LMFDB - Embedded newform 456.2.bk.a.61.27

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			61.27
Character	$\chi$	$=$	456.61
Dual form			456.2.bk.a.157.27

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.679291 - 1.24039i) q^{2} +(0.984808 - 0.173648i) q^{3} +(-1.07713 - 1.68517i) q^{4} +(-1.58746 - 1.89186i) q^{5} +(0.453580 - 1.33950i) q^{6} +(1.26268 - 2.18703i) q^{7} +(-2.82195 + 0.191334i) q^{8} +(0.939693 - 0.342020i) q^{9} +(-3.42499 + 0.683943i) q^{10} +(-3.77345 + 2.17860i) q^{11} +(-1.35339 - 1.47253i) q^{12} +(-0.844562 - 0.148919i) q^{13} +(-1.85504 - 3.05185i) q^{14} +(-1.89186 - 1.58746i) q^{15} +(-1.67960 + 3.63028i) 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} +(0.139042 + 6.16044i) q^{22} +(0.172021 + 0.144343i) q^{23} +(-2.74585 + 0.678454i) q^{24} +(-0.190869 + 1.08247i) q^{25} +(-0.758421 + 0.946425i) q^{26} +(0.866025 - 0.500000i) q^{27} +(-5.04559 + 0.227874i) q^{28} +(0.165642 + 0.455099i) q^{29} +(-3.25419 + 1.26830i) q^{30} +(1.69007 - 2.92729i) q^{31} +(3.36203 + 4.54937i) q^{32} +(-3.33781 + 2.80075i) q^{33} +(3.47157 - 3.04909i) q^{34} +(-6.14202 + 1.08300i) q^{35} +(-1.58853 - 1.21514i) q^{36} -10.9689i q^{37} +(-1.34598 - 6.01567i) q^{38} -0.857590 q^{39} +(4.84171 + 5.03500i) q^{40} +(0.556297 + 3.15492i) q^{41} +(-2.35680 - 2.68336i) q^{42} +(-1.59980 - 1.90657i) q^{43} +(7.73579 + 4.01227i) q^{44} +(-2.13878 - 1.23483i) q^{45} +(0.295894 - 0.115322i) q^{46} +(6.19504 - 2.25481i) q^{47} +(-1.02369 + 3.86679i) q^{48} +(0.311265 + 0.539127i) q^{49} +(1.21303 + 0.972067i) q^{50} +(3.21753 + 0.567337i) q^{51} +(0.658746 + 1.58363i) q^{52} +(3.77694 - 4.50118i) q^{53} +(-0.0319107 - 1.41385i) 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} +(-0.637366 + 4.89801i) q^{60} +(3.11777 - 3.71562i) q^{61} +(-2.48293 - 4.08483i) q^{62} +(0.438525 - 2.48700i) q^{63} +(7.92678 - 1.07987i) q^{64} +(1.05897 + 1.83420i) q^{65} +(1.20668 + 6.04271i) q^{66} +(5.06461 + 13.9149i) q^{67} +(-1.42385 - 6.37731i) q^{68} +(0.194473 + 0.112279i) q^{69} +(-2.82887 + 8.35416i) q^{70} +(0.316942 - 0.265946i) q^{71} +(-2.58632 + 1.14496i) q^{72} +(-1.86147 - 10.5569i) q^{73} +(-13.6056 - 7.45105i) q^{74} +1.09917i q^{75} +(-8.37609 - 2.41685i) q^{76} +11.0035i q^{77} +(-0.582554 + 1.06375i) q^{78} +(2.08407 + 11.8194i) q^{79} +(9.53429 - 2.58537i) q^{80} +(0.766044 - 0.642788i) q^{81} +(4.29121 + 1.45308i) q^{82} +(5.43961 + 3.14056i) q^{83} +(-4.92936 + 1.10057i) q^{84} +(-2.75968 - 7.58215i) q^{85} +(-3.45162 + 0.689260i) q^{86} +(0.242153 + 0.419421i) q^{87} +(10.2316 - 6.86989i) q^{88} +(2.20196 - 12.4879i) q^{89} +(-2.98452 + 1.81411i) q^{90} +(-1.39210 + 1.65904i) q^{91} +(0.0579537 - 0.445360i) 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} +(0.880167 - 0.0198654i) 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 $

$2$	0.679291	−	1.24039i	0.480331	−	0.877087i
$2$	0.679291	−	1.24039i	0.480331	−	0.877087i
$3$	0.984808	−	0.173648i	0.568579	−	0.100256i
$3$	0.984808	−	0.173648i	0.568579	−	0.100256i
$4$	−1.07713	−	1.68517i	−0.538563	−	0.842585i
$5$	−1.58746	−	1.89186i	−0.709934	−	0.846066i	0.283678	−	0.958920i	$-0.408445\pi$
$5$	−1.58746	−	1.89186i	−0.709934	−	0.846066i	−0.993612	+	0.112853i	$0.964001\pi$
$6$	0.453580	−	1.33950i	0.185173	−	0.546849i
$7$	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	$0.00830059\pi$
$8$	−2.82195	+	0.191334i	−0.997709	+	0.0676470i
$9$	0.939693	−	0.342020i	0.313231	−	0.114007i
$10$	−3.42499	+	0.683943i	−1.08308	+	0.216282i
$11$	−3.77345	+	2.17860i	−1.13774	+	0.656873i	−0.945869	−	0.324548i	$-0.894788\pi$
$11$	−3.77345	+	2.17860i	−1.13774	+	0.656873i	−0.191868	+	0.981421i	$0.561454\pi$
$12$	−1.35339	−	1.47253i	−0.390690	−	0.425082i
$13$	−0.844562	−	0.148919i	−0.234239	−	0.0413027i	0.0552962	−	0.998470i	$-0.482390\pi$
$13$	−0.844562	−	0.148919i	−0.234239	−	0.0413027i	−0.289535	+	0.957167i	$0.593501\pi$
$14$	−1.85504	−	3.05185i	−0.495780	−	0.815641i
$15$	−1.89186	−	1.58746i	−0.488477	−	0.409881i
$16$	−1.67960	+	3.63028i	−0.419899	+	0.907571i
$17$	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
$22$	0.139042	+	6.16044i	0.0296438	+	1.31341i
$23$	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	$0.714769\pi$
$24$	−2.74585	+	0.678454i	−0.560495	+	0.138489i
$25$	−0.190869	+	1.08247i	−0.0381739	+	0.216495i
$26$	−0.758421	+	0.946425i	−0.148739	+	0.185609i
$27$	0.866025	−	0.500000i	0.166667	−	0.0962250i
$28$	−5.04559	+	0.227874i	−0.953526	+	0.0430642i
$29$	0.165642	+	0.455099i	0.0307590	+	0.0845097i	0.954122	−	0.299419i	$-0.0967930\pi$
$29$	0.165642	+	0.455099i	0.0307590	+	0.0845097i	−0.923363	+	0.383929i	$0.874571\pi$
$30$	−3.25419	+	1.26830i	−0.594132	+	0.231558i
$31$	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	$0.0684961\pi$
$32$	3.36203	+	4.54937i	0.594328	+	0.804223i
$33$	−3.33781	+	2.80075i	−0.581038	+	0.487549i
$34$	3.47157	−	3.04909i	0.595369	−	0.522915i
$35$	−6.14202	+	1.08300i	−1.03819	+	0.183061i
$36$	−1.58853	−	1.21514i	−0.264755	−	0.202524i
$37$		−	10.9689i		−	1.80327i	−0.432499	−	0.901635i	$-0.642368\pi$
$37$		−	10.9689i		−	1.80327i	0.432499	−	0.901635i	$-0.357632\pi$
$38$	−1.34598	−	6.01567i	−0.218347	−	0.975871i
$39$	−0.857590			−0.137324
$40$	4.84171	+	5.03500i	0.765542	+	0.796103i
$41$	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	$0.863962\pi$
$42$	−2.35680	−	2.68336i	−0.363663	−	0.414051i
$43$	−1.59980	−	1.90657i	−0.243968	−	0.290749i	0.630140	−	0.776481i	$-0.282997\pi$
$43$	−1.59980	−	1.90657i	−0.243968	−	0.290749i	−0.874108	+	0.485732i	$0.838553\pi$
$44$	7.73579	+	4.01227i	1.16621	+	0.604872i
$45$	−2.13878	−	1.23483i	−0.318830	−	0.184077i
$46$	0.295894	−	0.115322i	0.0436271	−	0.0170033i
$47$	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	$0.229229\pi$
$48$	−1.02369	+	3.86679i	−0.147756	+	0.558123i
$49$	0.311265	+	0.539127i	0.0444665	+	0.0770182i
$50$	1.21303	+	0.972067i	0.171549	+	0.137471i
$51$	3.21753	+	0.567337i	0.450544	+	0.0794431i
$52$	0.658746	+	1.58363i	0.0913516	+	0.219611i
$53$	3.77694	−	4.50118i	0.518802	−	0.618284i	−0.441495	−	0.897264i	$-0.645552\pi$
$53$	3.77694	−	4.50118i	0.518802	−	0.618284i	0.960297	+	0.278980i	$0.0899962\pi$
$54$	−0.0319107	−	1.41385i	−0.00434250	−	0.192401i
$55$	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	$0.335255\pi$
$59$	−3.40158	+	9.34575i	−0.442847	+	1.21671i	−0.937611	+	0.347686i	$0.886968\pi$
$60$	−0.637366	+	4.89801i	−0.0822836	+	0.632330i
$61$	3.11777	−	3.71562i	0.399190	−	0.475736i	−0.528583	−	0.848882i	$-0.677276\pi$
$61$	3.11777	−	3.71562i	0.399190	−	0.475736i	0.927773	+	0.373146i	$0.121721\pi$
$62$	−2.48293	−	4.08483i	−0.315332	−	0.518774i
$63$	0.438525	−	2.48700i	0.0552490	−	0.313332i
$64$	7.92678	−	1.07987i	0.990848	−	0.134984i
$65$	1.05897	+	1.83420i	0.131350	+	0.227504i
$66$	1.20668	+	6.04271i	0.148532	+	0.743806i
$67$	5.06461	+	13.9149i	0.618740	+	1.69997i	0.710050	+	0.704152i	$0.248673\pi$
$67$	5.06461	+	13.9149i	0.618740	+	1.69997i	−0.0913095	+	0.995823i	$0.529105\pi$
$68$	−1.42385	−	6.37731i	−0.172667	−	0.773363i
$69$	0.194473	+	0.112279i	0.0234117	+	0.0135168i
$70$	−2.82887	+	8.35416i	−0.338115	+	0.998513i
$71$	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	$0.269962\pi$
$72$	−2.58632	+	1.14496i	−0.304801	+	0.134935i
$73$	−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	$-0.271407\pi$
$74$	−13.6056	−	7.45105i	−1.58162	−	0.866167i
$75$			1.09917i			0.126922i
$76$	−8.37609	−	2.41685i	−0.960803	−	0.277232i
$77$			11.0035i			1.25397i
$78$	−0.582554	+	1.06375i	−0.0659612	+	0.120445i
$79$	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	$0.708524\pi$
$80$	9.53429	−	2.58537i	1.06597	−	0.289053i
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$	4.29121	+	1.45308i	0.473885	+	0.160466i
$83$	5.43961	+	3.14056i	0.597074	+	0.344721i	0.767890	−	0.640582i	$-0.221307\pi$
$83$	5.43961	+	3.14056i	0.597074	+	0.344721i	−0.170815	+	0.985303i	$0.554640\pi$
$84$	−4.92936	+	1.10057i	−0.537838	+	0.120082i
$85$	−2.75968	−	7.58215i	−0.299329	−	0.822399i
$86$	−3.45162	+	0.689260i	−0.372198	+	0.0743248i
$87$	0.242153	+	0.419421i	0.0259615	+	0.0449667i
$88$	10.2316	−	6.86989i	1.09070	−	0.732333i
$89$	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	$-0.179039\pi$
$90$	−2.98452	+	1.81411i	−0.314596	+	0.191224i
$91$	−1.39210	+	1.65904i	−0.145932	+	0.173915i
$92$	0.0579537	−	0.445360i	0.00604209	−	0.0464320i
$93$	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	$0.562124\pi$
$98$	0.880167	−	0.0198654i	0.0889103	−	0.00200671i
$99$	−2.80075	+	3.33781i	−0.281486	+	0.335462i
$100$	2.02974	−	0.844314i	0.202974	−	0.0844314i
$101$	−8.82088	−	1.55536i	−0.877710	−	0.154764i	−0.283402	−	0.959001i	$-0.591463\pi$
$101$	−8.82088	−	1.55536i	−0.877710	−	0.154764i	−0.594308	+	0.804237i	$0.702574\pi$
$102$	2.88936	−	3.60560i	0.286089	−	0.357007i
$103$	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	$0.562005\pi$
$104$	2.41180	+	0.258648i	0.236497	+	0.0253625i
$105$	−5.86065	+	2.13310i	−0.571940	+	0.208169i
$106$	−3.01757	−	7.74248i	−0.293092	−	0.752016i
$107$	−5.85953	−	3.38300i	−0.566462	−	0.327047i	0.189273	−	0.981924i	$-0.439387\pi$
$107$	−5.85953	−	3.38300i	−0.566462	−	0.327047i	−0.755735	+	0.654878i	$0.772720\pi$
$108$	−1.77540	−	0.920837i	−0.170838	−	0.0886075i
$109$	7.59210	+	9.04791i	0.727191	+	0.866633i	0.995308	−	0.0967536i	$-0.0308459\pi$
$109$	7.59210	+	9.04791i	0.727191	+	0.866633i	−0.268117	+	0.963386i	$0.586401\pi$
$110$	11.4340	−	10.0425i	1.09019	−	0.957516i
$111$	−1.90472	−	10.8022i	−0.180788	−	1.02530i
$112$	5.81874	+	8.25722i	0.549820	+	0.780234i
$113$	−13.3230			−1.25332			−0.626662	−	0.779291i	$-0.715579\pi$
$113$	−13.3230			−1.25332			−0.626662	+	0.779291i	$0.715579\pi$
$114$	−2.37014	−	5.69055i	−0.221984	−	0.532969i
$115$		−	0.554579i		−	0.0517147i
$116$	0.588501	−	0.769334i	0.0546409	−	0.0714309i
$117$	−0.844562	+	0.148919i	−0.0780797	+	0.0137676i
$118$	9.28170	+	10.5678i	0.854450	+	0.972841i
$119$	6.32047	−	5.30350i	0.579396	−	0.486171i
$120$	5.64247	+	4.11775i	0.515085	+	0.375898i
$121$	3.99260	−	6.91539i	0.362964	−	0.628672i
$122$	−2.49093	−	6.39124i	−0.225518	−	0.578635i
$123$	1.09569	+	3.01039i	0.0987952	+	0.271437i
$124$	−6.75341	+	0.305005i	−0.606474	+	0.0273902i
$125$	−8.34301	+	4.81684i	−0.746222	+	0.430831i
$126$	−2.78696	−	2.23334i	−0.248282	−	0.198962i
$127$	−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	$0.0908416\pi$
$128$	4.04513	−	10.5658i	0.357543	−	0.933897i
$129$	−1.90657	−	1.59980i	−0.167864	−	0.140855i
$130$	2.99447	−	0.0675853i	0.262632	−	0.00592762i
$131$	−3.17506	+	8.72340i	−0.277406	+	0.762167i	0.720248	+	0.693716i	$0.244028\pi$
$131$	−3.17506	+	8.72340i	−0.277406	+	0.762167i	−0.997654	+	0.0684509i	$0.978194\pi$
$132$	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
$136$	−8.87755	−	2.56592i	−0.761244	−	0.220026i
$137$	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	$0.465098\pi$
$138$	0.271373	−	0.164951i	0.0231008	−	0.0140416i
$139$	17.3984	+	3.06781i	1.47571	+	0.260208i	0.852864	−	0.522134i	$-0.174864\pi$
$139$	17.3984	+	3.06781i	1.47571	+	0.260208i	0.622850	+	0.782342i	$0.285975\pi$
$140$	8.44078	+	9.18381i	0.713376	+	0.776174i
$141$	5.70938	−	3.29631i	0.480816	−	0.277600i
$142$	−0.114580	−	0.573785i	−0.00961536	−	0.0481510i
$143$	3.51134	−	1.27802i	0.293633	−	0.106874i
$144$	−0.336673	+	3.98581i	−0.0280561	+	0.332151i
$145$	0.598033	−	1.03582i	0.0496639	−	0.0860204i
$146$	−14.3592	−	4.86228i	−1.18837	−	0.402405i
$147$	0.400155	+	0.476886i	0.0330042	+	0.0393329i
$148$	−18.4844	+	11.8149i	−1.51941	+	0.971175i
$149$	1.59112	−	0.280558i	0.130350	−	0.0229842i	−0.108092	−	0.994141i	$-0.534474\pi$
$149$	1.59112	−	0.280558i	0.130350	−	0.0229842i	0.238442	+	0.971157i	$0.423363\pi$
$150$	1.36340	+	0.746658i	0.111321	+	0.0609644i
$151$	−18.7457			−1.52550			−0.762751	−	0.646692i	$-0.776152\pi$
$151$	−18.7457			−1.52550			−0.762751	+	0.646692i	$0.776152\pi$
$152$	−8.68764	+	8.74785i	−0.704661	+	0.709545i
$153$	3.26716			0.264135
$154$	13.6486	+	7.47460i	1.09984	+	0.602320i
$155$	−8.22095	+	1.44958i	−0.660323	+	0.116433i
$156$	0.923733	+	1.44519i	0.0739579	+	0.115707i
$157$	−4.31522	−	5.14268i	−0.344392	−	0.410430i	0.565849	−	0.824509i	$-0.308548\pi$
$157$	−4.31522	−	5.14268i	−0.344392	−	0.410430i	−0.910241	+	0.414078i	$0.864104\pi$
$158$	16.0763	+	5.44373i	1.27896	+	0.433080i
$159$	2.93793	−	5.08865i	0.232993	−	0.403556i
$160$	3.26970	−	13.5824i	0.258492	−	1.07379i
$161$	0.532890	−	0.193956i	0.0419976	−	0.0152859i
$162$	−0.276939	−	1.38683i	−0.0217584	−	0.108960i
$163$	17.0031	−	9.81674i	1.33179	−	0.768907i	0.346212	−	0.938156i	$-0.387468\pi$
$163$	17.0031	−	9.81674i	1.33179	−	0.768907i	0.985573	+	0.169250i	$0.0541344\pi$
$164$	4.71737	−	4.33570i	0.368365	−	0.338561i
$165$	10.5973	+	1.86859i	0.824997	+	0.145469i
$166$	7.59059	−	4.61387i	0.589144	−	0.358106i
$167$	−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	$0.724890\pi$
$168$	−1.98334	+	6.86193i	−0.153018	+	0.529410i
$169$	−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	$-0.689333\pi$
$173$	5.27824	−	14.5018i	0.401297	−	1.10255i	0.961645	−	0.274297i	$-0.0884451\pi$
$174$	0.684737	−	0.0154546i	0.0519098	−	0.00117161i
$175$	2.12640	+	1.78426i	0.160740	+	0.134877i
$176$	−1.57107	−	17.3578i	−0.118424	−	1.30840i
$177$	−1.72703	+	9.79445i	−0.129811	+	0.736196i
$178$	−13.9941	−	11.2142i	−1.04890	−	0.840543i
$179$	16.4466	−	9.49547i	1.22928	−	0.709724i	0.262400	−	0.964959i	$-0.415486\pi$
$179$	16.4466	−	9.49547i	1.22928	−	0.709724i	0.966879	+	0.255235i	$0.0821528\pi$
$180$	0.222847	+	4.93427i	0.0166100	+	0.367779i
$181$	7.75061	+	21.2946i	0.576098	+	1.58282i	0.794700	+	0.607003i	$0.207628\pi$
$181$	7.75061	+	21.2946i	0.576098	+	1.58282i	−0.218601	+	0.975814i	$0.570149\pi$
$182$	1.11222	+	2.85372i	0.0824429	+	0.211532i
$183$	2.42520	−	4.20056i	0.179276	−	0.310515i
$184$	−0.513052	−	0.374414i	−0.0378227	−	0.0276022i
$185$	−20.7516	+	17.4126i	−1.52569	+	1.28020i
$186$	−3.15453	−	3.59162i	−0.231301	−	0.263350i
$187$	−14.0194	+	2.47200i	−1.02520	+	0.180771i
$188$	−10.4726	−	8.01098i	−0.763792	−	0.584261i
$189$		−	2.52537i		−	0.183693i
$190$	−9.24413	+	12.0961i	−0.670640	+	0.877540i
$191$	−16.2374			−1.17490			−0.587450	−	0.809261i	$-0.699868\pi$
$191$	−16.2374			−1.17490			−0.587450	+	0.809261i	$0.699868\pi$
$192$	7.61884	−	2.43994i	0.549842	−	0.176087i
$193$	−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	$-0.156735\pi$
$194$	3.20838	−	2.81793i	0.230348	−	0.202316i
$195$	1.36139	+	1.62244i	0.0974912	+	0.116186i
$196$	0.573249	−	1.10524i	0.0409464	−	0.0789460i
$197$	−13.5219	−	7.80688i	−0.963396	−	0.556217i	−0.0661797	−	0.997808i	$-0.521081\pi$
$197$	−13.5219	−	7.80688i	−0.963396	−	0.556217i	−0.897217	+	0.441591i	$0.854414\pi$
$198$	2.23765	+	5.74137i	0.159023	+	0.408021i
$199$	−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	$0.653788\pi$
$200$	0.331509	−	3.09120i	0.0234412	−	0.218581i
$201$	7.40396	+	12.8240i	0.522235	+	0.904537i
$202$	−7.92119	+	9.88477i	−0.557333	+	0.695490i
$203$	1.20447	+	0.212380i	0.0845371	+	0.0149062i
$204$	−2.50963	−	6.03318i	−0.175709	−	0.422407i
$205$	5.08557	−	6.06074i	0.355191	−	0.423301i
$206$	21.6057	−	0.487643i	1.50534	−	0.0339757i
$207$	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	$0.306111\pi$
$211$	−5.71339	+	15.6974i	−0.393326	+	1.08065i	−0.965473	+	0.260503i	$0.916111\pi$
$212$	−11.6535	−	1.51644i	−0.800365	−	0.104150i
$213$	0.265946	−	0.316942i	0.0182223	−	0.0217165i
$214$	−8.17656	+	4.97005i	−0.558938	+	0.339745i
$215$	−1.06734	+	6.05321i	−0.0727923	+	0.412825i
$216$	−2.34821	+	1.57667i	−0.159776	+	0.107279i
$217$	−4.26805	−	7.39248i	−0.289734	−	0.501834i
$218$	16.3802	−	3.27099i	1.10941	−	0.221539i
$219$	−3.66638	−	10.0733i	−0.247751	−	0.680690i
$220$	−4.68961	−	21.0044i	−0.316173	−	1.41611i
$221$	−2.42651	−	1.40094i	−0.163224	−	0.0942377i
$222$	−14.6928	−	4.97526i	−0.986117	−	0.333917i
$223$	−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	$0.516787\pi$
$224$	14.1948	−	1.60844i	0.948429	−	0.107469i
$225$	0.190869	+	1.08247i	0.0127246	+	0.0721649i
$226$	−9.05021	+	16.5257i	−0.602011	+	1.09927i
$227$			0.316720i			0.0210214i	0.999945	+	0.0105107i	$0.00334573\pi$
$227$			0.316720i			0.0210214i	−0.999945	+	0.0105107i	$0.996654\pi$
$228$	−8.66852	−	0.925644i	−0.574087	−	0.0613023i
$229$			15.3602i			1.01503i	0.861643	+	0.507516i	$0.169436\pi$
$229$			15.3602i			1.01503i	−0.861643	+	0.507516i	$0.830564\pi$
$230$	−0.687893	−	0.376720i	−0.0453583	−	0.0248402i
$231$	1.91074	+	10.8364i	0.125718	+	0.712980i
$232$	−0.554510	−	1.25257i	−0.0364054	−	0.0822353i
$233$	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	$0.127901\pi$
$234$	−0.388986	+	1.14874i	−0.0254288	+	0.0750957i
$235$	−14.1002	−	8.14074i	−0.919794	−	0.531043i
$236$	19.4131	−	4.33433i	1.26369	−	0.282141i
$237$	4.10482	+	11.2779i	0.266637	+	0.732579i
$238$	−2.28496	−	11.4425i	−0.148112	−	0.741704i
$239$	−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	$-0.399394\pi$
$240$	8.94049	−	4.20170i	0.577106	−	0.271219i
$241$	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	$-0.121313\pi$
$242$	−5.86563	−	9.64994i	−0.377057	−	0.620321i
$243$	0.642788	−	0.766044i	0.0412348	−	0.0491418i
$244$	−9.61968	−	1.25179i	−0.615837	−	0.0801374i
$245$	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
$250$	0.307418	+	13.6206i	0.0194428	+	0.861443i
$251$	−15.7380	+	18.7558i	−0.993374	+	1.18386i	−0.0104308	+	0.999946i	$0.503320\pi$
$251$	−15.7380	+	18.7558i	−0.993374	+	1.18386i	−0.982943	+	0.183911i	$0.941124\pi$
$252$	−4.66336	+	1.93982i	−0.293764	+	0.122197i
$253$	−0.963578	−	0.169905i	−0.0605796	−	0.0106818i
$254$	2.75170	+	2.20508i	0.172657	+	0.138359i
$255$	−4.03438	−	6.98775i	−0.252642	−	0.437590i
$256$	−10.3579	−	12.1948i	−0.647370	−	0.762176i
$257$	−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	$0.454680\pi$
$258$	−3.27949	+	1.27816i	−0.204172	+	0.0795745i
$259$	−23.9892	−	13.8502i	−1.49062	−	0.860609i
$260$	1.95028	−	3.76021i	0.120951	−	0.233199i
$261$	0.311306	+	0.371000i	0.0192693	+	0.0229643i
$262$	8.66362	+	9.86404i	0.535240	+	0.609402i
$263$	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	$0.644270\pi$
$264$	8.88324	−	8.54222i	0.546726	−	0.525737i
$265$	−14.5113			−0.891425
$266$	−14.8560	−	4.65218i	−0.910880	−	0.285244i
$267$		−	12.6806i		−	0.776040i
$268$	17.9937	−	23.5228i	1.09914	−	1.43689i
$269$	−8.98328	+	1.58399i	−0.547720	+	0.0965778i	−0.440659	−	0.897675i	$-0.645255\pi$
$269$	−8.98328	+	1.58399i	−0.547720	+	0.0965778i	−0.107061	+	0.994252i	$0.534144\pi$
$270$	−2.62416	+	2.30481i	−0.159701	+	0.140266i
$271$	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	$0.268256\pi$
$272$	−9.21319	+	9.26860i	−0.558631	+	0.561992i
$273$	−1.08286	+	1.87558i	−0.0655379	+	0.113515i
$274$	22.2941	−	8.68893i	1.34683	−	0.524918i
$275$	−1.63804	−	4.50048i	−0.0987777	−	0.271389i
$276$	−0.0202628	−	0.448658i	−0.00121968	−	0.0270060i
$277$	−12.0878	+	6.97888i	−0.726284	+	0.419320i	−0.817061	−	0.576551i	$-0.804398\pi$
$277$	−12.0878	+	6.97888i	−0.726284	+	0.419320i	0.0907769	+	0.995871i	$0.471065\pi$
$278$	15.6239	−	19.4968i	0.937057	−	1.16934i
$279$	0.586956	−	3.32879i	0.0351401	−	0.199290i
$280$	17.1252	−	4.23136i	1.02343	−	0.252872i
$281$	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	$0.311108\pi$
$282$	−0.210376	−	9.32100i	−0.0125277	−	0.555058i
$283$	1.69472	−	4.65620i	0.100740	−	0.276782i	−0.879076	−	0.476682i	$-0.841839\pi$
$283$	1.69472	−	4.65620i	0.100740	−	0.276782i	0.979816	+	0.199900i	$0.0640616\pi$
$284$	−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
$288$	4.71525	+	3.12513i	0.277849	+	0.184150i
$289$	−4.84572	−	4.06604i	−0.285042	−	0.239179i
$290$	−0.878585	−	1.44542i	−0.0515923	−	0.0848779i
$291$	2.97360	+	0.524326i	0.174316	+	0.0307365i
$292$	−15.7852	+	14.5080i	−0.923756	+	0.849018i
$293$	−3.75889	+	2.17020i	−0.219597	+	0.126784i	−0.605764	−	0.795645i	$-0.707132\pi$
$293$	−3.75889	+	2.17020i	−0.219597	+	0.126784i	0.386167	+	0.922429i	$0.373799\pi$
$294$	0.863346	−	0.172403i	0.0503514	−	0.0100548i
$295$	23.0807	−	8.40070i	1.34381	−	0.489108i
$296$	2.09872	+	30.9535i	0.121986	+	1.79914i
$297$	−2.17860	+	3.77345i	−0.126415	+	0.218958i
$298$	0.732836	−	2.16419i	0.0424520	−	0.125368i
$299$	−0.123787	−	0.147524i	−0.00715879	−	0.00853151i
$300$	1.85229	−	1.18395i	0.106942	−	0.0683553i
$301$	−6.18977	+	1.09142i	−0.356772	+	0.0629086i
$302$	−12.7338	+	23.2519i	−0.732747	+	1.33800i
$303$	−8.95695			−0.514564
$304$	4.94930	+	16.7184i	0.283862	+	0.958865i
$305$	−11.9788			−0.685903
$306$	2.21936	−	4.05255i	0.126872	−	0.231669i
$307$	10.0064	−	1.76440i	0.571096	−	0.100700i	0.119360	−	0.992851i	$-0.461916\pi$
$307$	10.0064	−	1.76440i	0.571096	−	0.100700i	0.451736	+	0.892151i	$0.350805\pi$
$308$	18.5428	−	11.8522i	1.05657	−	0.675341i
$309$	9.82273	+	11.7063i	0.558796	+	0.665947i
$310$	−3.78638	+	11.1819i	−0.215052	+	0.635087i
$311$	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	$0.0854007\pi$
$312$	2.42008	−	0.164087i	0.137010	−	0.00928957i
$313$	−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	$0.619966\pi$
$314$	−9.31021	+	1.85917i	−0.525405	+	0.104919i
$315$	−5.40120	+	3.11838i	−0.304323	+	0.175701i
$316$	17.6728	−	16.2430i	0.994175	−	0.913739i
$317$	30.7475	+	5.42161i	1.72695	+	0.304508i	0.946976	−	0.321304i	$-0.104121\pi$
$317$	30.7475	+	5.42161i	1.72695	+	0.304508i	0.779974	+	0.625812i	$0.215232\pi$
$318$	−4.31619	−	7.10086i	−0.242040	−	0.398196i
$319$	−1.61652	−	1.35642i	−0.0905078	−	0.0759450i
$320$	−14.6264	−	13.2821i	−0.817642	−	0.742493i
$321$	−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
$326$	−0.626519	−	27.7589i	−0.0346997	−	1.53742i
$327$	9.04791	+	7.59210i	0.500351	+	0.419844i
$328$	−2.17349	−	8.79657i	−0.120011	−	0.485710i
$329$	2.89103	−	16.3958i	0.159388	−	0.903932i
$330$	9.51641	−	11.8754i	0.523861	−	0.653721i
$331$	15.9515	−	9.20963i	0.876776	−	0.506207i	0.00718193	−	0.999974i	$-0.497714\pi$
$331$	15.9515	−	9.20963i	0.876776	−	0.506207i	0.869594	+	0.493767i	$0.164381\pi$
$332$	−0.566772	−	12.5494i	−0.0311056	−	0.688740i
$333$	−3.75157	−	10.3074i	−0.205585	−	0.564840i
$334$	−0.285380	+	0.111224i	−0.0156153	+	0.00608593i
$335$	18.2852	−	31.6709i	0.999026	−	1.73036i
$336$	7.16420	+	7.12136i	0.390839	+	0.388502i
$337$	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	$0.126619\pi$
$338$	−13.0318	+	11.4459i	−0.708839	+	0.622576i
$339$	−13.1206	+	2.31352i	−0.712613	+	0.125653i
$340$	−9.80469	+	12.8175i	−0.531734	+	0.695124i
$341$			14.7280i			0.797564i
$342$	−3.32229	−	5.19253i	−0.179649	−	0.280780i
$343$	19.2497			1.03938
$344$	4.87935	+	5.07414i	0.263077	+	0.273579i
$345$	−0.0963016	−	0.546153i	−0.00518470	−	0.0294039i
$346$	−14.4024	−	16.3980i	−0.774280	−	0.881564i
$347$	7.58761	+	9.04256i	0.407324	+	0.485430i	0.930239	−	0.366955i	$-0.119600\pi$
$347$	7.58761	+	9.04256i	0.407324	+	0.485430i	−0.522915	+	0.852385i	$0.675155\pi$
$348$	0.445966	−	0.859838i	0.0239063	−	0.0460922i
$349$	5.61304	+	3.24069i	0.300459	+	0.173470i	0.642649	−	0.766161i	$-0.277835\pi$
$349$	5.61304	+	3.24069i	0.300459	+	0.173470i	−0.342190	+	0.939631i	$0.611169\pi$
$350$	3.65761	−	1.42553i	0.195508	−	0.0761975i
$351$	−0.805871	+	0.293313i	−0.0430142	+	0.0156559i
$352$	−22.5977	−	9.84229i	−1.20446	−	0.524596i
$353$	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	$0.693900\pi$
$354$	10.9758	+	8.79546i	0.583355	+	0.467474i
$355$	−1.00627	−	0.177432i	−0.0534070	−	0.00941710i
$356$	−23.4161	+	9.74042i	−1.24105	+	0.516241i
$357$	5.30350	−	6.32047i	0.280691	−	0.334515i
$358$	−0.606015	−	26.8504i	−0.0320289	−	1.41909i
$359$	−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
$364$	4.29524	+	0.558930i	0.225132	+	0.0292959i
$365$	−17.0172	+	20.2803i	−0.890722	+	1.06152i
$366$	−3.56292	−	5.86159i	−0.186237	−	0.306390i
$367$	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	$0.0246078\pi$
$368$	−0.812931	+	0.382048i	−0.0423770	+	0.0199156i
$369$	1.60179	+	2.77439i	0.0833860	+	0.144429i
$370$	7.50207	+	37.5682i	0.390014	+	1.95308i
$371$	−5.07514	−	13.9438i	−0.263488	−	0.723928i
$372$	−6.59784	+	1.47309i	−0.342082	+	0.0763760i
$373$	−15.9217	−	9.19242i	−0.824397	−	0.475966i	0.0275335	−	0.999621i	$-0.491235\pi$
$373$	−15.9217	−	9.19242i	−0.824397	−	0.475966i	−0.851930	+	0.523655i	$0.824568\pi$
$374$	−6.45703	+	19.0687i	−0.333885	+	0.986021i
$375$	−7.37983	+	6.19241i	−0.381093	+	0.319775i
$376$	−17.0507	+	7.54828i	−0.879321	+	0.389273i
$377$	−0.0721223	−	0.409026i	−0.00371449	−	0.0210659i
$378$	−3.13243	−	1.71546i	−0.161115	−	0.0882337i
$379$		−	22.9134i		−	1.17698i	−0.808504	−	0.588490i	$-0.799723\pi$
$379$		−	22.9134i		−	1.17698i	0.808504	−	0.588490i	$-0.200277\pi$
$380$	8.72435	+	19.6831i	0.447550	+	1.00972i
$381$			2.49342i			0.127742i
$382$	−11.0299	+	20.1407i	−0.564341	+	1.03049i
$383$	−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	$-0.243782\pi$
$384$	2.14894	−	11.1077i	0.109663	−	0.566840i
$385$	20.8171	−	17.4677i	1.06094	−	0.890234i
$386$	−11.6321	−	3.93883i	−0.592057	−	0.200481i
$387$	−2.15541	−	1.24443i	−0.109566	−	0.0632577i
$388$	−1.31591	−	5.89384i	−0.0668050	−	0.299214i
$389$	−2.77468	−	7.62337i	−0.140682	−	0.386520i	0.849264	−	0.527969i	$-0.177046\pi$
$389$	−2.77468	−	7.62337i	−0.140682	−	0.386520i	−0.989946	+	0.141449i	$0.954824\pi$
$390$	2.93724	−	0.586542i	0.148733	−	0.0297007i
$391$	0.366833	+	0.635374i	0.0185516	+	0.0321322i
$392$	−0.981528	−	1.46183i	−0.0495747	−	0.0738338i
$393$	−1.61202	+	9.14222i	−0.0813156	+	0.461164i
$394$	−18.8689	+	11.4693i	−0.950600	+	0.577814i
$395$	19.0522	−	22.7056i	0.958622	−	1.14244i
$396$	8.64154	+	1.12450i	0.434254	+	0.0565084i
$397$	−7.77830	+	21.3707i	−0.390382	+	1.07257i	0.576446	+	0.817135i	$0.304439\pi$
$397$	−7.77830	+	21.3707i	−0.390382	+	1.07257i	−0.966828	+	0.255430i	$0.917783\pi$
$398$	−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	$0.511535\pi$
$402$	20.9362	−	0.472532i	1.04420	−	0.0235677i
$403$	−1.86330	+	2.22059i	−0.0928175	+	0.110616i
$404$	6.88016	+	16.5400i	0.342301	+	0.822896i
$405$	−2.43213	−	0.428850i	−0.120854	−	0.0213097i
$406$	1.08162	−	1.34974i	0.0536798	−	0.0669865i
$407$	23.8968	+	41.3904i	1.18452	+	2.05165i
$408$	−9.18825	−	0.985372i	−0.454886	−	0.0487832i
$409$	−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	$0.576689\pi$
$410$	−4.06309	−	10.4251i	−0.200662	−	0.514858i
$411$	14.6525	+	8.45963i	0.722755	+	0.417283i
$412$	14.0717	−	27.1308i	0.693264	−	1.33664i
$413$	16.1443	+	19.2401i	0.794411	+	0.946742i
$414$	0.238606	−	0.209569i	0.0117269	−	0.0102997i
$415$	−2.69366	−	15.2765i	−0.132226	−	0.749894i
$416$	−2.16195	−	4.34289i	−0.105998	−	0.212928i
$417$	17.6668			0.865147
$418$	18.1847	+	19.7675i	0.889445	+	0.966858i
$419$		−	30.1260i		−	1.47175i	−0.677118	−	0.735875i	$-0.736771\pi$
$419$		−	30.1260i		−	1.47175i	0.677118	−	0.735875i	$-0.263229\pi$
$420$	9.90730	+	7.57856i	0.483427	+	0.369796i
$421$	19.8809	−	3.50555i	0.968938	−	0.170850i	0.333286	−	0.942826i	$-0.391843\pi$
$421$	19.8809	−	3.50555i	0.968938	−	0.170850i	0.635652	+	0.771976i	$0.280731\pi$
$422$	15.5898	+	17.7499i	0.758901	+	0.864054i
$423$	5.05024	−	4.23766i	0.245551	−	0.206042i
$424$	−9.79709	+	13.4247i	−0.475789	+	0.651963i
$425$	−1.79559	+	3.11005i	−0.0870988	+	0.150860i
$426$	−0.212476	−	0.545172i	−0.0102945	−	0.0264137i
$427$	−4.18941	−	11.5103i	−0.202740	−	0.557023i
$428$	0.610525	+	13.5182i	0.0295108	+	0.653428i
$429$	3.23607	−	1.86835i	0.156239	−	0.0902046i
$430$	6.78329	+	5.43581i	0.327119	+	0.262138i
$431$	−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	$0.974033\pi$
$432$	0.360569	+	3.98372i	0.0173479	+	0.191667i
$433$	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	$0.618524\pi$
$434$	−12.0688	+	0.272393i	−0.579321	+	0.0130753i
$435$	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	$0.389834\pi$
$440$	−29.2392	−	8.45115i	−1.39392	−	0.402893i
$441$	0.476886	+	0.400155i	0.0227089	+	0.0190550i
$442$	−3.38602	+	2.05816i	−0.161057	+	0.0978968i
$443$	20.7119	+	3.65206i	0.984051	+	0.173515i	0.642448	−	0.766330i	$-0.277919\pi$
$443$	20.7119	+	3.65206i	0.984051	+	0.173515i	0.341603	+	0.939844i	$0.389030\pi$
$444$	−16.1519	+	14.8451i	−0.766537	+	0.704519i
$445$	−27.1210	+	15.6583i	−1.28566	+	0.742275i
$446$	5.64321	+	28.2596i	0.267214	+	1.33813i
$447$	1.51823	−	0.552592i	0.0718100	−	0.0261367i
$448$	7.64730	−	18.6996i	0.361301	−	0.883475i
$449$	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	$-0.193989\pi$
$450$	1.47234	+	0.498563i	0.0694069	+	0.0235025i
$451$	−8.97246	−	10.6930i	−0.422497	−	0.503512i
$452$	14.3506	+	22.4515i	0.674994	+	1.05603i
$453$	−18.4609	+	3.25516i	−0.867369	+	0.152941i
$454$	0.392856	+	0.215145i	0.0184376	+	0.0100973i
$455$	5.34859			0.250746
$456$	−7.03661	+	10.1235i	−0.329519	+	0.474078i
$457$	2.73539			0.127956			0.0639782	−	0.997951i	$-0.479621\pi$
$457$	2.73539			0.127956			0.0639782	+	0.997951i	$0.479621\pi$
$458$	19.0526	+	10.4341i	0.890271	+	0.487551i
$459$	3.21753	−	0.567337i	0.150181	−	0.0264810i
$460$	−0.934559	+	0.597352i	−0.0435740	+	0.0278517i
$461$	23.0096	+	27.4218i	1.07166	+	1.27716i	0.958964	+	0.283529i	$0.0915053\pi$
$461$	23.0096	+	27.4218i	1.07166	+	1.27716i	0.112700	+	0.993629i	$0.464050\pi$
$462$	14.7392	+	4.99098i	0.685732	+	0.232201i
$463$	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	$0.100461\pi$
$464$	−1.93035	−	0.163053i	−0.0896142	−	0.00756954i
$465$	−7.84434	+	2.85511i	−0.363773	+	0.132402i
$466$	−3.83539	−	19.2065i	−0.177671	−	0.889726i
$467$	−22.1617	+	12.7950i	−1.02552	+	0.592084i	−0.915698	−	0.401868i	$-0.868361\pi$
$467$	−22.1617	+	12.7950i	−1.02552	+	0.592084i	−0.109821	+	0.993951i	$0.535028\pi$
$468$	1.16065	+	1.26283i	0.0536512	+	0.0583741i
$469$	36.8273	+	6.49364i	1.70053	+	0.299849i
$470$	−19.6758	+	11.9598i	−0.907577	+	0.551662i
$471$	−5.14268	−	4.31522i	−0.236962	−	0.198835i
$472$	7.81091	−	27.0241i	0.359526	−	1.24388i
$473$	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
$478$	−29.1893	+	0.658804i	−1.33509	+	0.0301330i
$479$	−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	$-0.623351\pi$
$480$	0.861456	−	13.9439i	0.0393199	−	0.636448i
$481$	−1.63347	+	9.26388i	−0.0744799	+	0.422396i
$482$	−18.0743	−	14.4839i	−0.823263	−	0.659724i
$483$	0.491114	−	0.283545i	0.0223465	−	0.0129017i
$484$	−15.9541	+	0.720539i	−0.725188	+	0.0327518i
$485$	−2.55046	−	7.00733i	−0.115810	−	0.318187i
$486$	−0.513553	−	1.31767i	−0.0232952	−	0.0597709i
$487$	−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	$0.988023\pi$
$488$	−8.08727	+	11.0818i	−0.366093	+	0.501650i
$489$	15.0401	−	12.6202i	0.680138	−	0.570703i
$490$	−1.43481	−	1.63362i	−0.0648183	−	0.0737994i
$491$	−3.90410	+	0.688399i	−0.176190	+	0.0310670i	−0.261047	−	0.965326i	$-0.584068\pi$
$491$	−3.90410	+	0.688399i	−0.176190	+	0.0310670i	0.0848572	+	0.996393i	$0.472957\pi$
$492$	3.89282	−	5.08899i	0.175502	−	0.229430i
$493$			1.58231i			0.0712635i
$494$	0.240917	+	5.28105i	0.0108394	+	0.237606i
$495$	10.7608			0.483660
$496$	7.78826	+	11.0521i	0.349703	+	0.496254i
$497$	−0.181435	−	1.02897i	−0.00813845	−	0.0461554i
$498$	6.67408	−	5.86187i	0.299073	−	0.262677i
$499$	19.1315	+	22.8001i	0.856445	+	1.02067i	0.999521	+	0.0309600i	$0.00985646\pi$
$499$	19.1315	+	22.8001i	0.856445	+	1.02067i	−0.143075	+	0.989712i	$0.545699\pi$
$500$	17.1037	+	8.87104i	0.764900	+	0.396725i
$501$	−0.187562	−	0.108289i	−0.00837967	−	0.00483800i
$502$	12.5738	+	32.2619i	0.561197	+	1.43992i
$503$	−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	$0.417709\pi$
$504$	−0.761646	+	7.10209i	−0.0339264	+	0.316352i
$505$	11.0603	+	19.1570i	0.492176	+	0.852473i
$506$	−0.865298	+	1.07980i	−0.0384672	+	0.0480028i
$507$	−12.0782	−	2.12971i	−0.536412	−	0.0945840i
$508$	4.60436	−	1.91528i	0.204286	−	0.0849769i
$509$	17.5821	−	20.9536i	0.779315	−	0.928751i	−0.219588	−	0.975593i	$-0.570471\pi$
$509$	17.5821	−	20.9536i	0.779315	−	0.928751i	0.998902	+	0.0468416i	$0.0149156\pi$
$510$	−11.4080	+	0.257480i	−0.505156	+	0.0114014i
$511$	−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
$516$	−0.642321	+	4.93608i	−0.0282766	+	0.217299i
$517$	−18.4643	+	22.0049i	−0.812060	+	0.967775i
$518$	−33.4753	+	20.3476i	−1.47082	+	0.894024i
$519$	2.67983	−	15.1981i	0.117632	−	0.667121i
$520$	−3.33931	−	4.97339i	−0.146439	−	0.218098i
$521$	−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	$0.978646\pi$
$522$	0.671651	−	0.134123i	0.0293974	−	0.00587041i
$523$	12.6367	+	34.7191i	0.552565	+	1.51816i	0.830195	+	0.557473i	$0.188229\pi$
$523$	12.6367	+	34.7191i	0.552565	+	1.51816i	−0.277630	+	0.960688i	$0.589549\pi$
$524$	18.1204	−	4.04570i	0.791592	−	0.176737i
$525$	2.40392	+	1.38791i	0.104916	+	0.0605732i
$526$	35.1627	+	11.9067i	1.53316	+	0.519158i
$527$	8.45980	−	7.09862i	0.368515	−	0.309221i
$528$	−4.56136	−	16.8213i	−0.198508	−	0.732054i
$529$	−3.98515	−	22.6009i	−0.173267	−	0.982649i
$530$	−9.85743	+	17.9997i	−0.428179	+	0.781857i
$531$			9.94554i			0.431600i
$532$	−15.8621	+	15.2670i	−0.687708	+	0.661910i
$533$		−	2.74736i		−	0.119002i
$534$	−15.7289	−	8.61382i	−0.680654	−	0.372756i
$535$	2.90160	+	16.4558i	0.125447	+	0.711446i
$536$	−16.9545	−	38.2981i	−0.732321	−	1.65422i
$537$	14.5479	−	12.2071i	0.627788	−	0.526777i
$538$	−4.13749	+	12.2187i	−0.178380	+	0.526788i
$539$	−2.34909	−	1.35625i	−0.101182	−	0.0584176i
$540$	1.07629	+	4.82061i	0.0463161	+	0.207446i
$541$	−6.91873	−	19.0090i	−0.297459	−	0.817263i	−0.994923	−	0.100642i	$-0.967910\pi$
$541$	−6.91873	−	19.0090i	−0.297459	−	0.817263i	0.697463	−	0.716620i	$-0.254312\pi$
$542$	−0.272717	−	1.36569i	−0.0117142	−	0.0586615i
$543$	11.3306	+	19.6252i	0.486244	+	0.842199i
$544$	5.23823	+	17.7240i	0.224587	+	0.759911i
$545$	5.06524	−	28.7264i	0.216971	−	1.23050i
$546$	1.59086	+	2.61723i	0.0680826	+	0.112007i
$547$	−3.37047	+	4.01676i	−0.144111	+	0.171744i	−0.833272	−	0.552864i	$-0.813535\pi$
$547$	−3.37047	+	4.01676i	−0.144111	+	0.171744i	0.689161	+	0.724608i	$0.257979\pi$
$548$	4.36651	−	33.5556i	0.186528	−	1.43343i
$549$	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
$554$	0.445403	+	19.7342i	0.0189234	+	0.838427i
$555$	−17.4126	+	20.7516i	−0.739125	+	0.880855i
$556$	−13.5705	−	32.6237i	−0.575518	−	1.38355i
$557$	12.7316	+	2.24492i	0.539455	+	0.0951204i	0.436735	−	0.899590i	$-0.356135\pi$
$557$	12.7316	+	2.24492i	0.539455	+	0.0951204i	0.102719	+	0.994710i	$0.467246\pi$
$558$	−3.73028	−	2.98927i	−0.157915	−	0.126546i
$559$	1.06721	+	1.84846i	0.0451380	+	0.0781814i
$560$	6.38450	−	24.1163i	0.269794	−	1.01910i
$561$	−13.3772	+	4.86889i	−0.564785	+	0.205565i
$562$	42.4653	−	16.5505i	1.79129	−	0.698141i
$563$	−12.6215	−	7.28702i	−0.531932	−	0.307111i	0.209871	−	0.977729i	$-0.432696\pi$
$563$	−12.6215	−	7.28702i	−0.531932	−	0.307111i	−0.741803	+	0.670618i	$0.766029\pi$
$564$	−11.7046	−	6.07073i	−0.492851	−	0.255624i
$565$	21.1498	+	25.2053i	0.889777	+	1.06039i
$566$	−4.62428	−	5.26502i	−0.194373	−	0.221305i
$567$	−0.438525	−	2.48700i	−0.0184163	−	0.104444i
$568$	−0.843509	+	0.811127i	−0.0353928	+	0.0340341i
$569$	9.82051			0.411697			0.205849	−	0.978584i	$-0.434005\pi$
$569$	9.82051			0.411697			0.205849	+	0.978584i	$0.434005\pi$
$570$	−7.00323	+	13.5175i	−0.293333	+	0.566187i
$571$		−	1.88885i		−	0.0790460i	−0.999219	−	0.0395230i	$-0.987416\pi$
$571$		−	1.88885i		−	0.0790460i	0.999219	−	0.0395230i	$-0.0125838\pi$
$572$	−5.93585	−	4.54062i	−0.248190	−	0.189853i
$573$	−15.9908	+	2.81960i	−0.668023	+	0.117791i
$574$	8.59637	−	7.55022i	0.358806	−	0.315140i
$575$	−0.189081	+	0.158658i	−0.00788521	+	0.00661648i
$576$	7.07940	−	3.72587i	0.294975	−	0.155244i
$577$	−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	$0.982850\pi$
$578$	−8.33513	+	3.24855i	−0.346696	+	0.135122i
$579$	−2.97006	−	8.16018i	−0.123432	−	0.339125i
$580$	−2.38970	+	0.107926i	−0.0992267	+	0.00448139i
$581$	13.7370	−	7.93106i	0.569906	−	0.329036i
$582$	2.67031	−	3.33225i	0.110688	−	0.138126i
$583$	−4.44580	+	25.2134i	−0.184126	+	1.04423i
$584$	7.27287	+	29.4349i	0.300954	+	1.21802i
$585$	1.62244	+	1.36139i	0.0670797	+	0.0562866i
$586$	0.138505	+	6.13668i	0.00572159	+	0.253504i
$587$	7.62316	−	20.9444i	0.314641	−	0.864470i	−0.677062	−	0.735926i	$-0.736747\pi$
$587$	7.62316	−	20.9444i	0.314641	−	0.864470i	0.991704	−	0.128544i	$-0.0410305\pi$
$588$	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
$592$	39.8201	+	18.4232i	1.63659	+	0.757191i
$593$	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	$0.640415\pi$
$594$	3.20064	+	5.26558i	0.131324	+	0.216049i
$595$	−20.0670	−	3.53835i	−0.822666	−	0.145058i
$596$	−2.18663	−	2.37912i	−0.0895679	−	0.0974525i
$597$	−18.0666	+	10.4308i	−0.739419	+	0.426904i
$598$	−0.267074	+	0.0533325i	−0.0109215	+	0.00218093i
$599$	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	$0.368393\pi$
$600$	−0.210310	−	3.10181i	−0.00858585	−	0.126631i
$601$	−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	$0.297013\pi$
$602$	−2.85087	+	8.41911i	−0.116193	+	0.343137i
$603$	9.51834	+	11.3435i	0.387617	+	0.461944i
$604$	20.1915	+	31.5897i	0.821580	+	1.28537i
$605$	−19.4211	+	3.42446i	−0.789578	+	0.139224i
$606$	−6.08438	+	11.1101i	−0.247161	+	0.451317i
$607$	0.358636			0.0145566			0.00727830	−	0.999974i	$-0.497683\pi$
$607$	0.358636			0.0145566			0.00727830	+	0.999974i	$0.497683\pi$
$608$	24.0993	+	5.21760i	0.977356	+	0.211602i
$609$	1.22305			0.0495604
$610$	−8.13708	+	14.8583i	−0.329461	+	0.601596i
$611$	−5.56788	+	0.981767i	−0.225252	+	0.0397180i
$612$	−3.51915	−	5.50573i	−0.142253	−	0.222556i
$613$	−29.1535	−	34.7438i	−1.17750	−	1.40329i	−0.896189	−	0.443672i	$-0.853675\pi$
$613$	−29.1535	−	34.7438i	−1.17750	−	1.40329i	−0.281310	−	0.959617i	$-0.590769\pi$
$614$	4.60873	−	13.6104i	0.185993	−	0.549270i
$615$	3.95587	−	6.85177i	0.159516	−	0.276290i
$616$	−2.10535	−	31.0514i	−0.0848271	−	1.25110i
$617$	−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	$0.539246\pi$
$618$	21.1928	−	4.23203i	0.852501	−	0.170237i
$619$	−8.09036	+	4.67097i	−0.325179	+	0.187742i	−0.653699	−	0.756755i	$-0.726784\pi$
$619$	−8.09036	+	4.67097i	−0.325179	+	0.187742i	0.328520	+	0.944497i	$0.393450\pi$
$620$	11.2978	+	12.2923i	0.453730	+	0.493672i
$621$	0.221146	+	0.0389940i	0.00887428	+	0.00156478i
$622$	−6.54288	−	10.7641i	−0.262346	−	0.431602i
$623$	−24.5311	−	20.5841i	−0.982819	−	0.824683i
$624$	1.44040	−	3.11330i	0.0576623	−	0.124632i
$625$	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
$630$	0.199020	+	8.81788i	0.00792914	+	0.351313i
$631$	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	$0.442399\pi$
$632$	−8.14260	−	32.9549i	−0.323895	−	1.31088i
$633$	−2.90077	+	16.4511i	−0.115295	+	0.653871i
$634$	27.6114	−	34.4560i	1.09659	−	1.36842i
$635$	5.33287	−	3.07893i	0.211628	−	0.122184i
$636$	−11.7398	+	0.530205i	−0.465512	+	0.0210240i
$637$	−0.182596	−	0.501680i	−0.00723474	−	0.0198773i
$638$	−2.78058	+	1.08371i	−0.110084	+	0.0429044i
$639$	0.206869	−	0.358308i	0.00818361	−	0.0141744i
$640$	−26.4106	+	9.12002i	−1.04397	+	0.360500i
$641$	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	$0.256610\pi$
$642$	−7.18930	+	6.31438i	−0.283739	+	0.249209i
$643$	5.26111	−	0.927676i	0.207478	−	0.0365840i	−0.0689431	−	0.997621i	$-0.521963\pi$
$643$	5.26111	−	0.927676i	0.207478	−	0.0365840i	0.276421	+	0.961037i	$0.410852\pi$
$644$	−0.900839	−	0.689095i	−0.0354980	−	0.0271541i
$645$			6.14659i			0.242022i
$646$	2.58979	−	19.9730i	0.101894	−	0.785825i
$647$	7.69396			0.302481			0.151240	−	0.988497i	$-0.451673\pi$
$647$	7.69396			0.302481			0.151240	+	0.988497i	$0.451673\pi$
$648$	−2.03875	+	1.96048i	−0.0800897	+	0.0770151i
$649$	−7.52500	−	42.6764i	−0.295382	−	1.67519i
$650$	−0.879721	−	1.00161i	−0.0345055	−	0.0392865i
$651$	−5.48690	−	6.53903i	−0.215049	−	0.256285i
$652$	−34.8574	−	18.0792i	−1.36512	−	0.708037i
$653$	24.3496	+	14.0582i	0.952872	+	0.550141i	0.893972	−	0.448123i	$-0.147907\pi$
$653$	24.3496	+	14.0582i	0.952872	+	0.550141i	0.0589004	+	0.998264i	$0.481241\pi$
$654$	15.5633	−	6.06568i	0.608574	−	0.237187i
$655$	21.5438	−	7.84129i	0.841784	−	0.306384i
$656$	−12.3876	−	3.27947i	−0.483654	−	0.128042i
$657$	−5.35989	−	9.28359i	−0.209109	−	0.362188i
$658$	−18.3734	−	14.7236i	−0.716269	−	0.573984i
$659$	−24.3390	−	4.29162i	−0.948111	−	0.167178i	−0.321850	−	0.946791i	$-0.604305\pi$
$659$	−24.3390	−	4.29162i	−0.948111	−	0.167178i	−0.626261	+	0.779613i	$0.715416\pi$
$660$	−8.26573	−	19.8709i	−0.321743	−	0.773475i
$661$	−5.85539	+	6.97818i	−0.227748	+	0.271420i	−0.867802	−	0.496911i	$-0.834468\pi$
$661$	−5.85539	+	6.97818i	−0.227748	+	0.271420i	0.640054	+	0.768330i	$0.278912\pi$
$662$	−0.587772	−	26.0421i	−0.0228444	−	1.01216i
$663$	−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
$668$	−0.0558944	+	0.429535i	−0.00216262	+	0.0166192i
$669$	−13.0981	+	15.6097i	−0.506403	+	0.603508i
$670$	−26.8632	−	44.1945i	−1.03782	−	1.70738i
$671$	−3.66990	+	20.8131i	−0.141675	+	0.803479i
$672$	13.6998	−	4.04891i	0.528482	−	0.156190i
$673$	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	$0.701222\pi$
$674$	−4.64906	−	23.2812i	−0.179075	−	0.896758i
$675$	0.375939	+	1.03288i	0.0144699	+	0.0397557i
$676$	5.34496	+	23.9397i	0.205575	+	0.920756i
$677$	−27.6169	−	15.9446i	−1.06140	−	0.612802i	−0.135584	−	0.990766i	$-0.543291\pi$
$677$	−27.6169	−	15.9446i	−1.06140	−	0.612802i	−0.925820	+	0.377964i	$0.876624\pi$
$678$	−6.04305	+	17.8462i	−0.232082	+	0.685379i
$679$	5.84130	−	4.90143i	0.224169	−	0.188100i
$680$	9.23839	+	20.8684i	0.354276	+	0.800267i
$681$	0.0549978	+	0.311908i	0.00210752	+	0.0119523i
$682$	18.2684	+	10.0046i	0.699533	+	0.383095i
$683$		−	22.3118i		−	0.853736i	−0.904314	−	0.426868i	$-0.859617\pi$
$683$		−	22.3118i		−	0.853736i	0.904314	−	0.426868i	$-0.140383\pi$
$684$	−8.69756	+	0.593691i	−0.332559	+	0.0227003i
$685$		−	41.7847i		−	1.59651i
$686$	13.0761	−	23.8771i	0.499249	−	0.911631i
$687$	2.66727	+	15.1269i	0.101763	+	0.577125i
$688$	9.60841	−	2.60547i	0.366317	−	0.0993326i
$689$	−3.86017	+	3.23906i	−0.147061	+	0.123398i
$690$	−0.742859	−	0.251546i	−0.0282802	−	0.00957619i
$691$	−32.7203	−	18.8911i	−1.24474	−	0.718650i	−0.274683	−	0.961535i	$-0.588573\pi$
$691$	−32.7203	−	18.8911i	−1.24474	−	0.718650i	−0.970055	+	0.242885i	$0.921906\pi$
$692$	−30.1234	+	6.72559i	−1.14512	+	0.255669i
$693$	3.76343	+	10.3399i	0.142961	+	0.392781i
$694$	16.3705	−	3.26905i	0.621415	−	0.124091i
$695$	−21.8154	−	37.7854i	−0.827506	−	1.43328i
$696$	−0.763593	−	1.13725i	−0.0289439	−	0.0431074i
$697$	−1.81751	+	10.3076i	−0.0688432	+	0.390429i
$698$	7.83261	−	4.76098i	0.296469	−	0.180206i
$699$	8.90210	−	10.6091i	0.336708	−	0.401274i
$700$	0.716380	−	5.50521i	0.0270766	−	0.208077i
$701$	15.1524	−	41.6308i	0.572297	−	1.57237i	−0.228567	−	0.973528i	$-0.573404\pi$
$701$	15.1524	−	41.6308i	0.572297	−	1.57237i	0.800864	−	0.598846i	$-0.204374\pi$
$702$	−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
$706$	22.5351	−	0.508619i	0.848121	−	0.0191421i
$707$	−14.5396	+	17.3276i	−0.546817	+	0.651672i
$708$	18.3655	−	7.63953i	0.690219	−	0.287111i
$709$	−0.561672	−	0.0990379i	−0.0210940	−	0.00371945i	0.163091	−	0.986611i	$-0.447854\pi$
$709$	−0.561672	−	0.0990379i	−0.0210940	−	0.00371945i	−0.184185	+	0.982892i	$0.558965\pi$
$710$	−0.903631	+	1.12763i	−0.0339127	+	0.0423193i
$711$	6.00085	+	10.3938i	0.225050	+	0.389797i
$712$	−3.82445	+	35.6617i	−0.143327	+	1.33648i
$713$	0.713261	−	0.259606i	0.0267119	−	0.00972232i
$714$	−4.23721	−	10.8718i	−0.158574	−	0.406868i
$715$	−7.99196	−	4.61416i	−0.298883	−	0.172560i
$716$	−33.7166	−	17.4875i	−1.26005	−	0.653540i
$717$	−13.2705	−	15.8152i	−0.495596	−	0.590628i
$718$	−12.1559	+	10.6766i	−0.453653	+	0.398445i
$719$	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	$0.760390\pi$
$720$	8.07505	−	5.69037i	0.300939	−	0.212068i
$721$	38.5913			1.43721
$722$	−21.7193	−	15.8200i	−0.808309	−	0.588759i
$723$		−	16.3778i		−	0.609097i
$724$	27.5367	−	35.9981i	1.02339	−	1.33786i
$725$	−0.524248	+	0.0924391i	−0.0194701	+	0.00343310i
$726$	−7.45221	−	8.48478i	−0.276577	−	0.314900i
$727$	−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	$0.370163\pi$
$728$	3.61101	−	4.94809i	0.133833	−	0.183389i
$729$	0.500000	−	0.866025i	0.0185185	−	0.0320750i
$730$	13.5958	+	34.8842i	0.503205	+	1.29112i
$731$	−2.78113	−	7.64109i	−0.102864	−	0.282616i
$732$	−9.69091	+	0.437672i	−0.358186	+	0.0161768i
$733$	−31.8660	+	18.3978i	−1.17700	+	0.679539i	−0.955318	−	0.295580i	$-0.904487\pi$
$733$	−31.8660	+	18.3978i	−1.17700	+	0.679539i	−0.221679	+	0.975120i	$0.571154\pi$
$734$	−4.10454	−	3.28919i	−0.151501	−	0.121406i
$735$	0.266972	−	1.51408i	0.00984743	−	0.0558475i
$736$	−0.0783294	+	1.26787i	−0.00288726	+	0.0467344i
$737$	−49.4260	−	41.4733i	−1.82063	−	1.52769i
$738$	4.52940	−	0.102229i	0.166730	−	0.00376310i
$739$	7.48438	−	20.5632i	0.275317	−	0.756428i	−0.722560	−	0.691308i	$-0.757035\pi$
$739$	7.48438	−	20.5632i	0.275317	−	0.756428i	0.997877	−	0.0651199i	$-0.0207430\pi$
$740$	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	$0.496954\pi$
$744$	−2.65466	+	9.18454i	−0.0973244	+	0.336722i
$745$	−3.05662	−	2.56481i	−0.111986	−	0.0939675i
$746$	−22.2177	+	13.5048i	−0.813447	+	0.494446i
$747$	6.18569	+	1.09070i	0.226323	+	0.0399068i
$748$	19.2664	+	20.9624i	0.704451	+	0.766463i
$749$	−14.7974	+	8.54331i	−0.540687	+	0.312166i
$750$	2.66794	+	13.3603i	0.0974195	+	0.487849i
$751$	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	$0.306067\pi$
$752$	−2.21956	+	26.2769i	−0.0809391	+	0.958221i
$753$	−12.2420	+	21.2037i	−0.446123	+	0.772708i
$754$	−0.556343	−	0.188388i	−0.0202608	−	0.00686069i
$755$	29.7580	+	35.4643i	1.08301	+	1.29068i
$756$	−4.25567	+	2.72014i	−0.154777	+	0.0989305i
$757$	22.0077	−	3.88055i	0.799882	−	0.141041i	0.241257	−	0.970461i	$-0.422440\pi$
$757$	22.0077	−	3.88055i	0.799882	−	0.141041i	0.558625	+	0.829420i	$0.311329\pi$
$758$	−28.4215	−	15.5648i	−1.03231	−	0.565341i
$759$	−0.978442			−0.0355152
$760$	30.3410	+	2.54894i	1.10058	+	0.0924598i
$761$	−46.4666			−1.68441			−0.842207	−	0.539155i	$-0.818744\pi$
$761$	−46.4666			−1.68441			−0.842207	+	0.539155i	$0.818744\pi$
$762$	3.09280	+	1.69375i	0.112040	+	0.0613583i
$763$	29.3745	−	5.17951i	1.06343	−	0.187511i
$764$	17.4898	+	27.3628i	0.632758	+	0.989953i
$765$	−5.18649	−	6.18102i	−0.187518	−	0.223475i
$766$	−29.2275	−	9.89696i	−1.05603	−	0.357592i
$767$	4.26460	−	7.38650i	0.153986	−	0.266711i
$768$	−12.3182	−	10.2109i	−0.444494	−	0.368455i
$769$	−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	$0.415700\pi$
$770$	−7.52578	−	37.6870i	−0.271210	−	1.35814i
$771$	−5.69837	+	3.28996i	−0.205222	+	0.118485i
$772$	−12.7872	+	11.7527i	−0.460223	+	0.422988i
$773$	1.36548	+	0.240771i	0.0491128	+	0.00865991i	0.198151	−	0.980172i	$-0.436506\pi$
$773$	1.36548	+	0.240771i	0.0491128	+	0.00865991i	−0.149038	+	0.988832i	$0.547618\pi$
$774$	−3.00772	+	1.82822i	−0.108110	+	0.0657138i
$775$	2.84613	+	2.38819i	0.102236	+	0.0857863i
$776$	−8.20453	−	2.37140i	−0.294525	−	0.0851282i
$777$	−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
$782$	1.03730	−	0.0234118i	0.0370937	−	0.000837206i
$783$	0.371000	+	0.311306i	0.0132584	+	0.0111252i
$784$	−2.47999	+	0.224466i	−0.0885709	+	0.00801663i
$785$	−2.87899	+	16.3276i	−0.102756	+	0.582757i
$786$	10.2449	+	8.20976i	0.365422	+	0.292832i
$787$	−25.2433	+	14.5742i	−0.899825	+	0.519514i	−0.877143	−	0.480228i	$-0.840554\pi$
$787$	−25.2433	+	14.5742i	−0.899825	+	0.519514i	−0.0226816	+	0.999743i	$0.507220\pi$
$788$	1.40890	+	31.1957i	0.0501898	+	1.11130i
$789$	8.97822	+	24.6674i	0.319633	+	0.878184i
$790$	−15.2217	−	39.0559i	−0.541564	−	1.38955i
$791$	−16.8227	+	29.1378i	−0.598148	+	1.03602i
$792$	7.26495	−	9.95501i	0.258149	−	0.353736i
$793$	−3.18648	+	2.67377i	−0.113155	+	0.0949484i
$794$	21.2243	+	24.1651i	0.753220	+	0.857586i
$795$	−14.2909	+	2.51987i	−0.506845	+	0.0893705i
$796$	33.1392	+	25.3498i	1.17459	+	0.898499i
$797$			9.70728i			0.343849i	0.985110	+	0.171925i	$0.0549986\pi$
$797$			9.70728i			0.343849i	−0.985110	+	0.171925i	$0.945001\pi$
$798$	−15.4382	−	2.00179i	−0.546505	−	0.0708624i
$799$	21.5392			0.762002
$800$	−5.56628	+	2.77097i	−0.196798	+	0.0979686i
$801$	−2.20196	−	12.4879i	−0.0778025	−	0.441240i
$802$	13.0965	−	11.5027i	0.462453	−	0.406174i
$803$	30.0235	+	35.7806i	1.05950	+	1.26267i
$804$	13.6357	−	26.2900i	0.480893	−	0.927178i
$805$	−1.21288	−	0.700257i	−0.0427484	−	0.0246808i
$806$	1.48868	+	3.81964i	0.0524364	+	0.134541i
$807$	−8.57175	+	3.11986i	−0.301740	+	0.109824i
$808$	25.1897	+	2.70140i	0.886169	+	0.0950350i
$809$	−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	$0.964036\pi$
$810$	−2.18407	+	2.72547i	−0.0767403	+	0.0957633i
$811$	31.6955	+	5.58877i	1.11298	+	0.196248i	0.699756	−	0.714382i	$-0.253292\pi$
$811$	31.6955	+	5.58877i	1.11298	+	0.196248i	0.413223	+	0.910630i	$0.364403\pi$
$812$	−0.939468	−	2.25849i	−0.0329689	−	0.0792576i
$813$	0.632989	−	0.754367i	0.0221999	−	0.0264568i
$814$	67.5730	−	1.52513i	2.36843	−	0.0534557i
$815$	−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
$820$	−15.6912	−	2.04186i	−0.547960	−	0.0713047i
$821$	15.5693	−	18.5547i	0.543371	−	0.647564i	−0.422569	−	0.906331i	$-0.638872\pi$
$821$	15.5693	−	18.5547i	0.543371	−	0.647564i	0.965940	+	0.258767i	$0.0833161\pi$
$822$	20.4466	−	12.4283i	0.713155	−	0.433485i
$823$	−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	$0.900976\pi$
$824$	−24.0939	−	35.8841i	−0.839350	−	1.25008i
$825$	−2.39466	−	4.14767i	−0.0833713	−	0.144403i
$826$	34.8319	−	6.95564i	1.21196	−	0.242018i
$827$	10.9195	+	30.0011i	0.379708	+	1.04324i	0.971477	+	0.237133i	$0.0762076\pi$
$827$	10.9195	+	30.0011i	0.379708	+	1.04324i	−0.591769	+	0.806108i	$0.701570\pi$
$828$	−0.0978635	−	0.438323i	−0.00340099	−	0.0152328i
$829$	−19.3534	−	11.1737i	−0.672173	−	0.388079i	0.124726	−	0.992191i	$-0.460195\pi$
$829$	−19.3534	−	11.1737i	−0.672173	−	0.388079i	−0.796900	+	0.604112i	$0.793528\pi$
$830$	−20.7786	−	7.03601i	−0.721235	−	0.244223i
$831$	−10.6923	+	8.97188i	−0.370911	+	0.311231i
$832$	−6.85547	−	0.268430i	−0.237671	−	0.00930614i
$833$	0.353185	+	2.00301i	0.0122371	+	0.0694002i
$834$	12.0009	−	21.9137i	0.415557	−	0.758809i
$835$			0.534873i			0.0185100i
$836$	36.8721	−	9.12828i	1.27525	−	0.315708i
$837$		−	3.38014i		−	0.116835i
$838$	−37.3679	−	20.4643i	−1.29085	−	0.706928i
$839$	−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	$-0.218836\pi$
$840$	16.1303	−	7.14084i	0.556548	−	0.246382i
$841$	22.0356	−	18.4901i	0.759849	−	0.637589i
$842$	9.15671	−	27.0414i	0.315561	−	0.931908i
$843$	27.9098	+	16.1137i	0.961265	+	0.554986i
$844$	32.6069	−	7.28007i	1.12237	−	0.250590i
$845$	10.3595	+	28.4625i	0.356377	+	0.979139i
$846$	−1.82575	−	9.14287i	−0.0627707	−	0.314338i
$847$	−10.0828	−	17.4639i	−0.346448	−	0.600066i
$848$	9.99682	+	21.2715i	0.343292	+	0.730466i
$849$	0.860430	−	4.87974i	0.0295299	−	0.167472i
$850$	2.63794	+	4.33986i	0.0904807	+	0.148856i
$851$	1.58328	−	1.88687i	0.0542740	−	0.0646812i
$852$	−0.820558	−	0.106777i	−0.0281119	−	0.00365813i
$853$	−7.08123	+	19.4555i	−0.242457	+	0.666144i	0.757455	+	0.652887i	$0.226442\pi$
$853$	−7.08123	+	19.4555i	−0.242457	+	0.666144i	−0.999912	+	0.0132575i	$0.995780\pi$
$854$	−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	$0.471712\pi$
$858$	−0.119241	−	5.28314i	−0.00407081	−	0.180363i
$859$	−13.8698	+	16.5294i	−0.473231	+	0.563974i	−0.948870	−	0.315666i	$-0.897772\pi$
$859$	−13.8698	+	16.5294i	−0.473231	+	0.563974i	0.475640	+	0.879640i	$0.342217\pi$
$860$	11.3504	−	4.72142i	0.387044	−	0.160999i
$861$	7.96732	+	1.40485i	0.271525	+	0.0478773i
$862$	11.6077	+	9.30184i	0.395359	+	0.316822i
$863$	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	$0.490191\pi$
$864$	5.18629	+	2.25886i	0.176441	+	0.0768479i
$865$	−35.8145	+	13.0354i	−1.21773	+	0.443217i
$866$	17.5507	−	6.84023i	0.596396	−	0.232440i
$867$	−5.47816	−	3.16282i	−0.186048	−	0.107415i
$868$	−7.86035	+	15.1550i	−0.266798	+	0.514395i
$869$	−33.6138	−	40.0594i	−1.14027	−	1.35892i
$870$	−1.11623	−	1.27089i	−0.0378438	−	0.0430874i
$871$	−2.20518	−	12.5062i	−0.0747197	−	0.423756i
$872$	−23.1557	−	24.0801i	−0.784151	−	0.815455i
$873$	3.01947			0.102194
$874$	0.636782	−	1.22911i	0.0215395	−	0.0415751i
$875$			24.3286i			0.822455i
$876$	−13.0261	+	17.0287i	−0.440110	+	0.575346i
$877$	23.4551	−	4.13577i	0.792023	−	0.139655i	0.237022	−	0.971504i	$-0.423829\pi$
$877$	23.4551	−	4.13577i	0.792023	−	0.139655i	0.555001	+	0.831849i	$0.312718\pi$
$878$	28.5196	−	25.0489i	0.962491	−	0.845359i
$879$	−3.32493	+	2.78995i	−0.112147	+	0.0941027i
$880$	−30.3446	+	30.5272i	−1.02292	+	1.02907i
$881$	−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	$0.759848\pi$
$882$	0.820292	−	0.319702i	0.0276207	−	0.0107649i
$883$	2.12527	+	5.83914i	0.0715211	+	0.196503i	0.970303	−	0.241894i	$-0.0777687\pi$
$883$	2.12527	+	5.83914i	0.0715211	+	0.196503i	−0.898782	+	0.438397i	$0.855546\pi$
$884$	0.252826	+	5.59807i	0.00850347	+	0.188283i
$885$	21.2713	−	12.2810i	0.715028	−	0.412821i
$886$	18.5994	−	23.2100i	0.624858	−	0.779754i
$887$	−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	$0.819310\pi$
$888$	7.44186	+	30.1189i	0.249733	+	1.01072i
$889$	4.82362	+	4.04749i	0.161779	+	0.135749i
$890$	0.999337	+	44.2771i	0.0334979	+	1.48417i
$891$	−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
$896$	−18.0001	−	22.1881i	−0.601341	−	0.741253i
$897$	−0.147524	−	0.123787i	−0.00492567	−	0.00413313i
$898$	−28.1947	−	46.3849i	−0.940868	−	1.54789i
$899$	1.61215	+	0.284266i	0.0537683	+	0.00948081i
$900$	1.61856	−	1.48761i	0.0539520	−	0.0495870i
$901$	16.6255	−	9.59871i	0.553874	−	0.319780i
$902$	−19.3583	+	3.86570i	−0.644562	+	0.128714i
$903$	−5.90621	+	2.14968i	−0.196546	+	0.0715370i
$904$	37.5968	−	2.54915i	1.25045	−	0.0847835i
$905$	27.9827	−	48.4675i	0.930176	−	1.61111i
$906$	−8.50267	+	25.1099i	−0.282482	+	0.834220i
$907$	6.45371	+	7.69123i	0.214292	+	0.255383i	0.862473	−	0.506103i	$-0.168914\pi$
$907$	6.45371	+	7.69123i	0.214292	+	0.255383i	−0.648181	+	0.761486i	$0.724470\pi$
$908$	0.533727	−	0.341147i	0.0177123	−	0.0113214i
$909$	−8.82088	+	1.55536i	−0.292570	+	0.0515880i
$910$	3.63325	−	6.63433i	0.120441	−	0.219926i
$911$	−7.57417			−0.250943			−0.125472	−	0.992097i	$-0.540044\pi$
$911$	−7.57417			−0.250943			−0.125472	+	0.992097i	$0.540044\pi$
$912$	7.77723	+	15.6050i	0.257530	+	0.516732i
$913$	−27.3681			−0.905751
$914$	1.85813	−	3.39295i	0.0614614	−	0.112229i
$915$	−11.7968	+	2.08009i	−0.389990	+	0.0687657i
$916$	25.8846	−	16.5449i	0.855250	−	0.546659i
$917$	15.0693	+	17.9588i	0.497631	+	0.593053i
$918$	1.48192	−	4.37637i	0.0489107	−	0.144442i
$919$	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	$0.0869379\pi$
$920$	0.106110	+	1.56499i	0.00349834	+	0.0515963i
$921$	9.54801	−	3.47519i	0.314618	−	0.114511i
$922$	49.6438	−	9.91346i	1.63493	−	0.326483i
$923$	−0.307281	+	0.177409i	−0.0101143	+	0.00583948i
$924$	16.2030	−	14.8921i	0.533039	−	0.489913i
$925$	11.8735	+	2.09362i	0.390398	+	0.0688377i
$926$	−6.52765	−	10.7391i	−0.214512	−	0.352908i
$927$	11.7063	+	9.82273i	0.384485	+	0.322621i
$928$	−1.51352	+	2.28362i	−0.0496837	+	0.0749636i
$929$	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
$934$	0.816598	+	36.1806i	0.0267199	+	1.18387i
$935$	26.9320	+	22.5986i	0.880769	+	0.739053i
$936$	2.35482	−	0.581835i	0.0769696	−	0.0190179i
$937$	−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	$0.715651\pi$
$938$	33.0711	−	41.2691i	1.07981	−	1.34748i
$939$	−20.3423	+	11.7446i	−0.663846	+	0.383272i
$940$	1.46915	+	32.5298i	0.0479183	+	1.06100i
$941$	6.38320	+	17.5377i	0.208087	+	0.571713i	0.999202	−	0.0399544i	$-0.0127213\pi$
$941$	6.38320	+	17.5377i	0.208087	+	0.571713i	−0.791115	+	0.611667i	$0.790499\pi$
$942$	−8.84592	+	3.44763i	−0.288216	+	0.112330i
$943$	−0.359695	+	0.623010i	−0.0117133	+	0.0202880i
$944$	−28.2145	−	28.0458i	−0.918303	−	0.912812i
$945$	−4.77764	+	4.00892i	−0.155417	+	0.130410i
$946$	11.5229	−	10.1206i	0.374641	−	0.329049i
$947$	−17.8459	+	3.14672i	−0.579914	+	0.102255i	−0.455908	−	0.890027i	$-0.650685\pi$
$947$	−17.8459	+	3.14672i	−0.579914	+	0.102255i	−0.124006	+	0.992281i	$0.539574\pi$
$948$	14.5838	−	19.0651i	0.473659	−	0.619205i
$949$			9.19317i			0.298423i
$950$	6.76871	−	0.308783i	0.219606	−	0.0100182i
$951$	31.2218			1.01244
$952$	−16.8213	+	16.1755i	−0.545181	+	0.524252i
$953$	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	$0.744725\pi$
$954$	−5.48367	−	6.24348i	−0.177540	−	0.202140i
$955$	25.7763	+	30.7190i	0.834101	+	0.994043i
$956$	−19.0109	+	36.6536i	−0.614856	+	1.18546i
$957$	−1.82750	−	1.05511i	−0.0590747	−	0.0341068i
$958$	−51.0218	+	19.8853i	−1.64844	+	0.642466i
$959$	40.1505	−	14.6136i	1.29653	−	0.471898i
$960$	−16.7106	−	10.5405i	−0.539333	−	0.340193i
$961$	9.78731	+	16.9521i	0.315720	+	0.546843i
$962$	10.3812	+	8.31901i	0.334703	+	0.268216i
$963$	−6.66321	−	1.17490i	−0.214719	−	0.0378607i
$964$	−30.2434	+	12.5804i	−0.974075	+	0.405187i
$965$	−13.7853	+	16.4287i	−0.443765	+	0.528858i
$966$	−0.0180963	−	0.801782i	−0.000582238	−	0.0257969i
$967$	−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	−0.963606	−	0.267325i	$-0.913860\pi$
$971$	−1.67046	+	4.58956i	−0.0536078	+	0.147286i	0.909999	+	0.414611i	$0.136082\pi$
$972$	−1.98328	−	0.258079i	−0.0636137	−	0.00827790i
$973$	28.6780	−	34.1772i	0.919376	−	1.09567i
$974$	17.2551	+	28.3875i	0.552889	+	0.909594i
$975$	0.163688	−	0.928319i	0.00524220	−	0.0297300i
$976$	8.25215	+	17.5591i	0.264145	+	0.562054i
$977$	−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	$0.953415\pi$
$978$	−5.43728	−	27.2284i	−0.173865	−	0.870667i
$979$	18.8973	+	51.9198i	0.603959	+	1.65936i
$980$	−3.00098	+	0.670023i	−0.0958628	+	0.0214031i
$981$	10.2288	+	5.90560i	0.326581	+	0.188551i
$982$	−1.79814	+	5.31023i	−0.0573810	+	0.169456i
$983$	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	$-0.0332722\pi$
$984$	−3.66797	−	8.28551i	−0.116931	−	0.264132i
$985$	6.69597	+	37.9747i	0.213351	+	1.20997i
$986$	1.96267	+	1.07485i	0.0625043	+	0.0342301i
$987$		−	16.6488i		−	0.529937i
$988$	6.71420	+	3.28854i	0.213607	+	0.104622i
$989$		−	0.558890i		−	0.0177717i
$990$	7.30969	−	13.3475i	0.232317	−	0.424212i
$991$	−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	$-0.215850\pi$
$992$	18.9994	−	2.15287i	0.603232	−	0.0683536i
$993$	14.1100	−	11.8397i	0.447766	−	0.375720i
$994$	−1.39956	−	0.473919i	−0.0443915	−	0.0150318i
$995$	44.6183	+	25.7604i	1.41450	+	0.816659i
$996$	−2.73735	−	12.2604i	−0.0867362	−	0.388485i
$997$	2.05862	+	5.65600i	0.0651970	+	0.179127i	0.968013	−	0.250899i	$-0.0807263\pi$
$997$	2.05862	+	5.65600i	0.0651970	+	0.179127i	−0.902816	+	0.430027i	$0.858504\pi$
$998$	41.2768	−	8.24265i	1.30660	−	0.260916i
$999$	−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.61.27	yes	240
8.5	even	2	inner	456.2.bk.a.61.18	✓	240
19.5	even	9	inner	456.2.bk.a.157.18	yes	240
152.5	even	18	inner	456.2.bk.a.157.27	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bk.a.61.18	✓	240	8.5	even	2	inner
456.2.bk.a.61.27	yes	240	1.1	even	1	trivial
456.2.bk.a.157.18	yes	240	19.5	even	9	inner
456.2.bk.a.157.27	yes	240	152.5	even	18	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+(0.679291 - 1.24039i) q^{2} +(0.984808 - 0.173648i) q^{3} +(-1.07713 - 1.68517i) q^{4} +(-1.58746 - 1.89186i) q^{5} +(0.453580 - 1.33950i) q^{6} +(1.26268 - 2.18703i) q^{7} +(-2.82195 + 0.191334i) q^{8} +(0.939693 - 0.342020i) q^{9} +(-3.42499 + 0.683943i) q^{10} +(-3.77345 + 2.17860i) q^{11} +(-1.35339 - 1.47253i) q^{12} +(-0.844562 - 0.148919i) q^{13} +(-1.85504 - 3.05185i) q^{14} +(-1.89186 - 1.58746i) q^{15} +(-1.67960 + 3.63028i) 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} +(0.139042 + 6.16044i) q^{22} +(0.172021 + 0.144343i) q^{23} +(-2.74585 + 0.678454i) q^{24} +(-0.190869 + 1.08247i) q^{25} +(-0.758421 + 0.946425i) q^{26} +(0.866025 - 0.500000i) q^{27} +(-5.04559 + 0.227874i) q^{28} +(0.165642 + 0.455099i) q^{29} +(-3.25419 + 1.26830i) q^{30} +(1.69007 - 2.92729i) q^{31} +(3.36203 + 4.54937i) q^{32} +(-3.33781 + 2.80075i) q^{33} +(3.47157 - 3.04909i) q^{34} +(-6.14202 + 1.08300i) q^{35} +(-1.58853 - 1.21514i) q^{36} -10.9689i q^{37} +(-1.34598 - 6.01567i) q^{38} -0.857590 q^{39} +(4.84171 + 5.03500i) q^{40} +(0.556297 + 3.15492i) q^{41} +(-2.35680 - 2.68336i) q^{42} +(-1.59980 - 1.90657i) q^{43} +(7.73579 + 4.01227i) q^{44} +(-2.13878 - 1.23483i) q^{45} +(0.295894 - 0.115322i) q^{46} +(6.19504 - 2.25481i) q^{47} +(-1.02369 + 3.86679i) q^{48} +(0.311265 + 0.539127i) q^{49} +(1.21303 + 0.972067i) q^{50} +(3.21753 + 0.567337i) q^{51} +(0.658746 + 1.58363i) q^{52} +(3.77694 - 4.50118i) q^{53} +(-0.0319107 - 1.41385i) 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} +(-0.637366 + 4.89801i) q^{60} +(3.11777 - 3.71562i) q^{61} +(-2.48293 - 4.08483i) q^{62} +(0.438525 - 2.48700i) q^{63} +(7.92678 - 1.07987i) q^{64} +(1.05897 + 1.83420i) q^{65} +(1.20668 + 6.04271i) q^{66} +(5.06461 + 13.9149i) q^{67} +(-1.42385 - 6.37731i) q^{68} +(0.194473 + 0.112279i) q^{69} +(-2.82887 + 8.35416i) q^{70} +(0.316942 - 0.265946i) q^{71} +(-2.58632 + 1.14496i) q^{72} +(-1.86147 - 10.5569i) q^{73} +(-13.6056 - 7.45105i) q^{74} +1.09917i q^{75} +(-8.37609 - 2.41685i) q^{76} +11.0035i q^{77} +(-0.582554 + 1.06375i) q^{78} +(2.08407 + 11.8194i) q^{79} +(9.53429 - 2.58537i) q^{80} +(0.766044 - 0.642788i) q^{81} +(4.29121 + 1.45308i) q^{82} +(5.43961 + 3.14056i) q^{83} +(-4.92936 + 1.10057i) q^{84} +(-2.75968 - 7.58215i) q^{85} +(-3.45162 + 0.689260i) q^{86} +(0.242153 + 0.419421i) q^{87} +(10.2316 - 6.86989i) q^{88} +(2.20196 - 12.4879i) q^{89} +(-2.98452 + 1.81411i) q^{90} +(-1.39210 + 1.65904i) q^{91} +(0.0579537 - 0.445360i) 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} +(0.880167 - 0.0198654i) 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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