LMFDB - Embedded newform 75.3.k.a.13.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,3,Mod(13,75)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 19]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("75.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	75.k (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.04360198270$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			13.8
Character	$\chi$	$=$	75.13
Dual form			75.3.k.a.52.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.52458 - 0.399854i) q^{2} +(0.786335 - 1.54327i) q^{3} +(2.40940 - 0.782861i) q^{4} +(2.98039 - 4.01464i) q^{5} +(1.36808 - 4.21053i) q^{6} +(-7.99303 + 7.99303i) q^{7} +(-3.34014 + 1.70189i) q^{8} +(-1.76336 - 2.42705i) q^{9} +O(q^{10})$	\(q+(2.52458 - 0.399854i) q^{2} +(0.786335 - 1.54327i) q^{3} +(2.40940 - 0.782861i) q^{4} +(2.98039 - 4.01464i) q^{5} +(1.36808 - 4.21053i) q^{6} +(-7.99303 + 7.99303i) q^{7} +(-3.34014 + 1.70189i) q^{8} +(-1.76336 - 2.42705i) q^{9} +(5.91896 - 11.3270i) q^{10} +(7.55171 + 5.48664i) q^{11} +(0.686429 - 4.33394i) q^{12} +(18.6042 + 2.94661i) q^{13} +(-16.9830 + 23.3751i) q^{14} +(-3.85208 - 7.75638i) q^{15} +(-15.9502 + 11.5885i) q^{16} +(-4.67525 - 9.17568i) q^{17} +(-5.42220 - 5.42220i) q^{18} +(-27.2439 - 8.85207i) q^{19} +(4.03804 - 12.0061i) q^{20} +(6.05019 + 18.6206i) q^{21} +(21.2587 + 10.8319i) q^{22} +(2.91575 + 18.4093i) q^{23} +6.49298i q^{24} +(-7.23459 - 23.9303i) q^{25} +48.1459 q^{26} +(-5.13218 + 0.812857i) q^{27} +(-13.0010 + 25.5158i) q^{28} +(-14.7153 + 4.78129i) q^{29} +(-12.8263 - 18.0413i) q^{30} +(14.6282 - 45.0210i) q^{31} +(-25.0308 + 25.0308i) q^{32} +(14.4055 - 7.33998i) q^{33} +(-15.4720 - 21.2953i) q^{34} +(8.26678 + 55.9114i) q^{35} +(-6.14867 - 4.46727i) q^{36} +(3.21245 - 20.2826i) q^{37} +(-72.3189 - 11.4542i) q^{38} +(19.1765 - 26.3942i) q^{39} +(-3.12245 + 18.4817i) q^{40} +(17.5771 - 12.7705i) q^{41} +(22.7197 + 44.5900i) q^{42} +(-2.49961 - 2.49961i) q^{43} +(22.4903 + 7.30756i) q^{44} +(-14.9992 - 0.154320i) q^{45} +(14.7221 + 45.3099i) q^{46} +(43.2168 + 22.0201i) q^{47} +(5.34196 + 33.7278i) q^{48} -78.7770i q^{49} +(-27.8330 - 57.5213i) q^{50} -17.8369 q^{51} +(47.1317 - 7.46492i) q^{52} +(-2.00554 + 3.93609i) q^{53} +(-12.6316 + 4.10425i) q^{54} +(44.5338 - 13.9650i) q^{55} +(13.0946 - 40.3010i) q^{56} +(-35.0839 + 35.0839i) q^{57} +(-35.2381 + 17.9547i) q^{58} +(24.1216 + 33.2005i) q^{59} +(-15.3534 - 15.6726i) q^{60} +(-30.0489 - 21.8318i) q^{61} +(18.9283 - 119.508i) q^{62} +(33.4940 + 5.30493i) q^{63} +(-6.82969 + 9.40026i) q^{64} +(67.2772 - 65.9069i) q^{65} +(33.4330 - 24.2905i) q^{66} +(35.0592 + 68.8075i) q^{67} +(-18.4478 - 18.4478i) q^{68} +(30.7033 + 9.97610i) q^{69} +(43.2266 + 137.847i) q^{70} +(-27.0431 - 83.2300i) q^{71} +(10.0204 + 5.10566i) q^{72} +(15.1994 + 95.9650i) q^{73} -52.4896i q^{74} +(-42.6197 - 7.65233i) q^{75} -72.5713 q^{76} +(-104.216 + 16.5062i) q^{77} +(37.8588 - 74.3021i) q^{78} +(-2.04034 + 0.662947i) q^{79} +(-1.01417 + 98.5722i) q^{80} +(-2.78115 + 8.55951i) q^{81} +(39.2684 - 39.2684i) q^{82} +(3.13930 - 1.59955i) q^{83} +(29.1547 + 40.1279i) q^{84} +(-50.7711 - 8.57769i) q^{85} +(-7.30994 - 5.31098i) q^{86} +(-4.19233 + 26.4693i) q^{87} +(-34.5614 - 5.47398i) q^{88} +(-47.0884 + 64.8116i) q^{89} +(-37.9284 + 5.60790i) q^{90} +(-172.256 + 125.151i) q^{91} +(21.4371 + 42.0728i) q^{92} +(-57.9769 - 57.9769i) q^{93} +(117.909 + 38.3110i) q^{94} +(-116.735 + 82.9916i) q^{95} +(18.9467 + 58.3118i) q^{96} +(-3.46493 - 1.76547i) q^{97} +(-31.4993 - 198.879i) q^{98} -28.0033i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8}+O(q^{10}) $ 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8	$ 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8} - 4 q^{10} - 24 q^{12} + 32 q^{13} - 24 q^{15} + 80 q^{16} - 100 q^{17} - 48 q^{18} - 100 q^{19} - 244 q^{20} - 100 q^{22} - 96 q^{23} - 16 q^{25} - 40 q^{26} + 196 q^{28} + 200 q^{29} + 264 q^{30} + 636 q^{32} + 216 q^{33} + 100 q^{34} + 260 q^{35} - 120 q^{36} - 184 q^{37} - 564 q^{38} - 948 q^{40} + 160 q^{41} - 12 q^{42} - 472 q^{43} - 700 q^{44} - 36 q^{45} - 288 q^{47} - 48 q^{48} + 16 q^{50} + 620 q^{52} + 304 q^{53} + 604 q^{55} + 72 q^{57} + 1272 q^{58} + 800 q^{59} + 84 q^{60} - 240 q^{61} + 1212 q^{62} - 12 q^{63} + 100 q^{64} + 272 q^{65} - 80 q^{67} + 104 q^{68} - 260 q^{70} + 36 q^{72} - 116 q^{73} - 24 q^{75} - 88 q^{77} - 120 q^{78} + 200 q^{79} - 164 q^{80} + 180 q^{81} - 168 q^{82} - 1264 q^{83} - 1200 q^{84} - 212 q^{85} - 876 q^{87} - 212 q^{88} - 1500 q^{89} - 444 q^{90} - 1504 q^{92} - 648 q^{93} - 200 q^{94} - 784 q^{95} + 60 q^{96} - 260 q^{97} - 92 q^{98}+O(q^{100}) $ 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8 - 4 * q^10 - 24 * q^12 + 32 * q^13 - 24 * q^15 + 80 * q^16 - 100 * q^17 - 48 * q^18 - 100 * q^19 - 244 * q^20 - 100 * q^22 - 96 * q^23 - 16 * q^25 - 40 * q^26 + 196 * q^28 + 200 * q^29 + 264 * q^30 + 636 * q^32 + 216 * q^33 + 100 * q^34 + 260 * q^35 - 120 * q^36 - 184 * q^37 - 564 * q^38 - 948 * q^40 + 160 * q^41 - 12 * q^42 - 472 * q^43 - 700 * q^44 - 36 * q^45 - 288 * q^47 - 48 * q^48 + 16 * q^50 + 620 * q^52 + 304 * q^53 + 604 * q^55 + 72 * q^57 + 1272 * q^58 + 800 * q^59 + 84 * q^60 - 240 * q^61 + 1212 * q^62 - 12 * q^63 + 100 * q^64 + 272 * q^65 - 80 * q^67 + 104 * q^68 - 260 * q^70 + 36 * q^72 - 116 * q^73 - 24 * q^75 - 88 * q^77 - 120 * q^78 + 200 * q^79 - 164 * q^80 + 180 * q^81 - 168 * q^82 - 1264 * q^83 - 1200 * q^84 - 212 * q^85 - 876 * q^87 - 212 * q^88 - 1500 * q^89 - 444 * q^90 - 1504 * q^92 - 648 * q^93 - 200 * q^94 - 784 * q^95 + 60 * q^96 - 260 * q^97 - 92 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{19}{20}\right)$

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 $

$2$	2.52458	−	0.399854i	1.26229	−	0.199927i	0.510816	−	0.859690i	$-0.329343\pi$
$2$	2.52458	−	0.399854i	1.26229	−	0.199927i	0.751474	+	0.659763i	$0.229343\pi$
$3$	0.786335	−	1.54327i	0.262112	−	0.514423i
$3$	0.786335	−	1.54327i	0.262112	−	0.514423i
$4$	2.40940	−	0.782861i	0.602350	−	0.195715i
$5$	2.98039	−	4.01464i	0.596077	−	0.802927i
$5$	2.98039	−	4.01464i	0.596077	−	0.802927i
$6$	1.36808	−	4.21053i	0.228014	−	0.701754i
$7$	−7.99303	+	7.99303i	−1.14186	+	1.14186i	−0.153752	+	0.988110i	$0.549136\pi$
$7$	−7.99303	+	7.99303i	−1.14186	+	1.14186i	−0.988110	+	0.153752i	$0.950864\pi$
$8$	−3.34014	+	1.70189i	−0.417517	+	0.212736i
$9$	−1.76336	−	2.42705i	−0.195928	−	0.269672i
$10$	5.91896	−	11.3270i	0.591896	−	1.13270i
$11$	7.55171	+	5.48664i	0.686519	+	0.498785i	0.875514	−	0.483193i	$-0.160523\pi$
$11$	7.55171	+	5.48664i	0.686519	+	0.498785i	−0.188995	+	0.981978i	$0.560523\pi$
$12$	0.686429	−	4.33394i	0.0572024	−	0.361162i
$13$	18.6042	+	2.94661i	1.43109	+	0.226662i	0.823377	−	0.567494i	$-0.192087\pi$
$13$	18.6042	+	2.94661i	1.43109	+	0.226662i	0.607713	+	0.794157i	$0.292087\pi$
$14$	−16.9830	+	23.3751i	−1.21307	+	1.66965i
$15$	−3.85208	−	7.75638i	−0.256805	−	0.517092i
$16$	−15.9502	+	11.5885i	−0.996886	+	0.724280i
$17$	−4.67525	−	9.17568i	−0.275014	−	0.539746i	0.711646	−	0.702538i	$-0.247950\pi$
$17$	−4.67525	−	9.17568i	−0.275014	−	0.539746i	−0.986660	+	0.162792i	$0.947950\pi$
$18$	−5.42220	−	5.42220i	−0.301233	−	0.301233i
$19$	−27.2439	−	8.85207i	−1.43389	−	0.465898i	−0.513902	−	0.857849i	$-0.671800\pi$
$19$	−27.2439	−	8.85207i	−1.43389	−	0.465898i	−0.919986	+	0.391951i	$0.871800\pi$
$20$	4.03804	−	12.0061i	0.201902	−	0.600304i
$21$	6.05019	+	18.6206i	0.288104	+	0.886694i
$22$	21.2587	+	10.8319i	0.966307	+	0.492358i
$23$	2.91575	+	18.4093i	0.126772	+	0.800405i	0.966362	+	0.257185i	$0.0827951\pi$
$23$	2.91575	+	18.4093i	0.126772	+	0.800405i	−0.839590	+	0.543220i	$0.817205\pi$
$24$			6.49298i			0.270541i
$25$	−7.23459	−	23.9303i	−0.289384	−	0.957213i
$26$	48.1459			1.85177
$27$	−5.13218	+	0.812857i	−0.190081	+	0.0301058i
$28$	−13.0010	+	25.5158i	−0.464320	+	0.911279i
$29$	−14.7153	+	4.78129i	−0.507424	+	0.164872i	−0.551530	−	0.834155i	$-0.685956\pi$
$29$	−14.7153	+	4.78129i	−0.507424	+	0.164872i	0.0441066	+	0.999027i	$0.485956\pi$
$30$	−12.8263	−	18.0413i	−0.427544	−	0.601378i
$31$	14.6282	−	45.0210i	0.471878	−	1.45229i	−0.378244	−	0.925706i	$-0.623472\pi$
$31$	14.6282	−	45.0210i	0.471878	−	1.45229i	0.850122	−	0.526586i	$-0.176528\pi$
$32$	−25.0308	+	25.0308i	−0.782212	+	0.782212i
$33$	14.4055	−	7.33998i	0.436531	−	0.222424i
$34$	−15.4720	−	21.2953i	−0.455058	−	0.626334i
$35$	8.26678	+	55.9114i	0.236194	+	1.59747i
$36$	−6.14867	−	4.46727i	−0.170796	−	0.124091i
$37$	3.21245	−	20.2826i	0.0868229	−	0.548178i	−0.905484	−	0.424379i	$-0.860492\pi$
$37$	3.21245	−	20.2826i	0.0868229	−	0.548178i	0.992307	−	0.123799i	$-0.0395077\pi$
$38$	−72.3189	−	11.4542i	−1.90313	−	0.301426i
$39$	19.1765	−	26.3942i	0.491706	−	0.676775i
$40$	−3.12245	+	18.4817i	−0.0780613	+	0.462043i
$41$	17.5771	−	12.7705i	0.428709	−	0.311476i	−0.352423	−	0.935841i	$-0.614642\pi$
$41$	17.5771	−	12.7705i	0.428709	−	0.311476i	0.781133	+	0.624365i	$0.214642\pi$
$42$	22.7197	+	44.5900i	0.540946	+	1.06167i
$43$	−2.49961	−	2.49961i	−0.0581304	−	0.0581304i	0.677444	−	0.735574i	$-0.263088\pi$
$43$	−2.49961	−	2.49961i	−0.0581304	−	0.0581304i	−0.735574	+	0.677444i	$0.763088\pi$
$44$	22.4903	+	7.30756i	0.511144	+	0.166081i
$45$	−14.9992	−	0.154320i	−0.333316	−	0.00342934i
$46$	14.7221	+	45.3099i	0.320045	+	0.984999i
$47$	43.2168	+	22.0201i	0.919506	+	0.468512i	0.848638	−	0.528974i	$-0.177423\pi$
$47$	43.2168	+	22.0201i	0.919506	+	0.468512i	0.0708681	+	0.997486i	$0.477423\pi$
$48$	5.34196	+	33.7278i	0.111291	+	0.702663i
$49$		−	78.7770i		−	1.60769i
$50$	−27.8330	−	57.5213i	−0.556659	−	1.15043i
$51$	−17.8369			−0.349742
$52$	47.1317	−	7.46492i	0.906378	−	0.143556i
$53$	−2.00554	+	3.93609i	−0.0378403	+	0.0742659i	−0.909153	−	0.416463i	$-0.863269\pi$
$53$	−2.00554	+	3.93609i	−0.0378403	+	0.0742659i	0.871312	+	0.490729i	$0.163269\pi$
$54$	−12.6316	+	4.10425i	−0.233918	+	0.0760046i
$55$	44.5338	−	13.9650i	0.809706	−	0.253910i
$56$	13.0946	−	40.3010i	0.233832	−	0.719661i
$57$	−35.0839	+	35.0839i	−0.615507	+	0.615507i
$58$	−35.2381	+	17.9547i	−0.607554	+	0.309564i
$59$	24.1216	+	33.2005i	0.408840	+	0.562721i	0.962935	−	0.269733i	$-0.0869355\pi$
$59$	24.1216	+	33.2005i	0.408840	+	0.562721i	−0.554095	+	0.832454i	$0.686935\pi$
$60$	−15.3534	−	15.6726i	−0.255889	−	0.261210i
$61$	−30.0489	−	21.8318i	−0.492604	−	0.357898i	0.313581	−	0.949562i	$-0.398471\pi$
$61$	−30.0489	−	21.8318i	−0.492604	−	0.357898i	−0.806185	+	0.591664i	$0.798471\pi$
$62$	18.9283	−	119.508i	0.305295	−	1.92755i
$63$	33.4940	+	5.30493i	0.531651	+	0.0842053i
$64$	−6.82969	+	9.40026i	−0.106714	+	0.146879i
$65$	67.2772	−	65.9069i	1.03503	−	1.01395i
$66$	33.4330	−	24.2905i	0.506560	−	0.368038i
$67$	35.0592	+	68.8075i	0.523271	+	1.02698i	0.989799	+	0.142471i	$0.0455049\pi$
$67$	35.0592	+	68.8075i	0.523271	+	1.02698i	−0.466527	+	0.884507i	$0.654495\pi$
$68$	−18.4478	−	18.4478i	−0.271291	−	0.271291i
$69$	30.7033	+	9.97610i	0.444975	+	0.144581i
$70$	43.2266	+	137.847i	0.617522	+	1.96925i
$71$	−27.0431	−	83.2300i	−0.380888	−	1.17225i	−0.939419	−	0.342770i	$-0.888635\pi$
$71$	−27.0431	−	83.2300i	−0.380888	−	1.17225i	0.558531	−	0.829484i	$-0.311365\pi$
$72$	10.0204	+	5.10566i	0.139172	+	0.0709119i
$73$	15.1994	+	95.9650i	0.208211	+	1.31459i	0.841324	+	0.540531i	$0.181776\pi$
$73$	15.1994	+	95.9650i	0.208211	+	1.31459i	−0.633114	+	0.774059i	$0.718224\pi$
$74$		−	52.4896i		−	0.709318i
$75$	−42.6197	−	7.65233i	−0.568263	−	0.102031i
$76$	−72.5713			−0.954885
$77$	−104.216	+	16.5062i	−1.35345	+	0.214366i
$78$	37.8588	−	74.3021i	0.485370	−	0.952591i
$79$	−2.04034	+	0.662947i	−0.0258271	+	0.00839173i	−0.321902	−	0.946773i	$-0.604322\pi$
$79$	−2.04034	+	0.662947i	−0.0258271	+	0.00839173i	0.296075	+	0.955165i	$0.404322\pi$
$80$	−1.01417	+	98.5722i	−0.0126771	+	1.23215i
$81$	−2.78115	+	8.55951i	−0.0343352	+	0.105673i
$82$	39.2684	−	39.2684i	0.478883	−	0.478883i
$83$	3.13930	−	1.59955i	0.0378229	−	0.0192717i	−0.434977	−	0.900442i	$-0.643243\pi$
$83$	3.13930	−	1.59955i	0.0378229	−	0.0192717i	0.472800	+	0.881170i	$0.343243\pi$
$84$	29.1547	+	40.1279i	0.347079	+	0.477714i
$85$	−50.7711	−	8.57769i	−0.597307	−	0.100914i
$86$	−7.30994	−	5.31098i	−0.0849993	−	0.0617556i
$87$	−4.19233	+	26.4693i	−0.0481877	+	0.304245i
$88$	−34.5614	−	5.47398i	−0.392743	−	0.0622043i
$89$	−47.0884	+	64.8116i	−0.529083	+	0.728220i	−0.986990	−	0.160780i	$-0.948599\pi$
$89$	−47.0884	+	64.8116i	−0.529083	+	0.728220i	0.457908	+	0.889000i	$0.348599\pi$
$90$	−37.9284	+	5.60790i	−0.421427	+	0.0623100i
$91$	−172.256	+	125.151i	−1.89292	+	1.37529i
$92$	21.4371	+	42.0728i	0.233012	+	0.457313i
$93$	−57.9769	−	57.9769i	−0.623407	−	0.623407i
$94$	117.909	+	38.3110i	1.25435	+	0.407564i
$95$	−116.735	+	82.9916i	−1.22879	+	0.873596i
$96$	18.9467	+	58.3118i	0.197361	+	0.607415i
$97$	−3.46493	−	1.76547i	−0.0357209	−	0.0182007i	0.436039	−	0.899928i	$-0.356381\pi$
$97$	−3.46493	−	1.76547i	−0.0357209	−	0.0182007i	−0.471760	+	0.881727i	$0.656381\pi$
$98$	−31.4993	−	198.879i	−0.321422	−	2.02938i
$99$		−	28.0033i		−	0.282861i
$100$	−36.1651	−	51.9940i	−0.361651	−	0.519940i
$101$	117.573			1.16409			0.582046	−	0.813156i	$-0.302253\pi$
$101$	117.573			1.16409			0.582046	+	0.813156i	$0.302253\pi$
$102$	−45.0306	+	7.13214i	−0.441476	+	0.0699230i
$103$	−22.0478	+	43.2712i	−0.214056	+	0.420109i	−0.972921	−	0.231140i	$-0.925754\pi$
$103$	−22.0478	+	43.2712i	−0.214056	+	0.420109i	0.758865	+	0.651249i	$0.225754\pi$
$104$	−67.1553	+	21.8201i	−0.645724	+	0.209808i
$105$	92.7868	+	31.2072i	0.883683	+	0.297212i
$106$	−3.48928	+	10.7389i	−0.0329177	+	0.101310i
$107$	−59.8859	+	59.8859i	−0.559682	+	0.559682i	−0.929217	−	0.369535i	$-0.879517\pi$
$107$	−59.8859	+	59.8859i	−0.559682	+	0.559682i	0.369535	+	0.929217i	$0.379517\pi$
$108$	−11.7291	+	5.97628i	−0.108603	+	0.0553359i
$109$	−36.6036	−	50.3806i	−0.335813	−	0.462207i	0.607399	−	0.794397i	$-0.292213\pi$
$109$	−36.6036	−	50.3806i	−0.335813	−	0.462207i	−0.943213	+	0.332189i	$0.892213\pi$
$110$	106.845	−	53.0629i	0.971321	−	0.482390i
$111$	−28.7754	−	20.9066i	−0.259238	−	0.188348i
$112$	34.8631	−	220.117i	0.311278	−	1.96533i
$113$	144.563	+	22.8965i	1.27932	+	0.202624i	0.758854	−	0.651260i	$-0.225759\pi$
$113$	144.563	+	22.8965i	1.27932	+	0.202624i	0.520463	+	0.853884i	$0.325759\pi$
$114$	−74.5437	+	102.601i	−0.653892	+	0.900006i
$115$	82.5968	+	43.1612i	0.718233	+	0.375315i
$116$	−31.7119	+	23.0400i	−0.273378	+	0.198621i
$117$	−25.6542	−	50.3492i	−0.219267	−	0.430335i
$118$	74.1723	+	74.1723i	0.628578	+	0.628578i
$119$	110.711	+	35.9721i	0.930343	+	0.302287i
$120$	26.0669	+	19.3516i	0.217225	+	0.161263i
$121$	−10.4660	−	32.2109i	−0.0864956	−	0.266206i
$122$	−84.5903	−	43.1009i	−0.693363	−	0.353286i
$123$	−5.88684	−	37.1681i	−0.0478605	−	0.302179i
$124$		−	119.925i		−	0.967141i
$125$	−117.633	−	42.2774i	−0.941067	−	0.338219i
$126$	86.6796			0.687933
$127$	−82.2861	+	13.0328i	−0.647922	+	0.102621i	−0.471741	−	0.881737i	$-0.656374\pi$
$127$	−82.2861	+	13.0328i	−0.647922	+	0.102621i	−0.176181	+	0.984358i	$0.556374\pi$
$128$	50.7997	−	99.7000i	0.396872	−	0.778906i
$129$	−5.82309	+	1.89204i	−0.0451402	+	0.0146670i
$130$	143.494	−	193.288i	1.10380	−	1.48683i
$131$	−59.9293	+	184.443i	−0.457476	+	1.40796i	0.410729	+	0.911758i	$0.365274\pi$
$131$	−59.9293	+	184.443i	−0.457476	+	1.40796i	−0.868204	+	0.496207i	$0.834726\pi$
$132$	28.9625	−	28.9625i	0.219413	−	0.219413i
$133$	288.516	−	147.006i	2.16929	−	1.10531i
$134$	116.023	+	159.692i	0.865841	+	1.19173i
$135$	−12.0326	+	23.0265i	−0.0891300	+	0.170566i
$136$	31.2319	+	22.6913i	0.229647	+	0.166848i
$137$	15.4352	−	97.4542i	0.112666	−	0.711345i	−0.865093	−	0.501612i	$-0.832741\pi$
$137$	15.4352	−	97.4542i	0.112666	−	0.711345i	0.977759	−	0.209733i	$-0.0672595\pi$
$138$	81.5019	+	12.9086i	0.590593	+	0.0935408i
$139$	22.8604	−	31.4646i	0.164463	−	0.226364i	−0.718829	−	0.695187i	$-0.755322\pi$
$139$	22.8604	−	31.4646i	0.164463	−	0.226364i	0.883292	+	0.468822i	$0.155322\pi$
$140$	63.6888	+	128.241i	0.454920	+	0.916008i
$141$	67.9657	−	49.3800i	0.482026	−	0.350213i
$142$	−101.552	−	199.308i	−0.715157	−	1.40357i
$143$	124.326	+	124.326i	0.869414	+	0.869414i
$144$	56.2516	+	18.2773i	0.390636	+	0.126925i
$145$	−24.6621	+	73.3266i	−0.170084	+	0.505701i
$146$	76.7441	+	236.194i	0.525644	+	1.61777i
$147$	−121.574	−	61.9451i	−0.827034	−	0.421395i
$148$	−8.13839	−	51.3838i	−0.0549891	−	0.347188i
$149$		−	86.4369i		−	0.580113i	−0.957009	−	0.290057i	$-0.906326\pi$
$149$		−	86.4369i		−	0.580113i	0.957009	−	0.290057i	$-0.0936742\pi$
$150$	−110.657	−	2.27724i	−0.737712	−	0.0151816i
$151$	−71.7582			−0.475220			−0.237610	−	0.971361i	$-0.576364\pi$
$151$	−71.7582			−0.475220			−0.237610	+	0.971361i	$0.576364\pi$
$152$	106.063	−	16.7988i	0.697786	−	0.110518i
$153$	−14.0257	+	27.5271i	−0.0916715	+	0.179915i
$154$	−256.501	+	83.3423i	−1.66559	+	0.541184i
$155$	−137.145	−	192.907i	−0.884808	−	1.24456i
$156$	25.5409	−	78.6067i	0.163724	−	0.503889i
$157$	−45.7787	+	45.7787i	−0.291584	+	0.291584i	−0.837706	−	0.546122i	$-0.816104\pi$
$157$	−45.7787	+	45.7787i	−0.291584	+	0.291584i	0.546122	+	0.837706i	$0.316104\pi$
$158$	−4.88592	+	2.48950i	−0.0309236	+	0.0157563i
$159$	4.49742	+	6.19017i	0.0282857	+	0.0389319i
$160$	25.8881	+	175.091i	0.161800	+	1.09432i
$161$	−170.452	−	123.841i	−1.05871	−	0.769196i
$162$	−3.59869	+	22.7212i	−0.0222141	+	0.140254i
$163$	−299.452	−	47.4285i	−1.83713	−	0.290972i	−0.861070	−	0.508487i	$-0.830205\pi$
$163$	−299.452	−	47.4285i	−1.83713	−	0.290972i	−0.976057	+	0.217514i	$0.930205\pi$
$164$	32.3527	−	44.5296i	0.197272	−	0.271522i
$165$	13.4667	−	79.7089i	0.0816162	−	0.483084i
$166$	7.28583	−	5.29347i	0.0438906	−	0.0318884i
$167$	51.5987	+	101.268i	0.308974	+	0.606397i	0.992320	−	0.123699i	$-0.0394756\pi$
$167$	51.5987	+	101.268i	0.308974	+	0.606397i	−0.683345	+	0.730095i	$0.739476\pi$
$168$	−51.8986	−	51.8986i	−0.308920	−	0.308920i
$169$	176.704	+	57.4146i	1.04559	+	0.339732i
$170$	−131.605	−	1.35403i	−0.774150	−	0.00796489i
$171$	26.5562	+	81.7316i	0.155299	+	0.477963i
$172$	−7.97939	−	4.06570i	−0.0463918	−	0.0236378i
$173$	28.3374	+	178.915i	0.163800	+	1.03419i	0.923411	+	0.383814i	$0.125390\pi$
$173$	28.3374	+	178.915i	0.163800	+	1.03419i	−0.759611	+	0.650378i	$0.774610\pi$
$174$			68.5003i			0.393680i
$175$	249.102	+	133.450i	1.42344	+	0.762569i
$176$	−184.033			−1.04564
$177$	70.2049	−	11.1194i	0.396638	−	0.0628213i
$178$	−92.9632	+	182.451i	−0.522265	+	1.02500i
$179$	174.999	−	56.8607i	0.977649	−	0.317657i	0.223749	−	0.974647i	$-0.428170\pi$
$179$	174.999	−	56.8607i	0.977649	−	0.317657i	0.753900	+	0.656989i	$0.228170\pi$
$180$	−36.2599	+	11.3705i	−0.201444	+	0.0631693i
$181$	62.6287	−	192.751i	0.346015	−	1.06492i	−0.615024	−	0.788509i	$-0.710854\pi$
$181$	62.6287	−	192.751i	0.346015	−	1.06492i	0.961038	−	0.276415i	$-0.0891465\pi$
$182$	−384.832	+	384.832i	−2.11446	+	2.11446i
$183$	−57.3208	+	29.2064i	−0.313228	+	0.159598i
$184$	−41.0696	−	56.5274i	−0.223204	−	0.307214i
$185$	−71.8529	−	73.3468i	−0.388394	−	0.396469i
$186$	−169.550	−	123.185i	−0.911557	−	0.662285i
$187$	15.0376	−	94.9434i	0.0804148	−	0.507719i
$188$	121.365	+	19.2223i	0.645559	+	0.102247i
$189$	34.5245	−	47.5188i	0.182669	−	0.251422i
$190$	−261.523	+	256.196i	−1.37643	+	1.34840i
$191$	71.6649	−	52.0676i	0.375209	−	0.272605i	−0.384159	−	0.923267i	$-0.625508\pi$
$191$	71.6649	−	52.0676i	0.375209	−	0.272605i	0.759368	+	0.650662i	$0.225508\pi$
$192$	9.13671	+	17.9318i	0.0475870	+	0.0933948i
$193$	7.66864	+	7.66864i	0.0397339	+	0.0397339i	0.726695	−	0.686961i	$-0.241056\pi$
$193$	7.66864	+	7.66864i	0.0397339	+	0.0397339i	−0.686961	+	0.726695i	$0.741056\pi$
$194$	−9.45342	−	3.07160i	−0.0487290	−	0.0158330i
$195$	−48.8097	−	155.652i	−0.250306	−	0.798214i
$196$	−61.6714	−	189.805i	−0.314650	−	0.968394i
$197$	240.613	+	122.598i	1.22139	+	0.622327i	0.941275	−	0.337641i	$-0.109629\pi$
$197$	240.613	+	122.598i	1.22139	+	0.622327i	0.280111	+	0.959968i	$0.409629\pi$
$198$	−11.1972	−	70.6965i	−0.0565516	−	0.357053i
$199$			21.6083i			0.108585i	0.998525	+	0.0542923i	$0.0172903\pi$
$199$			21.6083i			0.108585i	−0.998525	+	0.0542923i	$0.982710\pi$
$200$	64.8912	+	67.6182i	0.324456	+	0.338091i
$201$	133.757			0.665457
$202$	296.823	−	47.0122i	1.46942	−	0.232733i
$203$	79.4027	−	155.837i	0.391146	−	0.767668i
$204$	−42.9761	+	13.9638i	−0.210667	+	0.0684499i
$205$	1.11761	−	108.627i	0.00545177	−	0.529886i
$206$	−38.3592	+	118.057i	−0.186210	+	0.573095i
$207$	39.5389	−	39.5389i	0.191009	−	0.191009i
$208$	−330.886	+	168.595i	−1.59080	+	0.810553i
$209$	−157.170	−	216.325i	−0.752008	−	1.03505i
$210$	246.726	+	41.6839i	1.17489	+	0.198495i
$211$	204.226	+	148.379i	0.967894	+	0.703216i	0.954971	−	0.296700i	$-0.0958861\pi$
$211$	204.226	+	148.379i	0.967894	+	0.703216i	0.0129237	+	0.999916i	$0.495886\pi$
$212$	−1.75073	+	11.0537i	−0.00825816	+	0.0521399i
$213$	−149.711	−	23.7119i	−0.702869	−	0.111324i
$214$	−127.241	+	175.133i	−0.594585	+	0.818376i
$215$	−17.4848	+	2.58521i	−0.0813247	+	0.0120243i
$216$	15.7588	−	11.4494i	0.0729574	−	0.0530066i
$217$	242.931	+	476.778i	1.11950	+	2.19713i
$218$	−112.554	−	112.554i	−0.516302	−	0.516302i
$219$	160.052	+	52.0039i	0.730829	+	0.237461i
$220$	96.3671	−	68.5112i	0.438032	−	0.311414i
$221$	−59.9419	−	184.482i	−0.271230	−	0.834761i
$222$	−81.0055	−	41.2744i	−0.364890	−	0.185921i
$223$	−57.6796	−	364.174i	−0.258653	−	1.63307i	−0.685024	−	0.728521i	$-0.740208\pi$
$223$	−57.6796	−	364.174i	−0.258653	−	1.63307i	0.426371	−	0.904548i	$-0.359792\pi$
$224$		−	400.144i		−	1.78636i
$225$	−45.3230	+	59.7564i	−0.201435	+	0.265584i
$226$	374.116			1.65538
$227$	385.552	−	61.0654i	1.69847	−	0.269010i	0.769357	−	0.638819i	$-0.220577\pi$
$227$	385.552	−	61.0654i	1.69847	−	0.269010i	0.929108	+	0.369808i	$0.120577\pi$
$228$	−57.0653	+	111.997i	−0.250286	+	0.491215i
$229$	−166.732	+	54.1744i	−0.728085	+	0.236569i	−0.649525	−	0.760340i	$-0.725032\pi$
$229$	−166.732	+	54.1744i	−0.728085	+	0.236569i	−0.0785603	+	0.996909i	$0.525032\pi$
$230$	225.780	+	75.9373i	0.981654	+	0.330162i
$231$	−56.4751	+	173.812i	−0.244481	+	0.752434i
$232$	41.0139	−	41.0139i	0.176784	−	0.176784i
$233$	−273.193	+	139.199i	−1.17250	+	0.597420i	−0.928128	−	0.372261i	$-0.878583\pi$
$233$	−273.193	+	139.199i	−1.17250	+	0.597420i	−0.244375	+	0.969681i	$0.578583\pi$
$234$	−84.8984	−	116.853i	−0.362814	−	0.499370i
$235$	217.205	−	107.871i	0.924278	−	0.459027i
$236$	84.1099	+	61.1094i	0.356398	+	0.258938i
$237$	−0.581285	+	3.67009i	−0.00245268	+	0.0154856i
$238$	293.882	+	46.5464i	1.23480	+	0.195573i
$239$	−24.6293	+	33.8993i	−0.103051	+	0.141838i	−0.857428	−	0.514604i	$-0.827939\pi$
$239$	−24.6293	+	33.8993i	−0.103051	+	0.141838i	0.754377	+	0.656441i	$0.227939\pi$
$240$	151.326	+	79.0759i	0.630525	+	0.329483i
$241$	−325.379	+	236.401i	−1.35012	+	0.980919i	−0.351113	+	0.936333i	$0.614197\pi$
$241$	−325.379	+	236.401i	−1.35012	+	0.980919i	−0.999006	+	0.0445856i	$0.985803\pi$
$242$	−39.3019	−	77.1342i	−0.162404	−	0.318737i
$243$	11.0227	+	11.0227i	0.0453609	+	0.0453609i
$244$	−89.4910	−	29.0774i	−0.366766	−	0.119170i
$245$	−316.261	−	234.786i	−1.29086	−	0.958310i
$246$	−29.7236	−	91.4799i	−0.120828	−	0.371869i
$247$	−480.766	−	244.962i	−1.94642	−	0.991751i
$248$	27.7604	+	175.272i	0.111937	+	0.706742i
$249$		−	6.10257i		−	0.0245083i
$250$	−313.880	−	59.6965i	−1.25552	−	0.238786i
$251$	−345.021			−1.37459			−0.687293	−	0.726381i	$-0.741201\pi$
$251$	−345.021			−1.37459			−0.687293	+	0.726381i	$0.741201\pi$
$252$	84.8535	−	13.4395i	0.336720	−	0.0533313i
$253$	−78.9863	+	155.019i	−0.312199	+	0.612725i
$254$	−202.527	+	65.8049i	−0.797349	+	0.259074i
$255$	−53.1607	+	71.6085i	−0.208473	+	0.280817i
$256$	102.745	−	316.216i	0.401347	−	1.23522i
$257$	218.531	−	218.531i	0.850316	−	0.850316i	−0.139856	−	0.990172i	$-0.544664\pi$
$257$	218.531	−	218.531i	0.850316	−	0.850316i	0.990172	+	0.139856i	$0.0446639\pi$
$258$	−13.9443	+	7.10499i	−0.0540478	+	0.0275387i
$259$	136.442	+	187.797i	0.526804	+	0.725083i
$260$	110.502	−	211.465i	0.425006	−	0.813326i
$261$	37.5527	+	27.2836i	0.143880	+	0.104535i
$262$	−77.5459	+	489.605i	−0.295977	+	1.86872i
$263$	−143.194	−	22.6797i	−0.544463	−	0.0862345i	−0.121857	−	0.992548i	$-0.538885\pi$
$263$	−143.194	−	22.6797i	−0.544463	−	0.0862345i	−0.422607	+	0.906313i	$0.638885\pi$
$264$	−35.6246	+	49.0331i	−0.134942	+	0.185731i
$265$	9.82469	+	19.7826i	0.0370743	+	0.0746512i
$266$	669.600	−	486.493i	2.51729	−	1.82892i
$267$	62.9944	+	123.634i	0.235934	+	0.463047i
$268$	138.338	+	138.338i	0.516188	+	0.516188i
$269$	175.161	+	56.9134i	0.651157	+	0.211574i	0.615924	−	0.787805i	$-0.288783\pi$
$269$	175.161	+	56.9134i	0.651157	+	0.211574i	0.0352330	+	0.999379i	$0.488783\pi$
$270$	−21.1699	+	62.9434i	−0.0784071	+	0.233124i
$271$	−110.595	−	340.376i	−0.408099	−	1.25600i	−0.918279	−	0.395933i	$-0.870421\pi$
$271$	−110.595	−	340.376i	−0.408099	−	1.25600i	0.510180	−	0.860068i	$-0.329579\pi$
$272$	180.903	+	92.1748i	0.665085	+	0.338878i
$273$	57.6912	+	364.248i	0.211323	+	1.33424i
$274$		−	252.203i		−	0.920449i
$275$	76.6635	−	220.408i	0.278776	−	0.801485i
$276$	81.7863			0.296327
$277$	130.991	−	20.7469i	0.472890	−	0.0748984i	0.0845592	−	0.996418i	$-0.473052\pi$
$277$	130.991	−	20.7469i	0.472890	−	0.0748984i	0.388331	+	0.921520i	$0.373052\pi$
$278$	45.1317	−	88.5759i	0.162344	−	0.318618i
$279$	−135.063	+	43.8847i	−0.484097	+	0.157293i
$280$	−122.767	−	172.683i	−0.438453	−	0.616724i
$281$	−27.8287	+	85.6478i	−0.0990344	+	0.304797i	−0.988284	−	0.152626i	$-0.951227\pi$
$281$	−27.8287	+	85.6478i	−0.0990344	+	0.304797i	0.889250	+	0.457422i	$0.151227\pi$
$282$	151.840	−	151.840i	0.538440	−	0.538440i
$283$	196.084	−	99.9100i	0.692878	−	0.353039i	−0.0718292	−	0.997417i	$-0.522884\pi$
$283$	196.084	−	99.9100i	0.692878	−	0.353039i	0.764707	+	0.644378i	$0.222884\pi$
$284$	−130.315	−	179.363i	−0.458856	−	0.631561i
$285$	36.2855	+	245.413i	0.127317	+	0.861097i
$286$	363.584	+	264.159i	1.27127	+	0.923634i
$287$	−38.4192	+	242.569i	−0.133865	+	0.845189i
$288$	104.889	+	16.6128i	0.364199	+	0.0576834i
$289$	107.535	−	148.009i	0.372092	−	0.512141i
$290$	−32.9416	+	194.980i	−0.113592	+	0.672345i
$291$	−5.44919	+	3.95907i	−0.0187257	+	0.0136050i
$292$	111.749	+	219.319i	0.382701	+	0.751092i
$293$	−64.7980	−	64.7980i	−0.221153	−	0.221153i	0.587831	−	0.808984i	$-0.299982\pi$
$293$	−64.7980	−	64.7980i	−0.221153	−	0.221153i	−0.808984	+	0.587831i	$0.799982\pi$
$294$	−331.692	−	107.773i	−1.12821	−	0.366576i
$295$	205.180	+	2.11100i	0.695524	+	0.00715594i
$296$	23.7886	+	73.2139i	0.0803670	+	0.247344i
$297$	−43.2166	−	22.0199i	−0.145510	−	0.0741412i
$298$	−34.5622	−	218.217i	−0.115980	−	0.732271i
$299$			351.082i			1.17419i
$300$	−108.679	+	14.9278i	−0.362262	+	0.0497594i
$301$	39.9588			0.132754
$302$	−181.159	+	28.6928i	−0.599865	+	0.0950093i
$303$	92.4519	−	181.447i	0.305122	−	0.598835i
$304$	537.126	−	174.523i	1.76686	−	0.574088i
$305$	−177.204	+	55.5681i	−0.580996	+	0.182190i
$306$	−24.4023	+	75.1025i	−0.0797460	+	0.245433i
$307$	59.4433	−	59.4433i	0.193626	−	0.193626i	−0.603635	−	0.797261i	$-0.706281\pi$
$307$	59.4433	−	59.4433i	0.193626	−	0.193626i	0.797261	+	0.603635i	$0.206281\pi$
$308$	−238.175	+	121.356i	−0.773297	+	0.394014i
$309$	49.4421	+	68.0513i	0.160007	+	0.220231i
$310$	−423.369	−	432.171i	−1.36571	−	1.39410i
$311$	381.712	+	277.330i	1.22737	+	0.891735i	0.996690	−	0.0812949i	$-0.0259055\pi$
$311$	381.712	+	277.330i	1.22737	+	0.891735i	0.230678	+	0.973030i	$0.425906\pi$
$312$	−19.1323	+	120.797i	−0.0613214	+	0.387168i
$313$	−322.134	−	51.0211i	−1.02918	−	0.163007i	−0.381066	−	0.924548i	$-0.624443\pi$
$313$	−322.134	−	51.0211i	−1.02918	−	0.163007i	−0.648117	+	0.761541i	$0.724443\pi$
$314$	−97.2673	+	133.877i	−0.309768	+	0.426360i
$315$	121.123	−	118.656i	0.384516	−	0.376684i
$316$	−4.39700	+	3.19461i	−0.0139145	+	0.0101095i
$317$	−249.555	−	489.780i	−0.787240	−	1.54505i	−0.837580	−	0.546314i	$-0.816031\pi$
$317$	−249.555	−	489.780i	−0.787240	−	1.54505i	0.0503401	−	0.998732i	$-0.483969\pi$
$318$	13.8293	+	13.8293i	0.0434883	+	0.0434883i
$319$	−137.359	−	44.6305i	−0.430591	−	0.139908i
$320$	17.3835	+	55.4351i	0.0543234	+	0.173235i
$321$	45.3297	+	139.510i	0.141214	+	0.434612i
$322$	−479.838	−	244.490i	−1.49018	−	0.759284i
$323$	46.1480	+	291.367i	0.142873	+	0.902064i
$324$			22.8005i			0.0703720i
$325$	−64.0802	−	466.521i	−0.197170	−	1.43545i
$326$	−774.954			−2.37716
$327$	−106.534	+	16.8733i	−0.325791	+	0.0516002i
$328$	−36.9760	+	72.5694i	−0.112732	+	0.221248i
$329$	−521.440	+	169.426i	−1.58492	+	0.514973i
$330$	2.12578	−	206.616i	0.00644177	−	0.626110i
$331$	−101.582	+	312.637i	−0.306894	+	0.944524i	0.672069	+	0.740489i	$0.265406\pi$
$331$	−101.582	+	312.637i	−0.306894	+	0.944524i	−0.978963	+	0.204036i	$0.934594\pi$
$332$	6.31160	−	6.31160i	0.0190108	−	0.0190108i
$333$	−54.8916	+	27.9687i	−0.164840	+	0.0839900i
$334$	170.758	+	235.028i	0.511251	+	0.703676i
$335$	380.727	+	64.3232i	1.13650	+	0.192010i
$336$	−312.286	−	226.889i	−0.929422	−	0.675265i
$337$	−83.8137	+	529.179i	−0.248705	+	1.57026i	0.474894	+	0.880043i	$0.342486\pi$
$337$	−83.8137	+	529.179i	−0.248705	+	1.57026i	−0.723599	+	0.690220i	$0.757514\pi$
$338$	469.061	+	74.2920i	1.38776	+	0.219799i
$339$	149.010	−	205.095i	0.439558	−	0.605000i
$340$	−129.043	+	19.0796i	−0.379538	+	0.0561165i
$341$	357.482	−	259.726i	1.04833	−	0.761659i
$342$	99.7240	+	195.719i	0.291591	+	0.572279i
$343$	238.008	+	238.008i	0.693902	+	0.693902i
$344$	12.6031	+	4.09499i	0.0366368	+	0.0119040i
$345$	131.558	−	93.5298i	0.381328	−	0.271101i
$346$	143.080	+	440.355i	0.413526	+	1.27270i
$347$	−472.503	−	240.752i	−1.36168	−	0.693811i	−0.387985	−	0.921666i	$-0.626829\pi$
$347$	−472.503	−	240.752i	−1.36168	−	0.693811i	−0.973695	+	0.227855i	$0.926829\pi$
$348$	10.6208	+	67.0572i	0.0305196	+	0.192693i
$349$			381.118i			1.09203i	0.837776	+	0.546014i	$0.183855\pi$
$349$			381.118i			1.09203i	−0.837776	+	0.546014i	$0.816145\pi$
$350$	682.239	+	237.300i	1.94925	+	0.677999i
$351$	−97.8751			−0.278846
$352$	−326.360	+	51.6904i	−0.927159	+	0.146848i
$353$	−140.126	+	275.012i	−0.396956	+	0.779070i	−0.999824	−	0.0187708i	$-0.994025\pi$
$353$	−140.126	+	275.012i	−0.396956	+	0.779070i	0.602868	+	0.797841i	$0.294025\pi$
$354$	172.792	−	56.1435i	0.488113	−	0.158597i
$355$	−414.737	−	139.490i	−1.16827	−	0.392928i
$356$	−62.7162	+	193.021i	−0.176169	+	0.542193i
$357$	142.570	−	142.570i	0.399357	−	0.399357i
$358$	419.064	−	213.524i	1.17057	−	0.596435i
$359$	−160.270	−	220.592i	−0.446434	−	0.614463i	0.525193	−	0.850983i	$-0.323993\pi$
$359$	−160.270	−	220.592i	−0.446434	−	0.614463i	−0.971627	+	0.236520i	$0.923993\pi$
$360$	50.3620	−	25.0115i	0.139895	−	0.0694763i
$361$	371.814	+	270.139i	1.02996	+	0.748307i
$362$	81.0387	−	511.658i	0.223864	−	1.41342i
$363$	−57.9399	−	9.17677i	−0.159614	−	0.0252804i
$364$	−317.057	+	436.392i	−0.871037	+	1.19888i
$365$	430.565	+	224.993i	1.17963	+	0.616419i
$366$	−133.033	+	96.6539i	−0.363477	+	0.264082i
$367$	−167.988	−	329.695i	−0.457733	−	0.898351i	−0.998369	−	0.0570942i	$-0.981816\pi$
$367$	−167.988	−	329.695i	−0.457733	−	0.898351i	0.540636	−	0.841256i	$-0.318184\pi$
$368$	−259.843	−	259.843i	−0.706094	−	0.706094i
$369$	−61.9893	−	20.1416i	−0.167993	−	0.0545841i
$370$	−210.726	−	156.439i	−0.569531	−	0.422809i
$371$	−15.4310	−	47.4916i	−0.0415929	−	0.128010i
$372$	−185.077	−	94.3016i	−0.497519	−	0.253499i
$373$	−11.7805	−	74.3789i	−0.0315830	−	0.199407i	0.966852	−	0.255339i	$-0.0821871\pi$
$373$	−11.7805	−	74.3789i	−0.0315830	−	0.199407i	−0.998435	+	0.0559318i	$0.982187\pi$
$374$		−	245.705i		−	0.656966i
$375$	−157.745	+	148.296i	−0.420652	+	0.395455i
$376$	−181.826			−0.483579
$377$	−287.854	+	45.5916i	−0.763539	+	0.120933i
$378$	68.1592	−	133.770i	0.180315	−	0.353889i
$379$	−563.644	+	183.139i	−1.48719	+	0.483216i	−0.936251	−	0.351332i	$-0.885729\pi$
$379$	−563.644	+	183.139i	−1.48719	+	0.483216i	−0.550935	+	0.834548i	$0.685729\pi$
$380$	−216.290	+	291.347i	−0.569185	+	0.766703i
$381$	−44.5912	+	137.238i	−0.117037	+	0.360204i
$382$	160.104	−	160.104i	0.419122	−	0.419122i
$383$	511.078	−	260.407i	1.33441	−	0.679915i	0.366311	−	0.930492i	$-0.380621\pi$
$383$	511.078	−	260.407i	1.33441	−	0.679915i	0.968096	+	0.250578i	$0.0806206\pi$
$384$	−113.918	−	156.795i	−0.296662	−	0.408321i
$385$	−244.337	+	467.583i	−0.634642	+	1.21450i
$386$	22.4264	+	16.2938i	0.0580996	+	0.0422118i
$387$	−1.65898	+	10.4744i	−0.00428676	+	0.0270656i
$388$	−9.73051	−	1.54116i	−0.0250786	−	0.00397207i
$389$	−44.2279	+	60.8745i	−0.113697	+	0.156490i	−0.862073	−	0.506785i	$-0.830834\pi$
$389$	−44.2279	+	60.8745i	−0.113697	+	0.156490i	0.748376	+	0.663275i	$0.230834\pi$
$390$	−185.462	−	373.438i	−0.475544	−	0.957534i
$391$	155.286	−	112.822i	0.397152	−	0.288548i
$392$	134.069	+	263.126i	0.342014	+	0.671240i
$393$	237.521	+	237.521i	0.604380	+	0.604380i
$394$	656.468	+	213.300i	1.66616	+	0.541369i
$395$	−3.41951	+	10.1671i	−0.00865700	+	0.0257394i
$396$	−21.9227	−	67.4710i	−0.0553603	−	0.170381i
$397$	358.795	+	182.815i	0.903767	+	0.460492i	0.843156	−	0.537669i	$-0.180695\pi$
$397$	358.795	+	182.815i	0.903767	+	0.460492i	0.0606109	+	0.998161i	$0.480695\pi$
$398$	8.64018	+	54.5519i	0.0217090	+	0.137065i
$399$		−	560.853i		−	1.40565i
$400$	392.709	+	297.855i	0.981773	+	0.744637i
$401$	409.104			1.02021			0.510105	−	0.860112i	$-0.329607\pi$
$401$	409.104			1.02021			0.510105	+	0.860112i	$0.329607\pi$
$402$	337.680	−	53.4832i	0.839999	−	0.133043i
$403$	404.805	−	794.475i	1.00448	−	1.97140i
$404$	283.281	−	92.0435i	0.701190	−	0.227830i
$405$	26.0744	+	36.6760i	0.0643812	+	0.0905579i
$406$	138.147	−	425.172i	0.340263	−	1.04722i
$407$	135.543	−	135.543i	0.333029	−	0.333029i
$408$	59.5775	−	30.3563i	0.146023	−	0.0744026i
$409$	41.9264	+	57.7068i	0.102510	+	0.141092i	0.857190	−	0.515000i	$-0.172208\pi$
$409$	41.9264	+	57.7068i	0.102510	+	0.141092i	−0.754681	+	0.656092i	$0.772208\pi$
$410$	−40.6133	−	274.684i	−0.0990569	−	0.669960i
$411$	−138.261	−	100.452i	−0.336401	−	0.244410i
$412$	−19.2465	+	121.518i	−0.0467149	+	0.294946i
$413$	−458.177	−	72.5681i	−1.10939	−	0.175710i
$414$	84.0093	−	115.629i	0.202921	−	0.279297i
$415$	2.93471	−	17.3704i	0.00707158	−	0.0418565i
$416$	−539.433	+	391.921i	−1.29671	+	0.942118i
$417$	−30.5825	−	60.0215i	−0.0733393	−	0.143936i
$418$	−483.286	−	483.286i	−1.15619	−	1.15619i
$419$	233.315	+	75.8085i	0.556837	+	0.180927i	0.573897	−	0.818927i	$-0.305431\pi$
$419$	233.315	+	75.8085i	0.556837	+	0.180927i	−0.0170607	+	0.999854i	$0.505431\pi$
$420$	247.991	+	2.55147i	0.590455	+	0.00607494i
$421$	−169.787	−	522.551i	−0.403295	−	1.24121i	−0.922310	−	0.386450i	$-0.873701\pi$
$421$	−169.787	−	522.551i	−0.403295	−	1.24121i	0.519015	−	0.854765i	$-0.326299\pi$
$422$	574.914	+	292.933i	1.36236	+	0.694155i
$423$	−22.7628	−	143.719i	−0.0538127	−	0.339760i
$424$		−	16.5603i		−	0.0390573i
$425$	−185.754	+	178.262i	−0.437067	+	0.419441i
$426$	−387.439			−0.909482
$427$	414.683	−	65.6794i	0.971156	−	0.153816i
$428$	−97.4067	+	191.171i	−0.227586	+	0.446662i
$429$	289.631	−	94.1068i	0.675130	−	0.219363i
$430$	−43.1081	+	13.5180i	−0.100251	+	0.0314371i
$431$	−68.6900	+	211.406i	−0.159374	+	0.490501i	−0.998578	−	0.0533151i	$-0.983021\pi$
$431$	−68.6900	+	211.406i	−0.159374	+	0.490501i	0.839204	+	0.543816i	$0.183021\pi$
$432$	72.4393	−	72.4393i	0.167684	−	0.167684i
$433$	392.638	−	200.059i	0.906785	−	0.462030i	0.0625738	−	0.998040i	$-0.480069\pi$
$433$	392.638	−	200.059i	0.906785	−	0.462030i	0.844212	+	0.536010i	$0.180069\pi$
$434$	803.940	+	1106.53i	1.85240	+	2.54960i
$435$	93.7699	+	95.7195i	0.215563	+	0.220045i
$436$	−127.634	−	92.7314i	−0.292738	−	0.212687i
$437$	83.5243	−	527.351i	0.191131	−	1.20675i
$438$	424.857	+	67.2908i	0.969994	+	0.153632i
$439$	285.897	−	393.504i	0.651247	−	0.896364i	−0.347906	−	0.937530i	$-0.613107\pi$
$439$	285.897	−	393.504i	0.651247	−	0.896364i	0.999152	+	0.0411655i	$0.0131071\pi$
$440$	−124.982	+	122.437i	−0.284051	+	0.278265i
$441$	−191.196	+	138.912i	−0.433550	+	0.314993i
$442$	−225.094	−	441.772i	−0.509263	−	0.999484i
$443$	−344.919	−	344.919i	−0.778599	−	0.778599i	0.200994	−	0.979593i	$-0.435583\pi$
$443$	−344.919	−	344.919i	−0.778599	−	0.778599i	−0.979593	+	0.200994i	$0.935583\pi$
$444$	−85.6984	−	27.8451i	−0.193014	−	0.0627142i
$445$	119.853	+	382.206i	0.269333	+	0.858890i
$446$	−291.233	−	896.324i	−0.652990	−	2.00970i
$447$	−133.395	−	67.9683i	−0.298424	−	0.152054i
$448$	−20.5466	−	129.726i	−0.0458631	−	0.289568i
$449$			599.361i			1.33488i	0.744663	+	0.667440i	$0.232610\pi$
$449$			599.361i			1.33488i	−0.744663	+	0.667440i	$0.767390\pi$
$450$	−90.5277	+	168.982i	−0.201173	+	0.375517i
$451$	202.804			0.449676
$452$	366.234	−	58.0058i	0.810253	−	0.128331i
$453$	−56.4259	+	110.742i	−0.124561	+	0.244464i
$454$	948.939	−	308.329i	2.09017	−	0.679139i
$455$	−10.9526	+	1064.54i	−0.0240717	+	2.33966i
$456$	57.4763	−	176.894i	0.126045	−	0.387925i
$457$	−286.103	+	286.103i	−0.626046	+	0.626046i	−0.947071	−	0.321025i	$-0.895973\pi$
$457$	−286.103	+	286.103i	−0.626046	+	0.626046i	0.321025	+	0.947071i	$0.395973\pi$
$458$	−399.265	+	203.436i	−0.871759	+	0.444183i
$459$	31.4527	+	43.2910i	0.0685244	+	0.0943158i
$460$	232.798	+	39.3308i	0.506082	+	0.0855017i
$461$	−343.790	−	249.778i	−0.745749	−	0.541818i	0.148758	−	0.988874i	$-0.452473\pi$
$461$	−343.790	−	249.778i	−0.745749	−	0.541818i	−0.894506	+	0.447056i	$0.852473\pi$
$462$	−73.0762	+	461.385i	−0.158174	+	0.998669i
$463$	−336.055	−	53.2259i	−0.725821	−	0.114959i	−0.217419	−	0.976078i	$-0.569764\pi$
$463$	−336.055	−	53.2259i	−0.725821	−	0.114959i	−0.508402	+	0.861120i	$0.669764\pi$
$464$	179.303	−	246.790i	0.386430	−	0.531875i
$465$	−405.549	+	59.9625i	−0.872149	+	0.128952i
$466$	−634.039	+	460.656i	−1.36060	+	0.988533i
$467$	−300.950	−	590.647i	−0.644432	−	1.26477i	−0.949896	−	0.312565i	$-0.898812\pi$
$467$	−300.950	−	590.647i	−0.644432	−	1.26477i	0.305464	−	0.952203i	$-0.401188\pi$
$468$	−101.228	−	101.228i	−0.216298	−	0.216298i
$469$	−830.210	−	269.751i	−1.77017	−	0.575163i
$470$	505.219	−	359.180i	1.07493	−	0.764214i
$471$	34.6515	+	106.646i	0.0735700	+	0.226425i
$472$	−137.073	−	69.8421i	−0.290409	−	0.147971i
$473$	−5.16186	−	32.5907i	−0.0109130	−	0.0689022i
$474$			9.49787i			0.0200377i
$475$	−14.7347	+	715.996i	−0.0310204	+	1.50736i
$476$	294.908			0.619554
$477$	13.0896	−	2.07318i	0.0274414	−	0.00434630i
$478$	−48.6238	+	95.4295i	−0.101723	+	0.199643i
$479$	621.035	−	201.787i	1.29652	−	0.421266i	0.422154	−	0.906524i	$-0.361274\pi$
$479$	621.035	−	201.787i	1.29652	−	0.421266i	0.874371	+	0.485258i	$0.161274\pi$
$480$	290.569	+	97.7278i	0.605352	+	0.203600i
$481$	119.530	−	367.875i	0.248503	−	0.764813i
$482$	−726.918	+	726.918i	−1.50813	+	1.50813i
$483$	−325.151	+	165.673i	−0.673191	+	0.343008i
$484$	−50.4334	−	69.4156i	−0.104201	−	0.143421i
$485$	−17.4145	+	8.64865i	−0.0359063	+	0.0178323i
$486$	32.2352	+	23.4202i	0.0663275	+	0.0481898i
$487$	−67.2011	+	424.291i	−0.137990	+	0.871234i	0.817439	+	0.576015i	$0.195393\pi$
$487$	−67.2011	+	424.291i	−0.137990	+	0.871234i	−0.955429	+	0.295220i	$0.904607\pi$
$488$	137.523	+	21.7814i	0.281809	+	0.0446341i
$489$	−308.664	+	424.840i	−0.631215	+	0.868793i
$490$	−892.306	−	466.278i	−1.82103	−	0.951587i
$491$	−96.5536	+	70.1503i	−0.196647	+	0.142872i	−0.681752	−	0.731584i	$-0.738781\pi$
$491$	−96.5536	+	70.1503i	−0.196647	+	0.142872i	0.485105	+	0.874456i	$0.338781\pi$
$492$	−43.2812	−	84.9441i	−0.0879699	−	0.172651i
$493$	112.669	+	112.669i	0.228538	+	0.228538i
$494$	−1311.68	−	426.191i	−2.65523	−	0.862735i
$495$	−112.423	−	83.4606i	−0.227117	−	0.168607i
$496$	288.403	+	887.612i	0.581457	+	1.78954i
$497$	881.416	+	449.104i	1.77347	+	0.903629i
$498$	−2.44014	−	15.4064i	−0.00489988	−	0.0309366i
$499$			385.642i			0.772829i	0.922325	+	0.386414i	$0.126287\pi$
$499$			385.642i			0.772829i	−0.922325	+	0.386414i	$0.873713\pi$
$500$	−316.523	−	9.77246i	−0.633046	−	0.0195449i
$501$	196.858			0.392930
$502$	−871.033	+	137.958i	−1.73513	+	0.274817i
$503$	−143.312	+	281.266i	−0.284915	+	0.559177i	−0.988462	−	0.151472i	$-0.951599\pi$
$503$	−143.312	+	281.266i	−0.284915	+	0.559177i	0.703547	+	0.710649i	$0.251599\pi$
$504$	−120.903	+	39.2838i	−0.239887	+	0.0779440i
$505$	350.414	−	472.014i	0.693888	−	0.934680i
$506$	−137.422	+	422.942i	−0.271585	+	0.835854i
$507$	227.555	−	227.555i	0.448826	−	0.448826i
$508$	−188.057	+	95.8198i	−0.370191	+	0.188622i
$509$	−490.368	−	674.933i	−0.963394	−	1.32600i	−0.945314	−	0.326161i	$-0.894245\pi$
$509$	−490.368	−	674.933i	−0.963394	−	1.32600i	−0.0180799	−	0.999837i	$-0.505755\pi$
$510$	−105.576	+	202.038i	−0.207011	+	0.396153i
$511$	−888.540	−	645.562i	−1.73883	−	1.26333i
$512$	62.9296	−	397.322i	0.122909	−	0.776020i
$513$	147.016	+	23.2850i	0.286581	+	0.0453899i
$514$	464.319	−	639.080i	0.903344	−	1.24335i
$515$	108.007	+	217.479i	0.209723	+	0.422289i
$516$	−12.5489	+	9.11734i	−0.0243197	+	0.0176693i
$517$	205.544	+	403.404i	0.397572	+	0.780278i
$518$	419.550	+	419.550i	0.809943	+	0.809943i
$519$	298.397	+	96.9550i	0.574946	+	0.186811i
$520$	−112.549	+	334.636i	−0.216441	+	0.643531i
$521$	49.5899	+	152.622i	0.0951821	+	0.292940i	0.987301	−	0.158860i	$-0.0507819\pi$
$521$	49.5899	+	152.622i	0.0951821	+	0.292940i	−0.892119	+	0.451800i	$0.850782\pi$
$522$	105.714	+	53.8641i	0.202518	+	0.103188i
$523$	32.9063	+	207.762i	0.0629183	+	0.397250i	0.998969	+	0.0453866i	$0.0144520\pi$
$523$	32.9063	+	207.762i	0.0629183	+	0.397250i	−0.936051	+	0.351864i	$0.885548\pi$
$524$			491.314i			0.937622i
$525$	401.826	−	279.495i	0.765383	−	0.532372i
$526$	−370.573			−0.704511
$527$	−481.489	+	76.2604i	−0.913642	+	0.144707i
$528$	−144.711	+	284.012i	−0.274074	+	0.537901i
$529$	172.707	−	56.1160i	0.326479	−	0.106079i
$530$	32.7134	+	46.0143i	0.0617233	+	0.0868194i
$531$	38.0444	−	117.089i	0.0716467	−	0.220506i
$532$	580.064	−	580.064i	1.09035	−	1.09035i
$533$	364.637	−	185.792i	0.684122	−	0.348577i
$534$	208.470	+	286.934i	0.390393	+	0.537330i
$535$	61.9369	+	418.903i	0.115770	+	0.782997i
$536$	−234.205	−	170.160i	−0.436950	−	0.317463i
$537$	49.8566	−	314.782i	0.0928429	−	0.586187i
$538$	464.966	+	73.6434i	0.864249	+	0.136884i
$539$	432.221	−	594.901i	0.801893	−	1.10371i
$540$	−10.9647	+	64.8997i	−0.0203050	+	0.120185i
$541$	408.541	−	296.822i	0.755158	−	0.548655i	−0.142263	−	0.989829i	$-0.545438\pi$
$541$	408.541	−	296.822i	0.755158	−	0.548655i	0.897421	+	0.441174i	$0.145438\pi$
$542$	−415.307	−	815.085i	−0.766249	−	1.50385i
$543$	−248.220	−	248.220i	−0.457127	−	0.457127i
$544$	346.700	+	112.650i	0.637316	+	0.207076i
$545$	−311.353	−	3.20337i	−0.571289	−	0.00587775i
$546$	291.292	+	896.506i	0.533502	+	1.64195i
$547$	−64.4780	−	32.8532i	−0.117876	−	0.0600607i	0.394058	−	0.919085i	$-0.371071\pi$
$547$	−64.4780	−	32.8532i	−0.117876	−	0.0600607i	−0.511934	+	0.859025i	$0.671071\pi$
$548$	−39.1035	−	246.890i	−0.0713568	−	0.450529i
$549$			111.427i			0.202964i
$550$	105.412	−	587.093i	0.191658	−	1.06744i
$551$	443.225			0.804402
$552$	−119.531	+	18.9319i	−0.216542	+	0.0342969i
$553$	11.0095	−	21.6074i	0.0199088	−	0.0390731i
$554$	322.400	−	104.754i	0.581950	−	0.189087i
$555$	−169.694	+	53.2132i	−0.305755	+	0.0958796i
$556$	30.4474	−	93.7074i	0.0547615	−	0.168538i
$557$	−250.938	+	250.938i	−0.450516	+	0.450516i	−0.895526	−	0.445010i	$-0.853200\pi$
$557$	−250.938	+	250.938i	−0.450516	+	0.450516i	0.445010	+	0.895526i	$0.353200\pi$
$558$	−323.430	+	164.796i	−0.579624	+	0.295333i
$559$	−39.1377	−	53.8685i	−0.0700138	−	0.0963658i
$560$	−779.784	−	795.997i	−1.39247	−	1.42142i
$561$	−134.699	−	97.8643i	−0.240105	−	0.174446i
$562$	−36.0091	+	227.352i	−0.0640731	+	0.404541i
$563$	−556.798	−	88.1882i	−0.988985	−	0.156640i	−0.359076	−	0.933309i	$-0.616908\pi$
$563$	−556.798	−	88.1882i	−0.988985	−	0.156640i	−0.629909	+	0.776669i	$0.716908\pi$
$564$	125.099	−	172.184i	0.221806	−	0.305290i
$565$	522.774	−	512.127i	0.925264	−	0.906419i
$566$	455.082	−	330.636i	0.804031	−	0.584163i
$567$	−46.1866	−	90.6462i	−0.0814578	−	0.159870i
$568$	231.976	+	231.976i	0.408408	+	0.408408i
$569$	84.8785	+	27.5787i	0.149171	+	0.0484687i	0.382651	−	0.923893i	$-0.375011\pi$
$569$	84.8785	+	27.5787i	0.149171	+	0.0484687i	−0.233480	+	0.972362i	$0.575011\pi$
$570$	189.735	+	605.055i	0.332868	+	1.06150i
$571$	41.2619	+	126.991i	0.0722625	+	0.222401i	0.980664	−	0.195697i	$-0.0626969\pi$
$571$	41.2619	+	126.991i	0.0722625	+	0.222401i	−0.908402	+	0.418098i	$0.862697\pi$
$572$	396.882	+	202.221i	0.693849	+	0.353534i
$573$	−24.0017	−	151.541i	−0.0418878	−	0.264469i
$574$			627.747i			1.09364i
$575$	419.447	−	202.959i	0.729473	−	0.352972i
$576$	34.8581			0.0605175
$577$	−245.806	+	38.9318i	−0.426007	+	0.0674728i	−0.365757	−	0.930710i	$-0.619190\pi$
$577$	−245.806	+	38.9318i	−0.426007	+	0.0674728i	−0.0602500	+	0.998183i	$0.519190\pi$
$578$	212.298	−	416.658i	0.367298	−	0.720862i
$579$	17.8649	−	5.80466i	0.0308547	−	0.0100253i
$580$	−2.01635	+	195.980i	−0.00347647	+	0.337897i
$581$	−12.3072	+	37.8778i	−0.0211829	+	0.0651942i
$582$	−12.1739	+	12.1739i	−0.0209173	+	0.0209173i
$583$	−36.7411	+	18.7205i	−0.0630208	+	0.0321107i
$584$	−214.089	−	294.669i	−0.366591	−	0.504570i
$585$	−278.593	−	47.0678i	−0.476227	−	0.0804578i
$586$	−189.497	−	137.678i	−0.323375	−	0.234945i
$587$	44.1891	−	278.999i	0.0752796	−	0.475296i	−0.921032	−	0.389487i	$-0.872652\pi$
$587$	44.1891	−	278.999i	0.0752796	−	0.475296i	0.996312	−	0.0858096i	$-0.0273477\pi$
$588$	−341.415	−	54.0748i	−0.580637	−	0.0919639i
$589$	−797.059	+	1097.06i	−1.35324	+	1.86258i
$590$	518.837	−	76.7125i	0.879384	−	0.130021i
$591$	378.405	−	274.927i	0.640279	−	0.465190i
$592$	183.805	+	360.738i	0.310482	+	0.609355i
$593$	402.759	+	402.759i	0.679188	+	0.679188i	0.959817	−	0.280628i	$-0.0905428\pi$
$593$	402.759	+	402.759i	0.679188	+	0.679188i	−0.280628	+	0.959817i	$0.590543\pi$
$594$	−117.908	−	38.3108i	−0.198499	−	0.0644963i
$595$	474.376	−	337.253i	0.797271	−	0.566812i
$596$	−67.6681	−	208.261i	−0.113537	−	0.349431i
$597$	33.3474	+	16.9914i	0.0558584	+	0.0284613i
$598$	140.382	+	886.334i	0.234752	+	1.48216i
$599$		−	400.913i		−	0.669303i	−0.942342	−	0.334652i	$-0.891381\pi$
$599$		−	400.913i		−	0.669303i	0.942342	−	0.334652i	$-0.108619\pi$
$600$	155.379	−	46.9741i	0.258965	−	0.0782901i
$601$	1007.76			1.67681			0.838404	−	0.545049i	$-0.183489\pi$
$601$	1007.76			1.67681			0.838404	+	0.545049i	$0.183489\pi$
$602$	100.879	−	15.9777i	0.167574	−	0.0265411i
$603$	105.178	−	206.423i	0.174424	−	0.342326i
$604$	−172.894	+	56.1767i	−0.286248	+	0.0930078i
$605$	−160.508	−	53.9840i	−0.265302	−	0.0892297i
$606$	160.850	−	495.045i	0.265429	−	0.816906i
$607$	−44.3957	+	44.3957i	−0.0731395	+	0.0731395i	−0.742730	−	0.669591i	$-0.766470\pi$
$607$	−44.3957	+	44.3957i	−0.0731395	+	0.0731395i	0.669591	+	0.742730i	$0.266470\pi$
$608$	903.510	−	460.361i	1.48604	−	0.757173i
$609$	−178.061	−	245.079i	−0.292382	−	0.402429i
$610$	−425.146	+	211.142i	−0.696961	+	0.346134i
$611$	739.128	+	537.008i	1.20970	+	0.878900i
$612$	−12.2437	+	77.3039i	−0.0200061	+	0.126313i
$613$	−21.8479	−	3.46037i	−0.0356410	−	0.00564497i	0.138589	−	0.990350i	$-0.455743\pi$
$613$	−21.8479	−	3.46037i	−0.0356410	−	0.00564497i	−0.174229	+	0.984705i	$0.555743\pi$
$614$	126.301	−	173.838i	0.205702	−	0.283124i
$615$	−166.761	−	87.1417i	−0.271156	−	0.141694i
$616$	320.004	−	232.496i	0.519486	−	0.377429i
$617$	213.879	+	419.760i	0.346643	+	0.680325i	0.996840	−	0.0794412i	$-0.0253136\pi$
$617$	213.879	+	419.760i	0.346643	+	0.680325i	−0.650197	+	0.759766i	$0.725314\pi$
$618$	152.031	+	152.031i	0.246005	+	0.246005i
$619$	−421.942	−	137.097i	−0.681651	−	0.221482i	−0.0523327	−	0.998630i	$-0.516666\pi$
$619$	−421.942	−	137.097i	−0.681651	−	0.221482i	−0.629318	+	0.777148i	$0.716666\pi$
$620$	−481.457	−	357.424i	−0.776544	−	0.576491i
$621$	−29.9283	−	92.1098i	−0.0481937	−	0.148325i
$622$	1074.55	+	547.512i	1.72758	+	0.880245i
$623$	−141.662	−	894.419i	−0.227387	−	1.43566i
$624$			643.219i			1.03080i
$625$	−520.321	+	346.252i	−0.832514	+	0.554004i
$626$	−833.655			−1.33172
$627$	−457.436	+	72.4507i	−0.729563	+	0.115551i
$628$	−74.4608	+	146.138i	−0.118568	+	0.232703i
$629$	−201.126	+	65.3497i	−0.319755	+	0.103895i
$630$	258.339	−	347.987i	0.410061	−	0.552360i
$631$	−78.9246	+	242.905i	−0.125079	+	0.384952i	−0.993915	−	0.110146i	$-0.964868\pi$
$631$	−78.9246	+	242.905i	−0.125079	+	0.384952i	0.868837	+	0.495099i	$0.164868\pi$
$632$	5.68676	−	5.68676i	0.00899803	−	0.00899803i
$633$	389.578	−	198.500i	0.615447	−	0.313586i
$634$	−825.863	−	1136.70i	−1.30262	−	1.79291i
$635$	−192.922	+	369.191i	−0.303814	+	0.581404i
$636$	15.6821	+	11.3937i	0.0246574	+	0.0179147i
$637$	232.125	−	1465.58i	0.364404	−	2.30075i
$638$	−364.619	−	57.7499i	−0.571503	−	0.0905171i
$639$	−154.317	+	212.399i	−0.241498	+	0.332393i
$640$	−248.856	−	501.087i	−0.388838	−	0.782948i
$641$	−537.423	+	390.461i	−0.838414	+	0.609143i	−0.921927	−	0.387363i	$-0.873386\pi$
$641$	−537.423	+	390.461i	−0.838414	+	0.609143i	0.0835134	+	0.996507i	$0.473386\pi$
$642$	170.222	+	334.080i	0.265144	+	0.520374i
$643$	12.9642	+	12.9642i	0.0201621	+	0.0201621i	0.717116	−	0.696954i	$-0.245462\pi$
$643$	12.9642	+	12.9642i	0.0201621	+	0.0201621i	−0.696954	+	0.717116i	$0.745462\pi$
$644$	−507.636	−	164.941i	−0.788255	−	0.256120i
$645$	−9.75923	+	29.0166i	−0.0151306	+	0.0449870i
$646$	233.008	+	717.126i	0.360694	+	1.11010i
$647$	431.960	+	220.094i	0.667635	+	0.340177i	0.754742	−	0.656022i	$-0.227762\pi$
$647$	431.960	+	220.094i	0.667635	+	0.340177i	−0.0871069	+	0.996199i	$0.527762\pi$
$648$	−5.27787	−	33.3231i	−0.00814486	−	0.0514246i
$649$			383.067i			0.590242i
$650$	−348.316	−	1152.15i	−0.535871	−	1.77254i
$651$	926.821			1.42369
$652$	−758.628	+	120.155i	−1.16354	+	0.184287i
$653$	−350.096	+	687.102i	−0.536135	+	1.05222i	0.451029	+	0.892509i	$0.351057\pi$
$653$	−350.096	+	687.102i	−0.536135	+	1.05222i	−0.987163	+	0.159714i	$0.948943\pi$
$654$	−262.206	+	85.1958i	−0.400926	+	0.130269i
$655$	561.861	+	790.307i	0.857802	+	1.20658i
$656$	−132.367	+	407.383i	−0.201779	+	0.621011i
$657$	206.110	−	206.110i	0.313714	−	0.313714i
$658$	−1248.67	+	636.230i	−1.89768	+	0.966915i
$659$	41.4679	+	57.0757i	0.0629255	+	0.0866096i	0.839320	−	0.543638i	$-0.182953\pi$
$659$	41.4679	+	57.0757i	0.0629255	+	0.0866096i	−0.776394	+	0.630247i	$0.782953\pi$
$660$	−29.9544	−	202.593i	−0.0453854	−	0.306959i
$661$	191.151	+	138.880i	0.289185	+	0.210105i	0.722914	−	0.690938i	$-0.242802\pi$
$661$	191.151	+	138.880i	0.289185	+	0.210105i	−0.433729	+	0.901043i	$0.642802\pi$
$662$	−131.443	+	829.897i	−0.198554	+	1.25362i
$663$	−331.840	−	52.5583i	−0.500513	−	0.0792734i
$664$	−7.76344	+	10.6855i	−0.0116919	+	0.0160926i
$665$	269.713	−	1596.42i	0.405583	−	2.40063i
$666$	−127.395	+	92.5578i	−0.191284	+	0.138976i
$667$	−130.926	−	256.957i	−0.196291	−	0.385243i
$668$	203.601	+	203.601i	0.304792	+	0.304792i
$669$	−607.374	−	197.348i	−0.907884	−	0.294989i
$670$	986.896	+	10.1537i	1.47298	+	0.0151548i
$671$	−107.137	−	329.734i	−0.159668	−	0.491407i
$672$	−617.529	−	314.647i	−0.918942	−	0.468224i
$673$	−53.4053	−	337.188i	−0.0793541	−	0.501022i	−0.995068	−	0.0991920i	$-0.968374\pi$
$673$	−53.4053	−	337.188i	−0.0793541	−	0.501022i	0.915714	−	0.401830i	$-0.131626\pi$
$674$			1369.47i			2.03185i
$675$	56.5812	+	116.934i	0.0838239	+	0.173236i
$676$	470.698			0.696299
$677$	−505.902	+	80.1269i	−0.747270	+	0.118356i	−0.518444	−	0.855112i	$-0.673489\pi$
$677$	−505.902	+	80.1269i	−0.747270	+	0.118356i	−0.228826	+	0.973467i	$0.573489\pi$
$678$	294.180	−	577.361i	0.433894	−	0.851565i
$679$	41.8067	−	13.5838i	0.0615710	−	0.0200056i
$680$	184.181	−	57.7559i	0.270854	−	0.0849351i
$681$	208.932	−	643.027i	0.306802	−	0.944240i
$682$	798.640	−	798.640i	1.17103	−	1.17103i
$683$	707.255	−	360.364i	1.03551	−	0.527620i	0.148281	−	0.988945i	$-0.452626\pi$
$683$	707.255	−	360.364i	1.03551	−	0.527620i	0.887231	+	0.461326i	$0.152626\pi$
$684$	127.969	+	176.134i	0.187089	+	0.257506i
$685$	−345.240	−	352.418i	−0.504000	−	0.514479i
$686$	696.040	+	505.702i	1.01464	+	0.737176i
$687$	−47.5012	+	299.911i	−0.0691429	+	0.436551i
$688$	68.8358	+	10.9025i	0.100052	+	0.0158467i
$689$	−48.9095	+	67.3182i	−0.0709862	+	0.0977041i
$690$	294.731	−	288.728i	0.427146	−	0.418446i
$691$	−554.348	+	402.757i	−0.802240	+	0.582861i	−0.911570	−	0.411144i	$-0.865129\pi$
$691$	−554.348	+	402.757i	−0.802240	+	0.582861i	0.109331	+	0.994005i	$0.465129\pi$
$692$	208.342	+	408.894i	0.301072	+	0.590887i
$693$	223.831	+	223.831i	0.322988	+	0.322988i
$694$	−1289.14	−	418.866i	−1.85755	−	0.603554i
$695$	−58.1862	−	185.553i	−0.0837212	−	0.266983i
$696$	−31.0448	−	95.5461i	−0.0446046	−	0.137279i
$697$	−199.355	−	101.577i	−0.286019	−	0.145734i
$698$	152.392	+	962.162i	0.218326	+	1.37846i
$699$			531.067i			0.759753i
$700$	704.659	+	126.521i	1.00666	+	0.180744i
$701$	264.680			0.377574			0.188787	−	0.982018i	$-0.439544\pi$
$701$	264.680			0.377574			0.188787	+	0.982018i	$0.439544\pi$
$702$	−247.094	+	39.1358i	−0.351985	+	0.0557490i
$703$	−267.062	+	524.139i	−0.379890	+	0.745575i
$704$	−103.152	+	33.5160i	−0.146522	+	0.0476079i
$705$	4.32150	−	420.029i	0.00612978	−	0.595786i
$706$	−243.794	+	750.319i	−0.345317	+	1.06278i
$707$	−939.766	+	939.766i	−1.32923	+	1.32923i
$708$	160.447	−	81.7517i	0.226620	−	0.115469i
$709$	312.935	+	430.718i	0.441375	+	0.607501i	0.970517	−	0.241032i	$-0.0774860\pi$
$709$	312.935	+	430.718i	0.441375	+	0.607501i	−0.529142	+	0.848533i	$0.677486\pi$
$710$	−1102.81	−	186.318i	−1.55326	−	0.262420i
$711$	5.20685	+	3.78300i	0.00732328	+	0.00532067i
$712$	46.9798	−	296.619i	0.0659828	−	0.416599i
$713$	871.459	+	138.026i	1.22224	+	0.193584i
$714$	302.923	−	416.938i	0.424262	−	0.583947i
$715$	869.665	−	128.584i	1.21631	−	0.179838i
$716$	377.129	−	274.000i	0.526716	−	0.382682i
$717$	32.9488	+	64.6657i	0.0459537	+	0.0901893i
$718$	−492.819	−	492.819i	−0.686377	−	0.686377i
$719$	516.138	+	167.704i	0.717856	+	0.233245i	0.645093	−	0.764104i	$-0.276818\pi$
$719$	516.138	+	167.704i	0.717856	+	0.233245i	0.0727625	+	0.997349i	$0.476818\pi$
$720$	241.028	−	171.357i	0.334761	−	0.237995i
$721$	−169.639	−	522.096i	−0.235283	−	0.724128i
$722$	1046.69	+	533.315i	1.44971	+	0.738664i
$723$	108.974	+	688.037i	0.150725	+	0.951642i
$724$		−	513.444i		−	0.709177i
$725$	220.877	+	317.551i	0.304658	+	0.438001i
$726$	−149.943			−0.206533
$727$	196.791	−	31.1686i	0.270689	−	0.0428730i	−0.0196142	−	0.999808i	$-0.506244\pi$
$727$	196.791	−	31.1686i	0.270689	−	0.0428730i	0.290303	+	0.956935i	$0.406244\pi$
$728$	362.366	−	711.183i	0.497755	−	0.976899i
$729$	25.6785	−	8.34346i	0.0352243	−	0.0114451i
$730$	1176.96	+	395.850i	1.61227	+	0.542260i
$731$	−11.2493	+	34.6219i	−0.0153890	+	0.0473623i
$732$	−115.244	+	115.244i	−0.157437	+	0.157437i
$733$	−1173.65	+	598.003i	−1.60115	+	0.815829i	−0.601296	+	0.799026i	$0.705349\pi$
$733$	−1173.65	+	598.003i	−1.60115	+	0.815829i	−0.999859	+	0.0168026i	$0.994651\pi$
$734$	−555.929	−	765.170i	−0.757396	−	1.04247i
$735$	−611.024	+	303.455i	−0.831326	+	0.412864i
$736$	−533.783	−	387.816i	−0.725249	−	0.526924i
$737$	−112.765	+	711.971i	−0.153006	+	0.966040i
$738$	−164.551	−	26.0623i	−0.222968	−	0.0353147i
$739$	799.064	−	1099.82i	1.08128	−	1.48825i	0.223169	−	0.974780i	$-0.428360\pi$
$739$	799.064	−	1099.82i	1.08128	−	1.48825i	0.858108	−	0.513470i	$-0.171640\pi$
$740$	−230.543	−	120.471i	−0.311544	−	0.162798i
$741$	−756.086	+	549.328i	−1.02036	+	0.741334i
$742$	−57.9464	−	113.726i	−0.0780949	−	0.153270i
$743$	27.5132	+	27.5132i	0.0370299	+	0.0370299i	0.725379	−	0.688349i	$-0.241664\pi$
$743$	27.5132	+	27.5132i	0.0370299	+	0.0370299i	−0.688349	+	0.725379i	$0.741664\pi$
$744$	292.321	+	94.9808i	0.392904	+	0.127662i
$745$	−347.013	−	257.615i	−0.465789	−	0.345792i
$746$	−59.4814	−	183.065i	−0.0797338	−	0.245396i
$747$	−9.41790	−	4.79866i	−0.0126076	−	0.00642391i
$748$	−38.0960	−	240.529i	−0.0509305	−	0.321563i
$749$		−	957.340i		−	1.27816i
$750$	−338.942	+	437.460i	−0.451923	+	0.583279i
$751$	−622.402			−0.828764			−0.414382	−	0.910103i	$-0.636002\pi$
$751$	−622.402			−0.828764			−0.414382	+	0.910103i	$0.636002\pi$
$752$	−944.494	+	149.593i	−1.25598	+	0.198927i
$753$	−271.302	+	532.460i	−0.360295	+	0.707118i
$754$	−708.481	+	230.200i	−0.939630	+	0.305304i
$755$	−213.867	+	288.083i	−0.283268	+	0.381567i
$756$	45.9825	−	141.520i	0.0608235	−	0.187195i
$757$	371.664	−	371.664i	0.490970	−	0.490970i	−0.417642	−	0.908612i	$-0.637143\pi$
$757$	371.664	−	371.664i	0.490970	−	0.490970i	0.908612	+	0.417642i	$0.137143\pi$
$758$	−1349.74	+	687.724i	−1.78065	+	0.907288i
$759$	177.127	+	243.794i	0.233369	+	0.321205i
$760$	248.669	−	475.873i	0.327196	−	0.626149i
$761$	162.466	+	118.038i	0.213490	+	0.155110i	0.689391	−	0.724389i	$-0.257878\pi$
$761$	162.466	+	118.038i	0.213490	+	0.155110i	−0.475901	+	0.879499i	$0.657878\pi$
$762$	−57.6991	+	364.298i	−0.0757206	+	0.478081i
$763$	695.268	+	110.120i	0.911229	+	0.144324i
$764$	131.908	−	181.555i	0.172654	−	0.237638i
$765$	68.7090	+	138.349i	0.0898156	+	0.180849i
$766$	1186.13	−	861.776i	1.54848	−	1.12503i
$767$	350.933	+	688.745i	0.457540	+	0.897973i
$768$	−407.214	−	407.214i	−0.530227	−	0.530227i
$769$	−894.545	−	290.655i	−1.16326	−	0.377965i	−0.337135	−	0.941456i	$-0.609458\pi$
$769$	−894.545	−	290.655i	−1.16326	−	0.377965i	−0.826122	+	0.563491i	$0.809458\pi$
$770$	−429.884	+	1278.15i	−0.558291	+	1.65994i
$771$	−165.414	−	509.091i	−0.214544	−	0.660300i
$772$	24.4803	+	12.4733i	0.0317102	+	0.0161572i
$773$	−67.8200	−	428.199i	−0.0877361	−	0.553944i	−0.991926	−	0.126814i	$-0.959525\pi$
$773$	−67.8200	−	428.199i	−0.0877361	−	0.553944i	0.904190	−	0.427130i	$-0.140475\pi$
$774$			27.1067i			0.0350216i
$775$	−1183.20	−	24.3494i	−1.52671	−	0.0314186i
$776$	14.5780			0.0187860
$777$	397.110	−	62.8960i	0.511081	−	0.0809472i
$778$	−87.3161	+	171.367i	−0.112231	+	0.220267i
$779$	−591.913	+	192.324i	−0.759837	+	0.246886i
$780$	−239.456	−	336.816i	−0.306994	−	0.431815i
$781$	252.431	−	776.904i	0.323216	−	0.994755i
$782$	346.920	−	346.920i	0.443632	−	0.443632i
$783$	71.6350	−	36.4998i	0.0914878	−	0.0466154i
$784$	912.905	+	1256.51i	1.16442	+	1.60269i
$785$	47.3466	+	320.223i	0.0603141	+	0.407928i
$786$	694.615	+	504.668i	0.883735	+	0.642071i
$787$	43.5934	−	275.238i	0.0553919	−	0.349731i	−0.944390	−	0.328829i	$-0.893346\pi$
$787$	43.5934	−	275.238i	0.0553919	−	0.349731i	0.999782	−	0.0209021i	$-0.00665384\pi$
$788$	675.710	+	107.022i	0.857500	+	0.135815i
$789$	−147.599	+	203.153i	−0.187071	+	0.257481i
$790$	−4.56750	+	27.0349i	−0.00578164	+	0.0342214i
$791$	−1338.51	+	972.482i	−1.69217	+	1.22943i
$792$	47.6583	+	93.5348i	0.0601747	+	0.118099i
$793$	−494.705	−	494.705i	−0.623839	−	0.623839i
$794$	978.907	+	318.066i	1.23288	+	0.400587i
$795$	38.2553	+	0.393592i	0.0481199	+	0.000495085i
$796$	16.9163	+	52.0631i	0.0212516	+	0.0654058i
$797$	1030.21	+	524.916i	1.29260	+	0.658615i	0.958814	−	0.284033i	$-0.0916726\pi$
$797$	1030.21	+	524.916i	1.29260	+	0.658615i	0.333789	+	0.942648i	$0.391673\pi$
$798$	−224.260	−	1415.92i	−0.281027	−	1.77434i
$799$		−	499.493i		−	0.625147i
$800$	780.083	+	417.908i	0.975103	+	0.522385i
$801$	240.334			0.300043
$802$	1032.82	−	163.582i	1.28780	−	0.203968i
$803$	−411.744	+	808.093i	−0.512757	+	1.00634i
$804$	322.273	−	104.713i	0.400838	−	0.130240i
$805$	−1005.19	+	315.209i	−1.24868	+	0.391565i
$806$	704.290	−	2167.58i	0.873808	−	2.68931i
$807$	225.568	−	225.568i	0.279514	−	0.279514i
$808$	−392.711	+	200.096i	−0.486028	+	0.247644i
$809$	667.318	+	918.484i	0.824867	+	1.13533i	0.988857	+	0.148870i	$0.0475637\pi$
$809$	667.318	+	918.484i	0.824867	+	1.13533i	−0.163989	+	0.986462i	$0.552436\pi$
$810$	80.4920	+	82.1655i	0.0993728	+	0.101439i
$811$	−940.845	−	683.564i	−1.16010	−	0.842865i	−0.170313	−	0.985390i	$-0.554478\pi$
$811$	−940.845	−	683.564i	−1.16010	−	0.842865i	−0.989791	+	0.142525i	$0.954478\pi$
$812$	69.3144	−	437.634i	0.0853626	−	0.538958i
$813$	−612.257	−	96.9719i	−0.753083	−	0.119277i
$814$	287.991	−	396.386i	0.353797	−	0.486960i
$815$	−1082.89	+	1060.83i	−1.32870	+	1.30164i
$816$	284.501	−	206.702i	0.348653	−	0.253311i
$817$	45.9723	+	90.2256i	0.0562696	+	0.110435i
$818$	128.921	+	128.921i	0.157605	+	0.157605i
$819$	607.497	+	197.388i	0.741755	+	0.241011i
$820$	−82.3468	−	262.600i	−0.100423	−	0.320244i
$821$	113.047	+	347.923i	0.137694	+	0.423780i	0.995999	−	0.0893601i	$-0.0284822\pi$
$821$	113.047	+	347.923i	0.137694	+	0.423780i	−0.858305	+	0.513140i	$0.828482\pi$
$822$	−389.217	−	198.316i	−0.473500	−	0.241260i
$823$	47.8046	+	301.827i	0.0580858	+	0.366740i	0.999560	+	0.0296549i	$0.00944084\pi$
$823$	47.8046	+	301.827i	0.0580858	+	0.366740i	−0.941474	+	0.337085i	$0.890559\pi$
$824$		−	182.054i		−	0.220940i
$825$	−279.866	−	291.627i	−0.339232	−	0.353487i
$826$	−1185.72			−1.43550
$827$	−810.682	+	128.399i	−0.980268	+	0.155259i	−0.625948	−	0.779865i	$-0.715288\pi$
$827$	−810.682	+	128.399i	−0.980268	+	0.155259i	−0.354320	+	0.935124i	$0.615288\pi$
$828$	64.3114	−	126.218i	0.0776708	−	0.152438i
$829$	1334.02	−	433.448i	1.60919	−	0.522857i	0.639831	−	0.768516i	$-0.279004\pi$
$829$	1334.02	−	433.448i	1.60919	−	0.522857i	0.969356	+	0.245659i	$0.0790045\pi$
$830$	0.463258	−	45.0265i	0.000558143	−	0.0542488i
$831$	70.9844	−	218.468i	0.0854205	−	0.262897i
$832$	−154.760	+	154.760i	−0.186009	+	0.186009i
$833$	−722.833	+	368.302i	−0.867746	+	0.442139i
$834$	−101.208	−	139.301i	−0.121352	−	0.167027i
$835$	560.339	+	94.6684i	0.671065	+	0.113375i
$836$	−548.037	−	398.172i	−0.655547	−	0.476282i
$837$	−38.4790	+	242.947i	−0.0459725	+	0.290259i
$838$	619.334	+	98.0928i	0.739062	+	0.117056i
$839$	−261.207	+	359.520i	−0.311331	+	0.428510i	−0.935796	−	0.352543i	$-0.885317\pi$
$839$	−261.207	+	359.520i	−0.311331	+	0.428510i	0.624465	+	0.781053i	$0.285317\pi$
$840$	−363.032	+	53.6760i	−0.432181	+	0.0639000i
$841$	−486.704	+	353.611i	−0.578721	+	0.420465i
$842$	−637.586	−	1251.33i	−0.757228	−	1.48614i
$843$	110.295	+	110.295i	0.130836	+	0.130836i
$844$	608.221	+	197.623i	0.720641	+	0.234150i
$845$	757.145	−	538.285i	0.896030	−	0.637023i
$846$	−114.933	−	353.727i	−0.135855	−	0.418117i
$847$	341.118	+	173.808i	0.402736	+	0.205204i
$848$	−13.6246	−	86.0224i	−0.0160668	−	0.101442i
$849$		−	381.174i		−	0.448968i
$850$	−397.671	+	524.312i	−0.467848	+	0.616838i
$851$	382.755			0.449771
$852$	−379.277	+	60.0716i	−0.445161	+	0.0705065i
$853$	68.7406	−	134.911i	0.0805869	−	0.158161i	−0.847197	−	0.531279i	$-0.821712\pi$
$853$	68.7406	−	134.911i	0.0805869	−	0.158161i	0.927784	+	0.373119i	$0.121712\pi$
$854$	1020.64	−	331.626i	1.19513	−	0.388321i
$855$	407.270	+	136.978i	0.476340	+	0.160209i
$856$	98.1083	−	301.946i	0.114612	−	0.352741i
$857$	541.915	−	541.915i	0.632340	−	0.632340i	−0.316314	−	0.948654i	$-0.602445\pi$
$857$	541.915	−	541.915i	0.632340	−	0.632340i	0.948654	+	0.316314i	$0.102445\pi$
$858$	693.567	−	353.390i	0.808354	−	0.411877i
$859$	−363.808	−	500.738i	−0.423525	−	0.582932i	0.542927	−	0.839780i	$-0.317316\pi$
$859$	−363.808	−	500.738i	−0.423525	−	0.582932i	−0.966452	+	0.256848i	$0.917316\pi$
$860$	−40.1040	+	19.9170i	−0.0466326	+	0.0231593i
$861$	344.139	+	250.032i	0.399697	+	0.290397i
$862$	−88.8818	+	561.178i	−0.103111	+	0.651018i
$863$	−13.9183	−	2.20445i	−0.0161279	−	0.00255440i	0.148365	−	0.988933i	$-0.452599\pi$
$863$	−13.9183	−	2.20445i	−0.0161279	−	0.00255440i	−0.164493	+	0.986378i	$0.552599\pi$
$864$	108.116	−	148.809i	0.125134	−	0.172233i
$865$	802.736	+	419.472i	0.928018	+	0.484939i
$866$	911.252	−	662.063i	1.05225	−	0.764507i
$867$	−143.859	−	282.339i	−0.165927	−	0.325651i
$868$	958.568	+	958.568i	1.10434	+	1.10434i
$869$	−19.0454	−	6.18822i	−0.0219164	−	0.00712109i
$870$	275.004	+	204.157i	0.316096	+	0.234664i
$871$	449.498	+	1383.41i	0.516071	+	1.58830i
$872$	208.003	+	105.983i	0.238536	+	0.121540i
$873$	1.82502	+	11.5227i	0.00209051	+	0.0131990i
$874$		−	1364.74i		−	1.56149i
$875$	1278.17	−	602.323i	1.46077	−	0.688369i
$876$	426.340			0.486689
$877$	1228.75	−	194.614i	1.40108	−	0.221909i	0.590263	−	0.807211i	$-0.299024\pi$
$877$	1228.75	−	194.614i	1.40108	−	0.221909i	0.810816	+	0.585302i	$0.199024\pi$
$878$	564.427	−	1107.75i	0.642855	−	1.26167i
$879$	−150.954	+	49.0478i	−0.171733	+	0.0557995i
$880$	−548.489	+	738.824i	−0.623283	+	0.839573i
$881$	−248.533	+	764.907i	−0.282104	+	0.868226i	0.705148	+	0.709060i	$0.250880\pi$
$881$	−248.533	+	764.907i	−0.282104	+	0.868226i	−0.987252	+	0.159166i	$0.949120\pi$
$882$	−427.145	+	427.145i	−0.484291	+	0.484291i
$883$	611.272	−	311.459i	0.692268	−	0.352728i	−0.0721999	−	0.997390i	$-0.523002\pi$
$883$	611.272	−	311.459i	0.692268	−	0.352728i	0.764468	+	0.644662i	$0.223002\pi$
$884$	−288.848	−	397.565i	−0.326751	−	0.449734i
$885$	164.598	−	314.987i	0.185986	−	0.355918i
$886$	−1008.69	−	732.859i	−1.13848	−	0.827155i
$887$	131.944	−	833.059i	0.148753	−	0.939187i	−0.794537	−	0.607216i	$-0.792286\pi$
$887$	131.944	−	833.059i	0.148753	−	0.939187i	0.943290	−	0.331971i	$-0.107714\pi$
$888$	131.694	+	20.8584i	0.148305	+	0.0234891i
$889$	553.543	−	761.887i	0.622658	−	0.857015i
$890$	455.406	+	916.986i	0.511692	+	1.03032i
$891$	−67.9653	+	49.3797i	−0.0762799	+	0.0554206i
$892$	−424.071	−	832.286i	−0.475416	−	0.933056i
$893$	−982.469	−	982.469i	−1.10019	−	1.10019i
$894$	−363.945	−	118.253i	−0.407097	−	0.132274i
$895$	293.290	−	872.025i	0.327699	−	0.974329i
$896$	390.861	+	1202.95i	0.436229	+	1.34258i
$897$	541.813	+	276.068i	0.604028	+	0.307768i
$898$	239.657	+	1513.14i	0.266879	+	1.68501i
$899$			732.439i			0.814726i
$900$	−62.4201	+	179.459i	−0.0693557	+	0.199398i
$901$	45.4927			0.0504913
$902$	511.995	−	81.0921i	0.567622	−	0.0899025i
$903$	31.4210	−	61.6672i	0.0347963	−	0.0682915i
$904$	−521.827	+	169.552i	−0.577242	+	0.187557i
$905$	−587.168	−	825.904i	−0.648805	−	0.912601i
$906$	−98.1711	+	302.140i	−0.108357	+	0.333488i
$907$	−533.459	+	533.459i	−0.588158	+	0.588158i	−0.937132	−	0.348975i	$-0.886530\pi$
$907$	−533.459	+	533.459i	−0.588158	+	0.588158i	0.348975	+	0.937132i	$0.386530\pi$
$908$	881.142	−	448.964i	0.970420	−	0.494454i
$909$	−207.323	−	285.356i	−0.228079	−	0.313923i
$910$	398.012	+	2691.91i	0.437376	+	2.95814i
$911$	805.086	+	584.929i	0.883739	+	0.642074i	0.934238	−	0.356650i	$-0.116081\pi$
$911$	805.086	+	584.929i	0.883739	+	0.642074i	−0.0504991	+	0.998724i	$0.516081\pi$
$912$	153.025	−	966.163i	0.167791	−	1.05939i
$913$	32.4832	+	5.14484i	0.0355786	+	0.00563509i
$914$	−607.891	+	836.690i	−0.665089	+	0.915416i
$915$	−53.5851	+	317.168i	−0.0585629	+	0.346632i
$916$	−359.312	+	261.055i	−0.392262	+	0.284995i
$917$	−995.245	−	1953.28i	−1.08533	−	2.13007i
$918$	96.7150	+	96.7150i	0.105354	+	0.105354i
$919$	67.0182	+	21.7755i	0.0729251	+	0.0236948i	0.345252	−	0.938510i	$-0.387793\pi$
$919$	67.0182	+	21.7755i	0.0729251	+	0.0236948i	−0.272327	+	0.962205i	$0.587793\pi$
$920$	−349.340	−	3.59421i	−0.379717	−	0.00390675i
$921$	−44.9946	−	138.479i	−0.0488541	−	0.150358i
$922$	−967.801	−	493.119i	−1.04968	−	0.534836i
$923$	−257.867	−	1628.11i	−0.279380	−	1.76393i
$924$			462.995i			0.501077i
$925$	−508.610	+	69.8613i	−0.549849	+	0.0755258i
$926$	−869.681			−0.939180
$927$	143.899	−	22.7914i	0.155231	−	0.0245862i
$928$	248.656	−	488.015i	0.267948	−	0.525878i
$929$	1015.25	−	329.875i	1.09284	−	0.355086i	0.293498	−	0.955960i	$-0.405181\pi$
$929$	1015.25	−	329.875i	1.09284	−	0.355086i	0.799344	+	0.600874i	$0.205181\pi$
$930$	−999.866	+	313.541i	−1.07512	+	0.337141i
$931$	−697.339	+	2146.19i	−0.749022	+	2.30525i
$932$	−549.258	+	549.258i	−0.589332	+	0.589332i
$933$	728.147	−	371.009i	0.780436	−	0.397652i
$934$	−995.944	−	1370.80i	−1.06632	−	1.46767i
$935$	−336.346	−	343.338i	−0.359728	−	0.367207i
$936$	171.377	+	124.513i	0.183095	+	0.133026i
$937$	−273.749	+	1728.38i	−0.292155	+	1.84459i	0.207330	+	0.978271i	$0.433523\pi$
$937$	−273.749	+	1728.38i	−0.292155	+	1.84459i	−0.499485	+	0.866323i	$0.666477\pi$
$938$	−2203.79	−	349.046i	−2.34946	−	0.372118i
$939$	−332.045	+	457.020i	−0.353615	+	0.486709i
$940$	438.886	−	429.947i	0.466900	−	0.457390i
$941$	852.137	−	619.114i	0.905566	−	0.657932i	−0.0343239	−	0.999411i	$-0.510928\pi$
$941$	852.137	−	619.114i	0.905566	−	0.657932i	0.939889	+	0.341479i	$0.110928\pi$
$942$	130.123	+	255.382i	0.138135	+	0.271106i
$943$	286.347	+	286.347i	0.303655	+	0.303655i
$944$	−769.487	−	250.021i	−0.815134	−	0.264853i
$945$	−87.8746	−	280.228i	−0.0929890	−	0.296537i
$946$	−26.0631	−	80.2139i	−0.0275508	−	0.0847927i
$947$	−1525.74	−	777.405i	−1.61113	−	0.820914i	−0.999558	−	0.0297282i	$-0.990536\pi$
$947$	−1525.74	−	777.405i	−1.61113	−	0.820914i	−0.611576	−	0.791186i	$-0.709464\pi$
$948$	1.47262	+	9.29778i	0.00155340	+	0.00980778i
$949$			1830.14i			1.92849i
$950$	249.095	+	1813.48i	0.262205	+	1.90893i
$951$	−952.095			−1.00115
$952$	−431.010	+	68.2653i	−0.452742	+	0.0717072i
$953$	346.299	−	679.650i	0.363378	−	0.713169i	−0.634853	−	0.772633i	$-0.718939\pi$
$953$	346.299	−	679.650i	0.363378	−	0.713169i	0.998230	+	0.0594641i	$0.0189392\pi$
$954$	32.2167	−	10.4678i	0.0337701	−	0.0109726i
$955$	4.55670	−	442.890i	0.00477142	−	0.463759i
$956$	−32.8033	+	100.958i	−0.0343131	+	0.105605i
$957$	−176.887	+	176.887i	−0.184835	+	0.184835i
$958$	1487.17	−	757.750i	1.55237	−	0.790971i
$959$	655.580	+	902.329i	0.683608	+	0.940906i
$960$	99.2205	+	16.7631i	0.103355	+	0.0174616i
$961$	−1035.44	−	752.294i	−1.07746	−	0.782824i
$962$	154.666	−	976.525i	0.160776	−	1.01510i
$963$	250.946	+	39.7460i	0.260588	+	0.0412731i
$964$	−598.897	+	824.311i	−0.621263	+	0.855095i
$965$	53.6423	−	7.93128i	0.0555879	−	0.00821895i
$966$	−754.626	+	548.268i	−0.781186	+	0.567565i
$967$	−59.1646	−	116.117i	−0.0611837	−	0.120080i	0.858390	−	0.512998i	$-0.171465\pi$
$967$	−59.1646	−	116.117i	−0.0611837	−	0.120080i	−0.919573	+	0.392919i	$0.871465\pi$
$968$	89.7771	+	89.7771i	0.0927449	+	0.0927449i
$969$	485.945	+	157.893i	0.501491	+	0.162944i
$970$	−40.5062	+	28.7975i	−0.0417590	+	0.0296881i
$971$	−439.294	−	1352.01i	−0.452414	−	1.39239i	−0.874144	−	0.485666i	$-0.838577\pi$
$971$	−439.294	−	1352.01i	−0.452414	−	1.39239i	0.421730	−	0.906721i	$-0.361423\pi$
$972$	35.1873	+	17.9288i	0.0362010	+	0.0184453i
$973$	68.7740	+	434.222i	0.0706824	+	0.446271i
$974$			1098.03i			1.12734i
$975$	−770.356	−	267.949i	−0.790109	−	0.274820i
$976$	732.282			0.750289
$977$	933.290	−	147.819i	0.955261	−	0.151298i	0.340704	−	0.940171i	$-0.389335\pi$
$977$	933.290	−	147.819i	0.955261	−	0.151298i	0.614557	+	0.788872i	$0.289335\pi$
$978$	−609.374	+	1195.96i	−0.623081	+	1.22287i
$979$	−711.195	+	231.081i	−0.726450	+	0.236038i
$980$	−945.803	−	318.104i	−0.965105	−	0.324596i
$981$	−57.7310	+	177.678i	−0.0588492	+	0.181119i
$982$	−215.707	+	215.707i	−0.219661	+	0.219661i
$983$	−1206.61	+	614.797i	−1.22747	+	0.625429i	−0.942852	−	0.333210i	$-0.891868\pi$
$983$	−1206.61	+	614.797i	−1.22747	+	0.625429i	−0.284622	+	0.958640i	$0.591868\pi$
$984$	82.9186	+	114.128i	0.0842669	+	0.115983i
$985$	1209.31	−	600.583i	1.22772	−	0.609729i
$986$	329.494	+	239.391i	0.334172	+	0.242790i
$987$	−148.556	+	937.947i	−0.150513	+	0.950301i
$988$	−1350.13	−	213.839i	−1.36653	−	0.216437i
$989$	38.7278	−	53.3043i	0.0391586	−	0.0538972i
$990$	−317.193	−	165.750i	−0.320397	−	0.167424i
$991$	−835.755	+	607.212i	−0.843345	+	0.612726i	−0.923303	−	0.384072i	$-0.874521\pi$
$991$	−835.755	+	607.212i	−0.843345	+	0.612726i	0.0799579	+	0.996798i	$0.474521\pi$
$992$	760.756	+	1493.07i	0.766891	+	1.50511i
$993$	402.606	+	402.606i	0.405444	+	0.405444i
$994$	2404.78	+	781.361i	2.41930	+	0.786077i
$995$	86.7495	+	64.4011i	0.0871854	+	0.0647248i
$996$	−4.77746	−	14.7035i	−0.00479665	−	0.0147626i
$997$	−317.116	−	161.579i	−0.318071	−	0.162065i	0.287665	−	0.957731i	$-0.407121\pi$
$997$	−317.116	−	161.579i	−0.318071	−	0.162065i	−0.605736	+	0.795666i	$0.707121\pi$
$998$	154.200	+	973.583i	0.154509	+	0.975535i
$999$			106.705i			0.106812i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.3.k.a.13.8	✓	80
3.2	odd	2		225.3.r.b.163.3		80
5.2	odd	4		375.3.k.c.82.8		80
5.3	odd	4		375.3.k.b.82.3		80
5.4	even	2		375.3.k.a.43.3		80
25.2	odd	20	inner	75.3.k.a.52.8	yes	80
25.11	even	5		375.3.k.c.343.8		80
25.14	even	10		375.3.k.b.343.3		80
25.23	odd	20		375.3.k.a.157.3		80
75.2	even	20		225.3.r.b.127.3		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.k.a.13.8	✓	80	1.1	even	1	trivial
75.3.k.a.52.8	yes	80	25.2	odd	20	inner
225.3.r.b.127.3		80	75.2	even	20
225.3.r.b.163.3		80	3.2	odd	2
375.3.k.a.43.3		80	5.4	even	2
375.3.k.a.157.3		80	25.23	odd	20
375.3.k.b.82.3		80	5.3	odd	4
375.3.k.b.343.3		80	25.14	even	10
375.3.k.c.82.8		80	5.2	odd	4
375.3.k.c.343.8		80	25.11	even	5

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	75.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(2.52458 - 0.399854i) q^{2} +(0.786335 - 1.54327i) q^{3} +(2.40940 - 0.782861i) q^{4} +(2.98039 - 4.01464i) q^{5} +(1.36808 - 4.21053i) q^{6} +(-7.99303 + 7.99303i) q^{7} +(-3.34014 + 1.70189i) q^{8} +(-1.76336 - 2.42705i) q^{9} +O(q^{10})\)	\(q+(2.52458 - 0.399854i) q^{2} +(0.786335 - 1.54327i) q^{3} +(2.40940 - 0.782861i) q^{4} +(2.98039 - 4.01464i) q^{5} +(1.36808 - 4.21053i) q^{6} +(-7.99303 + 7.99303i) q^{7} +(-3.34014 + 1.70189i) q^{8} +(-1.76336 - 2.42705i) q^{9} +(5.91896 - 11.3270i) q^{10} +(7.55171 + 5.48664i) q^{11} +(0.686429 - 4.33394i) q^{12} +(18.6042 + 2.94661i) q^{13} +(-16.9830 + 23.3751i) q^{14} +(-3.85208 - 7.75638i) q^{15} +(-15.9502 + 11.5885i) q^{16} +(-4.67525 - 9.17568i) q^{17} +(-5.42220 - 5.42220i) q^{18} +(-27.2439 - 8.85207i) q^{19} +(4.03804 - 12.0061i) q^{20} +(6.05019 + 18.6206i) q^{21} +(21.2587 + 10.8319i) q^{22} +(2.91575 + 18.4093i) q^{23} +6.49298i q^{24} +(-7.23459 - 23.9303i) q^{25} +48.1459 q^{26} +(-5.13218 + 0.812857i) q^{27} +(-13.0010 + 25.5158i) q^{28} +(-14.7153 + 4.78129i) q^{29} +(-12.8263 - 18.0413i) q^{30} +(14.6282 - 45.0210i) q^{31} +(-25.0308 + 25.0308i) q^{32} +(14.4055 - 7.33998i) q^{33} +(-15.4720 - 21.2953i) q^{34} +(8.26678 + 55.9114i) q^{35} +(-6.14867 - 4.46727i) q^{36} +(3.21245 - 20.2826i) q^{37} +(-72.3189 - 11.4542i) q^{38} +(19.1765 - 26.3942i) q^{39} +(-3.12245 + 18.4817i) q^{40} +(17.5771 - 12.7705i) q^{41} +(22.7197 + 44.5900i) q^{42} +(-2.49961 - 2.49961i) q^{43} +(22.4903 + 7.30756i) q^{44} +(-14.9992 - 0.154320i) q^{45} +(14.7221 + 45.3099i) q^{46} +(43.2168 + 22.0201i) q^{47} +(5.34196 + 33.7278i) q^{48} -78.7770i q^{49} +(-27.8330 - 57.5213i) q^{50} -17.8369 q^{51} +(47.1317 - 7.46492i) q^{52} +(-2.00554 + 3.93609i) q^{53} +(-12.6316 + 4.10425i) q^{54} +(44.5338 - 13.9650i) q^{55} +(13.0946 - 40.3010i) q^{56} +(-35.0839 + 35.0839i) q^{57} +(-35.2381 + 17.9547i) q^{58} +(24.1216 + 33.2005i) q^{59} +(-15.3534 - 15.6726i) q^{60} +(-30.0489 - 21.8318i) q^{61} +(18.9283 - 119.508i) q^{62} +(33.4940 + 5.30493i) q^{63} +(-6.82969 + 9.40026i) q^{64} +(67.2772 - 65.9069i) q^{65} +(33.4330 - 24.2905i) q^{66} +(35.0592 + 68.8075i) q^{67} +(-18.4478 - 18.4478i) q^{68} +(30.7033 + 9.97610i) q^{69} +(43.2266 + 137.847i) q^{70} +(-27.0431 - 83.2300i) q^{71} +(10.0204 + 5.10566i) q^{72} +(15.1994 + 95.9650i) q^{73} -52.4896i q^{74} +(-42.6197 - 7.65233i) q^{75} -72.5713 q^{76} +(-104.216 + 16.5062i) q^{77} +(37.8588 - 74.3021i) q^{78} +(-2.04034 + 0.662947i) q^{79} +(-1.01417 + 98.5722i) q^{80} +(-2.78115 + 8.55951i) q^{81} +(39.2684 - 39.2684i) q^{82} +(3.13930 - 1.59955i) q^{83} +(29.1547 + 40.1279i) q^{84} +(-50.7711 - 8.57769i) q^{85} +(-7.30994 - 5.31098i) q^{86} +(-4.19233 + 26.4693i) q^{87} +(-34.5614 - 5.47398i) q^{88} +(-47.0884 + 64.8116i) q^{89} +(-37.9284 + 5.60790i) q^{90} +(-172.256 + 125.151i) q^{91} +(21.4371 + 42.0728i) q^{92} +(-57.9769 - 57.9769i) q^{93} +(117.909 + 38.3110i) q^{94} +(-116.735 + 82.9916i) q^{95} +(18.9467 + 58.3118i) q^{96} +(-3.46493 - 1.76547i) q^{97} +(-31.4993 - 198.879i) q^{98} -28.0033i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8}+O(q^{10}) \) 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8	\( 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8} - 4 q^{10} - 24 q^{12} + 32 q^{13} - 24 q^{15} + 80 q^{16} - 100 q^{17} - 48 q^{18} - 100 q^{19} - 244 q^{20} - 100 q^{22} - 96 q^{23} - 16 q^{25} - 40 q^{26} + 196 q^{28} + 200 q^{29} + 264 q^{30} + 636 q^{32} + 216 q^{33} + 100 q^{34} + 260 q^{35} - 120 q^{36} - 184 q^{37} - 564 q^{38} - 948 q^{40} + 160 q^{41} - 12 q^{42} - 472 q^{43} - 700 q^{44} - 36 q^{45} - 288 q^{47} - 48 q^{48} + 16 q^{50} + 620 q^{52} + 304 q^{53} + 604 q^{55} + 72 q^{57} + 1272 q^{58} + 800 q^{59} + 84 q^{60} - 240 q^{61} + 1212 q^{62} - 12 q^{63} + 100 q^{64} + 272 q^{65} - 80 q^{67} + 104 q^{68} - 260 q^{70} + 36 q^{72} - 116 q^{73} - 24 q^{75} - 88 q^{77} - 120 q^{78} + 200 q^{79} - 164 q^{80} + 180 q^{81} - 168 q^{82} - 1264 q^{83} - 1200 q^{84} - 212 q^{85} - 876 q^{87} - 212 q^{88} - 1500 q^{89} - 444 q^{90} - 1504 q^{92} - 648 q^{93} - 200 q^{94} - 784 q^{95} + 60 q^{96} - 260 q^{97} - 92 q^{98}+O(q^{100}) \) 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8 - 4 * q^10 - 24 * q^12 + 32 * q^13 - 24 * q^15 + 80 * q^16 - 100 * q^17 - 48 * q^18 - 100 * q^19 - 244 * q^20 - 100 * q^22 - 96 * q^23 - 16 * q^25 - 40 * q^26 + 196 * q^28 + 200 * q^29 + 264 * q^30 + 636 * q^32 + 216 * q^33 + 100 * q^34 + 260 * q^35 - 120 * q^36 - 184 * q^37 - 564 * q^38 - 948 * q^40 + 160 * q^41 - 12 * q^42 - 472 * q^43 - 700 * q^44 - 36 * q^45 - 288 * q^47 - 48 * q^48 + 16 * q^50 + 620 * q^52 + 304 * q^53 + 604 * q^55 + 72 * q^57 + 1272 * q^58 + 800 * q^59 + 84 * q^60 - 240 * q^61 + 1212 * q^62 - 12 * q^63 + 100 * q^64 + 272 * q^65 - 80 * q^67 + 104 * q^68 - 260 * q^70 + 36 * q^72 - 116 * q^73 - 24 * q^75 - 88 * q^77 - 120 * q^78 + 200 * q^79 - 164 * q^80 + 180 * q^81 - 168 * q^82 - 1264 * q^83 - 1200 * q^84 - 212 * q^85 - 876 * q^87 - 212 * q^88 - 1500 * q^89 - 444 * q^90 - 1504 * q^92 - 648 * q^93 - 200 * q^94 - 784 * q^95 + 60 * q^96 - 260 * q^97 - 92 * q^98

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