LMFDB - Embedded newform 456.2.bk.a.61.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [456,2,Mod(61,456)] 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("456.61"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(456, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.bk (of order $18$, degree $6$, 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:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			61.18
Character	$\chi$	$=$	456.61
Dual form			456.2.bk.a.157.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.276939 + 1.38683i) q^{2} +(-0.984808 + 0.173648i) q^{3} +(-1.84661 - 0.768136i) q^{4} +(1.58746 + 1.89186i) q^{5} +(0.0319107 - 1.41385i) q^{6} +(1.26268 - 2.18703i) q^{7} +(1.57667 - 2.34821i) q^{8} +(0.939693 - 0.342020i) q^{9} +(-3.06333 + 1.67761i) q^{10} +(3.77345 - 2.17860i) q^{11} +(1.95194 + 0.435806i) q^{12} +(0.844562 + 0.148919i) q^{13} +(2.68336 + 2.35680i) q^{14} +(-1.89186 - 1.58746i) q^{15} +(2.81993 + 2.83690i) q^{16} +(3.07013 + 1.11744i) q^{17} +(0.214087 + 1.39792i) q^{18} +(-3.27373 + 2.87797i) q^{19} +(-1.47821 - 4.71292i) q^{20} +(-0.863726 + 2.37307i) q^{21} +(1.97634 + 5.83648i) q^{22} +(0.172021 + 0.144343i) q^{23} +(-1.14496 + 2.58632i) q^{24} +(-0.190869 + 1.08247i) q^{25} +(-0.440418 + 1.13002i) q^{26} +(-0.866025 + 0.500000i) q^{27} +(-4.01162 + 3.06868i) q^{28} +(-0.165642 - 0.455099i) q^{29} +(2.72547 - 2.18407i) q^{30} +(1.69007 - 2.92729i) q^{31} +(-4.71525 + 3.12513i) q^{32} +(-3.33781 + 2.80075i) q^{33} +(-2.39994 + 3.94829i) q^{34} +(6.14202 - 1.08300i) q^{35} +(-1.99796 - 0.0902342i) q^{36} +10.9689i q^{37} +(-3.08464 - 5.33714i) q^{38} -0.857590 q^{39} +(6.94540 - 0.744843i) q^{40} +(0.556297 + 3.15492i) q^{41} +(-3.05185 - 1.85504i) q^{42} +(1.59980 + 1.90657i) q^{43} +(-8.64154 + 1.12450i) q^{44} +(2.13878 + 1.23483i) q^{45} +(-0.247819 + 0.198590i) q^{46} +(6.19504 - 2.25481i) q^{47} +(-3.26971 - 2.30412i) q^{48} +(0.311265 + 0.539127i) q^{49} +(-1.44835 - 0.564483i) q^{50} +(-3.21753 - 0.567337i) q^{51} +(-1.44519 - 0.923733i) q^{52} +(-3.77694 + 4.50118i) q^{53} +(-0.453580 - 1.33950i) q^{54} +(10.1118 + 3.68040i) q^{55} +(-3.14477 - 6.41328i) q^{56} +(2.72424 - 3.40272i) q^{57} +(0.677018 - 0.103684i) q^{58} +(3.40158 - 9.34575i) q^{59} +(2.27414 + 4.38463i) q^{60} +(-3.11777 + 3.71562i) q^{61} +(3.59162 + 3.15453i) q^{62} +(0.438525 - 2.48700i) q^{63} +(-3.02819 - 7.40473i) q^{64} +(1.05897 + 1.83420i) q^{65} +(-2.95981 - 5.40462i) q^{66} +(-5.06461 - 13.9149i) q^{67} +(-4.81099 - 4.42175i) q^{68} +(-0.194473 - 0.112279i) q^{69} +(-0.199020 + 8.81788i) q^{70} +(0.316942 - 0.265946i) q^{71} +(0.678454 - 2.74585i) q^{72} +(-1.86147 - 10.5569i) q^{73} +(-15.2120 - 3.03771i) q^{74} -1.09917i q^{75} +(8.25597 - 2.79981i) q^{76} -11.0035i q^{77} +(0.237500 - 1.18933i) q^{78} +(2.08407 + 11.8194i) q^{79} +(-0.890480 + 9.83838i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-4.52940 - 0.102229i) q^{82} +(-5.43961 - 3.14056i) q^{83} +(3.41780 - 3.71867i) q^{84} +(2.75968 + 7.58215i) q^{85} +(-3.08714 + 1.69065i) q^{86} +(0.242153 + 0.419421i) q^{87} +(0.833683 - 12.2958i) q^{88} +(2.20196 - 12.4879i) q^{89} +(-2.30481 + 2.62416i) q^{90} +(1.39210 - 1.65904i) q^{91} +(-0.206781 - 0.398680i) q^{92} +(-1.15608 + 3.17630i) q^{93} +(1.41140 + 9.21593i) q^{94} +(-10.6416 - 1.62478i) q^{95} +(4.10094 - 3.89645i) q^{96} +(2.83738 + 1.03272i) q^{97} +(-0.833881 + 0.282368i) q^{98} +(2.80075 - 3.33781i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48}+ \cdots - 12 q^{98}+O(q^{100}) $ 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$-1$	$1$	$1$

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 $

$2$	−0.276939	+	1.38683i	−0.195825	+	0.980639i
$2$	−0.276939	+	1.38683i	−0.195825	+	0.980639i
$3$	−0.984808	+	0.173648i	−0.568579	+	0.100256i
$3$	−0.984808	+	0.173648i	−0.568579	+	0.100256i
$4$	−1.84661	−	0.768136i	−0.923305	−	0.384068i
$5$	1.58746	+	1.89186i	0.709934	+	0.846066i	0.993612	−	0.112853i	$-0.0359990\pi$
$5$	1.58746	+	1.89186i	0.709934	+	0.846066i	−0.283678	+	0.958920i	$0.591555\pi$
$6$	0.0319107	−	1.41385i	0.0130275	−	0.577203i
$7$	1.26268	−	2.18703i	0.477249	−	0.826620i	−0.522411	−	0.852694i	$-0.674967\pi$
$7$	1.26268	−	2.18703i	0.477249	−	0.826620i	0.999660	+	0.0260741i	$0.00830059\pi$
$8$	1.57667	−	2.34821i	0.557439	−	0.830218i
$9$	0.939693	−	0.342020i	0.313231	−	0.114007i
$10$	−3.06333	+	1.67761i	−0.968709	+	0.530507i
$11$	3.77345	−	2.17860i	1.13774	−	0.656873i	0.191868	−	0.981421i	$-0.438546\pi$
$11$	3.77345	−	2.17860i	1.13774	−	0.656873i	0.945869	+	0.324548i	$0.105212\pi$
$12$	1.95194	+	0.435806i	0.563477	+	0.125806i
$13$	0.844562	+	0.148919i	0.234239	+	0.0413027i	0.289535	−	0.957167i	$-0.406499\pi$
$13$	0.844562	+	0.148919i	0.234239	+	0.0413027i	−0.0552962	+	0.998470i	$0.517610\pi$
$14$	2.68336	+	2.35680i	0.717158	+	0.629882i
$15$	−1.89186	−	1.58746i	−0.488477	−	0.409881i
$16$	2.81993	+	2.83690i	0.704983	+	0.709224i
$17$	3.07013	+	1.11744i	0.744616	+	0.271018i	0.686338	−	0.727282i	$-0.259217\pi$
$17$	3.07013	+	1.11744i	0.744616	+	0.271018i	0.0582776	+	0.998300i	$0.481439\pi$
$18$	0.214087	+	1.39792i	0.0504608	+	0.329492i
$19$	−3.27373	+	2.87797i	−0.751045	+	0.660251i
$19$	−3.27373	+	2.87797i	−0.751045	+	0.660251i
$20$	−1.47821	−	4.71292i	−0.330538	−	1.05384i
$21$	−0.863726	+	2.37307i	−0.188480	+	0.517846i
$22$	1.97634	+	5.83648i	0.421357	+	1.24434i
$23$	0.172021	+	0.144343i	0.0358689	+	0.0300976i	0.660546	−	0.750786i	$-0.270325\pi$
$23$	0.172021	+	0.144343i	0.0358689	+	0.0300976i	−0.624677	+	0.780883i	$0.714769\pi$
$24$	−1.14496	+	2.58632i	−0.233714	+	0.527931i
$25$	−0.190869	+	1.08247i	−0.0381739	+	0.216495i
$26$	−0.440418	+	1.13002i	−0.0863730	+	0.221616i
$27$	−0.866025	+	0.500000i	−0.166667	+	0.0962250i
$28$	−4.01162	+	3.06868i	−0.758125	+	0.579926i
$29$	−0.165642	−	0.455099i	−0.0307590	−	0.0845097i	0.923363	−	0.383929i	$-0.125429\pi$
$29$	−0.165642	−	0.455099i	−0.0307590	−	0.0845097i	−0.954122	+	0.299419i	$0.903207\pi$
$30$	2.72547	−	2.18407i	0.497601	−	0.398754i
$31$	1.69007	−	2.92729i	0.303546	−	0.525757i	−0.673391	−	0.739287i	$-0.735163\pi$
$31$	1.69007	−	2.92729i	0.303546	−	0.525757i	0.976937	+	0.213530i	$0.0684961\pi$
$32$	−4.71525	+	3.12513i	−0.833546	+	0.552450i
$33$	−3.33781	+	2.80075i	−0.581038	+	0.487549i
$34$	−2.39994	+	3.94829i	−0.411586	+	0.677127i
$35$	6.14202	−	1.08300i	1.03819	−	0.183061i
$36$	−1.99796	−	0.0902342i	−0.332994	−	0.0150390i
$37$			10.9689i			1.80327i	0.432499	+	0.901635i	$0.357632\pi$
$37$			10.9689i			1.80327i	−0.432499	+	0.901635i	$0.642368\pi$
$38$	−3.08464	−	5.33714i	−0.500394	−	0.865798i
$39$	−0.857590			−0.137324
$40$	6.94540	−	0.744843i	1.09816	−	0.117770i
$41$	0.556297	+	3.15492i	0.0868790	+	0.492715i	0.996935	+	0.0782306i	$0.0249270\pi$
$41$	0.556297	+	3.15492i	0.0868790	+	0.492715i	−0.910056	+	0.414485i	$0.863962\pi$
$42$	−3.05185	−	1.85504i	−0.470910	−	0.286239i
$43$	1.59980	+	1.90657i	0.243968	+	0.290749i	0.874108	−	0.485732i	$-0.161447\pi$
$43$	1.59980	+	1.90657i	0.243968	+	0.290749i	−0.630140	+	0.776481i	$0.717003\pi$
$44$	−8.64154	+	1.12450i	−1.30276	+	0.169525i
$45$	2.13878	+	1.23483i	0.318830	+	0.184077i
$46$	−0.247819	+	0.198590i	−0.0365389	+	0.0292805i
$47$	6.19504	−	2.25481i	0.903639	−	0.328898i	0.151929	−	0.988391i	$-0.451451\pi$
$47$	6.19504	−	2.25481i	0.903639	−	0.328898i	0.751710	+	0.659494i	$0.229229\pi$
$48$	−3.26971	−	2.30412i	−0.471943	−	0.332571i
$49$	0.311265	+	0.539127i	0.0444665	+	0.0770182i
$50$	−1.44835	−	0.564483i	−0.204828	−	0.0798299i
$51$	−3.21753	−	0.567337i	−0.450544	−	0.0794431i
$52$	−1.44519	−	0.923733i	−0.200411	−	0.128099i
$53$	−3.77694	+	4.50118i	−0.518802	+	0.618284i	−0.960297	−	0.278980i	$-0.910004\pi$
$53$	−3.77694	+	4.50118i	−0.518802	+	0.618284i	0.441495	+	0.897264i	$0.354448\pi$
$54$	−0.453580	−	1.33950i	−0.0617244	−	0.182283i
$55$	10.1118	+	3.68040i	1.36348	+	0.496265i
$56$	−3.14477	−	6.41328i	−0.420238	−	0.857011i
$57$	2.72424	−	3.40272i	0.360834	−	0.450702i
$58$	0.677018	−	0.103684i	0.0888969	−	0.0136143i
$59$	3.40158	−	9.34575i	0.442847	−	1.21671i	−0.494764	−	0.869028i	$-0.664745\pi$
$59$	3.40158	−	9.34575i	0.442847	−	1.21671i	0.937611	−	0.347686i	$-0.113032\pi$
$60$	2.27414	+	4.38463i	0.293591	+	0.566053i
$61$	−3.11777	+	3.71562i	−0.399190	+	0.475736i	−0.927773	−	0.373146i	$-0.878279\pi$
$61$	−3.11777	+	3.71562i	−0.399190	+	0.475736i	0.528583	+	0.848882i	$0.322724\pi$
$62$	3.59162	+	3.15453i	0.456136	+	0.400626i
$63$	0.438525	−	2.48700i	0.0552490	−	0.313332i
$64$	−3.02819	−	7.40473i	−0.378524	−	0.925591i
$65$	1.05897	+	1.83420i	0.131350	+	0.227504i
$66$	−2.95981	−	5.40462i	−0.364327	−	0.665263i
$67$	−5.06461	−	13.9149i	−0.618740	−	1.69997i	−0.710050	−	0.704152i	$-0.751327\pi$
$67$	−5.06461	−	13.9149i	−0.618740	−	1.69997i	0.0913095	−	0.995823i	$-0.470895\pi$
$68$	−4.81099	−	4.42175i	−0.583418	−	0.536215i
$69$	−0.194473	−	0.112279i	−0.0234117	−	0.0135168i
$70$	−0.199020	+	8.81788i	−0.0237874	+	1.05394i
$71$	0.316942	−	0.265946i	0.0376141	−	0.0315620i	−0.623787	−	0.781595i	$-0.714407\pi$
$71$	0.316942	−	0.265946i	0.0376141	−	0.0315620i	0.661401	+	0.750033i	$0.269962\pi$
$72$	0.678454	−	2.74585i	0.0799566	−	0.323602i
$73$	−1.86147	−	10.5569i	−0.217868	−	1.23559i	−0.875859	−	0.482567i	$-0.839704\pi$
$73$	−1.86147	−	10.5569i	−0.217868	−	1.23559i	0.657991	−	0.753026i	$-0.271407\pi$
$74$	−15.2120	−	3.03771i	−1.76836	−	0.353126i
$75$		−	1.09917i		−	0.126922i
$76$	8.25597	−	2.79981i	0.947025	−	0.321161i
$77$		−	11.0035i		−	1.25397i
$78$	0.237500	−	1.18933i	0.0268916	−	0.134666i
$79$	2.08407	+	11.8194i	0.234477	+	1.32978i	0.843713	+	0.536794i	$0.180365\pi$
$79$	2.08407	+	11.8194i	0.234477	+	1.32978i	−0.609236	+	0.792989i	$0.708524\pi$
$80$	−0.890480	+	9.83838i	−0.0995587	+	1.09996i
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$	−4.52940	−	0.102229i	−0.500189	−	0.0112893i
$83$	−5.43961	−	3.14056i	−0.597074	−	0.344721i	0.170815	−	0.985303i	$-0.445360\pi$
$83$	−5.43961	−	3.14056i	−0.597074	−	0.344721i	−0.767890	+	0.640582i	$0.778693\pi$
$84$	3.41780	−	3.71867i	0.372913	−	0.405740i
$85$	2.75968	+	7.58215i	0.299329	+	0.822399i
$86$	−3.08714	+	1.69065i	−0.332895	+	0.182308i
$87$	0.242153	+	0.419421i	0.0259615	+	0.0449667i
$88$	0.833683	−	12.2958i	0.0888709	−	1.31074i
$89$	2.20196	−	12.4879i	0.233408	−	1.32372i	−0.612534	−	0.790444i	$-0.709850\pi$
$89$	2.20196	−	12.4879i	0.233408	−	1.32372i	0.845942	−	0.533276i	$-0.179039\pi$
$90$	−2.30481	+	2.62416i	−0.242948	+	0.276611i
$91$	1.39210	−	1.65904i	0.145932	−	0.173915i
$92$	−0.206781	−	0.398680i	−0.0215584	−	0.0415653i
$93$	−1.15608	+	3.17630i	−0.119880	+	0.329367i
$94$	1.41140	+	9.21593i	0.145574	+	0.950550i
$95$	−10.6416	−	1.62478i	−1.09181	−	0.166699i
$96$	4.10094	−	3.89645i	0.418550	−	0.397679i
$97$	2.83738	+	1.03272i	0.288092	+	0.104857i	0.482024	−	0.876158i	$-0.339902\pi$
$97$	2.83738	+	1.03272i	0.288092	+	0.104857i	−0.193932	+	0.981015i	$0.562124\pi$
$98$	−0.833881	+	0.282368i	−0.0842347	+	0.0285234i
$99$	2.80075	−	3.33781i	0.281486	−	0.335462i
$100$	1.18395	−	1.85229i	0.118395	−	0.185229i
$101$	8.82088	+	1.55536i	0.877710	+	0.154764i	0.594308	−	0.804237i	$-0.297426\pi$
$101$	8.82088	+	1.55536i	0.877710	+	0.154764i	0.283402	+	0.959001i	$0.408537\pi$
$102$	1.67786	−	4.30506i	0.166133	−	0.426264i
$103$	7.64073	+	13.2341i	0.752863	+	1.30400i	0.946429	+	0.322911i	$0.104661\pi$
$103$	7.64073	+	13.2341i	0.752863	+	1.30400i	−0.193566	+	0.981087i	$0.562005\pi$
$104$	1.68129	−	1.74841i	0.164864	−	0.171446i
$105$	−5.86065	+	2.13310i	−0.571940	+	0.208169i
$106$	−5.19640	−	6.48453i	−0.504719	−	0.629833i
$107$	5.85953	+	3.38300i	0.566462	+	0.327047i	0.755735	−	0.654878i	$-0.227280\pi$
$107$	5.85953	+	3.38300i	0.566462	+	0.327047i	−0.189273	+	0.981924i	$0.560613\pi$
$108$	1.98328	−	0.258079i	0.190841	−	0.0248337i
$109$	−7.59210	−	9.04791i	−0.727191	−	0.866633i	0.268117	−	0.963386i	$-0.413599\pi$
$109$	−7.59210	−	9.04791i	−0.727191	−	0.866633i	−0.995308	+	0.0967536i	$0.969154\pi$
$110$	−7.90445	+	13.0041i	−0.753660	+	1.23990i
$111$	−1.90472	−	10.8022i	−0.180788	−	1.02530i
$112$	9.76506	−	2.58518i	0.922711	−	0.244277i
$113$	−13.3230			−1.25332			−0.626662	−	0.779291i	$-0.715579\pi$
$113$	−13.3230			−1.25332			−0.626662	+	0.779291i	$0.715579\pi$
$114$	3.96456	+	4.72041i	0.371315	+	0.442107i
$115$			0.554579i			0.0517147i
$116$	−0.0437010	+	0.967625i	−0.00405753	+	0.0898417i
$117$	0.844562	−	0.148919i	0.0780797	−	0.0137676i
$118$	12.0190	+	7.30562i	1.10644	+	0.672537i
$119$	6.32047	−	5.30350i	0.579396	−	0.486171i
$120$	−6.71054	+	1.93958i	−0.612586	+	0.177059i
$121$	3.99260	−	6.91539i	0.362964	−	0.628672i
$122$	−4.28951	−	5.35283i	−0.388354	−	0.484622i
$123$	−1.09569	−	3.01039i	−0.0987952	−	0.271437i
$124$	−5.36946	+	4.10736i	−0.482192	+	0.368852i
$125$	8.34301	−	4.81684i	0.746222	−	0.430831i
$126$	3.32761	+	1.29691i	0.296447	+	0.115538i
$127$	−0.432977	+	2.45553i	−0.0384205	+	0.217893i	−0.997973	−	0.0636356i	$-0.979730\pi$
$127$	−0.432977	+	2.45553i	−0.0384205	+	0.217893i	0.959553	+	0.281529i	$0.0908416\pi$
$128$	11.1077	−	2.14894i	0.981795	−	0.189941i
$129$	−1.90657	−	1.59980i	−0.167864	−	0.140855i
$130$	−2.83700	+	0.960659i	−0.248821	+	0.0842554i
$131$	3.17506	−	8.72340i	0.277406	−	0.762167i	−0.720248	−	0.693716i	$-0.755972\pi$
$131$	3.17506	−	8.72340i	0.277406	−	0.762167i	0.997654	−	0.0684509i	$-0.0218057\pi$
$132$	8.31499	−	2.60801i	0.723727	−	0.226998i
$133$	2.16052	+	10.7937i	0.187341	+	0.935933i
$134$	20.7002	−	3.17018i	1.78823	−	0.273862i
$135$	−2.32071	−	0.844670i	−0.199735	−	0.0726976i
$136$	7.46457	−	5.44748i	0.640082	−	0.467118i
$137$	12.9609	+	10.8755i	1.10733	+	0.929156i	0.997896	−	0.0648385i	$-0.0206532\pi$
$137$	12.9609	+	10.8755i	1.10733	+	0.929156i	0.109429	+	0.993995i	$0.465098\pi$
$138$	0.209569	−	0.238606i	0.0178397	−	0.0203115i
$139$	−17.3984	−	3.06781i	−1.47571	−	0.260208i	−0.622850	−	0.782342i	$-0.714025\pi$
$139$	−17.3984	−	3.06781i	−1.47571	−	0.260208i	−0.852864	+	0.522134i	$0.825136\pi$
$140$	−12.1738	−	2.71802i	−1.02887	−	0.229715i
$141$	−5.70938	+	3.29631i	−0.480816	+	0.277600i
$142$	0.281049	+	0.513196i	0.0235851	+	0.0430664i
$143$	3.51134	−	1.27802i	0.293633	−	0.106874i
$144$	3.62015	+	1.70134i	0.301679	+	0.141778i
$145$	0.598033	−	1.03582i	0.0496639	−	0.0860204i
$146$	15.1562	+	0.342076i	1.25433	+	0.0283104i
$147$	−0.400155	−	0.476886i	−0.0330042	−	0.0393329i
$148$	8.42558	−	20.2552i	0.692578	−	1.66497i
$149$	−1.59112	+	0.280558i	−0.130350	+	0.0229842i	−0.238442	−	0.971157i	$-0.576637\pi$
$149$	−1.59112	+	0.280558i	−0.130350	+	0.0229842i	0.108092	+	0.994141i	$0.465526\pi$
$150$	1.52437	+	0.304404i	0.124464	+	0.0248545i
$151$	−18.7457			−1.52550			−0.762751	−	0.646692i	$-0.776152\pi$
$151$	−18.7457			−1.52550			−0.762751	+	0.646692i	$0.776152\pi$
$152$	1.59647	+	12.2250i	0.129491	+	0.991581i
$153$	3.26716			0.264135
$154$	15.2600	+	3.04731i	1.22969	+	0.245559i
$155$	8.22095	−	1.44958i	0.660323	−	0.116433i
$156$	1.58363	+	0.658746i	0.126792	+	0.0527419i
$157$	4.31522	+	5.14268i	0.344392	+	0.410430i	0.910241	−	0.414078i	$-0.135896\pi$
$157$	4.31522	+	5.14268i	0.344392	+	0.410430i	−0.565849	+	0.824509i	$0.691452\pi$
$158$	−16.9686	−	0.382983i	−1.34995	−	0.0304685i
$159$	2.93793	−	5.08865i	0.232993	−	0.403556i
$160$	−13.3976	−	3.95958i	−1.05917	−	0.313032i
$161$	0.532890	−	0.193956i	0.0419976	−	0.0152859i
$162$	0.679291	+	1.24039i	0.0533702	+	0.0974541i
$163$	−17.0031	+	9.81674i	−1.33179	+	0.768907i	−0.985573	−	0.169250i	$-0.945866\pi$
$163$	−17.0031	+	9.81674i	−1.33179	+	0.768907i	−0.346212	+	0.938156i	$0.612532\pi$
$164$	1.39614	−	6.25321i	0.109020	−	0.488294i
$165$	−10.5973	−	1.86859i	−0.824997	−	0.145469i
$166$	5.86187	−	6.67408i	0.454969	−	0.518009i
$167$	−0.165909	−	0.139214i	−0.0128384	−	0.0107727i	0.636346	−	0.771404i	$-0.280445\pi$
$167$	−0.165909	−	0.139214i	−0.0128384	−	0.0107727i	−0.649184	+	0.760631i	$0.724890\pi$
$168$	4.21065	+	5.76977i	0.324859	+	0.445147i
$169$	−11.5249	−	4.19472i	−0.886531	−	0.322671i
$170$	−11.2794	+	1.72742i	−0.865093	+	0.132487i
$171$	−2.09198	+	3.82409i	−0.159977	+	0.292435i
$172$	−1.48970	−	4.74956i	−0.113589	−	0.362150i
$173$	−5.27824	+	14.5018i	−0.401297	+	1.10255i	0.560348	+	0.828257i	$0.310667\pi$
$173$	−5.27824	+	14.5018i	−0.401297	+	1.10255i	−0.961645	+	0.274297i	$0.911555\pi$
$174$	−0.648728	+	0.219671i	−0.0491800	+	0.0166532i
$175$	2.12640	+	1.78426i	0.160740	+	0.134877i
$176$	16.8213	+	4.56136i	1.26796	+	0.343826i
$177$	−1.72703	+	9.79445i	−0.129811	+	0.736196i
$178$	16.7089	+	6.51215i	1.25238	+	0.488107i
$179$	−16.4466	+	9.49547i	−1.22928	+	0.709724i	−0.966879	−	0.255235i	$-0.917847\pi$
$179$	−16.4466	+	9.49547i	−1.22928	+	0.709724i	−0.262400	+	0.964959i	$0.584514\pi$
$180$	−3.00098	−	3.92311i	−0.223680	−	0.292412i
$181$	−7.75061	−	21.2946i	−0.576098	−	1.58282i	−0.794700	−	0.607003i	$-0.792372\pi$
$181$	−7.75061	−	21.2946i	−0.576098	−	1.58282i	0.218601	−	0.975814i	$-0.429851\pi$
$182$	1.91529	+	2.39007i	0.141971	+	0.177164i
$183$	2.42520	−	4.20056i	0.179276	−	0.310515i
$184$	0.610169	−	0.176360i	0.0449822	−	0.0130014i
$185$	−20.7516	+	17.4126i	−1.52569	+	1.28020i
$186$	−4.08483	−	2.48293i	−0.299514	−	0.182057i
$187$	14.0194	−	2.47200i	1.02520	−	0.180771i
$188$	−13.1718	−	0.594880i	−0.960654	−	0.0433861i
$189$			2.52537i			0.183693i
$190$	5.20039	−	14.3082i	0.377276	−	1.03803i
$191$	−16.2374			−1.17490			−0.587450	−	0.809261i	$-0.699868\pi$
$191$	−16.2374			−1.17490			−0.587450	+	0.809261i	$0.699868\pi$
$192$	4.26801	+	6.76640i	0.308017	+	0.488323i
$193$	−1.50794	−	8.55195i	−0.108544	−	0.615583i	−0.989745	−	0.142842i	$-0.954376\pi$
$193$	−1.50794	−	8.55195i	−0.108544	−	0.615583i	0.881202	−	0.472741i	$-0.156735\pi$
$194$	−2.21799	+	3.64897i	−0.159243	+	0.261981i
$195$	−1.36139	−	1.62244i	−0.0974912	−	0.116186i
$196$	−0.160662	−	1.23465i	−0.0114759	−	0.0881894i
$197$	13.5219	+	7.80688i	0.963396	+	0.556217i	0.897217	−	0.441591i	$-0.145586\pi$
$197$	13.5219	+	7.80688i	0.963396	+	0.556217i	0.0661797	+	0.997808i	$0.478919\pi$
$198$	3.85335	+	4.80855i	0.273845	+	0.341729i
$199$	−19.6035	+	7.13508i	−1.38965	+	0.505792i	−0.925090	−	0.379748i	$-0.876011\pi$
$199$	−19.6035	+	7.13508i	−1.38965	+	0.505792i	−0.464563	+	0.885540i	$0.653788\pi$
$200$	2.24094	+	2.15491i	0.158458	+	0.152375i
$201$	7.40396	+	12.8240i	0.522235	+	0.904537i
$202$	−4.59987	+	11.8023i	−0.323646	+	0.830410i
$203$	−1.20447	−	0.212380i	−0.0845371	−	0.0149062i
$204$	5.50573	+	3.51915i	0.385478	+	0.246390i
$205$	−5.08557	+	6.06074i	−0.355191	+	0.423301i
$206$	−20.4695	+	6.93137i	−1.42618	+	0.482931i
$207$	0.211015	+	0.0768032i	0.0146666	+	0.00533819i
$208$	1.95914	+	2.81587i	0.135842	+	0.195246i
$209$	−6.08330	+	17.9920i	−0.420791	+	1.24453i
$210$	−1.33521	−	8.71847i	−0.0921384	−	0.601632i
$211$	5.71339	−	15.6974i	0.393326	−	1.08065i	−0.572147	−	0.820151i	$-0.693889\pi$
$211$	5.71339	−	15.6974i	0.393326	−	1.08065i	0.965473	−	0.260503i	$-0.0838885\pi$
$212$	10.4320	−	5.41072i	0.716476	−	0.371609i
$213$	−0.265946	+	0.316942i	−0.0182223	+	0.0217165i
$214$	−6.31438	+	7.18930i	−0.431642	+	0.491450i
$215$	−1.06734	+	6.05321i	−0.0727923	+	0.412825i
$216$	−0.191334	+	2.82195i	−0.0130187	+	0.192009i
$217$	−4.26805	−	7.39248i	−0.289734	−	0.501834i
$218$	14.6505	−	8.02325i	0.992256	−	0.543403i
$219$	3.66638	+	10.0733i	0.247751	+	0.680690i
$220$	−15.8455	−	14.5635i	−1.06830	−	0.981871i
$221$	2.42651	+	1.40094i	0.163224	+	0.0942377i
$222$	15.5084	+	0.350024i	1.04085	+	0.0234921i
$223$	−15.6097	+	13.0981i	−1.04531	+	0.877116i	−0.992592	−	0.121494i	$-0.961231\pi$
$223$	−15.6097	+	13.0981i	−1.04531	+	0.877116i	−0.0527136	+	0.998610i	$0.516787\pi$
$224$	0.880890	+	14.2584i	0.0588569	+	0.952682i
$225$	0.190869	+	1.08247i	0.0127246	+	0.0721649i
$226$	3.68966	−	18.4768i	0.245433	−	1.22906i
$227$		−	0.316720i		−	0.0210214i	−0.999945	−	0.0105107i	$-0.996654\pi$
$227$		−	0.316720i		−	0.0210214i	0.999945	−	0.0105107i	$-0.00334573\pi$
$228$	−7.64436	+	4.19091i	−0.506260	+	0.277550i
$229$		−	15.3602i		−	1.01503i	−0.861643	−	0.507516i	$-0.830564\pi$
$229$		−	15.3602i		−	1.01503i	0.861643	−	0.507516i	$-0.169436\pi$
$230$	−0.769108	−	0.153584i	−0.0507135	−	0.0101271i
$231$	1.91074	+	10.8364i	0.125718	+	0.712980i
$232$	−1.32983	−	0.328579i	−0.0873077	−	0.0215723i
$233$	10.6091	−	8.90210i	0.695026	−	0.583196i	−0.225328	−	0.974283i	$-0.572345\pi$
$233$	10.6091	−	8.90210i	0.695026	−	0.583196i	0.920354	+	0.391087i	$0.127901\pi$
$234$	−0.0273663	+	1.21251i	−0.00178899	+	0.0792641i
$235$	14.1002	+	8.14074i	0.919794	+	0.531043i
$236$	−13.4602	+	14.6451i	−0.876184	+	0.953314i
$237$	−4.10482	−	11.2779i	−0.266637	−	0.732579i
$238$	5.60468	+	10.2342i	0.363298	+	0.663383i
$239$	−10.3226	−	17.8793i	−0.667714	−	1.15651i	−0.978542	−	0.206048i	$-0.933940\pi$
$239$	−10.3226	−	17.8793i	−0.667714	−	1.15651i	0.310828	−	0.950466i	$-0.399394\pi$
$240$	−0.831466	−	9.84355i	−0.0536709	−	0.635398i
$241$	2.84398	−	16.1290i	0.183197	−	1.03896i	−0.745054	−	0.667004i	$-0.767576\pi$
$241$	2.84398	−	16.1290i	0.183197	−	1.03896i	0.928251	−	0.371956i	$-0.121313\pi$
$242$	8.48478	+	7.45221i	0.545422	+	0.479046i
$243$	−0.642788	+	0.766044i	−0.0412348	+	0.0491418i
$244$	8.61141	−	4.46642i	0.551289	−	0.285933i
$245$	−0.525833	+	1.44471i	−0.0335942	+	0.0922994i
$246$	4.47834	−	0.685847i	0.285529	−	0.0437280i
$247$	−3.19345	+	1.94310i	−0.203194	+	0.123637i
$248$	−4.20920	−	8.58403i	−0.267285	−	0.545087i
$249$	5.90232	+	2.14827i	0.374044	+	0.136141i
$250$	4.36965	+	12.9043i	0.276361	+	0.816142i
$251$	15.7380	−	18.7558i	0.993374	−	1.18386i	0.0104308	−	0.999946i	$-0.496680\pi$
$251$	15.7380	−	18.7558i	0.993374	−	1.18386i	0.982943	−	0.183911i	$-0.0588759\pi$
$252$	−2.72014	+	4.25567i	−0.171353	+	0.268082i
$253$	0.963578	+	0.169905i	0.0605796	+	0.0106818i
$254$	−3.28551	−	1.28050i	−0.206151	−	0.0803457i
$255$	−4.03438	−	6.98775i	−0.252642	−	0.437590i
$256$	−0.0959488	+	15.9997i	−0.00599680	+	0.999982i
$257$	−6.18309	+	2.25046i	−0.385691	+	0.140380i	−0.527586	−	0.849502i	$-0.676903\pi$
$257$	−6.18309	+	2.25046i	−0.385691	+	0.140380i	0.141895	+	0.989882i	$0.454680\pi$
$258$	2.74666	−	2.20105i	0.171000	−	0.137031i
$259$	23.9892	+	13.8502i	1.49062	+	0.860609i
$260$	−0.546599	−	4.20048i	−0.0338986	−	0.260503i
$261$	−0.311306	−	0.371000i	−0.0192693	−	0.0229643i
$262$	11.2186	+	6.81913i	0.693088	+	0.421287i
$263$	4.55836	+	25.8517i	0.281080	+	1.59409i	0.718959	+	0.695053i	$0.244619\pi$
$263$	4.55836	+	25.8517i	0.281080	+	1.59409i	−0.437878	+	0.899034i	$0.644270\pi$
$264$	1.31413	+	12.2538i	0.0808788	+	0.754167i
$265$	−14.5113			−0.891425
$266$	−15.5674	+	0.00708493i	−0.954498	+	0.000434405i
$267$			12.6806i			0.776040i
$268$	−1.33618	+	29.5857i	−0.0816202	+	1.80723i
$269$	8.98328	−	1.58399i	0.547720	−	0.0965778i	0.107061	−	0.994252i	$-0.465856\pi$
$269$	8.98328	−	1.58399i	0.547720	−	0.0965778i	0.440659	+	0.897675i	$0.354745\pi$
$270$	1.81411	−	2.98452i	0.110403	−	0.181632i
$271$	0.754367	−	0.632989i	0.0458245	−	0.0384514i	−0.619588	−	0.784927i	$-0.712700\pi$
$271$	0.754367	−	0.632989i	0.0458245	−	0.0384514i	0.665412	+	0.746476i	$0.268256\pi$
$272$	5.48751	+	11.8607i	0.332729	+	0.719163i
$273$	−1.08286	+	1.87558i	−0.0655379	+	0.113515i
$274$	−18.6719	+	14.9628i	−1.12801	+	0.903934i
$275$	1.63804	+	4.50048i	0.0987777	+	0.271389i
$276$	0.272869	+	0.356716i	0.0164248	+	0.0214718i
$277$	12.0878	−	6.97888i	0.726284	−	0.419320i	−0.0907769	−	0.995871i	$-0.528935\pi$
$277$	12.0878	−	6.97888i	0.726284	−	0.419320i	0.817061	+	0.576551i	$0.195602\pi$
$278$	9.07283	−	23.2791i	0.544152	−	1.39619i
$279$	0.586956	−	3.32879i	0.0351401	−	0.199290i
$280$	7.14084	−	16.1303i	0.426747	−	0.963970i
$281$	24.6877	+	20.7154i	1.47274	+	1.23578i	0.913541	+	0.406746i	$0.133337\pi$
$281$	24.6877	+	20.7154i	1.47274	+	1.23578i	0.559202	+	0.829032i	$0.311108\pi$
$282$	−2.99028	−	8.83083i	−0.178069	−	0.525868i
$283$	−1.69472	+	4.65620i	−0.100740	+	0.276782i	−0.979816	−	0.199900i	$-0.935938\pi$
$283$	−1.69472	+	4.65620i	−0.100740	+	0.276782i	0.879076	+	0.476682i	$0.158161\pi$
$284$	−0.789550	+	0.247643i	−0.0468512	+	0.0146949i
$285$	10.7621	−	0.247802i	0.637492	−	0.0146785i
$286$	0.799978	+	5.22358i	0.0473037	+	0.308877i
$287$	7.60233	+	2.76702i	0.448751	+	0.163332i
$288$	−3.36203	+	4.54937i	−0.198109	+	0.268074i
$289$	−4.84572	−	4.06604i	−0.285042	−	0.239179i
$290$	1.27089	+	1.11623i	0.0746295	+	0.0655474i
$291$	−2.97360	−	0.524326i	−0.174316	−	0.0307365i
$292$	−4.67174	+	20.9244i	−0.273393	+	1.22451i
$293$	3.75889	−	2.17020i	0.219597	−	0.126784i	−0.386167	−	0.922429i	$-0.626201\pi$
$293$	3.75889	−	2.17020i	0.219597	−	0.126784i	0.605764	+	0.795645i	$0.292868\pi$
$294$	0.772180	−	0.422880i	0.0450344	−	0.0246628i
$295$	23.0807	−	8.40070i	1.34381	−	0.489108i
$296$	25.7572	+	17.2943i	1.49711	+	1.00521i
$297$	−2.17860	+	3.77345i	−0.126415	+	0.218958i
$298$	0.0515572	−	2.28432i	0.00298663	−	0.132327i
$299$	0.123787	+	0.147524i	0.00715879	+	0.00853151i
$300$	−0.844314	+	2.02974i	−0.0487465	+	0.117187i
$301$	6.18977	−	1.09142i	0.356772	−	0.0629086i
$302$	5.19141	−	25.9971i	0.298732	−	1.49597i
$303$	−8.95695			−0.514564
$304$	−17.3962	−	1.17155i	−0.997740	−	0.0671929i
$305$	−11.9788			−0.685903
$306$	−0.904805	+	4.53101i	−0.0517243	+	0.259021i
$307$	−10.0064	+	1.76440i	−0.571096	+	0.100700i	−0.451736	−	0.892151i	$-0.649195\pi$
$307$	−10.0064	+	1.76440i	−0.571096	+	0.100700i	−0.119360	+	0.992851i	$0.538084\pi$
$308$	−8.45220	+	20.3192i	−0.481609	+	1.15779i
$309$	−9.82273	−	11.7063i	−0.558796	−	0.665947i
$310$	−0.266384	+	11.8025i	−0.0151296	+	0.670339i
$311$	4.45359	−	7.71385i	0.252540	−	0.437412i	−0.711684	−	0.702499i	$-0.752067\pi$
$311$	4.45359	−	7.71385i	0.252540	−	0.437412i	0.964224	+	0.265087i	$0.0854007\pi$
$312$	−1.35214	+	2.01380i	−0.0765499	+	0.114009i
$313$	−22.0727	+	8.03380i	−1.24762	+	0.454097i	−0.879598	−	0.475719i	$-0.842188\pi$
$313$	−22.0727	+	8.03380i	−1.24762	+	0.454097i	−0.368025	+	0.929816i	$0.619966\pi$
$314$	−8.32708	+	4.56028i	−0.469924	+	0.257351i
$315$	5.40120	−	3.11838i	0.304323	−	0.175701i
$316$	5.23042	−	23.4266i	0.294234	−	1.31785i
$317$	−30.7475	−	5.42161i	−1.72695	−	0.304508i	−0.779974	−	0.625812i	$-0.784768\pi$
$317$	−30.7475	−	5.42161i	−1.72695	−	0.304508i	−0.946976	+	0.321304i	$0.895879\pi$
$318$	6.24348	+	5.48367i	0.350117	+	0.307509i
$319$	−1.61652	−	1.35642i	−0.0905078	−	0.0759450i
$320$	9.20159	−	17.4836i	0.514384	−	0.977365i
$321$	−6.35796	−	2.31411i	−0.354867	−	0.129161i
$322$	0.121407	+	0.792743i	0.00676573	+	0.0441779i
$323$	−13.2667	+	5.17755i	−0.738180	+	0.288087i
$324$	−1.90833	+	0.598551i	−0.106019	+	0.0332528i
$325$	−0.322402	+	0.885791i	−0.0178836	+	0.0491349i
$326$	−8.90536	−	26.2991i	−0.493222	−	1.45657i
$327$	9.04791	+	7.59210i	0.500351	+	0.419844i
$328$	8.28551	+	3.66797i	0.457491	+	0.202530i
$329$	2.89103	−	16.3958i	0.159388	−	0.903932i
$330$	5.52622	−	14.1792i	0.304208	−	0.780538i
$331$	−15.9515	+	9.20963i	−0.876776	+	0.506207i	−0.869594	−	0.493767i	$-0.835619\pi$
$331$	−15.9515	+	9.20963i	−0.876776	+	0.506207i	−0.00718193	+	0.999974i	$0.502286\pi$
$332$	7.63245	+	9.97774i	0.418885	+	0.547600i
$333$	3.75157	+	10.3074i	0.205585	+	0.564840i
$334$	0.239013	−	0.191534i	0.0130782	−	0.0104803i
$335$	18.2852	−	31.6709i	0.999026	−	1.73036i
$336$	−9.16779	+	4.24159i	−0.500144	+	0.231398i
$337$	12.8598	−	10.7907i	0.700519	−	0.587805i	−0.221402	−	0.975183i	$-0.571063\pi$
$337$	12.8598	−	10.7907i	0.700519	−	0.587805i	0.921921	+	0.387377i	$0.126619\pi$
$338$	9.00907	−	14.8214i	0.490029	−	0.806179i
$339$	13.1206	−	2.31352i	0.712613	−	0.125653i
$340$	0.728078	−	16.1211i	0.0394856	−	0.874288i
$341$		−	14.7280i		−	0.797564i
$342$	−4.72402	−	3.96026i	−0.255446	−	0.214146i
$343$	19.2497			1.03938
$344$	6.99940	−	0.750633i	0.377382	−	0.0404714i
$345$	−0.0963016	−	0.546153i	−0.00518470	−	0.0294039i
$346$	−18.6499	−	11.3362i	−1.00262	−	0.609435i
$347$	−7.58761	−	9.04256i	−0.407324	−	0.485430i	0.522915	−	0.852385i	$-0.324845\pi$
$347$	−7.58761	−	9.04256i	−0.407324	−	0.485430i	−0.930239	+	0.366955i	$0.880400\pi$
$348$	−0.124989	−	0.960513i	−0.00670013	−	0.0514889i
$349$	−5.61304	−	3.24069i	−0.300459	−	0.173470i	0.342190	−	0.939631i	$-0.388831\pi$
$349$	−5.61304	−	3.24069i	−0.300459	−	0.173470i	−0.642649	+	0.766161i	$0.722165\pi$
$350$	−3.06335	+	2.45482i	−0.163743	+	0.131216i
$351$	−0.805871	+	0.293313i	−0.0430142	+	0.0156559i
$352$	−10.9843	+	22.0652i	−0.585467	+	1.17608i
$353$	7.96941	+	13.8034i	0.424169	+	0.734682i	0.996342	−	0.0854507i	$-0.0272330\pi$
$353$	7.96941	+	13.8034i	0.424169	+	0.734682i	−0.572174	+	0.820132i	$0.693900\pi$
$354$	−13.1050	−	5.10756i	−0.696522	−	0.271464i
$355$	1.00627	+	0.177432i	0.0534070	+	0.00941710i
$356$	−13.6586	+	21.3690i	−0.723905	+	1.13255i
$357$	−5.30350	+	6.32047i	−0.280691	+	0.334515i
$358$	−8.61391	−	25.4384i	−0.455259	−	1.34446i
$359$	−10.7502	−	3.91276i	−0.567375	−	0.206508i	0.0423743	−	0.999102i	$-0.486508\pi$
$359$	−10.7502	−	3.91276i	−0.567375	−	0.206508i	−0.609750	+	0.792594i	$0.708730\pi$
$360$	6.27179	−	3.07539i	0.330552	−	0.162087i
$361$	2.43460	−	18.8434i	0.128137	−	0.991756i
$362$	31.6785	−	4.85149i	1.66499	−	0.254988i
$363$	−2.73110	+	7.50363i	−0.143346	+	0.393839i
$364$	−3.84504	+	1.99428i	−0.201535	+	0.104529i
$365$	17.0172	−	20.2803i	0.890722	−	1.06152i
$366$	5.15385	+	4.52664i	0.269396	+	0.236611i
$367$	0.645845	−	3.66277i	0.0337128	−	0.191195i	−0.963300	−	0.268426i	$-0.913497\pi$
$367$	0.645845	−	3.66277i	0.0337128	−	0.191195i	0.997013	+	0.0772306i	$0.0246078\pi$
$368$	0.0756026	+	0.895043i	0.00394106	+	0.0466573i
$369$	1.60179	+	2.77439i	0.0833860	+	0.144429i
$370$	−18.4015	−	33.6012i	−0.956648	−	1.74684i
$371$	5.07514	+	13.9438i	0.263488	+	0.723928i
$372$	4.57465	−	4.97736i	0.237185	−	0.258064i
$373$	15.9217	+	9.19242i	0.824397	+	0.475966i	0.851930	−	0.523655i	$-0.175432\pi$
$373$	15.9217	+	9.19242i	0.824397	+	0.475966i	−0.0275335	+	0.999621i	$0.508765\pi$
$374$	−0.454272	+	20.1272i	−0.0234898	+	1.04075i
$375$	−7.37983	+	6.19241i	−0.381093	+	0.319775i
$376$	4.47279	−	18.1024i	0.230667	−	0.933558i
$377$	−0.0721223	−	0.409026i	−0.00371449	−	0.0210659i
$378$	−3.50226	−	0.699372i	−0.180137	−	0.0359718i
$379$			22.9134i			1.17698i	0.808504	+	0.588490i	$0.200277\pi$
$379$			22.9134i			1.17698i	−0.808504	+	0.588490i	$0.799723\pi$
$380$	18.4029	+	11.1746i	0.944048	+	0.573243i
$381$		−	2.49342i		−	0.127742i
$382$	4.49678	−	22.5186i	0.230075	−	1.15215i
$383$	−3.78894	−	21.4882i	−0.193606	−	1.09799i	−0.914390	−	0.404835i	$-0.867329\pi$
$383$	−3.78894	−	21.4882i	−0.193606	−	1.09799i	0.720784	−	0.693160i	$-0.243782\pi$
$384$	−10.5658	+	4.04513i	−0.539186	+	0.206427i
$385$	20.8171	−	17.4677i	1.06094	−	0.890234i
$386$	12.2777	+	0.277109i	0.624920	+	0.0141045i
$387$	2.15541	+	1.24443i	0.109566	+	0.0632577i
$388$	−4.44626	−	4.08653i	−0.225725	−	0.207462i
$389$	2.77468	+	7.62337i	0.140682	+	0.386520i	0.989946	−	0.141449i	$-0.0451760\pi$
$389$	2.77468	+	7.62337i	0.140682	+	0.386520i	−0.849264	+	0.527969i	$0.822954\pi$
$390$	2.62708	−	1.43870i	0.133027	−	0.0728516i
$391$	0.366833	+	0.635374i	0.0185516	+	0.0321322i
$392$	1.75675	+	0.119112i	0.0887293	+	0.00601604i
$393$	−1.61202	+	9.14222i	−0.0813156	+	0.461164i
$394$	−14.5716	+	16.5906i	−0.734106	+	0.835822i
$395$	−19.0522	+	22.7056i	−0.958622	+	1.14244i
$396$	−7.73579	+	4.01227i	−0.388738	+	0.201624i
$397$	7.77830	−	21.3707i	0.390382	−	1.07257i	−0.576446	−	0.817135i	$-0.695561\pi$
$397$	7.77830	−	21.3707i	0.390382	−	1.07257i	0.966828	−	0.255430i	$-0.0822170\pi$
$398$	−4.46619	−	29.1627i	−0.223870	−	1.46179i
$399$	−4.00201	−	10.2546i	−0.200351	−	0.513370i
$400$	−3.60910	+	2.51103i	−0.180455	+	0.125551i
$401$	11.5821	+	4.21553i	0.578381	+	0.210514i	0.614612	−	0.788830i	$-0.289313\pi$
$401$	11.5821	+	4.21553i	0.578381	+	0.210514i	−0.0362304	+	0.999343i	$0.511535\pi$
$402$	−19.8352	+	6.71658i	−0.989291	+	0.334992i
$403$	1.86330	−	2.22059i	0.0928175	−	0.110616i
$404$	−15.0940	−	9.64778i	−0.750954	−	0.479995i
$405$	2.43213	+	0.428850i	0.120854	+	0.0213097i
$406$	0.628100	−	1.61158i	0.0311721	−	0.0799813i
$407$	23.8968	+	41.3904i	1.18452	+	2.05165i
$408$	−6.40522	+	6.66093i	−0.317106	+	0.329765i
$409$	−21.1460	+	7.69651i	−1.04560	+	0.380568i	−0.807001	−	0.590550i	$-0.798911\pi$
$409$	−21.1460	+	7.69651i	−1.04560	+	0.380568i	−0.238601	+	0.971118i	$0.576689\pi$
$410$	−6.99685	−	8.73129i	−0.345550	−	0.431208i
$411$	−14.6525	−	8.45963i	−0.722755	−	0.417283i
$412$	−3.94383	−	30.3074i	−0.194299	−	1.49314i
$413$	−16.1443	−	19.2401i	−0.794411	−	0.946742i
$414$	−0.164951	+	0.271373i	−0.00810692	+	0.0133372i
$415$	−2.69366	−	15.2765i	−0.132226	−	0.749894i
$416$	−4.44771	+	1.93717i	−0.218067	+	0.0949778i
$417$	17.6668			0.865147
$418$	−23.2672	−	13.4192i	−1.13804	−	0.656355i
$419$			30.1260i			1.47175i	0.677118	+	0.735875i	$0.263229\pi$
$419$			30.1260i			1.47175i	−0.677118	+	0.735875i	$0.736771\pi$
$420$	12.4608	+	0.562770i	0.608027	+	0.0274604i
$421$	−19.8809	+	3.50555i	−0.968938	+	0.170850i	−0.635652	−	0.771976i	$-0.719269\pi$
$421$	−19.8809	+	3.50555i	−0.968938	+	0.170850i	−0.333286	+	0.942826i	$0.608157\pi$
$422$	20.1874	+	12.2707i	0.982709	+	0.597331i
$423$	5.05024	−	4.23766i	0.245551	−	0.206042i
$424$	4.61472	+	15.9659i	0.224110	+	0.775374i
$425$	−1.79559	+	3.11005i	−0.0870988	+	0.150860i
$426$	−0.365894	−	0.456596i	−0.0177276	−	0.0221221i
$427$	4.18941	+	11.5103i	0.202740	+	0.557023i
$428$	−8.22165	−	10.7480i	−0.397409	−	0.519524i
$429$	−3.23607	+	1.86835i	−0.156239	+	0.0902046i
$430$	−8.09920	−	3.15660i	−0.390578	−	0.152225i
$431$	−1.82645	+	10.3583i	−0.0879772	+	0.498943i	0.908697	+	0.417456i	$0.137078\pi$
$431$	−1.82645	+	10.3583i	−0.0879772	+	0.498943i	−0.996674	+	0.0814875i	$0.974033\pi$
$432$	−3.86058	−	1.04686i	−0.185742	−	0.0503669i
$433$	10.2033	+	8.56156i	0.490338	+	0.411443i	0.854147	−	0.520031i	$-0.174080\pi$
$433$	10.2033	+	8.56156i	0.490338	+	0.411443i	−0.363809	+	0.931473i	$0.618524\pi$
$434$	11.4341	−	3.87180i	0.548855	−	0.185853i
$435$	−0.409079	+	1.12393i	−0.0196138	+	0.0538885i
$436$	7.06961	+	22.5397i	0.338573	+	1.07946i
$437$	−0.978564	+	0.0225318i	−0.0468111	+	0.00107784i
$438$	−14.9853	+	2.29497i	−0.716027	+	0.109658i
$439$	25.2217	+	9.17996i	1.20377	+	0.438136i	0.864538	−	0.502568i	$-0.167611\pi$
$439$	25.2217	+	9.17996i	1.20377	+	0.438136i	0.339230	+	0.940703i	$0.389834\pi$
$440$	24.5854	−	17.9419i	1.17206	−	0.855345i
$441$	0.476886	+	0.400155i	0.0227089	+	0.0190550i
$442$	−2.61487	+	2.97718i	−0.124377	+	0.141610i
$443$	−20.7119	−	3.65206i	−0.984051	−	0.173515i	−0.341603	−	0.939844i	$-0.610970\pi$
$443$	−20.7119	−	3.65206i	−0.984051	−	0.173515i	−0.642448	+	0.766330i	$0.722081\pi$
$444$	−4.78030	+	21.4106i	−0.226863	+	1.01610i
$445$	27.1210	−	15.6583i	1.28566	−	0.742275i
$446$	−13.8420	−	25.2755i	−0.655436	−	1.19683i
$447$	1.51823	−	0.552592i	0.0718100	−	0.0261367i
$448$	−20.0180	−	2.72707i	−0.945763	−	0.128842i
$449$	19.1915	−	33.2406i	0.905702	−	1.56872i	0.0857297	−	0.996318i	$-0.472678\pi$
$449$	19.1915	−	33.2406i	0.905702	−	1.56872i	0.819972	−	0.572403i	$-0.193989\pi$
$450$	−1.55407	−	0.0350754i	−0.0732595	−	0.00165347i
$451$	8.97246	+	10.6930i	0.422497	+	0.503512i
$452$	24.6024	+	10.2339i	1.15720	+	0.481362i
$453$	18.4609	−	3.25516i	0.867369	−	0.152941i
$454$	0.439237	+	0.0877121i	0.0206144	+	0.00411653i
$455$	5.34859			0.250746
$456$	−3.69507	−	11.7621i	−0.173038	−	0.550810i
$457$	2.73539			0.127956			0.0639782	−	0.997951i	$-0.479621\pi$
$457$	2.73539			0.127956			0.0639782	+	0.997951i	$0.479621\pi$
$458$	21.3020	+	4.25384i	0.995379	+	0.198769i
$459$	−3.21753	+	0.567337i	−0.150181	+	0.0264810i
$460$	0.425992	−	1.02409i	0.0198620	−	0.0477484i
$461$	−23.0096	−	27.4218i	−1.07166	−	1.27716i	−0.958964	−	0.283529i	$-0.908495\pi$
$461$	−23.0096	−	27.4218i	−1.07166	−	1.27716i	−0.112700	−	0.993629i	$-0.535950\pi$
$462$	−15.5574	−	0.351131i	−0.723794	−	0.0163361i
$463$	4.44322	−	7.69589i	0.206494	−	0.357658i	−0.744114	−	0.668053i	$-0.767128\pi$
$463$	4.44322	−	7.69589i	0.206494	−	0.357658i	0.950608	+	0.310395i	$0.100461\pi$
$464$	0.823966	−	1.75326i	0.0382517	−	0.0813929i
$465$	−7.84434	+	2.85511i	−0.363773	+	0.132402i
$466$	9.40765	+	17.1784i	0.435801	+	0.795774i
$467$	22.1617	−	12.7950i	1.02552	−	0.592084i	0.109821	−	0.993951i	$-0.464972\pi$
$467$	22.1617	−	12.7950i	1.02552	−	0.592084i	0.915698	+	0.401868i	$0.131639\pi$
$468$	−1.67397	−	0.373743i	−0.0773791	−	0.0172763i
$469$	−36.8273	−	6.49364i	−1.70053	−	0.299849i
$470$	−15.1947	+	17.3001i	−0.700881	+	0.797994i
$471$	−5.14268	−	4.31522i	−0.236962	−	0.198835i
$472$	−16.5826	−	22.7228i	−0.763277	−	1.04590i
$473$	10.1904	+	3.70901i	0.468556	+	0.170540i
$474$	16.7774	−	2.56941i	0.770610	−	0.118017i
$475$	−2.49047	−	4.09304i	−0.114271	−	0.187802i
$476$	−15.7452	+	4.93852i	−0.721682	+	0.226357i
$477$	−2.00967	+	5.52151i	−0.0920163	+	0.252813i
$478$	27.6543	−	9.36426i	1.26488	−	0.428311i
$479$	−29.6621	−	24.8894i	−1.35530	−	1.13723i	−0.977404	−	0.211378i	$-0.932205\pi$
$479$	−29.6621	−	24.8894i	−1.35530	−	1.13723i	−0.377891	−	0.925850i	$-0.623351\pi$
$480$	13.8816	+	1.57296i	0.633606	+	0.0717954i
$481$	−1.63347	+	9.26388i	−0.0744799	+	0.422396i
$482$	21.5806	+	8.41087i	0.982970	+	0.383105i
$483$	−0.491114	+	0.283545i	−0.0223465	+	0.0129017i
$484$	−12.6847	+	9.70316i	−0.576579	+	0.441053i
$485$	2.55046	+	7.00733i	0.115810	+	0.318187i
$486$	−0.884362	−	1.10359i	−0.0401155	−	0.0500597i
$487$	−11.7451	+	20.3432i	−0.532223	+	0.921838i	0.467069	+	0.884221i	$0.345310\pi$
$487$	−11.7451	+	20.3432i	−0.532223	+	0.921838i	−0.999292	+	0.0376170i	$0.988023\pi$
$488$	3.80934	+	13.1795i	0.172441	+	0.596608i
$489$	15.0401	−	12.6202i	0.680138	−	0.570703i
$490$	−1.85795	−	1.12934i	−0.0839338	−	0.0510184i
$491$	3.90410	−	0.688399i	0.176190	−	0.0310670i	−0.0848572	−	0.996393i	$-0.527043\pi$
$491$	3.90410	−	0.688399i	0.176190	−	0.0310670i	0.261047	+	0.965326i	$0.415932\pi$
$492$	−0.289073	+	6.40065i	−0.0130324	+	0.288564i
$493$		−	1.58231i		−	0.0712635i
$494$	−1.81036	−	4.96690i	−0.0814521	−	0.223471i
$495$	10.7608			0.483660
$496$	13.0703	−	3.46021i	0.586874	−	0.155368i
$497$	−0.181435	−	1.02897i	−0.00813845	−	0.0461554i
$498$	−4.61387	+	7.59059i	−0.206752	+	0.340142i
$499$	−19.1315	−	22.8001i	−0.856445	−	1.02067i	−0.999521	−	0.0309600i	$-0.990144\pi$
$499$	−19.1315	−	22.8001i	−0.856445	−	1.02067i	0.143075	−	0.989712i	$-0.454301\pi$
$500$	−19.1063	+	2.48625i	−0.854459	+	0.111189i
$501$	0.187562	+	0.108289i	0.00837967	+	0.00483800i
$502$	21.6527	+	27.0202i	0.966408	+	1.20597i
$503$	−3.81115	+	1.38714i	−0.169931	+	0.0618497i	−0.425584	−	0.904919i	$-0.639931\pi$
$503$	−3.81115	+	1.38714i	−0.169931	+	0.0618497i	0.255654	+	0.966768i	$0.417709\pi$
$504$	−5.14859	−	4.95094i	−0.229336	−	0.220532i
$505$	11.0603	+	19.1570i	0.492176	+	0.852473i
$506$	−0.502482	+	1.28927i	−0.0223380	+	0.0573149i
$507$	12.0782	+	2.12971i	0.536412	+	0.0945840i
$508$	2.68572	−	4.20183i	0.119160	−	0.186426i
$509$	−17.5821	+	20.9536i	−0.779315	+	0.928751i	−0.998902	−	0.0468416i	$-0.985084\pi$
$509$	−17.5821	+	20.9536i	−0.779315	+	0.928751i	0.219588	+	0.975593i	$0.429529\pi$
$510$	10.8081	−	3.65983i	0.478591	−	0.162060i
$511$	−25.4387	−	9.25894i	−1.12534	−	0.409592i
$512$	−22.1624	−	4.56401i	−0.979447	−	0.201703i
$513$	1.39615	−	4.12926i	0.0616415	−	0.182311i
$514$	−1.40867	−	9.19816i	−0.0621340	−	0.405713i
$515$	−12.9078	+	35.4639i	−0.568785	+	1.56272i
$516$	2.29182	+	4.41872i	0.100892	+	0.194523i
$517$	18.4643	−	22.0049i	0.812060	−	0.967775i
$518$	−25.8514	+	29.4334i	−1.13585	+	1.29323i
$519$	2.67983	−	15.1981i	0.117632	−	0.667121i
$520$	5.97674	+	0.405237i	0.262097	+	0.0177708i
$521$	−10.0619	−	17.4277i	−0.440820	−	0.763523i	0.556930	−	0.830559i	$-0.311979\pi$
$521$	−10.0619	−	17.4277i	−0.440820	−	0.763523i	−0.997751	+	0.0670361i	$0.978646\pi$
$522$	0.600727	−	0.328985i	0.0262931	−	0.0143993i
$523$	−12.6367	−	34.7191i	−0.552565	−	1.51816i	−0.830195	−	0.557473i	$-0.811771\pi$
$523$	−12.6367	−	34.7191i	−0.552565	−	1.51816i	0.277630	−	0.960688i	$-0.410451\pi$
$524$	−12.5639	+	13.6698i	−0.548855	+	0.597170i
$525$	−2.40392	−	1.38791i	−0.104916	−	0.0605732i
$526$	−37.1144	−	0.837675i	−1.61827	−	0.0365243i
$527$	8.45980	−	7.09862i	0.368515	−	0.309221i
$528$	−17.3578	−	1.57107i	−0.755403	−	0.0683722i
$529$	−3.98515	−	22.6009i	−0.173267	−	0.982649i
$530$	4.01876	−	20.1248i	0.174564	−	0.874166i
$531$		−	9.94554i		−	0.431600i
$532$	4.30139	−	21.5913i	0.186489	−	0.936103i
$533$			2.74736i			0.119002i
$534$	−17.5859	−	3.51175i	−0.761015	−	0.151968i
$535$	2.90160	+	16.4558i	0.125447	+	0.711446i
$536$	−40.6603	−	10.0465i	−1.75626	−	0.433942i
$537$	14.5479	−	12.2071i	0.627788	−	0.526777i
$538$	−0.291085	+	12.8970i	−0.0125496	+	0.556028i
$539$	2.34909	+	1.35625i	0.101182	+	0.0584176i
$540$	3.63663	+	3.34240i	0.156496	+	0.143834i
$541$	6.91873	+	19.0090i	0.297459	+	0.817263i	0.994923	+	0.100642i	$0.0320898\pi$
$541$	6.91873	+	19.0090i	0.297459	+	0.817263i	−0.697463	+	0.716620i	$0.745688\pi$
$542$	0.668936	+	1.22148i	0.0287333	+	0.0524671i
$543$	11.3306	+	19.6252i	0.486244	+	0.842199i
$544$	−17.9686	+	4.32556i	−0.770396	+	0.185457i
$545$	5.06524	−	28.7264i	0.216971	−	1.23050i
$546$	−2.30122	−	2.02117i	−0.0984832	−	0.0864982i
$547$	3.37047	−	4.01676i	0.144111	−	0.171744i	−0.689161	−	0.724608i	$-0.742021\pi$
$547$	3.37047	−	4.01676i	0.144111	−	0.171744i	0.833272	+	0.552864i	$0.186465\pi$
$548$	−15.5799	−	30.0385i	−0.665539	−	1.28318i
$549$	−1.65893	+	4.55788i	−0.0708015	+	0.194526i
$550$	−6.69506	+	1.02533i	−0.285478	+	0.0437203i
$551$	1.85203	+	1.01316i	0.0788990	+	0.0431619i
$552$	−0.570274	+	0.279636i	−0.0242725	+	0.0119021i
$553$	28.4808	+	10.3662i	1.21113	+	0.440815i
$554$	6.33097	+	18.6965i	0.268977	+	0.794336i
$555$	17.4126	−	20.7516i	0.739125	−	0.880855i
$556$	29.7716	+	19.0294i	1.26260	+	0.807026i
$557$	−12.7316	−	2.24492i	−0.539455	−	0.0951204i	−0.102719	−	0.994710i	$-0.532754\pi$
$557$	−12.7316	−	2.24492i	−0.539455	−	0.0951204i	−0.436735	+	0.899590i	$0.643865\pi$
$558$	4.45393	+	1.73588i	0.188550	+	0.0734858i
$559$	1.06721	+	1.84846i	0.0451380	+	0.0781814i
$560$	20.3925	+	14.3703i	0.861738	+	0.607254i
$561$	−13.3772	+	4.86889i	−0.564785	+	0.205565i
$562$	−35.5658	+	28.5008i	−1.50025	+	1.20223i
$563$	12.6215	+	7.28702i	0.531932	+	0.307111i	0.741803	−	0.670618i	$-0.233971\pi$
$563$	12.6215	+	7.28702i	0.531932	+	0.307111i	−0.209871	+	0.977729i	$0.567304\pi$
$564$	13.0750	−	1.70142i	0.550557	−	0.0716427i
$565$	−21.1498	−	25.2053i	−0.889777	−	1.06039i
$566$	−5.98803	−	3.63977i	−0.251696	−	0.152991i
$567$	−0.438525	−	2.48700i	−0.0184163	−	0.104444i
$568$	−0.124783	−	1.16356i	−0.00523577	−	0.0488217i
$569$	9.82051			0.411697			0.205849	−	0.978584i	$-0.434005\pi$
$569$	9.82051			0.411697			0.205849	+	0.978584i	$0.434005\pi$
$570$	−2.63679	+	14.9939i	−0.110443	+	0.628024i
$571$			1.88885i			0.0790460i	0.999219	+	0.0395230i	$0.0125838\pi$
$571$			1.88885i			0.0790460i	−0.999219	+	0.0395230i	$0.987416\pi$
$572$	−7.46578	−	0.337178i	−0.312160	−	0.0140981i
$573$	15.9908	−	2.81960i	0.668023	−	0.117791i
$574$	−5.94278	+	9.77686i	−0.248047	+	0.408078i
$575$	−0.189081	+	0.158658i	−0.00788521	+	0.00661648i
$576$	−5.37814	−	5.92247i	−0.224089	−	0.246769i
$577$	−13.1133	+	22.7128i	−0.545913	+	0.945548i	0.452636	+	0.891695i	$0.350484\pi$
$577$	−13.1133	+	22.7128i	−0.545913	+	0.945548i	−0.998549	+	0.0538530i	$0.982850\pi$
$578$	6.98089	−	5.59416i	0.290367	−	0.232686i
$579$	2.97006	+	8.16018i	0.123432	+	0.339125i
$580$	−1.89999	+	1.45339i	−0.0788926	+	0.0603488i
$581$	−13.7370	+	7.93106i	−0.569906	+	0.329036i
$582$	1.55066	−	3.97868i	0.0642769	−	0.164922i
$583$	−4.44580	+	25.2134i	−0.184126	+	1.04423i
$584$	−27.7248	−	12.2737i	−1.14726	−	0.507889i
$585$	1.62244	+	1.36139i	0.0670797	+	0.0562866i
$586$	1.96872	+	5.81396i	0.0813269	+	0.240173i
$587$	−7.62316	+	20.9444i	−0.314641	+	0.864470i	0.677062	+	0.735926i	$0.263253\pi$
$587$	−7.62316	+	20.9444i	−0.314641	+	0.864470i	−0.991704	+	0.128544i	$0.958970\pi$
$588$	0.372617	+	1.18800i	0.0153664	+	0.0489921i
$589$	2.89181	+	14.4471i	0.119155	+	0.595284i
$590$	5.25841	+	34.3356i	0.216485	+	1.41357i
$591$	−14.6721	−	5.34022i	−0.603531	−	0.219667i
$592$	−31.1175	+	30.9315i	−1.27892	+	1.27127i
$593$	9.48331	+	7.95744i	0.389433	+	0.326773i	0.816392	−	0.577498i	$-0.195971\pi$
$593$	9.48331	+	7.95744i	0.389433	+	0.326773i	−0.426959	+	0.904271i	$0.640415\pi$
$594$	−4.62980	−	4.06637i	−0.189963	−	0.166845i
$595$	20.0670	+	3.53835i	0.822666	+	0.145058i
$596$	3.15369	+	0.704119i	0.129180	+	0.0288418i
$597$	18.0666	−	10.4308i	0.739419	−	0.426904i
$598$	−0.238872	+	0.130817i	−0.00976820	+	0.00534950i
$599$	2.95963	−	1.07722i	0.120927	−	0.0440139i	−0.280848	−	0.959752i	$-0.590616\pi$
$599$	2.95963	−	1.07722i	0.120927	−	0.0440139i	0.401775	+	0.915738i	$0.368393\pi$
$600$	−2.58109	−	1.73304i	−0.105373	−	0.0707510i
$601$	−9.76066	+	16.9060i	−0.398146	+	0.689609i	−0.993497	−	0.113857i	$-0.963680\pi$
$601$	−9.76066	+	16.9060i	−0.398146	+	0.689609i	0.595351	+	0.803465i	$0.297013\pi$
$602$	−0.200567	+	8.88643i	−0.00817451	+	0.362184i
$603$	−9.51834	−	11.3435i	−0.387617	−	0.461944i
$604$	34.6160	+	14.3992i	1.40850	+	0.585897i
$605$	19.4211	−	3.42446i	0.789578	−	0.139224i
$606$	2.48053	−	12.4218i	0.100765	−	0.504601i
$607$	0.358636			0.0145566			0.00727830	−	0.999974i	$-0.497683\pi$
$607$	0.358636			0.0145566			0.00727830	+	0.999974i	$0.497683\pi$
$608$	6.44243	−	23.8012i	0.261275	−	0.965264i
$609$	1.22305			0.0495604
$610$	3.31739	−	16.6126i	0.134317	−	0.672623i
$611$	5.56788	−	0.981767i	0.225252	−	0.0397180i
$612$	−6.03318	−	2.50963i	−0.243877	−	0.101446i
$613$	29.1535	+	34.7438i	1.17750	+	1.40329i	0.896189	+	0.443672i	$0.146325\pi$
$613$	29.1535	+	34.7438i	1.17750	+	1.40329i	0.281310	+	0.959617i	$0.409231\pi$
$614$	0.324238	−	14.3659i	0.0130852	−	0.579759i
$615$	3.95587	−	6.85177i	0.159516	−	0.276290i
$616$	−25.8386	−	17.3490i	−1.04107	−	0.699010i
$617$	−21.2403	+	7.73082i	−0.855100	+	0.311231i	−0.732118	−	0.681178i	$-0.761468\pi$
$617$	−21.2403	+	7.73082i	−0.855100	+	0.311231i	−0.122982	+	0.992409i	$0.539246\pi$
$618$	18.9549	−	10.3806i	0.762480	−	0.417567i
$619$	8.09036	−	4.67097i	0.325179	−	0.187742i	−0.328520	−	0.944497i	$-0.606550\pi$
$619$	8.09036	−	4.67097i	0.325179	−	0.187742i	0.653699	+	0.756755i	$0.273216\pi$
$620$	−16.2944	−	3.63801i	−0.654397	−	0.146106i
$621$	−0.221146	−	0.0389940i	−0.00887428	−	0.00156478i
$622$	9.46444	+	8.31265i	0.379490	+	0.333307i
$623$	−24.5311	−	20.5841i	−0.982819	−	0.824683i
$624$	−2.41835	−	2.43289i	−0.0968114	−	0.0973937i
$625$	27.5214	+	10.0170i	1.10086	+	0.400679i
$626$	−5.02875	−	32.8360i	−0.200989	−	1.31239i
$627$	2.86660	−	18.7750i	0.114481	−	0.749802i
$628$	−4.01825	−	12.8112i	−0.160345	−	0.511222i
$629$	−12.2570	+	33.6758i	−0.488718	+	1.34274i
$630$	2.82887	+	8.35416i	0.112705	+	0.332838i
$631$	29.6400	+	24.8709i	1.17995	+	0.990097i	0.999979	+	0.00642509i	$0.00204518\pi$
$631$	29.6400	+	24.8709i	1.17995	+	0.990097i	0.179972	+	0.983672i	$0.442399\pi$
$632$	31.0403	+	13.7415i	1.23472	+	0.546606i
$633$	−2.90077	+	16.4511i	−0.115295	+	0.653871i
$634$	16.0340	−	41.1401i	0.636793	−	1.63388i
$635$	−5.33287	+	3.07893i	−0.211628	+	0.122184i
$636$	−9.33400	+	7.14002i	−0.370117	+	0.283120i
$637$	0.182596	+	0.501680i	0.00723474	+	0.0198773i
$638$	2.32881	−	1.86620i	0.0921984	−	0.0738834i
$639$	0.206869	−	0.358308i	0.00818361	−	0.0141744i
$640$	21.6986	+	17.6030i	0.857713	+	0.695818i
$641$	2.57758	−	2.16285i	0.101808	−	0.0854274i	−0.590463	−	0.807065i	$-0.701055\pi$
$641$	2.57758	−	2.16285i	0.101808	−	0.0854274i	0.692271	+	0.721638i	$0.256610\pi$
$642$	4.97005	−	8.17656i	0.196152	−	0.322703i
$643$	−5.26111	+	0.927676i	−0.207478	+	0.0365840i	−0.276421	−	0.961037i	$-0.589148\pi$
$643$	−5.26111	+	0.927676i	−0.207478	+	0.0365840i	0.0689431	+	0.997621i	$0.478037\pi$
$644$	−1.13302	−	0.0511709i	−0.0446474	−	0.00201642i
$645$		−	6.14659i		−	0.242022i
$646$	−3.50633	−	19.8326i	−0.137955	−	0.780303i
$647$	7.69396			0.302481			0.151240	−	0.988497i	$-0.451673\pi$
$647$	7.69396			0.302481			0.151240	+	0.988497i	$0.451673\pi$
$648$	−0.301598	−	2.81230i	−0.0118479	−	0.110478i
$649$	−7.52500	−	42.6764i	−0.295382	−	1.67519i
$650$	−1.13916	−	0.692427i	−0.0446815	−	0.0271592i
$651$	5.48690	+	6.53903i	0.215049	+	0.256285i
$652$	38.9387	−	5.06700i	1.52496	−	0.198439i
$653$	−24.3496	−	14.0582i	−0.952872	−	0.550141i	−0.0589004	−	0.998264i	$-0.518759\pi$
$653$	−24.3496	−	14.0582i	−0.952872	−	0.550141i	−0.893972	+	0.448123i	$0.852093\pi$
$654$	−13.0347	+	10.4454i	−0.509697	+	0.408447i
$655$	21.5438	−	7.84129i	0.841784	−	0.306384i
$656$	−7.38145	+	10.4748i	−0.288197	+	0.408973i
$657$	−5.35989	−	9.28359i	−0.209109	−	0.362188i
$658$	21.9377	+	8.55003i	0.855219	+	0.333315i
$659$	24.3390	+	4.29162i	0.948111	+	0.167178i	0.626261	−	0.779613i	$-0.284584\pi$
$659$	24.3390	+	4.29162i	0.948111	+	0.167178i	0.321850	+	0.946791i	$0.395695\pi$
$660$	18.1337	+	11.5907i	0.705854	+	0.451168i
$661$	5.85539	−	6.97818i	0.227748	−	0.271420i	−0.640054	−	0.768330i	$-0.721088\pi$
$661$	5.85539	−	6.97818i	0.227748	−	0.271420i	0.867802	+	0.496911i	$0.165532\pi$
$662$	−8.35461	−	24.6726i	−0.324711	−	0.958929i
$663$	−2.63291	−	0.958302i	−0.102254	−	0.0372174i
$664$	−15.9512	+	7.82171i	−0.619026	+	0.303541i
$665$	−16.9905	+	21.2220i	−0.658862	+	0.822953i
$666$	−15.3335	+	2.34829i	−0.594162	+	0.0909944i
$667$	0.0371962	−	0.102196i	0.00144024	−	0.00395704i
$668$	0.199433	+	0.384514i	0.00771631	+	0.0148773i
$669$	13.0981	−	15.6097i	0.506403	−	0.603508i
$670$	38.8583	+	34.1294i	1.50123	+	1.31853i
$671$	−3.66990	+	20.8131i	−0.141675	+	0.803479i
$672$	−3.34346	−	13.8889i	−0.128977	−	0.535774i
$673$	10.4606	+	18.1183i	0.403226	+	0.698409i	0.994113	−	0.108346i	$-0.0345554\pi$
$673$	10.4606	+	18.1183i	0.403226	+	0.698409i	−0.590887	+	0.806754i	$0.701222\pi$
$674$	11.4035	+	20.8228i	0.439245	+	0.802063i
$675$	−0.375939	−	1.03288i	−0.0144699	−	0.0397557i
$676$	18.0599	+	16.5987i	0.694610	+	0.638411i
$677$	27.6169	+	15.9446i	1.06140	+	0.612802i	0.925820	−	0.377964i	$-0.123376\pi$
$677$	27.6169	+	15.9446i	1.06140	+	0.612802i	0.135584	+	0.990766i	$0.456709\pi$
$678$	−0.425147	+	18.8368i	−0.0163277	+	0.723422i
$679$	5.84130	−	4.90143i	0.224169	−	0.188100i
$680$	22.1556	+	5.47428i	0.849628	+	0.209929i
$681$	0.0549978	+	0.311908i	0.00210752	+	0.0119523i
$682$	20.4252	+	4.07875i	0.782122	+	0.156183i
$683$			22.3118i			0.853736i	0.904314	+	0.426868i	$0.140383\pi$
$683$			22.3118i			0.853736i	−0.904314	+	0.426868i	$0.859617\pi$
$684$	6.80048	−	5.45467i	0.260023	−	0.208565i
$685$			41.7847i			1.59651i
$686$	−5.33099	+	26.6961i	−0.203538	+	1.01926i
$687$	2.66727	+	15.1269i	0.101763	+	0.577125i
$688$	−0.897403	+	9.91487i	−0.0342132	+	0.378001i
$689$	−3.86017	+	3.23906i	−0.147061	+	0.123398i
$690$	0.784093	+	0.0176970i	0.0298499	+	0.000673714i
$691$	32.7203	+	18.8911i	1.24474	+	0.718650i	0.970055	−	0.242885i	$-0.0780937\pi$
$691$	32.7203	+	18.8911i	1.24474	+	0.718650i	0.274683	+	0.961535i	$0.411427\pi$
$692$	20.8862	−	22.7248i	0.793975	−	0.863868i
$693$	−3.76343	−	10.3399i	−0.142961	−	0.392781i
$694$	14.6418	−	8.01850i	0.555796	−	0.304378i
$695$	−21.8154	−	37.7854i	−0.827506	−	1.43328i
$696$	1.36669	+	0.0926644i	0.0518041	+	0.00351243i
$697$	−1.81751	+	10.3076i	−0.0688432	+	0.390429i
$698$	6.04877	−	6.88688i	0.228949	−	0.260672i
$699$	−8.90210	+	10.6091i	−0.336708	+	0.401274i
$700$	−2.55607	−	4.92819i	−0.0966103	−	0.186268i
$701$	−15.1524	+	41.6308i	−0.572297	+	1.57237i	0.228567	+	0.973528i	$0.426596\pi$
$701$	−15.1524	+	41.6308i	−0.572297	+	1.57237i	−0.800864	+	0.598846i	$0.795626\pi$
$702$	−0.183599	−	1.19884i	−0.00692950	−	0.0452472i
$703$	−31.5680	−	35.9091i	−1.19061	−	1.35434i
$704$	−27.5587	−	21.3441i	−1.03866	−	0.804437i
$705$	−15.2996	−	5.56859i	−0.576216	−	0.209725i
$706$	−21.3501	+	7.22953i	−0.803521	+	0.272087i
$707$	14.5396	−	17.3276i	0.546817	−	0.651672i
$708$	10.7126	−	16.7599i	0.402605	−	0.629877i
$709$	0.561672	+	0.0990379i	0.0210940	+	0.00371945i	0.184185	−	0.982892i	$-0.441035\pi$
$709$	0.561672	+	0.0990379i	0.0210940	+	0.00371945i	−0.163091	+	0.986611i	$0.552146\pi$
$710$	−0.524742	+	1.34638i	−0.0196932	+	0.0505289i
$711$	6.00085	+	10.3938i	0.225050	+	0.389797i
$712$	−25.8526	−	24.8601i	−0.968866	−	0.931672i
$713$	0.713261	−	0.259606i	0.0267119	−	0.00972232i
$714$	−7.29668	−	9.10545i	−0.273071	−	0.340763i
$715$	7.99196	+	4.61416i	0.298883	+	0.172560i
$716$	37.6643	−	4.90117i	1.40758	−	0.183165i
$717$	13.2705	+	15.8152i	0.495596	+	0.590628i
$718$	8.40350	−	13.8252i	0.313616	−	0.515951i
$719$	5.08960	+	28.8646i	0.189810	+	1.07647i	0.919618	+	0.392814i	$0.128499\pi$
$719$	5.08960	+	28.8646i	0.189810	+	1.07647i	−0.729808	+	0.683653i	$0.760390\pi$
$720$	2.52815	+	9.54962i	0.0942185	+	0.355893i
$721$	38.5913			1.43721
$722$	25.4584	+	8.59485i	0.947462	+	0.319867i
$723$			16.3778i			0.609097i
$724$	−2.04482	+	45.2764i	−0.0759952	+	1.68268i
$725$	0.524248	−	0.0924391i	0.0194701	−	0.00343310i
$726$	−9.64994	−	5.86563i	−0.358143	−	0.217694i
$727$	−11.8219	+	9.91975i	−0.438450	+	0.367903i	−0.835129	−	0.550054i	$-0.814607\pi$
$727$	−11.8219	+	9.91975i	−0.438450	+	0.367903i	0.396679	+	0.917957i	$0.370163\pi$
$728$	−1.70089	−	5.88473i	−0.0630393	−	0.218102i
$729$	0.500000	−	0.866025i	0.0185185	−	0.0320750i
$730$	23.4127	+	29.2164i	0.866543	+	1.08135i
$731$	2.78113	+	7.64109i	0.102864	+	0.282616i
$732$	−7.70500	+	5.89392i	−0.284785	+	0.217846i
$733$	31.8660	−	18.3978i	1.17700	−	0.679539i	0.221679	−	0.975120i	$-0.428846\pi$
$733$	31.8660	−	18.3978i	1.17700	−	0.679539i	0.955318	+	0.295580i	$0.0955130\pi$
$734$	4.90079	+	1.91004i	0.180891	+	0.0705010i
$735$	0.266972	−	1.51408i	0.00984743	−	0.0558475i
$736$	−1.26221	−	0.143024i	−0.0465257	−	0.00527194i
$737$	−49.4260	−	41.4733i	−1.82063	−	1.52769i
$738$	−4.29121	+	1.45308i	−0.157962	+	0.0534887i
$739$	−7.48438	+	20.5632i	−0.275317	+	0.756428i	0.722560	+	0.691308i	$0.242965\pi$
$739$	−7.48438	+	20.5632i	−0.275317	+	0.756428i	−0.997877	+	0.0651199i	$0.979257\pi$
$740$	51.6953	−	16.2143i	1.90036	−	0.596050i
$741$	2.80752	−	2.46812i	0.103137	−	0.0906685i
$742$	−20.7433	+	3.17678i	−0.761509	+	0.116623i
$743$	17.9809	+	6.54452i	0.659656	+	0.240095i	0.650088	−	0.759859i	$-0.274732\pi$
$743$	17.9809	+	6.54452i	0.659656	+	0.240095i	0.00956828	+	0.999954i	$0.496954\pi$
$744$	5.63586	+	7.72270i	0.206621	+	0.283128i
$745$	−3.05662	−	2.56481i	−0.111986	−	0.0939675i
$746$	−17.1577	+	19.5351i	−0.628188	+	0.715229i
$747$	−6.18569	−	1.09070i	−0.226323	−	0.0399068i
$748$	−27.7872	−	6.20400i	−1.01600	−	0.226841i
$749$	14.7974	−	8.54331i	0.540687	−	0.312166i
$750$	−6.54407	−	11.9495i	−0.238956	−	0.436334i
$751$	13.2502	−	4.82267i	0.483506	−	0.175982i	−0.0887549	−	0.996053i	$-0.528289\pi$
$751$	13.2502	−	4.82267i	0.483506	−	0.175982i	0.572261	+	0.820072i	$0.306067\pi$
$752$	23.8663	+	11.2163i	0.870313	+	0.409015i
$753$	−12.2420	+	21.2037i	−0.446123	+	0.772708i
$754$	0.587224	+	0.0132537i	0.0213854	+	0.000482670i
$755$	−29.7580	−	35.4643i	−1.08301	−	1.29068i
$756$	1.93982	−	4.66336i	0.0705507	−	0.169605i
$757$	−22.0077	+	3.88055i	−0.799882	+	0.141041i	−0.558625	−	0.829420i	$-0.688671\pi$
$757$	−22.0077	+	3.88055i	−0.799882	+	0.141041i	−0.241257	+	0.970461i	$0.577560\pi$
$758$	−31.7770	−	6.34561i	−1.15419	−	0.230483i
$759$	−0.978442			−0.0355152
$760$	−20.5937	+	22.4271i	−0.747013	+	0.813515i
$761$	−46.4666			−1.68441			−0.842207	−	0.539155i	$-0.818744\pi$
$761$	−46.4666			−1.68441			−0.842207	+	0.539155i	$0.818744\pi$
$762$	3.45795	+	0.690524i	0.125268	+	0.0250150i
$763$	−29.3745	+	5.17951i	−1.06343	+	0.187511i
$764$	29.9842	+	12.4726i	1.08479	+	0.451241i
$765$	5.18649	+	6.18102i	0.187518	+	0.223475i
$766$	30.8498	+	0.696282i	1.11465	+	0.0251577i
$767$	4.26460	−	7.38650i	0.153986	−	0.266711i
$768$	−2.68383	−	15.7733i	−0.0968444	−	0.569170i
$769$	−4.38453	+	1.59584i	−0.158110	+	0.0575474i	−0.419863	−	0.907588i	$-0.637922\pi$
$769$	−4.38453	+	1.59584i	−0.158110	+	0.0575474i	0.261753	+	0.965135i	$0.415700\pi$
$770$	18.4596	+	33.7074i	0.665239	+	1.21473i
$771$	5.69837	−	3.28996i	0.205222	−	0.118485i
$772$	−3.78449	+	16.9504i	−0.136207	+	0.610059i
$773$	−1.36548	−	0.240771i	−0.0491128	−	0.00865991i	0.149038	−	0.988832i	$-0.452382\pi$
$773$	−1.36548	−	0.240771i	−0.0491128	−	0.00865991i	−0.198151	+	0.980172i	$0.563494\pi$
$774$	−2.32273	+	2.64456i	−0.0834887	+	0.0950567i
$775$	2.84613	+	2.38819i	0.102236	+	0.0857863i
$776$	6.89867	−	5.03450i	0.247648	−	0.180728i
$777$	−26.0298	−	9.47409i	−0.933815	−	0.339881i
$778$	−11.3408	+	1.73681i	−0.406586	+	0.0622676i
$779$	−10.9009	−	8.72734i	−0.390566	−	0.312689i
$780$	1.26770	+	4.04175i	0.0453910	+	0.144718i
$781$	0.616573	−	1.69402i	0.0220627	−	0.0606169i
$782$	−0.982747	+	0.332776i	−0.0351430	+	0.0119001i
$783$	0.371000	+	0.311306i	0.0132584	+	0.0111252i
$784$	−0.651700	+	2.40333i	−0.0232750	+	0.0858332i
$785$	−2.87899	+	16.3276i	−0.102756	+	0.582757i
$786$	−12.2323	−	4.76744i	−0.436312	−	0.170049i
$787$	25.2433	−	14.5742i	0.899825	−	0.519514i	0.0226816	−	0.999743i	$-0.492780\pi$
$787$	25.2433	−	14.5742i	0.899825	−	0.519514i	0.877143	+	0.480228i	$0.159446\pi$
$788$	−18.9729	−	24.8029i	−0.675883	−	0.883568i
$789$	−8.97822	−	24.6674i	−0.319633	−	0.878184i
$790$	−26.2125	−	32.7103i	−0.932599	−	1.16378i
$791$	−16.8227	+	29.1378i	−0.598148	+	1.03602i
$792$	−3.42200	−	11.8394i	−0.121596	−	0.420695i
$793$	−3.18648	+	2.67377i	−0.113155	+	0.0949484i
$794$	27.4835	+	16.7056i	0.975352	+	0.592859i
$795$	14.2909	−	2.51987i	0.506845	−	0.0893705i
$796$	41.6806	+	1.88243i	1.47733	+	0.0667209i
$797$		−	9.70728i		−	0.343849i	−0.985110	−	0.171925i	$-0.945001\pi$
$797$		−	9.70728i		−	0.343849i	0.985110	−	0.171925i	$-0.0549986\pi$
$798$	15.3297	−	2.71023i	0.542664	−	0.0959410i
$799$	21.5392			0.762002
$800$	−2.48287	−	5.70062i	−0.0877828	−	0.201547i
$801$	−2.20196	−	12.4879i	−0.0778025	−	0.441240i
$802$	−9.05376	+	14.8950i	−0.319699	+	0.525959i
$803$	−30.0235	−	35.7806i	−1.05950	−	1.26267i
$804$	−3.82162	−	29.3682i	−0.134778	−	1.03574i
$805$	1.21288	+	0.700257i	0.0427484	+	0.0246808i
$806$	2.56357	+	3.19905i	0.0902980	+	0.112682i
$807$	−8.57175	+	3.11986i	−0.301740	+	0.109824i
$808$	17.5600	−	18.2610i	0.617757	−	0.642419i
$809$	−11.3536	−	19.6651i	−0.399172	−	0.691387i	0.594452	−	0.804131i	$-0.297369\pi$
$809$	−11.3536	−	19.6651i	−0.399172	−	0.691387i	−0.993624	+	0.112745i	$0.964036\pi$
$810$	−1.26830	+	3.25419i	−0.0445634	+	0.114341i
$811$	−31.6955	−	5.58877i	−1.11298	−	0.196248i	−0.413223	−	0.910630i	$-0.635597\pi$
$811$	−31.6955	−	5.58877i	−1.11298	−	0.196248i	−0.699756	+	0.714382i	$0.746708\pi$
$812$	2.06105	+	1.31738i	0.0723285	+	0.0462309i
$813$	−0.632989	+	0.754367i	−0.0221999	+	0.0264568i
$814$	−64.0195	+	21.6782i	−2.24388	+	0.759820i
$815$	−45.5637	−	16.5838i	−1.59603	−	0.580906i
$816$	−7.46374	−	10.7276i	−0.261283	−	0.375543i
$817$	−10.7244	−	1.63741i	−0.375198	−	0.0572859i
$818$	−4.81762	−	31.4574i	−0.168444	−	1.09988i
$819$	0.740723	−	2.03512i	0.0258829	−	0.0711128i
$820$	14.0465	−	7.28542i	0.490526	−	0.254418i
$821$	−15.5693	+	18.5547i	−0.543371	+	0.647564i	−0.965940	−	0.258767i	$-0.916684\pi$
$821$	−15.5693	+	18.5547i	−0.543371	+	0.647564i	0.422569	+	0.906331i	$0.361128\pi$
$822$	15.7899	−	17.9778i	0.550738	−	0.627047i
$823$	−4.65047	+	26.3741i	−0.162105	+	0.919344i	0.789894	+	0.613243i	$0.210136\pi$
$823$	−4.65047	+	26.3741i	−0.162105	+	0.919344i	−0.951999	+	0.306101i	$0.900976\pi$
$824$	43.1235	+	2.92387i	1.50228	+	0.101858i
$825$	−2.39466	−	4.14767i	−0.0833713	−	0.144403i
$826$	31.1538	−	17.0612i	1.08398	−	0.593634i
$827$	−10.9195	−	30.0011i	−0.379708	−	1.04324i	−0.971477	−	0.237133i	$-0.923792\pi$
$827$	−10.9195	−	30.0011i	−0.379708	−	1.04324i	0.591769	−	0.806108i	$-0.298430\pi$
$828$	−0.330667	−	0.303914i	−0.0114915	−	0.0105617i
$829$	19.3534	+	11.1737i	0.672173	+	0.388079i	0.796900	−	0.604112i	$-0.206472\pi$
$829$	19.3534	+	11.1737i	0.672173	+	0.388079i	−0.124726	+	0.992191i	$0.539805\pi$
$830$	21.9319	+	0.495005i	0.761268	+	0.0171819i
$831$	−10.6923	+	8.97188i	−0.370911	+	0.311231i
$832$	−1.45479	−	6.70471i	−0.0504358	−	0.232444i
$833$	0.353185	+	2.00301i	0.0122371	+	0.0694002i
$834$	−4.89263	+	24.5009i	−0.169418	+	0.848397i
$835$		−	0.534873i		−	0.0185100i
$836$	25.0538	−	28.5514i	0.866503	−	0.987471i
$837$			3.38014i			0.116835i
$838$	−41.7797	−	8.34306i	−1.44325	−	0.288206i
$839$	−4.93685	−	27.9983i	−0.170439	−	0.966608i	−0.943278	−	0.332005i	$-0.892275\pi$
$839$	−4.93685	−	27.9983i	−0.170439	−	0.966608i	0.772838	−	0.634603i	$-0.218836\pi$
$840$	−4.23136	+	17.1252i	−0.145996	+	0.590877i
$841$	22.0356	−	18.4901i	0.759849	−	0.637589i
$842$	0.644203	−	28.5424i	0.0222007	−	0.983635i
$843$	−27.9098	−	16.1137i	−0.961265	−	0.554986i
$844$	−22.6082	+	24.5983i	−0.778205	+	0.846710i
$845$	−10.3595	−	28.4625i	−0.356377	−	0.979139i
$846$	4.47831	+	8.17741i	0.153968	+	0.281145i
$847$	−10.0828	−	17.4639i	−0.346448	−	0.600066i
$848$	−23.4201	+	1.97825i	−0.804249	+	0.0679333i
$849$	0.860430	−	4.87974i	0.0295299	−	0.167472i
$850$	−3.81585	−	3.35147i	−0.130883	−	0.114955i
$851$	−1.58328	+	1.88687i	−0.0542740	+	0.0646812i
$852$	0.734552	−	0.380985i	0.0251653	−	0.0130523i
$853$	7.08123	−	19.4555i	0.242457	−	0.666144i	−0.757455	−	0.652887i	$-0.773558\pi$
$853$	7.08123	−	19.4555i	0.242457	−	0.666144i	0.999912	−	0.0132575i	$-0.00422011\pi$
$854$	−17.1231	+	2.62236i	−0.585940	+	0.0897352i
$855$	−10.5556	+	2.11286i	−0.360993	+	0.0722582i
$856$	17.1826	−	8.42552i	0.587288	−	0.287978i
$857$	23.3316	+	8.49200i	0.796991	+	0.290081i	0.708239	−	0.705973i	$-0.249490\pi$
$857$	23.3316	+	8.49200i	0.796991	+	0.290081i	0.0887522	+	0.996054i	$0.471712\pi$
$858$	−1.69489	−	5.00531i	−0.0578626	−	0.170878i
$859$	13.8698	−	16.5294i	0.473231	−	0.563974i	−0.475640	−	0.879640i	$-0.657783\pi$
$859$	13.8698	−	16.5294i	0.473231	−	0.563974i	0.948870	+	0.315666i	$0.102228\pi$
$860$	6.62066	−	10.3580i	0.225763	−	0.353207i
$861$	−7.96732	−	1.40485i	−0.271525	−	0.0478773i
$862$	−13.8595	−	5.40161i	−0.472055	−	0.183980i
$863$	25.8816	+	44.8282i	0.881020	+	1.52597i	0.850209	+	0.526445i	$0.176476\pi$
$863$	25.8816	+	44.8282i	0.881020	+	1.52597i	0.0308107	+	0.999525i	$0.490191\pi$
$864$	2.52096	−	5.06407i	0.0857648	−	0.172283i
$865$	−35.8145	+	13.0354i	−1.21773	+	0.443217i
$866$	−14.6991	+	11.7792i	−0.499497	+	0.400274i
$867$	5.47816	+	3.16282i	0.186048	+	0.107415i
$868$	2.20299	+	16.9295i	0.0747744	+	0.574624i
$869$	33.6138	+	40.0594i	1.14027	+	1.35892i
$870$	−1.44542	−	0.878585i	−0.0490043	−	0.0297868i
$871$	−2.20518	−	12.5062i	−0.0747197	−	0.423756i
$872$	−33.2167	+	3.56224i	−1.12486	+	0.120633i
$873$	3.01947			0.102194
$874$	0.239755	−	1.36334i	0.00810983	−	0.0461158i
$875$		−	24.3286i		−	0.822455i
$876$	0.967290	−	21.4177i	0.0326817	−	0.723637i
$877$	−23.4551	+	4.13577i	−0.792023	+	0.139655i	−0.555001	−	0.831849i	$-0.687282\pi$
$877$	−23.4551	+	4.13577i	−0.792023	+	0.139655i	−0.237022	+	0.971504i	$0.576171\pi$
$878$	−19.7160	+	32.4360i	−0.665381	+	1.09466i
$879$	−3.32493	+	2.78995i	−0.112147	+	0.0941027i
$880$	18.0737	+	39.0646i	0.609265	+	1.31687i
$881$	−28.4189	+	49.2230i	−0.957457	+	1.65836i	−0.228816	+	0.973470i	$0.573485\pi$
$881$	−28.4189	+	49.2230i	−0.957457	+	1.65836i	−0.728641	+	0.684895i	$0.759848\pi$
$882$	−0.687017	+	0.550543i	−0.0231330	+	0.0185377i
$883$	−2.12527	−	5.83914i	−0.0715211	−	0.196503i	0.898782	−	0.438397i	$-0.144454\pi$
$883$	−2.12527	−	5.83914i	−0.0715211	−	0.196503i	−0.970303	+	0.241894i	$0.922231\pi$
$884$	−3.40469	−	4.45088i	−0.114512	−	0.149699i
$885$	−21.2713	+	12.2810i	−0.715028	+	0.412821i
$886$	10.8007	−	27.7125i	0.362857	−	0.931020i
$887$	−6.99109	+	39.6484i	−0.234738	+	1.33126i	0.608427	+	0.793610i	$0.291801\pi$
$887$	−6.99109	+	39.6484i	−0.234738	+	1.33126i	−0.843165	+	0.537655i	$0.819310\pi$
$888$	−28.3690	−	12.5589i	−0.952002	−	0.421449i
$889$	4.82362	+	4.04749i	0.161779	+	0.135749i
$890$	14.2046	+	41.9487i	0.476139	+	1.40612i
$891$	1.49025	−	4.09443i	0.0499253	−	0.137169i
$892$	38.8862	−	12.1967i	1.30201	−	0.408376i
$893$	−13.7916	+	25.2108i	−0.461519	+	0.843646i
$894$	0.345894	+	2.25857i	0.0115684	+	0.0755379i
$895$	−44.0725	−	16.0411i	−1.47318	−	0.536194i
$896$	9.32576	−	27.0064i	0.311552	−	0.902221i
$897$	−0.147524	−	0.123787i	−0.00492567	−	0.00413313i
$898$	40.7843	+	35.8210i	1.36099	+	1.19536i
$899$	−1.61215	−	0.284266i	−0.0537683	−	0.00948081i
$900$	0.479026	−	2.14552i	0.0159675	−	0.0715173i
$901$	−16.6255	+	9.59871i	−0.553874	+	0.319780i
$902$	−17.3142	+	9.48200i	−0.576499	+	0.315716i
$903$	−5.90621	+	2.14968i	−0.196546	+	0.0715370i
$904$	−21.0061	+	31.2853i	−0.698651	+	1.04053i
$905$	27.9827	−	48.4675i	0.930176	−	1.61111i
$906$	−0.598189	+	26.5037i	−0.0198735	+	0.880525i
$907$	−6.45371	−	7.69123i	−0.214292	−	0.255383i	0.648181	−	0.761486i	$-0.275530\pi$
$907$	−6.45371	−	7.69123i	−0.214292	−	0.255383i	−0.862473	+	0.506103i	$0.831086\pi$
$908$	−0.243284	+	0.584858i	−0.00807366	+	0.0194092i
$909$	8.82088	−	1.55536i	0.292570	−	0.0515880i
$910$	−1.48123	+	7.41760i	−0.0491024	+	0.245891i
$911$	−7.57417			−0.250943			−0.125472	−	0.992097i	$-0.540044\pi$
$911$	−7.57417			−0.250943			−0.125472	+	0.992097i	$0.540044\pi$
$912$	17.3353	−	1.86707i	0.574031	−	0.0618248i
$913$	−27.3681			−0.905751
$914$	−0.757537	+	3.79353i	−0.0250571	+	0.125479i
$915$	11.7968	−	2.08009i	0.389990	−	0.0687657i
$916$	−11.7987	+	28.3643i	−0.389841	+	0.937183i
$917$	−15.0693	−	17.9588i	−0.497631	−	0.593053i
$918$	0.104258	−	4.61929i	0.00344102	−	0.152459i
$919$	7.51401	−	13.0147i	0.247864	−	0.429314i	−0.715069	−	0.699054i	$-0.753605\pi$
$919$	7.51401	−	13.0147i	0.247864	−	0.429314i	0.962933	+	0.269740i	$0.0869379\pi$
$920$	1.30227	+	0.874390i	0.0429345	+	0.0288278i
$921$	9.54801	−	3.47519i	0.314618	−	0.114511i
$922$	44.4016	−	24.3163i	1.46229	−	0.800814i
$923$	0.307281	−	0.177409i	0.0101143	−	0.00583948i
$924$	4.79540	−	21.4782i	0.157757	−	0.706582i
$925$	−11.8735	−	2.09362i	−0.390398	−	0.0688377i
$926$	9.44240	+	8.29330i	0.310297	+	0.272535i
$927$	11.7063	+	9.82273i	0.384485	+	0.322621i
$928$	2.20329	+	1.62825i	0.0723264	+	0.0534499i
$929$	9.27291	+	3.37506i	0.304234	+	0.110732i	0.489626	−	0.871932i	$-0.337133\pi$
$929$	9.27291	+	3.37506i	0.304234	+	0.110732i	−0.185392	+	0.982665i	$0.559355\pi$
$930$	−1.78715	−	11.6695i	−0.0586030	−	0.382657i
$931$	−2.57059	−	0.869145i	−0.0842477	−	0.0284851i
$932$	−26.4289	+	8.28947i	−0.865708	+	0.271530i
$933$	−3.04644	+	8.37002i	−0.0997358	+	0.274022i
$934$	11.6071	+	34.2780i	0.379798	+	1.12161i
$935$	26.9320	+	22.5986i	0.880769	+	0.739053i
$936$	0.981905	−	2.21801i	0.0320946	−	0.0724978i
$937$	−9.31439	+	52.8245i	−0.304288	+	1.72570i	0.322550	+	0.946552i	$0.395460\pi$
$937$	−9.31439	+	52.8245i	−0.304288	+	1.72570i	−0.626838	+	0.779150i	$0.715651\pi$
$938$	19.2045	−	49.2749i	0.627049	−	1.60888i
$939$	20.3423	−	11.7446i	0.663846	−	0.383272i
$940$	−19.7843	−	25.8636i	−0.645293	−	0.843578i
$941$	−6.38320	−	17.5377i	−0.208087	−	0.571713i	0.791115	−	0.611667i	$-0.209501\pi$
$941$	−6.38320	−	17.5377i	−0.208087	−	0.571713i	−0.999202	+	0.0399544i	$0.987279\pi$
$942$	7.40869	−	5.93698i	0.241388	−	0.193437i
$943$	−0.359695	+	0.623010i	−0.0117133	+	0.0202880i
$944$	36.1051	−	16.7045i	1.17512	−	0.543685i
$945$	−4.77764	+	4.00892i	−0.155417	+	0.130410i
$946$	−7.96590	+	13.1052i	−0.258994	+	0.426088i
$947$	17.8459	−	3.14672i	0.579914	−	0.102255i	0.124006	−	0.992281i	$-0.460426\pi$
$947$	17.8459	−	3.14672i	0.579914	−	0.102255i	0.455908	+	0.890027i	$0.349315\pi$
$948$	−1.08296	+	23.9790i	−0.0351731	+	0.778801i
$949$		−	9.19317i		−	0.298423i
$950$	6.36607	−	2.32034i	0.206543	−	0.0752818i
$951$	31.2218			1.01244
$952$	−2.48842	−	23.2037i	−0.0806503	−	0.752036i
$953$	6.29418	+	35.6960i	0.203888	+	1.15631i	0.899179	+	0.437580i	$0.144164\pi$
$953$	6.29418	+	35.6960i	0.203888	+	1.15631i	−0.695291	+	0.718728i	$0.744725\pi$
$954$	−7.10086	−	4.31619i	−0.229899	−	0.139742i
$955$	−25.7763	−	30.7190i	−0.834101	−	0.994043i
$956$	5.32810	+	40.9452i	0.172323	+	1.32426i
$957$	1.82750	+	1.05511i	0.0590747	+	0.0341068i
$958$	42.7321	−	34.2435i	1.38061	−	1.10636i
$959$	40.1505	−	14.6136i	1.29653	−	0.471898i
$960$	−6.02579	+	18.8159i	−0.194482	+	0.607280i
$961$	9.78731	+	16.9521i	0.315720	+	0.546843i
$962$	−12.3951	−	4.83088i	−0.399633	−	0.155754i
$963$	6.66321	+	1.17490i	0.214719	+	0.0378607i
$964$	−17.6410	+	27.5994i	−0.568178	+	0.888917i
$965$	13.7853	−	16.4287i	0.443765	−	0.528858i
$966$	−0.257221	−	0.759618i	−0.00827594	−	0.0244403i
$967$	−5.11016	−	1.85995i	−0.164332	−	0.0598118i	0.258544	−	0.965999i	$-0.416757\pi$
$967$	−5.11016	−	1.85995i	−0.164332	−	0.0598118i	−0.422876	+	0.906188i	$0.638979\pi$
$968$	−9.94376	−	20.2788i	−0.319605	−	0.651785i
$969$	12.1661	−	7.40264i	0.390831	−	0.237807i
$970$	−10.4243	+	1.59646i	−0.334705	+	0.0512592i
$971$	1.67046	−	4.58956i	0.0536078	−	0.147286i	−0.909999	−	0.414611i	$-0.863918\pi$
$971$	1.67046	−	4.58956i	0.0536078	−	0.147286i	0.963606	+	0.267325i	$0.0861398\pi$
$972$	1.77540	−	0.920837i	0.0569461	−	0.0295358i
$973$	−28.6780	+	34.1772i	−0.919376	+	1.09567i
$974$	−24.9599	−	21.9224i	−0.799767	−	0.702438i
$975$	0.163688	−	0.928319i	0.00524220	−	0.0297300i
$976$	−19.3327	+	1.63300i	−0.618826	+	0.0522710i
$977$	−11.5140	−	19.9428i	−0.368364	−	0.638026i	0.620946	−	0.783854i	$-0.286749\pi$
$977$	−11.5140	−	19.9428i	−0.368364	−	0.638026i	−0.989310	+	0.145828i	$0.953415\pi$
$978$	13.3369	+	24.3531i	0.426466	+	0.778728i
$979$	−18.8973	−	51.9198i	−0.603959	−	1.65936i
$980$	2.08075	−	2.26391i	0.0664670	−	0.0723180i
$981$	−10.2288	−	5.90560i	−0.326581	−	0.188551i
$982$	−0.126505	+	5.60498i	−0.00403693	+	0.178862i
$983$	39.8179	−	33.4112i	1.26999	−	1.06565i	0.275453	−	0.961315i	$-0.411172\pi$
$983$	39.8179	−	33.4112i	1.26999	−	1.06565i	0.994542	−	0.104338i	$-0.0332722\pi$
$984$	−8.79657	−	2.17349i	−0.280425	−	0.0692882i
$985$	6.69597	+	37.9747i	0.213351	+	1.20997i
$986$	2.19439	+	0.438202i	0.0698837	+	0.0139552i
$987$			16.6488i			0.529937i
$988$	7.38962	−	1.13514i	0.235095	−	0.0361137i
$989$			0.558890i			0.0177717i
$990$	−2.98008	+	14.9234i	−0.0947130	+	0.474296i
$991$	−5.27584	−	29.9208i	−0.167593	−	0.950465i	−0.946351	−	0.323141i	$-0.895261\pi$
$991$	−5.27584	−	29.9208i	−0.167593	−	0.950465i	0.778758	−	0.627324i	$-0.215850\pi$
$992$	1.17905	+	19.0846i	0.0374349	+	0.605937i
$993$	14.1100	−	11.8397i	0.447766	−	0.375720i
$994$	1.47725	+	0.0333416i	0.0468555	+	0.00105753i
$995$	−44.6183	−	25.7604i	−1.41450	−	0.816659i
$996$	−9.24911	−	8.50080i	−0.293069	−	0.269358i
$997$	−2.05862	−	5.65600i	−0.0651970	−	0.179127i	0.902816	−	0.430027i	$-0.141496\pi$
$997$	−2.05862	−	5.65600i	−0.0651970	−	0.179127i	−0.968013	+	0.250899i	$0.919274\pi$
$998$	36.9182	−	20.2180i	1.16862	−	0.639990i
$999$	−5.48443	−	9.49931i	−0.173520	−	0.300545i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.bk.a.61.18	✓	240
8.5	even	2	inner	456.2.bk.a.61.27	yes	240
19.5	even	9	inner	456.2.bk.a.157.27	yes	240
152.5	even	18	inner	456.2.bk.a.157.18	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bk.a.61.18	✓	240	1.1	even	1	trivial
456.2.bk.a.61.27	yes	240	8.5	even	2	inner
456.2.bk.a.157.18	yes	240	152.5	even	18	inner
456.2.bk.a.157.27	yes	240	19.5	even	9	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:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bk (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.276939 + 1.38683i) q^{2} +(-0.984808 + 0.173648i) q^{3} +(-1.84661 - 0.768136i) q^{4} +(1.58746 + 1.89186i) q^{5} +(0.0319107 - 1.41385i) q^{6} +(1.26268 - 2.18703i) q^{7} +(1.57667 - 2.34821i) q^{8} +(0.939693 - 0.342020i) q^{9} +(-3.06333 + 1.67761i) q^{10} +(3.77345 - 2.17860i) q^{11} +(1.95194 + 0.435806i) q^{12} +(0.844562 + 0.148919i) q^{13} +(2.68336 + 2.35680i) q^{14} +(-1.89186 - 1.58746i) q^{15} +(2.81993 + 2.83690i) q^{16} +(3.07013 + 1.11744i) q^{17} +(0.214087 + 1.39792i) q^{18} +(-3.27373 + 2.87797i) q^{19} +(-1.47821 - 4.71292i) q^{20} +(-0.863726 + 2.37307i) q^{21} +(1.97634 + 5.83648i) q^{22} +(0.172021 + 0.144343i) q^{23} +(-1.14496 + 2.58632i) q^{24} +(-0.190869 + 1.08247i) q^{25} +(-0.440418 + 1.13002i) q^{26} +(-0.866025 + 0.500000i) q^{27} +(-4.01162 + 3.06868i) q^{28} +(-0.165642 - 0.455099i) q^{29} +(2.72547 - 2.18407i) q^{30} +(1.69007 - 2.92729i) q^{31} +(-4.71525 + 3.12513i) q^{32} +(-3.33781 + 2.80075i) q^{33} +(-2.39994 + 3.94829i) q^{34} +(6.14202 - 1.08300i) q^{35} +(-1.99796 - 0.0902342i) q^{36} +10.9689i q^{37} +(-3.08464 - 5.33714i) q^{38} -0.857590 q^{39} +(6.94540 - 0.744843i) q^{40} +(0.556297 + 3.15492i) q^{41} +(-3.05185 - 1.85504i) q^{42} +(1.59980 + 1.90657i) q^{43} +(-8.64154 + 1.12450i) q^{44} +(2.13878 + 1.23483i) q^{45} +(-0.247819 + 0.198590i) q^{46} +(6.19504 - 2.25481i) q^{47} +(-3.26971 - 2.30412i) q^{48} +(0.311265 + 0.539127i) q^{49} +(-1.44835 - 0.564483i) q^{50} +(-3.21753 - 0.567337i) q^{51} +(-1.44519 - 0.923733i) q^{52} +(-3.77694 + 4.50118i) q^{53} +(-0.453580 - 1.33950i) q^{54} +(10.1118 + 3.68040i) q^{55} +(-3.14477 - 6.41328i) q^{56} +(2.72424 - 3.40272i) q^{57} +(0.677018 - 0.103684i) q^{58} +(3.40158 - 9.34575i) q^{59} +(2.27414 + 4.38463i) q^{60} +(-3.11777 + 3.71562i) q^{61} +(3.59162 + 3.15453i) q^{62} +(0.438525 - 2.48700i) q^{63} +(-3.02819 - 7.40473i) q^{64} +(1.05897 + 1.83420i) q^{65} +(-2.95981 - 5.40462i) q^{66} +(-5.06461 - 13.9149i) q^{67} +(-4.81099 - 4.42175i) q^{68} +(-0.194473 - 0.112279i) q^{69} +(-0.199020 + 8.81788i) q^{70} +(0.316942 - 0.265946i) q^{71} +(0.678454 - 2.74585i) q^{72} +(-1.86147 - 10.5569i) q^{73} +(-15.2120 - 3.03771i) q^{74} -1.09917i q^{75} +(8.25597 - 2.79981i) q^{76} -11.0035i q^{77} +(0.237500 - 1.18933i) q^{78} +(2.08407 + 11.8194i) q^{79} +(-0.890480 + 9.83838i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-4.52940 - 0.102229i) q^{82} +(-5.43961 - 3.14056i) q^{83} +(3.41780 - 3.71867i) q^{84} +(2.75968 + 7.58215i) q^{85} +(-3.08714 + 1.69065i) q^{86} +(0.242153 + 0.419421i) q^{87} +(0.833683 - 12.2958i) q^{88} +(2.20196 - 12.4879i) q^{89} +(-2.30481 + 2.62416i) q^{90} +(1.39210 - 1.65904i) q^{91} +(-0.206781 - 0.398680i) q^{92} +(-1.15608 + 3.17630i) q^{93} +(1.41140 + 9.21593i) q^{94} +(-10.6416 - 1.62478i) q^{95} +(4.10094 - 3.89645i) q^{96} +(2.83738 + 1.03272i) q^{97} +(-0.833881 + 0.282368i) q^{98} +(2.80075 - 3.33781i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48}+ \cdots - 12 q^{98}+O(q^{100}) \) 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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