LMFDB - Embedded newform 315.2.k.c.256.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [315,2,Mod(16,315)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(315, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("315.16"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.k (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [36] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			256.1
Character	$\chi$	$=$	315.256
Dual form			315.2.k.c.16.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37850 + 2.38764i) q^{2} +(-1.12222 + 1.31932i) q^{3} +(-2.80055 - 4.85069i) q^{4} +1.00000 q^{5} +(-1.60307 - 4.49816i) q^{6} +(2.15266 - 1.53820i) q^{7} +9.92824 q^{8} +(-0.481224 - 2.96115i) q^{9} +(-1.37850 + 2.38764i) q^{10} +2.28080 q^{11} +(9.54246 + 1.74874i) q^{12} +(1.37896 - 2.38844i) q^{13} +(0.705233 + 7.26018i) q^{14} +(-1.12222 + 1.31932i) q^{15} +(-8.08502 + 14.0037i) q^{16} +(1.01423 - 1.75669i) q^{17} +(7.73353 + 2.93297i) q^{18} +(-3.03493 - 5.25665i) q^{19} +(-2.80055 - 4.85069i) q^{20} +(-0.386375 + 4.56626i) q^{21} +(-3.14410 + 5.44574i) q^{22} +2.99113 q^{23} +(-11.1417 + 13.0985i) q^{24} +1.00000 q^{25} +(3.80182 + 6.58494i) q^{26} +(4.44676 + 2.68819i) q^{27} +(-13.4900 - 6.13405i) q^{28} +(-2.78655 - 4.82644i) q^{29} +(-1.60307 - 4.49816i) q^{30} +(0.166500 + 0.288386i) q^{31} +(-12.3622 - 21.4120i) q^{32} +(-2.55958 + 3.00912i) q^{33} +(2.79623 + 4.84321i) q^{34} +(2.15266 - 1.53820i) q^{35} +(-13.0159 + 10.6271i) q^{36} +(0.0601415 + 0.104168i) q^{37} +16.7347 q^{38} +(1.60361 + 4.49966i) q^{39} +9.92824 q^{40} +(-0.237341 + 0.411087i) q^{41} +(-10.3700 - 7.21713i) q^{42} +(3.43450 + 5.94872i) q^{43} +(-6.38750 - 11.0635i) q^{44} +(-0.481224 - 2.96115i) q^{45} +(-4.12329 + 7.14174i) q^{46} +(-3.60725 + 6.24794i) q^{47} +(-9.40214 - 26.3820i) q^{48} +(2.26785 - 6.62245i) q^{49} +(-1.37850 + 2.38764i) q^{50} +(1.17945 + 3.30949i) q^{51} -15.4474 q^{52} +(-4.25673 + 7.37287i) q^{53} +(-12.5483 + 6.91157i) q^{54} +2.28080 q^{55} +(21.3721 - 15.2717i) q^{56} +(10.3411 + 1.89509i) q^{57} +15.3651 q^{58} +(4.32075 + 7.48375i) q^{59} +(9.54246 + 1.74874i) q^{60} +(5.64787 - 9.78239i) q^{61} -0.918083 q^{62} +(-5.59077 - 5.63412i) q^{63} +35.8254 q^{64} +(1.37896 - 2.38844i) q^{65} +(-3.65630 - 10.2594i) q^{66} +(3.39059 + 5.87268i) q^{67} -11.3615 q^{68} +(-3.35672 + 3.94627i) q^{69} +(0.705233 + 7.26018i) q^{70} +12.3927 q^{71} +(-4.77770 - 29.3990i) q^{72} +(0.0952946 - 0.165055i) q^{73} -0.331621 q^{74} +(-1.12222 + 1.31932i) q^{75} +(-16.9989 + 29.4430i) q^{76} +(4.90979 - 3.50834i) q^{77} +(-12.9542 - 2.37396i) q^{78} +(5.77167 - 9.99682i) q^{79} +(-8.08502 + 14.0037i) q^{80} +(-8.53685 + 2.84995i) q^{81} +(-0.654352 - 1.13337i) q^{82} +(-3.98395 - 6.90040i) q^{83} +(23.2316 - 10.9138i) q^{84} +(1.01423 - 1.75669i) q^{85} -18.9379 q^{86} +(9.49476 + 1.74000i) q^{87} +22.6444 q^{88} +(1.05443 + 1.82633i) q^{89} +(7.73353 + 2.93297i) q^{90} +(-0.705469 - 7.26261i) q^{91} +(-8.37680 - 14.5090i) q^{92} +(-0.567325 - 0.103967i) q^{93} +(-9.94522 - 17.2256i) q^{94} +(-3.03493 - 5.25665i) q^{95} +(42.1225 + 7.71931i) q^{96} +(-3.42650 - 5.93488i) q^{97} +(12.6858 + 14.5439i) q^{98} +(-1.09758 - 6.75381i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9} - 2 q^{11} + 5 q^{12} + 2 q^{13} - 6 q^{14} - q^{15} - 30 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} - 22 q^{20} - 11 q^{21} - 19 q^{22} + 6 q^{23}+ \cdots - 89 q^{99}+O(q^{100}) $ 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9 - 2 * q^11 + 5 * q^12 + 2 * q^13 - 6 * q^14 - q^15 - 30 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 - 22 * q^20 - 11 * q^21 - 19 * q^22 + 6 * q^23 + 16 * q^24 + 36 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 - 4 * q^30 + 10 * q^32 - 5 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 + 44 * q^38 - 8 * q^39 - 4 * q^41 - 30 * q^42 - 29 * q^43 - 7 * q^44 + 3 * q^45 - 24 * q^46 - 23 * q^47 - 19 * q^48 - 7 * q^49 - 21 * q^51 + 14 * q^52 - 2 * q^55 + 33 * q^56 + 21 * q^57 + 40 * q^58 - 5 * q^59 + 5 * q^60 - 3 * q^61 - 12 * q^62 + 11 * q^63 + 128 * q^64 + 2 * q^65 - 30 * q^66 - 35 * q^67 + 34 * q^68 - 50 * q^69 - 6 * q^70 + 24 * q^71 + 5 * q^72 - 10 * q^73 - 44 * q^74 - q^75 + 10 * q^76 + 5 * q^77 + 66 * q^78 - 28 * q^79 - 30 * q^80 + 47 * q^81 - 8 * q^82 - 22 * q^83 - 2 * q^84 - 5 * q^85 - 38 * q^86 + 45 * q^87 + 100 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - 28 * q^93 - 2 * q^94 - 2 * q^95 + 79 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.37850	+	2.38764i	−0.974749	+	1.68832i	−0.293990	+	0.955809i	$0.594983\pi$
$2$	−1.37850	+	2.38764i	−0.974749	+	1.68832i	−0.680760	+	0.732507i	$0.738350\pi$
$3$	−1.12222	+	1.31932i	−0.647917	+	0.761711i
$3$	−1.12222	+	1.31932i	−0.647917	+	0.761711i
$4$	−2.80055	−	4.85069i	−1.40027	−	2.42534i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.60307	−	4.49816i	−0.654452	−	1.83637i
$7$	2.15266	−	1.53820i	0.813627	−	0.581387i
$7$	2.15266	−	1.53820i	0.813627	−	0.581387i
$8$	9.92824			3.51016
$9$	−0.481224	−	2.96115i	−0.160408	−	0.987051i
$10$	−1.37850	+	2.38764i	−0.435921	+	0.755038i
$11$	2.28080			0.687689			0.343844	−	0.939027i	$-0.388271\pi$
$11$	2.28080			0.687689			0.343844	+	0.939027i	$0.388271\pi$
$12$	9.54246	+	1.74874i	2.75467	+	0.504817i
$13$	1.37896	−	2.38844i	0.382456	−	0.662433i	−0.608957	−	0.793203i	$-0.708412\pi$
$13$	1.37896	−	2.38844i	0.382456	−	0.662433i	0.991413	+	0.130770i	$0.0417450\pi$
$14$	0.705233	+	7.26018i	0.188481	+	1.94037i
$15$	−1.12222	+	1.31932i	−0.289757	+	0.340648i
$16$	−8.08502	+	14.0037i	−2.02126	+	3.50092i
$17$	1.01423	−	1.75669i	0.245986	−	0.426060i	−0.716422	−	0.697667i	$-0.754222\pi$
$17$	1.01423	−	1.75669i	0.245986	−	0.426060i	0.962408	+	0.271607i	$0.0875550\pi$
$18$	7.73353	+	2.93297i	1.82281	+	0.691308i
$19$	−3.03493	−	5.25665i	−0.696261	−	1.20596i	−0.969754	−	0.244085i	$-0.921512\pi$
$19$	−3.03493	−	5.25665i	−0.696261	−	1.20596i	0.273493	−	0.961874i	$-0.411821\pi$
$20$	−2.80055	−	4.85069i	−0.626221	−	1.08465i
$21$	−0.386375	+	4.56626i	−0.0843140	+	0.996439i
$22$	−3.14410	+	5.44574i	−0.670324	+	1.16104i
$23$	2.99113			0.623694			0.311847	−	0.950132i	$-0.399052\pi$
$23$	2.99113			0.623694			0.311847	+	0.950132i	$0.399052\pi$
$24$	−11.1417	+	13.0985i	−2.27429	+	2.67373i
$25$	1.00000			0.200000
$26$	3.80182	+	6.58494i	0.745598	+	1.29141i
$27$	4.44676	+	2.68819i	0.855779	+	0.517342i
$28$	−13.4900	−	6.13405i	−2.54936	−	1.15923i
$29$	−2.78655	−	4.82644i	−0.517449	−	0.896248i	−0.999795	−	0.0202667i	$-0.993548\pi$
$29$	−2.78655	−	4.82644i	−0.517449	−	0.896248i	0.482346	−	0.875981i	$-0.339785\pi$
$30$	−1.60307	−	4.49816i	−0.292680	−	0.821248i
$31$	0.166500	+	0.288386i	0.0299043	+	0.0517957i	0.880590	−	0.473879i	$-0.157146\pi$
$31$	0.166500	+	0.288386i	0.0299043	+	0.0517957i	−0.850686	+	0.525674i	$0.823813\pi$
$32$	−12.3622	−	21.4120i	−2.18535	−	3.78514i
$33$	−2.55958	+	3.00912i	−0.445565	+	0.523820i
$34$	2.79623	+	4.84321i	0.479549	+	0.830604i
$35$	2.15266	−	1.53820i	0.363865	−	0.260004i
$36$	−13.0159	+	10.6271i	−2.16932	+	1.77118i
$37$	0.0601415	+	0.104168i	0.00988720	+	0.0171251i	0.870927	−	0.491413i	$-0.163519\pi$
$37$	0.0601415	+	0.104168i	0.00988720	+	0.0171251i	−0.861039	+	0.508538i	$0.830186\pi$
$38$	16.7347			2.71472
$39$	1.60361	+	4.49966i	0.256783	+	0.720523i
$40$	9.92824			1.56979
$41$	−0.237341	+	0.411087i	−0.0370665	+	0.0642010i	−0.883964	−	0.467556i	$-0.845135\pi$
$41$	−0.237341	+	0.411087i	−0.0370665	+	0.0642010i	0.846897	+	0.531757i	$0.178468\pi$
$42$	−10.3700	−	7.21713i	−1.60012	−	1.11363i
$43$	3.43450	+	5.94872i	0.523756	+	0.907171i	0.999618	+	0.0276514i	$0.00880283\pi$
$43$	3.43450	+	5.94872i	0.523756	+	0.907171i	−0.475862	+	0.879520i	$0.657864\pi$
$44$	−6.38750	−	11.0635i	−0.962952	−	1.66788i
$45$	−0.481224	−	2.96115i	−0.0717366	−	0.441423i
$46$	−4.12329	+	7.14174i	−0.607946	+	1.05299i
$47$	−3.60725	+	6.24794i	−0.526172	+	0.911356i	0.473363	+	0.880867i	$0.343040\pi$
$47$	−3.60725	+	6.24794i	−0.526172	+	0.911356i	−0.999535	+	0.0304891i	$0.990294\pi$
$48$	−9.40214	−	26.3820i	−1.35708	−	3.80791i
$49$	2.26785	−	6.62245i	0.323979	−	0.946064i
$50$	−1.37850	+	2.38764i	−0.194950	+	0.337663i
$51$	1.17945	+	3.30949i	0.165156	+	0.463422i
$52$	−15.4474			−2.14217
$53$	−4.25673	+	7.37287i	−0.584707	+	1.01274i	0.410205	+	0.911993i	$0.365457\pi$
$53$	−4.25673	+	7.37287i	−0.584707	+	1.01274i	−0.994912	+	0.100748i	$0.967876\pi$
$54$	−12.5483	+	6.91157i	−1.70761	+	0.940545i
$55$	2.28080			0.307544
$56$	21.3721	−	15.2717i	2.85596	−	2.04076i
$57$	10.3411	+	1.89509i	1.36971	+	0.251011i
$58$	15.3651			2.01753
$59$	4.32075	+	7.48375i	0.562513	+	0.974302i	0.997276	+	0.0737566i	$0.0234988\pi$
$59$	4.32075	+	7.48375i	0.562513	+	0.974302i	−0.434763	+	0.900545i	$0.643168\pi$
$60$	9.54246	+	1.74874i	1.23193	+	0.225761i
$61$	5.64787	−	9.78239i	0.723135	−	1.25251i	−0.236601	−	0.971607i	$-0.576034\pi$
$61$	5.64787	−	9.78239i	0.723135	−	1.25251i	0.959737	−	0.280901i	$-0.0906331\pi$
$62$	−0.918083			−0.116597
$63$	−5.59077	−	5.63412i	−0.704371	−	0.709832i
$64$	35.8254			4.47818
$65$	1.37896	−	2.38844i	0.171040	−	0.296249i
$66$	−3.65630	−	10.2594i	−0.450059	−	1.26285i
$67$	3.39059	+	5.87268i	0.414227	+	0.717462i	0.995347	−	0.0963558i	$-0.0307187\pi$
$67$	3.39059	+	5.87268i	0.414227	+	0.717462i	−0.581120	+	0.813818i	$0.697385\pi$
$68$	−11.3615			−1.37779
$69$	−3.35672	+	3.94627i	−0.404102	+	0.475075i
$70$	0.705233	+	7.26018i	0.0842914	+	0.867758i
$71$	12.3927			1.47074			0.735369	−	0.677667i	$-0.237009\pi$
$71$	12.3927			1.47074			0.735369	+	0.677667i	$0.237009\pi$
$72$	−4.77770	−	29.3990i	−0.563058	−	3.46471i
$73$	0.0952946	−	0.165055i	0.0111534	−	0.0193182i	−0.860395	−	0.509628i	$-0.829783\pi$
$73$	0.0952946	−	0.165055i	0.0111534	−	0.0193182i	0.871548	+	0.490310i	$0.163116\pi$
$74$	−0.331621			−0.0385502
$75$	−1.12222	+	1.31932i	−0.129583	+	0.152342i
$76$	−16.9989	+	29.4430i	−1.94991	+	3.37734i
$77$	4.90979	−	3.50834i	0.559522	−	0.399813i
$78$	−12.9542	−	2.37396i	−1.46677	−	0.268798i
$79$	5.77167	−	9.99682i	0.649363	−	1.12473i	−0.333912	−	0.942604i	$-0.608369\pi$
$79$	5.77167	−	9.99682i	0.649363	−	1.12473i	0.983275	−	0.182126i	$-0.0582978\pi$
$80$	−8.08502	+	14.0037i	−0.903933	+	1.56566i
$81$	−8.53685	+	2.84995i	−0.948539	+	0.316662i
$82$	−0.654352	−	1.13337i	−0.0722611	−	0.125160i
$83$	−3.98395	−	6.90040i	−0.437295	−	0.757418i	0.560185	−	0.828368i	$-0.310730\pi$
$83$	−3.98395	−	6.90040i	−0.437295	−	0.757418i	−0.997480	+	0.0709503i	$0.977397\pi$
$84$	23.2316	−	10.9138i	2.53477	−	1.19080i
$85$	1.01423	−	1.75669i	0.110008	−	0.190540i
$86$	−18.9379			−2.04212
$87$	9.49476	+	1.74000i	1.01795	+	0.186547i
$88$	22.6444			2.41390
$89$	1.05443	+	1.82633i	0.111770	+	0.193591i	0.916484	−	0.400072i	$-0.131015\pi$
$89$	1.05443	+	1.82633i	0.111770	+	0.193591i	−0.804714	+	0.593662i	$0.797681\pi$
$90$	7.73353	+	2.93297i	0.815186	+	0.309162i
$91$	−0.705469	−	7.26261i	−0.0739532	−	0.761329i
$92$	−8.37680	−	14.5090i	−0.873342	−	1.51267i
$93$	−0.567325	−	0.103967i	−0.0588289	−	0.0107809i
$94$	−9.94522	−	17.2256i	−1.02577	−	1.77669i
$95$	−3.03493	−	5.25665i	−0.311377	−	0.539321i
$96$	42.1225	+	7.71931i	4.29911	+	0.787849i
$97$	−3.42650	−	5.93488i	−0.347909	−	0.602596i	0.637969	−	0.770062i	$-0.279775\pi$
$97$	−3.42650	−	5.93488i	−0.347909	−	0.602596i	−0.985878	+	0.167466i	$0.946441\pi$
$98$	12.6858	+	14.5439i	1.28146	+	1.46915i
$99$	−1.09758	−	6.75381i	−0.110311	−	0.678784i
$100$	−2.80055	−	4.85069i	−0.280055	−	0.485069i
$101$	−12.5495			−1.24872			−0.624360	−	0.781137i	$-0.714640\pi$
$101$	−12.5495			−1.24872			−0.624360	+	0.781137i	$0.714640\pi$
$102$	−9.52775	−	1.74604i	−0.943388	−	0.172884i
$103$	−14.9056			−1.46870			−0.734348	−	0.678774i	$-0.762512\pi$
$103$	−14.9056			−1.46870			−0.734348	+	0.678774i	$0.762512\pi$
$104$	13.6907	−	23.7130i	1.34248	−	2.32525i
$105$	−0.386375	+	4.56626i	−0.0377064	+	0.445621i
$106$	−11.7358	−	20.3271i	−1.13989	−	1.97434i
$107$	8.79267	+	15.2293i	0.850019	+	1.47228i	0.881190	+	0.472762i	$0.156743\pi$
$107$	8.79267	+	15.2293i	0.850019	+	1.47228i	−0.0311708	+	0.999514i	$0.509924\pi$
$108$	0.586218	−	29.0982i	0.0564089	−	2.79998i
$109$	−2.07627	+	3.59620i	−0.198870	+	0.344454i	−0.948162	−	0.317786i	$-0.897061\pi$
$109$	−2.07627	+	3.59620i	−0.198870	+	0.344454i	0.749292	+	0.662240i	$0.230394\pi$
$110$	−3.14410	+	5.44574i	−0.299778	+	0.519231i
$111$	−0.204924	−	0.0375540i	−0.0194505	−	0.00356447i
$112$	4.13624	+	42.5815i	0.390838	+	4.02357i
$113$	3.40667	−	5.90053i	0.320473	−	0.555075i	−0.660113	−	0.751166i	$-0.729492\pi$
$113$	3.40667	−	5.90053i	0.320473	−	0.555075i	0.980586	+	0.196091i	$0.0628250\pi$
$114$	−18.7800	+	22.0784i	−1.75891	+	2.06783i
$115$	2.99113			0.278925
$116$	−15.6077	+	27.0333i	−1.44914	+	2.50998i
$117$	−7.73612	−	2.93395i	−0.715204	−	0.271244i
$118$	−23.8247			−2.19324
$119$	−0.518871	−	5.34164i	−0.0475648	−	0.489667i
$120$	−11.1417	+	13.0985i	−1.01709	+	1.19573i
$121$	−5.79793			−0.527084
$122$	15.5712	+	26.9701i	1.40975	+	2.44176i
$123$	−0.276006	−	0.774462i	−0.0248867	−	0.0698309i
$124$	0.932582	−	1.61528i	0.0837483	−	0.145056i
$125$	1.00000			0.0894427
$126$	21.1591	−	5.58208i	1.88501	−	0.497291i
$127$	15.5473			1.37960			0.689799	−	0.724001i	$-0.257699\pi$
$127$	15.5473			1.37960			0.689799	+	0.724001i	$0.257699\pi$
$128$	−24.6610	+	42.7142i	−2.17975	+	3.77543i
$129$	−11.7026	−	2.14459i	−1.03035	−	0.188821i
$130$	3.80182	+	6.58494i	0.333441	+	0.577537i
$131$	−8.79795			−0.768681			−0.384340	−	0.923191i	$-0.625571\pi$
$131$	−8.79795			−0.768681			−0.384340	+	0.923191i	$0.625571\pi$
$132$	21.7645	+	3.98853i	1.89436	+	0.347157i
$133$	−14.6190	−	6.64742i	−1.26763	−	0.576405i
$134$	−18.6958			−1.61507
$135$	4.44676	+	2.68819i	0.382716	+	0.231362i
$136$	10.0695	−	17.4408i	0.863450	−	1.49554i
$137$	0.433357			0.0370242			0.0185121	−	0.999829i	$-0.494107\pi$
$137$	0.433357			0.0370242			0.0185121	+	0.999829i	$0.494107\pi$
$138$	−4.79501	−	13.4546i	−0.408178	−	1.14533i
$139$	−1.11053	+	1.92350i	−0.0941940	+	0.163149i	−0.909272	−	0.416203i	$-0.863361\pi$
$139$	−1.11053	+	1.92350i	−0.0941940	+	0.163149i	0.815078	+	0.579351i	$0.196694\pi$
$140$	−13.4900	−	6.13405i	−1.14011	−	0.518422i
$141$	−4.19491	−	11.7707i	−0.353275	−	0.991274i
$142$	−17.0833	+	29.5892i	−1.43360	+	2.48307i
$143$	3.14515	−	5.44756i	0.263011	−	0.455548i
$144$	45.3577	+	17.2021i	3.77981	+	1.43351i
$145$	−2.78655	−	4.82644i	−0.231410	−	0.400814i
$146$	0.262728	+	0.455058i	0.0217435	+	0.0376609i
$147$	6.19211	+	10.4239i	0.510716	+	0.859749i
$148$	0.336858	−	0.583455i	0.0276895	−	0.0479597i
$149$	−8.31331			−0.681053			−0.340527	−	0.940235i	$-0.610605\pi$
$149$	−8.31331			−0.681053			−0.340527	+	0.940235i	$0.610605\pi$
$150$	−1.60307	−	4.49816i	−0.130890	−	0.367273i
$151$	20.7346			1.68736			0.843680	−	0.536846i	$-0.180384\pi$
$151$	20.7346			1.68736			0.843680	+	0.536846i	$0.180384\pi$
$152$	−30.1315	−	52.1893i	−2.44399	−	4.23311i
$153$	−5.68990	−	2.15792i	−0.460001	−	0.174457i
$154$	1.60850	+	16.5591i	0.129616	+	1.33437i
$155$	0.166500	+	0.288386i	0.0133736	+	0.0231638i
$156$	17.3355	−	20.3801i	1.38795	−	1.63172i
$157$	−7.11580	−	12.3249i	−0.567902	−	0.983636i	−0.996773	−	0.0802700i	$-0.974422\pi$
$157$	−7.11580	−	12.3249i	−0.567902	−	0.983636i	0.428871	−	0.903366i	$-0.358912\pi$
$158$	15.9125	+	27.5613i	1.26593	+	2.19266i
$159$	−4.95019	−	13.8900i	−0.392576	−	1.10155i
$160$	−12.3622	−	21.4120i	−0.977320	−	1.69277i
$161$	6.43888	−	4.60097i	0.507455	−	0.362608i
$162$	4.96342	−	24.3116i	0.389963	−	1.91010i
$163$	−3.08319	−	5.34024i	−0.241494	−	0.418280i	0.719646	−	0.694341i	$-0.244304\pi$
$163$	−3.08319	−	5.34024i	−0.241494	−	0.418280i	−0.961140	+	0.276061i	$0.910971\pi$
$164$	2.65874			0.207613
$165$	−2.55958	+	3.00912i	−0.199263	+	0.234259i
$166$	21.9676			1.70501
$167$	−2.22416	+	3.85236i	−0.172111	+	0.298105i	−0.939158	−	0.343487i	$-0.888392\pi$
$167$	−2.22416	+	3.85236i	−0.172111	+	0.298105i	0.767047	+	0.641591i	$0.221725\pi$
$168$	−3.83602	+	45.3349i	−0.295956	+	3.49766i
$169$	2.69691	+	4.67119i	0.207455	+	0.359322i
$170$	2.79623	+	4.84321i	0.214461	+	0.371457i
$171$	−14.1053	+	11.5165i	−1.07866	+	0.880690i
$172$	19.2369	−	33.3193i	1.46680	−	2.54057i
$173$	−8.95676	+	15.5136i	−0.680969	+	1.17947i	0.293716	+	0.955893i	$0.405108\pi$
$173$	−8.95676	+	15.5136i	−0.680969	+	1.17947i	−0.974685	+	0.223581i	$0.928225\pi$
$174$	−17.2431	+	20.2715i	−1.30719	+	1.53678i
$175$	2.15266	−	1.53820i	0.162725	−	0.116277i
$176$	−18.4404	+	31.9396i	−1.38999	+	2.40754i
$177$	−14.7223	−	2.69799i	−1.10660	−	0.202794i
$178$	−5.81415			−0.435789
$179$	−9.04272	+	15.6625i	−0.675885	+	1.17067i	0.300325	+	0.953837i	$0.402905\pi$
$179$	−9.04272	+	15.6625i	−0.675885	+	1.17067i	−0.976209	+	0.216830i	$0.930428\pi$
$180$	−13.0159	+	10.6271i	−0.970151	+	0.792098i
$181$	5.03221			0.374041			0.187021	−	0.982356i	$-0.440117\pi$
$181$	5.03221			0.374041			0.187021	+	0.982356i	$0.440117\pi$
$182$	18.3130	+	8.32714i	1.35745	+	0.617248i
$183$	6.56796	+	18.4294i	0.485517	+	1.36234i
$184$	29.6967			2.18927
$185$	0.0601415	+	0.104168i	0.00442169	+	0.00765859i
$186$	1.03030	−	1.21125i	0.0755450	−	0.0888130i
$187$	2.31325	−	4.00667i	0.169162	−	0.292997i
$188$	40.4091			2.94714
$189$	13.7073	−	1.05328i	0.997061	−	0.0766146i
$190$	16.7347			1.21406
$191$	6.00854	−	10.4071i	0.434763	−	0.753032i	−0.562513	−	0.826788i	$-0.690165\pi$
$191$	6.00854	−	10.4071i	0.434763	−	0.753032i	0.997276	+	0.0737566i	$0.0234988\pi$
$192$	−40.2042	+	47.2653i	−2.90149	+	3.41108i
$193$	5.09723	+	8.82866i	0.366907	+	0.635501i	0.989080	−	0.147378i	$-0.0470835\pi$
$193$	5.09723	+	8.82866i	0.366907	+	0.635501i	−0.622174	+	0.782879i	$0.713750\pi$
$194$	18.8938			1.35650
$195$	1.60361	+	4.49966i	0.114837	+	0.322227i
$196$	−38.4747	+	7.54583i	−2.74819	+	0.538988i
$197$	8.70110			0.619928			0.309964	−	0.950748i	$-0.399683\pi$
$197$	8.70110			0.619928			0.309964	+	0.950748i	$0.399683\pi$
$198$	17.6387	+	6.68953i	1.25353	+	0.475405i
$199$	−2.25588	+	3.90730i	−0.159915	+	0.276981i	−0.934838	−	0.355075i	$-0.884455\pi$
$199$	−2.25588	+	3.90730i	−0.159915	+	0.276981i	0.774923	+	0.632056i	$0.217789\pi$
$200$	9.92824			0.702032
$201$	−11.5530	−	2.11718i	−0.814883	−	0.149334i
$202$	17.2995	−	29.9636i	1.21719	−	2.10823i
$203$	−13.4225	−	6.10339i	−0.942077	−	0.428374i
$204$	12.7502	−	14.9895i	0.892693	−	1.04948i
$205$	−0.237341	+	0.411087i	−0.0165766	+	0.0287116i
$206$	20.5475	−	35.5893i	1.43161	−	2.47962i
$207$	−1.43940	−	8.85720i	−0.100046	−	0.615618i
$208$	22.2979	+	38.6211i	1.54608	+	2.67789i
$209$	−6.92208	−	11.9894i	−0.478811	−	0.829324i
$210$	−10.3700	−	7.21713i	−0.715595	−	0.498029i
$211$	−9.86770	+	17.0914i	−0.679320	+	1.17662i	0.295866	+	0.955230i	$0.404392\pi$
$211$	−9.86770	+	17.0914i	−0.679320	+	1.17662i	−0.975186	+	0.221388i	$0.928941\pi$
$212$	47.6847			3.27500
$213$	−13.9073	+	16.3499i	−0.952915	+	1.12028i
$214$	−48.4829			−3.31422
$215$	3.43450	+	5.94872i	0.234231	+	0.405699i
$216$	44.1484	+	26.6890i	3.00392	+	1.81595i
$217$	0.802014	+	0.364686i	0.0544443	+	0.0247565i
$218$	−5.72429	−	9.91476i	−0.387698	−	0.671512i
$219$	0.110819	+	0.310953i	0.00748845	+	0.0210123i
$220$	−6.38750	−	11.0635i	−0.430645	−	0.745899i
$221$	−2.79716	−	4.84483i	−0.188158	−	0.325898i
$222$	0.372153	−	0.437515i	0.0249773	−	0.0293641i
$223$	3.33721	+	5.78023i	0.223476	+	0.387073i	0.955861	−	0.293818i	$-0.0949261\pi$
$223$	3.33721	+	5.78023i	0.223476	+	0.387073i	−0.732385	+	0.680891i	$0.761593\pi$
$224$	−59.5477	−	27.0770i	−3.97870	−	1.80916i
$225$	−0.481224	−	2.96115i	−0.0320816	−	0.197410i
$226$	9.39222	+	16.2678i	0.624761	+	1.08212i
$227$	−2.73930			−0.181814			−0.0909068	−	0.995859i	$-0.528977\pi$
$227$	−2.73930			−0.181814			−0.0909068	+	0.995859i	$0.528977\pi$
$228$	−19.7682	−	55.4687i	−1.30918	−	3.67351i
$229$	4.72711			0.312376			0.156188	−	0.987727i	$-0.450079\pi$
$229$	4.72711			0.312376			0.156188	+	0.987727i	$0.450079\pi$
$230$	−4.12329	+	7.14174i	−0.271882	+	0.470913i
$231$	−0.881246	+	10.4147i	−0.0579818	+	0.685240i
$232$	−27.6655	−	47.9180i	−1.81633	−	3.14597i
$233$	−12.2018	−	21.1341i	−0.799365	−	1.38454i	−0.920030	−	0.391848i	$-0.871836\pi$
$233$	−12.2018	−	21.1341i	−0.799365	−	1.38454i	0.120665	−	0.992693i	$-0.461497\pi$
$234$	17.6695	−	14.4266i	1.15509	−	0.943096i
$235$	−3.60725	+	6.24794i	−0.235311	+	0.407571i
$236$	24.2009	−	41.9172i	1.57534	−	2.72858i
$237$	6.71192	+	18.8334i	0.435986	+	1.22336i
$238$	13.4692	+	6.12459i	0.873076	+	0.396998i
$239$	1.18546	−	2.05327i	0.0766809	−	0.132815i	−0.825135	−	0.564935i	$-0.808901\pi$
$239$	1.18546	−	2.05327i	0.0766809	−	0.132815i	0.901816	+	0.432120i	$0.142234\pi$
$240$	−9.40214	−	26.3820i	−0.606906	−	1.70295i
$241$	11.1539			0.718484			0.359242	−	0.933244i	$-0.383035\pi$
$241$	11.1539			0.718484			0.359242	+	0.933244i	$0.383035\pi$
$242$	7.99247	−	13.8434i	0.513775	−	0.889885i
$243$	5.82025	−	14.4611i	0.373369	−	0.927683i
$244$	−63.2685			−4.05035
$245$	2.26785	−	6.62245i	0.144888	−	0.423093i
$246$	2.22961	+	0.408595i	0.142155	+	0.0260511i
$247$	−16.7402			−1.06516
$248$	1.65305	+	2.86317i	0.104969	+	0.181811i
$249$	13.5747	+	2.48769i	0.860264	+	0.157651i
$250$	−1.37850	+	2.38764i	−0.0871842	+	0.151008i
$251$	−1.86691			−0.117838			−0.0589192	−	0.998263i	$-0.518765\pi$
$251$	−1.86691			−0.117838			−0.0589192	+	0.998263i	$0.518765\pi$
$252$	−11.6722	+	42.8977i	−0.735277	+	2.70230i
$253$	6.82219			0.428907
$254$	−21.4320	+	37.1213i	−1.34476	+	2.32920i
$255$	1.17945	+	3.30949i	0.0738602	+	0.207248i
$256$	−32.1652	−	55.7118i	−2.01033	−	3.48199i
$257$	−1.50775			−0.0940509			−0.0470254	−	0.998894i	$-0.514974\pi$
$257$	−1.50775			−0.0940509			−0.0470254	+	0.998894i	$0.514974\pi$
$258$	21.2525	−	24.9851i	1.32312	−	1.55551i
$259$	0.289696	+	0.131728i	0.0180008	+	0.00818519i
$260$	−15.4474			−0.958008
$261$	−12.9509	+	10.5740i	−0.801639	+	0.654513i
$262$	12.1280	−	21.0063i	0.749271	−	1.29778i
$263$	−1.92840			−0.118910			−0.0594551	−	0.998231i	$-0.518936\pi$
$263$	−1.92840			−0.118910			−0.0594551	+	0.998231i	$0.518936\pi$
$264$	−25.4121	+	29.8752i	−1.56400	+	1.83869i
$265$	−4.25673	+	7.37287i	−0.261489	+	0.452912i
$266$	36.0239	−	25.7413i	2.20877	−	1.57830i
$267$	−3.59283	−	0.658416i	−0.219878	−	0.0402944i
$268$	18.9910	−	32.8934i	1.16006	−	2.00929i
$269$	5.62853	−	9.74890i	0.343177	−	0.594401i	−0.641843	−	0.766836i	$-0.721830\pi$
$269$	5.62853	−	9.74890i	0.343177	−	0.594401i	0.985021	+	0.172435i	$0.0551634\pi$
$270$	−12.5483	+	6.91157i	−0.763665	+	0.420625i
$271$	9.11902	+	15.7946i	0.553941	+	0.959454i	0.997985	+	0.0634494i	$0.0202101\pi$
$271$	9.11902	+	15.7946i	0.553941	+	0.959454i	−0.444044	+	0.896005i	$0.646457\pi$
$272$	16.4001	+	28.4058i	0.994400	+	1.72235i
$273$	10.3734	+	7.21954i	0.627828	+	0.436947i
$274$	−0.597384	+	1.03470i	−0.0360893	+	0.0625085i
$275$	2.28080			0.137538
$276$	28.5428	+	5.23071i	1.71807	+	0.314852i
$277$	−5.03488			−0.302517			−0.151258	−	0.988494i	$-0.548333\pi$
$277$	−5.03488			−0.302517			−0.151258	+	0.988494i	$0.548333\pi$
$278$	−3.06174	−	5.30309i	−0.183631	−	0.318058i
$279$	0.773832	−	0.631810i	0.0463281	−	0.0378255i
$280$	21.3721	−	15.2717i	1.27723	−	0.912656i
$281$	−5.29241	−	9.16672i	−0.315719	−	0.546841i	0.663871	−	0.747847i	$-0.268912\pi$
$281$	−5.29241	−	9.16672i	−0.315719	−	0.546841i	−0.979590	+	0.201006i	$0.935579\pi$
$282$	33.8869	+	6.21007i	2.01794	+	0.369804i
$283$	−1.26176	−	2.18543i	−0.0750039	−	0.129911i	0.826084	−	0.563547i	$-0.190564\pi$
$283$	−1.26176	−	2.18543i	−0.0750039	−	0.129911i	−0.901088	+	0.433636i	$0.857230\pi$
$284$	−34.7062	−	60.1129i	−2.05943	−	3.56704i
$285$	10.3411	+	1.89509i	0.612554	+	0.112256i
$286$	8.67120	+	15.0190i	0.512739	+	0.888090i
$287$	0.121422	+	1.25001i	0.00716732	+	0.0737857i
$288$	−57.4552	+	46.9104i	−3.38558	+	2.76422i
$289$	6.44269	+	11.1591i	0.378982	+	0.656416i
$290$	15.3651			0.902268
$291$	11.6753	+	2.13960i	0.684420	+	0.125426i
$292$	−1.06751			−0.0624712
$293$	−12.4897	+	21.6328i	−0.729655	+	1.26380i	0.227374	+	0.973808i	$0.426986\pi$
$293$	−12.4897	+	21.6328i	−0.729655	+	1.26380i	−0.957029	+	0.289992i	$0.906347\pi$
$294$	−33.4244	+	0.415120i	−1.94935	+	0.0242103i
$295$	4.32075	+	7.48375i	0.251564	+	0.435721i
$296$	0.597099	+	1.03421i	0.0347057	+	0.0601120i
$297$	10.1422	+	6.13123i	0.588509	+	0.355770i
$298$	11.4599	−	19.8492i	0.663856	−	1.14983i
$299$	4.12467	−	7.14413i	0.238536	−	0.413156i
$300$	9.54246	+	1.74874i	0.550934	+	0.100963i
$301$	16.5436	+	7.52259i	0.953559	+	0.433595i
$302$	−28.5828	+	49.5068i	−1.64475	+	2.84880i
$303$	14.0833	−	16.5568i	0.809066	−	0.951164i
$304$	98.1499			5.62928
$305$	5.64787	−	9.78239i	0.323396	−	0.560138i
$306$	12.9959	−	10.6107i	0.742924	−	0.606575i
$307$	−16.5452			−0.944287			−0.472143	−	0.881522i	$-0.656520\pi$
$307$	−16.5452			−0.944287			−0.472143	+	0.881522i	$0.656520\pi$
$308$	−30.7680	−	13.9906i	−1.75317	−	0.797186i
$309$	16.7275	−	19.6653i	0.951592	−	1.11872i
$310$	−0.918083			−0.0521436
$311$	−5.11575	−	8.86074i	−0.290088	−	0.502447i	0.683743	−	0.729723i	$-0.260351\pi$
$311$	−5.11575	−	8.86074i	−0.290088	−	0.502447i	−0.973830	+	0.227277i	$0.927018\pi$
$312$	15.9210	+	44.6737i	0.901351	+	2.52915i
$313$	−5.83361	+	10.1041i	−0.329735	+	0.571118i	−0.982459	−	0.186477i	$-0.940293\pi$
$313$	−5.83361	+	10.1041i	−0.329735	+	0.571118i	0.652724	+	0.757596i	$0.273626\pi$
$314$	39.2366			2.21425
$315$	−5.59077	−	5.63412i	−0.315004	−	0.317447i
$316$	−64.6553			−3.63714
$317$	1.52848	−	2.64741i	0.0858482	−	0.148693i	−0.819904	−	0.572501i	$-0.805973\pi$
$317$	1.52848	−	2.64741i	0.0858482	−	0.148693i	0.905752	+	0.423807i	$0.139307\pi$
$318$	39.9882	+	7.32818i	2.24243	+	0.410944i
$319$	−6.35557	−	11.0082i	−0.355844	−	0.616339i
$320$	35.8254			2.00270
$321$	−29.9598	−	5.49038i	−1.67219	−	0.306443i
$322$	2.10944	+	21.7162i	0.117555	+	1.21020i
$323$	−12.3124			−0.685081
$324$	37.7321	+	33.4281i	2.09623	+	1.85712i
$325$	1.37896	−	2.38844i	0.0764912	−	0.132487i
$326$	17.0008			0.941585
$327$	−2.41451	−	6.77501i	−0.133523	−	0.374659i
$328$	−2.35638	+	4.08137i	−0.130109	+	0.225356i
$329$	1.84544	+	18.9984i	0.101743	+	1.04741i
$330$	−3.65630	−	10.2594i	−0.201273	−	0.564763i
$331$	−0.204487	+	0.354183i	−0.0112396	+	0.0194676i	−0.871591	−	0.490235i	$-0.836911\pi$
$331$	−0.204487	+	0.354183i	−0.0112396	+	0.0194676i	0.860351	+	0.509702i	$0.170244\pi$
$332$	−22.3145	+	38.6498i	−1.22467	+	2.12118i
$333$	0.279516	−	0.228216i	0.0153174	−	0.0125062i
$334$	−6.13203	−	10.6210i	−0.335530	−	0.581154i
$335$	3.39059	+	5.87268i	0.185248	+	0.320859i
$336$	−60.8205	−	42.3290i	−3.31803	−	2.30923i
$337$	5.32468	−	9.22262i	0.290054	−	0.502388i	−0.683768	−	0.729699i	$-0.739660\pi$
$337$	5.32468	−	9.22262i	0.290054	−	0.502388i	0.973822	+	0.227311i	$0.0729934\pi$
$338$	−14.8708			−0.808866
$339$	3.96165	+	11.1162i	0.215167	+	0.603750i
$340$	−11.3615			−0.616166
$341$	0.379754	+	0.657753i	0.0205648	+	0.0356193i
$342$	−8.05311	−	49.5539i	−0.435463	−	2.67957i
$343$	−5.30478	−	17.7443i	−0.286431	−	0.958101i
$344$	34.0985	+	59.0603i	1.83847	+	3.18432i
$345$	−3.35672	+	3.94627i	−0.180720	+	0.212460i
$346$	−24.6938	−	42.7710i	−1.32755	−	2.29938i
$347$	12.1555	+	21.0539i	0.652540	+	1.13023i	0.982504	+	0.186239i	$0.0596298\pi$
$347$	12.1555	+	21.0539i	0.652540	+	1.13023i	−0.329965	+	0.943993i	$0.607037\pi$
$348$	−18.1503	−	50.9291i	−0.972960	−	2.73008i
$349$	10.7597	+	18.6364i	0.575955	+	0.997584i	0.995937	+	0.0900511i	$0.0287030\pi$
$349$	10.7597	+	18.6364i	0.575955	+	0.997584i	−0.419982	+	0.907532i	$0.637964\pi$
$350$	0.705233	+	7.26018i	0.0376963	+	0.388073i
$351$	12.5525	−	6.91388i	0.670002	−	0.369036i
$352$	−28.1958	−	48.8366i	−1.50284	−	2.60300i
$353$	9.55165			0.508383			0.254192	−	0.967154i	$-0.418191\pi$
$353$	9.55165			0.508383			0.254192	+	0.967154i	$0.418191\pi$
$354$	26.7366	−	31.4324i	1.42104	−	1.67061i
$355$	12.3927			0.657734
$356$	5.90597	−	10.2294i	0.313016	−	0.542159i
$357$	7.62963	+	5.30996i	0.403803	+	0.281033i
$358$	−24.9309	−	43.1815i	−1.31764	−	2.28221i
$359$	−3.89960	−	6.75430i	−0.205813	−	0.356478i	0.744579	−	0.667535i	$-0.232650\pi$
$359$	−3.89960	−	6.75430i	−0.205813	−	0.356478i	−0.950391	+	0.311057i	$0.899317\pi$
$360$	−4.77770	−	29.3990i	−0.251807	−	1.54946i
$361$	−8.92161	+	15.4527i	−0.469558	+	0.813299i
$362$	−6.93692	+	12.0151i	−0.364596	+	0.631500i
$363$	6.50658	−	7.64934i	0.341507	−	0.401486i
$364$	−33.2530	+	23.7613i	−1.74293	+	1.24543i
$365$	0.0952946	−	0.165055i	0.00498795	−	0.00863938i
$366$	−53.0567	−	9.72310i	−2.77332	−	0.508234i
$367$	−16.3396			−0.852920			−0.426460	−	0.904506i	$-0.640240\pi$
$367$	−16.3396			−0.852920			−0.426460	+	0.904506i	$0.640240\pi$
$368$	−24.1834	+	41.8868i	−1.26065	+	2.18350i
$369$	1.33151	+	0.504979i	0.0693154	+	0.0262881i
$370$	−0.331621			−0.0172402
$371$	2.17771	+	22.4190i	0.113061	+	1.16394i
$372$	1.08451	+	3.04308i	0.0562291	+	0.157776i
$373$	8.91785			0.461749			0.230874	−	0.972984i	$-0.425841\pi$
$373$	8.91785			0.461749			0.230874	+	0.972984i	$0.425841\pi$
$374$	6.37765	+	11.0464i	0.329780	+	0.571197i
$375$	−1.12222	+	1.31932i	−0.0579514	+	0.0681295i
$376$	−35.8137	+	62.0311i	−1.84695	+	3.19901i
$377$	−15.3702			−0.791606
$378$	−16.3807	+	34.1801i	−0.842535	+	1.75803i
$379$	1.27870			0.0656824			0.0328412	−	0.999461i	$-0.489544\pi$
$379$	1.27870			0.0656824			0.0328412	+	0.999461i	$0.489544\pi$
$380$	−16.9989	+	29.4430i	−0.872026	+	1.51039i
$381$	−17.4475	+	20.5119i	−0.893864	+	1.05085i
$382$	16.5656	+	28.6925i	0.847570	+	1.46803i
$383$	1.37316			0.0701652			0.0350826	−	0.999384i	$-0.488831\pi$
$383$	1.37316			0.0701652			0.0350826	+	0.999384i	$0.488831\pi$
$384$	−28.6785	−	80.4707i	−1.46350	−	4.10651i
$385$	4.90979	−	3.50834i	0.250226	−	0.178802i
$386$	−28.1062			−1.43057
$387$	15.9623	−	13.0327i	0.811410	−	0.662491i
$388$	−19.1922	+	33.2418i	−0.974334	+	1.68760i
$389$	−10.7962			−0.547390			−0.273695	−	0.961817i	$-0.588246\pi$
$389$	−10.7962			−0.547390			−0.273695	+	0.961817i	$0.588246\pi$
$390$	−12.9542	−	2.37396i	−0.655959	−	0.120210i
$391$	3.03368	−	5.25449i	0.153420	−	0.265731i
$392$	22.5158	−	65.7492i	1.13722	−	3.32084i
$393$	9.87328	−	11.6073i	0.498041	−	0.585513i
$394$	−11.9945	+	20.7751i	−0.604274	+	1.04663i
$395$	5.77167	−	9.99682i	0.290404	−	0.502995i
$396$	−29.6868	+	24.2384i	−1.49182	+	1.21802i
$397$	1.10939	+	1.92153i	0.0556789	+	0.0964386i	0.892521	−	0.451005i	$-0.148934\pi$
$397$	1.10939	+	1.92153i	0.0556789	+	0.0964386i	−0.836843	+	0.547444i	$0.815601\pi$
$398$	−6.21948	−	10.7725i	−0.311754	−	0.539974i
$399$	25.1759	−	11.8272i	1.26037	−	0.592102i
$400$	−8.08502	+	14.0037i	−0.404251	+	0.700183i
$401$	−21.4891			−1.07311			−0.536557	−	0.843864i	$-0.680275\pi$
$401$	−21.4891			−1.07311			−0.536557	+	0.843864i	$0.680275\pi$
$402$	20.9809	−	24.6658i	1.04643	−	1.23022i
$403$	0.918390			0.0457483
$404$	35.1454	+	60.8736i	1.74855	+	3.02857i
$405$	−8.53685	+	2.84995i	−0.424199	+	0.141615i
$406$	33.0757	−	23.6346i	1.64152	−	1.17297i
$407$	0.137171	+	0.237587i	0.00679931	+	0.0117768i
$408$	11.7099	+	32.8574i	0.579725	+	1.62668i
$409$	−1.64155	−	2.84324i	−0.0811693	−	0.140589i	0.822583	−	0.568645i	$-0.192532\pi$
$409$	−1.64155	−	2.84324i	−0.0811693	−	0.140589i	−0.903752	+	0.428056i	$0.859199\pi$
$410$	−0.654352	−	1.13337i	−0.0323161	−	0.0559732i
$411$	−0.486324	+	0.571738i	−0.0239886	+	0.0282017i
$412$	41.7439	+	72.3025i	2.05657	+	3.56209i
$413$	20.8126	+	9.46375i	1.02412	+	0.465681i
$414$	23.1320	+	8.77291i	1.13688	+	0.431165i
$415$	−3.98395	−	6.90040i	−0.195564	−	0.338727i
$416$	−68.1883			−3.34321
$417$	−1.29145	−	3.62374i	−0.0632424	−	0.177455i
$418$	38.1685			1.86688
$419$	−15.4340	+	26.7325i	−0.754001	+	1.30597i	0.191869	+	0.981421i	$0.438545\pi$
$419$	−15.4340	+	26.7325i	−0.754001	+	1.30597i	−0.945870	+	0.324547i	$0.894788\pi$
$420$	23.2316	−	10.9138i	1.13358	−	0.532540i
$421$	14.4175	+	24.9718i	0.702665	+	1.21705i	0.967528	+	0.252765i	$0.0813401\pi$
$421$	14.4175	+	24.9718i	0.702665	+	1.21705i	−0.264863	+	0.964286i	$0.585327\pi$
$422$	−27.2053	−	47.1210i	−1.32433	−	2.29381i
$423$	20.2370	+	7.67496i	0.983957	+	0.373170i
$424$	−42.2618	+	73.1996i	−2.05242	+	3.55489i
$425$	1.01423	−	1.75669i	0.0491972	−	0.0852120i
$426$	−19.8663	−	55.7441i	−0.962528	−	2.70081i
$427$	−2.88941	−	29.7457i	−0.139828	−	1.43950i
$428$	49.2485	−	85.3010i	2.38052	−	4.12318i
$429$	3.65752	+	10.2629i	0.176587	+	0.495495i
$430$	−18.9379			−0.913265
$431$	11.0677	−	19.1699i	0.533114	−	0.923380i	−0.466138	−	0.884712i	$-0.654355\pi$
$431$	11.0677	−	19.1699i	0.533114	−	0.923380i	0.999252	−	0.0386684i	$-0.0123116\pi$
$432$	−73.5966	+	40.5368i	−3.54092	+	1.95033i
$433$	12.9721			0.623400			0.311700	−	0.950181i	$-0.399102\pi$
$433$	12.9721			0.623400			0.311700	+	0.950181i	$0.399102\pi$
$434$	−1.97632	+	1.41220i	−0.0948663	+	0.0677878i
$435$	9.49476	+	1.74000i	0.455239	+	0.0834264i
$436$	23.2587			1.11389
$437$	−9.07788	−	15.7233i	−0.434254	−	0.752150i
$438$	−0.895208	−	0.164055i	−0.0427747	−	0.00783883i
$439$	19.6247	−	33.9910i	0.936636	−	1.62230i	0.164946	−	0.986303i	$-0.447255\pi$
$439$	19.6247	−	33.9910i	0.936636	−	1.62230i	0.771690	−	0.635998i	$-0.219412\pi$
$440$	22.6444			1.07953
$441$	−20.7014	−	3.52858i	−0.985782	−	0.168027i
$442$	15.4236			0.733626
$443$	−2.59405	+	4.49302i	−0.123247	+	0.213470i	−0.921046	−	0.389453i	$-0.872664\pi$
$443$	−2.59405	+	4.49302i	−0.123247	+	0.213470i	0.797799	+	0.602923i	$0.205997\pi$
$444$	0.391735	+	1.09919i	0.0185909	+	0.0521653i
$445$	1.05443	+	1.82633i	0.0499849	+	0.0865763i
$446$	−18.4015			−0.871334
$447$	9.32940	−	10.9679i	0.441266	−	0.518766i
$448$	77.1198	−	55.1068i	3.64357	−	2.60355i
$449$	−14.2836			−0.674084			−0.337042	−	0.941490i	$-0.609426\pi$
$449$	−14.2836			−0.674084			−0.337042	+	0.941490i	$0.609426\pi$
$450$	7.73353	+	2.93297i	0.364562	+	0.138262i
$451$	−0.541329	+	0.937610i	−0.0254902	+	0.0441503i
$452$	−38.1621			−1.79500
$453$	−23.2689	+	27.3557i	−1.09327	+	1.28528i
$454$	3.77613	−	6.54045i	0.177223	−	0.306959i
$455$	−0.705469	−	7.26261i	−0.0330729	−	0.340477i
$456$	102.669	+	18.8149i	4.80791	+	0.881090i
$457$	−8.06768	+	13.9736i	−0.377390	+	0.653659i	−0.990682	−	0.136198i	$-0.956512\pi$
$457$	−8.06768	+	13.9736i	−0.377390	+	0.653659i	0.613292	+	0.789857i	$0.289845\pi$
$458$	−6.51633	+	11.2866i	−0.304488	+	0.527389i
$459$	9.23233	−	5.08514i	0.430928	−	0.237354i
$460$	−8.37680	−	14.5090i	−0.390570	−	0.676488i
$461$	−13.0362	−	22.5794i	−0.607157	−	1.05163i	−0.991707	−	0.128523i	$-0.958976\pi$
$461$	−13.0362	−	22.5794i	−0.607157	−	1.05163i	0.384549	−	0.923104i	$-0.374357\pi$
$462$	−23.6518	−	16.4609i	−1.10038	−	0.765829i
$463$	−17.6259	+	30.5290i	−0.819146	+	1.41880i	0.0871659	+	0.996194i	$0.472219\pi$
$463$	−17.6259	+	30.5290i	−0.819146	+	1.41880i	−0.906312	+	0.422609i	$0.861114\pi$
$464$	90.1172			4.18358
$465$	−0.567325	−	0.103967i	−0.0263091	−	0.00482136i
$466$	67.2808			3.11672
$467$	13.6311	+	23.6098i	0.630774	+	1.09253i	0.987394	+	0.158283i	$0.0505959\pi$
$467$	13.6311	+	23.6098i	0.630774	+	1.09253i	−0.356620	+	0.934250i	$0.616071\pi$
$468$	7.43366	+	45.7422i	0.343621	+	2.11443i
$469$	16.3322	+	7.42643i	0.754149	+	0.342921i
$470$	−9.94522	−	17.2256i	−0.458739	−	0.794559i
$471$	24.2461	+	4.44330i	1.11720	+	0.204736i
$472$	42.8974	+	74.3005i	1.97451	+	3.41996i
$473$	7.83341	+	13.5679i	0.360181	+	0.623851i
$474$	−54.2197	−	9.93622i	−2.49039	−	0.456386i
$475$	−3.03493	−	5.25665i	−0.139252	−	0.241192i
$476$	−24.4575	+	17.4764i	−1.12101	+	0.801028i
$477$	23.8806	+	9.05682i	1.09342	+	0.414683i
$478$	3.26832	+	5.66089i	0.149489	+	0.258923i
$479$	−8.42094			−0.384763			−0.192381	−	0.981320i	$-0.561621\pi$
$479$	−8.42094			−0.384763			−0.192381	+	0.981320i	$0.561621\pi$
$480$	42.1225	+	7.71931i	1.92262	+	0.352337i
$481$	0.331732			0.0151257
$482$	−15.3757	+	26.6314i	−0.700342	+	1.21303i
$483$	−1.15570	+	13.6583i	−0.0525861	+	0.621473i
$484$	16.2374	+	28.1239i	0.738062	+	1.27836i
$485$	−3.42650	−	5.93488i	−0.155589	−	0.269489i
$486$	26.5047	+	33.8314i	1.20228	+	1.53462i
$487$	−12.3605	+	21.4090i	−0.560108	+	0.970135i	0.437379	+	0.899278i	$0.355907\pi$
$487$	−12.3605	+	21.4090i	−0.560108	+	0.970135i	−0.997486	+	0.0708579i	$0.977426\pi$
$488$	56.0734	−	97.1219i	2.53832	−	4.39650i
$489$	10.5055	+	1.92523i	0.475077	+	0.0870619i
$490$	12.6858	+	14.5439i	0.573085	+	0.657026i
$491$	−2.31133	+	4.00335i	−0.104309	+	0.180668i	−0.913456	−	0.406938i	$-0.866596\pi$
$491$	−2.31133	+	4.00335i	−0.104309	+	0.180668i	0.809147	+	0.587607i	$0.199930\pi$
$492$	−2.98370	+	3.50774i	−0.134516	+	0.158141i
$493$	−11.3048			−0.509140
$494$	23.0765	−	39.9697i	1.03826	−	1.79832i
$495$	−1.09758	−	6.75381i	−0.0493324	−	0.303561i
$496$	−5.38462			−0.241777
$497$	26.6771	−	19.0624i	1.19663	−	0.855067i
$498$	−24.6525	+	28.9823i	−1.10471	+	1.29873i
$499$	−22.5611			−1.00997			−0.504987	−	0.863127i	$-0.668503\pi$
$499$	−22.5611			−1.00997			−0.504987	+	0.863127i	$0.668503\pi$
$500$	−2.80055	−	4.85069i	−0.125244	−	0.216929i
$501$	−2.58650	−	7.25760i	−0.115556	−	0.324246i
$502$	2.57354	−	4.45751i	0.114863	−	0.198948i
$503$	−14.9141			−0.664988			−0.332494	−	0.943105i	$-0.607890\pi$
$503$	−14.9141			−0.664988			−0.332494	+	0.943105i	$0.607890\pi$
$504$	−55.5065	−	55.9369i	−2.47245	−	2.49163i
$505$	−12.5495			−0.558444
$506$	−9.40441	+	16.2889i	−0.418077	+	0.724131i
$507$	−9.18935	−	1.68403i	−0.408113	−	0.0747902i
$508$	−43.5409	−	75.4150i	−1.93181	−	3.34600i
$509$	−1.23636			−0.0548007			−0.0274003	−	0.999625i	$-0.508723\pi$
$509$	−1.23636			−0.0548007			−0.0274003	+	0.999625i	$0.508723\pi$
$510$	−9.52775	−	1.74604i	−0.421896	−	0.0773160i
$511$	−0.0487520	−	0.501889i	−0.00215666	−	0.0222023i
$512$	78.7155			3.47876
$513$	0.635280	−	31.5335i	0.0280483	−	1.39224i
$514$	2.07844	−	3.59996i	0.0916760	−	0.158788i
$515$	−14.9056			−0.656821
$516$	22.3708	+	62.7715i	0.984819	+	2.76336i
$517$	−8.22744	+	14.2503i	−0.361842	+	0.626729i
$518$	−0.713866	+	0.510101i	−0.0313655	+	0.0224126i
$519$	−10.4159	−	29.2265i	−0.457207	−	1.28290i
$520$	13.6907	−	23.7130i	0.600376	−	1.03988i
$521$	21.3625	−	37.0009i	0.935908	−	1.62104i	0.162901	−	0.986642i	$-0.447915\pi$
$521$	21.3625	−	37.0009i	0.935908	−	1.62104i	0.773007	−	0.634398i	$-0.218752\pi$
$522$	−7.39403	−	45.4983i	−0.323628	−	1.99141i
$523$	19.9386	+	34.5347i	0.871855	+	1.51010i	0.860075	+	0.510167i	$0.170417\pi$
$523$	19.9386	+	34.5347i	0.871855	+	1.51010i	0.0117804	+	0.999931i	$0.496250\pi$
$524$	24.6391	+	42.6761i	1.07636	+	1.86431i
$525$	−0.386375	+	4.56626i	−0.0168628	+	0.199288i
$526$	2.65831	−	4.60432i	0.115908	−	0.200758i
$527$	0.675474			0.0294241
$528$	−21.4445	−	60.1722i	−0.933250	−	2.61866i
$529$	−14.0531			−0.611005
$530$	−11.7358	−	20.3271i	−0.509772	−	0.882951i
$531$	20.0813	−	16.3957i	0.871454	−	0.711515i
$532$	8.69653	+	89.5285i	0.377042	+	3.88155i
$533$	0.654571	+	1.13375i	0.0283526	+	0.0491081i
$534$	6.52479	−	7.67075i	0.282355	−	0.331946i
$535$	8.79267	+	15.2293i	0.380140	+	0.658422i
$536$	33.6626	+	58.3054i	1.45400	+	2.51841i
$537$	−10.5159	−	29.5071i	−0.453793	−	1.27332i
$538$	15.5179	+	26.8778i	0.669024	+	1.15878i
$539$	5.17253	−	15.1045i	0.222797	−	0.650598i
$540$	0.586218	−	29.0982i	0.0252268	−	1.25219i
$541$	8.42859	+	14.5987i	0.362373	+	0.627649i	0.988351	−	0.152192i	$-0.0486332\pi$
$541$	8.42859	+	14.5987i	0.362373	+	0.627649i	−0.625978	+	0.779841i	$0.715300\pi$
$542$	−50.2824			−2.15982
$543$	−5.64727	+	6.63911i	−0.242348	+	0.284911i
$544$	−50.1524			−2.15026
$545$	−2.07627	+	3.59620i	−0.0889376	+	0.154044i
$546$	−31.5375	+	14.8158i	−1.34968	+	0.634059i
$547$	−20.1819	−	34.9560i	−0.862915	−	1.49461i	−0.869103	−	0.494631i	$-0.835303\pi$
$547$	−20.1819	−	34.9560i	−0.862915	−	1.49461i	0.00618833	−	0.999981i	$-0.498030\pi$
$548$	−1.21364	−	2.10208i	−0.0518440	−	0.0897964i
$549$	−31.6851	−	12.0167i	−1.35229	−	0.512859i
$550$	−3.14410	+	5.44574i	−0.134065	+	0.232207i
$551$	−16.9140	+	29.2958i	−0.720559	+	1.24804i
$552$	−33.3263	+	39.1795i	−1.41846	+	1.66759i
$553$	−2.95274	−	30.3977i	−0.125563	−	1.29264i
$554$	6.94060	−	12.0215i	0.294878	−	0.510744i
$555$	−0.204924	−	0.0375540i	−0.00869852	−	0.00159408i
$556$	12.4404			0.527589
$557$	−2.17500	+	3.76721i	−0.0921578	+	0.159622i	−0.908419	−	0.418061i	$-0.862710\pi$
$557$	−2.17500	+	3.76721i	−0.0921578	+	0.159622i	0.816261	+	0.577683i	$0.196043\pi$
$558$	0.441804	+	2.71859i	0.0187030	+	0.115087i
$559$	18.9442			0.801254
$560$	4.13624	+	42.5815i	0.174788	+	1.79940i
$561$	2.69010	+	7.54831i	0.113576	+	0.318690i
$562$	29.1824			1.23099
$563$	−2.74111	−	4.74774i	−0.115524	−	0.200093i	0.802465	−	0.596699i	$-0.203521\pi$
$563$	−2.74111	−	4.74774i	−0.115524	−	0.200093i	−0.917989	+	0.396606i	$0.870188\pi$
$564$	−45.3481	+	53.3126i	−1.90950	+	2.24487i
$565$	3.40667	−	5.90053i	0.143320	−	0.248237i
$566$	6.95737			0.292440
$567$	−13.9931	+	19.2664i	−0.587654	+	0.809112i
$568$	123.037			5.16253
$569$	15.5379	−	26.9125i	0.651384	−	1.12823i	−0.331403	−	0.943489i	$-0.607522\pi$
$569$	15.5379	−	26.9125i	0.651384	−	1.12823i	0.982787	−	0.184741i	$-0.0591448\pi$
$570$	−18.7800	+	22.0784i	−0.786609	+	0.924763i
$571$	−3.39860	−	5.88655i	−0.142227	−	0.246345i	0.786108	−	0.618089i	$-0.212093\pi$
$571$	−3.39860	−	5.88655i	−0.142227	−	0.246345i	−0.928335	+	0.371745i	$0.878760\pi$
$572$	−35.2325			−1.47315
$573$	6.98739	+	19.6063i	0.291902	+	0.819066i
$574$	−3.15195	−	1.43323i	−0.131560	−	0.0598219i
$575$	2.99113			0.124739
$576$	−17.2401	−	106.085i	−0.718335	−	4.42019i
$577$	−7.43866	+	12.8841i	−0.309676	+	0.536374i	−0.978291	−	0.207234i	$-0.933554\pi$
$577$	−7.43866	+	12.8841i	−0.309676	+	0.536374i	0.668616	+	0.743608i	$0.266887\pi$
$578$	−35.5251			−1.47765
$579$	−17.3681	−	3.18285i	−0.721793	−	0.132275i
$580$	−15.6077	+	27.0333i	−0.648075	+	1.12250i
$581$	−19.1903	−	8.72606i	−0.796148	−	0.362018i
$582$	−21.2031	+	24.9270i	−0.878896	+	1.03326i
$583$	−9.70877	+	16.8161i	−0.402096	+	0.696451i
$584$	0.946107	−	1.63871i	0.0391502	−	0.0678101i
$585$	−7.73612	−	2.93395i	−0.319849	−	0.121304i
$586$	−34.4341	−	59.6417i	−1.42246	−	2.46378i
$587$	−20.2119	−	35.0081i	−0.834235	−	1.44494i	−0.894652	−	0.446764i	$-0.852576\pi$
$587$	−20.2119	−	35.0081i	−0.834235	−	1.44494i	0.0604165	−	0.998173i	$-0.480757\pi$
$588$	33.2218	−	59.2286i	1.37005	−	2.44255i
$589$	1.01063	−	1.75047i	0.0416424	−	0.0721267i
$590$	−23.8247			−0.980846
$591$	−9.76459	+	11.4796i	−0.401662	+	0.472206i
$592$	−1.94498			−0.0799382
$593$	−2.11725	−	3.66719i	−0.0869451	−	0.150593i	0.819273	−	0.573403i	$-0.194377\pi$
$593$	−2.11725	−	3.66719i	−0.0869451	−	0.150593i	−0.906218	+	0.422810i	$0.861044\pi$
$594$	−28.6202	+	15.7639i	−1.17430	+	0.646802i
$595$	−0.518871	−	5.34164i	−0.0212716	−	0.218986i
$596$	23.2818	+	40.3253i	0.953660	+	1.65179i
$597$	−2.62338	−	7.36110i	−0.107368	−	0.301270i
$598$	11.3717	+	19.6964i	0.465025	+	0.805447i
$599$	−2.05818	−	3.56488i	−0.0840951	−	0.145657i	0.820910	−	0.571057i	$-0.193467\pi$
$599$	−2.05818	−	3.56488i	−0.0840951	−	0.145657i	−0.905005	+	0.425400i	$0.860133\pi$
$600$	−11.1417	+	13.0985i	−0.454858	+	0.534746i
$601$	−21.2127	−	36.7416i	−0.865286	−	1.49872i	−0.866763	−	0.498720i	$-0.833803\pi$
$601$	−21.2127	−	36.7416i	−0.865286	−	1.49872i	0.00147704	−	0.999999i	$-0.499530\pi$
$602$	−40.7667	+	29.1303i	−1.66153	+	1.18726i
$603$	15.7583	−	12.8661i	0.641726	−	0.523950i
$604$	−58.0683	−	100.577i	−2.36277	−	4.09243i
$605$	−5.79793			−0.235719
$606$	20.1177	+	56.4495i	0.817227	+	2.29310i
$607$	−44.0566			−1.78820			−0.894102	−	0.447864i	$-0.852185\pi$
$607$	−44.0566			−1.78820			−0.894102	+	0.447864i	$0.852185\pi$
$608$	−75.0370	+	129.968i	−3.04315	+	5.27089i
$609$	23.1154	−	10.8593i	0.936684	−	0.440040i
$610$	15.5712	+	26.9701i	0.630460	+	1.09199i
$611$	9.94855	+	17.2314i	0.402475	+	0.697107i
$612$	5.46745	+	33.6433i	0.221008	+	1.35995i
$613$	6.78432	−	11.7508i	0.274016	−	0.474610i	−0.695870	−	0.718167i	$-0.744981\pi$
$613$	6.78432	−	11.7508i	0.274016	−	0.474610i	0.969886	+	0.243558i	$0.0783145\pi$
$614$	22.8077	−	39.5041i	0.920443	−	1.59425i
$615$	−0.276006	−	0.774462i	−0.0111297	−	0.0312293i
$616$	48.7455	−	34.8317i	1.96401	−	1.40341i
$617$	13.5005	−	23.3835i	0.543509	−	0.941384i	−0.455191	−	0.890394i	$-0.650429\pi$
$617$	13.5005	−	23.3835i	0.543509	−	0.941384i	0.998699	−	0.0509904i	$-0.0162378\pi$
$618$	23.8948	+	67.0479i	0.961191	+	2.69706i
$619$	−20.7063			−0.832256			−0.416128	−	0.909306i	$-0.636613\pi$
$619$	−20.7063			−0.832256			−0.416128	+	0.909306i	$0.636613\pi$
$620$	0.932582	−	1.61528i	0.0374534	−	0.0648712i
$621$	13.3008	+	8.04073i	0.533744	+	0.322663i
$622$	28.2083			1.13105
$623$	5.07910	+	2.30953i	0.203490	+	0.0925293i
$624$	−75.9770	−	13.9234i	−3.04151	−	0.557383i
$625$	1.00000			0.0400000
$626$	−16.0833	−	27.8571i	−0.642819	−	1.11339i
$627$	23.5860	+	4.32234i	0.941935	+	0.172618i
$628$	−39.8562	+	69.0330i	−1.59044	+	2.75472i
$629$	0.243988			0.00972844
$630$	21.1591	−	5.58208i	0.843000	−	0.222395i
$631$	10.8873			0.433416			0.216708	−	0.976237i	$-0.430468\pi$
$631$	10.8873			0.433416			0.216708	+	0.976237i	$0.430468\pi$
$632$	57.3025	−	99.2508i	2.27937	−	3.94798i
$633$	−11.4752	−	32.1990i	−0.456100	−	1.27980i
$634$	4.21404	+	7.29893i	0.167361	+	0.289878i
$635$	15.5473			0.616975
$636$	−53.5129	+	62.9114i	−2.12192	+	2.49460i
$637$	−12.6900	−	14.5487i	−0.502797	−	0.576442i
$638$	35.0447			1.38743
$639$	−5.96364	−	36.6965i	−0.235918	−	1.45169i
$640$	−24.6610	+	42.7142i	−0.974813	+	1.68843i
$641$	−16.4535			−0.649876			−0.324938	−	0.945735i	$-0.605343\pi$
$641$	−16.4535			−0.649876			−0.324938	+	0.945735i	$0.605343\pi$
$642$	54.4087	−	63.9646i	2.14734	−	2.52448i
$643$	17.2233	−	29.8317i	0.679221	−	1.17645i	−0.295994	−	0.955190i	$-0.595651\pi$
$643$	17.2233	−	29.8317i	0.679221	−	1.17645i	0.975216	−	0.221256i	$-0.0710157\pi$
$644$	−40.3503	−	18.3477i	−1.59002	−	0.723003i
$645$	−11.7026	−	2.14459i	−0.460788	−	0.0844433i
$646$	16.9727	−	29.3976i	0.667783	−	1.15663i
$647$	−6.32211	+	10.9502i	−0.248548	+	0.430498i	−0.963123	−	0.269061i	$-0.913287\pi$
$647$	−6.32211	+	10.9502i	−0.248548	+	0.430498i	0.714575	+	0.699559i	$0.246620\pi$
$648$	−84.7558	+	28.2950i	−3.32952	+	1.11153i
$649$	9.85478	+	17.0690i	0.386834	+	0.670016i
$650$	3.80182	+	6.58494i	0.149120	+	0.258283i
$651$	−1.38118	+	0.648857i	−0.0541326	+	0.0254307i
$652$	−17.2692	+	29.9112i	−0.676315	+	1.17141i
$653$	28.7663			1.12571			0.562856	−	0.826555i	$-0.309702\pi$
$653$	28.7663			1.12571			0.562856	+	0.826555i	$0.309702\pi$
$654$	19.5047	+	3.57440i	0.762694	+	0.139770i
$655$	−8.79795			−0.343764
$656$	−3.83782	−	6.64730i	−0.149842	−	0.259533i
$657$	−0.534611	−	0.202753i	−0.0208572	−	0.00791016i
$658$	−47.9052	−	21.7831i	−1.86754	−	0.849192i
$659$	16.4699	+	28.5267i	0.641576	+	1.11124i	0.985081	+	0.172091i	$0.0550523\pi$
$659$	16.4699	+	28.5267i	0.641576	+	1.11124i	−0.343506	+	0.939151i	$0.611614\pi$
$660$	21.7645	+	3.98853i	0.847182	+	0.155253i
$661$	18.2522	+	31.6138i	0.709930	+	1.22963i	0.964883	+	0.262681i	$0.0846066\pi$
$661$	18.2522	+	31.6138i	0.709930	+	1.22963i	−0.254953	+	0.966953i	$0.582060\pi$
$662$	−0.563773	−	0.976484i	−0.0219117	−	0.0379521i
$663$	9.53094	+	1.74663i	0.370151	+	0.0678333i
$664$	−39.5536	−	68.5088i	−1.53498	−	2.65866i
$665$	−14.6190	−	6.64742i	−0.566899	−	0.257776i
$666$	0.159584	+	0.981980i	0.00618375	+	0.0380510i
$667$	−8.33493	−	14.4365i	−0.322730	−	0.558984i
$668$	24.9155			0.964008
$669$	−11.3711	−	2.08385i	−0.439632	−	0.0805662i
$670$	−18.6958			−0.722281
$671$	12.8817	−	22.3117i	0.497292	−	0.861335i
$672$	102.549	−	48.1761i	3.95592	−	1.85843i
$673$	21.7574	+	37.6849i	0.838685	+	1.45265i	0.890994	+	0.454014i	$0.150008\pi$
$673$	21.7574	+	37.6849i	0.838685	+	1.45265i	−0.0523094	+	0.998631i	$0.516658\pi$
$674$	14.6802	+	25.4268i	0.565460	+	0.979405i
$675$	4.44676	+	2.68819i	0.171156	+	0.103468i
$676$	15.1057	−	26.1638i	0.580987	−	1.00630i
$677$	−21.1364	+	36.6092i	−0.812336	+	1.40701i	0.0988886	+	0.995099i	$0.468471\pi$
$677$	−21.1364	+	36.6092i	−0.812336	+	1.40701i	−0.911225	+	0.411909i	$0.864862\pi$
$678$	−32.0026	−	5.86476i	−1.22905	−	0.225235i
$679$	−16.5051	−	7.50508i	−0.633409	−	0.288019i
$680$	10.0695	−	17.4408i	0.386147	−	0.668826i
$681$	3.07411	−	3.61402i	0.117800	−	0.138489i
$682$	−2.09397			−0.0801822
$683$	−12.1766	+	21.0904i	−0.465923	+	0.807003i	−0.999243	−	0.0389112i	$-0.987611\pi$
$683$	−12.1766	+	21.0904i	−0.465923	+	0.807003i	0.533319	+	0.845914i	$0.320944\pi$
$684$	95.3655	+	36.1677i	3.64639	+	1.38291i
$685$	0.433357			0.0165577
$686$	49.6796	+	11.7947i	1.89677	+	0.450322i
$687$	−5.30487	+	6.23658i	−0.202394	+	0.237940i
$688$	−111.072			−4.23457
$689$	11.7398	+	20.3339i	0.447249	+	0.774658i
$690$	−4.79501	−	13.4546i	−0.182543	−	0.512207i
$691$	9.29449	−	16.0985i	0.353579	−	0.612417i	−0.633295	−	0.773911i	$-0.718298\pi$
$691$	9.29449	−	16.0985i	0.353579	−	0.612417i	0.986874	+	0.161494i	$0.0516312\pi$
$692$	100.335			3.81417
$693$	−12.7514	−	12.8503i	−0.484388	−	0.488144i
$694$	−67.0254			−2.54425
$695$	−1.11053	+	1.92350i	−0.0421248	+	0.0729623i
$696$	94.2663	+	17.2751i	3.57315	+	0.654811i
$697$	0.481435	+	0.833870i	0.0182357	+	0.0315851i
$698$	−59.3293			−2.24565
$699$	41.5758	+	7.61913i	1.57254	+	0.288182i
$700$	−13.4900	−	6.13405i	−0.509873	−	0.231845i
$701$	−23.3630			−0.882409			−0.441205	−	0.897407i	$-0.645449\pi$
$701$	−23.3630			−0.882409			−0.441205	+	0.897407i	$0.645449\pi$
$702$	−0.795807	+	39.5016i	−0.0300358	+	1.49089i
$703$	0.365050	−	0.632286i	0.0137681	−	0.0238471i
$704$	81.7108			3.07959
$705$	−4.19491	−	11.7707i	−0.157989	−	0.443311i
$706$	−13.1670	+	22.8059i	−0.495546	+	0.858311i
$707$	−27.0147	+	19.3037i	−1.01599	+	0.725989i
$708$	28.1434	+	78.9693i	1.05770	+	2.96785i
$709$	−21.6917	+	37.5711i	−0.814647	+	1.41101i	0.0949334	+	0.995484i	$0.469736\pi$
$709$	−21.6917	+	37.5711i	−0.814647	+	1.41101i	−0.909581	+	0.415527i	$0.863597\pi$
$710$	−17.0833	+	29.5892i	−0.641125	+	1.11046i
$711$	−32.3796	−	12.2801i	−1.21433	−	0.460539i
$712$	10.4687	+	18.1322i	0.392329	+	0.679534i
$713$	0.498024	+	0.862602i	0.0186511	+	0.0323047i
$714$	−23.1957	+	10.8970i	−0.868079	+	0.407810i
$715$	3.14515	−	5.44756i	0.117622	−	0.203727i
$716$	101.298			3.78569
$717$	1.37858	+	3.86824i	0.0514840	+	0.144462i
$718$	21.5024			0.802463
$719$	21.0553	+	36.4688i	0.785230	+	1.36006i	0.928862	+	0.370427i	$0.120789\pi$
$719$	21.0553	+	36.4688i	0.785230	+	1.36006i	−0.143632	+	0.989631i	$0.545878\pi$
$720$	45.3577	+	17.2021i	1.69038	+	0.641084i
$721$	−32.0867	+	22.9279i	−1.19497	+	0.853880i
$722$	−24.5969	−	42.6031i	−0.915403	−	1.58552i
$723$	−12.5171	+	14.7156i	−0.465518	+	0.547277i
$724$	−14.0929	−	24.4097i	−0.523760	−	0.907178i
$725$	−2.78655	−	4.82644i	−0.103490	−	0.179250i
$726$	9.29451	+	26.0800i	0.344952	+	0.967920i
$727$	−23.4220	−	40.5680i	−0.868673	−	1.50459i	−0.863354	−	0.504599i	$-0.831640\pi$
$727$	−23.4220	−	40.5680i	−0.868673	−	1.50459i	−0.00531918	−	0.999986i	$-0.501693\pi$
$728$	−7.00406	−	72.1049i	−0.259588	−	2.67239i
$729$	12.5473	+	23.9074i	0.464714	+	0.885461i
$730$	0.262728	+	0.455058i	0.00972400	+	0.0168425i
$731$	13.9334			0.515346
$732$	71.0014	−	83.4715i	2.62429	−	3.08520i
$733$	50.3761			1.86068			0.930341	−	0.366695i	$-0.119511\pi$
$733$	50.3761			1.86068			0.930341	+	0.366695i	$0.119511\pi$
$734$	22.5242	−	39.0131i	0.831383	−	1.44000i
$735$	6.19211	+	10.4239i	0.228399	+	0.384492i
$736$	−36.9771	−	64.0461i	−1.36299	−	2.36077i
$737$	7.73328	+	13.3944i	0.284859	+	0.493390i
$738$	−3.04119	+	2.48304i	−0.111948	+	0.0914020i
$739$	24.8224	−	42.9937i	0.913108	−	1.58155i	0.103460	−	0.994634i	$-0.467009\pi$
$739$	24.8224	−	42.9937i	0.913108	−	1.58155i	0.809648	−	0.586915i	$-0.199658\pi$
$740$	0.336858	−	0.583455i	0.0123831	−	0.0214482i
$741$	18.7863	−	22.0858i	0.690133	−	0.811342i
$742$	−56.5304	−	25.7051i	−2.07530	−	0.943662i
$743$	−6.76254	+	11.7131i	−0.248093	+	0.429710i	−0.962997	−	0.269513i	$-0.913137\pi$
$743$	−6.76254	+	11.7131i	−0.248093	+	0.429710i	0.714903	+	0.699223i	$0.246471\pi$
$744$	−5.63254	−	1.03221i	−0.206499	−	0.0378427i
$745$	−8.31331			−0.304576
$746$	−12.2933	+	21.2926i	−0.450089	+	0.779577i
$747$	−18.5160	+	15.1177i	−0.677464	+	0.553128i
$748$	−25.9135			−0.947490
$749$	42.3534	+	19.2586i	1.54756	+	0.703695i
$750$	−1.60307	−	4.49816i	−0.0585360	−	0.164250i
$751$	−40.5777			−1.48070			−0.740351	−	0.672220i	$-0.765341\pi$
$751$	−40.5777			−1.48070			−0.740351	+	0.672220i	$0.765341\pi$
$752$	−58.3294	−	101.030i	−2.12706	−	3.68417i
$753$	2.09509	−	2.46306i	0.0763494	−	0.0897588i
$754$	21.1879	−	36.6985i	0.771617	−	1.33648i
$755$	20.7346			0.754611
$756$	−43.4971	−	63.5402i	−1.58197	−	2.31093i
$757$	−0.0588390			−0.00213854			−0.00106927	−	0.999999i	$-0.500340\pi$
$757$	−0.0588390			−0.00213854			−0.00106927	+	0.999999i	$0.500340\pi$
$758$	−1.76269	+	3.05307i	−0.0640239	+	0.110893i
$759$	−7.65603	+	9.00067i	−0.277896	+	0.326704i
$760$	−30.1315	−	52.1893i	−1.09298	−	1.89310i
$761$	−1.74459			−0.0632415			−0.0316207	−	0.999500i	$-0.510067\pi$
$761$	−1.74459			−0.0632415			−0.0316207	+	0.999500i	$0.510067\pi$
$762$	−24.9234	−	69.9341i	−0.902881	−	2.53345i
$763$	1.06220	+	10.9351i	0.0384544	+	0.395878i
$764$	−67.3088			−2.43515
$765$	−5.68990	−	2.15792i	−0.205719	−	0.0780196i
$766$	−1.89291	+	3.27861i	−0.0683935	+	0.118461i
$767$	23.8326			0.860546
$768$	109.598	+	20.0849i	3.95479	+	0.724750i
$769$	−2.67448	+	4.63234i	−0.0964444	+	0.167047i	−0.910210	−	0.414146i	$-0.864080\pi$
$769$	−2.67448	+	4.63234i	−0.0964444	+	0.167047i	0.813766	+	0.581192i	$0.197414\pi$
$770$	1.60850	+	16.5591i	0.0579663	+	0.596747i
$771$	1.69203	−	1.98921i	0.0609371	−	0.0716396i
$772$	28.5500	−	49.4501i	1.02754	−	1.77975i
$773$	16.5833	−	28.7231i	0.596460	−	1.03310i	−0.396880	−	0.917871i	$-0.629907\pi$
$773$	16.5833	−	28.7231i	0.596460	−	1.03310i	0.993339	−	0.115228i	$-0.0367597\pi$
$774$	9.11335	+	56.0779i	0.327573	+	2.01568i
$775$	0.166500	+	0.288386i	0.00598086	+	0.0103591i
$776$	−34.0191	−	58.9229i	−1.22122	−	2.11521i
$777$	−0.498896	+	0.234374i	−0.0178978	+	0.00840810i
$778$	14.8826	−	25.7775i	0.533568	−	0.924167i
$779$	2.88126			0.103232
$780$	17.3355	−	20.3801i	0.620709	−	0.729725i
$781$	28.2652			1.01141
$782$	8.36389	+	14.4867i	0.299092	+	0.518043i
$783$	0.583288	−	28.9528i	0.0208450	−	1.03469i
$784$	74.4029	+	85.3009i	2.65725	+	3.04646i
$785$	−7.11580	−	12.3249i	−0.253974	−	0.439895i
$786$	14.1038	+	39.5746i	0.503065	+	1.41158i
$787$	−0.397349	−	0.688229i	−0.0141640	−	0.0245327i	0.858857	−	0.512216i	$-0.171175\pi$
$787$	−0.397349	−	0.688229i	−0.0141640	−	0.0245327i	−0.873021	+	0.487683i	$0.837842\pi$
$788$	−24.3678	−	42.2063i	−0.868068	−	1.50354i
$789$	2.16410	−	2.54418i	0.0770439	−	0.0905753i
$790$	15.9125	+	27.5613i	0.566142	+	0.980587i
$791$	−1.74283	−	17.9420i	−0.0619678	−	0.637943i
$792$	−10.8970	−	67.0534i	−0.387208	−	2.38264i
$793$	−15.5764	−	26.9792i	−0.553135	−	0.958058i
$794$	−6.11721			−0.217092
$795$	−4.95019	−	13.8900i	−0.175565	−	0.492628i
$796$	25.2708			0.895699
$797$	6.14419	−	10.6421i	0.217638	−	0.376961i	−0.736447	−	0.676495i	$-0.763498\pi$
$797$	6.14419	−	10.6421i	0.217638	−	0.376961i	0.954086	+	0.299534i	$0.0968313\pi$
$798$	−6.46585	+	76.4147i	−0.228889	+	2.70505i
$799$	7.31714	+	12.6737i	0.258862	+	0.448362i
$800$	−12.3622	−	21.4120i	−0.437071	−	0.757029i
$801$	4.90062	−	4.00121i	0.173155	−	0.141376i
$802$	29.6228	−	51.3082i	1.04602	−	1.81176i
$803$	0.217348	−	0.376458i	0.00767006	−	0.0132849i
$804$	22.0848	+	61.9691i	0.778872	+	2.18548i
$805$	6.43888	−	4.60097i	0.226941	−	0.162163i
$806$	−1.26600	+	2.19278i	−0.0445931	+	0.0772375i
$807$	6.54547	+	18.3663i	0.230411	+	0.646524i
$808$	−124.594			−4.38321
$809$	−7.69807	+	13.3334i	−0.270650	+	0.468779i	−0.969028	−	0.246950i	$-0.920572\pi$
$809$	−7.69807	+	13.3334i	−0.270650	+	0.468779i	0.698379	+	0.715728i	$0.253905\pi$
$810$	4.96342	−	24.3116i	0.174397	−	0.854222i
$811$	48.7158			1.71064			0.855321	−	0.518098i	$-0.173360\pi$
$811$	48.7158			1.71064			0.855321	+	0.518098i	$0.173360\pi$
$812$	7.98479	+	82.2013i	0.280211	+	2.88470i
$813$	−31.0718	−	5.69417i	−1.08974	−	0.199703i
$814$	−0.756363			−0.0265105
$815$	−3.08319	−	5.34024i	−0.107999	−	0.187061i
$816$	−55.8809	−	10.2407i	−1.95622	−	0.358495i
$817$	20.8469	−	36.1079i	0.729341	−	1.26326i
$818$	9.05152			0.316479
$819$	−21.1662	+	5.58394i	−0.739607	+	0.195119i
$820$	2.65874			0.0928473
$821$	20.7816	−	35.9947i	0.725282	−	1.25622i	−0.233576	−	0.972338i	$-0.575043\pi$
$821$	20.7816	−	35.9947i	0.725282	−	1.25622i	0.958858	−	0.283886i	$-0.0916238\pi$
$822$	−0.694704	−	1.94931i	−0.0242306	−	0.0679899i
$823$	9.12010	+	15.7965i	0.317907	+	0.550630i	0.980051	−	0.198746i	$-0.0636868\pi$
$823$	9.12010	+	15.7965i	0.317907	+	0.550630i	−0.662144	+	0.749376i	$0.730353\pi$
$824$	−147.987			−5.15536
$825$	−2.55958	+	3.00912i	−0.0891130	+	0.104764i
$826$	−51.2863	+	36.6472i	−1.78448	+	1.27512i
$827$	−42.1614			−1.46610			−0.733048	−	0.680177i	$-0.761903\pi$
$827$	−42.1614			−1.46610			−0.733048	+	0.680177i	$0.761903\pi$
$828$	−38.9324	+	31.7871i	−1.35299	+	1.10468i
$829$	−3.57036	+	6.18404i	−0.124004	+	0.214781i	−0.921343	−	0.388751i	$-0.872907\pi$
$829$	−3.57036	+	6.18404i	−0.124004	+	0.214781i	0.797339	+	0.603531i	$0.206240\pi$
$830$	21.9676			0.762505
$831$	5.65027	−	6.64263i	0.196006	−	0.230430i
$832$	49.4020	−	85.5668i	1.71271	−	2.96649i
$833$	−9.33348	−	10.7006i	−0.323386	−	0.370753i
$834$	10.4324	+	1.91184i	0.361246	+	0.0662014i
$835$	−2.22416	+	3.85236i	−0.0769703	+	0.133316i
$836$	−38.7712	+	67.1537i	−1.34093	+	2.32256i
$837$	−0.0348523	+	1.72997i	−0.00120467	+	0.0597964i
$838$	−42.5517	−	73.7017i	−1.46992	−	2.54598i
$839$	18.6903	+	32.3725i	0.645260	+	1.11762i	0.984241	+	0.176830i	$0.0565843\pi$
$839$	18.6903	+	32.3725i	0.645260	+	1.11762i	−0.338981	+	0.940793i	$0.610082\pi$
$840$	−3.83602	+	45.3349i	−0.132355	+	1.56420i
$841$	−1.02969	+	1.78347i	−0.0355065	+	0.0614990i
$842$	−79.4982			−2.73969
$843$	18.0331	+	3.30473i	0.621094	+	0.113821i
$844$	110.540			3.80494
$845$	2.69691	+	4.67119i	0.0927766	+	0.160694i
$846$	−46.2218	+	37.7387i	−1.58914	+	1.29748i
$847$	−12.4809	+	8.91840i	−0.428850	+	0.306440i
$848$	−68.8315	−	119.220i	−2.36368	−	4.09402i
$849$	4.29927	+	0.787878i	0.147551	+	0.0270399i
$850$	2.79623	+	4.84321i	0.0959098	+	0.166121i
$851$	0.179891	+	0.311581i	0.00616659	+	0.0106808i
$852$	118.256	+	21.6715i	4.05140	+	0.742453i
$853$	−2.46029	−	4.26134i	−0.0842386	−	0.145906i	0.820828	−	0.571176i	$-0.193512\pi$
$853$	−2.46029	−	4.26134i	−0.0842386	−	0.145906i	−0.905067	+	0.425270i	$0.860179\pi$
$854$	75.0051	+	34.1057i	2.56662	+	1.16707i
$855$	−14.1053	+	11.5165i	−0.482390	+	0.393857i
$856$	87.2957	+	151.201i	2.98370	+	5.16793i
$857$	48.1202			1.64376			0.821878	−	0.569663i	$-0.192926\pi$
$857$	48.1202			1.64376			0.821878	+	0.569663i	$0.192926\pi$
$858$	−29.5459	−	5.41454i	−1.00868	−	0.184849i
$859$	32.8500			1.12083			0.560414	−	0.828213i	$-0.310642\pi$
$859$	32.8500			1.12083			0.560414	+	0.828213i	$0.310642\pi$
$860$	19.2369	−	33.3193i	0.655974	−	1.13618i
$861$	−1.78543	−	1.24260i	−0.0608472	−	0.0423475i
$862$	30.5138	+	52.8515i	1.03930	+	1.80013i
$863$	20.3542	+	35.2544i	0.692864	+	1.20007i	0.970896	+	0.239503i	$0.0769845\pi$
$863$	20.3542	+	35.2544i	0.692864	+	1.20007i	−0.278032	+	0.960572i	$0.589682\pi$
$864$	2.58770	−	128.446i	0.0880352	−	4.36982i
$865$	−8.95676	+	15.5136i	−0.304539	+	0.527477i
$866$	−17.8821	+	30.9727i	−0.607659	+	1.05250i
$867$	−21.9526	−	4.02299i	−0.745548	−	0.136628i
$868$	−0.477102	−	4.91164i	−0.0161939	−	0.166712i
$869$	13.1640	−	22.8008i	0.446560	−	0.773464i
$870$	−17.2431	+	20.2715i	−0.584594	+	0.687267i
$871$	18.7020			0.633694
$872$	−20.6137	+	35.7039i	−0.698067	+	1.20909i
$873$	−15.9252	+	13.0024i	−0.538985	+	0.440065i
$874$	50.0556			1.69315
$875$	2.15266	−	1.53820i	0.0727730	−	0.0520008i
$876$	1.19798	−	1.40839i	0.0404761	−	0.0475850i
$877$	23.9564			0.808952			0.404476	−	0.914549i	$-0.367454\pi$
$877$	23.9564			0.808952			0.404476	+	0.914549i	$0.367454\pi$
$878$	54.1055	+	93.7134i	1.82597	+	3.16267i
$879$	−14.5244	−	40.7547i	−0.489895	−	1.37462i
$880$	−18.4404	+	31.9396i	−0.621624	+	1.07668i
$881$	−2.59131			−0.0873035			−0.0436518	−	0.999047i	$-0.513899\pi$
$881$	−2.59131			−0.0873035			−0.0436518	+	0.999047i	$0.513899\pi$
$882$	36.9620	−	44.5634i	1.24457	−	1.50053i
$883$	−38.0612			−1.28086			−0.640431	−	0.768015i	$-0.721244\pi$
$883$	−38.0612			−1.28086			−0.640431	+	0.768015i	$0.721244\pi$
$884$	−15.6672	+	27.1363i	−0.526944	+	0.912693i
$885$	−14.7223	−	2.69799i	−0.494886	−	0.0906920i
$886$	−7.15181	−	12.3873i	−0.240270	−	0.416160i
$887$	47.7337			1.60274			0.801371	−	0.598168i	$-0.204104\pi$
$887$	47.7337			1.60274			0.801371	+	0.598168i	$0.204104\pi$
$888$	−2.03453	−	0.372845i	−0.0682743	−	0.0125119i
$889$	33.4679	−	23.9149i	1.12248	−	0.802080i
$890$	−5.81415			−0.194891
$891$	−19.4709	+	6.50019i	−0.652299	+	0.217765i
$892$	18.6920	−	32.3756i	0.625856	−	1.08401i
$893$	43.7910			1.46541
$894$	13.3269	+	37.3946i	0.445717	+	1.25066i
$895$	−9.04272	+	15.6625i	−0.302265	+	0.523538i
$896$	12.6164	+	129.883i	0.421485	+	4.33907i
$897$	4.79661	+	13.4591i	0.160154	+	0.449386i
$898$	19.6900	−	34.1040i	0.657063	−	1.13807i
$899$	0.927920	−	1.60720i	0.0309479	−	0.0536033i
$900$	−13.0159	+	10.6271i	−0.433865	+	0.354237i
$901$	8.63457	+	14.9555i	0.287659	+	0.498240i
$902$	−1.49245	−	2.58500i	−0.0496931	−	0.0860710i
$903$	−28.4904	+	13.3844i	−0.948101	+	0.445403i
$904$	33.8222	−	58.5818i	1.12491	−	1.94840i
$905$	5.03221			0.167276
$906$	−33.2392	−	93.2677i	−1.10430	−	3.09861i
$907$	−14.2395			−0.472815			−0.236407	−	0.971654i	$-0.575970\pi$
$907$	−14.2395			−0.472815			−0.236407	+	0.971654i	$0.575970\pi$
$908$	7.67153	+	13.2875i	0.254589	+	0.440960i
$909$	6.03911	+	37.1609i	0.200305	+	1.23255i
$910$	18.3130	+	8.32714i	0.607070	+	0.276042i
$911$	15.6619	+	27.1272i	0.518902	+	0.898764i	0.999759	+	0.0219651i	$0.00699228\pi$
$911$	15.6619	+	27.1272i	0.518902	+	0.898764i	−0.480857	+	0.876799i	$0.659674\pi$
$912$	−110.146	+	129.491i	−3.64731	+	4.28789i
$913$	−9.08661	−	15.7385i	−0.300723	−	0.520867i
$914$	−22.2427	−	38.5254i	−0.735722	−	1.27431i
$915$	6.56796	+	18.4294i	0.217130	+	0.609257i
$916$	−13.2385	−	22.9297i	−0.437412	−	0.757619i
$917$	−18.9390	+	13.5331i	−0.625420	+	0.446901i
$918$	−0.585315	+	29.0534i	−0.0193183	+	0.958904i
$919$	14.9287	+	25.8572i	0.492451	+	0.852951i	0.999962	−	0.00869473i	$-0.00276765\pi$
$919$	14.9287	+	25.8572i	0.492451	+	0.852951i	−0.507511	+	0.861645i	$0.669434\pi$
$920$	29.6967			0.979070
$921$	18.5675	−	21.8285i	0.611819	−	0.719274i
$922$	71.8819			2.36730
$923$	17.0890	−	29.5991i	0.562492	−	0.974265i
$924$	52.9866	−	24.8923i	1.74313	−	0.818897i
$925$	0.0601415	+	0.104168i	0.00197744	+	0.00342503i
$926$	−48.5948	−	84.1687i	−1.59692	−	2.76595i
$927$	7.17294	+	44.1378i	0.235590	+	1.44968i
$928$	−68.8958	+	119.331i	−2.26162	+	3.91724i
$929$	10.4942	−	18.1764i	0.344302	−	0.596349i	−0.640925	−	0.767604i	$-0.721449\pi$
$929$	10.4942	−	18.1764i	0.344302	−	0.596349i	0.985227	+	0.171255i	$0.0547822\pi$
$930$	1.03030	−	1.21125i	0.0337847	−	0.0397184i
$931$	−41.6947	+	8.17736i	−1.36649	+	0.268002i
$932$	−68.3433	+	118.374i	−2.23866	+	3.87747i
$933$	17.4312	+	3.19442i	0.570672	+	0.104580i
$934$	−75.1624			−2.45939
$935$	2.31325	−	4.00667i	0.0756514	−	0.131032i
$936$	−76.8060	−	29.1290i	−2.51048	−	0.952110i
$937$	−22.0134			−0.719147			−0.359573	−	0.933117i	$-0.617078\pi$
$937$	−22.0134			−0.719147			−0.359573	+	0.933117i	$0.617078\pi$
$938$	−40.2456	+	28.7579i	−1.31406	+	0.938980i
$939$	−6.78396	−	19.0355i	−0.221386	−	0.621200i
$940$	40.4091			1.31800
$941$	27.6039	+	47.8114i	0.899862	+	1.55861i	0.827670	+	0.561215i	$0.189666\pi$
$941$	27.6039	+	47.8114i	0.899862	+	1.55861i	0.0721917	+	0.997391i	$0.477001\pi$
$942$	−44.0323	+	51.7657i	−1.43465	+	1.68662i
$943$	−0.709919	+	1.22962i	−0.0231182	+	0.0400418i
$944$	−139.733			−4.54793
$945$	13.7073	−	1.05328i	0.445899	−	0.0342631i
$946$	−43.1936			−1.40434
$947$	3.87939	−	6.71930i	0.126063	−	0.218348i	−0.796085	−	0.605185i	$-0.793099\pi$
$947$	3.87939	−	6.71930i	0.126063	−	0.218348i	0.922148	+	0.386837i	$0.126432\pi$
$948$	72.5577	−	85.3011i	2.35657	−	2.77045i
$949$	−0.262816	−	0.455210i	−0.00853136	−	0.0147768i
$950$	16.7347			0.542944
$951$	1.77749	+	4.98755i	0.0576390	+	0.161732i
$952$	−5.15147	−	53.0330i	−0.166960	−	1.71881i
$953$	−21.6205			−0.700356			−0.350178	−	0.936683i	$-0.613879\pi$
$953$	−21.6205			−0.700356			−0.350178	+	0.936683i	$0.613879\pi$
$954$	−54.5440	+	44.5335i	−1.76593	+	1.44182i
$955$	6.00854	−	10.4071i	0.194432	−	0.336766i
$956$	−13.2797			−0.429497
$957$	21.6557	+	3.96859i	0.700029	+	0.128286i
$958$	11.6083	−	20.1062i	0.375047	−	0.649601i
$959$	0.932868	−	0.666592i	0.0301239	−	0.0215254i
$960$	−40.2042	+	47.2653i	−1.29758	+	1.52548i
$961$	15.4446	−	26.7508i	0.498211	−	0.862928i
$962$	−0.457294	+	0.792056i	−0.0147437	+	0.0255369i
$963$	40.8652	−	33.3652i	1.31686	−	1.07518i
$964$	−31.2369	−	54.1039i	−1.00607	−	1.74257i
$965$	5.09723	+	8.82866i	0.164086	+	0.284205i
$966$	−31.0179	−	21.5874i	−0.997985	−	0.694563i
$967$	−28.5905	+	49.5202i	−0.919408	+	1.59246i	−0.119092	+	0.992883i	$0.537998\pi$
$967$	−28.5905	+	49.5202i	−0.919408	+	1.59246i	−0.800316	+	0.599579i	$0.795335\pi$
$968$	−57.5632			−1.85015
$969$	13.8173	−	16.2441i	0.443876	−	0.521834i
$970$	18.8938			0.606643
$971$	−7.15219	−	12.3879i	−0.229525	−	0.397548i	0.728143	−	0.685426i	$-0.240384\pi$
$971$	−7.15219	−	12.3879i	−0.229525	−	0.397548i	−0.957667	+	0.287877i	$0.907050\pi$
$972$	−86.4464	+	12.2669i	−2.77277	+	0.393460i
$973$	0.568140	+	5.84885i	0.0182137	+	0.187505i
$974$	−34.0780	−	59.0248i	−1.09193	−	1.89128i
$975$	1.60361	+	4.49966i	0.0513566	+	0.144105i
$976$	91.3263	+	158.182i	2.92328	+	5.06327i
$977$	6.22362	+	10.7796i	0.199111	+	0.344871i	0.948240	−	0.317553i	$-0.102861\pi$
$977$	6.22362	+	10.7796i	0.199111	+	0.344871i	−0.749129	+	0.662424i	$0.769528\pi$
$978$	−19.0787	+	22.4295i	−0.610069	+	0.717216i
$979$	2.40495	+	4.16550i	0.0768627	+	0.133130i
$980$	−38.4747	+	7.54583i	−1.22903	+	0.241043i
$981$	11.6481	+	4.41757i	0.371894	+	0.141042i
$982$	−6.37236	−	11.0373i	−0.203350	−	0.352213i
$983$	−15.6613			−0.499519			−0.249759	−	0.968308i	$-0.580352\pi$
$983$	−15.6613			−0.499519			−0.249759	+	0.968308i	$0.580352\pi$
$984$	−2.74026	−	7.68904i	−0.0873562	−	0.245118i
$985$	8.70110			0.277240
$986$	15.5836	−	26.9917i	0.496284	−	0.859590i
$987$	−27.1360	−	18.8857i	−0.863748	−	0.601138i
$988$	46.8818	+	81.2017i	1.49151	+	2.58337i
$989$	10.2730	+	17.7934i	0.326663	+	0.565798i
$990$	17.6387	+	6.68953i	0.560594	+	0.212607i
$991$	18.0010	−	31.1787i	0.571821	−	0.990423i	−0.424558	−	0.905401i	$-0.639570\pi$
$991$	18.0010	−	31.1787i	0.571821	−	0.990423i	0.996379	−	0.0850224i	$-0.0270962\pi$
$992$	4.11662	−	7.13020i	0.130703	−	0.226384i
$993$	−0.237800	−	0.667257i	−0.00754636	−	0.0211748i
$994$	8.73970	+	89.9729i	0.277207	+	2.85377i
$995$	−2.25588	+	3.90730i	−0.0715162	+	0.123870i
$996$	−25.9497	−	72.8137i	−0.822247	−	2.30719i
$997$	7.66503			0.242754			0.121377	−	0.992606i	$-0.461269\pi$
$997$	7.66503			0.242754			0.121377	+	0.992606i	$0.461269\pi$
$998$	31.1005	−	53.8677i	0.984471	−	1.70515i
$999$	−0.0125890	+	0.624882i	−0.000398298	+	0.0197704i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.k.c.256.1	yes	36
3.2	odd	2		945.2.k.c.361.18		36
7.2	even	3		315.2.l.c.121.18	yes	36
9.2	odd	6		945.2.l.c.46.1		36
9.7	even	3		315.2.l.c.151.18	yes	36
21.2	odd	6		945.2.l.c.226.1		36
63.2	odd	6		945.2.k.c.856.18		36
63.16	even	3	inner	315.2.k.c.16.1	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.c.16.1	✓	36	63.16	even	3	inner
315.2.k.c.256.1	yes	36	1.1	even	1	trivial
315.2.l.c.121.18	yes	36	7.2	even	3
315.2.l.c.151.18	yes	36	9.7	even	3
945.2.k.c.361.18		36	3.2	odd	2
945.2.k.c.856.18		36	63.2	odd	6
945.2.l.c.46.1		36	9.2	odd	6
945.2.l.c.226.1		36	21.2	odd	6

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37850 + 2.38764i) q^{2} +(-1.12222 + 1.31932i) q^{3} +(-2.80055 - 4.85069i) q^{4} +1.00000 q^{5} +(-1.60307 - 4.49816i) q^{6} +(2.15266 - 1.53820i) q^{7} +9.92824 q^{8} +(-0.481224 - 2.96115i) q^{9} +(-1.37850 + 2.38764i) q^{10} +2.28080 q^{11} +(9.54246 + 1.74874i) q^{12} +(1.37896 - 2.38844i) q^{13} +(0.705233 + 7.26018i) q^{14} +(-1.12222 + 1.31932i) q^{15} +(-8.08502 + 14.0037i) q^{16} +(1.01423 - 1.75669i) q^{17} +(7.73353 + 2.93297i) q^{18} +(-3.03493 - 5.25665i) q^{19} +(-2.80055 - 4.85069i) q^{20} +(-0.386375 + 4.56626i) q^{21} +(-3.14410 + 5.44574i) q^{22} +2.99113 q^{23} +(-11.1417 + 13.0985i) q^{24} +1.00000 q^{25} +(3.80182 + 6.58494i) q^{26} +(4.44676 + 2.68819i) q^{27} +(-13.4900 - 6.13405i) q^{28} +(-2.78655 - 4.82644i) q^{29} +(-1.60307 - 4.49816i) q^{30} +(0.166500 + 0.288386i) q^{31} +(-12.3622 - 21.4120i) q^{32} +(-2.55958 + 3.00912i) q^{33} +(2.79623 + 4.84321i) q^{34} +(2.15266 - 1.53820i) q^{35} +(-13.0159 + 10.6271i) q^{36} +(0.0601415 + 0.104168i) q^{37} +16.7347 q^{38} +(1.60361 + 4.49966i) q^{39} +9.92824 q^{40} +(-0.237341 + 0.411087i) q^{41} +(-10.3700 - 7.21713i) q^{42} +(3.43450 + 5.94872i) q^{43} +(-6.38750 - 11.0635i) q^{44} +(-0.481224 - 2.96115i) q^{45} +(-4.12329 + 7.14174i) q^{46} +(-3.60725 + 6.24794i) q^{47} +(-9.40214 - 26.3820i) q^{48} +(2.26785 - 6.62245i) q^{49} +(-1.37850 + 2.38764i) q^{50} +(1.17945 + 3.30949i) q^{51} -15.4474 q^{52} +(-4.25673 + 7.37287i) q^{53} +(-12.5483 + 6.91157i) q^{54} +2.28080 q^{55} +(21.3721 - 15.2717i) q^{56} +(10.3411 + 1.89509i) q^{57} +15.3651 q^{58} +(4.32075 + 7.48375i) q^{59} +(9.54246 + 1.74874i) q^{60} +(5.64787 - 9.78239i) q^{61} -0.918083 q^{62} +(-5.59077 - 5.63412i) q^{63} +35.8254 q^{64} +(1.37896 - 2.38844i) q^{65} +(-3.65630 - 10.2594i) q^{66} +(3.39059 + 5.87268i) q^{67} -11.3615 q^{68} +(-3.35672 + 3.94627i) q^{69} +(0.705233 + 7.26018i) q^{70} +12.3927 q^{71} +(-4.77770 - 29.3990i) q^{72} +(0.0952946 - 0.165055i) q^{73} -0.331621 q^{74} +(-1.12222 + 1.31932i) q^{75} +(-16.9989 + 29.4430i) q^{76} +(4.90979 - 3.50834i) q^{77} +(-12.9542 - 2.37396i) q^{78} +(5.77167 - 9.99682i) q^{79} +(-8.08502 + 14.0037i) q^{80} +(-8.53685 + 2.84995i) q^{81} +(-0.654352 - 1.13337i) q^{82} +(-3.98395 - 6.90040i) q^{83} +(23.2316 - 10.9138i) q^{84} +(1.01423 - 1.75669i) q^{85} -18.9379 q^{86} +(9.49476 + 1.74000i) q^{87} +22.6444 q^{88} +(1.05443 + 1.82633i) q^{89} +(7.73353 + 2.93297i) q^{90} +(-0.705469 - 7.26261i) q^{91} +(-8.37680 - 14.5090i) q^{92} +(-0.567325 - 0.103967i) q^{93} +(-9.94522 - 17.2256i) q^{94} +(-3.03493 - 5.25665i) q^{95} +(42.1225 + 7.71931i) q^{96} +(-3.42650 - 5.93488i) q^{97} +(12.6858 + 14.5439i) q^{98} +(-1.09758 - 6.75381i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9} - 2 q^{11} + 5 q^{12} + 2 q^{13} - 6 q^{14} - q^{15} - 30 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} - 22 q^{20} - 11 q^{21} - 19 q^{22} + 6 q^{23}+ \cdots - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9 - 2 * q^11 + 5 * q^12 + 2 * q^13 - 6 * q^14 - q^15 - 30 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 - 22 * q^20 - 11 * q^21 - 19 * q^22 + 6 * q^23 + 16 * q^24 + 36 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 - 4 * q^30 + 10 * q^32 - 5 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 + 44 * q^38 - 8 * q^39 - 4 * q^41 - 30 * q^42 - 29 * q^43 - 7 * q^44 + 3 * q^45 - 24 * q^46 - 23 * q^47 - 19 * q^48 - 7 * q^49 - 21 * q^51 + 14 * q^52 - 2 * q^55 + 33 * q^56 + 21 * q^57 + 40 * q^58 - 5 * q^59 + 5 * q^60 - 3 * q^61 - 12 * q^62 + 11 * q^63 + 128 * q^64 + 2 * q^65 - 30 * q^66 - 35 * q^67 + 34 * q^68 - 50 * q^69 - 6 * q^70 + 24 * q^71 + 5 * q^72 - 10 * q^73 - 44 * q^74 - q^75 + 10 * q^76 + 5 * q^77 + 66 * q^78 - 28 * q^79 - 30 * q^80 + 47 * q^81 - 8 * q^82 - 22 * q^83 - 2 * q^84 - 5 * q^85 - 38 * q^86 + 45 * q^87 + 100 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - 28 * q^93 - 2 * q^94 - 2 * q^95 + 79 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

Introduction

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