LMFDB - Embedded newform 525.2.z.b.64.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(64,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("525.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.z (of order $10$, degree $4$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			64.16
Character	$\chi$	$=$	525.64
Dual form			525.2.z.b.484.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.43938 + 1.98113i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-1.23505 + 3.80109i) q^{4} +(1.94961 + 1.09500i) q^{5} +(0.756726 + 2.32896i) q^{6} -1.00000i q^{7} +(-4.65025 + 1.51096i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(1.43938 + 1.98113i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-1.23505 + 3.80109i) q^{4} +(1.94961 + 1.09500i) q^{5} +(0.756726 + 2.32896i) q^{6} -1.00000i q^{7} +(-4.65025 + 1.51096i) q^{8} +(0.809017 + 0.587785i) q^{9} +(0.636883 + 5.43856i) q^{10} +(1.14497 - 0.831872i) q^{11} +(-2.34920 + 3.23340i) q^{12} +(1.65934 - 2.28388i) q^{13} +(1.98113 - 1.43938i) q^{14} +(1.51581 + 1.64387i) q^{15} +(-3.22008 - 2.33953i) q^{16} +(-5.64181 + 1.83313i) q^{17} +2.44882i q^{18} +(-2.35769 - 7.25621i) q^{19} +(-6.57006 + 6.05826i) q^{20} +(0.309017 - 0.951057i) q^{21} +(3.29610 + 1.07097i) q^{22} +(-4.70803 - 6.48005i) q^{23} -4.88957 q^{24} +(2.60195 + 4.26964i) q^{25} +6.91309 q^{26} +(0.587785 + 0.809017i) q^{27} +(3.80109 + 1.23505i) q^{28} +(-2.08926 + 6.43008i) q^{29} +(-1.07490 + 5.36918i) q^{30} +(-0.103802 - 0.319469i) q^{31} +0.0322471i q^{32} +(1.34600 - 0.437341i) q^{33} +(-11.7524 - 8.53860i) q^{34} +(1.09500 - 1.94961i) q^{35} +(-3.23340 + 2.34920i) q^{36} +(0.218940 - 0.301345i) q^{37} +(10.9819 - 15.1153i) q^{38} +(2.28388 - 1.65934i) q^{39} +(-10.7207 - 2.14625i) q^{40} +(-7.04205 - 5.11635i) q^{41} +(2.32896 - 0.756726i) q^{42} -2.82850i q^{43} +(1.74792 + 5.37956i) q^{44} +(0.933642 + 2.03182i) q^{45} +(6.06121 - 18.6545i) q^{46} +(9.80686 + 3.18644i) q^{47} +(-2.33953 - 3.22008i) q^{48} -1.00000 q^{49} +(-4.71355 + 11.3004i) q^{50} -5.93214 q^{51} +(6.63188 + 9.12800i) q^{52} +(-2.28246 - 0.741618i) q^{53} +(-0.756726 + 2.32896i) q^{54} +(3.14315 - 0.368079i) q^{55} +(1.51096 + 4.65025i) q^{56} -7.62964i q^{57} +(-15.7461 + 5.11622i) q^{58} +(7.63494 + 5.54711i) q^{59} +(-8.12061 + 3.73149i) q^{60} +(2.65741 - 1.93072i) q^{61} +(0.483501 - 0.665482i) q^{62} +(0.587785 - 0.809017i) q^{63} +(-6.50405 + 4.72547i) q^{64} +(5.73591 - 2.63570i) q^{65} +(2.80383 + 2.03710i) q^{66} +(-0.170770 + 0.0554867i) q^{67} -23.7090i q^{68} +(-2.47516 - 7.61776i) q^{69} +(5.43856 - 0.636883i) q^{70} +(-4.56842 + 14.0601i) q^{71} +(-4.65025 - 1.51096i) q^{72} +(2.05474 + 2.82811i) q^{73} +0.912143 q^{74} +(1.15521 + 4.86472i) q^{75} +30.4934 q^{76} +(-0.831872 - 1.14497i) q^{77} +(6.57474 + 2.13626i) q^{78} +(-1.05926 + 3.26007i) q^{79} +(-3.71612 - 8.08715i) q^{80} +(0.309017 + 0.951057i) q^{81} -21.3156i q^{82} +(10.5690 - 3.43407i) q^{83} +(3.23340 + 2.34920i) q^{84} +(-13.0066 - 2.60388i) q^{85} +(5.60364 - 4.07128i) q^{86} +(-3.97401 + 5.46975i) q^{87} +(-4.06749 + 5.59842i) q^{88} +(2.23362 - 1.62282i) q^{89} +(-2.68145 + 4.77424i) q^{90} +(-2.28388 - 1.65934i) q^{91} +(30.4459 - 9.89248i) q^{92} -0.335909i q^{93} +(7.80301 + 24.0152i) q^{94} +(3.34899 - 16.7284i) q^{95} +(-0.00996490 + 0.0306688i) q^{96} +(-6.26089 - 2.03428i) q^{97} +(-1.43938 - 1.98113i) q^{98} +1.41527 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 24 q^{4} - 2 q^{5} + 18 q^{9}+O(q^{10}) $ 72 * q + 24 * q^4 - 2 * q^5 + 18 * q^9	$ 72 q + 24 q^{4} - 2 q^{5} + 18 q^{9} - 28 q^{10} - 12 q^{11} - 20 q^{13} - 24 q^{16} + 10 q^{19} + 10 q^{20} - 18 q^{21} + 50 q^{22} - 10 q^{23} + 12 q^{25} + 36 q^{26} + 20 q^{28} - 2 q^{29} + 10 q^{30} - 16 q^{31} - 10 q^{33} + 24 q^{34} - 10 q^{35} - 24 q^{36} + 10 q^{37} - 100 q^{38} + 16 q^{39} - 14 q^{40} - 16 q^{41} - 18 q^{44} + 2 q^{45} - 44 q^{46} + 20 q^{47} - 72 q^{49} + 86 q^{50} + 32 q^{51} - 80 q^{52} + 70 q^{53} + 46 q^{55} - 40 q^{58} + 44 q^{59} - 62 q^{60} + 4 q^{61} - 50 q^{62} + 48 q^{64} + 38 q^{65} - 16 q^{66} - 20 q^{67} + 4 q^{69} + 10 q^{70} - 8 q^{71} - 20 q^{73} - 116 q^{74} - 8 q^{75} + 92 q^{76} + 20 q^{77} + 90 q^{78} + 28 q^{79} + 114 q^{80} - 18 q^{81} + 30 q^{83} + 24 q^{84} - 122 q^{85} + 40 q^{86} - 40 q^{87} - 270 q^{88} + 2 q^{89} - 12 q^{90} - 16 q^{91} - 100 q^{92} + 22 q^{94} + 116 q^{95} + 10 q^{96} + 190 q^{97} - 48 q^{99}+O(q^{100}) $ 72 * q + 24 * q^4 - 2 * q^5 + 18 * q^9 - 28 * q^10 - 12 * q^11 - 20 * q^13 - 24 * q^16 + 10 * q^19 + 10 * q^20 - 18 * q^21 + 50 * q^22 - 10 * q^23 + 12 * q^25 + 36 * q^26 + 20 * q^28 - 2 * q^29 + 10 * q^30 - 16 * q^31 - 10 * q^33 + 24 * q^34 - 10 * q^35 - 24 * q^36 + 10 * q^37 - 100 * q^38 + 16 * q^39 - 14 * q^40 - 16 * q^41 - 18 * q^44 + 2 * q^45 - 44 * q^46 + 20 * q^47 - 72 * q^49 + 86 * q^50 + 32 * q^51 - 80 * q^52 + 70 * q^53 + 46 * q^55 - 40 * q^58 + 44 * q^59 - 62 * q^60 + 4 * q^61 - 50 * q^62 + 48 * q^64 + 38 * q^65 - 16 * q^66 - 20 * q^67 + 4 * q^69 + 10 * q^70 - 8 * q^71 - 20 * q^73 - 116 * q^74 - 8 * q^75 + 92 * q^76 + 20 * q^77 + 90 * q^78 + 28 * q^79 + 114 * q^80 - 18 * q^81 + 30 * q^83 + 24 * q^84 - 122 * q^85 + 40 * q^86 - 40 * q^87 - 270 * q^88 + 2 * q^89 - 12 * q^90 - 16 * q^91 - 100 * q^92 + 22 * q^94 + 116 * q^95 + 10 * q^96 + 190 * q^97 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	1.43938	+	1.98113i	1.01779	+	1.40087i	0.913739	+	0.406302i	$0.133182\pi$
$2$	1.43938	+	1.98113i	1.01779	+	1.40087i	0.104056	+	0.994571i	$0.466818\pi$
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$4$	−1.23505	+	3.80109i	−0.617525	+	1.90055i
$5$	1.94961	+	1.09500i	0.871892	+	0.489699i
$5$	1.94961	+	1.09500i	0.871892	+	0.489699i
$6$	0.756726	+	2.32896i	0.308932	+	0.950795i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−4.65025	+	1.51096i	−1.64411	+	0.534205i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	0.636883	+	5.43856i	0.201400	+	1.71982i
$11$	1.14497	−	0.831872i	0.345223	−	0.250819i	−0.401639	−	0.915798i	$-0.631560\pi$
$11$	1.14497	−	0.831872i	0.345223	−	0.250819i	0.746862	+	0.664979i	$0.231560\pi$
$12$	−2.34920	+	3.23340i	−0.678157	+	0.933403i
$13$	1.65934	−	2.28388i	0.460217	−	0.633435i	−0.514337	−	0.857588i	$-0.671962\pi$
$13$	1.65934	−	2.28388i	0.460217	−	0.633435i	0.974554	+	0.224154i	$0.0719618\pi$
$14$	1.98113	−	1.43938i	0.529481	−	0.384690i
$15$	1.51581	+	1.64387i	0.391382	+	0.424445i
$16$	−3.22008	−	2.33953i	−0.805021	−	0.584882i
$17$	−5.64181	+	1.83313i	−1.36834	+	0.444600i	−0.898818	−	0.438321i	$-0.855573\pi$
$17$	−5.64181	+	1.83313i	−1.36834	+	0.444600i	−0.469520	+	0.882922i	$0.655573\pi$
$18$			2.44882i			0.577192i
$19$	−2.35769	−	7.25621i	−0.540891	−	1.66469i	−0.730565	−	0.682843i	$-0.760743\pi$
$19$	−2.35769	−	7.25621i	−0.540891	−	1.66469i	0.189675	−	0.981847i	$-0.439257\pi$
$20$	−6.57006	+	6.05826i	−1.46911	+	1.35467i
$21$	0.309017	−	0.951057i	0.0674330	−	0.207538i
$22$	3.29610	+	1.07097i	0.702731	+	0.228331i
$23$	−4.70803	−	6.48005i	−0.981693	−	1.35118i	−0.935912	−	0.352233i	$-0.885423\pi$
$23$	−4.70803	−	6.48005i	−0.981693	−	1.35118i	−0.0457803	−	0.998952i	$-0.514577\pi$
$24$	−4.88957			−0.998078
$25$	2.60195	+	4.26964i	0.520390	+	0.853929i
$26$	6.91309			1.35577
$27$	0.587785	+	0.809017i	0.113119	+	0.155695i
$28$	3.80109	+	1.23505i	0.718339	+	0.233402i
$29$	−2.08926	+	6.43008i	−0.387966	+	1.19404i	0.546340	+	0.837564i	$0.316021\pi$
$29$	−2.08926	+	6.43008i	−0.387966	+	1.19404i	−0.934306	+	0.356473i	$0.883979\pi$
$30$	−1.07490	+	5.36918i	−0.196248	+	0.980274i
$31$	−0.103802	−	0.319469i	−0.0186433	−	0.0573783i	0.941302	−	0.337566i	$-0.109603\pi$
$31$	−0.103802	−	0.319469i	−0.0186433	−	0.0573783i	−0.959945	+	0.280187i	$0.909603\pi$
$32$			0.0322471i			0.00570054i
$33$	1.34600	−	0.437341i	0.234308	−	0.0761313i
$34$	−11.7524	−	8.53860i	−2.01552	−	1.46436i
$35$	1.09500	−	1.94961i	0.185089	−	0.329544i
$36$	−3.23340	+	2.34920i	−0.538900	+	0.391534i
$37$	0.218940	−	0.301345i	0.0359935	−	0.0495408i	−0.790641	−	0.612280i	$-0.790252\pi$
$37$	0.218940	−	0.301345i	0.0359935	−	0.0495408i	0.826634	+	0.562739i	$0.190252\pi$
$38$	10.9819	−	15.1153i	1.78150	−	2.45203i
$39$	2.28388	−	1.65934i	0.365714	−	0.265706i
$40$	−10.7207	−	2.14625i	−1.69509	−	0.339352i
$41$	−7.04205	−	5.11635i	−1.09978	−	0.799040i	−0.118759	−	0.992923i	$-0.537892\pi$
$41$	−7.04205	−	5.11635i	−1.09978	−	0.799040i	−0.981025	+	0.193884i	$0.937892\pi$
$42$	2.32896	−	0.756726i	0.359367	−	0.116765i
$43$		−	2.82850i		−	0.431342i	−0.976466	−	0.215671i	$-0.930806\pi$
$43$		−	2.82850i		−	0.431342i	0.976466	−	0.215671i	$-0.0691939\pi$
$44$	1.74792	+	5.37956i	0.263509	+	0.810998i
$45$	0.933642	+	2.03182i	0.139179	+	0.302887i
$46$	6.06121	−	18.6545i	0.893677	−	2.75046i
$47$	9.80686	+	3.18644i	1.43048	+	0.464790i	0.918915	−	0.394456i	$-0.129067\pi$
$47$	9.80686	+	3.18644i	1.43048	+	0.464790i	0.511562	+	0.859246i	$0.329067\pi$
$48$	−2.33953	−	3.22008i	−0.337682	−	0.464779i
$49$	−1.00000			−0.142857
$50$	−4.71355	+	11.3004i	−0.666596	+	1.59812i
$51$	−5.93214			−0.830666
$52$	6.63188	+	9.12800i	0.919676	+	1.26583i
$53$	−2.28246	−	0.741618i	−0.313521	−	0.101869i	0.148030	−	0.988983i	$-0.452707\pi$
$53$	−2.28246	−	0.741618i	−0.313521	−	0.101869i	−0.461551	+	0.887114i	$0.652707\pi$
$54$	−0.756726	+	2.32896i	−0.102977	+	0.316932i
$55$	3.14315	−	0.368079i	0.423822	−	0.0496318i
$56$	1.51096	+	4.65025i	0.201910	+	0.621416i
$57$		−	7.62964i		−	1.01057i
$58$	−15.7461	+	5.11622i	−2.06756	+	0.671792i
$59$	7.63494	+	5.54711i	0.993985	+	0.722172i	0.960790	−	0.277277i	$-0.0894318\pi$
$59$	7.63494	+	5.54711i	0.993985	+	0.722172i	0.0331948	+	0.999449i	$0.489432\pi$
$60$	−8.12061	+	3.73149i	−1.04837	+	0.481733i
$61$	2.65741	−	1.93072i	0.340246	−	0.247203i	−0.404519	−	0.914529i	$-0.632561\pi$
$61$	2.65741	−	1.93072i	0.340246	−	0.247203i	0.744766	+	0.667326i	$0.232561\pi$
$62$	0.483501	−	0.665482i	0.0614047	−	0.0845163i
$63$	0.587785	−	0.809017i	0.0740540	−	0.101927i
$64$	−6.50405	+	4.72547i	−0.813007	+	0.590684i
$65$	5.73591	−	2.63570i	0.711452	−	0.326918i
$66$	2.80383	+	2.03710i	0.345128	+	0.250750i
$67$	−0.170770	+	0.0554867i	−0.0208629	+	0.00677877i	−0.319430	−	0.947610i	$-0.603491\pi$
$67$	−0.170770	+	0.0554867i	−0.0208629	+	0.00677877i	0.298567	+	0.954389i	$0.403491\pi$
$68$		−	23.7090i		−	2.87514i
$69$	−2.47516	−	7.61776i	−0.297974	−	0.917070i
$70$	5.43856	−	0.636883i	0.650032	−	0.0761221i
$71$	−4.56842	+	14.0601i	−0.542171	+	1.66863i	0.185451	+	0.982654i	$0.440625\pi$
$71$	−4.56842	+	14.0601i	−0.542171	+	1.66863i	−0.727622	+	0.685978i	$0.759375\pi$
$72$	−4.65025	−	1.51096i	−0.548038	−	0.178068i
$73$	2.05474	+	2.82811i	0.240489	+	0.331005i	0.912152	−	0.409852i	$-0.134420\pi$
$73$	2.05474	+	2.82811i	0.240489	+	0.331005i	−0.671663	+	0.740857i	$0.734420\pi$
$74$	0.912143			0.106034
$75$	1.15521	+	4.86472i	0.133392	+	0.561729i
$76$	30.4934			3.49783
$77$	−0.831872	−	1.14497i	−0.0948006	−	0.130482i
$78$	6.57474	+	2.13626i	0.744443	+	0.241884i
$79$	−1.05926	+	3.26007i	−0.119176	+	0.366786i	−0.992795	−	0.119824i	$-0.961767\pi$
$79$	−1.05926	+	3.26007i	−0.119176	+	0.366786i	0.873619	+	0.486610i	$0.161767\pi$
$80$	−3.71612	−	8.08715i	−0.415475	−	0.904171i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		−	21.3156i		−	2.35392i
$83$	10.5690	−	3.43407i	1.16010	−	0.376939i	0.335160	−	0.942161i	$-0.391210\pi$
$83$	10.5690	−	3.43407i	1.16010	−	0.376939i	0.824938	+	0.565223i	$0.191210\pi$
$84$	3.23340	+	2.34920i	0.352793	+	0.256319i
$85$	−13.0066	−	2.60388i	−1.41076	−	0.282431i
$86$	5.60364	−	4.07128i	0.604256	−	0.439017i
$87$	−3.97401	+	5.46975i	−0.426059	+	0.586419i
$88$	−4.06749	+	5.59842i	−0.433596	+	0.596794i
$89$	2.23362	−	1.62282i	0.236763	−	0.172019i	−0.463077	−	0.886318i	$-0.653255\pi$
$89$	2.23362	−	1.62282i	0.236763	−	0.172019i	0.699840	+	0.714300i	$0.253255\pi$
$90$	−2.68145	+	4.77424i	−0.282650	+	0.503249i
$91$	−2.28388	−	1.65934i	−0.239416	−	0.173946i
$92$	30.4459	−	9.89248i	3.17421	−	1.03136i
$93$		−	0.335909i		−	0.0348322i
$94$	7.80301	+	24.0152i	0.804819	+	2.47698i
$95$	3.34899	−	16.7284i	0.343599	−	1.71630i
$96$	−0.00996490	+	0.0306688i	−0.00101704	+	0.00313012i
$97$	−6.26089	−	2.03428i	−0.635697	−	0.206550i	−0.0265997	−	0.999646i	$-0.508468\pi$
$97$	−6.26089	−	2.03428i	−0.635697	−	0.206550i	−0.609097	+	0.793096i	$0.708468\pi$
$98$	−1.43938	−	1.98113i	−0.145399	−	0.200125i
$99$	1.41527			0.142240
$100$	−19.4428	+	4.61703i	−1.94428	+	0.461703i
$101$	14.0131			1.39436			0.697180	−	0.716896i	$-0.254438\pi$
$101$	14.0131			1.39436			0.697180	+	0.716896i	$0.254438\pi$
$102$	−8.53860	−	11.7524i	−0.845448	−	1.16366i
$103$	−12.1211	−	3.93838i	−1.19433	−	0.388060i	−0.356655	−	0.934236i	$-0.616083\pi$
$103$	−12.1211	−	3.93838i	−1.19433	−	0.388060i	−0.837670	+	0.546176i	$0.816083\pi$
$104$	−4.26549	+	13.1278i	−0.418265	+	1.28729i
$105$	1.64387	−	1.51581i	0.160425	−	0.147928i
$106$	−1.81609	−	5.58934i	−0.176394	−	0.542884i
$107$		−	7.25270i		−	0.701145i	−0.936536	−	0.350572i	$-0.885987\pi$
$107$		−	7.25270i		−	0.701145i	0.936536	−	0.350572i	$-0.114013\pi$
$108$	−3.80109	+	1.23505i	−0.365760	+	0.118843i
$109$	−8.06287	−	5.85802i	−0.772283	−	0.561097i	0.130370	−	0.991465i	$-0.458383\pi$
$109$	−8.06287	−	5.85802i	−0.772283	−	0.561097i	−0.902653	+	0.430369i	$0.858383\pi$
$110$	5.25340	+	5.69720i	0.500892	+	0.543207i
$111$	0.301345	−	0.218940i	0.0286024	−	0.0207809i
$112$	−2.33953	+	3.22008i	−0.221065	+	0.304269i
$113$	−0.598958	+	0.824395i	−0.0563453	+	0.0775526i	−0.836260	−	0.548333i	$-0.815262\pi$
$113$	−0.598958	+	0.824395i	−0.0563453	+	0.0775526i	0.779915	+	0.625886i	$0.215262\pi$
$114$	15.1153	−	10.9819i	1.41568	−	1.02855i
$115$	−2.08317	−	17.7889i	−0.194256	−	1.65882i
$116$	−21.8610	−	15.8829i	−2.02974	−	1.47469i
$117$	2.68486	−	0.872365i	0.248216	−	0.0806502i
$118$			23.1102i			2.12747i
$119$	1.83313	+	5.64181i	0.168043	+	0.517183i
$120$	−9.53274	−	5.35407i	−0.870216	−	0.488758i
$121$	−2.78023	+	8.55668i	−0.252748	+	0.777880i
$122$	7.65003	+	2.48565i	0.692602	+	0.225040i
$123$	−5.11635	−	7.04205i	−0.461326	−	0.634960i
$124$	1.34253			0.120563
$125$	0.397525	+	11.1733i	0.0355557	+	0.999368i
$126$	2.44882			0.218158
$127$	7.97110	+	10.9713i	0.707321	+	0.973543i	0.999851	+	0.0172871i	$0.00550292\pi$
$127$	7.97110	+	10.9713i	0.707321	+	0.973543i	−0.292530	+	0.956256i	$0.594497\pi$
$128$	−18.6623	−	6.06373i	−1.64953	−	0.535963i
$129$	0.874054	−	2.69006i	0.0769562	−	0.236847i
$130$	13.4778	+	7.56983i	1.18208	+	0.663918i
$131$	6.47097	+	19.9156i	0.565372	+	1.74003i	0.666845	+	0.745196i	$0.267644\pi$
$131$	6.47097	+	19.9156i	0.565372	+	1.74003i	−0.101474	+	0.994838i	$0.532356\pi$
$132$			5.65640i			0.492326i
$133$	−7.25621	+	2.35769i	−0.629194	+	0.204437i
$134$	−0.355730	−	0.258453i	−0.0307304	−	0.0223269i
$135$	0.260078	+	2.22089i	0.0223839	+	0.191144i
$136$	23.4660	−	17.0491i	2.01220	−	1.46195i
$137$	−5.32895	+	7.33467i	−0.455283	+	0.626643i	−0.973522	−	0.228592i	$-0.926588\pi$
$137$	−5.32895	+	7.33467i	−0.455283	+	0.626643i	0.518239	+	0.855236i	$0.326588\pi$
$138$	11.5291	−	15.8685i	0.981423	−	1.35081i
$139$	13.1525	−	9.55586i	1.11558	−	0.810518i	0.132048	−	0.991243i	$-0.457845\pi$
$139$	13.1525	−	9.55586i	1.11558	−	0.810518i	0.983534	+	0.180726i	$0.0578447\pi$
$140$	6.05826	+	6.57006i	0.512017	+	0.555271i
$141$	8.34221	+	6.06097i	0.702541	+	0.510426i
$142$	−34.4307	+	11.1872i	−2.88936	+	0.938810i
$143$		−	3.99534i		−	0.334107i
$144$	−1.22996	−	3.78544i	−0.102497	−	0.315453i
$145$	−11.1142	+	10.2484i	−0.922982	+	0.851084i
$146$	−2.64531	+	8.14143i	−0.218928	+	0.673790i
$147$	−0.951057	−	0.309017i	−0.0784418	−	0.0254873i
$148$	0.875039	+	1.20439i	0.0719277	+	0.0990000i
$149$	9.75942			0.799523			0.399761	−	0.916619i	$-0.369093\pi$
$149$	9.75942			0.799523			0.399761	+	0.916619i	$0.369093\pi$
$150$	−7.97488	+	9.29080i	−0.651146	+	0.758590i
$151$	−6.05080			−0.492407			−0.246204	−	0.969218i	$-0.579183\pi$
$151$	−6.05080			−0.492407			−0.246204	+	0.969218i	$0.579183\pi$
$152$	21.9277	+	30.1809i	1.77857	+	2.44799i
$153$	−5.64181	−	1.83313i	−0.456113	−	0.148200i
$154$	1.07097	−	3.29610i	0.0863011	−	0.265607i
$155$	0.147446	−	0.736502i	0.0118431	−	0.0591573i
$156$	3.48659	+	10.7306i	0.279150	+	0.859136i
$157$		−	4.02953i		−	0.321592i	−0.986988	−	0.160796i	$-0.948594\pi$
$157$		−	4.02953i		−	0.321592i	0.986988	−	0.160796i	$-0.0514061\pi$
$158$	−7.98331	+	2.59393i	−0.635118	+	0.206362i
$159$	−1.94158	−	1.41064i	−0.153977	−	0.111871i
$160$	−0.0353106	+	0.0628692i	−0.00279155	+	0.00497025i
$161$	−6.48005	+	4.70803i	−0.510700	+	0.371045i
$162$	−1.43938	+	1.98113i	−0.113088	+	0.155653i
$163$	5.90465	−	8.12705i	0.462488	−	0.636560i	−0.512535	−	0.858667i	$-0.671293\pi$
$163$	5.90465	−	8.12705i	0.462488	−	0.636560i	0.975022	+	0.222107i	$0.0712933\pi$
$164$	28.1450	−	20.4485i	2.19776	−	1.59676i
$165$	3.10306	+	0.621223i	0.241573	+	0.0483622i
$166$	22.0161	+	15.9957i	1.70878	+	1.24150i
$167$	−1.91680	+	0.622805i	−0.148326	+	0.0481941i	−0.382239	−	0.924063i	$-0.624847\pi$
$167$	−1.91680	+	0.622805i	−0.148326	+	0.0481941i	0.233913	+	0.972258i	$0.424847\pi$
$168$			4.88957i			0.377238i
$169$	1.55451	+	4.78428i	0.119577	+	0.368022i
$170$	−13.5628	−	29.5158i	−1.04022	−	2.26376i
$171$	2.35769	−	7.25621i	0.180297	−	0.554897i
$172$	10.7514	+	3.49334i	0.819785	+	0.266364i
$173$	−13.4061	−	18.4520i	−1.01925	−	1.40288i	−0.912729	−	0.408566i	$-0.866029\pi$
$173$	−13.4061	−	18.4520i	−1.01925	−	1.40288i	−0.106521	−	0.994310i	$-0.533971\pi$
$174$	−16.5564			−1.25514
$175$	4.26964	−	2.60195i	0.322755	−	0.196689i
$176$	−5.63310			−0.424611
$177$	5.54711	+	7.63494i	0.416946	+	0.573877i
$178$	6.43005	+	2.08925i	0.481953	+	0.156596i
$179$	−0.0423175	+	0.130240i	−0.00316296	+	0.00973458i	−0.952626	−	0.304146i	$-0.901629\pi$
$179$	−0.0423175	+	0.130240i	−0.00316296	+	0.00973458i	0.949463	+	0.313880i	$0.101629\pi$
$180$	−8.87625	+	1.03945i	−0.661597	+	0.0774763i
$181$	0.0679854	+	0.209238i	0.00505332	+	0.0155525i	0.953551	−	0.301230i	$-0.0973973\pi$
$181$	0.0679854	+	0.209238i	0.00505332	+	0.0155525i	−0.948498	+	0.316783i	$0.897397\pi$
$182$		−	6.91309i		−	0.512432i
$183$	3.12397	−	1.01504i	0.230931	−	0.0750339i
$184$	31.6846	+	23.0202i	2.33582	+	1.69707i
$185$	0.756820	−	0.347766i	0.0556425	−	0.0255682i
$186$	0.665482	−	0.483501i	0.0487955	−	0.0354520i
$187$	−4.93479	+	6.79215i	−0.360867	+	0.496691i
$188$	−24.2239	+	33.3414i	−1.76671	+	2.43167i
$189$	0.809017	−	0.587785i	0.0588473	−	0.0427551i
$190$	37.9618	−	17.4438i	2.75404	−	1.26550i
$191$	−2.82259	−	2.05073i	−0.204235	−	0.148386i	0.480966	−	0.876739i	$-0.340286\pi$
$191$	−2.82259	−	2.05073i	−0.204235	−	0.148386i	−0.685202	+	0.728354i	$0.740286\pi$
$192$	−7.64597	+	2.48433i	−0.551801	+	0.179291i
$193$			4.30859i			0.310139i	0.987904	+	0.155070i	$0.0495602\pi$
$193$			4.30859i			0.310139i	−0.987904	+	0.155070i	$0.950440\pi$
$194$	−4.98159	−	15.3318i	−0.357657	−	1.10076i
$195$	6.26965	−	0.734208i	0.448979	−	0.0525777i
$196$	1.23505	−	3.80109i	0.0882178	−	0.271507i
$197$	−10.2304	−	3.32405i	−0.728884	−	0.236829i	−0.0790132	−	0.996874i	$-0.525177\pi$
$197$	−10.2304	−	3.32405i	−0.728884	−	0.236829i	−0.649871	+	0.760045i	$0.725177\pi$
$198$	2.03710	+	2.80383i	0.144771	+	0.199260i
$199$	−0.527759			−0.0374118			−0.0187059	−	0.999825i	$-0.505955\pi$
$199$	−0.527759			−0.0374118			−0.0187059	+	0.999825i	$0.505955\pi$
$200$	−18.5510	−	15.9235i	−1.31175	−	1.12596i
$201$	−0.179559			−0.0126651
$202$	20.1702	+	27.7619i	1.41917	+	1.95332i
$203$	6.43008	+	2.08926i	0.451303	+	0.146637i
$204$	7.32649	−	22.5486i	0.512957	−	1.57872i
$205$	−8.12684	−	17.6859i	−0.567603	−	1.23524i
$206$	−9.64437	−	29.6823i	−0.671955	−	2.06806i
$207$		−	8.00978i		−	0.556718i
$208$	−10.6864	+	3.47222i	−0.740969	+	0.240755i
$209$	−8.73573	−	6.34688i	−0.604263	−	0.439023i
$210$	5.36918	+	1.07490i	0.370509	+	0.0741748i
$211$	−21.2271	+	15.4224i	−1.46134	+	1.06172i	−0.478323	+	0.878184i	$0.658755\pi$
$211$	−21.2271	+	15.4224i	−1.46134	+	1.06172i	−0.983013	+	0.183538i	$0.941245\pi$
$212$	5.63791	−	7.75992i	0.387213	−	0.532954i
$213$	−8.68964	+	11.9603i	−0.595405	+	0.819504i
$214$	14.3686	−	10.4394i	0.982215	−	0.713621i
$215$	3.09721	−	5.51447i	0.211228	−	0.376083i
$216$	−3.95574	−	2.87401i	−0.269154	−	0.195552i
$217$	−0.319469	+	0.103802i	−0.0216870	+	0.00704652i
$218$		−	24.4055i		−	1.65295i
$219$	1.08024	+	3.32464i	0.0729959	+	0.224658i
$220$	−2.48285	+	12.4020i	−0.167393	+	0.836143i
$221$	−5.17499	+	15.9270i	−0.348108	+	1.07137i
$222$	0.867499	+	0.281868i	0.0582227	+	0.0189177i
$223$	−1.26522	−	1.74142i	−0.0847252	−	0.116614i	0.764551	−	0.644564i	$-0.222961\pi$
$223$	−1.26522	−	1.74142i	−0.0847252	−	0.116614i	−0.849276	+	0.527950i	$0.822961\pi$
$224$	0.0322471			0.00215460
$225$	−0.404612	+	4.98360i	−0.0269741	+	0.332240i
$226$	−2.49537			−0.165989
$227$	−6.88305	−	9.47370i	−0.456844	−	0.628791i	0.517007	−	0.855981i	$-0.327046\pi$
$227$	−6.88305	−	9.47370i	−0.456844	−	0.628791i	−0.973850	+	0.227190i	$0.927046\pi$
$228$	29.0010	+	9.42298i	1.92063	+	0.624052i
$229$	3.08277	−	9.48779i	0.203715	−	0.626971i	−0.796049	−	0.605233i	$-0.793080\pi$
$229$	3.08277	−	9.48779i	0.203715	−	0.626971i	0.999764	−	0.0217379i	$-0.00691995\pi$
$230$	32.2437	−	29.7319i	2.12608	−	1.96047i
$231$	−0.437341	−	1.34600i	−0.0287749	−	0.0885601i
$232$		−	33.0583i		−	2.17038i
$233$	−0.251201	+	0.0816203i	−0.0164568	+	0.00534712i	−0.317234	−	0.948347i	$-0.602754\pi$
$233$	−0.251201	+	0.0816203i	−0.0164568	+	0.00534712i	0.300777	+	0.953694i	$0.402754\pi$
$234$	5.59281	+	4.06341i	0.365613	+	0.265634i
$235$	15.6304	+	16.9508i	1.01961	+	1.10575i
$236$	−30.5146	+	22.1702i	−1.98633	+	1.44315i
$237$	−2.01483	+	2.77318i	−0.130877	+	0.180137i
$238$	−8.53860	+	11.7524i	−0.553475	+	0.761793i
$239$	18.1408	−	13.1801i	1.17343	−	0.852547i	0.182015	−	0.983296i	$-0.441738\pi$
$239$	18.1408	−	13.1801i	1.17343	−	0.852547i	0.991416	+	0.130748i	$0.0417380\pi$
$240$	−1.03517	−	8.83969i	−0.0668201	−	0.570599i
$241$	−9.25264	−	6.72243i	−0.596015	−	0.433030i	0.248447	−	0.968645i	$-0.420080\pi$
$241$	−9.25264	−	6.72243i	−0.596015	−	0.433030i	−0.844462	+	0.535615i	$0.820080\pi$
$242$	−20.9537	+	6.80828i	−1.34696	+	0.437653i
$243$			1.00000i			0.0641500i
$244$	4.05682	+	12.4856i	0.259711	+	0.799308i
$245$	−1.94961	−	1.09500i	−0.124556	−	0.0699570i
$246$	6.58689	−	20.2724i	0.419965	−	1.29252i
$247$	−20.4845	−	6.65583i	−1.30340	−	0.423500i
$248$	0.965409	+	1.32877i	0.0613035	+	0.0843770i
$249$	11.1129			0.704251
$250$	−21.5636	+	16.8701i	−1.36380	+	1.06696i
$251$	−19.8428			−1.25246			−0.626232	−	0.779637i	$-0.715404\pi$
$251$	−19.8428			−1.25246			−0.626232	+	0.779637i	$0.715404\pi$
$252$	2.34920	+	3.23340i	0.147986	+	0.203685i
$253$	−10.7811	−	3.50301i	−0.677805	−	0.220232i
$254$	−10.2621	+	31.5836i	−0.643904	+	1.98173i
$255$	−11.5654	−	6.49570i	−0.724251	−	0.406776i
$256$	−9.88032	−	30.4085i	−0.617520	−	1.90053i
$257$			9.99835i			0.623680i	0.950135	+	0.311840i	$0.100945\pi$
$257$			9.99835i			0.623680i	−0.950135	+	0.311840i	$0.899055\pi$
$258$	6.58747	−	2.14040i	0.410118	−	0.133255i
$259$	−0.301345	−	0.218940i	−0.0187247	−	0.0136043i
$260$	2.93441	+	25.0579i	0.181985	+	1.55403i
$261$	−5.46975	+	3.97401i	−0.338569	+	0.245985i
$262$	−30.1413	+	41.4860i	−1.86214	+	2.56301i
$263$	−16.8906	+	23.2479i	−1.04152	+	1.43353i	−0.145579	+	0.989347i	$0.546505\pi$
$263$	−16.8906	+	23.2479i	−1.04152	+	1.43353i	−0.895938	+	0.444179i	$0.853495\pi$
$264$	−5.59842	+	4.06749i	−0.344559	+	0.250337i
$265$	−3.63784	−	3.94516i	−0.223471	−	0.242349i
$266$	−15.1153	−	10.9819i	−0.926781	−	0.673346i
$267$	2.62578	−	0.853168i	0.160695	−	0.0522130i
$268$		−	0.717643i		−	0.0438370i
$269$	9.91214	+	30.5064i	0.604354	+	1.86001i	0.501174	+	0.865347i	$0.332902\pi$
$269$	9.91214	+	30.5064i	0.604354	+	1.86001i	0.103180	+	0.994663i	$0.467098\pi$
$270$	−4.02553	+	3.71195i	−0.244986	+	0.225902i
$271$	6.27599	−	19.3155i	0.381239	−	1.17333i	−0.557933	−	0.829886i	$-0.688405\pi$
$271$	6.27599	−	19.3155i	0.381239	−	1.17333i	0.939172	−	0.343447i	$-0.111595\pi$
$272$	22.4557	+	7.29632i	1.36158	+	0.442404i
$273$	−1.65934	−	2.28388i	−0.100428	−	0.138227i
$274$	−22.2013			−1.34123
$275$	6.53096	+	2.72414i	0.393832	+	0.164272i
$276$	32.0127			1.92694
$277$	−13.4254	−	18.4785i	−0.806653	−	1.11026i	−0.991831	−	0.127558i	$-0.959286\pi$
$277$	−13.4254	−	18.4785i	−0.806653	−	1.11026i	0.185178	−	0.982705i	$-0.440714\pi$
$278$	37.8629	+	12.3024i	2.27087	+	0.737849i
$279$	0.103802	−	0.319469i	0.00621445	−	0.0191261i
$280$	−2.14625	+	10.7207i	−0.128263	+	0.640683i
$281$	−2.02306	−	6.22633i	−0.120685	−	0.371432i	0.872405	−	0.488784i	$-0.162559\pi$
$281$	−2.02306	−	6.22633i	−0.120685	−	0.371432i	−0.993090	+	0.117352i	$0.962559\pi$
$282$			25.2511i			1.50368i
$283$	−9.08111	+	2.95063i	−0.539816	+	0.175397i	−0.566219	−	0.824255i	$-0.691595\pi$
$283$	−9.08111	+	2.95063i	−0.539816	+	0.175397i	0.0264035	+	0.999651i	$0.491595\pi$
$284$	−47.8017	−	34.7299i	−2.83651	−	2.06084i
$285$	8.35445	−	14.8748i	0.494875	−	0.881107i
$286$	7.91531	−	5.75081i	0.468042	−	0.340052i
$287$	−5.11635	+	7.04205i	−0.302009	+	0.415679i
$288$	−0.0189544	+	0.0260884i	−0.00111690	+	0.00153728i
$289$	14.7163	−	10.6920i	0.865664	−	0.628942i
$290$	−36.3010	−	7.26735i	−2.13167	−	0.426754i
$291$	−5.32583	−	3.86944i	−0.312206	−	0.226831i
$292$	−13.2876	+	4.31740i	−0.777598	+	0.252657i
$293$		−	22.8224i		−	1.33330i	−0.745372	−	0.666649i	$-0.767728\pi$
$293$		−	22.8224i		−	1.33330i	0.745372	−	0.666649i	$-0.232272\pi$
$294$	−0.756726	−	2.32896i	−0.0441332	−	0.135828i
$295$	8.81107	+	19.1750i	0.513000	+	1.11641i
$296$	−0.562806	+	1.73214i	−0.0327125	+	0.100679i
$297$	1.34600	+	0.437341i	0.0781027	+	0.0253771i
$298$	14.0475	+	19.3347i	0.813750	+	1.12003i
$299$	−22.6119			−1.30768
$300$	−19.9180	−	1.61711i	−1.14997	−	0.0933641i
$301$	−2.82850			−0.163032
$302$	−8.70939	−	11.9875i	−0.501169	−	0.689800i
$303$	13.3273	+	4.33030i	0.765633	+	0.248769i
$304$	−9.38417	+	28.8815i	−0.538219	+	1.65647i
$305$	7.29505	−	0.854287i	0.417713	−	0.0489164i
$306$	−4.48901	−	13.8157i	−0.256620	−	0.789794i
$307$		−	21.1773i		−	1.20865i	−0.796737	−	0.604327i	$-0.793442\pi$
$307$		−	21.1773i		−	1.20865i	0.796737	−	0.604327i	$-0.206558\pi$
$308$	5.37956	−	1.74792i	0.306529	−	0.0995972i
$309$	−10.3108	−	7.49124i	−0.586561	−	0.426162i
$310$	1.67134	−	0.767996i	0.0949257	−	0.0436192i
$311$	−8.88365	+	6.45435i	−0.503745	+	0.365992i	−0.810446	−	0.585814i	$-0.800775\pi$
$311$	−8.88365	+	6.45435i	−0.503745	+	0.365992i	0.306700	+	0.951806i	$0.400775\pi$
$312$	−8.11344	+	11.1672i	−0.459333	+	0.632217i
$313$	2.23544	−	3.07682i	0.126354	−	0.173912i	−0.741153	−	0.671336i	$-0.765721\pi$
$313$	2.23544	−	3.07682i	0.126354	−	0.173912i	0.867507	+	0.497424i	$0.165721\pi$
$314$	7.98305	−	5.80002i	0.450509	−	0.327314i
$315$	2.03182	−	0.933642i	0.114480	−	0.0526048i
$316$	−11.0836	−	8.05269i	−0.623500	−	0.452999i
$317$	9.81359	−	3.18863i	0.551186	−	0.179091i	−0.0201653	−	0.999797i	$-0.506419\pi$
$317$	9.81359	−	3.18863i	0.551186	−	0.179091i	0.571352	+	0.820705i	$0.306419\pi$
$318$		−	5.87698i		−	0.329564i
$319$	2.95686	+	9.10027i	0.165552	+	0.509517i
$320$	−17.8547	+	2.09088i	−0.998111	+	0.116884i
$321$	2.24121	−	6.89772i	0.125092	−	0.384993i
$322$	−18.6545	−	6.06121i	−1.03957	−	0.337778i
$323$	26.6032	+	36.6162i	1.48024	+	2.03738i
$324$	−3.99671			−0.222039
$325$	14.0689	+	1.14223i	0.780400	+	0.0633596i
$326$	24.5998			1.36246
$327$	−5.85802	−	8.06287i	−0.323949	−	0.445878i
$328$	40.4779	+	13.1521i	2.23502	+	0.726202i
$329$	3.18644	−	9.80686i	0.175674	−	0.540669i
$330$	3.23575	+	7.04175i	0.178122	+	0.387636i
$331$	−7.79363	−	23.9863i	−0.428377	−	1.31841i	−0.899723	−	0.436460i	$-0.856232\pi$
$331$	−7.79363	−	23.9863i	−0.428377	−	1.31841i	0.471347	−	0.881948i	$-0.343768\pi$
$332$			44.4150i			2.43759i
$333$	0.354252	−	0.115104i	0.0194129	−	0.00630764i
$334$	−3.99286	−	2.90098i	−0.218479	−	0.158735i
$335$	−0.393693	−	0.0788163i	−0.0215098	−	0.00430619i
$336$	−3.22008	+	2.33953i	−0.175670	+	0.127632i
$337$	−3.03998	+	4.18417i	−0.165598	+	0.227926i	−0.883749	−	0.467961i	$-0.844989\pi$
$337$	−3.03998	+	4.18417i	−0.165598	+	0.227926i	0.718151	+	0.695887i	$0.244989\pi$
$338$	−7.24078	+	9.96608i	−0.393847	+	0.542083i
$339$	−0.824395	+	0.598958i	−0.0447750	+	0.0325310i
$340$	25.9614	−	46.2233i	1.40795	−	2.50681i
$341$	−0.384608	−	0.279434i	−0.0208277	−	0.0151322i
$342$	17.7691	−	5.77354i	0.960845	−	0.312198i
$343$			1.00000i			0.0539949i
$344$	4.27375	+	13.1532i	0.230425	+	0.709175i
$345$	3.51585	−	17.5619i	0.189287	−	0.945503i
$346$	17.2593	−	53.1187i	0.927867	−	2.85568i
$347$	29.8665	+	9.70423i	1.60332	+	0.520950i	0.967925	−	0.251237i	$-0.0808375\pi$
$347$	29.8665	+	9.70423i	1.60332	+	0.520950i	0.635395	+	0.772188i	$0.280837\pi$
$348$	−15.8829	−	21.8610i	−0.851415	−	1.17187i
$349$	14.5665			0.779728			0.389864	−	0.920872i	$-0.372522\pi$
$349$	14.5665			0.779728			0.389864	+	0.920872i	$0.372522\pi$
$350$	11.3004	+	4.71355i	0.604034	+	0.251950i
$351$	2.82303			0.150682
$352$	0.0268255	+	0.0369221i	0.00142980	+	0.00196795i
$353$	−23.6190	−	7.67427i	−1.25711	−	0.408460i	−0.396647	−	0.917971i	$-0.629826\pi$
$353$	−23.6190	−	7.67427i	−1.25711	−	0.408460i	−0.860464	+	0.509511i	$0.829826\pi$
$354$	−7.14146	+	21.9791i	−0.379564	+	1.16818i
$355$	−24.3025	+	22.4094i	−1.28984	+	1.18937i
$356$	3.40986	+	10.4945i	0.180722	+	0.556206i
$357$			5.93214i			0.313962i
$358$	−0.318933	+	0.103628i	−0.0168562	+	0.00547690i
$359$	17.1650	+	12.4711i	0.905932	+	0.658198i	0.939983	−	0.341222i	$-0.110841\pi$
$359$	17.1650	+	12.4711i	0.905932	+	0.658198i	−0.0340505	+	0.999420i	$0.510841\pi$
$360$	−7.41168	−	8.03781i	−0.390630	−	0.423630i
$361$	−31.7226	+	23.0478i	−1.66961	+	1.21304i
$362$	−0.316671	+	0.435861i	−0.0166439	+	0.0229083i
$363$	−5.28832	+	7.27874i	−0.277565	+	0.382035i
$364$	9.12800	−	6.63188i	0.478437	−	0.347605i
$365$	0.909162	+	7.76364i	0.0475877	+	0.406368i
$366$	6.50751	+	4.72798i	0.340153	+	0.247136i
$367$	9.99665	−	3.24811i	0.521821	−	0.169550i	−0.0362507	−	0.999343i	$-0.511541\pi$
$367$	9.99665	−	3.24811i	0.521821	−	0.169550i	0.558072	+	0.829793i	$0.311541\pi$
$368$			31.8809i			1.66191i
$369$	−2.68982	−	8.27843i	−0.140027	−	0.430958i
$370$	1.77832	+	0.998796i	0.0924505	+	0.0519249i
$371$	−0.741618	+	2.28246i	−0.0385029	+	0.118500i
$372$	1.27682	+	0.414865i	0.0662002	+	0.0215097i
$373$	−4.08210	−	5.61853i	−0.211363	−	0.290917i	0.690151	−	0.723665i	$-0.257544\pi$
$373$	−4.08210	−	5.61853i	−0.211363	−	0.290917i	−0.901515	+	0.432748i	$0.857544\pi$
$374$	−20.5592			−1.06309
$375$	−3.07466	+	10.7493i	−0.158775	+	0.555089i
$376$	−50.4189			−2.60016
$377$	11.2188	+	15.4413i	0.577795	+	0.795267i
$378$	2.32896	+	0.756726i	0.119789	+	0.0389218i
$379$	1.17309	−	3.61039i	0.0602574	−	0.185453i	−0.916397	−	0.400271i	$-0.868916\pi$
$379$	1.17309	−	3.61039i	0.0602574	−	0.185453i	0.976654	+	0.214818i	$0.0689159\pi$
$380$	59.4502	+	33.3903i	3.04973	+	1.71289i
$381$	4.19066	+	12.8975i	0.214694	+	0.660759i
$382$		−	8.54370i		−	0.437134i
$383$	30.8780	−	10.0329i	1.57779	−	0.512656i	0.616307	−	0.787506i	$-0.288628\pi$
$383$	30.8780	−	10.0329i	1.57779	−	0.512656i	0.961487	+	0.274850i	$0.0886281\pi$
$384$	−15.8751	−	11.5339i	−0.810121	−	0.588587i
$385$	−0.368079	−	3.14315i	−0.0187590	−	0.160190i
$386$	−8.53590	+	6.20169i	−0.434466	+	0.315658i
$387$	1.66255	−	2.28830i	0.0845122	−	0.116321i
$388$	15.4650	−	21.2858i	0.785117	−	1.08062i
$389$	−19.5773	+	14.2237i	−0.992607	+	0.721171i	−0.960491	−	0.278313i	$-0.910225\pi$
$389$	−19.5773	+	14.2237i	−0.992607	+	0.721171i	−0.0321168	+	0.999484i	$0.510225\pi$
$390$	10.4790	+	11.3642i	0.530623	+	0.575449i
$391$	38.4406	+	27.9287i	1.94402	+	1.41242i
$392$	4.65025	−	1.51096i	0.234873	−	0.0763149i
$393$			20.9405i			1.05631i
$394$	−8.13999	−	25.0523i	−0.410087	−	1.26212i
$395$	−5.63491	+	5.19596i	−0.283523	+	0.261437i
$396$	−1.74792	+	5.37956i	−0.0878365	+	0.270333i
$397$	−16.8237	−	5.46636i	−0.844359	−	0.274349i	−0.145277	−	0.989391i	$-0.546407\pi$
$397$	−16.8237	−	5.46636i	−0.844359	−	0.274349i	−0.699081	+	0.715042i	$0.746407\pi$
$398$	−0.759645	−	1.04556i	−0.0380775	−	0.0524092i
$399$	−7.62964			−0.381960
$400$	1.61045	−	19.8359i	0.0805226	−	0.991797i
$401$	29.4305			1.46969			0.734845	−	0.678235i	$-0.237255\pi$
$401$	29.4305			1.46969			0.734845	+	0.678235i	$0.237255\pi$
$402$	−0.258453	−	0.355730i	−0.0128905	−	0.0177422i
$403$	−0.901871	−	0.293036i	−0.0449254	−	0.0145971i
$404$	−17.3069	+	53.2652i	−0.861052	+	2.65005i
$405$	−0.438945	+	2.19256i	−0.0218113	+	0.108949i
$406$	5.11622	+	15.7461i	0.253914	+	0.781466i
$407$		−	0.527162i		−	0.0261305i
$408$	27.5860	−	8.96323i	1.36571	−	0.443746i
$409$	18.2618	+	13.2680i	0.902987	+	0.656059i	0.939232	−	0.343284i	$-0.111539\pi$
$409$	18.2618	+	13.2680i	0.902987	+	0.656059i	−0.0362443	+	0.999343i	$0.511539\pi$
$410$	23.3406	−	41.5571i	1.15271	−	2.05236i
$411$	−7.33467	+	5.32895i	−0.361793	+	0.262858i
$412$	29.9403	−	41.2092i	1.47505	−	2.03023i
$413$	5.54711	−	7.63494i	0.272955	−	0.375691i
$414$	15.8685	−	11.5291i	0.779892	−	0.566625i
$415$	24.3657	+	4.87795i	1.19607	+	0.239449i
$416$	0.0736485	+	0.0535088i	0.00361092	+	0.00262348i
$417$	15.4617	−	5.02381i	0.757163	−	0.246017i
$418$		−	26.4422i		−	1.29333i
$419$	10.5665	+	32.5203i	0.516206	+	1.58872i	0.781076	+	0.624435i	$0.214671\pi$
$419$	10.5665	+	32.5203i	0.516206	+	1.58872i	−0.264870	+	0.964284i	$0.585329\pi$
$420$	3.73149	+	8.12061i	0.182078	+	0.396245i
$421$	−10.7666	+	33.1362i	−0.524732	+	1.61496i	0.240114	+	0.970745i	$0.422815\pi$
$421$	−10.7666	+	33.1362i	−0.524732	+	1.61496i	−0.764845	+	0.644214i	$0.777185\pi$
$422$	−61.1077	−	19.8551i	−2.97468	−	0.966531i
$423$	6.06097	+	8.34221i	0.294694	+	0.405612i
$424$	11.7346			0.569882
$425$	−22.5065	−	19.3188i	−1.09173	−	0.937098i
$426$	−36.2026			−1.75402
$427$	−1.93072	−	2.65741i	−0.0934341	−	0.128601i
$428$	27.5682	+	8.95744i	1.33256	+	0.432974i
$429$	1.23463	−	3.79979i	0.0596084	−	0.183456i
$430$	15.3830	−	1.80142i	0.741832	−	0.0868723i
$431$	−1.92019	−	5.90972i	−0.0924921	−	0.284661i	0.894100	−	0.447868i	$-0.147816\pi$
$431$	−1.92019	−	5.90972i	−0.0924921	−	0.284661i	−0.986592	+	0.163206i	$0.947816\pi$
$432$		−	3.98024i		−	0.191499i
$433$	−3.92696	+	1.27595i	−0.188718	+	0.0613181i	−0.401851	−	0.915705i	$-0.631633\pi$
$433$	−3.92696	+	1.27595i	−0.188718	+	0.0613181i	0.213133	+	0.977023i	$0.431633\pi$
$434$	−0.665482	−	0.483501i	−0.0319442	−	0.0232088i
$435$	−13.7371	+	6.31234i	−0.658646	+	0.302654i
$436$	32.2249	−	23.4128i	1.54329	−	1.12127i
$437$	−35.9206	+	49.4404i	−1.71831	+	2.36506i
$438$	−5.03168	+	6.92552i	−0.240423	+	0.330914i
$439$	17.4417	−	12.6721i	0.832445	−	0.604807i	−0.0878051	−	0.996138i	$-0.527985\pi$
$439$	17.4417	−	12.6721i	0.832445	−	0.604807i	0.920250	+	0.391331i	$0.127985\pi$
$440$	−14.0603	+	6.46083i	−0.670298	+	0.308008i
$441$	−0.809017	−	0.587785i	−0.0385246	−	0.0279898i
$442$	−39.0023	+	12.6726i	−1.85515	+	0.602775i
$443$		−	28.4779i		−	1.35302i	−0.736431	−	0.676512i	$-0.763491\pi$
$443$		−	28.4779i		−	1.35302i	0.736431	−	0.676512i	$-0.236509\pi$
$444$	0.460035	+	1.41584i	0.0218323	+	0.0671929i
$445$	6.13168	−	0.718051i	0.290669	−	0.0340389i
$446$	1.62886	−	5.01313i	0.0771290	−	0.237379i
$447$	9.28176	+	3.01583i	0.439012	+	0.142644i
$448$	4.72547	+	6.50405i	0.223258	+	0.307288i
$449$	7.67110			0.362022			0.181011	−	0.983481i	$-0.442063\pi$
$449$	7.67110			0.362022			0.181011	+	0.983481i	$0.442063\pi$
$450$	−10.4556	+	6.37170i	−0.492881	+	0.300365i
$451$	−12.3191			−0.580084
$452$	−2.39386	−	3.29487i	−0.112598	−	0.154977i
$453$	−5.75465	−	1.86980i	−0.270377	−	0.0878509i
$454$	8.86137	−	27.2725i	0.415884	−	1.27996i
$455$	−2.63570	−	5.73591i	−0.123564	−	0.268903i
$456$	11.5281	+	35.4797i	0.539851	+	1.66149i
$457$		−	0.0671030i		−	0.00313895i	−0.999999	−	0.00156947i	$-0.999500\pi$
$457$		−	0.0671030i		−	0.00313895i	0.999999	−	0.00156947i	$-0.000499579\pi$
$458$	23.2339	−	7.54914i	1.08565	−	0.352748i
$459$	−4.79921	−	3.48683i	−0.224008	−	0.162751i
$460$	70.1899	+	14.0518i	3.27262	+	0.655170i
$461$	17.1203	−	12.4386i	0.797373	−	0.579325i	−0.112769	−	0.993621i	$-0.535972\pi$
$461$	17.1203	−	12.4386i	0.797373	−	0.579325i	0.910142	+	0.414296i	$0.135972\pi$
$462$	2.03710	−	2.80383i	0.0947746	−	0.130446i
$463$	3.32393	−	4.57500i	0.154476	−	0.212618i	−0.724764	−	0.688998i	$-0.758051\pi$
$463$	3.32393	−	4.57500i	0.154476	−	0.212618i	0.879240	+	0.476379i	$0.158051\pi$
$464$	21.7709	−	15.8175i	1.01069	−	0.734310i
$465$	0.367821	−	0.654892i	0.0170573	−	0.0303699i
$466$	−0.523275	−	0.380181i	−0.0242402	−	0.0176116i
$467$	−11.3208	+	3.67834i	−0.523862	+	0.170213i	−0.558997	−	0.829169i	$-0.688814\pi$
$467$	−11.3208	+	3.67834i	−0.523862	+	0.170213i	0.0351351	+	0.999383i	$0.488814\pi$
$468$			11.2828i			0.521549i
$469$	0.0554867	+	0.170770i	0.00256214	+	0.00788544i
$470$	−11.0838	+	55.3645i	−0.511259	+	2.55378i
$471$	1.24519	−	3.83231i	0.0573755	−	0.176584i
$472$	−43.8859	−	14.2594i	−2.02001	−	0.656341i
$473$	−2.35295	−	3.23856i	−0.108189	−	0.148909i
$474$	−8.39414			−0.385556
$475$	24.8469	−	28.9468i	1.14005	−	1.32817i
$476$	−23.7090			−1.08670
$477$	−1.41064	−	1.94158i	−0.0645888	−	0.0888988i
$478$	52.2230	+	16.9683i	2.38862	+	0.776111i
$479$	2.62591	−	8.08173i	0.119981	−	0.369264i	−0.872972	−	0.487770i	$-0.837811\pi$
$479$	2.62591	−	8.08173i	0.119981	−	0.369264i	0.992953	+	0.118506i	$0.0378106\pi$
$480$	−0.0530100	+	0.0488806i	−0.00241956	+	0.00223108i
$481$	−0.324941	−	1.00007i	−0.0148160	−	0.0455991i
$482$		−	28.0068i		−	1.27568i
$483$	−7.61776	+	2.47516i	−0.346620	+	0.112624i
$484$	−29.0910	−	21.1358i	−1.32232	−	0.960720i
$485$	−9.97874	−	10.8217i	−0.453111	−	0.491389i
$486$	−1.98113	+	1.43938i	−0.0898661	+	0.0652915i
$487$	15.4097	−	21.2096i	0.698280	−	0.961100i	−0.301690	−	0.953406i	$-0.597551\pi$
$487$	15.4097	−	21.2096i	0.698280	−	0.961100i	0.999970	−	0.00769426i	$-0.00244918\pi$
$488$	−9.44039	+	12.9936i	−0.427346	+	0.588192i
$489$	8.12705	−	5.90465i	0.367518	−	0.267017i
$490$	−0.636883	−	5.43856i	−0.0287714	−	0.245689i
$491$	20.6994	+	15.0390i	0.934150	+	0.678700i	0.947005	−	0.321218i	$-0.104092\pi$
$491$	20.6994	+	15.0390i	0.934150	+	0.678700i	−0.0128553	+	0.999917i	$0.504092\pi$
$492$	33.0864	−	10.7504i	1.49165	−	0.484667i
$493$		−	40.1072i		−	1.80634i
$494$	−16.2989	−	50.1629i	−0.733322	−	2.25693i
$495$	2.75921	+	1.54972i	0.124017	+	0.0696545i
$496$	−0.413156	+	1.27156i	−0.0185513	+	0.0570949i
$497$	14.0601	+	4.56842i	0.630683	+	0.204921i
$498$	15.9957	+	22.0161i	0.716783	+	0.986567i
$499$	28.3629			1.26970			0.634850	−	0.772636i	$-0.281062\pi$
$499$	28.3629			1.26970			0.634850	+	0.772636i	$0.281062\pi$
$500$	−42.9616	−	12.2885i	−1.92130	−	0.549559i
$501$	−2.01544			−0.0900432
$502$	−28.5612	−	39.3112i	−1.27475	−	1.75454i
$503$	−22.9229	−	7.44811i	−1.02208	−	0.332095i	−0.250427	−	0.968136i	$-0.580571\pi$
$503$	−22.9229	−	7.44811i	−1.02208	−	0.332095i	−0.771655	+	0.636041i	$0.780571\pi$
$504$	−1.51096	+	4.65025i	−0.0673035	+	0.207139i
$505$	27.3201	+	15.3444i	1.21573	+	0.682816i
$506$	−8.57823	−	26.4011i	−0.381349	−	1.17367i
$507$			5.03049i			0.223412i
$508$	−51.5475	+	16.7488i	−2.28705	+	0.743108i
$509$	4.12098	+	2.99406i	0.182659	+	0.132710i	0.675357	−	0.737491i	$-0.263989\pi$
$509$	4.12098	+	2.99406i	0.182659	+	0.132710i	−0.492698	+	0.870200i	$0.663989\pi$
$510$	−3.77808	−	32.2623i	−0.167296	−	1.42860i
$511$	2.82811	−	2.05474i	0.125108	−	0.0908964i
$512$	22.9540	−	31.5935i	1.01443	−	1.39625i
$513$	4.48459	−	6.17251i	0.197999	−	0.272523i
$514$	−19.8081	+	14.3914i	−0.873697	+	0.634778i
$515$	−19.3188	−	20.9509i	−0.851290	−	0.923206i
$516$	9.14567	+	6.64472i	0.402616	+	0.292518i
$517$	13.8793	−	4.50966i	0.610411	−	0.198335i
$518$		−	0.912143i		−	0.0400772i
$519$	−7.04802	−	21.6916i	−0.309374	−	0.952155i
$520$	−22.6910	+	20.9234i	−0.995065	+	0.917552i
$521$	−11.1187	+	34.2199i	−0.487120	+	1.49920i	0.341766	+	0.939785i	$0.388975\pi$
$521$	−11.1187	+	34.2199i	−0.487120	+	1.49920i	−0.828886	+	0.559417i	$0.811025\pi$
$522$	−15.7461	−	5.11622i	−0.689188	−	0.223931i
$523$	3.89350	+	5.35894i	0.170251	+	0.234330i	0.885613	−	0.464423i	$-0.153738\pi$
$523$	3.89350	+	5.35894i	0.170251	+	0.234330i	−0.715362	+	0.698754i	$0.753738\pi$
$524$	−83.6930			−3.65615
$525$	4.86472	−	1.15521i	0.212314	−	0.0504175i
$526$	−70.3691			−3.06824
$527$	1.17126	+	1.61210i	0.0510208	+	0.0702241i
$528$	−5.35740	−	1.74072i	−0.233151	−	0.0757553i
$529$	−12.7181	+	39.1423i	−0.552961	+	1.70184i
$530$	2.57967	−	12.8856i	0.112054	−	0.559716i
$531$	2.91629	+	8.97541i	0.126556	+	0.389500i
$532$		−	30.4934i		−	1.32206i
$533$	−23.3703	+	7.59346i	−1.01228	+	0.328909i
$534$	5.46973	+	3.97399i	0.236698	+	0.171971i
$535$	7.94170	−	14.1399i	0.343350	−	0.611322i
$536$	0.710288	−	0.516054i	0.0306797	−	0.0222901i
$537$	−0.0804926	+	0.110789i	−0.00347351	+	0.00478088i
$538$	−46.1700	+	63.5476i	−1.99053	+	2.73973i
$539$	−1.14497	+	0.831872i	−0.0493175	+	0.0358313i
$540$	−8.76302	−	1.75433i	−0.377100	−	0.0754944i
$541$	9.22320	+	6.70105i	0.396536	+	0.288100i	0.768129	−	0.640296i	$-0.221188\pi$
$541$	9.22320	+	6.70105i	0.396536	+	0.288100i	−0.371592	+	0.928396i	$0.621188\pi$
$542$	47.3001	−	15.3687i	2.03172	−	0.660144i
$543$			0.220006i			0.00944134i
$544$	−0.0591132	−	0.181932i	−0.00253446	−	0.00780026i
$545$	−9.30492	−	20.2497i	−0.398579	−	0.867402i
$546$	2.13626	−	6.57474i	0.0914236	−	0.281373i
$547$	28.0591	+	9.11697i	1.19972	+	0.389813i	0.839659	−	0.543114i	$-0.182755\pi$
$547$	28.0591	+	9.11697i	1.19972	+	0.389813i	0.360064	+	0.932928i	$0.382755\pi$
$548$	−21.2982	−	29.3145i	−0.909816	−	1.25225i
$549$	3.28474			0.140189
$550$	4.00364	+	16.8598i	0.170716	+	0.718904i
$551$	51.5839			2.19755
$552$	23.0202	+	31.6846i	0.979806	+	1.34859i
$553$	3.26007	+	1.05926i	0.138632	+	0.0450443i
$554$	17.2841	−	53.1950i	0.734331	−	2.26004i
$555$	0.827244	−	0.0968745i	0.0351146	−	0.00411210i
$556$	20.0787	+	61.7959i	0.851527	+	2.62073i
$557$			11.3372i			0.480372i	0.970727	+	0.240186i	$0.0772084\pi$
$557$			11.3372i			0.480372i	−0.970727	+	0.240186i	$0.922792\pi$
$558$	0.782321	−	0.254191i	0.0331183	−	0.0107608i
$559$	−6.45995	−	4.69343i	−0.273227	−	0.198511i
$560$	−8.08715	+	3.71612i	−0.341745	+	0.157035i
$561$	−6.79215	+	4.93479i	−0.286765	+	0.208347i
$562$	9.42325	−	12.9700i	0.397496	−	0.547106i
$563$	−1.78871	+	2.46195i	−0.0753853	+	0.103759i	−0.845044	−	0.534696i	$-0.820426\pi$
$563$	−1.78871	+	2.46195i	−0.0753853	+	0.103759i	0.769659	+	0.638455i	$0.220426\pi$
$564$	−33.3414	+	24.2239i	−1.40392	+	1.02001i
$565$	−2.07045	+	0.951389i	−0.0871044	+	0.0400253i
$566$	−18.9168	−	13.7438i	−0.795130	−	0.577696i
$567$	0.951057	−	0.309017i	0.0399406	−	0.0129775i
$568$		−	72.2859i		−	3.03305i
$569$	1.53791	+	4.73321i	0.0644727	+	0.198426i	0.978104	−	0.208118i	$-0.0667337\pi$
$569$	1.53791	+	4.73321i	0.0644727	+	0.198426i	−0.913631	+	0.406544i	$0.866734\pi$
$570$	41.4942	−	4.85918i	1.73800	−	0.203529i
$571$	−5.84148	+	17.9782i	−0.244459	+	0.752366i	0.751267	+	0.659999i	$0.229443\pi$
$571$	−5.84148	+	17.9782i	−0.244459	+	0.752366i	−0.995725	+	0.0923670i	$0.970557\pi$
$572$	15.1867	+	4.93444i	0.634986	+	0.206319i
$573$	−2.05073	−	2.82259i	−0.0856704	−	0.117915i
$574$	−21.3156			−0.889697
$575$	15.4174	−	36.9624i	0.642952	−	1.54144i
$576$	−8.03945			−0.334977
$577$	6.48120	+	8.92061i	0.269816	+	0.371370i	0.922328	−	0.386409i	$-0.126285\pi$
$577$	6.48120	+	8.92061i	0.269816	+	0.371370i	−0.652512	+	0.757779i	$0.726285\pi$
$578$	42.3646	+	13.7651i	1.76214	+	0.572553i
$579$	−1.33143	+	4.09771i	−0.0553322	+	0.170295i
$580$	−25.2286	−	54.9033i	−1.04756	−	2.27974i
$581$	−3.43407	−	10.5690i	−0.142469	−	0.438476i
$582$		−	16.1208i		−	0.668227i
$583$	−3.23029	+	1.04959i	−0.133785	+	0.0434694i
$584$	−13.8282	−	10.0468i	−0.572216	−	0.415739i
$585$	6.18967	+	1.23915i	0.255911	+	0.0512327i
$586$	45.2142	−	32.8501i	1.86778	−	1.35702i
$587$	15.2173	−	20.9448i	0.628083	−	0.864482i	−0.369827	−	0.929101i	$-0.620583\pi$
$587$	15.2173	−	20.9448i	0.628083	−	0.864482i	0.997910	+	0.0646183i	$0.0205830\pi$
$588$	2.34920	−	3.23340i	0.0968796	−	0.133343i
$589$	−2.07340	+	1.50642i	−0.0854331	+	0.0620708i
$590$	−25.3057	+	45.0559i	−1.04182	+	1.85492i
$591$	−8.70247	−	6.32272i	−0.357972	−	0.260082i
$592$	−1.41001	+	0.458140i	−0.0579511	+	0.0188294i
$593$			14.3472i			0.589168i	0.955626	+	0.294584i	$0.0951812\pi$
$593$			14.3472i			0.589168i	−0.955626	+	0.294584i	$0.904819\pi$
$594$	1.07097	+	3.29610i	0.0439424	+	0.135241i
$595$	−2.60388	+	13.0066i	−0.106749	+	0.533218i
$596$	−12.0534	+	37.0965i	−0.493725	+	1.51953i
$597$	−0.501928	−	0.163086i	−0.0205426	−	0.00667468i
$598$	−32.5471	−	44.7972i	−1.33095	−	1.83189i
$599$	36.3718			1.48611			0.743056	−	0.669229i	$-0.233376\pi$
$599$	36.3718			1.48611			0.743056	+	0.669229i	$0.233376\pi$
$600$	−12.7224	−	20.8767i	−0.519390	−	0.852288i
$601$	−7.07252			−0.288494			−0.144247	−	0.989542i	$-0.546076\pi$
$601$	−7.07252			−0.288494			−0.144247	+	0.989542i	$0.546076\pi$
$602$	−4.07128	−	5.60364i	−0.165933	−	0.228387i
$603$	−0.170770	−	0.0554867i	−0.00695431	−	0.00225959i
$604$	7.47304	−	22.9997i	0.304074	−	0.935843i
$605$	−14.7899	+	13.6378i	−0.601296	+	0.554456i
$606$	10.6041	+	32.6361i	0.430763	+	1.32575i
$607$		−	30.1220i		−	1.22261i	−0.791394	−	0.611306i	$-0.790644\pi$
$607$		−	30.1220i		−	1.22261i	0.791394	−	0.611306i	$-0.209356\pi$
$608$	0.233992	−	0.0760286i	0.00948962	−	0.00308337i
$609$	5.46975	+	3.97401i	0.221646	+	0.161035i
$610$	12.1928	+	13.2228i	0.493672	+	0.535377i
$611$	23.5503	−	17.1103i	0.952744	−	0.692209i
$612$	13.9358	−	19.1810i	0.563322	−	0.775346i
$613$	5.15325	−	7.09284i	0.208138	−	0.286477i	−0.692167	−	0.721738i	$-0.743344\pi$
$613$	5.15325	−	7.09284i	0.208138	−	0.286477i	0.900305	+	0.435260i	$0.143344\pi$
$614$	41.9551	−	30.4822i	1.69317	−	1.23016i
$615$	−2.26383	−	19.3316i	−0.0912866	−	0.779527i
$616$	5.59842	+	4.06749i	0.225567	+	0.163884i
$617$	−0.470805	+	0.152974i	−0.0189539	+	0.00615849i	−0.318479	−	0.947930i	$-0.603172\pi$
$617$	−0.470805	+	0.152974i	−0.0189539	+	0.00615849i	0.299525	+	0.954089i	$0.403172\pi$
$618$		−	31.2098i		−	1.25544i
$619$	8.76792	+	26.9849i	0.352413	+	1.08461i	0.957495	+	0.288451i	$0.0931403\pi$
$619$	8.76792	+	26.9849i	0.352413	+	1.08461i	−0.605082	+	0.796163i	$0.706860\pi$
$620$	2.61741	+	1.47007i	0.105118	+	0.0590395i
$621$	2.47516	−	7.61776i	0.0993247	−	0.305690i
$622$	−25.5739	−	8.30945i	−1.02542	−	0.333179i
$623$	−1.62282	−	2.23362i	−0.0650170	−	0.0894882i
$624$	−11.2364			−0.449814
$625$	−11.4597	+	22.2188i	−0.458388	+	0.888752i
$626$	9.31323			0.372232
$627$	−6.34688	−	8.73573i	−0.253470	−	0.348872i
$628$	15.3166	+	4.97667i	0.611200	+	0.198591i
$629$	−0.682811	+	2.10148i	−0.0272255	+	0.0837913i
$630$	4.77424	+	2.68145i	0.190210	+	0.106832i
$631$	−12.5160	−	38.5202i	−0.498253	−	1.53347i	−0.811825	−	0.583901i	$-0.801525\pi$
$631$	−12.5160	−	38.5202i	−0.498253	−	1.53347i	0.313571	−	0.949565i	$-0.398475\pi$
$632$		−	16.7606i		−	0.666702i
$633$	−24.9540	+	8.10804i	−0.991832	+	0.322266i
$634$	20.4426	+	14.8524i	0.811879	+	0.589864i
$635$	3.52698	+	30.1181i	0.139964	+	1.19520i
$636$	7.75992	−	5.63791i	0.307701	−	0.223558i
$637$	−1.65934	+	2.28388i	−0.0657453	+	0.0904907i
$638$	−13.7728	+	18.9567i	−0.545272	+	0.750502i
$639$	−11.9603	+	8.68964i	−0.473141	+	0.343757i
$640$	−29.7443	−	32.2571i	−1.17575	−	1.27507i
$641$	19.7903	+	14.3785i	0.781670	+	0.567917i	0.905480	−	0.424389i	$-0.139511\pi$
$641$	19.7903	+	14.3785i	0.781670	+	0.567917i	−0.123809	+	0.992306i	$0.539511\pi$
$642$	16.8913	−	5.48830i	0.666645	−	0.216606i
$643$			36.5738i			1.44233i	0.692764	+	0.721164i	$0.256393\pi$
$643$			36.5738i			1.44233i	−0.692764	+	0.721164i	$0.743607\pi$
$644$	−9.89248	−	30.4459i	−0.389818	−	1.19974i
$645$	4.64968	−	4.28748i	0.183081	−	0.168819i
$646$	−34.2495	+	105.409i	−1.34753	+	4.14727i
$647$	−13.1570	−	4.27498i	−0.517257	−	0.168067i	0.0387433	−	0.999249i	$-0.487665\pi$
$647$	−13.1570	−	4.27498i	−0.517257	−	0.168067i	−0.556000	+	0.831182i	$0.687665\pi$
$648$	−2.87401	−	3.95574i	−0.112902	−	0.155396i
$649$	13.3563			0.524281
$650$	17.9875	+	29.5164i	0.705528	+	1.15773i
$651$	−0.335909			−0.0131653
$652$	23.5991	+	32.4814i	0.924214	+	1.27207i
$653$	−21.9802	−	7.14181i	−0.860153	−	0.279481i	−0.154460	−	0.987999i	$-0.549364\pi$
$653$	−21.9802	−	7.14181i	−0.860153	−	0.279481i	−0.705692	+	0.708518i	$0.749364\pi$
$654$	7.54173	−	23.2111i	0.294905	−	0.907624i
$655$	−9.19172	+	45.9134i	−0.359150	+	1.79398i
$656$	10.7062	+	32.9501i	0.418005	+	1.28649i
$657$			3.49573i			0.136382i
$658$	24.0152	−	7.80301i	0.936210	−	0.304193i
$659$	−33.4699	−	24.3173i	−1.30380	−	0.947266i	−0.303815	−	0.952731i	$-0.598261\pi$
$659$	−33.4699	−	24.3173i	−1.30380	−	0.947266i	−0.999985	+	0.00546455i	$0.998261\pi$
$660$	−6.19376	+	11.0278i	−0.241092	+	0.429255i
$661$	17.5940	−	12.7828i	0.684329	−	0.497194i	−0.190462	−	0.981695i	$-0.560999\pi$
$661$	17.5940	−	12.7828i	0.684329	−	0.497194i	0.874791	+	0.484501i	$0.160999\pi$
$662$	36.3022	−	49.9657i	1.41092	−	1.94197i
$663$	−9.84342	+	13.5483i	−0.382287	+	0.526173i
$664$	−43.9598	+	31.9386i	−1.70597	+	1.23946i
$665$	−16.7284	−	3.34899i	−0.648701	−	0.129868i
$666$	0.737939	+	0.536144i	0.0285946	+	0.0207752i
$667$	51.5036	−	16.7345i	1.99423	−	0.647963i
$668$		−	8.05511i		−	0.311662i
$669$	−0.665164	−	2.04716i	−0.0257167	−	0.0791479i
$670$	−0.410528	−	0.893406i	−0.0158601	−	0.0345153i
$671$	1.43655	−	4.42125i	0.0554574	−	0.170680i
$672$	0.0306688	+	0.00996490i	0.00118308	+	0.000384404i
$673$	9.54645	+	13.1396i	0.367989	+	0.506493i	0.952353	−	0.304999i	$-0.0986560\pi$
$673$	9.54645	+	13.1396i	0.367989	+	0.506493i	−0.584364	+	0.811492i	$0.698656\pi$
$674$	−12.6651			−0.487841
$675$	−1.92483	+	4.61466i	−0.0740866	+	0.177618i
$676$	−20.1054			−0.773284
$677$	−23.2536	−	32.0058i	−0.893708	−	1.23008i	−0.972432	−	0.233187i	$-0.925084\pi$
$677$	−23.2536	−	32.0058i	−0.893708	−	1.23008i	0.0787237	−	0.996896i	$-0.474916\pi$
$678$	−2.37323	−	0.771111i	−0.0911435	−	0.0296143i
$679$	−2.03428	+	6.26089i	−0.0780687	+	0.240271i
$680$	64.4183	−	7.54372i	2.47033	−	0.289288i
$681$	−3.61863	−	11.1370i	−0.138666	−	0.426771i
$682$		−	1.16417i		−	0.0445784i
$683$	0.265798	−	0.0863631i	0.0101705	−	0.00330459i	−0.303927	−	0.952695i	$-0.598298\pi$
$683$	0.265798	−	0.0863631i	0.0101705	−	0.00330459i	0.314098	+	0.949391i	$0.398298\pi$
$684$	24.6697	+	17.9236i	0.943269	+	0.685325i
$685$	−18.4208	+	8.46454i	−0.703824	+	0.323413i
$686$	−1.98113	+	1.43938i	−0.0756401	+	0.0549557i
$687$	5.86378	−	8.07079i	0.223717	−	0.307920i
$688$	−6.61735	+	9.10800i	−0.252284	+	0.347239i
$689$	−5.48114	+	3.98228i	−0.208815	+	0.151713i
$690$	39.8532	−	18.3129i	1.51719	−	0.697161i
$691$	−1.99298	−	1.44799i	−0.0758167	−	0.0550840i	0.549231	−	0.835670i	$-0.314921\pi$
$691$	−1.99298	−	1.44799i	−0.0758167	−	0.0550840i	−0.625048	+	0.780586i	$0.714921\pi$
$692$	86.6949	−	28.1689i	3.29564	−	1.07082i
$693$		−	1.41527i		−	0.0537615i
$694$	23.7639	+	73.1377i	0.902065	+	2.77627i
$695$	36.1059	−	4.22819i	1.36958	−	0.160384i
$696$	10.2156	−	31.4403i	0.387220	−	1.19174i
$697$	49.1088	+	15.9564i	1.86013	+	0.604393i
$698$	20.9667	+	28.8582i	0.793603	+	1.09230i
$699$	−0.264129			−0.00999027
$700$	4.61703	+	19.4428i	0.174507	+	0.734871i
$701$	51.3215			1.93839			0.969193	−	0.246301i	$-0.0792151\pi$
$701$	51.3215			1.93839			0.969193	+	0.246301i	$0.0792151\pi$
$702$	4.06341	+	5.59281i	0.153364	+	0.211087i
$703$	−2.70282	−	0.878198i	−0.101939	−	0.0331219i
$704$	−3.51598	+	10.8211i	−0.132514	+	0.407835i
$705$	9.62728	+	20.9512i	0.362584	+	0.789069i
$706$	−18.7929	−	57.8386i	−0.707280	−	2.17678i
$707$		−	14.0131i		−	0.527018i
$708$	−35.8721	+	11.6555i	−1.34816	+	0.438042i
$709$	10.3052	+	7.48720i	0.387022	+	0.281188i	0.764234	−	0.644939i	$-0.223117\pi$
$709$	10.3052	+	7.48720i	0.387022	+	0.281188i	−0.377212	+	0.926127i	$0.623117\pi$
$710$	−79.3764	−	15.8909i	−2.97894	−	0.596376i
$711$	−2.77318	+	2.01483i	−0.104002	+	0.0755621i
$712$	−7.93489	+	10.9214i	−0.297373	+	0.409298i
$713$	−1.58147	+	2.17671i	−0.0592266	+	0.0815185i
$714$	−11.7524	+	8.53860i	−0.439822	+	0.319549i
$715$	4.37490	−	7.78935i	0.163612	−	0.291305i
$716$	−0.442789	−	0.321705i	−0.0165478	−	0.0120227i
$717$	21.3258	−	6.92917i	0.796426	−	0.258775i
$718$			51.9567i			1.93901i
$719$	−3.90274	−	12.0114i	−0.145548	−	0.447949i	0.851533	−	0.524300i	$-0.175673\pi$
$719$	−3.90274	−	12.0114i	−0.145548	−	0.447949i	−0.997081	+	0.0763510i	$0.975673\pi$
$720$	1.74711	−	8.72693i	0.0651108	−	0.325233i
$721$	−3.93838	+	12.1211i	−0.146673	+	0.451413i
$722$	−91.3218	−	29.6722i	−3.39864	−	1.10429i
$723$	−6.72243	−	9.25264i	−0.250010	−	0.344109i
$724$	−0.879297			−0.0326788
$725$	−32.8903	+	7.81036i	−1.22152	+	0.290069i
$726$	−22.0321			−0.817687
$727$	−2.04198	−	2.81055i	−0.0757329	−	0.104237i	0.769470	−	0.638683i	$-0.220520\pi$
$727$	−2.04198	−	2.81055i	−0.0757329	−	0.104237i	−0.845203	+	0.534446i	$0.820520\pi$
$728$	13.1278	+	4.26549i	0.486549	+	0.158089i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	−14.0722	+	12.9760i	−0.520835	+	0.480263i
$731$	5.18502	+	15.9578i	0.191775	+	0.590222i
$732$			13.1281i			0.485230i
$733$	25.2054	−	8.18974i	0.930984	−	0.302495i	0.196019	−	0.980600i	$-0.437199\pi$
$733$	25.2054	−	8.18974i	0.930984	−	0.302495i	0.734965	+	0.678105i	$0.237199\pi$
$734$	20.8239	+	15.1295i	0.768624	+	0.558438i
$735$	−1.51581	−	1.64387i	−0.0559117	−	0.0606350i
$736$	0.208963	−	0.151820i	0.00770247	−	0.00559617i
$737$	−0.149370	+	0.205590i	−0.00550211	+	0.00757300i
$738$	12.5290	−	17.2447i	0.461199	−	0.634786i
$739$	−22.4861	+	16.3371i	−0.827166	+	0.600971i	−0.918756	−	0.394826i	$-0.870805\pi$
$739$	−22.4861	+	16.3371i	−0.827166	+	0.600971i	0.0915902	+	0.995797i	$0.470805\pi$
$740$	0.387179	+	3.30625i	0.0142330	+	0.121540i
$741$	−17.4252	−	12.6601i	−0.640130	−	0.465082i
$742$	−5.58934	+	1.81609i	−0.205191	+	0.0666706i
$743$			2.39723i			0.0879459i	0.999033	+	0.0439729i	$0.0140015\pi$
$743$			2.39723i			0.0879459i	−0.999033	+	0.0439729i	$0.985998\pi$
$744$	0.507545	+	1.56206i	0.0186075	+	0.0572680i
$745$	19.0271	+	10.6866i	0.697097	+	0.391525i
$746$	5.25538	−	16.1744i	0.192413	−	0.592187i
$747$	10.5690	+	3.43407i	0.386699	+	0.125646i
$748$	−19.7229	−	27.1462i	−0.721140	−	0.992564i
$749$	−7.25270			−0.265008
$750$	−25.7213	+	9.38093i	−0.939210	+	0.342543i
$751$	−15.9908			−0.583511			−0.291756	−	0.956493i	$-0.594239\pi$
$751$	−15.9908			−0.583511			−0.291756	+	0.956493i	$0.594239\pi$
$752$	−24.1241	−	33.2040i	−0.879716	−	1.21083i
$753$	−18.8716	−	6.13175i	−0.687719	−	0.223453i
$754$	−14.4432	+	44.4517i	−0.525992	+	1.61884i
$755$	−11.7967	−	6.62563i	−0.429326	−	0.241131i
$756$	1.23505	+	3.80109i	0.0449183	+	0.138244i
$757$		−	10.3027i		−	0.374458i	−0.982316	−	0.187229i	$-0.940049\pi$
$757$		−	10.3027i		−	0.374458i	0.982316	−	0.187229i	$-0.0599507\pi$
$758$	8.84118	−	2.87267i	0.321126	−	0.104340i
$759$	−9.17099	−	6.66312i	−0.332886	−	0.241856i
$760$	9.70236	+	82.8517i	0.351942	+	3.00535i
$761$	−34.3160	+	24.9320i	−1.24395	+	0.903785i	−0.997855	−	0.0654594i	$-0.979149\pi$
$761$	−34.3160	+	24.9320i	−1.24395	+	0.903785i	−0.246099	+	0.969245i	$0.579149\pi$
$762$	−19.5198	+	26.8667i	−0.707127	+	0.973276i
$763$	−5.85802	+	8.06287i	−0.212075	+	0.291896i
$764$	11.2810	−	8.19616i	0.408134	−	0.296527i
$765$	−8.99203	−	9.75167i	−0.325108	−	0.352572i
$766$	64.3217	+	46.7324i	2.32404	+	1.68851i
$767$	25.3379	−	8.23278i	0.914898	−	0.297268i
$768$		−	31.9734i		−	1.15374i
$769$	−7.46028	−	22.9604i	−0.269025	−	0.827973i	−0.990739	−	0.135781i	$-0.956646\pi$
$769$	−7.46028	−	22.9604i	−0.269025	−	0.827973i	0.721714	−	0.692191i	$-0.243354\pi$
$770$	5.69720	−	5.25340i	0.205313	−	0.189319i
$771$	−3.08966	+	9.50900i	−0.111271	+	0.342458i
$772$	−16.3773	−	5.32132i	−0.589434	−	0.191519i
$773$	6.75207	+	9.29342i	0.242855	+	0.334261i	0.912993	−	0.407975i	$-0.133765\pi$
$773$	6.75207	+	9.29342i	0.242855	+	0.334261i	−0.670138	+	0.742237i	$0.733765\pi$
$774$	6.92648			0.248967
$775$	1.09393	−	1.27444i	0.0392952	−	0.0457792i
$776$	32.1884			1.15550
$777$	−0.218940	−	0.301345i	−0.00785443	−	0.0108107i
$778$	−56.3582	−	18.3119i	−2.02054	−	0.656513i
$779$	−20.5224	+	63.1614i	−0.735291	+	2.26299i
$780$	−4.95254	+	24.7383i	−0.177329	+	0.885773i
$781$	6.46552	+	19.8988i	0.231355	+	0.712036i
$782$			116.356i			4.16088i
$783$	−6.43008	+	2.08926i	−0.229792	+	0.0746641i
$784$	3.22008	+	2.33953i	0.115003	+	0.0835546i
$785$	4.41234	−	7.85601i	0.157483	−	0.280393i
$786$	−41.4860	+	30.1413i	−1.47976	+	1.07511i
$787$	12.0850	−	16.6335i	0.430782	−	0.592921i	−0.537350	−	0.843359i	$-0.680575\pi$
$787$	12.0850	−	16.6335i	0.430782	−	0.592921i	0.968133	+	0.250438i	$0.0805747\pi$
$788$	25.2700	−	34.7812i	0.900208	−	1.23903i
$789$	−23.2479	+	16.8906i	−0.827646	+	0.601320i
$790$	−18.4047	−	3.68456i	−0.654809	−	0.131091i
$791$	0.824395	+	0.598958i	0.0293121	+	0.0212965i
$792$	−6.58134	+	2.13841i	−0.233858	+	0.0759850i
$793$		−	9.27292i		−	0.329291i
$794$	−13.3861	−	41.1982i	−0.475056	−	1.46207i
$795$	−2.24067	−	4.87623i	−0.0794684	−	0.172942i
$796$	0.651808	−	2.00606i	0.0231027	−	0.0711029i
$797$	−44.7803	−	14.5500i	−1.58620	−	0.515387i	−0.622555	−	0.782576i	$-0.713905\pi$
$797$	−44.7803	−	14.5500i	−1.58620	−	0.515387i	−0.963644	+	0.267189i	$0.913905\pi$
$798$	−10.9819	−	15.1153i	−0.388756	−	0.535077i
$799$	−61.1695			−2.16402
$800$	−0.137684	+	0.0839053i	−0.00486785	+	0.00296650i
$801$	2.76091			0.0975519
$802$	42.3617	+	58.3058i	1.49584	+	2.05885i
$803$	4.70525	+	1.52883i	0.166045	+	0.0539512i
$804$	0.221764	−	0.682519i	0.00782101	−	0.0240706i
$805$	−17.7889	+	2.08317i	−0.626975	+	0.0734220i
$806$	−0.717591	−	2.20852i	−0.0252760	−	0.0777917i
$807$			32.0763i			1.12914i
$808$	−65.1647	+	21.1733i	−2.29248	+	0.744873i
$809$	−34.6275	−	25.1584i	−1.21744	−	0.884521i	−0.221554	−	0.975148i	$-0.571113\pi$
$809$	−34.6275	−	25.1584i	−1.21744	−	0.884521i	−0.995885	+	0.0906271i	$0.971113\pi$
$810$	−4.97557	+	2.28632i	−0.174824	+	0.0803330i
$811$	−43.3905	+	31.5251i	−1.52365	+	1.10700i	−0.564006	+	0.825771i	$0.690741\pi$
$811$	−43.3905	+	31.5251i	−1.52365	+	1.10700i	−0.959642	+	0.281225i	$0.909259\pi$
$812$	−15.8829	+	21.8610i	−0.557382	+	0.767171i
$813$	11.9376	−	16.4308i	0.418671	−	0.576252i
$814$	1.04438	−	0.758786i	0.0366055	−	0.0265954i
$815$	20.4109	−	9.37898i	0.714962	−	0.328531i
$816$	19.1020	+	13.8784i	0.668704	+	0.485842i
$817$	−20.5242	+	6.66872i	−0.718051	+	0.233309i
$818$			55.2767i			1.93270i
$819$	−0.872365	−	2.68486i	−0.0304829	−	0.0938167i
$820$	77.2629	−	9.04788i	2.69814	−	0.315966i
$821$	−6.48337	+	19.9537i	−0.226271	+	0.696391i	0.771889	+	0.635757i	$0.219312\pi$
$821$	−6.48337	+	19.9537i	−0.226271	+	0.696391i	−0.998160	+	0.0606334i	$0.980688\pi$
$822$	−21.1147	−	6.86059i	−0.736461	−	0.239291i
$823$	−24.5162	−	33.7437i	−0.854581	−	1.17623i	−0.982835	−	0.184489i	$-0.940937\pi$
$823$	−24.5162	−	33.7437i	−0.854581	−	1.17623i	0.128254	−	0.991741i	$-0.459063\pi$
$824$	62.3168			2.17091
$825$	5.36951	+	4.60899i	0.186942	+	0.160464i
$826$	23.1102			0.804108
$827$	−15.8327	−	21.7918i	−0.550555	−	0.757775i	0.439532	−	0.898227i	$-0.355144\pi$
$827$	−15.8327	−	21.7918i	−0.550555	−	0.757775i	−0.990087	+	0.140452i	$0.955144\pi$
$828$	30.4459	+	9.89248i	1.05807	+	0.343788i
$829$	−7.28898	+	22.4332i	−0.253157	+	0.779136i	0.741031	+	0.671471i	$0.234337\pi$
$829$	−7.28898	+	22.4332i	−0.253157	+	0.779136i	−0.994187	+	0.107665i	$0.965663\pi$
$830$	25.4076	+	55.2930i	0.881912	+	1.91925i
$831$	−7.05814	−	21.7227i	−0.244844	−	0.753553i
$832$			22.6956i			0.786829i
$833$	5.64181	−	1.83313i	0.195477	−	0.0635143i
$834$	32.2081	+	23.4006i	1.11528	+	0.810295i
$835$	−4.41897	−	0.884666i	−0.152925	−	0.0306151i
$836$	34.9142	−	25.3666i	1.20753	−	0.877323i
$837$	0.197443	−	0.271756i	0.00682462	−	0.00939328i
$838$	−49.2179	+	67.7426i	−1.70020	+	2.34013i
$839$	−0.563206	+	0.409193i	−0.0194440	+	0.0141269i	−0.597465	−	0.801895i	$-0.703825\pi$
$839$	−0.563206	+	0.409193i	−0.0194440	+	0.0141269i	0.578021	+	0.816022i	$0.303825\pi$
$840$	−5.35407	+	9.53274i	−0.184733	+	0.328911i
$841$	−13.5195	−	9.82246i	−0.466188	−	0.338706i
$842$	−81.1444	+	26.3654i	−2.79642	+	0.908613i
$843$		−	6.54675i		−	0.225482i
$844$	−32.4054	−	99.7337i	−1.11544	−	3.43298i
$845$	−2.20811	+	11.0297i	−0.0759612	+	0.379432i
$846$	−7.80301	+	24.0152i	−0.268273	+	0.825659i
$847$	8.55668	+	2.78023i	0.294011	+	0.0955299i
$848$	5.61469	+	7.72796i	0.192809	+	0.265379i
$849$	−9.54844			−0.327702
$850$	5.87769	−	72.3955i	0.201603	−	2.48314i
$851$	−2.98351			−0.102273
$852$	−34.7299	−	47.8017i	−1.18983	−	1.63766i
$853$	54.6639	+	17.7614i	1.87166	+	0.608139i	0.990905	+	0.134562i	$0.0429628\pi$
$853$	54.6639	+	17.7614i	1.87166	+	0.608139i	0.880753	+	0.473576i	$0.157037\pi$
$854$	2.48565	−	7.65003i	0.0850571	−	0.261779i
$855$	12.5421	−	11.5651i	0.428932	−	0.395519i
$856$	10.9585	+	33.7269i	0.374555	+	1.15276i
$857$			9.30808i			0.317958i	0.987282	+	0.158979i	$0.0508202\pi$
$857$			9.30808i			0.317958i	−0.987282	+	0.158979i	$0.949180\pi$
$858$	9.30500	−	3.02338i	0.317667	−	0.103216i
$859$	19.7210	+	14.3281i	0.672871	+	0.488870i	0.870985	−	0.491309i	$-0.163482\pi$
$859$	19.7210	+	14.3281i	0.672871	+	0.488870i	−0.198114	+	0.980179i	$0.563482\pi$
$860$	17.1358	+	18.5834i	0.584326	+	0.633689i
$861$	−7.04205	+	5.11635i	−0.239992	+	0.174365i
$862$	8.94408	−	12.3105i	0.304637	−	0.419297i
$863$	−7.74942	+	10.6662i	−0.263793	+	0.363080i	−0.920282	−	0.391255i	$-0.872041\pi$
$863$	−7.74942	+	10.6662i	−0.263793	+	0.363080i	0.656489	+	0.754336i	$0.272041\pi$
$864$	−0.0260884	+	0.0189544i	−0.000887547	+	0.000644841i
$865$	−5.93182	−	50.6538i	−0.201688	−	1.72228i
$866$	−8.18021	−	5.94327i	−0.277975	−	0.201961i
$867$	17.3000	−	5.62112i	0.587540	−	0.190903i
$868$		−	1.34253i		−	0.0455685i
$869$	1.49913	+	4.61386i	0.0508546	+	0.156514i
$870$	−32.2786	−	18.1293i	−1.09435	−	0.614640i
$871$	−0.156641	+	0.482090i	−0.00530756	+	0.0163350i
$872$	46.3456	+	15.0586i	1.56946	+	0.509949i
$873$	−3.86944	−	5.32583i	−0.130961	−	0.180252i
$874$	−149.651			−5.06204
$875$	11.1733	−	0.397525i	0.377725	−	0.0134388i
$876$	−13.9714			−0.472050
$877$	8.97052	+	12.3469i	0.302913	+	0.416924i	0.933155	−	0.359475i	$-0.117044\pi$
$877$	8.97052	+	12.3469i	0.302913	+	0.416924i	−0.630242	+	0.776399i	$0.717044\pi$
$878$	50.2103	+	16.3143i	1.69452	+	0.550581i
$879$	7.05251	−	21.7054i	0.237875	−	0.732105i
$880$	−10.9823	−	6.16824i	−0.370215	−	0.207931i
$881$	−8.01716	−	24.6743i	−0.270105	−	0.831298i	−0.990473	−	0.137706i	$-0.956027\pi$
$881$	−8.01716	−	24.6743i	−0.270105	−	0.831298i	0.720368	−	0.693592i	$-0.243973\pi$
$882$		−	2.44882i		−	0.0824560i
$883$	31.7533	−	10.3173i	1.06858	−	0.347204i	0.278648	−	0.960393i	$-0.410114\pi$
$883$	31.7533	−	10.3173i	1.06858	−	0.347204i	0.789936	+	0.613190i	$0.210114\pi$
$884$	−54.1486	−	39.3413i	−1.82121	−	1.32319i
$885$	2.45443	+	20.9592i	0.0825049	+	0.704537i
$886$	56.4185	−	40.9904i	1.89542	−	1.37710i
$887$	7.92211	−	10.9038i	0.265998	−	0.366115i	−0.655035	−	0.755598i	$-0.727346\pi$
$887$	7.92211	−	10.9038i	0.265998	−	0.366115i	0.921034	+	0.389483i	$0.127346\pi$
$888$	−1.07052	+	1.47345i	−0.0359244	+	0.0494456i
$889$	10.9713	−	7.97110i	0.367965	−	0.267342i
$890$	10.2484	+	11.1141i	0.343526	+	0.372547i
$891$	1.14497	+	0.831872i	0.0383581	+	0.0278688i
$892$	8.18191	−	2.65846i	0.273951	−	0.0890119i
$893$		−	78.6733i		−	2.63270i
$894$	7.38521	+	22.7293i	0.246998	+	0.760183i
$895$	−0.225115	+	0.207579i	−0.00752477	+	0.00693860i
$896$	−6.06373	+	18.6623i	−0.202575	+	0.623462i
$897$	−21.5052	−	6.98745i	−0.718037	−	0.233304i
$898$	11.0416	+	15.1975i	0.368463	+	0.507146i
$899$	2.27108			0.0757448
$900$	−18.4434	−	7.69296i	−0.614781	−	0.256432i
$901$	14.2367			0.474293
$902$	−17.7319	−	24.4058i	−0.590407	−	0.812625i
$903$	−2.69006	−	0.874054i	−0.0895197	−	0.0290867i
$904$	1.53968	−	4.73865i	0.0512090	−	0.157605i
$905$	−0.0965702	+	0.482376i	−0.00321010	+	0.0160347i
$906$	−4.57880	−	14.0921i	−0.152120	−	0.468179i
$907$			43.8872i			1.45725i	0.684913	+	0.728625i	$0.259840\pi$
$907$			43.8872i			1.45725i	−0.684913	+	0.728625i	$0.740160\pi$
$908$	44.5113	−	14.4626i	1.47716	−	0.479958i
$909$	11.3369	+	8.23672i	0.376020	+	0.273195i
$910$	7.56983	−	13.4778i	0.250937	−	0.446785i
$911$	2.71854	−	1.97514i	0.0900693	−	0.0654392i	−0.541839	−	0.840482i	$-0.682272\pi$
$911$	2.71854	−	1.97514i	0.0900693	−	0.0654392i	0.631909	+	0.775043i	$0.282272\pi$
$912$	−17.8497	+	24.5681i	−0.591064	+	0.813530i
$913$	9.24451	−	12.7240i	0.305949	−	0.421102i
$914$	0.132940	−	0.0965866i	0.00439727	−	0.00319480i
$915$	7.20199	+	1.44182i	0.238090	+	0.0476650i
$916$	32.2566	+	23.4358i	1.06579	+	0.774340i
$917$	19.9156	−	6.47097i	0.657671	−	0.213690i
$918$		−	14.5267i		−	0.479454i
$919$	−15.9311	−	49.0310i	−0.525520	−	1.61738i	−0.763286	−	0.646061i	$-0.776415\pi$
$919$	−15.9311	−	49.0310i	−0.525520	−	1.61738i	0.237766	−	0.971322i	$-0.423585\pi$
$920$	36.5655	+	79.5751i	1.20553	+	2.62351i
$921$	6.54415	−	20.1408i	0.215637	−	0.663663i
$922$	49.2853	+	16.0137i	1.62312	+	0.527385i
$923$	24.5311	+	33.7642i	0.807452	+	1.11136i
$924$	5.65640			0.186082
$925$	1.85631	+	0.150711i	0.0610350	+	0.00495535i
$926$	13.8481			0.455076
$927$	−7.49124	−	10.3108i	−0.246045	−	0.338651i
$928$	−0.207351	−	0.0673726i	−0.00680665	−	0.00221161i
$929$	−1.79914	+	5.53719i	−0.0590279	+	0.181669i	−0.976223	−	0.216770i	$-0.930448\pi$
$929$	−1.79914	+	5.53719i	−0.0590279	+	0.181669i	0.917195	+	0.398439i	$0.130448\pi$
$930$	1.82686	−	0.213935i	0.0599052	−	0.00701520i
$931$	2.35769	+	7.25621i	0.0772701	+	0.237813i
$932$		−	1.05564i		−	0.0345788i
$933$	−10.4434	+	3.39325i	−0.341900	+	0.111090i
$934$	−23.5821	−	17.1334i	−0.771631	−	0.560623i
$935$	−17.0583	+	7.83845i	−0.557866	+	0.256345i
$936$	−11.1672	+	8.11344i	−0.365011	+	0.265196i
$937$	−32.6670	+	44.9623i	−1.06719	+	1.46886i	−0.194293	+	0.980944i	$0.562241\pi$
$937$	−32.6670	+	44.9623i	−1.06719	+	1.46886i	−0.872893	+	0.487912i	$0.837759\pi$
$938$	−0.258453	+	0.355730i	−0.00843878	+	0.0116150i
$939$	3.07682	−	2.23544i	0.100408	−	0.0729508i
$940$	−83.7359	+	38.4774i	−2.73116	+	1.25499i
$941$	−14.4849	−	10.5239i	−0.472195	−	0.343070i	0.326101	−	0.945335i	$-0.394265\pi$
$941$	−14.4849	−	10.5239i	−0.472195	−	0.343070i	−0.798296	+	0.602265i	$0.794265\pi$
$942$	9.38464	−	3.04925i	0.305768	−	0.0993500i
$943$			69.7208i			2.27042i
$944$	−11.6075	−	35.7243i	−0.377793	−	1.16273i
$945$	2.22089	−	0.260078i	0.0722456	−	0.00846033i
$946$	3.02923	−	9.32302i	0.0984888	−	0.303118i
$947$	18.1948	+	5.91186i	0.591253	+	0.192110i	0.589335	−	0.807888i	$-0.299390\pi$
$947$	18.1948	+	5.91186i	0.591253	+	0.192110i	0.00191754	+	0.999998i	$0.499390\pi$
$948$	−8.05269	−	11.0836i	−0.261539	−	0.359978i
$949$	9.86857			0.320347
$950$	93.1115	+	7.55960i	3.02094	+	0.245266i
$951$	10.3186			0.334604
$952$	−17.0491	−	23.4660i	−0.552564	−	0.760539i
$953$	2.68559	+	0.872600i	0.0869946	+	0.0282663i	0.352191	−	0.935928i	$-0.385437\pi$
$953$	2.68559	+	0.872600i	0.0869946	+	0.0282663i	−0.265196	+	0.964194i	$0.585437\pi$
$954$	1.81609	−	5.58934i	0.0587979	−	0.180961i
$955$	−3.25739	−	7.08885i	−0.105407	−	0.229390i
$956$	27.6938	+	85.2329i	0.895683	+	2.75663i
$957$			9.56859i			0.309309i
$958$	19.7907	−	6.43038i	0.639408	−	0.207756i
$959$	7.33467	+	5.32895i	0.236849	+	0.172081i
$960$	−17.6270	−	3.52887i	−0.568909	−	0.113894i
$961$	24.9882	−	18.1550i	0.806072	−	0.585646i
$962$	1.51355	−	2.08323i	0.0487989	−	0.0671659i
$963$	4.26303	−	5.86755i	0.137374	−	0.189079i
$964$	36.9801	−	26.8676i	1.19105	−	0.865347i
$965$	−4.71791	+	8.40007i	−0.151875	+	0.270408i
$966$	−15.8685	−	11.5291i	−0.510559	−	0.370943i
$967$	−29.7991	+	9.68231i	−0.958274	+	0.311362i	−0.746073	−	0.665864i	$-0.768063\pi$
$967$	−29.7991	+	9.68231i	−0.958274	+	0.311362i	−0.212201	+	0.977226i	$0.568063\pi$
$968$		−	43.9915i		−	1.41394i
$969$	13.9861	+	43.0449i	0.449300	+	1.38280i
$970$	7.07612	−	35.3458i	0.227201	−	1.13488i
$971$	17.3134	−	53.2852i	0.555613	−	1.71000i	−0.138705	−	0.990334i	$-0.544294\pi$
$971$	17.3134	−	53.2852i	0.555613	−	1.71000i	0.694318	−	0.719668i	$-0.255706\pi$
$972$	−3.80109	−	1.23505i	−0.121920	−	0.0396142i
$973$	−9.55586	−	13.1525i	−0.306347	−	0.421650i
$974$	64.1995			2.05709
$975$	13.0273	+	5.43385i	0.417208	+	0.174022i
$976$	−13.0741			−0.418490
$977$	−19.0702	−	26.2479i	−0.610110	−	0.839745i	0.386476	−	0.922299i	$-0.373692\pi$
$977$	−19.0702	−	26.2479i	−0.610110	−	0.839745i	−0.996587	+	0.0825547i	$0.973692\pi$
$978$	23.3958	+	7.60176i	0.748116	+	0.243077i
$979$	1.20746	−	3.71618i	0.0385905	−	0.118769i
$980$	6.57006	−	6.05826i	0.209873	−	0.193524i
$981$	−3.07974	−	9.47848i	−0.0983286	−	0.302624i
$982$			62.6551i			1.99940i
$983$	13.6786	−	4.44445i	0.436280	−	0.141756i	−0.0826386	−	0.996580i	$-0.526335\pi$
$983$	13.6786	−	4.44445i	0.436280	−	0.141756i	0.518919	+	0.854824i	$0.326335\pi$
$984$	34.4326	+	25.0167i	1.09767	+	0.797504i
$985$	−16.3054	−	17.6829i	−0.519533	−	0.563423i
$986$	79.4577	−	57.7294i	2.53045	−	1.83848i
$987$	6.06097	−	8.34221i	0.192923	−	0.265535i
$988$	50.5988	−	69.6433i	1.60976	−	2.21565i
$989$	−18.3288	+	13.3167i	−0.582823	+	0.423445i
$990$	0.901358	+	7.69700i	0.0286471	+	0.244627i
$991$	−17.0385	−	12.3792i	−0.541246	−	0.393238i	0.283301	−	0.959031i	$-0.408570\pi$
$991$	−17.0385	−	12.3792i	−0.541246	−	0.393238i	−0.824548	+	0.565793i	$0.808570\pi$
$992$	0.0103019	−	0.00334730i	0.000327087	−	0.000106277i
$993$		−	25.2207i		−	0.800356i
$994$	11.1872	+	34.4307i	0.354837	+	1.09208i
$995$	−1.02892	−	0.577896i	−0.0326191	−	0.0183205i
$996$	−13.7250	+	42.2412i	−0.434893	+	1.33846i
$997$	5.95395	+	1.93456i	0.188563	+	0.0612680i	0.401777	−	0.915738i	$-0.368393\pi$
$997$	5.95395	+	1.93456i	0.188563	+	0.0612680i	−0.213213	+	0.977006i	$0.568393\pi$
$998$	40.8250	+	56.1908i	1.29229	+	1.77869i
$999$	0.372483			0.0117848

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.z.b.64.16	✓	72
25.9	even	10	inner	525.2.z.b.484.16	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.z.b.64.16	✓	72	1.1	even	1	trivial
525.2.z.b.484.16	yes	72	25.9	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.43938 + 1.98113i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-1.23505 + 3.80109i) q^{4} +(1.94961 + 1.09500i) q^{5} +(0.756726 + 2.32896i) q^{6} -1.00000i q^{7} +(-4.65025 + 1.51096i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(1.43938 + 1.98113i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-1.23505 + 3.80109i) q^{4} +(1.94961 + 1.09500i) q^{5} +(0.756726 + 2.32896i) q^{6} -1.00000i q^{7} +(-4.65025 + 1.51096i) q^{8} +(0.809017 + 0.587785i) q^{9} +(0.636883 + 5.43856i) q^{10} +(1.14497 - 0.831872i) q^{11} +(-2.34920 + 3.23340i) q^{12} +(1.65934 - 2.28388i) q^{13} +(1.98113 - 1.43938i) q^{14} +(1.51581 + 1.64387i) q^{15} +(-3.22008 - 2.33953i) q^{16} +(-5.64181 + 1.83313i) q^{17} +2.44882i q^{18} +(-2.35769 - 7.25621i) q^{19} +(-6.57006 + 6.05826i) q^{20} +(0.309017 - 0.951057i) q^{21} +(3.29610 + 1.07097i) q^{22} +(-4.70803 - 6.48005i) q^{23} -4.88957 q^{24} +(2.60195 + 4.26964i) q^{25} +6.91309 q^{26} +(0.587785 + 0.809017i) q^{27} +(3.80109 + 1.23505i) q^{28} +(-2.08926 + 6.43008i) q^{29} +(-1.07490 + 5.36918i) q^{30} +(-0.103802 - 0.319469i) q^{31} +0.0322471i q^{32} +(1.34600 - 0.437341i) q^{33} +(-11.7524 - 8.53860i) q^{34} +(1.09500 - 1.94961i) q^{35} +(-3.23340 + 2.34920i) q^{36} +(0.218940 - 0.301345i) q^{37} +(10.9819 - 15.1153i) q^{38} +(2.28388 - 1.65934i) q^{39} +(-10.7207 - 2.14625i) q^{40} +(-7.04205 - 5.11635i) q^{41} +(2.32896 - 0.756726i) q^{42} -2.82850i q^{43} +(1.74792 + 5.37956i) q^{44} +(0.933642 + 2.03182i) q^{45} +(6.06121 - 18.6545i) q^{46} +(9.80686 + 3.18644i) q^{47} +(-2.33953 - 3.22008i) q^{48} -1.00000 q^{49} +(-4.71355 + 11.3004i) q^{50} -5.93214 q^{51} +(6.63188 + 9.12800i) q^{52} +(-2.28246 - 0.741618i) q^{53} +(-0.756726 + 2.32896i) q^{54} +(3.14315 - 0.368079i) q^{55} +(1.51096 + 4.65025i) q^{56} -7.62964i q^{57} +(-15.7461 + 5.11622i) q^{58} +(7.63494 + 5.54711i) q^{59} +(-8.12061 + 3.73149i) q^{60} +(2.65741 - 1.93072i) q^{61} +(0.483501 - 0.665482i) q^{62} +(0.587785 - 0.809017i) q^{63} +(-6.50405 + 4.72547i) q^{64} +(5.73591 - 2.63570i) q^{65} +(2.80383 + 2.03710i) q^{66} +(-0.170770 + 0.0554867i) q^{67} -23.7090i q^{68} +(-2.47516 - 7.61776i) q^{69} +(5.43856 - 0.636883i) q^{70} +(-4.56842 + 14.0601i) q^{71} +(-4.65025 - 1.51096i) q^{72} +(2.05474 + 2.82811i) q^{73} +0.912143 q^{74} +(1.15521 + 4.86472i) q^{75} +30.4934 q^{76} +(-0.831872 - 1.14497i) q^{77} +(6.57474 + 2.13626i) q^{78} +(-1.05926 + 3.26007i) q^{79} +(-3.71612 - 8.08715i) q^{80} +(0.309017 + 0.951057i) q^{81} -21.3156i q^{82} +(10.5690 - 3.43407i) q^{83} +(3.23340 + 2.34920i) q^{84} +(-13.0066 - 2.60388i) q^{85} +(5.60364 - 4.07128i) q^{86} +(-3.97401 + 5.46975i) q^{87} +(-4.06749 + 5.59842i) q^{88} +(2.23362 - 1.62282i) q^{89} +(-2.68145 + 4.77424i) q^{90} +(-2.28388 - 1.65934i) q^{91} +(30.4459 - 9.89248i) q^{92} -0.335909i q^{93} +(7.80301 + 24.0152i) q^{94} +(3.34899 - 16.7284i) q^{95} +(-0.00996490 + 0.0306688i) q^{96} +(-6.26089 - 2.03428i) q^{97} +(-1.43938 - 1.98113i) q^{98} +1.41527 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 24 q^{4} - 2 q^{5} + 18 q^{9}+O(q^{10}) \) 72 * q + 24 * q^4 - 2 * q^5 + 18 * q^9	\( 72 q + 24 q^{4} - 2 q^{5} + 18 q^{9} - 28 q^{10} - 12 q^{11} - 20 q^{13} - 24 q^{16} + 10 q^{19} + 10 q^{20} - 18 q^{21} + 50 q^{22} - 10 q^{23} + 12 q^{25} + 36 q^{26} + 20 q^{28} - 2 q^{29} + 10 q^{30} - 16 q^{31} - 10 q^{33} + 24 q^{34} - 10 q^{35} - 24 q^{36} + 10 q^{37} - 100 q^{38} + 16 q^{39} - 14 q^{40} - 16 q^{41} - 18 q^{44} + 2 q^{45} - 44 q^{46} + 20 q^{47} - 72 q^{49} + 86 q^{50} + 32 q^{51} - 80 q^{52} + 70 q^{53} + 46 q^{55} - 40 q^{58} + 44 q^{59} - 62 q^{60} + 4 q^{61} - 50 q^{62} + 48 q^{64} + 38 q^{65} - 16 q^{66} - 20 q^{67} + 4 q^{69} + 10 q^{70} - 8 q^{71} - 20 q^{73} - 116 q^{74} - 8 q^{75} + 92 q^{76} + 20 q^{77} + 90 q^{78} + 28 q^{79} + 114 q^{80} - 18 q^{81} + 30 q^{83} + 24 q^{84} - 122 q^{85} + 40 q^{86} - 40 q^{87} - 270 q^{88} + 2 q^{89} - 12 q^{90} - 16 q^{91} - 100 q^{92} + 22 q^{94} + 116 q^{95} + 10 q^{96} + 190 q^{97} - 48 q^{99}+O(q^{100}) \) 72 * q + 24 * q^4 - 2 * q^5 + 18 * q^9 - 28 * q^10 - 12 * q^11 - 20 * q^13 - 24 * q^16 + 10 * q^19 + 10 * q^20 - 18 * q^21 + 50 * q^22 - 10 * q^23 + 12 * q^25 + 36 * q^26 + 20 * q^28 - 2 * q^29 + 10 * q^30 - 16 * q^31 - 10 * q^33 + 24 * q^34 - 10 * q^35 - 24 * q^36 + 10 * q^37 - 100 * q^38 + 16 * q^39 - 14 * q^40 - 16 * q^41 - 18 * q^44 + 2 * q^45 - 44 * q^46 + 20 * q^47 - 72 * q^49 + 86 * q^50 + 32 * q^51 - 80 * q^52 + 70 * q^53 + 46 * q^55 - 40 * q^58 + 44 * q^59 - 62 * q^60 + 4 * q^61 - 50 * q^62 + 48 * q^64 + 38 * q^65 - 16 * q^66 - 20 * q^67 + 4 * q^69 + 10 * q^70 - 8 * q^71 - 20 * q^73 - 116 * q^74 - 8 * q^75 + 92 * q^76 + 20 * q^77 + 90 * q^78 + 28 * q^79 + 114 * q^80 - 18 * q^81 + 30 * q^83 + 24 * q^84 - 122 * q^85 + 40 * q^86 - 40 * q^87 - 270 * q^88 + 2 * q^89 - 12 * q^90 - 16 * q^91 - 100 * q^92 + 22 * q^94 + 116 * q^95 + 10 * q^96 + 190 * q^97 - 48 * q^99

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