−	0.706013i	0.995848	−	0.0910343i	$-0.0290173\pi$
$798$	−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	−0.998936	−	0.0461160i	$-0.985316\pi$
$809$	−23.0708	+	26.6251i	−0.811126	+	0.936089i	0.187810	+	0.982205i	$0.439861\pi$
$810$	−0.844922	−	5.32591i	−0.0296875	−	0.187133i
$811$	−8.50865	−	9.81950i	−0.298779	−	0.344809i	0.586433	−	0.809998i	$-0.300532\pi$
$811$	−8.50865	−	9.81950i	−0.298779	−	0.344809i	−0.885212	+	0.465189i	$0.845986\pi$
$812$	−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	−0.640634	−	0.767847i	$-0.721328\pi$
$821$	−6.94200	−	48.2827i	−0.242278	−	1.68508i	0.398356	−	0.917231i	$-0.369581\pi$
$822$	−33.3281	+	28.8790i	−1.16245	+	1.00727i
$823$	−1.59367	+	2.47980i	−0.0555520	+	0.0864405i	−0.867919	−	0.496707i	$-0.834543\pi$
$823$	−1.59367	+	2.47980i	−0.0555520	+	0.0864405i	0.812367	+	0.583147i	$0.198179\pi$
$824$	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	$0.191278\pi$
$827$			32.5190i			1.13080i	−0.824818	+	0.565399i	$0.808722\pi$
$828$	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	−0.308157	−	0.951336i	$-0.599712\pi$
$839$	17.7447	−	38.8554i	0.612615	−	1.34144i	0.920771	−	0.390103i	$-0.127561\pi$
$840$	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	−0.715128	−	0.698994i	$-0.753632\pi$
$853$	−19.1351	+	8.73870i	−0.655173	+	0.299207i	0.0599550	+	0.998201i	$0.480904\pi$
$854$	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	0.205223	−	0.978715i	$-0.434208\pi$
$857$	35.2226	−	30.5206i	1.20318	−	1.04256i	0.997960	−	0.0638485i	$-0.0203375\pi$
$858$	−3.59739	+	0.517227i	−0.122813	+	0.0176578i
$859$	33.4154	+	9.81165i	1.14012	+	0.334769i	0.796677	−	0.604405i	$-0.206589\pi$
$859$	33.4154	+	9.81165i	1.14012	+	0.334769i	0.343441	+	0.939174i	$0.388407\pi$
$860$	−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	−0.413316	−	0.910587i	$-0.635630\pi$
$863$	−40.3097	−	18.4088i	−1.37216	−	0.626643i	−0.958841	+	0.283944i	$0.908357\pi$
$864$	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	0.992482	−	0.122390i	$-0.0390560\pi$
$877$	2.70626	+	9.21667i	0.0913838	+	0.311225i	−0.901098	+	0.433615i	$0.857238\pi$
$878$	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	−0.509033	−	0.860747i	$-0.669997\pi$
$881$	−7.80983	−	54.3186i	−0.263120	−	1.83004i	0.245913	−	0.969292i	$-0.420912\pi$
$882$	−3.67491	+	12.5156i	−0.123741	+	0.421422i
$883$	5.50320	+	8.56314i	0.185197	+	0.288173i	0.921421	−	0.388566i	$-0.127029\pi$
$883$	5.50320	+	8.56314i	0.185197	+	0.288173i	−0.736224	+	0.676738i	$0.763393\pi$
$884$	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	−0.177213	−	0.984173i	$-0.556708\pi$
$887$	−18.5998	−	2.67425i	−0.624521	−	0.0897925i	−0.447308	+	0.894380i	$0.647617\pi$
$888$	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	−0.184366	−	0.982858i	$-0.559023\pi$
$907$	−19.2193	−	2.76332i	−0.638167	−	0.0917545i	−0.453801	+	0.891103i	$0.649932\pi$
$908$	−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	−0.989451	−	0.144865i	$-0.953725\pi$
$911$	−38.2932	+	24.6096i	−1.26871	+	0.815351i	−0.279259	+	0.960216i	$0.590089\pi$
$912$	−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	0.330656	−	0.943751i	$-0.392730\pi$
$929$	40.4305	−	25.9831i	1.32648	−	0.852478i	0.995826	+	0.0912735i	$0.0290937\pi$
$930$	−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	−0.449678	−	0.893191i	$-0.648461\pi$
$937$	11.3389	−	9.82519i	0.370425	−	0.320975i	0.820103	+	0.572216i	$0.193916\pi$
$938$	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	0.865135	−	0.501540i	$-0.167233\pi$
$941$	−2.46775	−	5.40363i	−0.0804465	−	0.176153i	−0.945581	+	0.325386i	$0.894506\pi$
$942$		−	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	0.941515	−	0.336972i	$-0.109403\pi$
$947$	22.8327	+	19.7847i	0.741965	+	0.642916i	−0.199550	+	0.979888i	$0.563948\pi$
$948$	−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	−0.162258	−	0.986748i	$-0.551878\pi$
$953$	−18.3972	−	2.64512i	−0.595943	−	0.0856837i	−0.433685	+	0.901065i	$0.642787\pi$
$954$	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	$-0.908342\pi$
$967$		−	17.6623i		−	0.567980i	0.958827	−	0.283990i	$-0.0916582\pi$
$968$	−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	−0.0238811	−	0.999715i	$-0.507602\pi$
$971$	−29.3901	−	18.8879i	−0.943174	−	0.606141i	−0.919293	+	0.393574i	$0.871239\pi$
$972$	−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	0.990338	−	0.138674i	$-0.0442841\pi$
$977$	47.9504	+	21.8982i	1.53407	+	0.700586i	0.543731	+	0.839260i	$0.317011\pi$
$978$	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	−0.483951	−	0.875095i	$-0.660799\pi$
$983$	9.82485	−	8.51328i	0.313364	−	0.271532i	0.797315	+	0.603564i	$0.206253\pi$
$984$	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	0.969817	+	0.243835i	$0.0784054\pi$
$991$	16.3382	+	35.7757i	0.519000	+	1.13645i	−0.450817	+	0.892616i	$0.648867\pi$
$992$	−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	0.655548	+	0.755154i	$0.272438\pi$
$997$	−9.60524	+	32.7125i	−0.304201	+	1.03601i	−0.959749	+	0.280860i	$0.909380\pi$
$998$	−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.4.3	✓	240
5.4	even	2	inner	345.2.t.a.4.22	yes	240
23.6	even	11	inner	345.2.t.a.259.22	yes	240
115.29	even	22	inner	345.2.t.a.259.3	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.t.a.4.3	✓	240	1.1	even	1	trivial
345.2.t.a.4.22	yes	240	5.4	even	2	inner
345.2.t.a.259.3	yes	240	115.29	even	22	inner
345.2.t.a.259.22	yes	240	23.6	even	11	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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