LMFDB - Embedded newform 960.2.cn.a.731.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,2,Mod(11,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 5, 8, 0]))

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

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

chi := DirichletCharacter("960.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.cn (of order $16$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.66563859404$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$128$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			731.15
Character	$\chi$	$=$	960.731
Dual form			960.2.cn.a.851.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33138 + 0.476905i) q^{2} +(-1.53109 - 0.809797i) q^{3} +(1.54512 - 1.26988i) q^{4} +(-0.980785 - 0.195090i) q^{5} +(2.42465 + 0.347961i) q^{6} +(2.42385 + 1.00399i) q^{7} +(-1.45153 + 2.42756i) q^{8} +(1.68846 + 2.47974i) q^{9} +O(q^{10})$	\(q+(-1.33138 + 0.476905i) q^{2} +(-1.53109 - 0.809797i) q^{3} +(1.54512 - 1.26988i) q^{4} +(-0.980785 - 0.195090i) q^{5} +(2.42465 + 0.347961i) q^{6} +(2.42385 + 1.00399i) q^{7} +(-1.45153 + 2.42756i) q^{8} +(1.68846 + 2.47974i) q^{9} +(1.39883 - 0.208003i) q^{10} +(-1.37659 + 0.919810i) q^{11} +(-3.39406 + 0.693061i) q^{12} +(0.263379 + 1.32410i) q^{13} +(-3.70587 - 0.180744i) q^{14} +(1.34368 + 1.09294i) q^{15} +(0.774810 - 3.92424i) q^{16} +(-1.79441 - 1.79441i) q^{17} +(-3.43057 - 2.49623i) q^{18} +(-0.0729955 - 0.366973i) q^{19} +(-1.76318 + 0.944041i) q^{20} +(-2.89810 - 3.50003i) q^{21} +(1.39410 - 1.88112i) q^{22} +(-4.70276 + 1.94795i) q^{23} +(4.18825 - 2.54137i) q^{24} +(0.923880 + 0.382683i) q^{25} +(-0.982125 - 1.63726i) q^{26} +(-0.577090 - 5.16401i) q^{27} +(5.02010 - 1.52671i) q^{28} +(3.66572 - 5.48614i) q^{29} +(-2.31018 - 0.814300i) q^{30} +2.18217 q^{31} +(0.839928 + 5.59415i) q^{32} +(2.85254 - 0.293549i) q^{33} +(3.24479 + 1.53327i) q^{34} +(-2.18141 - 1.45757i) q^{35} +(5.75785 + 1.68737i) q^{36} +(-6.03442 - 1.20032i) q^{37} +(0.272196 + 0.453767i) q^{38} +(0.668993 - 2.24059i) q^{39} +(1.89723 - 2.09774i) q^{40} +(2.99233 + 7.22413i) q^{41} +(5.52764 + 3.27773i) q^{42} +(-9.63806 + 6.43995i) q^{43} +(-0.958957 + 3.16933i) q^{44} +(-1.17224 - 2.76149i) q^{45} +(5.33216 - 4.83622i) q^{46} +(-3.84817 + 3.84817i) q^{47} +(-4.36414 + 5.38092i) q^{48} +(-0.0826897 - 0.0826897i) q^{49} +(-1.41253 - 0.0688926i) q^{50} +(1.29429 + 4.20050i) q^{51} +(2.08840 + 1.71143i) q^{52} +(3.48365 + 5.21365i) q^{53} +(3.23107 + 6.60002i) q^{54} +(1.52959 - 0.633576i) q^{55} +(-5.95554 + 4.42673i) q^{56} +(-0.185411 + 0.620980i) q^{57} +(-2.26408 + 9.05231i) q^{58} +(0.0807657 - 0.406036i) q^{59} +(3.46406 - 0.0175953i) q^{60} +(2.14020 - 3.20303i) q^{61} +(-2.90528 + 1.04069i) q^{62} +(1.60293 + 7.70572i) q^{63} +(-3.78614 - 7.04735i) q^{64} -1.35004i q^{65} +(-3.65781 + 1.75122i) q^{66} +(-4.51773 - 3.01865i) q^{67} +(-5.05126 - 0.493898i) q^{68} +(8.77778 + 0.825804i) q^{69} +(3.59940 + 0.900249i) q^{70} +(-3.93633 + 9.50315i) q^{71} +(-8.47057 + 0.499430i) q^{72} +(4.39584 + 10.6125i) q^{73} +(8.60652 - 1.27977i) q^{74} +(-1.10464 - 1.33408i) q^{75} +(-0.578799 - 0.474323i) q^{76} +(-4.26014 + 0.847394i) q^{77} +(0.177869 + 3.30212i) q^{78} +(-0.462054 + 0.462054i) q^{79} +(-1.52550 + 3.69768i) q^{80} +(-3.29822 + 8.37387i) q^{81} +(-7.42914 - 8.19097i) q^{82} +(-8.92296 + 1.77489i) q^{83} +(-8.92254 - 1.72774i) q^{84} +(1.40986 + 2.11000i) q^{85} +(9.76064 - 13.1704i) q^{86} +(-10.0552 + 5.43127i) q^{87} +(-0.234736 - 4.67690i) q^{88} +(-0.842506 + 2.03399i) q^{89} +(2.87766 + 3.11754i) q^{90} +(-0.690991 + 3.47385i) q^{91} +(-4.79269 + 8.98176i) q^{92} +(-3.34109 - 1.76711i) q^{93} +(3.28814 - 6.95856i) q^{94} +0.374163i q^{95} +(3.24412 - 9.24530i) q^{96} +15.2920i q^{97} +(0.149526 + 0.0706559i) q^{98} +(-4.60521 - 1.86053i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q+O(q^{10}) $ 1024 * q	$ 1024 q + 80 q^{24} + 80 q^{42} - 96 q^{52} - 288 q^{58} - 96 q^{64} + 256 q^{67} - 112 q^{76} - 48 q^{78} + 32 q^{79} - 112 q^{84} - 160 q^{88} - 144 q^{90} - 16 q^{94} - 272 q^{96}+O(q^{100}) $ 1024 * q + 80 * q^24 + 80 * q^42 - 96 * q^52 - 288 * q^58 - 96 * q^64 + 256 * q^67 - 112 * q^76 - 48 * q^78 + 32 * q^79 - 112 * q^84 - 160 * q^88 - 144 * q^90 - 16 * q^94 - 272 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{9}{16}\right)$

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 $

$2$	−1.33138	+	0.476905i	−0.941425	+	0.337223i
$2$	−1.33138	+	0.476905i	−0.941425	+	0.337223i
$3$	−1.53109	−	0.809797i	−0.883974	−	0.467537i
$3$	−1.53109	−	0.809797i	−0.883974	−	0.467537i
$4$	1.54512	−	1.26988i	0.772561	−	0.634940i
$5$	−0.980785	−	0.195090i	−0.438621	−	0.0872470i
$5$	−0.980785	−	0.195090i	−0.438621	−	0.0872470i
$6$	2.42465	+	0.347961i	0.989859	+	0.142054i
$7$	2.42385	+	1.00399i	0.916130	+	0.379473i	0.790400	−	0.612591i	$-0.209873\pi$
$7$	2.42385	+	1.00399i	0.916130	+	0.379473i	0.125730	+	0.992065i	$0.459873\pi$
$8$	−1.45153	+	2.42756i	−0.513192	+	0.858274i
$9$	1.68846	+	2.47974i	0.562819	+	0.826580i
$10$	1.39883	−	0.208003i	0.442350	−	0.0657763i
$11$	−1.37659	+	0.919810i	−0.415058	+	0.277333i	−0.745516	−	0.666488i	$-0.767797\pi$
$11$	−1.37659	+	0.919810i	−0.415058	+	0.277333i	0.330458	+	0.943821i	$0.392797\pi$
$12$	−3.39406	+	0.693061i	−0.979782	+	0.200070i
$13$	0.263379	+	1.32410i	0.0730483	+	0.367238i	0.999968	−	0.00802169i	$-0.00255341\pi$
$13$	0.263379	+	1.32410i	0.0730483	+	0.367238i	−0.926920	+	0.375260i	$0.877553\pi$
$14$	−3.70587	−	0.180744i	−0.990435	−	0.0483058i
$15$	1.34368	+	1.09294i	0.346938	+	0.282195i
$16$	0.774810	−	3.92424i	0.193702	−	0.981060i
$17$	−1.79441	−	1.79441i	−0.435208	−	0.435208i	0.455188	−	0.890395i	$-0.349572\pi$
$17$	−1.79441	−	1.79441i	−0.435208	−	0.435208i	−0.890395	+	0.455188i	$0.849572\pi$
$18$	−3.43057	−	2.49623i	−0.808594	−	0.588367i
$19$	−0.0729955	−	0.366973i	−0.0167463	−	0.0841894i	0.971508	−	0.237005i	$-0.0761659\pi$
$19$	−0.0729955	−	0.366973i	−0.0167463	−	0.0841894i	−0.988255	+	0.152816i	$0.951166\pi$
$20$	−1.76318	+	0.944041i	−0.394258	+	0.211094i
$21$	−2.89810	−	3.50003i	−0.632417	−	0.763769i
$22$	1.39410	−	1.88112i	0.297223	−	0.401055i
$23$	−4.70276	+	1.94795i	−0.980594	+	0.406175i	−0.814646	−	0.579959i	$-0.803068\pi$
$23$	−4.70276	+	1.94795i	−0.980594	+	0.406175i	−0.165948	+	0.986134i	$0.553068\pi$
$24$	4.18825	−	2.54137i	0.854923	−	0.518755i
$25$	0.923880	+	0.382683i	0.184776	+	0.0765367i
$26$	−0.982125	−	1.63726i	−0.192611	−	0.321094i
$27$	−0.577090	−	5.16401i	−0.111061	−	0.993814i
$28$	5.02010	−	1.52671i	0.948710	−	0.288521i
$29$	3.66572	−	5.48614i	0.680707	−	1.01875i	−0.316821	−	0.948485i	$-0.602615\pi$
$29$	3.66572	−	5.48614i	0.680707	−	1.01875i	0.997528	−	0.0702651i	$-0.0223845\pi$
$30$	−2.31018	−	0.814300i	−0.421779	−	0.148670i
$31$	2.18217			0.391929			0.195964	−	0.980611i	$-0.437216\pi$
$31$	2.18217			0.391929			0.195964	+	0.980611i	$0.437216\pi$
$32$	0.839928	+	5.59415i	0.148480	+	0.988915i
$33$	2.85254	−	0.293549i	0.496564	−	0.0511003i
$34$	3.24479	+	1.53327i	0.556477	+	0.262953i
$35$	−2.18141	−	1.45757i	−0.368725	−	0.246374i
$36$	5.75785	+	1.68737i	0.959641	+	0.281228i
$37$	−6.03442	−	1.20032i	−0.992053	−	0.197332i	−0.327725	−	0.944773i	$-0.606282\pi$
$37$	−6.03442	−	1.20032i	−0.992053	−	0.197332i	−0.664328	+	0.747441i	$0.731282\pi$
$38$	0.272196	+	0.453767i	0.0441560	+	0.0736108i
$39$	0.668993	−	2.24059i	0.107125	−	0.358782i
$40$	1.89723	−	2.09774i	0.299979	−	0.331682i
$41$	2.99233	+	7.22413i	0.467324	+	1.12822i	0.965327	+	0.261044i	$0.0840669\pi$
$41$	2.99233	+	7.22413i	0.467324	+	1.12822i	−0.498003	+	0.867175i	$0.665933\pi$
$42$	5.52764	+	3.27773i	0.852933	+	0.505765i
$43$	−9.63806	+	6.43995i	−1.46979	+	0.982083i	−0.475017	+	0.879977i	$0.657558\pi$
$43$	−9.63806	+	6.43995i	−1.46979	+	0.982083i	−0.994774	+	0.102106i	$0.967442\pi$
$44$	−0.958957	+	3.16933i	−0.144568	+	0.477794i
$45$	−1.17224	−	2.76149i	−0.174747	−	0.411659i
$46$	5.33216	−	4.83622i	0.786184	−	0.713062i
$47$	−3.84817	+	3.84817i	−0.561313	+	0.561313i	−0.929680	−	0.368368i	$-0.879917\pi$
$47$	−3.84817	+	3.84817i	−0.561313	+	0.561313i	0.368368	+	0.929680i	$0.379917\pi$
$48$	−4.36414	+	5.38092i	−0.629909	+	0.776669i
$49$	−0.0826897	−	0.0826897i	−0.0118128	−	0.0118128i
$50$	−1.41253	−	0.0688926i	−0.199763	−	0.00974288i
$51$	1.29429	+	4.20050i	0.181237	+	0.588188i
$52$	2.08840	+	1.71143i	0.289609	+	0.237333i
$53$	3.48365	+	5.21365i	0.478516	+	0.716150i	0.989674	−	0.143337i	$-0.0457833\pi$
$53$	3.48365	+	5.21365i	0.478516	+	0.716150i	−0.511158	+	0.859487i	$0.670783\pi$
$54$	3.23107	+	6.60002i	0.439692	+	0.898148i
$55$	1.52959	−	0.633576i	0.206250	−	0.0854314i
$56$	−5.95554	+	4.42673i	−0.795843	+	0.591547i
$57$	−0.185411	+	0.620980i	−0.0245583	+	0.0822508i
$58$	−2.26408	+	9.05231i	−0.297289	+	1.18863i
$59$	0.0807657	−	0.406036i	0.0105148	−	0.0528614i	−0.975172	−	0.221450i	$-0.928921\pi$
$59$	0.0807657	−	0.406036i	0.0105148	−	0.0528614i	0.985686	+	0.168589i	$0.0539210\pi$
$60$	3.46406	−	0.0175953i	0.447208	−	0.00227155i
$61$	2.14020	−	3.20303i	0.274024	−	0.410106i	−0.668777	−	0.743464i	$-0.733182\pi$
$61$	2.14020	−	3.20303i	0.274024	−	0.410106i	0.942800	+	0.333358i	$0.108182\pi$
$62$	−2.90528	+	1.04069i	−0.368972	+	0.132167i
$63$	1.60293	+	7.70572i	0.201950	+	0.970830i
$64$	−3.78614	−	7.04735i	−0.473267	−	0.880919i
$65$		−	1.35004i		−	0.167452i
$66$	−3.65781	+	1.75122i	−0.450246	+	0.215560i
$67$	−4.51773	−	3.01865i	−0.551929	−	0.368787i	0.248113	−	0.968731i	$-0.420189\pi$
$67$	−4.51773	−	3.01865i	−0.551929	−	0.368787i	−0.800042	+	0.599944i	$0.795189\pi$
$68$	−5.05126	−	0.493898i	−0.612555	−	0.0598939i
$69$	8.77778	+	0.825804i	1.05672	+	0.0994152i
$70$	3.59940	+	0.900249i	0.430210	+	0.107600i
$71$	−3.93633	+	9.50315i	−0.467157	+	1.12782i	0.498242	+	0.867038i	$0.333979\pi$
$71$	−3.93633	+	9.50315i	−0.467157	+	1.12782i	−0.965399	+	0.260778i	$0.916021\pi$
$72$	−8.47057	+	0.499430i	−0.998266	+	0.0588584i
$73$	4.39584	+	10.6125i	0.514494	+	1.24210i	0.941244	+	0.337728i	$0.109658\pi$
$73$	4.39584	+	10.6125i	0.514494	+	1.24210i	−0.426750	+	0.904370i	$0.640342\pi$
$74$	8.60652	−	1.27977i	1.00049	−	0.148770i
$75$	−1.10464	−	1.33408i	−0.127553	−	0.154046i
$76$	−0.578799	−	0.474323i	−0.0663928	−	0.0544086i
$77$	−4.26014	+	0.847394i	−0.485488	+	0.0965696i
$78$	0.177869	+	3.30212i	0.0201397	+	0.373891i
$79$	−0.462054	+	0.462054i	−0.0519851	+	0.0519851i	−0.732621	−	0.680636i	$-0.761703\pi$
$79$	−0.462054	+	0.462054i	−0.0519851	+	0.0519851i	0.680636	+	0.732621i	$0.261703\pi$
$80$	−1.52550	+	3.69768i	−0.170556	+	0.413413i
$81$	−3.29822	+	8.37387i	−0.366469	+	0.930430i
$82$	−7.42914	−	8.19097i	−0.820412	−	0.904542i
$83$	−8.92296	+	1.77489i	−0.979423	+	0.194819i	−0.658743	−	0.752368i	$-0.728911\pi$
$83$	−8.92296	+	1.77489i	−0.979423	+	0.194819i	−0.320680	+	0.947188i	$0.603911\pi$
$84$	−8.92254	−	1.72774i	−0.973528	−	0.188511i
$85$	1.40986	+	2.11000i	0.152920	+	0.228862i
$86$	9.76064	−	13.1704i	1.05252	−	1.42020i
$87$	−10.0552	+	5.43127i	−1.07803	+	0.582293i
$88$	−0.234736	−	4.67690i	−0.0250230	−	0.498559i
$89$	−0.842506	+	2.03399i	−0.0893055	+	0.215602i	−0.962221	−	0.272268i	$-0.912226\pi$
$89$	−0.842506	+	2.03399i	−0.0893055	+	0.215602i	0.872916	+	0.487871i	$0.162226\pi$
$90$	2.87766	+	3.11754i	0.303332	+	0.328617i
$91$	−0.690991	+	3.47385i	−0.0724355	+	0.364158i
$92$	−4.79269	+	8.98176i	−0.499672	+	0.936414i
$93$	−3.34109	−	1.76711i	−0.346455	−	0.183241i
$94$	3.28814	−	6.95856i	0.339146	−	0.717721i
$95$			0.374163i			0.0383883i
$96$	3.24412	−	9.24530i	0.331102	−	0.943595i
$97$			15.2920i			1.55267i	0.630323	+	0.776333i	$0.282922\pi$
$97$			15.2920i			1.55267i	−0.630323	+	0.776333i	$0.717078\pi$
$98$	0.149526	+	0.0706559i	0.0151044	+	0.00713733i
$99$	−4.60521	−	1.86053i	−0.462841	−	0.186991i
$100$	1.91347	−	0.581923i	0.191347	−	0.0581923i
$101$	−0.371602	+	1.86817i	−0.0369758	+	0.185890i	−0.994859	−	0.101267i	$-0.967710\pi$
$101$	−0.371602	+	1.86817i	−0.0369758	+	0.185890i	0.957883	+	0.287157i	$0.0927103\pi$
$102$	−3.72642	−	4.97519i	−0.368971	−	0.492617i
$103$	−4.70678	+	11.3632i	−0.463773	+	1.11965i	0.503064	+	0.864249i	$0.332206\pi$
$103$	−4.70678	+	11.3632i	−0.463773	+	1.11965i	−0.966836	+	0.255397i	$0.917794\pi$
$104$	−3.59663	−	1.28259i	−0.352679	−	0.125769i
$105$	2.15959	+	3.99817i	0.210755	+	0.390181i
$106$	−7.12446	−	5.27996i	−0.691989	−	0.512835i
$107$	−5.70625	−	8.54000i	−0.551644	−	0.825593i	0.445940	−	0.895063i	$-0.352869\pi$
$107$	−5.70625	−	8.54000i	−0.551644	−	0.825593i	−0.997584	+	0.0694694i	$0.977869\pi$
$108$	−7.44934	−	7.24619i	−0.716813	−	0.697265i
$109$	−11.9854	+	2.38404i	−1.14799	+	0.228350i	−0.732187	−	0.681103i	$-0.761500\pi$
$109$	−11.9854	+	2.38404i	−1.14799	+	0.228350i	−0.415806	+	0.909453i	$0.636500\pi$
$110$	−1.73430	+	1.57300i	−0.165359	+	0.149979i
$111$	8.26721	+	6.72445i	0.784689	+	0.638257i
$112$	5.81793	−	8.73388i	0.549743	−	0.825274i
$113$	13.0483	−	13.0483i	1.22748	−	1.22748i	0.262563	−	0.964915i	$-0.415432\pi$
$113$	13.0483	−	13.0483i	1.22748	−	1.22748i	0.964915	−	0.262563i	$-0.0845678\pi$
$114$	−0.0492963	−	0.915181i	−0.00461702	−	0.0857145i
$115$	4.99243	−	0.993055i	0.465546	−	0.0926029i
$116$	−1.30275	−	13.1318i	−0.120957	−	1.21926i
$117$	−2.83871	+	2.88879i	−0.262439	+	0.267069i
$118$	0.0861114	+	0.579105i	0.00792720	+	0.0533109i
$119$	−2.54781	−	6.15095i	−0.233557	−	0.563857i
$120$	−4.60357	+	1.67545i	−0.420247	+	0.152947i
$121$	−3.16056	+	7.63027i	−0.287324	+	0.693661i
$122$	−1.32186	+	5.28510i	−0.119676	+	0.478491i
$123$	1.26856	−	13.4840i	0.114382	−	1.21581i
$124$	3.37172	−	2.77109i	0.302789	−	0.248851i
$125$	−0.831470	−	0.555570i	−0.0743689	−	0.0496917i
$126$	−5.80900	−	9.49476i	−0.517507	−	0.845861i
$127$			1.91702i			0.170108i	0.996376	+	0.0850539i	$0.0271062\pi$
$127$			1.91702i			0.170108i	−0.996376	+	0.0850539i	$0.972894\pi$
$128$	8.40169	+	7.57704i	0.742612	+	0.669722i
$129$	19.9718	−	2.05525i	1.75842	−	0.180955i
$130$	0.643840	+	1.79741i	0.0564685	+	0.157643i
$131$	−10.1639	+	15.2113i	−0.888023	+	1.32902i	0.0557562	+	0.998444i	$0.482243\pi$
$131$	−10.1639	+	15.2113i	−0.888023	+	1.32902i	−0.943779	+	0.330576i	$0.892757\pi$
$132$	4.03476	−	4.07596i	0.351181	−	0.354766i
$133$	0.191508	−	0.962776i	0.0166058	−	0.0834832i
$134$	7.45441	+	1.86443i	0.643963	+	0.161062i
$135$	−0.441446	+	5.17737i	−0.0379937	+	0.445597i
$136$	6.96067	−	1.75141i	0.596872	−	0.150182i
$137$	9.05091	−	3.74901i	0.773272	−	0.320300i	0.0390749	−	0.999236i	$-0.487559\pi$
$137$	9.05091	−	3.74901i	0.773272	−	0.320300i	0.734197	+	0.678937i	$0.237559\pi$
$138$	−12.0804	+	3.08671i	−1.02835	+	0.262759i
$139$	0.845121	+	1.26481i	0.0716822	+	0.107280i	0.865579	−	0.500773i	$-0.166951\pi$
$139$	0.845121	+	1.26481i	0.0716822	+	0.107280i	−0.793896	+	0.608053i	$0.791951\pi$
$140$	−5.22149	+	0.518001i	−0.441296	+	0.0437791i
$141$	9.00811	−	2.77564i	0.758620	−	0.233751i
$142$	0.708638	−	14.5295i	0.0594676	−	1.21929i
$143$	−1.58048	−	1.58048i	−0.132167	−	0.132167i
$144$	11.0393	−	4.70459i	0.919944	−	0.392049i
$145$	−4.66558	+	4.66558i	−0.387455	+	0.387455i
$146$	−10.9137	−	12.0328i	−0.903221	−	0.995843i
$147$	0.0596433	+	0.193567i	0.00491930	+	0.0159651i
$148$	−10.8482	+	5.80835i	−0.891716	+	0.477443i
$149$	5.18775	−	3.46634i	0.424997	−	0.283974i	−0.324622	−	0.945844i	$-0.605237\pi$
$149$	5.18775	−	3.46634i	0.424997	−	0.283974i	0.749619	+	0.661870i	$0.230237\pi$
$150$	2.10692	+	1.24935i	0.172030	+	0.102009i
$151$	−1.73552	−	4.18991i	−0.141234	−	0.340970i	0.837396	−	0.546597i	$-0.184077\pi$
$151$	−1.73552	−	4.18991i	−0.141234	−	0.340970i	−0.978631	+	0.205626i	$0.934077\pi$
$152$	0.996806	+	0.355470i	0.0808516	+	0.0288324i
$153$	1.41988	−	7.47944i	0.114791	−	0.604677i
$154$	5.26772	−	3.15988i	0.424485	−	0.254631i
$155$	−2.14024	−	0.425720i	−0.171908	−	0.0341946i
$156$	−1.81161	−	4.31153i	−0.145045	−	0.345199i
$157$	4.10272	+	2.74135i	0.327433	+	0.218783i	0.708410	−	0.705801i	$-0.249413\pi$
$157$	4.10272	+	2.74135i	0.327433	+	0.218783i	−0.380978	+	0.924584i	$0.624413\pi$
$158$	0.394812	−	0.835524i	0.0314095	−	0.0664707i
$159$	−1.11177	−	10.8036i	−0.0881694	−	0.856781i
$160$	0.267576	−	5.65052i	0.0211537	−	0.446713i
$161$	−13.3545			−1.05248
$162$	0.397631	−	12.7217i	0.0312408	−	0.999512i
$163$	−6.47394	+	9.68894i	−0.507078	+	0.758896i	−0.993378	−	0.114896i	$-0.963346\pi$
$163$	−6.47394	+	9.68894i	−0.507078	+	0.758896i	0.486299	+	0.873792i	$0.338346\pi$
$164$	13.7973	+	7.36227i	1.07739	+	0.574896i
$165$	−2.85500	−	0.268595i	−0.222262	−	0.0209101i
$166$	11.0334	−	6.61845i	0.856355	−	0.513691i
$167$	−7.00611	−	2.90203i	−0.542149	−	0.224566i	0.0947657	−	0.995500i	$-0.469790\pi$
$167$	−7.00611	−	2.90203i	−0.542149	−	0.224566i	−0.636915	+	0.770934i	$0.719790\pi$
$168$	12.7032	−	1.95494i	0.980074	−	0.150827i
$169$	10.3266	−	4.27741i	0.794352	−	0.329031i
$170$	−2.88332	−	2.13683i	−0.221140	−	0.163888i
$171$	0.786748	−	0.800629i	0.0601641	−	0.0612256i
$172$	−6.71403	+	22.1897i	−0.511940	+	1.69195i
$173$	−1.26873	−	6.37833i	−0.0964597	−	0.484936i	−0.998571	−	0.0534331i	$-0.982984\pi$
$173$	−1.26873	−	6.37833i	−0.0964597	−	0.484936i	0.902112	−	0.431503i	$-0.142016\pi$
$174$	10.7970	−	12.0264i	0.818522	−	0.911722i
$175$	1.85514	+	1.85514i	0.140235	+	0.140235i
$176$	2.54296	+	6.11476i	0.191683	+	0.460917i
$177$	−0.452466	+	0.556274i	−0.0340095	+	0.0418121i
$178$	0.151672	−	3.10980i	0.0113683	−	0.233089i
$179$	2.97427	+	14.9526i	0.222307	+	1.11761i	0.917178	+	0.398478i	$0.130462\pi$
$179$	2.97427	+	14.9526i	0.222307	+	1.11761i	−0.694871	+	0.719135i	$0.744538\pi$
$180$	−5.31802	−	2.77824i	−0.396382	−	0.207078i
$181$	−20.5750	+	13.7478i	−1.52933	+	1.02186i	−0.546475	+	0.837476i	$0.684031\pi$
$181$	−20.5750	+	13.7478i	−1.52933	+	1.02186i	−0.982853	+	0.184389i	$0.940969\pi$
$182$	−0.736726	−	4.95453i	−0.0546098	−	0.367254i
$183$	−5.87063	+	3.17099i	−0.433969	+	0.234407i
$184$	2.09742	−	14.2438i	0.154624	−	1.05006i
$185$	5.68430	+	2.35451i	0.417918	+	0.173107i
$186$	5.29099	+	0.759308i	0.387954	+	0.0556752i
$187$	4.12068	+	0.819655i	0.301334	+	0.0599391i
$188$	−1.05918	+	10.8326i	−0.0772487	+	0.790048i
$189$	3.78584	−	13.0962i	0.275380	−	0.952607i
$190$	−0.178440	−	0.498151i	−0.0129454	−	0.0361397i
$191$	−4.86708			−0.352170			−0.176085	−	0.984375i	$-0.556343\pi$
$191$	−4.86708			−0.352170			−0.176085	+	0.984375i	$0.556343\pi$
$192$	0.0899855	+	13.8561i	0.00649414	+	0.999979i
$193$	24.6063			1.77120			0.885599	−	0.464450i	$-0.153748\pi$
$193$	24.6063			1.77120			0.885599	+	0.464450i	$0.153748\pi$
$194$	−7.29283	−	20.3594i	−0.523595	−	1.46172i
$195$	−1.09326	+	2.06703i	−0.0782897	+	0.148023i
$196$	−0.232772	−	0.0227598i	−0.0166266	−	0.00162570i
$197$	4.31174	+	0.857659i	0.307199	+	0.0611056i	0.346282	−	0.938130i	$-0.387444\pi$
$197$	4.31174	+	0.857659i	0.307199	+	0.0611056i	−0.0390836	+	0.999236i	$0.512444\pi$
$198$	7.01856	+	0.280820i	0.498787	+	0.0199570i
$199$	−2.17846	−	0.902350i	−0.154427	−	0.0639659i	0.304131	−	0.952630i	$-0.401634\pi$
$199$	−2.17846	−	0.902350i	−0.154427	−	0.0639659i	−0.458558	+	0.888664i	$0.651634\pi$
$200$	−2.27002	+	1.68730i	−0.160515	+	0.119310i
$201$	4.47255	+	8.28026i	0.315469	+	0.584045i
$202$	−0.396198	−	2.66446i	−0.0278764	−	0.187471i
$203$	14.3932	−	9.61723i	1.01021	−	0.674997i
$204$	7.33397	+	4.84670i	0.513480	+	0.339337i
$205$	−1.52548	−	7.66910i	−0.106544	−	0.535633i
$206$	0.847337	−	17.3733i	0.0590368	−	1.21046i
$207$	−12.7708	−	8.37260i	−0.887633	−	0.581936i
$208$	5.40014	−	0.00764027i	0.374433	−	0.000529757i
$209$	0.438031	+	0.438031i	0.0302992	+	0.0302992i
$210$	−4.78197	−	4.29314i	−0.329988	−	0.296255i
$211$	0.153201	+	0.770193i	0.0105468	+	0.0530223i	0.985700	−	0.168508i	$-0.0538949\pi$
$211$	0.153201	+	0.770193i	0.0105468	+	0.0530223i	−0.975154	+	0.221530i	$0.928895\pi$
$212$	12.0034	+	3.63191i	0.824395	+	0.249441i
$213$	13.7225	−	11.3625i	0.940249	−	0.778547i
$214$	11.6699	+	8.64862i	0.797740	+	0.591207i
$215$	10.7092	−	4.43591i	0.730364	−	0.302527i
$216$	13.3736	+	6.09477i	0.909960	+	0.414697i
$217$	5.28925	+	2.19088i	0.359058	+	0.148727i
$218$	14.8201	−	8.88996i	1.00374	−	0.602104i
$219$	1.86355	−	19.8084i	0.125927	−	1.33853i
$220$	1.55884	−	2.92135i	0.105097	−	0.196957i
$221$	1.90336	−	2.84858i	0.128034	−	0.191616i
$222$	−14.2137	−	5.01010i	−0.953961	−	0.336256i
$223$	−14.6101			−0.978362			−0.489181	−	0.872182i	$-0.662704\pi$
$223$	−14.6101			−0.978362			−0.489181	+	0.872182i	$0.662704\pi$
$224$	−3.58062	+	14.4027i	−0.239241	+	0.962319i
$225$	0.610976	+	2.93713i	0.0407317	+	0.195808i
$226$	−11.1494	+	23.5949i	−0.741645	+	1.56951i
$227$	11.0632	+	7.39217i	0.734288	+	0.490636i	0.865619	−	0.500703i	$-0.166925\pi$
$227$	11.0632	+	7.39217i	0.734288	+	0.490636i	−0.131331	+	0.991339i	$0.541925\pi$
$228$	0.502086	+	1.19494i	0.0332515	+	0.0791368i
$229$	20.2462	+	4.02721i	1.33790	+	0.266126i	0.811622	−	0.584183i	$-0.198585\pi$
$229$	20.2462	+	4.02721i	1.33790	+	0.266126i	0.526283	+	0.850309i	$0.323585\pi$
$230$	−6.17320	+	3.70304i	−0.407049	+	0.244171i
$231$	7.20886	+	2.15241i	0.474308	+	0.141618i
$232$	7.99706	+	16.8621i	0.525033	+	1.10705i
$233$	−5.46144	−	13.1851i	−0.357791	−	0.863783i	−0.995610	−	0.0935971i	$-0.970163\pi$
$233$	−5.46144	−	13.1851i	−0.357791	−	0.863783i	0.637820	−	0.770186i	$-0.279837\pi$
$234$	2.40171	−	5.19987i	0.157005	−	0.339926i
$235$	4.52496	−	3.02348i	0.295176	−	0.197230i
$236$	−0.390825	−	0.729939i	−0.0254405	−	0.0475150i
$237$	1.08162	−	0.333275i	0.0702585	−	0.0216485i
$238$	6.32551	+	6.97416i	0.410022	+	0.452068i
$239$	0.786191	−	0.786191i	0.0508545	−	0.0508545i	−0.681222	−	0.732077i	$-0.738551\pi$
$239$	0.786191	−	0.786191i	0.0508545	−	0.0508545i	0.732077	+	0.681222i	$0.238551\pi$
$240$	5.33005	−	4.42612i	0.344053	−	0.285705i
$241$	−21.0399	−	21.0399i	−1.35530	−	1.35530i	−0.879618	−	0.475682i	$-0.842201\pi$
$241$	−21.0399	−	21.0399i	−1.35530	−	1.35530i	−0.475682	−	0.879618i	$-0.657799\pi$
$242$	0.568980	−	11.6660i	0.0365754	−	0.749921i
$243$	11.8310	−	10.1502i	0.758959	−	0.651138i
$244$	−0.760597	−	7.66686i	−0.0486922	−	0.490821i
$245$	0.0649689	+	0.0972328i	0.00415071	+	0.00621198i
$246$	4.74164	+	18.5572i	0.302316	+	1.18316i
$247$	0.466683	−	0.193306i	0.0296943	−	0.0122998i
$248$	−3.16748	+	5.29735i	−0.201135	+	0.336382i
$249$	15.0991	+	4.50828i	0.956869	+	0.285701i
$250$	1.37195	+	0.343141i	0.0867699	+	0.0217021i
$251$	1.46445	−	7.36229i	0.0924353	−	0.464704i	−0.906648	−	0.421889i	$-0.861367\pi$
$251$	1.46445	−	7.36229i	0.0924353	−	0.464704i	0.999083	−	0.0428152i	$-0.0136327\pi$
$252$	12.2621	+	9.87076i	0.772438	+	0.621799i
$253$	4.68205	−	7.00718i	0.294358	−	0.440538i
$254$	−0.914235	−	2.55227i	−0.0573642	−	0.160144i
$255$	−0.449942	−	4.37229i	−0.0281765	−	0.273804i
$256$	−14.7993	−	6.08108i	−0.924959	−	0.380068i
$257$		−	4.29685i		−	0.268030i	−0.990979	−	0.134015i	$-0.957213\pi$
$257$		−	4.29685i		−	0.268030i	0.990979	−	0.134015i	$-0.0427871\pi$
$258$	−25.6098	+	12.2609i	−1.59439	+	0.763333i
$259$	−13.4214	−	8.96791i	−0.833967	−	0.557239i
$260$	−1.71439	−	2.08597i	−0.106322	−	0.129367i
$261$	19.7936	−	0.173078i	1.22519	−	0.0107132i
$262$	6.27759	−	25.0992i	0.387831	−	1.55063i
$263$	10.2466	−	24.7375i	0.631833	−	1.52538i	−0.205483	−	0.978661i	$-0.565876\pi$
$263$	10.2466	−	24.7375i	0.631833	−	1.52538i	0.837316	−	0.546719i	$-0.184124\pi$
$264$	−3.42794	+	7.35083i	−0.210975	+	0.452412i
$265$	−2.39958	−	5.79310i	−0.147405	−	0.355867i
$266$	0.204184	+	1.37315i	0.0125193	+	0.0841931i
$267$	2.93707	−	2.43196i	0.179746	−	0.148833i
$268$	−10.8138	+	1.07279i	−0.660556	+	0.0655310i
$269$	−11.7350	+	2.33425i	−0.715498	+	0.142321i	−0.539398	−	0.842051i	$-0.681348\pi$
$269$	−11.7350	+	2.33425i	−0.715498	+	0.142321i	−0.176100	+	0.984372i	$0.556348\pi$
$270$	−1.88138	−	7.10355i	−0.114497	−	0.432308i
$271$	−10.5937	+	10.5937i	−0.643519	+	0.643519i	−0.951419	−	0.307900i	$-0.900374\pi$
$271$	−10.5937	+	10.5937i	−0.643519	+	0.643519i	0.307900	+	0.951419i	$0.400374\pi$
$272$	−8.43201	+	5.65136i	−0.511266	+	0.342664i
$273$	3.87108	−	4.75920i	0.234288	−	0.288040i
$274$	−10.2622	+	9.30777i	−0.619965	+	0.562303i
$275$	−1.62380	+	0.322994i	−0.0979190	+	0.0194773i
$276$	14.6114	−	9.87076i	0.879505	−	0.594150i
$277$	−10.8535	−	16.2434i	−0.652124	−	0.975972i	−0.999272	−	0.0381618i	$-0.987850\pi$
$277$	−10.8535	−	16.2434i	−0.652124	−	0.975972i	0.347148	−	0.937810i	$-0.387150\pi$
$278$	−1.72837	−	1.28090i	−0.103661	−	0.0768232i
$279$	3.68450	+	5.41121i	0.220585	+	0.323961i
$280$	6.70472	−	3.17981i	0.400684	−	0.190030i
$281$	−6.93627	+	16.7456i	−0.413783	+	0.998961i	0.570330	+	0.821416i	$0.306815\pi$
$281$	−6.93627	+	16.7456i	−0.413783	+	0.998961i	−0.984113	+	0.177545i	$0.943185\pi$
$282$	−10.6695	+	7.99144i	−0.635357	+	0.475883i
$283$	3.70447	−	18.6236i	0.220208	−	1.10706i	−0.699553	−	0.714581i	$-0.746617\pi$
$283$	3.70447	−	18.6236i	0.220208	−	1.10706i	0.919761	−	0.392480i	$-0.128383\pi$
$284$	5.98574	+	19.6822i	0.355188	+	1.16792i
$285$	0.302996	−	0.572876i	0.0179479	−	0.0339342i
$286$	2.85796	+	1.35048i	0.168995	+	0.0798554i
$287$			20.5145i			1.21093i
$288$	−12.4539	+	11.5283i	−0.733851	+	0.679311i
$289$		−	10.5602i		−	0.621189i
$290$	3.98660	−	8.43668i	0.234101	−	0.495419i
$291$	12.3834	−	23.4134i	0.725928	−	1.37252i
$292$	20.2687	+	10.8154i	1.18614	+	0.632924i
$293$	−4.50643	+	22.6553i	−0.263268	+	1.32354i	0.592245	+	0.805758i	$0.298242\pi$
$293$	−4.50643	+	22.6553i	−0.263268	+	1.32354i	−0.855513	+	0.517781i	$0.826758\pi$
$294$	−0.171721	−	0.229266i	−0.0100150	−	0.0133711i
$295$	−0.158428	+	0.382478i	−0.00922401	+	0.0222687i
$296$	11.6730	−	12.9066i	0.678478	−	0.750184i
$297$	5.54432	+	6.57792i	0.321714	+	0.381690i
$298$	−5.25373	+	7.08907i	−0.304340	+	0.410659i
$299$	−3.81788	−	5.71386i	−0.220794	−	0.330441i
$300$	−3.40093	−	0.658547i	−0.196353	−	0.0380212i
$301$	−29.8269	+	5.93294i	−1.71919	+	0.341969i
$302$	4.30882	+	4.75067i	0.247945	+	0.273370i
$303$	2.08180	−	2.55941i	0.119596	−	0.147034i
$304$	−1.49665	+	0.00211750i	−0.0858387	+	0.000121447i
$305$	−2.72395	+	2.72395i	−0.155973	+	0.155973i
$306$	1.67659	+	10.6351i	0.0958441	+	0.607968i
$307$	20.8141	−	4.14018i	1.18792	−	0.236293i	0.438715	−	0.898626i	$-0.355434\pi$
$307$	20.8141	−	4.14018i	1.18792	−	0.236293i	0.749209	+	0.662333i	$0.230434\pi$
$308$	−5.50635	+	6.71919i	−0.313753	+	0.382862i
$309$	16.4083	−	13.5865i	0.933438	−	0.772907i
$310$	3.05249	−	0.453897i	0.173370	−	0.0257796i
$311$	−2.71791	−	6.56161i	−0.154118	−	0.372075i	0.827896	−	0.560882i	$-0.189538\pi$
$311$	−2.71791	−	6.56161i	−0.154118	−	0.372075i	−0.982014	+	0.188807i	$0.939538\pi$
$312$	4.46812	+	4.87630i	0.252957	+	0.276066i
$313$	−2.18454	+	5.27395i	−0.123478	+	0.298101i	−0.973516	−	0.228620i	$-0.926579\pi$
$313$	−2.18454	+	5.27395i	−0.123478	+	0.298101i	0.850038	+	0.526721i	$0.176579\pi$
$314$	−6.76962	−	1.69316i	−0.382032	−	0.0955504i
$315$	−0.0688195	−	7.87037i	−0.00387754	−	0.443445i
$316$	−0.127177	+	1.30068i	−0.00715427	+	0.0731692i
$317$	−12.0789	−	8.07089i	−0.678421	−	0.453306i	0.168024	−	0.985783i	$-0.446261\pi$
$317$	−12.0789	−	8.07089i	−0.678421	−	0.453306i	−0.846445	+	0.532477i	$0.821261\pi$
$318$	6.63248	+	13.8534i	0.371931	+	0.776863i
$319$			10.9239i			0.611624i
$320$	2.33852	+	7.65058i	0.130727	+	0.427680i
$321$	1.82110	+	17.6964i	0.101644	+	0.987716i
$322$	17.7799	−	6.36884i	0.990835	−	0.354922i
$323$	−0.527516	+	0.789483i	−0.0293518	+	0.0439280i
$324$	5.53765	+	17.1270i	0.307647	+	0.951500i
$325$	−0.263379	+	1.32410i	−0.0146097	+	0.0734477i
$326$	3.99854	−	15.9871i	0.221459	−	0.885442i
$327$	20.2813	+	6.05556i	1.12156	+	0.334873i
$328$	−21.8805	−	3.22194i	−1.20815	−	0.177902i
$329$	−13.1909	+	5.46385i	−0.727239	+	0.301232i
$330$	3.92917	−	1.00396i	0.216294	−	0.0552664i
$331$	6.61927	+	9.90644i	0.363828	+	0.544507i	0.967547	−	0.252690i	$-0.0813153\pi$
$331$	6.61927	+	9.90644i	0.363828	+	0.544507i	−0.603719	+	0.797197i	$0.706315\pi$
$332$	−11.5332	+	14.0735i	−0.632966	+	0.772384i
$333$	−7.21238	−	16.9905i	−0.395236	−	0.931073i
$334$	10.7118	+	0.522437i	0.586122	+	0.0285865i
$335$	3.84201	+	3.84201i	0.209912	+	0.209912i
$336$	−15.9804	+	8.66098i	−0.871804	+	0.472495i
$337$	5.55189	−	5.55189i	0.302431	−	0.302431i	−0.539533	−	0.841964i	$-0.681399\pi$
$337$	5.55189	−	5.55189i	0.302431	−	0.302431i	0.841964	+	0.539533i	$0.181399\pi$
$338$	−11.7086	+	10.6196i	−0.636865	+	0.577632i
$339$	−30.5445	+	9.41159i	−1.65895	+	0.511167i
$340$	4.85785	+	1.46986i	0.263454	+	0.0797144i
$341$	−3.00396	+	2.00718i	−0.162673	+	0.108695i
$342$	−0.665634	+	1.44114i	−0.0359934	+	0.0779280i
$343$	−7.14535	−	17.2504i	−0.385813	−	0.931435i
$344$	−1.64348	−	32.7448i	−0.0886105	−	1.76548i
$345$	−8.44801	−	2.52240i	−0.454826	−	0.135801i
$346$	4.73102	+	7.88689i	0.254341	+	0.424002i
$347$	30.0361	+	5.97454i	1.61242	+	0.320730i	0.917310	−	0.398173i	$-0.130356\pi$
$347$	30.0361	+	5.97454i	1.61242	+	0.320730i	0.695110	+	0.718903i	$0.255356\pi$
$348$	−8.63946	+	21.1609i	−0.463124	+	1.13434i
$349$	−10.8673	−	7.26130i	−0.581713	−	0.388688i	0.229613	−	0.973282i	$-0.426254\pi$
$349$	−10.8673	−	7.26130i	−0.581713	−	0.388688i	−0.811326	+	0.584594i	$0.801254\pi$
$350$	−3.35461	−	1.58516i	−0.179311	−	0.0847303i
$351$	6.68565	−	2.12422i	0.356854	−	0.113382i
$352$	−6.30179	−	6.92829i	−0.335887	−	0.369279i
$353$	−23.5410			−1.25296			−0.626481	−	0.779437i	$-0.715505\pi$
$353$	−23.5410			−1.25296			−0.626481	+	0.779437i	$0.715505\pi$
$354$	0.337113	−	0.956393i	0.0179174	−	0.0508317i
$355$	5.71467	−	8.55261i	0.303303	−	0.453925i
$356$	1.28115	+	4.21265i	0.0679007	+	0.223270i
$357$	−1.08011	+	11.4808i	−0.0571652	+	0.607631i
$358$	−11.0909	−	18.4891i	−0.586170	−	0.977182i
$359$	27.9958	+	11.5962i	1.47756	+	0.612025i	0.968569	−	0.248747i	$-0.0800187\pi$
$359$	27.9958	+	11.5962i	1.47756	+	0.612025i	0.508991	+	0.860772i	$0.330019\pi$
$360$	8.40525	+	1.16269i	0.442995	+	0.0612793i
$361$	17.4244	−	7.21741i	0.917072	−	0.379864i
$362$	20.8367	−	28.1158i	1.09515	−	1.47773i
$363$	11.0181	−	9.12319i	0.578298	−	0.478843i
$364$	3.34370	+	6.24499i	0.175258	+	0.327327i
$365$	−2.24098	−	11.2662i	−0.117298	−	0.589698i
$366$	6.30375	−	7.02152i	0.329502	−	0.367021i
$367$	−23.2250	−	23.2250i	−1.21233	−	1.21233i	−0.970257	−	0.242076i	$-0.922172\pi$
$367$	−23.2250	−	23.2250i	−1.21233	−	1.21233i	−0.242076	−	0.970257i	$-0.577828\pi$
$368$	4.00047	+	19.9641i	0.208539	+	1.04070i
$369$	−12.8615	+	19.6178i	−0.669545	+	1.02126i
$370$	−8.69082	−	0.423871i	−0.451814	−	0.0220360i
$371$	3.20939	+	16.1347i	0.166623	+	0.837670i
$372$	−7.40641	+	1.51238i	−0.384005	+	0.0784130i
$373$	−31.6192	+	21.1273i	−1.63718	+	1.09393i	−0.721188	+	0.692739i	$0.756404\pi$
$373$	−31.6192	+	21.1273i	−1.63718	+	1.09393i	−0.915994	+	0.401191i	$0.868596\pi$
$374$	−5.87707	+	0.873906i	−0.303896	+	0.0451886i
$375$	0.823154	+	1.52395i	0.0425075	+	0.0786963i
$376$	−3.75595	−	14.9274i	−0.193699	−	0.769821i
$377$	8.22965	+	3.40883i	0.423849	+	0.175564i
$378$	1.20526	+	19.2414i	0.0619917	+	0.989672i
$379$	8.19740	+	1.63056i	0.421072	+	0.0837564i	0.401078	−	0.916044i	$-0.368635\pi$
$379$	8.19740	+	1.63056i	0.421072	+	0.0837564i	0.0199934	+	0.999800i	$0.493635\pi$
$380$	0.475142	+	0.578127i	0.0243742	+	0.0296573i
$381$	1.55240	−	2.93512i	0.0795316	−	0.150371i
$382$	6.47992	−	2.32114i	0.331541	−	0.118760i
$383$	−12.3824			−0.632711			−0.316355	−	0.948641i	$-0.602459\pi$
$383$	−12.3824			−0.632711			−0.316355	+	0.948641i	$0.602459\pi$
$384$	−6.72786	−	18.4048i	−0.343329	−	0.939215i
$385$	4.34360			0.221370
$386$	−32.7602	+	11.7349i	−1.66745	+	0.597289i
$387$	−32.2429	−	13.0263i	−1.63900	−	0.662165i
$388$	19.4190	+	23.6280i	0.985850	+	1.19953i
$389$	22.8543	+	4.54600i	1.15876	+	0.230492i	0.736792	−	0.676119i	$-0.236340\pi$
$389$	22.8543	+	4.54600i	1.15876	+	0.230492i	0.421967	+	0.906611i	$0.361340\pi$
$390$	0.469760	−	3.27337i	0.0237872	−	0.165753i
$391$	11.9341	+	4.94326i	0.603533	+	0.249991i
$392$	0.320761	−	0.0807083i	0.0162009	−	0.00407638i
$393$	27.8799	−	15.0592i	1.40635	−	0.759636i
$394$	−6.14957	+	0.914426i	−0.309811	+	0.0460681i
$395$	0.543318	−	0.363034i	0.0273373	−	0.0182662i
$396$	−9.47827	+	2.97331i	−0.476301	+	0.149414i
$397$	5.20296	+	26.1571i	0.261129	+	1.31279i	0.859323	+	0.511434i	$0.170885\pi$
$397$	5.20296	+	26.1571i	0.261129	+	1.31279i	−0.598194	+	0.801352i	$0.704115\pi$
$398$	3.33069	+	0.162445i	0.166952	+	0.00814265i
$399$	−1.07287	+	1.31901i	−0.0537106	+	0.0660331i
$400$	2.21757	−	3.32902i	0.110879	−	0.166451i
$401$	−12.8391	−	12.8391i	−0.641153	−	0.641153i	0.309686	−	0.950839i	$-0.399776\pi$
$401$	−12.8391	−	12.8391i	−0.641153	−	0.641153i	−0.950839	+	0.309686i	$0.899776\pi$
$402$	−9.90354	−	8.89116i	−0.493944	−	0.443451i
$403$	0.574738	+	2.88940i	0.0286297	+	0.143931i
$404$	1.79818	+	3.35844i	0.0894629	+	0.167089i
$405$	4.86851	−	7.56952i	0.241918	−	0.376132i
$406$	−14.5763	+	19.6683i	−0.723408	+	0.976124i
$407$	9.41101	−	3.89817i	0.466486	−	0.193225i
$408$	−12.0757	−	2.95517i	−0.597835	−	0.146303i
$409$	−2.20200	−	0.912099i	−0.108882	−	0.0451004i	0.327577	−	0.944824i	$-0.393768\pi$
$409$	−2.20200	−	0.912099i	−0.108882	−	0.0451004i	−0.436459	+	0.899724i	$0.643768\pi$
$410$	5.68842	+	9.48294i	0.280931	+	0.468329i
$411$	−16.8937	−	1.58934i	−0.833304	−	0.0783963i
$412$	7.15731	+	23.5345i	0.352615	+	1.15946i
$413$	0.603422	−	0.903084i	0.0296924	−	0.0444379i
$414$	20.9957	+	5.05661i	1.03188	+	0.248519i
$415$	9.09778			0.446592
$416$	−7.18598	+	2.58553i	−0.352322	+	0.126766i
$417$	−0.269712	−	2.62092i	−0.0132079	−	0.128347i
$418$	−0.792083	−	0.374284i	−0.0387420	−	0.0183068i
$419$	1.89228	+	1.26438i	0.0924441	+	0.0617692i	0.600933	−	0.799299i	$-0.294796\pi$
$419$	1.89228	+	1.26438i	0.0924441	+	0.0617692i	−0.508489	+	0.861068i	$0.669796\pi$
$420$	8.41403	+	3.43524i	0.410562	+	0.167622i
$421$	−12.1895	−	2.42464i	−0.594080	−	0.118170i	−0.111112	−	0.993808i	$-0.535441\pi$
$421$	−12.1895	−	2.42464i	−0.594080	−	0.118170i	−0.482968	+	0.875638i	$0.660441\pi$
$422$	−0.571277	−	0.952354i	−0.0278093	−	0.0463599i
$423$	−16.0399	−	3.04499i	−0.779887	−	0.148052i
$424$	−17.7131	+	0.889030i	−0.860223	+	0.0431751i
$425$	−0.971126	−	2.34451i	−0.0471065	−	0.113725i
$426$	−12.8509	+	21.6721i	−0.622630	+	1.05002i
$427$	8.40333	−	5.61493i	0.406666	−	0.271725i
$428$	−19.6616	−	5.94911i	−0.950381	−	0.287561i
$429$	1.13999	+	3.69973i	0.0550391	+	0.178625i
$430$	−12.1425	+	11.0132i	−0.585564	+	0.531102i
$431$	−22.2496	+	22.2496i	−1.07173	+	1.07173i	−0.0745047	+	0.997221i	$0.523738\pi$
$431$	−22.2496	+	22.2496i	−1.07173	+	1.07173i	−0.997221	+	0.0745047i	$0.976262\pi$
$432$	−20.7119	−	1.73648i	−0.996504	−	0.0835466i
$433$	3.28293	+	3.28293i	0.157768	+	0.157768i	0.781577	−	0.623809i	$-0.214416\pi$
$433$	3.28293	+	3.28293i	0.157768	+	0.157768i	−0.623809	+	0.781577i	$0.714416\pi$
$434$	−8.08682	−	0.394413i	−0.388180	−	0.0189324i
$435$	10.9216	−	3.36524i	0.523650	−	0.161351i
$436$	−15.4915	+	18.9037i	−0.741907	+	0.905321i
$437$	1.05813	+	1.58360i	0.0506170	+	0.0757537i
$438$	6.96563	+	27.2611i	0.332831	+	1.30259i
$439$	−24.9783	+	10.3464i	−1.19215	+	0.493805i	−0.888455	−	0.458965i	$-0.848220\pi$
$439$	−24.9783	+	10.3464i	−1.19215	+	0.493805i	−0.303695	+	0.952769i	$0.598220\pi$
$440$	−0.682192	+	4.63283i	−0.0325222	+	0.220861i
$441$	0.0654309	−	0.344667i	0.00311576	−	0.0164127i
$442$	−1.17558	+	4.70025i	−0.0559169	+	0.223568i
$443$	4.52836	−	22.7656i	0.215149	−	1.08163i	−0.710631	−	0.703565i	$-0.751590\pi$
$443$	4.52836	−	22.7656i	0.215149	−	1.08163i	0.925780	−	0.378062i	$-0.123410\pi$
$444$	21.3131	−	0.108258i	1.01148	−	0.00513769i
$445$	1.22313	−	1.83054i	0.0579819	−	0.0867760i
$446$	19.4515	−	6.96761i	0.921054	−	0.329926i
$447$	−10.7499	+	1.10625i	−0.508454	+	0.0523239i
$448$	−2.10155	−	20.8830i	−0.0992890	−	0.986629i
$449$		−	1.50669i		−	0.0711052i	−0.999368	−	0.0355526i	$-0.988681\pi$
$449$		−	1.50669i		−	0.0711052i	0.999368	−	0.0355526i	$-0.0113191\pi$
$450$	−2.21417	−	3.61904i	−0.104377	−	0.170603i
$451$	−10.7641	−	7.19231i	−0.506859	−	0.338673i
$452$	3.59145	−	36.7309i	0.168927	−	1.72768i
$453$	−0.735748	+	7.82054i	−0.0345685	+	0.367441i
$454$	−18.2546	−	4.56568i	−0.856731	−	0.214278i
$455$	1.35543	−	3.27229i	0.0635434	−	0.153407i
$456$	−1.23834	−	1.35147i	−0.0579905	−	0.0632882i
$457$	−1.18873	−	2.86986i	−0.0556066	−	0.134246i	0.893635	−	0.448795i	$-0.148147\pi$
$457$	−1.18873	−	2.86986i	−0.0556066	−	0.134246i	−0.949241	+	0.314549i	$0.898147\pi$
$458$	−28.8759	+	4.29377i	−1.34928	+	0.200635i
$459$	−8.23080	+	10.3019i	−0.384181	+	0.480850i
$460$	6.45285	−	7.87417i	0.300866	−	0.367135i
$461$	−26.2004	+	5.21158i	−1.22027	+	0.242728i	−0.762882	−	0.646538i	$-0.776216\pi$
$461$	−26.2004	+	5.21158i	−1.22027	+	0.242728i	−0.457392	+	0.889265i	$0.651216\pi$
$462$	−10.6242	+	0.572273i	−0.494283	+	0.0266246i
$463$	−3.24869	+	3.24869i	−0.150979	+	0.150979i	−0.778555	−	0.627576i	$-0.784047\pi$
$463$	−3.24869	+	3.24869i	−0.150979	+	0.150979i	0.627576	+	0.778555i	$0.284047\pi$
$464$	−18.6887	−	18.6359i	−0.867601	−	0.865149i
$465$	2.93214	+	2.38497i	0.135975	+	0.110600i
$466$	13.5593	+	14.9497i	0.628120	+	0.692532i
$467$	1.03737	−	0.206345i	0.0480036	−	0.00954852i	−0.171030	−	0.985266i	$-0.554710\pi$
$467$	1.03737	−	0.206345i	0.0480036	−	0.00954852i	0.219034	+	0.975717i	$0.429710\pi$
$468$	−0.717737	+	8.06836i	−0.0331774	+	0.372960i
$469$	−7.91961	−	11.8525i	−0.365694	−	0.547299i
$470$	−4.58251	+	6.18337i	−0.211376	+	0.285218i
$471$	−4.06168	−	7.51961i	−0.187153	−	0.346485i
$472$	0.868446	+	0.785437i	0.0399735	+	0.0361527i
$473$	7.34416	−	17.7304i	0.337685	−	0.815243i
$474$	−1.28110	+	0.959542i	−0.0588427	+	0.0440732i
$475$	0.0729955	−	0.366973i	0.00334926	−	0.0168379i
$476$	−11.7476	−	6.26856i	−0.538452	−	0.287319i
$477$	−7.04650	+	17.4416i	−0.322637	+	0.798595i
$478$	−0.671777	+	1.42165i	−0.0307264	+	0.0650250i
$479$		−	15.1077i		−	0.690287i	−0.938550	−	0.345143i	$-0.887830\pi$
$479$		−	15.1077i		−	0.690287i	0.938550	−	0.345143i	$-0.112170\pi$
$480$	−4.98546	+	8.43476i	−0.227554	+	0.384992i
$481$		−	8.30630i		−	0.378735i
$482$	38.0461	+	17.9780i	1.73295	+	0.818874i
$483$	20.4469	+	10.8145i	0.930368	+	0.492075i
$484$	4.80607	+	15.8032i	0.218458	+	0.718329i
$485$	2.98332	−	14.9982i	0.135466	−	0.681031i
$486$	−10.9108	+	19.1560i	−0.494924	+	0.868936i
$487$	−7.37838	+	17.8130i	−0.334346	+	0.807184i	0.663891	+	0.747830i	$0.268904\pi$
$487$	−7.37838	+	17.8130i	−0.334346	+	0.807184i	−0.998237	+	0.0593540i	$0.981096\pi$
$488$	4.66901	+	9.84474i	0.211356	+	0.445651i
$489$	17.7582	−	9.59203i	0.803056	−	0.433767i
$490$	−0.132869	−	0.0984694i	−0.00600240	−	0.00444840i
$491$	5.64938	+	8.45489i	0.254953	+	0.381564i	0.936763	−	0.349966i	$-0.113807\pi$
$491$	5.64938	+	8.45489i	0.254953	+	0.381564i	−0.681810	+	0.731530i	$0.738807\pi$
$492$	−15.1629	−	22.4453i	−0.683598	−	1.01191i
$493$	−16.4222	+	3.26657i	−0.739617	+	0.147119i
$494$	−0.529141	+	0.479927i	−0.0238072	+	0.0215929i
$495$	4.15375	+	2.72321i	0.186697	+	0.122399i
$496$	1.69077	−	8.56335i	0.0759176	−	0.384506i
$497$	−19.0822	+	19.0822i	−0.855952	+	0.855952i
$498$	−22.2527	+	1.19864i	−0.997165	+	0.0537123i
$499$	−16.1168	+	3.20583i	−0.721487	+	0.143513i	−0.542158	−	0.840276i	$-0.682393\pi$
$499$	−16.1168	+	3.20583i	−0.721487	+	0.143513i	−0.179329	+	0.983789i	$0.557393\pi$
$500$	−1.99023	+	0.197442i	−0.0890058	+	0.00882989i
$501$	8.37692	+	10.1168i	0.374253	+	0.451985i
$502$	1.56138	+	10.5004i	0.0696878	+	0.468655i
$503$	2.12269	+	5.12463i	0.0946462	+	0.228496i	0.964111	−	0.265498i	$-0.0855364\pi$
$503$	2.12269	+	5.12463i	0.0946462	+	0.228496i	−0.869465	+	0.493994i	$0.835536\pi$
$504$	−21.0328	−	7.29384i	−0.936877	−	0.324894i
$505$	0.728924	−	1.75978i	0.0324367	−	0.0783091i
$506$	−2.89180	+	11.5621i	−0.128556	+	0.513997i
$507$	−19.2747	−	1.81334i	−0.856020	−	0.0805334i
$508$	2.43438	+	2.96203i	0.108008	+	0.131419i
$509$	2.31496	+	1.54681i	0.102609	+	0.0685611i	0.605816	−	0.795605i	$-0.292847\pi$
$509$	2.31496	+	1.54681i	0.102609	+	0.0685611i	−0.503207	+	0.864166i	$0.667847\pi$
$510$	2.68421	+	5.60658i	0.118859	+	0.248264i
$511$			30.1365i			1.33316i
$512$	22.6036	+	1.03832i	0.998947	+	0.0458879i
$513$	−1.85293	+	0.588726i	−0.0818087	+	0.0259929i
$514$	2.04919	+	5.72072i	0.0903859	+	0.252330i
$515$	6.83318	−	10.2266i	0.301106	−	0.450637i
$516$	28.2489	−	28.5374i	1.24359	−	1.25629i
$517$	1.75778	−	8.83694i	0.0773069	−	0.388648i
$518$	22.1458	+	5.53891i	0.973031	+	0.243366i
$519$	−3.22262	+	10.7932i	−0.141457	+	0.473769i
$520$	3.27730	+	1.95962i	0.143719	+	0.0859348i
$521$	23.5128	−	9.73933i	1.03011	−	0.426688i	0.197361	−	0.980331i	$-0.436763\pi$
$521$	23.5128	−	9.73933i	1.03011	−	0.426688i	0.832754	+	0.553643i	$0.186763\pi$
$522$	−26.2702	+	9.67011i	−1.14982	+	0.423249i
$523$	−10.3099	−	15.4298i	−0.450820	−	0.674699i	0.534549	−	0.845138i	$-0.320482\pi$
$523$	−10.3099	−	15.4298i	−0.450820	−	0.674699i	−0.985368	+	0.170439i	$0.945482\pi$
$524$	3.61211	+	36.4103i	0.157796	+	1.59059i
$525$	−1.33809	−	4.34266i	−0.0583991	−	0.189529i
$526$	−1.84465	+	37.8216i	−0.0804304	+	1.64910i
$527$	−3.91570	−	3.91570i	−0.170570	−	0.170570i
$528$	1.05822	−	11.4215i	0.0460533	−	0.497058i
$529$	2.05802	−	2.05802i	0.0894791	−	0.0894791i
$530$	5.95750	+	6.56842i	0.258777	+	0.285314i
$531$	1.14323	−	0.485297i	0.0496121	−	0.0210601i
$532$	−0.926706	−	1.73080i	−0.0401778	−	0.0750396i
$533$	−8.77733	+	5.86482i	−0.380188	+	0.254034i
$534$	−2.75053	+	4.63855i	−0.119027	+	0.200730i
$535$	3.93053	+	9.48914i	0.169932	+	0.410251i
$536$	13.8856	−	6.58543i	0.599766	−	0.284447i
$537$	7.55475	−	25.3024i	0.326011	−	1.09188i
$538$	14.5105	−	8.70426i	0.625594	−	0.375267i
$539$	0.189889	+	0.0377713i	0.00817909	+	0.00162692i
$540$	5.89254	+	8.56025i	0.253575	+	0.368375i
$541$	0.235095	+	0.157085i	0.0101075	+	0.00675363i	0.560614	−	0.828077i	$-0.310565\pi$
$541$	0.235095	+	0.157085i	0.0101075	+	0.00675363i	−0.550506	+	0.834831i	$0.685565\pi$
$542$	9.05196	−	19.1563i	0.388815	−	0.822834i
$543$	42.6350	−	4.38747i	1.82964	−	0.188285i
$544$	8.53101	−	11.5454i	0.365764	−	0.495003i
$545$	12.2202			0.523456
$546$	−2.88417	+	8.18242i	−0.123431	+	0.350175i
$547$	11.9688	−	17.9126i	0.511749	−	0.765887i	−0.482161	−	0.876083i	$-0.660148\pi$
$547$	11.9688	−	17.9126i	0.511749	−	0.765887i	0.993910	+	0.110196i	$0.0351479\pi$
$548$	9.22398	−	17.2863i	0.394029	−	0.738432i
$549$	11.5563	−	0.101050i	0.493211	−	0.00431270i
$550$	2.00785	−	1.20443i	0.0856151	−	0.0513569i
$551$	−2.28085	−	0.944758i	−0.0971674	−	0.0402480i
$552$	−14.7459	+	20.1100i	−0.627626	+	0.855937i
$553$	−1.58385	+	0.656052i	−0.0673521	+	0.0278982i
$554$	22.1967	+	16.4500i	0.943046	+	0.698893i
$555$	−6.79648	−	8.20810i	−0.288495	−	0.348414i
$556$	2.91198	+	0.881089i	0.123495	+	0.0373665i
$557$	−8.35587	−	42.0078i	−0.354050	−	1.77993i	−0.589219	−	0.807973i	$-0.700564\pi$
$557$	−8.35587	−	42.0078i	−0.354050	−	1.77993i	0.235169	−	0.971954i	$-0.424436\pi$
$558$	−7.48608	−	5.44720i	−0.316911	−	0.230598i
$559$	−11.0656	−	11.0656i	−0.468024	−	0.468024i
$560$	−7.41004	+	7.43104i	−0.313131	+	0.314019i
$561$	−5.64537	−	4.59188i	−0.238348	−	0.193869i
$562$	1.24870	−	25.6027i	0.0526733	−	1.07998i
$563$	6.75454	+	33.9574i	0.284670	+	1.43113i	0.813084	+	0.582146i	$0.197787\pi$
$563$	6.75454	+	33.9574i	0.284670	+	1.43113i	−0.528414	+	0.848987i	$0.677213\pi$
$564$	10.3939	−	15.7279i	0.437662	−	0.662265i
$565$	−15.3431	+	10.2520i	−0.645491	+	0.431303i
$566$	3.94967	+	26.5618i	0.166017	+	1.11647i
$567$	−16.4017	+	16.9856i	−0.688807	+	0.713330i
$568$	−17.3558	−	23.3498i	−0.728234	−	0.979735i
$569$	19.0795	+	7.90298i	0.799854	+	0.331310i	0.744898	−	0.667179i	$-0.232498\pi$
$569$	19.0795	+	7.90298i	0.799854	+	0.331310i	0.0549557	+	0.998489i	$0.482498\pi$
$570$	−0.130194	+	0.907213i	−0.00545322	+	0.0379990i
$571$	29.3902	+	5.84608i	1.22994	+	0.244651i	0.766947	−	0.641710i	$-0.221775\pi$
$571$	29.3902	+	5.84608i	1.22994	+	0.244651i	0.462995	+	0.886361i	$0.346775\pi$
$572$	−4.44907	−	0.435017i	−0.186025	−	0.0181890i
$573$	7.45193	+	3.94135i	0.311309	+	0.164652i
$574$	−9.78347	−	27.3125i	−0.408354	−	1.14000i
$575$	−5.09023			−0.212277
$576$	11.0829	−	21.2878i	0.461786	−	0.886991i
$577$	44.4921			1.85223			0.926116	−	0.377239i	$-0.123126\pi$
$577$	44.4921			1.85223			0.926116	+	0.377239i	$0.123126\pi$
$578$	5.03622	+	14.0596i	0.209479	+	0.584802i
$579$	−37.6744	−	19.9261i	−1.56569	−	0.828100i
$580$	−1.28417	+	13.1336i	−0.0533222	+	0.545344i
$581$	−23.4099	−	4.65652i	−0.971207	−	0.193185i
$582$	−5.32101	+	37.0777i	−0.220563	+	1.53692i
$583$	−9.59113	−	3.97278i	−0.397224	−	0.164536i
$584$	−32.1432	−	4.73314i	−1.33009	−	0.195859i
$585$	3.34774	−	2.27948i	0.138412	−	0.0942449i
$586$	−4.80470	−	32.3119i	−0.198480	−	1.33479i
$587$	21.4838	−	14.3550i	0.886730	−	0.592494i	−0.0266306	−	0.999645i	$-0.508478\pi$
$587$	21.4838	−	14.3550i	0.886730	−	0.592494i	0.913361	+	0.407151i	$0.133478\pi$
$588$	0.337963	+	0.223345i	0.0139374	+	0.00921060i
$589$	−0.159288	−	0.800797i	−0.00656336	−	0.0329963i
$590$	0.0285209	−	0.584777i	0.00117419	−	0.0240749i
$591$	−5.90712	−	4.80479i	−0.242987	−	0.197642i
$592$	−9.38588	+	22.7505i	−0.385757	+	0.935040i
$593$	−22.7280	−	22.7280i	−0.933327	−	0.933327i	0.0645856	−	0.997912i	$-0.479427\pi$
$593$	−22.7280	−	22.7280i	−0.933327	−	0.933327i	−0.997912	+	0.0645856i	$0.979427\pi$
$594$	−10.5186	−	6.11357i	−0.431584	−	0.250843i
$595$	1.29886	+	6.52981i	0.0532481	+	0.267696i
$596$	3.61387	−	11.9437i	0.148030	−	0.489235i
$597$	2.60470	+	3.14569i	0.106603	+	0.128745i
$598$	7.80801	+	5.78653i	0.319293	+	0.236629i
$599$	33.9201	−	14.0501i	1.38594	−	0.574073i	0.439874	−	0.898060i	$-0.355023\pi$
$599$	33.9201	−	14.0501i	1.38594	−	0.574073i	0.946062	+	0.323986i	$0.105023\pi$
$600$	4.84198	−	0.745147i	0.197673	−	0.0304205i
$601$	23.5464	+	9.75324i	0.960478	+	0.397843i	0.807159	−	0.590334i	$-0.201004\pi$
$601$	23.5464	+	9.75324i	0.960478	+	0.397843i	0.153319	+	0.988177i	$0.451004\pi$
$602$	36.8814	−	22.1236i	1.50317	−	0.901689i
$603$	−0.142526	−	16.2997i	−0.00580411	−	0.663774i
$604$	−8.00228	−	4.27003i	−0.325608	−	0.173745i
$605$	4.58842	−	6.86706i	0.186546	−	0.279186i
$606$	−1.55106	+	4.40036i	−0.0630073	+	0.178752i
$607$	−0.753374			−0.0305785			−0.0152893	−	0.999883i	$-0.504867\pi$
$607$	−0.753374			−0.0305785			−0.0152893	+	0.999883i	$0.504867\pi$
$608$	1.99159	−	0.716579i	0.0807697	−	0.0290611i
$609$	−29.8253	+	3.06925i	−1.20858	+	0.124372i
$610$	2.32754	−	4.92567i	0.0942392	−	0.199435i
$611$	−6.10887	−	4.08182i	−0.247138	−	0.165133i
$612$	−7.30410	−	13.3597i	−0.295251	−	0.540036i
$613$	30.5640	+	6.07955i	1.23447	+	0.245551i	0.768846	−	0.639434i	$-0.220831\pi$
$613$	30.5640	+	6.07955i	1.23447	+	0.245551i	0.465620	+	0.884985i	$0.345831\pi$
$614$	−25.7369	+	15.4385i	−1.03866	+	0.623047i
$615$	−3.87477	+	12.9774i	−0.156246	+	0.523299i
$616$	4.12660	−	11.5718i	0.166266	−	0.466240i
$617$	13.9866	+	33.7665i	0.563078	+	1.35939i	0.907293	+	0.420499i	$0.138145\pi$
$617$	13.9866	+	33.7665i	0.563078	+	1.35939i	−0.344215	+	0.938891i	$0.611855\pi$
$618$	−15.3662	+	25.9139i	−0.618120	+	1.04241i
$619$	26.6012	−	17.7743i	1.06919	−	0.714411i	0.109081	−	0.994033i	$-0.465209\pi$
$619$	26.6012	−	17.7743i	1.06919	−	0.714411i	0.960110	+	0.279622i	$0.0902091\pi$
$620$	−3.84754	+	2.06006i	−0.154521	+	0.0827338i
$621$	12.7731	+	23.1610i	0.512568	+	0.929417i
$622$	6.74782	+	7.43978i	0.270563	+	0.298308i
$623$	−4.08422	+	4.08422i	−0.163631	+	0.163631i
$624$	−8.27428	−	4.36132i	−0.331236	−	0.174593i
$625$	0.707107	+	0.707107i	0.0282843	+	0.0282843i
$626$	0.393272	−	8.06343i	0.0157183	−	0.322280i
$627$	−0.315947	−	1.02538i	−0.0126177	−	0.0409497i
$628$	9.82039	−	0.974239i	0.391876	−	0.0388764i
$629$	8.67435	+	12.9821i	0.345869	+	0.517629i
$630$	3.84505	+	10.4456i	0.153190	+	0.416163i
$631$	32.5153	−	13.4683i	1.29442	−	0.536164i	0.374117	−	0.927382i	$-0.377946\pi$
$631$	32.5153	−	13.4683i	1.29442	−	0.536164i	0.920298	+	0.391217i	$0.127946\pi$
$632$	−0.450982	−	1.79235i	−0.0179391	−	0.0712959i
$633$	0.389136	−	1.30329i	0.0154668	−	0.0518013i
$634$	19.9307	+	4.98488i	0.791548	+	0.197975i
$635$	0.373992	−	1.88018i	0.0148414	−	0.0746128i
$636$	−15.4371	−	15.2811i	−0.612121	−	0.605934i
$637$	0.0877104	−	0.131268i	0.00347521	−	0.00520103i
$638$	−5.20969	−	14.5439i	−0.206253	−	0.575798i
$639$	−30.2117	+	6.28458i	−1.19515	+	0.248614i
$640$	−6.76205	−	9.07054i	−0.267293	−	0.358545i
$641$			12.2452i			0.483657i	0.970319	+	0.241829i	$0.0777472\pi$
$641$			12.2452i			0.483657i	−0.970319	+	0.241829i	$0.922253\pi$
$642$	−10.8641	−	22.6921i	−0.428770	−	0.895584i
$643$	9.30491	+	6.21734i	0.366950	+	0.245188i	0.725350	−	0.688380i	$-0.241678\pi$
$643$	9.30491	+	6.21734i	0.366950	+	0.245188i	−0.358400	+	0.933568i	$0.616678\pi$
$644$	−20.6344	+	16.9586i	−0.813109	+	0.668264i
$645$	−19.9890	−	1.88054i	−0.787065	−	0.0740462i
$646$	0.325813	−	1.30267i	0.0128189	−	0.0512530i
$647$	−16.3968	+	39.5853i	−0.644623	+	1.55626i	0.175753	+	0.984434i	$0.443764\pi$
$647$	−16.3968	+	39.5853i	−0.644623	+	1.55626i	−0.820377	+	0.571824i	$0.806236\pi$
$648$	−15.5407	−	20.1615i	−0.610495	−	0.792020i
$649$	0.262295	+	0.633236i	0.0102960	+	0.0248567i
$650$	−0.280812	−	1.88848i	−0.0110143	−	0.0740722i
$651$	−6.32414	−	7.63765i	−0.247863	−	0.299343i
$652$	2.30075	+	23.1917i	0.0901044	+	0.908258i
$653$	31.1914	−	6.20435i	1.22061	−	0.242795i	0.457588	−	0.889164i	$-0.348714\pi$
$653$	31.1914	−	6.20435i	1.22061	−	0.242795i	0.763025	+	0.646370i	$0.223714\pi$
$654$	−29.8899	+	1.61002i	−1.16879	+	0.0629569i
$655$	12.9362	−	12.9362i	0.505458	−	0.505458i
$656$	30.6677	−	6.14531i	1.19737	−	0.239934i
$657$	−18.8940	+	28.8193i	−0.737126	+	1.12435i
$658$	14.9563	−	13.5653i	0.583058	−	0.528829i
$659$	−33.9978	+	6.76258i	−1.32437	+	0.263433i	−0.806096	−	0.591785i	$-0.798423\pi$
$659$	−33.9978	+	6.76258i	−1.32437	+	0.263433i	−0.518269	+	0.855218i	$0.673423\pi$
$660$	−4.75241	+	3.21050i	−0.184987	+	0.124968i
$661$	−7.94811	−	11.8952i	−0.309146	−	0.462669i	0.644067	−	0.764969i	$-0.277246\pi$
$661$	−7.94811	−	11.8952i	−0.309146	−	0.462669i	−0.953213	+	0.302300i	$0.902246\pi$
$662$	−13.5372	−	10.0324i	−0.526137	−	0.389921i
$663$	−5.22098	+	2.82009i	−0.202766	+	0.109523i
$664$	8.64327	−	24.2374i	0.335424	−	0.940592i
$665$	−0.375656	+	0.906915i	−0.0145673	+	0.0351686i
$666$	17.7052	+	19.1811i	0.686064	+	0.743253i
$667$	−6.55230	+	32.9406i	−0.253706	+	1.27547i
$668$	−14.5105	+	4.41293i	−0.561429	+	0.170742i
$669$	22.3693	+	11.8312i	0.864846	+	0.457420i
$670$	−6.94744	−	3.28289i	−0.268403	−	0.126829i
$671$			6.37784i			0.246214i
$672$	17.1455	−	19.1522i	0.661402	−	0.738811i
$673$		−	21.1949i		−	0.817005i	−0.912757	−	0.408502i	$-0.866051\pi$
$673$		−	21.1949i		−	0.817005i	0.912757	−	0.408502i	$-0.133949\pi$
$674$	−4.74393	+	10.0394i	−0.182729	+	0.386702i
$675$	1.44302	−	4.99176i	0.0555418	−	0.192133i
$676$	10.5240	−	19.7226i	0.404770	−	0.758562i
$677$	−1.92432	+	9.67420i	−0.0739575	+	0.371810i	−0.999984	−	0.00564881i	$-0.998202\pi$
$677$	−1.92432	+	9.67420i	−0.0739575	+	0.371810i	0.926026	+	0.377459i	$0.123202\pi$
$678$	36.1778	−	27.0972i	1.38940	−	1.04066i
$679$	−15.3530	+	37.0655i	−0.589196	+	1.42244i
$680$	−7.16861	+	0.359796i	−0.274903	+	0.0137976i
$681$	−10.9525	−	20.2770i	−0.419701	−	0.777016i
$682$	3.04216	−	4.10491i	0.116490	−	0.157185i
$683$	24.9244	+	37.3020i	0.953706	+	1.42732i	0.903502	+	0.428583i	$0.140987\pi$
$683$	24.9244	+	37.3020i	0.953706	+	1.42732i	0.0502037	+	0.998739i	$0.484013\pi$
$684$	0.198921	−	2.23615i	0.00760593	−	0.0855012i
$685$	−9.60840	+	1.91123i	−0.367118	+	0.0730243i
$686$	17.7400	+	19.5591i	0.677315	+	0.746771i
$687$	−27.7374	−	22.5613i	−1.05825	−	0.860768i
$688$	17.8042	+	42.8118i	0.678780	+	1.63219i
$689$	−5.98586	+	5.98586i	−0.228043	+	0.228043i
$690$	12.4504	−	0.670643i	0.473980	−	0.0255309i
$691$	36.7856	−	7.31711i	1.39939	−	0.278356i	0.562985	−	0.826467i	$-0.309653\pi$
$691$	36.7856	−	7.31711i	1.39939	−	0.278356i	0.836406	+	0.548111i	$0.184653\pi$
$692$	−10.0601	−	8.24417i	−0.382426	−	0.313396i
$693$	−9.29438	−	9.13325i	−0.353064	−	0.346943i
$694$	−42.8386	+	6.36999i	−1.62613	+	0.241801i
$695$	−0.582129	−	1.40538i	−0.0220814	−	0.0533093i
$696$	1.41064	−	32.2933i	0.0534701	−	1.22407i
$697$	7.59357	−	18.3325i	0.287627	−	0.694393i
$698$	17.9314	+	4.48484i	0.678714	+	0.169754i
$699$	−2.31530	+	24.6102i	−0.0875726	+	0.930842i
$700$	5.22221	+	0.510613i	0.197381	+	0.0192994i
$701$	−38.3239	−	25.6072i	−1.44748	−	0.967172i	−0.997239	−	0.0742630i	$-0.976340\pi$
$701$	−38.3239	−	25.6072i	−1.44748	−	0.967172i	−0.450237	−	0.892909i	$-0.648660\pi$
$702$	−7.88807	+	6.01655i	−0.297716	+	0.227080i
$703$			2.30209i			0.0868249i
$704$	11.6942	+	6.21881i	0.440742	+	0.234380i
$705$	−9.37652	+	0.964916i	−0.353140	+	0.0363409i
$706$	31.3420	−	11.2268i	1.17957	−	0.422528i
$707$	−2.77634	+	4.15508i	−0.104415	+	0.156268i
$708$	0.00728432	+	1.43409i	0.000273761	+	0.0538964i
$709$	3.19478	−	16.0612i	0.119982	−	0.603193i	−0.873272	−	0.487234i	$-0.838006\pi$
$709$	3.19478	−	16.0612i	0.119982	−	0.603193i	0.993254	−	0.115959i	$-0.0369941\pi$
$710$	−3.52959	+	14.1121i	−0.132463	+	0.529617i
$711$	−1.92593	−	0.365615i	−0.0722281	−	0.0137116i
$712$	−3.71472	−	4.99763i	−0.139215	−	0.187294i
$713$	−10.2622	+	4.25075i	−0.384323	+	0.159192i
$714$	−4.03725	−	15.8004i	−0.151090	−	0.591316i
$715$	1.24178	+	1.85845i	0.0464399	+	0.0695022i
$716$	23.5837	+	19.3267i	0.881363	+	0.722273i
$717$	−1.84038	+	0.567072i	−0.0687304	+	0.0211777i
$718$	−42.8032	−	2.08761i	−1.59740	−	0.0779089i
$719$	20.8378	+	20.8378i	0.777120	+	0.777120i	0.979340	−	0.202220i	$-0.0648157\pi$
$719$	20.8378	+	20.8378i	0.777120	+	0.777120i	−0.202220	+	0.979340i	$0.564816\pi$
$720$	−11.7450	+	2.46052i	−0.437712	+	0.0916983i
$721$	−22.8171	+	22.8171i	−0.849752	+	0.849752i
$722$	−19.7564	+	17.9189i	−0.735256	+	0.666871i
$723$	15.1759	+	49.2520i	0.564397	+	1.83170i
$724$	−14.3329	+	47.3698i	−0.532677	+	1.76048i
$725$	5.48614	−	3.66572i	0.203750	−	0.136141i
$726$	−10.3183	+	17.4010i	−0.382947	+	0.645811i
$727$	−7.24860	−	17.4997i	−0.268836	−	0.649027i	0.730593	−	0.682813i	$-0.239244\pi$
$727$	−7.24860	−	17.4997i	−0.268836	−	0.649027i	−0.999429	+	0.0337859i	$0.989244\pi$
$728$	−7.42999	−	6.71980i	−0.275374	−	0.249053i
$729$	−26.3339	+	5.96019i	−0.975331	+	0.220748i
$730$	8.35647	+	13.9308i	0.309287	+	0.515600i
$731$	28.8505	+	5.73872i	1.06707	+	0.212254i
$732$	−5.04406	+	12.3546i	−0.186434	+	0.456638i
$733$	4.06730	+	2.71768i	0.150229	+	0.100380i	0.628413	−	0.777880i	$-0.283705\pi$
$733$	4.06730	+	2.71768i	0.150229	+	0.100380i	−0.478184	+	0.878260i	$0.658705\pi$
$734$	41.9973	+	19.8451i	1.55015	+	0.732494i
$735$	−0.0207342	−	0.201484i	−0.000764793	−	0.00743183i
$736$	−14.8471	−	24.6718i	−0.547271	−	0.909416i
$737$	8.99566			0.331359
$738$	7.76769	−	32.2525i	0.285933	−	1.18723i
$739$	−2.06393	+	3.08889i	−0.0759230	+	0.113627i	−0.867488	−	0.497458i	$-0.834267\pi$
$739$	−2.06393	+	3.08889i	−0.0759230	+	0.113627i	0.791565	+	0.611085i	$0.209267\pi$
$740$	11.7729	−	3.58037i	0.432780	−	0.131617i
$741$	−0.871071	−	0.0819494i	−0.0319996	−	0.00301049i
$742$	−11.9676	−	19.9507i	−0.439345	−	0.732415i
$743$	30.9640	+	12.8257i	1.13596	+	0.470530i	0.869803	−	0.493399i	$-0.164246\pi$
$743$	30.9640	+	12.8257i	1.13596	+	0.470530i	0.266157	+	0.963930i	$0.414246\pi$
$744$	9.13946	−	5.54570i	0.335069	−	0.203315i
$745$	−5.76432	+	2.38766i	−0.211188	+	0.0874771i
$746$	32.0214	−	43.2078i	1.17239	−	1.58195i
$747$	−19.4673	−	19.1298i	−0.712272	−	0.699923i
$748$	7.40782	−	3.96630i	0.270857	−	0.145022i
$749$	−5.25700	−	26.4287i	−0.192087	−	0.965685i
$750$	−1.82271	−	1.63638i	−0.0665558	−	0.0597522i
$751$	−21.6611	−	21.6611i	−0.790426	−	0.790426i	0.191138	−	0.981563i	$-0.438782\pi$
$751$	−21.6611	−	21.6611i	−0.790426	−	0.790426i	−0.981563	+	0.191138i	$0.938782\pi$
$752$	12.1195	+	18.0827i	0.441954	+	0.659409i
$753$	−8.20417	+	10.0864i	−0.298976	+	0.367569i
$754$	−12.5825	−	0.613675i	−0.458226	−	0.0223487i
$755$	0.884760	+	4.44799i	0.0321997	+	0.161879i
$756$	−10.7810	−	25.0428i	−0.392101	−	0.910797i
$757$	−1.57391	+	1.05165i	−0.0572046	+	0.0382229i	−0.583844	−	0.811866i	$-0.698452\pi$
$757$	−1.57391	+	1.05165i	−0.0572046	+	0.0382229i	0.526639	+	0.850089i	$0.323452\pi$
$758$	−11.6914	+	1.73849i	−0.424652	+	0.0631447i
$759$	−12.8430	+	6.93710i	−0.466172	+	0.251801i
$760$	−0.908304	−	0.543107i	−0.0329476	−	0.0197006i
$761$	−19.7501	−	8.18074i	−0.715939	−	0.296552i	−0.00517940	−	0.999987i	$-0.501649\pi$
$761$	−19.7501	−	8.18074i	−0.715939	−	0.296552i	−0.710760	+	0.703435i	$0.751649\pi$
$762$	−0.667047	+	4.64809i	−0.0241646	+	0.168383i
$763$	−31.4444	−	6.25468i	−1.13836	−	0.226435i
$764$	−7.52024	+	6.18061i	−0.272073	+	0.223607i
$765$	−2.85177	+	7.05872i	−0.103106	+	0.255209i
$766$	16.4856	−	5.90523i	0.595650	−	0.213365i
$767$	0.558904			0.0201808
$768$	17.7346	+	21.2951i	0.639944	+	0.768422i
$769$	28.1568			1.01536			0.507680	−	0.861546i	$-0.330503\pi$
$769$	28.1568			1.01536			0.507680	+	0.861546i	$0.330503\pi$
$770$	−5.78296	+	2.07149i	−0.208404	+	0.0746512i
$771$	−3.47958	+	6.57885i	−0.125314	+	0.236932i
$772$	38.0197	−	31.2470i	1.36836	−	1.12460i
$773$	18.9518	+	3.76974i	0.681648	+	0.135588i	0.523756	−	0.851868i	$-0.324530\pi$
$773$	18.9518	+	3.76974i	0.681648	+	0.135588i	0.157892	+	0.987456i	$0.449530\pi$
$774$	49.1397	+	1.96613i	1.76629	+	0.0706712i
$775$	2.01606	+	0.835079i	0.0724190	+	0.0299969i
$776$	−37.1223	−	22.1967i	−1.33261	−	0.796816i
$777$	13.2872	+	24.5993i	0.476676	+	0.882495i
$778$	−32.5957	+	4.84690i	−1.16861	+	0.173770i
$779$	2.43264	−	1.62543i	0.0871582	−	0.0582373i
$780$	0.935659	+	4.58211i	0.0335020	+	0.164066i
$781$	−3.32236	−	16.7026i	−0.118883	−	0.597668i
$782$	−18.2462	−	0.889910i	−0.652483	−	0.0318231i
$783$	−30.4459	−	15.7638i	−1.08805	−	0.563353i
$784$	−0.388563	+	0.260426i	−0.0138773	+	0.00930091i
$785$	−3.48907	−	3.48907i	−0.124530	−	0.124530i
$786$	−29.9368	+	33.3455i	−1.06781	+	1.18940i
$787$	4.30347	+	21.6350i	0.153402	+	0.771204i	0.978505	+	0.206222i	$0.0661169\pi$
$787$	4.30347	+	21.6350i	0.153402	+	0.771204i	−0.825103	+	0.564982i	$0.808883\pi$
$788$	7.75129	−	4.15021i	0.276128	−	0.147845i
$789$	−35.7208	+	29.5776i	−1.27169	+	1.05299i
$790$	−0.550228	+	0.742445i	−0.0195762	+	0.0264150i
$791$	44.7274	−	18.5267i	1.59032	−	0.658734i
$792$	11.2011	−	8.47883i	0.398015	−	0.301282i
$793$	4.80480	+	1.99021i	0.170624	+	0.0706746i
$794$	−19.4015	−	32.3436i	−0.688535	−	1.14783i
$795$	−1.01727	+	10.8129i	−0.0360787	+	0.383494i
$796$	−4.51187	+	1.37215i	−0.159919	+	0.0486345i
$797$	−8.08231	+	12.0960i	−0.286290	+	0.428463i	−0.946542	−	0.322581i	$-0.895450\pi$
$797$	−8.08231	+	12.0960i	−0.286290	+	0.428463i	0.660252	+	0.751044i	$0.270450\pi$
$798$	0.799348	−	2.26776i	0.0282966	−	0.0802777i
$799$	13.8104			0.488575
$800$	−1.36480	+	5.48975i	−0.0482529	+	0.194092i
$801$	−6.46630	+	1.34511i	−0.228475	+	0.0475271i
$802$	23.2167	+	10.9706i	0.819808	+	0.387386i
$803$	−15.8128	−	10.5657i	−0.558020	−	0.372857i
$804$	17.4256	+	7.11443i	0.614553	+	0.250907i
$805$	13.0979	+	2.60534i	0.461641	+	0.0918261i
$806$	−2.14316	−	3.57278i	−0.0754897	−	0.125846i
$807$	19.8576	+	5.92907i	0.699022	+	0.208713i
$808$	−3.99572	−	3.61379i	−0.140569	−	0.127133i
$809$	−13.7176	−	33.1172i	−0.482284	−	1.16434i	−0.958521	−	0.285020i	$-0.908000\pi$
$809$	−13.7176	−	33.1172i	−0.482284	−	1.16434i	0.476237	−	0.879317i	$-0.342000\pi$
$810$	−2.87187	+	12.3997i	−0.100907	+	0.435681i
$811$	30.6718	−	20.4942i	1.07703	−	0.719649i	0.115214	−	0.993341i	$-0.463245\pi$
$811$	30.6718	−	20.4942i	1.07703	−	0.719649i	0.961818	+	0.273691i	$0.0882446\pi$
$812$	10.0265	−	33.1375i	0.351863	−	1.16290i
$813$	24.7985	−	7.64110i	0.869722	−	0.267985i
$814$	−10.6705	+	9.67809i	−0.374002	+	0.339217i
$815$	8.23977	−	8.23977i	0.288626	−	0.288626i
$816$	17.4866	−	1.82451i	0.612154	−	0.0638707i
$817$	3.06682	+	3.06682i	0.107295	+	0.107295i
$818$	3.36668	+	0.164201i	0.117713	+	0.00574114i
$819$	−9.78094	+	4.15196i	−0.341774	+	0.145081i
$820$	−12.0959	−	9.91252i	−0.422407	−	0.346160i
$821$	14.4106	+	21.5669i	0.502932	+	0.752691i	0.992887	−	0.119057i	$-0.0379870\pi$
$821$	14.4106	+	21.5669i	0.502932	+	0.752691i	−0.489956	+	0.871747i	$0.662987\pi$
$822$	23.2498	−	5.94067i	0.810930	−	0.207205i
$823$	3.81170	−	1.57886i	0.132868	−	0.0550355i	−0.315259	−	0.949006i	$-0.602091\pi$
$823$	3.81170	−	1.57886i	0.132868	−	0.0550355i	0.448127	+	0.893970i	$0.352091\pi$
$824$	−20.7528	−	27.9200i	−0.722958	−	0.972638i
$825$	2.74774	+	0.820418i	0.0956641	+	0.0285633i
$826$	−0.372695	+	1.49012i	−0.0129677	+	0.0518479i
$827$	4.65161	−	23.3852i	0.161752	−	0.813183i	−0.811661	−	0.584128i	$-0.801437\pi$
$827$	4.65161	−	23.3852i	0.161752	−	0.813183i	0.973414	−	0.229055i	$-0.0735635\pi$
$828$	−30.3647	+	3.28071i	−1.05525	+	0.114013i
$829$	−25.4301	+	38.0588i	−0.883223	+	1.32184i	0.0628972	+	0.998020i	$0.479966\pi$
$829$	−25.4301	+	38.0588i	−0.883223	+	1.32184i	−0.946120	+	0.323816i	$0.895034\pi$
$830$	−12.1126	+	4.33878i	−0.420433	+	0.150601i
$831$	3.46379	+	33.6592i	0.120158	+	1.16763i
$832$	8.33418	−	6.86934i	0.288936	−	0.238151i
$833$			0.296758i			0.0102821i
$834$	1.60902	+	3.36080i	0.0557157	+	0.116375i
$835$	6.30534	+	4.21309i	0.218205	+	0.145800i
$836$	1.23306	+	0.120565i	0.0426462	+	0.00416982i
$837$	−1.25931	−	11.2687i	−0.0435280	−	0.389504i
$838$	−3.12233	−	0.780930i	−0.107859	−	0.0269768i
$839$	17.6041	−	42.5002i	0.607763	−	1.46727i	−0.257665	−	0.966234i	$-0.582953\pi$
$839$	17.6041	−	42.5002i	0.607763	−	1.46727i	0.865427	−	0.501034i	$-0.167047\pi$
$840$	−12.8405	−	0.560900i	−0.443040	−	0.0193529i
$841$	−5.56239	−	13.4288i	−0.191807	−	0.463062i
$842$	17.3851	−	2.58513i	0.599131	−	0.0890893i
$843$	24.1806	−	20.0221i	0.832824	−	0.689596i
$844$	1.21477	+	0.995496i	0.0418140	+	0.0342664i
$845$	−10.9626	+	2.18060i	−0.377126	+	0.0750150i
$846$	22.8073	−	3.59550i	0.784132	−	0.123616i
$847$	−15.3215	+	15.3215i	−0.526452	+	0.526452i
$848$	23.1588	−	9.63109i	0.795276	−	0.330733i
$849$	−20.7532	+	25.5146i	−0.712250	+	0.875657i
$850$	2.41104	+	2.65828i	0.0826980	+	0.0911784i
$851$	30.7166	−	6.10992i	1.05295	−	0.209445i
$852$	6.77390	−	34.9824i	0.232070	−	1.19848i
$853$	2.80078	+	4.19167i	0.0958970	+	0.143520i	0.876316	−	0.481737i	$-0.159994\pi$
$853$	2.80078	+	4.19167i	0.0958970	+	0.143520i	−0.780419	+	0.625257i	$0.784994\pi$
$854$	−8.51021	+	11.4832i	−0.291213	+	0.392946i
$855$	−0.927826	+	0.631758i	−0.0317310	+	0.0216057i
$856$	29.0142	−	1.45624i	0.991684	−	0.0497732i
$857$	3.77266	−	9.10801i	0.128872	−	0.311124i	−0.846253	−	0.532781i	$-0.821147\pi$
$857$	3.77266	−	9.10801i	0.128872	−	0.311124i	0.975125	+	0.221658i	$0.0711468\pi$
$858$	−3.28217	−	4.38206i	−0.112051	−	0.149601i
$859$	−10.7890	+	54.2401i	−0.368117	+	1.85065i	0.141081	+	0.989998i	$0.454942\pi$
$859$	−10.7890	+	54.2401i	−0.368117	+	1.85065i	−0.509198	+	0.860650i	$0.670058\pi$
$860$	10.9140	−	20.4535i	0.372165	−	0.697458i
$861$	16.6126	−	31.4095i	0.566155	−	1.07043i
$862$	19.0116	−	40.2335i	0.647539	−	1.37036i
$863$		−	47.7943i		−	1.62694i	−0.581609	−	0.813469i	$-0.697577\pi$
$863$		−	47.7943i		−	1.62694i	0.581609	−	0.813469i	$-0.302423\pi$
$864$	28.4035	−	7.56572i	0.966307	−	0.257391i
$865$			6.50329i			0.221119i
$866$	−5.93646	−	2.80517i	−0.201729	−	0.0953235i
$867$	−8.55162	+	16.1686i	−0.290428	+	0.549114i
$868$	10.9547	−	3.33154i	0.371827	−	0.113080i
$869$	0.211058	−	1.06106i	0.00715967	−	0.0359941i
$870$	−12.9358	+	9.68895i	−0.438566	+	0.328486i
$871$	2.80711	−	6.77696i	0.0951153	−	0.229629i
$872$	11.6097	−	32.5558i	0.393154	−	1.10248i
$873$	−37.9202	+	25.8199i	−1.28340	+	0.873870i
$874$	−2.16399	−	1.60374i	−0.0731980	−	0.0542472i
$875$	−1.45757	−	2.18141i	−0.0492749	−	0.0737451i
$876$	−22.2749	−	32.9729i	−0.752598	−	1.11405i
$877$	23.8390	−	4.74187i	0.804985	−	0.160122i	0.224587	−	0.974454i	$-0.427897\pi$
$877$	23.8390	−	4.74187i	0.804985	−	0.160122i	0.580399	+	0.814333i	$0.302897\pi$
$878$	28.3213	−	25.6872i	0.955797	−	0.866900i
$879$	25.2460	−	31.0380i	0.851525	−	1.04689i
$880$	−1.30117	−	6.49337i	−0.0438623	−	0.218892i
$881$	29.5853	−	29.5853i	0.996754	−	0.996754i	−0.00324111	−	0.999995i	$-0.501032\pi$
$881$	29.5853	−	29.5853i	0.996754	−	0.996754i	0.999995	+	0.00324111i	$0.00103168\pi$
$882$	0.0772604	+	0.490086i	0.00260149	+	0.0165020i
$883$	27.8516	−	5.54003i	0.937281	−	0.186437i	0.297262	−	0.954796i	$-0.403926\pi$
$883$	27.8516	−	5.54003i	0.937281	−	0.186437i	0.640019	+	0.768359i	$0.278926\pi$
$884$	−0.676428	−	6.81844i	−0.0227508	−	0.229329i
$885$	0.552296	−	0.457313i	0.0185652	−	0.0153724i
$886$	4.82809	+	32.4692i	0.162203	+	1.09082i
$887$	21.1354	+	51.0254i	0.709658	+	1.71327i	0.700855	+	0.713304i	$0.252802\pi$
$887$	21.1354	+	51.0254i	0.709658	+	1.71327i	0.00880298	+	0.999961i	$0.497198\pi$
$888$	−28.3241	+	10.3085i	−0.950495	+	0.345929i
$889$	−1.92467	+	4.64657i	−0.0645514	+	0.155841i
$890$	−0.755450	+	3.02046i	−0.0253227	+	0.101246i
$891$	−3.16206	−	14.5612i	−0.105933	−	0.487817i
$892$	−22.5743	+	18.5530i	−0.755845	+	0.621201i
$893$	1.69307	+	1.13127i	0.0566565	+	0.0378567i
$894$	13.7846	−	6.59953i	0.461027	−	0.220721i
$895$		−	15.2456i		−	0.509604i
$896$	12.7572	+	26.8009i	0.426187	+	0.895354i
$897$	1.21844	+	11.8401i	0.0406826	+	0.395331i
$898$	0.718549	+	2.00597i	0.0239783	+	0.0669402i
$899$	7.99922	−	11.9717i	0.266789	−	0.399278i
$900$	4.67383	+	3.76235i	0.155794	+	0.125412i
$901$	3.10433	−	15.6065i	0.103420	−	0.519928i
$902$	17.7610	+	4.44223i	0.591378	+	0.147910i
$903$	50.4721	+	15.0699i	1.67960	+	0.501494i
$904$	12.7356	+	50.6154i	0.423580	+	1.68344i
$905$	22.8617	−	9.46963i	0.759949	−	0.314781i
$906$	−2.75010	−	10.7630i	−0.0913659	−	0.357575i
$907$	−5.57886	−	8.34935i	−0.185243	−	0.277236i	0.727212	−	0.686413i	$-0.240816\pi$
$907$	−5.57886	−	8.34935i	−0.185243	−	0.277236i	−0.912455	+	0.409177i	$0.865816\pi$
$908$	26.4811	−	2.62708i	0.878807	−	0.0871827i
$909$	−5.26001	+	2.23285i	−0.174464	+	0.0740590i
$910$	−0.244011	+	5.00306i	−0.00808887	+	0.165850i
$911$	−21.8703	−	21.8703i	−0.724597	−	0.724597i	0.244941	−	0.969538i	$-0.421231\pi$
$911$	−21.8703	−	21.8703i	−0.724597	−	0.724597i	−0.969538	+	0.244941i	$0.921231\pi$
$912$	2.29322	+	1.20874i	0.0759359	+	0.0400254i
$913$	10.6507	−	10.6507i	0.352488	−	0.352488i
$914$	2.95130	+	3.25395i	0.0976204	+	0.107631i
$915$	6.37646	−	1.96476i	0.210799	−	0.0649530i
$916$	36.3969	−	19.4877i	1.20259	−	0.643891i
$917$	−39.9078	+	26.6656i	−1.31787	+	0.880574i
$918$	6.04527	−	17.6410i	0.199524	−	0.582239i
$919$	−15.5747	−	37.6006i	−0.513761	−	1.24033i	−0.941679	−	0.336511i	$-0.890753\pi$
$919$	−15.5747	−	37.6006i	−0.513761	−	1.24033i	0.427919	−	0.903817i	$-0.359247\pi$
$920$	−4.83594	+	13.5609i	−0.159436	+	0.447089i
$921$	−35.2209	−	10.5162i	−1.16057	−	0.346521i
$922$	32.3971	−	19.4337i	1.06694	−	0.640014i
$923$	−13.6198	−	2.70915i	−0.448302	−	0.0891729i
$924$	13.8719	−	5.82865i	0.456352	−	0.191748i
$925$	−5.11574	−	3.41823i	−0.168204	−	0.112391i
$926$	2.77591	−	5.87454i	0.0912220	−	0.193049i
$927$	−36.1249	+	7.51464i	−1.18650	+	0.246813i
$928$	33.7692	+	15.8986i	1.10853	+	0.521898i
$929$	−20.4535			−0.671058			−0.335529	−	0.942030i	$-0.608915\pi$
$929$	−20.4535			−0.671058			−0.335529	+	0.942030i	$0.608915\pi$
$930$	−5.04119	−	1.77694i	−0.165307	−	0.0582681i
$931$	−0.0243089	+	0.0363809i	−0.000796693	+	0.00119234i
$932$	−25.1821	−	13.4372i	−0.824866	−	0.440150i
$933$	−1.15222	+	12.2473i	−0.0377219	+	0.400960i
$934$	−1.28272	+	0.769449i	−0.0419718	+	0.0251771i
$935$	−3.88160	−	1.60781i	−0.126942	−	0.0525810i
$936$	−2.89227	−	11.0843i	−0.0945367	−	0.362302i
$937$	40.6179	−	16.8245i	1.32693	−	0.549631i	0.397150	−	0.917754i	$-0.369999\pi$
$937$	40.6179	−	16.8245i	1.32693	−	0.549631i	0.929777	+	0.368122i	$0.119999\pi$
$938$	16.1965	+	12.0033i	0.528835	+	0.391921i
$939$	7.61556	−	6.30585i	0.248524	−	0.205783i
$940$	3.15216	−	10.4178i	0.102812	−	0.339792i
$941$	2.96128	+	14.8874i	0.0965350	+	0.485314i	0.998561	+	0.0536321i	$0.0170798\pi$
$941$	2.96128	+	14.8874i	0.0965350	+	0.485314i	−0.902026	+	0.431682i	$0.857920\pi$
$942$	8.99377	+	8.07439i	0.293033	+	0.263078i
$943$	−28.1445	−	28.1445i	−0.916510	−	0.916510i
$944$	−1.53081	−	0.631545i	−0.0498235	−	0.0205550i
$945$	−6.26804	+	12.1060i	−0.203899	+	0.393807i
$946$	−1.32213	+	27.1083i	−0.0429862	+	0.881365i
$947$	−10.3181	−	51.8727i	−0.335294	−	1.68564i	−0.669242	−	0.743044i	$-0.733381\pi$
$947$	−10.3181	−	51.8727i	−0.335294	−	1.68564i	0.333949	−	0.942591i	$-0.391619\pi$
$948$	1.24801	−	1.88847i	0.0405334	−	0.0613347i
$949$	−12.8942	+	8.61562i	−0.418563	+	0.279675i
$950$	0.0778270	+	0.523391i	0.00252504	+	0.0169811i
$951$	11.9581	+	22.1387i	0.387769	+	0.717897i
$952$	18.6300	+	2.74330i	0.603803	+	0.0889110i
$953$	−56.9155	−	23.5752i	−1.84367	−	0.763675i	−0.947270	−	0.320437i	$-0.896170\pi$
$953$	−56.9155	−	23.5752i	−1.84367	−	0.763675i	−0.896404	−	0.443237i	$-0.853830\pi$
$954$	1.06357	−	26.5818i	0.0344343	−	0.860618i
$955$	4.77356	+	0.949521i	0.154469	+	0.0307258i
$956$	0.216394	−	2.21313i	0.00699867	−	0.0715778i
$957$	8.84618	−	16.7255i	0.285956	−	0.540659i
$958$	7.20492	+	20.1140i	0.232780	+	0.649853i
$959$	25.7021			0.829963
$960$	2.61494	−	13.6074i	0.0843967	−	0.439178i
$961$	−26.2381			−0.846392
$962$	3.96132	+	11.0588i	0.127718	+	0.356550i
$963$	11.5422	−	28.5694i	0.371943	−	0.920638i
$964$	−59.2274	−	5.79109i	−1.90759	−	0.186518i
$965$	−24.1335	−	4.80045i	−0.776884	−	0.154532i
$966$	−32.3800	−	4.64685i	−1.04181	−	0.149510i
$967$	−26.9983	−	11.1831i	−0.868207	−	0.359623i	−0.0962954	−	0.995353i	$-0.530699\pi$
$967$	−26.9983	−	11.1831i	−0.868207	−	0.359623i	−0.771912	+	0.635730i	$0.780699\pi$
$968$	−13.9353	−	18.7480i	−0.447898	−	0.602584i
$969$	1.44699	−	0.781587i	0.0464841	−	0.0251082i
$970$	3.18078	+	21.3909i	0.102129	+	0.686822i
$971$	4.83106	−	3.22801i	0.155036	−	0.103592i	−0.475632	−	0.879644i	$-0.657781\pi$
$971$	4.83106	−	3.22801i	0.155036	−	0.103592i	0.630669	+	0.776052i	$0.282781\pi$
$972$	5.39077	−	30.7073i	0.172909	−	0.984938i
$973$	0.778586	+	3.91421i	0.0249603	+	0.125484i
$974$	1.32829	−	27.2346i	0.0425613	−	0.872652i
$975$	1.47551	−	1.81402i	0.0472540	−	0.0580953i
$976$	−10.9112	−	10.8804i	−0.349259	−	0.348272i
$977$	39.1546	+	39.1546i	1.25267	+	1.25267i	0.954520	+	0.298147i	$0.0963686\pi$
$977$	39.1546	+	39.1546i	1.25267	+	1.25267i	0.298147	+	0.954520i	$0.403631\pi$
$978$	−19.0684	+	21.2396i	−0.609740	+	0.679168i
$979$	−0.711096	−	3.57492i	−0.0227267	−	0.114255i
$980$	0.223859	+	0.0677340i	0.00715091	+	0.00216368i
$981$	−26.1487	−	25.6953i	−0.834862	−	0.820389i
$982$	−11.5536	−	8.56242i	−0.368691	−	0.273238i
$983$	−11.4783	+	4.75449i	−0.366102	+	0.151645i	−0.558148	−	0.829741i	$-0.688488\pi$
$983$	−11.4783	+	4.75449i	−0.366102	+	0.151645i	0.192046	+	0.981386i	$0.438488\pi$
$984$	30.8918	+	22.6518i	0.984796	+	0.722114i
$985$	−4.06157	−	1.68236i	−0.129412	−	0.0536044i
$986$	20.3062	−	12.1808i	0.646682	−	0.387917i
$987$	24.6211	+	2.31632i	0.783697	+	0.0737293i
$988$	0.475606	−	0.891313i	0.0151310	−	0.0283564i
$989$	32.7808	−	49.0600i	1.04237	−	1.56002i
$990$	−6.82892	−	1.64468i	−0.217037	−	0.0522713i
$991$	59.2566			1.88235			0.941173	−	0.337924i	$-0.109725\pi$
$991$	59.2566			1.88235			0.941173	+	0.337924i	$0.109725\pi$
$992$	1.83286	+	12.2074i	0.0581935	+	0.387584i
$993$	−2.11248	−	20.5279i	−0.0670374	−	0.651433i
$994$	16.3052	−	34.5059i	0.517168	−	1.09446i
$995$	1.96057	+	1.31001i	0.0621541	+	0.0415301i
$996$	29.0550	−	12.2082i	0.920643	−	0.386833i
$997$	29.3444	+	5.83697i	0.929347	+	0.184859i	0.636479	−	0.771294i	$-0.280390\pi$
$997$	29.3444	+	5.83697i	0.929347	+	0.184859i	0.292868	+	0.956153i	$0.405390\pi$
$998$	19.9286	−	11.9544i	0.630830	−	0.378408i
$999$	−2.71606	+	31.8545i	−0.0859324	+	1.00783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.cn.a.731.15	✓	1024
3.2	odd	2	inner	960.2.cn.a.731.114	yes	1024
64.19	odd	16	inner	960.2.cn.a.851.114	yes	1024
192.83	even	16	inner	960.2.cn.a.851.15	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
960.2.cn.a.731.15	✓	1024	1.1	even	1	trivial
960.2.cn.a.731.114	yes	1024	3.2	odd	2	inner
960.2.cn.a.851.15	yes	1024	192.83	even	16	inner
960.2.cn.a.851.114	yes	1024	64.19	odd	16	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:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.cn (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33138 + 0.476905i) q^{2} +(-1.53109 - 0.809797i) q^{3} +(1.54512 - 1.26988i) q^{4} +(-0.980785 - 0.195090i) q^{5} +(2.42465 + 0.347961i) q^{6} +(2.42385 + 1.00399i) q^{7} +(-1.45153 + 2.42756i) q^{8} +(1.68846 + 2.47974i) q^{9} +O(q^{10})\)	\(q+(-1.33138 + 0.476905i) q^{2} +(-1.53109 - 0.809797i) q^{3} +(1.54512 - 1.26988i) q^{4} +(-0.980785 - 0.195090i) q^{5} +(2.42465 + 0.347961i) q^{6} +(2.42385 + 1.00399i) q^{7} +(-1.45153 + 2.42756i) q^{8} +(1.68846 + 2.47974i) q^{9} +(1.39883 - 0.208003i) q^{10} +(-1.37659 + 0.919810i) q^{11} +(-3.39406 + 0.693061i) q^{12} +(0.263379 + 1.32410i) q^{13} +(-3.70587 - 0.180744i) q^{14} +(1.34368 + 1.09294i) q^{15} +(0.774810 - 3.92424i) q^{16} +(-1.79441 - 1.79441i) q^{17} +(-3.43057 - 2.49623i) q^{18} +(-0.0729955 - 0.366973i) q^{19} +(-1.76318 + 0.944041i) q^{20} +(-2.89810 - 3.50003i) q^{21} +(1.39410 - 1.88112i) q^{22} +(-4.70276 + 1.94795i) q^{23} +(4.18825 - 2.54137i) q^{24} +(0.923880 + 0.382683i) q^{25} +(-0.982125 - 1.63726i) q^{26} +(-0.577090 - 5.16401i) q^{27} +(5.02010 - 1.52671i) q^{28} +(3.66572 - 5.48614i) q^{29} +(-2.31018 - 0.814300i) q^{30} +2.18217 q^{31} +(0.839928 + 5.59415i) q^{32} +(2.85254 - 0.293549i) q^{33} +(3.24479 + 1.53327i) q^{34} +(-2.18141 - 1.45757i) q^{35} +(5.75785 + 1.68737i) q^{36} +(-6.03442 - 1.20032i) q^{37} +(0.272196 + 0.453767i) q^{38} +(0.668993 - 2.24059i) q^{39} +(1.89723 - 2.09774i) q^{40} +(2.99233 + 7.22413i) q^{41} +(5.52764 + 3.27773i) q^{42} +(-9.63806 + 6.43995i) q^{43} +(-0.958957 + 3.16933i) q^{44} +(-1.17224 - 2.76149i) q^{45} +(5.33216 - 4.83622i) q^{46} +(-3.84817 + 3.84817i) q^{47} +(-4.36414 + 5.38092i) q^{48} +(-0.0826897 - 0.0826897i) q^{49} +(-1.41253 - 0.0688926i) q^{50} +(1.29429 + 4.20050i) q^{51} +(2.08840 + 1.71143i) q^{52} +(3.48365 + 5.21365i) q^{53} +(3.23107 + 6.60002i) q^{54} +(1.52959 - 0.633576i) q^{55} +(-5.95554 + 4.42673i) q^{56} +(-0.185411 + 0.620980i) q^{57} +(-2.26408 + 9.05231i) q^{58} +(0.0807657 - 0.406036i) q^{59} +(3.46406 - 0.0175953i) q^{60} +(2.14020 - 3.20303i) q^{61} +(-2.90528 + 1.04069i) q^{62} +(1.60293 + 7.70572i) q^{63} +(-3.78614 - 7.04735i) q^{64} -1.35004i q^{65} +(-3.65781 + 1.75122i) q^{66} +(-4.51773 - 3.01865i) q^{67} +(-5.05126 - 0.493898i) q^{68} +(8.77778 + 0.825804i) q^{69} +(3.59940 + 0.900249i) q^{70} +(-3.93633 + 9.50315i) q^{71} +(-8.47057 + 0.499430i) q^{72} +(4.39584 + 10.6125i) q^{73} +(8.60652 - 1.27977i) q^{74} +(-1.10464 - 1.33408i) q^{75} +(-0.578799 - 0.474323i) q^{76} +(-4.26014 + 0.847394i) q^{77} +(0.177869 + 3.30212i) q^{78} +(-0.462054 + 0.462054i) q^{79} +(-1.52550 + 3.69768i) q^{80} +(-3.29822 + 8.37387i) q^{81} +(-7.42914 - 8.19097i) q^{82} +(-8.92296 + 1.77489i) q^{83} +(-8.92254 - 1.72774i) q^{84} +(1.40986 + 2.11000i) q^{85} +(9.76064 - 13.1704i) q^{86} +(-10.0552 + 5.43127i) q^{87} +(-0.234736 - 4.67690i) q^{88} +(-0.842506 + 2.03399i) q^{89} +(2.87766 + 3.11754i) q^{90} +(-0.690991 + 3.47385i) q^{91} +(-4.79269 + 8.98176i) q^{92} +(-3.34109 - 1.76711i) q^{93} +(3.28814 - 6.95856i) q^{94} +0.374163i q^{95} +(3.24412 - 9.24530i) q^{96} +15.2920i q^{97} +(0.149526 + 0.0706559i) q^{98} +(-4.60521 - 1.86053i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q+O(q^{10}) \) 1024 * q	\( 1024 q + 80 q^{24} + 80 q^{42} - 96 q^{52} - 288 q^{58} - 96 q^{64} + 256 q^{67} - 112 q^{76} - 48 q^{78} + 32 q^{79} - 112 q^{84} - 160 q^{88} - 144 q^{90} - 16 q^{94} - 272 q^{96}+O(q^{100}) \) 1024 * q + 80 * q^24 + 80 * q^42 - 96 * q^52 - 288 * q^58 - 96 * q^64 + 256 * q^67 - 112 * q^76 - 48 * q^78 + 32 * q^79 - 112 * q^84 - 160 * q^88 - 144 * q^90 - 16 * q^94 - 272 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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