LMFDB - Embedded newform 930.2.j.h.497.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [930,2,Mod(497,930)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("930.497"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(930, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,-4,0,0,8,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			497.13
Character	$\chi$	$=$	930.497
Dual form			930.2.j.h.683.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 0.707107i) q^{2} +(-0.860137 + 1.50338i) q^{3} -1.00000i q^{4} +(-2.19538 + 0.424609i) q^{5} +(0.454844 + 1.67126i) q^{6} +(-0.358790 - 0.358790i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.52033 - 2.58623i) q^{9} +(-1.25213 + 1.85261i) q^{10} +1.95505i q^{11} +(1.50338 + 0.860137i) q^{12} +(1.74122 - 1.74122i) q^{13} -0.507406 q^{14} +(1.24998 - 3.66573i) q^{15} -1.00000 q^{16} +(3.65749 - 3.65749i) q^{17} +(-2.90378 - 0.753709i) q^{18} -3.69824i q^{19} +(0.424609 + 2.19538i) q^{20} +(0.848008 - 0.230791i) q^{21} +(1.38243 + 1.38243i) q^{22} +(6.27796 + 6.27796i) q^{23} +(1.67126 - 0.454844i) q^{24} +(4.63941 - 1.86436i) q^{25} -2.46246i q^{26} +(5.19579 - 0.0611210i) q^{27} +(-0.358790 + 0.358790i) q^{28} +8.51841 q^{29} +(-1.70819 - 3.47593i) q^{30} -1.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.93919 - 1.68161i) q^{33} -5.17247i q^{34} +(0.940028 + 0.635336i) q^{35} +(-2.58623 + 1.52033i) q^{36} +(-1.92806 - 1.92806i) q^{37} +(-2.61505 - 2.61505i) q^{38} +(1.12003 + 4.11541i) q^{39} +(1.85261 + 1.25213i) q^{40} +9.77147i q^{41} +(0.436439 - 0.762826i) q^{42} +(-1.51772 + 1.51772i) q^{43} +1.95505 q^{44} +(4.43584 + 5.03223i) q^{45} +8.87838 q^{46} +(4.14558 - 4.14558i) q^{47} +(0.860137 - 1.50338i) q^{48} -6.74254i q^{49} +(1.96226 - 4.59886i) q^{50} +(2.35267 + 8.64455i) q^{51} +(-1.74122 - 1.74122i) q^{52} +(-9.34225 - 9.34225i) q^{53} +(3.63076 - 3.71720i) q^{54} +(-0.830133 - 4.29208i) q^{55} +0.507406i q^{56} +(5.55987 + 3.18099i) q^{57} +(6.02342 - 6.02342i) q^{58} +1.87779 q^{59} +(-3.66573 - 1.24998i) q^{60} +10.5206 q^{61} +(-0.707107 + 0.707107i) q^{62} +(-0.382436 + 1.47339i) q^{63} +1.00000i q^{64} +(-3.08330 + 4.56198i) q^{65} +(-3.26740 + 0.889243i) q^{66} +(-7.86226 - 7.86226i) q^{67} +(-3.65749 - 3.65749i) q^{68} +(-14.8381 + 4.03828i) q^{69} +(1.11395 - 0.215449i) q^{70} +2.88620i q^{71} +(-0.753709 + 2.90378i) q^{72} +(9.70365 - 9.70365i) q^{73} -2.72669 q^{74} +(-1.18768 + 8.57843i) q^{75} -3.69824 q^{76} +(0.701453 - 0.701453i) q^{77} +(3.70202 + 2.11805i) q^{78} -1.35078i q^{79} +(2.19538 - 0.424609i) q^{80} +(-4.37721 + 7.86385i) q^{81} +(6.90947 + 6.90947i) q^{82} +(2.46289 + 2.46289i) q^{83} +(-0.230791 - 0.848008i) q^{84} +(-6.47658 + 9.58259i) q^{85} +2.14639i q^{86} +(-7.32700 + 12.8064i) q^{87} +(1.38243 - 1.38243i) q^{88} -0.192825 q^{89} +(6.69494 + 0.421709i) q^{90} -1.24946 q^{91} +(6.27796 - 6.27796i) q^{92} +(0.860137 - 1.50338i) q^{93} -5.86273i q^{94} +(1.57031 + 8.11905i) q^{95} +(-0.454844 - 1.67126i) q^{96} +(1.01182 + 1.01182i) q^{97} +(-4.76770 - 4.76770i) q^{98} +(5.05622 - 2.97232i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7} + 4 q^{12} + 24 q^{13} - 12 q^{15} - 40 q^{16} - 56 q^{21} + 16 q^{22} - 48 q^{25} + 8 q^{27} - 8 q^{28} + 4 q^{30} - 40 q^{31} - 20 q^{33} - 8 q^{37} - 8 q^{40} + 12 q^{42}+ \cdots + 24 q^{97}+O(q^{100}) $ 40 * q - 4 * q^3 + 8 * q^6 - 8 * q^7 + 4 * q^12 + 24 * q^13 - 12 * q^15 - 40 * q^16 - 56 * q^21 + 16 * q^22 - 48 * q^25 + 8 * q^27 - 8 * q^28 + 4 * q^30 - 40 * q^31 - 20 * q^33 - 8 * q^37 - 8 * q^40 + 12 * q^42 - 16 * q^43 + 76 * q^45 - 8 * q^46 + 4 * q^48 + 16 * q^51 - 24 * q^52 - 48 * q^55 + 56 * q^57 - 56 * q^58 + 12 * q^60 + 128 * q^61 - 24 * q^63 + 16 * q^66 + 8 * q^67 + 32 * q^70 + 248 * q^73 - 8 * q^75 + 56 * q^76 + 8 * q^78 + 40 * q^81 - 8 * q^82 - 48 * q^85 + 12 * q^87 + 16 * q^88 + 16 * q^90 - 192 * q^91 + 4 * q^93 - 8 * q^96 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−0.860137	+	1.50338i	−0.496600	+	0.867979i
$3$	−0.860137	+	1.50338i	−0.496600	+	0.867979i
$4$		−	1.00000i		−	0.500000i
$5$	−2.19538	+	0.424609i	−0.981805	+	0.189891i
$5$	−2.19538	+	0.424609i	−0.981805	+	0.189891i
$6$	0.454844	+	1.67126i	0.185689	+	0.682290i
$7$	−0.358790	−	0.358790i	−0.135610	−	0.135610i	0.636043	−	0.771653i	$-0.280570\pi$
$7$	−0.358790	−	0.358790i	−0.135610	−	0.135610i	−0.771653	+	0.636043i	$0.780570\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−1.52033	−	2.58623i	−0.506776	−	0.862078i
$10$	−1.25213	+	1.85261i	−0.395957	+	0.585848i
$11$			1.95505i			0.589470i	0.955579	+	0.294735i	$0.0952313\pi$
$11$			1.95505i			0.589470i	−0.955579	+	0.294735i	$0.904769\pi$
$12$	1.50338	+	0.860137i	0.433990	+	0.248300i
$13$	1.74122	−	1.74122i	0.482927	−	0.482927i	−0.423138	−	0.906065i	$-0.639071\pi$
$13$	1.74122	−	1.74122i	0.482927	−	0.482927i	0.906065	+	0.423138i	$0.139071\pi$
$14$	−0.507406			−0.135610
$15$	1.24998	−	3.66573i	0.322743	−	0.946487i
$16$	−1.00000			−0.250000
$17$	3.65749	−	3.65749i	0.887071	−	0.887071i	−0.107170	−	0.994241i	$-0.534179\pi$
$17$	3.65749	−	3.65749i	0.887071	−	0.887071i	0.994241	+	0.107170i	$0.0341789\pi$
$18$	−2.90378	−	0.753709i	−0.684427	−	0.177651i
$19$		−	3.69824i		−	0.848434i	−0.905561	−	0.424217i	$-0.860549\pi$
$19$		−	3.69824i		−	0.848434i	0.905561	−	0.424217i	$-0.139451\pi$
$20$	0.424609	+	2.19538i	0.0949456	+	0.490903i
$21$	0.848008	−	0.230791i	0.185051	−	0.0503626i
$22$	1.38243	+	1.38243i	0.294735	+	0.294735i
$23$	6.27796	+	6.27796i	1.30905	+	1.30905i	0.922104	+	0.386942i	$0.126469\pi$
$23$	6.27796	+	6.27796i	1.30905	+	1.30905i	0.386942	+	0.922104i	$0.373531\pi$
$24$	1.67126	−	0.454844i	0.341145	−	0.0928447i
$25$	4.63941	−	1.86436i	0.927883	−	0.372872i
$26$		−	2.46246i		−	0.482927i
$27$	5.19579	−	0.0611210i	0.999931	−	0.0117627i
$28$	−0.358790	+	0.358790i	−0.0678050	+	0.0678050i
$29$	8.51841			1.58183			0.790914	−	0.611927i	$-0.209605\pi$
$29$	8.51841			1.58183			0.790914	+	0.611927i	$0.209605\pi$
$30$	−1.70819	−	3.47593i	−0.311872	−	0.634615i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−2.93919	−	1.68161i	−0.511647	−	0.292731i
$34$		−	5.17247i		−	0.887071i
$35$	0.940028	+	0.635336i	0.158894	+	0.107391i
$36$	−2.58623	+	1.52033i	−0.431039	+	0.253388i
$37$	−1.92806	−	1.92806i	−0.316972	−	0.316972i	0.530631	−	0.847603i	$-0.321955\pi$
$37$	−1.92806	−	1.92806i	−0.316972	−	0.316972i	−0.847603	+	0.530631i	$0.821955\pi$
$38$	−2.61505	−	2.61505i	−0.424217	−	0.424217i
$39$	1.12003	+	4.11541i	0.179349	+	0.658993i
$40$	1.85261	+	1.25213i	0.292924	+	0.197979i
$41$			9.77147i			1.52605i	0.646371	+	0.763024i	$0.276286\pi$
$41$			9.77147i			1.52605i	−0.646371	+	0.763024i	$0.723714\pi$
$42$	0.436439	−	0.762826i	0.0673440	−	0.117707i
$43$	−1.51772	+	1.51772i	−0.231451	+	0.231451i	−0.813298	−	0.581847i	$-0.802330\pi$
$43$	−1.51772	+	1.51772i	−0.231451	+	0.231451i	0.581847	+	0.813298i	$0.302330\pi$
$44$	1.95505			0.294735
$45$	4.43584	+	5.03223i	0.661256	+	0.750160i
$46$	8.87838			1.30905
$47$	4.14558	−	4.14558i	0.604695	−	0.604695i	−0.336860	−	0.941555i	$-0.609365\pi$
$47$	4.14558	−	4.14558i	0.604695	−	0.604695i	0.941555	+	0.336860i	$0.109365\pi$
$48$	0.860137	−	1.50338i	0.124150	−	0.216995i
$49$		−	6.74254i		−	0.963220i
$50$	1.96226	−	4.59886i	0.277505	−	0.650377i
$51$	2.35267	+	8.64455i	0.329439	+	1.21048i
$52$	−1.74122	−	1.74122i	−0.241464	−	0.241464i
$53$	−9.34225	−	9.34225i	−1.28326	−	1.28326i	−0.938804	−	0.344452i	$-0.888065\pi$
$53$	−9.34225	−	9.34225i	−1.28326	−	1.28326i	−0.344452	−	0.938804i	$-0.611935\pi$
$54$	3.63076	−	3.71720i	0.494084	−	0.505847i
$55$	−0.830133	−	4.29208i	−0.111935	−	0.578744i
$56$			0.507406i			0.0678050i
$57$	5.55987	+	3.18099i	0.736423	+	0.421333i
$58$	6.02342	−	6.02342i	0.790914	−	0.790914i
$59$	1.87779			0.244468			0.122234	−	0.992501i	$-0.460994\pi$
$59$	1.87779			0.244468			0.122234	+	0.992501i	$0.460994\pi$
$60$	−3.66573	−	1.24998i	−0.473243	−	0.161372i
$61$	10.5206			1.34702			0.673510	−	0.739178i	$-0.264786\pi$
$61$	10.5206			1.34702			0.673510	+	0.739178i	$0.264786\pi$
$62$	−0.707107	+	0.707107i	−0.0898027	+	0.0898027i
$63$	−0.382436	+	1.47339i	−0.0481825	+	0.185630i
$64$			1.00000i			0.125000i
$65$	−3.08330	+	4.56198i	−0.382437	+	0.565844i
$66$	−3.26740	+	0.889243i	−0.402189	+	0.109458i
$67$	−7.86226	−	7.86226i	−0.960528	−	0.960528i	0.0387218	−	0.999250i	$-0.487671\pi$
$67$	−7.86226	−	7.86226i	−0.960528	−	0.960528i	−0.999250	+	0.0387218i	$0.987671\pi$
$68$	−3.65749	−	3.65749i	−0.443535	−	0.443535i
$69$	−14.8381	+	4.03828i	−1.78630	+	0.486152i
$70$	1.11395	−	0.215449i	0.133143	−	0.0257511i
$71$			2.88620i			0.342529i	0.985225	+	0.171264i	$0.0547852\pi$
$71$			2.88620i			0.342529i	−0.985225	+	0.171264i	$0.945215\pi$
$72$	−0.753709	+	2.90378i	−0.0888255	+	0.342213i
$73$	9.70365	−	9.70365i	1.13573	−	1.13573i	0.146518	−	0.989208i	$-0.453193\pi$
$73$	9.70365	−	9.70365i	1.13573	−	1.13573i	0.989208	−	0.146518i	$-0.0468067\pi$
$74$	−2.72669			−0.316972
$75$	−1.18768	+	8.57843i	−0.137142	+	0.990551i
$76$	−3.69824			−0.424217
$77$	0.701453	−	0.701453i	0.0799379	−	0.0799379i
$78$	3.70202	+	2.11805i	0.419171	+	0.239822i
$79$		−	1.35078i		−	0.151974i	−0.997109	−	0.0759872i	$-0.975789\pi$
$79$		−	1.35078i		−	0.151974i	0.997109	−	0.0759872i	$-0.0242108\pi$
$80$	2.19538	−	0.424609i	0.245451	−	0.0474728i
$81$	−4.37721	+	7.86385i	−0.486356	+	0.873761i
$82$	6.90947	+	6.90947i	0.763024	+	0.763024i
$83$	2.46289	+	2.46289i	0.270337	+	0.270337i	0.829236	−	0.558899i	$-0.188776\pi$
$83$	2.46289	+	2.46289i	0.270337	+	0.270337i	−0.558899	+	0.829236i	$0.688776\pi$
$84$	−0.230791	−	0.848008i	−0.0251813	−	0.0925253i
$85$	−6.47658	+	9.58259i	−0.702484	+	1.03938i
$86$			2.14639i			0.231451i
$87$	−7.32700	+	12.8064i	−0.785537	+	1.37299i
$88$	1.38243	−	1.38243i	0.147367	−	0.147367i
$89$	−0.192825			−0.0204395			−0.0102197	−	0.999948i	$-0.503253\pi$
$89$	−0.192825			−0.0204395			−0.0102197	+	0.999948i	$0.503253\pi$
$90$	6.69494	+	0.421709i	0.705708	+	0.0444520i
$91$	−1.24946			−0.130979
$92$	6.27796	−	6.27796i	0.654523	−	0.654523i
$93$	0.860137	−	1.50338i	0.0891921	−	0.155894i
$94$		−	5.86273i		−	0.604695i
$95$	1.57031	+	8.11905i	0.161110	+	0.832997i
$96$	−0.454844	−	1.67126i	−0.0464223	−	0.170572i
$97$	1.01182	+	1.01182i	0.102735	+	0.102735i	0.756606	−	0.653871i	$-0.226856\pi$
$97$	1.01182	+	1.01182i	0.102735	+	0.102735i	−0.653871	+	0.756606i	$0.726856\pi$
$98$	−4.76770	−	4.76770i	−0.481610	−	0.481610i
$99$	5.05622	−	2.97232i	0.508169	−	0.298729i
$100$	−1.86436	−	4.63941i	−0.186436	−	0.463941i
$101$		−	0.318549i		−	0.0316969i	−0.999874	−	0.0158484i	$-0.994955\pi$
$101$		−	0.318549i		−	0.0316969i	0.999874	−	0.0158484i	$-0.00504492\pi$
$102$	7.77620	+	4.44903i	0.769959	+	0.440520i
$103$	11.0476	−	11.0476i	1.08856	−	1.08856i	0.0928796	−	0.995677i	$-0.470393\pi$
$103$	11.0476	−	11.0476i	1.08856	−	1.08856i	0.995677	−	0.0928796i	$-0.0296072\pi$
$104$	−2.46246			−0.241464
$105$	−1.76371	+	0.866746i	−0.172120	+	0.0845858i
$106$	−13.2119			−1.28326
$107$	−1.88705	+	1.88705i	−0.182428	+	0.182428i	−0.792413	−	0.609985i	$-0.791176\pi$
$107$	−1.88705	+	1.88705i	−0.182428	+	0.182428i	0.609985	+	0.792413i	$0.291176\pi$
$108$	−0.0611210	−	5.19579i	−0.00588137	−	0.499965i
$109$		−	0.0819468i		−	0.00784908i	−0.999992	−	0.00392454i	$-0.998751\pi$
$109$		−	0.0819468i		−	0.00784908i	0.999992	−	0.00392454i	$-0.00124922\pi$
$110$	−3.62195	−	2.44797i	−0.345340	−	0.233405i
$111$	4.55702	−	1.24022i	0.432533	−	0.117717i
$112$	0.358790	+	0.358790i	0.0339025	+	0.0339025i
$113$	−9.29128	−	9.29128i	−0.874050	−	0.874050i	0.118861	−	0.992911i	$-0.462076\pi$
$113$	−9.29128	−	9.29128i	−0.874050	−	0.874050i	−0.992911	+	0.118861i	$0.962076\pi$
$114$	6.18072	−	1.68212i	0.578878	−	0.157545i
$115$	−16.4482	−	11.1169i	−1.53380	−	1.03665i
$116$		−	8.51841i		−	0.790914i
$117$	−7.15042	−	1.85598i	−0.661057	−	0.171585i
$118$	1.32780	−	1.32780i	0.122234	−	0.122234i
$119$	−2.62454			−0.240591
$120$	−3.47593	+	1.70819i	−0.317307	+	0.155936i
$121$	7.17778			0.652525
$122$	7.43916	−	7.43916i	0.673510	−	0.673510i
$123$	−14.6903	−	8.40481i	−1.32458	−	0.757836i
$124$			1.00000i			0.0898027i
$125$	−9.39366	+	6.06293i	−0.840195	+	0.542284i
$126$	0.771423	+	1.31227i	0.0687238	+	0.116906i
$127$	5.42117	+	5.42117i	0.481051	+	0.481051i	0.905467	−	0.424416i	$-0.139521\pi$
$127$	5.42117	+	5.42117i	0.481051	+	0.481051i	−0.424416	+	0.905467i	$0.639521\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−0.976271	−	3.58717i	−0.0859559	−	0.315833i
$130$	1.04558	+	5.40603i	0.0917036	+	0.474141i
$131$			15.0074i			1.31120i	0.755107	+	0.655601i	$0.227585\pi$
$131$			15.0074i			1.31120i	−0.755107	+	0.655601i	$0.772415\pi$
$132$	−1.68161	+	2.93919i	−0.146365	+	0.255824i
$133$	−1.32689	+	1.32689i	−0.115056	+	0.115056i
$134$	−11.1189			−0.960528
$135$	−11.3808	+	2.34037i	−0.979504	+	0.201427i
$136$	−5.17247			−0.443535
$137$	2.32290	−	2.32290i	0.198459	−	0.198459i	−0.600880	−	0.799339i	$-0.705183\pi$
$137$	2.32290	−	2.32290i	0.198459	−	0.198459i	0.799339	+	0.600880i	$0.205183\pi$
$138$	−7.63663	+	13.3476i	−0.650073	+	1.13622i
$139$			9.23533i			0.783331i	0.920108	+	0.391665i	$0.128101\pi$
$139$			9.23533i			0.783331i	−0.920108	+	0.391665i	$0.871899\pi$
$140$	0.635336	−	0.940028i	0.0536957	−	0.0794468i
$141$	2.66663	+	9.79816i	0.224571	+	0.825154i
$142$	2.04085	+	2.04085i	0.171264	+	0.171264i
$143$	3.40417	+	3.40417i	0.284671	+	0.284671i
$144$	1.52033	+	2.58623i	0.126694	+	0.215519i
$145$	−18.7012	+	3.61700i	−1.55305	+	0.300375i
$146$		−	13.7230i		−	1.13573i
$147$	10.1366	+	5.79951i	0.836055	+	0.478335i
$148$	−1.92806	+	1.92806i	−0.158486	+	0.158486i
$149$	−0.823443			−0.0674591			−0.0337295	−	0.999431i	$-0.510738\pi$
$149$	−0.823443			−0.0674591			−0.0337295	+	0.999431i	$0.510738\pi$
$150$	5.22605	+	6.90568i	0.426705	+	0.563847i
$151$	−11.6623			−0.949068			−0.474534	−	0.880237i	$-0.657383\pi$
$151$	−11.6623			−0.949068			−0.474534	+	0.880237i	$0.657383\pi$
$152$	−2.61505	+	2.61505i	−0.212108	+	0.212108i
$153$	−15.0197	−	3.89854i	−1.21427	−	0.315178i
$154$		−	0.992004i		−	0.0799379i
$155$	2.19538	−	0.424609i	0.176337	−	0.0341055i
$156$	4.11541	−	1.12003i	0.329496	−	0.0896745i
$157$	−14.8439	−	14.8439i	−1.18467	−	1.18467i	−0.978520	−	0.206152i	$-0.933906\pi$
$157$	−14.8439	−	14.8439i	−1.18467	−	1.18467i	−0.206152	−	0.978520i	$-0.566094\pi$
$158$	−0.955144	−	0.955144i	−0.0759872	−	0.0759872i
$159$	22.0806	−	6.00937i	1.75111	−	0.476574i
$160$	1.25213	−	1.85261i	0.0989893	−	0.146462i
$161$		−	4.50494i		−	0.355039i
$162$	2.46543	+	8.65573i	0.193702	+	0.680058i
$163$	−13.7523	+	13.7523i	−1.07716	+	1.07716i	−0.0803969	+	0.996763i	$0.525619\pi$
$163$	−13.7523	+	13.7523i	−1.07716	+	1.07716i	−0.996763	+	0.0803969i	$0.974381\pi$
$164$	9.77147			0.763024
$165$	7.16668	+	2.44377i	0.557925	+	0.190247i
$166$	3.48305			0.270337
$167$	17.7715	−	17.7715i	1.37520	−	1.37520i	0.522652	−	0.852546i	$-0.324943\pi$
$167$	17.7715	−	17.7715i	1.37520	−	1.37520i	0.852546	−	0.522652i	$-0.175057\pi$
$168$	−0.762826	−	0.436439i	−0.0588533	−	0.0336720i
$169$			6.93631i			0.533562i
$170$	2.19628	+	11.3555i	0.168447	+	0.870931i
$171$	−9.56450	+	5.62253i	−0.731416	+	0.429966i
$172$	1.51772	+	1.51772i	0.115725	+	0.115725i
$173$	2.20529	+	2.20529i	0.167665	+	0.167665i	0.785952	−	0.618287i	$-0.212173\pi$
$173$	2.20529	+	2.20529i	0.167665	+	0.167665i	−0.618287	+	0.785952i	$0.712173\pi$
$174$	3.87455	+	14.2365i	0.293729	+	1.07927i
$175$	−2.33349	−	0.995662i	−0.176395	−	0.0752649i
$176$		−	1.95505i		−	0.147367i
$177$	−1.61516	+	2.82304i	−0.121403	+	0.212193i
$178$	−0.136348	+	0.136348i	−0.0102197	+	0.0102197i
$179$	3.73765			0.279365			0.139682	−	0.990196i	$-0.455392\pi$
$179$	3.73765			0.279365			0.139682	+	0.990196i	$0.455392\pi$
$180$	5.03223	−	4.43584i	0.375080	−	0.330628i
$181$	−17.5399			−1.30373			−0.651863	−	0.758336i	$-0.726012\pi$
$181$	−17.5399			−1.30373			−0.651863	+	0.758336i	$0.726012\pi$
$182$	−0.883505	+	0.883505i	−0.0654897	+	0.0654897i
$183$	−9.04913	+	15.8164i	−0.668931	+	1.16919i
$184$		−	8.87838i		−	0.654523i
$185$	5.05151	+	3.41416i	0.371394	+	0.251014i
$186$	−0.454844	−	1.67126i	−0.0333508	−	0.122543i
$187$	7.15057	+	7.15057i	0.522901	+	0.522901i
$188$	−4.14558	−	4.14558i	−0.302347	−	0.302347i
$189$	−1.88613	−	1.84227i	−0.137196	−	0.134005i
$190$	6.85141	+	4.63066i	0.497053	+	0.335943i
$191$		−	2.42501i		−	0.175468i	−0.996144	−	0.0877339i	$-0.972037\pi$
$191$		−	2.42501i		−	0.175468i	0.996144	−	0.0877339i	$-0.0279625\pi$
$192$	−1.50338	−	0.860137i	−0.108497	−	0.0620751i
$193$	−8.58471	+	8.58471i	−0.617941	+	0.617941i	−0.945003	−	0.327062i	$-0.893941\pi$
$193$	−8.58471	+	8.58471i	−0.617941	+	0.617941i	0.327062	+	0.945003i	$0.393941\pi$
$194$	1.43093			0.102735
$195$	−4.20634	−	8.55932i	−0.301223	−	0.612946i
$196$	−6.74254			−0.481610
$197$	−17.2273	+	17.2273i	−1.22740	+	1.22740i	−0.262452	+	0.964945i	$0.584531\pi$
$197$	−17.2273	+	17.2273i	−1.22740	+	1.22740i	−0.964945	+	0.262452i	$0.915469\pi$
$198$	1.47354	−	5.67703i	0.104720	−	0.403449i
$199$			13.5961i			0.963801i	0.876226	+	0.481900i	$0.160053\pi$
$199$			13.5961i			0.963801i	−0.876226	+	0.481900i	$0.839947\pi$
$200$	−4.59886	−	1.96226i	−0.325189	−	0.138753i
$201$	18.5826	−	5.05738i	1.31072	−	0.356720i
$202$	−0.225248	−	0.225248i	−0.0158484	−	0.0158484i
$203$	−3.05632	−	3.05632i	−0.214512	−	0.214512i
$204$	8.64455	−	2.35267i	0.605239	−	0.164720i
$205$	−4.14906	−	21.4521i	−0.289783	−	1.49828i
$206$		−	15.6237i		−	1.08856i
$207$	6.69172	−	25.7808i	0.465107	−	1.79189i
$208$	−1.74122	+	1.74122i	−0.120732	+	0.120732i
$209$	7.23024			0.500126
$210$	−0.634247	+	1.86001i	−0.0437672	+	0.128353i
$211$	26.5004			1.82436			0.912182	−	0.409785i	$-0.134396\pi$
$211$	26.5004			1.82436			0.912182	+	0.409785i	$0.134396\pi$
$212$	−9.34225	+	9.34225i	−0.641628	+	0.641628i
$213$	−4.33906	−	2.48253i	−0.297308	−	0.170100i
$214$			2.66870i			0.182428i
$215$	2.68755	−	3.97643i	0.183289	−	0.271190i
$216$	−3.71720	−	3.63076i	−0.252923	−	0.247042i
$217$	0.358790	+	0.358790i	0.0243563	+	0.0243563i
$218$	−0.0579452	−	0.0579452i	−0.00392454	−	0.00392454i
$219$	6.24184	+	22.9348i	0.421785	+	1.54979i
$220$	−4.29208	+	0.830133i	−0.289372	+	0.0559675i
$221$		−	12.7370i		−	0.856781i
$222$	2.34533	−	4.09927i	0.157408	−	0.275125i
$223$	19.1668	−	19.1668i	1.28350	−	1.28350i	0.344842	−	0.938661i	$-0.387933\pi$
$223$	19.1668	−	19.1668i	1.28350	−	1.28350i	0.938661	−	0.344842i	$-0.112067\pi$
$224$	0.507406			0.0339025
$225$	−11.8751	−	9.16417i	−0.791673	−	0.610944i
$226$	−13.1399			−0.874050
$227$	1.96350	−	1.96350i	0.130322	−	0.130322i	−0.638937	−	0.769259i	$-0.720626\pi$
$227$	1.96350	−	1.96350i	0.130322	−	0.130322i	0.769259	+	0.638937i	$0.220626\pi$
$228$	3.18099	−	5.55987i	0.210666	−	0.368211i
$229$			1.32660i			0.0876644i	0.999039	+	0.0438322i	$0.0139567\pi$
$229$			1.32660i			0.0876644i	−0.999039	+	0.0438322i	$0.986043\pi$
$230$	−19.4914	+	3.76984i	−1.28523	+	0.248576i
$231$	0.451207	+	1.65790i	0.0296873	+	0.109082i
$232$	−6.02342	−	6.02342i	−0.395457	−	0.395457i
$233$	7.07940	+	7.07940i	0.463787	+	0.463787i	0.899894	−	0.436108i	$-0.143643\pi$
$233$	7.07940	+	7.07940i	0.463787	+	0.463787i	−0.436108	+	0.899894i	$0.643643\pi$
$234$	−6.36849	+	3.74374i	−0.416321	+	0.244736i
$235$	−7.34088	+	10.8614i	−0.478866	+	0.708519i
$236$		−	1.87779i		−	0.122234i
$237$	2.03074	+	1.16185i	0.131911	+	0.0754705i
$238$	−1.85583	+	1.85583i	−0.120296	+	0.120296i
$239$	−9.69880			−0.627363			−0.313682	−	0.949528i	$-0.601562\pi$
$239$	−9.69880			−0.627363			−0.313682	+	0.949528i	$0.601562\pi$
$240$	−1.24998	+	3.66573i	−0.0806858	+	0.236622i
$241$	1.35150			0.0870581			0.0435290	−	0.999052i	$-0.486140\pi$
$241$	1.35150			0.0870581			0.0435290	+	0.999052i	$0.486140\pi$
$242$	5.07546	−	5.07546i	0.326263	−	0.326263i
$243$	−8.05738	−	13.3446i	−0.516881	−	0.856057i
$244$		−	10.5206i		−	0.673510i
$245$	2.86295	+	14.8025i	0.182907	+	0.945694i
$246$	−16.3307	+	4.44450i	−1.04121	+	0.283371i
$247$	−6.43944	−	6.43944i	−0.409732	−	0.409732i
$248$	0.707107	+	0.707107i	0.0449013	+	0.0449013i
$249$	−5.82109	+	1.58425i	−0.368897	+	0.100398i
$250$	−2.35519	+	10.9295i	−0.148955	+	0.691240i
$251$			20.3533i			1.28469i	0.766417	+	0.642343i	$0.222038\pi$
$251$			20.3533i			1.28469i	−0.766417	+	0.642343i	$0.777962\pi$
$252$	1.47339	+	0.382436i	0.0928151	+	0.0240912i
$253$	−12.2737	+	12.2737i	−0.771643	+	0.771643i
$254$	7.66669			0.481051
$255$	−8.83556	−	17.9791i	−0.553304	−	1.12590i
$256$	1.00000			0.0625000
$257$	17.9170	−	17.9170i	1.11763	−	1.11763i	0.125546	−	0.992088i	$-0.459932\pi$
$257$	17.9170	−	17.9170i	1.11763	−	1.11763i	0.992088	−	0.125546i	$-0.0400682\pi$
$258$	−3.22684	−	1.84619i	−0.200894	−	0.114939i
$259$			1.38354i			0.0859690i
$260$	4.56198	+	3.08330i	0.282922	+	0.191218i
$261$	−12.9508	−	22.0306i	−0.801633	−	1.36366i
$262$	10.6118	+	10.6118i	0.655601	+	0.655601i
$263$	14.2853	+	14.2853i	0.880869	+	0.880869i	0.993623	−	0.112754i	$-0.0359672\pi$
$263$	14.2853	+	14.2853i	0.880869	+	0.880869i	−0.112754	+	0.993623i	$0.535967\pi$
$264$	0.889243	+	3.26740i	0.0547291	+	0.201095i
$265$	24.4766	+	16.5430i	1.50359	+	1.01623i
$266$			1.87651i			0.115056i
$267$	0.165856	−	0.289891i	0.0101502	−	0.0177410i
$268$	−7.86226	+	7.86226i	−0.480264	+	0.480264i
$269$	−2.28146			−0.139103			−0.0695514	−	0.997578i	$-0.522157\pi$
$269$	−2.28146			−0.139103			−0.0695514	+	0.997578i	$0.522157\pi$
$270$	−6.39255	+	9.70233i	−0.389038	+	0.590465i
$271$	16.6154			1.00931			0.504657	−	0.863320i	$-0.331619\pi$
$271$	16.6154			1.00931			0.504657	+	0.863320i	$0.331619\pi$
$272$	−3.65749	+	3.65749i	−0.221768	+	0.221768i
$273$	1.07471	−	1.87843i	0.0650445	−	0.113687i
$274$		−	3.28508i		−	0.198459i
$275$	3.64492	+	9.07028i	0.219797	+	0.546959i
$276$	4.03828	+	14.8381i	0.243076	+	0.893149i
$277$	−8.63825	−	8.63825i	−0.519022	−	0.519022i	0.398253	−	0.917275i	$-0.369616\pi$
$277$	−8.63825	−	8.63825i	−0.519022	−	0.519022i	−0.917275	+	0.398253i	$0.869616\pi$
$278$	6.53037	+	6.53037i	0.391665	+	0.391665i
$279$	1.52033	+	2.58623i	0.0910196	+	0.154834i
$280$	−0.215449	−	1.11395i	−0.0128756	−	0.0665713i
$281$		−	1.91141i		−	0.114025i	−0.998373	−	0.0570126i	$-0.981842\pi$
$281$		−	1.91141i		−	0.114025i	0.998373	−	0.0570126i	$-0.0181575\pi$
$282$	8.81394	+	5.04276i	0.524862	+	0.300292i
$283$	18.8289	−	18.8289i	1.11926	−	1.11926i	0.127413	−	0.991850i	$-0.459333\pi$
$283$	18.8289	−	18.8289i	1.11926	−	1.11926i	0.991850	−	0.127413i	$-0.0406672\pi$
$284$	2.88620			0.171264
$285$	−13.5567	−	4.62272i	−0.803031	−	0.273826i
$286$	4.81422			0.284671
$287$	3.50591	−	3.50591i	0.206947	−	0.206947i
$288$	2.90378	+	0.753709i	0.171107	+	0.0444127i
$289$		−	9.75441i		−	0.573789i
$290$	−10.6661	+	15.7813i	−0.626336	+	0.926711i
$291$	−2.39146	+	0.650852i	−0.140190	+	0.0381536i
$292$	−9.70365	−	9.70365i	−0.567863	−	0.567863i
$293$	−13.7308	−	13.7308i	−0.802162	−	0.802162i	0.181271	−	0.983433i	$-0.441979\pi$
$293$	−13.7308	−	13.7308i	−0.802162	−	0.802162i	−0.983433	+	0.181271i	$0.941979\pi$
$294$	11.2685	−	3.06681i	0.657195	−	0.178860i
$295$	−4.12247	+	0.797328i	−0.240019	+	0.0464222i
$296$			2.72669i			0.158486i
$297$	0.119495	+	10.1580i	0.00693377	+	0.589429i
$298$	−0.582262	+	0.582262i	−0.0337295	+	0.0337295i
$299$	21.8626			1.26435
$300$	8.57843	+	1.18768i	0.495276	+	0.0685709i
$301$	1.08909			0.0627741
$302$	−8.24652	+	8.24652i	−0.474534	+	0.474534i
$303$	0.478902	+	0.273996i	0.0275122	+	0.0157407i
$304$			3.69824i			0.212108i
$305$	−23.0967	+	4.46713i	−1.32251	+	0.255787i
$306$	−13.3772	+	7.86385i	−0.764724	+	0.449546i
$307$	19.1173	+	19.1173i	1.09108	+	1.09108i	0.995413	+	0.0956661i	$0.0304981\pi$
$307$	19.1173	+	19.1173i	1.09108	+	1.09108i	0.0956661	+	0.995413i	$0.469502\pi$
$308$	−0.701453	−	0.701453i	−0.0399690	−	0.0399690i
$309$	7.10636	+	26.1113i	0.404267	+	1.48542i
$310$	1.25213	−	1.85261i	0.0711160	−	0.105221i
$311$		−	6.25550i		−	0.354717i	−0.984146	−	0.177359i	$-0.943245\pi$
$311$		−	6.25550i		−	0.354717i	0.984146	−	0.177359i	$-0.0567552\pi$
$312$	2.11805	−	3.70202i	0.119911	−	0.209585i
$313$	−18.9730	+	18.9730i	−1.07242	+	1.07242i	−0.0752511	+	0.997165i	$0.523976\pi$
$313$	−18.9730	+	18.9730i	−1.07242	+	1.07242i	−0.997165	+	0.0752511i	$0.976024\pi$
$314$	−20.9924			−1.18467
$315$	0.213978	−	3.39705i	0.0120563	−	0.191402i
$316$	−1.35078			−0.0759872
$317$	−10.3258	+	10.3258i	−0.579954	+	0.579954i	−0.934890	−	0.354937i	$-0.884502\pi$
$317$	−10.3258	+	10.3258i	−0.579954	+	0.579954i	0.354937	+	0.934890i	$0.384502\pi$
$318$	11.3641	−	19.8626i	0.637266	−	1.11384i
$319$			16.6539i			0.932440i
$320$	−0.424609	−	2.19538i	−0.0237364	−	0.122726i
$321$	−1.21384	−	4.46009i	−0.0677501	−	0.248938i
$322$	−3.18548	−	3.18548i	−0.177520	−	0.177520i
$323$	−13.5263	−	13.5263i	−0.752621	−	0.752621i
$324$	7.86385	+	4.37721i	0.436880	+	0.243178i
$325$	4.83197	−	11.3245i	0.268030	−	0.628170i
$326$			19.4486i			1.07716i
$327$	0.123198	+	0.0704855i	0.00681284	+	0.00389786i
$328$	6.90947	−	6.90947i	0.381512	−	0.381512i
$329$	−2.97479			−0.164005
$330$	6.79561	−	3.33960i	0.374086	−	0.183839i
$331$	2.07714			0.114170			0.0570850	−	0.998369i	$-0.481819\pi$
$331$	2.07714			0.114170			0.0570850	+	0.998369i	$0.481819\pi$
$332$	2.46289	−	2.46289i	0.135169	−	0.135169i
$333$	−2.05513	+	7.91771i	−0.112621	+	0.433888i
$334$		−	25.1327i		−	1.37520i
$335$	20.5991	+	13.9223i	1.12545	+	0.760656i
$336$	−0.848008	+	0.230791i	−0.0462626	+	0.0125907i
$337$	7.26005	+	7.26005i	0.395480	+	0.395480i	0.876635	−	0.481155i	$-0.159783\pi$
$337$	7.26005	+	7.26005i	0.395480	+	0.395480i	−0.481155	+	0.876635i	$0.659783\pi$
$338$	4.90471	+	4.90471i	0.266781	+	0.266781i
$339$	21.9601	−	5.97659i	1.19271	−	0.324604i
$340$	9.58259	+	6.47658i	0.519689	+	0.351242i
$341$		−	1.95505i		−	0.105872i
$342$	−2.78739	+	10.7389i	−0.150725	+	0.580691i
$343$	−4.93069	+	4.93069i	−0.266232	+	0.266232i
$344$	2.14639			0.115725
$345$	30.8606	−	15.1660i	1.66148	−	0.816508i
$346$	3.11875			0.167665
$347$	−9.72013	+	9.72013i	−0.521804	+	0.521804i	−0.918116	−	0.396312i	$-0.870290\pi$
$347$	−9.72013	+	9.72013i	−0.521804	+	0.521804i	0.396312	+	0.918116i	$0.370290\pi$
$348$	12.8064	+	7.32700i	0.686497	+	0.392768i
$349$		−	5.23665i		−	0.280311i	−0.990129	−	0.140156i	$-0.955240\pi$
$349$		−	5.23665i		−	0.280311i	0.990129	−	0.140156i	$-0.0447603\pi$
$350$	−2.35407	+	0.945988i	−0.125830	+	0.0505652i
$351$	8.94059	−	9.15344i	0.477213	−	0.488574i
$352$	−1.38243	−	1.38243i	−0.0736837	−	0.0736837i
$353$	9.32810	+	9.32810i	0.496485	+	0.496485i	0.910342	−	0.413857i	$-0.135819\pi$
$353$	9.32810	+	9.32810i	0.496485	+	0.496485i	−0.413857	+	0.910342i	$0.635819\pi$
$354$	0.854102	+	3.13828i	0.0453950	+	0.166798i
$355$	−1.22551	−	6.33631i	−0.0650431	−	0.336296i
$356$			0.192825i			0.0102197i
$357$	2.25746	−	3.94569i	0.119478	−	0.208828i
$358$	2.64291	−	2.64291i	0.139682	−	0.139682i
$359$	−15.9315			−0.840833			−0.420417	−	0.907331i	$-0.638116\pi$
$359$	−15.9315			−0.840833			−0.420417	+	0.907331i	$0.638116\pi$
$360$	0.421709	−	6.69494i	0.0222260	−	0.352854i
$361$	5.32305			0.280160
$362$	−12.4025	+	12.4025i	−0.651863	+	0.651863i
$363$	−6.17388	+	10.7910i	−0.324044	+	0.566379i
$364$			1.24946i			0.0654897i
$365$	−17.1830	+	25.4235i	−0.899398	+	1.33073i
$366$	4.78522	+	17.5826i	0.250127	+	0.919058i
$367$	2.44539	+	2.44539i	0.127648	+	0.127648i	0.768045	−	0.640396i	$-0.221230\pi$
$367$	2.44539	+	2.44539i	0.127648	+	0.127648i	−0.640396	+	0.768045i	$0.721230\pi$
$368$	−6.27796	−	6.27796i	−0.327262	−	0.327262i
$369$	25.2713	−	14.8558i	1.31557	−	0.773364i
$370$	5.98614	−	1.15778i	0.311204	−	0.0601901i
$371$			6.70381i			0.348045i
$372$	−1.50338	−	0.860137i	−0.0779468	−	0.0445960i
$373$	14.3557	−	14.3557i	0.743308	−	0.743308i	−0.229905	−	0.973213i	$-0.573841\pi$
$373$	14.3557	−	14.3557i	0.743308	−	0.743308i	0.973213	+	0.229905i	$0.0738415\pi$
$374$	10.1124			0.522901
$375$	−1.03506	−	19.3372i	−0.0534505	−	0.998571i
$376$	−5.86273			−0.302347
$377$	14.8324	−	14.8324i	0.763908	−	0.763908i
$378$	−2.63638	+	0.0310131i	−0.135601	+	0.00159514i
$379$			13.9990i			0.719082i	0.933129	+	0.359541i	$0.117067\pi$
$379$			13.9990i			0.719082i	−0.933129	+	0.359541i	$0.882933\pi$
$380$	8.11905	−	1.57031i	0.416498	−	0.0805550i
$381$	−12.8130	+	3.48715i	−0.656432	+	0.178652i
$382$	−1.71474	−	1.71474i	−0.0877339	−	0.0877339i
$383$	−13.5580	−	13.5580i	−0.692781	−	0.692781i	0.270062	−	0.962843i	$-0.412956\pi$
$383$	−13.5580	−	13.5580i	−0.692781	−	0.692781i	−0.962843	+	0.270062i	$0.912956\pi$
$384$	−1.67126	+	0.454844i	−0.0852862	+	0.0232112i
$385$	−1.24211	+	1.83780i	−0.0633040	+	0.0936630i
$386$			12.1406i			0.617941i
$387$	6.23263	+	1.61775i	0.316822	+	0.0822349i
$388$	1.01182	−	1.01182i	0.0513675	−	0.0513675i
$389$	−7.92369			−0.401747			−0.200874	−	0.979617i	$-0.564378\pi$
$389$	−7.92369			−0.401747			−0.200874	+	0.979617i	$0.564378\pi$
$390$	−9.02669	−	3.07802i	−0.457084	−	0.155862i
$391$	45.9231			2.32243
$392$	−4.76770	+	4.76770i	−0.240805	+	0.240805i
$393$	−22.5619	−	12.9084i	−1.13810	−	0.651144i
$394$			24.3631i			1.22740i
$395$	0.573553	+	2.96547i	0.0288586	+	0.149209i
$396$	−2.97232	−	5.05622i	−0.149365	−	0.254084i
$397$	−24.9906	−	24.9906i	−1.25424	−	1.25424i	−0.953801	−	0.300440i	$-0.902866\pi$
$397$	−24.9906	−	24.9906i	−1.25424	−	1.25424i	−0.300440	−	0.953801i	$-0.597134\pi$
$398$	9.61388	+	9.61388i	0.481900	+	0.481900i
$399$	−0.853518	−	3.13614i	−0.0427294	−	0.157003i
$400$	−4.63941	+	1.86436i	−0.231971	+	0.0932180i
$401$		−	22.0069i		−	1.09897i	−0.835502	−	0.549487i	$-0.814823\pi$
$401$		−	22.0069i		−	1.09897i	0.835502	−	0.549487i	$-0.185177\pi$
$402$	9.56380	−	16.7160i	0.476999	−	0.833719i
$403$	−1.74122	+	1.74122i	−0.0867363	+	0.0867363i
$404$	−0.318549			−0.0158484
$405$	6.27058	−	19.1228i	0.311588	−	0.950217i
$406$	−4.32229			−0.214512
$407$	3.76946	−	3.76946i	0.186845	−	0.186845i
$408$	4.44903	−	7.77620i	0.220260	−	0.384979i
$409$			10.8865i			0.538304i	0.963098	+	0.269152i	$0.0867434\pi$
$409$			10.8865i			0.538304i	−0.963098	+	0.269152i	$0.913257\pi$
$410$	−18.1028	−	12.2351i	−0.894032	−	0.604249i
$411$	1.49420	+	5.49023i	0.0737034	+	0.270813i
$412$	−11.0476	−	11.0476i	−0.544278	−	0.544278i
$413$	−0.673733	−	0.673733i	−0.0331522	−	0.0331522i
$414$	−13.4981	−	22.9616i	−0.663393	−	1.12850i
$415$	−6.45275	−	4.36122i	−0.316753	−	0.214084i
$416$			2.46246i			0.120732i
$417$	−13.8843	−	7.94365i	−0.679915	−	0.389002i
$418$	5.11255	−	5.11255i	0.250063	−	0.250063i
$419$	2.09340			0.102269			0.0511346	−	0.998692i	$-0.483716\pi$
$419$	2.09340			0.102269			0.0511346	+	0.998692i	$0.483716\pi$
$420$	0.866746	+	1.76371i	0.0422929	+	0.0860601i
$421$	34.4422			1.67861			0.839306	−	0.543659i	$-0.182962\pi$
$421$	34.4422			1.67861			0.839306	+	0.543659i	$0.182962\pi$
$422$	18.7386	−	18.7386i	0.912182	−	0.912182i
$423$	−17.0241	−	4.41880i	−0.827739	−	0.214849i
$424$			13.2119i			0.641628i
$425$	10.1497	−	23.7875i	0.492334	−	1.15386i
$426$	−4.82359	+	1.31277i	−0.233704	+	0.0636039i
$427$	−3.77467	−	3.77467i	−0.182669	−	0.182669i
$428$	1.88705	+	1.88705i	0.0912142	+	0.0912142i
$429$	−8.04583	+	2.18972i	−0.388456	+	0.105721i
$430$	−0.911376	−	4.71214i	−0.0439504	−	0.227240i
$431$		−	24.8456i		−	1.19677i	−0.801208	−	0.598386i	$-0.795809\pi$
$431$		−	24.8456i		−	1.19677i	0.801208	−	0.598386i	$-0.204191\pi$
$432$	−5.19579	+	0.0611210i	−0.249983	+	0.00294068i
$433$	−3.57481	+	3.57481i	−0.171794	+	0.171794i	−0.787767	−	0.615973i	$-0.788763\pi$
$433$	−3.57481	+	3.57481i	−0.171794	+	0.171794i	0.615973	+	0.787767i	$0.288763\pi$
$434$	0.507406			0.0243563
$435$	10.6478	−	31.2261i	0.510525	−	1.49718i
$436$	−0.0819468			−0.00392454
$437$	23.2174	−	23.2174i	1.11064	−	1.11064i
$438$	20.6310	+	11.8037i	0.985787	+	0.564002i
$439$			11.5796i			0.552664i	0.961062	+	0.276332i	$0.0891190\pi$
$439$			11.5796i			0.552664i	−0.961062	+	0.276332i	$0.910881\pi$
$440$	−2.44797	+	3.62195i	−0.116702	+	0.172670i
$441$	−17.4378	+	10.2509i	−0.830370	+	0.488137i
$442$	−9.00640	−	9.00640i	−0.428391	−	0.428391i
$443$	8.88709	+	8.88709i	0.422238	+	0.422238i	0.885974	−	0.463735i	$-0.153491\pi$
$443$	8.88709	+	8.88709i	0.422238	+	0.422238i	−0.463735	+	0.885974i	$0.653491\pi$
$444$	−1.24022	−	4.55702i	−0.0588583	−	0.216267i
$445$	0.423326	−	0.0818755i	0.0200676	−	0.00388127i
$446$		−	27.1059i		−	1.28350i
$447$	0.708274	−	1.23795i	0.0335002	−	0.0585531i
$448$	0.358790	−	0.358790i	0.0169512	−	0.0169512i
$449$	−9.67396			−0.456543			−0.228271	−	0.973598i	$-0.573307\pi$
$449$	−9.67396			−0.456543			−0.228271	+	0.973598i	$0.573307\pi$
$450$	−14.8770	+	1.91692i	−0.701309	+	0.0903645i
$451$	−19.1037			−0.899559
$452$	−9.29128	+	9.29128i	−0.437025	+	0.437025i
$453$	10.0312	−	17.5330i	0.471308	−	0.823772i
$454$		−	2.77681i		−	0.130322i
$455$	2.74305	−	0.530534i	0.128596	−	0.0248718i
$456$	−1.68212	−	6.18072i	−0.0787726	−	0.289439i
$457$	−4.89450	−	4.89450i	−0.228955	−	0.228955i	0.583301	−	0.812256i	$-0.301761\pi$
$457$	−4.89450	−	4.89450i	−0.228955	−	0.228955i	−0.812256	+	0.583301i	$0.801761\pi$
$458$	0.938050	+	0.938050i	0.0438322	+	0.0438322i
$459$	18.7800	−	19.2271i	0.876575	−	0.897444i
$460$	−11.1169	+	16.4482i	−0.518326	+	0.766902i
$461$		−	26.4567i		−	1.23221i	−0.787663	−	0.616107i	$-0.788709\pi$
$461$		−	26.4567i		−	1.23221i	0.787663	−	0.616107i	$-0.211291\pi$
$462$	1.49136	+	0.853259i	0.0693845	+	0.0396972i
$463$	−22.0172	+	22.0172i	−1.02323	+	1.02323i	−0.0235013	+	0.999724i	$0.507481\pi$
$463$	−22.0172	+	22.0172i	−1.02323	+	1.02323i	−0.999724	+	0.0235013i	$0.992519\pi$
$464$	−8.51841			−0.395457
$465$	−1.24998	+	3.66573i	−0.0579664	+	0.169994i
$466$	10.0118			0.463787
$467$	−12.2168	+	12.2168i	−0.565327	+	0.565327i	−0.930816	−	0.365489i	$-0.880902\pi$
$467$	−12.2168	+	12.2168i	−0.565327	+	0.565327i	0.365489	+	0.930816i	$0.380902\pi$
$468$	−1.85598	+	7.15042i	−0.0857925	+	0.330528i
$469$			5.64180i			0.260514i
$470$	2.48937	+	12.8709i	0.114826	+	0.593692i
$471$	35.0839	−	9.54829i	1.61658	−	0.439962i
$472$	−1.32780	−	1.32780i	−0.0611169	−	0.0611169i
$473$	−2.96723	−	2.96723i	−0.136433	−	0.136433i
$474$	2.25750	−	0.614393i	0.103691	−	0.0282200i
$475$	−6.89485	−	17.1576i	−0.316357	−	0.787247i
$476$			2.62454i			0.120296i
$477$	−9.95795	+	38.3645i	−0.455943	+	1.75659i
$478$	−6.85809	+	6.85809i	−0.313682	+	0.313682i
$479$	−1.13514			−0.0518660			−0.0259330	−	0.999664i	$-0.508256\pi$
$479$	−1.13514			−0.0518660			−0.0259330	+	0.999664i	$0.508256\pi$
$480$	1.70819	+	3.47593i	0.0779679	+	0.158654i
$481$	−6.71436			−0.306149
$482$	0.955658	−	0.955658i	0.0435290	−	0.0435290i
$483$	6.77266	+	3.87487i	0.308167	+	0.176313i
$484$		−	7.17778i		−	0.326263i
$485$	−2.65097	−	1.79171i	−0.120374	−	0.0813573i
$486$	−15.1335	−	3.73863i	−0.686469	−	0.169588i
$487$	−25.5727	−	25.5727i	−1.15881	−	1.15881i	−0.984732	−	0.174080i	$-0.944305\pi$
$487$	−25.5727	−	25.5727i	−1.15881	−	1.15881i	−0.174080	−	0.984732i	$-0.555695\pi$
$488$	−7.43916	−	7.43916i	−0.336755	−	0.336755i
$489$	−8.84610	−	32.5038i	−0.400034	−	1.46987i
$490$	12.4913	+	8.44251i	0.564301	+	0.381394i
$491$		−	6.43538i		−	0.290425i	−0.989401	−	0.145212i	$-0.953613\pi$
$491$		−	6.43538i		−	0.290425i	0.989401	−	0.145212i	$-0.0463865\pi$
$492$	−8.40481	+	14.6903i	−0.378918	+	0.662289i
$493$	31.1560	−	31.1560i	1.40319	−	1.40319i
$494$	−9.10674			−0.409732
$495$	−9.83826	+	8.67229i	−0.442197	+	0.389790i
$496$	1.00000			0.0449013
$497$	1.03554	−	1.03554i	0.0464503	−	0.0464503i
$498$	−2.99590	+	5.23637i	−0.134250	+	0.234647i
$499$			2.13426i			0.0955426i	0.998858	+	0.0477713i	$0.0152119\pi$
$499$			2.13426i			0.0955426i	−0.998858	+	0.0477713i	$0.984788\pi$
$500$	6.06293	+	9.39366i	0.271142	+	0.420097i
$501$	11.4314	+	42.0033i	0.510719	+	1.87657i
$502$	14.3919	+	14.3919i	0.642343	+	0.642343i
$503$	−16.0055	−	16.0055i	−0.713652	−	0.713652i	0.253645	−	0.967297i	$-0.418370\pi$
$503$	−16.0055	−	16.0055i	−0.713652	−	0.713652i	−0.967297	+	0.253645i	$0.918370\pi$
$504$	1.31227	−	0.771423i	0.0584532	−	0.0343619i
$505$	0.135259	+	0.699338i	0.00601895	+	0.0311201i
$506$			17.3577i			0.771643i
$507$	−10.4279	−	5.96618i	−0.463121	−	0.264967i
$508$	5.42117	−	5.42117i	0.240525	−	0.240525i
$509$	0.206280			0.00914319			0.00457160	−	0.999990i	$-0.498545\pi$
$509$	0.206280			0.00914319			0.00457160	+	0.999990i	$0.498545\pi$
$510$	−18.9608	−	6.46548i	−0.839601	−	0.286296i
$511$	−6.96315			−0.308032
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−0.226040	−	19.2153i	−0.00997990	−	0.848375i
$514$		−	25.3385i		−	1.11763i
$515$	−19.5629	+	28.9448i	−0.862044	+	1.27546i
$516$	−3.58717	+	0.976271i	−0.157917	+	0.0429780i
$517$	8.10481	+	8.10481i	0.356449	+	0.356449i
$518$	0.978311	+	0.978311i	0.0429845	+	0.0429845i
$519$	−5.21225	+	1.41854i	−0.228792	+	0.0622672i
$520$	5.40603	−	1.04558i	0.237070	−	0.0458518i
$521$			16.7588i			0.734215i	0.930178	+	0.367108i	$0.119652\pi$
$521$			16.7588i			0.734215i	−0.930178	+	0.367108i	$0.880348\pi$
$522$	−24.7356	−	6.42040i	−1.08265	−	0.281013i
$523$	17.4085	−	17.4085i	0.761219	−	0.761219i	−0.215324	−	0.976543i	$-0.569081\pi$
$523$	17.4085	−	17.4085i	0.761219	−	0.761219i	0.976543	+	0.215324i	$0.0690807\pi$
$524$	15.0074			0.655601
$525$	3.50398	−	2.65173i	0.152926	−	0.115731i
$526$	20.2025			0.880869
$527$	−3.65749	+	3.65749i	−0.159323	+	0.159323i
$528$	2.93919	+	1.68161i	0.127912	+	0.0731827i
$529$			55.8257i			2.42720i
$530$	29.0052	−	5.60991i	1.25991	−	0.243679i
$531$	−2.85486	−	4.85641i	−0.123890	−	0.210750i
$532$	1.32689	+	1.32689i	0.0575280	+	0.0575280i
$533$	17.0143	+	17.0143i	0.736970	+	0.736970i
$534$	−0.0877056	−	0.322262i	−0.00379539	−	0.0139456i
$535$	3.34155	−	4.94407i	0.144468	−	0.213751i
$536$			11.1189i			0.480264i
$537$	−3.21489	+	5.61912i	−0.138733	+	0.242483i
$538$	−1.61323	+	1.61323i	−0.0695514	+	0.0695514i
$539$	13.1820			0.567789
$540$	2.34037	+	11.3808i	0.100713	+	0.489752i
$541$	−29.6653			−1.27541			−0.637705	−	0.770281i	$-0.720116\pi$
$541$	−29.6653			−1.27541			−0.637705	+	0.770281i	$0.720116\pi$
$542$	11.7489	−	11.7489i	0.504657	−	0.504657i
$543$	15.0867	−	26.3691i	0.647431	−	1.13161i
$544$			5.17247i			0.221768i
$545$	0.0347954	+	0.179905i	0.00149047	+	0.00770627i
$546$	−0.568312	−	2.08818i	−0.0243215	−	0.0893660i
$547$	−2.72287	−	2.72287i	−0.116421	−	0.116421i	0.646496	−	0.762917i	$-0.276234\pi$
$547$	−2.72287	−	2.72287i	−0.116421	−	0.116421i	−0.762917	+	0.646496i	$0.776234\pi$
$548$	−2.32290	−	2.32290i	−0.0992295	−	0.0992295i
$549$	−15.9947	−	27.2086i	−0.682637	−	1.16124i
$550$	8.99101	+	3.83631i	0.383378	+	0.163581i
$551$		−	31.5031i		−	1.34208i
$552$	13.3476	+	7.63663i	0.568112	+	0.325036i
$553$	−0.484646	+	0.484646i	−0.0206092	+	0.0206092i
$554$	−12.2163			−0.519022
$555$	−9.47779	+	4.65771i	−0.402310	+	0.197709i
$556$	9.23533			0.391665
$557$	−10.5384	+	10.5384i	−0.446526	+	0.446526i	−0.894198	−	0.447672i	$-0.852253\pi$
$557$	−10.5384	+	10.5384i	−0.446526	+	0.446526i	0.447672	+	0.894198i	$0.352253\pi$
$558$	2.90378	+	0.753709i	0.122927	+	0.0319071i
$559$			5.28538i			0.223548i
$560$	−0.940028	−	0.635336i	−0.0397234	−	0.0268479i
$561$	−16.9005	+	4.59958i	−0.713541	+	0.194194i
$562$	−1.35157	−	1.35157i	−0.0570126	−	0.0570126i
$563$	23.4280	+	23.4280i	0.987372	+	0.987372i	0.999921	−	0.0125491i	$-0.00399462\pi$
$563$	23.4280	+	23.4280i	0.987372	+	0.987372i	−0.0125491	+	0.999921i	$0.503995\pi$
$564$	9.79816	−	2.66663i	0.412577	−	0.112285i
$565$	24.3431	+	16.4528i	1.02412	+	0.692173i
$566$		−	26.6281i		−	1.11926i
$567$	4.39197	−	1.25097i	0.184445	−	0.0525359i
$568$	2.04085	−	2.04085i	0.0856321	−	0.0856321i
$569$	7.44387			0.312063			0.156032	−	0.987752i	$-0.450130\pi$
$569$	7.44387			0.312063			0.156032	+	0.987752i	$0.450130\pi$
$570$	−12.8548	+	6.31729i	−0.538429	+	0.264602i
$571$	−11.8316			−0.495136			−0.247568	−	0.968870i	$-0.579631\pi$
$571$	−11.8316			−0.495136			−0.247568	+	0.968870i	$0.579631\pi$
$572$	3.40417	−	3.40417i	0.142335	−	0.142335i
$573$	3.64573	+	2.08584i	0.152302	+	0.0871374i
$574$		−	4.95810i		−	0.206947i
$575$	40.8305	+	17.4217i	1.70275	+	0.726534i
$576$	2.58623	−	1.52033i	0.107760	−	0.0633470i
$577$	−14.3674	−	14.3674i	−0.598122	−	0.598122i	0.341691	−	0.939812i	$-0.389000\pi$
$577$	−14.3674	−	14.3674i	−0.598122	−	0.598122i	−0.939812	+	0.341691i	$0.889000\pi$
$578$	−6.89741	−	6.89741i	−0.286895	−	0.286895i
$579$	−5.52209	−	20.2901i	−0.229490	−	0.843230i
$580$	3.61700	+	18.7012i	0.150188	+	0.776524i
$581$		−	1.76732i		−	0.0733209i
$582$	−1.23080	+	2.15124i	−0.0510183	+	0.0891719i
$583$	18.2646	−	18.2646i	0.756441	−	0.756441i
$584$	−13.7230			−0.567863
$585$	16.4860	+	1.03844i	0.681611	+	0.0429342i
$586$	−19.4183			−0.802162
$587$	4.80609	−	4.80609i	0.198368	−	0.198368i	−0.600932	−	0.799300i	$-0.705204\pi$
$587$	4.80609	−	4.80609i	0.198368	−	0.198368i	0.799300	+	0.600932i	$0.205204\pi$
$588$	5.79951	−	10.1366i	0.239168	−	0.418027i
$589$			3.69824i			0.152383i
$590$	−2.35123	+	3.47882i	−0.0967986	+	0.143221i
$591$	−11.0814	−	40.7172i	−0.455829	−	1.67488i
$592$	1.92806	+	1.92806i	0.0792429	+	0.0792429i
$593$	14.6591	+	14.6591i	0.601979	+	0.601979i	0.940837	−	0.338859i	$-0.110041\pi$
$593$	14.6591	+	14.6591i	0.601979	+	0.601979i	−0.338859	+	0.940837i	$0.610041\pi$
$594$	7.26731	+	7.09832i	0.298181	+	0.291248i
$595$	5.76187	−	1.11440i	0.236214	−	0.0456861i
$596$			0.823443i			0.0337295i
$597$	−20.4401	−	11.6945i	−0.836559	−	0.478624i
$598$	15.4592	−	15.4592i	0.632174	−	0.632174i
$599$	−39.4780			−1.61303			−0.806514	−	0.591215i	$-0.798648\pi$
$599$	−39.4780			−1.61303			−0.806514	+	0.591215i	$0.798648\pi$
$600$	6.90568	−	5.22605i	0.281923	−	0.213352i
$601$	−15.1492			−0.617950			−0.308975	−	0.951070i	$-0.599986\pi$
$601$	−15.1492			−0.617950			−0.308975	+	0.951070i	$0.599986\pi$
$602$	0.770102	−	0.770102i	0.0313870	−	0.0313870i
$603$	−8.38043	+	32.2869i	−0.341277	+	1.31482i
$604$			11.6623i			0.474534i
$605$	−15.7580	+	3.04775i	−0.640653	+	0.123909i
$606$	0.532380	−	0.144890i	0.0216264	−	0.00588577i
$607$	14.2742	+	14.2742i	0.579373	+	0.579373i	0.934730	−	0.355357i	$-0.115641\pi$
$607$	14.2742	+	14.2742i	0.579373	+	0.579373i	−0.355357	+	0.934730i	$0.615641\pi$
$608$	2.61505	+	2.61505i	0.106054	+	0.106054i
$609$	7.22368	−	1.96597i	0.292718	−	0.0796651i
$610$	−13.1731	+	19.4905i	−0.533362	+	0.789149i
$611$		−	14.4367i		−	0.584047i
$612$	−3.89854	+	15.0197i	−0.157589	+	0.607135i
$613$	9.44047	−	9.44047i	0.381297	−	0.381297i	−0.490272	−	0.871569i	$-0.663103\pi$
$613$	9.44047	−	9.44047i	0.381297	−	0.381297i	0.871569	+	0.490272i	$0.163103\pi$
$614$	27.0359			1.09108
$615$	35.8195	+	12.2141i	1.44438	+	0.492522i
$616$	−0.992004			−0.0399690
$617$	33.3329	−	33.3329i	1.34193	−	1.34193i	0.447800	−	0.894134i	$-0.352208\pi$
$617$	33.3329	−	33.3329i	1.34193	−	1.34193i	0.894134	−	0.447800i	$-0.147792\pi$
$618$	23.4885	+	13.4386i	0.944845	+	0.540578i
$619$		−	33.8700i		−	1.36135i	−0.732584	−	0.680676i	$-0.761686\pi$
$619$		−	33.8700i		−	1.36135i	0.732584	−	0.680676i	$-0.238314\pi$
$620$	−0.424609	−	2.19538i	−0.0170527	−	0.0881687i
$621$	33.0027	+	32.2353i	1.32435	+	1.29356i
$622$	−4.42331	−	4.42331i	−0.177359	−	0.177359i
$623$	0.0691839	+	0.0691839i	0.00277179	+	0.00277179i
$624$	−1.12003	−	4.11541i	−0.0448372	−	0.164748i
$625$	18.0483	−	17.2991i	0.721933	−	0.691963i
$626$			26.8318i			1.07242i
$627$	−6.21900	+	10.8698i	−0.248363	+	0.434099i
$628$	−14.8439	+	14.8439i	−0.592336	+	0.592336i
$629$	−14.1037			−0.562353
$630$	−2.25077	−	2.55338i	−0.0896729	−	0.101729i
$631$	2.45690			0.0978076			0.0489038	−	0.998803i	$-0.484427\pi$
$631$	2.45690			0.0978076			0.0489038	+	0.998803i	$0.484427\pi$
$632$	−0.955144	+	0.955144i	−0.0379936	+	0.0379936i
$633$	−22.7940	+	39.8403i	−0.905980	+	1.58351i
$634$			14.6029i			0.579954i
$635$	−14.2034	−	9.59966i	−0.563645	−	0.380951i
$636$	−6.00937	−	22.0806i	−0.238287	−	0.875553i
$637$	−11.7402	−	11.7402i	−0.465165	−	0.465165i
$638$	11.7761	+	11.7761i	0.466220	+	0.466220i
$639$	7.46438	−	4.38796i	0.295286	−	0.173585i
$640$	−1.85261	−	1.25213i	−0.0732310	−	0.0494946i
$641$			25.5355i			1.00859i	0.863531	+	0.504297i	$0.168248\pi$
$641$			25.5355i			1.00859i	−0.863531	+	0.504297i	$0.831752\pi$
$642$	−4.01208	−	2.29545i	−0.158344	−	0.0905941i
$643$	−14.0125	+	14.0125i	−0.552597	+	0.552597i	−0.927190	−	0.374592i	$-0.877783\pi$
$643$	−14.0125	+	14.0125i	−0.552597	+	0.552597i	0.374592	+	0.927190i	$0.377783\pi$
$644$	−4.50494			−0.177520
$645$	3.66644	+	7.46069i	0.144366	+	0.293764i
$646$	−19.1290			−0.752621
$647$	19.0335	−	19.0335i	0.748283	−	0.748283i	−0.225874	−	0.974157i	$-0.572524\pi$
$647$	19.0335	−	19.0335i	0.748283	−	0.748283i	0.974157	+	0.225874i	$0.0725238\pi$
$648$	8.65573	−	2.46543i	0.340029	−	0.0968511i
$649$			3.67117i			0.144106i
$650$	−4.59091	−	11.4244i	−0.180070	−	0.448100i
$651$	−0.848008	+	0.230791i	−0.0332361	+	0.00904540i
$652$	13.7523	+	13.7523i	0.538580	+	0.538580i
$653$	12.3516	+	12.3516i	0.483355	+	0.483355i	0.906201	−	0.422846i	$-0.138969\pi$
$653$	12.3516	+	12.3516i	0.483355	+	0.483355i	−0.422846	+	0.906201i	$0.638969\pi$
$654$	0.136955	−	0.0372730i	0.00535535	−	0.00145749i
$655$	−6.37228	−	32.9470i	−0.248986	−	1.28735i
$656$		−	9.77147i		−	0.381512i
$657$	−39.8486	−	10.3432i	−1.55464	−	0.403526i
$658$	−2.10349	+	2.10349i	−0.0820026	+	0.0820026i
$659$	−35.0699			−1.36613			−0.683065	−	0.730358i	$-0.739353\pi$
$659$	−35.0699			−1.36613			−0.683065	+	0.730358i	$0.739353\pi$
$660$	2.44377	−	7.16668i	0.0951237	−	0.278963i
$661$	1.85106			0.0719978			0.0359989	−	0.999352i	$-0.488539\pi$
$661$	1.85106			0.0719978			0.0359989	+	0.999352i	$0.488539\pi$
$662$	1.46876	−	1.46876i	0.0570850	−	0.0570850i
$663$	19.1486	+	10.9555i	0.743668	+	0.425478i
$664$		−	3.48305i		−	0.135169i
$665$	2.34962	−	3.47644i	0.0911145	−	0.134811i
$666$	4.14547	+	7.05186i	0.160634	+	0.273254i
$667$	53.4782	+	53.4782i	2.07069	+	2.07069i
$668$	−17.7715	−	17.7715i	−0.687599	−	0.687599i
$669$	12.3290	+	45.3011i	0.476666	+	1.75144i
$670$	24.4103	−	4.72120i	0.943052	−	0.182396i
$671$			20.5682i			0.794027i
$672$	−0.436439	+	0.762826i	−0.0168360	+	0.0294267i
$673$	−8.95618	+	8.95618i	−0.345236	+	0.345236i	−0.858331	−	0.513096i	$-0.828499\pi$
$673$	−8.95618	+	8.95618i	−0.345236	+	0.345236i	0.513096	+	0.858331i	$0.328499\pi$
$674$	10.2673			0.395480
$675$	23.9915	−	9.97040i	0.923433	−	0.383761i
$676$	6.93631			0.266781
$677$	18.2690	−	18.2690i	0.702136	−	0.702136i	−0.262733	−	0.964869i	$-0.584624\pi$
$677$	18.2690	−	18.2690i	0.702136	−	0.702136i	0.964869	+	0.262733i	$0.0846237\pi$
$678$	11.3021	−	19.7543i	0.434054	−	0.758658i
$679$		−	0.726064i		−	0.0278638i
$680$	11.3555	−	2.19628i	0.435465	−	0.0842234i
$681$	1.26302	+	4.64078i	0.0483989	+	0.177835i
$682$	−1.38243	−	1.38243i	−0.0529359	−	0.0529359i
$683$	10.9514	+	10.9514i	0.419044	+	0.419044i	0.884874	−	0.465830i	$-0.154244\pi$
$683$	10.9514	+	10.9514i	0.419044	+	0.419044i	−0.465830	+	0.884874i	$0.654244\pi$
$684$	5.62253	+	9.56450i	0.214983	+	0.365708i
$685$	−4.11333	+	6.08599i	−0.157162	+	0.232534i
$686$			6.97305i			0.266232i
$687$	−1.99439	−	1.14106i	−0.0760909	−	0.0435342i
$688$	1.51772	−	1.51772i	0.0578627	−	0.0578627i
$689$	−32.5338			−1.23944
$690$	11.0978	−	32.5457i	0.422486	−	1.23899i
$691$	−27.1310			−1.03211			−0.516056	−	0.856555i	$-0.672600\pi$
$691$	−27.1310			−1.03211			−0.516056	+	0.856555i	$0.672600\pi$
$692$	2.20529	−	2.20529i	0.0838325	−	0.0838325i
$693$	−2.88056	−	0.747682i	−0.109423	−	0.0284021i
$694$			13.7463i			0.521804i
$695$	−3.92141	−	20.2751i	−0.148748	−	0.769078i
$696$	14.2365	−	3.87455i	0.539633	−	0.146864i
$697$	35.7390	+	35.7390i	1.35371	+	1.35371i
$698$	−3.70287	−	3.70287i	−0.140156	−	0.140156i
$699$	−16.7323	+	4.55380i	−0.632874	+	0.172241i
$700$	−0.995662	+	2.33349i	−0.0376325	+	0.0881976i
$701$			31.7577i			1.19947i	0.800198	+	0.599736i	$0.204728\pi$
$701$			31.7577i			1.19947i	−0.800198	+	0.599736i	$0.795272\pi$
$702$	−0.150508	−	12.7944i	−0.00568054	−	0.482894i
$703$	−7.13043	+	7.13043i	−0.268929	+	0.268929i
$704$	−1.95505			−0.0736837
$705$	−10.0147	−	20.3784i	−0.377174	−	0.767497i
$706$	13.1919			0.496485
$707$	−0.114292	+	0.114292i	−0.00429841	+	0.00429841i
$708$	2.82304	+	1.61516i	0.106096	+	0.0607013i
$709$			5.36101i			0.201337i	0.994920	+	0.100668i	$0.0320981\pi$
$709$			5.36101i			0.201337i	−0.994920	+	0.100668i	$0.967902\pi$
$710$	−5.34701	−	3.61388i	−0.200670	−	0.135627i
$711$	−3.49343	+	2.05362i	−0.131014	+	0.0770169i
$712$	0.136348	+	0.136348i	0.00510986	+	0.00510986i
$713$	−6.27796	−	6.27796i	−0.235112	−	0.235112i
$714$	−1.19376	−	4.38629i	−0.0446752	−	0.164153i
$715$	−8.91890	−	6.02801i	−0.333548	−	0.225435i
$716$		−	3.73765i		−	0.139682i
$717$	8.34230	−	14.5810i	0.311549	−	0.544538i
$718$	−11.2653	+	11.2653i	−0.420417	+	0.420417i
$719$	−15.2611			−0.569144			−0.284572	−	0.958655i	$-0.591852\pi$
$719$	−15.2611			−0.569144			−0.284572	+	0.958655i	$0.591852\pi$
$720$	−4.43584	−	5.03223i	−0.165314	−	0.187540i
$721$	−7.92757			−0.295238
$722$	3.76396	−	3.76396i	0.140080	−	0.140080i
$723$	−1.16248	+	2.03183i	−0.0432331	+	0.0755646i
$724$			17.5399i			0.651863i
$725$	39.5204	−	15.8814i	1.46775	−	0.589820i
$726$	3.26477	+	11.9960i	0.121167	+	0.445212i
$727$	14.7117	+	14.7117i	0.545625	+	0.545625i	0.925172	−	0.379547i	$-0.123920\pi$
$727$	14.7117	+	14.7117i	0.545625	+	0.545625i	−0.379547	+	0.925172i	$0.623920\pi$
$728$	0.883505	+	0.883505i	0.0327449	+	0.0327449i
$729$	26.9925	−	0.635144i	0.999723	−	0.0235238i
$730$	5.82693	+	30.1273i	0.215664	+	1.11506i
$731$			11.1021i			0.410626i
$732$	15.8164	+	9.04913i	0.584593	+	0.334465i
$733$	−21.1638	+	21.1638i	−0.781704	+	0.781704i	−0.980118	−	0.198414i	$-0.936421\pi$
$733$	−21.1638	+	21.1638i	−0.781704	+	0.781704i	0.198414	+	0.980118i	$0.436421\pi$
$734$	3.45830			0.127648
$735$	−24.7163	−	8.42804i	−0.911675	−	0.310873i
$736$	−8.87838			−0.327262
$737$	15.3711	−	15.3711i	0.566202	−	0.566202i
$738$	7.36485	−	28.3742i	0.271104	−	1.04447i
$739$			25.5918i			0.941410i	0.882291	+	0.470705i	$0.156000\pi$
$739$			25.5918i			0.941410i	−0.882291	+	0.470705i	$0.844000\pi$
$740$	3.41416	−	5.05151i	0.125507	−	0.185697i
$741$	15.2198	−	4.14215i	0.559112	−	0.152166i
$742$	4.74031	+	4.74031i	0.174022	+	0.174022i
$743$	−13.6274	−	13.6274i	−0.499939	−	0.499939i	0.411480	−	0.911419i	$-0.365012\pi$
$743$	−13.6274	−	13.6274i	−0.499939	−	0.499939i	−0.911419	+	0.411480i	$0.865012\pi$
$744$	−1.67126	+	0.454844i	−0.0612714	+	0.0166754i
$745$	1.80777	−	0.349642i	0.0662317	−	0.0128099i
$746$		−	20.3020i		−	0.743308i
$747$	2.62521	−	10.1140i	0.0960514	−	0.370052i
$748$	7.15057	−	7.15057i	0.261451	−	0.261451i
$749$	1.35411			0.0494782
$750$	−14.4054	−	12.9416i	−0.526010	−	0.472560i
$751$	3.34996			0.122242			0.0611209	−	0.998130i	$-0.480532\pi$
$751$	3.34996			0.122242			0.0611209	+	0.998130i	$0.480532\pi$
$752$	−4.14558	+	4.14558i	−0.151174	+	0.151174i
$753$	−30.5988	−	17.5066i	−1.11508	−	0.637976i
$754$		−	20.9762i		−	0.763908i
$755$	25.6033	−	4.95194i	0.931800	−	0.180220i
$756$	−1.84227	+	1.88613i	−0.0670027	+	0.0685978i
$757$	−11.0695	−	11.0695i	−0.402329	−	0.402329i	0.476724	−	0.879053i	$-0.341824\pi$
$757$	−11.0695	−	11.0695i	−0.402329	−	0.402329i	−0.879053	+	0.476724i	$0.841824\pi$
$758$	9.89882	+	9.89882i	0.359541	+	0.359541i
$759$	−7.89504	−	29.0092i	−0.286572	−	1.05297i
$760$	4.63066	−	6.85141i	0.167972	−	0.248527i
$761$			13.9912i			0.507180i	0.967312	+	0.253590i	$0.0816114\pi$
$761$			13.9912i			0.507180i	−0.967312	+	0.253590i	$0.918389\pi$
$762$	−6.59440	+	11.5260i	−0.238890	+	0.417542i
$763$	−0.0294017	+	0.0294017i	−0.00106441	+	0.00106441i
$764$	−2.42501			−0.0877339
$765$	34.6293	+	2.18128i	1.25203	+	0.0788642i
$766$	−19.1739			−0.692781
$767$	3.26965	−	3.26965i	0.118060	−	0.118060i
$768$	−0.860137	+	1.50338i	−0.0310375	+	0.0542487i
$769$			1.44997i			0.0522874i	0.999658	+	0.0261437i	$0.00832275\pi$
$769$			1.44997i			0.0522874i	−0.999658	+	0.0261437i	$0.991677\pi$
$770$	0.421214	+	2.17783i	0.0151795	+	0.0784835i
$771$	11.5251	+	42.3473i	0.415065	+	1.52510i
$772$	8.58471	+	8.58471i	0.308970	+	0.308970i
$773$	6.72297	+	6.72297i	0.241808	+	0.241808i	0.817598	−	0.575790i	$-0.195305\pi$
$773$	6.72297	+	6.72297i	0.241808	+	0.241808i	−0.575790	+	0.817598i	$0.695305\pi$
$774$	5.55106	−	3.26321i	0.199529	−	0.117294i
$775$	−4.63941	+	1.86436i	−0.166653	+	0.0669698i
$776$		−	1.43093i		−	0.0513675i
$777$	−2.07999	−	1.19003i	−0.0746193	−	0.0426922i
$778$	−5.60289	+	5.60289i	−0.200874	+	0.200874i
$779$	36.1372			1.29475
$780$	−8.55932	+	4.20634i	−0.306473	+	0.150611i
$781$	−5.64266			−0.201910
$782$	32.4726	−	32.4726i	1.16122	−	1.16122i
$783$	44.2599	−	0.520653i	1.58172	−	0.0186066i
$784$			6.74254i			0.240805i
$785$	38.8909	+	26.2852i	1.38808	+	0.938159i
$786$	−25.0813	+	6.82603i	−0.894620	+	0.243476i
$787$	−7.53390	−	7.53390i	−0.268555	−	0.268555i	0.559963	−	0.828518i	$-0.310815\pi$
$787$	−7.53390	−	7.53390i	−0.268555	−	0.268555i	−0.828518	+	0.559963i	$0.810815\pi$
$788$	17.2273	+	17.2273i	0.613698	+	0.613698i
$789$	−33.7636	+	9.18897i	−1.20202	+	0.327136i
$790$	2.50247	+	1.69134i	0.0890339	+	0.0601753i
$791$			6.66724i			0.237060i
$792$	−5.67703	−	1.47354i	−0.201724	−	0.0523599i
$793$	18.3186	−	18.3186i	0.650513	−	0.650513i
$794$	−35.3420			−1.25424
$795$	−45.9237	+	22.5685i	−1.62875	+	0.800422i
$796$	13.5961			0.481900
$797$	−36.9287	+	36.9287i	−1.30808	+	1.30808i	−0.385282	+	0.922799i	$0.625896\pi$
$797$	−36.9287	+	36.9287i	−1.30808	+	1.30808i	−0.922799	+	0.385282i	$0.874104\pi$
$798$	−2.82111	−	1.61405i	−0.0998662	−	0.0571369i
$799$		−	30.3248i		−	1.07281i
$800$	−1.96226	+	4.59886i	−0.0693763	+	0.162594i
$801$	0.293158	+	0.498692i	0.0103582	+	0.0176204i
$802$	−15.5613	−	15.5613i	−0.549487	−	0.549487i
$803$	18.9711	+	18.9711i	0.669476	+	0.669476i
$804$	−5.05738	−	18.5826i	−0.178360	−	0.655359i
$805$	1.91284	+	9.89008i	0.0674188	+	0.348579i
$806$			2.46246i			0.0867363i
$807$	1.96237	−	3.42990i	0.0690785	−	0.120738i
$808$	−0.225248	+	0.225248i	−0.00792421	+	0.00792421i
$809$	−46.4784			−1.63409			−0.817046	−	0.576573i	$-0.804390\pi$
$809$	−46.4784			−1.63409			−0.817046	+	0.576573i	$0.804390\pi$
$810$	−9.08786	−	17.9558i	−0.319315	−	0.630903i
$811$	−3.32637			−0.116805			−0.0584023	−	0.998293i	$-0.518601\pi$
$811$	−3.32637			−0.116805			−0.0584023	+	0.998293i	$0.518601\pi$
$812$	−3.05632	+	3.05632i	−0.107256	+	0.107256i
$813$	−14.2915	+	24.9793i	−0.501226	+	0.876064i
$814$		−	5.33082i		−	0.186845i
$815$	24.3521	−	36.0308i	0.853018	−	1.26210i
$816$	−2.35267	−	8.64455i	−0.0823598	−	0.302620i
$817$	5.61290	+	5.61290i	0.196371	+	0.196371i
$818$	7.69794	+	7.69794i	0.269152	+	0.269152i
$819$	1.89960	+	3.23141i	0.0663772	+	0.112914i
$820$	−21.4521	+	4.14906i	−0.749140	+	0.144891i
$821$		−	6.46893i		−	0.225767i	−0.993608	−	0.112884i	$-0.963991\pi$
$821$		−	6.46893i		−	0.225767i	0.993608	−	0.112884i	$-0.0360087\pi$
$822$	4.93874	+	2.82562i	0.172258	+	0.0985548i
$823$	−25.1379	+	25.1379i	−0.876252	+	0.876252i	−0.993145	−	0.116892i	$-0.962707\pi$
$823$	−25.1379	+	25.1379i	−0.876252	+	0.876252i	0.116892	+	0.993145i	$0.462707\pi$
$824$	−15.6237			−0.544278
$825$	−16.7713	−	2.32198i	−0.583900	−	0.0808409i
$826$	−0.952802			−0.0331522
$827$	−25.7731	+	25.7731i	−0.896220	+	0.896220i	−0.995099	−	0.0988794i	$-0.968474\pi$
$827$	−25.7731	+	25.7731i	−0.896220	+	0.896220i	0.0988794	+	0.995099i	$0.468474\pi$
$828$	−25.7808	−	6.69172i	−0.895946	−	0.232553i
$829$			42.8699i			1.48893i	0.667659	+	0.744467i	$0.267296\pi$
$829$			42.8699i			1.48893i	−0.667659	+	0.744467i	$0.732704\pi$
$830$	−7.64664	+	1.47894i	−0.265419	+	0.0513347i
$831$	20.4167	−	5.55653i	0.708247	−	0.192754i
$832$	1.74122	+	1.74122i	0.0603659	+	0.0603659i
$833$	−24.6607	−	24.6607i	−0.854444	−	0.854444i
$834$	−15.4347	+	4.20064i	−0.534459	+	0.145456i
$835$	−31.4693	+	46.5611i	−1.08904	+	1.61131i
$836$		−	7.23024i		−	0.250063i
$837$	−5.19579	+	0.0611210i	−0.179593	+	0.00211265i
$838$	1.48026	−	1.48026i	0.0511346	−	0.0511346i
$839$	−15.0781			−0.520553			−0.260276	−	0.965534i	$-0.583814\pi$
$839$	−15.0781			−0.520553			−0.260276	+	0.965534i	$0.583814\pi$
$840$	1.86001	+	0.634247i	0.0641765	+	0.0218836i
$841$	43.5632			1.50218
$842$	24.3543	−	24.3543i	0.839306	−	0.839306i
$843$	2.87359	+	1.64408i	0.0989716	+	0.0566250i
$844$		−	26.5004i		−	0.912182i
$845$	−2.94522	−	15.2279i	−0.101319	−	0.523854i
$846$	−15.1624	+	8.91328i	−0.521294	+	0.306445i
$847$	−2.57532	−	2.57532i	−0.0884889	−	0.0884889i
$848$	9.34225	+	9.34225i	0.320814	+	0.320814i
$849$	12.1116	+	44.5025i	0.415670	+	1.52732i
$850$	−9.64334	−	23.9972i	−0.330764	−	0.823098i
$851$		−	24.2086i		−	0.829861i
$852$	−2.48253	+	4.33906i	−0.0850499	+	0.148654i
$853$	−32.7061	+	32.7061i	−1.11984	+	1.11984i	−0.128070	+	0.991765i	$0.540878\pi$
$853$	−32.7061	+	32.7061i	−1.11984	+	1.11984i	−0.991765	+	0.128070i	$0.959122\pi$
$854$	−5.33820			−0.182669
$855$	18.6104	−	16.4048i	0.636461	−	0.561032i
$856$	2.66870			0.0912142
$857$	7.36603	−	7.36603i	0.251619	−	0.251619i	−0.570015	−	0.821634i	$-0.693063\pi$
$857$	7.36603	−	7.36603i	0.251619	−	0.251619i	0.821634	+	0.570015i	$0.193063\pi$
$858$	−4.14089	+	7.23763i	−0.141368	+	0.247089i
$859$			4.64716i			0.158559i	0.996852	+	0.0792796i	$0.0252620\pi$
$859$			4.64716i			0.158559i	−0.996852	+	0.0792796i	$0.974738\pi$
$860$	−3.97643	−	2.68755i	−0.135595	−	0.0916446i
$861$	2.25516	+	8.28629i	0.0768558	+	0.282396i
$862$	−17.5685	−	17.5685i	−0.598386	−	0.598386i
$863$	−23.5547	−	23.5547i	−0.801810	−	0.801810i	0.181568	−	0.983378i	$-0.441883\pi$
$863$	−23.5547	−	23.5547i	−0.801810	−	0.801810i	−0.983378	+	0.181568i	$0.941883\pi$
$864$	−3.63076	+	3.71720i	−0.123521	+	0.126462i
$865$	−5.77784	−	3.90507i	−0.196452	−	0.132776i
$866$			5.05554i			0.171794i
$867$	14.6646	+	8.39013i	0.498037	+	0.284944i
$868$	0.358790	−	0.358790i	0.0121781	−	0.0121781i
$869$	2.64084			0.0895842
$870$	−14.5511	−	29.6094i	−0.493327	−	1.00385i
$871$	−27.3798			−0.927731
$872$	−0.0579452	+	0.0579452i	−0.00196227	+	0.00196227i
$873$	1.07851	−	4.15511i	0.0365019	−	0.140629i
$874$		−	32.8344i		−	1.11064i
$875$	5.54567	+	1.19504i	0.187478	+	0.0403996i
$876$	22.9348	−	6.24184i	0.774894	−	0.210892i
$877$	25.9850	+	25.9850i	0.877452	+	0.877452i	0.993270	−	0.115818i	$-0.0369490\pi$
$877$	25.9850	+	25.9850i	0.877452	+	0.877452i	−0.115818	+	0.993270i	$0.536949\pi$
$878$	8.18801	+	8.18801i	0.276332	+	0.276332i
$879$	32.4531	−	8.83230i	1.09461	−	0.297906i
$880$	0.830133	+	4.29208i	0.0279838	+	0.144686i
$881$		−	57.2613i		−	1.92918i	−0.263747	−	0.964592i	$-0.584958\pi$
$881$		−	57.2613i		−	1.92918i	0.263747	−	0.964592i	$-0.415042\pi$
$882$	−5.08191	+	19.5788i	−0.171117	+	0.659254i
$883$	−6.65521	+	6.65521i	−0.223966	+	0.223966i	−0.810166	−	0.586200i	$-0.800623\pi$
$883$	−6.65521	+	6.65521i	−0.223966	+	0.223966i	0.586200	+	0.810166i	$0.300623\pi$
$884$	−12.7370			−0.428391
$885$	2.34720	−	6.88347i	0.0789003	−	0.231385i
$886$	12.5682			0.422238
$887$	−40.0415	+	40.0415i	−1.34446	+	1.34446i	−0.452901	+	0.891561i	$0.649611\pi$
$887$	−40.0415	+	40.0415i	−1.34446	+	1.34446i	−0.891561	+	0.452901i	$0.850389\pi$
$888$	−4.09927	−	2.34533i	−0.137562	−	0.0787041i
$889$		−	3.89012i		−	0.130470i
$890$	0.241442	−	0.357231i	0.00809315	−	0.0119744i
$891$	−15.3742	−	8.55766i	−0.515055	−	0.286692i
$892$	−19.1668	−	19.1668i	−0.641751	−	0.641751i
$893$	−15.3313	−	15.3313i	−0.513043	−	0.513043i
$894$	−0.374538	−	1.37619i	−0.0125264	−	0.0460266i
$895$	−8.20557	+	1.58704i	−0.274282	+	0.0530489i
$896$		−	0.507406i		−	0.0169512i
$897$	−18.8049	+	32.8679i	−0.627876	+	1.09743i
$898$	−6.84052	+	6.84052i	−0.228271	+	0.228271i
$899$	−8.51841			−0.284105
$900$	−9.16417	+	11.8751i	−0.305472	+	0.395837i
$901$	−68.3383			−2.27668
$902$	−13.5084	+	13.5084i	−0.449779	+	0.449779i
$903$	−0.936766	+	1.63732i	−0.0311736	+	0.0544866i
$904$			13.1399i			0.437025i
$905$	38.5067	−	7.44759i	1.28001	−	0.247566i
$906$	−5.30455	−	19.4908i	−0.176232	−	0.647540i
$907$	−1.45442	−	1.45442i	−0.0482933	−	0.0482933i	0.682548	−	0.730841i	$-0.260872\pi$
$907$	−1.45442	−	1.45442i	−0.0482933	−	0.0482933i	−0.730841	+	0.682548i	$0.760872\pi$
$908$	−1.96350	−	1.96350i	−0.0651611	−	0.0651611i
$909$	−0.823843	+	0.484300i	−0.0273252	+	0.0160632i
$910$	1.56449	−	2.31478i	0.0518622	−	0.0767341i
$911$		−	4.45072i		−	0.147459i	−0.997278	−	0.0737294i	$-0.976510\pi$
$911$		−	4.45072i		−	0.147459i	0.997278	−	0.0737294i	$-0.0234901\pi$
$912$	−5.55987	−	3.18099i	−0.184106	−	0.105333i
$913$	−4.81507	+	4.81507i	−0.159356	+	0.159356i
$914$	−6.92187			−0.228955
$915$	13.1505	−	38.5655i	0.434742	−	1.27494i
$916$	1.32660			0.0438322
$917$	5.38451	−	5.38451i	0.177812	−	0.177812i
$918$	−0.316146	−	26.8751i	−0.0104344	−	0.887009i
$919$			2.60868i			0.0860525i	0.999074	+	0.0430263i	$0.0136999\pi$
$919$			2.60868i			0.0860525i	−0.999074	+	0.0430263i	$0.986300\pi$
$920$	3.76984	+	19.4914i	0.124288	+	0.642614i
$921$	−45.1841	+	12.2971i	−1.48887	+	0.405204i
$922$	−18.7077	−	18.7077i	−0.616107	−	0.616107i
$923$	5.02550	+	5.02550i	0.165416	+	0.165416i
$924$	1.65790	−	0.451207i	0.0545408	−	0.0148436i
$925$	−12.5397	−	5.35048i	−0.412302	−	0.175923i
$926$			31.1370i			1.02323i
$927$	−45.3678	−	11.7757i	−1.49008	−	0.386766i
$928$	−6.02342	+	6.02342i	−0.197729	+	0.197729i
$929$	−23.7156			−0.778084			−0.389042	−	0.921220i	$-0.627194\pi$
$929$	−23.7156			−0.778084			−0.389042	+	0.921220i	$0.627194\pi$
$930$	1.70819	+	3.47593i	0.0560138	+	0.113980i
$931$	−24.9355			−0.817228
$932$	7.07940	−	7.07940i	0.231893	−	0.231893i
$933$	9.40443	+	5.38059i	0.307887	+	0.176153i
$934$			17.2772i			0.565327i
$935$	−18.7344	−	12.6620i	−0.612682	−	0.414093i
$936$	3.74374	+	6.36849i	0.122368	+	0.208160i
$937$	−12.5016	−	12.5016i	−0.408408	−	0.408408i	0.472775	−	0.881183i	$-0.343252\pi$
$937$	−12.5016	−	12.5016i	−0.408408	−	0.408408i	−0.881183	+	0.472775i	$0.843252\pi$
$938$	3.98936	+	3.98936i	0.130257	+	0.130257i
$939$	−12.2043	−	44.8430i	−0.398272	−	1.46340i
$940$	10.8614	+	7.34088i	0.354259	+	0.239433i
$941$			16.3893i			0.534277i	0.963658	+	0.267139i	$0.0860782\pi$
$941$			16.3893i			0.534277i	−0.963658	+	0.267139i	$0.913922\pi$
$942$	18.0564	−	31.5597i	0.588309	−	1.02827i
$943$	−61.3449	+	61.3449i	−1.99767	+	1.99767i
$944$	−1.87779			−0.0611169
$945$	4.92302	+	3.24362i	0.160146	+	0.105515i
$946$	−4.19629			−0.136433
$947$	−34.5084	+	34.5084i	−1.12137	+	1.12137i	−0.129837	+	0.991535i	$0.541445\pi$
$947$	−34.5084	+	34.5084i	−1.12137	+	1.12137i	−0.991535	+	0.129837i	$0.958555\pi$
$948$	1.16185	−	2.03074i	0.0377353	−	0.0659553i
$949$		−	33.7924i		−	1.09695i
$950$	−17.0077	−	7.25690i	−0.551802	−	0.235445i
$951$	−6.64202	−	24.4052i	−0.215382	−	0.791393i
$952$	1.85583	+	1.85583i	0.0601478	+	0.0601478i
$953$	35.3174	+	35.3174i	1.14404	+	1.14404i	0.987703	+	0.156339i	$0.0499692\pi$
$953$	35.3174	+	35.3174i	1.14404	+	1.14404i	0.156339	+	0.987703i	$0.450031\pi$
$954$	20.0865	+	34.1691i	0.650323	+	1.10627i
$955$	1.02968	+	5.32383i	0.0333198	+	0.172275i
$956$			9.69880i			0.313682i
$957$	−25.0372	−	14.3246i	−0.809338	−	0.463050i
$958$	−0.802667	+	0.802667i	−0.0259330	+	0.0259330i
$959$	−1.66687			−0.0538260
$960$	3.66573	+	1.24998i	0.118311	+	0.0403429i
$961$	1.00000			0.0322581
$962$	−4.74777	+	4.74777i	−0.153074	+	0.153074i
$963$	7.74930	+	2.01142i	0.249718	+	0.0648172i
$964$		−	1.35150i		−	0.0435290i
$965$	15.2016	−	22.4919i	0.489356	−	0.724039i
$966$	7.52894	−	2.04905i	0.242240	−	0.0659270i
$967$	19.7749	+	19.7749i	0.635918	+	0.635918i	0.949546	−	0.313628i	$-0.101544\pi$
$967$	19.7749	+	19.7749i	0.635918	+	0.635918i	−0.313628	+	0.949546i	$0.601544\pi$
$968$	−5.07546	−	5.07546i	−0.163131	−	0.163131i
$969$	31.9696	−	8.70072i	1.02701	−	0.279507i
$970$	−3.14145	+	0.607588i	−0.100866	+	0.0195085i
$971$			16.1832i			0.519344i	0.965697	+	0.259672i	$0.0836144\pi$
$971$			16.1832i			0.519344i	−0.965697	+	0.259672i	$0.916386\pi$
$972$	−13.3446	+	8.05738i	−0.428029	+	0.258441i
$973$	3.31355	−	3.31355i	0.106227	−	0.106227i
$974$	−36.1653			−1.15881
$975$	12.8689	+	17.0049i	0.412135	+	0.544594i
$976$	−10.5206			−0.336755
$977$	−3.95607	+	3.95607i	−0.126566	+	0.126566i	−0.767552	−	0.640986i	$-0.778526\pi$
$977$	−3.95607	+	3.95607i	−0.126566	+	0.126566i	0.640986	+	0.767552i	$0.278526\pi$
$978$	−29.2388	−	16.7285i	−0.934952	−	0.534918i
$979$		−	0.376983i		−	0.0120484i
$980$	14.8025	−	2.86295i	0.472847	−	0.0914535i
$981$	−0.211934	+	0.124586i	−0.00676652	+	0.00397773i
$982$	−4.55050	−	4.55050i	−0.145212	−	0.145212i
$983$	25.3353	+	25.3353i	0.808072	+	0.808072i	0.984342	−	0.176270i	$-0.0564032\pi$
$983$	25.3353	+	25.3353i	0.808072	+	0.808072i	−0.176270	+	0.984342i	$0.556403\pi$
$984$	4.44450	+	16.3307i	0.141685	+	0.520603i
$985$	30.5057	−	45.1355i	0.971993	−	1.43814i
$986$		−	44.0612i		−	1.40319i
$987$	2.55872	−	4.47225i	0.0814451	−	0.142353i
$988$	−6.43944	+	6.43944i	−0.204866	+	0.204866i
$989$	−19.0564			−0.605959
$990$	−0.824462	+	13.0889i	−0.0262031	+	0.415994i
$991$	−55.7498			−1.77095			−0.885475	−	0.464687i	$-0.846167\pi$
$991$	−55.7498			−1.77095			−0.885475	+	0.464687i	$0.846167\pi$
$992$	0.707107	−	0.707107i	0.0224507	−	0.0224507i
$993$	−1.78663	+	3.12274i	−0.0566969	+	0.0990972i
$994$		−	1.46447i		−	0.0464503i
$995$	−5.77302	−	29.8486i	−0.183017	−	0.946264i
$996$	1.58425	+	5.82109i	0.0501988	+	0.184448i
$997$	−9.22969	−	9.22969i	−0.292307	−	0.292307i	0.545684	−	0.837991i	$-0.316270\pi$
$997$	−9.22969	−	9.22969i	−0.292307	−	0.292307i	−0.837991	+	0.545684i	$0.816270\pi$
$998$	1.50915	+	1.50915i	0.0477713	+	0.0477713i
$999$	−10.1357	−	9.89997i	−0.320678	−	0.313221i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.j.h.497.13	yes	40
3.2	odd	2	inner	930.2.j.h.497.3	✓	40
5.3	odd	4	inner	930.2.j.h.683.3	yes	40
15.8	even	4	inner	930.2.j.h.683.13	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.h.497.3	✓	40	3.2	odd	2	inner
930.2.j.h.497.13	yes	40	1.1	even	1	trivial
930.2.j.h.683.3	yes	40	5.3	odd	4	inner
930.2.j.h.683.13	yes	40	15.8	even	4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.860137 + 1.50338i) q^{3} -1.00000i q^{4} +(-2.19538 + 0.424609i) q^{5} +(0.454844 + 1.67126i) q^{6} +(-0.358790 - 0.358790i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.52033 - 2.58623i) q^{9} +(-1.25213 + 1.85261i) q^{10} +1.95505i q^{11} +(1.50338 + 0.860137i) q^{12} +(1.74122 - 1.74122i) q^{13} -0.507406 q^{14} +(1.24998 - 3.66573i) q^{15} -1.00000 q^{16} +(3.65749 - 3.65749i) q^{17} +(-2.90378 - 0.753709i) q^{18} -3.69824i q^{19} +(0.424609 + 2.19538i) q^{20} +(0.848008 - 0.230791i) q^{21} +(1.38243 + 1.38243i) q^{22} +(6.27796 + 6.27796i) q^{23} +(1.67126 - 0.454844i) q^{24} +(4.63941 - 1.86436i) q^{25} -2.46246i q^{26} +(5.19579 - 0.0611210i) q^{27} +(-0.358790 + 0.358790i) q^{28} +8.51841 q^{29} +(-1.70819 - 3.47593i) q^{30} -1.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.93919 - 1.68161i) q^{33} -5.17247i q^{34} +(0.940028 + 0.635336i) q^{35} +(-2.58623 + 1.52033i) q^{36} +(-1.92806 - 1.92806i) q^{37} +(-2.61505 - 2.61505i) q^{38} +(1.12003 + 4.11541i) q^{39} +(1.85261 + 1.25213i) q^{40} +9.77147i q^{41} +(0.436439 - 0.762826i) q^{42} +(-1.51772 + 1.51772i) q^{43} +1.95505 q^{44} +(4.43584 + 5.03223i) q^{45} +8.87838 q^{46} +(4.14558 - 4.14558i) q^{47} +(0.860137 - 1.50338i) q^{48} -6.74254i q^{49} +(1.96226 - 4.59886i) q^{50} +(2.35267 + 8.64455i) q^{51} +(-1.74122 - 1.74122i) q^{52} +(-9.34225 - 9.34225i) q^{53} +(3.63076 - 3.71720i) q^{54} +(-0.830133 - 4.29208i) q^{55} +0.507406i q^{56} +(5.55987 + 3.18099i) q^{57} +(6.02342 - 6.02342i) q^{58} +1.87779 q^{59} +(-3.66573 - 1.24998i) q^{60} +10.5206 q^{61} +(-0.707107 + 0.707107i) q^{62} +(-0.382436 + 1.47339i) q^{63} +1.00000i q^{64} +(-3.08330 + 4.56198i) q^{65} +(-3.26740 + 0.889243i) q^{66} +(-7.86226 - 7.86226i) q^{67} +(-3.65749 - 3.65749i) q^{68} +(-14.8381 + 4.03828i) q^{69} +(1.11395 - 0.215449i) q^{70} +2.88620i q^{71} +(-0.753709 + 2.90378i) q^{72} +(9.70365 - 9.70365i) q^{73} -2.72669 q^{74} +(-1.18768 + 8.57843i) q^{75} -3.69824 q^{76} +(0.701453 - 0.701453i) q^{77} +(3.70202 + 2.11805i) q^{78} -1.35078i q^{79} +(2.19538 - 0.424609i) q^{80} +(-4.37721 + 7.86385i) q^{81} +(6.90947 + 6.90947i) q^{82} +(2.46289 + 2.46289i) q^{83} +(-0.230791 - 0.848008i) q^{84} +(-6.47658 + 9.58259i) q^{85} +2.14639i q^{86} +(-7.32700 + 12.8064i) q^{87} +(1.38243 - 1.38243i) q^{88} -0.192825 q^{89} +(6.69494 + 0.421709i) q^{90} -1.24946 q^{91} +(6.27796 - 6.27796i) q^{92} +(0.860137 - 1.50338i) q^{93} -5.86273i q^{94} +(1.57031 + 8.11905i) q^{95} +(-0.454844 - 1.67126i) q^{96} +(1.01182 + 1.01182i) q^{97} +(-4.76770 - 4.76770i) q^{98} +(5.05622 - 2.97232i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7} + 4 q^{12} + 24 q^{13} - 12 q^{15} - 40 q^{16} - 56 q^{21} + 16 q^{22} - 48 q^{25} + 8 q^{27} - 8 q^{28} + 4 q^{30} - 40 q^{31} - 20 q^{33} - 8 q^{37} - 8 q^{40} + 12 q^{42}+ \cdots + 24 q^{97}+O(q^{100}) \) 40 * q - 4 * q^3 + 8 * q^6 - 8 * q^7 + 4 * q^12 + 24 * q^13 - 12 * q^15 - 40 * q^16 - 56 * q^21 + 16 * q^22 - 48 * q^25 + 8 * q^27 - 8 * q^28 + 4 * q^30 - 40 * q^31 - 20 * q^33 - 8 * q^37 - 8 * q^40 + 12 * q^42 - 16 * q^43 + 76 * q^45 - 8 * q^46 + 4 * q^48 + 16 * q^51 - 24 * q^52 - 48 * q^55 + 56 * q^57 - 56 * q^58 + 12 * q^60 + 128 * q^61 - 24 * q^63 + 16 * q^66 + 8 * q^67 + 32 * q^70 + 248 * q^73 - 8 * q^75 + 56 * q^76 + 8 * q^78 + 40 * q^81 - 8 * q^82 - 48 * q^85 + 12 * q^87 + 16 * q^88 + 16 * q^90 - 192 * q^91 + 4 * q^93 - 8 * q^96 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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