LMFDB - Embedded newform 475.2.u.b.424.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [475,2,Mod(24,475)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(475, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 16])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("475.24"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.u (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [36,0,0,6,0,-12,0,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			424.6
Character	$\chi$	$=$	475.424
Dual form			475.2.u.b.149.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.47196 + 1.75422i) q^{2} +(-1.13116 + 3.10785i) q^{3} +(-0.563307 + 3.19467i) q^{4} +(-7.11687 + 2.59033i) q^{6} +(2.54534 + 1.46955i) q^{7} +(-2.46697 + 1.42431i) q^{8} +(-6.08105 - 5.10261i) q^{9} +(0.288800 + 0.500217i) q^{11} +(-9.29136 - 5.36437i) q^{12} +(-0.229289 - 0.629967i) q^{13} +(1.16873 + 6.62820i) q^{14} +(-0.0331972 - 0.0120828i) q^{16} +(-0.226198 - 0.269572i) q^{17} -18.1783i q^{18} +(3.86230 - 2.02056i) q^{19} +(-7.44633 + 6.24822i) q^{21} +(-0.452386 + 1.24292i) q^{22} +(4.05820 + 0.715571i) q^{23} +(-1.63598 - 9.27810i) q^{24} +(0.767594 - 1.32951i) q^{26} +(14.1442 - 8.16613i) q^{27} +(-6.12854 + 7.30371i) q^{28} +(-2.30426 - 1.93351i) q^{29} +(-0.148853 + 0.257821i) q^{31} +(1.92090 + 5.27762i) q^{32} +(-1.88128 + 0.331720i) q^{33} +(0.139933 - 0.793600i) q^{34} +(19.7266 - 16.5526i) q^{36} -8.30595i q^{37} +(9.22966 + 3.80111i) q^{38} +2.21721 q^{39} +(-2.51099 - 0.913926i) q^{41} +(-21.9215 - 3.86534i) q^{42} +(-6.49806 + 1.14578i) q^{43} +(-1.76071 + 0.640846i) q^{44} +(4.71826 + 8.17226i) q^{46} +(-7.09153 + 8.45135i) q^{47} +(0.0751029 - 0.0895041i) q^{48} +(0.819160 + 1.41883i) q^{49} +(1.09366 - 0.398058i) q^{51} +(2.14170 - 0.377639i) q^{52} +(4.04421 + 0.713104i) q^{53} +(35.1449 + 12.7917i) q^{54} -8.37237 q^{56} +(1.91071 + 14.2890i) q^{57} -6.88822i q^{58} +(-0.467725 + 0.392468i) q^{59} +(0.178325 - 1.01133i) q^{61} +(-0.671381 + 0.118383i) q^{62} +(-7.97978 - 21.9243i) q^{63} +(-6.46593 + 11.1993i) q^{64} +(-3.35108 - 2.81189i) q^{66} +(2.14429 - 2.55547i) q^{67} +(0.988612 - 0.570776i) q^{68} +(-6.81438 + 11.8028i) q^{69} +(-2.29645 - 13.0238i) q^{71} +(22.2695 + 3.92671i) q^{72} +(-2.44161 + 6.70827i) q^{73} +(14.5704 - 12.2261i) q^{74} +(4.27938 + 13.4770i) q^{76} +1.69763i q^{77} +(3.26364 + 3.88946i) q^{78} +(1.44931 + 0.527504i) q^{79} +(5.24435 + 29.7422i) q^{81} +(-2.09286 - 5.75009i) q^{82} +(11.5342 + 6.65930i) q^{83} +(-15.7664 - 27.3082i) q^{84} +(-11.5749 - 9.71246i) q^{86} +(8.61554 - 4.97418i) q^{87} +(-1.42492 - 0.822680i) q^{88} +(-6.17500 + 2.24752i) q^{89} +(0.342150 - 1.94043i) q^{91} +(-4.57203 + 12.5615i) q^{92} +(-0.632892 - 0.754252i) q^{93} -25.2640 q^{94} -18.5749 q^{96} +(7.84066 + 9.34414i) q^{97} +(-1.28316 + 3.52545i) q^{98} +(0.796200 - 4.51548i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{4} - 12 q^{6} - 6 q^{9} + 24 q^{14} - 6 q^{16} - 42 q^{21} + 30 q^{24} + 6 q^{26} - 30 q^{29} - 36 q^{31} + 24 q^{34} + 150 q^{36} - 72 q^{39} - 60 q^{41} - 84 q^{44} + 18 q^{46} - 18 q^{49}+ \cdots + 186 q^{99}+O(q^{100}) $ 36 * q + 6 * q^4 - 12 * q^6 - 6 * q^9 + 24 * q^14 - 6 * q^16 - 42 * q^21 + 30 * q^24 + 6 * q^26 - 30 * q^29 - 36 * q^31 + 24 * q^34 + 150 * q^36 - 72 * q^39 - 60 * q^41 - 84 * q^44 + 18 * q^46 - 18 * q^49 - 90 * q^51 + 132 * q^54 - 36 * q^59 - 60 * q^61 - 72 * q^64 + 78 * q^66 - 30 * q^69 - 24 * q^71 + 30 * q^74 - 66 * q^76 + 102 * q^79 + 54 * q^81 - 96 * q^84 + 126 * q^86 + 108 * q^89 + 60 * q^91 - 60 * q^94 - 132 * q^96 + 186 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	1.47196	+	1.75422i	1.04084	+	1.24042i	0.970044	+	0.242928i	$0.0781078\pi$
$2$	1.47196	+	1.75422i	1.04084	+	1.24042i	0.0707907	+	0.997491i	$0.477448\pi$
$3$	−1.13116	+	3.10785i	−0.653078	+	1.79432i	−0.0470226	+	0.998894i	$0.514973\pi$
$3$	−1.13116	+	3.10785i	−0.653078	+	1.79432i	−0.606055	+	0.795423i	$0.707249\pi$
$4$	−0.563307	+	3.19467i	−0.281653	+	1.59734i
$5$		0			0
$5$		0			0
$6$	−7.11687	+	2.59033i	−2.90545	+	1.05750i
$7$	2.54534	+	1.46955i	0.962047	+	0.555438i	0.896802	−	0.442431i	$-0.145884\pi$
$7$	2.54534	+	1.46955i	0.962047	+	0.555438i	0.0652445	+	0.997869i	$0.479217\pi$
$8$	−2.46697	+	1.42431i	−0.872206	+	0.503569i
$9$	−6.08105	−	5.10261i	−2.02702	−	1.70087i
$10$		0			0
$11$	0.288800	+	0.500217i	0.0870766	+	0.150821i	0.906274	−	0.422690i	$-0.138914\pi$
$11$	0.288800	+	0.500217i	0.0870766	+	0.150821i	−0.819198	+	0.573511i	$0.805581\pi$
$12$	−9.29136	−	5.36437i	−2.68218	−	1.54856i
$13$	−0.229289	−	0.629967i	−0.0635934	−	0.174721i	0.903826	−	0.427900i	$-0.140746\pi$
$13$	−0.229289	−	0.629967i	−0.0635934	−	0.174721i	−0.967420	+	0.253178i	$0.918524\pi$
$14$	1.16873	+	6.62820i	0.312356	+	1.77146i
$15$		0			0
$16$	−0.0331972	−	0.0120828i	−0.00829929	−	0.00302070i
$17$	−0.226198	−	0.269572i	−0.0548610	−	0.0653808i	0.737916	−	0.674892i	$-0.235810\pi$
$17$	−0.226198	−	0.269572i	−0.0548610	−	0.0653808i	−0.792777	+	0.609512i	$0.791366\pi$
$18$		−	18.1783i		−	4.28467i
$19$	3.86230	−	2.02056i	0.886071	−	0.463549i
$19$	3.86230	−	2.02056i	0.886071	−	0.463549i
$20$		0			0
$21$	−7.44633	+	6.24822i	−1.62492	+	1.36347i
$22$	−0.452386	+	1.24292i	−0.0964489	+	0.264991i
$23$	4.05820	+	0.715571i	0.846194	+	0.149207i	0.579903	−	0.814686i	$-0.303091\pi$
$23$	4.05820	+	0.715571i	0.846194	+	0.149207i	0.266291	+	0.963893i	$0.414202\pi$
$24$	−1.63598	−	9.27810i	−0.333943	−	1.89388i
$25$		0			0
$26$	0.767594	−	1.32951i	0.150538	−	0.260739i
$27$	14.1442	−	8.16613i	2.72204	−	1.57157i
$28$	−6.12854	+	7.30371i	−1.15818	+	1.38027i
$29$	−2.30426	−	1.93351i	−0.427891	−	0.359043i	0.403264	−	0.915083i	$-0.367875\pi$
$29$	−2.30426	−	1.93351i	−0.427891	−	0.359043i	−0.831155	+	0.556041i	$0.812320\pi$
$30$		0			0
$31$	−0.148853	+	0.257821i	−0.0267348	+	0.0463061i	−0.879083	−	0.476668i	$-0.841844\pi$
$31$	−0.148853	+	0.257821i	−0.0267348	+	0.0463061i	0.852348	+	0.522974i	$0.175178\pi$
$32$	1.92090	+	5.27762i	0.339570	+	0.932961i
$33$	−1.88128	+	0.331720i	−0.327488	+	0.0577450i
$34$	0.139933	−	0.793600i	0.0239983	−	0.136101i
$35$		0			0
$36$	19.7266	−	16.5526i	3.28777	−	2.75877i
$37$		−	8.30595i		−	1.36549i	−0.730657	−	0.682745i	$-0.760786\pi$
$37$		−	8.30595i		−	1.36549i	0.730657	−	0.682745i	$-0.239214\pi$
$38$	9.22966	+	3.80111i	1.49725	+	0.616622i
$39$	2.21721			0.355037
$40$		0			0
$41$	−2.51099	−	0.913926i	−0.392151	−	0.142731i	0.138416	−	0.990374i	$-0.455799\pi$
$41$	−2.51099	−	0.913926i	−0.392151	−	0.142731i	−0.530567	+	0.847643i	$0.678021\pi$
$42$	−21.9215	−	3.86534i	−3.38255	−	0.596436i
$43$	−6.49806	+	1.14578i	−0.990945	+	0.174730i	−0.645543	−	0.763724i	$-0.723369\pi$
$43$	−6.49806	+	1.14578i	−0.990945	+	0.174730i	−0.345403	+	0.938455i	$0.612258\pi$
$44$	−1.76071	+	0.640846i	−0.265437	+	0.0966112i
$45$		0			0
$46$	4.71826	+	8.17226i	0.695669	+	1.20493i
$47$	−7.09153	+	8.45135i	−1.03441	+	1.23276i	−0.0623379	+	0.998055i	$0.519856\pi$
$47$	−7.09153	+	8.45135i	−1.03441	+	1.23276i	−0.972068	+	0.234701i	$0.924589\pi$
$48$	0.0751029	−	0.0895041i	0.0108402	−	0.0129188i
$49$	0.819160	+	1.41883i	0.117023	+	0.202690i
$50$		0			0
$51$	1.09366	−	0.398058i	0.153142	−	0.0557393i
$52$	2.14170	−	0.377639i	0.297000	−	0.0523691i
$53$	4.04421	+	0.713104i	0.555515	+	0.0979523i	0.444356	−	0.895850i	$-0.353433\pi$
$53$	4.04421	+	0.713104i	0.555515	+	0.0979523i	0.111159	+	0.993803i	$0.464544\pi$
$54$	35.1449	+	12.7917i	4.78261	+	1.74073i
$55$		0			0
$56$	−8.37237			−1.11880
$57$	1.91071	+	14.2890i	0.253080	+	1.89263i
$58$		−	6.88822i		−	0.904468i
$59$	−0.467725	+	0.392468i	−0.0608926	+	0.0510950i	−0.672726	−	0.739892i	$-0.734877\pi$
$59$	−0.467725	+	0.392468i	−0.0608926	+	0.0510950i	0.611833	+	0.790987i	$0.290432\pi$
$60$		0			0
$61$	0.178325	−	1.01133i	0.0228322	−	0.129488i	−0.971261	−	0.238016i	$-0.923503\pi$
$61$	0.178325	−	1.01133i	0.0228322	−	0.129488i	0.994093	+	0.108529i	$0.0346139\pi$
$62$	−0.671381	+	0.118383i	−0.0852655	+	0.0150346i
$63$	−7.97978	−	21.9243i	−1.00536	−	2.76220i
$64$	−6.46593	+	11.1993i	−0.808242	+	1.39992i
$65$		0			0
$66$	−3.35108	−	2.81189i	−0.412489	−	0.346120i
$67$	2.14429	−	2.55547i	0.261967	−	0.312200i	−0.618988	−	0.785401i	$-0.712457\pi$
$67$	2.14429	−	2.55547i	0.261967	−	0.312200i	0.880955	+	0.473201i	$0.156901\pi$
$68$	0.988612	−	0.570776i	0.119887	−	0.0692167i
$69$	−6.81438	+	11.8028i	−0.820355	+	1.42090i
$70$		0			0
$71$	−2.29645	−	13.0238i	−0.272538	−	1.54564i	−0.746675	−	0.665189i	$-0.768351\pi$
$71$	−2.29645	−	13.0238i	−0.272538	−	1.54564i	0.474137	−	0.880451i	$-0.342760\pi$
$72$	22.2695	+	3.92671i	2.62448	+	0.462767i
$73$	−2.44161	+	6.70827i	−0.285769	+	0.785143i	0.710878	+	0.703316i	$0.248298\pi$
$73$	−2.44161	+	6.70827i	−0.285769	+	0.785143i	−0.996647	+	0.0818275i	$0.973924\pi$
$74$	14.5704	−	12.2261i	1.69378	−	1.42125i
$75$		0			0
$76$	4.27938	+	13.4770i	0.490878	+	1.54591i
$77$			1.69763i			0.193463i
$78$	3.26364	+	3.88946i	0.369535	+	0.440395i
$79$	1.44931	+	0.527504i	0.163060	+	0.0593489i	0.422260	−	0.906475i	$-0.361237\pi$
$79$	1.44931	+	0.527504i	0.163060	+	0.0593489i	−0.259201	+	0.965824i	$0.583459\pi$
$80$		0			0
$81$	5.24435	+	29.7422i	0.582706	+	3.30469i
$82$	−2.09286	−	5.75009i	−0.231118	−	0.634991i
$83$	11.5342	+	6.65930i	1.26605	+	0.730953i	0.974238	−	0.225524i	$-0.0724093\pi$
$83$	11.5342	+	6.65930i	1.26605	+	0.730953i	0.291809	+	0.956476i	$0.405743\pi$
$84$	−15.7664	−	27.3082i	−1.72026	−	2.97957i
$85$		0			0
$86$	−11.5749	−	9.71246i	−1.24815	−	1.04732i
$87$	8.61554	−	4.97418i	0.923683	−	0.533288i
$88$	−1.42492	−	0.822680i	−0.151897	−	0.0876980i
$89$	−6.17500	+	2.24752i	−0.654549	+	0.238236i	−0.647881	−	0.761741i	$-0.724345\pi$
$89$	−6.17500	+	2.24752i	−0.654549	+	0.238236i	−0.00666773	+	0.999978i	$0.502122\pi$
$90$		0			0
$91$	0.342150	−	1.94043i	0.0358671	−	0.203412i
$92$	−4.57203	+	12.5615i	−0.476667	+	1.30963i
$93$	−0.632892	−	0.754252i	−0.0656279	−	0.0782123i
$94$	−25.2640			−2.60578
$95$		0			0
$96$	−18.5749			−1.89579
$97$	7.84066	+	9.34414i	0.796099	+	0.948754i	0.999540	−	0.0303336i	$-0.00965696\pi$
$97$	7.84066	+	9.34414i	0.796099	+	0.948754i	−0.203441	+	0.979087i	$0.565213\pi$
$98$	−1.28316	+	3.52545i	−0.129618	+	0.356124i
$99$	0.796200	−	4.51548i	0.0800211	−	0.453822i
$100$		0			0
$101$	0.545793	−	0.198653i	0.0543085	−	0.0197667i	−0.314723	−	0.949184i	$-0.601912\pi$
$101$	0.545793	−	0.198653i	0.0543085	−	0.0197667i	0.369032	+	0.929417i	$0.379689\pi$
$102$	2.30810	+	1.33258i	0.228536	+	0.131945i
$103$	5.60414	−	3.23555i	0.552193	−	0.318809i	−0.197813	−	0.980240i	$-0.563384\pi$
$103$	5.60414	−	3.23555i	0.552193	−	0.318809i	0.750006	+	0.661431i	$0.230051\pi$
$104$	1.46292	+	1.22753i	0.143451	+	0.120370i
$105$		0			0
$106$	4.70199	+	8.14409i	0.456698	+	0.791024i
$107$	−15.9165	−	9.18942i	−1.53871	−	0.888374i	−0.998915	−	0.0465776i	$-0.985169\pi$
$107$	−15.9165	−	9.18942i	−1.53871	−	0.888374i	−0.539795	−	0.841797i	$-0.681498\pi$
$108$	18.1206	+	49.7860i	1.74366	+	4.79066i
$109$	0.435803	+	2.47156i	0.0417424	+	0.236733i	0.998540	−	0.0540230i	$-0.0172044\pi$
$109$	0.435803	+	2.47156i	0.0417424	+	0.236733i	−0.956797	+	0.290756i	$0.906093\pi$
$110$		0			0
$111$	25.8136	+	9.39539i	2.45012	+	0.891771i
$112$	−0.0667417	−	0.0795397i	−0.00630650	−	0.00751579i
$113$			11.3386i			1.06665i	0.845911	+	0.533325i	$0.179058\pi$
$113$			11.3386i			1.06665i	−0.845911	+	0.533325i	$0.820942\pi$
$114$	−22.2535	+	24.3847i	−2.08423	+	2.28384i
$115$		0			0
$116$	7.47492	−	6.27220i	0.694029	−	0.582359i
$117$	−1.82015	+	5.00083i	−0.168273	+	0.462327i
$118$	−1.37695	−	0.242793i	−0.126758	−	0.0223509i
$119$	−0.179600	−	1.01856i	−0.0164639	−	0.0933713i
$120$		0			0
$121$	5.33319	−	9.23735i	0.484835	−	0.839759i
$122$	2.03658	−	1.17582i	0.184383	−	0.106454i
$123$	5.68068	−	6.76997i	0.512210	−	0.610428i
$124$	−0.739805	−	0.620770i	−0.0664364	−	0.0557468i
$125$		0			0
$126$	26.7140	−	46.2700i	2.37987	−	4.12206i
$127$	−6.56408	−	18.0347i	−0.582468	−	1.60032i	−0.783949	−	0.620826i	$-0.786797\pi$
$127$	−6.56408	−	18.0347i	−0.582468	−	1.60032i	0.201480	−	0.979493i	$-0.435425\pi$
$128$	−18.1017	+	3.19181i	−1.59998	+	0.282119i
$129$	3.78945	−	21.4911i	0.333643	−	1.89218i
$130$		0			0
$131$	−5.24756	+	4.40322i	−0.458481	+	0.384711i	−0.842572	−	0.538584i	$-0.818959\pi$
$131$	−5.24756	+	4.40322i	−0.458481	+	0.384711i	0.384091	+	0.923295i	$0.374515\pi$
$132$		−	6.19692i		−	0.539373i
$133$	12.8002	+	0.532827i	1.10991	+	0.0462019i
$134$	7.63916			0.659923
$135$		0			0
$136$	0.941977	+	0.342852i	0.0807738	+	0.0293993i
$137$	13.0406	+	2.29941i	1.11413	+	0.196452i	0.700264	−	0.713884i	$-0.253066\pi$
$137$	13.0406	+	2.29941i	1.11413	+	0.196452i	0.413870	+	0.910336i	$0.364177\pi$
$138$	−30.7353	+	5.41946i	−2.61636	+	0.461335i
$139$	2.73439	−	0.995237i	0.231928	−	0.0844149i	−0.223442	−	0.974717i	$-0.571729\pi$
$139$	2.73439	−	0.995237i	0.231928	−	0.0844149i	0.455370	+	0.890302i	$0.349507\pi$
$140$		0			0
$141$	−18.2438	−	31.5992i	−1.53641	−	2.66114i
$142$	19.4663	−	23.1990i	1.63357	−	1.94682i
$143$	0.248901	−	0.296629i	0.0208142	−	0.0248054i
$144$	0.140220	+	0.242868i	0.0116850	+	0.0202390i
$145$		0			0
$146$	−15.3617	+	5.59121i	−1.27134	+	0.462732i
$147$	−5.33610	+	0.940899i	−0.440114	+	0.0776040i
$148$	26.5348	+	4.67880i	2.18115	+	0.384595i
$149$	−8.32247	−	3.02913i	−0.681804	−	0.248156i	−0.0221819	−	0.999754i	$-0.507061\pi$
$149$	−8.32247	−	3.02913i	−0.681804	−	0.248156i	−0.659622	+	0.751598i	$0.729284\pi$
$150$		0			0
$151$	8.37160			0.681271			0.340636	−	0.940195i	$-0.389358\pi$
$151$	8.37160			0.681271			0.340636	+	0.940195i	$0.389358\pi$
$152$	−6.65027	+	10.4858i	−0.539408	+	0.850508i
$153$			2.79348i			0.225839i
$154$	−2.97801	+	2.49884i	−0.239975	+	0.201363i
$155$		0			0
$156$	−1.24897	+	7.08324i	−0.0999973	+	0.567113i
$157$	15.6255	−	2.75519i	1.24705	−	0.219888i	0.489115	−	0.872219i	$-0.337320\pi$
$157$	15.6255	−	2.75519i	1.24705	−	0.219888i	0.757934	+	0.652331i	$0.226209\pi$
$158$	1.20797	+	3.31887i	0.0961008	+	0.264035i
$159$	−6.79088	+	11.7622i	−0.538552	+	0.932799i
$160$		0			0
$161$	9.27793	+	7.78511i	0.731203	+	0.613552i
$162$	−44.4548	+	52.9791i	−3.49270	+	4.16243i
$163$	−8.42002	+	4.86130i	−0.659507	+	0.380766i	−0.792089	−	0.610406i	$-0.791006\pi$
$163$	−8.42002	+	4.86130i	−0.659507	+	0.380766i	0.132582	+	0.991172i	$0.457673\pi$
$164$	4.33415	−	7.50697i	0.338440	−	0.586195i
$165$		0			0
$166$	5.29612	+	30.0358i	0.411059	+	2.33123i
$167$	0.277863	+	0.0489947i	0.0215017	+	0.00379132i	0.184389	−	0.982853i	$-0.440969\pi$
$167$	0.277863	+	0.0489947i	0.0215017	+	0.00379132i	−0.162887	+	0.986645i	$0.552081\pi$
$168$	9.47052	−	26.0200i	0.730666	−	2.00749i
$169$	9.61429	−	8.06735i	0.739561	−	0.620565i
$170$		0			0
$171$	−33.7969	−	7.42063i	−2.58452	−	0.567470i
$172$		−	21.4046i		−	1.63208i
$173$	−9.72470	−	11.5894i	−0.739355	−	0.881129i	0.257002	−	0.966411i	$-0.417265\pi$
$173$	−9.72470	−	11.5894i	−0.739355	−	0.881129i	−0.996357	+	0.0852817i	$0.972821\pi$
$174$	21.4075	+	7.79171i	1.62290	+	0.590688i
$175$		0			0
$176$	−0.00354334	−	0.0200953i	−0.000267089	−	0.00151474i
$177$	−0.690657	−	1.89756i	−0.0519129	−	0.142630i
$178$	−13.0320	−	7.52403i	−0.976790	−	0.563950i
$179$	−7.22664	−	12.5169i	−0.540145	−	0.935558i	−0.998895	−	0.0469929i	$-0.985036\pi$
$179$	−7.22664	−	12.5169i	−0.540145	−	0.935558i	0.458751	−	0.888565i	$-0.348297\pi$
$180$		0			0
$181$	−5.33540	−	4.47693i	−0.396577	−	0.332768i	0.422592	−	0.906320i	$-0.361120\pi$
$181$	−5.33540	−	4.47693i	−0.396577	−	0.332768i	−0.819169	+	0.573552i	$0.805565\pi$
$182$	3.90757	−	2.25604i	0.289648	−	0.167229i
$183$	2.94135	+	1.69819i	0.217431	+	0.125534i
$184$	−11.0307	+	4.01483i	−0.813192	+	0.295978i
$185$		0			0
$186$	0.391527	−	2.22046i	0.0287082	−	0.162812i
$187$	0.0695184	−	0.191000i	0.00508369	−	0.0139673i
$188$	−23.0046	−	27.4158i	−1.67778	−	1.99950i
$189$	48.0022			3.49165
$190$		0			0
$191$	5.49050			0.397279			0.198639	−	0.980073i	$-0.436348\pi$
$191$	5.49050			0.397279			0.198639	+	0.980073i	$0.436348\pi$
$192$	−27.4918	−	32.7634i	−1.98405	−	2.36450i
$193$	2.21521	−	6.08625i	0.159455	−	0.438098i	−0.834078	−	0.551647i	$-0.814000\pi$
$193$	2.21521	−	6.08625i	0.159455	−	0.438098i	0.993532	+	0.113549i	$0.0362219\pi$
$194$	−4.85048	+	27.5085i	−0.348244	+	1.97499i
$195$		0			0
$196$	−4.99412	+	1.81771i	−0.356723	+	0.129837i
$197$	8.04931	+	4.64727i	0.573490	+	0.331104i	0.758542	−	0.651624i	$-0.225912\pi$
$197$	8.04931	+	4.64727i	0.573490	+	0.331104i	−0.185052	+	0.982729i	$0.559245\pi$
$198$	9.09310	−	5.24991i	0.646219	−	0.373095i
$199$	18.6201	+	15.6242i	1.31995	+	1.10757i	0.986317	+	0.164863i	$0.0527181\pi$
$199$	18.6201	+	15.6242i	1.31995	+	1.10757i	0.333630	+	0.942704i	$0.391726\pi$
$200$		0			0
$201$	5.51646	+	9.55478i	0.389101	+	0.673942i
$202$	1.15187	+	0.665031i	0.0810451	+	0.0467914i
$203$	−3.02374	−	8.30765i	−0.212225	−	0.583083i
$204$	0.655601	+	3.71810i	0.0459012	+	0.260319i
$205$		0			0
$206$	13.9250	+	5.06827i	0.970198	+	0.353123i
$207$	−21.0269	−	25.0588i	−1.46147	−	1.74171i
$208$			0.0236836i			0.00164216i
$209$	2.12615	+	1.34845i	0.147069	+	0.0932739i
$210$		0			0
$211$	18.3601	−	15.4060i	1.26396	−	1.06059i	0.268715	−	0.963220i	$-0.413401\pi$
$211$	18.3601	−	15.4060i	1.26396	−	1.06059i	0.995248	−	0.0973716i	$-0.0310435\pi$
$212$	−4.55626	+	12.5182i	−0.312925	+	0.859755i
$213$	43.0736	+	7.59504i	2.95136	+	0.520404i
$214$	−7.30832	−	41.4475i	−0.499586	−	2.83330i
$215$		0			0
$216$	−23.2622	+	40.2913i	−1.58279	+	2.74147i
$217$	−0.757764	+	0.437495i	−0.0514403	+	0.0296991i
$218$	−3.69417	+	4.40254i	−0.250201	+	0.298178i
$219$	−18.0864	−	15.1763i	−1.22217	−	1.02552i
$220$		0			0
$221$	−0.117957	+	0.204307i	−0.00793463	+	0.0137432i
$222$	21.5152	+	59.1124i	1.44400	+	3.96736i
$223$	20.2565	−	3.57177i	1.35648	−	0.239183i	0.552336	−	0.833622i	$-0.313737\pi$
$223$	20.2565	−	3.57177i	1.35648	−	0.239183i	0.804141	+	0.594438i	$0.202626\pi$
$224$	−2.86640	+	16.2562i	−0.191520	+	1.08616i
$225$		0			0
$226$	−19.8904	+	16.6901i	−1.32309	+	1.11021i
$227$			12.6949i			0.842593i	0.906923	+	0.421297i	$0.138425\pi$
$227$			12.6949i			0.842593i	−0.906923	+	0.421297i	$0.861575\pi$
$228$	−46.7250	−	1.94500i	−3.09444	−	0.128811i
$229$	−5.76019			−0.380644			−0.190322	−	0.981722i	$-0.560953\pi$
$229$	−5.76019			−0.380644			−0.190322	+	0.981722i	$0.560953\pi$
$230$		0			0
$231$	−5.27596	−	1.92029i	−0.347133	−	0.126346i
$232$	8.43845	+	1.48793i	0.554012	+	0.0976872i
$233$	−2.73631	+	0.482485i	−0.179262	+	0.0316087i	−0.262558	−	0.964916i	$-0.584566\pi$
$233$	−2.73631	+	0.482485i	−0.179262	+	0.0316087i	0.0832967	+	0.996525i	$0.473455\pi$
$234$	−11.4517	+	4.16810i	−0.748624	+	0.272477i
$235$		0			0
$236$	−0.990333	−	1.71531i	−0.0644652	−	0.111657i
$237$	−3.27881	+	3.90753i	−0.212981	+	0.253821i
$238$	1.52241	−	1.81434i	0.0986834	−	0.117606i
$239$	9.72936	+	16.8518i	0.629340	+	1.09005i	0.987684	+	0.156460i	$0.0500081\pi$
$239$	9.72936	+	16.8518i	0.629340	+	1.09005i	−0.358344	+	0.933590i	$0.616659\pi$
$240$		0			0
$241$	6.80304	−	2.47610i	0.438222	−	0.159500i	−0.113481	−	0.993540i	$-0.536200\pi$
$241$	6.80304	−	2.47610i	0.438222	−	0.159500i	0.551704	+	0.834040i	$0.313978\pi$
$242$	24.0546	−	4.24147i	1.54629	−	0.272652i
$243$	−50.1140	−	8.83644i	−3.21481	−	0.566858i
$244$	3.13042	+	1.13938i	0.200404	+	0.0729412i
$245$		0			0
$246$	20.2378			1.29031
$247$	−2.15847	−	1.96983i	−0.137340	−	0.125337i
$248$		−	0.848051i		−	0.0538513i
$249$	−33.7432	+	28.3139i	−2.13839	+	1.79432i
$250$		0			0
$251$	2.57969	−	14.6301i	0.162829	−	0.923446i	−0.788447	−	0.615103i	$-0.789114\pi$
$251$	2.57969	−	14.6301i	0.162829	−	0.923446i	0.951275	−	0.308343i	$-0.0997745\pi$
$252$	74.5359	−	13.1427i	4.69532	−	0.827911i
$253$	0.814070	+	2.23664i	0.0511801	+	0.140616i
$254$	21.9746	−	38.0612i	1.37881	−	2.38817i
$255$		0			0
$256$	−12.4313	−	10.4311i	−0.776958	−	0.651946i
$257$	−12.6988	+	15.1338i	−0.792128	+	0.944021i	−0.999413	−	0.0342591i	$-0.989093\pi$
$257$	−12.6988	+	15.1338i	−0.792128	+	0.944021i	0.207285	+	0.978281i	$0.433537\pi$
$258$	43.2779	−	24.9865i	2.69436	−	1.55559i
$259$	12.2060	−	21.1414i	0.758445	−	1.31367i
$260$		0			0
$261$	4.14641	+	23.5155i	0.256657	+	1.45557i
$262$	−15.4484	−	2.72397i	−0.954407	−	0.168288i
$263$	−4.05337	+	11.1365i	−0.249942	+	0.686709i	0.749746	+	0.661725i	$0.230176\pi$
$263$	−4.05337	+	11.1365i	−0.249942	+	0.686709i	−0.999688	+	0.0249835i	$0.992047\pi$
$264$	4.16859	−	3.49786i	0.256559	−	0.215278i
$265$		0			0
$266$	17.9067	+	23.2386i	1.09793	+	1.42485i
$267$		−	21.7333i		−	1.33005i
$268$	6.95598	+	8.28982i	0.424904	+	0.506381i
$269$	−10.2199	−	3.71975i	−0.623120	−	0.226797i	0.0111138	−	0.999938i	$-0.496462\pi$
$269$	−10.2199	−	3.71975i	−0.623120	−	0.226797i	−0.634234	+	0.773141i	$0.718685\pi$
$270$		0			0
$271$	−1.01974	−	5.78324i	−0.0619448	−	0.351307i	−0.999989	−	0.00478962i	$-0.998475\pi$
$271$	−1.01974	−	5.78324i	−0.0619448	−	0.351307i	0.938044	−	0.346517i	$-0.112636\pi$
$272$	0.00425195	+	0.0116821i	0.000257812	+	0.000708333i
$273$	5.64353	+	3.25830i	0.341562	+	0.197201i
$274$	15.1616	+	26.2607i	0.915947	+	1.58647i
$275$		0			0
$276$	−33.8676	−	28.4183i	−2.03859	−	1.71058i
$277$	−20.6224	+	11.9064i	−1.23908	+	0.715385i	−0.968907	−	0.247426i	$-0.920415\pi$
$277$	−20.6224	+	11.9064i	−1.23908	+	0.715385i	−0.270176	+	0.962811i	$0.587082\pi$
$278$	5.77079	+	3.33176i	0.346109	+	0.199826i
$279$	2.22075	−	0.808285i	0.132953	−	0.0483908i
$280$		0			0
$281$	−1.23971	+	7.03074i	−0.0739549	+	0.419419i	0.925243	+	0.379375i	$0.123861\pi$
$281$	−1.23971	+	7.03074i	−0.0739549	+	0.419419i	−0.999198	+	0.0400440i	$0.987250\pi$
$282$	28.5777	−	78.5166i	1.70178	−	4.67559i
$283$	−17.1844	−	20.4796i	−1.02151	−	1.21739i	−0.975853	−	0.218428i	$-0.929907\pi$
$283$	−17.1844	−	20.4796i	−1.02151	−	1.21739i	−0.0456547	−	0.998957i	$-0.514537\pi$
$284$	42.9003			2.54567
$285$		0			0
$286$	0.886725			0.0524332
$287$	−5.04825	−	6.01628i	−0.297989	−	0.355130i
$288$	15.2486	−	41.8951i	0.898530	−	2.46869i
$289$	2.93052	−	16.6198i	0.172383	−	0.977634i
$290$		0			0
$291$	−37.9092	+	13.7978i	−2.22228	+	0.808843i
$292$	−20.0553	−	11.5789i	−1.17365	−	0.677607i
$293$	−0.929566	+	0.536685i	−0.0543058	+	0.0313535i	−0.526907	−	0.849923i	$-0.676648\pi$
$293$	−0.929566	+	0.536685i	−0.0543058	+	0.0313535i	0.472601	+	0.881276i	$0.343315\pi$
$294$	−9.50508	−	7.97571i	−0.554348	−	0.465153i
$295$		0			0
$296$	11.8302	+	20.4906i	0.687618	+	1.19099i
$297$	8.16967	+	4.71676i	0.474053	+	0.273694i
$298$	−6.93662	−	19.0582i	−0.401827	−	1.10401i
$299$	−0.479716	−	2.72061i	−0.0277427	−	0.157337i
$300$		0			0
$301$	−18.2235	−	6.63283i	−1.05039	−	0.382310i
$302$	12.3227	+	14.6856i	0.709091	+	0.845062i
$303$			1.92095i			0.110356i
$304$	−0.152631	+	0.0204097i	−0.00875400	+	0.00117058i
$305$		0			0
$306$	−4.90037	+	4.11190i	−0.280135	+	0.235062i
$307$	−8.88231	+	24.4039i	−0.506940	+	1.39281i	0.377438	+	0.926035i	$0.376805\pi$
$307$	−8.88231	+	24.4039i	−0.506940	+	1.39281i	−0.884378	+	0.466772i	$0.845417\pi$
$308$	−5.42336	−	0.956284i	−0.309025	−	0.0544894i
$309$	3.71640	+	21.0768i	0.211419	+	1.19901i
$310$		0			0
$311$	−9.52546	+	16.4986i	−0.540139	+	0.935548i	0.458756	+	0.888562i	$0.348295\pi$
$311$	−9.52546	+	16.4986i	−0.540139	+	0.935548i	−0.998896	+	0.0469862i	$0.985038\pi$
$312$	−5.46978	+	3.15798i	−0.309666	+	0.178785i
$313$	−9.89844	+	11.7965i	−0.559493	+	0.666777i	−0.969439	−	0.245332i	$-0.921103\pi$
$313$	−9.89844	+	11.7965i	−0.559493	+	0.666777i	0.409946	+	0.912110i	$0.365547\pi$
$314$	27.8333	+	23.3549i	1.57073	+	1.31800i
$315$		0			0
$316$	−2.50161	+	4.33291i	−0.140726	+	0.243745i
$317$	−8.73532	−	24.0001i	−0.490624	−	1.34798i	−0.900110	−	0.435663i	$-0.856514\pi$
$317$	−8.73532	−	24.0001i	−0.490624	−	1.34798i	0.409485	−	0.912317i	$-0.365708\pi$
$318$	−30.6293	+	5.40077i	−1.71761	+	0.302860i
$319$	0.301700	−	1.71103i	0.0168920	−	0.0957991i
$320$		0			0
$321$	46.5635	−	39.0714i	2.59892	−	2.18075i
$322$			27.7349i			1.54560i
$323$	−1.41833	−	0.584120i	−0.0789180	−	0.0325013i
$324$	−97.9707			−5.44282
$325$		0			0
$326$	−20.9217	−	7.61489i	−1.15875	−	0.421750i
$327$	−8.17420	−	1.44133i	−0.452034	−	0.0797058i
$328$	7.49625	−	1.32179i	0.413911	−	0.0729837i
$329$	−30.4700	+	11.0902i	−1.67987	+	0.611421i
$330$		0			0
$331$	−2.26589	−	3.92464i	−0.124545	−	0.215718i	0.797010	−	0.603966i	$-0.206414\pi$
$331$	−2.26589	−	3.92464i	−0.124545	−	0.215718i	−0.921555	+	0.388248i	$0.873080\pi$
$332$	−27.7716	+	33.0969i	−1.52416	+	1.81643i
$333$	−42.3820	+	50.5089i	−2.32252	+	2.76787i
$334$	0.323056	+	0.559550i	0.0176768	+	0.0306172i
$335$		0			0
$336$	0.322693	−	0.117451i	0.0176043	−	0.00640746i
$337$	−20.0306	+	3.53193i	−1.09114	+	0.192397i	−0.690135	−	0.723681i	$-0.742449\pi$
$337$	−20.0306	+	3.53193i	−1.09114	+	0.192397i	−0.401001	+	0.916078i	$0.631338\pi$
$338$	28.3038	+	4.99072i	1.53952	+	0.271459i
$339$	−35.2388	−	12.8259i	−1.91391	−	0.696605i
$340$		0			0
$341$	−0.171955			−0.00931191
$342$	−36.7305	−	70.2101i	−1.98616	−	3.79653i
$343$		−	15.7585i		−	0.850880i
$344$	14.3986	−	12.0819i	0.776320	−	0.651410i
$345$		0			0
$346$	6.01601	−	34.1185i	0.323423	−	1.83422i
$347$	−26.8521	+	4.73475i	−1.44150	+	0.254175i	−0.839080	−	0.544008i	$-0.816906\pi$
$347$	−26.8521	+	4.73475i	−1.44150	+	0.254175i	−0.602416	+	0.798182i	$0.705795\pi$
$348$	11.0377	+	30.3258i	0.591682	+	1.62563i
$349$	6.31115	−	10.9312i	0.337828	−	0.585135i	−0.646196	−	0.763171i	$-0.723641\pi$
$349$	6.31115	−	10.9312i	0.337828	−	0.585135i	0.984024	+	0.178036i	$0.0569745\pi$
$350$		0			0
$351$	−8.38750	−	7.03795i	−0.447692	−	0.375658i
$352$	−2.08520	+	2.48504i	−0.111142	+	0.132453i
$353$	−26.6728	+	15.3996i	−1.41965	+	0.819636i	−0.996268	−	0.0863140i	$-0.972491\pi$
$353$	−26.6728	+	15.3996i	−1.41965	+	0.819636i	−0.423384	+	0.905950i	$0.639158\pi$
$354$	2.31212	−	4.00471i	0.122888	−	0.212848i
$355$		0			0
$356$	−3.70166	−	20.9931i	−0.196187	−	1.11263i
$357$	3.36869	+	0.593991i	0.178290	+	0.0314373i
$358$	11.3200	−	31.1015i	0.598282	−	1.64377i
$359$	13.2039	−	11.0794i	0.696877	−	0.584749i	−0.224007	−	0.974588i	$-0.571914\pi$
$359$	13.2039	−	11.0794i	0.696877	−	0.584749i	0.920883	+	0.389839i	$0.127469\pi$
$360$		0			0
$361$	10.8347	−	15.6080i	0.570245	−	0.821475i
$362$		−	15.9493i		−	0.838278i
$363$	22.6756	+	27.0237i	1.19016	+	1.41838i
$364$	6.00630	+	2.18612i	0.314816	+	0.114584i
$365$		0			0
$366$	1.35056	+	7.65943i	0.0705951	+	0.400365i
$367$	10.2927	+	28.2788i	0.537272	+	1.47614i	0.850248	+	0.526383i	$0.176452\pi$
$367$	10.2927	+	28.2788i	0.537272	+	1.47614i	−0.312975	+	0.949761i	$0.601326\pi$
$368$	−0.126075	−	0.0727893i	−0.00657210	−	0.00379440i
$369$	10.6061	+	18.3702i	0.552129	+	0.956315i
$370$		0			0
$371$	9.24594	+	7.75826i	0.480025	+	0.402789i
$372$	2.76610	−	1.59701i	0.143416	−	0.0828010i
$373$	−5.31178	−	3.06676i	−0.275034	−	0.158791i	0.356139	−	0.934433i	$-0.384093\pi$
$373$	−5.31178	−	3.06676i	−0.275034	−	0.158791i	−0.631173	+	0.775642i	$0.717426\pi$
$374$	0.437385	−	0.159195i	0.0226166	−	0.00823178i
$375$		0			0
$376$	5.45728	−	30.9498i	0.281438	−	1.59611i
$377$	−0.689702	+	1.89494i	−0.0355215	+	0.0975944i
$378$	70.6575	+	84.2063i	3.63423	+	4.33110i
$379$	−30.8958			−1.58701			−0.793505	−	0.608564i	$-0.791746\pi$
$379$	−30.8958			−1.58701			−0.793505	+	0.608564i	$0.791746\pi$
$380$		0			0
$381$	63.4741			3.25187
$382$	8.08181	+	9.63153i	0.413501	+	0.492792i
$383$	−1.59079	+	4.37066i	−0.0812855	+	0.223330i	−0.973677	−	0.227932i	$-0.926804\pi$
$383$	−1.59079	+	4.37066i	−0.0812855	+	0.223330i	0.892392	+	0.451262i	$0.149026\pi$
$384$	10.5563	−	59.8677i	0.538698	−	3.05511i
$385$		0			0
$386$	13.9373	−	5.07277i	0.709391	−	0.258197i
$387$	45.3615	+	26.1895i	2.30586	+	1.33129i
$388$	−34.2681	+	19.7847i	−1.73970	+	1.00442i
$389$	12.3923	+	10.3984i	0.628315	+	0.527219i	0.900405	−	0.435053i	$-0.143270\pi$
$389$	12.3923	+	10.3984i	0.628315	+	0.527219i	−0.272090	+	0.962272i	$0.587715\pi$
$390$		0			0
$391$	−0.725059	−	1.25584i	−0.0366678	−	0.0635105i
$392$	−4.04169	−	2.33347i	−0.204136	−	0.117858i
$393$	−7.74870	−	21.2894i	−0.390870	−	1.07391i
$394$	3.69596	+	20.9609i	0.186200	+	1.05599i
$395$		0			0
$396$	13.9770	+	5.08720i	0.702368	+	0.255641i
$397$	−6.38613	−	7.61069i	−0.320511	−	0.381970i	0.581600	−	0.813475i	$-0.302427\pi$
$397$	−6.38613	−	7.61069i	−0.320511	−	0.381970i	−0.902110	+	0.431506i	$0.857983\pi$
$398$			55.6619i			2.79008i
$399$	−16.1350	+	39.1782i	−0.807762	+	1.96137i
$400$		0			0
$401$	−9.90801	+	8.31381i	−0.494783	+	0.415172i	−0.855737	−	0.517412i	$-0.826896\pi$
$401$	−9.90801	+	8.31381i	−0.494783	+	0.415172i	0.360954	+	0.932584i	$0.382451\pi$
$402$	−8.64114	+	23.7413i	−0.430981	+	1.18411i
$403$	0.196550	+	0.0346570i	0.00979083	+	0.00172639i
$404$	0.327180	+	1.85553i	0.0162778	+	0.0923162i
$405$		0			0
$406$	10.1226	−	17.5329i	0.502376	−	0.870141i
$407$	4.15478	−	2.39876i	0.205945	−	0.118902i
$408$	−2.13106	+	2.53970i	−0.105503	+	0.125734i
$409$	4.78036	+	4.01120i	0.236373	+	0.198341i	0.753278	−	0.657702i	$-0.228471\pi$
$409$	4.78036	+	4.01120i	0.236373	+	0.198341i	−0.516905	+	0.856043i	$0.672916\pi$
$410$		0			0
$411$	−21.8973	+	37.9272i	−1.08011	+	1.87081i
$412$	7.17968	+	19.7260i	0.353717	+	0.971830i
$413$	−1.76727	+	0.311617i	−0.0869616	+	0.0153337i
$414$	13.0079	−	73.7714i	0.639302	−	3.62566i
$415$		0			0
$416$	2.88429	−	2.42020i	0.141414	−	0.118660i
$417$			9.62385i			0.471282i
$418$	0.764149	+	5.71459i	0.0373758	+	0.279510i
$419$	30.5403			1.49199			0.745995	−	0.665951i	$-0.231974\pi$
$419$	30.5403			1.49199			0.745995	+	0.665951i	$0.231974\pi$
$420$		0			0
$421$	−34.3641	−	12.5075i	−1.67480	−	0.609578i	−0.682219	−	0.731148i	$-0.738985\pi$
$421$	−34.3641	−	12.5075i	−1.67480	−	0.609578i	−0.992583	+	0.121569i	$0.961207\pi$
$422$	54.0509	+	9.53063i	2.63115	+	0.463944i
$423$	86.2478	−	15.2078i	4.19351	−	0.739430i
$424$	−10.9926	+	4.00099i	−0.533850	+	0.194305i
$425$		0			0
$426$	50.0794	+	86.7401i	2.42636	+	4.20257i
$427$	1.94010	−	2.31212i	0.0938880	−	0.111891i
$428$	38.3230	−	45.6716i	1.85241	−	2.20762i
$429$	0.640329	+	1.10908i	0.0309154	+	0.0535470i
$430$		0			0
$431$	−22.4618	+	8.17542i	−1.08195	+	0.393796i	−0.820631	−	0.571458i	$-0.806378\pi$
$431$	−22.4618	+	8.17542i	−1.08195	+	0.393796i	−0.261314	+	0.965254i	$0.584156\pi$
$432$	−0.568216	+	0.100192i	−0.0273383	+	0.00482048i
$433$	14.4318	+	2.54471i	0.693547	+	0.122291i	0.509300	−	0.860589i	$-0.329904\pi$
$433$	14.4318	+	2.54471i	0.693547	+	0.122291i	0.184247	+	0.982880i	$0.441015\pi$
$434$	−1.88286	−	0.685305i	−0.0903802	−	0.0328957i
$435$		0			0
$436$	−8.14132			−0.389898
$437$	17.1198	−	5.43611i	0.818953	−	0.260044i
$438$		−	54.0664i		−	2.58339i
$439$	13.0414	−	10.9430i	0.622433	−	0.522283i	−0.276134	−	0.961119i	$-0.589053\pi$
$439$	13.0414	−	10.9430i	0.622433	−	0.522283i	0.898567	+	0.438836i	$0.144609\pi$
$440$		0			0
$441$	2.25836	−	12.8078i	0.107541	−	0.609896i
$442$	−0.532027	+	0.0938107i	−0.0253059	+	0.00446212i
$443$	−12.3097	−	33.8207i	−0.584854	−	1.60687i	−0.779780	−	0.626054i	$-0.784669\pi$
$443$	−12.3097	−	33.8207i	−0.584854	−	1.60687i	0.194926	−	0.980818i	$-0.437553\pi$
$444$	−44.5562	+	77.1736i	−2.11454	+	3.66250i
$445$		0			0
$446$	36.0825	+	30.2768i	1.70856	+	1.43365i
$447$	18.8282	−	22.4385i	0.890542	−	1.06131i
$448$	−32.9160	+	19.0040i	−1.55513	+	0.897856i
$449$	1.77883	−	3.08102i	0.0839481	−	0.145402i	−0.820994	−	0.570936i	$-0.806580\pi$
$449$	1.77883	−	3.08102i	0.0839481	−	0.145402i	0.904942	+	0.425534i	$0.139914\pi$
$450$		0			0
$451$	−0.268014	−	1.51998i	−0.0126203	−	0.0715731i
$452$	−36.2232	−	6.38713i	−1.70380	−	0.300425i
$453$	−9.46966	+	26.0177i	−0.444923	+	1.22242i
$454$	−22.2697	+	18.6865i	−1.04517	+	0.877001i
$455$		0			0
$456$	−25.0656	−	32.5292i	−1.17380	−	1.52332i
$457$		−	4.61695i		−	0.215972i	−0.994152	−	0.107986i	$-0.965560\pi$
$457$		−	4.61695i		−	0.215972i	0.994152	−	0.107986i	$-0.0344401\pi$
$458$	−8.47879	−	10.1046i	−0.396188	−	0.472158i
$459$	−5.40074	−	1.96571i	−0.252085	−	0.0917514i
$460$		0			0
$461$	−5.06596	−	28.7305i	−0.235945	−	1.33811i	−0.840614	−	0.541634i	$-0.817806\pi$
$461$	−5.06596	−	28.7305i	−0.235945	−	1.33811i	0.604669	−	0.796477i	$-0.293305\pi$
$462$	−4.39741	−	12.0818i	−0.204586	−	0.562096i
$463$	−15.2747	−	8.81888i	−0.709877	−	0.409848i	0.101138	−	0.994872i	$-0.467752\pi$
$463$	−15.2747	−	8.81888i	−0.709877	−	0.409848i	−0.811016	+	0.585024i	$0.801085\pi$
$464$	0.0531328	+	0.0920288i	0.00246663	+	0.00427233i
$465$		0			0
$466$	−4.87413	−	4.08988i	−0.225790	−	0.189460i
$467$	14.6735	−	8.47175i	0.679009	−	0.392026i	−0.120473	−	0.992717i	$-0.538441\pi$
$467$	14.6735	−	8.47175i	0.679009	−	0.392026i	0.799482	+	0.600691i	$0.205108\pi$
$468$	−14.9507	−	8.63180i	−0.691097	−	0.399005i
$469$	9.21333	−	3.35338i	0.425432	−	0.154845i
$470$		0			0
$471$	−9.11226	+	51.6782i	−0.419871	+	2.38120i
$472$	0.594870	−	1.63439i	0.0273811	−	0.0752290i
$473$	−2.44978	−	2.91954i	−0.112641	−	0.134240i
$474$	−11.6809			−0.536523
$475$		0			0
$476$	3.35514			0.153782
$477$	−20.9544	−	24.9724i	−0.959434	−	1.14341i
$478$	−15.2404	+	41.8726i	−0.697078	+	1.91521i
$479$	2.51117	−	14.2416i	0.114738	−	0.650714i	−0.872141	−	0.489255i	$-0.837269\pi$
$479$	2.51117	−	14.2416i	0.114738	−	0.650714i	0.986879	−	0.161459i	$-0.0516201\pi$
$480$		0			0
$481$	−5.23248	+	1.90447i	−0.238580	+	0.0868362i
$482$	14.3574	+	8.28927i	0.653964	+	0.377566i
$483$	−34.6898	+	20.0282i	−1.57844	+	0.911312i
$484$	26.5061	+	22.2412i	1.20482	+	1.01097i
$485$		0			0
$486$	−58.2649	−	100.918i	−2.64295	−	4.57772i
$487$	0.287462	+	0.165966i	0.0130261	+	0.00752064i	0.506499	−	0.862241i	$-0.330939\pi$
$487$	0.287462	+	0.165966i	0.0130261	+	0.00752064i	−0.493473	+	0.869761i	$0.664273\pi$
$488$	1.00052	+	2.74891i	0.0452915	+	0.124437i
$489$	−5.58376	−	31.6671i	−0.252506	−	1.43203i
$490$		0			0
$491$	3.14034	+	1.14299i	0.141721	+	0.0515824i	0.411907	−	0.911226i	$-0.364863\pi$
$491$	3.14034	+	1.14299i	0.141721	+	0.0515824i	−0.270186	+	0.962808i	$0.587085\pi$
$492$	18.4279	+	21.9615i	0.830792	+	0.990100i
$493$			1.05852i			0.0476733i
$494$	0.278313	−	6.68594i	0.0125219	−	0.300815i
$495$		0			0
$496$	0.00805671	−	0.00676038i	0.000361757	−	0.000303550i
$497$	13.2939	−	36.5247i	0.596313	−	1.63836i
$498$	−99.3375	−	17.5159i	−4.45142	−	0.784905i
$499$	2.44695	+	13.8773i	0.109540	+	0.621235i	0.989309	+	0.145833i	$0.0465862\pi$
$499$	2.44695	+	13.8773i	0.109540	+	0.621235i	−0.879769	+	0.475402i	$0.842303\pi$
$500$		0			0
$501$	−0.466576	+	0.808133i	−0.0208451	+	0.0361047i
$502$	29.4617	−	17.0097i	1.31494	−	0.759180i
$503$	−2.38217	+	2.83896i	−0.106216	+	0.126583i	−0.816533	−	0.577299i	$-0.804107\pi$
$503$	−2.38217	+	2.83896i	−0.106216	+	0.126583i	0.710318	+	0.703881i	$0.248551\pi$
$504$	50.9128	+	42.7209i	2.26784	+	1.90294i
$505$		0			0
$506$	−2.72527	+	4.72030i	−0.121153	+	0.209843i
$507$	14.1967	+	39.0052i	0.630500	+	1.73228i
$508$	61.3124	−	10.8110i	2.72030	−	0.479662i
$509$	−6.13731	+	34.8064i	−0.272032	+	1.54277i	0.476204	+	0.879335i	$0.342012\pi$
$509$	−6.13731	+	34.8064i	−0.272032	+	1.54277i	−0.748236	+	0.663433i	$0.769099\pi$
$510$		0			0
$511$	−16.0729	+	13.4867i	−0.711021	+	0.596618i
$512$		−	0.399682i		−	0.0176636i
$513$	38.1287	−	60.1192i	1.68342	−	2.65433i
$514$	−45.2401			−1.99546
$515$		0			0
$516$	66.5222	+	24.2121i	2.92848	+	1.06588i
$517$	−6.27554	−	1.10655i	−0.275998	−	0.0486659i
$518$	55.0535	−	9.70742i	2.41891	−	0.426520i
$519$	47.0185	−	17.1133i	2.06388	−	0.751191i
$520$		0			0
$521$	−2.52454	−	4.37264i	−0.110602	−	0.191569i	0.805411	−	0.592717i	$-0.201945\pi$
$521$	−2.52454	−	4.37264i	−0.110602	−	0.191569i	−0.916013	+	0.401148i	$0.868611\pi$
$522$	−35.1479	+	41.8876i	−1.53838	+	1.83337i
$523$	15.0194	−	17.8994i	0.656752	−	0.782686i	−0.330164	−	0.943924i	$-0.607104\pi$
$523$	15.0194	−	17.8994i	0.656752	−	0.782686i	0.986916	+	0.161238i	$0.0515485\pi$
$524$	−11.1109	−	19.2446i	−0.485380	−	0.840704i
$525$		0			0
$526$	−25.5023	+	9.28209i	−1.11195	+	0.404718i
$527$	0.103172	−	0.0181920i	0.00449423	−	0.000792454i
$528$	0.0664612	+	0.0117189i	0.00289235	+	0.000510000i
$529$	−5.65596	−	2.05860i	−0.245911	−	0.0895043i
$530$		0			0
$531$	4.84687			0.210336
$532$	−8.91262	+	40.5922i	−0.386411	+	1.75989i
$533$			1.79139i			0.0775939i
$534$	38.1249	−	31.9906i	1.64982	−	1.38437i
$535$		0			0
$536$	−1.65014	+	9.35839i	−0.0712751	+	0.404221i
$537$	47.0752	−	8.30062i	2.03144	−	0.358198i
$538$	−8.51811	−	23.4033i	−0.367242	−	1.00899i
$539$	−0.473147	+	0.819515i	−0.0203799	+	0.0352990i
$540$		0			0
$541$	24.3992	+	20.4734i	1.04900	+	0.880219i	0.992988	−	0.118211i	$-0.0377160\pi$
$541$	24.3992	+	20.4734i	1.04900	+	0.880219i	0.0560152	+	0.998430i	$0.482160\pi$
$542$	8.64403	−	10.3016i	0.371293	−	0.442490i
$543$	19.9488	−	11.5175i	0.856086	−	0.494262i
$544$	0.988197	−	1.71161i	0.0423686	−	0.0733845i
$545$		0			0
$546$	2.59131	+	14.6961i	0.110898	+	0.628934i
$547$	29.2567	+	5.15875i	1.25093	+	0.220572i	0.759593	−	0.650399i	$-0.225398\pi$
$547$	29.2567	+	5.15875i	1.25093	+	0.220572i	0.491334	+	0.870971i	$0.336510\pi$
$548$	−14.6917	+	40.3651i	−0.627599	+	1.72431i
$549$	−6.24483	+	5.24003i	−0.266523	+	0.223639i
$550$		0			0
$551$	−12.8065	−	2.81186i	−0.545576	−	0.119789i
$552$		−	38.8231i		−	1.65242i
$553$	2.91378	+	3.47251i	0.123906	+	0.147666i
$554$	−51.2418	−	18.6505i	−2.17706	−	0.792384i
$555$		0			0
$556$	1.63915	+	9.29611i	0.0695156	+	0.394243i
$557$	7.40274	+	20.3389i	0.313664	+	0.861785i	0.991909	+	0.126950i	$0.0405186\pi$
$557$	7.40274	+	20.3389i	0.313664	+	0.861785i	−0.678245	+	0.734836i	$0.737259\pi$
$558$	4.68676	+	2.70590i	0.198407	+	0.114550i
$559$	2.21174	+	3.83085i	0.0935467	+	0.162028i
$560$		0			0
$561$	0.514963	+	0.432105i	0.0217418	+	0.0182435i
$562$	−14.1583	+	8.17427i	−0.597230	+	0.344811i
$563$	−5.13413	−	2.96419i	−0.216378	−	0.124926i	0.387894	−	0.921704i	$-0.373203\pi$
$563$	−5.13413	−	2.96419i	−0.216378	−	0.124926i	−0.604272	+	0.796778i	$0.706536\pi$
$564$	111.226	−	40.4830i	4.68346	−	1.70464i
$565$		0			0
$566$	10.6308	−	60.2904i	0.446847	−	2.53420i
$567$	−30.3590	+	83.4107i	−1.27496	+	3.50292i
$568$	24.2151	+	28.8585i	1.01605	+	1.21088i
$569$	5.27877			0.221297			0.110649	−	0.993860i	$-0.464707\pi$
$569$	5.27877			0.221297			0.110649	+	0.993860i	$0.464707\pi$
$570$		0			0
$571$	16.5322			0.691852			0.345926	−	0.938262i	$-0.387565\pi$
$571$	16.5322			0.691852			0.345926	+	0.938262i	$0.387565\pi$
$572$	0.807424	+	0.962251i	0.0337601	+	0.0402337i
$573$	−6.21065	+	17.0636i	−0.259454	+	0.712843i
$574$	3.12301	−	17.7115i	0.130352	−	0.739263i
$575$		0			0
$576$	96.4654	−	35.1105i	4.01939	−	1.46294i
$577$	−31.4050	−	18.1317i	−1.30741	−	0.754832i	−0.325745	−	0.945458i	$-0.605615\pi$
$577$	−31.4050	−	18.1317i	−1.30741	−	0.754832i	−0.981663	+	0.190625i	$0.938948\pi$
$578$	33.4683	−	19.3229i	1.39210	−	0.803728i
$579$	16.4094	+	13.7691i	0.681950	+	0.572224i
$580$		0			0
$581$	19.5723	+	33.9003i	0.811998	+	1.40642i
$582$	−80.0054	−	46.1911i	−3.31633	−	1.91468i
$583$	0.811263	+	2.22893i	0.0335991	+	0.0923127i
$584$	−3.53125	−	20.0267i	−0.146124	−	0.828711i
$585$		0			0
$586$	−2.30975	−	0.840680i	−0.0954148	−	0.0347282i
$587$	−17.1315	−	20.4165i	−0.707093	−	0.842680i	0.286217	−	0.958165i	$-0.407602\pi$
$587$	−17.1315	−	20.4165i	−0.707093	−	0.842680i	−0.993309	+	0.115485i	$0.963158\pi$
$588$		−	17.5771i		−	0.724867i
$589$	−0.0539709	+	1.29655i	−0.00222383	+	0.0534234i
$590$		0			0
$591$	−23.5481	+	19.7592i	−0.968640	+	0.812785i
$592$	−0.100359	+	0.275734i	−0.00412473	+	0.0113326i
$593$	27.2630	+	4.80721i	1.11956	+	0.197408i	0.702647	−	0.711539i	$-0.252001\pi$
$593$	27.2630	+	4.80721i	1.11956	+	0.197408i	0.416911	+	0.908947i	$0.363113\pi$
$594$	3.75123	+	21.2743i	0.153915	+	0.872895i
$595$		0			0
$596$	14.3652	−	24.8812i	0.588421	−	1.01918i
$597$	−69.6199	+	40.1951i	−2.84935	+	1.64507i
$598$	4.06641	−	4.84616i	0.166288	−	0.198174i
$599$	26.3171	+	22.0826i	1.07529	+	0.902272i	0.995521	−	0.0945415i	$-0.0301385\pi$
$599$	26.3171	+	22.0826i	1.07529	+	0.902272i	0.0797652	+	0.996814i	$0.474583\pi$
$600$		0			0
$601$	−8.44516	+	14.6274i	−0.344485	+	0.596666i	−0.985260	−	0.171063i	$-0.945280\pi$
$601$	−8.44516	+	14.6274i	−0.344485	+	0.596666i	0.640775	+	0.767729i	$0.278613\pi$
$602$	−15.1890	−	41.7313i	−0.619056	−	1.70084i
$603$	−26.0791	+	4.59845i	−1.06202	+	0.187263i
$604$	−4.71578	+	26.7445i	−0.191882	+	1.08822i
$605$		0			0
$606$	−3.36977	+	2.82757i	−0.136887	+	0.114862i
$607$		−	4.71187i		−	0.191249i	−0.995417	−	0.0956245i	$-0.969515\pi$
$607$		−	4.71187i		−	0.191249i	0.995417	−	0.0956245i	$-0.0304848\pi$
$608$	18.0828	+	16.5024i	0.733356	+	0.669262i
$609$	29.2393			1.18483
$610$		0			0
$611$	6.95008	+	2.52962i	0.281170	+	0.102338i
$612$	−8.92424	−	1.57359i	−0.360741	−	0.0636084i
$613$	−40.4229	+	7.12765i	−1.63267	+	0.287883i	−0.913464	−	0.406919i	$-0.866603\pi$
$613$	−40.4229	+	7.12765i	−1.63267	+	0.287883i	−0.719201	+	0.694802i	$0.755492\pi$
$614$	−55.8842	+	20.3402i	−2.25530	+	0.820864i
$615$		0			0
$616$	−2.41794	−	4.18800i	−0.0974216	−	0.168739i
$617$	4.16404	−	4.96251i	0.167638	−	0.199783i	−0.675685	−	0.737191i	$-0.736152\pi$
$617$	4.16404	−	4.96251i	0.167638	−	0.199783i	0.843323	+	0.537408i	$0.180596\pi$
$618$	−31.5028	+	37.5436i	−1.26723	+	1.51022i
$619$	−18.3222	−	31.7349i	−0.736429	−	1.27553i	−0.954093	−	0.299509i	$-0.903177\pi$
$619$	−18.3222	−	31.7349i	−0.736429	−	1.27553i	0.217664	−	0.976024i	$-0.430156\pi$
$620$		0			0
$621$	63.2433	−	23.0187i	2.53787	−	0.923708i
$622$	−42.9632	+	7.57557i	−1.72267	+	0.303753i
$623$	−19.0203	−	3.35379i	−0.762032	−	0.134367i
$624$	−0.0736049	−	0.0267900i	−0.00294656	−	0.00107246i
$625$		0			0
$626$	−35.2637			−1.40942
$627$	−6.59579	+	5.08244i	−0.263410	+	0.202973i
$628$			51.4703i			2.05389i
$629$	−2.23905	+	1.87879i	−0.0892769	+	0.0749122i
$630$		0			0
$631$	−2.62539	+	14.8893i	−0.104515	+	0.592734i	0.886898	+	0.461965i	$0.152856\pi$
$631$	−2.62539	+	14.8893i	−0.104515	+	0.592734i	−0.991413	+	0.130769i	$0.958256\pi$
$632$	−4.32673	+	0.762919i	−0.172108	+	0.0303473i
$633$	27.1111	+	74.4872i	1.07757	+	2.96060i
$634$	29.2433	−	50.6509i	1.16140	−	2.01160i
$635$		0			0
$636$	−33.7509	−	28.3203i	−1.33831	−	1.12297i
$637$	0.705990	−	0.841366i	0.0279723	−	0.0333361i
$638$	3.44561	−	1.98932i	0.136413	−	0.0787580i
$639$	−52.4905	+	90.9162i	−2.07649	+	3.59659i
$640$		0			0
$641$	−1.83609	−	10.4130i	−0.0725210	−	0.411287i	−0.999358	−	0.0358234i	$-0.988595\pi$
$641$	−1.83609	−	10.4130i	−0.0725210	−	0.411287i	0.926837	−	0.375464i	$-0.122517\pi$
$642$	137.080	+	24.1708i	5.41010	+	0.953946i
$643$	1.19500	−	3.28323i	0.0471261	−	0.129478i	−0.913897	−	0.405946i	$-0.866942\pi$
$643$	1.19500	−	3.28323i	0.0471261	−	0.129478i	0.961023	+	0.276469i	$0.0891642\pi$
$644$	−30.0972	+	25.2545i	−1.18599	+	0.995168i
$645$		0			0
$646$	−1.06306	−	3.34786i	−0.0418254	−	0.131720i
$647$			21.5689i			0.847961i	0.905671	+	0.423981i	$0.139368\pi$
$647$			21.5689i			0.847961i	−0.905671	+	0.423981i	$0.860632\pi$
$648$	−55.2997	−	65.9036i	−2.17238	−	2.58894i
$649$	−0.331398	−	0.120619i	−0.0130085	−	0.00473471i
$650$		0			0
$651$	−0.502513	−	2.84989i	−0.0196950	−	0.111696i
$652$	−10.7872	−	29.6376i	−0.422459	−	1.16070i
$653$	−24.2297	−	13.9890i	−0.948181	−	0.547432i	−0.0556654	−	0.998449i	$-0.517728\pi$
$653$	−24.2297	−	13.9890i	−0.948181	−	0.547432i	−0.892515	+	0.451017i	$0.851061\pi$
$654$	−9.50371	−	16.4609i	−0.371625	−	0.643673i
$655$		0			0
$656$	0.0723150	+	0.0606795i	0.00282343	+	0.00236914i
$657$	49.0772	−	28.3347i	1.91468	−	1.10544i
$658$	−64.3053	−	37.1267i	−2.50688	−	1.44735i
$659$	5.32402	−	1.93779i	0.207395	−	0.0754854i	−0.236234	−	0.971696i	$-0.575913\pi$
$659$	5.32402	−	1.93779i	0.207395	−	0.0754854i	0.443629	+	0.896211i	$0.353691\pi$
$660$		0			0
$661$	−0.0226150	+	0.128256i	−0.000879623	+	0.00498859i	−0.985244	−	0.171153i	$-0.945251\pi$
$661$	−0.0226150	+	0.128256i	−0.000879623	+	0.00498859i	0.984365	+	0.176142i	$0.0563618\pi$
$662$	3.54936	−	9.75178i	0.137950	−	0.379014i
$663$	−0.501527	−	0.597696i	−0.0194777	−	0.0232126i
$664$	−37.9395			−1.47234
$665$		0			0
$666$	−150.988			−5.85068
$667$	−7.96760	−	9.49542i	−0.308507	−	0.367664i
$668$	−0.313044	+	0.860080i	−0.0121120	+	0.0332775i
$669$	−11.8129	+	66.9944i	−0.456714	+	2.59015i
$670$		0			0
$671$	0.557385	−	0.202871i	0.0215176	−	0.00783177i
$672$	−47.2794	−	27.2968i	−1.82384	−	1.05300i
$673$	35.8812	−	20.7160i	1.38312	−	0.798543i	0.390590	−	0.920565i	$-0.372271\pi$
$673$	35.8812	−	20.7160i	1.38312	−	0.798543i	0.992528	+	0.122021i	$0.0389376\pi$
$674$	−35.6801	−	29.9391i	−1.37434	−	1.15321i
$675$		0			0
$676$	20.3567	+	35.2589i	0.782951	+	1.35611i
$677$	−16.6833	−	9.63213i	−0.641193	−	0.370193i	0.143881	−	0.989595i	$-0.454042\pi$
$677$	−16.6833	−	9.63213i	−0.641193	−	0.370193i	−0.785074	+	0.619402i	$0.787375\pi$
$678$	−29.3708	−	80.6956i	−1.12798	−	3.09910i
$679$	6.22544	+	35.3062i	0.238911	+	1.35493i
$680$		0			0
$681$	−39.4540	−	14.3601i	−1.51188	−	0.550279i
$682$	−0.253112	−	0.301647i	−0.00969216	−	0.0115507i
$683$		−	14.0647i		−	0.538170i	−0.963116	−	0.269085i	$-0.913279\pi$
$683$		−	14.0647i		−	0.538170i	0.963116	−	0.269085i	$-0.0867213\pi$
$684$	42.7445	−	103.790i	1.63438	−	3.96851i
$685$		0			0
$686$	27.6439	−	23.1960i	1.05545	−	0.885626i
$687$	6.51572	−	17.9018i	0.248590	−	0.682996i
$688$	0.229561	+	0.0404779i	0.00875195	+	0.00154320i
$689$	−0.478063	−	2.71123i	−0.0182127	−	0.103290i
$690$		0			0
$691$	5.66284	−	9.80833i	0.215425	−	0.373126i	−0.737979	−	0.674823i	$-0.764220\pi$
$691$	5.66284	−	9.80833i	0.215425	−	0.373126i	0.953404	+	0.301697i	$0.0975531\pi$
$692$	42.5025	−	24.5388i	1.61570	−	0.932825i
$693$	8.66232	−	10.3234i	0.329054	−	0.392152i
$694$	−47.8311	−	40.1350i	−1.81564	−	1.52350i
$695$		0			0
$696$	−14.1695	+	24.5423i	−0.537094	+	0.930275i
$697$	0.321612	+	0.883620i	0.0121819	+	0.0334695i
$698$	28.4655	−	5.01924i	1.07744	−	0.189981i
$699$	1.59572	−	9.04980i	0.0603558	−	0.342295i
$700$		0			0
$701$	−11.8225	+	9.92029i	−0.446531	+	0.374684i	−0.838147	−	0.545445i	$-0.816361\pi$
$701$	−11.8225	+	9.92029i	−0.446531	+	0.374684i	0.391615	+	0.920129i	$0.371916\pi$
$702$		−	25.0731i		−	0.946323i
$703$	−16.7827	−	32.0800i	−0.632972	−	1.20992i
$704$	−7.46945			−0.281516
$705$		0			0
$706$	−66.2756	−	24.1224i	−2.49432	−	0.907857i
$707$	1.68116	+	0.296434i	0.0632265	+	0.0111485i
$708$	6.45114	−	1.13751i	0.242449	−	0.0427503i
$709$	17.9320	−	6.52671i	0.673450	−	0.245116i	0.0174175	−	0.999848i	$-0.494456\pi$
$709$	17.9320	−	6.52671i	0.673450	−	0.245116i	0.656033	+	0.754733i	$0.272233\pi$
$710$		0			0
$711$	−6.12166	−	10.6030i	−0.229580	−	0.397644i
$712$	12.0324	−	14.3397i	0.450933	−	0.537401i
$713$	−0.788566	+	0.939777i	−0.0295320	+	0.0351949i
$714$	3.91660	+	6.78374i	0.146575	+	0.253875i
$715$		0			0
$716$	44.0582	−	16.0359i	1.64653	−	0.599289i
$717$	−63.3782	+	11.1753i	−2.36690	+	0.417349i
$718$	38.8714	+	6.85407i	1.45067	+	0.255792i
$719$	−10.7312	−	3.90584i	−0.400207	−	0.145663i	0.134072	−	0.990972i	$-0.457195\pi$
$719$	−10.7312	−	3.90584i	−0.400207	−	0.145663i	−0.534279	+	0.845308i	$0.679417\pi$
$720$		0			0
$721$	19.0192			0.708314
$722$	43.3281	−	3.96810i	1.61250	−	0.147677i
$723$			23.9437i			0.890475i
$724$	17.3078	−	14.5230i	0.643239	−	0.539742i
$725$		0			0
$726$	−14.0278	+	79.5558i	−0.520622	+	2.95259i
$727$	10.7592	−	1.89714i	0.399036	−	0.0703609i	0.0294711	−	0.999566i	$-0.490618\pi$
$727$	10.7592	−	1.89714i	0.399036	−	0.0703609i	0.369565	+	0.929205i	$0.379507\pi$
$728$	1.91969	+	5.27432i	0.0711486	+	0.195479i
$729$	38.8479	−	67.2865i	1.43881	−	2.49209i
$730$		0			0
$731$	1.77872	+	1.49252i	0.0657883	+	0.0552029i
$732$	−7.08203	+	8.44003i	−0.261759	+	0.311953i
$733$	−20.4147	+	11.7865i	−0.754036	+	0.435343i	−0.827150	−	0.561981i	$-0.810039\pi$
$733$	−20.4147	+	11.7865i	−0.754036	+	0.435343i	0.0731146	+	0.997324i	$0.476706\pi$
$734$	−34.4568	+	59.6810i	−1.27182	+	2.20286i
$735$		0			0
$736$	4.01888	+	22.7922i	0.148138	+	0.840132i
$737$	1.89756	+	0.334591i	0.0698975	+	0.0123248i
$738$	−16.6136	+	45.6456i	−0.611557	+	1.68024i
$739$	1.72100	−	1.44409i	0.0633081	−	0.0531218i	−0.610585	−	0.791951i	$-0.709065\pi$
$739$	1.72100	−	1.44409i	0.0633081	−	0.0531218i	0.673893	+	0.738829i	$0.264621\pi$
$740$		0			0
$741$	8.56350	−	4.48000i	0.314588	−	0.164577i
$742$			27.6393i			1.01467i
$743$	17.3031	+	20.6210i	0.634788	+	0.756511i	0.983537	−	0.180705i	$-0.0578381\pi$
$743$	17.3031	+	20.6210i	0.634788	+	0.756511i	−0.348750	+	0.937216i	$0.613394\pi$
$744$	2.63561	+	0.959285i	0.0966263	+	0.0351691i
$745$		0			0
$746$	−2.43899	−	13.8322i	−0.0892976	−	0.506432i
$747$	−36.1605	−	99.3502i	−1.32304	−	3.63503i
$748$	0.571023	+	0.329680i	0.0208787	+	0.0120543i
$749$	−27.0086	−	46.7803i	−0.986874	−	1.70932i
$750$		0			0
$751$	−26.1495	−	21.9420i	−0.954209	−	0.800676i	0.0257926	−	0.999667i	$-0.491789\pi$
$751$	−26.1495	−	21.9420i	−0.954209	−	0.800676i	−0.980001	+	0.198991i	$0.936234\pi$
$752$	0.337534	−	0.194876i	0.0123086	−	0.00710638i
$753$	42.5502	+	24.5664i	1.55062	+	0.895248i
$754$	−4.33935	+	1.57940i	−0.158030	+	0.0575182i
$755$		0			0
$756$	−27.0400	+	153.351i	−0.983434	+	5.57733i
$757$	6.44514	−	17.7079i	0.234253	−	0.643604i	−0.765747	−	0.643142i	$-0.777631\pi$
$757$	6.44514	−	17.7079i	0.234253	−	0.643604i	1.00000		0.000462353i	$-0.000147171\pi$
$758$	−45.4775	−	54.1979i	−1.65182	−	1.96856i
$759$	−7.87198			−0.285735
$760$		0			0
$761$	−10.8012			−0.391544			−0.195772	−	0.980649i	$-0.562721\pi$
$761$	−10.8012			−0.391544			−0.195772	+	0.980649i	$0.562721\pi$
$762$	93.4315	+	111.347i	3.38467	+	4.03369i
$763$	−2.52282	+	6.93139i	−0.0913322	+	0.250933i
$764$	−3.09283	+	17.5403i	−0.111895	+	0.634587i
$765$		0			0
$766$	−10.0087	+	3.64286i	−0.361628	+	0.131622i
$767$	0.354486	+	0.204663i	0.0127998	+	0.00738994i
$768$	46.4802	−	26.8354i	1.67721	−	0.968338i
$769$	−37.4804	−	31.4498i	−1.35158	−	1.13411i	−0.978486	−	0.206313i	$-0.933854\pi$
$769$	−37.4804	−	31.4498i	−1.35158	−	1.13411i	−0.373091	−	0.927795i	$-0.621702\pi$
$770$		0			0
$771$	−32.6692	−	56.5847i	−1.17655	−	2.03785i
$772$	18.1957	+	10.5053i	0.654878	+	0.378094i
$773$	−9.15095	−	25.1420i	−0.329137	−	0.904296i	−0.988331	−	0.152323i	$-0.951325\pi$
$773$	−9.15095	−	25.1420i	−0.329137	−	0.904296i	0.659194	−	0.751973i	$-0.270898\pi$
$774$	20.8284	+	118.124i	0.748662	+	4.24588i
$775$		0			0
$776$	−32.6516	−	11.8842i	−1.17212	−	0.426619i
$777$	51.8974	+	61.8489i	1.86181	+	2.21882i
$778$			37.0448i			1.32812i
$779$	−11.5448	+	1.54376i	−0.413636	+	0.0553110i
$780$		0			0
$781$	5.85150	−	4.91000i	0.209383	−	0.175693i
$782$	1.13575	−	3.12046i	0.0406145	−	0.111587i
$783$	−48.3811	−	8.53090i	−1.72900	−	0.304869i
$784$	−0.0100504	−	0.0569988i	−0.000358944	−	0.00203567i
$785$		0			0
$786$	25.9404	−	44.9301i	0.925263	−	1.60260i
$787$	18.9093	−	10.9173i	0.674045	−	0.389160i	−0.123563	−	0.992337i	$-0.539432\pi$
$787$	18.9093	−	10.9173i	0.674045	−	0.389160i	0.797607	+	0.603177i	$0.206099\pi$
$788$	−19.3807	+	23.0971i	−0.690410	+	0.822799i
$789$	−30.0257	−	25.1945i	−1.06894	−	0.896949i
$790$		0			0
$791$	−16.6627	+	28.8607i	−0.592458	+	1.02617i
$792$	4.46722	+	12.2736i	0.158736	+	0.436123i
$793$	−0.677993	+	0.119548i	−0.0240762	+	0.00424529i
$794$	3.95066	−	22.4053i	0.140204	−	0.795135i
$795$		0			0
$796$	−60.4029	+	50.6840i	−2.14092	+	1.79645i
$797$		−	13.0244i		−	0.461347i	−0.973031	−	0.230673i	$-0.925907\pi$
$797$		−	13.0244i		−	0.461347i	0.973031	−	0.230673i	$-0.0740929\pi$
$798$	−92.4773	+	29.3646i	−3.27366	+	1.03949i
$799$	3.88234			0.137347
$800$		0			0
$801$	49.0187	+	17.8413i	1.73199	+	0.630393i
$802$	−29.1685	−	5.14319i	−1.02997	−	0.181612i
$803$	−4.06072	+	0.716015i	−0.143300	+	0.0252676i
$804$	−33.6318	+	12.2410i	−1.18610	+	0.431706i
$805$		0			0
$806$	0.228518	+	0.395804i	0.00804919	+	0.0139416i
$807$	23.1208	−	27.5543i	0.813892	−	0.969959i
$808$	−1.06351	+	1.26745i	−0.0374143	+	0.0445886i
$809$	−4.51134	−	7.81388i	−0.158610	−	0.274721i	0.775757	−	0.631031i	$-0.217368\pi$
$809$	−4.51134	−	7.81388i	−0.158610	−	0.274721i	−0.934368	+	0.356310i	$0.884035\pi$
$810$		0			0
$811$	21.0062	−	7.64565i	0.737629	−	0.268475i	0.0542386	−	0.998528i	$-0.482727\pi$
$811$	21.0062	−	7.64565i	0.737629	−	0.268475i	0.683391	+	0.730053i	$0.260505\pi$
$812$	28.2435	−	4.98009i	0.991153	−	0.174767i
$813$	19.1269	+	3.37259i	0.670810	+	0.118282i
$814$	10.3236	+	3.75749i	0.361843	+	0.131700i
$815$		0			0
$816$	−0.0411159			−0.00143934
$817$	−22.7823	+	17.5551i	−0.797052	+	0.614175i
$818$			14.2901i			0.499642i
$819$	−11.9819	+	10.0540i	−0.418681	+	0.351315i
$820$		0			0
$821$	−6.05598	+	34.3451i	−0.211355	+	1.19865i	0.675766	+	0.737116i	$0.263813\pi$
$821$	−6.05598	+	34.3451i	−0.211355	+	1.19865i	−0.887121	+	0.461537i	$0.847298\pi$
$822$	−98.7645	+	17.4148i	−3.44481	+	0.607412i
$823$	−1.72647	−	4.74344i	−0.0601809	−	0.165346i	0.905958	−	0.423367i	$-0.139152\pi$
$823$	−1.72647	−	4.74344i	−0.0601809	−	0.165346i	−0.966139	+	0.258021i	$0.916930\pi$
$824$	−9.21684	+	15.9640i	−0.321084	+	0.556134i
$825$		0			0
$826$	−3.14800	−	2.64149i	−0.109533	−	0.0919090i
$827$	−32.2938	+	38.4862i	−1.12296	+	1.33830i	−0.188569	+	0.982060i	$0.560385\pi$
$827$	−32.2938	+	38.4862i	−1.12296	+	1.33830i	−0.934395	+	0.356237i	$0.884059\pi$
$828$	91.8993	−	53.0581i	3.19372	−	1.84390i
$829$	8.13553	−	14.0911i	0.282559	−	0.489406i	−0.689456	−	0.724328i	$-0.742150\pi$
$829$	8.13553	−	14.0911i	0.282559	−	0.489406i	0.972014	+	0.234922i	$0.0754835\pi$
$830$		0			0
$831$	−13.6758	−	77.5595i	−0.474409	−	2.69051i
$832$	8.53778	+	1.50544i	0.295994	+	0.0521918i
$833$	0.197184	−	0.541758i	0.00683201	−	0.0187708i
$834$	−16.8823	+	14.1659i	−0.584587	+	0.490527i
$835$		0			0
$836$	−5.50551	+	6.03276i	−0.190412	+	0.208648i
$837$			4.86222i			0.168063i
$838$	44.9542	+	53.5743i	1.55292	+	1.85069i
$839$	−20.3201	−	7.39592i	−0.701528	−	0.255335i	−0.0334650	−	0.999440i	$-0.510654\pi$
$839$	−20.3201	−	7.39592i	−0.701528	−	0.255335i	−0.668063	+	0.744105i	$0.732876\pi$
$840$		0			0
$841$	−3.46462	−	19.6488i	−0.119470	−	0.677545i
$842$	−28.6418	−	78.6926i	−0.987061	−	2.71193i
$843$	−20.4482	−	11.8058i	−0.704272	−	0.406612i
$844$	38.8746	+	67.3329i	1.33812	+	2.31769i
$845$		0			0
$846$	153.631	+	128.912i	5.28196	+	4.43209i
$847$	27.1495	−	15.6748i	0.932869	−	0.538592i
$848$	−0.125640	−	0.0725383i	−0.00431450	−	0.00249098i
$849$	83.0858	−	30.2408i	2.85150	−	1.03786i
$850$		0			0
$851$	5.94350	−	33.7072i	0.203740	−	1.15547i
$852$	−48.5273	+	133.328i	−1.66252	+	4.56773i
$853$	25.3918	+	30.2607i	0.869397	+	1.03611i	0.999007	+	0.0445424i	$0.0141830\pi$
$853$	25.3918	+	30.2607i	0.869397	+	1.03611i	−0.129610	+	0.991565i	$0.541373\pi$
$854$	6.91172			0.236514
$855$		0			0
$856$	52.3542			1.78943
$857$	−8.00863	−	9.54432i	−0.273570	−	0.326028i	0.611714	−	0.791079i	$-0.290480\pi$
$857$	−8.00863	−	9.54432i	−0.273570	−	0.326028i	−0.885284	+	0.465051i	$0.846036\pi$
$858$	−1.00303	+	2.75581i	−0.0342429	+	0.0940817i
$859$	−5.73773	+	32.5403i	−0.195769	+	1.11026i	0.715551	+	0.698561i	$0.246176\pi$
$859$	−5.73773	+	32.5403i	−0.195769	+	1.11026i	−0.911319	+	0.411700i	$0.864935\pi$
$860$		0			0
$861$	24.4081	−	8.88381i	0.831825	−	0.302759i
$862$	−47.4044	−	27.3689i	−1.61460	−	0.932189i
$863$	7.67835	−	4.43310i	0.261374	−	0.150904i	−0.363587	−	0.931560i	$-0.618448\pi$
$863$	7.67835	−	4.43310i	0.261374	−	0.150904i	0.624961	+	0.780656i	$0.285115\pi$
$864$	70.2673	+	58.9612i	2.39054	+	2.00590i
$865$		0			0
$866$	16.7791	+	29.0622i	0.570176	+	0.987573i
$867$	48.3368	+	27.9073i	1.64161	+	0.947781i
$868$	−0.970799	−	2.66725i	−0.0329511	−	0.0905323i
$869$	0.154694	+	0.877311i	0.00524762	+	0.0297607i
$870$		0			0
$871$	−2.10152	−	0.764892i	−0.0712074	−	0.0259174i
$872$	−4.59538	−	5.47656i	−0.155619	−	0.185460i
$873$		−	96.8300i		−	3.27720i
$874$	34.7359	+	22.0302i	1.17496	+	0.745181i
$875$		0			0
$876$	58.6715	−	49.2312i	1.98232	−	1.66337i
$877$	3.79669	−	10.4313i	0.128205	−	0.352241i	−0.858938	−	0.512080i	$-0.828875\pi$
$877$	3.79669	−	10.4313i	0.128205	−	0.352241i	0.987143	+	0.159839i	$0.0510974\pi$
$878$	38.3930	+	6.76972i	1.29570	+	0.228467i
$879$	−0.616444	−	3.49603i	−0.0207921	−	0.117918i
$880$		0			0
$881$	−20.9588	+	36.3016i	−0.706119	+	1.22303i	0.260168	+	0.965563i	$0.416222\pi$
$881$	−20.9588	+	36.3016i	−0.706119	+	1.22303i	−0.966286	+	0.257470i	$0.917111\pi$
$882$	25.7919	−	14.8910i	0.868458	−	0.501405i
$883$	17.0960	−	20.3742i	0.575325	−	0.685646i	−0.397390	−	0.917650i	$-0.630084\pi$
$883$	17.0960	−	20.3742i	0.575325	−	0.685646i	0.972715	+	0.232004i	$0.0745283\pi$
$884$	−0.586248	−	0.491921i	−0.0197177	−	0.0165451i
$885$		0			0
$886$	41.2094	−	71.3768i	1.38446	−	2.39795i
$887$	−7.11802	−	19.5566i	−0.239000	−	0.656646i	−0.999969	−	0.00785834i	$-0.997499\pi$
$887$	−7.11802	−	19.5566i	−0.239000	−	0.656646i	0.760970	−	0.648788i	$-0.224724\pi$
$888$	−77.0634	+	13.5884i	−2.58608	+	0.455996i
$889$	9.79506	−	55.5506i	0.328516	−	1.86311i
$890$		0			0
$891$	−13.3630	+	11.2129i	−0.447676	+	0.375645i
$892$			66.7249i			2.23412i
$893$	−10.3131	+	46.9705i	−0.345114	+	1.57181i
$894$	67.0764			2.24337
$895$		0			0
$896$	−50.7654	−	18.4771i	−1.69595	−	0.617276i
$897$	8.99787	+	1.58657i	0.300430	+	0.0529739i
$898$	8.02315	−	1.41470i	0.267736	−	0.0472091i
$899$	0.841496	−	0.306280i	0.0280655	−	0.0102150i
$900$		0			0
$901$	−0.722559	−	1.25151i	−0.0240719	−	0.0416938i
$902$	2.27187	−	2.70751i	0.0756450	−	0.0901502i
$903$	41.2276	−	49.1332i	1.37197	−	1.63505i
$904$	−16.1497	−	27.9721i	−0.537131	−	0.930338i
$905$		0			0
$906$	−59.5796	+	21.6852i	−1.97940	+	0.720443i
$907$	0.792997	−	0.139827i	0.0263310	−	0.00464287i	−0.160467	−	0.987041i	$-0.551300\pi$
$907$	0.792997	−	0.139827i	0.0263310	−	0.00464287i	0.186798	+	0.982398i	$0.440189\pi$
$908$	−40.5562	−	7.15115i	−1.34590	−	0.237319i
$909$	−4.33264	−	1.57695i	−0.143705	−	0.0523042i
$910$		0			0
$911$	33.6958			1.11639			0.558196	−	0.829709i	$-0.311494\pi$
$911$	33.6958			1.11639			0.558196	+	0.829709i	$0.311494\pi$
$912$	0.109221	−	0.497441i	0.00361666	−	0.0164719i
$913$			7.69283i			0.254595i
$914$	8.09913	−	6.79598i	0.267895	−	0.224791i
$915$		0			0
$916$	3.24475	−	18.4019i	0.107210	−	0.608016i
$917$	−19.8276	+	3.49613i	−0.654764	+	0.115453i
$918$	−4.50141	−	12.3675i	−0.148569	−	0.408189i
$919$	−7.14677	+	12.3786i	−0.235750	+	0.408331i	−0.959490	−	0.281741i	$-0.909088\pi$
$919$	−7.14677	+	12.3786i	−0.235750	+	0.408331i	0.723740	+	0.690072i	$0.242421\pi$
$920$		0			0
$921$	−65.7964	−	55.2097i	−2.16806	−	1.81922i
$922$	42.9426	−	51.1770i	1.41424	−	1.68542i
$923$	−7.67801	+	4.43290i	−0.252725	+	0.145911i
$924$	9.10669	−	15.7733i	0.299588	−	0.518902i
$925$		0			0
$926$	−7.01363	−	39.7763i	−0.230482	−	1.30713i
$927$	−50.5888	−	8.92017i	−1.66155	−	0.292977i
$928$	5.77806	−	15.8751i	0.189674	−	0.521125i
$929$	−11.3513	+	9.52484i	−0.372423	+	0.312500i	−0.809719	−	0.586818i	$-0.800381\pi$
$929$	−11.3513	+	9.52484i	−0.372423	+	0.312500i	0.437296	+	0.899317i	$0.355936\pi$
$930$		0			0
$931$	6.03067	+	3.82476i	0.197647	+	0.125352i
$932$		−	9.01339i		−	0.295244i
$933$	−40.5002	−	48.2663i	−1.32592	−	1.58017i
$934$	36.4602	+	13.2704i	1.19301	+	0.434221i
$935$		0			0
$936$	−2.63245	−	14.9294i	−0.0860444	−	0.487982i
$937$	16.6085	+	45.6316i	0.542577	+	1.49072i	0.843531	+	0.537080i	$0.180473\pi$
$937$	16.6085	+	45.6316i	0.542577	+	1.49072i	−0.300954	+	0.953639i	$0.597305\pi$
$938$	19.4442	+	11.2261i	0.634877	+	0.366546i
$939$	−25.4650	−	44.1066i	−0.831017	−	1.43936i
$940$		0			0
$941$	14.5770	+	12.2315i	0.475195	+	0.398736i	0.848685	−	0.528898i	$-0.177395\pi$
$941$	14.5770	+	12.2315i	0.475195	+	0.398736i	−0.373490	+	0.927634i	$0.621839\pi$
$942$	−104.068	+	60.0835i	−3.39071	+	1.95763i
$943$	−9.53613	−	5.50569i	−0.310539	−	0.179290i
$944$	0.0202693	−	0.00737740i	0.000659708	−	0.000240114i
$945$		0			0
$946$	1.51551	−	8.59490i	0.0492736	−	0.279444i
$947$	−13.8679	+	38.1018i	−0.450646	+	1.23814i	0.481624	+	0.876378i	$0.340047\pi$
$947$	−13.8679	+	38.1018i	−0.450646	+	1.23814i	−0.932270	+	0.361763i	$0.882175\pi$
$948$	−10.6363	−	12.6758i	−0.345451	−	0.411692i
$949$	4.78582			0.155354
$950$		0			0
$951$	84.4697			2.73912
$952$	1.89381	+	2.25696i	0.0613788	+	0.0731484i
$953$	12.9385	−	35.5481i	0.419118	−	1.15152i	−0.533088	−	0.846060i	$-0.678968\pi$
$953$	12.9385	−	35.5481i	0.419118	−	1.15152i	0.952206	−	0.305457i	$-0.0988093\pi$
$954$	12.9630	−	73.5170i	0.419694	−	2.38020i
$955$		0			0
$956$	−59.3164	+	21.5894i	−1.91843	+	0.698251i
$957$	4.97634	+	2.87309i	0.160862	+	0.0928738i
$958$	28.6792	−	16.5579i	0.926582	−	0.534962i
$959$	29.8136	+	25.0166i	0.962732	+	0.807828i
$960$		0			0
$961$	15.4557	+	26.7700i	0.498570	+	0.863549i
$962$	−11.0429	−	6.37560i	−0.356036	−	0.205558i
$963$	49.8993	+	137.097i	1.60798	+	4.41789i
$964$	4.07814	+	23.1283i	0.131348	+	0.744911i
$965$		0			0
$966$	−86.1958	−	31.3727i	−2.77330	−	1.00940i
$967$	18.0465	+	21.5070i	0.580336	+	0.691618i	0.973718	−	0.227758i	$-0.0731394\pi$
$967$	18.0465	+	21.5070i	0.580336	+	0.691618i	−0.393382	+	0.919375i	$0.628695\pi$
$968$			30.3844i			0.976591i
$969$	3.41972	−	3.74722i	0.109857	−	0.120378i
$970$		0			0
$971$	−26.9547	+	22.6176i	−0.865016	+	0.725835i	−0.963043	−	0.269349i	$-0.913191\pi$
$971$	−26.9547	+	22.6176i	−0.865016	+	0.725835i	0.0980264	+	0.995184i	$0.468747\pi$
$972$	56.4590	−	155.120i	1.81092	−	4.97548i
$973$	8.42250	+	1.48511i	0.270013	+	0.0476106i
$974$	0.131992	+	0.748566i	0.00422931	+	0.0239856i
$975$		0			0
$976$	−0.0181396	+	0.0314187i	−0.000580633	+	0.00100569i
$977$	46.1619	−	26.6516i	1.47685	−	0.852659i	0.477191	−	0.878799i	$-0.341655\pi$
$977$	46.1619	−	26.6516i	1.47685	−	0.852659i	0.999658	+	0.0261400i	$0.00832156\pi$
$978$	47.3318	−	56.4079i	1.51350	−	1.80372i
$979$	−2.90759	−	2.43976i	−0.0929269	−	0.0779749i
$980$		0			0
$981$	9.96127	−	17.2534i	0.318039	−	0.550859i
$982$	2.61741	+	7.19127i	0.0835249	+	0.229483i
$983$	−50.0417	+	8.82370i	−1.59608	+	0.281432i	−0.899789	−	0.436325i	$-0.856280\pi$
$983$	−50.0417	+	8.82370i	−1.59608	+	0.281432i	−0.696293	+	0.717757i	$0.745169\pi$
$984$	−4.37156	+	24.7924i	−0.139360	+	0.790352i
$985$		0			0
$986$	−1.85687	+	1.55810i	−0.0591349	+	0.0496200i
$987$		−	107.241i		−	3.41352i
$988$	7.50883	−	5.78599i	0.238888	−	0.184077i
$989$	−27.1903			−0.864603
$990$		0			0
$991$	52.8203	+	19.2250i	1.67789	+	0.610703i	0.993018	−	0.117960i	$-0.0376354\pi$
$991$	52.8203	+	19.2250i	1.67789	+	0.610703i	0.684873	+	0.728662i	$0.259858\pi$
$992$	−1.64662	−	0.290343i	−0.0522801	−	0.00921840i
$993$	14.7603	−	2.60263i	0.468403	−	0.0825920i
$994$	83.6404	−	30.4426i	2.65291	−	0.965581i
$995$		0			0
$996$	−71.4458	−	123.748i	−2.26385	−	3.92110i
$997$	−24.0867	+	28.7054i	−0.762834	+	0.909110i	−0.998024	−	0.0628394i	$-0.979984\pi$
$997$	−24.0867	+	28.7054i	−0.762834	+	0.909110i	0.235190	+	0.971949i	$0.424429\pi$
$998$	−20.7420	+	24.7194i	−0.656578	+	0.782479i
$999$	−67.8275	−	117.481i	−2.14597	−	3.71693i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.u.b.424.6		36
5.2	odd	4		475.2.l.c.101.1		18
5.3	odd	4		95.2.k.a.6.3	✓	18
5.4	even	2	inner	475.2.u.b.424.1		36
15.8	even	4		855.2.bs.c.766.1		18
19.16	even	9	inner	475.2.u.b.149.1		36
95.23	odd	36		1805.2.a.v.1.8		9
95.42	odd	36		9025.2.a.cc.1.2		9
95.53	even	36		1805.2.a.s.1.2		9
95.54	even	18	inner	475.2.u.b.149.6		36
95.72	even	36		9025.2.a.cf.1.8		9
95.73	odd	36		95.2.k.a.16.3	yes	18
95.92	odd	36		475.2.l.c.301.1		18
285.263	even	36		855.2.bs.c.586.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.6.3	✓	18	5.3	odd	4
95.2.k.a.16.3	yes	18	95.73	odd	36
475.2.l.c.101.1		18	5.2	odd	4
475.2.l.c.301.1		18	95.92	odd	36
475.2.u.b.149.1		36	19.16	even	9	inner
475.2.u.b.149.6		36	95.54	even	18	inner
475.2.u.b.424.1		36	5.4	even	2	inner
475.2.u.b.424.6		36	1.1	even	1	trivial
855.2.bs.c.586.1		18	285.263	even	36
855.2.bs.c.766.1		18	15.8	even	4
1805.2.a.s.1.2		9	95.53	even	36
1805.2.a.v.1.8		9	95.23	odd	36
9025.2.a.cc.1.2		9	95.42	odd	36
9025.2.a.cf.1.8		9	95.72	even	36

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.47196 + 1.75422i) q^{2} +(-1.13116 + 3.10785i) q^{3} +(-0.563307 + 3.19467i) q^{4} +(-7.11687 + 2.59033i) q^{6} +(2.54534 + 1.46955i) q^{7} +(-2.46697 + 1.42431i) q^{8} +(-6.08105 - 5.10261i) q^{9} +(0.288800 + 0.500217i) q^{11} +(-9.29136 - 5.36437i) q^{12} +(-0.229289 - 0.629967i) q^{13} +(1.16873 + 6.62820i) q^{14} +(-0.0331972 - 0.0120828i) q^{16} +(-0.226198 - 0.269572i) q^{17} -18.1783i q^{18} +(3.86230 - 2.02056i) q^{19} +(-7.44633 + 6.24822i) q^{21} +(-0.452386 + 1.24292i) q^{22} +(4.05820 + 0.715571i) q^{23} +(-1.63598 - 9.27810i) q^{24} +(0.767594 - 1.32951i) q^{26} +(14.1442 - 8.16613i) q^{27} +(-6.12854 + 7.30371i) q^{28} +(-2.30426 - 1.93351i) q^{29} +(-0.148853 + 0.257821i) q^{31} +(1.92090 + 5.27762i) q^{32} +(-1.88128 + 0.331720i) q^{33} +(0.139933 - 0.793600i) q^{34} +(19.7266 - 16.5526i) q^{36} -8.30595i q^{37} +(9.22966 + 3.80111i) q^{38} +2.21721 q^{39} +(-2.51099 - 0.913926i) q^{41} +(-21.9215 - 3.86534i) q^{42} +(-6.49806 + 1.14578i) q^{43} +(-1.76071 + 0.640846i) q^{44} +(4.71826 + 8.17226i) q^{46} +(-7.09153 + 8.45135i) q^{47} +(0.0751029 - 0.0895041i) q^{48} +(0.819160 + 1.41883i) q^{49} +(1.09366 - 0.398058i) q^{51} +(2.14170 - 0.377639i) q^{52} +(4.04421 + 0.713104i) q^{53} +(35.1449 + 12.7917i) q^{54} -8.37237 q^{56} +(1.91071 + 14.2890i) q^{57} -6.88822i q^{58} +(-0.467725 + 0.392468i) q^{59} +(0.178325 - 1.01133i) q^{61} +(-0.671381 + 0.118383i) q^{62} +(-7.97978 - 21.9243i) q^{63} +(-6.46593 + 11.1993i) q^{64} +(-3.35108 - 2.81189i) q^{66} +(2.14429 - 2.55547i) q^{67} +(0.988612 - 0.570776i) q^{68} +(-6.81438 + 11.8028i) q^{69} +(-2.29645 - 13.0238i) q^{71} +(22.2695 + 3.92671i) q^{72} +(-2.44161 + 6.70827i) q^{73} +(14.5704 - 12.2261i) q^{74} +(4.27938 + 13.4770i) q^{76} +1.69763i q^{77} +(3.26364 + 3.88946i) q^{78} +(1.44931 + 0.527504i) q^{79} +(5.24435 + 29.7422i) q^{81} +(-2.09286 - 5.75009i) q^{82} +(11.5342 + 6.65930i) q^{83} +(-15.7664 - 27.3082i) q^{84} +(-11.5749 - 9.71246i) q^{86} +(8.61554 - 4.97418i) q^{87} +(-1.42492 - 0.822680i) q^{88} +(-6.17500 + 2.24752i) q^{89} +(0.342150 - 1.94043i) q^{91} +(-4.57203 + 12.5615i) q^{92} +(-0.632892 - 0.754252i) q^{93} -25.2640 q^{94} -18.5749 q^{96} +(7.84066 + 9.34414i) q^{97} +(-1.28316 + 3.52545i) q^{98} +(0.796200 - 4.51548i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{4} - 12 q^{6} - 6 q^{9} + 24 q^{14} - 6 q^{16} - 42 q^{21} + 30 q^{24} + 6 q^{26} - 30 q^{29} - 36 q^{31} + 24 q^{34} + 150 q^{36} - 72 q^{39} - 60 q^{41} - 84 q^{44} + 18 q^{46} - 18 q^{49}+ \cdots + 186 q^{99}+O(q^{100}) \) 36 * q + 6 * q^4 - 12 * q^6 - 6 * q^9 + 24 * q^14 - 6 * q^16 - 42 * q^21 + 30 * q^24 + 6 * q^26 - 30 * q^29 - 36 * q^31 + 24 * q^34 + 150 * q^36 - 72 * q^39 - 60 * q^41 - 84 * q^44 + 18 * q^46 - 18 * q^49 - 90 * q^51 + 132 * q^54 - 36 * q^59 - 60 * q^61 - 72 * q^64 + 78 * q^66 - 30 * q^69 - 24 * q^71 + 30 * q^74 - 66 * q^76 + 102 * q^79 + 54 * q^81 - 96 * q^84 + 126 * q^86 + 108 * q^89 + 60 * q^91 - 60 * q^94 - 132 * q^96 + 186 * q^99

Introduction

L-functions

Modular forms

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Database

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