LMFDB - Embedded newform 456.2.bk.a.253.36

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [456,2,Mod(61,456)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("456.61"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(456, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.bk (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			253.36
Character	$\chi$	$=$	456.253
Dual form			456.2.bk.a.301.36

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.34083 - 0.449648i) q^{2} +(-0.342020 + 0.939693i) q^{3} +(1.59563 - 1.20580i) q^{4} +(-3.77792 + 0.666150i) q^{5} +(-0.0360593 + 1.41375i) q^{6} +(-1.80901 + 3.13331i) q^{7} +(1.59728 - 2.33424i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(-4.76601 + 2.59193i) q^{10} +(-4.93409 + 2.84870i) q^{11} +(0.587342 + 1.91181i) q^{12} +(1.84697 + 5.07450i) q^{13} +(-1.01669 + 5.01464i) q^{14} +(0.666150 - 3.77792i) q^{15} +(1.09210 - 3.84803i) q^{16} +(0.763925 - 0.641009i) q^{17} +(-1.31616 - 0.517417i) q^{18} +(2.66790 - 3.44707i) q^{19} +(-5.22494 + 5.61835i) q^{20} +(-2.32562 - 2.77157i) q^{21} +(-5.33485 + 6.03822i) q^{22} +(-0.0616151 + 0.349436i) q^{23} +(1.64717 + 2.29931i) q^{24} +(9.13050 - 3.32323i) q^{25} +(4.75820 + 5.97354i) q^{26} +(0.866025 - 0.500000i) q^{27} +(0.891612 + 7.18092i) q^{28} +(1.84760 - 2.20189i) q^{29} +(-0.805543 - 5.36508i) q^{30} +(-4.47323 + 7.74786i) q^{31} +(-0.265945 - 5.65060i) q^{32} +(-0.989343 - 5.61084i) q^{33} +(0.736063 - 1.20298i) q^{34} +(4.74707 - 13.0425i) q^{35} +(-1.99740 - 0.101958i) q^{36} -1.40865i q^{37} +(2.02722 - 5.82154i) q^{38} -5.40017 q^{39} +(-4.47947 + 9.88262i) q^{40} +(-3.99665 - 1.45466i) q^{41} +(-4.36449 - 2.67049i) q^{42} +(-3.02833 + 0.533975i) q^{43} +(-4.43805 + 10.4950i) q^{44} +(3.32225 + 1.91810i) q^{45} +(0.0745081 + 0.496239i) q^{46} +(5.76564 + 4.83795i) q^{47} +(3.24245 + 2.34234i) q^{48} +(-3.04507 - 5.27422i) q^{49} +(10.7481 - 8.56138i) q^{50} +(0.341074 + 0.937093i) q^{51} +(9.06591 + 5.86997i) q^{52} +(-4.57524 - 0.806739i) q^{53} +(0.936366 - 1.05982i) q^{54} +(16.7430 - 14.0490i) q^{55} +(4.42438 + 9.22746i) q^{56} +(2.32671 + 3.68597i) q^{57} +(1.48724 - 3.78312i) q^{58} +(3.00014 + 3.57543i) q^{59} +(-3.49249 - 6.83143i) q^{60} +(-0.689588 - 0.121593i) q^{61} +(-2.51402 + 12.3999i) q^{62} +(3.39984 - 1.23744i) q^{63} +(-2.89737 - 7.45689i) q^{64} +(-10.3581 - 17.9407i) q^{65} +(-3.84944 - 7.07832i) q^{66} +(-3.13505 + 3.73621i) q^{67} +(0.446016 - 1.94396i) q^{68} +(-0.307289 - 0.177414i) q^{69} +(0.500485 - 19.6222i) q^{70} +(1.41816 + 8.04280i) q^{71} +(-2.72401 + 0.761418i) q^{72} +(10.1399 + 3.69063i) q^{73} +(-0.633397 - 1.88876i) q^{74} +9.71647i q^{75} +(0.100510 - 8.71722i) q^{76} -20.6134i q^{77} +(-7.24070 + 2.42817i) q^{78} +(-2.12163 - 0.772211i) q^{79} +(-1.56249 + 15.2651i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-6.01291 - 0.153366i) q^{82} +(11.7365 + 6.77608i) q^{83} +(-7.05281 - 1.61818i) q^{84} +(-2.45904 + 2.93057i) q^{85} +(-3.82036 + 2.07765i) q^{86} +(1.43718 + 2.48927i) q^{87} +(-1.23160 + 16.0675i) q^{88} +(-9.67914 + 3.52292i) q^{89} +(5.31703 + 1.07800i) q^{90} +(-19.2412 - 3.39273i) q^{91} +(0.323035 + 0.631868i) q^{92} +(-5.75067 - 6.85338i) q^{93} +(9.90610 + 3.89435i) q^{94} +(-7.78285 + 14.8000i) q^{95} +(5.40079 + 1.68271i) q^{96} +(3.10012 - 2.60131i) q^{97} +(-6.45445 - 5.70260i) q^{98} +(5.61084 + 0.989343i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48}+ \cdots - 12 q^{98}+O(q^{100}) $ 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$	$1$	$1$

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 $

$2$	1.34083	−	0.449648i	0.948108	−	0.317949i
$2$	1.34083	−	0.449648i	0.948108	−	0.317949i
$3$	−0.342020	+	0.939693i	−0.197465	+	0.542532i
$3$	−0.342020	+	0.939693i	−0.197465	+	0.542532i
$4$	1.59563	−	1.20580i	0.797817	−	0.602900i
$5$	−3.77792	+	0.666150i	−1.68954	+	0.297911i	−0.934022	−	0.357217i	$-0.883726\pi$
$5$	−3.77792	+	0.666150i	−1.68954	+	0.297911i	−0.755518	+	0.655128i	$0.772615\pi$
$6$	−0.0360593	+	1.41375i	−0.0147211	+	0.577163i
$7$	−1.80901	+	3.13331i	−0.683743	+	1.18428i	0.290087	+	0.957000i	$0.406316\pi$
$7$	−1.80901	+	3.13331i	−0.683743	+	1.18428i	−0.973830	+	0.227278i	$0.927017\pi$
$8$	1.59728	−	2.33424i	0.564725	−	0.825279i
$9$	−0.766044	−	0.642788i	−0.255348	−	0.214263i
$10$	−4.76601	+	2.59193i	−1.50714	+	0.819639i
$11$	−4.93409	+	2.84870i	−1.48769	+	0.858915i	−0.999901	−	0.0140490i	$-0.995528\pi$
$11$	−4.93409	+	2.84870i	−1.48769	+	0.858915i	−0.487784	+	0.872964i	$0.662195\pi$
$12$	0.587342	+	1.91181i	0.169551	+	0.551893i
$13$	1.84697	+	5.07450i	0.512257	+	1.40741i	0.878880	+	0.477044i	$0.158292\pi$
$13$	1.84697	+	5.07450i	0.512257	+	1.40741i	−0.366623	+	0.930370i	$0.619486\pi$
$14$	−1.01669	+	5.01464i	−0.271723	+	1.34022i
$15$	0.666150	−	3.77792i	0.171999	−	0.975456i
$16$	1.09210	−	3.84803i	0.273024	−	0.962007i
$17$	0.763925	−	0.641009i	0.185279	−	0.155468i	−0.545431	−	0.838156i	$-0.683634\pi$
$17$	0.763925	−	0.641009i	0.185279	−	0.155468i	0.730710	+	0.682688i	$0.239189\pi$
$18$	−1.31616	−	0.517417i	−0.310222	−	0.121956i
$19$	2.66790	−	3.44707i	0.612058	−	0.790813i
$19$	2.66790	−	3.44707i	0.612058	−	0.790813i
$20$	−5.22494	+	5.61835i	−1.16833	+	1.25630i
$21$	−2.32562	−	2.77157i	−0.507493	−	0.604807i
$22$	−5.33485	+	6.03822i	−1.13739	+	1.28735i
$23$	−0.0616151	+	0.349436i	−0.0128476	+	0.0728625i	−0.990557	−	0.137098i	$-0.956222\pi$
$23$	−0.0616151	+	0.349436i	−0.0128476	+	0.0728625i	0.977710	+	0.209961i	$0.0673336\pi$
$24$	1.64717	+	2.29931i	0.336226	+	0.469345i
$25$	9.13050	−	3.32323i	1.82610	−	0.664646i
$26$	4.75820	+	5.97354i	0.933160	+	1.17151i
$27$	0.866025	−	0.500000i	0.166667	−	0.0962250i
$28$	0.891612	+	7.18092i	0.168499	+	1.35707i
$29$	1.84760	−	2.20189i	0.343091	−	0.408880i	−0.566715	−	0.823914i	$-0.691786\pi$
$29$	1.84760	−	2.20189i	0.343091	−	0.408880i	0.909806	+	0.415034i	$0.136230\pi$
$30$	−0.805543	−	5.36508i	−0.147071	−	0.979524i
$31$	−4.47323	+	7.74786i	−0.803416	+	1.39156i	0.113940	+	0.993488i	$0.463653\pi$
$31$	−4.47323	+	7.74786i	−0.803416	+	1.39156i	−0.917355	+	0.398069i	$0.869680\pi$
$32$	−0.265945	−	5.65060i	−0.0470129	−	0.998894i
$33$	−0.989343	−	5.61084i	−0.172223	−	0.976723i
$34$	0.736063	−	1.20298i	0.126234	−	0.206309i
$35$	4.74707	−	13.0425i	0.802401	−	2.20458i
$36$	−1.99740	−	0.101958i	−0.332900	−	0.0169930i
$37$		−	1.40865i		−	0.231581i	−0.993274	−	0.115791i	$-0.963060\pi$
$37$		−	1.40865i		−	0.231581i	0.993274	−	0.115791i	$-0.0369401\pi$
$38$	2.02722	−	5.82154i	0.328859	−	0.944379i
$39$	−5.40017			−0.864719
$40$	−4.47947	+	9.88262i	−0.708266	+	1.56258i
$41$	−3.99665	−	1.45466i	−0.624173	−	0.227180i	0.0105204	−	0.999945i	$-0.496651\pi$
$41$	−3.99665	−	1.45466i	−0.624173	−	0.227180i	−0.634693	+	0.772764i	$0.718873\pi$
$42$	−4.36449	−	2.67049i	−0.673456	−	0.412065i
$43$	−3.02833	+	0.533975i	−0.461815	+	0.0814305i	−0.399715	−	0.916639i	$-0.630891\pi$
$43$	−3.02833	+	0.533975i	−0.461815	+	0.0814305i	−0.0621002	+	0.998070i	$0.519780\pi$
$44$	−4.43805	+	10.4950i	−0.669061	+	1.58218i
$45$	3.32225	+	1.91810i	0.495252	+	0.285934i
$46$	0.0745081	+	0.496239i	0.0109856	+	0.0731664i
$47$	5.76564	+	4.83795i	0.841006	+	0.705687i	0.957790	−	0.287470i	$-0.0928141\pi$
$47$	5.76564	+	4.83795i	0.841006	+	0.705687i	−0.116784	+	0.993157i	$0.537259\pi$
$48$	3.24245	+	2.34234i	0.468007	+	0.338087i
$49$	−3.04507	−	5.27422i	−0.435010	−	0.753459i
$50$	10.7481	−	8.56138i	1.52002	−	1.21076i
$51$	0.341074	+	0.937093i	0.0477599	+	0.131219i
$52$	9.06591	+	5.86997i	1.25722	+	0.814019i
$53$	−4.57524	−	0.806739i	−0.628458	−	0.110814i	−0.149658	−	0.988738i	$-0.547817\pi$
$53$	−4.57524	−	0.806739i	−0.628458	−	0.110814i	−0.478800	+	0.877924i	$0.658928\pi$
$54$	0.936366	−	1.05982i	0.127423	−	0.144223i
$55$	16.7430	−	14.0490i	2.25762	−	1.89437i
$56$	4.42438	+	9.22746i	0.591233	+	1.23307i
$57$	2.32671	+	3.68597i	0.308181	+	0.488219i
$58$	1.48724	−	3.78312i	0.195284	−	0.496748i
$59$	3.00014	+	3.57543i	0.390585	+	0.465481i	0.925125	−	0.379662i	$-0.123960\pi$
$59$	3.00014	+	3.57543i	0.390585	+	0.465481i	−0.534540	+	0.845143i	$0.679515\pi$
$60$	−3.49249	−	6.83143i	−0.450878	−	0.881934i
$61$	−0.689588	−	0.121593i	−0.0882926	−	0.0155684i	0.129327	−	0.991602i	$-0.458718\pi$
$61$	−0.689588	−	0.121593i	−0.0882926	−	0.0155684i	−0.217620	+	0.976034i	$0.569829\pi$
$62$	−2.51402	+	12.3999i	−0.319281	+	1.57479i
$63$	3.39984	−	1.23744i	0.428339	−	0.155903i
$64$	−2.89737	−	7.45689i	−0.362171	−	0.932112i
$65$	−10.3581	−	17.9407i	−1.28476	−	2.22527i
$66$	−3.84944	−	7.07832i	−0.473833	−	0.871280i
$67$	−3.13505	+	3.73621i	−0.383007	+	0.456450i	−0.922761	−	0.385373i	$-0.874073\pi$
$67$	−3.13505	+	3.73621i	−0.383007	+	0.456450i	0.539754	+	0.841823i	$0.318517\pi$
$68$	0.446016	−	1.94396i	0.0540874	−	0.235739i
$69$	−0.307289	−	0.177414i	−0.0369933	−	0.0213581i
$70$	0.500485	−	19.6222i	0.0598194	−	2.34530i
$71$	1.41816	+	8.04280i	0.168305	+	0.954505i	0.945591	+	0.325358i	$0.105485\pi$
$71$	1.41816	+	8.04280i	0.168305	+	0.954505i	−0.777286	+	0.629147i	$0.783404\pi$
$72$	−2.72401	+	0.761418i	−0.321028	+	0.0897340i
$73$	10.1399	+	3.69063i	1.18679	+	0.431955i	0.858594	−	0.512656i	$-0.171338\pi$
$73$	10.1399	+	3.69063i	1.18679	+	0.431955i	0.328193	+	0.944611i	$0.393560\pi$
$74$	−0.633397	−	1.88876i	−0.0736309	−	0.219564i
$75$			9.71647i			1.12196i
$76$	0.100510	−	8.71722i	0.0115293	−	0.999934i
$77$		−	20.6134i		−	2.34911i
$78$	−7.24070	+	2.42817i	−0.819847	+	0.274937i
$79$	−2.12163	−	0.772211i	−0.238702	−	0.0868805i	0.219899	−	0.975523i	$-0.429427\pi$
$79$	−2.12163	−	0.772211i	−0.238702	−	0.0868805i	−0.458601	+	0.888642i	$0.651649\pi$
$80$	−1.56249	+	15.2651i	−0.174692	+	1.70669i
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$	−6.01291	−	0.153366i	−0.664015	−	0.0169364i
$83$	11.7365	+	6.77608i	1.28825	+	0.743772i	0.978342	−	0.206995i	$-0.0663683\pi$
$83$	11.7365	+	6.77608i	1.28825	+	0.743772i	0.309908	+	0.950766i	$0.399702\pi$
$84$	−7.05281	−	1.61818i	−0.769524	−	0.176558i
$85$	−2.45904	+	2.93057i	−0.266721	+	0.317865i
$86$	−3.82036	+	2.07765i	−0.411960	+	0.224039i
$87$	1.43718	+	2.48927i	0.154082	+	0.266878i
$88$	−1.23160	+	16.0675i	−0.131289	+	1.71281i
$89$	−9.67914	+	3.52292i	−1.02599	+	0.373429i	−0.799552	−	0.600597i	$-0.794929\pi$
$89$	−9.67914	+	3.52292i	−1.02599	+	0.373429i	−0.226435	+	0.974026i	$0.572707\pi$
$90$	5.31703	+	1.07800i	0.560465	+	0.113631i
$91$	−19.2412	−	3.39273i	−2.01702	−	0.355655i
$92$	0.323035	+	0.631868i	0.0336787	+	0.0658768i
$93$	−5.75067	−	6.85338i	−0.596317	−	0.710663i
$94$	9.90610	+	3.89435i	1.02174	+	0.401671i
$95$	−7.78285	+	14.8000i	−0.798504	+	1.51845i
$96$	5.40079	+	1.68271i	0.551215	+	0.171741i
$97$	3.10012	−	2.60131i	0.314769	−	0.264123i	−0.471691	−	0.881764i	$-0.656356\pi$
$97$	3.10012	−	2.60131i	0.314769	−	0.264123i	0.786460	+	0.617641i	$0.211912\pi$
$98$	−6.45445	−	5.70260i	−0.651998	−	0.576050i
$99$	5.61084	+	0.989343i	0.563911	+	0.0994327i
$100$	10.5618	−	16.3122i	1.05618	−	1.63122i
$101$	−2.09424	−	5.75387i	−0.208384	−	0.572531i	0.790835	−	0.612029i	$-0.209646\pi$
$101$	−2.09424	−	5.75387i	−0.208384	−	0.572531i	−0.999220	+	0.0394978i	$0.987424\pi$
$102$	0.878683	+	1.10312i	0.0870025	+	0.109225i
$103$	5.88315	+	10.1899i	0.579684	+	1.00404i	0.995515	+	0.0946000i	$0.0301572\pi$
$103$	5.88315	+	10.1899i	0.579684	+	1.00404i	−0.415832	+	0.909442i	$0.636509\pi$
$104$	14.7952	+	3.79415i	1.45079	+	0.372047i
$105$	10.6323	+	8.92157i	1.03761	+	0.870657i
$106$	−6.49736	+	0.975550i	−0.631079	+	0.0947538i
$107$	−4.96831	−	2.86845i	−0.480304	−	0.277304i	0.240239	−	0.970714i	$-0.422774\pi$
$107$	−4.96831	−	2.86845i	−0.480304	−	0.277304i	−0.720543	+	0.693410i	$0.756108\pi$
$108$	0.778960	−	1.84207i	0.0749555	−	0.177253i
$109$	12.0968	−	2.13300i	1.15867	−	0.204304i	0.438910	−	0.898531i	$-0.355365\pi$
$109$	12.0968	−	2.13300i	1.15867	−	0.204304i	0.719756	+	0.694227i	$0.244254\pi$
$110$	16.1323	−	26.3657i	1.53816	−	2.51388i
$111$	1.32370	+	0.481788i	0.125640	+	0.0457293i
$112$	10.0814	+	10.3830i	0.952606	+	0.981102i
$113$	8.30114			0.780906			0.390453	−	0.920623i	$-0.372318\pi$
$113$	8.30114			0.780906			0.390453	+	0.920623i	$0.372318\pi$
$114$	4.77711	+	3.89605i	0.447417	+	0.364899i
$115$		−	1.36119i		−	0.126932i
$116$	0.293064	−	5.74124i	0.0272103	−	0.533061i
$117$	1.84697	−	5.07450i	0.170752	−	0.469138i
$118$	5.63035	+	3.44503i	0.518316	+	0.317140i
$119$	0.626526	+	3.55321i	0.0574336	+	0.325722i
$120$	−7.75456	−	7.58938i	−0.707891	−	0.692812i
$121$	10.7302	−	18.5852i	0.975472	−	1.68957i
$122$	−0.979292	+	0.147036i	−0.0886609	+	0.0133120i
$123$	2.73387	−	3.25810i	0.246505	−	0.293773i
$124$	2.20473	+	17.7566i	0.197990	+	1.59459i
$125$	−15.6693	+	9.04668i	−1.40151	+	0.809160i
$126$	4.00218	−	3.18792i	0.356543	−	0.284002i
$127$	−7.31820	+	2.66361i	−0.649385	+	0.236357i	−0.645647	−	0.763636i	$-0.723412\pi$
$127$	−7.31820	+	2.66361i	−0.649385	+	0.236357i	−0.00373836	+	0.999993i	$0.501190\pi$
$128$	−7.23784	−	8.69561i	−0.639741	−	0.768591i
$129$	0.533975	−	3.02833i	0.0470139	−	0.266629i
$130$	−21.9554	−	19.3979i	−1.92562	−	1.70131i
$131$	−0.116927	−	0.139349i	−0.0102160	−	0.0121750i	0.760912	−	0.648855i	$-0.224752\pi$
$131$	−0.116927	−	0.139349i	−0.0102160	−	0.0121750i	−0.771128	+	0.636680i	$0.780307\pi$
$132$	−8.34418	−	7.75990i	−0.726268	−	0.675413i
$133$	5.97447	+	14.5951i	0.518052	+	1.26556i
$134$	−2.52358	+	6.41928i	−0.218004	+	0.554541i
$135$	−2.93870	+	2.46587i	−0.252923	+	0.212228i
$136$	−0.276065	−	2.80706i	−0.0236724	−	0.240703i
$137$	0.335499	−	1.90271i	0.0286636	−	0.162560i	−0.967116	−	0.254336i	$-0.918143\pi$
$137$	0.335499	−	1.90271i	0.0286636	−	0.162560i	0.995780	+	0.0917760i	$0.0292544\pi$
$138$	−0.491795	−	0.0997090i	−0.0418644	−	0.00848779i
$139$	5.82304	+	15.9987i	0.493904	+	1.35699i	0.897080	+	0.441868i	$0.145684\pi$
$139$	5.82304	+	15.9987i	0.493904	+	1.35699i	−0.403176	+	0.915122i	$0.632094\pi$
$140$	−8.15201	−	26.5350i	−0.688971	−	2.24262i
$141$	−6.51815	+	3.76326i	−0.548927	+	0.316923i
$142$	5.51794	+	10.1463i	0.463055	+	0.851461i
$143$	−23.5688	−	19.7766i	−1.97093	−	1.65380i
$144$	−3.31006	+	2.24578i	−0.275838	+	0.187148i
$145$	−5.51332	+	9.54934i	−0.457856	+	0.793030i
$146$	15.2554	+	0.389104i	1.26254	+	0.0322025i
$147$	5.99762	−	1.05754i	0.494675	−	0.0872246i
$148$	−1.69855	−	2.24769i	−0.139620	−	0.184759i
$149$	−1.50613	+	4.13806i	−0.123387	+	0.339003i	−0.985972	−	0.166909i	$-0.946622\pi$
$149$	−1.50613	+	4.13806i	−0.123387	+	0.339003i	0.862585	+	0.505911i	$0.168844\pi$
$150$	4.36899	+	13.0281i	0.356726	+	1.06374i
$151$	−3.34409			−0.272138			−0.136069	−	0.990699i	$-0.543447\pi$
$151$	−3.34409			−0.272138			−0.136069	+	0.990699i	$0.543447\pi$
$152$	−3.78491	−	11.7335i	−0.306997	−	0.951711i
$153$	−0.997233			−0.0806215
$154$	−9.26875	−	27.6390i	−0.746897	−	2.22721i
$155$	11.7383	−	32.2507i	0.942842	−	2.59044i
$156$	−8.61670	+	6.51152i	−0.689888	+	0.521339i
$157$	−20.9677	+	3.69717i	−1.67340	+	0.295066i	−0.928286	−	0.371867i	$-0.878718\pi$
$157$	−20.9677	+	3.69717i	−1.67340	+	0.295066i	−0.745118	+	0.666933i	$0.767607\pi$
$158$	−3.19197	−	0.0814145i	−0.253939	−	0.00647699i
$159$	2.32291	−	4.02340i	0.184219	−	0.319077i
$160$	4.76887	+	21.1704i	0.377012	+	1.67367i
$161$	−0.983429	−	0.825195i	−0.0775050	−	0.0650345i
$162$	0.675649	+	1.24238i	0.0530840	+	0.0976103i
$163$	18.5508	−	10.7103i	1.45301	−	0.838898i	0.454363	−	0.890817i	$-0.349867\pi$
$163$	18.5508	−	10.7103i	1.45301	−	0.838898i	0.998651	+	0.0519185i	$0.0165336\pi$
$164$	−8.13123	+	2.49805i	−0.634942	+	0.195065i
$165$	7.47533	+	20.5383i	0.581954	+	1.59890i
$166$	18.7835	+	3.80826i	1.45788	+	0.295578i
$167$	1.62463	−	9.21373i	0.125718	−	0.712980i	−0.855161	−	0.518362i	$-0.826542\pi$
$167$	1.62463	−	9.21373i	0.125718	−	0.712980i	0.980879	−	0.194618i	$-0.0623468\pi$
$168$	−10.1842	+	1.00158i	−0.785728	+	0.0772737i
$169$	−12.3807	+	10.3886i	−0.952361	+	0.799126i
$170$	−1.97943	+	5.03510i	−0.151815	+	0.386174i
$171$	−4.25947	+	0.925720i	−0.325729	+	0.0707916i
$172$	−4.18823	+	4.50358i	−0.319350	+	0.343395i
$173$	0.801246	+	0.954888i	0.0609176	+	0.0725988i	0.795643	−	0.605766i	$-0.207133\pi$
$173$	0.801246	+	0.954888i	0.0609176	+	0.0725988i	−0.734725	+	0.678365i	$0.762689\pi$
$174$	3.04630	+	2.69145i	0.230940	+	0.204039i
$175$	−6.10451	+	34.6204i	−0.461458	+	2.61706i
$176$	5.57338	+	22.0976i	0.420109	+	1.66567i
$177$	−4.38591	+	1.59634i	−0.329665	+	0.119988i
$178$	−11.3940	+	9.07583i	−0.854015	+	0.680262i
$179$	−7.08442	+	4.09019i	−0.529515	+	0.305715i	−0.740819	−	0.671705i	$-0.765562\pi$
$179$	−7.08442	+	4.09019i	−0.529515	+	0.305715i	0.211304	+	0.977420i	$0.432229\pi$
$180$	7.61394	−	0.945378i	0.567510	−	0.0704644i
$181$	11.6325	−	13.8631i	0.864638	−	1.03044i	−0.134580	−	0.990903i	$-0.542968\pi$
$181$	11.6325	−	13.8631i	0.864638	−	1.03044i	0.999218	−	0.0395332i	$-0.0125871\pi$
$182$	−27.3246	+	4.10267i	−2.02543	+	0.304110i
$183$	0.350113	−	0.606413i	0.0258811	−	0.0448274i
$184$	0.717252	+	0.701974i	0.0528765	+	0.0517502i
$185$	0.938374	+	5.32178i	0.0689906	+	0.391265i
$186$	−10.7923	−	6.60343i	−0.791327	−	0.484187i
$187$	−1.94323	+	5.33899i	−0.142103	+	0.390426i
$188$	15.0335	+	0.767388i	1.09643	+	0.0559675i
$189$			3.61803i			0.263173i
$190$	−3.78067	+	23.3438i	−0.274279	+	1.69354i
$191$	−12.9330			−0.935801			−0.467900	−	0.883781i	$-0.654989\pi$
$191$	−12.9330			−0.935801			−0.467900	+	0.883781i	$0.654989\pi$
$192$	7.99815	−	0.172224i	0.577216	−	0.0124292i
$193$	−0.184835	−	0.0672744i	−0.0133047	−	0.00484252i	0.335359	−	0.942090i	$-0.391142\pi$
$193$	−0.184835	−	0.0672744i	−0.0133047	−	0.00484252i	−0.348664	+	0.937248i	$0.613365\pi$
$194$	2.98705	−	4.88186i	0.214458	−	0.350497i
$195$	20.4014	−	3.59732i	1.46098	−	0.257610i
$196$	−11.2185	−	4.74398i	−0.801319	−	0.338855i
$197$	−6.87786	−	3.97094i	−0.490027	−	0.282917i	0.234558	−	0.972102i	$-0.424636\pi$
$197$	−6.87786	−	3.97094i	−0.490027	−	0.282917i	−0.724586	+	0.689185i	$0.757969\pi$
$198$	7.96803	−	1.19636i	0.566263	−	0.0850219i
$199$	−12.4834	−	10.4748i	−0.884926	−	0.742541i	0.0822600	−	0.996611i	$-0.473786\pi$
$199$	−12.4834	−	10.4748i	−0.884926	−	0.742541i	−0.967186	+	0.254070i	$0.918231\pi$
$200$	6.82678	−	26.6209i	0.482726	−	1.88238i
$201$	−2.43864	−	4.22384i	−0.172008	−	0.297927i
$202$	−5.39522	−	6.77327i	−0.379606	−	0.476566i
$203$	3.55684	+	9.77235i	0.249642	+	0.685884i
$204$	1.67418	+	1.08399i	0.117216	+	0.0758945i
$205$	16.0681	+	2.83324i	1.12224	+	0.197882i
$206$	12.4702	+	11.0176i	0.868837	+	0.767630i
$207$	0.271813	−	0.228078i	0.0188923	−	0.0158525i
$208$	21.5439	−	1.56534i	1.49380	−	0.108537i
$209$	−3.34398	+	24.6082i	−0.231308	+	1.70219i
$210$	18.2677	+	7.18149i	1.26059	+	0.495570i
$211$	4.22762	+	5.03828i	0.291042	+	0.346850i	0.891676	−	0.452674i	$-0.149530\pi$
$211$	4.22762	+	5.03828i	0.291042	+	0.346850i	−0.600635	+	0.799524i	$0.705085\pi$
$212$	−8.27318	+	4.22957i	−0.568204	+	0.290488i
$213$	−8.04280	−	1.41816i	−0.551084	−	0.0971709i
$214$	−7.95143	−	1.61211i	−0.543549	−	0.110202i
$215$	11.0851	−	4.03464i	0.755996	−	0.275160i
$216$	0.216168	−	2.82015i	0.0147084	−	0.191887i
$217$	−16.1843	−	28.0320i	−1.09866	−	1.90294i
$218$	15.2607	−	8.29929i	1.03358	−	0.562099i
$219$	−6.93611	+	8.26613i	−0.468699	+	0.558574i
$220$	9.77536	−	42.6058i	0.659054	−	2.87248i
$221$	4.66375	+	2.69262i	0.313718	+	0.181125i
$222$	1.99149	+	0.0507950i	0.133660	+	0.00340914i
$223$	−1.24412	−	7.05575i	−0.0833123	−	0.472488i	−0.997708	−	0.0676662i	$-0.978445\pi$
$223$	−1.24412	−	7.05575i	−0.0833123	−	0.472488i	0.914396	−	0.404822i	$-0.132666\pi$
$224$	18.1862	+	9.38873i	1.21511	+	0.627311i
$225$	−9.13050	−	3.32323i	−0.608700	−	0.221549i
$226$	11.1304	−	3.73259i	0.740383	−	0.248288i
$227$			13.5335i			0.898249i	0.893469	+	0.449124i	$0.148264\pi$
$227$			13.5335i			0.898249i	−0.893469	+	0.449124i	$0.851736\pi$
$228$	8.15713	+	3.07591i	0.540219	+	0.203707i
$229$			25.9972i			1.71794i	0.512022	+	0.858972i	$0.328897\pi$
$229$			25.9972i			1.71794i	−0.512022	+	0.858972i	$0.671103\pi$
$230$	−0.612056	−	1.82512i	−0.0403578	−	0.120345i
$231$	19.3702	+	7.05019i	1.27447	+	0.463868i
$232$	−2.18859	−	7.82979i	−0.143688	−	0.514051i
$233$	0.277217	+	1.57218i	0.0181611	+	0.102997i	0.992541	−	0.121912i	$-0.0389026\pi$
$233$	0.277217	+	1.57218i	0.0181611	+	0.102997i	−0.974380	+	0.224909i	$0.927792\pi$
$234$	0.194726	−	7.63451i	0.0127297	−	0.499084i
$235$	−25.0050	−	14.4366i	−1.63114	−	0.941742i
$236$	9.09838	+	2.08751i	0.592254	+	0.135885i
$237$	1.45128	−	1.72957i	0.0942709	−	0.112348i
$238$	2.43775	+	4.48252i	0.158016	+	0.290559i
$239$	2.56176	+	4.43709i	0.165706	+	0.287011i	0.936906	−	0.349582i	$-0.113676\pi$
$239$	2.56176	+	4.43709i	0.165706	+	0.287011i	−0.771200	+	0.636593i	$0.780343\pi$
$240$	−13.8101	−	6.68922i	−0.891436	−	0.431787i
$241$	−15.0575	+	5.48048i	−0.969939	+	0.353029i	−0.777921	−	0.628363i	$-0.783725\pi$
$241$	−15.0575	+	5.48048i	−0.969939	+	0.353029i	−0.192018	+	0.981391i	$0.561503\pi$
$242$	6.03052	−	29.7444i	0.387657	−	1.91204i
$243$	−0.984808	−	0.173648i	−0.0631754	−	0.0111395i
$244$	−1.24695	+	0.637487i	−0.0798275	+	0.0408109i
$245$	15.0175	+	17.8971i	0.959431	+	1.14340i
$246$	2.20065	−	5.59783i	0.140308	−	0.356905i
$247$	22.4197	+	7.17162i	1.42653	+	0.456319i
$248$	10.9404	+	22.8171i	0.694713	+	1.44889i
$249$	−10.3816	+	8.71117i	−0.657905	+	0.552048i
$250$	−16.9420	+	19.1757i	−1.07151	+	1.21278i
$251$	19.4780	+	3.43450i	1.22944	+	0.216784i	0.750386	−	0.661000i	$-0.229868\pi$
$251$	19.4780	+	3.43450i	1.22944	+	0.216784i	0.479056	+	0.877784i	$0.340979\pi$
$252$	3.93279	−	6.07402i	0.247743	−	0.382627i
$253$	−0.691425	−	1.89968i	−0.0434695	−	0.119432i
$254$	−8.61476	+	6.86205i	−0.540538	+	0.430563i
$255$	−1.91280	−	3.31306i	−0.119784	−	0.207472i
$256$	−13.6147	−	8.40483i	−0.850916	−	0.525302i
$257$	23.2734	+	19.5287i	1.45176	+	1.21817i	0.931287	+	0.364286i	$0.118687\pi$
$257$	23.2734	+	19.5287i	1.45176	+	1.21817i	0.520468	+	0.853881i	$0.325757\pi$
$258$	−0.645711	−	4.30056i	−0.0402002	−	0.267741i
$259$	4.41374	+	2.54827i	0.274256	+	0.158342i
$260$	−38.1606	−	16.1371i	−2.36662	−	1.00078i
$261$	−2.83069	+	0.499127i	−0.175215	+	0.0308952i
$262$	−0.219437	−	0.134266i	−0.0135569	−	0.00829500i
$263$	−20.4721	−	7.45124i	−1.26236	−	0.459463i	−0.377803	−	0.925886i	$-0.623320\pi$
$263$	−20.4721	−	7.45124i	−1.26236	−	0.459463i	−0.884562	+	0.466423i	$0.845542\pi$
$264$	−14.6773	−	6.65275i	−0.903327	−	0.409448i
$265$	17.8223			1.09482
$266$	14.5734	+	16.8832i	0.893553	+	1.03517i
$267$		−	10.3003i		−	0.630370i
$268$	−0.497277	+	9.74186i	−0.0303760	+	0.595079i
$269$	−2.74641	+	7.54571i	−0.167452	+	0.460070i	−0.994827	−	0.101579i	$-0.967611\pi$
$269$	−2.74641	+	7.54571i	−0.167452	+	0.460070i	0.827376	+	0.561649i	$0.189833\pi$
$270$	−2.83152	+	4.62768i	−0.172321	+	0.281632i
$271$	−1.55933	−	8.84342i	−0.0947228	−	0.537200i	−0.994832	−	0.101535i	$-0.967625\pi$
$271$	−1.55933	−	8.84342i	−0.0947228	−	0.537200i	0.900109	−	0.435664i	$-0.143487\pi$
$272$	−1.63234	−	3.63965i	−0.0989753	−	0.220686i
$273$	9.76899	−	16.9204i	0.591246	−	1.02407i
$274$	−0.405703	−	2.70206i	−0.0245094	−	0.163238i
$275$	−35.5838	+	42.4072i	−2.14579	+	2.55725i
$276$	−0.704246	+	0.0874421i	−0.0423907	+	0.00526340i
$277$	22.2770	−	12.8616i	1.33850	−	0.772782i	0.351913	−	0.936033i	$-0.385531\pi$
$277$	22.2770	−	12.8616i	1.33850	−	0.772782i	0.986585	+	0.163251i	$0.0521981\pi$
$278$	15.0015	+	18.8331i	0.899728	+	1.12954i
$279$	8.40692	−	3.05987i	0.503309	−	0.183190i
$280$	−22.8618	−	31.9133i	−1.36626	−	1.90719i
$281$	−4.01514	+	22.7710i	−0.239523	+	1.35840i	0.593353	+	0.804943i	$0.297804\pi$
$281$	−4.01514	+	22.7710i	−0.239523	+	1.35840i	−0.832876	+	0.553460i	$0.813307\pi$
$282$	−7.04757	+	7.97675i	−0.419677	+	0.475008i
$283$	−11.7261	−	13.9746i	−0.697044	−	0.830704i	0.295145	−	0.955453i	$-0.404632\pi$
$283$	−11.7261	−	13.9746i	−0.697044	−	0.830704i	−0.992188	+	0.124748i	$0.960188\pi$
$284$	11.9609	+	11.1233i	0.709747	+	0.660049i
$285$	−11.2456	−	12.3754i	−0.666130	−	0.733055i
$286$	−40.4942	−	15.9193i	−2.39447	−	0.941330i
$287$	11.7879	−	9.89123i	0.695818	−	0.583861i
$288$	−3.42841	+	4.49956i	−0.202021	+	0.265139i
$289$	−2.77933	+	15.7624i	−0.163490	+	0.927198i
$290$	−3.09856	+	15.2831i	−0.181954	+	0.897453i
$291$	1.38413	+	3.80285i	0.0811389	+	0.222927i
$292$	20.6297	−	6.33781i	1.20726	−	0.370892i
$293$	24.2635	−	14.0086i	1.41749	−	0.818389i	0.421413	−	0.906869i	$-0.361534\pi$
$293$	24.2635	−	14.0086i	1.41749	−	0.818389i	0.996078	+	0.0884804i	$0.0282011\pi$
$294$	7.56625	−	4.11479i	0.441272	−	0.239980i
$295$	−13.7161	−	11.5092i	−0.798581	−	0.670089i
$296$	−3.28814	−	2.25002i	−0.191119	−	0.130780i
$297$	−2.84870	+	4.93409i	−0.165298	+	0.286305i
$298$	−0.158792	+	6.22565i	−0.00919856	+	0.360642i
$299$	−1.88702	+	0.332732i	−0.109129	+	0.0192424i
$300$	11.7161	+	15.5039i	0.676430	+	0.895120i
$301$	3.80518	−	10.4546i	0.219327	−	0.602595i
$302$	−4.48385	+	1.50366i	−0.258016	+	0.0865261i
$303$	6.12314			0.351765
$304$	−10.3508	−	14.0307i	−0.593661	−	0.804715i
$305$	2.68621			0.153812
$306$	−1.33712	+	0.448404i	−0.0764379	+	0.0256335i
$307$	−1.46098	+	4.01400i	−0.0833823	+	0.229091i	−0.974376	−	0.224924i	$-0.927787\pi$
$307$	−1.46098	+	4.01400i	−0.0833823	+	0.229091i	0.890994	+	0.454015i	$0.150009\pi$
$308$	−24.8556	−	32.8914i	−1.41628	−	1.87416i
$309$	−11.5875	+	2.04320i	−0.659192	+	0.116233i
$310$	1.23757	−	48.5207i	0.0702893	−	2.75579i
$311$	−0.757646	+	1.31228i	−0.0429622	+	0.0744127i	−0.886707	−	0.462332i	$-0.847013\pi$
$311$	−0.757646	+	1.31228i	−0.0429622	+	0.0744127i	0.843745	+	0.536745i	$0.180346\pi$
$312$	−8.62561	+	12.6053i	−0.488329	+	0.713635i
$313$	−3.59129	−	3.01345i	−0.202992	−	0.170330i	0.535625	−	0.844456i	$-0.320076\pi$
$313$	−3.59129	−	3.01345i	−0.202992	−	0.170330i	−0.738617	+	0.674126i	$0.764521\pi$
$314$	−26.4516	+	14.3853i	−1.49275	+	0.811812i
$315$	−12.0200	+	6.93975i	−0.677251	+	0.391011i
$316$	−4.31648	+	1.32610i	−0.242821	+	0.0745988i
$317$	4.53344	+	12.4555i	0.254624	+	0.699573i	0.999477	+	0.0323443i	$0.0102973\pi$
$317$	4.53344	+	12.4555i	0.254624	+	0.699573i	−0.744853	+	0.667228i	$0.767480\pi$
$318$	1.30551	−	6.43918i	0.0732094	−	0.361091i
$319$	−2.84373	+	16.1276i	−0.159218	+	0.902971i
$320$	15.9134	+	26.2415i	0.889588	+	1.46694i
$321$	4.39472	−	3.68761i	0.245290	−	0.205822i
$322$	−1.68965	−	0.664247i	−0.0941608	−	0.0370170i
$323$	−0.171532	−	4.34345i	−0.00954428	−	0.241676i
$324$	1.46456	+	1.36201i	0.0813644	+	0.0756671i
$325$	33.7275	+	40.1948i	1.87086	+	2.22961i
$326$	20.0576	−	22.7020i	1.11089	−	1.25735i
$327$	−2.13300	+	12.0968i	−0.117955	+	0.668956i
$328$	−9.77933	+	7.00564i	−0.539973	+	0.386822i
$329$	−25.5889	+	9.31360i	−1.41076	+	0.513475i
$330$	19.2581	+	24.1770i	1.06012	+	1.33090i
$331$	3.69548	−	2.13359i	0.203122	−	0.117273i	−0.394989	−	0.918686i	$-0.629252\pi$
$331$	3.69548	−	2.13359i	0.203122	−	0.117273i	0.598111	+	0.801413i	$0.295918\pi$
$332$	26.8978	−	3.33974i	1.47621	−	0.183292i
$333$	−0.905464	+	1.07909i	−0.0496191	+	0.0591338i
$334$	−1.96459	−	13.0845i	−0.107497	−	0.715954i
$335$	9.35511	−	16.2035i	0.511124	−	0.885293i
$336$	−13.2049	+	5.92225i	−0.720386	+	0.323085i
$337$	−5.08408	−	28.8332i	−0.276947	−	1.57065i	−0.732707	−	0.680544i	$-0.761744\pi$
$337$	−5.08408	−	28.8332i	−0.276947	−	1.57065i	0.455760	−	0.890103i	$-0.349368\pi$
$338$	−11.9291	+	19.4963i	−0.648860	+	1.06046i
$339$	−2.83916	+	7.80052i	−0.154202	+	0.423666i
$340$	−0.390049	+	7.64124i	−0.0211534	+	0.414404i
$341$		−	50.9716i		−	2.76026i
$342$	−5.29496	+	3.15649i	−0.286319	+	0.170683i
$343$	−3.29190			−0.177746
$344$	−3.59067	+	7.92175i	−0.193596	+	0.427112i
$345$	1.27910	+	0.465554i	0.0688644	+	0.0250646i
$346$	1.50370	+	0.920061i	0.0808392	+	0.0494628i
$347$	−19.0068	+	3.35142i	−1.02034	+	0.179914i	−0.658701	−	0.752404i	$-0.728894\pi$
$347$	−19.0068	+	3.35142i	−1.02034	+	0.179914i	−0.361639	+	0.932318i	$0.617783\pi$
$348$	5.29477	+	2.23901i	0.283829	+	0.120024i
$349$	1.72747	+	0.997354i	0.0924692	+	0.0533871i	0.545522	−	0.838097i	$-0.316332\pi$
$349$	1.72747	+	0.997354i	0.0924692	+	0.0533871i	−0.453052	+	0.891484i	$0.649665\pi$
$350$	7.38189	+	49.1649i	0.394579	+	2.62797i
$351$	4.13677	+	3.47116i	0.220805	+	0.185277i
$352$	17.4091	+	27.1230i	0.927906	+	1.44566i
$353$	−3.78713	−	6.55951i	−0.201569	−	0.349127i	0.747465	−	0.664301i	$-0.231271\pi$
$353$	−3.78713	−	6.55951i	−0.201569	−	0.349127i	−0.949034	+	0.315173i	$0.897937\pi$
$354$	−5.16296	+	4.11253i	−0.274408	+	0.218579i
$355$	−10.7154	−	29.4404i	−0.568716	−	1.56253i
$356$	−11.1964	+	17.2924i	−0.593410	+	0.916495i
$357$	−3.55321	−	0.626526i	−0.188056	−	0.0331593i
$358$	−7.65984	+	8.66973i	−0.404835	+	0.458210i
$359$	11.9395	−	10.0184i	0.630143	−	0.528753i	−0.270830	−	0.962627i	$-0.587298\pi$
$359$	11.9395	−	10.0184i	0.630143	−	0.528753i	0.900973	+	0.433874i	$0.142854\pi$
$360$	9.78389	−	4.69118i	0.515657	−	0.247247i
$361$	−4.76464	−	18.3929i	−0.250770	−	0.968047i
$362$	9.36369	−	23.8185i	0.492145	−	1.25188i
$363$	13.7945	+	16.4396i	0.724021	+	0.862855i
$364$	−34.7928	+	17.7874i	−1.82364	+	0.932314i
$365$	−40.7663	−	7.18821i	−2.13381	−	0.376248i
$366$	0.196768	−	0.970523i	0.0102853	−	0.0507300i
$367$	17.6056	−	6.40793i	0.919007	−	0.334491i	0.161164	−	0.986928i	$-0.448475\pi$
$367$	17.6056	−	6.40793i	0.919007	−	0.334491i	0.757843	+	0.652436i	$0.226253\pi$
$368$	1.27735	+	0.618715i	0.0665866	+	0.0322527i
$369$	2.12658	+	3.68334i	0.110705	+	0.191747i
$370$	3.65112	+	6.71365i	0.189813	+	0.349026i
$371$	10.8044	−	12.8762i	0.560939	−	0.668501i
$372$	−17.4398	−	4.00134i	−0.904210	−	0.207460i
$373$	−0.308144	−	0.177907i	−0.0159551	−	0.00921167i	0.492001	−	0.870594i	$-0.336266\pi$
$373$	−0.308144	−	0.177907i	−0.0159551	−	0.00921167i	−0.507956	+	0.861383i	$0.669599\pi$
$374$	−0.204876	+	8.03244i	−0.0105939	+	0.415347i
$375$	−3.14188	−	17.8185i	−0.162246	−	0.920142i
$376$	20.5023	−	5.73082i	1.05733	−	0.295545i
$377$	14.5859	+	5.30885i	0.751214	+	0.273420i
$378$	1.62684	+	4.85115i	0.0836755	+	0.249516i
$379$			10.2559i			0.526808i	0.964686	+	0.263404i	$0.0848452\pi$
$379$			10.2559i			0.526808i	−0.964686	+	0.263404i	$0.915155\pi$
$380$	5.42726	+	33.0000i	0.278412	+	1.69286i
$381$		−	7.78787i		−	0.398984i
$382$	−17.3410	+	5.81530i	−0.887240	+	0.297537i
$383$	−18.6332	−	6.78193i	−0.952112	−	0.346540i	−0.181174	−	0.983451i	$-0.557990\pi$
$383$	−18.6332	−	6.78193i	−0.952112	−	0.346540i	−0.770938	+	0.636911i	$0.780212\pi$
$384$	10.6467	−	3.82727i	0.543312	−	0.195310i
$385$	13.7316	+	77.8757i	0.699827	+	3.96892i
$386$	−0.278082	−	0.00709277i	−0.0141540	−	0.000361012i
$387$	2.66306	+	1.53752i	0.135371	+	0.0781566i
$388$	1.81000	−	7.88885i	0.0918887	−	0.400496i
$389$	1.57736	−	1.87983i	0.0799754	−	0.0953109i	−0.724573	−	0.689198i	$-0.757963\pi$
$389$	1.57736	−	1.87983i	0.0799754	−	0.0953109i	0.804548	+	0.593887i	$0.202407\pi$
$390$	25.7373	−	13.9968i	1.30326	−	0.708758i
$391$	0.176923	+	0.306439i	0.00894737	+	0.0154973i
$392$	−17.1751	−	1.31649i	−0.867475	−	0.0664930i
$393$	0.170936	−	0.0622158i	0.00862260	−	0.00313837i
$394$	−11.0075	−	2.23172i	−0.554552	−	0.112433i
$395$	8.52978	+	1.50403i	0.429180	+	0.0756760i
$396$	10.1458	−	5.18692i	0.509846	−	0.260653i
$397$	−20.9048	−	24.9133i	−1.04918	−	1.25036i	−0.967276	−	0.253725i	$-0.918344\pi$
$397$	−20.9048	−	24.9133i	−1.04918	−	1.25036i	−0.0819043	−	0.996640i	$-0.526100\pi$
$398$	−21.4481	−	8.43180i	−1.07510	−	0.422648i
$399$	−15.7583	+	0.622329i	−0.788904	+	0.0311554i
$400$	−2.81650	−	38.7637i	−0.140825	−	1.93819i
$401$	27.8168	−	23.3410i	1.38910	−	1.16560i	0.423401	−	0.905943i	$-0.360836\pi$
$401$	27.8168	−	23.3410i	1.38910	−	1.16560i	0.965702	−	0.259653i	$-0.0836081\pi$
$402$	−5.16903	−	4.56691i	−0.257808	−	0.227777i
$403$	−47.5784	−	8.38936i	−2.37005	−	0.417904i
$404$	−10.2796	−	6.65584i	−0.511431	−	0.331140i
$405$	−1.31206	−	3.60485i	−0.0651968	−	0.179127i
$406$	9.16323	+	11.5037i	0.454763	+	0.570919i
$407$	4.01283	+	6.95042i	0.198909	+	0.344520i
$408$	2.73219	+	0.700655i	0.135264	+	0.0346876i
$409$	−19.3706	−	16.2538i	−0.957813	−	0.803700i	0.0227833	−	0.999740i	$-0.492747\pi$
$409$	−19.3706	−	16.2538i	−0.957813	−	0.803700i	−0.980596	+	0.196040i	$0.937192\pi$
$410$	22.8185	−	3.42610i	1.12692	−	0.169203i
$411$	1.67322	+	0.966031i	0.0825336	+	0.0476508i
$412$	21.6743	+	9.16547i	1.06782	+	0.451550i
$413$	−16.6302	+	2.93235i	−0.818319	+	0.144292i
$414$	0.261900	−	0.428034i	0.0128717	−	0.0210367i
$415$	−48.8536	−	17.7813i	−2.39813	−	0.872847i
$416$	28.1828	−	11.7860i	1.38177	−	0.577857i
$417$	−17.0254			−0.833739
$418$	6.58133	+	34.4990i	0.321904	+	1.68740i
$419$		−	10.1163i		−	0.494214i	−0.968988	−	0.247107i	$-0.920520\pi$
$419$		−	10.1163i		−	0.494214i	0.968988	−	0.247107i	$-0.0794799\pi$
$420$	27.7229	+	1.41513i	1.35274	+	0.0690511i
$421$	−4.65481	+	12.7890i	−0.226862	+	0.623298i	−0.999939	−	0.0110139i	$-0.996494\pi$
$421$	−4.65481	+	12.7890i	−0.226862	+	0.623298i	0.773078	+	0.634311i	$0.218716\pi$
$422$	7.93396	+	4.85453i	0.386219	+	0.236315i
$423$	−1.30697	−	7.41217i	−0.0635468	−	0.360392i
$424$	−9.19109	+	9.39113i	−0.446359	+	0.456074i
$425$	4.84480	−	8.39143i	0.235007	−	0.407044i
$426$	−11.4217	+	1.71492i	−0.553382	+	0.0830879i
$427$	1.62846	−	1.94073i	0.0788068	−	0.0939183i
$428$	−11.3864	+	1.41378i	−0.550381	+	0.0683376i
$429$	26.6450	−	15.3835i	1.28643	−	0.742721i
$430$	13.0490	−	10.3941i	0.629279	−	0.501249i
$431$	23.5253	−	8.56251i	1.13317	−	0.412442i	0.293730	−	0.955888i	$-0.405103\pi$
$431$	23.5253	−	8.56251i	1.13317	−	0.412442i	0.839444	+	0.543447i	$0.182881\pi$
$432$	−0.978232	−	3.87854i	−0.0470652	−	0.186606i
$433$	0.0356525	−	0.202195i	0.00171335	−	0.00971689i	−0.983939	−	0.178505i	$-0.942874\pi$
$433$	0.0356525	−	0.202195i	0.00171335	−	0.00971689i	0.985652	+	0.168788i	$0.0539852\pi$
$434$	−34.3048	−	30.3088i	−1.64668	−	1.45487i
$435$	−7.08778	−	8.44689i	−0.339833	−	0.404997i
$436$	16.7301	−	17.9898i	0.801228	−	0.861556i
$437$	1.04015	+	1.14465i	0.0497572	+	0.0547562i
$438$	−5.58328	+	14.2023i	−0.266779	+	0.678610i
$439$	14.2067	−	11.9208i	0.678048	−	0.568950i	−0.237387	−	0.971415i	$-0.576291\pi$
$439$	14.2067	−	11.9208i	0.678048	−	0.568950i	0.915435	+	0.402465i	$0.131847\pi$
$440$	−6.05052	−	61.5224i	−0.288447	−	2.93297i
$441$	−1.05754	+	5.99762i	−0.0503591	+	0.285601i
$442$	7.46401	+	1.51329i	0.355027	+	0.0719798i
$443$	7.54611	+	20.7328i	0.358526	+	0.985043i	0.979541	+	0.201244i	$0.0644985\pi$
$443$	7.54611	+	20.7328i	0.358526	+	0.985043i	−0.621015	+	0.783799i	$0.713279\pi$
$444$	2.69308	−	0.827360i	0.127808	−	0.0392648i
$445$	34.2203	−	19.7571i	1.62220	−	0.936576i
$446$	−4.84075	−	8.90112i	−0.229216	−	0.421480i
$447$	−3.37337	−	2.83060i	−0.159555	−	0.133883i
$448$	28.6061	+	4.41130i	1.35151	+	0.208414i
$449$	10.8573	−	18.8053i	0.512386	−	0.887479i	−0.487511	−	0.873117i	$-0.662095\pi$
$449$	10.8573	−	18.8053i	0.512386	−	0.887479i	0.999897	−	0.0143617i	$-0.00457164\pi$
$450$	−13.7367	−	0.350369i	−0.647554	−	0.0165166i
$451$	23.8638	−	4.20783i	1.12370	−	0.198139i
$452$	13.2456	−	10.0095i	0.623020	−	0.470808i
$453$	1.14375	−	3.14242i	0.0537379	−	0.147644i
$454$	6.08530	+	18.1461i	0.285597	+	0.851636i
$455$	74.9517			3.51379
$456$	12.3204	+	0.456433i	0.576954	+	0.0213744i
$457$	5.54150			0.259220			0.129610	−	0.991565i	$-0.458627\pi$
$457$	5.54150			0.259220			0.129610	+	0.991565i	$0.458627\pi$
$458$	11.6896	+	34.8578i	0.546219	+	1.62880i
$459$	0.341074	−	0.937093i	0.0159200	−	0.0437397i
$460$	−1.64132	−	2.17196i	−0.0765270	−	0.101268i
$461$	24.0454	−	4.23985i	1.11990	−	0.197469i	0.417106	−	0.908858i	$-0.363044\pi$
$461$	24.0454	−	4.23985i	1.11990	−	0.197469i	0.702799	+	0.711388i	$0.251933\pi$
$462$	29.1422	+	0.743303i	1.35582	+	0.0345816i
$463$	14.9654	−	25.9208i	0.695501	−	1.20464i	−0.274510	−	0.961584i	$-0.588516\pi$
$463$	14.9654	−	25.9208i	0.695501	−	1.20464i	0.970011	−	0.243059i	$-0.0781509\pi$
$464$	−6.45516	−	9.51430i	−0.299673	−	0.441690i
$465$	26.2910	+	22.0608i	1.21922	+	1.02304i
$466$	1.07863	+	1.98337i	0.0499664	+	0.0918777i
$467$	11.0706	−	6.39164i	0.512288	−	0.295770i	−0.221485	−	0.975164i	$-0.571091\pi$
$467$	11.0706	−	6.39164i	0.512288	−	0.295770i	0.733774	+	0.679394i	$0.237757\pi$
$468$	−3.17175	−	10.3241i	−0.146614	−	0.477233i
$469$	−6.03533	−	16.5819i	−0.278686	−	0.765682i
$470$	−40.0187	−	8.11359i	−1.84593	−	0.374252i
$471$	3.69717	−	20.9677i	0.170357	−	0.966140i
$472$	13.1380	−	1.29208i	0.604725	−	0.0594726i
$473$	13.4209	−	11.2615i	0.617094	−	0.517803i
$474$	1.16822	−	2.97162i	0.0536582	−	0.136491i
$475$	12.9038	−	40.3395i	0.592068	−	1.85090i
$476$	5.28416	+	4.91415i	0.242199	+	0.225240i
$477$	2.98628	+	3.55891i	0.136732	+	0.162951i
$478$	5.43000	+	4.79748i	0.248362	+	0.219432i
$479$	−7.32296	+	41.5306i	−0.334595	+	1.89758i	0.0966036	+	0.995323i	$0.469202\pi$
$479$	−7.32296	+	41.5306i	−0.334595	+	1.89758i	−0.431198	+	0.902257i	$0.641909\pi$
$480$	−21.5247	−	2.75943i	−0.982464	−	0.125950i
$481$	7.14821	−	2.60174i	0.325930	−	0.118629i
$482$	−17.7252	+	14.1189i	−0.807361	+	0.643100i
$483$	1.11178	−	0.641888i	0.0505878	−	0.0292069i
$484$	−5.28860	−	42.5937i	−0.240391	−	1.93608i
$485$	−9.97914	+	11.8927i	−0.453130	+	0.540019i
$486$	−1.39854	+	0.209984i	−0.0634389	+	0.00952508i
$487$	17.1419	−	29.6907i	0.776775	−	1.34541i	−0.157016	−	0.987596i	$-0.550187\pi$
$487$	17.1419	−	29.6907i	0.776775	−	1.34541i	0.933791	−	0.357818i	$-0.116479\pi$
$488$	−1.38529	+	1.41545i	−0.0627093	+	0.0640742i
$489$	3.71966	+	21.0952i	0.168209	+	0.953960i
$490$	28.1832	+	17.2444i	1.27319	+	0.779021i
$491$	10.7027	−	29.4053i	0.483004	−	1.32704i	−0.423901	−	0.905709i	$-0.639339\pi$
$491$	10.7027	−	29.4053i	0.483004	−	1.32704i	0.906905	−	0.421335i	$-0.138438\pi$
$492$	0.433642	−	8.49524i	0.0195501	−	0.382995i
$493$		−	2.86641i		−	0.129096i
$494$	33.2856	−	0.465063i	1.49759	−	0.0209242i
$495$	−21.8564			−0.982372
$496$	24.9288	+	25.6745i	1.11934	+	1.15282i
$497$	−27.7660	−	10.1060i	−1.24548	−	0.453316i
$498$	−10.0029	+	16.3482i	−0.448242	+	0.732581i
$499$	−13.8697	+	2.44561i	−0.620894	+	0.109480i	−0.475242	−	0.879855i	$-0.657639\pi$
$499$	−13.8697	+	2.44561i	−0.620894	+	0.109480i	−0.145653	+	0.989336i	$0.546528\pi$
$500$	−14.0940	+	33.3292i	−0.630303	+	1.49053i
$501$	8.10242	+	4.67793i	0.361989	+	0.208995i
$502$	27.6610	−	4.15318i	1.23457	−	0.185365i
$503$	−4.00948	−	3.36435i	−0.178774	−	0.150009i	0.549010	−	0.835816i	$-0.315005\pi$
$503$	−4.00948	−	3.36435i	−0.178774	−	0.150009i	−0.727784	+	0.685807i	$0.759449\pi$
$504$	2.54202	−	9.91258i	0.113231	−	0.441541i
$505$	11.7448	+	20.3426i	0.522637	+	0.905234i
$506$	−1.78127	−	2.23624i	−0.0791869	−	0.0994129i
$507$	−5.52768	−	15.1872i	−0.245493	−	0.674486i
$508$	−8.46539	+	13.0744i	−0.375591	+	0.580084i
$509$	29.5862	+	5.21685i	1.31139	+	0.231233i	0.785256	−	0.619171i	$-0.212531\pi$
$509$	29.5862	+	5.21685i	1.31139	+	0.231233i	0.526130	+	0.850404i	$0.323642\pi$
$510$	−4.05444	−	3.58216i	−0.179534	−	0.158621i
$511$	−29.9071	+	25.0951i	−1.32301	+	1.11014i
$512$	−22.0341	−	5.14763i	−0.973779	−	0.227495i
$513$	0.586931	−	4.31920i	0.0259136	−	0.190697i
$514$	39.9866	+	15.7198i	1.76374	+	0.693370i
$515$	−29.0141	−	34.5777i	−1.27851	−	1.52367i
$516$	−2.79952	−	5.47597i	−0.123242	−	0.241066i
$517$	−42.2301	−	7.44630i	−1.85728	−	0.327488i
$518$	7.06389	+	1.43217i	0.310369	+	0.0629258i
$519$	−1.17134	+	0.426334i	−0.0514163	+	0.0187140i
$520$	−58.4228	−	4.47818i	−2.56201	−	0.196381i
$521$	8.48019	+	14.6881i	0.371524	+	0.643498i	0.989800	−	0.142463i	$-0.0455021\pi$
$521$	8.48019	+	14.6881i	0.371524	+	0.643498i	−0.618276	+	0.785961i	$0.712169\pi$
$522$	−3.57104	+	1.94206i	−0.156300	+	0.0850015i
$523$	−7.43448	+	8.86007i	−0.325087	+	0.387424i	−0.903691	−	0.428185i	$-0.859153\pi$
$523$	−7.43448	+	8.86007i	−0.325087	+	0.387424i	0.578604	+	0.815609i	$0.303598\pi$
$524$	−0.354600	−	0.0813585i	−0.0154908	−	0.00355416i
$525$	−30.4447	−	17.5772i	−1.32871	−	0.767134i
$526$	−30.8000	−	0.785587i	−1.34294	−	0.0342532i
$527$	1.54924	+	8.78617i	0.0674859	+	0.382731i
$528$	−22.6711	−	2.32056i	−0.986635	−	0.100989i
$529$	21.4946	+	7.82340i	0.934549	+	0.340148i
$530$	23.8967	−	8.01377i	1.03800	−	0.348096i
$531$		−	4.66739i		−	0.202548i
$532$	27.1319	+	16.0845i	1.17632	+	0.697352i
$533$		−	22.9677i		−	0.994843i
$534$	−4.63152	−	13.8110i	−0.200425	−	0.597659i
$535$	20.6807	+	7.52716i	0.894105	+	0.325428i
$536$	3.71364	+	13.2858i	0.160405	+	0.573857i
$537$	−1.42051	−	8.05611i	−0.0612995	−	0.347647i
$538$	−0.289555	+	11.3524i	−0.0124836	+	0.489437i
$539$	30.0493	+	17.3490i	1.29432	+	0.747274i
$540$	−1.71576	+	7.47811i	−0.0738344	+	0.321806i
$541$	−19.9536	+	23.7797i	−0.857871	+	1.02237i	0.141602	+	0.989924i	$0.454775\pi$
$541$	−19.9536	+	23.7797i	−0.857871	+	1.02237i	−0.999473	+	0.0324472i	$0.989670\pi$
$542$	−6.06722	−	11.1564i	−0.260609	−	0.479206i
$543$	9.04849	+	15.6725i	0.388308	+	0.672569i
$544$	−3.82525	−	4.14616i	−0.164006	−	0.177765i
$545$	−44.2800	+	16.1166i	−1.89675	+	0.690359i
$546$	5.49031	−	27.0799i	0.234964	−	1.15891i
$547$	−24.8564	−	4.38286i	−1.06278	−	0.187397i	−0.385192	−	0.922836i	$-0.625865\pi$
$547$	−24.8564	−	4.38286i	−1.06278	−	0.187397i	−0.677591	+	0.735439i	$0.736976\pi$
$548$	−1.75895	−	3.44057i	−0.0751388	−	0.146974i
$549$	0.450096	+	0.536404i	0.0192096	+	0.0228932i
$550$	−28.6435	+	72.8609i	−1.22136	+	3.10680i
$551$	−2.66085	−	12.2432i	−0.113356	−	0.521579i
$552$	−0.904954	+	0.433907i	−0.0385174	+	0.0184683i
$553$	6.25764	−	5.25078i	0.266102	−	0.223286i
$554$	24.0864	−	27.2621i	1.02333	−	1.15825i
$555$	−5.32178	−	0.938374i	−0.225897	−	0.0398318i
$556$	28.5826	+	18.5066i	1.21217	+	0.784855i
$557$	11.0489	+	30.3565i	0.468156	+	1.28625i	0.919216	+	0.393754i	$0.128824\pi$
$557$	11.0489	+	30.3565i	0.468156	+	1.28625i	−0.451060	+	0.892494i	$0.648954\pi$
$558$	9.89636	−	7.88291i	0.418946	−	0.333710i
$559$	−8.30288	−	14.3810i	−0.351174	−	0.608252i
$560$	−45.0035	−	32.5105i	−1.90175	−	1.37382i
$561$	−4.35239	−	3.65209i	−0.183758	−	0.154191i
$562$	4.85531	+	32.3373i	0.204809	+	1.36407i
$563$	−10.1963	−	5.88682i	−0.429722	−	0.248100i	0.269506	−	0.962999i	$-0.413139\pi$
$563$	−10.1963	−	5.88682i	−0.429722	−	0.248100i	−0.699228	+	0.714899i	$0.746473\pi$
$564$	−5.86285	+	13.8644i	−0.246871	+	0.583795i
$565$	−31.3611	+	5.52981i	−1.31937	+	0.232641i
$566$	−22.0063	−	13.4649i	−0.924994	−	0.565973i
$567$	−3.39984	−	1.23744i	−0.142780	−	0.0519676i
$568$	21.0390	+	9.53631i	0.882779	+	0.400135i
$569$	−10.8627			−0.455388			−0.227694	−	0.973733i	$-0.573119\pi$
$569$	−10.8627			−0.455388			−0.227694	+	0.973733i	$0.573119\pi$
$570$	−20.6429	−	11.5367i	−0.864637	−	0.483220i
$571$		−	13.7600i		−	0.575839i	−0.957655	−	0.287920i	$-0.907036\pi$
$571$		−	13.7600i		−	0.575839i	0.957655	−	0.287920i	$-0.0929636\pi$
$572$	−61.4539	−	3.13693i	−2.56952	−	0.131162i
$573$	4.42336	−	12.1531i	0.184788	−	0.507702i
$574$	11.3580	−	18.5628i	0.474073	−	0.774798i
$575$	0.598681	+	3.39529i	0.0249667	+	0.141593i
$576$	−2.57369	+	7.57470i	−0.107237	+	0.315613i
$577$	−1.51763	+	2.62862i	−0.0631799	+	0.109431i	−0.895885	−	0.444286i	$-0.853458\pi$
$577$	−1.51763	+	2.62862i	−0.0631799	+	0.109431i	0.832705	+	0.553716i	$0.186791\pi$
$578$	3.36091	+	22.3843i	0.139795	+	0.931065i
$579$	0.126435	−	0.150679i	0.00525444	−	0.00626200i
$580$	2.71736	+	21.8852i	0.112832	+	0.908734i
$581$	−42.4631	+	24.5161i	−1.76167	+	1.01710i
$582$	3.56582	+	4.47660i	0.147808	+	0.185561i
$583$	24.8728	−	9.05297i	1.03013	−	0.374936i
$584$	24.8111	−	17.7740i	1.02669	−	0.735494i
$585$	−3.59732	+	20.4014i	−0.148731	+	0.843496i
$586$	26.2343	−	29.6931i	1.08373	−	1.22661i
$587$	12.3054	+	14.6650i	0.507897	+	0.605288i	0.957675	−	0.287853i	$-0.0929413\pi$
$587$	12.3054	+	14.6650i	0.507897	+	0.605288i	−0.449778	+	0.893140i	$0.648497\pi$
$588$	8.29482	−	8.91937i	0.342073	−	0.367829i
$589$	14.7733	+	36.0901i	0.608724	+	1.48706i
$590$	−23.5660	−	9.26439i	−0.970195	−	0.381409i
$591$	6.08383	−	5.10494i	0.250255	−	0.209989i
$592$	−5.42054	−	1.53838i	−0.222783	−	0.0632272i
$593$	−3.24548	+	18.4061i	−0.133276	+	0.755846i	0.842769	+	0.538276i	$0.180924\pi$
$593$	−3.24548	+	18.4061i	−0.133276	+	0.755846i	−0.976045	+	0.217570i	$0.930187\pi$
$594$	−1.60101	+	7.89668i	−0.0656903	+	0.324005i
$595$	−4.73394	−	13.0064i	−0.194073	−	0.533210i
$596$	2.58643	+	8.41891i	0.105944	+	0.344852i
$597$	14.1127	−	8.14797i	0.577594	−	0.333474i
$598$	−2.38055	+	1.29463i	−0.0973480	+	0.0529413i
$599$	26.1284	+	21.9244i	1.06758	+	0.895805i	0.994831	−	0.101545i	$-0.0323787\pi$
$599$	26.1284	+	21.9244i	1.06758	+	0.895805i	0.0727478	+	0.997350i	$0.476823\pi$
$600$	22.6806	+	15.5200i	0.925931	+	0.633600i
$601$	7.35132	−	12.7329i	0.299867	−	0.519384i	−0.676239	−	0.736683i	$-0.736391\pi$
$601$	7.35132	−	12.7329i	0.299867	−	0.519384i	0.976105	+	0.217298i	$0.0697245\pi$
$602$	0.401181	−	15.7289i	0.0163509	−	0.641060i
$603$	4.80318	−	0.846929i	0.195600	−	0.0344896i
$604$	−5.33595	+	4.03230i	−0.217117	+	0.164072i
$605$	−28.1573	+	77.3615i	−1.14476	+	3.14519i
$606$	8.21007	−	2.75325i	0.333511	−	0.111843i
$607$	−48.1929			−1.95609			−0.978045	−	0.208395i	$-0.933176\pi$
$607$	−48.1929			−1.95609			−0.978045	+	0.208395i	$0.933176\pi$
$608$	−20.1875	−	14.1585i	−0.818713	−	0.574203i
$609$	−10.3995			−0.421410
$610$	3.60174	−	1.20785i	0.145830	−	0.0489043i
$611$	−13.9012	+	38.1933i	−0.562383	+	1.54514i
$612$	−1.59122	+	1.20246i	−0.0643212	+	0.0486067i
$613$	24.9530	−	4.39988i	1.00784	−	0.177709i	0.354727	−	0.934970i	$-0.384574\pi$
$613$	24.9530	−	4.39988i	1.00784	−	0.177709i	0.653113	+	0.757260i	$0.273463\pi$
$614$	−0.154031	+	6.03900i	−0.00621619	+	0.243714i
$615$	−8.15798	+	14.1300i	−0.328961	+	0.569778i
$616$	−48.1166	−	32.9254i	−1.93867	−	1.32660i
$617$	36.3219	+	30.4777i	1.46227	+	1.22699i	0.922971	+	0.384869i	$0.125753\pi$
$617$	36.3219	+	30.4777i	1.46227	+	1.22699i	0.539294	+	0.842118i	$0.318691\pi$
$618$	−14.6182	+	7.94988i	−0.588029	+	0.319791i
$619$	−23.9629	+	13.8350i	−0.963150	+	0.556075i	−0.897141	−	0.441744i	$-0.854360\pi$
$619$	−23.9629	+	13.8350i	−0.963150	+	0.556075i	−0.0660088	+	0.997819i	$0.521027\pi$
$620$	−20.1578	−	65.6143i	−0.809558	−	2.63513i
$621$	0.121358	+	0.333428i	0.00486993	+	0.0133800i
$622$	−0.425808	+	2.10022i	−0.0170734	+	0.0842110i
$623$	6.47133	−	36.7007i	0.259268	−	1.47038i
$624$	−5.89751	+	20.7800i	−0.236089	+	0.831866i
$625$	15.9548	−	13.3876i	0.638191	−	0.535506i
$626$	−6.17029	−	2.42570i	−0.246615	−	0.0969506i
$627$	−21.9805	−	11.5588i	−0.877815	−	0.461615i
$628$	−28.9987	+	31.1822i	−1.15717	+	1.24430i
$629$	−0.902959	−	1.07611i	−0.0360033	−	0.0429071i
$630$	−12.9963	+	14.7098i	−0.517785	+	0.586051i
$631$	1.38102	−	7.83218i	0.0549777	−	0.311794i	−0.944901	−	0.327356i	$-0.893842\pi$
$631$	1.38102	−	7.83218i	0.0549777	−	0.311794i	0.999879	+	0.0155615i	$0.00495358\pi$
$632$	−5.19138	+	3.71896i	−0.206502	+	0.147932i
$633$	−6.18037	+	2.24947i	−0.245648	+	0.0894084i
$634$	11.6792	+	14.6623i	0.463839	+	0.582313i
$635$	25.8732	−	14.9379i	1.02675	−	0.592794i
$636$	−1.14490	−	9.22084i	−0.0453981	−	0.365630i
$637$	21.1399	−	25.1935i	0.837592	−	0.998203i
$638$	3.43878	+	22.9030i	0.136143	+	0.906737i
$639$	4.08344	−	7.07272i	0.161538	−	0.279793i
$640$	33.1366	+	28.0299i	1.30984	+	1.10798i
$641$	−1.79505	−	10.1802i	−0.0709001	−	0.402094i	−0.999518	−	0.0310560i	$-0.990113\pi$
$641$	−1.79505	−	10.1802i	−0.0709001	−	0.402094i	0.928618	−	0.371038i	$-0.120998\pi$
$642$	4.23444	−	6.92053i	0.167120	−	0.273131i
$643$	−3.42630	+	9.41367i	−0.135120	+	0.371239i	−0.988737	−	0.149662i	$-0.952182\pi$
$643$	−3.42630	+	9.41367i	−0.135120	+	0.371239i	0.853617	+	0.520901i	$0.174404\pi$
$644$	−2.56421	−	0.130891i	−0.101044	−	0.00515783i
$645$			11.7965i			0.464486i
$646$	−2.18302	−	5.74669i	−0.0858897	−	0.226101i
$647$	−0.789462			−0.0310370			−0.0155185	−	0.999880i	$-0.504940\pi$
$647$	−0.789462			−0.0310370			−0.0155185	+	0.999880i	$0.504940\pi$
$648$	2.57614	+	1.16768i	0.101201	+	0.0458709i
$649$	−24.9883	−	9.09500i	−0.980877	−	0.357010i
$650$	63.2962	+	38.7288i	2.48268	+	1.51907i
$651$	31.8768	−	5.62074i	1.24935	−	0.220294i
$652$	16.6858	−	39.4584i	0.653468	−	1.54531i
$653$	1.01171	+	0.584112i	0.0395913	+	0.0228581i	0.519665	−	0.854370i	$-0.326057\pi$
$653$	1.01171	+	0.584112i	0.0395913	+	0.0228581i	−0.480074	+	0.877228i	$0.659390\pi$
$654$	2.57933	+	17.1788i	0.100860	+	0.671746i
$655$	0.534570	+	0.448558i	0.0208874	+	0.0175266i
$656$	−9.96232	+	13.7906i	−0.388963	+	0.538433i
$657$	−5.39534	−	9.34499i	−0.210492	−	0.364583i
$658$	−30.1225	+	23.9939i	−1.17430	+	0.935380i
$659$	5.03799	+	13.8418i	0.196252	+	0.539199i	0.998314	−	0.0580423i	$-0.0184858\pi$
$659$	5.03799	+	13.8418i	0.196252	+	0.539199i	−0.802062	+	0.597241i	$0.796264\pi$
$660$	36.6930	+	23.7579i	1.42827	+	0.924773i
$661$	−42.5719	−	7.50657i	−1.65585	−	0.291972i	−0.733896	−	0.679261i	$-0.762300\pi$
$661$	−42.5719	−	7.50657i	−1.65585	−	0.291972i	−0.921958	+	0.387290i	$0.873411\pi$
$662$	3.99564	−	4.52244i	0.155295	−	0.175770i
$663$	−4.12533	+	3.46156i	−0.160214	+	0.134436i
$664$	34.5636	−	16.5725i	1.34133	−	0.643139i
$665$	−32.2937	−	51.1595i	−1.25229	−	1.98388i
$666$	−0.728861	+	1.85401i	−0.0282428	+	0.0718416i
$667$	0.655579	+	0.781289i	0.0253841	+	0.0302516i
$668$	−8.51760	−	16.6607i	−0.329556	−	0.644623i
$669$	7.05575	+	1.24412i	0.272791	+	0.0481004i
$670$	5.25771	−	25.9326i	0.203123	−	1.00186i
$671$	3.74887	−	1.36448i	0.144724	−	0.0526751i
$672$	−15.0426	+	13.8783i	−0.580279	+	0.535366i
$673$	16.8855	+	29.2466i	0.650889	+	1.12737i	0.982907	+	0.184100i	$0.0589372\pi$
$673$	16.8855	+	29.2466i	0.650889	+	1.12737i	−0.332018	+	0.943273i	$0.607729\pi$
$674$	−19.7817	−	36.3743i	−0.761961	−	1.40109i
$675$	6.24563	−	7.44325i	0.240394	−	0.286491i
$676$	−7.22845	+	31.5051i	−0.278017	+	1.21173i
$677$	33.0756	+	19.0962i	1.27120	+	0.733927i	0.975214	−	0.221266i	$-0.0710188\pi$
$677$	33.0756	+	19.0962i	1.27120	+	0.733927i	0.295985	+	0.955193i	$0.404352\pi$
$678$	−0.299333	+	11.7358i	−0.0114958	+	0.450710i
$679$	2.54253	+	14.4194i	0.0975734	+	0.553366i
$680$	2.91287	+	10.4210i	0.111704	+	0.399626i
$681$	−12.7173	−	4.62872i	−0.487328	−	0.177373i
$682$	−22.9192	−	68.3440i	−0.877623	−	2.61703i
$683$			5.27971i			0.202022i	0.994885	+	0.101011i	$0.0322078\pi$
$683$			5.27971i			0.202022i	−0.994885	+	0.101011i	$0.967792\pi$
$684$	−5.68032	+	6.61317i	−0.217192	+	0.252861i
$685$			7.41179i			0.283190i
$686$	−4.41387	+	1.48019i	−0.168522	+	0.0565141i
$687$	−24.4294	−	8.89157i	−0.932040	−	0.339235i
$688$	−1.25247	+	12.2362i	−0.0477499	+	0.466502i
$689$	−4.35653	−	24.7071i	−0.165971	−	0.941266i
$690$	1.92439	+	0.0490835i	0.0732602	+	0.00186858i
$691$	37.2331	+	21.4965i	1.41641	+	0.817766i	0.995982	−	0.0895583i	$-0.0285455\pi$
$691$	37.2331	+	21.4965i	1.41641	+	0.817766i	0.420431	+	0.907325i	$0.361879\pi$
$692$	2.42990	+	0.557510i	0.0923709	+	0.0211933i
$693$	−13.2500	+	15.7908i	−0.503326	+	0.599841i
$694$	−23.9779	+	13.0401i	−0.910190	+	0.494994i
$695$	−32.6565	−	56.5628i	−1.23873	−	2.14555i
$696$	8.10614	+	0.621345i	0.307262	+	0.0235520i
$697$	−3.98560	+	1.45064i	−0.150965	+	0.0549469i
$698$	2.76469	+	0.560527i	0.104645	+	0.0212163i
$699$	−1.57218	−	0.277217i	−0.0594652	−	0.0104853i
$700$	32.0047	+	62.6023i	1.20966	+	2.36615i
$701$	2.49533	+	2.97382i	0.0942474	+	0.112320i	0.811107	−	0.584898i	$-0.198866\pi$
$701$	2.49533	+	2.97382i	0.0942474	+	0.112320i	−0.716859	+	0.697218i	$0.754421\pi$
$702$	7.10749	+	2.79414i	0.268255	+	0.105458i
$703$	−4.85573	−	3.75814i	−0.183137	−	0.141741i
$704$	35.5383	+	28.5393i	1.33940	+	1.07561i
$705$	22.1182	−	18.5594i	0.833019	−	0.698986i
$706$	−8.02736	−	7.09229i	−0.302114	−	0.266922i
$707$	21.8171	+	3.84695i	0.820518	+	0.144679i
$708$	−5.07344	+	7.83571i	−0.190672	+	0.294484i
$709$	−1.04990	−	2.88457i	−0.0394298	−	0.108332i	0.918415	−	0.395618i	$-0.129469\pi$
$709$	−1.04990	−	2.88457i	−0.0394298	−	0.108332i	−0.957845	+	0.287285i	$0.907247\pi$
$710$	−27.6053	−	34.6563i	−1.03601	−	1.30063i
$711$	1.12890	+	1.95531i	0.0423370	+	0.0733298i
$712$	−7.23700	+	28.2206i	−0.271218	+	1.05761i
$713$	−2.43177	−	2.04049i	−0.0910704	−	0.0764171i
$714$	−5.04595	+	0.757628i	−0.188840	+	0.0283535i
$715$	102.216	+	59.0142i	3.82264	+	2.20700i
$716$	−6.37219	+	15.0688i	−0.238140	+	0.563149i
$717$	−5.04567	+	0.889688i	−0.188434	+	0.0332260i
$718$	11.5040	−	18.8016i	0.429327	−	0.701668i
$719$	−22.8888	−	8.33085i	−0.853609	−	0.310688i	−0.122098	−	0.992518i	$-0.538962\pi$
$719$	−22.8888	−	8.33085i	−0.853609	−	0.310688i	−0.731511	+	0.681830i	$0.761185\pi$
$720$	11.0091	−	10.6894i	0.410286	−	0.398369i
$721$	−42.5708			−1.58542
$722$	−14.6589	−	22.5193i	−0.545547	−	0.838080i
$723$		−	16.0239i		−	0.595933i
$724$	1.84513	−	36.1469i	0.0685738	−	1.34339i
$725$	9.55215	−	26.2443i	0.354758	−	0.974690i
$726$	25.8880	+	15.8400i	0.960794	+	0.587878i
$727$	2.38159	+	13.5067i	0.0883285	+	0.500936i	0.996589	+	0.0825297i	$0.0262999\pi$
$727$	2.38159	+	13.5067i	0.0883285	+	0.500936i	−0.908260	+	0.418406i	$0.862589\pi$
$728$	−38.6531	+	39.4943i	−1.43258	+	1.46376i
$729$	0.500000	−	0.866025i	0.0185185	−	0.0320750i
$730$	−57.8928	+	8.69235i	−2.14271	+	0.321718i
$731$	−1.97113	+	2.34910i	−0.0729049	+	0.0868847i
$732$	−0.172561	−	1.38978i	−0.00637803	−	0.0513677i
$733$	19.6955	−	11.3712i	0.727469	−	0.420004i	−0.0900265	−	0.995939i	$-0.528695\pi$
$733$	19.6955	−	11.3712i	0.727469	−	0.420004i	0.817496	+	0.575935i	$0.195362\pi$
$734$	20.7248	−	16.5083i	0.764967	−	0.609331i
$735$	−21.9541	+	7.99063i	−0.809788	+	0.294739i
$736$	1.99091	+	0.255231i	0.0733860	+	0.00940795i
$737$	4.82530	−	27.3656i	0.177742	−	1.00803i
$738$	4.50757	+	3.98251i	0.165926	+	0.146598i
$739$	14.1452	+	16.8576i	0.520340	+	0.620117i	0.960661	−	0.277723i	$-0.0895798\pi$
$739$	14.1452	+	16.8576i	0.520340	+	0.620117i	−0.440321	+	0.897840i	$0.645135\pi$
$740$	7.91430	+	7.36013i	0.290936	+	0.270564i
$741$	−14.4071	+	18.6148i	−0.529258	+	0.683831i
$742$	8.69712	−	22.1230i	0.319281	−	0.812161i
$743$	13.2901	−	11.1517i	0.487565	−	0.409116i	−0.365588	−	0.930777i	$-0.619132\pi$
$743$	13.2901	−	11.1517i	0.487565	−	0.409116i	0.853153	+	0.521661i	$0.174688\pi$
$744$	−25.1829	+	2.47665i	−0.923250	+	0.0907985i
$745$	2.93348	−	16.6366i	0.107474	−	0.609517i
$746$	−0.493163	−	0.0999863i	−0.0180560	−	0.00366076i
$747$	−4.63511	−	12.7349i	−0.169590	−	0.465945i
$748$	3.33706	+	10.8622i	0.122015	+	0.397162i
$749$	17.9755	−	10.3781i	0.656810	−	0.379209i
$750$	−12.2248	−	22.4788i	−0.446385	−	0.820808i
$751$	25.8362	+	21.6791i	0.942776	+	0.791083i	0.978066	−	0.208294i	$-0.0667910\pi$
$751$	25.8362	+	21.6791i	0.942776	+	0.791083i	−0.0352899	+	0.999377i	$0.511235\pi$
$752$	24.9132	−	16.9029i	0.908491	−	0.616384i
$753$	−9.88925	+	17.1287i	−0.360384	+	0.624204i
$754$	21.9443	+	0.559713i	0.799165	+	0.0203836i
$755$	12.6337	−	2.22767i	0.459788	−	0.0810731i
$756$	4.36262	+	5.77305i	0.158667	+	0.209964i
$757$	14.7774	−	40.6006i	0.537095	−	1.47566i	−0.313374	−	0.949630i	$-0.601459\pi$
$757$	14.7774	−	40.6006i	0.537095	−	1.47566i	0.850469	−	0.526026i	$-0.176318\pi$
$758$	4.61152	+	13.7513i	0.167498	+	0.499471i
$759$	2.02159			0.0733791
$760$	22.1154	+	41.8069i	0.802208	+	1.51649i
$761$	−15.8911			−0.576051			−0.288025	−	0.957623i	$-0.592999\pi$
$761$	−15.8911			−0.576051			−0.288025	+	0.957623i	$0.592999\pi$
$762$	−3.50180	−	10.4422i	−0.126857	−	0.378280i
$763$	−15.2000	+	41.7617i	−0.550277	+	1.51187i
$764$	−20.6364	+	15.5946i	−0.746598	+	0.564194i
$765$	3.76747	−	0.664307i	0.136213	−	0.0240181i
$766$	−28.0334	−	0.715021i	−1.01289	−	0.0258348i
$767$	−12.6024	+	21.8279i	−0.455045	+	0.788160i
$768$	12.5544	−	9.91897i	0.453020	−	0.357920i
$769$	30.3504	+	25.4670i	1.09446	+	0.918364i	0.997040	−	0.0768795i	$-0.0244957\pi$
$769$	30.3504	+	25.4670i	1.09446	+	0.918364i	0.0974228	+	0.995243i	$0.468940\pi$
$770$	53.4283	+	98.2435i	1.92542	+	3.54045i
$771$	−26.3110	+	15.1906i	−0.947566	+	0.547077i
$772$	−0.376049	+	0.115529i	−0.0135343	+	0.00415796i
$773$	−6.27192	−	17.2320i	−0.225585	−	0.619791i	0.774330	−	0.632782i	$-0.218087\pi$
$773$	−6.27192	−	17.2320i	−0.225585	−	0.619791i	−0.999916	+	0.0129910i	$0.995865\pi$
$774$	4.26205	+	0.864109i	0.153196	+	0.0310598i
$775$	−15.0949	+	85.6074i	−0.542225	+	3.07511i
$776$	−1.12031	−	11.3914i	−0.0402168	−	0.408929i
$777$	−3.90418	+	3.27600i	−0.140062	+	0.117526i
$778$	1.26971	−	3.22978i	0.0455213	−	0.115793i
$779$	−15.6770	+	9.89587i	−0.561687	+	0.354556i
$780$	28.2156	−	30.3401i	1.01028	−	1.08635i
$781$	−29.9089	−	35.6440i	−1.07022	−	1.27544i
$782$	0.375012	+	0.331329i	0.0134104	+	0.0118483i
$783$	0.499127	−	2.83069i	0.0178374	−	0.101161i
$784$	−23.6208	+	5.95757i	−0.843602	+	0.212770i
$785$	76.7515	−	27.9353i	2.73938	−	0.997052i
$786$	0.201221	−	0.160282i	0.00717732	−	0.00571706i
$787$	−34.9513	+	20.1791i	−1.24588	+	0.719308i	−0.970285	−	0.241967i	$-0.922208\pi$
$787$	−34.9513	+	20.1791i	−1.24588	+	0.719308i	−0.275593	+	0.961274i	$0.588874\pi$
$788$	−15.7627	+	1.95716i	−0.561523	+	0.0697210i
$789$	14.0038	−	16.6890i	0.498547	−	0.594145i
$790$	12.1132	−	1.81875i	0.430970	−	0.0647082i
$791$	−15.0169	+	26.0100i	−0.533939	+	0.924810i
$792$	11.2715	−	11.5168i	0.400515	−	0.409232i
$793$	−0.656623	−	3.72389i	−0.0233173	−	0.132239i
$794$	−39.2319	−	24.0047i	−1.39229	−	0.851895i
$795$	−6.09560	+	16.7475i	−0.216189	+	0.593973i
$796$	−32.5495	−	1.66150i	−1.15369	−	0.0588903i
$797$			2.69717i			0.0955387i	0.998858	+	0.0477694i	$0.0152112\pi$
$797$			2.69717i			0.0955387i	−0.998858	+	0.0477694i	$0.984789\pi$
$798$	−20.8494	+	7.92014i	−0.738060	+	0.280370i
$799$	7.50569			0.265532
$800$	−21.2064	−	50.7090i	−0.749761	−	1.79283i
$801$	9.67914	+	3.52292i	0.341996	+	0.124476i
$802$	26.8022	−	43.8040i	0.946419	−	1.54677i
$803$	−60.5448	+	10.6757i	−2.13658	+	0.376736i
$804$	−8.98428	−	3.79920i	−0.316851	−	0.133987i
$805$	4.26502	+	2.46241i	0.150322	+	0.0867886i
$806$	−67.5667	+	10.1448i	−2.37994	+	0.357337i
$807$	−6.15132	−	5.16157i	−0.216537	−	0.181696i
$808$	−16.7760	−	4.30211i	−0.590178	−	0.151348i
$809$	−3.75997	−	6.51245i	−0.132193	−	0.228966i	0.792328	−	0.610095i	$-0.208869\pi$
$809$	−3.75997	−	6.51245i	−0.132193	−	0.228966i	−0.924522	+	0.381129i	$0.875535\pi$
$810$	−3.38016	−	4.24352i	−0.118767	−	0.149102i
$811$	−12.4267	−	34.1421i	−0.436360	−	1.19889i	−0.941843	−	0.336053i	$-0.890908\pi$
$811$	−12.4267	−	34.1421i	−0.436360	−	1.19889i	0.505483	−	0.862837i	$-0.331314\pi$
$812$	17.4589	+	11.3043i	0.612688	+	0.396701i
$813$	8.84342	+	1.55933i	0.310152	+	0.0546882i
$814$	8.50575	+	7.51496i	0.298126	+	0.263399i
$815$	−62.9490	+	52.8205i	−2.20501	+	1.85022i
$816$	3.97845	−	0.289067i	0.139273	−	0.0101194i
$817$	−6.23861	+	11.8635i	−0.218261	+	0.415050i
$818$	−33.2811	−	13.0836i	−1.16365	−	0.457459i
$819$	12.5588	+	14.9670i	0.438839	+	0.522988i
$820$	29.0551	−	14.8541i	1.01465	−	0.518727i
$821$	−23.9358	−	4.22052i	−0.835364	−	0.147297i	−0.260426	−	0.965494i	$-0.583863\pi$
$821$	−23.9358	−	4.22052i	−0.835364	−	0.147297i	−0.574938	+	0.818197i	$0.694974\pi$
$822$	2.67787	+	0.542924i	0.0934013	+	0.0189366i
$823$	27.7640	−	10.1053i	0.967791	−	0.352247i	0.190709	−	0.981647i	$-0.438921\pi$
$823$	27.7640	−	10.1053i	0.967791	−	0.352247i	0.777082	+	0.629399i	$0.216699\pi$
$824$	33.1828	+	2.54350i	1.15598	+	0.0886070i
$825$	−27.6793	−	47.9420i	−0.963670	−	1.66913i
$826$	−20.9797	+	11.4095i	−0.729977	+	0.396988i
$827$	−16.7992	+	20.0205i	−0.584165	+	0.696180i	−0.974473	−	0.224504i	$-0.927924\pi$
$827$	−16.7992	+	20.0205i	−0.584165	+	0.696180i	0.390308	+	0.920684i	$0.372368\pi$
$828$	0.158698	−	0.691682i	0.00551513	−	0.0240376i
$829$	9.81563	+	5.66706i	0.340911	+	0.196825i	0.660675	−	0.750672i	$-0.270270\pi$
$829$	9.81563	+	5.66706i	0.340911	+	0.196825i	−0.319764	+	0.947497i	$0.603604\pi$
$830$	−73.4995	−	1.87468i	−2.55120	−	0.0650712i
$831$	4.46680	+	25.3325i	0.154952	+	0.878775i
$832$	32.4887	−	28.4753i	1.12634	−	0.987204i
$833$	−5.70703	−	2.07719i	−0.197737	−	0.0719703i
$834$	−22.8282	+	7.65545i	−0.790475	+	0.265086i
$835$			35.8910i			1.24206i
$836$	24.3368	+	43.2979i	0.841706	+	1.49749i
$837$			8.94646i			0.309235i
$838$	−4.54877	−	13.5642i	−0.157135	−	0.468568i
$839$	16.1375	+	5.87357i	0.557129	+	0.202778i	0.605211	−	0.796065i	$-0.293089\pi$
$839$	16.1375	+	5.87357i	0.557129	+	0.202778i	−0.0480823	+	0.998843i	$0.515311\pi$
$840$	37.8079	−	10.5681i	1.30450	−	0.364634i
$841$	3.60113	+	20.4230i	0.124177	+	0.704241i
$842$	−0.490758	+	19.2409i	−0.0169127	+	0.663084i
$843$	−20.0245	−	11.5611i	−0.689679	−	0.398186i
$844$	12.8209	+	2.94159i	0.441313	+	0.101254i
$845$	39.8529	−	47.4949i	1.37098	−	1.63387i
$846$	−5.08528	−	9.35076i	−0.174835	−	0.321486i
$847$	38.8221	+	67.2419i	1.33394	+	2.31046i
$848$	−8.10096	+	16.7246i	−0.278188	+	0.574326i
$849$	17.1424	−	6.23932i	0.588326	−	0.214133i
$850$	2.72285	−	13.4299i	0.0933928	−	0.460642i
$851$	0.492235	+	0.0867942i	0.0168736	+	0.00297527i
$852$	−14.5434	+	7.43514i	−0.498248	+	0.254724i
$853$	12.5981	+	15.0138i	0.431350	+	0.514062i	0.937311	−	0.348494i	$-0.113307\pi$
$853$	12.5981	+	15.0138i	0.431350	+	0.514062i	−0.505962	+	0.862556i	$0.668862\pi$
$854$	1.31084	−	3.33441i	0.0448561	−	0.114101i
$855$	15.4753	−	6.33474i	0.529243	−	0.216644i
$856$	−14.6315	+	7.01549i	−0.500093	+	0.239785i
$857$	28.6187	−	24.0140i	0.977598	−	0.820302i	−0.00612744	−	0.999981i	$-0.501950\pi$
$857$	28.6187	−	24.0140i	0.977598	−	0.820302i	0.983725	+	0.179679i	$0.0575060\pi$
$858$	28.8091	−	32.6074i	0.983527	−	1.11320i
$859$	19.8715	+	3.50388i	0.678006	+	0.119551i	0.502039	−	0.864845i	$-0.332584\pi$
$859$	19.8715	+	3.50388i	0.678006	+	0.119551i	0.175968	+	0.984396i	$0.443695\pi$
$860$	12.8228	−	19.8042i	0.437253	−	0.675317i
$861$	5.26301	+	14.4600i	0.179363	+	0.492796i
$862$	27.6932	−	22.0589i	0.943236	−	0.751330i
$863$	10.2476	+	17.7494i	0.348832	+	0.604195i	0.986042	−	0.166495i	$-0.0532449\pi$
$863$	10.2476	+	17.7494i	0.348832	+	0.604195i	−0.637210	+	0.770690i	$0.719912\pi$
$864$	−3.05562	−	4.76059i	−0.103954	−	0.161959i
$865$	−3.66315	−	3.07374i	−0.124551	−	0.104510i
$866$	−0.0431128	−	0.287140i	−0.00146503	−	0.00975741i
$867$	−13.8612	−	8.00276i	−0.470751	−	0.271788i
$868$	−59.6251	−	25.2138i	−2.02381	−	0.855812i
$869$	12.6681	−	2.23373i	0.429737	−	0.0757742i
$870$	−13.3016	−	8.13881i	−0.450967	−	0.275932i
$871$	−24.7497	−	9.00816i	−0.838612	−	0.305230i
$872$	14.3431	−	31.6439i	0.485720	−	1.07160i
$873$	−4.04691			−0.136967
$874$	1.90935	+	1.06708i	0.0645848	+	0.0360945i
$875$		−	65.4623i		−	2.21303i
$876$	−1.10019	+	21.5533i	−0.0371721	+	0.728218i
$877$	−0.506419	+	1.39137i	−0.0171006	+	0.0469834i	−0.947949	−	0.318422i	$-0.896847\pi$
$877$	−0.506419	+	1.39137i	−0.0171006	+	0.0469834i	0.930849	+	0.365405i	$0.119069\pi$
$878$	13.6885	−	22.3718i	0.461966	−	0.755011i
$879$	4.86512	+	27.5915i	0.164096	+	0.930637i
$880$	−35.7761	−	79.7703i	−1.20601	−	2.68906i
$881$	−24.5334	+	42.4930i	−0.826550	+	1.43163i	0.0741792	+	0.997245i	$0.476366\pi$
$881$	−24.5334	+	42.4930i	−0.826550	+	1.43163i	−0.900729	+	0.434381i	$0.856967\pi$
$882$	1.27883	+	8.51729i	0.0430606	+	0.286792i
$883$	6.81061	−	8.11657i	0.229195	−	0.273144i	−0.639174	−	0.769062i	$-0.720724\pi$
$883$	6.81061	−	8.11657i	0.229195	−	0.273144i	0.868370	+	0.495918i	$0.165168\pi$
$884$	10.6884	−	1.32711i	0.359489	−	0.0446357i
$885$	15.5062	−	8.95253i	0.521237	−	0.300936i
$886$	19.4405	+	24.4060i	0.653115	+	0.819934i
$887$	−6.50290	+	2.36686i	−0.218346	+	0.0794714i	−0.448877	−	0.893594i	$-0.648176\pi$
$887$	−6.50290	+	2.36686i	−0.218346	+	0.0794714i	0.230531	+	0.973065i	$0.425954\pi$
$888$	3.23893	−	2.32028i	0.108692	−	0.0778636i
$889$	4.89284	−	27.7487i	0.164101	−	0.930660i
$890$	36.9997	−	41.8779i	1.24023	−	1.40375i
$891$	−3.66222	−	4.36446i	−0.122689	−	0.146215i
$892$	−10.4930	−	9.75823i	−0.351331	−	0.326730i
$893$	32.0589	−	6.96744i	1.07281	−	0.233157i
$894$	−5.79588	−	2.27851i	−0.193843	−	0.0762048i
$895$	24.0397	−	20.1717i	0.803560	−	0.674267i
$896$	40.3394	−	6.94787i	1.34764	−	0.232112i
$897$	0.332732	−	1.88702i	0.0111096	−	0.0630057i
$898$	6.10194	−	30.0966i	0.203624	−	1.00434i
$899$	8.79516	+	24.1645i	0.293335	+	0.805932i
$900$	−18.5761	+	5.70689i	−0.619203	+	0.190230i
$901$	−4.01227	+	2.31649i	−0.133668	+	0.0771733i
$902$	30.1051	−	16.3723i	1.00239	−	0.545136i
$903$	8.52270	+	7.15139i	0.283618	+	0.237983i
$904$	13.2593	−	19.3769i	0.440997	−	0.644465i
$905$	−34.7119	+	60.1227i	−1.15386	+	1.99855i
$906$	0.120586	−	4.72772i	0.00400619	−	0.157068i
$907$	11.2033	−	1.97544i	0.371998	−	0.0655933i	0.0154760	−	0.999880i	$-0.495074\pi$
$907$	11.2033	−	1.97544i	0.371998	−	0.0655933i	0.356522	+	0.934287i	$0.383963\pi$
$908$	16.3187	+	21.5945i	0.541554	+	0.716638i
$909$	−2.09424	+	5.75387i	−0.0694614	+	0.190844i
$910$	100.497	−	33.7019i	3.33145	−	1.11721i
$911$	−3.51817			−0.116562			−0.0582810	−	0.998300i	$-0.518562\pi$
$911$	−3.51817			−0.116562			−0.0582810	+	0.998300i	$0.518562\pi$
$912$	16.7247	−	4.92783i	0.553811	−	0.163177i
$913$	−77.2121			−2.55535
$914$	7.43019	−	2.49172i	0.245769	−	0.0824188i
$915$	−0.918738	+	2.52421i	−0.0303725	+	0.0834478i
$916$	31.3474	+	41.4821i	1.03575	+	1.37061i
$917$	0.648146	−	0.114286i	0.0214037	−	0.00377404i
$918$	0.0359595	−	1.40984i	0.00118684	−	0.0465317i
$919$	−6.32116	+	10.9486i	−0.208516	+	0.361160i	−0.951247	−	0.308430i	$-0.900197\pi$
$919$	−6.32116	+	10.9486i	−0.208516	+	0.361160i	0.742731	+	0.669589i	$0.233530\pi$
$920$	−3.17735	−	2.17421i	−0.104754	−	0.0716815i
$921$	−3.27224	−	2.74574i	−0.107824	−	0.0904751i
$922$	30.3343	−	16.4968i	0.999005	−	0.543295i
$923$	−38.1939	+	22.0513i	−1.25717	+	0.725826i
$924$	39.4089	−	12.1071i	1.29646	−	0.398294i
$925$	−4.68128	−	12.8617i	−0.153919	−	0.422890i
$926$	8.41077	−	41.4845i	0.276395	−	1.36327i
$927$	2.04320	−	11.5875i	0.0671073	−	0.380585i
$928$	−12.9333	−	9.85448i	−0.424558	−	0.323489i
$929$	−21.4671	+	18.0131i	−0.704314	+	0.590989i	−0.922997	−	0.384807i	$-0.874268\pi$
$929$	−21.4671	+	18.0131i	−0.704314	+	0.590989i	0.218684	+	0.975796i	$0.429824\pi$
$930$	45.1712	+	17.7580i	1.48122	+	0.582307i
$931$	−26.3046	−	3.57449i	−0.862097	−	0.117149i
$932$	2.33807	+	2.17435i	0.0765859	+	0.0712232i
$933$	−0.974011	−	1.16078i	−0.0318877	−	0.0380023i
$934$	11.9698	−	13.5480i	0.391665	−	0.443303i
$935$	3.78482	−	21.4648i	0.123777	−	0.701974i
$936$	−8.89498	−	12.4167i	−0.290741	−	0.405852i
$937$	−15.7600	+	5.73619i	−0.514858	+	0.187393i	−0.586365	−	0.810047i	$-0.699441\pi$
$937$	−15.7600	+	5.73619i	−0.514858	+	0.187393i	0.0715068	+	0.997440i	$0.477219\pi$
$938$	−15.5484	−	19.5197i	−0.507672	−	0.637342i
$939$	4.06001	−	2.34405i	0.132494	−	0.0764952i
$940$	−57.3065	+	7.11540i	−1.86913	+	0.232079i
$941$	−31.9750	+	38.1063i	−1.04235	+	1.24223i	−0.0728008	+	0.997347i	$0.523194\pi$
$941$	−31.9750	+	38.1063i	−1.04235	+	1.24223i	−0.969553	+	0.244882i	$0.921251\pi$
$942$	−4.47081	−	29.7765i	−0.145667	−	0.970170i
$943$	0.754567	−	1.30695i	0.0245721	−	0.0425601i
$944$	17.0348	−	7.63992i	0.554435	−	0.248658i
$945$	−2.41015	−	13.6686i	−0.0784022	−	0.444641i
$946$	12.9314	−	21.1344i	0.420437	−	0.687138i
$947$	18.9907	−	52.1766i	0.617116	−	1.69551i	−0.0968197	−	0.995302i	$-0.530867\pi$
$947$	18.9907	−	52.1766i	0.617116	−	1.69551i	0.713936	−	0.700211i	$-0.246911\pi$
$948$	0.230200	−	4.50972i	0.00747655	−	0.146469i
$949$			58.2715i			1.89157i
$950$	−0.836784	−	59.8905i	−0.0271489	−	1.94310i
$951$	−13.2549			−0.429820
$952$	9.29478	+	4.21302i	0.301246	+	0.136545i
$953$	47.1391	+	17.1572i	1.52699	+	0.555778i	0.962881	−	0.269926i	$-0.0869991\pi$
$953$	47.1391	+	17.1572i	1.52699	+	0.555778i	0.564105	+	0.825703i	$0.309221\pi$
$954$	5.60434	+	3.42911i	0.181447	+	0.111021i
$955$	48.8600	−	8.61534i	1.58107	−	0.278786i
$956$	9.43786	+	3.99101i	0.305242	+	0.129078i
$957$	−14.1824	−	8.18819i	−0.458450	−	0.264687i
$958$	8.85530	+	58.9781i	0.286102	+	1.90549i
$959$	5.35485	+	4.49325i	0.172917	+	0.145095i
$960$	−30.1017	+	5.97862i	−0.971527	+	0.192959i
$961$	−24.5196	−	42.4691i	−0.790954	−	1.36997i
$962$	8.41465	−	6.70265i	0.271299	−	0.216102i
$963$	1.96214	+	5.39093i	0.0632290	+	0.173720i
$964$	−17.4179	+	26.9012i	−0.560993	+	0.866428i
$965$	0.743108	+	0.131030i	0.0239215	+	0.00421800i
$966$	1.20208	−	1.36057i	0.0386764	−	0.0437756i
$967$	5.73173	−	4.80949i	0.184320	−	0.154663i	−0.545959	−	0.837812i	$-0.683835\pi$
$967$	5.73173	−	4.80949i	0.184320	−	0.154663i	0.730279	+	0.683149i	$0.239390\pi$
$968$	−26.2432	−	54.7327i	−0.843490	−	1.75918i
$969$	4.14018	+	1.32436i	0.133002	+	0.0425446i
$970$	−8.03279	+	20.4331i	−0.257917	+	0.656068i
$971$	−18.7204	−	22.3101i	−0.600767	−	0.715967i	0.376870	−	0.926266i	$-0.377001\pi$
$971$	−18.7204	−	22.3101i	−0.600767	−	0.715967i	−0.977637	+	0.210300i	$0.932556\pi$
$972$	−1.78078	+	0.910402i	−0.0571185	+	0.0292011i
$973$	−60.6627	−	10.6965i	−1.94476	−	0.342913i
$974$	9.63402	−	47.5179i	0.308694	−	1.52257i
$975$	−49.3063	+	17.9460i	−1.57906	+	0.574732i
$976$	−1.22099	+	2.52076i	−0.0390829	+	0.0806876i
$977$	−26.9513	−	46.6810i	−0.862247	−	1.49346i	−0.869755	−	0.493484i	$-0.835723\pi$
$977$	−26.9513	−	46.6810i	−0.862247	−	1.49346i	0.00750739	−	0.999972i	$-0.497610\pi$
$978$	14.4728	+	26.6125i	0.462791	+	0.850975i
$979$	37.7221	−	44.9554i	1.20560	−	1.43678i
$980$	45.5427	+	10.4492i	1.45481	+	0.333788i
$981$	−10.6378	−	6.14172i	−0.339638	−	0.196090i
$982$	1.12839	−	44.2399i	0.0360082	−	1.41175i
$983$	−2.91498	−	16.5317i	−0.0929734	−	0.527278i	−0.995350	−	0.0963290i	$-0.969290\pi$
$983$	−2.91498	−	16.5317i	−0.0929734	−	0.527278i	0.902376	−	0.430949i	$-0.141821\pi$
$984$	−3.23843	−	11.5856i	−0.103237	−	0.369337i
$985$	28.6293	+	10.4202i	0.912205	+	0.332015i
$986$	−1.28887	−	3.84336i	−0.0410461	−	0.122397i
$987$		−	27.2311i		−	0.866777i
$988$	44.4212	−	15.5904i	1.41323	−	0.495996i
$989$		−	1.09111i		−	0.0346952i
$990$	−29.3057	+	9.82768i	−0.931395	+	0.312344i
$991$	−28.0888	−	10.2235i	−0.892270	−	0.324760i	−0.145119	−	0.989414i	$-0.546357\pi$
$991$	−28.0888	−	10.2235i	−0.892270	−	0.324760i	−0.747151	+	0.664654i	$0.768579\pi$
$992$	44.9697	+	23.2159i	1.42779	+	0.737106i
$993$	0.740988	+	4.20235i	0.0235145	+	0.133358i
$994$	−41.7736	−	1.06548i	−1.32498	−	0.0337950i
$995$	54.1392	+	31.2573i	1.71633	+	0.990923i
$996$	−6.06126	+	26.4179i	−0.192058	+	0.837084i
$997$	−15.5000	+	18.4722i	−0.490890	+	0.585020i	−0.953444	−	0.301571i	$-0.902489\pi$
$997$	−15.5000	+	18.4722i	−0.490890	+	0.585020i	0.462554	+	0.886591i	$0.346933\pi$
$998$	−17.4972	+	9.51563i	−0.553866	+	0.301212i
$999$	−0.704326	−	1.21993i	−0.0222839	−	0.0385968i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.bk.a.253.36	yes	240
8.5	even	2	inner	456.2.bk.a.253.26	✓	240
19.16	even	9	inner	456.2.bk.a.301.26	yes	240
152.149	even	18	inner	456.2.bk.a.301.36	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bk.a.253.26	✓	240	8.5	even	2	inner
456.2.bk.a.253.36	yes	240	1.1	even	1	trivial
456.2.bk.a.301.26	yes	240	19.16	even	9	inner
456.2.bk.a.301.36	yes	240	152.149	even	18	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:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bk (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34083 - 0.449648i) q^{2} +(-0.342020 + 0.939693i) q^{3} +(1.59563 - 1.20580i) q^{4} +(-3.77792 + 0.666150i) q^{5} +(-0.0360593 + 1.41375i) q^{6} +(-1.80901 + 3.13331i) q^{7} +(1.59728 - 2.33424i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(-4.76601 + 2.59193i) q^{10} +(-4.93409 + 2.84870i) q^{11} +(0.587342 + 1.91181i) q^{12} +(1.84697 + 5.07450i) q^{13} +(-1.01669 + 5.01464i) q^{14} +(0.666150 - 3.77792i) q^{15} +(1.09210 - 3.84803i) q^{16} +(0.763925 - 0.641009i) q^{17} +(-1.31616 - 0.517417i) q^{18} +(2.66790 - 3.44707i) q^{19} +(-5.22494 + 5.61835i) q^{20} +(-2.32562 - 2.77157i) q^{21} +(-5.33485 + 6.03822i) q^{22} +(-0.0616151 + 0.349436i) q^{23} +(1.64717 + 2.29931i) q^{24} +(9.13050 - 3.32323i) q^{25} +(4.75820 + 5.97354i) q^{26} +(0.866025 - 0.500000i) q^{27} +(0.891612 + 7.18092i) q^{28} +(1.84760 - 2.20189i) q^{29} +(-0.805543 - 5.36508i) q^{30} +(-4.47323 + 7.74786i) q^{31} +(-0.265945 - 5.65060i) q^{32} +(-0.989343 - 5.61084i) q^{33} +(0.736063 - 1.20298i) q^{34} +(4.74707 - 13.0425i) q^{35} +(-1.99740 - 0.101958i) q^{36} -1.40865i q^{37} +(2.02722 - 5.82154i) q^{38} -5.40017 q^{39} +(-4.47947 + 9.88262i) q^{40} +(-3.99665 - 1.45466i) q^{41} +(-4.36449 - 2.67049i) q^{42} +(-3.02833 + 0.533975i) q^{43} +(-4.43805 + 10.4950i) q^{44} +(3.32225 + 1.91810i) q^{45} +(0.0745081 + 0.496239i) q^{46} +(5.76564 + 4.83795i) q^{47} +(3.24245 + 2.34234i) q^{48} +(-3.04507 - 5.27422i) q^{49} +(10.7481 - 8.56138i) q^{50} +(0.341074 + 0.937093i) q^{51} +(9.06591 + 5.86997i) q^{52} +(-4.57524 - 0.806739i) q^{53} +(0.936366 - 1.05982i) q^{54} +(16.7430 - 14.0490i) q^{55} +(4.42438 + 9.22746i) q^{56} +(2.32671 + 3.68597i) q^{57} +(1.48724 - 3.78312i) q^{58} +(3.00014 + 3.57543i) q^{59} +(-3.49249 - 6.83143i) q^{60} +(-0.689588 - 0.121593i) q^{61} +(-2.51402 + 12.3999i) q^{62} +(3.39984 - 1.23744i) q^{63} +(-2.89737 - 7.45689i) q^{64} +(-10.3581 - 17.9407i) q^{65} +(-3.84944 - 7.07832i) q^{66} +(-3.13505 + 3.73621i) q^{67} +(0.446016 - 1.94396i) q^{68} +(-0.307289 - 0.177414i) q^{69} +(0.500485 - 19.6222i) q^{70} +(1.41816 + 8.04280i) q^{71} +(-2.72401 + 0.761418i) q^{72} +(10.1399 + 3.69063i) q^{73} +(-0.633397 - 1.88876i) q^{74} +9.71647i q^{75} +(0.100510 - 8.71722i) q^{76} -20.6134i q^{77} +(-7.24070 + 2.42817i) q^{78} +(-2.12163 - 0.772211i) q^{79} +(-1.56249 + 15.2651i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-6.01291 - 0.153366i) q^{82} +(11.7365 + 6.77608i) q^{83} +(-7.05281 - 1.61818i) q^{84} +(-2.45904 + 2.93057i) q^{85} +(-3.82036 + 2.07765i) q^{86} +(1.43718 + 2.48927i) q^{87} +(-1.23160 + 16.0675i) q^{88} +(-9.67914 + 3.52292i) q^{89} +(5.31703 + 1.07800i) q^{90} +(-19.2412 - 3.39273i) q^{91} +(0.323035 + 0.631868i) q^{92} +(-5.75067 - 6.85338i) q^{93} +(9.90610 + 3.89435i) q^{94} +(-7.78285 + 14.8000i) q^{95} +(5.40079 + 1.68271i) q^{96} +(3.10012 - 2.60131i) q^{97} +(-6.45445 - 5.70260i) q^{98} +(5.61084 + 0.989343i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48}+ \cdots - 12 q^{98}+O(q^{100}) \) 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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