LMFDB - Embedded newform 370.2.r.d.177.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [370,2,Mod(23,370)] 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("370.23"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(370, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.r (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} - 4x^{10} + 6x^{8} + 44x^{7} + 56x^{6} + 32x^{5} + 92x^{4} - 16x^{3} + 36x^{2} - 24x + 4 $ x^12 - 2x^11 - 4x^10 + 6x^8 + 44x^7 + 56x^6 + 32x^5 + 92x^4 - 16x^3 + 36x^2 - 24x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			177.3
Root			$-1.69087 - 0.453068i$ of defining polynomial
Character	$\chi$	$=$	370.177
Dual form			370.2.r.d.23.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +(2.26997 - 0.608236i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.514372 + 2.17610i) q^{5} +(1.66173 - 1.66173i) q^{6} +(-0.991227 + 0.265598i) q^{7} -1.00000i q^{8} +(2.18472 - 1.26135i) q^{9} +(1.53351 + 1.62737i) q^{10} -1.09386i q^{11} +(0.608236 - 2.26997i) q^{12} +(0.393937 + 0.227440i) q^{13} +(-0.725629 + 0.725629i) q^{14} +(2.49119 + 4.62682i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.44647 - 2.50536i) q^{17} +(1.26135 - 2.18472i) q^{18} +(0.134218 - 0.0359636i) q^{19} +(2.14175 + 0.642592i) q^{20} +(-2.08851 + 1.20580i) q^{21} +(-0.546932 - 0.947314i) q^{22} +0.390557i q^{23} +(-0.608236 - 2.26997i) q^{24} +(-4.47084 + 2.23865i) q^{25} +0.454879 q^{26} +(-0.793148 + 0.793148i) q^{27} +(-0.265598 + 0.991227i) q^{28} +(-1.28518 + 1.28518i) q^{29} +(4.47084 + 2.76135i) q^{30} +(-0.795949 - 0.795949i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-0.665327 - 2.48303i) q^{33} +(-2.50536 - 1.44647i) q^{34} +(-1.08783 - 2.02040i) q^{35} -2.52270i q^{36} +(-5.85486 + 1.64941i) q^{37} +(0.0982545 - 0.0982545i) q^{38} +(1.03256 + 0.276674i) q^{39} +(2.17610 - 0.514372i) q^{40} +(-6.11196 - 3.52874i) q^{41} +(-1.20580 + 2.08851i) q^{42} -8.52588i q^{43} +(-0.947314 - 0.546932i) q^{44} +(3.86858 + 4.10537i) q^{45} +(0.195278 + 0.338232i) q^{46} +(6.69408 + 6.69408i) q^{47} +(-1.66173 - 1.66173i) q^{48} +(-5.15019 + 2.97346i) q^{49} +(-2.75254 + 4.17415i) q^{50} +(-4.80728 - 4.80728i) q^{51} +(0.393937 - 0.227440i) q^{52} +(7.58864 + 2.03337i) q^{53} +(-0.290312 + 1.08346i) q^{54} +(2.38036 - 0.562653i) q^{55} +(0.265598 + 0.991227i) q^{56} +(0.282796 - 0.163272i) q^{57} +(-0.470410 + 1.75559i) q^{58} +(0.934291 - 3.48682i) q^{59} +(5.25254 + 0.155976i) q^{60} +(4.90553 - 1.31443i) q^{61} +(-1.08729 - 0.291337i) q^{62} +(-1.83054 + 1.83054i) q^{63} -1.00000 q^{64} +(-0.292302 + 0.974235i) q^{65} +(-1.81771 - 1.81771i) q^{66} +(3.30819 + 12.3464i) q^{67} -2.89294 q^{68} +(0.237550 + 0.886550i) q^{69} +(-1.95228 - 1.20580i) q^{70} +(3.63611 - 6.29793i) q^{71} +(-1.26135 - 2.18472i) q^{72} +(-1.40473 - 1.40473i) q^{73} +(-4.24575 + 4.35587i) q^{74} +(-8.78704 + 7.80099i) q^{75} +(0.0359636 - 0.134218i) q^{76} +(0.290529 + 1.08427i) q^{77} +(1.03256 - 0.276674i) q^{78} +(4.98605 - 1.33601i) q^{79} +(1.62737 - 1.53351i) q^{80} +(-5.10205 + 8.83700i) q^{81} -7.05749 q^{82} +(-4.04446 - 1.08371i) q^{83} +2.41160i q^{84} +(4.70789 - 4.43635i) q^{85} +(-4.26294 - 7.38363i) q^{86} +(-2.13563 + 3.69902i) q^{87} -1.09386 q^{88} +(13.3347 + 3.57303i) q^{89} +(5.40298 + 1.62107i) q^{90} +(-0.450888 - 0.120815i) q^{91} +(0.338232 + 0.195278i) q^{92} +(-2.29090 - 1.32265i) q^{93} +(9.14429 + 2.45020i) q^{94} +(0.147299 + 0.273574i) q^{95} +(-2.26997 - 0.608236i) q^{96} -11.8906 q^{97} +(-2.97346 + 5.15019i) q^{98} +(-1.37974 - 2.38979i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} + 6 q^{4} - 8 q^{5} + 6 q^{6} - 4 q^{7} - 18 q^{9} - 4 q^{10} - 6 q^{13} - 8 q^{14} - 14 q^{15} - 6 q^{16} + 12 q^{17} + 10 q^{18} + 8 q^{19} - 4 q^{20} + 54 q^{21} - 10 q^{22} - 10 q^{25}+ \cdots - 28 q^{99}+O(q^{100}) $ 12 * q + 6 * q^3 + 6 * q^4 - 8 * q^5 + 6 * q^6 - 4 * q^7 - 18 * q^9 - 4 * q^10 - 6 * q^13 - 8 * q^14 - 14 * q^15 - 6 * q^16 + 12 * q^17 + 10 * q^18 + 8 * q^19 - 4 * q^20 + 54 * q^21 - 10 * q^22 - 10 * q^25 - 18 * q^27 + 4 * q^28 - 4 * q^29 + 10 * q^30 - 2 * q^31 - 28 * q^33 - 12 * q^34 + 14 * q^35 + 12 * q^37 + 16 * q^38 + 30 * q^39 - 2 * q^40 + 12 * q^41 - 22 * q^42 - 6 * q^44 + 24 * q^45 + 2 * q^46 - 28 * q^47 - 6 * q^48 - 24 * q^49 + 16 * q^50 - 8 * q^51 - 6 * q^52 + 14 * q^53 + 18 * q^54 - 32 * q^55 - 4 * q^56 - 72 * q^57 - 10 * q^58 + 14 * q^60 + 24 * q^61 - 16 * q^62 + 8 * q^63 - 12 * q^64 - 26 * q^65 + 8 * q^66 + 18 * q^67 + 24 * q^68 + 40 * q^69 + 6 * q^70 - 10 * q^72 + 28 * q^73 - 38 * q^74 - 30 * q^75 - 8 * q^76 + 26 * q^77 + 30 * q^78 + 56 * q^79 + 4 * q^80 + 4 * q^81 - 28 * q^82 + 14 * q^83 + 28 * q^85 - 22 * q^86 - 10 * q^87 - 20 * q^88 + 2 * q^89 + 42 * q^90 + 38 * q^91 - 18 * q^92 + 18 * q^93 + 16 * q^94 - 56 * q^95 - 6 * q^96 - 44 * q^97 + 22 * q^98 - 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	2.26997	−	0.608236i	1.31057	−	0.351165i	0.465130	−	0.885242i	$-0.346008\pi$
$3$	2.26997	−	0.608236i	1.31057	−	0.351165i	0.845436	+	0.534077i	$0.179341\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.514372	+	2.17610i	0.230034	+	0.973183i
$5$	0.514372	+	2.17610i	0.230034	+	0.973183i
$6$	1.66173	−	1.66173i	0.678399	−	0.678399i
$7$	−0.991227	+	0.265598i	−0.374649	+	0.100387i	−0.441230	−	0.897394i	$-0.645458\pi$
$7$	−0.991227	+	0.265598i	−0.374649	+	0.100387i	0.0665810	+	0.997781i	$0.478791\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.18472	−	1.26135i	0.728240	−	0.420450i
$10$	1.53351	+	1.62737i	0.484939	+	0.514621i
$11$		−	1.09386i		−	0.329812i	−0.986309	−	0.164906i	$-0.947268\pi$
$11$		−	1.09386i		−	0.329812i	0.986309	−	0.164906i	$-0.0527321\pi$
$12$	0.608236	−	2.26997i	0.175583	−	0.655283i
$13$	0.393937	+	0.227440i	0.109258	+	0.0630804i	0.553633	−	0.832760i	$-0.313241\pi$
$13$	0.393937	+	0.227440i	0.109258	+	0.0630804i	−0.444375	+	0.895841i	$0.646574\pi$
$14$	−0.725629	+	0.725629i	−0.193932	+	0.193932i
$15$	2.49119	+	4.62682i	0.643222	+	1.19464i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.44647	−	2.50536i	−0.350820	−	0.607638i	0.635573	−	0.772040i	$-0.280764\pi$
$17$	−1.44647	−	2.50536i	−0.350820	−	0.607638i	−0.986393	+	0.164403i	$0.947430\pi$
$18$	1.26135	−	2.18472i	0.297303	−	0.514943i
$19$	0.134218	−	0.0359636i	0.0307917	−	0.00825062i	−0.243390	−	0.969928i	$-0.578260\pi$
$19$	0.134218	−	0.0359636i	0.0307917	−	0.00825062i	0.274182	+	0.961678i	$0.411593\pi$
$20$	2.14175	+	0.642592i	0.478909	+	0.143688i
$21$	−2.08851	+	1.20580i	−0.455749	+	0.263127i
$22$	−0.546932	−	0.947314i	−0.116606	−	0.201968i
$23$			0.390557i			0.0814367i	0.999171	+	0.0407183i	$0.0129646\pi$
$23$			0.390557i			0.0814367i	−0.999171	+	0.0407183i	$0.987035\pi$
$24$	−0.608236	−	2.26997i	−0.124156	−	0.463355i
$25$	−4.47084	+	2.23865i	−0.894169	+	0.447730i
$26$	0.454879			0.0892091
$27$	−0.793148	+	0.793148i	−0.152641	+	0.152641i
$28$	−0.265598	+	0.991227i	−0.0501934	+	0.187324i
$29$	−1.28518	+	1.28518i	−0.238653	+	0.238653i	−0.816292	−	0.577639i	$-0.803974\pi$
$29$	−1.28518	+	1.28518i	−0.238653	+	0.238653i	0.577639	+	0.816292i	$0.303974\pi$
$30$	4.47084	+	2.76135i	0.816261	+	0.504151i
$31$	−0.795949	−	0.795949i	−0.142957	−	0.142957i	0.632006	−	0.774963i	$-0.282232\pi$
$31$	−0.795949	−	0.795949i	−0.142957	−	0.142957i	−0.774963	+	0.632006i	$0.782232\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−0.665327	−	2.48303i	−0.115819	−	0.432241i
$34$	−2.50536	−	1.44647i	−0.429665	−	0.248067i
$35$	−1.08783	−	2.02040i	−0.183877	−	0.341509i
$36$		−	2.52270i		−	0.420450i
$37$	−5.85486	+	1.64941i	−0.962534	+	0.271162i
$37$	−5.85486	+	1.64941i	−0.962534	+	0.271162i
$38$	0.0982545	−	0.0982545i	0.0159390	−	0.0159390i
$39$	1.03256	+	0.276674i	0.165342	+	0.0443032i
$40$	2.17610	−	0.514372i	0.344072	−	0.0813293i
$41$	−6.11196	−	3.52874i	−0.954528	−	0.551097i	−0.0600436	−	0.998196i	$-0.519124\pi$
$41$	−6.11196	−	3.52874i	−0.954528	−	0.551097i	−0.894485	+	0.447099i	$0.852457\pi$
$42$	−1.20580	+	2.08851i	−0.186059	+	0.322263i
$43$		−	8.52588i		−	1.30018i	−0.759855	−	0.650092i	$-0.774730\pi$
$43$		−	8.52588i		−	1.30018i	0.759855	−	0.650092i	$-0.225270\pi$
$44$	−0.947314	−	0.546932i	−0.142813	−	0.0824531i
$45$	3.86858	+	4.10537i	0.576694	+	0.611993i
$46$	0.195278	+	0.338232i	0.0287922	+	0.0498696i
$47$	6.69408	+	6.69408i	0.976432	+	0.976432i	0.999729	−	0.0232961i	$-0.00741606\pi$
$47$	6.69408	+	6.69408i	0.976432	+	0.976432i	−0.0232961	+	0.999729i	$0.507416\pi$
$48$	−1.66173	−	1.66173i	−0.239850	−	0.239850i
$49$	−5.15019	+	2.97346i	−0.735741	+	0.424780i
$50$	−2.75254	+	4.17415i	−0.389268	+	0.590314i
$51$	−4.80728	−	4.80728i	−0.673154	−	0.673154i
$52$	0.393937	−	0.227440i	0.0546292	−	0.0315402i
$53$	7.58864	+	2.03337i	1.04238	+	0.279305i	0.739099	−	0.673597i	$-0.235251\pi$
$53$	7.58864	+	2.03337i	1.04238	+	0.279305i	0.303280	+	0.952901i	$0.401918\pi$
$54$	−0.290312	+	1.08346i	−0.0395065	+	0.147440i
$55$	2.38036	−	0.562653i	0.320968	−	0.0758681i
$56$	0.265598	+	0.991227i	0.0354921	+	0.132458i
$57$	0.282796	−	0.163272i	0.0374573	−	0.0216260i
$58$	−0.470410	+	1.75559i	−0.0617679	+	0.230521i
$59$	0.934291	−	3.48682i	0.121634	−	0.453946i	−0.878063	−	0.478545i	$-0.841164\pi$
$59$	0.934291	−	3.48682i	0.121634	−	0.453946i	0.999697	+	0.0245994i	$0.00783103\pi$
$60$	5.25254	+	0.155976i	0.678100	+	0.0201365i
$61$	4.90553	−	1.31443i	0.628089	−	0.168296i	0.0692867	−	0.997597i	$-0.477928\pi$
$61$	4.90553	−	1.31443i	0.628089	−	0.168296i	0.558802	+	0.829301i	$0.311261\pi$
$62$	−1.08729	−	0.291337i	−0.138085	−	0.0369999i
$63$	−1.83054	+	1.83054i	−0.230627	+	0.230627i
$64$	−1.00000			−0.125000
$65$	−0.292302	+	0.974235i	−0.0362556	+	0.120839i
$66$	−1.81771	−	1.81771i	−0.223744	−	0.223744i
$67$	3.30819	+	12.3464i	0.404160	+	1.50835i	0.805599	+	0.592461i	$0.201844\pi$
$67$	3.30819	+	12.3464i	0.404160	+	1.50835i	−0.401439	+	0.915886i	$0.631490\pi$
$68$	−2.89294			−0.350820
$69$	0.237550	+	0.886550i	0.0285977	+	0.106728i
$70$	−1.95228	−	1.20580i	−0.233343	−	0.144121i
$71$	3.63611	−	6.29793i	0.431527	−	0.747426i	−0.565478	−	0.824763i	$-0.691308\pi$
$71$	3.63611	−	6.29793i	0.431527	−	0.747426i	0.997005	+	0.0773369i	$0.0246417\pi$
$72$	−1.26135	−	2.18472i	−0.148651	−	0.257472i
$73$	−1.40473	−	1.40473i	−0.164411	−	0.164411i	0.620107	−	0.784518i	$-0.287089\pi$
$73$	−1.40473	−	1.40473i	−0.164411	−	0.164411i	−0.784518	+	0.620107i	$0.787089\pi$
$74$	−4.24575	+	4.35587i	−0.493559	+	0.506359i
$75$	−8.78704	+	7.80099i	−1.01464	+	0.900781i
$76$	0.0359636	−	0.134218i	0.00412531	−	0.0153959i
$77$	0.290529	+	1.08427i	0.0331088	+	0.123564i
$78$	1.03256	−	0.276674i	0.116914	−	0.0313271i
$79$	4.98605	−	1.33601i	0.560975	−	0.150313i	0.0328206	−	0.999461i	$-0.489551\pi$
$79$	4.98605	−	1.33601i	0.560975	−	0.150313i	0.528154	+	0.849149i	$0.322884\pi$
$80$	1.62737	−	1.53351i	0.181946	−	0.171452i
$81$	−5.10205	+	8.83700i	−0.566894	+	0.981889i
$82$	−7.05749			−0.779369
$83$	−4.04446	−	1.08371i	−0.443938	−	0.118953i	0.0299237	−	0.999552i	$-0.490474\pi$
$83$	−4.04446	−	1.08371i	−0.443938	−	0.118953i	−0.473861	+	0.880599i	$0.657140\pi$
$84$			2.41160i			0.263127i
$85$	4.70789	−	4.43635i	0.510642	−	0.481189i
$86$	−4.26294	−	7.38363i	−0.459685	−	0.796197i
$87$	−2.13563	+	3.69902i	−0.228964	+	0.396577i
$88$	−1.09386			−0.116606
$89$	13.3347	+	3.57303i	1.41348	+	0.378741i	0.883166	−	0.469061i	$-0.155407\pi$
$89$	13.3347	+	3.57303i	1.41348	+	0.378741i	0.530314	+	0.847801i	$0.322074\pi$
$90$	5.40298	+	1.62107i	0.569524	+	0.170875i
$91$	−0.450888	−	0.120815i	−0.0472660	−	0.0126649i
$92$	0.338232	+	0.195278i	0.0352631	+	0.0203592i
$93$	−2.29090	−	1.32265i	−0.237555	−	0.137153i
$94$	9.14429	+	2.45020i	0.943161	+	0.252719i
$95$	0.147299	+	0.273574i	0.0151125	+	0.0280681i
$96$	−2.26997	−	0.608236i	−0.231677	−	0.0620778i
$97$	−11.8906			−1.20731			−0.603656	−	0.797245i	$-0.706290\pi$
$97$	−11.8906			−1.20731			−0.603656	+	0.797245i	$0.706290\pi$
$98$	−2.97346	+	5.15019i	−0.300365	+	0.520248i
$99$	−1.37974	−	2.38979i	−0.138669	−	0.240183i
$100$	−0.296693	+	4.99119i	−0.0296693	+	0.499119i
$101$		−	2.62938i		−	0.261633i	−0.991407	−	0.130816i	$-0.958240\pi$
$101$		−	2.62938i		−	0.261633i	0.991407	−	0.130816i	$-0.0417598\pi$
$102$	−6.56687	−	1.75959i	−0.650217	−	0.174225i
$103$	−6.18963			−0.609882			−0.304941	−	0.952371i	$-0.598637\pi$
$103$	−6.18963			−0.609882			−0.304941	+	0.952371i	$0.598637\pi$
$104$	0.227440	−	0.393937i	0.0223023	−	0.0386287i
$105$	−3.69821	−	3.92457i	−0.360908	−	0.382999i
$106$	7.58864	−	2.03337i	0.737074	−	0.197498i
$107$	7.39938	−	1.98266i	0.715325	−	0.191671i	0.117240	−	0.993104i	$-0.462595\pi$
$107$	7.39938	−	1.98266i	0.715325	−	0.191671i	0.598085	+	0.801433i	$0.295929\pi$
$108$	0.290312	+	1.08346i	0.0279353	+	0.104256i
$109$	−0.145164	+	0.541758i	−0.0139041	+	0.0518910i	−0.972529	−	0.232780i	$-0.925218\pi$
$109$	−0.145164	+	0.541758i	−0.0139041	+	0.0518910i	0.958625	+	0.284671i	$0.0918844\pi$
$110$	1.78013	−	1.67745i	0.169728	−	0.159939i
$111$	−12.2871	+	7.30525i	−1.16624	+	0.693384i
$112$	0.725629	+	0.725629i	0.0685655	+	0.0685655i
$113$	−2.49186	−	4.31602i	−0.234414	−	0.406017i	0.724688	−	0.689077i	$-0.241984\pi$
$113$	−2.49186	−	4.31602i	−0.234414	−	0.406017i	−0.959102	+	0.283060i	$0.908651\pi$
$114$	0.163272	−	0.282796i	0.0152919	−	0.0264863i
$115$	−0.849891	+	0.200891i	−0.0792528	+	0.0187332i
$116$	0.470410	+	1.75559i	0.0436765	+	0.163003i
$117$	1.14752			0.106088
$118$	−0.934291	−	3.48682i	−0.0860085	−	0.320988i
$119$	2.09920	+	2.09920i	0.192433	+	0.192433i
$120$	4.62682	−	2.49119i	0.422369	−	0.227413i
$121$	9.80346			0.891224
$122$	3.59110	−	3.59110i	0.325123	−	0.325123i
$123$	−16.0203	−	4.29262i	−1.44450	−	0.387052i
$124$	−1.08729	+	0.291337i	−0.0976412	+	0.0261629i
$125$	−7.17121	−	8.57751i	−0.641413	−	0.767196i
$126$	−0.670025	+	2.50057i	−0.0596905	+	0.222768i
$127$	−5.45148	+	20.3452i	−0.483741	+	1.80535i	0.101924	+	0.994792i	$0.467500\pi$
$127$	−5.45148	+	20.3452i	−0.483741	+	1.80535i	−0.585665	+	0.810553i	$0.699167\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−5.18575	−	19.3535i	−0.456579	−	1.70398i
$130$	0.233977	+	0.989863i	0.0205211	+	0.0868168i
$131$	4.71929	−	17.6126i	0.412327	−	1.53882i	−0.377804	−	0.925885i	$-0.623321\pi$
$131$	4.71929	−	17.6126i	0.412327	−	1.53882i	0.790131	−	0.612938i	$-0.210012\pi$
$132$	−2.48303	−	0.665327i	−0.216120	−	0.0579093i
$133$	−0.123489	+	0.0712962i	−0.0107078	+	0.00618217i
$134$	9.03816	+	9.03816i	0.780778	+	0.780778i
$135$	−2.13395	−	1.31800i	−0.183661	−	0.113435i
$136$	−2.50536	+	1.44647i	−0.214832	+	0.124034i
$137$	−11.0845	−	11.0845i	−0.947009	−	0.947009i	0.0516564	−	0.998665i	$-0.483550\pi$
$137$	−11.0845	−	11.0845i	−0.947009	−	0.947009i	−0.998665	+	0.0516564i	$0.983550\pi$
$138$	0.649000	+	0.649000i	0.0552465	+	0.0552465i
$139$	6.67857	+	11.5676i	0.566469	+	0.981152i	0.996911	+	0.0785346i	$0.0250241\pi$
$139$	6.67857	+	11.5676i	0.566469	+	0.981152i	−0.430443	+	0.902618i	$0.641643\pi$
$140$	−2.29363	−	0.0681103i	−0.193847	−	0.00575637i
$141$	19.2669	+	11.1238i	1.62257	+	0.936790i
$142$		−	7.27222i		−	0.610271i
$143$	0.248788	−	0.430913i	0.0208047	−	0.0360348i
$144$	−2.18472	−	1.26135i	−0.182060	−	0.105112i
$145$	−3.45776	−	2.13563i	−0.287151	−	0.177354i
$146$	−1.91889	−	0.514166i	−0.158809	−	0.0425527i
$147$	−9.88219	+	9.88219i	−0.815069	+	0.815069i
$148$	−1.49900	+	5.89517i	−0.123217	+	0.484580i
$149$			2.61183i			0.213969i	0.994261	+	0.106985i	$0.0341196\pi$
$149$			2.61183i			0.213969i	−0.994261	+	0.106985i	$0.965880\pi$
$150$	−3.70930	+	11.1494i	−0.302863	+	0.910342i
$151$	19.3408	+	11.1664i	1.57393	+	0.908711i	0.995680	+	0.0928532i	$0.0295987\pi$
$151$	19.3408	+	11.1664i	1.57393	+	0.908711i	0.578253	+	0.815857i	$0.303735\pi$
$152$	−0.0359636	−	0.134218i	−0.00291704	−	0.0108865i
$153$	−6.32025	−	3.64900i	−0.510962	−	0.295004i
$154$	0.793739	+	0.793739i	0.0639613	+	0.0639613i
$155$	1.32265	−	2.14148i	0.106238	−	0.172008i
$156$	0.755886	−	0.755886i	0.0605194	−	0.0605194i
$157$	−0.830175	+	3.09826i	−0.0662552	+	0.247268i	−0.991108	−	0.133056i	$-0.957521\pi$
$157$	−0.830175	+	3.09826i	−0.0662552	+	0.247268i	0.924853	+	0.380324i	$0.124188\pi$
$158$	3.65004	−	3.65004i	0.290382	−	0.290382i
$159$	18.4627			1.46419
$160$	0.642592	−	2.14175i	0.0508014	−	0.169320i
$161$	−0.103731	−	0.387130i	−0.00817517	−	0.0305101i
$162$			10.2041i			0.801709i
$163$	10.0203	+	17.3556i	0.784847	+	1.35940i	0.929090	+	0.369853i	$0.120592\pi$
$163$	10.0203	+	17.3556i	0.784847	+	1.35940i	−0.144243	+	0.989542i	$0.546075\pi$
$164$	−6.11196	+	3.52874i	−0.477264	+	0.275549i
$165$	5.06111	−	2.72502i	0.394007	−	0.212143i
$166$	−4.04446	+	1.08371i	−0.313911	+	0.0841123i
$167$	−2.44027	+	4.22666i	−0.188833	+	0.327069i	−0.944862	−	0.327470i	$-0.893804\pi$
$167$	−2.44027	+	4.22666i	−0.188833	+	0.327069i	0.756028	+	0.654539i	$0.227137\pi$
$168$	1.20580	+	2.08851i	0.0930294	+	0.161132i
$169$	−6.39654	−	11.0791i	−0.492042	−	0.852241i
$170$	1.85898	−	6.19593i	0.142577	−	0.475206i
$171$	0.247866	−	0.247866i	0.0189548	−	0.0189548i
$172$	−7.38363	−	4.26294i	−0.562997	−	0.325046i
$173$	4.13508	−	15.4323i	0.314384	−	1.17330i	−0.610177	−	0.792265i	$-0.708902\pi$
$173$	4.13508	−	15.4323i	0.314384	−	1.17330i	0.924561	−	0.381033i	$-0.124432\pi$
$174$			4.27126i			0.323803i
$175$	3.83704	−	3.40646i	0.290053	−	0.257504i
$176$	−0.947314	+	0.546932i	−0.0714065	+	0.0412265i
$177$		−	8.48324i		−	0.637639i
$178$	13.3347	−	3.57303i	0.999481	−	0.267810i
$179$	8.92638	−	8.92638i	0.667189	−	0.667189i	−0.289875	−	0.957064i	$-0.593614\pi$
$179$	8.92638	−	8.92638i	0.667189	−	0.667189i	0.957064	+	0.289875i	$0.0936139\pi$
$180$	5.48965	−	1.29760i	0.409174	−	0.0967177i
$181$	8.68014	−	15.0344i	0.645190	−	1.11750i	−0.339068	−	0.940762i	$-0.610112\pi$
$181$	8.68014	−	15.0344i	0.645190	−	1.11750i	0.984258	−	0.176740i	$-0.0565550\pi$
$182$	−0.450888	+	0.120815i	−0.0334221	+	0.00895542i
$183$	10.3359	−	5.96744i	0.764052	−	0.441126i
$184$	0.390557			0.0287922
$185$	−6.60087	−	11.8924i	−0.485306	−	0.874345i
$186$	−2.64530			−0.193963
$187$	−2.74052	+	1.58224i	−0.200406	+	0.115705i
$188$	9.14429	−	2.45020i	0.666916	−	0.178700i
$189$	0.575531	−	0.996849i	0.0418637	−	0.0725101i
$190$	0.264351	+	0.163272i	0.0191780	+	0.0118450i
$191$	7.40119	−	7.40119i	0.535531	−	0.535531i	−0.386682	−	0.922213i	$-0.626379\pi$
$191$	7.40119	−	7.40119i	0.535531	−	0.535531i	0.922213	+	0.386682i	$0.126379\pi$
$192$	−2.26997	+	0.608236i	−0.163821	+	0.0438956i
$193$		−	5.47453i		−	0.394065i	−0.980397	−	0.197033i	$-0.936870\pi$
$193$		−	5.47453i		−	0.394065i	0.980397	−	0.197033i	$-0.0631305\pi$
$194$	−10.2976	+	5.94532i	−0.739325	+	0.426849i
$195$	−0.0709504	+	2.38927i	−0.00508086	+	0.171099i
$196$			5.94693i			0.424780i
$197$	1.45086	−	5.41467i	0.103369	−	0.385779i	−0.894786	−	0.446496i	$-0.852672\pi$
$197$	1.45086	−	5.41467i	0.103369	−	0.385779i	0.998155	+	0.0607164i	$0.0193385\pi$
$198$	−2.38979	−	1.37974i	−0.169835	−	0.0980541i
$199$	10.8649	−	10.8649i	0.770191	−	0.770191i	−0.207948	−	0.978140i	$-0.566679\pi$
$199$	10.8649	−	10.8649i	0.770191	−	0.770191i	0.978140	+	0.207948i	$0.0666786\pi$
$200$	2.23865	+	4.47084i	0.158297	+	0.316136i
$201$	15.0190	+	26.0136i	1.05936	+	1.83486i
$202$	−1.31469	−	2.27711i	−0.0925011	−	0.160217i
$203$	0.932566	−	1.61525i	0.0654533	−	0.113368i
$204$	−6.56687	+	1.75959i	−0.459773	+	0.123196i
$205$	4.53509	−	15.1153i	0.316744	−	1.05570i
$206$	−5.36037	+	3.09481i	−0.373475	+	0.215626i
$207$	0.492628	+	0.853257i	0.0342400	+	0.0593054i
$208$		−	0.454879i		−	0.0315402i
$209$	−0.0393393	−	0.146816i	−0.00272116	−	0.0101555i
$210$	−5.16503	−	1.54967i	−0.356421	−	0.106938i
$211$	4.61625			0.317796			0.158898	−	0.987295i	$-0.449206\pi$
$211$	4.61625			0.317796			0.158898	+	0.987295i	$0.449206\pi$
$212$	5.55527	−	5.55527i	0.381537	−	0.381537i
$213$	4.42322	−	16.5077i	0.303074	−	1.13109i
$214$	5.41672	−	5.41672i	0.370280	−	0.370280i
$215$	18.5532	−	4.38547i	1.26532	−	0.299087i
$216$	0.793148	+	0.793148i	0.0539669	+	0.0539669i
$217$	1.00037	+	0.577563i	0.0679094	+	0.0392075i
$218$	0.145164	+	0.541758i	0.00983172	+	0.0366925i
$219$	−4.04309	−	2.33428i	−0.273207	−	0.157736i
$220$	0.702908	−	2.34278i	0.0473901	−	0.157950i
$221$		−	1.31594i		−	0.0885194i
$222$	−6.98833	+	12.4701i	−0.469026	+	0.836938i
$223$	−13.3465	+	13.3465i	−0.893748	+	0.893748i	−0.994874	−	0.101126i	$-0.967756\pi$
$223$	−13.3465	+	13.3465i	−0.893748	+	0.893748i	0.101126	+	0.994874i	$0.467756\pi$
$224$	0.991227	+	0.265598i	0.0662291	+	0.0177460i
$225$	−6.94382	+	10.5301i	−0.462921	+	0.702008i
$226$	−4.31602	−	2.49186i	−0.287098	−	0.165756i
$227$	5.11973	−	8.86763i	0.339808	−	0.588565i	−0.644588	−	0.764530i	$-0.722971\pi$
$227$	5.11973	−	8.86763i	0.339808	−	0.588565i	0.984396	+	0.175965i	$0.0563044\pi$
$228$		−	0.326545i		−	0.0216260i
$229$	−0.542093	−	0.312978i	−0.0358225	−	0.0206822i	0.481982	−	0.876181i	$-0.339917\pi$
$229$	−0.542093	−	0.312978i	−0.0358225	−	0.0206822i	−0.517804	+	0.855499i	$0.673250\pi$
$230$	−0.635582	+	0.598923i	−0.0419090	+	0.0394918i
$231$	1.31898	+	2.28454i	0.0867825	+	0.150312i
$232$	1.28518	+	1.28518i	0.0843765	+	0.0843765i
$233$	4.49284	+	4.49284i	0.294335	+	0.294335i	0.838790	−	0.544455i	$-0.183263\pi$
$233$	4.49284	+	4.49284i	0.294335	+	0.294335i	−0.544455	+	0.838790i	$0.683263\pi$
$234$	0.993783	−	0.573761i	0.0649657	−	0.0375079i
$235$	−11.1238	+	18.0103i	−0.725634	+	1.17486i
$236$	−2.55253	−	2.55253i	−0.166156	−	0.166156i
$237$	10.5056	−	6.06539i	0.682410	−	0.393989i
$238$	2.86756	+	0.768359i	0.185876	+	0.0498053i
$239$	−4.58065	+	17.0952i	−0.296298	+	1.10580i	0.643884	+	0.765123i	$0.277322\pi$
$239$	−4.58065	+	17.0952i	−0.296298	+	1.10580i	−0.940181	+	0.340674i	$0.889345\pi$
$240$	2.76135	−	4.47084i	0.178244	−	0.288592i
$241$	−0.941745	−	3.51464i	−0.0606631	−	0.226398i	0.928938	−	0.370235i	$-0.120723\pi$
$241$	−0.941745	−	3.51464i	−0.0606631	−	0.226398i	−0.989601	+	0.143837i	$0.954056\pi$
$242$	8.49005	−	4.90173i	0.545761	−	0.315095i
$243$	−5.33555	+	19.9126i	−0.342276	+	1.27739i
$244$	1.31443	−	4.90553i	0.0841480	−	0.314045i
$245$	−9.11967	−	9.67787i	−0.582635	−	0.618297i
$246$	−16.0203	+	4.29262i	−1.02141	+	0.273687i
$247$	0.0610530	+	0.0163591i	0.00388471	+	0.00104090i
$248$	−0.795949	+	0.795949i	−0.0505428	+	0.0505428i
$249$	−9.83995			−0.623581
$250$	−10.4992	−	3.84274i	−0.664028	−	0.243036i
$251$	−15.8289	−	15.8289i	−0.999112	−	0.999112i	0.000887213	−	1.00000i	$-0.499718\pi$
$251$	−15.8289	−	15.8289i	−0.999112	−	0.999112i	−1.00000		0.000887213i	$0.999718\pi$
$252$	0.670025	+	2.50057i	0.0422076	+	0.157521i
$253$	0.427216			0.0268588
$254$	5.45148	+	20.3452i	0.342056	+	1.27657i
$255$	7.98840	−	12.9339i	0.500253	−	0.809950i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−10.9325	−	18.9356i	−0.681949	−	1.18117i	−0.974385	−	0.224886i	$-0.927799\pi$
$257$	−10.9325	−	18.9356i	−0.681949	−	1.18117i	0.292436	−	0.956285i	$-0.405534\pi$
$258$	−14.1677	−	14.1677i	−0.882044	−	0.882044i
$259$	5.36542	−	3.18999i	0.333391	−	0.198216i
$260$	0.697562	+	0.740258i	0.0432609	+	0.0459089i
$261$	−1.18670	+	4.42883i	−0.0734550	+	0.274138i
$262$	−4.71929	−	17.6126i	−0.291559	−	1.08811i
$263$	−8.31336	+	2.22756i	−0.512624	+	0.137357i	−0.505852	−	0.862620i	$-0.668822\pi$
$263$	−8.31336	+	2.22756i	−0.512624	+	0.137357i	−0.00677111	+	0.999977i	$0.502155\pi$
$264$	−2.48303	+	0.665327i	−0.152820	+	0.0409480i
$265$	−0.521439	+	17.5596i	−0.0320317	+	1.07868i
$266$	−0.0712962	+	0.123489i	−0.00437145	+	0.00757158i
$267$	32.4427			1.98546
$268$	12.3464	+	3.30819i	0.754173	+	0.202080i
$269$		−	5.72668i		−	0.349162i	−0.984643	−	0.174581i	$-0.944143\pi$
$269$		−	5.72668i		−	0.349162i	0.984643	−	0.174581i	$-0.0558570\pi$
$270$	−2.50705	−	0.0744480i	−0.152574	−	0.00453076i
$271$	3.30228	+	5.71972i	0.200599	+	0.347448i	0.948722	−	0.316113i	$-0.102378\pi$
$271$	3.30228	+	5.71972i	0.200599	+	0.347448i	−0.748122	+	0.663561i	$0.769044\pi$
$272$	−1.44647	+	2.50536i	−0.0877050	+	0.151909i
$273$	−1.09699			−0.0663926
$274$	−15.1416	−	4.05719i	−0.914740	−	0.245104i
$275$	2.44878	+	4.89049i	0.147667	+	0.294908i
$276$	0.886550	+	0.237550i	0.0533641	+	0.0142989i
$277$	−7.70387	−	4.44783i	−0.462881	−	0.267244i	0.250374	−	0.968149i	$-0.419446\pi$
$277$	−7.70387	−	4.44783i	−0.462881	−	0.267244i	−0.713255	+	0.700905i	$0.752780\pi$
$278$	11.5676	+	6.67857i	0.693780	+	0.400554i
$279$	−2.74289	−	0.734956i	−0.164213	−	0.0440007i
$280$	−2.02040	+	1.08783i	−0.120742	+	0.0650102i
$281$	1.59322	+	0.426903i	0.0950437	+	0.0254669i	0.306027	−	0.952023i	$-0.401000\pi$
$281$	1.59322	+	0.426903i	0.0950437	+	0.0254669i	−0.210984	+	0.977490i	$0.567667\pi$
$282$	22.2475			1.32482
$283$	−16.3099	+	28.2496i	−0.969522	+	1.67926i	−0.272582	+	0.962133i	$0.587878\pi$
$283$	−16.3099	+	28.2496i	−0.969522	+	1.67926i	−0.696940	+	0.717129i	$0.745456\pi$
$284$	−3.63611	−	6.29793i	−0.215763	−	0.373713i
$285$	0.500760	+	0.531411i	0.0296625	+	0.0314781i
$286$		−	0.497576i		−	0.0294223i
$287$	6.99557	+	1.87446i	0.412936	+	0.110646i
$288$	−2.52270			−0.148651
$289$	4.31546	−	7.47460i	0.253851	−	0.439682i
$290$	−4.06232	−	0.120632i	−0.238548	−	0.00708378i
$291$	−26.9914	+	7.23232i	−1.58226	+	0.423966i
$292$	−1.91889	+	0.514166i	−0.112295	+	0.0300893i
$293$	6.21218	+	23.1842i	0.362919	+	1.35443i	0.870220	+	0.492664i	$0.163977\pi$
$293$	6.21218	+	23.1842i	0.362919	+	1.35443i	−0.507300	+	0.861769i	$0.669357\pi$
$294$	−3.61713	+	13.4993i	−0.210955	+	0.787296i
$295$	8.06825	+	0.239590i	0.469752	+	0.0139495i
$296$	1.64941	+	5.85486i	0.0958702	+	0.340307i
$297$	0.867596	+	0.867596i	0.0503430	+	0.0503430i
$298$	1.30592	+	2.26191i	0.0756496	+	0.131029i
$299$	−0.0888280	+	0.153855i	−0.00513706	+	0.00889764i
$300$	2.36234	+	11.5103i	0.136390	+	0.664547i
$301$	2.26446	+	8.45108i	0.130521	+	0.487112i
$302$	22.3328			1.28511
$303$	−1.59928	−	5.96860i	−0.0918763	−	0.342887i
$304$	−0.0982545	−	0.0982545i	−0.00563528	−	0.00563528i
$305$	5.38361	+	9.99884i	0.308265	+	0.572532i
$306$	−7.29800			−0.417199
$307$	14.2681	−	14.2681i	0.814321	−	0.814321i	−0.170957	−	0.985278i	$-0.554686\pi$
$307$	14.2681	−	14.2681i	0.814321	−	0.814321i	0.985278	+	0.170957i	$0.0546860\pi$
$308$	1.08427	+	0.290529i	0.0617819	+	0.0165544i
$309$	−14.0502	+	3.76475i	−0.799291	+	0.214169i
$310$	0.0747108	−	2.51590i	0.00424329	−	0.142894i
$311$	1.96729	−	7.34201i	0.111555	−	0.416327i	−0.887452	−	0.460901i	$-0.847526\pi$
$311$	1.96729	−	7.34201i	0.111555	−	0.416327i	0.999006	+	0.0445738i	$0.0141930\pi$
$312$	0.276674	−	1.03256i	0.0156636	−	0.0584572i
$313$	−28.1999	+	16.2812i	−1.59395	+	0.920270i	−0.601335	+	0.798997i	$0.705364\pi$
$313$	−28.1999	+	16.2812i	−1.59395	+	0.920270i	−0.992619	+	0.121273i	$0.961302\pi$
$314$	0.830175	+	3.09826i	0.0468495	+	0.174845i
$315$	−4.92502	−	3.04187i	−0.277494	−	0.171390i
$316$	1.33601	−	4.98605i	0.0751564	−	0.280487i
$317$	25.2620	+	6.76893i	1.41885	+	0.380181i	0.885077	−	0.465444i	$-0.154106\pi$
$317$	25.2620	+	6.76893i	1.41885	+	0.380181i	0.533777	+	0.845625i	$0.320772\pi$
$318$	15.9892	−	9.23136i	0.896629	−	0.517669i
$319$	1.40582	+	1.40582i	0.0787106	+	0.0787106i
$320$	−0.514372	−	2.17610i	−0.0287543	−	0.121648i
$321$	15.5904	−	9.00114i	0.870173	−	0.502394i
$322$	−0.283399	−	0.283399i	−0.0157932	−	0.0157932i
$323$	−0.284244	−	0.284244i	−0.0158157	−	0.0158157i
$324$	5.10205	+	8.83700i	0.283447	+	0.490945i
$325$	−2.27039	−	0.134959i	−0.125938	−	0.00748620i
$326$	17.3556	+	10.0203i	0.961238	+	0.554971i
$327$			1.31807i			0.0728892i
$328$	−3.52874	+	6.11196i	−0.194842	+	0.337477i
$329$	−8.41330	−	4.85742i	−0.463840	−	0.267798i
$330$	3.02054	−	4.89049i	0.166275	−	0.269213i
$331$	−16.9750	−	4.54843i	−0.933029	−	0.250004i	−0.239883	−	0.970802i	$-0.577109\pi$
$331$	−16.9750	−	4.54843i	−0.933029	−	0.250004i	−0.693146	+	0.720798i	$0.743776\pi$
$332$	−2.96075	+	2.96075i	−0.162492	+	0.162492i
$333$	−10.7108	+	10.9885i	−0.586946	+	0.602168i
$334$			4.88053i			0.267051i
$335$	−25.1653	+	13.5496i	−1.37493	+	0.740293i
$336$	2.08851	+	1.20580i	0.113937	+	0.0657817i
$337$	−5.68810	−	21.2283i	−0.309851	−	1.15638i	−0.928689	−	0.370860i	$-0.879063\pi$
$337$	−5.68810	−	21.2283i	−0.309851	−	1.15638i	0.618838	−	0.785519i	$-0.287604\pi$
$338$	−11.0791	−	6.39654i	−0.602626	−	0.347926i
$339$	−8.28159	−	8.28159i	−0.449794	−	0.449794i
$340$	−1.48804	−	6.29532i	−0.0807005	−	0.341412i
$341$	−0.870660	+	0.870660i	−0.0471489	+	0.0471489i
$342$	0.0907254	−	0.338592i	0.00490587	−	0.0183089i
$343$	9.39466	−	9.39466i	0.507264	−	0.507264i
$344$	−8.52588			−0.459685
$345$	−1.80703	+	0.972951i	−0.0972875	+	0.0523819i
$346$	−4.13508	−	15.4323i	−0.222303	−	0.829647i
$347$			12.3387i			0.662377i	0.943565	+	0.331189i	$0.107450\pi$
$347$			12.3387i			0.662377i	−0.943565	+	0.331189i	$0.892550\pi$
$348$	2.13563	+	3.69902i	0.114482	+	0.198288i
$349$	−19.7732	+	11.4160i	−1.05843	+	0.611087i	−0.924999	−	0.379971i	$-0.875934\pi$
$349$	−19.7732	+	11.4160i	−1.05843	+	0.611087i	−0.133435	+	0.991058i	$0.542601\pi$
$350$	1.61974	−	4.86860i	0.0865789	−	0.260238i
$351$	−0.492844	+	0.132057i	−0.0263061	+	0.00704869i
$352$	−0.546932	+	0.947314i	−0.0291516	+	0.0504920i
$353$	8.53634	+	14.7854i	0.454343	+	0.786946i	0.998650	−	0.0519405i	$-0.0165406\pi$
$353$	8.53634	+	14.7854i	0.454343	+	0.786946i	−0.544307	+	0.838886i	$0.683207\pi$
$354$	−4.24162	−	7.34670i	−0.225439	−	0.390473i
$355$	15.5752	+	4.67307i	0.826648	+	0.248021i
$356$	9.76171	−	9.76171i	0.517369	−	0.517369i
$357$	6.04191	+	3.48830i	0.319772	+	0.184620i
$358$	3.26728	−	12.1937i	0.172681	−	0.644455i
$359$		−	20.3975i		−	1.07654i	−0.842773	−	0.538269i	$-0.819078\pi$
$359$		−	20.3975i		−	1.07654i	0.842773	−	0.538269i	$-0.180922\pi$
$360$	4.10537	−	3.86858i	0.216372	−	0.203892i
$361$	−16.4378	+	9.49035i	−0.865145	+	0.499492i
$362$		−	17.3603i		−	0.912436i
$363$	22.2535	−	5.96281i	1.16801	−	0.312967i
$364$	−0.330073	+	0.330073i	−0.0173005	+	0.0173005i
$365$	2.33428	−	3.77938i	0.122182	−	0.197822i
$366$	5.96744	−	10.3359i	0.311923	−	0.540267i
$367$	−12.8836	+	3.45216i	−0.672521	+	0.180201i	−0.578890	−	0.815406i	$-0.696514\pi$
$367$	−12.8836	+	3.45216i	−0.672521	+	0.180201i	−0.0936308	+	0.995607i	$0.529847\pi$
$368$	0.338232	−	0.195278i	0.0176316	−	0.0101796i
$369$	−17.8039			−0.926834
$370$	−11.6627	−	6.99866i	−0.606315	−	0.363843i
$371$	−8.06212			−0.418565
$372$	−2.29090	+	1.32265i	−0.118778	+	0.0685763i
$373$	−16.8544	+	4.51612i	−0.872688	+	0.233836i	−0.667250	−	0.744834i	$-0.732529\pi$
$373$	−16.8544	+	4.51612i	−0.872688	+	0.233836i	−0.205438	+	0.978670i	$0.565862\pi$
$374$	−1.58224	+	2.74052i	−0.0818156	+	0.141709i
$375$	−21.4956	−	15.1089i	−1.11003	−	0.780219i
$376$	6.69408	−	6.69408i	0.345221	−	0.345221i
$377$	−0.798583	+	0.213980i	−0.0411291	+	0.0110205i
$378$		−	1.15106i		−	0.0592043i
$379$	−21.7843	+	12.5772i	−1.11898	+	0.646045i	−0.941141	−	0.338014i	$-0.890245\pi$
$379$	−21.7843	+	12.5772i	−1.11898	+	0.646045i	−0.177842	+	0.984059i	$0.556911\pi$
$380$	0.310571	+	0.00922254i	0.0159320	+	0.000473106i
$381$			49.4987i			2.53590i
$382$	2.70902	−	10.1102i	0.138606	−	0.517284i
$383$	9.29874	+	5.36863i	0.475143	+	0.274324i	0.718390	−	0.695640i	$-0.244879\pi$
$383$	9.29874	+	5.36863i	0.475143	+	0.274324i	−0.243247	+	0.969964i	$0.578213\pi$
$384$	−1.66173	+	1.66173i	−0.0847998	+	0.0847998i
$385$	−2.21004	+	1.18994i	−0.112634	+	0.0606448i
$386$	−2.73726	−	4.74108i	−0.139323	−	0.241315i
$387$	−10.7541	−	18.6267i	−0.546662	−	0.946847i
$388$	−5.94532	+	10.2976i	−0.301828	+	0.522782i
$389$	−29.4549	+	7.89241i	−1.49342	+	0.400161i	−0.910891	−	0.412647i	$-0.864604\pi$
$389$	−29.4549	+	7.89241i	−1.49342	+	0.400161i	−0.582531	+	0.812808i	$0.697938\pi$
$390$	1.13319	+	2.10464i	0.0573813	+	0.106573i
$391$	0.978483	−	0.564927i	0.0494840	−	0.0285696i
$392$	2.97346	+	5.15019i	0.150183	+	0.260124i
$393$		−	42.8505i		−	2.16152i
$394$	−1.45086	−	5.41467i	−0.0730931	−	0.272787i
$395$	5.47198	+	10.1630i	0.275325	+	0.511354i
$396$	−2.75949			−0.138669
$397$	−14.1042	+	14.1042i	−0.707867	+	0.707867i	−0.966086	−	0.258219i	$-0.916864\pi$
$397$	−14.1042	+	14.1042i	−0.707867	+	0.707867i	0.258219	+	0.966086i	$0.416864\pi$
$398$	3.97682	−	14.8417i	0.199340	−	0.743948i
$399$	−0.236950	+	0.236950i	−0.0118624	+	0.0118624i
$400$	4.17415	+	2.75254i	0.208708	+	0.137627i
$401$	9.57043	+	9.57043i	0.477925	+	0.477925i	0.904467	−	0.426543i	$-0.140269\pi$
$401$	9.57043	+	9.57043i	0.477925	+	0.477925i	−0.426543	+	0.904467i	$0.640269\pi$
$402$	26.0136	+	15.0190i	1.29744	+	0.749079i
$403$	−0.132523	−	0.494584i	−0.00660146	−	0.0246370i
$404$	−2.27711	−	1.31469i	−0.113290	−	0.0654082i
$405$	−21.8546	−	6.55707i	−1.08596	−	0.325823i
$406$		−	1.86513i		−	0.0925650i
$407$	1.80423	+	6.40442i	0.0894325	+	0.317456i
$408$	−4.80728	+	4.80728i	−0.237996	+	0.237996i
$409$	26.7076	+	7.15628i	1.32061	+	0.353855i	0.849205	−	0.528064i	$-0.177082\pi$
$409$	26.7076	+	7.15628i	1.32061	+	0.353855i	0.471401	+	0.881919i	$0.343749\pi$
$410$	−3.63017	−	15.3578i	−0.179281	−	0.758468i
$411$	−31.9033	−	18.4194i	−1.57367	−	0.908561i
$412$	−3.09481	+	5.36037i	−0.152471	+	0.264087i
$413$			3.70438i			0.182281i
$414$	0.853257	+	0.492628i	0.0419353	+	0.0242113i
$415$	0.277908	−	9.35860i	0.0136420	−	0.459396i
$416$	−0.227440	−	0.393937i	−0.0111511	−	0.0193143i
$417$	22.1960	+	22.1960i	1.08694	+	1.08694i
$418$	−0.107477	−	0.107477i	−0.00525687	−	0.00525687i
$419$	0.732348	−	0.422822i	0.0357776	−	0.0206562i	−0.482005	−	0.876169i	$-0.660091\pi$
$419$	0.732348	−	0.422822i	0.0357776	−	0.0206562i	0.517782	+	0.855513i	$0.326758\pi$
$420$	−5.24788	+	1.24046i	−0.256071	+	0.0605282i
$421$	−5.01009	−	5.01009i	−0.244177	−	0.244177i	0.574399	−	0.818576i	$-0.305236\pi$
$421$	−5.01009	−	5.01009i	−0.244177	−	0.244177i	−0.818576	+	0.574399i	$0.805236\pi$
$422$	3.99779	−	2.30813i	0.194609	−	0.112358i
$423$	23.0683	+	6.18112i	1.12162	+	0.300537i
$424$	2.03337	−	7.58864i	0.0987491	−	0.368537i
$425$	12.0755	+	7.96291i	0.585750	+	0.386258i
$426$	−4.42322	−	16.5077i	−0.214306	−	0.799800i
$427$	−4.51339	+	2.60580i	−0.218418	+	0.126104i
$428$	1.98266	−	7.39938i	0.0958354	−	0.357663i
$429$	0.302643	−	1.12948i	0.0146118	−	0.0545318i
$430$	13.8748	−	13.0745i	0.669102	−	0.630510i
$431$	15.3592	−	4.11547i	0.739824	−	0.198235i	0.130824	−	0.991406i	$-0.458238\pi$
$431$	15.3592	−	4.11547i	0.739824	−	0.198235i	0.609000	+	0.793170i	$0.291571\pi$
$432$	1.08346	+	0.290312i	0.0521280	+	0.0139677i
$433$	−19.2276	+	19.2276i	−0.924022	+	0.924022i	−0.997311	−	0.0732891i	$-0.976650\pi$
$433$	−19.2276	+	19.2276i	−0.924022	+	0.924022i	0.0732891	+	0.997311i	$0.476650\pi$
$434$	1.15513			0.0554478
$435$	−9.14795	−	2.74468i	−0.438611	−	0.131597i
$436$	0.396594	+	0.396594i	0.0189934	+	0.0189934i
$437$	0.0140458	+	0.0524198i	0.000671903	+	0.00250758i
$438$	−4.66856			−0.223072
$439$	−0.975860	−	3.64196i	−0.0465752	−	0.173821i	0.938720	−	0.344680i	$-0.112013\pi$
$439$	−0.975860	−	3.64196i	−0.0465752	−	0.173821i	−0.985296	+	0.170859i	$0.945346\pi$
$440$	−0.562653	−	2.38036i	−0.0268234	−	0.113479i
$441$	−7.50115	+	12.9924i	−0.357198	+	0.618684i
$442$	−0.657968	−	1.13963i	−0.0312963	−	0.0542068i
$443$	16.0819	+	16.0819i	0.764074	+	0.764074i	0.977056	−	0.212982i	$-0.0683177\pi$
$443$	16.0819	+	16.0819i	0.764074	+	0.764074i	−0.212982	+	0.977056i	$0.568318\pi$
$444$	0.182976	+	14.2936i	0.00868364	+	0.678343i
$445$	−0.916271	+	30.8556i	−0.0434354	+	1.46270i
$446$	−4.88516	+	18.2317i	−0.231319	+	0.863294i
$447$	1.58861	+	5.92877i	0.0751386	+	0.280421i
$448$	0.991227	−	0.265598i	0.0468311	−	0.0125483i
$449$	−3.02946	+	0.811742i	−0.142969	+	0.0383085i	−0.329594	−	0.944123i	$-0.606912\pi$
$449$	−3.02946	+	0.811742i	−0.142969	+	0.0383085i	0.186625	+	0.982431i	$0.440245\pi$
$450$	−0.748466	+	12.5913i	−0.0352830	+	0.593558i
$451$	−3.85996	+	6.68566i	−0.181759	+	0.314815i
$452$	−4.98372			−0.234414
$453$	50.6948	+	13.5836i	2.38185	+	0.638215i
$454$		−	10.2395i		−	0.480562i
$455$	0.0309819	−	1.04332i	0.00145246	−	0.0489118i
$456$	−0.163272	−	0.282796i	−0.00764593	−	0.0132431i
$457$	18.4520	−	31.9599i	0.863150	−	1.49502i	−0.00572214	−	0.999984i	$-0.501821\pi$
$457$	18.4520	−	31.9599i	0.863150	−	1.49502i	0.868872	−	0.495036i	$-0.164845\pi$
$458$	−0.625956			−0.0292490
$459$	3.13438	+	0.839855i	0.146300	+	0.0392011i
$460$	−0.250969	+	0.836473i	−0.0117015	+	0.0390008i
$461$	−23.7875	−	6.37384i	−1.10789	−	0.296859i	−0.341919	−	0.939730i	$-0.611077\pi$
$461$	−23.7875	−	6.37384i	−1.10789	−	0.296859i	−0.765975	+	0.642870i	$0.777743\pi$
$462$	2.28454	+	1.31898i	0.106286	+	0.0613645i
$463$	1.40692	+	0.812285i	0.0653850	+	0.0377501i	0.532336	−	0.846533i	$-0.321314\pi$
$463$	1.40692	+	0.812285i	0.0653850	+	0.0377501i	−0.466951	+	0.884283i	$0.654648\pi$
$464$	1.75559	+	0.470410i	0.0815014	+	0.0218382i
$465$	1.69985	−	5.66557i	0.0788288	−	0.262735i
$466$	6.13733	+	1.64449i	0.284306	+	0.0761796i
$467$	−30.6174			−1.41680			−0.708401	−	0.705810i	$-0.750583\pi$
$467$	−30.6174			−1.41680			−0.708401	+	0.705810i	$0.750583\pi$
$468$	0.573761	−	0.993783i	0.0265221	−	0.0459377i
$469$	−6.55834	−	11.3594i	−0.302836	−	0.524528i
$470$	−0.628332	+	21.1592i	−0.0289828	+	0.976002i
$471$			7.53788i			0.347327i
$472$	−3.48682	−	0.934291i	−0.160494	−	0.0430042i
$473$	−9.32615			−0.428817
$474$	6.06539	−	10.5056i	0.278593	−	0.482537i
$475$	−0.519558	+	0.461255i	−0.0238390	+	0.0211638i
$476$	2.86756	−	0.768359i	0.131434	−	0.0352177i
$477$	19.1438	−	5.12958i	0.876536	−	0.234867i
$478$	4.58065	+	17.0952i	0.209514	+	0.781917i
$479$	−1.07888	+	4.02643i	−0.0492952	+	0.183972i	−0.986183	−	0.165657i	$-0.947026\pi$
$479$	−1.07888	+	4.02643i	−0.0492952	+	0.183972i	0.936888	+	0.349629i	$0.113692\pi$
$480$	0.155976	−	5.25254i	0.00711932	−	0.239744i
$481$	−2.68159	−	0.681863i	−0.122270	−	0.0310903i
$482$	−2.57289	−	2.57289i	−0.117192	−	0.117192i
$483$	−0.470933	−	0.815680i	−0.0214282	−	0.0371147i
$484$	4.90173	−	8.49005i	0.222806	−	0.385911i
$485$	−6.11621	−	25.8753i	−0.277723	−	1.17494i
$486$	5.33555	+	19.9126i	0.242026	+	0.903252i
$487$	8.40797			0.381002			0.190501	−	0.981687i	$-0.438989\pi$
$487$	8.40797			0.381002			0.190501	+	0.981687i	$0.438989\pi$
$488$	−1.31443	−	4.90553i	−0.0595016	−	0.222063i
$489$	33.3019	+	33.3019i	1.50597	+	1.50597i
$490$	−12.7368	−	3.82145i	−0.575390	−	0.172635i
$491$	−10.8980			−0.491819			−0.245909	−	0.969293i	$-0.579087\pi$
$491$	−10.8980			−0.491819			−0.245909	+	0.969293i	$0.579087\pi$
$492$	−11.7276	+	11.7276i	−0.528723	+	0.528723i
$493$	5.07882	+	1.36087i	0.228739	+	0.0612903i
$494$	0.0610530	−	0.0163591i	0.00274690	−	0.000736031i
$495$	4.49072	−	4.23170i	0.201843	−	0.190201i
$496$	−0.291337	+	1.08729i	−0.0130814	+	0.0488206i
$497$	−1.93149	+	7.20842i	−0.0866392	+	0.323342i
$498$	−8.52165	+	4.91997i	−0.381864	+	0.220469i
$499$	−3.97714	−	14.8429i	−0.178041	−	0.664459i	−0.996014	−	0.0892013i	$-0.971569\pi$
$499$	−3.97714	−	14.8429i	−0.178041	−	0.664459i	0.817972	−	0.575257i	$-0.195098\pi$
$500$	−11.0140	+	1.92169i	−0.492559	+	0.0859407i
$501$	−2.96851	+	11.0786i	−0.132623	+	0.494957i
$502$	−21.6227	−	5.79379i	−0.965068	−	0.258589i
$503$	28.0700	−	16.2062i	1.25158	−	0.722600i	0.280156	−	0.959954i	$-0.409614\pi$
$503$	28.0700	−	16.2062i	1.25158	−	0.722600i	0.971423	+	0.237355i	$0.0762804\pi$
$504$	1.83054	+	1.83054i	0.0815388	+	0.0815388i
$505$	5.72179	−	1.35248i	0.254616	−	0.0601844i
$506$	0.369980	−	0.213608i	0.0164476	−	0.00949603i
$507$	−21.2587	−	21.2587i	−0.944130	−	0.944130i
$508$	14.8937	+	14.8937i	0.660802	+	0.660802i
$509$	16.9629	+	29.3806i	0.751867	+	1.30227i	0.946917	+	0.321478i	$0.104180\pi$
$509$	16.9629	+	29.3806i	0.751867	+	1.30227i	−0.195050	+	0.980793i	$0.562487\pi$
$510$	0.451230	−	15.1953i	0.0199808	−	0.672857i
$511$	1.76550	+	1.01931i	0.0781010	+	0.0450916i
$512$			1.00000i			0.0441942i
$513$	−0.0779304	+	0.134979i	−0.00344071	+	0.00595949i
$514$	−18.9356	−	10.9325i	−0.835214	−	0.482211i
$515$	−3.18377	−	13.4693i	−0.140294	−	0.593527i
$516$	−19.3535	−	5.18575i	−0.851989	−	0.228290i
$517$	7.32242	−	7.32242i	0.322039	−	0.322039i
$518$	3.05160	−	5.44532i	0.134079	−	0.239254i
$519$		−	37.5460i		−	1.64809i
$520$	0.974235	+	0.292302i	0.0427230	+	0.0128183i
$521$	6.63535	+	3.83092i	0.290700	+	0.167836i	0.638258	−	0.769823i	$-0.279655\pi$
$521$	6.63535	+	3.83092i	0.290700	+	0.167836i	−0.347557	+	0.937659i	$0.612989\pi$
$522$	1.18670	+	4.42883i	0.0519406	+	0.193845i
$523$	−10.4476	−	6.03193i	−0.456842	−	0.263758i	0.253873	−	0.967237i	$-0.418295\pi$
$523$	−10.4476	−	6.03193i	−0.456842	−	0.263758i	−0.710716	+	0.703479i	$0.751629\pi$
$524$	−12.8933	−	12.8933i	−0.563248	−	0.563248i
$525$	6.63802	−	10.0664i	0.289707	−	0.439333i
$526$	−6.08580	+	6.08580i	−0.265354	+	0.265354i
$527$	−0.842820	+	3.14545i	−0.0367138	+	0.137018i
$528$	−1.81771	+	1.81771i	−0.0791055	+	0.0791055i
$529$	22.8475			0.993368
$530$	8.32820	+	15.4677i	0.361754	+	0.671876i
$531$	−2.35693	−	8.79620i	−0.102282	−	0.381722i
$532$			0.142592i			0.00618217i
$533$	−1.60515	−	2.78020i	−0.0695268	−	0.120424i
$534$	28.0962	−	16.2213i	1.21584	−	0.701965i
$535$	8.12050	+	15.0820i	0.351080	+	0.652051i
$536$	12.3464	−	3.30819i	0.533281	−	0.142892i
$537$	14.8332	−	25.6919i	0.640102	−	1.10869i
$538$	−2.86334	−	4.95945i	−0.123447	−	0.213817i
$539$	3.25256	+	5.63361i	0.140098	+	0.242657i
$540$	−2.20839	+	1.18905i	−0.0950341	+	0.0511686i
$541$	22.7977	−	22.7977i	0.980151	−	0.980151i	−0.0196559	−	0.999807i	$-0.506257\pi$
$541$	22.7977	−	22.7977i	0.980151	−	0.980151i	0.999807	+	0.0196559i	$0.00625705\pi$
$542$	5.71972	+	3.30228i	0.245683	+	0.141845i
$543$	10.5591	−	39.4073i	0.453136	−	1.69113i
$544$			2.89294i			0.124034i
$545$	−1.25359	−	0.0372259i	−0.0536978	−	0.00159458i
$546$	−0.950017	+	0.548493i	−0.0406570	+	0.0234733i
$547$			32.5413i			1.39137i	0.718349	+	0.695683i	$0.244898\pi$
$547$			32.5413i			1.39137i	−0.718349	+	0.695683i	$0.755102\pi$
$548$	−15.1416	+	4.05719i	−0.646819	+	0.173315i
$549$	9.05926	−	9.05926i	0.386640	−	0.386640i
$550$	4.56595	+	3.01090i	0.194693	+	0.128385i
$551$	−0.126275	+	0.218715i	−0.00537950	+	0.00931757i
$552$	0.886550	−	0.237550i	0.0377341	−	0.0101108i
$553$	−4.58747	+	2.64858i	−0.195079	+	0.112629i
$554$	−8.89566			−0.377940
$555$	−22.2171	−	22.9804i	−0.943064	−	0.975464i
$556$	13.3571			0.566469
$557$	3.54898	−	2.04900i	0.150375	−	0.0868190i	−0.422925	−	0.906165i	$-0.638996\pi$
$557$	3.54898	−	2.04900i	0.150375	−	0.0868190i	0.573300	+	0.819346i	$0.305663\pi$
$558$	−2.74289	+	0.734956i	−0.116116	+	0.0311132i
$559$	1.93912	−	3.35866i	0.0820162	−	0.142056i
$560$	−1.20580	+	1.95228i	−0.0509543	+	0.0824991i
$561$	−5.25851	+	5.25851i	−0.222014	+	0.222014i
$562$	1.59322	−	0.426903i	0.0672061	−	0.0180078i
$563$		−	38.2228i		−	1.61090i	−0.592665	−	0.805449i	$-0.701924\pi$
$563$		−	38.2228i		−	1.61090i	0.592665	−	0.805449i	$-0.298076\pi$
$564$	19.2669	−	11.1238i	0.811284	−	0.468395i
$565$	8.11037	−	7.64258i	0.341206	−	0.321526i
$566$			32.6198i			1.37111i
$567$	2.71019	−	10.1146i	0.113817	−	0.424772i
$568$	−6.29793	−	3.63611i	−0.264255	−	0.152568i
$569$	5.18626	−	5.18626i	0.217420	−	0.217420i	−0.589991	−	0.807410i	$-0.700869\pi$
$569$	5.18626	−	5.18626i	0.217420	−	0.217420i	0.807410	+	0.589991i	$0.200869\pi$
$570$	0.699376	+	0.209835i	0.0292936	+	0.00878903i
$571$	1.43605	+	2.48731i	0.0600968	+	0.104091i	0.894508	−	0.447051i	$-0.147526\pi$
$571$	1.43605	+	2.48731i	0.0600968	+	0.104091i	−0.834412	+	0.551142i	$0.814192\pi$
$572$	−0.248788	−	0.430913i	−0.0104023	−	0.0180174i
$573$	12.2988	−	21.3021i	0.513789	−	0.889909i
$574$	6.99557	−	1.87446i	0.291990	−	0.0782384i
$575$	−0.874320	−	1.74612i	−0.0364617	−	0.0728181i
$576$	−2.18472	+	1.26135i	−0.0910300	+	0.0525562i
$577$	16.6152	+	28.7785i	0.691702	+	1.19806i	0.971280	+	0.237940i	$0.0764721\pi$
$577$	16.6152	+	28.7785i	0.691702	+	1.19806i	−0.279578	+	0.960123i	$0.590195\pi$
$578$		−	8.63093i		−	0.358999i
$579$	−3.32980	−	12.4270i	−0.138382	−	0.516448i
$580$	−3.57839	+	1.92669i	−0.148584	+	0.0800014i
$581$	4.29681			0.178262
$582$	−19.7591	+	19.7591i	−0.819039	+	0.819039i
$583$	2.22423	−	8.30094i	0.0921182	−	0.343790i
$584$	−1.40473	+	1.40473i	−0.0581280	+	0.0581280i
$585$	0.590253	+	2.49713i	0.0244040	+	0.103243i
$586$	16.9720	+	16.9720i	0.701106	+	0.701106i
$587$	−5.07079	−	2.92762i	−0.209294	−	0.120836i	0.391689	−	0.920098i	$-0.371891\pi$
$587$	−5.07079	−	2.92762i	−0.209294	−	0.120836i	−0.600983	+	0.799262i	$0.705224\pi$
$588$	3.61713	+	13.4993i	0.149168	+	0.556703i
$589$	−0.135456	−	0.0782055i	−0.00558136	−	0.00322240i
$590$	7.10711	−	3.82664i	0.292595	−	0.157540i
$591$		−	13.1736i		−	0.541889i
$592$	4.35587	+	4.24575i	0.179025	+	0.174499i
$593$	−6.25765	+	6.25765i	−0.256971	+	0.256971i	−0.823821	−	0.566850i	$-0.808162\pi$
$593$	−6.25765	+	6.25765i	−0.256971	+	0.256971i	0.566850	+	0.823821i	$0.308162\pi$
$594$	1.18516	+	0.317562i	0.0486277	+	0.0130297i
$595$	−3.48830	+	5.64783i	−0.143006	+	0.231539i
$596$	2.26191	+	1.30592i	0.0926515	+	0.0534924i
$597$	18.0545	−	31.2713i	0.738922	−	1.27985i
$598$			0.177656i			0.00726489i
$599$	10.8652	+	6.27302i	0.443940	+	0.256309i	0.705267	−	0.708941i	$-0.250827\pi$
$599$	10.8652	+	6.27302i	0.443940	+	0.256309i	−0.261328	+	0.965250i	$0.584160\pi$
$600$	7.80099	+	8.78704i	0.318474	+	0.358729i
$601$	9.26076	+	16.0401i	0.377754	+	0.654290i	0.990735	−	0.135808i	$-0.0433631\pi$
$601$	9.26076	+	16.0401i	0.377754	+	0.654290i	−0.612981	+	0.790098i	$0.710030\pi$
$602$	6.18662	+	6.18662i	0.252148	+	0.252148i
$603$	22.8005	+	22.8005i	0.928509	+	0.928509i
$604$	19.3408	−	11.1664i	0.786966	−	0.454355i
$605$	5.04262	+	21.3333i	0.205012	+	0.867323i
$606$	−4.36932	−	4.36932i	−0.177491	−	0.177491i
$607$	−0.675992	+	0.390284i	−0.0274377	+	0.0158412i	−0.513656	−	0.857996i	$-0.671709\pi$
$607$	−0.675992	+	0.390284i	−0.0274377	+	0.0158412i	0.486218	+	0.873837i	$0.338376\pi$
$608$	−0.134218	−	0.0359636i	−0.00544326	−	0.00145852i
$609$	1.13444	−	4.23379i	0.0459698	−	0.171562i
$610$	9.66176	+	5.96744i	0.391193	+	0.241615i
$611$	1.11455	+	4.15955i	0.0450897	+	0.168277i
$612$	−6.32025	+	3.64900i	−0.255481	+	0.147502i
$613$	−5.57619	+	20.8106i	−0.225220	+	0.840533i	0.757096	+	0.653304i	$0.226617\pi$
$613$	−5.57619	+	20.8106i	−0.225220	+	0.840533i	−0.982316	+	0.187229i	$0.940049\pi$
$614$	5.22247	−	19.4905i	0.210762	−	0.786574i
$615$	1.10080	−	37.0697i	0.0443886	−	1.49480i
$616$	1.08427	−	0.290529i	0.0436864	−	0.0117057i
$617$	23.2095	+	6.21897i	0.934380	+	0.250366i	0.693722	−	0.720243i	$-0.255970\pi$
$617$	23.2095	+	6.21897i	0.934380	+	0.250366i	0.240659	+	0.970610i	$0.422637\pi$
$618$	−10.2855	+	10.2855i	−0.413743	+	0.413743i
$619$	−6.63573			−0.266713			−0.133356	−	0.991068i	$-0.542575\pi$
$619$	−6.63573			−0.266713			−0.133356	+	0.991068i	$0.542575\pi$
$620$	−1.19325	−	2.21619i	−0.0479221	−	0.0890043i
$621$	−0.309769	−	0.309769i	−0.0124306	−	0.0124306i
$622$	−1.96729	−	7.34201i	−0.0788810	−	0.294388i
$623$	−14.1667			−0.567579
$624$	−0.276674	−	1.03256i	−0.0110758	−	0.0413355i
$625$	14.9769	−	20.0173i	0.599075	−	0.800693i
$626$	−16.2812	+	28.1999i	−0.650729	+	1.12710i
$627$	−0.178598	−	0.309341i	−0.00713251	−	0.0123539i
$628$	2.26808	+	2.26808i	0.0905063	+	0.0905063i
$629$	12.6012	+	12.2827i	0.502444	+	0.489743i
$630$	−5.78613	−	0.171822i	−0.230525	−	0.00684554i
$631$	−2.82761	+	10.5528i	−0.112565	+	0.420100i	−0.999093	−	0.0425753i	$-0.986444\pi$
$631$	−2.82761	+	10.5528i	−0.112565	+	0.420100i	0.886528	+	0.462675i	$0.153110\pi$
$632$	−1.33601	−	4.98605i	−0.0531436	−	0.198335i
$633$	10.4787	−	2.80777i	0.416492	−	0.111599i
$634$	25.2620	−	6.76893i	1.00328	−	0.268828i
$635$	−47.0773	−	1.39798i	−1.86821	−	0.0554772i
$636$	9.23136	−	15.9892i	0.366047	−	0.634012i
$637$	−2.70513			−0.107181
$638$	1.92038	+	0.514565i	0.0760286	+	0.0203718i
$639$		−	18.3456i		−	0.725741i
$640$	−1.53351	−	1.62737i	−0.0606173	−	0.0643276i
$641$	21.2426	+	36.7932i	0.839031	+	1.45324i	0.890706	+	0.454580i	$0.150211\pi$
$641$	21.2426	+	36.7932i	0.839031	+	1.45324i	−0.0516750	+	0.998664i	$0.516456\pi$
$642$	9.00114	−	15.5904i	0.355246	−	0.615305i
$643$	18.2603			0.720117			0.360058	−	0.932930i	$-0.382757\pi$
$643$	18.2603			0.720117			0.360058	+	0.932930i	$0.382757\pi$
$644$	−0.387130	−	0.103731i	−0.0152551	−	0.00408758i
$645$	39.4477	−	21.2396i	1.55325	−	0.836308i
$646$	−0.388284	−	0.104040i	−0.0152768	−	0.00409342i
$647$	11.9953	+	6.92548i	0.471583	+	0.272269i	0.716902	−	0.697174i	$-0.245559\pi$
$647$	11.9953	+	6.92548i	0.471583	+	0.272269i	−0.245319	+	0.969442i	$0.578893\pi$
$648$	8.83700	+	5.10205i	0.347150	+	0.200427i
$649$	−3.81411	−	1.02199i	−0.149717	−	0.0401165i
$650$	−2.03369	+	1.01832i	−0.0797680	+	0.0399416i
$651$	2.62210	+	0.702589i	0.102768	+	0.0275366i
$652$	20.0405			0.784847
$653$	−0.834191	+	1.44486i	−0.0326444	+	0.0565418i	−0.881886	−	0.471463i	$-0.843726\pi$
$653$	−0.834191	+	1.44486i	−0.0326444	+	0.0565418i	0.849242	+	0.528004i	$0.177060\pi$
$654$	0.659033	+	1.14148i	0.0257702	+	0.0446353i
$655$	40.7544	+	1.21022i	1.59241	+	0.0472872i
$656$			7.05749i			0.275549i
$657$	−4.84079	−	1.29708i	−0.188857	−	0.0506041i
$658$	−9.71484			−0.378724
$659$	4.01747	−	6.95846i	0.156498	−	0.271063i	−0.777105	−	0.629371i	$-0.783313\pi$
$659$	4.01747	−	6.95846i	0.156498	−	0.271063i	0.933604	+	0.358307i	$0.116646\pi$
$660$	0.170617	−	5.74556i	0.00664126	−	0.223646i
$661$	−27.5450	+	7.38067i	−1.07138	+	0.287075i	−0.751059	−	0.660235i	$-0.770457\pi$
$661$	−27.5450	+	7.38067i	−1.07138	+	0.287075i	−0.320319	+	0.947310i	$0.603790\pi$
$662$	−16.9750	+	4.54843i	−0.659751	+	0.176780i
$663$	−0.800399	−	2.98713i	−0.0310849	−	0.116010i
$664$	−1.08371	+	4.04446i	−0.0420561	+	0.156956i
$665$	−0.218667	−	0.232051i	−0.00847954	−	0.00899856i
$666$	−3.78152	+	14.8717i	−0.146531	+	0.576268i
$667$	−0.501937	−	0.501937i	−0.0194351	−	0.0194351i
$668$	2.44027	+	4.22666i	0.0944167	+	0.163535i
$669$	−22.1783	+	38.4139i	−0.857463	+	1.48517i
$670$	−15.0190	+	24.3169i	−0.580234	+	0.939445i
$671$	−1.43781	−	5.36599i	−0.0555061	−	0.207152i
$672$	2.41160			0.0930294
$673$	−11.4717	−	42.8128i	−0.442200	−	1.65031i	−0.723224	−	0.690613i	$-0.757341\pi$
$673$	−11.4717	−	42.8128i	−0.442200	−	1.65031i	0.281024	−	0.959701i	$-0.409326\pi$
$674$	−15.5402	−	15.5402i	−0.598586	−	0.598586i
$675$	1.77046	−	5.32163i	0.0681450	−	0.204829i
$676$	−12.7931			−0.492042
$677$	−36.0280	+	36.0280i	−1.38467	+	1.38467i	−0.548549	+	0.836118i	$0.684820\pi$
$677$	−36.0280	+	36.0280i	−1.38467	+	1.38467i	−0.836118	+	0.548549i	$0.815180\pi$
$678$	−11.3129	−	3.03127i	−0.434468	−	0.116415i
$679$	11.7863	−	3.15814i	0.452318	−	0.121198i
$680$	−4.43635	−	4.70789i	−0.170126	−	0.180539i
$681$	6.22800	−	23.2432i	0.238658	−	0.890682i
$682$	−0.318684	+	1.18934i	−0.0122030	+	0.0455423i
$683$	−35.6056	+	20.5569i	−1.36241	+	0.786588i	−0.989944	−	0.141457i	$-0.954821\pi$
$683$	−35.6056	+	20.5569i	−1.36241	+	0.786588i	−0.372467	+	0.928046i	$0.621488\pi$
$684$	−0.0907254	−	0.338592i	−0.00346897	−	0.0129464i
$685$	18.4194	−	29.8224i	0.703768	−	1.13946i
$686$	3.43868	−	12.8333i	0.131290	−	0.489979i
$687$	−1.42090	−	0.380729i	−0.0542106	−	0.0145257i
$688$	−7.38363	+	4.26294i	−0.281498	+	0.162523i
$689$	2.52698	+	2.52698i	0.0962701	+	0.0962701i
$690$	−1.07846	+	1.74612i	−0.0410564	+	0.0664736i
$691$	28.4645	−	16.4340i	1.08284	−	0.625179i	0.151181	−	0.988506i	$-0.451693\pi$
$691$	28.4645	−	16.4340i	1.08284	−	0.625179i	0.931662	+	0.363327i	$0.118359\pi$
$692$	−11.2972	−	11.2972i	−0.429457	−	0.429457i
$693$	2.00236	+	2.00236i	0.0760635	+	0.0760635i
$694$	6.16936	+	10.6856i	0.234186	+	0.405622i
$695$	−21.7371	+	20.4833i	−0.824533	+	0.776976i
$696$	3.69902	+	2.13563i	0.140211	+	0.0809509i
$697$			20.4169i			0.773343i
$698$	−11.4160	+	19.7732i	−0.432104	+	0.748425i
$699$	12.9313	+	7.46588i	0.489106	+	0.282386i
$700$	−1.03156	−	5.02620i	−0.0389894	−	0.189973i
$701$	−43.3904	−	11.6264i	−1.63883	−	0.439124i	−0.682376	−	0.731001i	$-0.739053\pi$
$701$	−43.3904	−	11.6264i	−1.63883	−	0.439124i	−0.956456	+	0.291878i	$0.905720\pi$
$702$	−0.360787	+	0.360787i	−0.0136170	+	0.0136170i
$703$	−0.726510	+	0.431943i	−0.0274008	+	0.0162911i
$704$			1.09386i			0.0412265i
$705$	−14.2961	+	47.6486i	−0.538422	+	1.79455i
$706$	14.7854	+	8.53634i	0.556455	+	0.321269i
$707$	0.698358	+	2.60631i	0.0262645	+	0.0980203i
$708$	−7.34670	−	4.24162i	−0.276106	−	0.159410i
$709$	−1.37574	−	1.37574i	−0.0516669	−	0.0516669i	0.680801	−	0.732468i	$-0.261632\pi$
$709$	−1.37574	−	1.37574i	−0.0516669	−	0.0516669i	−0.732468	+	0.680801i	$0.761632\pi$
$710$	15.8251	−	3.74062i	0.593905	−	0.140383i
$711$	9.20796	−	9.20796i	0.345325	−	0.345325i
$712$	3.57303	−	13.3347i	0.133905	−	0.499741i
$713$	0.310863	−	0.310863i	0.0116419	−	0.0116419i
$714$	6.97660			0.261093
$715$	1.06568	+	0.319738i	0.0398542	+	0.0119575i
$716$	−3.26728	−	12.1937i	−0.122104	−	0.455699i
$717$			41.5917i			1.55327i
$718$	−10.1987	−	17.6647i	−0.380614	−	0.659243i
$719$	−32.0917	+	18.5282i	−1.19682	+	0.690984i	−0.959845	−	0.280532i	$-0.909489\pi$
$719$	−32.0917	+	18.5282i	−1.19682	+	0.690984i	−0.236975	+	0.971516i	$0.576156\pi$
$720$	1.62107	−	5.40298i	0.0604135	−	0.201357i
$721$	6.13533	−	1.64396i	0.228491	−	0.0612241i
$722$	−9.49035	+	16.4378i	−0.353194	+	0.611750i
$723$	−4.27546	−	7.40531i	−0.159006	−	0.275406i
$724$	−8.68014	−	15.0344i	−0.322595	−	0.558751i
$725$	2.86878	−	8.62294i	0.106544	−	0.320248i
$726$	16.2907	−	16.2907i	0.604605	−	0.604605i
$727$	−7.03346	−	4.06077i	−0.260856	−	0.150606i	0.363869	−	0.931450i	$-0.381456\pi$
$727$	−7.03346	−	4.06077i	−0.260856	−	0.150606i	−0.624725	+	0.780845i	$0.714789\pi$
$728$	−0.120815	+	0.450888i	−0.00447771	+	0.0167110i
$729$			17.8338i			0.660512i
$730$	0.131853	−	4.44018i	0.00488010	−	0.164338i
$731$	−21.3604	+	12.3324i	−0.790042	+	0.456131i
$732$		−	11.9349i		−	0.441126i
$733$	−48.4318	+	12.9773i	−1.78887	+	0.479326i	−0.992153	−	0.125027i	$-0.960098\pi$
$733$	−48.4318	+	12.9773i	−1.78887	+	0.479326i	−0.796717	+	0.604353i	$0.793432\pi$
$734$	−9.43149	+	9.43149i	−0.348122	+	0.348122i
$735$	−26.5878	−	16.4215i	−0.980705	−	0.605718i
$736$	0.195278	−	0.338232i	0.00719805	−	0.0124674i
$737$	13.5052	−	3.61871i	0.497471	−	0.133297i
$738$	−15.4186	+	8.90195i	−0.567568	+	0.327685i
$739$	−12.7958			−0.470701			−0.235351	−	0.971911i	$-0.575624\pi$
$739$	−12.7958			−0.470701			−0.235351	+	0.971911i	$0.575624\pi$
$740$	−13.5995	−	0.229666i	−0.499929	−	0.00844268i
$741$	0.148538			0.00545670
$742$	−6.98200	+	4.03106i	−0.256317	+	0.147985i
$743$	46.3327	−	12.4148i	1.69978	−	0.455455i	0.726897	−	0.686746i	$-0.240962\pi$
$743$	46.3327	−	12.4148i	1.69978	−	0.455455i	0.972885	+	0.231291i	$0.0742950\pi$
$744$	−1.32265	+	2.29090i	−0.0484908	+	0.0839885i
$745$	−5.68361	+	1.34345i	−0.208231	+	0.0492203i
$746$	−12.3383	+	12.3383i	−0.451737	+	0.451737i
$747$	−10.2030	+	2.73387i	−0.373307	+	0.100027i
$748$			3.16448i			0.115705i
$749$	−6.80788	+	3.93053i	−0.248754	+	0.143618i
$750$	−26.1701	−	2.33690i	−0.955598	−	0.0853314i
$751$		−	8.75628i		−	0.319521i	−0.987156	−	0.159761i	$-0.948928\pi$
$751$		−	8.75628i		−	0.319521i	0.987156	−	0.159761i	$-0.0510722\pi$
$752$	2.45020	−	9.14429i	0.0893498	−	0.333458i
$753$	−45.5588	−	26.3034i	−1.66026	−	0.958549i
$754$	−0.584603	+	0.584603i	−0.0212900	+	0.0212900i
$755$	−14.3509	+	47.8313i	−0.522283	+	1.74076i
$756$	−0.575531	−	0.996849i	−0.0209319	−	0.0362551i
$757$	−24.7395	−	42.8500i	−0.899172	−	1.55741i	−0.828555	−	0.559908i	$-0.810837\pi$
$757$	−24.7395	−	42.8500i	−0.899172	−	1.55741i	−0.0706169	−	0.997504i	$-0.522497\pi$
$758$	−12.5772	+	21.7843i	−0.456823	+	0.791240i
$759$	0.969765	−	0.259848i	0.0352003	−	0.00943188i
$760$	0.273574	−	0.147299i	0.00992356	−	0.00534308i
$761$	3.14495	−	1.81574i	0.114004	−	0.0658204i	−0.441914	−	0.897058i	$-0.645700\pi$
$761$	3.14495	−	1.81574i	0.114004	−	0.0658204i	0.555918	+	0.831237i	$0.312367\pi$
$762$	24.7494	+	42.8672i	0.896575	+	1.55291i
$763$		−	0.575560i		−	0.0208367i
$764$	−2.70902	−	10.1102i	−0.0980090	−	0.365775i
$765$	4.68964	−	15.6305i	0.169554	−	0.565120i
$766$	10.7373			0.387953
$767$	1.16109	−	1.16109i	0.0419246	−	0.0419246i
$768$	−0.608236	+	2.26997i	−0.0219478	+	0.0819104i
$769$	−36.4223	+	36.4223i	−1.31342	+	1.31342i	−0.394543	+	0.918877i	$0.629097\pi$
$769$	−36.4223	+	36.4223i	−1.31342	+	1.31342i	−0.918877	+	0.394543i	$0.870903\pi$
$770$	−1.31898	+	2.13553i	−0.0475327	+	0.0769593i
$771$	−36.3337	−	36.3337i	−1.30852	−	1.30852i
$772$	−4.74108	−	2.73726i	−0.170635	−	0.0985163i
$773$	−5.61641	−	20.9607i	−0.202008	−	0.753905i	−0.990341	−	0.138656i	$-0.955722\pi$
$773$	−5.61641	−	20.9607i	−0.202008	−	0.753905i	0.788332	−	0.615250i	$-0.210945\pi$
$774$	−18.6267	−	10.7541i	−0.669522	−	0.386549i
$775$	5.34041	+	1.77671i	0.191833	+	0.0638213i
$776$			11.8906i			0.426849i
$777$	10.2391	−	10.5046i	0.367324	−	0.376850i
$778$	−21.5625	+	21.5625i	−0.773052	+	0.773052i
$779$	−0.947243	−	0.253813i	−0.0339385	−	0.00909379i
$780$	2.03369	+	1.25608i	0.0728179	+	0.0449749i
$781$	−6.88907	−	3.97741i	−0.246510	−	0.142323i
$782$	0.564927	−	0.978483i	0.0202018	−	0.0349905i
$783$		−	2.03868i		−	0.0728566i
$784$	5.15019	+	2.97346i	0.183935	+	0.106195i
$785$	−7.16914	−	0.212891i	−0.255878	−	0.00759840i
$786$	−21.4253	−	37.1097i	−0.764214	−	1.32366i
$787$	−19.1328	−	19.1328i	−0.682009	−	0.682009i	0.278443	−	0.960453i	$-0.410182\pi$
$787$	−19.1328	−	19.1328i	−0.682009	−	0.682009i	−0.960453	+	0.278443i	$0.910182\pi$
$788$	−3.96381	−	3.96381i	−0.141205	−	0.141205i
$789$	−17.5162	+	10.1130i	−0.623592	+	0.360031i
$790$	9.82035	+	6.06539i	0.349392	+	0.215797i
$791$	3.61633	+	3.61633i	0.128582	+	0.128582i
$792$	−2.38979	+	1.37974i	−0.0849174	+	0.0490271i
$793$	2.23142	+	0.597908i	0.0792402	+	0.0212323i
$794$	−5.16248	+	19.2666i	−0.183210	+	0.683747i
$795$	9.49670	+	40.1768i	0.336813	+	1.42492i
$796$	−3.97682	−	14.8417i	−0.140955	−	0.526050i
$797$	−48.0413	+	27.7366i	−1.70171	+	0.982482i	−0.757675	+	0.652632i	$0.773665\pi$
$797$	−48.0413	+	27.7366i	−1.70171	+	0.982482i	−0.944033	+	0.329850i	$0.893002\pi$
$798$	−0.0867298	+	0.323680i	−0.00307020	+	0.0114582i
$799$	7.08828	−	26.4538i	0.250765	−	0.935869i
$800$	4.99119	+	0.296693i	0.176465	+	0.0104897i
$801$	33.6395	−	9.01368i	1.18859	−	0.318483i
$802$	13.0735	+	3.50302i	0.461640	+	0.123696i
$803$	−1.53658	+	1.53658i	−0.0542247	+	0.0542247i
$804$	30.0380			1.05936
$805$	0.789079	−	0.424859i	0.0278114	−	0.0149743i
$806$	−0.362060	−	0.362060i	−0.0127530	−	0.0127530i
$807$	−3.48317	−	12.9994i	−0.122613	−	0.457599i
$808$	−2.62938			−0.0925011
$809$	−5.75814	−	21.4897i	−0.202445	−	0.755537i	−0.990213	−	0.139564i	$-0.955430\pi$
$809$	−5.75814	−	21.4897i	−0.202445	−	0.755537i	0.787768	−	0.615973i	$-0.211237\pi$
$810$	−22.2051	+	5.24870i	−0.780209	+	0.184420i
$811$	18.3417	−	31.7688i	0.644066	−	1.11555i	−0.340451	−	0.940262i	$-0.610580\pi$
$811$	18.3417	−	31.7688i	0.644066	−	1.11555i	0.984516	−	0.175292i	$-0.0560870\pi$
$812$	−0.932566	−	1.61525i	−0.0327267	−	0.0566842i
$813$	10.9750	+	10.9750i	0.384910	+	0.384910i
$814$	4.76472	+	4.64428i	0.167004	+	0.162782i
$815$	−32.6134	+	30.7323i	−1.14240	+	1.07651i
$816$	−1.75959	+	6.56687i	−0.0615978	+	0.229886i
$817$	−0.306622	−	1.14433i	−0.0107273	−	0.0400350i
$818$	26.7076	−	7.15628i	0.933809	−	0.250213i
$819$	−1.13746	+	0.304780i	−0.0397459	+	0.0106499i
$820$	−10.8227	−	11.4852i	−0.377946	−	0.401080i
$821$	21.5031	−	37.2444i	0.750462	−	1.29984i	−0.197137	−	0.980376i	$-0.563164\pi$
$821$	21.5031	−	37.2444i	0.750462	−	1.29984i	0.947599	−	0.319462i	$-0.103502\pi$
$822$	−36.8387			−1.28490
$823$	34.2248	+	9.17050i	1.19300	+	0.319663i	0.800071	−	0.599905i	$-0.204795\pi$
$823$	34.2248	+	9.17050i	1.19300	+	0.319663i	0.392929	+	0.919569i	$0.371462\pi$
$824$			6.18963i			0.215626i
$825$	8.53322	+	9.61182i	0.297089	+	0.334641i
$826$	1.85219	+	3.20809i	0.0644459	+	0.111624i
$827$	18.2882	−	31.6761i	0.635943	−	1.10149i	−0.350372	−	0.936611i	$-0.613945\pi$
$827$	18.2882	−	31.6761i	0.635943	−	1.10149i	0.986315	−	0.164875i	$-0.0527220\pi$
$828$	0.985256			0.0342400
$829$	−19.8506	−	5.31896i	−0.689440	−	0.184735i	−0.102944	−	0.994687i	$-0.532826\pi$
$829$	−19.8506	−	5.31896i	−0.689440	−	0.184735i	−0.586496	+	0.809952i	$0.699493\pi$
$830$	−4.43862	−	8.24374i	−0.154067	−	0.286144i
$831$	−20.1929	−	5.41066i	−0.700482	−	0.187694i
$832$	−0.393937	−	0.227440i	−0.0136573	−	0.00788505i
$833$	14.8992	+	8.60204i	0.516225	+	0.298043i
$834$	30.3202	+	8.12428i	1.04990	+	0.281321i
$835$	−10.4529	−	3.13619i	−0.361736	−	0.108532i
$836$	−0.146816	−	0.0393393i	−0.00507775	−	0.00136058i
$837$	1.26261			0.0436422
$838$	0.422822	−	0.732348i	0.0146061	−	0.0252986i
$839$	23.8810	+	41.3632i	0.824465	+	1.42802i	0.902328	+	0.431051i	$0.141857\pi$
$839$	23.8810	+	41.3632i	0.824465	+	1.42802i	−0.0778627	+	0.996964i	$0.524810\pi$
$840$	−3.92457	+	3.69821i	−0.135411	+	0.127600i
$841$			25.6966i			0.886090i
$842$	−6.84391	−	1.83382i	−0.235857	−	0.0631976i
$843$	3.87622			0.133504
$844$	2.30813	−	3.99779i	0.0794489	−	0.137610i
$845$	20.8191	−	19.6183i	0.716200	−	0.674891i
$846$	23.0683	−	6.18112i	0.793104	−	0.212511i
$847$	−9.71746	+	2.60378i	−0.333896	+	0.0894671i
$848$	−2.03337	−	7.58864i	−0.0698262	−	0.260595i
$849$	−19.8405	+	74.0458i	−0.680925	+	2.54125i
$850$	14.4392	+	0.858313i	0.495260	+	0.0294399i
$851$	−0.644189	−	2.28666i	−0.0220825	−	0.0783856i
$852$	−12.0845	−	12.0845i	−0.414007	−	0.414007i
$853$	5.01838	+	8.69210i	0.171826	+	0.297612i	0.939058	−	0.343758i	$-0.111700\pi$
$853$	5.01838	+	8.69210i	0.171826	+	0.297612i	−0.767232	+	0.641369i	$0.778367\pi$
$854$	−2.60580	+	4.51339i	−0.0891688	+	0.154445i
$855$	0.666878	+	0.411887i	0.0228067	+	0.0140862i
$856$	−1.98266	−	7.39938i	−0.0677659	−	0.252906i
$857$	−12.1187			−0.413968			−0.206984	−	0.978344i	$-0.566365\pi$
$857$	−12.1187			−0.413968			−0.206984	+	0.978344i	$0.566365\pi$
$858$	−0.302643	−	1.12948i	−0.0103321	−	0.0385598i
$859$	4.37193	+	4.37193i	0.149168	+	0.149168i	0.777746	−	0.628578i	$-0.216363\pi$
$859$	4.37193	+	4.37193i	0.149168	+	0.149168i	−0.628578	+	0.777746i	$0.716363\pi$
$860$	5.47867	−	18.2603i	0.186821	−	0.622670i
$861$	17.0198			0.580034
$862$	11.2437	−	11.2437i	0.382961	−	0.382961i
$863$	−32.2954	−	8.65353i	−1.09935	−	0.294570i	−0.336849	−	0.941559i	$-0.609361\pi$
$863$	−32.2954	−	8.65353i	−1.09935	−	0.294570i	−0.762499	+	0.646989i	$0.776028\pi$
$864$	1.08346	−	0.290312i	0.0368601	−	0.00987663i
$865$	35.7093	+	1.06040i	1.21415	+	0.0360548i
$866$	−7.03781	+	26.2655i	−0.239154	+	0.892536i
$867$	5.24964	−	19.5919i	0.178287	−	0.665376i
$868$	1.00037	−	0.577563i	0.0339547	−	0.0196038i
$869$	−1.46141	−	5.45406i	−0.0495750	−	0.185016i
$870$	−9.29470	+	2.19702i	−0.315120	+	0.0744858i
$871$	−1.50483	+	5.61610i	−0.0509892	+	0.190294i
$872$	0.541758	+	0.145164i	0.0183462	+	0.00491586i
$873$	−25.9777	+	14.9983i	−0.879213	+	0.507614i
$874$	0.0383739	+	0.0383739i	0.00129802	+	0.00129802i
$875$	9.38647	+	6.59760i	0.317321	+	0.223040i
$876$	−4.04309	+	2.33428i	−0.136603	+	0.0788679i
$877$	8.44407	+	8.44407i	0.285136	+	0.285136i	0.835153	−	0.550017i	$-0.185379\pi$
$877$	8.44407	+	8.44407i	0.285136	+	0.285136i	−0.550017	+	0.835153i	$0.685379\pi$
$878$	−2.66610	−	2.66610i	−0.0899765	−	0.0899765i
$879$	28.2029	+	48.8488i	0.951259	+	1.64763i
$880$	−1.67745	−	1.78013i	−0.0565469	−	0.0600080i
$881$	−25.1839	−	14.5399i	−0.848466	−	0.489862i	0.0116671	−	0.999932i	$-0.496286\pi$
$881$	−25.1839	−	14.5399i	−0.848466	−	0.489862i	−0.860133	+	0.510070i	$0.829620\pi$
$882$			15.0023i			0.505154i
$883$	6.97147	−	12.0749i	0.234609	−	0.406354i	−0.724550	−	0.689222i	$-0.757953\pi$
$883$	6.97147	−	12.0749i	0.234609	−	0.406354i	0.959159	+	0.282868i	$0.0912858\pi$
$884$	−1.13963	−	0.657968i	−0.0383300	−	0.0221299i
$885$	18.4604	−	4.36354i	0.620539	−	0.146679i
$886$	21.9683	+	5.88638i	0.738038	+	0.197757i
$887$	−13.4845	+	13.4845i	−0.452766	+	0.452766i	−0.896272	−	0.443506i	$-0.853735\pi$
$887$	−13.4845	+	13.4845i	−0.452766	+	0.452766i	0.443506	+	0.896272i	$0.353735\pi$
$888$	7.30525	+	12.2871i	0.245148	+	0.412328i
$889$		−	21.6146i		−	0.724931i
$890$	14.6343	+	27.1799i	0.490543	+	0.911072i
$891$	9.66648	+	5.58094i	0.323839	+	0.186969i
$892$	4.88516	+	18.2317i	0.163567	+	0.610441i
$893$	1.13921	+	0.657724i	0.0381222	+	0.0220099i
$894$	4.34016	+	4.34016i	0.145157	+	0.145157i
$895$	24.0162	+	14.8332i	0.802773	+	0.495821i
$896$	0.725629	−	0.725629i	0.0242415	−	0.0242415i
$897$	−0.108057	+	0.403273i	−0.00360791	+	0.0134649i
$898$	−2.21772	+	2.21772i	−0.0740063	+	0.0740063i
$899$	2.04588			0.0682340
$900$	5.64744	+	11.2786i	0.188248	+	0.375953i
$901$	−5.88241	−	21.9534i	−0.195971	−	0.731375i
$902$			7.71993i			0.257046i
$903$	10.2805	+	17.8064i	0.342114	+	0.592558i
$904$	−4.31602	+	2.49186i	−0.143549	+	0.0828780i
$905$	37.1813	+	11.1556i	1.23595	+	0.370824i
$906$	50.6948	−	13.5836i	1.68422	−	0.451286i
$907$	3.54706	−	6.14368i	0.117778	−	0.203998i	−0.801109	−	0.598519i	$-0.795756\pi$
$907$	3.54706	−	6.14368i	0.117778	−	0.203998i	0.918887	+	0.394521i	$0.129090\pi$
$908$	−5.11973	−	8.86763i	−0.169904	−	0.294283i
$909$	−3.31656	−	5.74445i	−0.110003	−	0.190531i
$910$	−0.494831	−	0.919035i	−0.0164035	−	0.0304657i
$911$	−0.294391	+	0.294391i	−0.00975361	+	0.00975361i	−0.711967	−	0.702213i	$-0.752195\pi$
$911$	−0.294391	+	0.294391i	−0.00975361	+	0.00975361i	0.702213	+	0.711967i	$0.252195\pi$
$912$	−0.282796	−	0.163272i	−0.00936432	−	0.00540649i
$913$	−1.18543	+	4.42409i	−0.0392321	+	0.146416i
$914$		−	36.9041i		−	1.22068i
$915$	18.3023	+	19.4225i	0.605054	+	0.642089i
$916$	−0.542093	+	0.312978i	−0.0179113	+	0.0103411i
$917$			18.7116i			0.617910i
$918$	3.13438	−	0.839855i	0.103450	−	0.0277194i
$919$	17.6615	−	17.6615i	0.582600	−	0.582600i	−0.353017	−	0.935617i	$-0.614844\pi$
$919$	17.6615	−	17.6615i	0.582600	−	0.582600i	0.935617	+	0.353017i	$0.114844\pi$
$920$	0.200891	+	0.849891i	0.00662319	+	0.0280201i
$921$	23.7097	−	41.0664i	0.781260	−	1.35318i
$922$	−23.7875	+	6.37384i	−0.783399	+	0.209911i
$923$	2.86480	−	1.65399i	0.0942959	−	0.0544417i
$924$	2.63796			0.0867825
$925$	22.4837	−	20.4813i	0.739260	−	0.673420i
$926$	1.62457			0.0533867
$927$	−13.5226	+	7.80728i	−0.444141	+	0.256425i
$928$	1.75559	−	0.470410i	0.0576302	−	0.0154420i
$929$	−17.4188	+	30.1703i	−0.571492	+	0.989854i	0.424921	+	0.905231i	$0.360302\pi$
$929$	−17.4188	+	30.1703i	−0.571492	+	0.989854i	−0.996413	+	0.0846232i	$0.973031\pi$
$930$	−1.36067	−	5.75645i	−0.0446181	−	0.188762i
$931$	−0.584312	+	0.584312i	−0.0191501	+	0.0191501i
$932$	6.13733	−	1.64449i	0.201035	−	0.0538671i
$933$		−	17.8627i		−	0.584798i
$934$	−26.5154	+	15.3087i	−0.867611	+	0.500915i
$935$	−4.85276	−	5.14979i	−0.158702	−	0.168416i
$936$		−	1.14752i		−	0.0375079i
$937$	8.61118	−	32.1374i	0.281315	−	1.04988i	−0.670175	−	0.742203i	$-0.733781\pi$
$937$	8.61118	−	32.1374i	0.281315	−	1.04988i	0.951490	−	0.307679i	$-0.0995523\pi$
$938$	−11.3594	−	6.55834i	−0.370897	−	0.214138i
$939$	−54.1101	+	54.1101i	−1.76581	+	1.76581i
$940$	10.0355	+	18.6386i	0.327321	+	0.607924i
$941$	5.33349	+	9.23787i	0.173867	+	0.301146i	0.939768	−	0.341812i	$-0.111040\pi$
$941$	5.33349	+	9.23787i	0.173867	+	0.301146i	−0.765902	+	0.642958i	$0.777707\pi$
$942$	3.76894	+	6.52799i	0.122799	+	0.212694i
$943$	1.37817	−	2.38707i	0.0448795	−	0.0777336i
$944$	−3.48682	+	0.934291i	−0.113486	+	0.0304086i
$945$	2.46528	+	0.739664i	0.0801957	+	0.0240613i
$946$	−8.07669	+	4.66308i	−0.262596	+	0.151610i
$947$	−11.8834	−	20.5826i	−0.386158	−	0.668846i	0.605771	−	0.795639i	$-0.292865\pi$
$947$	−11.8834	−	20.5826i	−0.386158	−	0.668846i	−0.991929	+	0.126793i	$0.959531\pi$
$948$		−	12.1308i		−	0.393989i
$949$	−0.233883	−	0.872864i	−0.00759217	−	0.0283344i
$950$	−0.219323	+	0.659238i	−0.00711577	+	0.0213885i
$951$	61.4609			1.99301
$952$	2.09920	−	2.09920i	0.0680353	−	0.0680353i
$953$	12.8095	−	47.8057i	0.414941	−	1.54858i	−0.370014	−	0.929026i	$-0.620647\pi$
$953$	12.8095	−	47.8057i	0.414941	−	1.54858i	0.784955	−	0.619553i	$-0.212686\pi$
$954$	14.0143	−	14.0143i	0.453728	−	0.453728i
$955$	19.9127	+	12.2988i	0.644360	+	0.397979i
$956$	12.5146	+	12.5146i	0.404750	+	0.404750i
$957$	4.04622	+	2.33609i	0.130796	+	0.0755150i
$958$	1.07888	+	4.02643i	0.0348570	+	0.130088i
$959$	13.9312	+	8.04319i	0.449863	+	0.259728i
$960$	−2.49119	−	4.62682i	−0.0804028	−	0.149330i
$961$		−	29.7329i		−	0.959127i
$962$	−2.66326	+	0.750284i	−0.0858668	+	0.0241901i
$963$	13.6648	−	13.6648i	0.440341	−	0.440341i
$964$	−3.51464	−	0.941745i	−0.113199	−	0.0303316i
$965$	11.9131	−	2.81594i	0.383497	−	0.0906484i
$966$	−0.815680	−	0.470933i	−0.0262441	−	0.0151520i
$967$	27.5163	−	47.6596i	0.884863	−	1.53263i	0.0389927	−	0.999239i	$-0.487585\pi$
$967$	27.5163	−	47.6596i	0.884863	−	1.53263i	0.845870	−	0.533388i	$-0.179082\pi$
$968$		−	9.80346i		−	0.315095i
$969$	−0.818111	−	0.472337i	−0.0262815	−	0.0151736i
$970$	−18.2344	−	19.3505i	−0.585472	−	0.621308i
$971$	−18.4759	−	32.0011i	−0.592919	−	1.02697i	−0.993837	−	0.110852i	$-0.964642\pi$
$971$	−18.4759	−	32.0011i	−0.592919	−	1.02697i	0.400918	−	0.916114i	$-0.368691\pi$
$972$	14.5770	+	14.5770i	0.467558	+	0.467558i
$973$	−9.69232	−	9.69232i	−0.310721	−	0.310721i
$974$	7.28152	−	4.20399i	0.233315	−	0.134704i
$975$	−5.23579	+	1.07458i	−0.167679	+	0.0344140i
$976$	−3.59110	−	3.59110i	−0.114948	−	0.114948i
$977$	−14.7800	+	8.53326i	−0.472855	+	0.273003i	−0.717434	−	0.696626i	$-0.754684\pi$
$977$	−14.7800	+	8.53326i	−0.472855	+	0.273003i	0.244579	+	0.969629i	$0.421350\pi$
$978$	45.4913	+	12.1894i	1.45465	+	0.389773i
$979$	3.90841	−	14.5864i	0.124913	−	0.466183i
$980$	−12.9411	+	3.05893i	−0.413389	+	0.0977140i
$981$	0.366204	+	1.36669i	0.0116920	+	0.0436351i
$982$	−9.43792	+	5.44899i	−0.301176	+	0.173884i
$983$	−6.93932	+	25.8979i	−0.221330	+	0.826014i	0.762512	+	0.646974i	$0.223966\pi$
$983$	−6.93932	+	25.8979i	−0.221330	+	0.826014i	−0.983842	+	0.179040i	$0.942701\pi$
$984$	−4.29262	+	16.0203i	−0.136844	+	0.510707i
$985$	12.5292	+	0.372059i	0.399212	+	0.0118548i
$986$	5.07882	−	1.36087i	0.161743	−	0.0433388i
$987$	−22.0524	−	5.90891i	−0.701934	−	0.188083i
$988$	0.0446939	−	0.0446939i	0.00142190	−	0.00142190i
$989$	3.32984			0.105883
$990$	1.77323	−	5.91012i	0.0563568	−	0.187836i
$991$	21.3229	+	21.3229i	0.677345	+	0.677345i	0.959399	−	0.282053i	$-0.0910155\pi$
$991$	21.3229	+	21.3229i	0.677345	+	0.677345i	−0.282053	+	0.959399i	$0.591015\pi$
$992$	0.291337	+	1.08729i	0.00924997	+	0.0345214i
$993$	−41.2991			−1.31059
$994$	1.93149	+	7.20842i	0.0612632	+	0.228637i
$995$	29.2317	+	18.0545i	0.926707	+	0.572367i
$996$	−4.91997	+	8.52165i	−0.155895	+	0.270019i
$997$	4.00639	+	6.93928i	0.126884	+	0.219769i	0.922468	−	0.386074i	$-0.126169\pi$
$997$	4.00639	+	6.93928i	0.126884	+	0.219769i	−0.795584	+	0.605843i	$0.792836\pi$
$998$	−10.8657	−	10.8657i	−0.343949	−	0.343949i
$999$	3.33555	−	5.95201i	0.105532	−	0.188313i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.r.d.177.3	yes	12
5.3	odd	4		370.2.q.d.103.3	yes	12
37.23	odd	12		370.2.q.d.97.3	✓	12
185.23	even	12	inner	370.2.r.d.23.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.q.d.97.3	✓	12	37.23	odd	12
370.2.q.d.103.3	yes	12	5.3	odd	4
370.2.r.d.23.3	yes	12	185.23	even	12	inner
370.2.r.d.177.3	yes	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.r (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(2.26997 - 0.608236i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.514372 + 2.17610i) q^{5} +(1.66173 - 1.66173i) q^{6} +(-0.991227 + 0.265598i) q^{7} -1.00000i q^{8} +(2.18472 - 1.26135i) q^{9} +(1.53351 + 1.62737i) q^{10} -1.09386i q^{11} +(0.608236 - 2.26997i) q^{12} +(0.393937 + 0.227440i) q^{13} +(-0.725629 + 0.725629i) q^{14} +(2.49119 + 4.62682i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.44647 - 2.50536i) q^{17} +(1.26135 - 2.18472i) q^{18} +(0.134218 - 0.0359636i) q^{19} +(2.14175 + 0.642592i) q^{20} +(-2.08851 + 1.20580i) q^{21} +(-0.546932 - 0.947314i) q^{22} +0.390557i q^{23} +(-0.608236 - 2.26997i) q^{24} +(-4.47084 + 2.23865i) q^{25} +0.454879 q^{26} +(-0.793148 + 0.793148i) q^{27} +(-0.265598 + 0.991227i) q^{28} +(-1.28518 + 1.28518i) q^{29} +(4.47084 + 2.76135i) q^{30} +(-0.795949 - 0.795949i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-0.665327 - 2.48303i) q^{33} +(-2.50536 - 1.44647i) q^{34} +(-1.08783 - 2.02040i) q^{35} -2.52270i q^{36} +(-5.85486 + 1.64941i) q^{37} +(0.0982545 - 0.0982545i) q^{38} +(1.03256 + 0.276674i) q^{39} +(2.17610 - 0.514372i) q^{40} +(-6.11196 - 3.52874i) q^{41} +(-1.20580 + 2.08851i) q^{42} -8.52588i q^{43} +(-0.947314 - 0.546932i) q^{44} +(3.86858 + 4.10537i) q^{45} +(0.195278 + 0.338232i) q^{46} +(6.69408 + 6.69408i) q^{47} +(-1.66173 - 1.66173i) q^{48} +(-5.15019 + 2.97346i) q^{49} +(-2.75254 + 4.17415i) q^{50} +(-4.80728 - 4.80728i) q^{51} +(0.393937 - 0.227440i) q^{52} +(7.58864 + 2.03337i) q^{53} +(-0.290312 + 1.08346i) q^{54} +(2.38036 - 0.562653i) q^{55} +(0.265598 + 0.991227i) q^{56} +(0.282796 - 0.163272i) q^{57} +(-0.470410 + 1.75559i) q^{58} +(0.934291 - 3.48682i) q^{59} +(5.25254 + 0.155976i) q^{60} +(4.90553 - 1.31443i) q^{61} +(-1.08729 - 0.291337i) q^{62} +(-1.83054 + 1.83054i) q^{63} -1.00000 q^{64} +(-0.292302 + 0.974235i) q^{65} +(-1.81771 - 1.81771i) q^{66} +(3.30819 + 12.3464i) q^{67} -2.89294 q^{68} +(0.237550 + 0.886550i) q^{69} +(-1.95228 - 1.20580i) q^{70} +(3.63611 - 6.29793i) q^{71} +(-1.26135 - 2.18472i) q^{72} +(-1.40473 - 1.40473i) q^{73} +(-4.24575 + 4.35587i) q^{74} +(-8.78704 + 7.80099i) q^{75} +(0.0359636 - 0.134218i) q^{76} +(0.290529 + 1.08427i) q^{77} +(1.03256 - 0.276674i) q^{78} +(4.98605 - 1.33601i) q^{79} +(1.62737 - 1.53351i) q^{80} +(-5.10205 + 8.83700i) q^{81} -7.05749 q^{82} +(-4.04446 - 1.08371i) q^{83} +2.41160i q^{84} +(4.70789 - 4.43635i) q^{85} +(-4.26294 - 7.38363i) q^{86} +(-2.13563 + 3.69902i) q^{87} -1.09386 q^{88} +(13.3347 + 3.57303i) q^{89} +(5.40298 + 1.62107i) q^{90} +(-0.450888 - 0.120815i) q^{91} +(0.338232 + 0.195278i) q^{92} +(-2.29090 - 1.32265i) q^{93} +(9.14429 + 2.45020i) q^{94} +(0.147299 + 0.273574i) q^{95} +(-2.26997 - 0.608236i) q^{96} -11.8906 q^{97} +(-2.97346 + 5.15019i) q^{98} +(-1.37974 - 2.38979i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} + 6 q^{4} - 8 q^{5} + 6 q^{6} - 4 q^{7} - 18 q^{9} - 4 q^{10} - 6 q^{13} - 8 q^{14} - 14 q^{15} - 6 q^{16} + 12 q^{17} + 10 q^{18} + 8 q^{19} - 4 q^{20} + 54 q^{21} - 10 q^{22} - 10 q^{25}+ \cdots - 28 q^{99}+O(q^{100}) \) 12 * q + 6 * q^3 + 6 * q^4 - 8 * q^5 + 6 * q^6 - 4 * q^7 - 18 * q^9 - 4 * q^10 - 6 * q^13 - 8 * q^14 - 14 * q^15 - 6 * q^16 + 12 * q^17 + 10 * q^18 + 8 * q^19 - 4 * q^20 + 54 * q^21 - 10 * q^22 - 10 * q^25 - 18 * q^27 + 4 * q^28 - 4 * q^29 + 10 * q^30 - 2 * q^31 - 28 * q^33 - 12 * q^34 + 14 * q^35 + 12 * q^37 + 16 * q^38 + 30 * q^39 - 2 * q^40 + 12 * q^41 - 22 * q^42 - 6 * q^44 + 24 * q^45 + 2 * q^46 - 28 * q^47 - 6 * q^48 - 24 * q^49 + 16 * q^50 - 8 * q^51 - 6 * q^52 + 14 * q^53 + 18 * q^54 - 32 * q^55 - 4 * q^56 - 72 * q^57 - 10 * q^58 + 14 * q^60 + 24 * q^61 - 16 * q^62 + 8 * q^63 - 12 * q^64 - 26 * q^65 + 8 * q^66 + 18 * q^67 + 24 * q^68 + 40 * q^69 + 6 * q^70 - 10 * q^72 + 28 * q^73 - 38 * q^74 - 30 * q^75 - 8 * q^76 + 26 * q^77 + 30 * q^78 + 56 * q^79 + 4 * q^80 + 4 * q^81 - 28 * q^82 + 14 * q^83 + 28 * q^85 - 22 * q^86 - 10 * q^87 - 20 * q^88 + 2 * q^89 + 42 * q^90 + 38 * q^91 - 18 * q^92 + 18 * q^93 + 16 * q^94 - 56 * q^95 - 6 * q^96 - 44 * q^97 + 22 * q^98 - 28 * q^99

Introduction

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