LMFDB - Embedded newform 740.2.be.a.251.76

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [740,2,Mod(51,740)] 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("740.51"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(740, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 0, 11])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.be (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$304$
Relative dimension:	$76$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			251.76
Character	$\chi$	$=$	740.251
Dual form			740.2.be.a.171.76

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41416 + 0.0123313i) q^{2} +(-0.552492 + 0.956944i) q^{3} +(1.99970 + 0.0348769i) q^{4} +(-0.258819 - 0.965926i) q^{5} +(-0.793112 + 1.34646i) q^{6} +(-0.911932 - 0.526504i) q^{7} +(2.82746 + 0.0739805i) q^{8} +(0.889506 + 1.54067i) q^{9} +(-0.354100 - 1.36917i) q^{10} -1.69195 q^{11} +(-1.13819 + 1.89433i) q^{12} +(1.28004 + 4.77717i) q^{13} +(-1.28313 - 0.755807i) q^{14} +(1.06733 + 0.285991i) q^{15} +(3.99757 + 0.139487i) q^{16} +(4.61990 + 1.23790i) q^{17} +(1.23890 + 2.18972i) q^{18} +(6.49847 - 1.74126i) q^{19} +(-0.483871 - 1.94058i) q^{20} +(1.00767 - 0.581779i) q^{21} +(-2.39269 - 0.0208640i) q^{22} +(-1.00871 - 1.00871i) q^{23} +(-1.63294 + 2.66485i) q^{24} +(-0.866025 + 0.500000i) q^{25} +(1.75127 + 6.77147i) q^{26} -5.28073 q^{27} +(-1.80522 - 1.08465i) q^{28} +(4.46668 + 4.46668i) q^{29} +(1.50585 + 0.417598i) q^{30} +(0.275132 - 0.275132i) q^{31} +(5.65148 + 0.246552i) q^{32} +(0.934788 - 1.61910i) q^{33} +(6.51802 + 1.80756i) q^{34} +(-0.272539 + 1.01713i) q^{35} +(1.72501 + 3.11189i) q^{36} +(-2.53258 - 5.53046i) q^{37} +(9.21135 - 2.38229i) q^{38} +(-5.27870 - 1.41442i) q^{39} +(-0.660341 - 2.75026i) q^{40} +(-5.53989 - 3.19846i) q^{41} +(1.43218 - 0.810302i) q^{42} +(-7.72604 - 7.72604i) q^{43} +(-3.38339 - 0.0590100i) q^{44} +(1.25795 - 1.25795i) q^{45} +(-1.41403 - 1.43891i) q^{46} +3.49426i q^{47} +(-2.34210 + 3.74838i) q^{48} +(-2.94559 - 5.10190i) q^{49} +(-1.23086 + 0.696401i) q^{50} +(-3.73706 + 3.73706i) q^{51} +(2.39308 + 9.59754i) q^{52} +(5.09943 + 8.83247i) q^{53} +(-7.46779 - 0.0651184i) q^{54} +(0.437909 + 1.63430i) q^{55} +(-2.53950 - 1.55614i) q^{56} +(-1.92406 + 7.18071i) q^{57} +(6.26152 + 6.37168i) q^{58} +(1.22270 - 4.56316i) q^{59} +(2.12437 + 0.609120i) q^{60} +(-1.89645 + 0.508152i) q^{61} +(0.392473 - 0.385687i) q^{62} -1.87331i q^{63} +(7.98905 + 0.418353i) q^{64} +(4.28310 - 2.47285i) q^{65} +(1.34191 - 2.27814i) q^{66} +(-7.60563 + 13.1733i) q^{67} +(9.19523 + 2.63655i) q^{68} +(1.52258 - 0.407973i) q^{69} +(-0.397956 + 1.43502i) q^{70} +(-1.55425 - 0.897347i) q^{71} +(2.40106 + 4.42198i) q^{72} -16.0678i q^{73} +(-3.51328 - 7.85219i) q^{74} -1.10498i q^{75} +(13.0557 - 3.25535i) q^{76} +(1.54294 + 0.890819i) q^{77} +(-7.44748 - 2.06531i) q^{78} +(-2.99879 + 0.803523i) q^{79} +(-0.899913 - 3.89746i) q^{80} +(0.249043 - 0.431354i) q^{81} +(-7.79485 - 4.59144i) q^{82} +(-11.4458 + 6.60821i) q^{83} +(2.03532 - 1.12824i) q^{84} -4.78288i q^{85} +(-10.8306 - 11.0211i) q^{86} +(-6.74217 + 1.80656i) q^{87} +(-4.78392 - 0.125171i) q^{88} +(1.14117 - 4.25890i) q^{89} +(1.79446 - 1.76343i) q^{90} +(1.34789 - 5.03040i) q^{91} +(-1.98192 - 2.05228i) q^{92} +(0.111278 + 0.415293i) q^{93} +(-0.0430888 + 4.94144i) q^{94} +(-3.36386 - 5.82637i) q^{95} +(-3.35833 + 5.27193i) q^{96} +(-5.15561 + 5.15561i) q^{97} +(-4.10262 - 7.25123i) q^{98} +(-1.50500 - 2.60673i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 304 q + 4 q^{2} - 12 q^{4} - 8 q^{8} - 152 q^{9} + 16 q^{13} - 24 q^{14} + 20 q^{16} - 60 q^{18} - 16 q^{22} - 24 q^{24} - 32 q^{29} - 56 q^{32} - 32 q^{37} + 40 q^{38} + 20 q^{42} + 12 q^{44} - 8 q^{46}+ \cdots - 36 q^{98}+O(q^{100}) $ 304 * q + 4 * q^2 - 12 * q^4 - 8 * q^8 - 152 * q^9 + 16 * q^13 - 24 * q^14 + 20 * q^16 - 60 * q^18 - 16 * q^22 - 24 * q^24 - 32 * q^29 - 56 * q^32 - 32 * q^37 + 40 * q^38 + 20 * q^42 + 12 * q^44 - 8 * q^46 + 104 * q^49 + 4 * q^50 - 40 * q^52 + 40 * q^54 + 4 * q^56 - 48 * q^57 - 12 * q^58 - 28 * q^60 - 16 * q^61 - 60 * q^62 + 24 * q^65 - 52 * q^66 - 200 * q^68 - 196 * q^72 + 20 * q^74 - 40 * q^76 + 96 * q^77 - 48 * q^78 - 152 * q^81 + 32 * q^82 - 112 * q^84 + 12 * q^88 - 8 * q^89 + 140 * q^92 - 16 * q^93 - 28 * q^94 - 132 * q^96 + 48 * q^97 - 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.41416	+	0.0123313i	0.999962	+	0.00871956i
$2$	1.41416	+	0.0123313i	0.999962	+	0.00871956i
$3$	−0.552492	+	0.956944i	−0.318981	+	0.552492i	−0.980276	−	0.197635i	$-0.936674\pi$
$3$	−0.552492	+	0.956944i	−0.318981	+	0.552492i	0.661294	+	0.750126i	$0.270007\pi$
$4$	1.99970	+	0.0348769i	0.999848	+	0.0174385i
$5$	−0.258819	−	0.965926i	−0.115747	−	0.431975i
$5$	−0.258819	−	0.965926i	−0.115747	−	0.431975i
$6$	−0.793112	+	1.34646i	−0.323787	+	0.549689i
$7$	−0.911932	−	0.526504i	−0.344678	−	0.199000i	0.317661	−	0.948204i	$-0.397103\pi$
$7$	−0.911932	−	0.526504i	−0.344678	−	0.199000i	−0.662339	+	0.749204i	$0.730436\pi$
$8$	2.82746	+	0.0739805i	0.999658	+	0.0261560i
$9$	0.889506	+	1.54067i	0.296502	+	0.513556i
$10$	−0.354100	−	1.36917i	−0.111976	−	0.432968i
$11$	−1.69195			−0.510142			−0.255071	−	0.966922i	$-0.582099\pi$
$11$	−1.69195			−0.510142			−0.255071	+	0.966922i	$0.582099\pi$
$12$	−1.13819	+	1.89433i	−0.328567	+	0.546845i
$13$	1.28004	+	4.77717i	0.355019	+	1.32495i	0.880461	+	0.474119i	$0.157234\pi$
$13$	1.28004	+	4.77717i	0.355019	+	1.32495i	−0.525441	+	0.850830i	$0.676100\pi$
$14$	−1.28313	−	0.755807i	−0.342930	−	0.201998i
$15$	1.06733	+	0.285991i	0.275584	+	0.0738425i
$16$	3.99757	+	0.139487i	0.999392	+	0.0348716i
$17$	4.61990	+	1.23790i	1.12049	+	0.300235i	0.771082	−	0.636736i	$-0.219716\pi$
$17$	4.61990	+	1.23790i	1.12049	+	0.300235i	0.349409	+	0.936970i	$0.386382\pi$
$18$	1.23890	+	2.18972i	0.292013	+	0.516122i
$19$	6.49847	−	1.74126i	1.49085	−	0.399473i	0.580828	−	0.814027i	$-0.302729\pi$
$19$	6.49847	−	1.74126i	1.49085	−	0.399473i	0.910025	+	0.414554i	$0.136062\pi$
$20$	−0.483871	−	1.94058i	−0.108197	−	0.433928i
$21$	1.00767	−	0.581779i	0.219892	−	0.126955i
$22$	−2.39269	−	0.0208640i	−0.510123	−	0.00444822i
$23$	−1.00871	−	1.00871i	−0.210330	−	0.210330i	0.594078	−	0.804408i	$-0.297517\pi$
$23$	−1.00871	−	1.00871i	−0.210330	−	0.210330i	−0.804408	+	0.594078i	$0.797517\pi$
$24$	−1.63294	+	2.66485i	−0.333323	+	0.543959i
$25$	−0.866025	+	0.500000i	−0.173205	+	0.100000i
$26$	1.75127	+	6.77147i	0.343453	+	1.32799i
$27$	−5.28073			−1.01628
$28$	−1.80522	−	1.08465i	−0.341155	−	0.204980i
$29$	4.46668	+	4.46668i	0.829442	+	0.829442i	0.987439	−	0.157998i	$-0.0505039\pi$
$29$	4.46668	+	4.46668i	0.829442	+	0.829442i	−0.157998	+	0.987439i	$0.550504\pi$
$30$	1.50585	+	0.417598i	0.274930	+	0.0762427i
$31$	0.275132	−	0.275132i	0.0494151	−	0.0494151i	−0.681967	−	0.731383i	$-0.738875\pi$
$31$	0.275132	−	0.275132i	0.0494151	−	0.0494151i	0.731383	+	0.681967i	$0.238875\pi$
$32$	5.65148	+	0.246552i	0.999050	+	0.0435846i
$33$	0.934788	−	1.61910i	0.162726	−	0.281849i
$34$	6.51802	+	1.80756i	1.11783	+	0.309993i
$35$	−0.272539	+	1.01713i	−0.0460675	+	0.171926i
$36$	1.72501	+	3.11189i	0.287501	+	0.518649i
$37$	−2.53258	−	5.53046i	−0.416354	−	0.909203i
$37$	−2.53258	−	5.53046i	−0.416354	−	0.909203i
$38$	9.21135	−	2.38229i	1.49428	−	0.386458i
$39$	−5.27870	−	1.41442i	−0.845268	−	0.226489i
$40$	−0.660341	−	2.75026i	−0.104409	−	0.434855i
$41$	−5.53989	−	3.19846i	−0.865185	−	0.499515i	0.000560008	−	1.00000i	$-0.499822\pi$
$41$	−5.53989	−	3.19846i	−0.865185	−	0.499515i	−0.865745	+	0.500485i	$0.833155\pi$
$42$	1.43218	−	0.810302i	0.220990	−	0.125032i
$43$	−7.72604	−	7.72604i	−1.17821	−	1.17821i	−0.980200	−	0.198010i	$-0.936552\pi$
$43$	−7.72604	−	7.72604i	−1.17821	−	1.17821i	−0.198010	−	0.980200i	$-0.563448\pi$
$44$	−3.38339	−	0.0590100i	−0.510065	−	0.00889610i
$45$	1.25795	−	1.25795i	0.187524	−	0.187524i
$46$	−1.41403	−	1.43891i	−0.208488	−	0.212156i
$47$			3.49426i			0.509689i	0.966982	+	0.254845i	$0.0820244\pi$
$47$			3.49426i			0.509689i	−0.966982	+	0.254845i	$0.917976\pi$
$48$	−2.34210	+	3.74838i	−0.338054	+	0.541032i
$49$	−2.94559	−	5.10190i	−0.420798	−	0.728844i
$50$	−1.23086	+	0.696401i	−0.174070	+	0.0984859i
$51$	−3.73706	+	3.73706i	−0.523293	+	0.523293i
$52$	2.39308	+	9.59754i	0.331860	+	1.33094i
$53$	5.09943	+	8.83247i	0.700461	+	1.21323i	0.968305	+	0.249771i	$0.0803554\pi$
$53$	5.09943	+	8.83247i	0.700461	+	1.21323i	−0.267844	+	0.963462i	$0.586311\pi$
$54$	−7.46779	−	0.0651184i	−1.01624	−	0.00886149i
$55$	0.437909	+	1.63430i	0.0590476	+	0.220369i
$56$	−2.53950	−	1.55614i	−0.339355	−	0.207947i
$57$	−1.92406	+	7.18071i	−0.254849	+	0.951108i
$58$	6.26152	+	6.37168i	0.822178	+	0.836642i
$59$	1.22270	−	4.56316i	0.159181	−	0.594073i	−0.839529	−	0.543314i	$-0.817169\pi$
$59$	1.22270	−	4.56316i	0.159181	−	0.594073i	0.998711	−	0.0507591i	$-0.0161641\pi$
$60$	2.12437	+	0.609120i	0.274254	+	0.0786370i
$61$	−1.89645	+	0.508152i	−0.242815	+	0.0650621i	−0.378174	−	0.925734i	$-0.623448\pi$
$61$	−1.89645	+	0.508152i	−0.242815	+	0.0650621i	0.135359	+	0.990797i	$0.456781\pi$
$62$	0.392473	−	0.385687i	0.0498441	−	0.0489823i
$63$		−	1.87331i		−	0.236015i
$64$	7.98905	+	0.418353i	0.998632	+	0.0522942i
$65$	4.28310	−	2.47285i	0.531253	−	0.306719i
$66$	1.34191	−	2.27814i	0.165177	−	0.280420i
$67$	−7.60563	+	13.1733i	−0.929176	+	1.60938i	−0.144472	+	0.989509i	$0.546148\pi$
$67$	−7.60563	+	13.1733i	−0.929176	+	1.60938i	−0.784704	+	0.619871i	$0.787185\pi$
$68$	9.19523	+	2.63655i	1.11508	+	0.319729i
$69$	1.52258	−	0.407973i	0.183297	−	0.0491142i
$70$	−0.397956	+	1.43502i	−0.0475648	+	0.171518i
$71$	−1.55425	−	0.897347i	−0.184456	−	0.106495i	0.404929	−	0.914348i	$-0.367296\pi$
$71$	−1.55425	−	0.897347i	−0.184456	−	0.106495i	−0.589384	+	0.807853i	$0.700630\pi$
$72$	2.40106	+	4.42198i	0.282968	+	0.521136i
$73$		−	16.0678i		−	1.88060i	−0.340348	−	0.940300i	$-0.610545\pi$
$73$		−	16.0678i		−	1.88060i	0.340348	−	0.940300i	$-0.389455\pi$
$74$	−3.51328	−	7.85219i	−0.408410	−	0.912799i
$75$		−	1.10498i		−	0.127593i
$76$	13.0557	−	3.25535i	1.49759	−	0.373414i
$77$	1.54294	+	0.890819i	0.175835	+	0.101518i
$78$	−7.44748	−	2.06531i	−0.843261	−	0.233851i
$79$	−2.99879	+	0.803523i	−0.337390	+	0.0904034i	−0.423536	−	0.905879i	$-0.639211\pi$
$79$	−2.99879	+	0.803523i	−0.337390	+	0.0904034i	0.0861463	+	0.996282i	$0.472545\pi$
$80$	−0.899913	−	3.89746i	−0.100613	−	0.435749i
$81$	0.249043	−	0.431354i	0.0276714	−	0.0479283i
$82$	−7.79485	−	4.59144i	−0.860797	−	0.507040i
$83$	−11.4458	+	6.60821i	−1.25633	+	0.725345i	−0.972360	−	0.233486i	$-0.924987\pi$
$83$	−11.4458	+	6.60821i	−1.25633	+	0.725345i	−0.283975	+	0.958832i	$0.591653\pi$
$84$	2.03532	−	1.12824i	0.222072	−	0.123101i
$85$		−	4.78288i		−	0.518776i
$86$	−10.8306	−	11.0211i	−1.16789	−	1.18844i
$87$	−6.74217	+	1.80656i	−0.722836	+	0.193683i
$88$	−4.78392	−	0.125171i	−0.509968	−	0.0133433i
$89$	1.14117	−	4.25890i	0.120964	−	0.451442i	−0.878700	−	0.477374i	$-0.841589\pi$
$89$	1.14117	−	4.25890i	0.120964	−	0.451442i	0.999664	+	0.0259320i	$0.00825533\pi$
$90$	1.79446	−	1.76343i	0.189152	−	0.185882i
$91$	1.34789	−	5.03040i	0.141298	−	0.527330i
$92$	−1.98192	−	2.05228i	−0.206630	−	0.213965i
$93$	0.111278	+	0.415293i	0.0115389	+	0.0430639i
$94$	−0.0430888	+	4.94144i	−0.00444427	+	0.509670i
$95$	−3.36386	−	5.82637i	−0.345125	−	0.597773i
$96$	−3.35833	+	5.27193i	−0.342758	+	0.538064i
$97$	−5.15561	+	5.15561i	−0.523473	+	0.523473i	−0.918619	−	0.395146i	$-0.870694\pi$
$97$	−5.15561	+	5.15561i	−0.523473	+	0.523473i	0.395146	+	0.918619i	$0.370694\pi$
$98$	−4.10262	−	7.25123i	−0.414427	−	0.732485i
$99$	−1.50500	−	2.60673i	−0.151258	−	0.261987i
$100$	−1.74923	+	0.969644i	−0.174923	+	0.0969644i
$101$		−	13.5949i		−	1.35274i	−0.736560	−	0.676372i	$-0.763551\pi$
$101$		−	13.5949i		−	1.35274i	0.736560	−	0.676372i	$-0.236449\pi$
$102$	−5.33088	+	5.23871i	−0.527836	+	0.518710i
$103$	13.7799	−	13.7799i	1.35778	−	1.35778i	0.481124	−	0.876652i	$-0.340229\pi$
$103$	13.7799	−	13.7799i	1.35778	−	1.35778i	0.876652	−	0.481124i	$-0.159771\pi$
$104$	3.26584	+	13.6020i	0.320242	+	1.33378i
$105$	−0.822759	−	0.822759i	−0.0802931	−	0.0802931i
$106$	7.10249	+	12.5534i	0.689855	+	1.21929i
$107$	2.25565	+	1.30230i	0.218061	+	0.125898i	0.605052	−	0.796186i	$-0.293152\pi$
$107$	2.25565	+	1.30230i	0.218061	+	0.125898i	−0.386991	+	0.922084i	$0.626486\pi$
$108$	−10.5599	−	0.184176i	−1.01612	−	0.0177223i
$109$	11.2350	+	3.01040i	1.07612	+	0.288344i	0.753004	−	0.658016i	$-0.228604\pi$
$109$	11.2350	+	3.01040i	1.07612	+	0.288344i	0.323112	+	0.946361i	$0.395271\pi$
$110$	0.599120	+	2.31656i	0.0571239	+	0.220875i
$111$	6.69157	+	0.631998i	0.635136	+	0.0599866i
$112$	−3.57207	−	2.23194i	−0.337529	−	0.210898i
$113$	2.37167	−	8.85119i	0.223108	−	0.832649i	−0.760046	−	0.649869i	$-0.774824\pi$
$113$	2.37167	−	8.85119i	0.223108	−	0.832649i	0.983154	−	0.182780i	$-0.0585097\pi$
$114$	−2.80948	+	10.1309i	−0.263132	+	0.948850i
$115$	−0.713262	+	1.23541i	−0.0665121	+	0.115202i
$116$	8.77622	+	9.08779i	0.814851	+	0.843780i
$117$	−6.22144	+	6.22144i	−0.575172	+	0.575172i
$118$	1.78536	−	6.43796i	0.164355	−	0.592663i
$119$	−3.56128	−	3.56128i	−0.326462	−	0.326462i
$120$	2.99668	+	0.887589i	0.273558	+	0.0810254i
$121$	−8.13731			−0.739755
$122$	−2.68815	+	0.695222i	−0.243373	+	0.0629424i
$123$	6.12149	−	3.53424i	0.551956	−	0.318672i
$124$	0.559775	−	0.540584i	0.0502693	−	0.0485459i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	0.0231005	−	2.64917i	0.00205795	−	0.236006i
$127$	−11.3254	+	6.53870i	−1.00496	+	0.580216i	−0.909713	−	0.415237i	$-0.863699\pi$
$127$	−11.3254	+	6.53870i	−1.00496	+	0.580216i	−0.0952506	+	0.995453i	$0.530365\pi$
$128$	11.2926	+	0.690134i	0.998138	+	0.0609998i
$129$	11.6620	−	3.12481i	1.02678	−	0.275124i
$130$	6.08748	−	3.44418i	0.533907	−	0.302075i
$131$	2.57540	+	0.690076i	0.225014	+	0.0602923i	0.369564	−	0.929205i	$-0.379507\pi$
$131$	2.57540	+	0.690076i	0.225014	+	0.0602923i	−0.144551	+	0.989497i	$0.546174\pi$
$132$	1.92576	−	3.20511i	0.167616	−	0.278969i
$133$	−6.84295	−	1.83356i	−0.593359	−	0.158990i
$134$	−10.9180	+	18.5354i	−0.943174	+	1.60122i
$135$	1.36675	+	5.10079i	0.117631	+	0.439006i
$136$	12.9710	+	3.84189i	1.11225	+	0.329440i
$137$	−20.0963			−1.71695			−0.858473	−	0.512859i	$-0.828586\pi$
$137$	−20.0963			−1.71695			−0.858473	+	0.512859i	$0.828586\pi$
$138$	2.15820	−	0.558164i	0.183718	−	0.0475140i
$139$	−7.04286	−	12.1986i	−0.597367	−	1.03467i	−0.993208	−	0.116351i	$-0.962880\pi$
$139$	−7.04286	−	12.1986i	−0.597367	−	1.03467i	0.395841	−	0.918319i	$-0.370453\pi$
$140$	−0.580469	+	2.02444i	−0.0490586	+	0.171097i
$141$	−3.34381	−	1.93055i	−0.281599	−	0.162581i
$142$	−2.18689	−	1.28816i	−0.183520	−	0.108100i
$143$	−2.16576	−	8.08274i	−0.181110	−	0.675912i
$144$	3.34096	+	6.28300i	0.278413	+	0.523583i
$145$	3.15842	−	5.47054i	0.262292	−	0.454304i
$146$	0.198138	−	22.7225i	0.0163980	−	1.88053i
$147$	6.50965			0.536907
$148$	−4.87151	−	11.1476i	−0.400435	−	0.916325i
$149$	0.987449			0.0808950			0.0404475	−	0.999182i	$-0.487122\pi$
$149$	0.987449			0.0808950			0.0404475	+	0.999182i	$0.487122\pi$
$150$	0.0136259	−	1.56262i	0.00111255	−	0.127588i
$151$	9.85444	−	17.0684i	0.801943	−	1.38901i	−0.116393	−	0.993203i	$-0.537133\pi$
$151$	9.85444	−	17.0684i	0.801943	−	1.38901i	0.918336	−	0.395803i	$-0.129534\pi$
$152$	18.5030	−	4.44258i	1.50079	−	0.360341i
$153$	2.20224	+	8.21886i	0.178040	+	0.664455i
$154$	2.17098	+	1.27879i	0.174943	+	0.103048i
$155$	−0.336966	−	0.194547i	−0.0270658	−	0.0156264i
$156$	−10.5065	−	3.01252i	−0.841190	−	0.241195i
$157$	4.75359	+	8.23346i	0.379378	+	0.657102i	0.990972	−	0.134070i	$-0.0428047\pi$
$157$	4.75359	+	8.23346i	0.379378	+	0.657102i	−0.611594	+	0.791172i	$0.709471\pi$
$158$	−4.25067	+	1.09933i	−0.338166	+	0.0874581i
$159$	−11.2696			−0.893735
$160$	−1.22456	−	5.52272i	−0.0968100	−	0.436609i
$161$	0.388783	+	1.45096i	0.0306404	+	0.114352i
$162$	0.357505	−	0.606933i	0.0280883	−	0.0476852i
$163$	3.94338	+	1.05663i	0.308869	+	0.0827613i	0.409924	−	0.912120i	$-0.365555\pi$
$163$	3.94338	+	1.05663i	0.308869	+	0.0827613i	−0.101055	+	0.994881i	$0.532222\pi$
$164$	−10.9665	−	6.58915i	−0.856343	−	0.514526i
$165$	−1.80587	−	0.483882i	−0.140587	−	0.0376702i
$166$	−16.2676	+	9.20392i	−1.26261	+	0.714363i
$167$	8.25996	−	2.21325i	0.639175	−	0.171266i	0.0753450	−	0.997158i	$-0.475994\pi$
$167$	8.25996	−	2.21325i	0.639175	−	0.171266i	0.563829	+	0.825891i	$0.309328\pi$
$168$	2.89219	−	1.57041i	0.223137	−	0.121160i
$169$	−9.92454	+	5.72994i	−0.763426	+	0.440764i
$170$	0.0589792	−	6.76375i	0.00452350	−	0.518756i
$171$	8.46314	+	8.46314i	0.647192	+	0.647192i
$172$	−15.1803	−	15.7192i	−1.15748	−	1.19858i
$173$	−8.37247	+	4.83384i	−0.636547	+	0.367510i	−0.783283	−	0.621665i	$-0.786456\pi$
$173$	−8.37247	+	4.83384i	−0.636547	+	0.367510i	0.146736	+	0.989176i	$0.453123\pi$
$174$	−9.55678	+	2.47162i	−0.724497	+	0.187373i
$175$	1.05301			0.0796000
$176$	−6.76368	−	0.236004i	−0.509832	−	0.0177895i
$177$	3.69116	+	3.69116i	0.277445	+	0.277445i
$178$	1.66631	−	6.00869i	0.124895	−	0.450370i
$179$	−2.50419	+	2.50419i	−0.187172	+	0.187172i	−0.794472	−	0.607300i	$-0.792252\pi$
$179$	−2.50419	+	2.50419i	−0.187172	+	0.187172i	0.607300	+	0.794472i	$0.292252\pi$
$180$	2.55939	−	2.47165i	0.190766	−	0.184226i
$181$	8.58824	−	14.8753i	0.638359	−	1.10567i	−0.347434	−	0.937704i	$-0.612947\pi$
$181$	8.58824	−	14.8753i	0.638359	−	1.10567i	0.985793	−	0.167966i	$-0.0537197\pi$
$182$	1.96817	−	7.09717i	0.145890	−	0.526078i
$183$	0.561499	−	2.09554i	0.0415072	−	0.154907i
$184$	−2.77745	−	2.92670i	−0.204756	−	0.215759i
$185$	−4.68654	+	3.87767i	−0.344561	+	0.285092i
$186$	0.152243	+	0.588664i	0.0111630	+	0.0431629i
$187$	−7.81664	−	2.09446i	−0.571610	−	0.153162i
$188$	−0.121869	+	6.98745i	−0.00888820	+	0.509612i
$189$	4.81567	+	2.78033i	0.350288	+	0.202239i
$190$	−4.68519	−	8.28090i	−0.339899	−	0.600760i
$191$	16.6732	+	16.6732i	1.20643	+	1.20643i	0.972175	+	0.234257i	$0.0752656\pi$
$191$	16.6732	+	16.6732i	1.20643	+	1.20643i	0.234257	+	0.972175i	$0.424734\pi$
$192$	−4.81423	+	7.41394i	−0.347437	+	0.535055i
$193$	−9.93880	+	9.93880i	−0.715410	+	0.715410i	−0.967662	−	0.252251i	$-0.918829\pi$
$193$	−9.93880	+	9.93880i	−0.715410	+	0.715410i	0.252251	+	0.967662i	$0.418829\pi$
$194$	−7.35443	+	7.22728i	−0.528018	+	0.518889i
$195$			5.46491i			0.391350i
$196$	−5.71234	−	10.3050i	−0.408024	−	0.736071i
$197$	−0.373419	−	0.646781i	−0.0266050	−	0.0460812i	0.852416	−	0.522864i	$-0.175136\pi$
$197$	−0.373419	−	0.646781i	−0.0266050	−	0.0460812i	−0.879021	+	0.476782i	$0.841803\pi$
$198$	−2.09616	−	3.70490i	−0.148968	−	0.263296i
$199$	16.6292	−	16.6292i	1.17882	−	1.17882i	0.198770	−	0.980046i	$-0.436305\pi$
$199$	16.6292	−	16.6292i	1.17882	−	1.17882i	0.980046	−	0.198770i	$-0.0636947\pi$
$200$	−2.48564	+	1.34966i	−0.175761	+	0.0954354i
$201$	−8.40410	−	14.5563i	−0.592779	−	1.02672i
$202$	0.167643	−	19.2254i	0.0117953	−	1.35269i
$203$	−1.72158	−	6.42504i	−0.120831	−	0.450949i
$204$	−7.60332	+	7.34264i	−0.532339	+	0.514088i
$205$	−1.65564	+	6.17894i	−0.115635	+	0.431556i
$206$	19.6569	−	19.3171i	1.36956	−	1.34589i
$207$	0.656832	−	2.45133i	0.0456530	−	0.170379i
$208$	4.45069	+	19.2756i	0.308600	+	1.33652i
$209$	−10.9951	+	2.94613i	−0.760547	+	0.203788i
$210$	−1.15337	−	1.17366i	−0.0795899	−	0.0809902i
$211$			0.478764i			0.0329594i	0.999864	+	0.0164797i	$0.00524590\pi$
$211$			0.478764i			0.0329594i	−0.999864	+	0.0164797i	$0.994754\pi$
$212$	9.88926	+	17.8401i	0.679197	+	1.22526i
$213$	1.71742	−	0.991553i	0.117676	−	0.0679401i
$214$	3.17378	+	1.86947i	0.216955	+	0.127794i
$215$	−5.46313	+	9.46243i	−0.372583	+	0.645332i
$216$	−14.9310	−	0.390671i	−1.01593	−	0.0265818i
$217$	−0.395759	+	0.106043i	−0.0268659	+	0.00719870i
$218$	15.8509	+	4.39573i	1.07356	+	0.297717i
$219$	15.3760	+	8.87735i	1.03902	+	0.599876i
$220$	0.818685	+	3.28337i	0.0551957	+	0.221365i
$221$			23.6546i			1.59118i
$222$	9.45516	+	0.976262i	0.634589	+	0.0655224i
$223$		−	13.1300i		−	0.879248i	−0.898182	−	0.439624i	$-0.855112\pi$
$223$		−	13.1300i		−	0.879248i	0.898182	−	0.439624i	$-0.144888\pi$
$224$	−5.02396	−	3.20037i	−0.335677	−	0.213834i
$225$	−1.54067	−	0.889506i	−0.102711	−	0.0593004i
$226$	3.46306	−	12.4877i	0.230360	−	0.830672i
$227$	−0.647028	+	0.173371i	−0.0429447	+	0.0115070i	−0.280227	−	0.959934i	$-0.590410\pi$
$227$	−0.647028	+	0.173371i	−0.0429447	+	0.0115070i	0.237283	+	0.971441i	$0.423743\pi$
$228$	−4.09799	+	14.2921i	−0.271396	+	0.946519i
$229$	−9.21274	+	15.9569i	−0.608795	+	1.05446i	0.382644	+	0.923896i	$0.375013\pi$
$229$	−9.21274	+	15.9569i	−0.608795	+	1.05446i	−0.991439	+	0.130568i	$0.958320\pi$
$230$	−1.02390	+	1.73827i	−0.0675141	+	0.114618i
$231$	−1.70493	+	0.984341i	−0.112176	+	0.0647649i
$232$	12.2989	+	12.9598i	0.807463	+	0.850853i
$233$			9.34851i			0.612441i	0.951961	+	0.306221i	$0.0990645\pi$
$233$			9.34851i			0.612441i	−0.951961	+	0.306221i	$0.900935\pi$
$234$	−8.87483	+	8.72139i	−0.580166	+	0.570135i
$235$	3.37519	−	0.904380i	0.220173	−	0.0589952i
$236$	2.60417	−	9.08229i	0.169517	−	0.591207i
$237$	0.887880	−	3.31361i	0.0576740	−	0.215242i
$238$	−4.99230	−	5.08013i	−0.323603	−	0.329296i
$239$	0.790104	−	2.94871i	0.0511076	−	0.190736i	−0.935653	−	0.352923i	$-0.885188\pi$
$239$	0.790104	−	2.94871i	0.0511076	−	0.190736i	0.986760	+	0.162186i	$0.0518546\pi$
$240$	4.22684	+	1.29215i	0.272841	+	0.0834077i
$241$	−3.95717	−	14.7684i	−0.254904	−	0.951314i	−0.968144	−	0.250394i	$-0.919440\pi$
$241$	−3.95717	−	14.7684i	−0.254904	−	0.951314i	0.713240	−	0.700920i	$-0.247227\pi$
$242$	−11.5075	−	0.100344i	−0.739727	−	0.00645034i
$243$	−7.64591	−	13.2431i	−0.490485	−	0.849545i
$244$	−3.81004	+	0.950006i	−0.243913	+	0.0608179i
$245$	−4.16569	+	4.16569i	−0.266136	+	0.266136i
$246$	8.70034	−	4.92250i	0.554714	−	0.313847i
$247$	16.6366	+	28.8155i	1.05856	+	1.83348i
$248$	0.798278	−	0.757569i	0.0506907	−	0.0481057i
$249$		−	14.6039i		−	0.925486i
$250$	0.991242	+	1.00868i	0.0626917	+	0.0637946i
$251$	−12.4016	+	12.4016i	−0.782780	+	0.782780i	−0.980299	−	0.197519i	$-0.936711\pi$
$251$	−12.4016	+	12.4016i	−0.782780	+	0.782780i	0.197519	+	0.980299i	$0.436711\pi$
$252$	0.0653355	−	3.74606i	0.00411575	−	0.235980i
$253$	1.70668	+	1.70668i	0.107298	+	0.107298i
$254$	−16.0965	+	9.10711i	−1.00998	+	0.571431i
$255$	4.57694	+	2.64250i	0.286619	+	0.165480i
$256$	15.9611	+	1.11521i	0.997568	+	0.0697008i
$257$	12.4497	+	3.33590i	0.776593	+	0.208088i	0.625282	−	0.780399i	$-0.284984\pi$
$257$	12.4497	+	3.33590i	0.776593	+	0.208088i	0.151311	+	0.988486i	$0.451650\pi$
$258$	16.5304	−	4.27518i	1.02914	−	0.266161i
$259$	−0.602271	+	6.37682i	−0.0374233	+	0.396237i
$260$	8.65113	−	4.79556i	0.536521	−	0.297408i
$261$	−2.90854	+	10.8548i	−0.180034	+	0.671896i
$262$	3.63352	+	1.00764i	0.224479	+	0.0622520i
$263$	−11.3646	+	19.6841i	−0.700774	+	1.21378i	0.267421	+	0.963580i	$0.413828\pi$
$263$	−11.3646	+	19.6841i	−0.700774	+	1.21378i	−0.968195	+	0.250196i	$0.919505\pi$
$264$	2.76286	−	4.50879i	0.170042	−	0.277497i
$265$	7.21168	−	7.21168i	0.443010	−	0.443010i
$266$	−9.65442	−	2.67733i	−0.591950	−	0.164158i
$267$	3.44504	+	3.44504i	0.210833	+	0.210833i
$268$	−15.6684	+	26.0774i	−0.957100	+	1.59293i
$269$	4.86269			0.296484			0.148242	−	0.988951i	$-0.452639\pi$
$269$	4.86269			0.296484			0.148242	+	0.988951i	$0.452639\pi$
$270$	1.86991	+	7.23019i	0.113799	+	0.440015i
$271$	11.8465	−	6.83956i	0.719621	−	0.415473i	−0.0949922	−	0.995478i	$-0.530283\pi$
$271$	11.8465	−	6.83956i	0.719621	−	0.415473i	0.814613	+	0.580005i	$0.196949\pi$
$272$	18.2957	+	5.59300i	1.10934	+	0.339125i
$273$	4.06912	+	4.06912i	0.246274	+	0.246274i
$274$	−28.4194	−	0.247814i	−1.71688	−	0.0149710i
$275$	1.46527	−	0.845975i	0.0883592	−	0.0510142i
$276$	3.05892	−	0.762719i	0.184125	−	0.0459103i
$277$	−1.84242	+	0.493676i	−0.110701	+	0.0296621i	−0.313744	−	0.949508i	$-0.601583\pi$
$277$	−1.84242	+	0.493676i	−0.110701	+	0.0296621i	0.203043	+	0.979170i	$0.434917\pi$
$278$	−9.80930	−	17.3376i	−0.588323	−	1.03984i
$279$	0.668618	+	0.179156i	0.0400291	+	0.0107258i
$280$	−0.845840	+	2.85573i	−0.0505486	+	0.170662i
$281$	11.2369	+	3.01093i	0.670339	+	0.179617i	0.577908	−	0.816102i	$-0.303869\pi$
$281$	11.2369	+	3.01093i	0.670339	+	0.179617i	0.0924317	+	0.995719i	$0.470536\pi$
$282$	−4.70487	−	2.77134i	−0.280171	−	0.165031i
$283$	5.13478	+	19.1633i	0.305231	+	1.13914i	0.932746	+	0.360533i	$0.117405\pi$
$283$	5.13478	+	19.1633i	0.305231	+	1.13914i	−0.627515	+	0.778604i	$0.715928\pi$
$284$	−3.07673	−	1.84863i	−0.182570	−	0.109696i
$285$	7.43402			0.440353
$286$	−2.96306	−	11.4570i	−0.175210	−	0.677466i
$287$	3.36800	+	5.83355i	0.198807	+	0.344344i
$288$	4.64717	+	8.92637i	0.273837	+	0.525991i
$289$	5.08867	+	2.93795i	0.299334	+	0.172820i
$290$	4.53397	−	7.69728i	0.266244	−	0.452000i
$291$	−2.08520	−	7.78206i	−0.122236	−	0.456193i
$292$	0.560397	−	32.1308i	0.0327948	−	1.88031i
$293$	1.08893	−	1.88608i	0.0636161	−	0.110186i	−0.832463	−	0.554080i	$-0.813070\pi$
$293$	1.08893	−	1.88608i	0.0636161	−	0.110186i	0.896079	+	0.443894i	$0.146403\pi$
$294$	9.20568	+	0.0802726i	0.536886	+	0.00468159i
$295$	−4.72413			−0.275050
$296$	−6.75162	−	15.8245i	−0.392430	−	0.919782i
$297$	8.93473			0.518446
$298$	1.39641	+	0.0121766i	0.0808919	+	0.000705369i
$299$	3.52758	−	6.10994i	0.204005	−	0.353347i
$300$	0.0385384	−	2.20963i	0.00222502	−	0.127573i
$301$	2.97783	+	11.1134i	0.171639	+	0.640567i
$302$	14.1462	−	24.0159i	0.814024	−	1.38196i
$303$	13.0096	+	7.51108i	0.747380	+	0.431500i
$304$	26.2210	−	6.05436i	1.50388	−	0.347241i
$305$	0.981673	+	1.70031i	0.0562105	+	0.0973594i
$306$	3.01296	+	11.6499i	0.172240	+	0.665983i
$307$	−6.08919			−0.347528			−0.173764	−	0.984787i	$-0.555593\pi$
$307$	−6.08919			−0.347528			−0.173764	+	0.984787i	$0.555593\pi$
$308$	3.05435	+	1.83518i	0.174038	+	0.104569i
$309$	5.57332	+	20.7999i	0.317055	+	1.18327i
$310$	−0.474125	−	0.279276i	−0.0269285	−	0.0158618i
$311$	−14.8991	−	3.99219i	−0.844849	−	0.226376i	−0.189667	−	0.981848i	$-0.560741\pi$
$311$	−14.8991	−	3.99219i	−0.844849	−	0.226376i	−0.655181	+	0.755472i	$0.727408\pi$
$312$	−14.8207	−	4.38974i	−0.839055	−	0.248520i
$313$	−10.7583	−	2.88267i	−0.608094	−	0.162938i	−0.0583847	−	0.998294i	$-0.518595\pi$
$313$	−10.7583	−	2.88267i	−0.608094	−	0.162938i	−0.549710	+	0.835356i	$0.685262\pi$
$314$	6.62081	+	11.7020i	0.373634	+	0.660385i
$315$	−1.80948	+	0.484849i	−0.101953	+	0.0273182i
$316$	−6.02469	+	1.50221i	−0.338915	+	0.0845061i
$317$	16.3603	−	9.44561i	0.918884	−	0.530518i	0.0356054	−	0.999366i	$-0.488664\pi$
$317$	16.3603	−	9.44561i	0.918884	−	0.530518i	0.883279	+	0.468848i	$0.155331\pi$
$318$	−15.9370	−	0.138969i	−0.893701	−	0.00779298i
$319$	−7.55740	−	7.55740i	−0.423133	−	0.423133i
$320$	−1.66362	−	7.82511i	−0.0929992	−	0.437437i
$321$	−2.49245	+	1.43902i	−0.139115	+	0.0803181i
$322$	0.531909	+	2.05668i	0.0296422	+	0.114614i
$323$	32.1778			1.79042
$324$	0.513054	−	0.853892i	0.0285030	−	0.0474384i
$325$	−3.49713	−	3.49713i	−0.193986	−	0.193986i
$326$	5.56354	+	1.54287i	0.308136	+	0.0854514i
$327$	−9.08802	+	9.08802i	−0.502569	+	0.502569i
$328$	−15.4272	−	9.45335i	−0.851824	−	0.521974i
$329$	1.83974	−	3.18652i	0.101428	−	0.175679i
$330$	−2.54783	−	0.706555i	−0.140253	−	0.0388946i
$331$	−1.50247	+	5.60728i	−0.0825830	+	0.308204i	−0.994846	−	0.101402i	$-0.967667\pi$
$331$	−1.50247	+	5.60728i	−0.0825830	+	0.308204i	0.912263	+	0.409606i	$0.134334\pi$
$332$	−23.1185	+	12.8152i	−1.26879	+	0.703326i
$333$	6.26787	−	8.82125i	0.343477	−	0.483401i
$334$	11.7082	−	3.02803i	0.640644	−	0.165686i
$335$	14.6930	+	3.93697i	0.802762	+	0.215099i
$336$	4.10938	−	2.18514i	0.224185	−	0.119209i
$337$	−20.8549	−	12.0406i	−1.13604	−	0.655892i	−0.190591	−	0.981669i	$-0.561041\pi$
$337$	−20.8549	−	12.0406i	−1.13604	−	0.655892i	−0.945446	+	0.325778i	$0.894374\pi$
$338$	−14.1055	+	7.98067i	−0.767241	+	0.434091i
$339$	7.15976	+	7.15976i	0.388865	+	0.388865i
$340$	0.166812	−	9.56430i	0.00904665	−	0.518697i
$341$	−0.465509	+	0.465509i	−0.0252087	+	0.0252087i
$342$	11.8639	+	12.0726i	0.641524	+	0.652811i
$343$			13.5745i			0.732955i
$344$	−21.2735	−	22.4166i	−1.14699	−	1.20862i
$345$	−0.788143	−	1.36510i	−0.0424322	−	0.0734947i
$346$	−11.8996	+	6.73259i	−0.639727	+	0.361946i
$347$	−25.8892	+	25.8892i	−1.38981	+	1.38981i	−0.564099	+	0.825707i	$0.690776\pi$
$347$	−25.8892	+	25.8892i	−1.38981	+	1.38981i	−0.825707	+	0.564099i	$0.809224\pi$
$348$	−13.5453	+	3.37742i	−0.726104	+	0.181049i
$349$	−0.868423	−	1.50415i	−0.0464856	−	0.0805154i	0.841846	−	0.539717i	$-0.181469\pi$
$349$	−0.868423	−	1.50415i	−0.0464856	−	0.0805154i	−0.888332	+	0.459202i	$0.848135\pi$
$350$	1.48912	+	0.0129850i	0.0795970	+	0.000694077i
$351$	−6.75954	−	25.2270i	−0.360798	−	1.34652i
$352$	−9.56202	−	0.417153i	−0.509657	−	0.0222343i
$353$	6.77435	−	25.2822i	0.360562	−	1.34564i	−0.512776	−	0.858523i	$-0.671383\pi$
$353$	6.77435	−	25.2822i	0.360562	−	1.34564i	0.873338	−	0.487115i	$-0.161951\pi$
$354$	5.17437	+	5.26541i	0.275015	+	0.279853i
$355$	−0.464501	+	1.73354i	−0.0246531	+	0.0920068i
$356$	2.43053	−	8.47670i	0.128818	−	0.449264i
$357$	5.37552	−	1.44037i	0.284503	−	0.0762323i
$358$	−3.57221	+	3.51045i	−0.188797	+	0.185533i
$359$			7.68296i			0.405491i	0.979231	+	0.202745i	$0.0649864\pi$
$359$			7.68296i			0.405491i	−0.979231	+	0.202745i	$0.935014\pi$
$360$	3.64987	−	3.46374i	0.192365	−	0.182555i
$361$	22.7437	−	13.1311i	1.19704	−	0.691110i
$362$	12.3286	−	20.9301i	0.647976	−	1.10006i
$363$	4.49579	−	7.78694i	0.235968	−	0.408709i
$364$	2.87082	−	10.0123i	0.150472	−	0.524785i
$365$	−15.5203	+	4.15866i	−0.812372	+	0.217674i
$366$	0.819890	−	2.95651i	0.0428564	−	0.154539i
$367$	17.9329	+	10.3536i	0.936090	+	0.540452i	0.888732	−	0.458426i	$-0.151587\pi$
$367$	17.9329	+	10.3536i	0.936090	+	0.540452i	0.0473575	+	0.998878i	$0.484920\pi$
$368$	−3.89167	−	4.17307i	−0.202867	−	0.217536i
$369$		−	11.3802i		−	0.592428i
$370$	−6.67533	+	5.42586i	−0.347034	+	0.282077i
$371$		−	10.7395i		−	0.557566i
$372$	0.208037	+	0.834342i	0.0107862	+	0.0432586i
$373$	−5.45051	−	3.14685i	−0.282217	−	0.162938i	0.352210	−	0.935921i	$-0.385430\pi$
$373$	−5.45051	−	3.14685i	−0.282217	−	0.162938i	−0.634427	+	0.772983i	$0.718764\pi$
$374$	−11.0282	−	3.05830i	−0.570252	−	0.158141i
$375$	−1.06733	+	0.285991i	−0.0551168	+	0.0147685i
$376$	−0.258507	+	9.87986i	−0.0133315	+	0.509515i
$377$	−15.6206	+	27.0556i	−0.804500	+	1.39344i
$378$	6.77584	+	3.99121i	0.348512	+	0.205286i
$379$	−0.213923	+	0.123508i	−0.0109885	+	0.00634420i	−0.505484	−	0.862836i	$-0.668686\pi$
$379$	−0.213923	+	0.123508i	−0.0109885	+	0.00634420i	0.494496	+	0.869180i	$0.335353\pi$
$380$	−6.52349	−	11.7683i	−0.334648	−	0.603701i
$381$		−	14.4503i		−	0.740312i
$382$	23.3730	+	23.7842i	1.19587	+	1.21691i
$383$	−21.9453	+	5.88022i	−1.12135	+	0.300465i	−0.771430	−	0.636314i	$-0.780458\pi$
$383$	−21.9453	+	5.88022i	−1.12135	+	0.300465i	−0.349921	+	0.936779i	$0.613792\pi$
$384$	−6.89951	+	10.4251i	−0.352089	+	0.532005i
$385$	0.461122	−	1.72093i	0.0235009	−	0.0877067i
$386$	−14.1776	+	13.9325i	−0.721621	+	0.709145i
$387$	5.03091	−	18.7756i	0.255736	−	0.954419i
$388$	−10.4895	+	10.1298i	−0.532522	+	0.514265i
$389$	6.06664	+	22.6410i	0.307591	+	1.14794i	0.930692	+	0.365804i	$0.119206\pi$
$389$	6.06664	+	22.6410i	0.307591	+	1.14794i	−0.623101	+	0.782141i	$0.714128\pi$
$390$	−0.0673896	+	7.72826i	−0.00341240	+	0.391335i
$391$	−3.41145	−	5.90880i	−0.172524	−	0.298821i
$392$	−7.95108	−	14.6433i	−0.401590	−	0.739601i
$393$	−2.08325	+	2.08325i	−0.105086	+	0.105086i
$394$	−0.520099	−	0.919257i	−0.0262022	−	0.0463115i
$395$	1.55229	+	2.68864i	0.0781040	+	0.135280i
$396$	−2.91863	−	5.26517i	−0.146666	−	0.264585i
$397$			5.76309i			0.289241i	0.989487	+	0.144621i	$0.0461962\pi$
$397$			5.76309i			0.289241i	−0.989487	+	0.144621i	$0.953804\pi$
$398$	23.7215	−	23.3114i	1.18905	−	1.16849i
$399$	5.53529	−	5.53529i	0.277111	−	0.277111i
$400$	−3.53174	+	1.87798i	−0.176587	+	0.0938992i
$401$	2.22009	+	2.22009i	0.110866	+	0.110866i	0.760364	−	0.649498i	$-0.225021\pi$
$401$	2.22009	+	2.22009i	0.110866	+	0.110866i	−0.649498	+	0.760364i	$0.725021\pi$
$402$	−11.7052	−	20.6886i	−0.583804	−	1.03185i
$403$	1.66653	+	0.962172i	0.0830158	+	0.0479292i
$404$	0.474149	−	27.1857i	0.0235898	−	1.35254i
$405$	−0.481113	−	0.128914i	−0.0239067	−	0.00640579i
$406$	−2.35536	−	9.10726i	−0.116895	−	0.451986i
$407$	4.28500	+	9.35727i	0.212400	+	0.463823i
$408$	−10.8429	+	10.2899i	−0.536801	+	0.509427i
$409$	2.98517	−	11.1408i	0.147607	−	0.550877i	−0.852018	−	0.523512i	$-0.824622\pi$
$409$	2.98517	−	11.1408i	0.147607	−	0.550877i	0.999625	−	0.0273653i	$-0.00871174\pi$
$410$	−2.41754	+	8.71760i	−0.119394	+	0.430531i
$411$	11.1031	−	19.2311i	0.547674	−	0.948598i
$412$	28.0363	−	27.0751i	1.38125	−	1.33389i
$413$	−3.51754	+	3.51754i	−0.173087	+	0.173087i
$414$	0.959094	−	3.45847i	0.0471369	−	0.169975i
$415$	9.34542	+	9.34542i	0.458749	+	0.458749i
$416$	6.05630	+	27.3137i	0.296934	+	1.33916i
$417$	15.5645			0.762196
$418$	−15.5851	+	4.03071i	−0.762295	+	0.197148i
$419$	26.5700	−	15.3402i	1.29803	−	0.749416i	0.317964	−	0.948103i	$-0.397001\pi$
$419$	26.5700	−	15.3402i	1.29803	−	0.749416i	0.980063	+	0.198686i	$0.0636676\pi$
$420$	−1.61657	−	1.67396i	−0.0788807	−	0.0816811i
$421$	20.2356	+	20.2356i	0.986221	+	0.986221i	0.999906	−	0.0136850i	$-0.00435620\pi$
$421$	20.2356	+	20.2356i	0.986221	+	0.986221i	−0.0136850	+	0.999906i	$0.504356\pi$
$422$	−0.00590379	+	0.677048i	−0.000287392	+	0.0329582i
$423$	−5.38349	+	3.10816i	−0.261754	+	0.151124i
$424$	13.7650	+	25.3507i	0.668487	+	1.23114i
$425$	−4.61990	+	1.23790i	−0.224098	+	0.0600469i
$426$	2.44093	−	1.38104i	0.118264	−	0.0669115i
$427$	1.99698	+	0.535088i	0.0966404	+	0.0258947i
$428$	4.46519	+	2.68287i	0.215833	+	0.129681i
$429$	8.93129	+	2.39313i	0.431207	+	0.115542i
$430$	−7.84243	+	13.3140i	−0.378196	+	0.642059i
$431$	−3.00253	−	11.2056i	−0.144627	−	0.539754i	−0.999772	−	0.0213655i	$-0.993199\pi$
$431$	−3.00253	−	11.2056i	−0.144627	−	0.539754i	0.855145	−	0.518389i	$-0.173468\pi$
$432$	−21.1101	−	0.736590i	−1.01566	−	0.0354392i
$433$	15.8936			0.763797			0.381899	−	0.924204i	$-0.375270\pi$
$433$	15.8936			0.763797			0.381899	+	0.924204i	$0.375270\pi$
$434$	−0.560975	+	0.145082i	−0.0269277	+	0.00696416i
$435$	3.49000	+	6.04486i	0.167333	+	0.289829i
$436$	22.3615	+	6.41173i	1.07092	+	0.307066i
$437$	−8.31147	−	4.79863i	−0.397591	−	0.229549i
$438$	21.6347	+	12.7436i	1.03375	+	0.608913i
$439$	−3.52559	−	13.1577i	−0.168267	−	0.627981i	−0.997601	−	0.0692278i	$-0.977946\pi$
$439$	−3.52559	−	13.1577i	−0.168267	−	0.627981i	0.829334	−	0.558753i	$-0.188720\pi$
$440$	1.11726	+	4.65331i	0.0532634	+	0.221838i
$441$	5.24023	−	9.07635i	0.249535	−	0.432207i
$442$	−0.291693	+	33.4514i	−0.0138744	+	1.59112i
$443$	−0.922277			−0.0438187			−0.0219093	−	0.999760i	$-0.506975\pi$
$443$	−0.922277			−0.0438187			−0.0219093	+	0.999760i	$0.506975\pi$
$444$	13.3591	+	1.49719i	0.633993	+	0.0710533i
$445$	−4.40913			−0.209013
$446$	0.161910	−	18.5679i	0.00766666	−	0.879214i
$447$	−0.545557	+	0.944933i	−0.0258040	+	0.0446938i
$448$	−7.06521	−	4.58778i	−0.333800	−	0.216752i
$449$	−4.55115	−	16.9851i	−0.214782	−	0.801577i	−0.986243	−	0.165301i	$-0.947140\pi$
$449$	−4.55115	−	16.9851i	−0.214782	−	0.801577i	0.771461	−	0.636276i	$-0.219526\pi$
$450$	−2.16778	−	1.27690i	−0.102190	−	0.0601937i
$451$	9.37321	+	5.41163i	0.441367	+	0.254824i
$452$	5.05132	−	17.6170i	0.237594	−	0.828632i
$453$	10.8890	+	18.8603i	0.511610	+	0.886134i
$454$	−0.917139	+	0.237195i	−0.0430434	+	0.0111321i
$455$	−5.20786			−0.244148
$456$	−5.97145	+	20.1608i	−0.279639	+	0.944117i
$457$	−4.93618	−	18.4221i	−0.230905	−	0.861749i	−0.979952	−	0.199232i	$-0.936155\pi$
$457$	−4.93618	−	18.4221i	−0.230905	−	0.861749i	0.749047	−	0.662516i	$-0.230512\pi$
$458$	−13.2251	+	22.4521i	−0.617966	+	1.04912i
$459$	−24.3965	−	6.53701i	−1.13873	−	0.305122i
$460$	−1.46940	+	2.44556i	−0.0685109	+	0.114025i
$461$	−25.9733	−	6.95953i	−1.20970	−	0.324137i	−0.403054	−	0.915176i	$-0.632051\pi$
$461$	−25.9733	−	6.95953i	−1.20970	−	0.324137i	−0.806643	+	0.591039i	$0.798718\pi$
$462$	−2.42318	+	1.37099i	−0.112736	+	0.0637843i
$463$	22.8284	−	6.11686i	1.06093	−	0.284274i	0.314167	−	0.949368i	$-0.398275\pi$
$463$	22.8284	−	6.11686i	1.06093	−	0.284274i	0.746760	+	0.665093i	$0.231608\pi$
$464$	17.2328	+	18.4789i	0.800013	+	0.857861i
$465$	0.372342	−	0.214972i	0.0172669	−	0.00996908i
$466$	−0.115280	+	13.2203i	−0.00534022	+	0.612418i
$467$	21.8740	+	21.8740i	1.01221	+	1.01221i	0.999925	+	0.0122850i	$0.00391053\pi$
$467$	21.8740	+	21.8740i	1.01221	+	1.01221i	0.0122850	+	0.999925i	$0.496089\pi$
$468$	−12.6580	+	12.2240i	−0.585115	+	0.565055i
$469$	13.8716	−	8.00880i	0.640533	−	0.369812i
$470$	4.78421	−	1.23732i	0.220679	−	0.0570732i
$471$	−10.5053			−0.484058
$472$	3.79471	−	12.8117i	0.174666	−	0.589706i
$473$	13.0721	+	13.0721i	0.601054	+	0.601054i
$474$	1.29647	−	4.67503i	0.0595486	−	0.214731i
$475$	−4.75721	+	4.75721i	−0.218276	+	0.218276i
$476$	−6.99727	−	7.24568i	−0.320719	−	0.332105i
$477$	−9.07194	+	15.7131i	−0.415376	+	0.719452i
$478$	1.15370	−	4.16020i	0.0527688	−	0.190283i
$479$	0.922439	−	3.44259i	0.0421473	−	0.157296i	−0.941645	−	0.336608i	$-0.890720\pi$
$479$	0.922439	−	3.44259i	0.0421473	−	0.157296i	0.983792	+	0.179312i	$0.0573871\pi$
$480$	5.96149	+	1.87942i	0.272104	+	0.0857835i
$481$	23.1782	−	19.1778i	1.05683	−	0.874432i
$482$	−5.41396	−	20.9336i	−0.246599	−	0.953500i
$483$	−1.60329	−	0.429599i	−0.0729520	−	0.0195474i
$484$	−16.2721	−	0.283804i	−0.739643	−	0.0129002i
$485$	6.31431	+	3.64557i	0.286718	+	0.165537i
$486$	−10.6492	−	18.8221i	−0.483059	−	0.853790i
$487$	−10.0773	−	10.0773i	−0.456647	−	0.456647i	0.440906	−	0.897553i	$-0.354657\pi$
$487$	−10.0773	−	10.0773i	−0.456647	−	0.456647i	−0.897553	+	0.440906i	$0.854657\pi$
$488$	−5.39972	+	1.29648i	−0.244434	+	0.0586888i
$489$	−3.18982	+	3.18982i	−0.144249	+	0.144249i
$490$	−5.94232	+	5.83958i	−0.268447	+	0.263805i
$491$			31.9496i			1.44187i	0.693005	+	0.720933i	$0.256286\pi$
$491$			31.9496i			1.44187i	−0.693005	+	0.720933i	$0.743714\pi$
$492$	12.3644	−	6.85391i	0.557429	−	0.308998i
$493$	15.1063	+	26.1649i	0.680355	+	1.17841i
$494$	23.1715	+	40.9548i	1.04253	+	1.84264i
$495$	−2.12839	+	2.12839i	−0.0956640	+	0.0956640i
$496$	1.13823	−	1.06148i	0.0511082	−	0.0476619i
$497$	0.944914	+	1.63664i	0.0423852	+	0.0734133i
$498$	0.180086	−	20.6523i	0.00806984	−	0.925451i
$499$	−1.02679	−	3.83203i	−0.0459654	−	0.171545i	0.939127	−	0.343569i	$-0.111636\pi$
$499$	−1.02679	−	3.83203i	−0.0459654	−	0.171545i	−0.985093	+	0.172024i	$0.944969\pi$
$500$	1.38934	+	1.43866i	0.0621330	+	0.0643388i
$501$	−2.44560	+	9.12711i	−0.109261	+	0.407769i
$502$	−17.6907	+	17.3849i	−0.789575	+	0.775924i
$503$	−4.74673	+	17.7151i	−0.211646	+	0.789875i	0.775674	+	0.631134i	$0.217410\pi$
$503$	−4.74673	+	17.7151i	−0.211646	+	0.789875i	−0.987320	+	0.158741i	$0.949256\pi$
$504$	0.138589	−	5.29672i	0.00617323	−	0.235935i
$505$	−13.1317	+	3.51862i	−0.584352	+	0.156577i
$506$	2.39247	+	2.43456i	0.106358	+	0.108230i
$507$		−	12.6630i		−	0.562383i
$508$	−22.8753	+	12.6804i	−1.01493	+	0.562603i
$509$	−35.5113	+	20.5024i	−1.57401	+	0.908754i	−0.578339	+	0.815797i	$0.696299\pi$
$509$	−35.5113	+	20.5024i	−1.57401	+	0.908754i	−0.995670	+	0.0929576i	$0.970368\pi$
$510$	6.43994	+	3.79336i	0.285165	+	0.167973i
$511$	−8.45979	+	14.6528i	−0.374239	+	0.648201i
$512$	22.5578	+	1.77391i	0.996922	+	0.0783965i
$513$	−34.3167	+	9.19513i	−1.51512	+	0.405975i
$514$	17.5648	+	4.87101i	0.774749	+	0.214851i
$515$	−16.8769	−	9.74388i	−0.743685	−	0.429367i
$516$	23.4294	−	5.84194i	1.03142	−	0.257177i
$517$		−	5.91210i		−	0.260014i
$518$	−0.930342	+	9.01042i	−0.0408769	+	0.395895i
$519$		−	10.6826i		−	0.468916i
$520$	12.2932	−	6.67501i	0.539093	−	0.292718i
$521$	18.0179	+	10.4026i	0.789379	+	0.455748i	0.839744	−	0.542983i	$-0.182705\pi$
$521$	18.0179	+	10.4026i	0.789379	+	0.455748i	−0.0503650	+	0.998731i	$0.516038\pi$
$522$	−4.24699	+	15.3146i	−0.185886	+	0.670301i
$523$	2.44655	−	0.655550i	0.106980	−	0.0286652i	−0.204932	−	0.978776i	$-0.565697\pi$
$523$	2.44655	−	0.655550i	0.106980	−	0.0286652i	0.311912	+	0.950111i	$0.399031\pi$
$524$	5.12595	+	1.46977i	0.223928	+	0.0642070i
$525$	−0.581779	+	1.00767i	−0.0253909	+	0.0439783i
$526$	−16.3142	+	27.6964i	−0.711331	+	1.20762i
$527$	1.61167	−	0.930496i	0.0702053	−	0.0405330i
$528$	3.96272	−	6.34208i	0.172455	−	0.276003i
$529$		−	20.9650i		−	0.911523i
$530$	10.2874	−	10.1095i	0.446856	−	0.439130i
$531$	8.11792	−	2.17519i	0.352288	−	0.0943952i
$532$	−13.6199	−	3.90523i	−0.590496	−	0.169313i
$533$	8.18830	−	30.5592i	0.354675	−	1.32366i
$534$	4.82935	+	4.91432i	0.208987	+	0.212663i
$535$	0.674119	−	2.51585i	0.0291447	−	0.108769i
$536$	−22.4792	+	36.6844i	−0.970953	+	1.58453i
$537$	−1.01283	−	3.77991i	−0.0437066	−	0.163115i
$538$	6.87662	+	0.0599634i	0.296472	+	0.00258521i
$539$	4.98378	+	8.63217i	0.214667	+	0.371814i
$540$	2.55519	+	10.2477i	0.109958	+	0.440991i
$541$	−24.2672	+	24.2672i	−1.04333	+	1.04333i	−0.0443085	+	0.999018i	$0.514108\pi$
$541$	−24.2672	+	24.2672i	−1.04333	+	1.04333i	−0.999018	+	0.0443085i	$0.985892\pi$
$542$	16.8371	−	9.52614i	0.723216	−	0.409183i
$543$	9.48986	+	16.4369i	0.407249	+	0.705376i
$544$	25.8041	+	8.13500i	1.10634	+	0.348785i
$545$		−	11.6313i		−	0.498230i
$546$	5.70420	+	5.80456i	0.244117	+	0.248412i
$547$	−24.0987	+	24.0987i	−1.03039	+	1.03039i	−0.0308643	+	0.999524i	$0.509826\pi$
$547$	−24.0987	+	24.0987i	−1.03039	+	1.03039i	−0.999524	+	0.0308643i	$0.990174\pi$
$548$	−40.1866	−	0.700898i	−1.71668	−	0.0299409i
$549$	−2.46979	−	2.46979i	−0.105408	−	0.105408i
$550$	2.08256	−	1.17828i	0.0888007	−	0.0502418i
$551$	36.8043	+	21.2490i	1.56791	+	0.905236i
$552$	4.33520	−	1.04089i	0.184519	−	0.0443031i
$553$	3.15775	+	0.846117i	0.134281	+	0.0359805i
$554$	−2.61157	+	0.675418i	−0.110955	+	0.0286957i
$555$	−1.12144	−	6.62714i	−0.0476026	−	0.281306i
$556$	−13.6581	−	24.6391i	−0.579233	−	1.04493i
$557$	8.04908	−	30.0396i	0.341051	−	1.27282i	−0.556108	−	0.831110i	$-0.687706\pi$
$557$	8.04908	−	30.0396i	0.341051	−	1.27282i	0.897159	−	0.441708i	$-0.145627\pi$
$558$	0.943323	+	0.261600i	0.0399341	+	0.0110744i
$559$	27.0190	−	46.7983i	1.14278	−	1.97936i
$560$	−1.23137	+	4.02802i	−0.0520348	+	0.170215i
$561$	6.32292	−	6.32292i	0.266954	−	0.266954i
$562$	15.8537	+	4.39650i	0.668748	+	0.185455i
$563$	21.1687	+	21.1687i	0.892156	+	0.892156i	0.994726	−	0.102569i	$-0.0327064\pi$
$563$	21.1687	+	21.1687i	0.892156	+	0.892156i	−0.102569	+	0.994726i	$0.532706\pi$
$564$	−6.61926	−	3.97713i	−0.278721	−	0.167467i
$565$	−9.16342			−0.385508
$566$	7.02509	+	27.1632i	0.295287	+	1.14176i
$567$	−0.454220	+	0.262244i	−0.0190754	+	0.0110132i
$568$	−4.32819	−	2.65220i	−0.181607	−	0.111284i
$569$	−14.7740	−	14.7740i	−0.619359	−	0.619359i	0.326008	−	0.945367i	$-0.394296\pi$
$569$	−14.7740	−	14.7740i	−0.619359	−	0.619359i	−0.945367	+	0.326008i	$0.894296\pi$
$570$	10.5129	+	0.0916713i	0.440336	+	0.00383969i
$571$	−11.6423	+	6.72170i	−0.487216	+	0.281294i	−0.723419	−	0.690410i	$-0.757430\pi$
$571$	−11.6423	+	6.72170i	−0.487216	+	0.281294i	0.236203	+	0.971704i	$0.424097\pi$
$572$	−4.04897	−	16.2386i	−0.169296	−	0.678968i
$573$	−25.1671	+	6.74352i	−1.05137	+	0.281714i
$574$	4.69096	+	8.29111i	0.195797	+	0.346064i
$575$	1.37792	+	0.369212i	0.0574631	+	0.0153972i
$576$	6.46176	+	12.6806i	0.269240	+	0.528359i
$577$	−19.3790	−	5.19258i	−0.806757	−	0.216170i	−0.168209	−	0.985751i	$-0.553798\pi$
$577$	−19.3790	−	5.19258i	−0.806757	−	0.216170i	−0.638549	+	0.769581i	$0.720465\pi$
$578$	7.15997	+	4.21748i	0.297815	+	0.175424i
$579$	−4.01977	−	15.0020i	−0.167056	−	0.623461i
$580$	6.50667	−	10.8293i	0.270175	−	0.449661i
$581$	13.9170			0.577375
$582$	−2.85284	−	11.0308i	−0.118254	−	0.457241i
$583$	−8.62798	−	14.9441i	−0.357334	−	0.618921i
$584$	1.18871	−	45.4312i	0.0491890	−	1.87996i
$585$	7.61968	+	4.39922i	0.315035	+	0.181885i
$586$	1.56318	−	2.65380i	0.0645744	−	0.109627i
$587$	8.04147	+	30.0112i	0.331907	+	1.23869i	0.907184	+	0.420734i	$0.138228\pi$
$587$	8.04147	+	30.0112i	0.331907	+	1.23869i	−0.575277	+	0.817959i	$0.695106\pi$
$588$	13.0173	+	0.227037i	0.536825	+	0.00936283i
$589$	1.30886	−	2.26701i	0.0539306	−	0.0934106i
$590$	−6.68068	−	0.0582548i	−0.275039	−	0.00239831i
$591$	0.825244			0.0339460
$592$	−9.35274	−	22.4617i	−0.384395	−	0.923169i
$593$	−0.568919			−0.0233627			−0.0116814	−	0.999932i	$-0.503718\pi$
$593$	−0.568919			−0.0233627			−0.0116814	+	0.999932i	$0.503718\pi$
$594$	12.6351	+	0.110177i	0.518426	+	0.00452062i
$595$	−2.51820	+	4.36166i	−0.103236	+	0.178811i
$596$	1.97460	+	0.0344392i	0.0808827	+	0.00141068i
$597$	6.72573	+	25.1008i	0.275266	+	1.02731i
$598$	5.06390	−	8.59694i	0.207078	−	0.351555i
$599$	−7.22583	−	4.17183i	−0.295239	−	0.170457i	0.345063	−	0.938580i	$-0.387858\pi$
$599$	−7.22583	−	4.17183i	−0.295239	−	0.170457i	−0.640302	+	0.768123i	$0.721191\pi$
$600$	0.0817472	−	3.12430i	0.00333731	−	0.127549i
$601$	−13.2932	−	23.0245i	−0.542242	−	0.939190i	−0.998775	−	0.0494839i	$-0.984242\pi$
$601$	−13.2932	−	23.0245i	−0.542242	−	0.939190i	0.456533	−	0.889706i	$-0.349091\pi$
$602$	4.07409	+	15.7529i	0.166047	+	0.642039i
$603$	−27.0610			−1.10201
$604$	20.3012	−	33.7879i	0.826043	−	1.37481i
$605$	2.10609	+	7.86003i	0.0856247	+	0.319556i
$606$	18.3050	+	10.7823i	0.743589	+	0.438001i
$607$	−21.9054	−	5.86953i	−0.889111	−	0.238237i	−0.214777	−	0.976663i	$-0.568903\pi$
$607$	−21.9054	−	5.86953i	−0.889111	−	0.238237i	−0.674334	+	0.738426i	$0.735569\pi$
$608$	37.1553	−	8.23849i	1.50685	−	0.334115i
$609$	7.09956	+	1.90232i	0.287689	+	0.0770860i
$610$	1.36728	+	2.41661i	0.0553594	+	0.0978458i
$611$	−16.6927	+	4.47278i	−0.675313	+	0.180949i
$612$	4.11715	+	16.5120i	0.166426	+	0.667459i
$613$	34.9825	−	20.1972i	1.41293	−	0.815756i	0.417268	−	0.908784i	$-0.362988\pi$
$613$	34.9825	−	20.1972i	1.41293	−	0.815756i	0.995664	+	0.0930271i	$0.0296543\pi$
$614$	−8.61109	−	0.0750878i	−0.347515	−	0.00303030i
$615$	−4.99817	−	4.99817i	−0.201546	−	0.201546i
$616$	4.29671	+	2.63290i	0.173119	+	0.106083i
$617$	−3.63300	+	2.09751i	−0.146259	+	0.0844427i	−0.571344	−	0.820711i	$-0.693578\pi$
$617$	−3.63300	+	2.09751i	−0.146259	+	0.0844427i	0.425085	+	0.905154i	$0.360244\pi$
$618$	7.62508	+	29.4831i	0.306726	+	1.18599i
$619$	18.3190			0.736302			0.368151	−	0.929766i	$-0.379991\pi$
$619$	18.3190			0.736302			0.368151	+	0.929766i	$0.379991\pi$
$620$	−0.667044	−	0.400788i	−0.0267891	−	0.0160960i
$621$	5.32670	+	5.32670i	0.213753	+	0.213753i
$622$	−21.0204	−	5.82932i	−0.842843	−	0.233735i
$623$	−3.28300	+	3.28300i	−0.131530	+	0.131530i
$624$	−20.9047	−	6.39056i	−0.836856	−	0.255827i
$625$	0.500000	−	0.866025i	0.0200000	−	0.0346410i
$626$	−15.1784	−	4.20923i	−0.606651	−	0.168235i
$627$	3.25542	−	12.1494i	0.130009	−	0.485200i
$628$	9.21858	+	16.6302i	0.367861	+	0.663618i
$629$	−4.85412	−	28.6853i	−0.193546	−	1.14376i
$630$	−2.56488	+	0.663341i	−0.102187	+	0.0264282i
$631$	−21.9099	−	5.87074i	−0.872220	−	0.233711i	−0.205172	−	0.978726i	$-0.565775\pi$
$631$	−21.9099	−	5.87074i	−0.872220	−	0.233711i	−0.667047	+	0.745015i	$0.732442\pi$
$632$	−8.53840	+	2.05008i	−0.339639	+	0.0815477i
$633$	−0.458150	−	0.264513i	−0.0182098	−	0.0105134i
$634$	23.2525	−	13.1559i	0.923475	−	0.522486i
$635$	9.24712	+	9.24712i	0.366961	+	0.366961i
$636$	−22.5357	−	0.393048i	−0.893599	−	0.0155854i
$637$	20.6022	−	20.6022i	0.816289	−	0.816289i
$638$	−10.5942	−	10.7806i	−0.419427	−	0.426807i
$639$		−	3.19278i		−	0.126304i
$640$	−2.25613	−	11.0865i	−0.0891814	−	0.438231i
$641$	20.6707	+	35.8027i	0.816443	+	1.41412i	0.908287	+	0.418347i	$0.137391\pi$
$641$	20.6707	+	35.8027i	0.816443	+	1.41412i	−0.0918442	+	0.995773i	$0.529276\pi$
$642$	−3.54247	+	2.00427i	−0.139810	+	0.0791020i
$643$	27.3621	−	27.3621i	1.07906	−	1.07906i	0.0824614	−	0.996594i	$-0.473722\pi$
$643$	27.3621	−	27.3621i	1.07906	−	1.07906i	0.996594	−	0.0824614i	$-0.0262781\pi$
$644$	0.726843	+	2.91504i	0.0286416	+	0.114869i
$645$	−6.03667	−	10.4558i	−0.237694	−	0.411698i
$646$	45.5046	+	0.396795i	1.79035	+	0.0156117i
$647$	−0.724790	−	2.70495i	−0.0284944	−	0.106343i	0.950214	−	0.311598i	$-0.100864\pi$
$647$	−0.724790	−	2.70495i	−0.0284944	−	0.106343i	−0.978708	+	0.205255i	$0.934198\pi$
$648$	0.736070	−	1.20121i	0.0289155	−	0.0471881i
$649$	−2.06874	+	7.72064i	−0.0812052	+	0.303062i
$650$	−4.90238	−	4.98863i	−0.192287	−	0.195670i
$651$	0.117176	−	0.437308i	0.00459250	−	0.0171394i
$652$	7.84871	+	2.25046i	0.307379	+	0.0881350i
$653$	−23.8468	+	6.38973i	−0.933198	+	0.250050i	−0.693218	−	0.720728i	$-0.743808\pi$
$653$	−23.8468	+	6.38973i	−0.933198	+	0.250050i	−0.239980	+	0.970778i	$0.577141\pi$
$654$	−12.9640	+	12.7398i	−0.506932	+	0.498167i
$655$		−	2.66625i		−	0.104179i
$656$	−21.6999	−	13.5588i	−0.847240	−	0.529382i
$657$	24.7552	−	14.2924i	0.965794	−	0.557601i
$658$	2.64098	−	4.48357i	0.102956	−	0.174788i
$659$	4.11911	−	7.13450i	0.160458	−	0.277921i	−0.774575	−	0.632482i	$-0.782036\pi$
$659$	4.11911	−	7.13450i	0.160458	−	0.277921i	0.935033	+	0.354561i	$0.115370\pi$
$660$	−3.59432	−	1.03060i	−0.139909	−	0.0401161i
$661$	−21.4137	+	5.73777i	−0.832895	+	0.223174i	−0.649976	−	0.759955i	$-0.725221\pi$
$661$	−21.4137	+	5.73777i	−0.832895	+	0.223174i	−0.182919	+	0.983128i	$0.558555\pi$
$662$	−2.19387	+	7.91106i	−0.0852672	+	0.307472i
$663$	−22.6362	−	13.0690i	−0.879115	−	0.507557i
$664$	−32.8513	+	17.8377i	−1.27488	+	0.692236i
$665$			7.08434i			0.274719i
$666$	8.97255	−	12.3974i	0.347679	−	0.480388i
$667$		−	9.01113i		−	0.348912i
$668$	16.5946	−	4.13774i	0.642064	−	0.160094i
$669$	12.5646	+	7.25420i	0.485777	+	0.280464i
$670$	20.7296	+	5.74868i	0.800856	+	0.222091i
$671$	3.20869	−	0.859767i	0.123870	−	0.0331909i
$672$	5.83827	−	3.03947i	0.225216	−	0.117250i
$673$	−2.01517	+	3.49038i	−0.0776792	+	0.134544i	−0.902248	−	0.431217i	$-0.858084\pi$
$673$	−2.01517	+	3.49038i	−0.0776792	+	0.134544i	0.824569	+	0.565761i	$0.191418\pi$
$674$	−29.3437	−	17.2845i	−1.13028	−	0.665772i
$675$	4.57325	−	2.64036i	0.176024	−	0.101628i
$676$	−20.0459	+	11.1120i	−0.770997	+	0.427384i
$677$			21.0006i			0.807119i	0.914953	+	0.403560i	$0.132227\pi$
$677$			21.0006i			0.807119i	−0.914953	+	0.403560i	$0.867773\pi$
$678$	10.0368	+	10.2133i	0.385459	+	0.392241i
$679$	7.41602	−	1.98712i	0.284601	−	0.0762585i
$680$	0.353839	−	13.5234i	0.0135691	−	0.518598i
$681$	0.191572	−	0.714955i	0.00734104	−	0.0273971i
$682$	−0.664044	+	0.652564i	−0.0254276	+	0.0249880i
$683$	9.93853	−	37.0911i	0.380287	−	1.41925i	−0.465176	−	0.885218i	$-0.654009\pi$
$683$	9.93853	−	37.0911i	0.380287	−	1.41925i	0.845463	−	0.534033i	$-0.179324\pi$
$684$	16.6285	+	17.2189i	0.635808	+	0.658380i
$685$	5.20131	+	19.4116i	0.198732	+	0.741678i
$686$	−0.167392	+	19.1965i	−0.00639105	+	0.732927i
$687$	−10.1799	−	17.6322i	−0.388388	−	0.672709i
$688$	−29.8077	−	31.9630i	−1.13641	−	1.21858i
$689$	−35.6668	+	35.6668i	−1.35880	+	1.35880i
$690$	−1.09773	−	1.94019i	−0.0417898	−	0.0738619i
$691$	−14.1559	−	24.5187i	−0.538514	−	0.932734i	−0.998984	−	0.0450591i	$-0.985652\pi$
$691$	−14.1559	−	24.5187i	−0.538514	−	0.932734i	0.460470	−	0.887675i	$-0.347681\pi$
$692$	−16.9110	+	9.37421i	−0.642859	+	0.356354i
$693$			3.16955i			0.120401i
$694$	−36.9307	+	36.2922i	−1.40187	+	1.37763i
$695$	−9.96010	+	9.96010i	−0.377808	+	0.377808i
$696$	−19.1969	+	4.60918i	−0.727655	+	0.174711i
$697$	−21.6344	−	21.6344i	−0.819461	−	0.819461i
$698$	−1.20954	−	2.13782i	−0.0457818	−	0.0809177i
$699$	−8.94600	−	5.16497i	−0.338369	−	0.195357i
$700$	2.10570	+	0.0367257i	0.0795879	+	0.00138810i
$701$	7.39614	+	1.98179i	0.279348	+	0.0748512i	0.395773	−	0.918348i	$-0.370477\pi$
$701$	7.39614	+	1.98179i	0.279348	+	0.0748512i	−0.116425	+	0.993200i	$0.537143\pi$
$702$	−9.24799	−	35.7583i	−0.349043	−	1.34961i
$703$	−26.0879	−	31.5297i	−0.983924	−	1.18917i
$704$	−13.5171	−	0.707833i	−0.509444	−	0.0266775i
$705$	−0.999325	+	3.72953i	−0.0376367	+	0.140462i
$706$	9.89178	−	35.6696i	0.372282	−	1.34244i
$707$	−7.15778	+	12.3976i	−0.269196	+	0.466261i
$708$	7.25246	+	7.50994i	0.272564	+	0.282241i
$709$	−21.4925	+	21.4925i	−0.807167	+	0.807167i	−0.984204	−	0.177037i	$-0.943349\pi$
$709$	−21.4925	+	21.4925i	−0.807167	+	0.807167i	0.177037	+	0.984204i	$0.443349\pi$
$710$	−0.678255	+	2.44578i	−0.0254545	+	0.0917883i
$711$	−3.90540	−	3.90540i	−0.146464	−	0.146464i
$712$	3.54168	−	11.9574i	0.132730	−	0.448124i
$713$	−0.555054			−0.0207869
$714$	7.61961	−	1.97062i	0.285157	−	0.0737487i
$715$	−7.24678	+	4.18393i	−0.271014	+	0.156470i
$716$	−5.09496	+	4.92028i	−0.190408	+	0.183880i
$717$	2.38522	+	2.38522i	0.0890778	+	0.0890778i
$718$	−0.0947410	+	10.8649i	−0.00353570	+	0.405476i
$719$	−37.5851	+	21.6998i	−1.40169	+	0.809265i	−0.994566	−	0.104109i	$-0.966801\pi$
$719$	−37.5851	+	21.6998i	−1.40169	+	0.809265i	−0.407122	+	0.913374i	$0.633468\pi$
$720$	5.20421	−	4.85328i	0.193949	−	0.180871i
$721$	−19.8216	+	5.31117i	−0.738193	+	0.197798i
$722$	32.3251	−	18.2890i	1.20302	−	0.680646i
$723$	16.3188	+	4.37261i	0.606903	+	0.162619i
$724$	17.6927	−	29.4465i	0.657543	−	1.09437i
$725$	−6.10160	−	1.63492i	−0.226608	−	0.0607193i
$726$	6.45380	−	10.9565i	0.239523	−	0.406636i
$727$	1.04748	+	3.90923i	0.0388487	+	0.144985i	0.982626	−	0.185596i	$-0.0594217\pi$
$727$	1.04748	+	3.90923i	0.0388487	+	0.144985i	−0.943777	+	0.330582i	$0.892755\pi$
$728$	4.18326	−	14.1235i	0.155042	−	0.523453i
$729$	18.3915			0.681165
$730$	−21.9995	+	5.68963i	−0.814239	+	0.210583i
$731$	−26.1295	−	45.2576i	−0.966434	−	1.67391i
$732$	1.19591	−	4.17087i	0.0442022	−	0.154160i
$733$	24.2970	+	14.0279i	0.897429	+	0.518131i	0.876365	−	0.481647i	$-0.159961\pi$
$733$	24.2970	+	14.0279i	0.897429	+	0.518131i	0.0210641	+	0.999778i	$0.493295\pi$
$734$	25.2323	+	14.8627i	0.931342	+	0.548594i
$735$	−1.68482	−	6.28784i	−0.0621456	−	0.231930i
$736$	−5.45198	−	5.94938i	−0.200963	−	0.219297i
$737$	12.8683	−	22.2886i	0.474012	−	0.821012i
$738$	0.140333	−	16.0934i	0.00516572	−	0.592406i
$739$	−4.59475			−0.169021			−0.0845103	−	0.996423i	$-0.526933\pi$
$739$	−4.59475			−0.169021			−0.0845103	+	0.996423i	$0.526933\pi$
$740$	−9.50689	+	7.59072i	−0.349480	+	0.279040i
$741$	−36.7664			−1.35065
$742$	0.132432	−	15.1874i	0.00486174	−	0.557545i
$743$	−7.36785	+	12.7615i	−0.270300	+	0.468174i	−0.968939	−	0.247301i	$-0.920456\pi$
$743$	−7.36785	+	12.7615i	−0.270300	+	0.468174i	0.698638	+	0.715475i	$0.253790\pi$
$744$	0.283909	+	1.18246i	0.0104086	+	0.0433510i
$745$	−0.255571	−	0.953802i	−0.00936338	−	0.0349446i
$746$	−7.66909	−	4.51737i	−0.280785	−	0.165393i
$747$	−20.3621	−	11.7561i	−0.745011	−	0.430132i
$748$	−15.5579	−	4.46091i	−0.568852	−	0.163107i
$749$	−1.37133	−	2.37521i	−0.0501073	−	0.0867885i
$750$	−1.51290	+	0.391275i	−0.0552435	+	0.0142873i
$751$	1.15188			0.0420326			0.0210163	−	0.999779i	$-0.493310\pi$
$751$	1.15188			0.0420326			0.0210163	+	0.999779i	$0.493310\pi$
$752$	−0.487401	+	13.9685i	−0.0177737	+	0.509379i
$753$	−5.01584	−	18.7194i	−0.182787	−	0.682171i
$754$	−22.4236	+	38.0684i	−0.816620	+	1.38637i
$755$	−19.0373	−	5.10103i	−0.692839	−	0.185646i
$756$	9.53290	+	5.72776i	0.346708	+	0.208317i
$757$	−24.8456	−	6.65737i	−0.903030	−	0.241966i	−0.222713	−	0.974884i	$-0.571491\pi$
$757$	−24.8456	−	6.65737i	−0.903030	−	0.241966i	−0.680317	+	0.732918i	$0.738158\pi$
$758$	−0.304044	+	0.172023i	−0.0110434	+	0.00624814i
$759$	−2.57612	+	0.690270i	−0.0935073	+	0.0250552i
$760$	−9.08013	−	16.7227i	−0.329371	−	0.606596i
$761$	5.04530	−	2.91291i	0.182892	−	0.105593i	−0.405759	−	0.913980i	$-0.632993\pi$
$761$	5.04530	−	2.91291i	0.182892	−	0.105593i	0.588651	+	0.808387i	$0.299659\pi$
$762$	0.178192	−	20.4351i	0.00645520	−	0.740284i
$763$	−8.66055	−	8.66055i	−0.313533	−	0.313533i
$764$	32.7598	+	33.9229i	1.18521	+	1.22729i
$765$	7.36883	−	4.25439i	0.266421	−	0.153818i
$766$	−31.1066	+	8.04496i	−1.12393	+	0.290676i
$767$	23.3641			0.843629
$768$	−9.88557	+	14.6577i	−0.356715	+	0.528915i
$769$	19.9838	+	19.9838i	0.720633	+	0.720633i	0.968734	−	0.248101i	$-0.0798066\pi$
$769$	19.9838	+	19.9838i	0.720633	+	0.720633i	−0.248101	+	0.968734i	$0.579807\pi$
$770$	0.673321	−	2.42798i	0.0242648	−	0.0874985i
$771$	−10.0706	+	10.0706i	−0.362685	+	0.362685i
$772$	−20.2212	+	19.5279i	−0.727777	+	0.702826i
$773$	12.6211	−	21.8603i	0.453949	−	0.786262i	−0.544679	−	0.838645i	$-0.683348\pi$
$773$	12.6211	−	21.8603i	0.453949	−	0.786262i	0.998627	+	0.0523830i	$0.0166817\pi$
$774$	7.34604	−	26.4897i	0.264048	−	0.952152i
$775$	−0.100705	+	0.375837i	−0.00361744	+	0.0135005i
$776$	−14.9587	+	14.1959i	−0.536986	+	0.509602i
$777$	−5.76951	−	4.09948i	−0.206980	−	0.147068i
$778$	8.30001	+	32.0928i	0.297570	+	1.15058i
$779$	−41.5702	−	11.1387i	−1.48941	−	0.399085i
$780$	−0.190599	+	10.9282i	−0.00682455	+	0.391291i
$781$	2.62971	+	1.51827i	0.0940986	+	0.0543278i
$782$	−4.75147	−	8.39805i	−0.169912	−	0.300314i
$783$	−23.5873	−	23.5873i	−0.842942	−	0.842942i
$784$	−11.0635	−	20.8061i	−0.395126	−	0.743074i
$785$	6.72259	−	6.72259i	0.239940	−	0.239940i
$786$	−2.97174	+	2.92036i	−0.105998	+	0.104166i
$787$		−	37.8970i		−	1.35088i	−0.737414	−	0.675441i	$-0.763953\pi$
$787$		−	37.8970i		−	1.35088i	0.737414	−	0.675441i	$-0.236047\pi$
$788$	−0.724167	−	1.30639i	−0.0257974	−	0.0465382i
$789$	−12.5577	−	21.7506i	−0.447067	−	0.774344i
$790$	2.16203	+	3.82131i	0.0769215	+	0.135956i
$791$	−6.82299	+	6.82299i	−0.242598	+	0.242598i
$792$	−4.06248	−	7.48178i	−0.144354	−	0.265853i
$793$	−4.85506	−	8.40920i	−0.172408	−	0.298620i
$794$	−0.0710666	+	8.14994i	−0.00252206	+	0.289230i
$795$	2.91678	+	10.8856i	0.103448	+	0.386071i
$796$	33.8334	−	32.6735i	1.19919	−	1.15808i
$797$	−1.14226	+	4.26298i	−0.0404610	+	0.151002i	−0.983201	−	0.182526i	$-0.941573\pi$
$797$	−1.14226	+	4.26298i	−0.0404610	+	0.151002i	0.942740	+	0.333528i	$0.108239\pi$
$798$	7.89604	−	7.75953i	0.279517	−	0.274684i
$799$	−4.32554	+	16.1431i	−0.153026	+	0.571102i
$800$	−5.01760	+	2.61222i	−0.177399	+	0.0923559i
$801$	7.57662	−	2.03015i	0.267707	−	0.0717318i
$802$	3.11218	+	3.16693i	0.109895	+	0.111828i
$803$			27.1860i			0.959373i
$804$	−16.2980	−	29.4013i	−0.574785	−	1.03691i
$805$	1.30089	−	0.751072i	0.0458505	−	0.0264718i
$806$	2.34488	+	1.38122i	0.0825947	+	0.0486512i
$807$	−2.68660	+	4.65332i	−0.0945727	+	0.163805i
$808$	1.00576	−	38.4391i	0.0353824	−	1.35228i
$809$	−3.02693	+	0.811062i	−0.106421	+	0.0285154i	−0.311637	−	0.950201i	$-0.600877\pi$
$809$	−3.02693	+	0.811062i	−0.106421	+	0.0285154i	0.205216	+	0.978717i	$0.434210\pi$
$810$	−0.678782	−	0.188238i	−0.0238500	−	0.00661400i
$811$	41.5928	+	24.0136i	1.46052	+	0.843233i	0.999035	−	0.0439147i	$-0.0139830\pi$
$811$	41.5928	+	24.0136i	1.46052	+	0.843233i	0.461486	+	0.887147i	$0.347316\pi$
$812$	−3.21856	−	12.9082i	−0.112949	−	0.452988i
$813$			15.1152i			0.530113i
$814$	5.94429	+	13.2855i	0.208347	+	0.465657i
$815$		−	4.08249i		−	0.143003i
$816$	−15.4604	+	14.4179i	−0.541223	+	0.504726i
$817$	−63.6605	−	36.7544i	−2.22720	−	1.28587i
$818$	4.35889	−	15.7181i	0.152405	−	0.549569i
$819$	8.94915	−	2.39792i	0.312708	−	0.0837900i
$820$	−3.52628	+	12.2983i	−0.123143	+	0.429474i
$821$	−1.70202	+	2.94798i	−0.0594008	+	0.102885i	−0.894197	−	0.447674i	$-0.852252\pi$
$821$	−1.70202	+	2.94798i	−0.0594008	+	0.102885i	0.834796	+	0.550560i	$0.185586\pi$
$822$	15.9386	−	27.0589i	0.555924	−	0.943787i
$823$	26.8314	−	15.4911i	0.935282	−	0.539986i	0.0468041	−	0.998904i	$-0.485096\pi$
$823$	26.8314	−	15.4911i	0.935282	−	0.539986i	0.888478	+	0.458919i	$0.151763\pi$
$824$	39.9816	−	37.9427i	1.39283	−	1.32180i
$825$			1.86958i			0.0650903i
$826$	−5.01774	+	4.93099i	−0.174590	+	0.171571i
$827$	−2.90452	+	0.778265i	−0.101000	+	0.0270629i	−0.308965	−	0.951073i	$-0.599983\pi$
$827$	−2.90452	+	0.778265i	−0.101000	+	0.0270629i	0.207965	+	0.978136i	$0.433316\pi$
$828$	1.39896	−	4.87901i	0.0486172	−	0.169557i
$829$	8.55478	−	31.9269i	0.297120	−	1.10887i	−0.642399	−	0.766370i	$-0.722061\pi$
$829$	8.55478	−	31.9269i	0.297120	−	1.10887i	0.939519	−	0.342496i	$-0.111272\pi$
$830$	13.1007	+	13.3312i	0.454731	+	0.462731i
$831$	0.545504	−	2.03585i	0.0189233	−	0.0706228i
$832$	8.22776	+	38.7006i	0.285246	+	1.34170i
$833$	−7.29268	−	27.2166i	−0.252676	−	0.943001i
$834$	22.0107	+	0.191931i	0.762167	+	0.00664601i
$835$	−4.27567	−	7.40567i	−0.147966	−	0.256284i
$836$	−22.0896	+	5.50788i	−0.763985	+	0.190494i
$837$	−1.45290	+	1.45290i	−0.0502194	+	0.0502194i
$838$	37.7633	−	21.3658i	1.30451	−	0.738070i
$839$	23.1360	+	40.0727i	0.798743	+	1.38346i	0.920435	+	0.390896i	$0.127835\pi$
$839$	23.1360	+	40.0727i	0.798743	+	1.38346i	−0.121691	+	0.992568i	$0.538832\pi$
$840$	−2.26545	−	2.38719i	−0.0781655	−	0.0823658i
$841$			10.9025i			0.375947i
$842$	28.3668	+	28.8659i	0.977584	+	0.994783i
$843$	−9.08960	+	9.08960i	−0.313063	+	0.313063i
$844$	−0.0166978	+	0.957382i	−0.000574762	+	0.0329544i
$845$	8.10336	+	8.10336i	0.278764	+	0.278764i
$846$	−7.65144	+	4.32905i	−0.263062	+	0.148836i
$847$	7.42067	+	4.28433i	0.254977	+	0.147211i
$848$	19.1533	+	36.0197i	0.657727	+	1.23692i
$849$	−21.1751	−	5.67385i	−0.726727	−	0.194726i
$850$	−6.54855	+	1.69362i	−0.224613	+	0.0580906i
$851$	−3.02398	+	8.13324i	−0.103661	+	0.278804i
$852$	3.46890	−	1.92291i	0.118843	−	0.0658777i
$853$	11.7568	−	43.8769i	0.402545	−	1.50232i	−0.405995	−	0.913875i	$-0.633075\pi$
$853$	11.7568	−	43.8769i	0.402545	−	1.50232i	0.808539	−	0.588442i	$-0.200258\pi$
$854$	2.81744	+	0.781325i	0.0964110	+	0.0267364i
$855$	5.98434	−	10.3652i	0.204660	−	0.354482i
$856$	6.28140	+	3.84907i	0.214694	+	0.131558i
$857$	−19.2043	+	19.2043i	−0.656007	+	0.656007i	−0.954433	−	0.298426i	$-0.903539\pi$
$857$	−19.2043	+	19.2043i	−0.656007	+	0.656007i	0.298426	+	0.954433i	$0.403539\pi$
$858$	12.6008	+	3.49441i	0.430183	+	0.119297i
$859$	5.82331	+	5.82331i	0.198689	+	0.198689i	0.799438	−	0.600749i	$-0.205131\pi$
$859$	5.82331	+	5.82331i	0.198689	+	0.198689i	−0.600749	+	0.799438i	$0.705131\pi$
$860$	−11.2546	+	18.7314i	−0.383780	+	0.638737i
$861$	−7.44318			−0.253663
$862$	−4.10788	−	15.8835i	−0.139915	−	0.540995i
$863$	−39.6526	+	22.8934i	−1.34979	+	0.779301i	−0.988219	−	0.153044i	$-0.951092\pi$
$863$	−39.6526	+	22.8934i	−1.34979	+	0.779301i	−0.361570	+	0.932345i	$0.617759\pi$
$864$	−29.8439	−	1.30197i	−1.01531	−	0.0442940i
$865$	6.83609	+	6.83609i	0.232434	+	0.232434i
$866$	22.4761	+	0.195989i	0.763768	+	0.00665998i
$867$	−5.62290	+	3.24638i	−0.190964	+	0.110253i
$868$	−0.795097	+	0.198252i	−0.0269874	+	0.00672910i
$869$	5.07380	−	1.35952i	0.172117	−	0.0461186i
$870$	4.86088	+	8.59144i	0.164799	+	0.291277i
$871$	−72.6668	−	19.4710i	−2.46222	−	0.659750i
$872$	31.5437	+	9.34296i	1.06821	+	0.316393i
$873$	−12.5290	−	3.35714i	−0.424044	−	0.113622i
$874$	−11.6946	−	6.88852i	−0.395575	−	0.233008i
$875$	−0.272539	−	1.01713i	−0.00921349	−	0.0343852i
$876$	30.4378	+	18.2883i	1.02840	+	0.617904i
$877$	40.0554			1.35257			0.676287	−	0.736638i	$-0.263588\pi$
$877$	40.0554			1.35257			0.676287	+	0.736638i	$0.263588\pi$
$878$	−4.82349	−	18.6505i	−0.162785	−	0.629425i
$879$	1.20325	+	2.08409i	0.0405847	+	0.0702947i
$880$	1.52261	+	6.59430i	0.0513271	+	0.222294i
$881$	−28.9272	−	16.7011i	−0.974582	−	0.562675i	−0.0739523	−	0.997262i	$-0.523561\pi$
$881$	−28.9272	−	16.7011i	−0.974582	−	0.562675i	−0.900630	+	0.434586i	$0.856895\pi$
$882$	7.52245	−	12.7708i	0.253294	−	0.430015i
$883$	−12.6812	−	47.3270i	−0.426757	−	1.59268i	−0.760056	−	0.649858i	$-0.774828\pi$
$883$	−12.6812	−	47.3270i	−0.426757	−	1.59268i	0.333299	−	0.942821i	$-0.391838\pi$
$884$	−0.825001	+	47.3021i	−0.0277478	+	1.59094i
$885$	2.61005	−	4.52073i	0.0877357	−	0.151963i
$886$	−1.30425	−	0.0113729i	−0.0438170	−	0.000382080i
$887$	−5.29365			−0.177743			−0.0888717	−	0.996043i	$-0.528326\pi$
$887$	−5.29365			−0.177743			−0.0888717	+	0.996043i	$0.528326\pi$
$888$	18.8734	+	2.28200i	0.633350	+	0.0765787i
$889$	13.7706			0.461852
$890$	−6.23522	−	0.0543705i	−0.209005	−	0.00182250i
$891$	−0.421368	+	0.729830i	−0.0141163	+	0.0244502i
$892$	0.457933	−	26.2559i	0.0153327	−	0.879114i
$893$	6.08441	+	22.7073i	0.203607	+	0.759872i
$894$	−0.783158	+	1.32956i	−0.0261927	+	0.0444671i
$895$	3.06699	+	1.77073i	0.102518	+	0.0591890i
$896$	−9.93477	−	6.57498i	−0.331897	−	0.219655i
$897$	3.89791	+	6.75139i	0.130148	+	0.225422i
$898$	−6.22660	−	24.0758i	−0.207784	−	0.803419i
$899$	2.45785			0.0819739
$900$	−3.04985	−	1.83247i	−0.101662	−	0.0610825i
$901$	12.6252	+	47.1177i	0.420605	+	1.56972i
$902$	13.1885	+	7.76849i	0.439129	+	0.258662i
$903$	−12.2801	−	3.29045i	−0.408658	−	0.109499i
$904$	7.36061	−	24.8509i	0.244810	−	0.826529i
$905$	−16.5912	−	4.44560i	−0.551510	−	0.147777i
$906$	15.1662	+	26.8057i	0.503863	+	0.890561i
$907$	−24.7166	+	6.62279i	−0.820701	+	0.219906i	−0.644653	−	0.764475i	$-0.722998\pi$
$907$	−24.7166	+	6.62279i	−0.820701	+	0.219906i	−0.176048	+	0.984382i	$0.556331\pi$
$908$	−1.29991	+	0.324122i	−0.0431389	+	0.0107564i
$909$	20.9453	−	12.0928i	0.694710	−	0.401091i
$910$	−7.36474	−	0.0642198i	−0.244139	−	0.00212887i
$911$	24.9072	+	24.9072i	0.825213	+	0.825213i	0.986850	−	0.161638i	$-0.0516776\pi$
$911$	24.9072	+	24.9072i	0.825213	+	0.825213i	−0.161638	+	0.986850i	$0.551678\pi$
$912$	−8.69319	+	28.4370i	−0.287860	+	0.941643i
$913$	19.3656	−	11.1808i	0.640909	−	0.370029i
$914$	−6.75338	−	26.1126i	−0.223382	−	0.863729i
$915$	−2.16947			−0.0717203
$916$	−18.9792	+	31.5877i	−0.627091	+	1.04369i
$917$	−1.98526	−	1.98526i	−0.0655592	−	0.0655592i
$918$	−34.4199	−	9.54522i	−1.13603	−	0.315039i
$919$	−17.9598	+	17.9598i	−0.592440	+	0.592440i	−0.938290	−	0.345850i	$-0.887591\pi$
$919$	−17.9598	+	17.9598i	−0.592440	+	0.592440i	0.345850	+	0.938290i	$0.387591\pi$
$920$	−2.10812	+	3.44030i	−0.0695025	+	0.113423i
$921$	3.36423	−	5.82701i	0.110855	−	0.192007i
$922$	−36.6446	−	10.1622i	−1.20683	−	0.334673i
$923$	2.29728	−	8.57356i	0.0756158	−	0.282202i
$924$	−3.44367	+	1.90892i	−0.113288	+	0.0627988i
$925$	4.95851	+	3.52323i	0.163035	+	0.115843i
$926$	32.3585	−	8.36871i	1.06337	−	0.275013i
$927$	33.4876	+	8.97298i	1.09988	+	0.294711i
$928$	24.1421	+	26.3446i	0.792503	+	0.864804i
$929$	−25.8369	−	14.9170i	−0.847682	−	0.489409i	0.0121861	−	0.999926i	$-0.496121\pi$
$929$	−25.8369	−	14.9170i	−0.847682	−	0.489409i	−0.859868	+	0.510516i	$0.829454\pi$
$930$	0.529202	−	0.299413i	0.0173532	−	0.00981814i
$931$	−28.0256	−	28.0256i	−0.918501	−	0.918501i
$932$	−0.326047	+	18.6942i	−0.0106800	+	0.612348i
$933$	12.0519	−	12.0519i	0.394562	−	0.394562i
$934$	30.6636	+	31.2031i	1.00335	+	1.02100i
$935$			8.09239i			0.264649i
$936$	−18.0511	+	17.1306i	−0.590020	+	0.559931i
$937$	−9.28511	−	16.0823i	−0.303331	−	0.525385i	0.673557	−	0.739135i	$-0.264766\pi$
$937$	−9.28511	−	16.0823i	−0.303331	−	0.525385i	−0.976888	+	0.213750i	$0.931432\pi$
$938$	19.7155	−	11.1547i	0.643733	−	0.364213i
$939$	8.70242	−	8.70242i	0.283993	−	0.283993i
$940$	6.78090	−	1.69077i	0.221169	−	0.0551468i
$941$	25.7478	+	44.5966i	0.839355	+	1.45381i	0.890434	+	0.455112i	$0.150401\pi$
$941$	25.7478	+	44.5966i	0.839355	+	1.45381i	−0.0510791	+	0.998695i	$0.516266\pi$
$942$	−14.8561	−	0.129544i	−0.484039	−	0.00422077i
$943$	2.36182	+	8.81442i	0.0769113	+	0.287037i
$944$	5.52431	−	18.0710i	0.179801	−	0.588161i
$945$	1.43920	−	5.37118i	0.0468173	−	0.174724i
$946$	18.3248	+	18.6472i	0.595791	+	0.606273i
$947$	11.2109	−	41.8395i	0.364304	−	1.35960i	−0.504058	−	0.863670i	$-0.668160\pi$
$947$	11.2109	−	41.8395i	0.364304	−	1.35960i	0.868362	−	0.495931i	$-0.165173\pi$
$948$	1.89106	−	6.59525i	0.0614187	−	0.214204i
$949$	76.7589	−	20.5675i	2.49170	−	0.667649i
$950$	−6.78612	+	6.66880i	−0.220171	+	0.216364i
$951$			20.8745i			0.676901i
$952$	−9.80591	−	10.3328i	−0.317811	−	0.334889i
$953$	11.9781	−	6.91556i	0.388009	−	0.224017i	−0.293288	−	0.956024i	$-0.594750\pi$
$953$	11.9781	−	6.91556i	0.388009	−	0.224017i	0.681297	+	0.732007i	$0.261416\pi$
$954$	−13.0229	+	22.1089i	−0.421633	+	0.715803i
$955$	11.7897	−	20.4204i	0.381507	−	0.660790i
$956$	1.68281	−	5.86896i	0.0544260	−	0.189816i
$957$	11.4074	−	3.05661i	0.368749	−	0.0988060i
$958$	1.34693	−	4.85700i	0.0435173	−	0.156922i
$959$	18.3265	+	10.5808i	0.591794	+	0.341672i
$960$	8.40733	+	2.73132i	0.271345	+	0.0881529i
$961$			30.8486i			0.995116i
$962$	33.0141	−	26.8346i	1.06442	−	0.865184i
$963$			4.63360i			0.149316i
$964$	−7.39806	−	29.6702i	−0.238276	−	0.955614i
$965$	12.1725	+	7.02779i	0.391846	+	0.226233i
$966$	−2.26201	−	0.627293i	−0.0727788	−	0.0201828i
$967$	37.2041	−	9.96881i	1.19640	−	0.320575i	0.394990	−	0.918686i	$-0.370748\pi$
$967$	37.2041	−	9.96881i	1.19640	−	0.320575i	0.801414	+	0.598110i	$0.204082\pi$
$968$	−23.0079	−	0.602002i	−0.739502	−	0.0193491i
$969$	−17.7780	+	30.7924i	−0.571111	+	0.989194i
$970$	8.88449	+	5.23328i	0.285264	+	0.168030i
$971$	11.6802	−	6.74359i	0.374837	−	0.216412i	−0.300733	−	0.953708i	$-0.597231\pi$
$971$	11.6802	−	6.74359i	0.374837	−	0.216412i	0.675569	+	0.737296i	$0.263898\pi$
$972$	−14.8276	−	26.7488i	−0.475596	−	0.857969i
$973$			14.8324i			0.475504i
$974$	−14.1267	−	14.3752i	−0.452648	−	0.460612i
$975$	5.27870	−	1.41442i	0.169054	−	0.0452978i
$976$	−7.65206	+	1.76684i	−0.244936	+	0.0565552i
$977$	9.38643	−	35.0306i	0.300298	−	1.12073i	−0.636619	−	0.771178i	$-0.719668\pi$
$977$	9.38643	−	35.0306i	0.300298	−	1.12073i	0.936918	−	0.349550i	$-0.113666\pi$
$978$	−4.55025	+	4.47158i	−0.145501	+	0.142985i
$979$	−1.93080	+	7.20584i	−0.0617086	+	0.230300i
$980$	−8.47540	+	8.18482i	−0.270737	+	0.261455i
$981$	5.35554	+	19.9872i	0.170989	+	0.638141i
$982$	−0.393981	+	45.1819i	−0.0125724	+	1.44181i
$983$	11.1023	+	19.2297i	0.354107	+	0.613331i	0.986965	−	0.160937i	$-0.0514515\pi$
$983$	11.1023	+	19.2297i	0.354107	+	0.613331i	−0.632858	+	0.774268i	$0.718118\pi$
$984$	17.5697	−	9.54005i	0.560102	−	0.304126i
$985$	−0.528095	+	0.528095i	−0.0168265	+	0.0168265i
$986$	21.0401	+	37.1877i	0.670054	+	1.18430i
$987$	2.03288	+	3.52106i	0.0647074	+	0.112076i
$988$	32.2632	+	58.2024i	1.02643	+	1.85166i
$989$			15.5866i			0.495625i
$990$	−3.03613	+	2.98364i	−0.0964945	+	0.0948262i
$991$	−22.6734	+	22.6734i	−0.720244	+	0.720244i	−0.968655	−	0.248411i	$-0.920092\pi$
$991$	−22.6734	+	22.6734i	−0.720244	+	0.720244i	0.248411	+	0.968655i	$0.420092\pi$
$992$	1.62273	−	1.48707i	0.0515219	−	0.0472144i
$993$	−4.53575	−	4.53575i	−0.143938	−	0.143938i
$994$	1.31608	+	2.32612i	0.0417434	+	0.0737801i
$995$	−20.3666	−	11.7587i	−0.645664	−	0.372774i
$996$	0.509340	−	29.2034i	0.0161391	−	0.925346i
$997$	42.9864	+	11.5182i	1.36139	+	0.364784i	0.864327	−	0.502930i	$-0.167745\pi$
$997$	42.9864	+	11.5182i	1.36139	+	0.364784i	0.497064	+	0.867714i	$0.334411\pi$
$998$	−1.40479	−	5.43177i	−0.0444679	−	0.171940i
$999$	13.3739	+	29.2049i	0.423131	+	0.924002i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.be.a.251.76	yes	304
4.3	odd	2	inner	740.2.be.a.251.13	yes	304
37.23	odd	12	inner	740.2.be.a.171.13	✓	304
148.23	even	12	inner	740.2.be.a.171.76	yes	304

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.be.a.171.13	✓	304	37.23	odd	12	inner
740.2.be.a.171.76	yes	304	148.23	even	12	inner
740.2.be.a.251.13	yes	304	4.3	odd	2	inner
740.2.be.a.251.76	yes	304	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41416 + 0.0123313i) q^{2} +(-0.552492 + 0.956944i) q^{3} +(1.99970 + 0.0348769i) q^{4} +(-0.258819 - 0.965926i) q^{5} +(-0.793112 + 1.34646i) q^{6} +(-0.911932 - 0.526504i) q^{7} +(2.82746 + 0.0739805i) q^{8} +(0.889506 + 1.54067i) q^{9} +(-0.354100 - 1.36917i) q^{10} -1.69195 q^{11} +(-1.13819 + 1.89433i) q^{12} +(1.28004 + 4.77717i) q^{13} +(-1.28313 - 0.755807i) q^{14} +(1.06733 + 0.285991i) q^{15} +(3.99757 + 0.139487i) q^{16} +(4.61990 + 1.23790i) q^{17} +(1.23890 + 2.18972i) q^{18} +(6.49847 - 1.74126i) q^{19} +(-0.483871 - 1.94058i) q^{20} +(1.00767 - 0.581779i) q^{21} +(-2.39269 - 0.0208640i) q^{22} +(-1.00871 - 1.00871i) q^{23} +(-1.63294 + 2.66485i) q^{24} +(-0.866025 + 0.500000i) q^{25} +(1.75127 + 6.77147i) q^{26} -5.28073 q^{27} +(-1.80522 - 1.08465i) q^{28} +(4.46668 + 4.46668i) q^{29} +(1.50585 + 0.417598i) q^{30} +(0.275132 - 0.275132i) q^{31} +(5.65148 + 0.246552i) q^{32} +(0.934788 - 1.61910i) q^{33} +(6.51802 + 1.80756i) q^{34} +(-0.272539 + 1.01713i) q^{35} +(1.72501 + 3.11189i) q^{36} +(-2.53258 - 5.53046i) q^{37} +(9.21135 - 2.38229i) q^{38} +(-5.27870 - 1.41442i) q^{39} +(-0.660341 - 2.75026i) q^{40} +(-5.53989 - 3.19846i) q^{41} +(1.43218 - 0.810302i) q^{42} +(-7.72604 - 7.72604i) q^{43} +(-3.38339 - 0.0590100i) q^{44} +(1.25795 - 1.25795i) q^{45} +(-1.41403 - 1.43891i) q^{46} +3.49426i q^{47} +(-2.34210 + 3.74838i) q^{48} +(-2.94559 - 5.10190i) q^{49} +(-1.23086 + 0.696401i) q^{50} +(-3.73706 + 3.73706i) q^{51} +(2.39308 + 9.59754i) q^{52} +(5.09943 + 8.83247i) q^{53} +(-7.46779 - 0.0651184i) q^{54} +(0.437909 + 1.63430i) q^{55} +(-2.53950 - 1.55614i) q^{56} +(-1.92406 + 7.18071i) q^{57} +(6.26152 + 6.37168i) q^{58} +(1.22270 - 4.56316i) q^{59} +(2.12437 + 0.609120i) q^{60} +(-1.89645 + 0.508152i) q^{61} +(0.392473 - 0.385687i) q^{62} -1.87331i q^{63} +(7.98905 + 0.418353i) q^{64} +(4.28310 - 2.47285i) q^{65} +(1.34191 - 2.27814i) q^{66} +(-7.60563 + 13.1733i) q^{67} +(9.19523 + 2.63655i) q^{68} +(1.52258 - 0.407973i) q^{69} +(-0.397956 + 1.43502i) q^{70} +(-1.55425 - 0.897347i) q^{71} +(2.40106 + 4.42198i) q^{72} -16.0678i q^{73} +(-3.51328 - 7.85219i) q^{74} -1.10498i q^{75} +(13.0557 - 3.25535i) q^{76} +(1.54294 + 0.890819i) q^{77} +(-7.44748 - 2.06531i) q^{78} +(-2.99879 + 0.803523i) q^{79} +(-0.899913 - 3.89746i) q^{80} +(0.249043 - 0.431354i) q^{81} +(-7.79485 - 4.59144i) q^{82} +(-11.4458 + 6.60821i) q^{83} +(2.03532 - 1.12824i) q^{84} -4.78288i q^{85} +(-10.8306 - 11.0211i) q^{86} +(-6.74217 + 1.80656i) q^{87} +(-4.78392 - 0.125171i) q^{88} +(1.14117 - 4.25890i) q^{89} +(1.79446 - 1.76343i) q^{90} +(1.34789 - 5.03040i) q^{91} +(-1.98192 - 2.05228i) q^{92} +(0.111278 + 0.415293i) q^{93} +(-0.0430888 + 4.94144i) q^{94} +(-3.36386 - 5.82637i) q^{95} +(-3.35833 + 5.27193i) q^{96} +(-5.15561 + 5.15561i) q^{97} +(-4.10262 - 7.25123i) q^{98} +(-1.50500 - 2.60673i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 304 q + 4 q^{2} - 12 q^{4} - 8 q^{8} - 152 q^{9} + 16 q^{13} - 24 q^{14} + 20 q^{16} - 60 q^{18} - 16 q^{22} - 24 q^{24} - 32 q^{29} - 56 q^{32} - 32 q^{37} + 40 q^{38} + 20 q^{42} + 12 q^{44} - 8 q^{46}+ \cdots - 36 q^{98}+O(q^{100}) \) 304 * q + 4 * q^2 - 12 * q^4 - 8 * q^8 - 152 * q^9 + 16 * q^13 - 24 * q^14 + 20 * q^16 - 60 * q^18 - 16 * q^22 - 24 * q^24 - 32 * q^29 - 56 * q^32 - 32 * q^37 + 40 * q^38 + 20 * q^42 + 12 * q^44 - 8 * q^46 + 104 * q^49 + 4 * q^50 - 40 * q^52 + 40 * q^54 + 4 * q^56 - 48 * q^57 - 12 * q^58 - 28 * q^60 - 16 * q^61 - 60 * q^62 + 24 * q^65 - 52 * q^66 - 200 * q^68 - 196 * q^72 + 20 * q^74 - 40 * q^76 + 96 * q^77 - 48 * q^78 - 152 * q^81 + 32 * q^82 - 112 * q^84 + 12 * q^88 - 8 * q^89 + 140 * q^92 - 16 * q^93 - 28 * q^94 - 132 * q^96 + 48 * q^97 - 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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