LMFDB - Embedded newform 275.2.l.d.71.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,2,Mod(31,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([4, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.l (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [100,2,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$25$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			71.7
Character	$\chi$	$=$	275.71
Dual form			275.2.l.d.31.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.49148 q^{2} +(0.0955568 + 0.294094i) q^{3} +0.224502 q^{4} +(-1.68887 + 1.46551i) q^{5} +(-0.142521 - 0.438634i) q^{6} +(2.02744 - 1.47302i) q^{7} +2.64811 q^{8} +(2.34969 - 1.70715i) q^{9} +(2.51891 - 2.18577i) q^{10} +(-2.71315 + 1.90756i) q^{11} +(0.0214527 + 0.0660247i) q^{12} +(-4.85916 + 3.53039i) q^{13} +(-3.02387 + 2.19697i) q^{14} +(-0.592380 - 0.356646i) q^{15} -4.39860 q^{16} +(2.31272 + 7.11782i) q^{17} +(-3.50451 + 2.54618i) q^{18} -3.20317 q^{19} +(-0.379156 + 0.329011i) q^{20} +(0.626940 + 0.455499i) q^{21} +(4.04661 - 2.84509i) q^{22} +(-2.19113 + 6.74361i) q^{23} +(0.253045 + 0.778793i) q^{24} +(0.704565 - 4.95011i) q^{25} +(7.24733 - 5.26549i) q^{26} +(1.47710 + 1.07318i) q^{27} +(0.455164 - 0.330696i) q^{28} -0.361668 q^{29} +(0.883521 + 0.531930i) q^{30} +(0.885177 + 0.643119i) q^{31} +1.26419 q^{32} +(-0.820262 - 0.615640i) q^{33} +(-3.44937 - 10.6161i) q^{34} +(-1.26535 + 5.45896i) q^{35} +(0.527511 - 0.383260i) q^{36} +(6.33247 + 4.60081i) q^{37} +4.77745 q^{38} +(-1.50259 - 1.09170i) q^{39} +(-4.47232 + 3.88083i) q^{40} +(0.788105 - 2.42554i) q^{41} +(-0.935067 - 0.679366i) q^{42} -6.81097 q^{43} +(-0.609110 + 0.428253i) q^{44} +(-1.46648 + 6.32665i) q^{45} +(3.26802 - 10.0579i) q^{46} +(-0.0229839 - 0.0707371i) q^{47} +(-0.420316 - 1.29360i) q^{48} +(-0.222407 + 0.684499i) q^{49} +(-1.05084 + 7.38297i) q^{50} +(-1.87231 + 1.36031i) q^{51} +(-1.09089 + 0.792581i) q^{52} +(-0.761946 + 2.34503i) q^{53} +(-2.20307 - 1.60062i) q^{54} +(1.78661 - 7.19778i) q^{55} +(5.36888 - 3.90072i) q^{56} +(-0.306085 - 0.942032i) q^{57} +0.539420 q^{58} +(2.91380 + 2.11700i) q^{59} +(-0.132991 - 0.0800680i) q^{60} +(-9.13449 - 6.63659i) q^{61} +(-1.32022 - 0.959197i) q^{62} +(2.24918 - 6.92227i) q^{63} +6.91170 q^{64} +(3.03268 - 13.0835i) q^{65} +(1.22340 + 0.918213i) q^{66} +(12.9188 - 9.38603i) q^{67} +(0.519212 + 1.59797i) q^{68} -2.19263 q^{69} +(1.88724 - 8.14191i) q^{70} +(-0.357383 + 0.259654i) q^{71} +(6.22225 - 4.52073i) q^{72} +(3.05976 + 9.41698i) q^{73} +(-9.44473 - 6.86200i) q^{74} +(1.52312 - 0.265809i) q^{75} -0.719120 q^{76} +(-2.69087 + 7.86398i) q^{77} +(2.24108 + 1.62824i) q^{78} +(0.998303 - 3.07246i) q^{79} +(7.42867 - 6.44619i) q^{80} +(2.51804 - 7.74973i) q^{81} +(-1.17544 + 3.61763i) q^{82} +(0.390798 + 1.20275i) q^{83} +(0.140750 + 0.102261i) q^{84} +(-14.3371 - 8.63176i) q^{85} +10.1584 q^{86} +(-0.0345599 - 0.106364i) q^{87} +(-7.18474 + 5.05144i) q^{88} +(-0.357172 + 1.09926i) q^{89} +(2.18722 - 9.43605i) q^{90} +(-4.65131 + 14.3153i) q^{91} +(-0.491914 + 1.51396i) q^{92} +(-0.104552 + 0.321779i) q^{93} +(0.0342799 + 0.105503i) q^{94} +(5.40974 - 4.69428i) q^{95} +(0.120802 + 0.371790i) q^{96} +(0.553288 - 1.70285i) q^{97} +(0.331715 - 1.02091i) q^{98} +(-3.11858 + 9.11395i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 2 q^{2} - 2 q^{3} + 106 q^{4} + 5 q^{5} + 5 q^{6} + 5 q^{7} - 30 q^{8} - 25 q^{9} - 22 q^{10} - 53 q^{12} - 18 q^{13} - 10 q^{14} + 16 q^{15} + 62 q^{16} + q^{17} - 21 q^{18} + 6 q^{19} + q^{20}+ \cdots - 84 q^{99}+O(q^{100}) $ 100 * q + 2 * q^2 - 2 * q^3 + 106 * q^4 + 5 * q^5 + 5 * q^6 + 5 * q^7 - 30 * q^8 - 25 * q^9 - 22 * q^10 - 53 * q^12 - 18 * q^13 - 10 * q^14 + 16 * q^15 + 62 * q^16 + q^17 - 21 * q^18 + 6 * q^19 + q^20 - 22 * q^21 + 6 * q^22 + 20 * q^23 - 18 * q^24 + q^25 - 37 * q^26 + 10 * q^27 - 64 * q^28 - 28 * q^29 + 15 * q^30 + 9 * q^31 - 98 * q^32 + 13 * q^33 - 14 * q^34 + 13 * q^35 - 30 * q^36 - 21 * q^37 + 18 * q^38 + 44 * q^39 + 9 * q^40 + 28 * q^41 + 31 * q^42 + 82 * q^43 - 4 * q^44 - 25 * q^45 - 16 * q^46 - 10 * q^47 - 72 * q^48 - 26 * q^49 - 46 * q^50 - 14 * q^51 - 23 * q^52 - 5 * q^53 - 22 * q^54 + 32 * q^55 + q^56 - 85 * q^57 + 80 * q^58 - 3 * q^59 + 61 * q^60 + 35 * q^61 + 43 * q^62 - 47 * q^63 - 54 * q^64 - 64 * q^65 - 13 * q^66 - 20 * q^67 + 5 * q^68 + 76 * q^69 - 23 * q^70 + 28 * q^71 - 53 * q^72 + 33 * q^73 - 3 * q^74 - 34 * q^75 - 156 * q^76 + 45 * q^77 + 30 * q^78 + 4 * q^79 - 144 * q^80 - 27 * q^81 - 59 * q^82 - 92 * q^83 + 9 * q^84 - 26 * q^85 - 56 * q^86 + 38 * q^87 + 18 * q^88 + 39 * q^89 + 114 * q^90 - 11 * q^91 - 60 * q^92 - 19 * q^93 + 46 * q^94 - 46 * q^95 + 9 * q^96 + 20 * q^97 + 122 * q^98 - 84 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−1.49148			−1.05463			−0.527317	−	0.849669i	$-0.676802\pi$
$2$	−1.49148			−1.05463			−0.527317	+	0.849669i	$0.676802\pi$
$3$	0.0955568	+	0.294094i	0.0551697	+	0.169795i	0.974845	−	0.222886i	$-0.0715477\pi$
$3$	0.0955568	+	0.294094i	0.0551697	+	0.169795i	−0.919675	+	0.392681i	$0.871548\pi$
$4$	0.224502			0.112251
$5$	−1.68887	+	1.46551i	−0.755286	+	0.655396i
$5$	−1.68887	+	1.46551i	−0.755286	+	0.655396i
$6$	−0.142521	−	0.438634i	−0.0581838	−	0.179071i
$7$	2.02744	−	1.47302i	0.766298	−	0.556748i	−0.134537	−	0.990909i	$-0.542955\pi$
$7$	2.02744	−	1.47302i	0.766298	−	0.556748i	0.900836	+	0.434160i	$0.142955\pi$
$8$	2.64811			0.936249
$9$	2.34969	−	1.70715i	0.783230	−	0.569050i
$10$	2.51891	−	2.18577i	0.796549	−	0.691202i
$11$	−2.71315	+	1.90756i	−0.818047	+	0.575152i
$11$	−2.71315	+	1.90756i	−0.818047	+	0.575152i
$12$	0.0214527	+	0.0660247i	0.00619287	+	0.0190597i
$13$	−4.85916	+	3.53039i	−1.34769	+	0.979154i	−0.348567	+	0.937284i	$0.613331\pi$
$13$	−4.85916	+	3.53039i	−1.34769	+	0.979154i	−0.999123	+	0.0418699i	$0.986669\pi$
$14$	−3.02387	+	2.19697i	−0.808164	+	0.587165i
$15$	−0.592380	−	0.356646i	−0.152952	−	0.0920857i
$16$	−4.39860			−1.09965
$17$	2.31272	+	7.11782i	0.560917	+	1.72633i	0.679781	+	0.733415i	$0.262075\pi$
$17$	2.31272	+	7.11782i	0.560917	+	1.72633i	−0.118864	+	0.992911i	$0.537925\pi$
$18$	−3.50451	+	2.54618i	−0.826021	+	0.600139i
$19$	−3.20317			−0.734858			−0.367429	−	0.930052i	$-0.619762\pi$
$19$	−3.20317			−0.734858			−0.367429	+	0.930052i	$0.619762\pi$
$20$	−0.379156	+	0.329011i	−0.0847818	+	0.0735690i
$21$	0.626940	+	0.455499i	0.136810	+	0.0993980i
$22$	4.04661	−	2.84509i	0.862739	−	0.606574i
$23$	−2.19113	+	6.74361i	−0.456882	+	1.40614i	0.412029	+	0.911171i	$0.364820\pi$
$23$	−2.19113	+	6.74361i	−0.456882	+	1.40614i	−0.868911	+	0.494968i	$0.835180\pi$
$24$	0.253045	+	0.778793i	0.0516526	+	0.158970i
$25$	0.704565	−	4.95011i	0.140913	−	0.990022i
$26$	7.24733	−	5.26549i	1.42132	−	1.03265i
$27$	1.47710	+	1.07318i	0.284269	+	0.206533i
$28$	0.455164	−	0.330696i	0.0860180	−	0.0624957i
$29$	−0.361668			−0.0671601			−0.0335801	−	0.999436i	$-0.510691\pi$
$29$	−0.361668			−0.0671601			−0.0335801	+	0.999436i	$0.510691\pi$
$30$	0.883521	+	0.531930i	0.161308	+	0.0971167i
$31$	0.885177	+	0.643119i	0.158983	+	0.115508i	0.664432	−	0.747348i	$-0.268673\pi$
$31$	0.885177	+	0.643119i	0.158983	+	0.115508i	−0.505450	+	0.862856i	$0.668673\pi$
$32$	1.26419			0.223479
$33$	−0.820262	−	0.615640i	−0.142789	−	0.107169i
$34$	−3.44937	−	10.6161i	−0.591562	−	1.82064i
$35$	−1.26535	+	5.45896i	−0.213884	+	0.922733i
$36$	0.527511	−	0.383260i	0.0879186	−	0.0638766i
$37$	6.33247	+	4.60081i	1.04105	+	0.756368i	0.970491	−	0.241139i	$-0.0775210\pi$
$37$	6.33247	+	4.60081i	1.04105	+	0.756368i	0.0705612	+	0.997507i	$0.477521\pi$
$38$	4.77745			0.775006
$39$	−1.50259	−	1.09170i	−0.240607	−	0.174811i
$40$	−4.47232	+	3.88083i	−0.707136	+	0.613614i
$41$	0.788105	−	2.42554i	0.123081	−	0.378805i	−0.870465	−	0.492230i	$-0.836182\pi$
$41$	0.788105	−	2.42554i	0.123081	−	0.378805i	0.993547	+	0.113424i	$0.0361820\pi$
$42$	−0.935067	−	0.679366i	−0.144284	−	0.104828i
$43$	−6.81097			−1.03866			−0.519332	−	0.854573i	$-0.673819\pi$
$43$	−6.81097			−1.03866			−0.519332	+	0.854573i	$0.673819\pi$
$44$	−0.609110	+	0.428253i	−0.0918267	+	0.0645615i
$45$	−1.46648	+	6.32665i	−0.218610	+	0.943121i
$46$	3.26802	−	10.0579i	0.481843	−	1.48296i
$47$	−0.0229839	−	0.0707371i	−0.00335254	−	0.0103181i	0.949366	−	0.314171i	$-0.101727\pi$
$47$	−0.0229839	−	0.0707371i	−0.00335254	−	0.0103181i	−0.952719	+	0.303853i	$0.901727\pi$
$48$	−0.420316	−	1.29360i	−0.0606675	−	0.186715i
$49$	−0.222407	+	0.684499i	−0.0317725	+	0.0977856i
$50$	−1.05084	+	7.38297i	−0.148611	+	1.04411i
$51$	−1.87231	+	1.36031i	−0.262176	+	0.190482i
$52$	−1.09089	+	0.792581i	−0.151280	+	0.109911i
$53$	−0.761946	+	2.34503i	−0.104661	+	0.322114i	−0.989651	−	0.143497i	$-0.954165\pi$
$53$	−0.761946	+	2.34503i	−0.104661	+	0.322114i	0.884990	+	0.465611i	$0.154165\pi$
$54$	−2.20307	−	1.60062i	−0.299799	−	0.217817i
$55$	1.78661	−	7.19778i	0.240907	−	0.970548i
$56$	5.36888	−	3.90072i	0.717446	−	0.521255i
$57$	−0.306085	−	0.942032i	−0.0405419	−	0.124775i
$58$	0.539420			0.0708293
$59$	2.91380	+	2.11700i	0.379344	+	0.275610i	0.761075	−	0.648664i	$-0.224672\pi$
$59$	2.91380	+	2.11700i	0.379344	+	0.275610i	−0.381731	+	0.924274i	$0.624672\pi$
$60$	−0.132991	−	0.0800680i	−0.0171690	−	0.0103367i
$61$	−9.13449	−	6.63659i	−1.16955	−	0.849729i	−0.178596	−	0.983922i	$-0.557156\pi$
$61$	−9.13449	−	6.63659i	−1.16955	−	0.849729i	−0.990955	+	0.134194i	$0.957156\pi$
$62$	−1.32022	−	0.959197i	−0.167668	−	0.121818i
$63$	2.24918	−	6.92227i	0.283370	−	0.872125i
$64$	6.91170			0.863962
$65$	3.03268	−	13.0835i	0.376157	−	1.62281i
$66$	1.22340	+	0.918213i	0.150590	+	0.113024i
$67$	12.9188	−	9.38603i	1.57828	−	1.14669i	0.659644	−	0.751578i	$-0.270707\pi$
$67$	12.9188	−	9.38603i	1.57828	−	1.14669i	0.918635	−	0.395108i	$-0.129293\pi$
$68$	0.519212	+	1.59797i	0.0629636	+	0.193782i
$69$	−2.19263			−0.263961
$70$	1.88724	−	8.14191i	0.225569	−	0.973145i
$71$	−0.357383	+	0.259654i	−0.0424136	+	0.0308153i	−0.608790	−	0.793331i	$-0.708345\pi$
$71$	−0.357383	+	0.259654i	−0.0424136	+	0.0308153i	0.566376	+	0.824147i	$0.308345\pi$
$72$	6.22225	−	4.52073i	0.733299	−	0.532773i
$73$	3.05976	+	9.41698i	0.358118	+	1.10217i	0.954179	+	0.299235i	$0.0967316\pi$
$73$	3.05976	+	9.41698i	0.358118	+	1.10217i	−0.596061	+	0.802939i	$0.703268\pi$
$74$	−9.44473	−	6.86200i	−1.09793	−	0.797691i
$75$	1.52312	−	0.265809i	0.175875	−	0.0306930i
$76$	−0.719120			−0.0824887
$77$	−2.69087	+	7.86398i	−0.306653	+	0.896184i
$78$	2.24108	+	1.62824i	0.253752	+	0.184362i
$79$	0.998303	−	3.07246i	0.112318	−	0.345679i	−0.879060	−	0.476711i	$-0.841829\pi$
$79$	0.998303	−	3.07246i	0.112318	−	0.345679i	0.991378	+	0.131032i	$0.0418290\pi$
$80$	7.42867	−	6.44619i	0.830551	−	0.720706i
$81$	2.51804	−	7.74973i	0.279782	−	0.861081i
$82$	−1.17544	+	3.61763i	−0.129806	+	0.399501i
$83$	0.390798	+	1.20275i	0.0428956	+	0.132019i	0.970211	−	0.242262i	$-0.0778894\pi$
$83$	0.390798	+	1.20275i	0.0428956	+	0.132019i	−0.927315	+	0.374281i	$0.877889\pi$
$84$	0.140750	+	0.102261i	0.0153570	+	0.0111575i
$85$	−14.3371	−	8.63176i	−1.55508	−	0.936246i
$86$	10.1584			1.09541
$87$	−0.0345599	−	0.106364i	−0.00370521	−	0.0114035i
$88$	−7.18474	+	5.05144i	−0.765896	+	0.538486i
$89$	−0.357172	+	1.09926i	−0.0378601	+	0.116521i	−0.968200	−	0.250176i	$-0.919512\pi$
$89$	−0.357172	+	1.09926i	−0.0378601	+	0.116521i	0.930340	+	0.366697i	$0.119512\pi$
$90$	2.18722	−	9.43605i	0.230553	−	0.994647i
$91$	−4.65131	+	14.3153i	−0.487590	+	1.50065i
$92$	−0.491914	+	1.51396i	−0.0512856	+	0.157841i
$93$	−0.104552	+	0.321779i	−0.0108416	+	0.0333670i
$94$	0.0342799	+	0.105503i	0.00353570	+	0.0108818i
$95$	5.40974	−	4.69428i	0.555028	−	0.481623i
$96$	0.120802	+	0.371790i	0.0123293	+	0.0379456i
$97$	0.553288	−	1.70285i	0.0561779	−	0.172898i	−0.919030	−	0.394187i	$-0.871026\pi$
$97$	0.553288	−	1.70285i	0.0561779	−	0.172898i	0.975208	+	0.221289i	$0.0710263\pi$
$98$	0.331715	−	1.02091i	0.0335083	−	0.103128i
$99$	−3.11858	+	9.11395i	−0.313429	+	0.915986i
$100$	0.158176	−	1.11131i	0.0158176	−	0.111131i
$101$	4.15124	+	12.7762i	0.413063	+	1.27128i	0.913972	+	0.405778i	$0.132999\pi$
$101$	4.15124	+	12.7762i	0.413063	+	1.27128i	−0.500908	+	0.865500i	$0.667001\pi$
$102$	2.79251	−	2.02887i	0.276499	−	0.200889i
$103$	7.20892			0.710316			0.355158	−	0.934806i	$-0.384427\pi$
$103$	7.20892			0.710316			0.355158	+	0.934806i	$0.384427\pi$
$104$	−12.8676	+	9.34887i	−1.26177	+	0.916732i
$105$	−1.72636	+	0.149509i	−0.168475	+	0.0145905i
$106$	1.13642	−	3.49755i	0.110379	−	0.339712i
$107$	−10.9968	−	7.98966i	−1.06310	−	0.772390i	−0.0884436	−	0.996081i	$-0.528189\pi$
$107$	−10.9968	−	7.98966i	−1.06310	−	0.772390i	−0.974660	+	0.223691i	$0.928189\pi$
$108$	0.331613	+	0.240931i	0.0319095	+	0.0231836i
$109$	3.02626	+	9.31386i	0.289863	+	0.892106i	0.984899	+	0.173131i	$0.0553885\pi$
$109$	3.02626	+	9.31386i	0.289863	+	0.892106i	−0.695036	+	0.718975i	$0.744611\pi$
$110$	−2.66469	+	10.7353i	−0.254068	+	1.02357i
$111$	−0.747958	+	2.30198i	−0.0709930	+	0.218494i
$112$	−8.91788	+	6.47922i	−0.842661	+	0.612229i
$113$	2.09877	−	6.45936i	0.197436	−	0.607645i	−0.802504	−	0.596647i	$-0.796499\pi$
$113$	2.09877	−	6.45936i	0.197436	−	0.607645i	0.999940	−	0.0109980i	$-0.00350083\pi$
$114$	0.456518	+	1.40502i	0.0427569	+	0.131592i
$115$	−6.18228	−	14.6002i	−0.576501	−	1.36148i
$116$	−0.0811954			−0.00753881
$117$	−5.39063	+	16.5906i	−0.498364	+	1.53381i
$118$	−4.34586	−	3.15746i	−0.400069	−	0.290667i
$119$	15.1736	+	11.0242i	1.39096	+	1.01059i
$120$	−1.56869	−	0.944440i	−0.143201	−	0.0862152i
$121$	3.72241	−	10.3510i	0.338401	−	0.941002i
$122$	13.6239	+	9.89832i	1.23345	+	0.896152i
$123$	0.788644			0.0711096
$124$	0.198725	+	0.144382i	0.0178460	+	0.0129659i
$125$	6.06451	+	9.39264i	0.542427	+	0.840103i
$126$	−3.35460	+	10.3244i	−0.298852	+	0.919771i
$127$	−8.33487	−	6.05563i	−0.739600	−	0.537351i	0.152986	−	0.988228i	$-0.451111\pi$
$127$	−8.33487	−	6.05563i	−0.739600	−	0.537351i	−0.892586	+	0.450878i	$0.851111\pi$
$128$	−12.8370			−1.13464
$129$	−0.650835	−	2.00306i	−0.0573028	−	0.176360i
$130$	−4.52317	+	19.5138i	−0.396708	+	1.71147i
$131$	7.18936	−	5.22337i	0.628137	−	0.456368i	−0.227617	−	0.973751i	$-0.573094\pi$
$131$	7.18936	−	5.22337i	0.628137	−	0.456368i	0.855754	+	0.517382i	$0.173094\pi$
$132$	−0.184151	−	0.138213i	−0.0160283	−	0.0120299i
$133$	−6.49422	+	4.71833i	−0.563120	+	0.409131i
$134$	−19.2680	+	13.9990i	−1.66450	+	1.20933i
$135$	−4.06739	+	0.352250i	−0.350065	+	0.0303169i
$136$	6.12435	+	18.8488i	0.525158	+	1.61627i
$137$	−6.55083			−0.559675			−0.279837	−	0.960047i	$-0.590281\pi$
$137$	−6.55083			−0.559675			−0.279837	+	0.960047i	$0.590281\pi$
$138$	3.27025			0.278383
$139$	−4.91034	−	15.1125i	−0.416490	−	1.28182i	−0.910912	−	0.412601i	$-0.864620\pi$
$139$	−4.91034	−	15.1125i	−0.416490	−	1.28182i	0.494422	−	0.869222i	$-0.335380\pi$
$140$	−0.284075	+	1.22555i	−0.0240087	+	0.103578i
$141$	0.0186071	−	0.0135188i	0.00156700	−	0.00113849i
$142$	0.533029	−	0.387268i	0.0447308	−	0.0324988i
$143$	6.44922	−	18.8477i	0.539311	−	1.57612i
$144$	−10.3354	+	7.50908i	−0.861280	+	0.625757i
$145$	0.610811	−	0.530028i	0.0507251	−	0.0440165i
$146$	−4.56357	−	14.0452i	−0.377683	−	1.16239i
$147$	−0.222559			−0.0183564
$148$	1.42166	+	1.03289i	0.116859	+	0.0849033i
$149$	−0.434883	+	1.33843i	−0.0356270	+	0.109649i	−0.967289	−	0.253679i	$-0.918359\pi$
$149$	−0.434883	+	1.33843i	−0.0356270	+	0.109649i	0.931661	+	0.363328i	$0.118359\pi$
$150$	−2.27170	+	0.396448i	−0.185484	+	0.0323698i
$151$	7.58986	+	5.51435i	0.617654	+	0.448752i	0.852101	−	0.523377i	$-0.175328\pi$
$151$	7.58986	+	5.51435i	0.617654	+	0.448752i	−0.234447	+	0.972129i	$0.575328\pi$
$152$	−8.48236			−0.688010
$153$	17.5854	+	12.7765i	1.42169	+	1.03292i
$154$	4.01337	−	11.7289i	0.323406	−	0.945146i
$155$	−2.43745	+	0.211091i	−0.195780	+	0.0169553i
$156$	−0.337335	−	0.245089i	−0.0270085	−	0.0196228i
$157$	4.69905	+	3.41406i	0.375025	+	0.272472i	0.759292	−	0.650750i	$-0.225546\pi$
$157$	4.69905	+	3.41406i	0.375025	+	0.272472i	−0.384266	+	0.923222i	$0.625546\pi$
$158$	−1.48895	+	4.58250i	−0.118454	+	0.364564i
$159$	−0.762467			−0.0604675
$160$	−2.13505	+	1.85268i	−0.168791	+	0.146467i
$161$	5.49108	+	16.8998i	0.432758	+	1.33189i
$162$	−3.75560	+	11.5585i	−0.295067	+	0.908124i
$163$	17.6254	−	12.8056i	1.38053	−	1.00301i	0.383697	−	0.923459i	$-0.374651\pi$
$163$	17.6254	−	12.8056i	1.38053	−	1.00301i	0.996831	−	0.0795525i	$-0.0253491\pi$
$164$	0.176932	−	0.544539i	0.0138160	−	0.0425214i
$165$	2.28754	−	0.162365i	0.178085	−	0.0126401i
$166$	−0.582866	−	1.79388i	−0.0452392	−	0.139232i
$167$	7.57079	+	5.50050i	0.585846	+	0.425642i	0.840827	−	0.541304i	$-0.182069\pi$
$167$	7.57079	+	5.50050i	0.585846	+	0.425642i	−0.254981	+	0.966946i	$0.582069\pi$
$168$	1.66021	+	1.20621i	0.128088	+	0.0930613i
$169$	7.13061	−	21.9458i	0.548508	−	1.68813i
$170$	21.3835	+	12.8741i	1.64004	+	0.987396i
$171$	−7.52646	+	5.46830i	−0.575563	+	0.418171i
$172$	−1.52908			−0.116591
$173$	−10.4290	+	7.57712i	−0.792903	+	0.576078i	−0.908824	−	0.417181i	$-0.863018\pi$
$173$	−10.4290	+	7.57712i	−0.792903	+	0.576078i	0.115920	+	0.993258i	$0.463018\pi$
$174$	0.0515452	+	0.158640i	0.00390763	+	0.0120265i
$175$	−5.86314	−	11.0739i	−0.443212	−	0.837105i
$176$	11.9341	−	8.39061i	0.899566	−	0.632466i
$177$	−0.344163	+	1.05922i	−0.0258688	+	0.0796161i
$178$	0.532713	−	1.63952i	0.0399285	−	0.122887i
$179$	2.12661	+	6.54502i	0.158950	+	0.489198i	0.998540	−	0.0540233i	$-0.0172045\pi$
$179$	2.12661	+	6.54502i	0.158950	+	0.489198i	−0.839590	+	0.543221i	$0.817205\pi$
$180$	−0.329228	+	1.42035i	−0.0245392	+	0.105867i
$181$	−0.818738	−	2.51982i	−0.0608564	−	0.187297i	0.916006	−	0.401164i	$-0.131394\pi$
$181$	−0.818738	−	2.51982i	−0.0608564	−	0.187297i	−0.976863	+	0.213867i	$0.931394\pi$
$182$	6.93733	−	21.3509i	0.514229	−	1.58263i
$183$	1.07892	−	3.32057i	0.0797559	−	0.245463i
$184$	−5.80236	+	17.8578i	−0.427756	+	1.31650i
$185$	−17.4372	+	1.51013i	−1.28201	+	0.111027i
$186$	0.155938	−	0.479927i	0.0114339	−	0.0351899i
$187$	−19.8525	−	14.9001i	−1.45176	−	1.08960i
$188$	−0.00515994	−	0.0158806i	−0.000376327	−	0.00115822i
$189$	4.57554			0.332822
$190$	−8.06850	+	7.00140i	−0.585351	+	0.507935i
$191$	−17.4896	−	12.7069i	−1.26550	−	0.919440i	−0.266487	−	0.963839i	$-0.585863\pi$
$191$	−17.4896	−	12.7069i	−1.26550	−	0.919440i	−0.999014	+	0.0443985i	$0.985863\pi$
$192$	0.660460	+	2.03269i	0.0476646	+	0.146697i
$193$	−6.34646	+	19.5324i	−0.456828	+	1.40597i	0.412148	+	0.911117i	$0.364779\pi$
$193$	−6.34646	+	19.5324i	−0.456828	+	1.40597i	−0.868976	+	0.494855i	$0.835221\pi$
$194$	−0.825217	+	2.53976i	−0.0592471	+	0.182344i
$195$	4.13757	−	0.358328i	0.296298	−	0.0256604i
$196$	−0.0499310	+	0.153672i	−0.00356650	+	0.0109766i
$197$	−16.4307	−	11.9376i	−1.17064	−	0.850519i	−0.179554	−	0.983748i	$-0.557465\pi$
$197$	−16.4307	−	11.9376i	−1.17064	−	0.850519i	−0.991085	+	0.133229i	$0.957465\pi$
$198$	4.65128	−	13.5932i	0.330552	−	0.966029i
$199$	14.7091			1.04270			0.521349	−	0.853344i	$-0.325429\pi$
$199$	14.7091			1.04270			0.521349	+	0.853344i	$0.325429\pi$
$200$	1.86577	−	13.1085i	0.131930	−	0.926907i
$201$	3.99485	+	2.90243i	0.281775	+	0.204721i
$202$	−6.19147	−	19.0554i	−0.435630	−	1.34073i
$203$	−0.733259	+	0.532744i	−0.0514647	+	0.0373913i
$204$	−0.420338	+	0.305394i	−0.0294296	+	0.0213818i
$205$	2.22364	+	5.25139i	0.155306	+	0.366773i
$206$	−10.7519			−0.749123
$207$	6.36387	+	19.5860i	0.442320	+	1.36132i
$208$	21.3735	−	15.5288i	1.48199	−	1.07673i
$209$	8.69070	−	6.11025i	0.601148	−	0.422655i
$210$	2.57482	−	0.222989i	0.177680	−	0.0153877i
$211$	7.41444			0.510431			0.255216	−	0.966884i	$-0.417854\pi$
$211$	7.41444			0.510431			0.255216	+	0.966884i	$0.417854\pi$
$212$	−0.171059	+	0.526465i	−0.0117484	+	0.0361577i
$213$	−0.110513	−	0.0802924i	−0.00757223	−	0.00550155i
$214$	16.4015	+	11.9164i	1.12118	+	0.814588i
$215$	11.5029	−	9.98155i	0.784488	−	0.680736i
$216$	3.91154	+	2.84190i	0.266146	+	0.193367i
$217$	2.74197			0.186137
$218$	−4.51359	−	13.8914i	−0.305699	−	0.940845i
$219$	−2.47709	+	1.79971i	−0.167386	+	0.121613i
$220$	0.401099	−	1.61592i	0.0270421	−	0.108945i
$221$	−36.3666	−	26.4219i	−2.44628	−	1.77733i
$222$	1.11556	−	3.43335i	0.0748716	−	0.230431i
$223$	−8.51324	+	6.18523i	−0.570089	+	0.414194i	−0.835137	−	0.550041i	$-0.814612\pi$
$223$	−8.51324	+	6.18523i	−0.570089	+	0.414194i	0.265049	+	0.964235i	$0.414612\pi$
$224$	2.56306	−	1.86217i	0.171252	−	0.124422i
$225$	−6.79507	−	12.8340i	−0.453005	−	0.855602i
$226$	−3.13027	+	9.63398i	−0.208222	+	0.640843i
$227$	2.48455	+	7.64665i	0.164905	+	0.507526i	0.999029	−	0.0440508i	$-0.0140263\pi$
$227$	2.48455	+	7.64665i	0.164905	+	0.507526i	−0.834124	+	0.551577i	$0.814026\pi$
$228$	−0.0687168	−	0.211489i	−0.00455088	−	0.0140062i
$229$	−3.23111	+	9.94435i	−0.213518	+	0.657141i	0.785737	+	0.618560i	$0.212284\pi$
$229$	−3.23111	+	9.94435i	−0.213518	+	0.657141i	−0.999255	+	0.0385809i	$0.987716\pi$
$230$	9.22073	+	21.7759i	0.607997	+	1.43586i
$231$	−2.56988	−	0.0399100i	−0.169086	−	0.00262589i
$232$	−0.957739			−0.0628786
$233$	−1.89932	−	1.37994i	−0.124429	−	0.0904027i	0.523830	−	0.851823i	$-0.324503\pi$
$233$	−1.89932	−	1.37994i	−0.124429	−	0.0904027i	−0.648259	+	0.761420i	$0.724503\pi$
$234$	8.04000	−	24.7446i	0.525591	−	1.61760i
$235$	0.142483	+	0.0857826i	0.00929454	+	0.00559584i
$236$	0.654155	+	0.475272i	0.0425819	+	0.0309376i
$237$	0.998985			0.0648911
$238$	−22.6310	−	16.4424i	−1.46695	−	1.06580i
$239$	14.2451	−	10.3497i	0.921442	−	0.669467i	−0.0224406	−	0.999748i	$-0.507144\pi$
$239$	14.2451	−	10.3497i	0.921442	−	0.669467i	0.943882	+	0.330281i	$0.107144\pi$
$240$	2.60564	+	1.56875i	0.168194	+	0.101262i
$241$	7.42141	+	22.8407i	0.478055	+	1.47130i	0.841793	+	0.539801i	$0.181500\pi$
$241$	7.42141	+	22.8407i	0.478055	+	1.47130i	−0.363738	+	0.931501i	$0.618500\pi$
$242$	−5.55188	+	15.4383i	−0.356888	+	0.992412i
$243$	7.99716			0.513018
$244$	−2.05072	−	1.48993i	−0.131284	−	0.0953831i
$245$	−0.627523	−	1.48197i	−0.0400910	−	0.0946796i
$246$	−1.17624			−0.0749946
$247$	15.5647	−	11.3084i	0.990360	−	0.719539i
$248$	2.34405	+	1.70305i	0.148847	+	0.108144i
$249$	−0.316378	+	0.229862i	−0.0200497	+	0.0145669i
$250$	−9.04508	−	14.0089i	−0.572061	−	0.886001i
$251$	−1.72690	−	5.31485i	−0.109001	−	0.335470i	0.881648	−	0.471908i	$-0.156435\pi$
$251$	−1.72690	−	5.31485i	−0.109001	−	0.335470i	−0.990649	+	0.136438i	$0.956435\pi$
$252$	0.504947	−	1.55407i	0.0318087	−	0.0978971i
$253$	−6.91898	−	22.4762i	−0.434993	−	1.41306i
$254$	12.4313	+	9.03184i	0.780007	+	0.566708i
$255$	1.16854	−	5.04128i	0.0731766	−	0.315697i
$256$	5.32271			0.332669
$257$	6.33627	−	4.60357i	0.395246	−	0.287163i	−0.372356	−	0.928090i	$-0.621450\pi$
$257$	6.33627	−	4.60357i	0.395246	−	0.287163i	0.767602	+	0.640927i	$0.221450\pi$
$258$	0.970705	+	2.98752i	0.0604335	+	0.185995i
$259$	19.6157			1.21886
$260$	0.680844	−	2.93728i	0.0422241	−	0.182163i
$261$	−0.849809	+	0.617422i	−0.0526018	+	0.0382175i
$262$	−10.7228	+	7.79054i	−0.662454	+	0.481301i
$263$	−1.99985	−	6.15489i	−0.123316	−	0.379527i	0.870275	−	0.492567i	$-0.163941\pi$
$263$	−1.99985	−	6.15489i	−0.123316	−	0.379527i	−0.993590	+	0.113040i	$0.963941\pi$
$264$	−2.17215	−	1.63029i	−0.133686	−	0.100337i
$265$	−2.14983	−	5.07709i	−0.132063	−	0.311883i
$266$	9.68598	−	7.03728i	0.593886	−	0.431483i
$267$	−0.357416			−0.0218735
$268$	2.90030	−	2.10719i	0.177164	−	0.128717i
$269$	−1.56262	−	4.80924i	−0.0952744	−	0.293224i	0.892051	−	0.451935i	$-0.149266\pi$
$269$	−1.56262	−	4.80924i	−0.0952744	−	0.293224i	−0.987325	+	0.158711i	$0.949266\pi$
$270$	6.06642	−	0.525373i	0.369190	−	0.0319732i
$271$	2.86770			0.174200			0.0871002	−	0.996200i	$-0.472240\pi$
$271$	2.86770			0.174200			0.0871002	+	0.996200i	$0.472240\pi$
$272$	−10.1727	−	31.3085i	−0.616813	−	1.89836i
$273$	−4.65449			−0.281703
$274$	9.77041			0.590252
$275$	7.53106	+	14.7744i	0.454140	+	0.890930i
$276$	−0.492251			−0.0296300
$277$	18.5027			1.11172			0.555860	−	0.831276i	$-0.312389\pi$
$277$	18.5027			1.11172			0.555860	+	0.831276i	$0.312389\pi$
$278$	7.32366	+	22.5399i	0.439244	+	1.35185i
$279$	3.17779			0.190250
$280$	−3.35080	+	14.4559i	−0.200248	+	0.863908i
$281$	3.22557	+	9.92729i	0.192421	+	0.592212i	0.999997	+	0.00244828i	$0.000779313\pi$
$281$	3.22557	+	9.92729i	0.192421	+	0.592212i	−0.807576	+	0.589764i	$0.799221\pi$
$282$	−0.0277520	+	0.0201630i	−0.00165261	+	0.00120069i
$283$	13.2187			0.785769			0.392884	−	0.919588i	$-0.371477\pi$
$283$	13.2187			0.785769			0.392884	+	0.919588i	$0.371477\pi$
$284$	−0.0802334	+	0.0582930i	−0.00476098	+	0.00345905i
$285$	1.89749	+	1.14240i	0.112398	+	0.0676699i
$286$	−9.61886	+	28.1108i	−0.568775	+	1.66223i
$287$	−1.97503	−	6.07851i	−0.116582	−	0.358803i
$288$	2.97045	−	2.15816i	0.175036	−	0.127171i
$289$	−31.5614	+	22.9307i	−1.85655	+	1.34887i
$290$	−0.911010	+	0.790525i	−0.0534963	+	0.0464212i
$291$	0.553667			0.0324565
$292$	0.686924	+	2.11414i	0.0401992	+	0.123720i
$293$	−8.31595	+	6.04189i	−0.485823	+	0.352971i	−0.803576	−	0.595202i	$-0.797072\pi$
$293$	−8.31595	+	6.04189i	−0.485823	+	0.352971i	0.317753	+	0.948174i	$0.397072\pi$
$294$	0.331942			0.0193593
$295$	−8.02351	+	0.694864i	−0.467147	+	0.0404565i
$296$	16.7691	+	12.1835i	0.974684	+	0.708149i
$297$	−6.05477	−	0.0940300i	−0.351333	−	0.00545618i
$298$	0.648619	−	1.99624i	0.0375735	−	0.115639i
$299$	−13.1605	−	40.5038i	−0.761091	−	2.34240i
$300$	0.341945	−	0.0596747i	0.0197422	−	0.00344532i
$301$	−13.8088	+	10.0327i	−0.795927	+	0.578274i
$302$	−11.3201	−	8.22453i	−0.651398	−	0.473269i
$303$	−3.36072	+	2.44170i	−0.193068	+	0.140272i
$304$	14.0895			0.808087
$305$	25.1530	−	2.17833i	1.44025	−	0.124731i
$306$	−26.2282	−	19.0559i	−1.49936	−	1.08935i
$307$	−21.9100			−1.25047			−0.625234	−	0.780437i	$-0.714996\pi$
$307$	−21.9100			−1.25047			−0.625234	+	0.780437i	$0.714996\pi$
$308$	−0.604107	+	1.76548i	−0.0344222	+	0.100598i
$309$	0.688861	+	2.12010i	0.0391880	+	0.120608i
$310$	3.63540	−	0.314838i	0.206477	−	0.0178816i
$311$	7.17384	−	5.21210i	0.406791	−	0.295551i	−0.365510	−	0.930807i	$-0.619106\pi$
$311$	7.17384	−	5.21210i	0.406791	−	0.295551i	0.772301	+	0.635256i	$0.219106\pi$
$312$	−3.97903	−	2.89094i	−0.225268	−	0.163667i
$313$	−3.62067			−0.204652			−0.102326	−	0.994751i	$-0.532629\pi$
$313$	−3.62067			−0.204652			−0.102326	+	0.994751i	$0.532629\pi$
$314$	−7.00853	−	5.09199i	−0.395514	−	0.287358i
$315$	6.34608	+	14.9870i	0.357561	+	0.844423i
$316$	0.224121	−	0.689775i	0.0126078	−	0.0388029i
$317$	22.8397	+	16.5940i	1.28280	+	0.932012i	0.999634	−	0.0270577i	$-0.00861380\pi$
$317$	22.8397	+	16.5940i	1.28280	+	0.932012i	0.283170	+	0.959070i	$0.408614\pi$
$318$	1.13720			0.0637711
$319$	0.981262	−	0.689905i	0.0549401	−	0.0386273i
$320$	−11.6730	+	10.1292i	−0.652538	+	0.566237i
$321$	1.29889	−	3.99756i	0.0724968	−	0.223122i
$322$	−8.18981	−	25.2057i	−0.456400	−	1.40466i
$323$	−7.40804	−	22.7996i	−0.412194	−	1.26860i
$324$	0.565306	−	1.73983i	0.0314059	−	0.0966574i
$325$	14.0522	+	26.5408i	0.779477	+	1.47222i
$326$	−26.2879	+	19.0992i	−1.45595	+	1.05781i
$327$	−2.44997	+	1.78001i	−0.135484	+	0.0984346i
$328$	2.08699	−	6.42310i	0.115235	−	0.354656i
$329$	−0.150795	−	0.109559i	−0.00831361	−	0.00604019i
$330$	−3.41182	+	0.242164i	−0.187814	+	0.0133307i
$331$	10.3568	−	7.52467i	0.569262	−	0.413593i	−0.265575	−	0.964090i	$-0.585562\pi$
$331$	10.3568	−	7.52467i	0.569262	−	0.413593i	0.834837	+	0.550497i	$0.185562\pi$
$332$	0.0877351	+	0.270021i	0.00481509	+	0.0148193i
$333$	22.7336			1.24579
$334$	−11.2917	−	8.20387i	−0.617852	−	0.448896i
$335$	−8.06280	+	34.7844i	−0.440518	+	1.90047i
$336$	−2.75766	−	2.00356i	−0.150443	−	0.109303i
$337$	−7.71007	−	5.60169i	−0.419994	−	0.305144i	0.357641	−	0.933859i	$-0.383581\pi$
$337$	−7.71007	−	5.60169i	−0.419994	−	0.305144i	−0.777635	+	0.628715i	$0.783581\pi$
$338$	−10.6351	+	32.7316i	−0.578475	+	1.78036i
$339$	2.10021			0.114068
$340$	−3.21872	−	1.93785i	−0.174560	−	0.105095i
$341$	−3.62841	−	0.0563490i	−0.196490	−	0.00305147i
$342$	11.2255	−	8.15583i	0.607008	−	0.441017i
$343$	5.97824	+	18.3991i	0.322795	+	0.993460i
$344$	−18.0362			−0.972448
$345$	3.70307	−	3.21332i	0.199366	−	0.172999i
$346$	15.5546	−	11.3011i	0.836222	−	0.607551i
$347$	15.6488	−	11.3695i	0.840070	−	0.610347i	−0.0823203	−	0.996606i	$-0.526233\pi$
$347$	15.6488	−	11.3695i	0.840070	−	0.610347i	0.922390	+	0.386259i	$0.126233\pi$
$348$	−0.00775878	−	0.0238791i	−0.000415914	−	0.00128005i
$349$	1.42217	+	1.03326i	0.0761268	+	0.0553093i	0.625198	−	0.780466i	$-0.285018\pi$
$349$	1.42217	+	1.03326i	0.0761268	+	0.0553093i	−0.549071	+	0.835776i	$0.685018\pi$
$350$	8.74474	+	16.5164i	0.467426	+	0.882839i
$351$	−10.9662			−0.585334
$352$	−3.42994	+	2.41152i	−0.182816	+	0.128534i
$353$	−0.877645	−	0.637646i	−0.0467123	−	0.0339385i	0.564184	−	0.825649i	$-0.309191\pi$
$353$	−0.877645	−	0.637646i	−0.0467123	−	0.0339385i	−0.610896	+	0.791711i	$0.709191\pi$
$354$	0.513311	−	1.57981i	0.0272821	−	0.0839658i
$355$	0.223048	−	0.962271i	0.0118382	−	0.0510720i
$356$	−0.0801859	+	0.246787i	−0.00424984	+	0.0130797i
$357$	−1.79222	+	5.51589i	−0.0948544	+	0.291932i
$358$	−3.17178	−	9.76174i	−0.167634	−	0.515924i
$359$	−1.99400	−	1.44873i	−0.105239	−	0.0764608i	0.533921	−	0.845534i	$-0.320718\pi$
$359$	−1.99400	−	1.44873i	−0.105239	−	0.0764608i	−0.639160	+	0.769074i	$0.720718\pi$
$360$	−3.88340	+	16.7537i	−0.204673	+	0.882997i
$361$	−8.73969			−0.459984
$362$	1.22113	+	3.75825i	0.0641811	+	0.197529i
$363$	3.39987	+	0.105625i	0.178447	+	0.00554387i
$364$	−1.04423	+	3.21381i	−0.0547326	+	0.168450i
$365$	−18.9682	−	11.4199i	−0.992842	−	0.597747i
$366$	−1.60918	+	4.95255i	−0.0841132	+	0.258874i
$367$	−4.24978	+	13.0795i	−0.221837	+	0.682744i	0.776760	+	0.629796i	$0.216862\pi$
$367$	−4.24978	+	13.0795i	−0.221837	+	0.682744i	−0.998597	+	0.0529474i	$0.983138\pi$
$368$	9.63791	−	29.6625i	0.502411	−	1.54626i
$369$	−2.28895	−	7.04468i	−0.119158	−	0.366731i
$370$	26.0072	−	2.25232i	1.35205	−	0.117092i
$371$	1.90947	+	5.87675i	0.0991349	+	0.305106i
$372$	−0.0234723	+	0.0722403i	−0.00121698	+	0.00374548i
$373$	1.96925	−	6.06074i	0.101964	−	0.313813i	−0.887042	−	0.461689i	$-0.847244\pi$
$373$	1.96925	−	6.06074i	0.101964	−	0.313813i	0.989006	+	0.147876i	$0.0472436\pi$
$374$	29.6095	+	22.2231i	1.53107	+	1.14913i
$375$	−2.18281	+	2.68107i	−0.112720	+	0.138450i
$376$	−0.0608639	−	0.187320i	−0.00313881	−	0.00966028i
$377$	1.75741	−	1.27683i	0.0905110	−	0.0657601i
$378$	−6.82432			−0.351005
$379$	24.8927	−	18.0856i	1.27865	−	0.928997i	0.279142	−	0.960250i	$-0.409950\pi$
$379$	24.8927	−	18.0856i	1.27865	−	0.928997i	0.999511	+	0.0312532i	$0.00994982\pi$
$380$	1.21450	−	1.05388i	0.0623025	−	0.0540627i
$381$	0.984470	−	3.02989i	0.0504359	−	0.155226i
$382$	26.0853	+	18.9521i	1.33464	+	0.969672i
$383$	−25.8818	−	18.8042i	−1.32250	−	0.960851i	−0.999898	−	0.0143164i	$-0.995443\pi$
$383$	−25.8818	−	18.8042i	−1.32250	−	0.960851i	−0.322601	−	0.946535i	$-0.604557\pi$
$384$	−1.22666	−	3.77528i	−0.0625979	−	0.192657i
$385$	−6.98022	−	17.2247i	−0.355745	−	0.877854i
$386$	9.46559	−	29.1321i	0.481786	−	1.48278i
$387$	−16.0037	+	11.6274i	−0.813513	+	0.591052i
$388$	0.124215	−	0.382293i	0.00630604	−	0.0194080i
$389$	2.92913	+	9.01493i	0.148513	+	0.457075i	0.997446	−	0.0714249i	$-0.0227546\pi$
$389$	2.92913	+	9.01493i	0.148513	+	0.457075i	−0.848933	+	0.528500i	$0.822755\pi$
$390$	−6.17109	+	0.534438i	−0.312485	+	0.0270623i
$391$	−53.0673			−2.68373
$392$	−0.588960	+	1.81263i	−0.0297470	+	0.0915517i
$393$	2.22315	+	1.61522i	0.112143	+	0.0814768i
$394$	24.5060	+	17.8047i	1.23460	+	0.896986i
$395$	2.81672	+	6.65201i	0.141724	+	0.334699i
$396$	−0.700128	+	2.04610i	−0.0351828	+	0.102821i
$397$	23.5711	+	17.1254i	1.18300	+	0.859498i	0.992507	−	0.122191i	$-0.0389920\pi$
$397$	23.5711	+	17.1254i	1.18300	+	0.859498i	0.190491	+	0.981689i	$0.438992\pi$
$398$	−21.9382			−1.09966
$399$	−2.00820	−	1.45904i	−0.100536	−	0.0730434i
$400$	−3.09910	+	21.7736i	−0.154955	+	1.08868i
$401$	4.39110	−	13.5144i	0.219281	−	0.674877i	−0.779541	−	0.626351i	$-0.784548\pi$
$401$	4.39110	−	13.5144i	0.219281	−	0.674877i	0.998822	−	0.0485259i	$-0.0154524\pi$
$402$	−5.95822	−	4.32890i	−0.297169	−	0.215906i
$403$	−6.57168			−0.327359
$404$	0.931963	+	2.86829i	0.0463669	+	0.142703i
$405$	7.10466	+	16.7785i	0.353033	+	0.833730i
$406$	1.09364	−	0.794575i	0.0542764	−	0.0394341i
$407$	−25.9573	−	0.403115i	−1.28666	−	0.0199817i
$408$	−4.95809	+	3.60226i	−0.245462	+	0.178339i
$409$	13.6469	−	9.91509i	0.674798	−	0.490269i	−0.196830	−	0.980438i	$-0.563065\pi$
$409$	13.6469	−	9.91509i	0.674798	−	0.490269i	0.871628	+	0.490168i	$0.163065\pi$
$410$	−3.31651	−	7.83233i	−0.163791	−	0.386811i
$411$	−0.625976	−	1.92656i	−0.0308771	−	0.0950300i
$412$	1.61842			0.0797339
$413$	9.02592			0.444136
$414$	−9.49156	−	29.2120i	−0.466485	−	1.43569i
$415$	−2.42265	−	1.45857i	−0.118923	−	0.0715986i
$416$	−6.14290	+	4.46308i	−0.301180	+	0.218820i
$417$	3.97527	−	2.88820i	0.194670	−	0.141436i
$418$	−12.9620	+	9.11330i	−0.633991	+	0.445746i
$419$	11.2547	−	8.17698i	0.549826	−	0.399472i	−0.277896	−	0.960611i	$-0.589637\pi$
$419$	11.2547	−	8.17698i	0.549826	−	0.399472i	0.827721	+	0.561140i	$0.189637\pi$
$420$	−0.387572	+	0.0335651i	−0.0189116	+	0.00163781i
$421$	1.04236	+	3.20806i	0.0508016	+	0.156351i	0.973239	−	0.229796i	$-0.0738058\pi$
$421$	1.04236	+	3.20806i	0.0508016	+	0.156351i	−0.922437	+	0.386147i	$0.873806\pi$
$422$	−11.0585			−0.538318
$423$	−0.174764	−	0.126973i	−0.00849731	−	0.00617365i
$424$	−2.01772	+	6.20990i	−0.0979891	+	0.301579i
$425$	36.8635	−	6.43326i	1.78814	−	0.312059i
$426$	0.164828	+	0.119754i	0.00798592	+	0.00580211i
$427$	−28.2954			−1.36931
$428$	−2.46882	−	1.79370i	−0.119335	−	0.0867017i
$429$	6.15924	+	0.0956525i	0.297371	+	0.00461815i
$430$	−17.1562	+	14.8872i	−0.827347	+	0.717927i
$431$	−6.90016	−	5.01326i	−0.332369	−	0.241480i	0.409066	−	0.912505i	$-0.365855\pi$
$431$	−6.90016	−	5.01326i	−0.332369	−	0.241480i	−0.741435	+	0.671024i	$0.765855\pi$
$432$	−6.49719	−	4.72049i	−0.312596	−	0.227115i
$433$	−5.39006	+	16.5889i	−0.259030	+	0.797212i	0.733979	+	0.679172i	$0.237661\pi$
$433$	−5.39006	+	16.5889i	−0.259030	+	0.797212i	−0.993009	+	0.118040i	$0.962339\pi$
$434$	−4.08958			−0.196306
$435$	0.214245	+	0.128988i	0.0102723	+	0.00618449i
$436$	0.679402	+	2.09099i	0.0325375	+	0.100140i
$437$	7.01857	−	21.6009i	0.335744	−	1.03331i
$438$	3.69453	−	2.68423i	0.176531	−	0.128258i
$439$	−4.67547	+	14.3896i	−0.223148	+	0.686779i	0.775326	+	0.631561i	$0.217585\pi$
$439$	−4.67547	+	14.3896i	−0.223148	+	0.686779i	−0.998474	+	0.0552179i	$0.982415\pi$
$440$	4.73115	−	19.0605i	0.225549	−	0.908675i
$441$	0.645955	+	1.98804i	0.0307598	+	0.0946688i
$442$	54.2399	+	39.4076i	2.57993	+	1.87443i
$443$	16.9775	+	12.3348i	0.806624	+	0.586046i	0.912850	−	0.408296i	$-0.133877\pi$
$443$	16.9775	+	12.3348i	0.806624	+	0.586046i	−0.106226	+	0.994342i	$0.533877\pi$
$444$	−0.167918	+	0.516800i	−0.00796905	+	0.0245262i
$445$	−1.00776	−	2.37995i	−0.0477725	−	0.112820i
$446$	12.6973	−	9.22513i	0.601234	−	0.436822i
$447$	−0.435181			−0.0205833
$448$	14.0130	−	10.1811i	0.662053	−	0.481010i
$449$	5.29288	+	16.2898i	0.249786	+	0.768763i	0.994812	+	0.101728i	$0.0324370\pi$
$449$	5.29288	+	16.2898i	0.249786	+	0.768763i	−0.745026	+	0.667035i	$0.767563\pi$
$450$	10.1347	+	19.1417i	0.477754	+	0.902346i
$451$	2.48862	+	8.08422i	0.117184	+	0.380671i
$452$	0.471180	−	1.45014i	0.0221624	−	0.0682089i
$453$	−0.896474	+	2.75906i	−0.0421200	+	0.129632i
$454$	−3.70564	−	11.4048i	−0.173915	−	0.535254i
$455$	−13.1237	−	30.9932i	−0.615249	−	1.45298i
$456$	−0.810547	−	2.49461i	−0.0379573	−	0.116821i
$457$	4.27935	−	13.1705i	0.200179	−	0.616089i	−0.799697	−	0.600403i	$-0.795007\pi$
$457$	4.27935	−	13.1705i	0.200179	−	0.616089i	0.999877	−	0.0156859i	$-0.00499319\pi$
$458$	4.81913	−	14.8318i	0.225183	−	0.693043i
$459$	−4.22257	+	12.9957i	−0.197093	+	0.606588i
$460$	−1.38794	−	3.27778i	−0.0647129	−	0.152827i
$461$	−3.68075	+	11.3282i	−0.171430	+	0.527606i	−0.999452	−	0.0330883i	$-0.989466\pi$
$461$	−3.68075	+	11.3282i	−0.171430	+	0.527606i	0.828023	+	0.560694i	$0.189466\pi$
$462$	3.83291	+	0.0595248i	0.178323	+	0.00276935i
$463$	12.7070	+	39.1081i	0.590544	+	1.81751i	0.575761	+	0.817618i	$0.304706\pi$
$463$	12.7070	+	39.1081i	0.590544	+	1.81751i	0.0147830	+	0.999891i	$0.495294\pi$
$464$	1.59084			0.0738527
$465$	−0.294995	−	0.696666i	−0.0136801	−	0.0323071i
$466$	2.83279	+	2.05814i	0.131227	+	0.0953417i
$467$	−5.16913	−	15.9089i	−0.239199	−	0.736178i	−0.996537	−	0.0831546i	$-0.973500\pi$
$467$	−5.16913	−	15.9089i	−0.239199	−	0.736178i	0.757338	−	0.653023i	$-0.226500\pi$
$468$	−1.21021	+	3.72464i	−0.0559420	+	0.172172i
$469$	12.3662	−	38.0591i	0.571017	−	1.75741i
$470$	−0.212509	−	0.127943i	−0.00980233	−	0.00590156i
$471$	−0.555027	+	1.70820i	−0.0255743	+	0.0787096i
$472$	7.71607	+	5.60605i	0.355161	+	0.258040i
$473$	18.4792	−	12.9924i	0.849675	−	0.597390i
$474$	−1.48996			−0.0684363
$475$	−2.25684	+	15.8560i	−0.103551	+	0.727525i
$476$	3.40650	+	2.47497i	0.156137	+	0.113440i
$477$	2.21298	+	6.81085i	0.101325	+	0.311847i
$478$	−21.2463	+	15.4363i	−0.971783	+	0.706042i
$479$	−10.1634	+	7.38417i	−0.464379	+	0.337391i	−0.795247	−	0.606286i	$-0.792659\pi$
$479$	−10.1634	+	7.38417i	−0.464379	+	0.337391i	0.330868	+	0.943677i	$0.392659\pi$
$480$	−0.748880	−	0.450868i	−0.0341815	−	0.0205792i
$481$	−47.0132			−2.14362
$482$	−11.0689	−	34.0664i	−0.504173	−	1.55168i
$483$	−4.44541	+	3.22978i	−0.202273	+	0.146960i
$484$	0.835689	−	2.32383i	0.0379859	−	0.105629i
$485$	1.56111	+	3.68674i	0.0708861	+	0.167406i
$486$	−11.9276			−0.541046
$487$	−7.82411	+	24.0801i	−0.354544	+	1.09118i	0.601729	+	0.798700i	$0.294479\pi$
$487$	−7.82411	+	24.0801i	−0.354544	+	1.09118i	−0.956273	+	0.292475i	$0.905521\pi$
$488$	−24.1892	−	17.5744i	−1.09499	−	0.795558i
$489$	5.45027	+	3.95985i	0.246470	+	0.179071i
$490$	0.935936	+	2.21032i	0.0422813	+	0.0998523i
$491$	−0.695828	−	0.505548i	−0.0314023	−	0.0228151i	0.571973	−	0.820272i	$-0.306178\pi$
$491$	−0.695828	−	0.505548i	−0.0314023	−	0.0228151i	−0.603376	+	0.797457i	$0.706178\pi$
$492$	0.177053			0.00798214
$493$	−0.836438	−	2.57429i	−0.0376713	−	0.115940i
$494$	−23.2144	+	16.8663i	−1.04447	+	0.758850i
$495$	−8.08970	−	19.9626i	−0.363605	−	0.897251i
$496$	−3.89354	−	2.82883i	−0.174825	−	0.127018i
$497$	−0.342096	+	1.05286i	−0.0153451	+	0.0472274i
$498$	0.471871	−	0.342834i	0.0211450	−	0.0153628i
$499$	−17.3125	+	12.5783i	−0.775014	+	0.563081i	−0.903478	−	0.428634i	$-0.858995\pi$
$499$	−17.3125	+	12.5783i	−0.775014	+	0.563081i	0.128465	+	0.991714i	$0.458995\pi$
$500$	1.36150	+	2.10867i	0.0608881	+	0.0943026i
$501$	−0.894222	+	2.75213i	−0.0399509	+	0.122956i
$502$	2.57563	+	7.92697i	0.114956	+	0.353798i
$503$	4.40171	+	13.5471i	0.196263	+	0.604034i	0.999960	+	0.00899547i	$0.00286339\pi$
$503$	4.40171	+	13.5471i	0.196263	+	0.604034i	−0.803697	+	0.595039i	$0.797137\pi$
$504$	5.95609	−	18.3310i	0.265305	−	0.816526i
$505$	−25.7345	−	15.4937i	−1.14517	−	0.689458i
$506$	10.3195	+	33.5227i	0.458758	+	1.49026i
$507$	7.13548			0.316898
$508$	−1.87120	−	1.35951i	−0.0830210	−	0.0603183i
$509$	−11.8135	+	36.3581i	−0.523623	+	1.61154i	0.243401	+	0.969926i	$0.421737\pi$
$509$	−11.8135	+	36.3581i	−0.523623	+	1.61154i	−0.767023	+	0.641619i	$0.778263\pi$
$510$	−1.74285	+	7.51895i	−0.0771745	+	0.332945i
$511$	20.0749	+	14.5852i	0.888059	+	0.645213i
$512$	17.7353			0.783798
$513$	−4.73142	−	3.43758i	−0.208897	−	0.151773i
$514$	−9.45040	+	6.86611i	−0.416839	+	0.302851i
$515$	−12.1749	+	10.5647i	−0.536492	+	0.465538i
$516$	−0.146114	−	0.449693i	−0.00643231	−	0.0197966i
$517$	0.197294	+	0.148077i	0.00867699	+	0.00651243i
$518$	−29.2564			−1.28545
$519$	−3.22495	−	2.34306i	−0.141559	−	0.102849i
$520$	8.03088	−	34.6466i	0.352177	−	1.51936i
$521$	26.3444			1.15417			0.577085	−	0.816684i	$-0.304190\pi$
$521$	26.3444			1.15417			0.577085	+	0.816684i	$0.304190\pi$
$522$	1.26747	−	0.920871i	0.0554757	−	0.0403054i
$523$	22.9806	+	16.6963i	1.00487	+	0.730080i	0.963127	−	0.269048i	$-0.0867091\pi$
$523$	22.9806	+	16.6963i	1.00487	+	0.730080i	0.0417426	+	0.999128i	$0.486709\pi$
$524$	1.61403	−	1.17266i	0.0705092	−	0.0512279i
$525$	2.69649	−	2.78250i	0.117684	−	0.121438i
$526$	2.98272	+	9.17988i	0.130053	+	0.400262i
$527$	−2.53044	+	7.78789i	−0.110228	+	0.339246i
$528$	3.60801	+	2.70796i	0.157018	+	0.117849i
$529$	−22.0678	−	16.0332i	−0.959469	−	0.697095i
$530$	3.20643	+	7.57235i	0.139278	+	0.328922i
$531$	10.4606			0.453950
$532$	−1.45797	+	1.05928i	−0.0632110	+	0.0459255i
$533$	4.73356	+	14.5684i	0.205033	+	0.631028i
$534$	0.533077			0.0230685
$535$	30.2811	−	2.62245i	1.30917	−	0.113378i
$536$	34.2104	−	24.8553i	1.47766	−	1.07358i
$537$	−1.72164	+	1.25084i	−0.0742941	+	0.0539778i
$538$	2.33061	+	7.17287i	0.100480	+	0.309244i
$539$	−0.702300	−	2.28141i	−0.0302502	−	0.0982672i
$540$	−0.913139	+	0.0790810i	−0.0392953	+	0.00340310i
$541$	34.9990	−	25.4283i	1.50472	−	1.09325i	0.536273	−	0.844045i	$-0.319832\pi$
$541$	34.9990	−	25.4283i	1.50472	−	1.09325i	0.968452	−	0.249201i	$-0.0801681\pi$
$542$	−4.27711			−0.183718
$543$	0.662826	−	0.481571i	0.0284446	−	0.0206662i
$544$	2.92371	+	8.99827i	0.125353	+	0.385798i
$545$	−18.7605	−	11.2949i	−0.803612	−	0.483820i
$546$	6.94207			0.297093
$547$	9.21335	+	28.3558i	0.393935	+	1.21241i	0.929788	+	0.368095i	$0.119990\pi$
$547$	9.21335	+	28.3558i	0.393935	+	1.21241i	−0.535854	+	0.844311i	$0.680010\pi$
$548$	−1.47068			−0.0628242
$549$	−32.7929			−1.39957
$550$	−11.2324	−	22.0357i	−0.478951	−	0.939605i
$551$	1.15849			0.0493531
$552$	−5.80633			−0.247134
$553$	−2.50179	−	7.69973i	−0.106387	−	0.327426i
$554$	−27.5964			−1.17246
$555$	−2.11037	−	4.98388i	−0.0895801	−	0.211554i
$556$	−1.10238	−	3.39279i	−0.0467515	−	0.143886i
$557$	−16.5976	+	12.0589i	−0.703264	+	0.510951i	−0.880994	−	0.473128i	$-0.843125\pi$
$557$	−16.5976	+	12.0589i	−0.703264	+	0.510951i	0.177729	+	0.984079i	$0.443125\pi$
$558$	−4.73961			−0.200644
$559$	33.0956	−	24.0454i	1.39980	−	1.01701i
$560$	5.56579	−	24.0118i	0.235197	−	1.01468i
$561$	2.48498	−	7.26229i	0.104916	−	0.306614i
$562$	−4.81087	−	14.8063i	−0.202934	−	0.624567i
$563$	−6.91389	+	5.02324i	−0.291386	+	0.211704i	−0.723868	−	0.689938i	$-0.757638\pi$
$563$	−6.91389	+	5.02324i	−0.291386	+	0.211704i	0.432483	+	0.901642i	$0.357638\pi$
$564$	0.00417733	−	0.00303501i	0.000175897	−	0.000127797i
$565$	5.92169	+	13.9848i	0.249128	+	0.588344i
$566$	−19.7153			−0.828698
$567$	−6.31032	−	19.4212i	−0.265009	−	0.815613i
$568$	−0.946391	+	0.687594i	−0.0397097	+	0.0288508i
$569$	−7.91647			−0.331876			−0.165938	−	0.986136i	$-0.553065\pi$
$569$	−7.91647			−0.331876			−0.165938	+	0.986136i	$0.553065\pi$
$570$	−2.83007	−	1.70386i	−0.118539	−	0.0713669i
$571$	−6.09902	−	4.43120i	−0.255236	−	0.185440i	0.452808	−	0.891608i	$-0.350422\pi$
$571$	−6.09902	−	4.43120i	−0.255236	−	0.185440i	−0.708044	+	0.706168i	$0.750422\pi$
$572$	1.44787	−	4.23134i	0.0605383	−	0.176921i
$573$	2.06578	−	6.35780i	0.0862990	−	0.265601i
$574$	2.94571	+	9.06596i	0.122952	+	0.378406i
$575$	31.8378	+	15.5976i	1.32773	+	0.650467i
$576$	16.2404	−	11.7993i	0.676682	−	0.491638i
$577$	7.07440	+	5.13985i	0.294511	+	0.213975i	0.725222	−	0.688515i	$-0.241737\pi$
$577$	7.07440	+	5.13985i	0.294511	+	0.213975i	−0.430711	+	0.902490i	$0.641737\pi$
$578$	47.0731	−	34.2006i	1.95798	−	1.42256i
$579$	−6.35080			−0.263930
$580$	0.137129	−	0.118993i	0.00569395	−	0.00494090i
$581$	2.56399	+	1.86285i	0.106372	+	0.0772840i
$582$	−0.825781			−0.0342297
$583$	−2.40601	−	7.81588i	−0.0996469	−	0.323701i
$584$	8.10260	+	24.9372i	0.335288	+	1.03191i
$585$	−15.2097	−	35.9195i	−0.628843	−	1.48509i
$586$	12.4031	−	9.01134i	0.512365	−	0.372255i
$587$	3.01918	+	2.19356i	0.124615	+	0.0905379i	0.648347	−	0.761345i	$-0.275461\pi$
$587$	3.01918	+	2.19356i	0.124615	+	0.0905379i	−0.523732	+	0.851883i	$0.675461\pi$
$588$	−0.0499651			−0.00206053
$589$	−2.83538	−	2.06002i	−0.116830	−	0.0848817i
$590$	11.9669	−	1.03637i	0.492669	−	0.0426668i
$591$	1.94071	−	5.97288i	0.0798301	−	0.245692i
$592$	−27.8540	−	20.2371i	−1.14479	−	0.831741i
$593$	3.53924			0.145339			0.0726697	−	0.997356i	$-0.476848\pi$
$593$	3.53924			0.145339			0.0726697	+	0.997356i	$0.476848\pi$
$594$	9.03054	+	0.140244i	0.370528	+	0.00575426i
$595$	−41.7823	+	3.61849i	−1.71291	+	0.148344i
$596$	−0.0976324	+	0.300482i	−0.00399918	+	0.0123082i
$597$	1.40555	+	4.32584i	0.0575254	+	0.177045i
$598$	19.6286	+	60.4105i	0.802672	+	2.47037i
$599$	4.08694	−	12.5783i	0.166988	−	0.513936i	−0.832189	−	0.554492i	$-0.812913\pi$
$599$	4.08694	−	12.5783i	0.166988	−	0.513936i	0.999177	+	0.0405554i	$0.0129127\pi$
$600$	4.03340	−	0.703892i	0.164663	−	0.0287363i
$601$	21.3749	−	15.5298i	0.871900	−	0.633473i	−0.0591960	−	0.998246i	$-0.518854\pi$
$601$	21.3749	−	15.5298i	0.871900	−	0.633473i	0.931096	+	0.364774i	$0.118854\pi$
$602$	20.5955	−	14.9635i	0.839411	−	0.609867i
$603$	14.3317	−	44.1086i	0.583634	−	1.79624i
$604$	1.70394	+	1.23799i	0.0693324	+	0.0503729i
$605$	8.88286	+	22.9368i	0.361140	+	0.932512i
$606$	5.01243	−	3.64174i	0.203616	−	0.147936i
$607$	−4.43491	−	13.6493i	−0.180007	−	0.554006i	0.819819	−	0.572622i	$-0.194074\pi$
$607$	−4.43491	−	13.6493i	−0.180007	−	0.554006i	−0.999827	+	0.0186164i	$0.994074\pi$
$608$	−4.04941			−0.164225
$609$	−0.226744	−	0.164739i	−0.00918815	−	0.00667558i
$610$	−37.5150	+	3.24893i	−1.51894	+	0.131545i
$611$	0.361412	+	0.262581i	0.0146212	+	0.0106229i
$612$	3.94796	+	2.86836i	0.159587	+	0.115947i
$613$	6.43081	−	19.7920i	0.259738	−	0.799392i	−0.733121	−	0.680098i	$-0.761937\pi$
$613$	6.43081	−	19.7920i	0.259738	−	0.799392i	0.992859	−	0.119293i	$-0.0380629\pi$
$614$	32.6782			1.31878
$615$	−1.33192	+	1.15577i	−0.0537081	+	0.0466049i
$616$	−7.12572	+	20.8247i	−0.287104	+	0.839052i
$617$	−20.2083	+	14.6822i	−0.813557	+	0.591084i	−0.914860	−	0.403772i	$-0.867699\pi$
$617$	−20.2083	+	14.6822i	−0.813557	+	0.591084i	0.101302	+	0.994856i	$0.467699\pi$
$618$	−1.02742	−	3.16208i	−0.0413289	−	0.127197i
$619$	15.4151			0.619586			0.309793	−	0.950804i	$-0.399740\pi$
$619$	15.4151			0.619586			0.309793	+	0.950804i	$0.399740\pi$
$620$	−0.547213	+	0.0473905i	−0.0219766	+	0.00190325i
$621$	−10.4736	+	7.60953i	−0.420292	+	0.305360i
$622$	−10.6996	+	7.77372i	−0.429015	+	0.311698i
$623$	0.895089	+	2.75480i	0.0358610	+	0.110369i
$624$	6.60930	+	4.80194i	0.264584	+	0.192231i
$625$	−24.0072	−	6.97534i	−0.960287	−	0.279014i
$626$	5.40014			0.215833
$627$	2.62744	+	1.97200i	0.104930	+	0.0787542i
$628$	1.05495	+	0.766465i	0.0420970	+	0.0305853i
$629$	−18.1025	+	55.7138i	−0.721794	+	2.22145i
$630$	−9.46503	−	22.3528i	−0.377096	−	0.890556i
$631$	−12.4364	+	38.2752i	−0.495083	+	1.52371i	0.321743	+	0.946827i	$0.395731\pi$
$631$	−12.4364	+	38.2752i	−0.495083	+	1.52371i	−0.816827	+	0.576883i	$0.804269\pi$
$632$	2.64362	−	8.13622i	0.105157	−	0.323641i
$633$	0.708501	+	2.18054i	0.0281604	+	0.0866687i
$634$	−34.0648	−	24.7496i	−1.35289	−	0.982931i
$635$	22.9511	−	1.98764i	0.910786	−	0.0788772i
$636$	−0.171176			−0.00678756
$637$	−1.33584	−	4.11128i	−0.0529277	−	0.162895i
$638$	−1.46353	+	1.02898i	−0.0579417	+	0.0407376i
$639$	−0.396472	+	1.22021i	−0.0156842	+	0.0482709i
$640$	21.6801	−	18.8128i	0.856979	−	0.743640i
$641$	1.82228	−	5.60839i	0.0719756	−	0.221518i	−0.908597	−	0.417673i	$-0.862846\pi$
$641$	1.82228	−	5.60839i	0.0719756	−	0.221518i	0.980573	+	0.196155i	$0.0628457\pi$
$642$	−1.93726	+	5.96227i	−0.0764576	+	0.235312i
$643$	8.40696	−	25.8740i	0.331538	−	1.02037i	−0.636864	−	0.770976i	$-0.719769\pi$
$643$	8.40696	−	25.8740i	0.331538	−	1.02037i	0.968402	−	0.249393i	$-0.0802312\pi$
$644$	1.23276	+	3.79405i	0.0485776	+	0.149506i
$645$	4.03468	+	2.42911i	0.158866	+	0.0956461i
$646$	11.0489	+	34.0051i	0.434714	+	1.33791i
$647$	8.51838	−	26.2169i	0.334892	−	1.03069i	−0.631883	−	0.775064i	$-0.717718\pi$
$647$	8.51838	−	26.2169i	0.334892	−	1.03069i	0.966775	−	0.255628i	$-0.0822824\pi$
$648$	6.66805	−	20.5222i	0.261946	−	0.806186i
$649$	−11.9439	−	0.185488i	−0.468839	−	0.00728103i
$650$	−20.9586	−	39.5850i	−0.822062	−	1.55265i
$651$	0.262013	+	0.806395i	0.0102691	+	0.0316051i
$652$	3.95694	−	2.87489i	0.154966	−	0.112589i
$653$	5.25938			0.205815			0.102908	−	0.994691i	$-0.467185\pi$
$653$	5.25938			0.205815			0.102908	+	0.994691i	$0.467185\pi$
$654$	3.65407	−	2.65484i	0.142885	−	0.103812i
$655$	−4.48699	+	19.3577i	−0.175321	+	0.756367i
$656$	−3.46656	+	10.6690i	−0.135346	+	0.416554i
$657$	23.2657	+	16.9035i	0.907682	+	0.659469i
$658$	0.224908	+	0.163405i	0.00876781	+	0.00637019i
$659$	−2.59805	−	7.99599i	−0.101206	−	0.311479i	0.887615	−	0.460585i	$-0.152360\pi$
$659$	−2.59805	−	7.99599i	−0.101206	−	0.311479i	−0.988821	+	0.149106i	$0.952360\pi$
$660$	0.513559	−	0.0364514i	0.0199903	−	0.00141887i
$661$	12.1895	−	37.5153i	0.474115	−	1.45918i	−0.373031	−	0.927819i	$-0.621682\pi$
$661$	12.1895	−	37.5153i	0.474115	−	1.45918i	0.847147	−	0.531359i	$-0.178318\pi$
$662$	−15.4470	+	11.2229i	−0.600363	+	0.436189i
$663$	4.29543	−	13.2200i	0.166821	−	0.513421i
$664$	1.03488	+	3.18502i	0.0401610	+	0.123603i
$665$	4.05314	−	17.4860i	0.157174	−	0.678077i
$666$	−33.9067			−1.31386
$667$	0.792462	−	2.43895i	0.0306843	−	0.0944365i
$668$	1.69966	+	1.23488i	0.0657619	+	0.0477788i
$669$	−2.63253	−	1.91265i	−0.101780	−	0.0739473i
$670$	12.0255	−	51.8801i	0.464585	−	2.00430i
$671$	37.4430	+	0.581487i	1.44547	+	0.0224480i
$672$	0.792571	+	0.575836i	0.0305741	+	0.0222134i
$673$	−8.30085			−0.319974			−0.159987	−	0.987119i	$-0.551145\pi$
$673$	−8.30085			−0.319974			−0.159987	+	0.987119i	$0.551145\pi$
$674$	11.4994	+	8.35479i	0.442940	+	0.321815i
$675$	6.35307	−	6.55570i	0.244530	−	0.252329i
$676$	1.60084	−	4.92688i	0.0615707	−	0.189495i
$677$	−27.4572	−	19.9488i	−1.05527	−	0.766696i	−0.0820595	−	0.996627i	$-0.526150\pi$
$677$	−27.4572	−	19.9488i	−1.05527	−	0.766696i	−0.973207	+	0.229932i	$0.926150\pi$
$678$	−3.13241			−0.120299
$679$	−1.38657	−	4.26741i	−0.0532116	−	0.163768i
$680$	−37.9663	−	22.8579i	−1.45594	−	0.876560i
$681$	−2.01142	+	1.46138i	−0.0770776	+	0.0560002i
$682$	5.41169	+	0.0840432i	0.207224	+	0.00321818i
$683$	−28.3208	+	20.5763i	−1.08367	+	0.787330i	−0.978319	−	0.207106i	$-0.933596\pi$
$683$	−28.3208	+	20.5763i	−1.08367	+	0.787330i	−0.105348	+	0.994435i	$0.533596\pi$
$684$	−1.68971	+	1.22765i	−0.0646077	+	0.0469402i
$685$	11.0635	−	9.60030i	0.422714	−	0.366809i
$686$	−8.91641	−	27.4419i	−0.340430	−	1.04774i
$687$	−3.23332			−0.123359
$688$	29.9588			1.14217
$689$	−4.57644	−	14.0848i	−0.174349	−	0.536590i
$690$	−5.52304	+	4.79259i	−0.210258	+	0.182451i
$691$	21.5591	−	15.6636i	0.820148	−	0.595873i	−0.0966066	−	0.995323i	$-0.530799\pi$
$691$	21.5591	−	15.6636i	0.820148	−	0.595873i	0.916755	+	0.399450i	$0.130799\pi$
$692$	−2.34134	+	1.70108i	−0.0890044	+	0.0646655i
$693$	7.10229	+	23.0717i	0.269794	+	0.876420i
$694$	−23.3398	+	16.9573i	−0.885966	+	0.643692i
$695$	30.4404	+	18.3269i	1.15467	+	0.695177i
$696$	−0.0915184	−	0.281665i	−0.00346900	−	0.0106765i
$697$	19.0872			0.722980
$698$	−2.12113	−	1.54109i	−0.0802858	−	0.0583311i
$699$	0.224338	−	0.690441i	0.00848523	−	0.0261149i
$700$	−1.31629	−	2.48611i	−0.0497511	−	0.0939661i
$701$	29.7061	+	21.5828i	1.12199	+	0.815170i	0.984509	−	0.175335i	$-0.0561008\pi$
$701$	29.7061	+	21.5828i	1.12199	+	0.815170i	0.137477	+	0.990505i	$0.456101\pi$
$702$	16.3559			0.617313
$703$	−20.2840	−	14.7372i	−0.765025	−	0.555823i
$704$	−18.7525	+	13.1845i	−0.706762	+	0.496910i
$705$	−0.0116129	+	0.0501003i	−0.000437369	+	0.00188689i
$706$	1.30899	+	0.951035i	0.0492644	+	0.0357927i
$707$	27.2359	+	19.7881i	1.02431	+	0.744206i
$708$	−0.0772654	+	0.237798i	−0.00290381	+	0.00893701i
$709$	−21.4868			−0.806955			−0.403478	−	0.914990i	$-0.632199\pi$
$709$	−21.4868			−0.806955			−0.403478	+	0.914990i	$0.632199\pi$
$710$	−0.332671	+	1.43520i	−0.0124849	+	0.0538623i
$711$	−2.89945	−	8.92358i	−0.108738	−	0.334661i
$712$	−0.945831	+	2.91097i	−0.0354465	+	0.109093i
$713$	−6.27648	+	4.56013i	−0.235056	+	0.170778i
$714$	2.67306	−	8.22682i	0.100037	−	0.307881i
$715$	16.7295	+	41.2826i	0.625649	+	1.54388i
$716$	0.477428	+	1.46937i	0.0178423	+	0.0549131i
$717$	4.40500	+	3.20042i	0.164508	+	0.119522i
$718$	2.97401	+	2.16074i	0.110989	+	0.0806382i
$719$	−9.50569	+	29.2555i	−0.354502	+	1.09105i	0.601795	+	0.798651i	$0.294452\pi$
$719$	−9.50569	+	29.2555i	−0.354502	+	1.09105i	−0.956297	+	0.292396i	$0.905548\pi$
$720$	6.45046	−	27.8284i	0.240394	−	1.03710i
$721$	14.6156	−	10.6189i	0.544314	−	0.395467i
$722$	13.0350			0.485114
$723$	−6.00815	+	4.36518i	−0.223446	+	0.162343i
$724$	−0.183809	−	0.565705i	−0.00683120	−	0.0210243i
$725$	−0.254819	+	1.79030i	−0.00946373	+	0.0664900i
$726$	−5.07083	−	0.157537i	−0.188196	−	0.00584675i
$727$	−2.94379	+	9.06005i	−0.109179	+	0.336019i	−0.990689	−	0.136148i	$-0.956528\pi$
$727$	−2.94379	+	9.06005i	−0.109179	+	0.336019i	0.881509	+	0.472166i	$0.156528\pi$
$728$	−12.3172	+	37.9085i	−0.456506	+	1.40498i
$729$	−6.78993	−	20.8973i	−0.251479	−	0.773973i
$730$	28.2907	+	17.0326i	1.04708	+	0.630404i
$731$	−15.7519	−	48.4793i	−0.582604	−	1.79307i
$732$	0.242220	−	0.745475i	0.00895269	−	0.0275536i
$733$	−2.93552	+	9.03461i	−0.108426	+	0.333701i	−0.990519	−	0.137374i	$-0.956134\pi$
$733$	−2.93552	+	9.03461i	−0.108426	+	0.333701i	0.882093	+	0.471075i	$0.156134\pi$
$734$	6.33845	−	19.5077i	0.233956	−	0.720044i
$735$	0.375874	−	0.326163i	0.0138643	−	0.0120307i
$736$	−2.77000	+	8.52519i	−0.102104	+	0.314243i
$737$	−17.1461	+	50.1091i	−0.631586	+	1.84579i
$738$	3.41392	+	10.5070i	0.125668	+	0.386767i
$739$	−19.3312			−0.711110			−0.355555	−	0.934655i	$-0.615708\pi$
$739$	−19.3312			−0.711110			−0.355555	+	0.934655i	$0.615708\pi$
$740$	−3.91471	+	0.339027i	−0.143907	+	0.0124629i
$741$	4.81306	+	3.49689i	0.176812	+	0.128461i
$742$	−2.84793	−	8.76504i	−0.104551	−	0.321775i
$743$	−7.03300	+	21.6454i	−0.258016	+	0.794091i	0.735205	+	0.677845i	$0.237086\pi$
$743$	−7.03300	+	21.6454i	−0.258016	+	0.794091i	−0.993220	+	0.116246i	$0.962914\pi$
$744$	−0.276867	+	0.852108i	−0.0101504	+	0.0312398i
$745$	−1.22703	−	2.89777i	−0.0449547	−	0.106166i
$746$	−2.93709	+	9.03945i	−0.107535	+	0.330958i
$747$	2.97153	+	2.15895i	0.108723	+	0.0789917i
$748$	−4.45693	−	3.34511i	−0.162961	−	0.122309i
$749$	−34.0643			−1.24468
$750$	3.25561	−	3.99875i	0.118878	−	0.146014i
$751$	−27.5785	−	20.0370i	−1.00636	−	0.731160i	−0.0429137	−	0.999079i	$-0.513664\pi$
$751$	−27.5785	−	20.0370i	−1.00636	−	0.731160i	−0.963441	+	0.267919i	$0.913664\pi$
$752$	0.101097	+	0.311144i	0.00368663	+	0.0113463i
$753$	1.39805	−	1.01574i	0.0509476	−	0.0370156i
$754$	−2.62113	+	1.90436i	−0.0954559	+	0.0693528i
$755$	−20.8996	+	1.80998i	−0.760615	+	0.0658719i
$756$	1.02722			0.0373597
$757$	−3.80972	−	11.7251i	−0.138467	−	0.426156i	0.857647	−	0.514240i	$-0.171926\pi$
$757$	−3.80972	−	11.7251i	−0.138467	−	0.426156i	−0.996113	+	0.0880834i	$0.971926\pi$
$758$	−37.1269	+	26.9743i	−1.34851	+	0.979751i
$759$	5.94894	−	4.18258i	0.215933	−	0.151818i
$760$	14.3256	−	12.4310i	0.519644	−	0.450919i
$761$	49.8759			1.80800			0.904000	−	0.427532i	$-0.140617\pi$
$761$	49.8759			1.80800			0.904000	+	0.427532i	$0.140617\pi$
$762$	−1.46831	+	4.51901i	−0.0531914	+	0.163706i
$763$	19.8550	+	14.4255i	0.718800	+	0.522239i
$764$	−3.92645	−	2.85273i	−0.142054	−	0.103208i
$765$	−48.4235	+	4.19364i	−1.75076	+	0.151622i
$766$	38.6021	+	28.0461i	1.39475	+	1.01335i
$767$	−21.6325			−0.781103
$768$	0.508621	+	1.56537i	0.0183533	+	0.0564856i
$769$	10.1343	−	7.36301i	0.365453	−	0.265517i	−0.389870	−	0.920870i	$-0.627480\pi$
$769$	10.1343	−	7.36301i	0.365453	−	0.265517i	0.755323	+	0.655353i	$0.227480\pi$
$770$	10.4108	+	25.6903i	0.375180	+	0.925814i
$771$	1.95935	+	1.42355i	0.0705644	+	0.0512680i
$772$	−1.42479	+	4.38507i	−0.0512795	+	0.157822i
$773$	−28.3661	+	20.6091i	−1.02026	+	0.741260i	−0.966335	−	0.257286i	$-0.917172\pi$
$773$	−28.3661	+	20.6091i	−1.02026	+	0.741260i	−0.0539209	+	0.998545i	$0.517172\pi$
$774$	23.8691	−	17.3419i	0.857958	−	0.623343i
$775$	3.80717	−	3.92861i	0.136758	−	0.141120i
$776$	1.46517	−	4.50933i	0.0525965	−	0.161876i
$777$	1.87442	+	5.76887i	0.0672444	+	0.206957i
$778$	−4.36873	−	13.4456i	−0.156626	−	0.482047i
$779$	−2.52444	+	7.76941i	−0.0904473	+	0.278368i
$780$	0.928895	−	0.0804455i	0.0332598	−	0.00288041i
$781$	0.474329	−	1.38621i	0.0169728	−	0.0496026i
$782$	79.1486			2.83035
$783$	−0.534222	−	0.388135i	−0.0190915	−	0.0138708i
$784$	0.978281	−	3.01084i	0.0349386	−	0.107530i
$785$	−12.9394	+	1.12060i	−0.461828	+	0.0399959i
$786$	−3.31578	−	2.40906i	−0.118270	−	0.0859282i
$787$	1.06338			0.0379053			0.0189527	−	0.999820i	$-0.493967\pi$
$787$	1.06338			0.0379053			0.0189527	+	0.999820i	$0.493967\pi$
$788$	−3.68873	−	2.68002i	−0.131406	−	0.0954718i
$789$	1.61902	−	1.17628i	0.0576385	−	0.0418768i
$790$	−4.20106	−	9.92131i	−0.149467	−	0.352985i
$791$	−5.25962	−	16.1875i	−0.187011	−	0.575560i
$792$	−8.25834	+	24.1348i	−0.293447	+	0.857591i
$793$	67.8157			2.40821
$794$	−35.1557	−	25.5421i	−1.24763	−	0.906455i
$795$	1.28771	−	1.11740i	0.0456703	−	0.0396302i
$796$	3.30222			0.117044
$797$	−10.8878	+	7.91048i	−0.385667	+	0.280203i	−0.763678	−	0.645598i	$-0.776608\pi$
$797$	−10.8878	+	7.91048i	−0.385667	+	0.280203i	0.378011	+	0.925801i	$0.376608\pi$
$798$	2.99518	+	2.17613i	0.106028	+	0.0770340i
$799$	0.450339	−	0.327190i	0.0159318	−	0.0115752i
$800$	0.890702	−	6.25787i	0.0314911	−	0.221249i
$801$	1.03736	+	3.19267i	0.0366534	+	0.112807i
$802$	−6.54922	+	20.1564i	−0.231261	+	0.711748i
$803$	−26.2651	−	19.7130i	−0.926875	−	0.695658i
$804$	0.896853	+	0.651602i	0.0316296	+	0.0229802i
$805$	−34.0405	−	20.4943i	−1.19977	−	0.722331i
$806$	9.80151			0.345244
$807$	1.26505	−	0.919111i	0.0445318	−	0.0323542i
$808$	10.9929	+	33.8328i	0.386730	+	1.19023i
$809$	−32.0842			−1.12802			−0.564010	−	0.825768i	$-0.690742\pi$
$809$	−32.0842			−1.12802			−0.564010	+	0.825768i	$0.690742\pi$
$810$	−10.5964	−	25.0247i	−0.372321	−	0.879279i
$811$	7.12937	−	5.17979i	0.250346	−	0.181887i	−0.455534	−	0.890218i	$-0.650552\pi$
$811$	7.12937	−	5.17979i	0.250346	−	0.181887i	0.705880	+	0.708331i	$0.250552\pi$
$812$	−0.164618	+	0.119602i	−0.00577698	+	0.00419722i
$813$	0.274028	+	0.843372i	0.00961059	+	0.0295784i
$814$	38.7147	+	0.601236i	1.35695	+	0.0210733i
$815$	−11.0003	+	47.4572i	−0.385323	+	1.66235i
$816$	8.23555	−	5.98348i	0.288302	−	0.209464i
$817$	21.8167			0.763270
$818$	−20.3541	+	14.7881i	−0.711664	+	0.517054i
$819$	13.5092	+	41.5770i	0.472049	+	1.45282i
$820$	0.499213	+	1.17895i	0.0174333	+	0.0411708i
$821$	48.3893			1.68880			0.844400	−	0.535713i	$-0.179957\pi$
$821$	48.3893			1.68880			0.844400	+	0.535713i	$0.179957\pi$
$822$	0.933629	+	2.87341i	0.0325640	+	0.100222i
$823$	13.9184			0.485164			0.242582	−	0.970131i	$-0.422006\pi$
$823$	13.9184			0.485164			0.242582	+	0.970131i	$0.422006\pi$
$824$	19.0900			0.665033
$825$	−3.62542	+	3.62663i	−0.126221	+	0.126263i
$826$	−13.4619			−0.468401
$827$	−12.3426			−0.429195			−0.214597	−	0.976703i	$-0.568844\pi$
$827$	−12.3426			−0.429195			−0.214597	+	0.976703i	$0.568844\pi$
$828$	1.42870	+	4.39710i	0.0496509	+	0.152810i
$829$	10.8286			0.376094			0.188047	−	0.982160i	$-0.439784\pi$
$829$	10.8286			0.376094			0.188047	+	0.982160i	$0.439784\pi$
$830$	3.61333	+	2.17543i	0.125420	+	0.0755103i
$831$	1.76806	+	5.44153i	0.0613333	+	0.188765i
$832$	−33.5851	+	24.4010i	−1.16435	+	0.845952i
$833$	−5.38651			−0.186631
$834$	−5.92902	+	4.30768i	−0.205305	+	0.149163i
$835$	−20.8471	+	1.80543i	−0.721445	+	0.0624796i
$836$	1.95108	−	1.37177i	0.0674796	−	0.0474435i
$837$	0.617317	+	1.89991i	0.0213376	+	0.0656704i
$838$	−16.7860	+	12.1958i	−0.579864	+	0.421296i
$839$	−8.37057	+	6.08158i	−0.288984	+	0.209959i	−0.722827	−	0.691029i	$-0.757157\pi$
$839$	−8.37057	+	6.08158i	−0.288984	+	0.209959i	0.433842	+	0.900989i	$0.357157\pi$
$840$	−4.57159	+	0.395916i	−0.157735	+	0.0136604i
$841$	−28.8692			−0.995490
$842$	−1.55466	−	4.78475i	−0.0535771	−	0.164893i
$843$	−2.61133	+	1.89724i	−0.0899389	+	0.0653444i
$844$	1.66456			0.0572966
$845$	20.1190	+	47.5135i	0.692116	+	1.63451i
$846$	0.260656	+	0.189378i	0.00896154	+	0.00651094i
$847$	−7.70031	−	26.4692i	−0.264586	−	0.909492i
$848$	3.35150	−	10.3148i	0.115091	−	0.354213i
$849$	1.26313	+	3.88753i	0.0433507	+	0.133420i
$850$	−54.9810	+	9.59505i	−1.88583	+	0.329108i
$851$	−44.9013	+	32.6227i	−1.53920	+	1.11829i
$852$	−0.0248104	−	0.0180258i	−0.000849992	−	0.000617555i
$853$	−41.3133	+	30.0159i	−1.41454	+	1.02772i	−0.421899	+	0.906643i	$0.638636\pi$
$853$	−41.3133	+	30.0159i	−1.41454	+	1.02772i	−0.992643	+	0.121081i	$0.961364\pi$
$854$	42.2019			1.44412
$855$	4.69738	−	20.2653i	0.160647	−	0.693060i
$856$	−29.1208	−	21.1575i	−0.995330	−	0.723150i
$857$	−44.8864			−1.53329			−0.766644	−	0.642072i	$-0.778075\pi$
$857$	−44.8864			−1.53329			−0.766644	+	0.642072i	$0.778075\pi$
$858$	−9.18636	−	0.142663i	−0.313617	−	0.00487045i
$859$	−0.615385	−	1.89396i	−0.0209967	−	0.0646211i	0.940009	−	0.341149i	$-0.110816\pi$
$859$	−0.615385	−	1.89396i	−0.0209967	−	0.0646211i	−0.961006	+	0.276528i	$0.910816\pi$
$860$	2.58242	−	2.24088i	0.0880597	−	0.0764134i
$861$	1.59892	−	1.16169i	0.0544912	−	0.0395902i
$862$	10.2914	+	7.47716i	0.350527	+	0.254673i
$863$	53.4583			1.81974			0.909871	−	0.414890i	$-0.136180\pi$
$863$	53.4583			1.81974			0.909871	+	0.414890i	$0.136180\pi$
$864$	1.86734	+	1.35670i	0.0635281	+	0.0461559i
$865$	6.50891	−	28.0806i	0.221309	−	0.954769i
$866$	8.03915	−	24.7420i	0.273181	−	0.840766i
$867$	−9.75969	−	7.09083i	−0.331456	−	0.240817i
$868$	0.615578			0.0208941
$869$	3.15236	+	10.2404i	0.106937	+	0.347381i
$870$	−0.319541	−	0.192382i	−0.0108335	−	0.00652237i
$871$	−29.6381	+	91.2166i	−1.00425	+	3.09076i
$872$	8.01387	+	24.6642i	0.271384	+	0.835234i
$873$	−1.60696	−	4.94571i	−0.0543873	−	0.167387i
$874$	−10.4680	+	32.2173i	−0.354086	+	1.08977i
$875$	26.1309	+	10.1098i	0.883387	+	0.341775i
$876$	−0.556114	+	0.404040i	−0.0187893	+	0.0136513i
$877$	4.50955	−	3.27638i	0.152277	−	0.110636i	−0.509038	−	0.860744i	$-0.669999\pi$
$877$	4.50955	−	3.27638i	0.152277	−	0.110636i	0.661315	+	0.750108i	$0.269999\pi$
$878$	6.97335	−	21.4618i	0.235339	−	0.724300i
$879$	−2.57153	−	1.86832i	−0.0867355	−	0.0630170i
$880$	−7.85860	+	31.6602i	−0.264913	+	1.06726i
$881$	34.9606	−	25.4004i	1.17785	−	0.855760i	0.185925	−	0.982564i	$-0.440472\pi$
$881$	34.9606	−	25.4004i	1.17785	−	0.855760i	0.991928	+	0.126803i	$0.0404717\pi$
$882$	−0.963426	−	2.96512i	−0.0324403	−	0.0998408i
$883$	−37.5809			−1.26470			−0.632350	−	0.774683i	$-0.717909\pi$
$883$	−37.5809			−1.26470			−0.632350	+	0.774683i	$0.717909\pi$
$884$	−8.16439	−	5.93177i	−0.274598	−	0.199507i
$885$	−0.971056	−	2.29326i	−0.0326417	−	0.0770873i
$886$	−25.3215	−	18.3971i	−0.850692	−	0.618064i
$887$	19.4062	+	14.0995i	0.651597	+	0.473413i	0.863815	−	0.503809i	$-0.168069\pi$
$887$	19.4062	+	14.0995i	0.651597	+	0.473413i	−0.212218	+	0.977222i	$0.568069\pi$
$888$	−1.98068	+	6.09590i	−0.0664672	+	0.204565i
$889$	−25.8185			−0.865923
$890$	1.50305	+	3.54964i	0.0503824	+	0.118984i
$891$	7.95127	+	25.8295i	0.266377	+	0.865321i
$892$	−1.91124	+	1.38860i	−0.0639932	+	0.0464938i
$893$	0.0736213	+	0.226583i	0.00246364	+	0.00758231i
$894$	0.649062			0.0217079
$895$	−13.1833	−	7.93713i	−0.440671	−	0.265309i
$896$	−26.0262	+	18.9092i	−0.869475	+	0.631710i
$897$	10.6543	−	7.74083i	0.355738	−	0.258459i
$898$	−7.89420	−	24.2959i	−0.263433	−	0.810763i
$899$	−0.320141	−	0.232596i	−0.0106773	−	0.00775750i
$900$	−1.52551	−	2.88127i	−0.0508504	−	0.0960424i
$901$	−18.4537			−0.614780
$902$	−3.71171	−	12.0574i	−0.123587	−	0.401468i
$903$	−4.27007	−	3.10239i	−0.142099	−	0.103241i
$904$	5.55779	−	17.1051i	0.184849	−	0.568907i
$905$	5.07556	+	3.05578i	0.168717	+	0.101577i
$906$	1.33707	−	4.11508i	0.0444212	−	0.136714i
$907$	−0.415545	+	1.27892i	−0.0137980	+	0.0424657i	−0.957718	−	0.287707i	$-0.907107\pi$
$907$	−0.415545	+	1.27892i	−0.0137980	+	0.0424657i	0.943920	+	0.330173i	$0.107107\pi$
$908$	0.557787	+	1.71669i	0.0185108	+	0.0569704i
$909$	31.5650	+	22.9333i	1.04695	+	0.760650i
$910$	19.5737	+	46.2256i	0.648862	+	1.53236i
$911$	−44.0724			−1.46018			−0.730092	−	0.683349i	$-0.760523\pi$
$911$	−44.0724			−1.46018			−0.730092	+	0.683349i	$0.760523\pi$
$912$	1.34635	+	4.14363i	0.0445820	+	0.137209i
$913$	−3.35462	−	2.51778i	−0.111022	−	0.0833263i
$914$	−6.38255	+	19.6435i	−0.211116	+	0.649748i
$915$	3.04417	+	7.18917i	0.100637	+	0.237667i
$916$	−0.725393	+	2.23253i	−0.0239677	+	0.0737649i
$917$	6.88183	−	21.1801i	0.227258	−	0.699429i
$918$	6.29786	−	19.3828i	0.207860	−	0.639728i
$919$	11.8595	+	36.4997i	0.391207	+	1.20401i	0.931876	+	0.362777i	$0.118171\pi$
$919$	11.8595	+	36.4997i	0.391207	+	1.20401i	−0.540668	+	0.841236i	$0.681829\pi$
$920$	−16.3714	−	38.6630i	−0.539749	−	1.27468i
$921$	−2.09365	−	6.44358i	−0.0689880	−	0.212323i
$922$	5.48975	−	16.8957i	0.180795	−	0.556431i
$923$	0.819904	−	2.52340i	0.0269875	−	0.0830589i
$924$	−0.576944	−	0.00895990i	−0.0189801	−	0.000294759i
$925$	27.2361	−	28.1049i	0.895519	−	0.924082i
$926$	−18.9522	−	58.3288i	−0.622808	−	1.91680i
$927$	16.9387	−	12.3067i	0.556341	−	0.404206i
$928$	−0.457217			−0.0150089
$929$	−3.65412	+	2.65488i	−0.119888	+	0.0871036i	−0.646113	−	0.763241i	$-0.723607\pi$
$929$	−3.65412	+	2.65488i	−0.119888	+	0.0871036i	0.526226	+	0.850345i	$0.323607\pi$
$930$	0.439978	+	1.03906i	0.0144275	+	0.0340722i
$931$	0.712409	−	2.19257i	0.0233482	−	0.0718585i
$932$	−0.426402	−	0.309799i	−0.0139673	−	0.0101478i
$933$	2.21835	+	1.61173i	0.0726256	+	0.0527656i
$934$	7.70963	+	23.7278i	0.252267	+	0.776397i
$935$	55.3644	−	3.92966i	1.81061	−	0.128514i
$936$	−14.2750	+	43.9339i	−0.466593	+	1.43602i
$937$	18.5232	−	13.4579i	0.605126	−	0.439650i	−0.242569	−	0.970134i	$-0.577990\pi$
$937$	18.5232	−	13.4579i	0.605126	−	0.439650i	0.847695	+	0.530485i	$0.177990\pi$
$938$	−18.4438	+	56.7643i	−0.602213	+	1.85342i
$939$	−0.345979	−	1.06482i	−0.0112906	−	0.0347489i
$940$	0.0319877	+	0.0192584i	0.00104332	+	0.000628140i
$941$	45.6273			1.48741			0.743705	−	0.668508i	$-0.233067\pi$
$941$	45.6273			1.48741			0.743705	+	0.668508i	$0.233067\pi$
$942$	0.827810	−	2.54774i	0.0269715	−	0.0830098i
$943$	14.6300	+	10.6293i	0.476419	+	0.346139i
$944$	−12.8167	−	9.31184i	−0.417146	−	0.303075i
$945$	−7.72750	+	6.70550i	−0.251376	+	0.218130i
$946$	−27.5613	+	19.3778i	−0.896096	+	0.630027i
$947$	−11.6400	−	8.45699i	−0.378251	−	0.274815i	0.382373	−	0.924008i	$-0.375107\pi$
$947$	−11.6400	−	8.45699i	−0.378251	−	0.274815i	−0.760624	+	0.649193i	$0.775107\pi$
$948$	0.224275			0.00728410
$949$	−48.1135	−	34.9565i	−1.56183	−	1.13474i
$950$	3.36603	−	23.6489i	0.109208	−	0.767273i
$951$	−2.69770	+	8.30267i	−0.0874790	+	0.269233i
$952$	40.1813	+	29.1934i	1.30228	+	0.946165i
$953$	8.52795			0.276247			0.138124	−	0.990415i	$-0.455893\pi$
$953$	8.52795			0.276247			0.138124	+	0.990415i	$0.455893\pi$
$954$	−3.30061	−	10.1582i	−0.106861	−	0.328884i
$955$	48.1597	−	4.17080i	1.55841	−	0.134964i
$956$	3.19807	−	2.32353i	0.103433	−	0.0751485i
$957$	0.296663	+	0.222658i	0.00958975	+	0.00719750i
$958$	15.1585	−	11.0133i	0.489750	−	0.355824i
$959$	−13.2814	+	9.64949i	−0.428878	+	0.311598i
$960$	−4.09435	−	2.46503i	−0.132145	−	0.0795586i
$961$	−9.20959	−	28.3442i	−0.297084	−	0.914329i
$962$	70.1190			2.26073
$963$	−39.4787			−1.27218
$964$	1.66612	+	5.12780i	0.0536623	+	0.165155i
$965$	−17.9065	−	42.2884i	−0.576432	−	1.36131i
$966$	6.63023	−	4.81714i	0.213324	−	0.154989i
$967$	38.8419	−	28.2203i	1.24907	−	0.907503i	0.250904	−	0.968012i	$-0.419272\pi$
$967$	38.8419	−	28.2203i	1.24907	−	0.907503i	0.998168	+	0.0605088i	$0.0192723\pi$
$968$	9.85735	−	27.4107i	0.316827	−	0.881013i
$969$	5.99733	−	4.35731i	0.192662	−	0.139977i
$970$	−2.32835	−	5.49868i	−0.0747589	−	0.176552i
$971$	2.68378	+	8.25983i	0.0861266	+	0.265070i	0.984840	−	0.173466i	$-0.0554968\pi$
$971$	2.68378	+	8.25983i	0.0861266	+	0.265070i	−0.898713	+	0.438537i	$0.855497\pi$
$972$	1.79538			0.0575869
$973$	−32.2163	−	23.4065i	−1.03281	−	0.750379i
$974$	11.6695	−	35.9150i	0.373914	−	1.15079i
$975$	−6.46269	+	6.66882i	−0.206972	+	0.213573i
$976$	40.1790	+	29.1917i	1.28610	+	0.934405i
$977$	8.22015			0.262986			0.131493	−	0.991317i	$-0.458023\pi$
$977$	8.22015			0.262986			0.131493	+	0.991317i	$0.458023\pi$
$978$	−8.12895	−	5.90603i	−0.259935	−	0.188854i
$979$	−1.12785	−	3.66379i	−0.0360462	−	0.117095i
$980$	−0.140880	−	0.332706i	−0.00450026	−	0.0106279i
$981$	23.0109	+	16.7184i	0.734683	+	0.533778i
$982$	1.03781	+	0.754013i	0.0331179	+	0.0240615i
$983$	12.2718	−	37.7686i	0.391409	−	1.20463i	−0.540315	−	0.841463i	$-0.681695\pi$
$983$	12.2718	−	37.7686i	0.391409	−	1.20463i	0.931723	−	0.363169i	$-0.118305\pi$
$984$	2.08842			0.0665763
$985$	45.2440	−	3.91829i	1.44159	−	0.124847i
$986$	1.24753	+	3.83949i	0.0397294	+	0.122274i
$987$	0.0178111	−	0.0548170i	0.000566935	−	0.00174485i
$988$	3.49432	−	2.53877i	0.111169	−	0.0807691i
$989$	14.9237	−	45.9305i	0.474547	−	1.46051i
$990$	12.0656	+	29.7737i	0.383470	+	0.946271i
$991$	6.86301	+	21.1222i	0.218011	+	0.670968i	0.998926	+	0.0463310i	$0.0147529\pi$
$991$	6.86301	+	21.1222i	0.218011	+	0.670968i	−0.780916	+	0.624637i	$0.785247\pi$
$992$	1.11903	+	0.813024i	0.0355293	+	0.0258135i
$993$	3.20262	+	2.32684i	0.101632	+	0.0738401i
$994$	0.510229	−	1.57032i	0.0161835	−	0.0498076i
$995$	−24.8417	+	21.5563i	−0.787535	+	0.683380i
$996$	−0.0710277	+	0.0516047i	−0.00225060	+	0.00163516i
$997$	−21.2734			−0.673737			−0.336868	−	0.941552i	$-0.609368\pi$
$997$	−21.2734			−0.673737			−0.336868	+	0.941552i	$0.609368\pi$
$998$	25.8212	−	18.7602i	0.817355	−	0.593843i
$999$	4.41623	+	13.5917i	0.139723	+	0.430024i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.l.d.71.7	yes	100
11.9	even	5		275.2.k.d.196.19	yes	100
25.6	even	5		275.2.k.d.181.19	✓	100
275.31	even	5	inner	275.2.l.d.31.7	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.2.k.d.181.19	✓	100	25.6	even	5
275.2.k.d.196.19	yes	100	11.9	even	5
275.2.l.d.31.7	yes	100	275.31	even	5	inner
275.2.l.d.71.7	yes	100	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.l (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-1.49148 q^{2} +(0.0955568 + 0.294094i) q^{3} +0.224502 q^{4} +(-1.68887 + 1.46551i) q^{5} +(-0.142521 - 0.438634i) q^{6} +(2.02744 - 1.47302i) q^{7} +2.64811 q^{8} +(2.34969 - 1.70715i) q^{9} +(2.51891 - 2.18577i) q^{10} +(-2.71315 + 1.90756i) q^{11} +(0.0214527 + 0.0660247i) q^{12} +(-4.85916 + 3.53039i) q^{13} +(-3.02387 + 2.19697i) q^{14} +(-0.592380 - 0.356646i) q^{15} -4.39860 q^{16} +(2.31272 + 7.11782i) q^{17} +(-3.50451 + 2.54618i) q^{18} -3.20317 q^{19} +(-0.379156 + 0.329011i) q^{20} +(0.626940 + 0.455499i) q^{21} +(4.04661 - 2.84509i) q^{22} +(-2.19113 + 6.74361i) q^{23} +(0.253045 + 0.778793i) q^{24} +(0.704565 - 4.95011i) q^{25} +(7.24733 - 5.26549i) q^{26} +(1.47710 + 1.07318i) q^{27} +(0.455164 - 0.330696i) q^{28} -0.361668 q^{29} +(0.883521 + 0.531930i) q^{30} +(0.885177 + 0.643119i) q^{31} +1.26419 q^{32} +(-0.820262 - 0.615640i) q^{33} +(-3.44937 - 10.6161i) q^{34} +(-1.26535 + 5.45896i) q^{35} +(0.527511 - 0.383260i) q^{36} +(6.33247 + 4.60081i) q^{37} +4.77745 q^{38} +(-1.50259 - 1.09170i) q^{39} +(-4.47232 + 3.88083i) q^{40} +(0.788105 - 2.42554i) q^{41} +(-0.935067 - 0.679366i) q^{42} -6.81097 q^{43} +(-0.609110 + 0.428253i) q^{44} +(-1.46648 + 6.32665i) q^{45} +(3.26802 - 10.0579i) q^{46} +(-0.0229839 - 0.0707371i) q^{47} +(-0.420316 - 1.29360i) q^{48} +(-0.222407 + 0.684499i) q^{49} +(-1.05084 + 7.38297i) q^{50} +(-1.87231 + 1.36031i) q^{51} +(-1.09089 + 0.792581i) q^{52} +(-0.761946 + 2.34503i) q^{53} +(-2.20307 - 1.60062i) q^{54} +(1.78661 - 7.19778i) q^{55} +(5.36888 - 3.90072i) q^{56} +(-0.306085 - 0.942032i) q^{57} +0.539420 q^{58} +(2.91380 + 2.11700i) q^{59} +(-0.132991 - 0.0800680i) q^{60} +(-9.13449 - 6.63659i) q^{61} +(-1.32022 - 0.959197i) q^{62} +(2.24918 - 6.92227i) q^{63} +6.91170 q^{64} +(3.03268 - 13.0835i) q^{65} +(1.22340 + 0.918213i) q^{66} +(12.9188 - 9.38603i) q^{67} +(0.519212 + 1.59797i) q^{68} -2.19263 q^{69} +(1.88724 - 8.14191i) q^{70} +(-0.357383 + 0.259654i) q^{71} +(6.22225 - 4.52073i) q^{72} +(3.05976 + 9.41698i) q^{73} +(-9.44473 - 6.86200i) q^{74} +(1.52312 - 0.265809i) q^{75} -0.719120 q^{76} +(-2.69087 + 7.86398i) q^{77} +(2.24108 + 1.62824i) q^{78} +(0.998303 - 3.07246i) q^{79} +(7.42867 - 6.44619i) q^{80} +(2.51804 - 7.74973i) q^{81} +(-1.17544 + 3.61763i) q^{82} +(0.390798 + 1.20275i) q^{83} +(0.140750 + 0.102261i) q^{84} +(-14.3371 - 8.63176i) q^{85} +10.1584 q^{86} +(-0.0345599 - 0.106364i) q^{87} +(-7.18474 + 5.05144i) q^{88} +(-0.357172 + 1.09926i) q^{89} +(2.18722 - 9.43605i) q^{90} +(-4.65131 + 14.3153i) q^{91} +(-0.491914 + 1.51396i) q^{92} +(-0.104552 + 0.321779i) q^{93} +(0.0342799 + 0.105503i) q^{94} +(5.40974 - 4.69428i) q^{95} +(0.120802 + 0.371790i) q^{96} +(0.553288 - 1.70285i) q^{97} +(0.331715 - 1.02091i) q^{98} +(-3.11858 + 9.11395i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 2 q^{2} - 2 q^{3} + 106 q^{4} + 5 q^{5} + 5 q^{6} + 5 q^{7} - 30 q^{8} - 25 q^{9} - 22 q^{10} - 53 q^{12} - 18 q^{13} - 10 q^{14} + 16 q^{15} + 62 q^{16} + q^{17} - 21 q^{18} + 6 q^{19} + q^{20}+ \cdots - 84 q^{99}+O(q^{100}) \) 100 * q + 2 * q^2 - 2 * q^3 + 106 * q^4 + 5 * q^5 + 5 * q^6 + 5 * q^7 - 30 * q^8 - 25 * q^9 - 22 * q^10 - 53 * q^12 - 18 * q^13 - 10 * q^14 + 16 * q^15 + 62 * q^16 + q^17 - 21 * q^18 + 6 * q^19 + q^20 - 22 * q^21 + 6 * q^22 + 20 * q^23 - 18 * q^24 + q^25 - 37 * q^26 + 10 * q^27 - 64 * q^28 - 28 * q^29 + 15 * q^30 + 9 * q^31 - 98 * q^32 + 13 * q^33 - 14 * q^34 + 13 * q^35 - 30 * q^36 - 21 * q^37 + 18 * q^38 + 44 * q^39 + 9 * q^40 + 28 * q^41 + 31 * q^42 + 82 * q^43 - 4 * q^44 - 25 * q^45 - 16 * q^46 - 10 * q^47 - 72 * q^48 - 26 * q^49 - 46 * q^50 - 14 * q^51 - 23 * q^52 - 5 * q^53 - 22 * q^54 + 32 * q^55 + q^56 - 85 * q^57 + 80 * q^58 - 3 * q^59 + 61 * q^60 + 35 * q^61 + 43 * q^62 - 47 * q^63 - 54 * q^64 - 64 * q^65 - 13 * q^66 - 20 * q^67 + 5 * q^68 + 76 * q^69 - 23 * q^70 + 28 * q^71 - 53 * q^72 + 33 * q^73 - 3 * q^74 - 34 * q^75 - 156 * q^76 + 45 * q^77 + 30 * q^78 + 4 * q^79 - 144 * q^80 - 27 * q^81 - 59 * q^82 - 92 * q^83 + 9 * q^84 - 26 * q^85 - 56 * q^86 + 38 * q^87 + 18 * q^88 + 39 * q^89 + 114 * q^90 - 11 * q^91 - 60 * q^92 - 19 * q^93 + 46 * q^94 - 46 * q^95 + 9 * q^96 + 20 * q^97 + 122 * q^98 - 84 * q^99

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