LMFDB - Embedded newform 961.2.g.v.732.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(235,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([26]))

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

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

chi := DirichletCharacter("961.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.g (of order $15$, degree $8$, not 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:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			732.10
Character	$\chi$	$=$	961.732
Dual form			961.2.g.v.235.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.45837 + 1.05957i) q^{2} +(0.174457 + 0.0776734i) q^{3} +(0.386120 + 1.18836i) q^{4} +(1.23318 - 2.13593i) q^{5} +(0.172123 + 0.298125i) q^{6} +(-0.704026 + 0.781900i) q^{7} +(0.418057 - 1.28665i) q^{8} +(-1.98299 - 2.20233i) q^{9} +(4.06159 - 1.80834i) q^{10} +(5.25223 + 1.11640i) q^{11} +(-0.0249421 + 0.237309i) q^{12} +(0.128930 + 1.22669i) q^{13} +(-1.85520 + 0.394336i) q^{14} +(0.381043 - 0.276844i) q^{15} +(3.99472 - 2.90233i) q^{16} +(-5.54991 + 1.17967i) q^{17} +(-0.558410 - 5.31292i) q^{18} +(0.487397 - 4.63728i) q^{19} +(3.01441 + 0.640732i) q^{20} +(-0.183555 + 0.0817242i) q^{21} +(6.47678 + 7.19320i) q^{22} +(1.84912 - 5.69101i) q^{23} +(0.172872 - 0.191993i) q^{24} +(-0.541477 - 0.937865i) q^{25} +(-1.11173 + 1.92557i) q^{26} +(-0.351921 - 1.08310i) q^{27} +(-1.20101 - 0.534726i) q^{28} +(2.91890 + 2.12070i) q^{29} +0.849035 q^{30} +6.19525 q^{32} +(0.829576 + 0.602723i) q^{33} +(-9.34374 - 4.16010i) q^{34} +(0.801895 + 2.46798i) q^{35} +(1.85148 - 3.20686i) q^{36} +(2.67703 + 4.63676i) q^{37} +(5.62430 - 6.24642i) q^{38} +(-0.0727883 + 0.224019i) q^{39} +(-2.23265 - 2.47961i) q^{40} +(9.64964 - 4.29630i) q^{41} +(-0.354283 - 0.0753052i) q^{42} +(-0.316071 + 3.00721i) q^{43} +(0.701317 + 6.67258i) q^{44} +(-7.14943 + 1.51966i) q^{45} +(8.72670 - 6.34032i) q^{46} +(-4.55810 + 3.31166i) q^{47} +(0.922342 - 0.196050i) q^{48} +(0.615984 + 5.86070i) q^{49} +(0.204058 - 1.94148i) q^{50} +(-1.05985 - 0.225279i) q^{51} +(-1.40796 + 0.626864i) q^{52} +(-0.608029 - 0.675285i) q^{53} +(0.634387 - 1.95244i) q^{54} +(8.86151 - 9.84170i) q^{55} +(0.711707 + 1.23271i) q^{56} +(0.445223 - 0.771149i) q^{57} +(2.00980 + 6.18552i) q^{58} +(2.80017 + 1.24671i) q^{59} +(0.476117 + 0.345920i) q^{60} -9.12376 q^{61} +3.11808 q^{63} +(1.04551 + 0.759607i) q^{64} +(2.77912 + 1.23734i) q^{65} +(0.571202 + 1.75798i) q^{66} +(-3.98244 + 6.89779i) q^{67} +(-3.54480 - 6.13978i) q^{68} +(0.764633 - 0.849211i) q^{69} +(-1.44553 + 4.44888i) q^{70} +(4.06068 + 4.50985i) q^{71} +(-3.66263 + 1.63071i) q^{72} +(-3.70617 - 0.787770i) q^{73} +(-1.00885 + 9.59858i) q^{74} +(-0.0216174 - 0.205676i) q^{75} +(5.69893 - 1.21134i) q^{76} +(-4.57062 + 3.32075i) q^{77} +(-0.343515 + 0.249578i) q^{78} +(-8.32417 + 1.76936i) q^{79} +(-1.27298 - 12.1116i) q^{80} +(-0.906587 + 8.62560i) q^{81} +(18.6249 + 3.95885i) q^{82} +(-12.0893 + 5.38249i) q^{83} +(-0.167992 - 0.186574i) q^{84} +(-4.32436 + 13.3090i) q^{85} +(-3.64729 + 4.05072i) q^{86} +(0.344501 + 0.596693i) q^{87} +(3.63214 - 6.29106i) q^{88} +(-0.272533 - 0.838769i) q^{89} +(-12.0367 - 5.35907i) q^{90} +(-1.04992 - 0.762810i) q^{91} +7.47693 q^{92} -10.1563 q^{94} +(-9.30387 - 6.75966i) q^{95} +(1.08081 + 0.481206i) q^{96} +(2.67052 + 8.21902i) q^{97} +(-5.31146 + 9.19972i) q^{98} +(-7.95645 - 13.7810i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 32 q^{4} - 32 q^{5} + 8 q^{7} - 24 q^{8} + 20 q^{9} + 20 q^{10} + 28 q^{14} + 32 q^{16} - 8 q^{18} + 16 q^{19} - 20 q^{20} - 48 q^{25} - 20 q^{28} + 192 q^{32} + 80 q^{33} - 112 q^{35} - 160 q^{36}+ \cdots - 16 q^{98}+O(q^{100}) $ 96 * q - 32 * q^4 - 32 * q^5 + 8 * q^7 - 24 * q^8 + 20 * q^9 + 20 * q^10 + 28 * q^14 + 32 * q^16 - 8 * q^18 + 16 * q^19 - 20 * q^20 - 48 * q^25 - 20 * q^28 + 192 * q^32 + 80 * q^33 - 112 * q^35 - 160 * q^36 + 36 * q^38 + 32 * q^39 - 16 * q^40 + 32 * q^41 + 16 * q^45 - 96 * q^47 - 20 * q^49 + 20 * q^50 + 16 * q^51 + 32 * q^56 + 40 * q^59 - 64 * q^63 + 56 * q^64 - 48 * q^66 - 64 * q^67 + 24 * q^69 - 24 * q^70 + 72 * q^71 + 36 * q^72 + 36 * q^76 + 208 * q^78 - 20 * q^80 - 36 * q^81 - 4 * q^82 - 256 * q^87 - 44 * q^90 + 128 * q^94 - 80 * q^95 + 16 * q^97 - 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{15}\right)$

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 $

$2$	1.45837	+	1.05957i	1.03122	+	0.749226i	0.968553	−	0.248809i	$-0.0800390\pi$
$2$	1.45837	+	1.05957i	1.03122	+	0.749226i	0.0626681	+	0.998034i	$0.480039\pi$
$3$	0.174457	+	0.0776734i	0.100723	+	0.0448448i	0.456480	−	0.889734i	$-0.349110\pi$
$3$	0.174457	+	0.0776734i	0.100723	+	0.0448448i	−0.355757	+	0.934579i	$0.615777\pi$
$4$	0.386120	+	1.18836i	0.193060	+	0.594178i
$5$	1.23318	−	2.13593i	0.551496	−	0.955219i	−0.446671	−	0.894698i	$-0.647391\pi$
$5$	1.23318	−	2.13593i	0.551496	−	0.955219i	0.998167	−	0.0605206i	$-0.0192761\pi$
$6$	0.172123	+	0.298125i	0.0702688	+	0.121709i
$7$	−0.704026	+	0.781900i	−0.266097	+	0.295531i	−0.861354	−	0.508004i	$-0.830383\pi$
$7$	−0.704026	+	0.781900i	−0.266097	+	0.295531i	0.595258	+	0.803535i	$0.297050\pi$
$8$	0.418057	−	1.28665i	0.147806	−	0.454899i
$9$	−1.98299	−	2.20233i	−0.660997	−	0.734111i
$10$	4.06159	−	1.80834i	1.28439	−	0.571847i
$11$	5.25223	+	1.11640i	1.58361	+	0.336606i	0.913875	−	0.405996i	$-0.133075\pi$
$11$	5.25223	+	1.11640i	1.58361	+	0.336606i	0.669733	+	0.742602i	$0.266409\pi$
$12$	−0.0249421	+	0.237309i	−0.00720018	+	0.0685051i
$13$	0.128930	+	1.22669i	0.0357588	+	0.340222i	0.997745	+	0.0671230i	$0.0213820\pi$
$13$	0.128930	+	1.22669i	0.0357588	+	0.340222i	−0.961986	+	0.273099i	$0.911951\pi$
$14$	−1.85520	+	0.394336i	−0.495824	+	0.105391i
$15$	0.381043	−	0.276844i	0.0983849	−	0.0714808i
$16$	3.99472	−	2.90233i	0.998680	−	0.725583i
$17$	−5.54991	+	1.17967i	−1.34605	+	0.286112i	−0.823897	−	0.566739i	$-0.808205\pi$
$17$	−5.54991	+	1.17967i	−1.34605	+	0.286112i	−0.522154	+	0.852851i	$0.674871\pi$
$18$	−0.558410	−	5.31292i	−0.131618	−	1.25227i
$19$	0.487397	−	4.63728i	0.111817	−	1.06386i	−0.784402	−	0.620252i	$-0.787030\pi$
$19$	0.487397	−	4.63728i	0.111817	−	1.06386i	0.896219	−	0.443612i	$-0.146303\pi$
$20$	3.01441	+	0.640732i	0.674042	+	0.143272i
$21$	−0.183555	+	0.0817242i	−0.0400551	+	0.0178337i
$22$	6.47678	+	7.19320i	1.38086	+	1.53360i
$23$	1.84912	−	5.69101i	0.385569	−	1.18666i	−0.550498	−	0.834836i	$-0.685562\pi$
$23$	1.84912	−	5.69101i	0.385569	−	1.18666i	0.936067	−	0.351822i	$-0.114438\pi$
$24$	0.172872	−	0.191993i	0.0352873	−	0.0391905i
$25$	−0.541477	−	0.937865i	−0.108295	−	0.187573i
$26$	−1.11173	+	1.92557i	−0.218028	+	0.377635i
$27$	−0.351921	−	1.08310i	−0.0677272	−	0.208443i
$28$	−1.20101	−	0.534726i	−0.226970	−	0.101054i
$29$	2.91890	+	2.12070i	0.542026	+	0.393805i	0.824837	−	0.565371i	$-0.191267\pi$
$29$	2.91890	+	2.12070i	0.542026	+	0.393805i	−0.282811	+	0.959176i	$0.591267\pi$
$30$	0.849035			0.155012
$31$		0			0
$31$		0			0
$32$	6.19525			1.09518
$33$	0.829576	+	0.602723i	0.144411	+	0.104921i
$34$	−9.34374	−	4.16010i	−1.60244	−	0.713452i
$35$	0.801895	+	2.46798i	0.135545	+	0.417165i
$36$	1.85148	−	3.20686i	0.308580	−	0.534477i
$37$	2.67703	+	4.63676i	0.440102	+	0.762278i	0.997697	−	0.0678348i	$-0.0216091\pi$
$37$	2.67703	+	4.63676i	0.440102	+	0.762278i	−0.557595	+	0.830113i	$0.688276\pi$
$38$	5.62430	−	6.24642i	0.912382	−	1.01330i
$39$	−0.0727883	+	0.224019i	−0.0116554	+	0.0358718i
$40$	−2.23265	−	2.47961i	−0.353014	−	0.392061i
$41$	9.64964	−	4.29630i	1.50702	−	0.670969i	0.523543	−	0.851999i	$-0.324610\pi$
$41$	9.64964	−	4.29630i	1.50702	−	0.670969i	0.983477	+	0.181031i	$0.0579433\pi$
$42$	−0.354283	−	0.0753052i	−0.0546671	−	0.0116198i
$43$	−0.316071	+	3.00721i	−0.0482004	+	0.458596i	0.943627	+	0.331010i	$0.107389\pi$
$43$	−0.316071	+	3.00721i	−0.0482004	+	0.458596i	−0.991828	+	0.127586i	$0.959277\pi$
$44$	0.701317	+	6.67258i	0.105727	+	1.00593i
$45$	−7.14943	+	1.51966i	−1.06577	+	0.226537i
$46$	8.72670	−	6.34032i	1.28668	−	0.934829i
$47$	−4.55810	+	3.31166i	−0.664868	+	0.483055i	−0.868303	−	0.496034i	$-0.834789\pi$
$47$	−4.55810	+	3.31166i	−0.664868	+	0.483055i	0.203436	+	0.979088i	$0.434789\pi$
$48$	0.922342	−	0.196050i	0.133129	−	0.0282974i
$49$	0.615984	+	5.86070i	0.0879977	+	0.837242i
$50$	0.204058	−	1.94148i	0.0288581	−	0.274567i
$51$	−1.05985	−	0.225279i	−0.148409	−	0.0315453i
$52$	−1.40796	+	0.626864i	−0.195249	+	0.0869304i
$53$	−0.608029	−	0.675285i	−0.0835193	−	0.0927575i	0.699937	−	0.714205i	$-0.253212\pi$
$53$	−0.608029	−	0.675285i	−0.0835193	−	0.0927575i	−0.783456	+	0.621447i	$0.786545\pi$
$54$	0.634387	−	1.95244i	0.0863291	−	0.265694i
$55$	8.86151	−	9.84170i	1.19489	−	1.32706i
$56$	0.711707	+	1.23271i	0.0951059	+	0.164728i
$57$	0.445223	−	0.771149i	0.0589713	−	0.102141i
$58$	2.00980	+	6.18552i	0.263899	+	0.812199i
$59$	2.80017	+	1.24671i	0.364551	+	0.162308i	0.580834	−	0.814022i	$-0.302727\pi$
$59$	2.80017	+	1.24671i	0.364551	+	0.162308i	−0.216283	+	0.976331i	$0.569393\pi$
$60$	0.476117	+	0.345920i	0.0614665	+	0.0446580i
$61$	−9.12376			−1.16818			−0.584089	−	0.811690i	$-0.698548\pi$
$61$	−9.12376			−1.16818			−0.584089	+	0.811690i	$0.698548\pi$
$62$		0			0
$63$	3.11808			0.392841
$64$	1.04551	+	0.759607i	0.130689	+	0.0949508i
$65$	2.77912	+	1.23734i	0.344707	+	0.153474i
$66$	0.571202	+	1.75798i	0.0703102	+	0.216392i
$67$	−3.98244	+	6.89779i	−0.486532	+	0.842699i	−0.999880	−	0.0154820i	$-0.995072\pi$
$67$	−3.98244	+	6.89779i	−0.486532	+	0.842699i	0.513348	+	0.858181i	$0.328405\pi$
$68$	−3.54480	−	6.13978i	−0.429870	−	0.744557i
$69$	0.764633	−	0.849211i	0.0920510	−	0.102233i
$70$	−1.44553	+	4.44888i	−0.172774	+	0.531743i
$71$	4.06068	+	4.50985i	0.481914	+	0.535220i	0.934246	−	0.356630i	$-0.116074\pi$
$71$	4.06068	+	4.50985i	0.481914	+	0.535220i	−0.452331	+	0.891850i	$0.649408\pi$
$72$	−3.66263	+	1.63071i	−0.431645	+	0.192181i
$73$	−3.70617	−	0.787770i	−0.433774	−	0.0922015i	−0.0141507	−	0.999900i	$-0.504504\pi$
$73$	−3.70617	−	0.787770i	−0.433774	−	0.0922015i	−0.419623	+	0.907698i	$0.637838\pi$
$74$	−1.00885	+	9.59858i	−0.117277	+	1.11581i
$75$	−0.0216174	−	0.205676i	−0.00249616	−	0.0237494i
$76$	5.69893	−	1.21134i	0.653712	−	0.138951i
$77$	−4.57062	+	3.32075i	−0.520871	+	0.378435i
$78$	−0.343515	+	0.249578i	−0.0388954	+	0.0282592i
$79$	−8.32417	+	1.76936i	−0.936543	+	0.199068i	−0.650810	−	0.759241i	$-0.725570\pi$
$79$	−8.32417	+	1.76936i	−0.936543	+	0.199068i	−0.285733	+	0.958309i	$0.592237\pi$
$80$	−1.27298	−	12.1116i	−0.142323	−	1.35411i
$81$	−0.906587	+	8.62560i	−0.100732	+	0.958400i
$82$	18.6249	+	3.95885i	2.05678	+	0.437182i
$83$	−12.0893	+	5.38249i	−1.32697	+	0.590805i	−0.943078	−	0.332572i	$-0.892083\pi$
$83$	−12.0893	+	5.38249i	−1.32697	+	0.590805i	−0.383893	+	0.923378i	$0.625417\pi$
$84$	−0.167992	−	0.186574i	−0.0183294	−	0.0203569i
$85$	−4.32436	+	13.3090i	−0.469042	+	1.44356i
$86$	−3.64729	+	4.05072i	−0.393297	+	0.436801i
$87$	0.344501	+	0.596693i	0.0369344	+	0.0639722i
$88$	3.63214	−	6.29106i	0.387188	−	0.670629i
$89$	−0.272533	−	0.838769i	−0.0288884	−	0.0889093i	0.935573	−	0.353134i	$-0.114884\pi$
$89$	−0.272533	−	0.838769i	−0.0288884	−	0.0889093i	−0.964461	+	0.264225i	$0.914884\pi$
$90$	−12.0367	−	5.35907i	−1.26878	−	0.564895i
$91$	−1.04992	−	0.762810i	−0.110061	−	0.0799642i
$92$	7.47693			0.779524
$93$		0			0
$94$	−10.1563			−1.04754
$95$	−9.30387	−	6.75966i	−0.954557	−	0.693526i
$96$	1.08081	+	0.481206i	0.110309	+	0.0491129i
$97$	2.67052	+	8.21902i	0.271150	+	0.834515i	0.990212	+	0.139569i	$0.0445717\pi$
$97$	2.67052	+	8.21902i	0.271150	+	0.834515i	−0.719062	+	0.694946i	$0.755428\pi$
$98$	−5.31146	+	9.19972i	−0.536538	+	0.929312i
$99$	−7.95645	−	13.7810i	−0.799653	−	1.38504i
$100$	0.905442	−	1.00560i	0.0905442	−	0.100560i
$101$	3.07204	−	9.45476i	0.305679	−	0.940783i	−0.673744	−	0.738965i	$-0.735315\pi$
$101$	3.07204	−	9.45476i	0.305679	−	0.940783i	0.979423	−	0.201818i	$-0.0646851\pi$
$102$	−1.30696	−	1.45152i	−0.129408	−	0.143722i
$103$	−8.22927	+	3.66391i	−0.810854	+	0.361016i	−0.769915	−	0.638146i	$-0.779702\pi$
$103$	−8.22927	+	3.66391i	−0.810854	+	0.361016i	−0.0409390	+	0.999162i	$0.513035\pi$
$104$	1.63222	+	0.346938i	0.160052	+	0.0340201i
$105$	−0.0517999	+	0.492843i	−0.00505515	+	0.0480966i
$106$	−0.171221	−	1.62906i	−0.0166305	−	0.158228i
$107$	−0.288410	+	0.0613034i	−0.0278816	+	0.00592643i	−0.221831	−	0.975085i	$-0.571203\pi$
$107$	−0.288410	+	0.0613034i	−0.0278816	+	0.00592643i	0.193950	+	0.981011i	$0.437870\pi$
$108$	1.15123	−	0.836414i	0.110777	−	0.0804840i
$109$	−1.76844	+	1.28485i	−0.169386	+	0.123066i	−0.669248	−	0.743039i	$-0.733384\pi$
$109$	−1.76844	+	1.28485i	−0.169386	+	0.123066i	0.499863	+	0.866105i	$0.333384\pi$
$110$	23.3513	−	4.96346i	2.22645	−	0.473248i
$111$	0.106875	+	1.01685i	0.0101442	+	0.0965152i
$112$	−0.543052	+	5.16679i	−0.0513136	+	0.488216i
$113$	−10.3759	−	2.20548i	−0.976087	−	0.207474i	−0.307860	−	0.951432i	$-0.599613\pi$
$113$	−10.3759	−	2.20548i	−0.976087	−	0.207474i	−0.668227	+	0.743958i	$0.732946\pi$
$114$	1.46638	−	0.652875i	0.137339	−	0.0611474i
$115$	−9.87532	−	10.9677i	−0.920879	−	1.02274i
$116$	−1.39310	+	4.28753i	−0.129346	+	0.398087i
$117$	2.44591	−	2.71646i	0.226124	−	0.251137i
$118$	2.76269	+	4.78512i	0.254326	+	0.440506i
$119$	2.98490	−	5.17000i	0.273625	−	0.473933i
$120$	−0.196903	−	0.606005i	−0.0179747	−	0.0553204i
$121$	16.2906	+	7.25305i	1.48096	+	0.659368i
$122$	−13.3058	−	9.66722i	−1.20465	−	0.875229i
$123$	2.01716			0.181881
$124$		0			0
$125$	9.66086			0.864094
$126$	4.54731	+	3.30381i	0.405106	+	0.294327i
$127$	18.5752	+	8.27020i	1.64828	+	0.733862i	0.999629	−	0.0272241i	$-0.00866679\pi$
$127$	18.5752	+	8.27020i	1.64828	+	0.733862i	0.648651	+	0.761086i	$0.275333\pi$
$128$	−3.10899	−	9.56850i	−0.274799	−	0.845744i
$129$	−0.288721	+	0.500080i	−0.0254205	+	0.0440296i
$130$	2.74193	+	4.74916i	0.240483	+	0.416529i
$131$	3.63965	−	4.04224i	0.317998	−	0.353172i	−0.562861	−	0.826552i	$-0.690299\pi$
$131$	3.63965	−	4.04224i	0.317998	−	0.353172i	0.880859	+	0.473379i	$0.156966\pi$
$132$	−0.395932	+	1.21855i	−0.0344615	+	0.106062i
$133$	3.28275	+	3.64586i	0.284650	+	0.316136i
$134$	−13.1165	+	5.83985i	−1.13309	+	0.504486i
$135$	−2.74742	−	0.583981i	−0.236460	−	0.0502611i
$136$	−0.802361	+	7.63395i	−0.0688019	+	0.654606i
$137$	−0.458865	−	4.36581i	−0.0392035	−	0.372996i	−0.996481	−	0.0838239i	$-0.973287\pi$
$137$	−0.458865	−	4.36581i	−0.0392035	−	0.372996i	0.957277	−	0.289172i	$-0.0933800\pi$
$138$	2.01491	−	0.428282i	0.171521	−	0.0364578i
$139$	5.44078	−	3.95296i	0.461481	−	0.335286i	−0.332631	−	0.943057i	$-0.607936\pi$
$139$	5.44078	−	3.95296i	0.461481	−	0.335286i	0.794112	+	0.607771i	$0.207936\pi$
$140$	−2.62321	+	1.90587i	−0.221702	+	0.161076i
$141$	−1.05242	+	0.223699i	−0.0886300	+	0.0188389i
$142$	1.14349	+	10.8796i	0.0959594	+	0.912993i
$143$	−0.692299	+	6.58679i	−0.0578930	+	0.550815i
$144$	−14.3134	−	3.04241i	−1.19278	−	0.253534i
$145$	8.12921	−	3.61936i	0.675094	−	0.300571i
$146$	−4.57025	−	5.07578i	−0.378237	−	0.420075i
$147$	−0.347757	+	1.07029i	−0.0286825	+	0.0882758i
$148$	−4.47646	+	4.97161i	−0.367963	+	0.408664i
$149$	−1.10847	−	1.91993i	−0.0908097	−	0.157287i	0.817042	−	0.576578i	$-0.195612\pi$
$149$	−1.10847	−	1.91993i	−0.0908097	−	0.157287i	−0.907852	+	0.419291i	$0.862279\pi$
$150$	0.186401	−	0.322856i	0.0152196	−	0.0263611i
$151$	−1.46631	−	4.51283i	−0.119326	−	0.367249i	0.873498	−	0.486827i	$-0.161846\pi$
$151$	−1.46631	−	4.51283i	−0.119326	−	0.367249i	−0.992825	+	0.119578i	$0.961846\pi$
$152$	−5.76278	−	2.56576i	−0.467423	−	0.208110i
$153$	13.6034	+	9.88348i	1.09977	+	0.799032i
$154$	−10.1842			−0.820666
$155$		0			0
$156$	−0.294319			−0.0235644
$157$	−3.27521	−	2.37958i	−0.261391	−	0.189911i	0.449369	−	0.893346i	$-0.351649\pi$
$157$	−3.27521	−	2.37958i	−0.261391	−	0.189911i	−0.710760	+	0.703435i	$0.751649\pi$
$158$	−14.0144	−	6.23963i	−1.11493	−	0.496398i
$159$	−0.0536235	−	0.165036i	−0.00425262	−	0.0130882i
$160$	7.63987	−	13.2327i	0.603985	−	1.04613i
$161$	3.14797	+	5.45245i	0.248095	+	0.429713i
$162$	−10.4615	+	11.6187i	−0.821935	+	0.912851i
$163$	−0.335065	+	1.03122i	−0.0262443	+	0.0807717i	−0.963321	−	0.268352i	$-0.913521\pi$
$163$	−0.335065	+	1.03122i	−0.0262443	+	0.0807717i	0.937076	+	0.349124i	$0.113521\pi$
$164$	8.83145	+	9.80832i	0.689620	+	0.765901i
$165$	2.31039	−	1.02865i	0.179864	−	0.0800806i
$166$	−23.3337	−	4.95973i	−1.81105	−	0.384950i
$167$	1.16549	−	11.0889i	0.0901886	−	0.858088i	−0.852121	−	0.523345i	$-0.824684\pi$
$167$	1.16549	−	11.0889i	0.0901886	−	0.858088i	0.942310	−	0.334743i	$-0.108649\pi$
$168$	0.0284135	+	0.270337i	0.00219215	+	0.0208569i
$169$	11.2278	−	2.38654i	0.863675	−	0.183580i
$170$	−20.4082	+	14.8275i	−1.56524	+	1.13721i
$171$	−11.1793	+	8.12226i	−0.854905	+	0.621125i
$172$	−3.69568	+	0.785541i	−0.281793	+	0.0598969i
$173$	0.798406	+	7.59633i	0.0607017	+	0.577538i	0.982026	+	0.188744i	$0.0604416\pi$
$173$	0.798406	+	7.59633i	0.0607017	+	0.577538i	−0.921325	+	0.388794i	$0.872892\pi$
$174$	−0.129827	+	1.23522i	−0.00984213	+	0.0936416i
$175$	1.11453	+	0.236901i	0.0842506	+	0.0179080i
$176$	24.2213	−	10.7840i	1.82575	−	0.812878i
$177$	0.391673	+	0.434997i	0.0294399	+	0.0326964i
$178$	0.491278	−	1.51200i	0.0368228	−	0.113329i
$179$	−8.92057	+	9.90729i	−0.666755	+	0.740506i	−0.977720	−	0.209915i	$-0.932681\pi$
$179$	−8.92057	+	9.90729i	−0.666755	+	0.740506i	0.310965	+	0.950421i	$0.399348\pi$
$180$	−4.56643	−	7.90929i	−0.340362	−	0.589524i
$181$	−10.4890	+	18.1674i	−0.779638	+	1.35037i	0.152513	+	0.988301i	$0.451263\pi$
$181$	−10.4890	+	18.1674i	−0.779638	+	1.35037i	−0.932151	+	0.362070i	$0.882070\pi$
$182$	−0.722918	−	2.22491i	−0.0535863	−	0.164922i
$183$	−1.59171	−	0.708674i	−0.117662	−	0.0523867i
$184$	−6.54929	−	4.75834i	−0.482820	−	0.350789i
$185$	13.2051			0.970857
$186$		0			0
$187$	−30.4664			−2.22793
$188$	−5.69540	−	4.13795i	−0.415380	−	0.301791i
$189$	1.09464	+	0.487365i	0.0796233	+	0.0354506i
$190$	−6.40615	−	19.7161i	−0.464751	−	1.43036i
$191$	−3.78330	+	6.55288i	−0.273750	+	0.474149i	−0.969819	−	0.243826i	$-0.921598\pi$
$191$	−3.78330	+	6.55288i	−0.273750	+	0.474149i	0.696069	+	0.717975i	$0.254931\pi$
$192$	0.123395	+	0.213727i	0.00890530	+	0.0154244i
$193$	−8.58325	+	9.53266i	−0.617836	+	0.686176i	−0.968126	−	0.250465i	$-0.919416\pi$
$193$	−8.58325	+	9.53266i	−0.617836	+	0.686176i	0.350290	+	0.936641i	$0.386083\pi$
$194$	−4.81399	+	14.8159i	−0.345624	+	1.06372i
$195$	0.388729	+	0.431727i	0.0278375	+	0.0309166i
$196$	−6.72675	+	2.99494i	−0.480482	+	0.213924i
$197$	17.3342	+	3.68449i	1.23501	+	0.262509i	0.778748	−	0.627337i	$-0.215855\pi$
$197$	17.3342	+	3.68449i	1.23501	+	0.262509i	0.456261	+	0.889846i	$0.349188\pi$
$198$	2.99842	−	28.5281i	0.213089	−	2.02740i
$199$	−0.0245109	−	0.233206i	−0.00173753	−	0.0165315i	0.993619	−	0.112791i	$-0.0359789\pi$
$199$	−0.0245109	−	0.233206i	−0.00173753	−	0.0165315i	−0.995356	+	0.0962591i	$0.969312\pi$
$200$	−1.43307	+	0.304609i	−0.101333	+	0.0215391i
$201$	−1.23054	+	0.894040i	−0.0867956	+	0.0630607i
$202$	14.4981	−	10.5335i	1.02008	−	0.741133i
$203$	−3.71316	+	0.789256i	−0.260613	+	0.0553949i
$204$	−0.141519	−	1.34647i	−0.00990833	−	0.0942715i
$205$	2.72316	−	25.9091i	0.190194	−	1.80957i
$206$	−15.8834	−	3.37613i	−1.10665	−	0.235226i
$207$	−16.2003	+	7.21284i	−1.12600	+	0.501327i
$208$	4.07530	+	4.52608i	0.282571	+	0.313827i
$209$	7.73697	−	23.8119i	0.535177	−	1.64711i
$210$	−0.597743	+	0.663861i	−0.0412482	+	0.0458107i
$211$	−8.18778	−	14.1817i	−0.563670	−	0.976305i	−0.997172	−	0.0751525i	$-0.976056\pi$
$211$	−8.18778	−	14.1817i	−0.563670	−	0.976305i	0.433502	−	0.901153i	$-0.357278\pi$
$212$	0.567706	−	0.983296i	0.0389902	−	0.0675331i
$213$	0.358121	+	1.10218i	0.0245380	+	0.0755203i
$214$	−0.485562	−	0.216186i	−0.0331924	−	0.0147782i
$215$	6.03344	+	4.38355i	0.411477	+	0.298956i
$216$	−1.54069			−0.104831
$217$		0			0
$218$	−3.94041			−0.266878
$219$	−0.585379	−	0.425303i	−0.0395563	−	0.0287393i
$220$	15.1170	+	6.73054i	1.01919	+	0.453773i
$221$	−2.16264	−	6.65592i	−0.145475	−	0.447725i
$222$	−0.921556	+	1.59618i	−0.0618508	+	0.107129i
$223$	4.89874	+	8.48486i	0.328044	+	0.568188i	0.982124	−	0.188237i	$-0.0602773\pi$
$223$	4.89874	+	8.48486i	0.328044	+	0.568188i	−0.654080	+	0.756426i	$0.726944\pi$
$224$	−4.36162	+	4.84407i	−0.291423	+	0.323658i
$225$	−0.991749	+	3.05229i	−0.0661166	+	0.203486i
$226$	−12.7951	−	14.2104i	−0.851116	−	0.945261i
$227$	−1.31794	+	0.586786i	−0.0874750	+	0.0389464i	−0.450008	−	0.893025i	$-0.648579\pi$
$227$	−1.31794	+	0.586786i	−0.0874750	+	0.0389464i	0.362533	+	0.931971i	$0.381912\pi$
$228$	1.08831	+	0.231327i	0.0720750	+	0.0153200i
$229$	2.91195	−	27.7053i	0.192427	−	1.83082i	−0.292501	−	0.956265i	$-0.594488\pi$
$229$	2.91195	−	27.7053i	0.192427	−	1.83082i	0.484928	−	0.874554i	$-0.338846\pi$
$230$	−2.78089	−	26.4584i	−0.183367	−	1.74462i
$231$	−1.05531	+	0.224314i	−0.0694345	+	0.0147588i
$232$	3.94886	−	2.86902i	0.259256	−	0.188360i
$233$	12.3606	−	8.98047i	0.809767	−	0.588330i	−0.103996	−	0.994578i	$-0.533163\pi$
$233$	12.3606	−	8.98047i	0.809767	−	0.588330i	0.913763	+	0.406248i	$0.133163\pi$
$234$	6.44529	−	1.36999i	0.421342	−	0.0895590i
$235$	1.45251	+	13.8197i	0.0947511	+	0.901497i
$236$	−0.400339	+	3.80897i	−0.0260599	+	0.247943i
$237$	−1.58965	−	0.337890i	−0.103259	−	0.0219483i
$238$	9.83103	−	4.37706i	0.637251	−	0.283722i
$239$	3.04991	+	3.38727i	0.197283	+	0.219105i	0.833667	−	0.552268i	$-0.186237\pi$
$239$	3.04991	+	3.38727i	0.197283	+	0.219105i	−0.636384	+	0.771372i	$0.719571\pi$
$240$	0.718666	−	2.21183i	0.0463897	−	0.142773i
$241$	−5.36676	+	5.96039i	−0.345703	+	0.383942i	−0.890773	−	0.454448i	$-0.849836\pi$
$241$	−5.36676	+	5.96039i	−0.345703	+	0.383942i	0.545070	+	0.838391i	$0.316503\pi$
$242$	16.0726	+	27.8386i	1.03319	+	1.78953i
$243$	−2.53640	+	4.39317i	−0.162710	+	0.281822i
$244$	−3.52287	−	10.8423i	−0.225529	−	0.694105i
$245$	13.2777	+	5.91161i	0.848280	+	0.377679i
$246$	2.94176	+	2.13731i	0.187560	+	0.136270i
$247$	5.75133			0.365949
$248$		0			0
$249$	−2.52714			−0.160151
$250$	14.0891	+	10.2363i	0.891072	+	0.647401i
$251$	−10.7833	−	4.80104i	−0.680637	−	0.303039i	0.0371423	−	0.999310i	$-0.488175\pi$
$251$	−10.7833	−	4.80104i	−0.680637	−	0.303039i	−0.717779	+	0.696271i	$0.754841\pi$
$252$	1.20395	+	3.70539i	0.0758420	+	0.233418i
$253$	16.0654	−	27.8262i	1.01003	−	1.74942i
$254$	18.3266	+	31.7426i	1.14991	+	1.99171i
$255$	−1.78817	+	1.98597i	−0.111980	+	0.124366i
$256$	6.40309	−	19.7067i	0.400193	−	1.23167i
$257$	0.0710691	+	0.0789302i	0.00443317	+	0.00492353i	0.745357	−	0.666665i	$-0.232279\pi$
$257$	0.0710691	+	0.0789302i	0.00443317	+	0.00492353i	−0.740924	+	0.671589i	$0.765612\pi$
$258$	−0.950929	+	0.423381i	−0.0592023	+	0.0263586i
$259$	−5.51019	−	1.17123i	−0.342386	−	0.0727764i
$260$	−0.397330	+	3.78035i	−0.0246414	+	0.234447i
$261$	−1.11765	−	10.6337i	−0.0691807	−	0.658210i
$262$	9.59096	−	2.03862i	0.592532	−	0.125947i
$263$	−19.2231	+	13.9664i	−1.18535	+	0.861205i	−0.992765	−	0.120075i	$-0.961686\pi$
$263$	−19.2231	+	13.9664i	−1.18535	+	0.861205i	−0.192583	+	0.981281i	$0.561686\pi$
$264$	1.12230	−	0.815400i	0.0690729	−	0.0501844i
$265$	−2.19218	+	0.465961i	−0.134664	+	0.0286238i
$266$	0.924422	+	8.79529i	0.0566800	+	0.539274i
$267$	0.0176047	−	0.167498i	0.00107739	−	0.0102507i
$268$	−9.73472	−	2.06918i	−0.594643	−	0.126395i
$269$	2.35438	−	1.04824i	0.143549	−	0.0639120i	−0.333705	−	0.942678i	$-0.608299\pi$
$269$	2.35438	−	1.04824i	0.143549	−	0.0639120i	0.477254	+	0.878766i	$0.341632\pi$
$270$	−3.38797	−	3.76272i	−0.206185	−	0.228992i
$271$	−8.98627	+	27.6569i	−0.545877	+	1.68004i	0.173019	+	0.984919i	$0.444648\pi$
$271$	−8.98627	+	27.6569i	−0.545877	+	1.68004i	−0.718896	+	0.695118i	$0.755352\pi$
$272$	−18.7465	+	20.8202i	−1.13668	+	1.26241i
$273$	−0.123916	−	0.214629i	−0.00749973	−	0.0129899i
$274$	3.95666	−	6.85314i	0.239031	−	0.414014i
$275$	−1.79693	−	5.53039i	−0.108359	−	0.333495i
$276$	1.30441	+	0.580759i	0.0785160	+	0.0349576i
$277$	−9.73377	−	7.07200i	−0.584845	−	0.424915i	0.255622	−	0.966777i	$-0.417720\pi$
$277$	−9.73377	−	7.07200i	−0.584845	−	0.424915i	−0.840468	+	0.541862i	$0.817720\pi$
$278$	12.1231			0.727094
$279$		0			0
$280$	3.51066			0.209802
$281$	25.1909	+	18.3023i	1.50276	+	1.09182i	0.969264	+	0.246021i	$0.0791232\pi$
$281$	25.1909	+	18.3023i	1.50276	+	1.09182i	0.533499	+	0.845801i	$0.320877\pi$
$282$	−1.77184	−	0.788875i	−0.105512	−	0.0469768i
$283$	1.77314	+	5.45718i	0.105402	+	0.324395i	0.989825	−	0.142292i	$-0.0454472\pi$
$283$	1.77314	+	5.45718i	0.105402	+	0.324395i	−0.884422	+	0.466688i	$0.845447\pi$
$284$	−3.79139	+	6.56688i	−0.224978	+	0.389673i
$285$	−1.09808	−	1.90194i	−0.0650448	−	0.112661i
$286$	−7.98876	+	8.87241i	−0.472385	+	0.524637i
$287$	−3.43432	+	10.5698i	−0.202722	+	0.623913i
$288$	−12.2851	−	13.6440i	−0.723908	−	0.803981i
$289$	13.8796	−	6.17961i	0.816450	−	0.363507i
$290$	15.6903	+	3.33508i	0.921367	+	0.195843i
$291$	−0.172507	+	1.64130i	−0.0101126	+	0.0962145i
$292$	−0.494874	−	4.70842i	−0.0289603	−	0.275539i
$293$	−1.25108	+	0.265925i	−0.0730887	+	0.0155355i	−0.244311	−	0.969697i	$-0.578562\pi$
$293$	−1.25108	+	0.265925i	−0.0730887	+	0.0155355i	0.171222	+	0.985232i	$0.445228\pi$
$294$	−1.64120	+	1.19240i	−0.0957165	+	0.0695421i
$295$	6.11601	−	4.44354i	0.356088	−	0.258713i
$296$	7.08503	−	1.50597i	0.411809	−	0.0875327i
$297$	−0.639200	−	6.08158i	−0.0370901	−	0.352889i
$298$	0.417733	−	3.97446i	0.0241986	−	0.230235i
$299$	7.21950	+	1.53455i	0.417515	+	0.0887455i
$300$	0.236069	−	0.105105i	0.0136295	−	0.00606822i
$301$	−2.12882	−	2.36429i	−0.122703	−	0.136276i
$302$	2.64322	−	8.13500i	0.152100	−	0.468117i
$303$	1.27032	−	1.41084i	0.0729781	−	0.0810504i
$304$	−11.5119	−	19.9392i	−0.660253	−	1.14359i
$305$	−11.2513	+	19.4878i	−0.644245	+	1.11587i
$306$	9.36662	+	28.8275i	0.535454	+	1.64796i
$307$	−14.3364	−	6.38299i	−0.818223	−	0.364296i	−0.0454405	−	0.998967i	$-0.514469\pi$
$307$	−14.3364	−	6.38299i	−0.818223	−	0.364296i	−0.772783	+	0.634671i	$0.781136\pi$
$308$	−5.71104	−	4.14931i	−0.325417	−	0.236429i
$309$	−1.72025			−0.0978613
$310$		0			0
$311$	27.4565			1.55692			0.778459	−	0.627695i	$-0.216002\pi$
$311$	27.4565			1.55692			0.778459	+	0.627695i	$0.216002\pi$
$312$	0.257804	+	0.187306i	0.0145953	+	0.0106041i
$313$	11.7009	+	5.20956i	0.661371	+	0.294462i	0.709840	−	0.704363i	$-0.248767\pi$
$313$	11.7009	+	5.20956i	0.661371	+	0.294462i	−0.0484683	+	0.998825i	$0.515434\pi$
$314$	−2.25514	−	6.94060i	−0.127265	−	0.391681i
$315$	3.84516	−	6.66002i	0.216650	−	0.375250i
$316$	−5.31676	−	9.20889i	−0.299091	−	0.518041i
$317$	−6.37203	+	7.07686i	−0.357889	+	0.397476i	−0.895022	−	0.446021i	$-0.852841\pi$
$317$	−6.37203	+	7.07686i	−0.357889	+	0.397476i	0.537133	+	0.843497i	$0.319507\pi$
$318$	0.0966639	−	0.297501i	0.00542064	−	0.0166830i
$319$	12.9632	+	14.3971i	0.725799	+	0.806081i
$320$	2.91177	−	1.29640i	0.162773	−	0.0724712i
$321$	−0.0550769	−	0.0117070i	−0.00307409	−	0.000653418i
$322$	−1.18633	+	11.2872i	−0.0661115	+	0.629009i
$323$	2.76545	+	26.3115i	0.153873	+	1.46401i
$324$	−10.6003	+	2.25317i	−0.588907	+	0.125176i
$325$	1.08066	−	0.785142i	0.0599440	−	0.0435518i
$326$	−1.58130	+	1.14888i	−0.0875799	+	0.0636305i
$327$	−0.408316	+	0.0867901i	−0.0225799	+	0.00479951i
$328$	−1.49372	−	14.2118i	−0.0824768	−	0.784715i
$329$	0.619640	−	5.89548i	0.0341618	−	0.325028i
$330$	4.45933	+	0.947859i	0.245478	+	0.0521779i
$331$	19.7172	−	8.77866i	1.08376	−	0.482519i	0.214420	−	0.976742i	$-0.431214\pi$
$331$	19.7172	−	8.77866i	1.08376	−	0.482519i	0.869335	+	0.494223i	$0.164547\pi$
$332$	−11.0642	−	12.2881i	−0.607228	−	0.674395i
$333$	4.90316	−	15.0904i	0.268691	−	0.826947i
$334$	13.4492	−	14.9368i	0.735906	−	0.817306i
$335$	9.82214	+	17.0125i	0.536641	+	0.929490i
$336$	−0.496062	+	0.859204i	−0.0270624	+	0.0468734i
$337$	−1.40540	−	4.32539i	−0.0765572	−	0.235619i	0.905453	−	0.424446i	$-0.139531\pi$
$337$	−1.40540	−	4.32539i	−0.0765572	−	0.235619i	−0.982010	+	0.188828i	$0.939531\pi$
$338$	18.9029	+	8.41612i	1.02818	+	0.457776i
$339$	−1.63885	−	1.19070i	−0.0890103	−	0.0646698i
$340$	−17.4855			−0.948287
$341$		0			0
$342$	−24.9096			−1.34696
$343$	−10.9746	−	7.97352i	−0.592573	−	0.430529i
$344$	3.73709	+	1.66386i	0.201490	+	0.0897093i
$345$	−0.870927	−	2.68044i	−0.0468892	−	0.144310i
$346$	−6.88444	+	11.9242i	−0.370110	+	0.641049i
$347$	−14.6947	−	25.4520i	−0.788855	−	1.36634i	−0.926669	−	0.375879i	$-0.877341\pi$
$347$	−14.6947	−	25.4520i	−0.788855	−	1.36634i	0.137813	−	0.990458i	$-0.455993\pi$
$348$	−0.576065	+	0.639785i	−0.0308803	+	0.0342961i
$349$	−2.08625	+	6.42082i	−0.111674	+	0.343698i	−0.991239	−	0.132081i	$-0.957834\pi$
$349$	−2.08625	+	6.42082i	−0.111674	+	0.343698i	0.879565	+	0.475780i	$0.157834\pi$
$350$	1.37438	+	1.52641i	0.0734639	+	0.0815899i
$351$	1.28325	−	0.571341i	0.0684950	−	0.0304960i
$352$	32.5389	+	6.91636i	1.73433	+	0.368643i
$353$	−0.813303	+	7.73806i	−0.0432878	+	0.411855i	0.951325	+	0.308191i	$0.0997235\pi$
$353$	−0.813303	+	7.73806i	−0.0432878	+	0.411855i	−0.994612	+	0.103665i	$0.966943\pi$
$354$	0.110295	+	1.04939i	0.00586212	+	0.0557743i
$355$	14.6403	−	3.11189i	0.777026	−	0.165162i
$356$	0.891525	−	0.647731i	0.0472507	−	0.0343297i
$357$	0.922309	−	0.670097i	0.0488138	−	0.0354653i
$358$	−23.5069	+	4.99654i	−1.24238	+	0.264075i
$359$	−0.270453	−	2.57319i	−0.0142740	−	0.135808i	0.985064	−	0.172188i	$-0.0550838\pi$
$359$	−0.270453	−	2.57319i	−0.0142740	−	0.135808i	−0.999338	+	0.0363806i	$0.988417\pi$
$360$	−1.03361	+	9.83410i	−0.0544758	+	0.518302i
$361$	−2.68198	−	0.570072i	−0.141157	−	0.0300038i
$362$	−34.5463	+	15.3810i	−1.81571	+	0.808407i
$363$	2.27865	+	2.53069i	0.119598	+	0.132827i
$364$	0.501095	−	1.54221i	0.0262645	−	0.0808339i
$365$	−6.25300	+	6.94466i	−0.327297	+	0.363500i
$366$	−1.57041	−	2.72002i	−0.0820865	−	0.142178i
$367$	17.6139	−	30.5081i	0.919437	−	1.59251i	0.119166	−	0.992874i	$-0.461978\pi$
$367$	17.6139	−	30.5081i	0.919437	−	1.59251i	0.800271	−	0.599638i	$-0.204689\pi$
$368$	−9.13049	−	28.1008i	−0.475960	−	1.46485i
$369$	−28.5970	−	12.7322i	−1.48870	−	0.662812i
$370$	19.2578	+	13.9916i	1.00117	+	0.727391i
$371$	0.956075			0.0496369
$372$		0			0
$373$	6.68493			0.346133			0.173066	−	0.984910i	$-0.444632\pi$
$373$	6.68493			0.346133			0.173066	+	0.984910i	$0.444632\pi$
$374$	−44.4312	−	32.2812i	−2.29748	−	1.66922i
$375$	1.68541	+	0.750392i	0.0870341	+	0.0387501i
$376$	2.35539	+	7.24914i	0.121470	+	0.373846i
$377$	−2.22511	+	3.85400i	−0.114599	+	0.198491i
$378$	1.07999	+	1.87060i	0.0555487	+	0.0962131i
$379$	11.7626	−	13.0636i	0.604202	−	0.671034i	−0.360992	−	0.932569i	$-0.617562\pi$
$379$	11.7626	−	13.0636i	0.604202	−	0.671034i	0.965194	+	0.261535i	$0.0842286\pi$
$380$	4.44046	−	13.6663i	0.227791	−	0.701069i
$381$	2.59820	+	2.88560i	0.133110	+	0.147834i
$382$	−12.4606	+	5.54784i	−0.637542	+	0.283852i
$383$	−31.8658	−	6.77329i	−1.62827	−	0.346099i	−0.698890	−	0.715229i	$-0.746322\pi$
$383$	−31.8658	−	6.77329i	−1.62827	−	0.346099i	−0.929378	+	0.369130i	$0.879656\pi$
$384$	0.200831	−	1.91078i	0.0102486	−	0.0975092i
$385$	1.45650	+	13.8576i	0.0742299	+	0.706251i
$386$	−22.6180	+	4.80760i	−1.15123	+	0.244701i
$387$	7.24965	−	5.26718i	0.368520	−	0.267746i
$388$	−8.73597	+	6.34706i	−0.443502	+	0.322223i
$389$	−8.20471	+	1.74396i	−0.415995	+	0.0884225i	−0.411154	−	0.911566i	$-0.634874\pi$
$389$	−8.20471	+	1.74396i	−0.415995	+	0.0884225i	−0.00484086	+	0.999988i	$0.501541\pi$
$390$	0.109466	+	1.04150i	0.00554303	+	0.0527384i
$391$	−3.54895	+	33.7660i	−0.179478	+	1.70762i
$392$	7.79817	+	1.65755i	0.393867	+	0.0837190i
$393$	0.948939	−	0.422495i	0.0478676	−	0.0213120i
$394$	21.3756	+	23.7400i	1.07689	+	1.19601i
$395$	−6.48599	+	19.9618i	−0.326346	+	1.00439i
$396$	13.3045	−	14.7762i	0.668579	−	0.742532i
$397$	−13.1250	−	22.7332i	−0.658727	−	1.14095i	−0.980946	−	0.194283i	$-0.937762\pi$
$397$	−13.1250	−	22.7332i	−0.658727	−	1.14095i	0.322219	−	0.946665i	$-0.395571\pi$
$398$	0.211351	−	0.366071i	0.0105941	−	0.0183495i
$399$	0.289513	+	0.891030i	0.0144938	+	0.0446073i
$400$	−4.88504	−	2.17496i	−0.244252	−	0.108748i
$401$	−2.17484	−	1.58011i	−0.108606	−	0.0789070i	0.532157	−	0.846646i	$-0.321382\pi$
$401$	−2.17484	−	1.58011i	−0.108606	−	0.0789070i	−0.640763	+	0.767739i	$0.721382\pi$
$402$	−2.74187			−0.136752
$403$		0			0
$404$	12.4218			0.618007
$405$	17.3057	+	12.5733i	0.859929	+	0.624775i
$406$	−6.25141	−	2.78331i	−0.310253	−	0.138133i
$407$	8.88394	+	27.3420i	0.440361	+	1.35529i
$408$	−0.732933	+	1.26948i	−0.0362856	+	0.0628485i
$409$	−1.54776	−	2.68079i	−0.0765316	−	0.132557i	0.825220	−	0.564812i	$-0.191051\pi$
$409$	−1.54776	−	2.68079i	−0.0765316	−	0.132557i	−0.901751	+	0.432255i	$0.857718\pi$
$410$	31.4238	−	34.8996i	1.55191	−	1.72357i
$411$	0.259055	−	0.797289i	0.0127782	−	0.0393274i
$412$	−7.53151	−	8.36459i	−0.371051	−	0.412094i
$413$	−2.94620	+	1.31173i	−0.144973	+	0.0645461i
$414$	−31.2684	−	6.64631i	−1.53676	−	0.326648i
$415$	−3.41163	+	32.4595i	−0.167470	+	1.59337i
$416$	0.798755	+	7.59964i	0.0391622	+	0.372603i
$417$	1.25622	−	0.267019i	0.0615176	−	0.0130760i
$418$	36.5136	−	26.5287i	1.78594	−	1.29756i
$419$	−26.4383	+	19.2086i	−1.29160	+	0.938400i	−0.999836	−	0.0180919i	$-0.994241\pi$
$419$	−26.4383	+	19.2086i	−1.29160	+	0.938400i	−0.291760	+	0.956492i	$0.594241\pi$
$420$	−0.605674	+	0.128740i	−0.0295539	+	0.00628187i
$421$	−1.42518	−	13.5596i	−0.0694588	−	0.660857i	−0.972754	−	0.231838i	$-0.925526\pi$
$421$	−1.42518	−	13.5596i	−0.0694588	−	0.660857i	0.903296	−	0.429019i	$-0.141141\pi$
$422$	3.08560	−	29.3575i	0.150205	−	1.42910i
$423$	16.3320	+	3.47148i	0.794091	+	0.168789i
$424$	−1.12305	+	0.500012i	−0.0545399	+	0.0242827i
$425$	4.11152	+	4.56631i	0.199438	+	0.221498i
$426$	−0.645563	+	1.98684i	−0.0312776	+	0.0962627i
$427$	6.42337	−	7.13387i	0.310849	−	0.345232i
$428$	−0.184211	−	0.319063i	−0.00890418	−	0.0154225i
$429$	−0.632395	+	1.09534i	−0.0305323	+	0.0528835i
$430$	4.15431	+	12.7856i	0.200338	+	0.616578i
$431$	25.4209	+	11.3181i	1.22448	+	0.545174i	0.914120	−	0.405445i	$-0.132883\pi$
$431$	25.4209	+	11.3181i	1.22448	+	0.545174i	0.310361	+	0.950619i	$0.399550\pi$
$432$	−4.54935	−	3.30529i	−0.218880	−	0.159026i
$433$	2.12857			0.102292			0.0511462	−	0.998691i	$-0.483713\pi$
$433$	2.12857			0.102292			0.0511462	+	0.998691i	$0.483713\pi$
$434$		0			0
$435$	1.69933			0.0814766
$436$	−2.20968	−	1.60543i	−0.105825	−	0.0768861i
$437$	−25.4895	−	11.3487i	−1.21933	−	0.542881i
$438$	−0.403061	−	1.24049i	−0.0192590	−	0.0592731i
$439$	−4.69991	+	8.14048i	−0.224314	+	0.388524i	−0.956114	−	0.292997i	$-0.905348\pi$
$439$	−4.69991	+	8.14048i	−0.224314	+	0.388524i	0.731799	+	0.681520i	$0.238681\pi$
$440$	−8.95819	−	15.5160i	−0.427065	−	0.739698i
$441$	11.6857	−	12.9783i	0.556463	−	0.618014i
$442$	3.89846	−	11.9982i	0.185431	−	0.570697i
$443$	21.0162	+	23.3408i	0.998508	+	1.10896i	0.994046	+	0.108965i	$0.0347537\pi$
$443$	21.0162	+	23.3408i	0.998508	+	1.10896i	0.00446214	+	0.999990i	$0.498580\pi$
$444$	−1.16711	+	0.519632i	−0.0553888	+	0.0246607i
$445$	−2.12764	−	0.452243i	−0.100860	−	0.0214384i
$446$	−1.84611	+	17.5646i	−0.0874159	+	0.831707i
$447$	−0.0442536	−	0.421045i	−0.00209313	−	0.0199148i
$448$	−1.33000	+	0.282701i	−0.0628367	+	0.0133564i
$449$	19.5094	−	14.1744i	0.920707	−	0.668933i	−0.0229929	−	0.999736i	$-0.507320\pi$
$449$	19.5094	−	14.1744i	0.920707	−	0.668933i	0.943700	+	0.330803i	$0.107320\pi$
$450$	−4.68043	+	3.40053i	−0.220638	+	0.160303i
$451$	55.4785	−	11.7923i	2.61238	−	0.555279i
$452$	−1.38547	−	13.1819i	−0.0651671	−	0.620024i
$453$	0.0947188	−	0.901189i	0.00445028	−	0.0423416i
$454$	−2.54378	−	0.540698i	−0.119386	−	0.0253762i
$455$	−2.92405	+	1.30187i	−0.137082	+	0.0610327i
$456$	−0.806069	−	0.895230i	−0.0377476	−	0.0419230i
$457$	1.14526	−	3.52473i	0.0535728	−	0.164880i	−0.920690	−	0.390294i	$-0.872373\pi$
$457$	1.14526	−	3.52473i	0.0535728	−	0.164880i	0.974263	+	0.225414i	$0.0723734\pi$
$458$	33.6023	−	37.3191i	1.57013	−	1.74381i
$459$	3.23083	+	5.59597i	0.150802	+	0.261197i
$460$	9.22042	−	15.9702i	0.429904	−	0.744616i
$461$	5.27568	+	16.2369i	0.245713	+	0.756227i	0.995518	+	0.0945683i	$0.0301471\pi$
$461$	5.27568	+	16.2369i	0.245713	+	0.756227i	−0.749805	+	0.661658i	$0.769853\pi$
$462$	−1.77671	−	0.791041i	−0.0826599	−	0.0368026i
$463$	−3.97426	−	2.88747i	−0.184699	−	0.134192i	0.491593	−	0.870825i	$-0.336415\pi$
$463$	−3.97426	−	2.88747i	−0.184699	−	0.134192i	−0.676293	+	0.736633i	$0.736415\pi$
$464$	17.8152			0.827048
$465$		0			0
$466$	27.5416			1.27584
$467$	2.07955	+	1.51088i	0.0962302	+	0.0699153i	0.634860	−	0.772627i	$-0.281058\pi$
$467$	2.07955	+	1.51088i	0.0962302	+	0.0699153i	−0.538630	+	0.842543i	$0.681058\pi$
$468$	4.17253	+	1.85773i	0.192875	+	0.0858736i
$469$	−2.58964	−	7.97009i	−0.119578	−	0.368025i
$470$	−12.5246	+	21.6932i	−0.577715	+	1.00063i
$471$	−0.386555	−	0.669533i	−0.0178115	−	0.0308504i
$472$	2.77471	−	3.08163i	0.127716	−	0.141843i
$473$	−5.01732	+	15.4417i	−0.230697	+	0.710011i
$474$	−1.96027	−	2.17710i	−0.0900381	−	0.0999975i
$475$	−4.61306	+	2.05386i	−0.211661	+	0.0942378i
$476$	7.29633	+	1.55088i	0.334427	+	0.0710846i
$477$	−0.281487	+	2.67817i	−0.0128884	+	0.122625i
$478$	0.858856	+	8.17147i	0.0392832	+	0.373754i
$479$	−2.00836	+	0.426890i	−0.0917642	+	0.0195051i	−0.253565	−	0.967318i	$-0.581603\pi$
$479$	−2.00836	+	0.426890i	−0.0917642	+	0.0195051i	0.161801	+	0.986823i	$0.448270\pi$
$480$	2.36066	−	1.71512i	0.107749	−	0.0782841i
$481$	−5.34271	+	3.88170i	−0.243606	+	0.176990i
$482$	−14.1421	+	3.00600i	−0.644156	+	0.136920i
$483$	0.125677	+	1.19573i	0.00571849	+	0.0544078i
$484$	−2.32907	+	22.1596i	−0.105867	+	1.00725i
$485$	20.8485	+	4.43149i	0.946683	+	0.201224i
$486$	−8.35386	+	3.71938i	−0.378939	+	0.168714i
$487$	−11.8512	−	13.1621i	−0.537030	−	0.596432i	0.412170	−	0.911107i	$-0.364771\pi$
$487$	−11.8512	−	13.1621i	−0.537030	−	0.596432i	−0.949199	+	0.314675i	$0.898104\pi$
$488$	−3.81425	+	11.7391i	−0.172663	+	0.531403i
$489$	−0.138553	+	0.153879i	−0.00626560	+	0.00695865i
$490$	13.1000	+	22.6899i	0.591797	+	1.02502i
$491$	−11.2360	+	19.4613i	−0.507072	+	0.878275i	0.492894	+	0.870089i	$0.335939\pi$
$491$	−11.2360	+	19.4613i	−0.507072	+	0.878275i	−0.999966	+	0.00818549i	$0.997394\pi$
$492$	0.778866	+	2.39710i	0.0351140	+	0.108070i
$493$	−18.7014	−	8.32638i	−0.842267	−	0.375001i
$494$	8.38755	+	6.09391i	0.377374	+	0.274178i
$495$	−39.2470			−1.76402
$496$		0			0
$497$	−6.38508			−0.286410
$498$	−3.68550	−	2.67767i	−0.165151	−	0.119989i
$499$	−18.2712	−	8.13486i	−0.817931	−	0.364166i	−0.0452615	−	0.998975i	$-0.514412\pi$
$499$	−18.2712	−	8.13486i	−0.817931	−	0.364166i	−0.772669	+	0.634809i	$0.781079\pi$
$500$	3.73025	+	11.4805i	0.166822	+	0.513425i
$501$	1.06464	−	1.84402i	0.0475648	−	0.0823847i
$502$	−10.6390	−	18.4273i	−0.474842	−	0.822451i
$503$	8.38470	−	9.31215i	0.373855	−	0.415208i	−0.526630	−	0.850095i	$-0.676545\pi$
$503$	8.38470	−	9.31215i	0.373855	−	0.415208i	0.900485	+	0.434886i	$0.143211\pi$
$504$	1.30354	−	4.01187i	0.0580641	−	0.178703i
$505$	−16.4064	−	18.2211i	−0.730073	−	0.810828i
$506$	52.9129	−	23.5584i	2.35227	−	1.04730i
$507$	2.14414	+	0.455751i	0.0952246	+	0.0202406i
$508$	−2.65569	+	25.2672i	−0.117827	+	1.12105i
$509$	2.76024	+	26.2620i	0.122346	+	1.16404i	0.867601	+	0.497262i	$0.165661\pi$
$509$	2.76024	+	26.2620i	0.122346	+	1.16404i	−0.745255	+	0.666779i	$0.767672\pi$
$510$	−4.71207	+	1.00158i	−0.208654	+	0.0443508i
$511$	3.22520	−	2.34324i	0.142674	−	0.103659i
$512$	13.9397	−	10.1278i	0.616053	−	0.447589i
$513$	−5.19417	+	1.10405i	−0.229328	+	0.0487452i
$514$	0.0200130	+	0.190411i	0.000882738	+	0.00839869i
$515$	−2.32233	+	22.0955i	−0.102334	+	0.973642i
$516$	−0.705754	−	0.150013i	−0.0310691	−	0.00660394i
$517$	−27.6373	+	12.3049i	−1.21549	+	0.541171i
$518$	−6.79488	−	7.54648i	−0.298550	−	0.331573i
$519$	−0.450745	+	1.38725i	−0.0197855	+	0.0608935i
$520$	2.75386	−	3.05847i	0.120765	−	0.134123i
$521$	12.1247	+	21.0006i	0.531193	+	0.920053i	0.999337	+	0.0364011i	$0.0115894\pi$
$521$	12.1247	+	21.0006i	0.531193	+	0.920053i	−0.468144	+	0.883652i	$0.655077\pi$
$522$	9.63717	−	16.6921i	0.421808	−	0.730592i
$523$	11.0794	+	34.0988i	0.484468	+	1.49104i	0.832750	+	0.553649i	$0.186765\pi$
$523$	11.0794	+	34.0988i	0.484468	+	1.49104i	−0.348282	+	0.937390i	$0.613235\pi$
$524$	6.20896	+	2.76441i	0.271240	+	0.120764i
$525$	0.176037	+	0.127899i	0.00768290	+	0.00558195i
$526$	−42.8327			−1.86759
$527$		0			0
$528$	5.06323			0.220349
$529$	−10.3610	−	7.52769i	−0.450477	−	0.327291i
$530$	−3.69071	−	1.64321i	−0.160314	−	0.0713765i
$531$	−2.80702	−	8.63912i	−0.121814	−	0.374906i
$532$	−3.06504	+	5.30881i	−0.132887	+	0.230166i
$533$	6.51434	+	11.2832i	0.282168	+	0.488729i
$534$	0.203149	−	0.225620i	0.00879112	−	0.00976353i
$535$	−0.224722	+	0.691623i	−0.00971558	+	0.0299015i
$536$	7.21013	+	8.00766i	0.311430	+	0.345878i
$537$	−2.32579	+	1.03551i	−0.100365	+	0.0446855i
$538$	4.54422	+	0.965903i	0.195915	+	0.0416430i
$539$	−3.30757	+	31.4694i	−0.142467	+	1.35548i
$540$	−0.366855	−	3.49039i	−0.0157869	−	0.150203i
$541$	−14.7086	+	3.12641i	−0.632373	+	0.134415i	−0.512936	−	0.858427i	$-0.671442\pi$
$541$	−14.7086	+	3.12641i	−0.632373	+	0.134415i	−0.119437	+	0.992842i	$0.538109\pi$
$542$	−42.4096	+	30.8123i	−1.82165	+	1.32350i
$543$	−3.24100	+	2.35472i	−0.139085	+	0.101051i
$544$	−34.3831	+	7.30836i	−1.47416	+	0.313343i
$545$	0.563539	+	5.36172i	0.0241394	+	0.229671i
$546$	0.0466982	−	0.444304i	0.00199850	−	0.0190145i
$547$	39.6138	+	8.42018i	1.69377	+	0.360021i	0.950919	−	0.309441i	$-0.100142\pi$
$547$	39.6138	+	8.42018i	1.69377	+	0.360021i	0.742847	+	0.669462i	$0.233475\pi$
$548$	5.01095	−	2.23102i	0.214057	−	0.0953045i
$549$	18.0923	+	20.0936i	0.772162	+	0.857572i
$550$	3.23922	−	9.96930i	0.138121	−	0.425092i
$551$	11.2569	−	12.5021i	0.479562	−	0.532608i
$552$	−0.772976	−	1.33883i	−0.0329000	−	0.0569845i
$553$	4.47698	−	7.75435i	0.190380	−	0.329748i
$554$	−6.70216	−	20.6271i	−0.284747	−	0.876362i
$555$	2.30372	+	1.02568i	0.0977876	+	0.0435379i
$556$	6.79832	+	4.93927i	0.288313	+	0.209472i
$557$	32.3465			1.37057			0.685284	−	0.728276i	$-0.259678\pi$
$557$	32.3465			1.37057			0.685284	+	0.728276i	$0.259678\pi$
$558$		0			0
$559$	−3.72966			−0.157748
$560$	10.3662	+	7.53152i	0.438054	+	0.318265i
$561$	−5.31509	−	2.36643i	−0.224403	−	0.0999108i
$562$	17.3451	+	53.3828i	0.731660	+	2.25182i
$563$	−14.3093	+	24.7844i	−0.603064	+	1.04454i	0.389290	+	0.921115i	$0.372720\pi$
$563$	−14.3093	+	24.7844i	−0.603064	+	1.04454i	−0.992354	+	0.123422i	$0.960613\pi$
$564$	−0.672196	−	1.16428i	−0.0283045	−	0.0490249i
$565$	−17.5062	+	19.4426i	−0.736491	+	0.817956i
$566$	−3.19634	+	9.83732i	−0.134352	+	0.413494i
$567$	−6.10610	−	6.78151i	−0.256432	−	0.284797i
$568$	7.50018	−	3.33930i	0.314701	−	0.140114i
$569$	36.5337	+	7.76547i	1.53157	+	0.325545i	0.895139	−	0.445787i	$-0.147076\pi$
$569$	36.5337	+	7.76547i	1.53157	+	0.325545i	0.636432	+	0.771333i	$0.280410\pi$
$570$	0.413817	−	3.93721i	0.0173329	−	0.164912i
$571$	−1.04327	−	9.92602i	−0.0436594	−	0.415391i	−0.994422	−	0.105472i	$-0.966365\pi$
$571$	−1.04327	−	9.92602i	−0.0436594	−	0.415391i	0.950763	−	0.309919i	$-0.100302\pi$
$572$	−8.09476	+	1.72059i	−0.338459	+	0.0719416i
$573$	−1.16901	+	0.849335i	−0.0488361	+	0.0354815i
$574$	−16.2079	+	11.7757i	−0.676503	+	0.491508i
$575$	−6.33866	+	1.34732i	−0.264340	+	0.0561873i
$576$	−0.400326	−	3.80885i	−0.0166803	−	0.158702i
$577$	4.01727	−	38.2218i	0.167241	−	1.59119i	−0.513119	−	0.858317i	$-0.671510\pi$
$577$	4.01727	−	38.2218i	0.167241	−	1.59119i	0.680361	−	0.732877i	$-0.261823\pi$
$578$	26.7893	+	5.69424i	1.11429	+	0.236849i
$579$	−2.23785	+	0.996353i	−0.0930017	+	0.0414070i
$580$	7.43994	+	8.26289i	0.308927	+	0.343098i
$581$	4.30260	−	13.2420i	0.178502	−	0.549372i
$582$	−1.99064	+	2.21083i	−0.0825147	+	0.0916418i
$583$	−2.43963	−	4.22556i	−0.101039	−	0.175005i
$584$	−2.56297	+	4.43920i	−0.106057	+	0.183695i
$585$	−2.78592	−	8.57419i	−0.115184	−	0.354499i
$586$	−2.10629	−	0.937782i	−0.0870102	−	0.0387394i
$587$	−24.5189	−	17.8141i	−1.01200	−	0.735265i	−0.0473763	−	0.998877i	$-0.515086\pi$
$587$	−24.5189	−	17.8141i	−1.01200	−	0.735265i	−0.964629	+	0.263612i	$0.915086\pi$
$588$	−1.40616			−0.0579890
$589$		0			0
$590$	13.6276			0.561040
$591$	2.73789	+	1.98919i	0.112622	+	0.0818244i
$592$	24.1514	+	10.7529i	0.992617	+	0.441942i
$593$	0.668894	+	2.05864i	0.0274682	+	0.0845384i	0.963851	−	0.266442i	$-0.0858482\pi$
$593$	0.668894	+	2.05864i	0.0274682	+	0.0845384i	−0.936383	+	0.350981i	$0.885848\pi$
$594$	5.51165	−	9.54645i	0.226146	−	0.391696i
$595$	−7.36185	−	12.7511i	−0.301806	−	0.522744i
$596$	1.85356	−	2.05858i	0.0759247	−	0.0843229i
$597$	0.0138378	−	0.0425884i	0.000566343	−	0.00174303i
$598$	8.90272	+	9.88748i	0.364059	+	0.404329i
$599$	−24.1860	+	10.7683i	−0.988211	+	0.439980i	−0.836215	−	0.548401i	$-0.815237\pi$
$599$	−24.1860	+	10.7683i	−0.988211	+	0.439980i	−0.151996	+	0.988381i	$0.548570\pi$
$600$	−0.273670	−	0.0581703i	−0.0111725	−	0.00237479i
$601$	4.29317	−	40.8468i	0.175122	−	1.66618i	−0.455613	−	0.890178i	$-0.650580\pi$
$601$	4.29317	−	40.8468i	0.175122	−	1.66618i	0.630735	−	0.775998i	$-0.282753\pi$
$602$	−0.599476	−	5.70363i	−0.0244328	−	0.232463i
$603$	23.0884	−	4.90758i	0.940230	−	0.199852i
$604$	4.79667	−	3.48499i	0.195174	−	0.141802i
$605$	35.5813	−	25.8513i	1.44659	−	1.05101i
$606$	3.34747	−	0.711526i	0.135982	−	0.0289038i
$607$	−4.09965	−	39.0055i	−0.166399	−	1.58319i	−0.685242	−	0.728315i	$-0.740304\pi$
$607$	−4.09965	−	39.0055i	−0.166399	−	1.58319i	0.518843	−	0.854870i	$-0.326363\pi$
$608$	3.01955	−	28.7291i	0.122459	−	1.16512i
$609$	−0.709092	−	0.150722i	−0.0287339	−	0.00610757i
$610$	−37.0570	+	16.4988i	−1.50039	+	0.668019i
$611$	−4.65005	−	5.16440i	−0.188121	−	0.208929i
$612$	−6.49253	+	19.9819i	−0.262445	+	0.807722i
$613$	−14.5430	+	16.1516i	−0.587386	+	0.652358i	−0.961429	−	0.275053i	$-0.911305\pi$
$613$	−14.5430	+	16.1516i	−0.587386	+	0.652358i	0.374043	+	0.927411i	$0.377971\pi$
$614$	−14.1446	−	24.4991i	−0.570829	−	0.988704i
$615$	2.48752	−	4.30852i	0.100307	−	0.173736i
$616$	2.36186	+	7.26904i	0.0951619	+	0.292878i
$617$	−12.3750	−	5.50972i	−0.498201	−	0.221813i	0.142224	−	0.989835i	$-0.454575\pi$
$617$	−12.3750	−	5.50972i	−0.498201	−	0.221813i	−0.640424	+	0.768021i	$0.721241\pi$
$618$	−2.50875	−	1.82271i	−0.100917	−	0.0733202i
$619$	42.3785			1.70334			0.851668	−	0.524082i	$-0.175592\pi$
$619$	42.3785			1.70334			0.851668	+	0.524082i	$0.175592\pi$
$620$		0			0
$621$	−6.81469			−0.273464
$622$	40.0417	+	29.0920i	1.60553	+	1.16648i
$623$	0.847704	+	0.377422i	0.0339625	+	0.0151211i
$624$	0.359410	+	1.10615i	0.0143879	+	0.0442814i
$625$	14.6210	−	25.3243i	0.584840	−	1.01297i
$626$	11.5443	+	19.9953i	0.461402	+	0.799171i
$627$	3.19932	−	3.55321i	0.127769	−	0.141902i
$628$	1.56316	−	4.81092i	0.0623770	−	0.191977i
$629$	−20.3272	−	22.5756i	−0.810497	−	0.900148i
$630$	12.6644	−	5.63855i	0.504561	−	0.224645i
$631$	−22.3842	−	4.75791i	−0.891102	−	0.189409i	−0.260461	−	0.965484i	$-0.583874\pi$
$631$	−22.3842	−	4.75791i	−0.891102	−	0.189409i	−0.630641	+	0.776075i	$0.717208\pi$
$632$	−1.20344	+	11.4500i	−0.0478703	+	0.455455i
$633$	−0.326881	−	3.11007i	−0.0129924	−	0.123614i
$634$	−16.7912	+	3.56907i	−0.666862	+	0.141746i
$635$	40.5712	−	29.4767i	1.61002	−	1.16975i
$636$	0.175417	−	0.127448i	0.00695572	−	0.00505363i
$637$	−7.10983	+	1.51124i	−0.281702	+	0.0598775i
$638$	3.65043	+	34.7315i	0.144522	+	1.37503i
$639$	1.87989	−	17.8860i	0.0743673	−	0.707557i
$640$	−24.2716	−	5.15910i	−0.959421	−	0.203931i
$641$	21.4254	−	9.53921i	0.846253	−	0.376776i	0.0626484	−	0.998036i	$-0.480045\pi$
$641$	21.4254	−	9.53921i	0.846253	−	0.376776i	0.783605	+	0.621259i	$0.213379\pi$
$642$	−0.0679180	−	0.0754306i	−0.00268051	−	0.00297701i
$643$	4.49137	−	13.8230i	0.177122	−	0.545127i	−0.822602	−	0.568618i	$-0.807478\pi$
$643$	4.49137	−	13.8230i	0.177122	−	0.545127i	0.999724	+	0.0234915i	$0.00747826\pi$
$644$	−5.26396	+	5.84621i	−0.207429	+	0.230373i
$645$	0.712092	+	1.23338i	0.0280386	+	0.0485643i
$646$	−23.8457	+	41.3019i	−0.938195	+	1.62500i
$647$	−1.52771	−	4.70179i	−0.0600603	−	0.184847i	0.916525	−	0.399978i	$-0.130982\pi$
$647$	−1.52771	−	4.70179i	−0.0600603	−	0.184847i	−0.976585	+	0.215131i	$0.930982\pi$
$648$	10.7191	+	4.77245i	0.421086	+	0.187480i
$649$	13.3153	+	9.67413i	0.522671	+	0.379743i
$650$	2.40790			0.0944456
$651$		0			0
$652$	−1.35484			−0.0530595
$653$	−12.8139	−	9.30982i	−0.501445	−	0.364321i	0.308124	−	0.951346i	$-0.400299\pi$
$653$	−12.8139	−	9.30982i	−0.501445	−	0.364321i	−0.809569	+	0.587025i	$0.800299\pi$
$654$	−0.687433	−	0.306065i	−0.0268808	−	0.0119681i
$655$	−4.14561	−	12.7589i	−0.161982	−	0.498531i
$656$	26.0783	−	45.1690i	1.01819	−	1.76355i
$657$	5.61436	+	9.72435i	0.219037	+	0.379383i
$658$	7.15030	−	7.94122i	0.278748	−	0.309581i
$659$	7.36102	−	22.6549i	0.286745	−	0.882510i	−0.699125	−	0.714999i	$-0.746427\pi$
$659$	7.36102	−	22.6549i	0.286745	−	0.882510i	0.985870	−	0.167511i	$-0.0535729\pi$
$660$	2.11450	+	2.34839i	0.0823067	+	0.0914108i
$661$	37.6472	−	16.7616i	1.46430	−	0.651951i	0.488894	−	0.872343i	$-0.337401\pi$
$661$	37.6472	−	16.7616i	1.46430	−	0.651951i	0.975411	+	0.220393i	$0.0707339\pi$
$662$	38.0565	+	8.08915i	1.47911	+	0.314394i
$663$	0.139700	−	1.32915i	0.00542548	−	0.0516200i
$664$	1.87136	+	17.8048i	0.0726230	+	0.690961i
$665$	11.8355	−	2.51572i	0.458963	−	0.0975556i
$666$	23.1398	−	16.8121i	0.896650	−	0.651454i
$667$	17.4663	−	12.6900i	0.676300	−	0.491360i
$668$	13.6276	−	2.89664i	0.527268	−	0.112074i
$669$	0.195573	+	1.86075i	0.00756127	+	0.0719407i
$670$	−3.70152	+	35.2176i	−0.143002	+	1.36057i
$671$	−47.9201	−	10.1857i	−1.84994	−	0.393216i
$672$	−1.13717	+	0.506302i	−0.0438674	+	0.0195310i
$673$	26.9042	+	29.8801i	1.03708	+	1.15179i	0.988228	+	0.152987i	$0.0488892\pi$
$673$	26.9042	+	29.8801i	1.03708	+	1.15179i	0.0488506	+	0.998806i	$0.484444\pi$
$674$	2.53344	−	7.79711i	0.0975843	−	0.300334i
$675$	−0.825246	+	0.916528i	−0.0317637	+	0.0352772i
$676$	7.17133	+	12.4211i	0.275820	+	0.477735i
$677$	15.8290	−	27.4165i	0.608356	−	1.05370i	−0.383155	−	0.923684i	$-0.625163\pi$
$677$	15.8290	−	27.4165i	0.608356	−	1.05370i	0.991511	−	0.130020i	$-0.0415040\pi$
$678$	−1.12843	−	3.47294i	−0.0433370	−	0.133378i
$679$	−8.30657	−	3.69832i	−0.318777	−	0.141929i
$680$	15.3162	+	11.1278i	0.587348	+	0.426733i
$681$	−0.275503			−0.0105573
$682$		0			0
$683$	10.8397			0.414771			0.207386	−	0.978259i	$-0.433505\pi$
$683$	10.8397			0.414771			0.207386	+	0.978259i	$0.433505\pi$
$684$	−13.9687	−	10.1489i	−0.534107	−	0.388051i
$685$	−9.89094	−	4.40373i	−0.377913	−	0.168258i
$686$	−7.55653	−	23.2566i	−0.288510	−	0.887942i
$687$	2.65998	−	4.60722i	0.101484	−	0.175776i
$688$	7.46532	+	12.9303i	0.284613	+	0.492964i
$689$	0.749971	−	0.832927i	0.0285716	−	0.0317320i
$690$	1.56997	−	4.83187i	0.0597677	−	0.183946i
$691$	−17.7159	−	19.6755i	−0.673944	−	0.748490i	0.305060	−	0.952333i	$-0.401324\pi$
$691$	−17.7159	−	19.6755i	−0.673944	−	0.748490i	−0.979004	+	0.203843i	$0.934657\pi$
$692$	−8.71886	+	3.88189i	−0.331441	+	0.147567i
$693$	16.3769	+	3.48102i	0.622107	+	0.132233i
$694$	5.53778	−	52.6884i	0.210211	−	2.00003i
$695$	−1.73379	−	16.4959i	−0.0657663	−	0.625724i
$696$	0.911755	−	0.193799i	0.0345600	−	0.00734595i
$697$	−48.4864	+	35.2275i	−1.83656	+	1.33434i
$698$	−9.84579	+	7.15339i	−0.372669	+	0.270760i
$699$	2.85393	−	0.606622i	0.107946	−	0.0229446i
$700$	0.148820	+	1.41593i	0.00562488	+	0.0535172i
$701$	−1.12124	+	10.6679i	−0.0423487	+	0.402921i	0.952729	+	0.303822i	$0.0982627\pi$
$701$	−1.12124	+	10.6679i	−0.0423487	+	0.402921i	−0.995078	+	0.0990991i	$0.968404\pi$
$702$	2.47683	+	0.526466i	0.0934819	+	0.0198702i
$703$	22.8067	−	10.1542i	0.860171	−	0.382973i
$704$	4.64323	+	5.15683i	0.174998	+	0.194355i
$705$	−0.820022	+	2.52377i	−0.0308838	+	0.0950506i
$706$	−9.38507	+	10.4232i	−0.353212	+	0.392282i
$707$	5.22988	+	9.05842i	0.196690	+	0.340677i
$708$	−0.365698	+	0.633408i	−0.0137438	+	0.0238049i
$709$	−10.3715	−	31.9202i	−0.389510	−	1.19879i	−0.933155	−	0.359473i	$-0.882956\pi$
$709$	−10.3715	−	31.9202i	−0.389510	−	1.19879i	0.543646	−	0.839315i	$-0.317044\pi$
$710$	24.6482	+	10.9741i	0.925029	+	0.411850i
$711$	20.4035	+	14.8240i	0.765190	+	0.555943i
$712$	−1.19313			−0.0447146
$713$		0			0
$714$	2.05508			0.0769093
$715$	13.2152	+	9.60142i	0.494221	+	0.359073i
$716$	−15.2178	−	6.77540i	−0.568716	−	0.253209i
$717$	0.268979	+	0.827832i	0.0100452	+	0.0309160i
$718$	2.33204	−	4.03922i	0.0870311	−	0.150742i
$719$	4.62689	+	8.01401i	0.172554	+	0.298872i	0.939312	−	0.343064i	$-0.111465\pi$
$719$	4.62689	+	8.01401i	0.172554	+	0.298872i	−0.766758	+	0.641936i	$0.778131\pi$
$720$	−24.1494	+	26.8206i	−0.899995	+	0.999546i
$721$	2.92881	−	9.01396i	0.109075	−	0.335697i
$722$	−3.30728	−	3.67311i	−0.123084	−	0.136699i
$723$	−1.39923	+	0.622979i	−0.0520381	+	0.0231688i
$724$	−25.6393	−	5.44981i	−0.952878	−	0.202540i
$725$	0.408419	−	3.88584i	0.0151683	−	0.144317i
$726$	0.641667	+	6.10506i	0.0238145	+	0.226580i
$727$	−44.6082	+	9.48176i	−1.65443	+	0.351659i	−0.938169	−	0.346178i	$-0.887479\pi$
$727$	−44.6082	+	9.48176i	−1.65443	+	0.351659i	−0.716257	+	0.697837i	$0.754146\pi$
$728$	−1.42039	+	1.03198i	−0.0526433	+	0.0382476i
$729$	20.2664	−	14.7244i	0.750606	−	0.545347i
$730$	−16.4775	+	3.50240i	−0.609859	+	0.129630i
$731$	−1.79336	−	17.0626i	−0.0663296	−	0.631084i
$732$	0.227566	−	2.16515i	0.00841109	−	0.0800262i
$733$	−37.1402	−	7.89440i	−1.37181	−	0.291586i	−0.537675	−	0.843152i	$-0.680697\pi$
$733$	−37.1402	−	7.89440i	−1.37181	−	0.291586i	−0.834131	+	0.551566i	$0.814031\pi$
$734$	58.0129	−	25.8290i	2.14129	−	0.953366i
$735$	1.85721	+	2.06265i	0.0685044	+	0.0760818i
$736$	11.4558	−	35.2573i	0.422266	−	1.29960i
$737$	−28.6174	+	31.7828i	−1.05413	+	1.17073i
$738$	−28.2143	−	48.8686i	−1.03858	−	1.79888i
$739$	−13.1610	+	22.7955i	−0.484134	+	0.838545i	−0.999834	−	0.0182243i	$-0.994199\pi$
$739$	−13.1610	+	22.7955i	−0.484134	+	0.838545i	0.515700	+	0.856769i	$0.327532\pi$
$740$	5.09875	+	15.6923i	0.187434	+	0.576861i
$741$	1.00336	+	0.446726i	0.0368594	+	0.0164109i
$742$	1.39431	+	1.01302i	0.0511866	+	0.0371893i
$743$	−53.3973			−1.95896			−0.979479	−	0.201545i	$-0.935404\pi$
$743$	−53.3973			−1.95896			−0.979479	+	0.201545i	$0.935404\pi$
$744$		0			0
$745$	−5.46780			−0.200325
$746$	9.74908	+	7.08312i	0.356939	+	0.259332i
$747$	35.8269	+	15.9512i	1.31084	+	0.583623i
$748$	−11.7637	−	36.2049i	−0.430123	−	1.32378i
$749$	0.155115	−	0.268667i	0.00566778	−	0.00981688i
$750$	1.66285	+	2.88015i	0.0607188	+	0.105168i
$751$	5.94696	−	6.60477i	0.217008	−	0.241011i	−0.624806	−	0.780780i	$-0.714822\pi$
$751$	5.94696	−	6.60477i	0.217008	−	0.241011i	0.841813	+	0.539769i	$0.181488\pi$
$752$	−8.59681	+	26.4583i	−0.313494	+	0.964834i
$753$	−1.50832	−	1.67515i	−0.0549661	−	0.0610460i
$754$	−7.32858	+	3.26290i	−0.266891	+	0.118828i
$755$	−11.4473	−	2.43320i	−0.416611	−	0.0885534i
$756$	−0.156500	+	1.48900i	−0.00569186	+	0.0541545i
$757$	−4.09107	−	38.9239i	−0.148692	−	1.41471i	−0.773432	−	0.633879i	$-0.781462\pi$
$757$	−4.09107	−	38.9239i	−0.148692	−	1.41471i	0.624740	−	0.780833i	$-0.285205\pi$
$758$	30.9959	−	6.58838i	1.12582	−	0.239301i
$759$	4.96409	−	3.60662i	0.180185	−	0.130912i
$760$	−12.5868	+	9.14488i	−0.456573	+	0.331720i
$761$	−16.3875	+	3.48328i	−0.594047	+	0.126269i	−0.495118	−	0.868826i	$-0.664875\pi$
$761$	−16.3875	+	3.48328i	−0.594047	+	0.126269i	−0.0989295	+	0.995094i	$0.531542\pi$
$762$	0.731654	+	6.96122i	0.0265050	+	0.252178i
$763$	0.240406	−	2.28731i	0.00870327	−	0.0828061i
$764$	−9.24796	−	1.96571i	−0.334579	−	0.0711170i
$765$	37.8860	−	16.8679i	1.36977	−	0.609861i
$766$	−39.2953	−	43.6419i	−1.41980	−	1.57684i
$767$	−1.16830	+	3.59567i	−0.0421850	+	0.129832i
$768$	2.64775	−	2.94063i	0.0955426	−	0.106111i
$769$	−8.61075	−	14.9142i	−0.310511	−	0.537822i	0.667962	−	0.744196i	$-0.267167\pi$
$769$	−8.61075	−	14.9142i	−0.310511	−	0.537822i	−0.978473	+	0.206374i	$0.933834\pi$
$770$	−12.5590	+	21.7528i	−0.452594	+	0.783915i
$771$	0.00626774	+	0.0192901i	0.000225727	+	0.000694717i
$772$	−14.6424	−	6.51920i	−0.526990	−	0.234631i
$773$	−23.8619	−	17.3367i	−0.858253	−	0.623557i	0.0691560	−	0.997606i	$-0.477969\pi$
$773$	−23.8619	−	17.3367i	−0.858253	−	0.623557i	−0.927409	+	0.374048i	$0.877969\pi$
$774$	16.1536			0.580628
$775$		0			0
$776$	11.6914			0.419697
$777$	−0.870319	−	0.632324i	−0.0312225	−	0.0226845i
$778$	−13.8133	−	6.15008i	−0.495231	−	0.220491i
$779$	−15.2199	−	46.8421i	−0.545310	−	1.67829i
$780$	−0.362950	+	0.628647i	−0.0129957	+	0.0225092i
$781$	16.2929	+	28.2201i	0.583005	+	1.00979i
$782$	−40.9529	+	45.4828i	−1.46447	+	1.62646i
$783$	1.26971	−	3.90778i	0.0453759	−	0.139653i
$784$	19.4704	+	21.6240i	0.695371	+	0.772287i
$785$	−9.12157	+	4.06118i	−0.325563	+	0.144950i
$786$	1.83156	+	0.389310i	0.0653296	+	0.0138862i
$787$	1.57891	−	15.0223i	0.0562819	−	0.535486i	−0.929662	−	0.368412i	$-0.879901\pi$
$787$	1.57891	−	15.0223i	0.0562819	−	0.535486i	0.985944	−	0.167074i	$-0.0534319\pi$
$788$	2.31459	+	22.0218i	0.0824537	+	0.784495i
$789$	−4.43843	+	0.943418i	−0.158012	+	0.0335866i
$790$	−30.6098	+	22.2393i	−1.08905	+	0.791240i
$791$	9.02940	−	6.56024i	0.321049	−	0.233255i
$792$	−21.0575	+	4.47591i	−0.748246	+	0.159045i
$793$	−1.17633	−	11.1920i	−0.0417726	−	0.397440i
$794$	4.94623	−	47.0602i	0.175535	−	1.67010i
$795$	−0.418634	−	0.0889834i	−0.0148474	−	0.00315592i
$796$	0.267668	−	0.119173i	0.00948722	−	0.00422398i
$797$	27.6076	+	30.6613i	0.977910	+	1.08608i	0.996274	+	0.0862473i	$0.0274875\pi$
$797$	27.6076	+	30.6613i	0.977910	+	1.08608i	−0.0183641	+	0.999831i	$0.505846\pi$
$798$	−0.521888	+	1.60621i	−0.0184746	+	0.0568591i
$799$	21.3904	−	23.7565i	0.756739	−	0.840443i
$800$	−3.35458	−	5.81031i	−0.118602	−	0.205426i
$801$	−1.30682	+	2.26348i	−0.0461742	+	0.0799760i
$802$	−1.49748	−	4.60876i	−0.0528778	−	0.162741i
$803$	−18.5862	−	8.27510i	−0.655892	−	0.292022i
$804$	−1.53757	−	1.11711i	−0.0542260	−	0.0393975i
$805$	15.5281			0.547294
$806$		0			0
$807$	0.492158			0.0173248
$808$	−10.8807	−	7.90526i	−0.382780	−	0.278106i
$809$	−17.7677	−	7.91071i	−0.624681	−	0.278126i	0.0698850	−	0.997555i	$-0.477737\pi$
$809$	−17.7677	−	7.91071i	−0.624681	−	0.278126i	−0.694566	+	0.719429i	$0.744403\pi$
$810$	11.9158	+	36.6731i	0.418679	+	1.28856i
$811$	−8.01689	+	13.8857i	−0.281511	+	0.487591i	−0.971757	−	0.235983i	$-0.924169\pi$
$811$	−8.01689	+	13.8857i	−0.281511	+	0.487591i	0.690246	+	0.723575i	$0.257502\pi$
$812$	−2.37164	−	4.10781i	−0.0832283	−	0.144156i
$813$	−3.71593	+	4.12695i	−0.130323	+	0.144739i
$814$	−16.0145	+	49.2877i	−0.561310	+	1.72753i
$815$	1.78943	+	1.98736i	0.0626810	+	0.0696143i
$816$	−4.88765	+	2.17612i	−0.171102	+	0.0761794i
$817$	13.7912	+	2.93142i	0.482494	+	0.102557i
$818$	0.583279	−	5.54953i	0.0203939	−	0.194035i
$819$	0.402015	+	3.82491i	0.0140475	+	0.133653i
$820$	31.8407	−	6.76795i	1.11193	−	0.236347i
$821$	−16.6055	+	12.0646i	−0.579537	+	0.421058i	−0.838557	−	0.544813i	$-0.816600\pi$
$821$	−16.6055	+	12.0646i	−0.579537	+	0.421058i	0.259020	+	0.965872i	$0.416600\pi$
$822$	1.22258	−	0.888254i	0.0426422	−	0.0309814i
$823$	26.0699	−	5.54132i	0.908738	−	0.193158i	0.270250	−	0.962790i	$-0.412894\pi$
$823$	26.0699	−	5.54132i	0.908738	−	0.193158i	0.638488	+	0.769632i	$0.279560\pi$
$824$	1.27385	+	12.1199i	0.0443768	+	0.422217i
$825$	0.116076	−	1.10439i	0.00404125	−	0.0384500i
$826$	−5.68650	−	1.20870i	−0.197859	−	0.0420561i
$827$	−23.3956	+	10.4164i	−0.813546	+	0.362214i	−0.770964	−	0.636879i	$-0.780225\pi$
$827$	−23.3956	+	10.4164i	−0.813546	+	0.362214i	−0.0425823	+	0.999093i	$0.513558\pi$
$828$	−14.8267	−	16.4667i	−0.515263	−	0.572257i
$829$	10.8972	−	33.5382i	0.378476	−	1.16483i	−0.562627	−	0.826711i	$-0.690209\pi$
$829$	10.8972	−	33.5382i	0.378476	−	1.16483i	0.941103	−	0.338119i	$-0.109791\pi$
$830$	−39.3684	+	43.7230i	−1.36650	+	1.51765i
$831$	−1.14882	−	1.98982i	−0.0398522	−	0.0690260i
$832$	−0.797003	+	1.38045i	−0.0276311	+	0.0478585i
$833$	−10.3323	−	31.7997i	−0.357995	−	1.10179i
$834$	2.11496	+	0.941641i	0.0732351	+	0.0326064i
$835$	−22.2480	−	16.1641i	−0.769923	−	0.559382i
$836$	31.2844			1.08199
$837$		0			0
$838$	−58.9095			−2.03499
$839$	−17.2858	−	12.5589i	−0.596773	−	0.433581i	0.247959	−	0.968771i	$-0.420240\pi$
$839$	−17.2858	−	12.5589i	−0.596773	−	0.433581i	−0.844732	+	0.535190i	$0.820240\pi$
$840$	0.612460	+	0.272685i	0.0211319	+	0.00940852i
$841$	−4.93891	−	15.2004i	−0.170307	−	0.524152i
$842$	12.2889	−	21.2850i	0.423504	−	0.733530i
$843$	2.97314	+	5.14963i	0.102400	+	0.177363i
$844$	13.6914	−	15.2058i	0.471277	−	0.523406i
$845$	8.74841	−	26.9248i	0.300954	−	0.926242i
$846$	20.1398	+	22.3676i	0.692422	+	0.769012i
$847$	−17.1402	+	7.63130i	−0.588943	+	0.262215i
$848$	−4.38881	−	0.932870i	−0.150712	−	0.0320349i
$849$	−0.114540	+	1.08977i	−0.00393099	+	0.0374008i
$850$	1.15780	+	11.0158i	0.0397124	+	0.377838i
$851$	31.3380	−	6.66110i	1.07425	−	0.228340i
$852$	−1.17151	+	0.851150i	−0.0401352	+	0.0291599i
$853$	−14.4680	+	10.5116i	−0.495376	+	0.359912i	−0.807248	−	0.590212i	$-0.799044\pi$
$853$	−14.4680	+	10.5116i	−0.495376	+	0.359912i	0.311872	+	0.950124i	$0.399044\pi$
$854$	16.9264	−	3.59782i	0.579210	−	0.123115i
$855$	3.56246	+	33.8945i	0.121834	+	1.15917i
$856$	−0.0416959	+	0.396710i	−0.00142514	+	0.0135593i
$857$	20.0630	+	4.26453i	0.685340	+	0.145674i	0.537406	−	0.843324i	$-0.319404\pi$
$857$	20.0630	+	4.26453i	0.685340	+	0.145674i	0.147934	+	0.988997i	$0.452738\pi$
$858$	−2.08285	+	0.927344i	−0.0711073	+	0.0316590i
$859$	−18.6689	−	20.7339i	−0.636974	−	0.707431i	0.335080	−	0.942190i	$-0.391237\pi$
$859$	−18.6689	−	20.7339i	−0.636974	−	0.707431i	−0.972054	+	0.234759i	$0.924570\pi$
$860$	−2.87958	+	8.86244i	−0.0981930	+	0.302207i
$861$	−1.42013	+	1.57722i	−0.0483980	+	0.0537514i
$862$	25.0807	+	43.4410i	0.854252	+	1.47961i
$863$	18.0809	−	31.3170i	0.615480	−	1.06604i	−0.374820	−	0.927097i	$-0.622296\pi$
$863$	18.0809	−	31.3170i	0.615480	−	1.06604i	0.990300	−	0.138945i	$-0.0443710\pi$
$864$	−2.18024	−	6.71008i	−0.0741732	−	0.228282i
$865$	17.2098	+	7.66231i	0.585152	+	0.260526i
$866$	3.10423	+	2.25535i	0.105486	+	0.0766401i
$867$	2.90140			0.0985366
$868$		0			0
$869$	−45.6958			−1.55012
$870$	2.47824	+	1.80055i	0.0840204	+	0.0610444i
$871$	−8.97489	−	3.99588i	−0.304102	−	0.135395i
$872$	0.913836	+	2.81250i	0.0309464	+	0.0952432i
$873$	12.8054	−	22.1796i	0.433397	−	0.750666i
$874$	−25.1484	−	43.5584i	−0.850658	−	1.47338i
$875$	−6.80150	+	7.55383i	−0.229933	+	0.255366i
$876$	0.279384	−	0.859856i	0.00943952	−	0.0290519i
$877$	−12.3103	−	13.6720i	−0.415690	−	0.461670i	0.498540	−	0.866867i	$-0.333870\pi$
$877$	−12.3103	−	13.6720i	−0.415690	−	0.461670i	−0.914230	+	0.405197i	$0.867203\pi$
$878$	−15.4796	+	6.89194i	−0.522410	+	0.232592i
$879$	−0.238915	−	0.0507829i	−0.00805840	−	0.00171287i
$880$	6.83534	−	65.0339i	0.230419	−	2.19229i
$881$	−3.47994	−	33.1094i	−0.117242	−	1.11548i	−0.882027	−	0.471198i	$-0.843822\pi$
$881$	−3.47994	−	33.1094i	−0.117242	−	1.11548i	0.764785	−	0.644285i	$-0.222845\pi$
$882$	30.7934	−	6.54534i	1.03687	−	0.220393i
$883$	−4.25326	+	3.09018i	−0.143134	+	0.103993i	−0.657048	−	0.753849i	$-0.728195\pi$
$883$	−4.25326	+	3.09018i	−0.143134	+	0.103993i	0.513914	+	0.857842i	$0.328195\pi$
$884$	7.07456	−	5.13997i	0.237943	−	0.172876i
$885$	1.41213	−	0.300157i	0.0474682	−	0.0100897i
$886$	5.91815	+	56.3074i	0.198824	+	1.89169i
$887$	−3.78685	+	36.0295i	−0.127150	+	1.20975i	0.725854	+	0.687849i	$0.241445\pi$
$887$	−3.78685	+	36.0295i	−0.127150	+	1.20975i	−0.853004	+	0.521904i	$0.825222\pi$
$888$	1.35301	+	0.287591i	0.0454040	+	0.00965092i
$889$	−19.5439	+	8.70150i	−0.655481	+	0.291839i
$890$	−2.62369	−	2.91391i	−0.0879464	−	0.0976744i
$891$	−14.3912	+	44.2916i	−0.482123	+	1.48382i
$892$	−8.19153	+	9.09762i	−0.274273	+	0.304611i
$893$	13.1355	+	22.7513i	0.439561	+	0.761343i
$894$	0.381587	−	0.660928i	0.0127622	−	0.0221047i
$895$	10.1606	+	31.2712i	0.339633	+	1.04528i
$896$	9.67043	+	4.30555i	0.323066	+	0.143838i
$897$	1.14030	+	0.828478i	0.0380736	+	0.0276621i
$898$	43.4706			1.45063
$899$		0			0
$900$	−4.01014			−0.133671
$901$	4.17112	+	3.03050i	0.138960	+	0.100961i
$902$	93.4027	+	41.5856i	3.10997	+	1.38465i
$903$	−0.187745	−	0.577821i	−0.00624778	−	0.0192287i
$904$	−7.17541	+	12.4282i	−0.238651	+	0.413355i
$905$	25.8696	+	44.8074i	0.859934	+	1.48945i
$906$	1.09300	−	1.21390i	0.0363126	−	0.0403292i
$907$	−5.38673	+	16.5786i	−0.178863	+	0.550485i	−0.999789	−	0.0205505i	$-0.993458\pi$
$907$	−5.38673	+	16.5786i	−0.178863	+	0.550485i	0.820925	+	0.571035i	$0.193458\pi$
$908$	−1.20620	−	1.33962i	−0.0400290	−	0.0444567i
$909$	−26.9143	+	11.9830i	−0.892692	+	0.397452i
$910$	−5.64376	−	1.19962i	−0.187089	−	0.0397669i
$911$	−1.92171	+	18.2839i	−0.0636692	+	0.605772i	0.915442	+	0.402449i	$0.131841\pi$
$911$	−1.92171	+	18.2839i	−0.0636692	+	0.605772i	−0.979112	+	0.203323i	$0.934826\pi$
$912$	−0.459590	−	4.37271i	−0.0152186	−	0.144795i
$913$	−69.5047	+	14.7737i	−2.30027	+	0.488937i
$914$	5.40489	−	3.92688i	0.178778	−	0.129890i
$915$	−3.47655	+	2.52586i	−0.114931	+	0.0835023i
$916$	34.0481	−	7.23715i	1.12498	−	0.239122i
$917$	0.598221	+	5.69169i	0.0197550	+	0.187956i
$918$	−1.21755	+	11.5842i	−0.0401853	+	0.382337i
$919$	−37.9890	−	8.07480i	−1.25314	−	0.266363i	−0.466914	−	0.884303i	$-0.654634\pi$
$919$	−37.9890	−	8.07480i	−1.25314	−	0.266363i	−0.786226	+	0.617939i	$0.787968\pi$
$920$	−18.2400	+	8.12096i	−0.601354	+	0.267740i
$921$	−2.00531	−	2.22712i	−0.0660771	−	0.0733861i
$922$	−9.51015	+	29.2692i	−0.313200	+	0.963931i
$923$	−5.00863	+	5.56265i	−0.164861	+	0.183097i
$924$	−0.674042	−	1.16747i	−0.0221743	−	0.0384071i
$925$	2.89910	−	5.02139i	0.0953219	−	0.165102i
$926$	−2.73646	−	8.42197i	−0.0899258	−	0.276763i
$927$	24.3877	+	10.8581i	0.800997	+	0.356627i
$928$	18.0833	+	13.1383i	0.593613	+	0.431285i
$929$	−45.3781			−1.48881			−0.744404	−	0.667729i	$-0.767266\pi$
$929$	−45.3781			−1.48881			−0.744404	+	0.667729i	$0.767266\pi$
$930$		0			0
$931$	27.4779			0.900552
$932$	15.4446	+	11.2212i	0.505906	+	0.367562i
$933$	4.79000	+	2.13264i	0.156817	+	0.0698196i
$934$	1.43187	+	4.40684i	0.0468522	+	0.144196i
$935$	−37.5706	+	65.0743i	−1.22869	+	2.12816i
$936$	−2.47259	−	4.28266i	−0.0808192	−	0.139983i
$937$	−17.4304	+	19.3584i	−0.569425	+	0.632411i	−0.957229	−	0.289331i	$-0.906567\pi$
$937$	−17.4304	+	19.3584i	−0.569425	+	0.632411i	0.387804	+	0.921742i	$0.373234\pi$
$938$	4.66819	−	14.3672i	0.152422	−	0.469106i
$939$	1.63666	+	1.81769i	0.0534103	+	0.0593181i
$940$	−15.8619	+	7.06215i	−0.517357	+	0.230342i
$941$	−40.0138	−	8.50520i	−1.30441	−	0.277261i	−0.497259	−	0.867602i	$-0.665660\pi$
$941$	−40.0138	−	8.50520i	−1.30441	−	0.277261i	−0.807154	+	0.590341i	$0.798993\pi$
$942$	0.145675	−	1.38600i	0.00474634	−	0.0451585i
$943$	−6.60691	−	62.8606i	−0.215151	−	2.04702i
$944$	14.8043	−	3.14674i	0.481837	−	0.102418i
$945$	2.39087	−	1.73707i	0.0777749	−	0.0565068i
$946$	−23.6786	+	17.2035i	−0.769858	+	0.559335i
$947$	38.2007	−	8.11980i	1.24135	−	0.263858i	0.459985	−	0.887927i	$-0.347855\pi$
$947$	38.2007	−	8.11980i	1.24135	−	0.263858i	0.781370	+	0.624069i	$0.214521\pi$
$948$	−0.212261	−	2.01953i	−0.00689392	−	0.0655913i
$949$	0.488511	−	4.64788i	0.0158578	−	0.150876i
$950$	−8.90373	−	1.89255i	−0.288875	−	0.0614023i
$951$	−1.66133	+	0.739673i	−0.0538724	+	0.0239855i
$952$	−5.40411	−	6.00187i	−0.175148	−	0.194522i
$953$	−2.44519	+	7.52551i	−0.0792073	+	0.243775i	−0.982817	−	0.184581i	$-0.940907\pi$
$953$	−2.44519	+	7.52551i	−0.0792073	+	0.243775i	0.903610	+	0.428356i	$0.140907\pi$
$954$	−3.24820	+	3.60749i	−0.105164	+	0.116797i
$955$	9.33101	+	16.1618i	0.301944	+	0.522983i
$956$	−2.84765	+	4.93228i	−0.0920996	+	0.159521i
$957$	1.14325	+	3.51857i	0.0369561	+	0.113739i
$958$	−3.38124	−	1.50542i	−0.109243	−	0.0486380i
$959$	3.73668	+	2.71486i	0.120664	+	0.0876673i
$960$	0.608676			0.0196449
$961$		0			0
$962$	−11.9045			−0.383818
$963$	0.706925	+	0.513611i	0.0227803	+	0.0165509i
$964$	−9.15527	−	4.07619i	−0.294871	−	0.131285i
$965$	9.77643	+	30.0888i	0.314715	+	0.968592i
$966$	−1.08368	+	1.87698i	−0.0348667	+	0.0603909i
$967$	−5.71906	−	9.90569i	−0.183912	−	0.318546i	0.759297	−	0.650744i	$-0.225543\pi$
$967$	−5.71906	−	9.90569i	−0.183912	−	0.318546i	−0.943210	+	0.332198i	$0.892210\pi$
$968$	16.1425	−	17.9281i	0.518840	−	0.576231i
$969$	−1.56125	+	4.80503i	−0.0501545	+	0.154360i
$970$	25.7093	+	28.5531i	0.825477	+	0.916785i
$971$	−29.1753	+	12.9897i	−0.936279	+	0.416858i	−0.817413	−	0.576052i	$-0.804593\pi$
$971$	−29.1753	+	12.9897i	−0.936279	+	0.416858i	−0.118866	+	0.992910i	$0.537926\pi$
$972$	−6.20001	−	1.31785i	−0.198865	−	0.0422701i
$973$	−0.739633	+	7.03714i	−0.0237116	+	0.225600i
$974$	−3.33730	−	31.7523i	−0.106934	−	1.01741i
$975$	0.249513	−	0.0530356i	0.00799081	−	0.00169850i
$976$	−36.4469	+	26.4802i	−1.16664	+	0.847610i
$977$	9.52177	−	6.91797i	0.304628	−	0.221326i	−0.424960	−	0.905212i	$-0.639712\pi$
$977$	9.52177	−	6.91797i	0.304628	−	0.221326i	0.729588	+	0.683887i	$0.239712\pi$
$978$	−0.365106	+	0.0776057i	−0.0116748	+	0.00248156i
$979$	−0.495006	−	4.70966i	−0.0158204	−	0.150522i
$980$	−1.89831	+	18.0612i	−0.0606392	+	0.576944i
$981$	6.33645	+	1.34685i	0.202307	+	0.0430018i
$982$	−37.0066	+	16.4764i	−1.18093	+	0.525784i
$983$	−35.7077	−	39.6575i	−1.13890	−	1.26488i	−0.959689	−	0.281066i	$-0.909312\pi$
$983$	−35.7077	−	39.6575i	−1.13890	−	1.26488i	−0.179211	−	0.983811i	$-0.557355\pi$
$984$	0.843288	−	2.59537i	0.0268830	−	0.0827375i
$985$	29.2460	−	32.4810i	0.931856	−	1.03493i
$986$	−18.4511	−	31.9582i	−0.587602	−	1.01776i
$987$	0.566023	−	0.980380i	0.0180167	−	0.0312058i
$988$	2.22071	+	6.83463i	0.0706500	+	0.217438i
$989$	16.5296	+	7.35947i	0.525612	+	0.234017i
$990$	−57.2365	−	41.5847i	−1.81910	−	1.32165i
$991$	−11.6584			−0.370343			−0.185171	−	0.982706i	$-0.559284\pi$
$991$	−11.6584			−0.370343			−0.185171	+	0.982706i	$0.559284\pi$
$992$		0			0
$993$	4.12168			0.130798
$994$	−9.31178	−	6.76541i	−0.295352	−	0.214586i
$995$	−0.528339	−	0.235232i	−0.0167495	−	0.00745735i
$996$	−0.975779	−	3.00314i	−0.0309188	−	0.0951581i
$997$	−13.0744	+	22.6455i	−0.414071	+	0.717191i	−0.995330	−	0.0965266i	$-0.969227\pi$
$997$	−13.0744	+	22.6455i	−0.414071	+	0.717191i	0.581260	+	0.813718i	$0.302560\pi$
$998$	−18.0267	−	31.2231i	−0.570624	−	0.988350i
$999$	4.07997	−	4.53127i	0.129085	−	0.143363i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.v.732.10		96
31.2	even	5	inner	961.2.g.v.448.4		96
31.3	odd	30		961.2.d.r.388.10		48
31.4	even	5		961.2.c.k.521.3		24
31.5	even	3	inner	961.2.g.v.816.9		96
31.6	odd	6		961.2.d.r.374.10		48
31.7	even	15		961.2.a.k.1.4	yes	12
31.8	even	5	inner	961.2.g.v.844.3		96
31.9	even	15	inner	961.2.g.v.547.4		96
31.10	even	15	inner	961.2.g.v.846.3		96
31.11	odd	30		961.2.c.k.439.4		24
31.12	odd	30		961.2.d.r.628.3		48
31.13	odd	30	inner	961.2.g.v.235.9		96
31.14	even	15		961.2.d.r.531.4		48
31.15	odd	10	inner	961.2.g.v.338.10		96
31.16	even	5	inner	961.2.g.v.338.9		96
31.17	odd	30		961.2.d.r.531.3		48
31.18	even	15	inner	961.2.g.v.235.10		96
31.19	even	15		961.2.d.r.628.4		48
31.20	even	15		961.2.c.k.439.3		24
31.21	odd	30	inner	961.2.g.v.846.4		96
31.22	odd	30	inner	961.2.g.v.547.3		96
31.23	odd	10	inner	961.2.g.v.844.4		96
31.24	odd	30		961.2.a.k.1.3	✓	12
31.25	even	3		961.2.d.r.374.9		48
31.26	odd	6	inner	961.2.g.v.816.10		96
31.27	odd	10		961.2.c.k.521.4		24
31.28	even	15		961.2.d.r.388.9		48
31.29	odd	10	inner	961.2.g.v.448.3		96
31.30	odd	2	inner	961.2.g.v.732.9		96
93.38	odd	30		8649.2.a.bp.1.10		12
93.86	even	30		8649.2.a.bp.1.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.k.1.3	✓	12	31.24	odd	30
961.2.a.k.1.4	yes	12	31.7	even	15
961.2.c.k.439.3		24	31.20	even	15
961.2.c.k.439.4		24	31.11	odd	30
961.2.c.k.521.3		24	31.4	even	5
961.2.c.k.521.4		24	31.27	odd	10
961.2.d.r.374.9		48	31.25	even	3
961.2.d.r.374.10		48	31.6	odd	6
961.2.d.r.388.9		48	31.28	even	15
961.2.d.r.388.10		48	31.3	odd	30
961.2.d.r.531.3		48	31.17	odd	30
961.2.d.r.531.4		48	31.14	even	15
961.2.d.r.628.3		48	31.12	odd	30
961.2.d.r.628.4		48	31.19	even	15
961.2.g.v.235.9		96	31.13	odd	30	inner
961.2.g.v.235.10		96	31.18	even	15	inner
961.2.g.v.338.9		96	31.16	even	5	inner
961.2.g.v.338.10		96	31.15	odd	10	inner
961.2.g.v.448.3		96	31.29	odd	10	inner
961.2.g.v.448.4		96	31.2	even	5	inner
961.2.g.v.547.3		96	31.22	odd	30	inner
961.2.g.v.547.4		96	31.9	even	15	inner
961.2.g.v.732.9		96	31.30	odd	2	inner
961.2.g.v.732.10		96	1.1	even	1	trivial
961.2.g.v.816.9		96	31.5	even	3	inner
961.2.g.v.816.10		96	31.26	odd	6	inner
961.2.g.v.844.3		96	31.8	even	5	inner
961.2.g.v.844.4		96	31.23	odd	10	inner
961.2.g.v.846.3		96	31.10	even	15	inner
961.2.g.v.846.4		96	31.21	odd	30	inner
8649.2.a.bp.1.9		12	93.86	even	30
8649.2.a.bp.1.10		12	93.38	odd	30

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.45837 + 1.05957i) q^{2} +(0.174457 + 0.0776734i) q^{3} +(0.386120 + 1.18836i) q^{4} +(1.23318 - 2.13593i) q^{5} +(0.172123 + 0.298125i) q^{6} +(-0.704026 + 0.781900i) q^{7} +(0.418057 - 1.28665i) q^{8} +(-1.98299 - 2.20233i) q^{9} +(4.06159 - 1.80834i) q^{10} +(5.25223 + 1.11640i) q^{11} +(-0.0249421 + 0.237309i) q^{12} +(0.128930 + 1.22669i) q^{13} +(-1.85520 + 0.394336i) q^{14} +(0.381043 - 0.276844i) q^{15} +(3.99472 - 2.90233i) q^{16} +(-5.54991 + 1.17967i) q^{17} +(-0.558410 - 5.31292i) q^{18} +(0.487397 - 4.63728i) q^{19} +(3.01441 + 0.640732i) q^{20} +(-0.183555 + 0.0817242i) q^{21} +(6.47678 + 7.19320i) q^{22} +(1.84912 - 5.69101i) q^{23} +(0.172872 - 0.191993i) q^{24} +(-0.541477 - 0.937865i) q^{25} +(-1.11173 + 1.92557i) q^{26} +(-0.351921 - 1.08310i) q^{27} +(-1.20101 - 0.534726i) q^{28} +(2.91890 + 2.12070i) q^{29} +0.849035 q^{30} +6.19525 q^{32} +(0.829576 + 0.602723i) q^{33} +(-9.34374 - 4.16010i) q^{34} +(0.801895 + 2.46798i) q^{35} +(1.85148 - 3.20686i) q^{36} +(2.67703 + 4.63676i) q^{37} +(5.62430 - 6.24642i) q^{38} +(-0.0727883 + 0.224019i) q^{39} +(-2.23265 - 2.47961i) q^{40} +(9.64964 - 4.29630i) q^{41} +(-0.354283 - 0.0753052i) q^{42} +(-0.316071 + 3.00721i) q^{43} +(0.701317 + 6.67258i) q^{44} +(-7.14943 + 1.51966i) q^{45} +(8.72670 - 6.34032i) q^{46} +(-4.55810 + 3.31166i) q^{47} +(0.922342 - 0.196050i) q^{48} +(0.615984 + 5.86070i) q^{49} +(0.204058 - 1.94148i) q^{50} +(-1.05985 - 0.225279i) q^{51} +(-1.40796 + 0.626864i) q^{52} +(-0.608029 - 0.675285i) q^{53} +(0.634387 - 1.95244i) q^{54} +(8.86151 - 9.84170i) q^{55} +(0.711707 + 1.23271i) q^{56} +(0.445223 - 0.771149i) q^{57} +(2.00980 + 6.18552i) q^{58} +(2.80017 + 1.24671i) q^{59} +(0.476117 + 0.345920i) q^{60} -9.12376 q^{61} +3.11808 q^{63} +(1.04551 + 0.759607i) q^{64} +(2.77912 + 1.23734i) q^{65} +(0.571202 + 1.75798i) q^{66} +(-3.98244 + 6.89779i) q^{67} +(-3.54480 - 6.13978i) q^{68} +(0.764633 - 0.849211i) q^{69} +(-1.44553 + 4.44888i) q^{70} +(4.06068 + 4.50985i) q^{71} +(-3.66263 + 1.63071i) q^{72} +(-3.70617 - 0.787770i) q^{73} +(-1.00885 + 9.59858i) q^{74} +(-0.0216174 - 0.205676i) q^{75} +(5.69893 - 1.21134i) q^{76} +(-4.57062 + 3.32075i) q^{77} +(-0.343515 + 0.249578i) q^{78} +(-8.32417 + 1.76936i) q^{79} +(-1.27298 - 12.1116i) q^{80} +(-0.906587 + 8.62560i) q^{81} +(18.6249 + 3.95885i) q^{82} +(-12.0893 + 5.38249i) q^{83} +(-0.167992 - 0.186574i) q^{84} +(-4.32436 + 13.3090i) q^{85} +(-3.64729 + 4.05072i) q^{86} +(0.344501 + 0.596693i) q^{87} +(3.63214 - 6.29106i) q^{88} +(-0.272533 - 0.838769i) q^{89} +(-12.0367 - 5.35907i) q^{90} +(-1.04992 - 0.762810i) q^{91} +7.47693 q^{92} -10.1563 q^{94} +(-9.30387 - 6.75966i) q^{95} +(1.08081 + 0.481206i) q^{96} +(2.67052 + 8.21902i) q^{97} +(-5.31146 + 9.19972i) q^{98} +(-7.95645 - 13.7810i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 32 q^{4} - 32 q^{5} + 8 q^{7} - 24 q^{8} + 20 q^{9} + 20 q^{10} + 28 q^{14} + 32 q^{16} - 8 q^{18} + 16 q^{19} - 20 q^{20} - 48 q^{25} - 20 q^{28} + 192 q^{32} + 80 q^{33} - 112 q^{35} - 160 q^{36}+ \cdots - 16 q^{98}+O(q^{100}) \) 96 * q - 32 * q^4 - 32 * q^5 + 8 * q^7 - 24 * q^8 + 20 * q^9 + 20 * q^10 + 28 * q^14 + 32 * q^16 - 8 * q^18 + 16 * q^19 - 20 * q^20 - 48 * q^25 - 20 * q^28 + 192 * q^32 + 80 * q^33 - 112 * q^35 - 160 * q^36 + 36 * q^38 + 32 * q^39 - 16 * q^40 + 32 * q^41 + 16 * q^45 - 96 * q^47 - 20 * q^49 + 20 * q^50 + 16 * q^51 + 32 * q^56 + 40 * q^59 - 64 * q^63 + 56 * q^64 - 48 * q^66 - 64 * q^67 + 24 * q^69 - 24 * q^70 + 72 * q^71 + 36 * q^72 + 36 * q^76 + 208 * q^78 - 20 * q^80 - 36 * q^81 - 4 * q^82 - 256 * q^87 - 44 * q^90 + 128 * q^94 - 80 * q^95 + 16 * q^97 - 16 * q^98

Introduction

L-functions

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