LMFDB - Embedded newform 605.2.m.d.457.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [605,2,Mod(112,605)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(605, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([5, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("605.112"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.m (of order $20$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,6,0,-2,0,20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			457.4
Character	$\chi$	$=$	605.457
Dual form			605.2.m.d.233.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.16745 + 1.10437i) q^{2} +(-0.590657 + 0.0935509i) q^{3} +(2.30265 + 3.16932i) q^{4} +(-2.23491 + 0.0720754i) q^{5} +(-1.38354 - 0.449539i) q^{6} +(-0.403870 + 2.54993i) q^{7} +(0.729688 + 4.60707i) q^{8} +(-2.51305 + 0.816538i) q^{9} +(-4.92366 - 2.31195i) q^{10} +(-1.65657 - 1.65657i) q^{12} +(-1.27517 + 2.50266i) q^{13} +(-3.69145 + 5.08085i) q^{14} +(1.31332 - 0.251649i) q^{15} +(-1.08521 + 3.33993i) q^{16} +(0.428708 + 0.841386i) q^{17} +(-6.34868 - 1.00553i) q^{18} +(3.35726 + 2.43919i) q^{19} +(-5.37463 - 6.91718i) q^{20} -1.54392i q^{21} +(0.104710 - 0.104710i) q^{23} +(-0.861991 - 2.65293i) q^{24} +(4.98961 - 0.322163i) q^{25} +(-5.52773 + 4.01613i) q^{26} +(3.00648 - 1.53188i) q^{27} +(-9.01154 + 4.59161i) q^{28} +(5.61462 - 4.07926i) q^{29} +(3.12448 + 0.904958i) q^{30} +(2.80047 + 8.61895i) q^{31} +(0.555921 - 0.555921i) q^{32} +2.29712i q^{34} +(0.718824 - 5.72797i) q^{35} +(-8.37454 - 6.08446i) q^{36} +(-7.50462 - 1.18862i) q^{37} +(4.58292 + 8.99450i) q^{38} +(0.519061 - 1.59750i) q^{39} +(-1.96284 - 10.2438i) q^{40} +(2.02641 - 2.78912i) q^{41} +(1.70506 - 3.34638i) q^{42} +(-3.91833 - 3.91833i) q^{43} +(5.55757 - 2.00601i) q^{45} +(0.342592 - 0.111315i) q^{46} +(0.165396 + 1.04427i) q^{47} +(0.328533 - 2.07428i) q^{48} +(0.318339 + 0.103435i) q^{49} +(11.1705 + 4.81212i) q^{50} +(-0.331932 - 0.456865i) q^{51} +(-10.8680 + 1.72132i) q^{52} +(3.67328 + 1.87163i) q^{53} +8.20817 q^{54} -12.0424 q^{56} +(-2.21118 - 1.12665i) q^{57} +(16.6745 - 2.64097i) q^{58} +(3.80993 + 5.24392i) q^{59} +(3.82167 + 3.58288i) q^{60} +(-9.05905 - 2.94346i) q^{61} +(-3.44865 + 21.7739i) q^{62} +(-1.06717 - 6.73788i) q^{63} +(8.49874 - 2.76141i) q^{64} +(2.66950 - 5.68511i) q^{65} +(2.94509 + 2.94509i) q^{67} +(-1.67946 + 3.29613i) q^{68} +(-0.0520518 + 0.0716431i) q^{69} +(7.88384 - 11.6213i) q^{70} +(0.391234 - 1.20409i) q^{71} +(-5.59558 - 10.9820i) q^{72} +(1.74957 + 0.277105i) q^{73} +(-14.9533 - 10.8642i) q^{74} +(-2.91701 + 0.657071i) q^{75} +16.2568i q^{76} +(2.88928 - 2.88928i) q^{78} +(-1.34174 - 4.12944i) q^{79} +(2.18461 - 7.54265i) q^{80} +(4.78068 - 3.47337i) q^{81} +(7.47238 - 3.80737i) q^{82} +(7.38775 - 3.76425i) q^{83} +(4.89318 - 3.55511i) q^{84} +(-1.01876 - 1.84952i) q^{85} +(-4.16551 - 12.8201i) q^{86} +(-2.93470 + 2.93470i) q^{87} +4.23092i q^{89} +(14.2612 + 1.78969i) q^{90} +(-5.86661 - 4.26234i) q^{91} +(0.572968 + 0.0907492i) q^{92} +(-2.46043 - 4.82886i) q^{93} +(-0.794777 + 2.44607i) q^{94} +(-7.67896 - 5.20938i) q^{95} +(-0.276352 + 0.380366i) q^{96} +(-6.54815 + 12.8515i) q^{97} +(0.575755 + 0.575755i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 6 q^{3} - 2 q^{5} + 20 q^{7} - 20 q^{8} + 12 q^{12} - 20 q^{13} + 4 q^{15} + 12 q^{16} + 30 q^{18} + 16 q^{20} - 24 q^{23} - 24 q^{25} - 20 q^{26} + 24 q^{27} - 20 q^{28} + 40 q^{30} + 32 q^{31}+ \cdots - 38 q^{97}+O(q^{100}) $ 32 * q + 6 * q^3 - 2 * q^5 + 20 * q^7 - 20 * q^8 + 12 * q^12 - 20 * q^13 + 4 * q^15 + 12 * q^16 + 30 * q^18 + 16 * q^20 - 24 * q^23 - 24 * q^25 - 20 * q^26 + 24 * q^27 - 20 * q^28 + 40 * q^30 + 32 * q^31 + 30 * q^35 - 36 * q^36 - 8 * q^37 + 10 * q^38 - 50 * q^40 - 20 * q^42 - 28 * q^45 + 20 * q^46 + 42 * q^47 + 26 * q^48 + 80 * q^50 - 100 * q^51 - 20 * q^52 - 34 * q^53 - 80 * q^56 - 40 * q^57 + 90 * q^58 - 86 * q^60 + 10 * q^62 - 10 * q^63 - 8 * q^67 - 70 * q^68 + 10 * q^70 - 36 * q^71 - 70 * q^72 + 30 * q^73 + 4 * q^75 + 60 * q^78 - 102 * q^80 + 8 * q^81 + 20 * q^82 - 60 * q^83 + 60 * q^85 - 80 * q^86 + 130 * q^90 - 60 * q^91 + 42 * q^92 - 8 * q^93 - 30 * q^95 - 38 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{9}{10}\right)$

Coefficient data

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

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

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

$2$	2.16745	+	1.10437i	1.53262	+	0.780910i	0.997941	−	0.0641439i	$-0.0204317\pi$
$2$	2.16745	+	1.10437i	1.53262	+	0.780910i	0.534681	+	0.845054i	$0.320432\pi$
$3$	−0.590657	+	0.0935509i	−0.341016	+	0.0540116i	−0.324594	−	0.945854i	$-0.605228\pi$
$3$	−0.590657	+	0.0935509i	−0.341016	+	0.0540116i	−0.0164223	+	0.999865i	$0.505228\pi$
$4$	2.30265	+	3.16932i	1.15132	+	1.58466i
$5$	−2.23491	+	0.0720754i	−0.999480	+	0.0322331i
$5$	−2.23491	+	0.0720754i	−0.999480	+	0.0322331i
$6$	−1.38354	−	0.449539i	−0.564827	−	0.183523i
$7$	−0.403870	+	2.54993i	−0.152649	+	0.963785i	0.785829	+	0.618444i	$0.212237\pi$
$7$	−0.403870	+	2.54993i	−0.152649	+	0.963785i	−0.938477	+	0.345341i	$0.887763\pi$
$8$	0.729688	+	4.60707i	0.257984	+	1.62884i
$9$	−2.51305	+	0.816538i	−0.837682	+	0.272179i
$10$	−4.92366	−	2.31195i	−1.55700	−	0.731103i
$11$		0			0
$11$		0			0
$12$	−1.65657	−	1.65657i	−0.478210	−	0.478210i
$13$	−1.27517	+	2.50266i	−0.353668	+	0.694112i	−0.997471	−	0.0710794i	$-0.977356\pi$
$13$	−1.27517	+	2.50266i	−0.353668	+	0.694112i	0.643803	+	0.765191i	$0.277356\pi$
$14$	−3.69145	+	5.08085i	−0.986582	+	1.35791i
$15$	1.31332	−	0.251649i	0.339098	−	0.0649756i
$16$	−1.08521	+	3.33993i	−0.271302	+	0.834983i
$17$	0.428708	+	0.841386i	0.103977	+	0.204066i	0.937134	−	0.348971i	$-0.113469\pi$
$17$	0.428708	+	0.841386i	0.103977	+	0.204066i	−0.833157	+	0.553037i	$0.813469\pi$
$18$	−6.34868	−	1.00553i	−1.49640	−	0.237006i
$19$	3.35726	+	2.43919i	0.770207	+	0.559588i	0.902024	−	0.431686i	$-0.142081\pi$
$19$	3.35726	+	2.43919i	0.770207	+	0.559588i	−0.131817	+	0.991274i	$0.542081\pi$
$20$	−5.37463	−	6.91718i	−1.20180	−	1.54673i
$21$		−	1.54392i		−	0.336911i
$22$		0			0
$23$	0.104710	−	0.104710i	0.0218334	−	0.0218334i	−0.696106	−	0.717939i	$-0.745086\pi$
$23$	0.104710	−	0.104710i	0.0218334	−	0.0218334i	0.717939	+	0.696106i	$0.245086\pi$
$24$	−0.861991	−	2.65293i	−0.175953	−	0.541528i
$25$	4.98961	−	0.322163i	0.997922	−	0.0644327i
$26$	−5.52773	+	4.01613i	−1.08408	+	0.787629i
$27$	3.00648	−	1.53188i	0.578597	−	0.294810i
$28$	−9.01154	+	4.59161i	−1.70302	+	0.867733i
$29$	5.61462	−	4.07926i	1.04261	−	0.757499i	0.0718154	−	0.997418i	$-0.477121\pi$
$29$	5.61462	−	4.07926i	1.04261	−	0.757499i	0.970793	+	0.239919i	$0.0771208\pi$
$30$	3.12448	+	0.904958i	0.570449	+	0.165222i
$31$	2.80047	+	8.61895i	0.502979	+	1.54801i	0.804143	+	0.594436i	$0.202625\pi$
$31$	2.80047	+	8.61895i	0.502979	+	1.54801i	−0.301164	+	0.953572i	$0.597375\pi$
$32$	0.555921	−	0.555921i	0.0982739	−	0.0982739i
$33$		0			0
$34$			2.29712i			0.393953i
$35$	0.718824	−	5.72797i	0.121503	−	0.968204i
$36$	−8.37454	−	6.08446i	−1.39576	−	1.01408i
$37$	−7.50462	−	1.18862i	−1.23375	−	0.195407i	−0.494705	−	0.869061i	$-0.664724\pi$
$37$	−7.50462	−	1.18862i	−1.23375	−	0.195407i	−0.739047	+	0.673654i	$0.764724\pi$
$38$	4.58292	+	8.99450i	0.743448	+	1.45910i
$39$	0.519061	−	1.59750i	0.0831162	−	0.255805i
$40$	−1.96284	−	10.2438i	−0.310352	−	1.61968i
$41$	2.02641	−	2.78912i	0.316472	−	0.435587i	−0.620914	−	0.783879i	$-0.713238\pi$
$41$	2.02641	−	2.78912i	0.316472	−	0.435587i	0.937386	+	0.348292i	$0.113238\pi$
$42$	1.70506	−	3.34638i	0.263097	−	0.516357i
$43$	−3.91833	−	3.91833i	−0.597540	−	0.597540i	0.342117	−	0.939657i	$-0.388856\pi$
$43$	−3.91833	−	3.91833i	−0.597540	−	0.597540i	−0.939657	+	0.342117i	$0.888856\pi$
$44$		0			0
$45$	5.55757	−	2.00601i	0.828473	−	0.299039i
$46$	0.342592	−	0.111315i	0.0505124	−	0.0164125i
$47$	0.165396	+	1.04427i	0.0241255	+	0.152323i	0.996810	−	0.0798074i	$-0.0254305\pi$
$47$	0.165396	+	1.04427i	0.0241255	+	0.152323i	−0.972685	+	0.232130i	$0.925431\pi$
$48$	0.328533	−	2.07428i	0.0474197	−	0.299396i
$49$	0.318339	+	0.103435i	0.0454770	+	0.0147764i
$50$	11.1705	+	4.81212i	1.57975	+	0.680536i
$51$	−0.331932	−	0.456865i	−0.0464797	−	0.0639739i
$52$	−10.8680	+	1.72132i	−1.50712	+	0.238704i
$53$	3.67328	+	1.87163i	0.504564	+	0.257088i	0.687694	−	0.726000i	$-0.258623\pi$
$53$	3.67328	+	1.87163i	0.504564	+	0.257088i	−0.183130	+	0.983089i	$0.558623\pi$
$54$	8.20817			1.11699
$55$		0			0
$56$	−12.0424			−1.60924
$57$	−2.21118	−	1.12665i	−0.292877	−	0.149228i
$58$	16.6745	−	2.64097i	2.18946	−	0.346777i
$59$	3.80993	+	5.24392i	0.496011	+	0.682701i	0.981483	−	0.191552i	$-0.0613520\pi$
$59$	3.80993	+	5.24392i	0.496011	+	0.682701i	−0.485471	+	0.874253i	$0.661352\pi$
$60$	3.82167	+	3.58288i	0.493376	+	0.462548i
$61$	−9.05905	−	2.94346i	−1.15989	−	0.376872i	−0.335031	−	0.942207i	$-0.608747\pi$
$61$	−9.05905	−	2.94346i	−1.15989	−	0.376872i	−0.824861	+	0.565335i	$0.808747\pi$
$62$	−3.44865	+	21.7739i	−0.437979	+	2.76529i
$63$	−1.06717	−	6.73788i	−0.134451	−	0.848893i
$64$	8.49874	−	2.76141i	1.06234	−	0.345176i
$65$	2.66950	−	5.68511i	0.331111	−	0.705151i
$66$		0			0
$67$	2.94509	+	2.94509i	0.359801	+	0.359801i	0.863739	−	0.503939i	$-0.168116\pi$
$67$	2.94509	+	2.94509i	0.359801	+	0.359801i	−0.503939	+	0.863739i	$0.668116\pi$
$68$	−1.67946	+	3.29613i	−0.203665	+	0.399715i
$69$	−0.0520518	+	0.0716431i	−0.00626629	+	0.00862481i
$70$	7.88384	−	11.6213i	0.942299	−	1.38901i
$71$	0.391234	−	1.20409i	0.0464309	−	0.142900i	−0.925153	−	0.379594i	$-0.876064\pi$
$71$	0.391234	−	1.20409i	0.0464309	−	0.142900i	0.971584	+	0.236694i	$0.0760639\pi$
$72$	−5.59558	−	10.9820i	−0.659446	−	1.29424i
$73$	1.74957	+	0.277105i	0.204772	+	0.0324326i	0.257977	−	0.966151i	$-0.416944\pi$
$73$	1.74957	+	0.277105i	0.204772	+	0.0324326i	−0.0532059	+	0.998584i	$0.516944\pi$
$74$	−14.9533	−	10.8642i	−1.73828	−	1.26293i
$75$	−2.91701	+	0.657071i	−0.336827	+	0.0758720i
$76$			16.2568i			1.86479i
$77$		0			0
$78$	2.88928	−	2.88928i	0.327147	−	0.327147i
$79$	−1.34174	−	4.12944i	−0.150957	−	0.464598i	0.846772	−	0.531957i	$-0.178543\pi$
$79$	−1.34174	−	4.12944i	−0.150957	−	0.464598i	−0.997729	+	0.0673580i	$0.978543\pi$
$80$	2.18461	−	7.54265i	0.244247	−	0.843294i
$81$	4.78068	−	3.47337i	0.531187	−	0.385930i
$82$	7.47238	−	3.80737i	0.825187	−	0.420454i
$83$	7.38775	−	3.76425i	0.810911	−	0.413180i	0.00119325	−	0.999999i	$-0.499620\pi$
$83$	7.38775	−	3.76425i	0.810911	−	0.413180i	0.809718	+	0.586819i	$0.199620\pi$
$84$	4.89318	−	3.55511i	0.533890	−	0.387894i
$85$	−1.01876	−	1.84952i	−0.110501	−	0.200609i
$86$	−4.16551	−	12.8201i	−0.449178	−	1.38243i
$87$	−2.93470	+	2.93470i	−0.314632	+	0.314632i
$88$		0			0
$89$			4.23092i			0.448477i	0.974534	+	0.224238i	$0.0719894\pi$
$89$			4.23092i			0.448477i	−0.974534	+	0.224238i	$0.928011\pi$
$90$	14.2612	+	1.78969i	1.50326	+	0.188649i
$91$	−5.86661	−	4.26234i	−0.614988	−	0.446815i
$92$	0.572968	+	0.0907492i	0.0597360	+	0.00946125i
$93$	−2.46043	−	4.82886i	−0.255134	−	0.500729i
$94$	−0.794777	+	2.44607i	−0.0819749	+	0.252293i
$95$	−7.67896	−	5.20938i	−0.787844	−	0.534471i
$96$	−0.276352	+	0.380366i	−0.0282050	+	0.0388209i
$97$	−6.54815	+	12.8515i	−0.664864	+	1.30487i	0.274381	+	0.961621i	$0.411527\pi$
$97$	−6.54815	+	12.8515i	−0.664864	+	1.30487i	−0.939245	+	0.343248i	$0.888473\pi$
$98$	0.575755	+	0.575755i	0.0581600	+	0.0581600i
$99$		0			0
$100$	12.5104	+	15.0719i	1.25104	+	1.50719i
$101$	−1.84046	+	0.598002i	−0.183133	+	0.0595034i	−0.399148	−	0.916887i	$-0.630694\pi$
$101$	−1.84046	+	0.598002i	−0.183133	+	0.0595034i	0.216015	+	0.976390i	$0.430694\pi$
$102$	−0.214898	−	1.35681i	−0.0212780	−	0.134344i
$103$	−0.268951	+	1.69809i	−0.0265005	+	0.167318i	−0.997389	−	0.0722135i	$-0.976994\pi$
$103$	−0.268951	+	1.69809i	−0.0265005	+	0.167318i	0.970889	+	0.239531i	$0.0769937\pi$
$104$	−12.4604	−	4.04862i	−1.22184	−	0.397000i
$105$	0.111279	+	3.45052i	0.0108597	+	0.336736i
$106$	5.89470	+	8.11335i	0.572544	+	0.788039i
$107$	4.10781	−	0.650614i	0.397117	−	0.0628972i	0.0453180	−	0.998973i	$-0.485570\pi$
$107$	4.10781	−	0.650614i	0.397117	−	0.0628972i	0.351799	+	0.936075i	$0.385570\pi$
$108$	11.7779	+	6.00113i	1.13333	+	0.577459i
$109$	3.22321			0.308728			0.154364	−	0.988014i	$-0.450667\pi$
$109$	3.22321			0.308728			0.154364	+	0.988014i	$0.450667\pi$
$110$		0			0
$111$	4.54385			0.431284
$112$	−8.07832	−	4.11611i	−0.763330	−	0.388936i
$113$	11.0159	−	1.74475i	1.03629	−	0.164132i	0.384964	−	0.922932i	$-0.374214\pi$
$113$	11.0159	−	1.74475i	1.03629	−	0.164132i	0.651324	+	0.758800i	$0.274214\pi$
$114$	−3.54838	−	4.88393i	−0.332336	−	0.457422i
$115$	−0.226469	+	0.241563i	−0.0211183	+	0.0225259i
$116$	25.8570	+	8.40145i	2.40076	+	0.780055i
$117$	1.16104	−	7.33051i	0.107338	−	0.677706i
$118$	2.46661	+	15.5736i	0.227070	+	1.43366i
$119$	−2.31862	+	0.753366i	−0.212548	+	0.0690609i
$120$	2.11768	+	5.86693i	0.193317	+	0.535575i
$121$		0			0
$122$	−16.3844	−	16.3844i	−1.48337	−	1.48337i
$123$	−0.935990	+	1.83698i	−0.0843954	+	0.165635i
$124$	−20.8678	+	28.7220i	−1.87398	+	2.57931i
$125$	−11.1281	+	1.07963i	−0.995327	+	0.0965653i
$126$	5.12808	−	15.7826i	0.456846	−	1.40603i
$127$	1.07825	+	2.11618i	0.0956788	+	0.187780i	0.933885	−	0.357573i	$-0.116396\pi$
$127$	1.07825	+	2.11618i	0.0956788	+	0.187780i	−0.838206	+	0.545353i	$0.816396\pi$
$128$	19.9172	+	3.15458i	1.76045	+	0.278828i
$129$	2.68095	+	1.94783i	0.236045	+	0.171497i
$130$	12.0645	−	9.37409i	1.05813	−	0.822162i
$131$		−	3.12466i		−	0.273003i	−0.990640	−	0.136501i	$-0.956414\pi$
$131$		−	3.12466i		−	0.273003i	0.990640	−	0.136501i	$-0.0435858\pi$
$132$		0			0
$133$	−7.57567	+	7.57567i	−0.656894	+	0.656894i
$134$	3.13088	+	9.63584i	0.270466	+	0.832410i
$135$	−6.60879	+	3.64030i	−0.568794	+	0.313307i
$136$	−3.56350	+	2.58903i	−0.305568	+	0.222008i
$137$	−14.7336	+	7.50715i	−1.25878	+	0.641379i	−0.950738	−	0.309995i	$-0.899673\pi$
$137$	−14.7336	+	7.50715i	−1.25878	+	0.641379i	−0.308039	+	0.951374i	$0.599673\pi$
$138$	−0.191941	+	0.0977986i	−0.0163391	+	0.00832517i
$139$	3.49534	−	2.53951i	0.296470	−	0.215398i	−0.429599	−	0.903020i	$-0.641345\pi$
$139$	3.49534	−	2.53951i	0.296470	−	0.215398i	0.726069	+	0.687621i	$0.241345\pi$
$140$	19.8090	−	10.9113i	1.67417	−	0.922175i
$141$	−0.195385	−	0.601333i	−0.0164544	−	0.0506414i
$142$	2.17775	−	2.17775i	0.182753	−	0.182753i
$143$		0			0
$144$		−	9.27951i		−	0.773293i
$145$	−12.2541	+	9.52144i	−1.01765	+	0.790712i
$146$	3.48609	+	2.53279i	0.288511	+	0.209615i
$147$	−0.197706	−	0.0313135i	−0.0163065	−	0.00258269i
$148$	−13.5134	−	26.5215i	−1.11079	−	2.18006i
$149$	2.60955	−	8.03136i	0.213782	−	0.657954i	−0.785455	−	0.618918i	$-0.787571\pi$
$149$	2.60955	−	8.03136i	0.213782	−	0.657954i	0.999238	−	0.0390361i	$-0.0124288\pi$
$150$	−7.04814	−	1.79730i	−0.575478	−	0.146749i
$151$	7.01365	−	9.65346i	0.570763	−	0.785587i	−0.421882	−	0.906651i	$-0.638630\pi$
$151$	7.01365	−	9.65346i	0.570763	−	0.785587i	0.992645	+	0.121063i	$0.0386304\pi$
$152$	−8.78776	+	17.2470i	−0.712782	+	1.39891i
$153$	−1.76439	−	1.76439i	−0.142642	−	0.142642i
$154$		0			0
$155$	−6.87999	−	19.0607i	−0.552614	−	1.53099i
$156$	6.25823	−	2.03342i	0.501059	−	0.162804i
$157$	0.212989	+	1.34476i	0.0169983	+	0.107323i	0.994729	−	0.102542i	$-0.0326975\pi$
$157$	0.212989	+	1.34476i	0.0169983	+	0.107323i	−0.977730	+	0.209865i	$0.932698\pi$
$158$	1.65229	−	10.4322i	0.131449	−	0.829938i
$159$	−2.34474	−	0.761854i	−0.185950	−	0.0604189i
$160$	−1.20236	+	1.28250i	−0.0950551	+	0.101390i
$161$	0.224713	+	0.309291i	0.0177099	+	0.0243756i
$162$	14.1978	−	2.24871i	1.11549	−	0.176676i
$163$	−20.4427	−	10.4161i	−1.60120	−	0.815852i	−0.999858	−	0.0168592i	$-0.994633\pi$
$163$	−20.4427	−	10.4161i	−1.60120	−	0.815852i	−0.601341	−	0.798992i	$-0.705367\pi$
$164$	13.5057			1.05462
$165$		0			0
$166$	20.1698			1.56548
$167$	−12.7952	−	6.51948i	−0.990123	−	0.504493i	−0.117597	−	0.993061i	$-0.537519\pi$
$167$	−12.7952	−	6.51948i	−0.990123	−	0.504493i	−0.872525	+	0.488569i	$0.837519\pi$
$168$	7.11294	−	1.12658i	0.548775	−	0.0869175i
$169$	3.00397	+	4.13461i	0.231075	+	0.318047i
$170$	−0.165566	−	5.13385i	−0.0126983	−	0.393748i
$171$	−10.4286	−	3.38847i	−0.797497	−	0.259122i
$172$	3.39592	−	21.4410i	0.258937	−	1.63486i
$173$	3.48873	+	22.0270i	0.265243	+	1.67468i	0.656444	+	0.754375i	$0.272060\pi$
$173$	3.48873	+	22.0270i	0.265243	+	1.67468i	−0.391201	+	0.920305i	$0.627940\pi$
$174$	−9.60182	+	3.11982i	−0.727912	+	0.236513i
$175$	−1.19366	+	12.8533i	−0.0902321	+	0.971618i
$176$		0			0
$177$	−2.74094	−	2.74094i	−0.206022	−	0.206022i
$178$	−4.67252	+	9.17033i	−0.350220	+	0.687345i
$179$	2.56757	−	3.53396i	0.191909	−	0.264140i	−0.702210	−	0.711970i	$-0.747803\pi$
$179$	2.56757	−	3.53396i	0.191909	−	0.264140i	0.894119	+	0.447830i	$0.147803\pi$
$180$	19.1548	+	12.9946i	1.42772	+	0.968560i
$181$	2.91705	−	8.97777i	0.216823	−	0.667312i	−0.782196	−	0.623032i	$-0.785901\pi$
$181$	2.91705	−	8.97777i	0.216823	−	0.667312i	0.999019	−	0.0442801i	$-0.0140994\pi$
$182$	−8.00839	−	15.7174i	−0.593622	−	1.16505i
$183$	5.62616	+	0.891096i	0.415897	+	0.0658717i
$184$	0.558809	+	0.405999i	0.0411960	+	0.0299306i
$185$	16.8578	+	2.11554i	1.23941	+	0.155538i
$186$		−	13.1836i		−	0.966665i
$187$		0			0
$188$	−2.92879	+	2.92879i	−0.213604	+	0.213604i
$189$	2.69196	+	8.28500i	0.195811	+	0.602645i
$190$	−10.8907	−	19.7715i	−0.790093	−	1.43438i
$191$	5.23658	−	3.80460i	0.378906	−	0.275291i	−0.381988	−	0.924167i	$-0.624761\pi$
$191$	5.23658	−	3.80460i	0.378906	−	0.275291i	0.760894	+	0.648876i	$0.224761\pi$
$192$	−4.76151	+	2.42611i	−0.343632	+	0.175089i
$193$	0.896922	−	0.457004i	0.0645618	−	0.0328959i	−0.421412	−	0.906870i	$-0.638465\pi$
$193$	0.896922	−	0.457004i	0.0645618	−	0.0328959i	0.485973	+	0.873974i	$0.338465\pi$
$194$	−28.3856	+	20.6234i	−2.03797	+	1.48067i
$195$	−1.04491	+	3.60768i	−0.0748277	+	0.258352i
$196$	0.405205	+	1.24709i	0.0289432	+	0.0890781i
$197$	−17.3425	+	17.3425i	−1.23560	+	1.23560i	−0.273821	+	0.961781i	$0.588287\pi$
$197$	−17.3425	+	17.3425i	−1.23560	+	1.23560i	−0.961781	+	0.273821i	$0.911713\pi$
$198$		0			0
$199$		−	3.25580i		−	0.230797i	−0.993319	−	0.115399i	$-0.963185\pi$
$199$		−	3.25580i		−	0.230797i	0.993319	−	0.115399i	$-0.0368146\pi$
$200$	5.12509	+	22.7524i	0.362398	+	1.60884i
$201$	−2.01506	−	1.46403i	−0.142131	−	0.103264i
$202$	−4.64953	−	0.736413i	−0.327140	−	0.0518138i
$203$	8.13427	+	15.9644i	0.570914	+	1.12048i
$204$	0.683631	−	2.10400i	0.0478637	−	0.147309i
$205$	−4.32781	+	6.37947i	−0.302268	+	0.445561i
$206$	−2.45826	+	3.38351i	−0.171275	+	0.235740i
$207$	−0.177640	+	0.348639i	−0.0123469	+	0.0242321i
$208$	−6.97487	−	6.97487i	−0.483621	−	0.483621i
$209$		0			0
$210$	−3.56947	+	7.60173i	−0.246317	+	0.524569i
$211$	23.6255	−	7.67640i	1.62645	−	0.528465i	0.652997	−	0.757360i	$-0.273511\pi$
$211$	23.6255	−	7.67640i	1.62645	−	0.528465i	0.973451	+	0.228895i	$0.0735113\pi$
$212$	2.52648	+	15.9515i	0.173519	+	1.09556i
$213$	−0.118441	+	0.747807i	−0.00811544	+	0.0512389i
$214$	9.62202	+	3.12638i	0.657748	+	0.213715i
$215$	9.03952	+	8.47469i	0.616490	+	0.577969i
$216$	9.25126	+	12.7333i	0.629468	+	0.866389i
$217$	−23.1088	+	3.66007i	−1.56873	+	0.248462i
$218$	6.98617	+	3.55963i	0.473163	+	0.241089i
$219$	−1.05932			−0.0715822
$220$		0			0
$221$	−2.65237			−0.178418
$222$	9.84860	+	5.01811i	0.660995	+	0.336794i
$223$	−19.3488	+	3.06455i	−1.29569	+	0.205218i	−0.765928	−	0.642926i	$-0.777720\pi$
$223$	−19.3488	+	3.06455i	−1.29569	+	0.205218i	−0.529766	+	0.848144i	$0.677720\pi$
$224$	1.19304	+	1.64208i	0.0797135	+	0.109716i
$225$	−12.2761	+	4.88382i	−0.818404	+	0.325588i
$226$	25.8033	+	8.38400i	1.71641	+	0.557695i
$227$	−0.160020	+	1.01032i	−0.0106209	+	0.0670576i	−0.992430	−	0.122815i	$-0.960808\pi$
$227$	−0.160020	+	1.01032i	−0.0106209	+	0.0670576i	0.981809	+	0.189873i	$0.0608077\pi$
$228$	−1.52084	−	9.60221i	−0.100720	−	0.635922i
$229$	0.0968640	−	0.0314730i	0.00640095	−	0.00207980i	−0.305815	−	0.952091i	$-0.598929\pi$
$229$	0.0968640	−	0.0314730i	0.00640095	−	0.00207980i	0.312216	+	0.950011i	$0.398929\pi$
$230$	−0.757637	+	0.273470i	−0.0499571	+	0.0180321i
$231$		0			0
$232$	22.8903	+	22.8903i	1.50282	+	1.50282i
$233$	9.71543	−	19.0676i	0.636479	−	1.24916i	−0.317207	−	0.948356i	$-0.602745\pi$
$233$	9.71543	−	19.0676i	0.636479	−	1.24916i	0.953686	−	0.300804i	$-0.0972549\pi$
$234$	10.6121	−	14.6063i	0.693736	−	0.954846i
$235$	−0.444912	−	2.32193i	−0.0290228	−	0.151466i
$236$	−7.84676	+	24.1498i	−0.510780	+	1.57202i
$237$	1.17882	+	2.31356i	0.0765726	+	0.150282i
$238$	−5.85751	−	0.927738i	−0.379686	−	0.0601363i
$239$	−7.00907	−	5.09239i	−0.453379	−	0.329399i	0.337549	−	0.941308i	$-0.390402\pi$
$239$	−7.00907	−	5.09239i	−0.453379	−	0.329399i	−0.790929	+	0.611909i	$0.790402\pi$
$240$	−0.584736	+	4.65949i	−0.0377446	+	0.300769i
$241$			10.6492i			0.685976i	0.939340	+	0.342988i	$0.111439\pi$
$241$			10.6492i			0.685976i	−0.939340	+	0.342988i	$0.888561\pi$
$242$		0			0
$243$	−9.65667	+	9.65667i	−0.619476	+	0.619476i
$244$	−11.5310	−	35.4888i	−0.738198	−	2.27194i
$245$	−0.718913	−	0.208222i	−0.0459297	−	0.0133028i
$246$	−4.05743	+	2.94790i	−0.258693	+	0.187951i
$247$	−10.3855	+	5.29168i	−0.660814	+	0.336702i
$248$	−37.6646	+	19.1911i	−2.39171	+	1.21863i
$249$	−4.01148	+	2.91451i	−0.254217	+	0.184700i
$250$	−25.3120	−	9.94951i	−1.60087	−	0.629262i
$251$	−2.90262	−	8.93333i	−0.183211	−	0.563867i	0.816701	−	0.577060i	$-0.195800\pi$
$251$	−2.90262	−	8.93333i	−0.183211	−	0.563867i	−0.999913	+	0.0131934i	$0.995800\pi$
$252$	18.8972	−	18.8972i	1.19041	−	1.19041i
$253$		0			0
$254$			5.77750i			0.362513i
$255$	0.774765	+	0.997126i	0.0485177	+	0.0624424i
$256$	25.2270	+	18.3285i	1.57668	+	1.14553i
$257$	18.2128	+	2.88462i	1.13608	+	0.179938i	0.696015	−	0.718027i	$-0.254955\pi$
$257$	18.2128	+	2.88462i	1.13608	+	0.179938i	0.440067	+	0.897965i	$0.354955\pi$
$258$	3.65972	+	7.18260i	0.227844	+	0.447169i
$259$	6.06178	−	18.6562i	0.376661	−	1.15924i
$260$	24.1649	−	4.63030i	1.49864	−	0.287159i
$261$	−10.7789	+	14.8359i	−0.667198	+	0.918320i
$262$	3.45079	−	6.77256i	0.213191	−	0.418410i
$263$	11.8928	+	11.8928i	0.733342	+	0.733342i	0.971280	−	0.237938i	$-0.0764717\pi$
$263$	11.8928	+	11.8928i	0.733342	+	0.733342i	−0.237938	+	0.971280i	$0.576472\pi$
$264$		0			0
$265$	−8.34434	−	3.91817i	−0.512589	−	0.240691i
$266$	−24.7863	+	8.05355i	−1.51974	+	0.493795i
$267$	−0.395807	−	2.49902i	−0.0242230	−	0.152938i
$268$	−2.55244	+	16.1155i	−0.155915	+	0.984410i
$269$	27.0639	+	8.79360i	1.65012	+	0.536155i	0.978765	−	0.204985i	$-0.0657146\pi$
$269$	27.0639	+	8.79360i	1.65012	+	0.536155i	0.671350	+	0.741140i	$0.265715\pi$
$270$	−18.3445	+	0.591607i	−1.11641	+	0.0360041i
$271$	−17.4468	−	24.0135i	−1.05982	−	1.45871i	−0.879976	−	0.475018i	$-0.842442\pi$
$271$	−17.4468	−	24.0135i	−1.05982	−	1.45871i	−0.179841	−	0.983696i	$-0.557558\pi$
$272$	−3.27541	+	0.518774i	−0.198601	+	0.0314553i
$273$	3.86390	+	1.96876i	0.233854	+	0.119154i
$274$	−40.2251			−2.43009
$275$		0			0
$276$	−0.346917			−0.0208820
$277$	−11.0660	−	5.63843i	−0.664894	−	0.338780i	0.0887589	−	0.996053i	$-0.471710\pi$
$277$	−11.0660	−	5.63843i	−0.664894	−	0.338780i	−0.753653	+	0.657273i	$0.771710\pi$
$278$	10.3805	−	1.64412i	0.622584	−	0.0986076i
$279$	−14.0754	−	19.3731i	−0.842672	−	1.15984i
$280$	26.9137	−	0.867962i	1.60840	−	0.0518706i
$281$	−20.8044	−	6.75975i	−1.24108	−	0.403253i	−0.386366	−	0.922345i	$-0.626270\pi$
$281$	−20.8044	−	6.75975i	−1.24108	−	0.403253i	−0.854718	+	0.519093i	$0.826270\pi$
$282$	0.240608	−	1.51914i	0.0143280	−	0.0904635i
$283$	−4.25463	−	26.8627i	−0.252912	−	1.59682i	−0.707892	−	0.706320i	$-0.750354\pi$
$283$	−4.25463	−	26.8627i	−0.252912	−	1.59682i	0.454981	−	0.890501i	$-0.349646\pi$
$284$	4.71704	−	1.53266i	0.279905	−	0.0909465i
$285$	5.02297	+	2.35859i	0.297535	+	0.139711i
$286$		0			0
$287$	6.29366	+	6.29366i	0.371503	+	0.371503i
$288$	−0.943124	+	1.85099i	−0.0555741	+	0.109070i
$289$	9.46821	−	13.0319i	0.556953	−	0.766581i
$290$	−37.0755	+	7.10415i	−2.17715	+	0.417170i
$291$	2.66545	−	8.20340i	0.156251	−	0.480892i
$292$	3.15041	+	6.18303i	0.184364	+	0.361834i
$293$	19.8646	+	3.14625i	1.16050	+	0.183806i	0.706844	−	0.707369i	$-0.250118\pi$
$293$	19.8646	+	3.14625i	1.16050	+	0.183806i	0.453660	+	0.891175i	$0.350118\pi$
$294$	−0.393936	−	0.286211i	−0.0229748	−	0.0166922i
$295$	−8.89280	−	11.4451i	−0.517759	−	0.666358i
$296$		−	35.4416i		−	2.06000i
$297$		0			0
$298$	14.5257	−	14.5257i	0.841450	−	0.841450i
$299$	0.128530	+	0.395574i	0.00743307	+	0.0228766i
$300$	−8.79932	−	7.73195i	−0.508029	−	0.446404i
$301$	11.5740	−	8.40900i	0.667114	−	0.484686i
$302$	25.8628	−	13.1777i	1.48824	−	0.758294i
$303$	1.03114	−	0.525391i	0.0592373	−	0.0301829i
$304$	−11.7900	+	8.56597i	−0.676206	+	0.491292i
$305$	20.4583	+	5.92543i	1.17144	+	0.339289i
$306$	−1.87569	−	5.77277i	−0.107226	−	0.330007i
$307$	14.6921	−	14.6921i	0.838520	−	0.838520i	−0.150144	−	0.988664i	$-0.547974\pi$
$307$	14.6921	−	14.6921i	0.838520	−	0.838520i	0.988664	+	0.150144i	$0.0479738\pi$
$308$		0			0
$309$		−	1.02815i		−	0.0584893i
$310$	6.13805	−	48.9113i	0.348618	−	2.77797i
$311$	−18.8330	−	13.6830i	−1.06792	−	0.775892i	−0.0923861	−	0.995723i	$-0.529449\pi$
$311$	−18.8330	−	13.6830i	−1.06792	−	0.775892i	−0.975538	+	0.219831i	$0.929449\pi$
$312$	7.73857	+	1.22567i	0.438110	+	0.0693898i
$313$	6.36402	+	12.4901i	0.359716	+	0.705982i	0.997959	−	0.0638526i	$-0.0203388\pi$
$313$	6.36402	+	12.4901i	0.359716	+	0.705982i	−0.638244	+	0.769834i	$0.720339\pi$
$314$	−1.02347	+	3.14992i	−0.0577578	+	0.177760i
$315$	2.87067	+	14.9816i	0.161744	+	0.844118i
$316$	9.99799	−	13.7611i	0.562431	−	0.774120i
$317$	13.3927	−	26.2847i	0.752211	−	1.47630i	−0.122922	−	0.992416i	$-0.539227\pi$
$317$	13.3927	−	26.2847i	0.752211	−	1.47630i	0.875134	−	0.483881i	$-0.160773\pi$
$318$	−4.24076	−	4.24076i	−0.237810	−	0.237810i
$319$		0			0
$320$	−18.7949	+	6.78404i	−1.05066	+	0.379239i
$321$	−2.36544	+	0.768580i	−0.132026	+	0.0428979i
$322$	0.145483	+	0.918543i	0.00810744	+	0.0511884i
$323$	−0.613019	+	3.87045i	−0.0341093	+	0.215357i
$324$	22.0165	+	7.15358i	1.22314	+	0.397421i
$325$	−5.55632	+	12.8981i	−0.308209	+	0.715457i
$326$	−32.8055	−	45.1528i	−1.81693	−	2.50078i
$327$	−1.90381	+	0.301535i	−0.105281	+	0.0166749i
$328$	14.3283	+	7.30063i	0.791148	+	0.403110i
$329$	−2.72962			−0.150489
$330$		0			0
$331$	2.18560			0.120131			0.0600657	−	0.998194i	$-0.480869\pi$
$331$	2.18560			0.120131			0.0600657	+	0.998194i	$0.480869\pi$
$332$	28.9415	+	14.7464i	1.58837	+	0.809316i
$333$	19.8300	−	3.14076i	1.08668	−	0.172113i
$334$	−20.5331	−	28.2614i	−1.12352	−	1.54639i
$335$	−6.79428	−	6.36974i	−0.371211	−	0.348016i
$336$	5.15658	+	1.67548i	0.281315	+	0.0914047i
$337$	0.281896	−	1.77982i	0.0153559	−	0.0969531i	−0.978820	−	0.204722i	$-0.934371\pi$
$337$	0.281896	−	1.77982i	0.0153559	−	0.0969531i	0.994176	+	0.107769i	$0.0343708\pi$
$338$	1.94482	+	12.2791i	0.105784	+	0.667894i
$339$	−6.34339	+	2.06109i	−0.344526	+	0.111943i
$340$	3.51587	−	7.48759i	0.190675	−	0.406072i
$341$		0			0
$342$	−18.8614	−	18.8614i	−1.01991	−	1.01991i
$343$	−8.59685	+	16.8723i	−0.464186	+	0.911017i
$344$	15.1929	−	20.9112i	0.819144	−	1.12746i
$345$	0.111167	−	0.163867i	0.00598503	−	0.00882231i
$346$	−16.7643	+	51.5953i	−0.901257	+	2.77378i
$347$	9.74821	+	19.1319i	0.523311	+	1.02706i	0.989791	+	0.142525i	$0.0455220\pi$
$347$	9.74821	+	19.1319i	0.523311	+	1.02706i	−0.466480	+	0.884532i	$0.654478\pi$
$348$	−16.0586	−	2.54343i	−0.860830	−	0.136342i
$349$	8.62120	+	6.26367i	0.461482	+	0.335286i	0.794112	−	0.607771i	$-0.207936\pi$
$349$	8.62120	+	6.26367i	0.461482	+	0.335286i	−0.332630	+	0.943057i	$0.607936\pi$
$350$	−16.7820	+	26.5407i	−0.897038	+	1.41866i
$351$			9.47758i			0.505876i
$352$		0			0
$353$	−7.73857	+	7.73857i	−0.411883	+	0.411883i	−0.882394	−	0.470511i	$-0.844069\pi$
$353$	−7.73857	+	7.73857i	−0.411883	+	0.411883i	0.470511	+	0.882394i	$0.344069\pi$
$354$	−2.91384	−	8.96788i	−0.154869	−	0.476637i
$355$	−0.787585	+	2.71923i	−0.0418007	+	0.144322i
$356$	−13.4092	+	9.74233i	−0.710684	+	0.516342i
$357$	1.29903	−	0.661890i	0.0687521	−	0.0350309i
$358$	9.46790	−	4.82414i	0.500394	−	0.254963i
$359$	2.64887	−	1.92452i	0.139802	−	0.101572i	−0.515686	−	0.856778i	$-0.672463\pi$
$359$	2.64887	−	1.92452i	0.139802	−	0.101572i	0.655488	+	0.755205i	$0.272463\pi$
$360$	13.2971	+	24.1403i	0.700821	+	1.27231i
$361$	−0.549801	−	1.69211i	−0.0289369	−	0.0890586i
$362$	16.2374	−	16.2374i	0.853418	−	0.853418i
$363$		0			0
$364$		−	28.4079i		−	1.48898i
$365$	−3.93010	−	0.493202i	−0.205711	−	0.0258154i
$366$	11.2103	+	8.14479i	0.585974	+	0.425735i
$367$	−18.0053	−	2.85177i	−0.939871	−	0.148861i	−0.332342	−	0.943159i	$-0.607839\pi$
$367$	−18.0053	−	2.85177i	−0.939871	−	0.148861i	−0.607529	+	0.794298i	$0.707839\pi$
$368$	0.236091	+	0.463354i	0.0123071	+	0.0241540i
$369$	−2.81505	+	8.66382i	−0.146545	+	0.451020i
$370$	34.2022	+	23.2026i	1.77809	+	1.20625i
$371$	−6.25607	+	8.61074i	−0.324799	+	0.447047i
$372$	9.63872	−	18.9171i	0.499744	−	0.980803i
$373$	−12.4917	−	12.4917i	−0.646795	−	0.646795i	0.305422	−	0.952217i	$-0.401202\pi$
$373$	−12.4917	−	12.4917i	−0.646795	−	0.646795i	−0.952217	+	0.305422i	$0.901202\pi$
$374$		0			0
$375$	6.47189	−	1.67874i	0.334207	−	0.0866895i
$376$	−4.69034	+	1.52398i	−0.241886	+	0.0785935i
$377$	3.04941	+	19.2532i	0.157052	+	0.991590i
$378$	−3.31503	+	20.9303i	−0.170507	+	1.07654i
$379$	−20.9834	−	6.81794i	−1.07785	−	0.350214i	−0.284308	−	0.958733i	$-0.591764\pi$
$379$	−20.9834	−	6.81794i	−1.07785	−	0.350214i	−0.793539	+	0.608519i	$0.791764\pi$
$380$	−1.17172	−	36.3325i	−0.0601078	−	1.86382i
$381$	−0.834843	−	1.14906i	−0.0427703	−	0.0588683i
$382$	15.5518	−	2.46316i	0.795697	−	0.126026i
$383$	17.5437	+	8.93896i	0.896441	+	0.456759i	0.840585	−	0.541680i	$-0.182211\pi$
$383$	17.5437	+	8.93896i	0.896441	+	0.456759i	0.0558556	+	0.998439i	$0.482211\pi$
$384$	−12.0594			−0.615402
$385$		0			0
$386$	2.44874			0.124638
$387$	13.0464	+	6.64748i	0.663187	+	0.337910i
$388$	−55.8086	+	8.83921i	−2.83325	+	0.448743i
$389$	10.0633	+	13.8509i	0.510227	+	0.702268i	0.983958	−	0.178402i	$-0.0570929\pi$
$389$	10.0633	+	13.8509i	0.510227	+	0.702268i	−0.473730	+	0.880670i	$0.657093\pi$
$390$	−6.24903	+	6.66552i	−0.316432	+	0.337522i
$391$	0.132991	+	0.0432114i	0.00672564	+	0.00218529i
$392$	−0.244242	+	1.54208i	−0.0123361	+	0.0778870i
$393$	0.292315	+	1.84560i	0.0147453	+	0.0930983i
$394$	−56.7417	+	18.4365i	−2.85860	+	0.928816i
$395$	3.29629	+	9.13221i	0.165854	+	0.459491i
$396$		0			0
$397$	5.24887	+	5.24887i	0.263433	+	0.263433i	0.826447	−	0.563014i	$-0.190358\pi$
$397$	5.24887	+	5.24887i	0.263433	+	0.263433i	−0.563014	+	0.826447i	$0.690358\pi$
$398$	3.59562	−	7.05679i	0.180232	−	0.353725i
$399$	3.76591	−	5.18333i	0.188531	−	0.259491i
$400$	−4.33877	+	17.0146i	−0.216938	+	0.850728i
$401$	3.79327	−	11.6745i	0.189427	−	0.582996i	−0.810570	−	0.585642i	$-0.800842\pi$
$401$	3.79327	−	11.6745i	0.189427	−	0.582996i	0.999996	+	0.00264628i	$0.000842338\pi$
$402$	−2.75072	−	5.39858i	−0.137193	−	0.269257i
$403$	−25.1413	−	3.98199i	−1.25238	−	0.198357i
$404$	−6.13319	−	4.45603i	−0.305138	−	0.221696i
$405$	−10.4340	+	8.10722i	−0.518471	+	0.402851i
$406$			43.5854i			2.16311i
$407$		0			0
$408$	1.86260	−	1.86260i	0.0922125	−	0.0922125i
$409$	8.26899	+	25.4493i	0.408875	+	1.25839i	0.917616	+	0.397469i	$0.130111\pi$
$409$	8.26899	+	25.4493i	0.408875	+	1.25839i	−0.508740	+	0.860920i	$0.669889\pi$
$410$	−16.4257	+	9.04769i	−0.811205	+	0.446833i
$411$	8.00021	−	5.81249i	0.394621	−	0.286709i
$412$	−6.00109	+	3.05771i	−0.295653	+	0.150643i
$413$	−14.9104	+	7.59722i	−0.733692	+	0.373835i
$414$	−0.770055	+	0.559478i	−0.0378462	+	0.0274968i
$415$	−16.2396	+	8.94521i	−0.797172	+	0.439103i
$416$	0.682387	+	2.10017i	0.0334568	+	0.102969i
$417$	−1.82697	+	1.82697i	−0.0894672	+	0.0894672i
$418$		0			0
$419$		−	14.2401i		−	0.695676i	−0.937555	−	0.347838i	$-0.886916\pi$
$419$		−	14.2401i		−	0.695676i	0.937555	−	0.347838i	$-0.113084\pi$
$420$	−10.6796	+	8.29800i	−0.521110	+	0.404901i
$421$	5.58723	+	4.05936i	0.272305	+	0.197841i	0.715554	−	0.698557i	$-0.246174\pi$
$421$	5.58723	+	4.05936i	0.272305	+	0.197841i	−0.443249	+	0.896398i	$0.646174\pi$
$422$	59.6849	+	9.45316i	2.90541	+	0.460172i
$423$	−1.26834	−	2.48925i	−0.0616686	−	0.121031i
$424$	−5.94238	+	18.2888i	−0.288588	+	0.888181i
$425$	2.41015	+	4.06007i	0.116909	+	0.196943i
$426$	−1.08257	+	1.49003i	−0.0524508	+	0.0721924i
$427$	11.1643	−	21.9112i	0.540279	−	1.06036i
$428$	11.5209	+	11.5209i	0.556882	+	0.556882i
$429$		0			0
$430$	10.2335	+	28.3515i	0.493505	+	1.36723i
$431$	6.78988	−	2.20617i	0.327057	−	0.106267i	−0.140886	−	0.990026i	$-0.544995\pi$
$431$	6.78988	−	2.20617i	0.327057	−	0.106267i	0.467943	+	0.883759i	$0.344995\pi$
$432$	1.85371	+	11.7038i	0.0891865	+	0.563101i
$433$	−2.62850	+	16.5957i	−0.126318	+	0.797540i	0.840451	+	0.541888i	$0.182290\pi$
$433$	−2.62850	+	16.5957i	−0.126318	+	0.797540i	−0.966769	+	0.255652i	$0.917710\pi$
$434$	−54.1293	−	17.5877i	−2.59829	−	0.844236i
$435$	6.34725	−	6.77029i	0.304327	−	0.324611i
$436$	7.42193	+	10.2154i	0.355446	+	0.489229i
$437$	0.606943	−	0.0961303i	0.0290340	−	0.00459854i
$438$	−2.29603	−	1.16988i	−0.109708	−	0.0558992i
$439$	−0.772934			−0.0368901			−0.0184451	−	0.999830i	$-0.505872\pi$
$439$	−0.772934			−0.0368901			−0.0184451	+	0.999830i	$0.505872\pi$
$440$		0			0
$441$	−0.884459			−0.0421171
$442$	−5.74890	−	2.92921i	−0.273447	−	0.139328i
$443$	−18.5585	+	2.93938i	−0.881741	+	0.139654i	−0.580856	−	0.814007i	$-0.697282\pi$
$443$	−18.5585	+	2.93938i	−0.881741	+	0.139654i	−0.300885	+	0.953660i	$0.597282\pi$
$444$	10.4629	+	14.4009i	0.496547	+	0.683439i
$445$	−0.304945	−	9.45571i	−0.0144558	−	0.448244i
$446$	−45.3221	−	14.7261i	−2.14607	−	0.697299i
$447$	−0.790006	+	4.98790i	−0.0373660	+	0.235920i
$448$	3.60902	+	22.7865i	0.170510	+	1.07656i
$449$	−0.678469	+	0.220448i	−0.0320189	+	0.0104036i	−0.324983	−	0.945720i	$-0.605358\pi$
$449$	−0.678469	+	0.220448i	−0.0320189	+	0.0104036i	0.292964	+	0.956124i	$0.405358\pi$
$450$	−32.0014	−	2.97190i	−1.50856	−	0.140097i
$451$		0			0
$452$	30.8954	+	30.8954i	1.45320	+	1.45320i
$453$	−3.23957	+	6.35802i	−0.152208	+	0.298726i
$454$	−1.46261	+	2.01311i	−0.0686437	+	0.0944800i
$455$	13.4185	+	9.10309i	0.629070	+	0.426760i
$456$	3.57709	−	11.0091i	0.167512	−	0.515550i
$457$	8.78244	+	17.2365i	0.410825	+	0.806290i	0.999999	−	0.00171662i	$-0.000546419\pi$
$457$	8.78244	+	17.2365i	0.410825	+	0.806290i	−0.589173	+	0.808007i	$0.700546\pi$
$458$	0.244706	+	0.0387577i	0.0114344	+	0.00181103i
$459$	2.57780	+	1.87288i	0.120321	+	0.0874186i
$460$	−1.28707	−	0.161519i	−0.0600099	−	0.00753086i
$461$		−	36.5277i		−	1.70126i	−0.525761	−	0.850632i	$-0.676219\pi$
$461$		−	36.5277i		−	1.70126i	0.525761	−	0.850632i	$-0.323781\pi$
$462$		0			0
$463$	−17.1422	+	17.1422i	−0.796664	+	0.796664i	−0.982568	−	0.185904i	$-0.940479\pi$
$463$	−17.1422	+	17.1422i	−0.796664	+	0.796664i	0.185904	+	0.982568i	$0.440479\pi$
$464$	7.53141	+	23.1793i	0.349637	+	1.07607i
$465$	5.84686	+	10.6147i	0.271142	+	0.492245i
$466$	42.1155	−	30.5987i	1.95096	−	1.41746i
$467$	13.2045	−	6.72802i	0.611031	−	0.311336i	−0.120953	−	0.992658i	$-0.538595\pi$
$467$	13.2045	−	6.72802i	0.611031	−	0.311336i	0.731983	+	0.681323i	$0.238595\pi$
$468$	25.9062	−	13.1999i	1.19752	−	0.610165i
$469$	−8.69924	+	6.32036i	−0.401693	+	0.291847i
$470$	1.59995	−	5.52402i	0.0738002	−	0.254804i
$471$	−0.251606	−	0.774365i	−0.0115934	−	0.0356808i
$472$	−21.3791	+	21.3791i	−0.984051	+	0.984051i
$473$		0			0
$474$			6.31640i			0.290122i
$475$	17.5372	+	11.0890i	0.804663	+	0.508799i
$476$	−7.72663	−	5.61373i	−0.354150	−	0.257305i
$477$	−10.7594	−	1.70412i	−0.492638	−	0.0780263i
$478$	−9.56795	−	18.7782i	−0.437628	−	0.858893i
$479$	8.52455	−	26.2359i	0.389496	−	1.19875i	−0.543669	−	0.839300i	$-0.682965\pi$
$479$	8.52455	−	26.2359i	0.389496	−	1.19875i	0.933165	−	0.359447i	$-0.117035\pi$
$480$	0.590205	−	0.870000i	0.0269391	−	0.0397099i
$481$	12.5443	−	17.2658i	0.571973	−	0.787253i
$482$	−11.7607	+	23.0817i	−0.535685	+	1.05134i
$483$	−0.161663	−	0.161663i	−0.00735592	−	0.00735592i
$484$		0			0
$485$	13.7082	−	29.1938i	0.622459	−	1.32562i
$486$	−31.5950	+	10.2658i	−1.43318	+	0.465667i
$487$	6.08463	+	38.4169i	0.275721	+	1.74083i	0.604661	+	0.796483i	$0.293309\pi$
$487$	6.08463	+	38.4169i	0.275721	+	1.74083i	−0.328940	+	0.944351i	$0.606691\pi$
$488$	6.95046	−	43.8835i	0.314632	−	1.98651i
$489$	13.0491	+	4.23990i	0.590100	+	0.191735i
$490$	−1.32826	−	1.24526i	−0.0600045	−	0.0562551i
$491$	11.0511	+	15.2106i	0.498730	+	0.686443i	0.981968	−	0.189046i	$-0.0605395\pi$
$491$	11.0511	+	15.2106i	0.498730	+	0.686443i	−0.483238	+	0.875489i	$0.660539\pi$
$492$	−7.97726	+	1.26347i	−0.359643	+	0.0569618i
$493$	5.83926	+	2.97525i	0.262987	+	0.133999i
$494$	−28.3541			−1.27571
$495$		0			0
$496$	−31.8258			−1.42902
$497$	2.91235	+	1.48392i	0.130637	+	0.0665628i
$498$	−11.9134	+	1.88690i	−0.533853	+	0.0845539i
$499$	3.07983	+	4.23902i	0.137872	+	0.189765i	0.872370	−	0.488846i	$-0.162582\pi$
$499$	3.07983	+	4.23902i	0.137872	+	0.189765i	−0.734498	+	0.678611i	$0.762582\pi$
$500$	−29.0458	−	32.7825i	−1.29897	−	1.46608i
$501$	8.16748	+	2.65378i	0.364896	+	0.118562i
$502$	3.57445	−	22.5682i	0.159535	−	1.00727i
$503$	−2.06374	−	13.0299i	−0.0920176	−	0.580976i	−0.990014	−	0.140973i	$-0.954977\pi$
$503$	−2.06374	−	13.0299i	−0.0920176	−	0.580976i	0.897996	−	0.440004i	$-0.145023\pi$
$504$	30.2632	−	9.83310i	1.34803	−	0.438001i
$505$	4.07015	−	1.46913i	0.181119	−	0.0653754i
$506$		0			0
$507$	−2.16111	−	2.16111i	−0.0959784	−	0.0959784i
$508$	−4.22403	+	8.29012i	−0.187411	+	0.367815i
$509$	3.28913	−	4.52710i	0.145788	−	0.200660i	−0.729878	−	0.683578i	$-0.760423\pi$
$509$	3.28913	−	4.52710i	0.145788	−	0.200660i	0.875666	+	0.482918i	$0.160423\pi$
$510$	0.578069	+	3.01685i	0.0255973	+	0.133589i
$511$	−1.41320	+	4.34937i	−0.0625162	+	0.192405i
$512$	16.1269	+	31.6509i	0.712716	+	1.39878i
$513$	13.8301	+	2.19047i	0.610612	+	0.0967114i
$514$	36.2897	+	26.3660i	1.60067	+	1.16295i
$515$	0.478689	−	3.81445i	0.0210936	−	0.168085i
$516$			12.9820i			0.571500i
$517$		0			0
$518$	33.7421	−	33.7421i	1.48254	−	1.48254i
$519$	−4.12129	−	12.6840i	−0.180904	−	0.556767i
$520$	28.1396	+	8.15021i	1.23400	+	0.357410i
$521$	−15.4337	+	11.2132i	−0.676163	+	0.491261i	−0.872082	−	0.489359i	$-0.837231\pi$
$521$	−15.4337	+	11.2132i	−0.676163	+	0.491261i	0.195920	+	0.980620i	$0.437231\pi$
$522$	−39.7472	+	20.2522i	−1.73969	+	0.886415i
$523$	31.2730	−	15.9344i	1.36747	−	0.696762i	0.392638	−	0.919693i	$-0.371563\pi$
$523$	31.2730	−	15.9344i	1.36747	−	0.696762i	0.974834	+	0.222932i	$0.0715627\pi$
$524$	9.90306	−	7.19499i	0.432617	−	0.314315i
$525$	−0.497394	−	7.70356i	−0.0217081	−	0.336211i
$526$	12.6430	+	38.9112i	0.551262	+	1.69661i
$527$	−6.05128	+	6.05128i	−0.263598	+	0.263598i
$528$		0			0
$529$			22.9781i			0.999047i
$530$	−13.7589	−	17.7077i	−0.597647	−	0.769174i
$531$	−13.8564	−	10.0673i	−0.601317	−	0.436882i
$532$	−41.4539	−	6.56565i	−1.79725	−	0.284657i
$533$	4.39619	+	8.62800i	0.190420	+	0.373720i
$534$	1.90196	−	5.85364i	0.0823060	−	0.253312i
$535$	−9.13369	+	1.75013i	−0.394884	+	0.0756649i
$536$	−11.4193	+	15.7173i	−0.493237	+	0.678882i
$537$	−1.18595	+	2.32756i	−0.0511775	+	0.100441i
$538$	48.9484	+	48.9484i	2.11031	+	2.11031i
$539$		0			0
$540$	−26.7550	−	12.5631i	−1.15135	−	0.540628i
$541$	2.41645	−	0.785152i	0.103891	−	0.0337563i	−0.256610	−	0.966515i	$-0.582606\pi$
$541$	2.41645	−	0.785152i	0.103891	−	0.0337563i	0.360501	+	0.932759i	$0.382606\pi$
$542$	−11.2953	−	71.3159i	−0.485176	−	3.06328i
$543$	−0.883100	+	5.57568i	−0.0378975	+	0.239275i
$544$	0.706072	+	0.229417i	0.0302726	+	0.00983616i
$545$	−7.20358	+	0.232314i	−0.308567	+	0.00995125i
$546$	6.20059	+	8.53438i	0.265361	+	0.365238i
$547$	14.6420	−	2.31906i	0.626045	−	0.0991559i	0.164652	−	0.986352i	$-0.447350\pi$
$547$	14.6420	−	2.31906i	0.626045	−	0.0991559i	0.461393	+	0.887196i	$0.347350\pi$
$548$	−57.7189	−	29.4093i	−2.46563	−	1.25630i
$549$	25.1693			1.07420
$550$		0			0
$551$	28.7998			1.22691
$552$	−0.368046	−	0.187529i	−0.0156651	−	0.00798176i
$553$	11.0717	−	1.75358i	0.470816	−	0.0745700i
$554$	−17.7582	−	24.4421i	−0.754474	−	1.03844i
$555$	−10.1551	+	0.327500i	−0.431059	+	0.0139016i
$556$	16.0971	+	5.23025i	0.682667	+	0.221812i
$557$	−1.99631	+	12.6042i	−0.0845865	+	0.534058i	0.908614	+	0.417638i	$0.137142\pi$
$557$	−1.99631	+	12.6042i	−0.0845865	+	0.534058i	−0.993200	+	0.116420i	$0.962858\pi$
$558$	−9.11263	−	57.5349i	−0.385768	−	2.43564i
$559$	14.8028	−	4.80971i	0.626090	−	0.203429i
$560$	18.3510	+	8.61687i	0.775470	+	0.364129i
$561$		0			0
$562$	−37.6272	−	37.6272i	−1.58721	−	1.58721i
$563$	15.2231	−	29.8770i	0.641578	−	1.25917i	−0.309701	−	0.950834i	$-0.600229\pi$
$563$	15.2231	−	29.8770i	0.641578	−	1.25917i	0.951278	−	0.308333i	$-0.0997712\pi$
$564$	1.45592	−	2.00390i	0.0613052	−	0.0843794i
$565$	−24.4937	+	4.69332i	−1.03046	+	0.197449i
$566$	20.4447	−	62.9224i	0.859356	−	2.64483i
$567$	6.92609	+	13.5932i	0.290868	+	0.570862i
$568$	5.83282	+	0.923828i	0.244740	+	0.0387629i
$569$	6.73005	+	4.88967i	0.282139	+	0.204986i	0.719850	−	0.694130i	$-0.244211\pi$
$569$	6.73005	+	4.88967i	0.282139	+	0.204986i	−0.437711	+	0.899116i	$0.644211\pi$
$570$	8.28231	+	10.6594i	0.346908	+	0.446472i
$571$		−	45.2601i		−	1.89408i	−0.321118	−	0.947039i	$-0.604059\pi$
$571$		−	45.2601i		−	1.89408i	0.321118	−	0.947039i	$-0.395941\pi$
$572$		0			0
$573$	−2.73710	+	2.73710i	−0.114344	+	0.114344i
$574$	6.69067	+	20.5918i	0.279263	+	0.859484i
$575$	0.488726	−	0.556193i	0.0203813	−	0.0231949i
$576$	−19.1029	+	13.8791i	−0.795955	+	0.578295i
$577$	20.4344	−	10.4119i	0.850697	−	0.433452i	0.0264283	−	0.999651i	$-0.491587\pi$
$577$	20.4344	−	10.4119i	0.850697	−	0.433452i	0.824269	+	0.566199i	$0.191587\pi$
$578$	34.9140	−	17.7896i	1.45223	−	0.739948i
$579$	−0.487020	+	0.353841i	−0.0202399	+	0.0147051i
$580$	−58.3935	−	16.9128i	−2.42466	−	0.702265i
$581$	6.61489	+	20.3586i	0.274432	+	0.844615i
$582$	14.8369	−	14.8369i	0.615007	−	0.615007i
$583$		0			0
$584$			8.26259i			0.341908i
$585$	−2.06646	+	16.4667i	−0.0854378	+	0.680814i
$586$	39.5811	+	28.7573i	1.63508	+	1.18795i
$587$	−9.97239	−	1.57947i	−0.411605	−	0.0651917i	−0.0528014	−	0.998605i	$-0.516815\pi$
$587$	−9.97239	−	1.57947i	−0.411605	−	0.0651917i	−0.358803	+	0.933413i	$0.616815\pi$
$588$	−0.356004	−	0.698697i	−0.0146814	−	0.0288138i
$589$	−11.6214	+	35.7669i	−0.478850	+	1.47375i
$590$	−6.63511	−	34.6277i	−0.273163	−	1.42560i
$591$	8.62106	−	11.8659i	0.354623	−	0.488097i
$592$	12.1140	−	23.7750i	0.497881	−	0.977147i
$593$	−9.47168	−	9.47168i	−0.388955	−	0.388955i	0.485359	−	0.874315i	$-0.338689\pi$
$593$	−9.47168	−	9.47168i	−0.388955	−	0.388955i	−0.874315	+	0.485359i	$0.838689\pi$
$594$		0			0
$595$	5.12760	−	1.85082i	0.210211	−	0.0758761i
$596$	31.4628	−	10.2229i	1.28877	−	0.418746i
$597$	0.304583	+	1.92306i	0.0124657	+	0.0787056i
$598$	−0.158279	+	0.999334i	−0.00647251	+	0.0408658i
$599$	38.0508	+	12.3635i	1.55471	+	0.505157i	0.955390	−	0.295349i	$-0.0954358\pi$
$599$	38.0508	+	12.3635i	1.55471	+	0.505157i	0.599325	+	0.800506i	$0.295436\pi$
$600$	−5.15568	−	12.9594i	−0.210480	−	0.529066i
$601$	21.3719	+	29.4160i	0.871780	+	1.19990i	0.978630	+	0.205627i	$0.0659234\pi$
$601$	21.3719	+	29.4160i	0.871780	+	1.19990i	−0.106850	+	0.994275i	$0.534077\pi$
$602$	34.3728	−	5.44411i	1.40093	−	0.221885i
$603$	−9.80594	−	4.99638i	−0.399329	−	0.203468i
$604$	46.7449			1.90202
$605$		0			0
$606$	2.81517			0.114358
$607$	−22.2128	−	11.3180i	−0.901590	−	0.459383i	−0.0591966	−	0.998246i	$-0.518854\pi$
$607$	−22.2128	−	11.3180i	−0.901590	−	0.459383i	−0.842393	+	0.538863i	$0.818854\pi$
$608$	3.22236	−	0.510372i	0.130684	−	0.0206983i
$609$	−6.29805	−	8.66852i	−0.255210	−	0.351266i
$610$	37.7985	+	35.4367i	1.53042	+	1.43479i
$611$	−2.82436	−	0.917690i	−0.114261	−	0.0371258i
$612$	1.52915	−	9.65467i	0.0618122	−	0.390267i
$613$	1.82887	+	11.5470i	0.0738674	+	0.466380i	0.996700	+	0.0811783i	$0.0258683\pi$
$613$	1.82887	+	11.5470i	0.0738674	+	0.466380i	−0.922832	+	0.385202i	$0.874132\pi$
$614$	48.0699	−	15.6188i	1.93994	−	0.630325i
$615$	1.95945	−	4.17295i	0.0790126	−	0.168270i
$616$		0			0
$617$	6.18386	+	6.18386i	0.248953	+	0.248953i	0.820541	−	0.571588i	$-0.193672\pi$
$617$	6.18386	+	6.18386i	0.248953	+	0.248953i	−0.571588	+	0.820541i	$0.693672\pi$
$618$	1.13546	−	2.22847i	0.0456749	−	0.0896420i
$619$	0.645775	−	0.888833i	0.0259559	−	0.0357252i	−0.795842	−	0.605505i	$-0.792971\pi$
$619$	0.645775	−	0.888833i	0.0259559	−	0.0357252i	0.821798	+	0.569779i	$0.192971\pi$
$620$	44.5673	−	65.6950i	1.78987	−	2.63838i
$621$	0.154405	−	0.475209i	0.00619605	−	0.0190695i
$622$	−25.7086	−	50.4560i	−1.03082	−	2.02310i
$623$	−10.7886	−	1.70874i	−0.432235	−	0.0684593i
$624$	4.77227	+	3.46725i	0.191044	+	0.138801i
$625$	24.7924	−	3.21494i	0.991697	−	0.128598i
$626$			34.1000i			1.36291i
$627$		0			0
$628$	−3.77153	+	3.77153i	−0.150501	+	0.150501i
$629$	−2.21720	−	6.82385i	−0.0884057	−	0.272085i
$630$	−10.3232	+	35.6422i	−0.411288	+	1.42002i
$631$	2.63807	−	1.91667i	0.105020	−	0.0763014i	−0.534036	−	0.845462i	$-0.679325\pi$
$631$	2.63807	−	1.91667i	0.105020	−	0.0763014i	0.639056	+	0.769160i	$0.279325\pi$
$632$	18.0456	−	9.19468i	0.717814	−	0.365745i
$633$	−13.2365	+	6.74431i	−0.526102	+	0.268062i
$634$	58.0563	−	42.1804i	2.30571	−	1.67520i
$635$	−2.56230	−	4.65174i	−0.101682	−	0.184599i
$636$	−2.98456	−	9.18554i	−0.118346	−	0.364230i
$637$	−0.664797	+	0.664797i	−0.0263402	+	0.0263402i
$638$		0			0
$639$			3.34540i			0.132342i
$640$	−44.7405	−	5.61465i	−1.76852	−	0.221938i
$641$	7.21025	+	5.23855i	0.284788	+	0.206910i	0.721003	−	0.692932i	$-0.243681\pi$
$641$	7.21025	+	5.23855i	0.284788	+	0.206910i	−0.436215	+	0.899842i	$0.643681\pi$
$642$	−5.97579	−	0.946473i	−0.235846	−	0.0373543i
$643$	−16.8433	−	33.0569i	−0.664237	−	1.30364i	−0.939592	−	0.342296i	$-0.888796\pi$
$643$	−16.8433	−	33.0569i	−0.664237	−	1.30364i	0.275355	−	0.961342i	$-0.411204\pi$
$644$	−0.462809	+	1.42438i	−0.0182372	+	0.0561284i
$645$	−6.13207	−	4.15998i	−0.241450	−	0.163799i
$646$	−5.60311	+	7.71202i	−0.220451	+	0.303425i
$647$	−10.0113	+	19.6483i	−0.393585	+	0.772455i	−0.999738	−	0.0228938i	$-0.992712\pi$
$647$	−10.0113	+	19.6483i	−0.393585	+	0.772455i	0.606153	+	0.795348i	$0.292712\pi$
$648$	19.4905	+	19.4905i	0.765657	+	0.765657i
$649$		0			0
$650$	−26.2874	+	21.8198i	−1.03108	+	0.855842i
$651$	13.3070	−	4.32369i	0.521541	−	0.169459i
$652$	−14.0605	−	88.7743i	−0.550650	−	3.47667i
$653$	7.59976	−	47.9830i	0.297402	−	1.87772i	−0.158008	−	0.987438i	$-0.550507\pi$
$653$	7.59976	−	47.9830i	0.297402	−	1.87772i	0.455409	−	0.890282i	$-0.349493\pi$
$654$	−4.45944	−	1.44896i	−0.174378	−	0.0566588i
$655$	0.225211	+	6.98332i	0.00879972	+	0.272861i
$656$	7.11638	+	9.79485i	0.277848	+	0.382425i
$657$	−4.62301	+	0.732213i	−0.180361	+	0.0285664i
$658$	−5.91633	−	3.01452i	−0.230643	−	0.117518i
$659$	47.3029			1.84266			0.921329	−	0.388783i	$-0.127104\pi$
$659$	47.3029			1.84266			0.921329	+	0.388783i	$0.127104\pi$
$660$		0			0
$661$	−26.7159			−1.03913			−0.519564	−	0.854432i	$-0.673906\pi$
$661$	−26.7159			−1.03913			−0.519564	+	0.854432i	$0.673906\pi$
$662$	4.73719	+	2.41372i	0.184116	+	0.0938118i
$663$	1.56664	−	0.248132i	0.0608434	−	0.00963665i
$664$	22.7329	+	31.2891i	0.882207	+	1.21425i
$665$	16.3849	−	17.4769i	0.635379	−	0.677726i
$666$	46.4492	+	15.0923i	1.79987	+	0.584813i
$667$	0.160767	−	1.01504i	0.00622491	−	0.0393025i
$668$	−8.80051	−	55.5642i	−0.340502	−	2.14985i
$669$	11.1418	−	3.62020i	0.430768	−	0.139965i
$670$	−7.69172	−	21.3095i	−0.297157	−	0.823260i
$671$		0			0
$672$	−0.858297	−	0.858297i	−0.0331095	−	0.0331095i
$673$	−6.00870	+	11.7927i	−0.231618	+	0.454576i	−0.977338	−	0.211683i	$-0.932106\pi$
$673$	−6.00870	+	11.7927i	−0.231618	+	0.454576i	0.745720	+	0.666259i	$0.232106\pi$
$674$	2.57659	−	3.54637i	0.0992464	−	0.136601i
$675$	14.5076	−	8.61205i	0.558399	−	0.331478i
$676$	−6.18684	+	19.0411i	−0.237955	+	0.732351i
$677$	−15.6128	−	30.6419i	−0.600050	−	1.17767i	−0.968732	−	0.248110i	$-0.920191\pi$
$677$	−15.6128	−	30.6419i	−0.600050	−	1.17767i	0.368682	−	0.929556i	$-0.379809\pi$
$678$	−16.0252	−	2.53815i	−0.615446	−	0.0974770i
$679$	−30.1258	−	21.8877i	−1.15612	−	0.839972i
$680$	7.77748	−	6.04309i	0.298253	−	0.231742i
$681$		−	0.611726i		−	0.0234414i
$682$		0			0
$683$	27.9495	−	27.9495i	1.06946	−	1.06946i	0.0720555	−	0.997401i	$-0.477044\pi$
$683$	27.9495	−	27.9495i	1.06946	−	1.06946i	0.997401	−	0.0720555i	$-0.0229559\pi$
$684$	−13.2743	−	40.8541i	−0.507556	−	1.56210i
$685$	32.3872	−	17.8397i	1.23745	−	0.681620i
$686$	−37.2666	+	27.0758i	−1.42284	+	1.03376i
$687$	−0.0542691	+	0.0276515i	−0.00207050	+	0.00105497i
$688$	17.3392	−	8.83475i	0.661050	−	0.336822i
$689$	−9.36810	+	6.80632i	−0.356896	+	0.259300i
$690$	0.421920	−	0.232405i	0.0160622	−	0.00884750i
$691$	1.01180	+	3.11399i	0.0384905	+	0.118462i	0.968456	−	0.249186i	$-0.0801631\pi$
$691$	1.01180	+	3.11399i	0.0384905	+	0.118462i	−0.929965	+	0.367648i	$0.880163\pi$
$692$	−61.7773	+	61.7773i	−2.34842	+	2.34842i
$693$		0			0
$694$			52.2333i			1.98275i
$695$	−7.62871	+	5.92749i	−0.289373	+	0.224843i
$696$	−15.6618	−	11.3789i	−0.593657	−	0.431317i
$697$	3.21546	+	0.509279i	0.121794	+	0.0192903i
$698$	11.7686	+	23.0972i	0.445449	+	0.874243i
$699$	−3.95470	+	12.1713i	−0.149580	+	0.460361i
$700$	−43.4848	+	25.8135i	−1.64357	+	0.975660i
$701$	−3.43439	+	4.72703i	−0.129715	+	0.178538i	−0.868934	−	0.494927i	$-0.835195\pi$
$701$	−3.43439	+	4.72703i	−0.129715	+	0.178538i	0.739219	+	0.673465i	$0.235195\pi$
$702$	−10.4668	+	20.5422i	−0.395044	+	0.775317i
$703$	−22.2957	−	22.2957i	−0.840897	−	0.840897i
$704$		0			0
$705$	0.480009	+	1.32984i	0.0180782	+	0.0500847i
$706$	−25.3193	+	8.22673i	−0.952904	+	0.309617i
$707$	−0.781559	−	4.93457i	−0.0293935	−	0.185583i
$708$	2.37550	−	14.9983i	0.0892769	−	0.563672i
$709$	−38.0265	−	12.3555i	−1.42811	−	0.464022i	−0.509943	−	0.860208i	$-0.670334\pi$
$709$	−38.0265	−	12.3555i	−1.42811	−	0.464022i	−0.918170	+	0.396186i	$0.870334\pi$
$710$	−4.71010	+	5.02403i	−0.176767	+	0.188548i
$711$	6.74369	+	9.28190i	0.252908	+	0.348098i
$712$	−19.4921	+	3.08725i	−0.730499	+	0.115700i
$713$	1.19572	+	0.609250i	0.0447801	+	0.0228166i
$714$	3.54657			0.132727
$715$		0			0
$716$	17.1125			0.639523
$717$	4.61636	+	2.35215i	0.172401	+	0.0878427i
$718$	7.86670	−	1.24596i	0.293583	−	0.0464989i
$719$	11.8728	+	16.3415i	0.442781	+	0.609435i	0.970827	−	0.239780i	$-0.0770753\pi$
$719$	11.8728	+	16.3415i	0.442781	+	0.609435i	−0.528047	+	0.849215i	$0.677075\pi$
$720$	0.668824	+	20.7388i	0.0249256	+	0.772891i
$721$	−4.22139	−	1.37161i	−0.157213	−	0.0510816i
$722$	0.677056	−	4.27476i	0.0251974	−	0.159090i
$723$	−0.996243	−	6.29003i	−0.0370507	−	0.233929i
$724$	35.1704	−	11.4276i	1.30710	−	0.424702i
$725$	26.7006	−	22.1627i	0.991634	−	0.823103i
$726$		0			0
$727$	26.5141	+	26.5141i	0.983354	+	0.983354i	0.999864	−	0.0165102i	$-0.00525558\pi$
$727$	26.5141	+	26.5141i	0.983354	+	0.983354i	−0.0165102	+	0.999864i	$0.505256\pi$
$728$	15.3561	−	30.1380i	0.569135	−	1.11699i
$729$	−5.61971	+	7.73487i	−0.208138	+	0.286477i
$730$	−7.97363	−	5.40929i	−0.295117	−	0.200207i
$731$	1.61701	−	4.97665i	0.0598073	−	0.184068i
$732$	10.1309	+	19.8830i	0.374449	+	0.734897i
$733$	31.5047	+	4.98986i	1.16365	+	0.184305i	0.708238	−	0.705974i	$-0.249490\pi$
$733$	31.5047	+	4.98986i	1.16365	+	0.184305i	0.455416	+	0.890279i	$0.349490\pi$
$734$	−35.8763	−	26.0657i	−1.32422	−	0.962102i
$735$	0.444110	+	0.0557330i	0.0163813	+	0.00205574i
$736$		−	0.116420i		−	0.00429131i
$737$		0			0
$738$	−15.6696	+	15.6696i	−0.576805	+	0.576805i
$739$	12.1034	+	37.2504i	0.445231	+	1.37028i	0.882230	+	0.470818i	$0.156041\pi$
$739$	12.1034	+	37.2504i	0.445231	+	1.37028i	−0.437000	+	0.899462i	$0.643959\pi$
$740$	32.1127	+	58.2992i	1.18049	+	2.14312i
$741$	5.63924	−	4.09714i	0.207162	−	0.150512i
$742$	−23.0692	+	11.7544i	−0.846897	+	0.431516i
$743$	6.04541	−	3.08029i	0.221785	−	0.113005i	−0.339568	−	0.940581i	$-0.610281\pi$
$743$	6.04541	−	3.08029i	0.221785	−	0.113005i	0.561353	+	0.827576i	$0.310281\pi$
$744$	20.4515	−	14.8589i	0.749789	−	0.544754i
$745$	−5.25323	+	18.1374i	−0.192463	+	0.664503i
$746$	−13.2797	−	40.8706i	−0.486203	−	1.49638i
$747$	−15.4921	+	15.4921i	−0.566826	+	0.566826i
$748$		0			0
$749$			10.7374i			0.392337i
$750$	15.8815	+	3.50879i	0.579909	+	0.128123i
$751$	17.8734	+	12.9858i	0.652209	+	0.473858i	0.864023	−	0.503452i	$-0.167937\pi$
$751$	17.8734	+	12.9858i	0.652209	+	0.473858i	−0.211814	+	0.977310i	$0.567937\pi$
$752$	−3.66728	−	0.580841i	−0.133732	−	0.0211811i
$753$	2.55017	+	5.00499i	0.0929334	+	0.182392i
$754$	−14.6533	+	45.0981i	−0.533640	+	1.64238i
$755$	−14.9791	+	22.0801i	−0.545144	+	0.803577i
$756$	−20.0592	+	27.6092i	−0.729547	+	1.00414i
$757$	−15.1880	+	29.8080i	−0.552016	+	1.08339i	0.431423	+	0.902150i	$0.358012\pi$
$757$	−15.1880	+	29.8080i	−0.552016	+	1.08339i	−0.983439	+	0.181242i	$0.941988\pi$
$758$	−37.9511	−	37.9511i	−1.37845	−	1.37845i
$759$		0			0
$760$	18.3967	−	39.1787i	0.667320	−	1.42116i
$761$	24.7800	−	8.05150i	0.898273	−	0.291867i	0.176749	−	0.984256i	$-0.443442\pi$
$761$	24.7800	−	8.05150i	0.898273	−	0.291867i	0.721524	+	0.692389i	$0.243442\pi$
$762$	−0.540490	−	3.41252i	−0.0195799	−	0.123623i
$763$	−1.30176	+	8.21898i	−0.0471269	+	0.297547i
$764$	24.1160	+	7.83577i	0.872487	+	0.283488i
$765$	4.07040	+	3.81607i	0.147166	+	0.137970i
$766$	28.1532	+	38.7496i	1.01722	+	1.40008i
$767$	−17.9820	+	2.84808i	−0.649294	+	0.102838i
$768$	−16.6151	−	8.46583i	−0.599547	−	0.305484i
$769$	−51.2907			−1.84959			−0.924794	−	0.380468i	$-0.875763\pi$
$769$	−51.2907			−1.84959			−0.924794	+	0.380468i	$0.875763\pi$
$770$		0			0
$771$	−11.0274			−0.397141
$772$	3.51369	+	1.79032i	0.126461	+	0.0644349i
$773$	−16.3111	+	2.58343i	−0.586670	+	0.0929194i	−0.442711	−	0.896664i	$-0.645983\pi$
$773$	−16.3111	+	2.58343i	−0.586670	+	0.0929194i	−0.143959	+	0.989584i	$0.545983\pi$
$774$	20.9362	+	28.8162i	0.752537	+	1.03578i
$775$	16.7499	+	42.1030i	0.601676	+	1.51238i
$776$	−63.9857	−	20.7902i	−2.29695	−	0.746325i
$777$	−1.83513	+	11.5865i	−0.0658348	+	0.415665i
$778$	6.51510	+	41.1348i	0.233578	+	1.47475i
$779$	13.6064	−	4.42098i	0.487499	−	0.158398i
$780$	−13.8400	+	4.99557i	−0.495551	+	0.178870i
$781$		0			0
$782$	0.240530	+	0.240530i	0.00860135	+	0.00860135i
$783$	10.6313	−	20.8651i	0.379932	−	0.745658i
$784$	−0.690929	+	0.950982i	−0.0246760	+	0.0339636i
$785$	−0.572933	−	2.99005i	−0.0204489	−	0.106720i
$786$	−1.40466	+	4.32308i	−0.0501024	+	0.154199i
$787$	−2.01012	−	3.94509i	−0.0716531	−	0.140627i	0.852401	−	0.522888i	$-0.175146\pi$
$787$	−2.01012	−	3.94509i	−0.0716531	−	0.140627i	−0.924054	+	0.382261i	$0.875146\pi$
$788$	−94.8977	−	15.0303i	−3.38059	−	0.535433i
$789$	−8.13715	−	5.91199i	−0.289690	−	0.210472i
$790$	−2.94081	+	23.4340i	−0.104629	+	0.833744i
$791$			28.7945i			1.02381i
$792$		0			0
$793$	18.9183	−	18.9183i	0.671808	−	0.671808i
$794$	5.57997	+	17.1734i	0.198026	+	0.609461i
$795$	5.29519	+	1.53367i	0.187801	+	0.0543938i
$796$	10.3187	−	7.49696i	0.365736	−	0.265723i
$797$	−17.1266	+	8.72643i	−0.606655	+	0.309106i	−0.730201	−	0.683233i	$-0.760573\pi$
$797$	−17.1266	+	8.72643i	−0.606655	+	0.309106i	0.123546	+	0.992339i	$0.460573\pi$
$798$	13.8868	−	7.07567i	0.491587	−	0.250476i
$799$	−0.807729	+	0.586849i	−0.0285754	+	0.0207612i
$800$	2.59473	−	2.95293i	0.0917376	−	0.104402i
$801$	−3.45471	−	10.6325i	−0.122066	−	0.375681i
$802$	21.1147	−	21.1147i	0.745587	−	0.745587i
$803$		0			0
$804$		−	9.75751i		−	0.344121i
$805$	−0.524506	−	0.675041i	−0.0184864	−	0.0237921i
$806$	−50.0951	−	36.3962i	−1.76452	−	1.28200i
$807$	−16.8081	−	2.66215i	−0.591674	−	0.0937120i
$808$	−4.09799	−	8.04277i	−0.144167	−	0.282944i
$809$	9.54622	−	29.3802i	0.335627	−	1.03295i	−0.630785	−	0.775957i	$-0.717267\pi$
$809$	9.54622	−	29.3802i	0.335627	−	1.03295i	0.966412	−	0.256996i	$-0.0827329\pi$
$810$	−31.5687	+	6.04897i	−1.10921	+	0.212539i
$811$	14.7148	−	20.2531i	0.516705	−	0.711184i	−0.468327	−	0.883555i	$-0.655143\pi$
$811$	14.7148	−	20.2531i	0.516705	−	0.711184i	0.985032	+	0.172372i	$0.0551430\pi$
$812$	−31.8660	+	62.5405i	−1.11828	+	2.19474i
$813$	12.5516	+	12.5516i	0.440202	+	0.440202i
$814$		0			0
$815$	46.4383	+	21.8056i	1.62666	+	0.763816i
$816$	1.88611	−	0.612835i	0.0660271	−	0.0214535i
$817$	−3.59729	−	22.7124i	−0.125853	−	0.794606i
$818$	−10.1829	+	64.2923i	−0.356037	+	2.24793i
$819$	18.2234	+	5.92115i	0.636778	+	0.206902i
$820$	−30.1840	+	0.973431i	−1.05407	+	0.0339937i
$821$	−13.3959	−	18.4379i	−0.467520	−	0.643486i	0.508527	−	0.861046i	$-0.330190\pi$
$821$	−13.3959	−	18.4379i	−0.467520	−	0.643486i	−0.976047	+	0.217560i	$0.930190\pi$
$822$	23.7593	−	3.76310i	0.828699	−	0.131253i
$823$	−15.7218	−	8.01068i	−0.548029	−	0.279235i	0.157974	−	0.987443i	$-0.449504\pi$
$823$	−15.7218	−	8.01068i	−0.548029	−	0.279235i	−0.706003	+	0.708209i	$0.749504\pi$
$824$	−8.01946			−0.279371
$825$		0			0
$826$	−40.7077			−1.41640
$827$	−14.8438	−	7.56328i	−0.516168	−	0.263001i	0.176444	−	0.984311i	$-0.443540\pi$
$827$	−14.8438	−	7.56328i	−0.516168	−	0.263001i	−0.692613	+	0.721310i	$0.743540\pi$
$828$	−1.51399	+	0.239793i	−0.0526149	+	0.00833339i
$829$	24.5888	+	33.8436i	0.854004	+	1.17544i	0.982966	+	0.183786i	$0.0588353\pi$
$829$	24.5888	+	33.8436i	0.854004	+	1.17544i	−0.128963	+	0.991649i	$0.541165\pi$
$830$	−45.0775	+	1.45374i	−1.56466	+	0.0504601i
$831$	7.06372	+	2.29514i	0.245038	+	0.0796175i
$832$	−3.92646	+	24.7907i	−0.136125	+	0.859462i
$833$	0.0494459	+	0.312189i	0.00171320	+	0.0108167i
$834$	−5.97754	+	1.94222i	−0.206985	+	0.0672536i
$835$	29.0660	+	13.6482i	1.00587	+	0.472316i
$836$		0			0
$837$	21.6227	+	21.6227i	0.747390	+	0.747390i
$838$	15.7264	−	30.8648i	0.543260	−	1.06621i
$839$	−30.5197	+	42.0067i	−1.05366	+	1.45023i	−0.168059	+	0.985777i	$0.553750\pi$
$839$	−30.5197	+	42.0067i	−1.05366	+	1.45023i	−0.885597	+	0.464455i	$0.846250\pi$
$840$	−15.8156	+	3.03047i	−0.545689	+	0.104561i
$841$	5.92209	−	18.2263i	0.204210	−	0.628494i
$842$	7.62701	+	14.9689i	0.262844	+	0.515861i
$843$	12.9206	+	2.04643i	0.445010	+	0.0704827i
$844$	78.7303	+	57.2009i	2.71001	+	1.96894i
$845$	−7.01160	−	9.02396i	−0.241206	−	0.310434i
$846$		−	6.79605i		−	0.233653i
$847$		0			0
$848$	−10.2374	+	10.2374i	−0.351554	+	0.351554i
$849$	5.02606	+	15.4686i	0.172494	+	0.530882i
$850$	0.740048	+	11.4617i	0.0253834	+	0.393134i
$851$	−0.910264	+	0.661346i	−0.0312035	+	0.0226706i
$852$	−2.64277	+	1.34656i	−0.0905398	+	0.0461323i
$853$	−12.4787	+	6.35820i	−0.427262	+	0.217701i	−0.654379	−	0.756167i	$-0.727070\pi$
$853$	−12.4787	+	6.35820i	−0.427262	+	0.217701i	0.227117	+	0.973867i	$0.427070\pi$
$854$	48.3963	−	35.1620i	1.65609	−	1.20322i
$855$	23.5512	+	6.82126i	0.805435	+	0.233282i
$856$	5.99485	+	18.4502i	0.204900	+	0.630616i
$857$	10.2364	−	10.2364i	0.349669	−	0.349669i	−0.510317	−	0.859986i	$-0.670472\pi$
$857$	10.2364	−	10.2364i	0.349669	−	0.349669i	0.859986	+	0.510317i	$0.170472\pi$
$858$		0			0
$859$		−	56.0426i		−	1.91215i	−0.293125	−	0.956074i	$-0.594695\pi$
$859$		−	56.0426i		−	1.91215i	0.293125	−	0.956074i	$-0.405305\pi$
$860$	−6.04420	+	48.1634i	−0.206105	+	1.64236i
$861$	−4.30617	−	3.12862i	−0.146754	−	0.106623i
$862$	17.1532	+	2.71680i	0.584240	+	0.0925345i
$863$	−7.82527	−	15.3580i	−0.266375	−	0.522791i	0.718613	−	0.695410i	$-0.244777\pi$
$863$	−7.82527	−	15.3580i	−0.266375	−	0.522791i	−0.984989	+	0.172619i	$0.944777\pi$
$864$	0.819762	−	2.52297i	0.0278889	−	0.0858331i
$865$	−9.38459	−	48.9768i	−0.319086	−	1.66526i
$866$	−24.0250	+	33.0676i	−0.816404	+	1.12368i
$867$	−4.37332	+	8.58313i	−0.148526	+	0.291498i
$868$	−64.8114	−	64.8114i	−2.19984	−	2.19984i
$869$		0			0
$870$	21.2343	−	7.66456i	0.719910	−	0.259853i
$871$	−11.1260	+	3.61507i	−0.376992	+	0.122492i
$872$	2.35194	+	14.8496i	0.0796467	+	0.502870i
$873$	5.96209	−	37.6431i	0.201786	−	1.27403i
$874$	1.42168	+	0.461933i	0.0480892	+	0.0156251i
$875$	1.74131	−	28.8119i	0.0588670	−	0.974021i
$876$	−2.43924	−	3.35733i	−0.0824143	−	0.113434i
$877$	6.96326	−	1.10287i	0.235133	−	0.0372413i	−0.0377560	−	0.999287i	$-0.512021\pi$
$877$	6.96326	−	1.10287i	0.235133	−	0.0372413i	0.272889	+	0.962046i	$0.412021\pi$
$878$	−1.67530	−	0.853608i	−0.0565386	−	0.0288079i
$879$	−12.0275			−0.405678
$880$		0			0
$881$	−46.6330			−1.57111			−0.785553	−	0.618794i	$-0.787622\pi$
$881$	−46.6330			−1.57111			−0.785553	+	0.618794i	$0.787622\pi$
$882$	−1.91702	−	0.976773i	−0.0645496	−	0.0328896i
$883$	−10.8716	+	1.72190i	−0.365859	+	0.0579464i	−0.336658	−	0.941627i	$-0.609296\pi$
$883$	−10.8716	+	1.72190i	−0.365859	+	0.0579464i	−0.0292016	+	0.999574i	$0.509296\pi$
$884$	−6.10749	−	8.40623i	−0.205417	−	0.282732i
$885$	6.32329	+	5.92819i	0.212555	+	0.199274i
$886$	−43.4709	−	14.1245i	−1.46043	−	0.474523i
$887$	6.09743	−	38.4977i	0.204732	−	1.29262i	−0.644500	−	0.764604i	$-0.722934\pi$
$887$	6.09743	−	38.4977i	0.204732	−	1.29262i	0.849232	−	0.528020i	$-0.177066\pi$
$888$	3.31560	+	20.9338i	0.111264	+	0.702494i
$889$	−5.83158	+	1.89480i	−0.195585	+	0.0635494i
$890$	9.78168	−	20.8316i	0.327883	−	0.698277i
$891$		0			0
$892$	−54.2662	−	54.2662i	−1.81697	−	1.81697i
$893$	−1.99190	+	3.90932i	−0.0666563	+	0.130820i
$894$	−7.22081	+	9.93859i	−0.241500	+	0.332396i
$895$	−5.48357	+	8.08312i	−0.183295	+	0.270189i
$896$	−16.0879	+	49.5136i	−0.537461	+	1.65413i
$897$	−0.112923	−	0.221625i	−0.00377040	−	0.00739983i
$898$	−1.71401	−	0.271472i	−0.0571972	−	0.00905914i
$899$	50.8825	+	36.9683i	1.69703	+	1.23296i
$900$	−43.7459	−	27.6611i	−1.45820	−	0.922037i
$901$			3.89303i			0.129696i
$902$		0			0
$903$	−6.04959	+	6.04959i	−0.201318	+	0.201318i
$904$	16.0763	+	49.4779i	0.534691	+	1.64561i
$905$	−5.87226	+	20.2747i	−0.195201	+	0.673954i
$906$	−14.0433	+	10.2030i	−0.466556	+	0.338973i
$907$	25.0506	−	12.7639i	0.831793	−	0.423820i	0.0143971	−	0.999896i	$-0.495417\pi$
$907$	25.0506	−	12.7639i	0.831793	−	0.423820i	0.817396	+	0.576077i	$0.195417\pi$
$908$	−3.57052	+	1.81927i	−0.118492	+	0.0603746i
$909$	4.13687	−	3.00561i	0.137211	−	0.0996898i
$910$	19.0308	+	34.5496i	0.630866	+	1.14531i
$911$	−9.11103	−	28.0409i	−0.301862	−	0.929035i	−0.980830	−	0.194867i	$-0.937572\pi$
$911$	−9.11103	−	28.0409i	−0.301862	−	0.929035i	0.678968	−	0.734168i	$-0.262428\pi$
$912$	6.16252	−	6.16252i	0.204061	−	0.204061i
$913$		0			0
$914$			47.0585i			1.55656i
$915$	−12.6382	−	1.58601i	−0.417805	−	0.0524318i
$916$	0.322792	+	0.234522i	0.0106654	+	0.00774883i
$917$	7.96768	+	1.26196i	0.263116	+	0.0416735i
$918$	3.51891	+	6.90624i	0.116141	+	0.227940i
$919$	−12.6027	+	38.7871i	−0.415725	+	1.27947i	0.495877	+	0.868393i	$0.334847\pi$
$919$	−12.6027	+	38.7871i	−0.415725	+	1.27947i	−0.911601	+	0.411076i	$0.865153\pi$
$920$	−1.27815	−	0.867092i	−0.0421393	−	0.0285872i
$921$	−7.30351	+	10.0524i	−0.240659	+	0.331239i
$922$	40.3402	−	79.1721i	1.32853	−	2.60740i
$923$	2.51454	+	2.51454i	0.0827672	+	0.0827672i
$924$		0			0
$925$	−37.8281	−	3.51301i	−1.24378	−	0.115507i
$926$	−56.0862	+	18.2235i	−1.84311	+	0.598862i
$927$	−0.710668	−	4.48698i	−0.0233414	−	0.147372i
$928$	0.853538	−	5.38903i	0.0280188	−	0.176904i
$929$	−48.7643	−	15.8445i	−1.59990	−	0.519840i	−0.632820	−	0.774299i	$-0.718103\pi$
$929$	−48.7643	−	15.8445i	−1.59990	−	0.519840i	−0.967084	+	0.254458i	$0.918103\pi$
$930$	0.950210	+	29.4640i	0.0311586	+	0.966163i
$931$	0.816449	+	1.12375i	0.0267580	+	0.0368293i
$932$	82.8026	−	13.1146i	2.71229	−	0.429585i
$933$	12.4039	+	6.32012i	0.406086	+	0.206911i
$934$	36.0504			1.17960
$935$		0			0
$936$	34.6194			1.13157
$937$	2.74472	+	1.39850i	0.0896660	+	0.0456871i	0.498248	−	0.867034i	$-0.333977\pi$
$937$	2.74472	+	1.39850i	0.0896660	+	0.0456871i	−0.408582	+	0.912721i	$0.633977\pi$
$938$	−25.8352	+	4.09190i	−0.843551	+	0.133605i
$939$	−4.92741	−	6.78200i	−0.160800	−	0.221322i
$940$	6.33447	−	6.75665i	0.206608	−	0.220378i
$941$	27.0435	+	8.78695i	0.881592	+	0.286447i	0.714618	−	0.699515i	$-0.246601\pi$
$941$	27.0435	+	8.78695i	0.881592	+	0.286447i	0.166974	+	0.985961i	$0.446601\pi$
$942$	0.309842	−	1.95627i	0.0100952	−	0.0637387i
$943$	−0.0798625	−	0.504232i	−0.00260068	−	0.0164200i
$944$	−21.6489	+	7.03416i	−0.704612	+	0.228942i
$945$	−6.61343	−	18.3222i	−0.215135	−	0.596021i
$946$		0			0
$947$	−40.6526	−	40.6526i	−1.32103	−	1.32103i	−0.912941	−	0.408091i	$-0.866195\pi$
$947$	−40.6526	−	40.6526i	−1.32103	−	1.32103i	−0.408091	−	0.912941i	$-0.633805\pi$
$948$	−4.61803	+	9.06339i	−0.149987	+	0.294365i
$949$	−2.92449	+	4.02522i	−0.0949330	+	0.130664i
$950$	25.7647	+	43.4026i	0.835917	+	1.40817i
$951$	−5.45156	+	16.7782i	−0.176779	+	0.544069i
$952$	−5.16268	−	10.1323i	−0.167323	−	0.328391i
$953$	−18.9002	−	2.99349i	−0.612237	−	0.0969688i	−0.157387	−	0.987537i	$-0.550307\pi$
$953$	−18.9002	−	2.99349i	−0.612237	−	0.0969688i	−0.454850	+	0.890568i	$0.650307\pi$
$954$	−21.4385	−	15.5760i	−0.694097	−	0.504291i
$955$	−11.4291	+	8.88035i	−0.369835	+	0.287361i
$956$		−	33.9400i		−	1.09770i
$957$		0			0
$958$	47.4507	−	47.4507i	1.53306	−	1.53306i
$959$	−13.1923	−	40.6017i	−0.426001	−	1.31110i
$960$	10.4667	−	5.76532i	0.337810	−	0.186075i
$961$	−41.3641	+	30.0528i	−1.33433	+	0.969445i
$962$	46.2572	−	23.5692i	1.49139	−	0.759902i
$963$	−9.79187	+	4.98921i	−0.315539	+	0.160775i
$964$	−33.7508	+	24.5214i	−1.08704	+	0.789781i
$965$	−1.97160	+	1.08601i	−0.0634680	+	0.0349598i
$966$	−0.171861	−	0.528934i	−0.00552954	−	0.0170182i
$967$	−12.6930	+	12.6930i	−0.408178	+	0.408178i	−0.881103	−	0.472925i	$-0.843198\pi$
$967$	−12.6930	+	12.6930i	−0.408178	+	0.408178i	0.472925	+	0.881103i	$0.343198\pi$
$968$		0			0
$969$		−	2.34346i		−	0.0752826i
$970$	61.9528	−	48.1372i	1.98919	−	1.54559i
$971$	2.82019	+	2.04898i	0.0905040	+	0.0657550i	0.632117	−	0.774873i	$-0.282186\pi$
$971$	2.82019	+	2.04898i	0.0905040	+	0.0657550i	−0.541613	+	0.840628i	$0.682186\pi$
$972$	−52.8411	−	8.36920i	−1.69488	−	0.268442i
$973$	5.06392	+	9.93851i	0.162342	+	0.318614i
$974$	−29.2384	+	89.9865i	−0.936858	+	2.88335i
$975$	2.07525	−	8.13815i	0.0664613	−	0.260629i
$976$	19.6619	−	27.0623i	0.629363	−	0.866244i
$977$	11.7295	−	23.0204i	0.375259	−	0.736487i	−0.623721	−	0.781647i	$-0.714380\pi$
$977$	11.7295	−	23.0204i	0.375259	−	0.736487i	0.998980	+	0.0451603i	$0.0143799\pi$
$978$	23.6009	+	23.6009i	0.754672	+	0.754672i
$979$		0			0
$980$	−0.995480	−	2.75793i	−0.0317994	−	0.0880989i
$981$	−8.10008	+	2.63188i	−0.258616	+	0.0840293i
$982$	7.15466	+	45.1728i	0.228315	+	1.44152i
$983$	−4.88486	+	30.8418i	−0.155803	+	0.983701i	0.778610	+	0.627508i	$0.215925\pi$
$983$	−4.88486	+	30.8418i	−0.155803	+	0.983701i	−0.934413	+	0.356192i	$0.884075\pi$
$984$	−9.14609	−	2.97175i	−0.291567	−	0.0947358i
$985$	37.5089	−	40.0088i	1.19513	−	1.27479i
$986$	9.37055	+	12.8974i	0.298419	+	0.410738i
$987$	1.61227	−	0.255359i	0.0513192	−	0.00812816i
$988$	−40.6853	−	20.7302i	−1.29437	−	0.659515i
$989$	−0.820573			−0.0260927
$990$		0			0
$991$	−19.5868			−0.622196			−0.311098	−	0.950378i	$-0.600697\pi$
$991$	−19.5868			−0.622196			−0.311098	+	0.950378i	$0.600697\pi$
$992$	6.34829	+	3.23462i	0.201558	+	0.102699i
$993$	−1.29094	+	0.204465i	−0.0409667	+	0.00648850i
$994$	4.67359	+	6.43265i	0.148237	+	0.204031i
$995$	0.234663	+	7.27640i	0.00743931	+	0.230677i
$996$	−18.4741	−	6.00259i	−0.585373	−	0.190199i
$997$	−4.42928	+	27.9653i	−0.140277	+	0.885671i	0.812712	+	0.582665i	$0.197990\pi$
$997$	−4.42928	+	27.9653i	−0.140277	+	0.885671i	−0.952989	+	0.303006i	$0.902010\pi$
$998$	1.99393	+	12.5892i	0.0631167	+	0.398503i
$999$	−24.3833	+	7.92261i	−0.771453	+	0.250660i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.m.d.457.4		32
5.3	odd	4	inner	605.2.m.d.578.4		32
11.2	odd	10	inner	605.2.m.d.112.4		32
11.3	even	5		605.2.e.b.362.15		32
11.4	even	5		605.2.m.e.602.1		32
11.5	even	5		55.2.l.a.7.1	✓	32
11.6	odd	10		605.2.m.e.282.4		32
11.7	odd	10		55.2.l.a.52.4	yes	32
11.8	odd	10		605.2.e.b.362.2		32
11.9	even	5		605.2.m.c.112.1		32
11.10	odd	2		605.2.m.c.457.1		32
33.5	odd	10		495.2.bj.a.172.4		32
33.29	even	10		495.2.bj.a.217.1		32
44.7	even	10		880.2.cm.a.657.2		32
44.27	odd	10		880.2.cm.a.337.3		32
55.3	odd	20		605.2.e.b.483.2		32
55.7	even	20		275.2.bm.b.118.4		32
55.8	even	20		605.2.e.b.483.15		32
55.13	even	20	inner	605.2.m.d.233.4		32
55.18	even	20		55.2.l.a.8.1	yes	32
55.27	odd	20		275.2.bm.b.18.1		32
55.28	even	20		605.2.m.e.403.1		32
55.29	odd	10		275.2.bm.b.107.1		32
55.38	odd	20		55.2.l.a.18.4	yes	32
55.43	even	4		605.2.m.c.578.1		32
55.48	odd	20		605.2.m.e.118.4		32
55.49	even	10		275.2.bm.b.7.4		32
55.53	odd	20		605.2.m.c.233.1		32
165.38	even	20		495.2.bj.a.73.1		32
165.128	odd	20		495.2.bj.a.118.4		32
220.183	odd	20		880.2.cm.a.833.3		32
220.203	even	20		880.2.cm.a.513.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.7.1	✓	32	11.5	even	5
55.2.l.a.8.1	yes	32	55.18	even	20
55.2.l.a.18.4	yes	32	55.38	odd	20
55.2.l.a.52.4	yes	32	11.7	odd	10
275.2.bm.b.7.4		32	55.49	even	10
275.2.bm.b.18.1		32	55.27	odd	20
275.2.bm.b.107.1		32	55.29	odd	10
275.2.bm.b.118.4		32	55.7	even	20
495.2.bj.a.73.1		32	165.38	even	20
495.2.bj.a.118.4		32	165.128	odd	20
495.2.bj.a.172.4		32	33.5	odd	10
495.2.bj.a.217.1		32	33.29	even	10
605.2.e.b.362.2		32	11.8	odd	10
605.2.e.b.362.15		32	11.3	even	5
605.2.e.b.483.2		32	55.3	odd	20
605.2.e.b.483.15		32	55.8	even	20
605.2.m.c.112.1		32	11.9	even	5
605.2.m.c.233.1		32	55.53	odd	20
605.2.m.c.457.1		32	11.10	odd	2
605.2.m.c.578.1		32	55.43	even	4
605.2.m.d.112.4		32	11.2	odd	10	inner
605.2.m.d.233.4		32	55.13	even	20	inner
605.2.m.d.457.4		32	1.1	even	1	trivial
605.2.m.d.578.4		32	5.3	odd	4	inner
605.2.m.e.118.4		32	55.48	odd	20
605.2.m.e.282.4		32	11.6	odd	10
605.2.m.e.403.1		32	55.28	even	20
605.2.m.e.602.1		32	11.4	even	5
880.2.cm.a.337.3		32	44.27	odd	10
880.2.cm.a.513.2		32	220.203	even	20
880.2.cm.a.657.2		32	44.7	even	10
880.2.cm.a.833.3		32	220.183	odd	20

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.m (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.16745 + 1.10437i) q^{2} +(-0.590657 + 0.0935509i) q^{3} +(2.30265 + 3.16932i) q^{4} +(-2.23491 + 0.0720754i) q^{5} +(-1.38354 - 0.449539i) q^{6} +(-0.403870 + 2.54993i) q^{7} +(0.729688 + 4.60707i) q^{8} +(-2.51305 + 0.816538i) q^{9} +(-4.92366 - 2.31195i) q^{10} +(-1.65657 - 1.65657i) q^{12} +(-1.27517 + 2.50266i) q^{13} +(-3.69145 + 5.08085i) q^{14} +(1.31332 - 0.251649i) q^{15} +(-1.08521 + 3.33993i) q^{16} +(0.428708 + 0.841386i) q^{17} +(-6.34868 - 1.00553i) q^{18} +(3.35726 + 2.43919i) q^{19} +(-5.37463 - 6.91718i) q^{20} -1.54392i q^{21} +(0.104710 - 0.104710i) q^{23} +(-0.861991 - 2.65293i) q^{24} +(4.98961 - 0.322163i) q^{25} +(-5.52773 + 4.01613i) q^{26} +(3.00648 - 1.53188i) q^{27} +(-9.01154 + 4.59161i) q^{28} +(5.61462 - 4.07926i) q^{29} +(3.12448 + 0.904958i) q^{30} +(2.80047 + 8.61895i) q^{31} +(0.555921 - 0.555921i) q^{32} +2.29712i q^{34} +(0.718824 - 5.72797i) q^{35} +(-8.37454 - 6.08446i) q^{36} +(-7.50462 - 1.18862i) q^{37} +(4.58292 + 8.99450i) q^{38} +(0.519061 - 1.59750i) q^{39} +(-1.96284 - 10.2438i) q^{40} +(2.02641 - 2.78912i) q^{41} +(1.70506 - 3.34638i) q^{42} +(-3.91833 - 3.91833i) q^{43} +(5.55757 - 2.00601i) q^{45} +(0.342592 - 0.111315i) q^{46} +(0.165396 + 1.04427i) q^{47} +(0.328533 - 2.07428i) q^{48} +(0.318339 + 0.103435i) q^{49} +(11.1705 + 4.81212i) q^{50} +(-0.331932 - 0.456865i) q^{51} +(-10.8680 + 1.72132i) q^{52} +(3.67328 + 1.87163i) q^{53} +8.20817 q^{54} -12.0424 q^{56} +(-2.21118 - 1.12665i) q^{57} +(16.6745 - 2.64097i) q^{58} +(3.80993 + 5.24392i) q^{59} +(3.82167 + 3.58288i) q^{60} +(-9.05905 - 2.94346i) q^{61} +(-3.44865 + 21.7739i) q^{62} +(-1.06717 - 6.73788i) q^{63} +(8.49874 - 2.76141i) q^{64} +(2.66950 - 5.68511i) q^{65} +(2.94509 + 2.94509i) q^{67} +(-1.67946 + 3.29613i) q^{68} +(-0.0520518 + 0.0716431i) q^{69} +(7.88384 - 11.6213i) q^{70} +(0.391234 - 1.20409i) q^{71} +(-5.59558 - 10.9820i) q^{72} +(1.74957 + 0.277105i) q^{73} +(-14.9533 - 10.8642i) q^{74} +(-2.91701 + 0.657071i) q^{75} +16.2568i q^{76} +(2.88928 - 2.88928i) q^{78} +(-1.34174 - 4.12944i) q^{79} +(2.18461 - 7.54265i) q^{80} +(4.78068 - 3.47337i) q^{81} +(7.47238 - 3.80737i) q^{82} +(7.38775 - 3.76425i) q^{83} +(4.89318 - 3.55511i) q^{84} +(-1.01876 - 1.84952i) q^{85} +(-4.16551 - 12.8201i) q^{86} +(-2.93470 + 2.93470i) q^{87} +4.23092i q^{89} +(14.2612 + 1.78969i) q^{90} +(-5.86661 - 4.26234i) q^{91} +(0.572968 + 0.0907492i) q^{92} +(-2.46043 - 4.82886i) q^{93} +(-0.794777 + 2.44607i) q^{94} +(-7.67896 - 5.20938i) q^{95} +(-0.276352 + 0.380366i) q^{96} +(-6.54815 + 12.8515i) q^{97} +(0.575755 + 0.575755i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 6 q^{3} - 2 q^{5} + 20 q^{7} - 20 q^{8} + 12 q^{12} - 20 q^{13} + 4 q^{15} + 12 q^{16} + 30 q^{18} + 16 q^{20} - 24 q^{23} - 24 q^{25} - 20 q^{26} + 24 q^{27} - 20 q^{28} + 40 q^{30} + 32 q^{31}+ \cdots - 38 q^{97}+O(q^{100}) \) 32 * q + 6 * q^3 - 2 * q^5 + 20 * q^7 - 20 * q^8 + 12 * q^12 - 20 * q^13 + 4 * q^15 + 12 * q^16 + 30 * q^18 + 16 * q^20 - 24 * q^23 - 24 * q^25 - 20 * q^26 + 24 * q^27 - 20 * q^28 + 40 * q^30 + 32 * q^31 + 30 * q^35 - 36 * q^36 - 8 * q^37 + 10 * q^38 - 50 * q^40 - 20 * q^42 - 28 * q^45 + 20 * q^46 + 42 * q^47 + 26 * q^48 + 80 * q^50 - 100 * q^51 - 20 * q^52 - 34 * q^53 - 80 * q^56 - 40 * q^57 + 90 * q^58 - 86 * q^60 + 10 * q^62 - 10 * q^63 - 8 * q^67 - 70 * q^68 + 10 * q^70 - 36 * q^71 - 70 * q^72 + 30 * q^73 + 4 * q^75 + 60 * q^78 - 102 * q^80 + 8 * q^81 + 20 * q^82 - 60 * q^83 + 60 * q^85 - 80 * q^86 + 130 * q^90 - 60 * q^91 + 42 * q^92 - 8 * q^93 - 30 * q^95 - 38 * q^97

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