LMFDB - Embedded newform 370.2.q.d.103.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [370,2,Mod(97,370)] 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("370.97"); 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([3, 5])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [12,-6,0] 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			103.3
Root			$-1.69087 + 0.453068i$ of defining polynomial
Character	$\chi$	$=$	370.103
Dual form			370.2.q.d.97.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.608236 + 2.26997i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.642592 + 2.14175i) q^{5} +(1.66173 - 1.66173i) q^{6} +(0.265598 + 0.991227i) q^{7} +1.00000 q^{8} +(-2.18472 + 1.26135i) q^{9} +(1.53351 - 1.62737i) q^{10} -1.09386i q^{11} +(-2.26997 - 0.608236i) q^{12} +(-0.227440 + 0.393937i) q^{13} +(0.725629 - 0.725629i) q^{14} +(-4.47084 + 2.76135i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.50536 + 1.44647i) q^{17} +(2.18472 + 1.26135i) q^{18} +(-0.134218 + 0.0359636i) q^{19} +(-2.17610 - 0.514372i) q^{20} +(-2.08851 + 1.20580i) q^{21} +(-0.947314 + 0.546932i) q^{22} -0.390557 q^{23} +(0.608236 + 2.26997i) q^{24} +(-4.17415 + 2.75254i) q^{25} +0.454879 q^{26} +(0.793148 + 0.793148i) q^{27} +(-0.991227 - 0.265598i) q^{28} +(1.28518 - 1.28518i) q^{29} +(4.62682 + 2.49119i) q^{30} +(-0.795949 - 0.795949i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.48303 - 0.665327i) q^{33} +(2.50536 + 1.44647i) q^{34} +(-1.95228 + 1.20580i) q^{35} -2.52270i q^{36} +(1.64941 + 5.85486i) q^{37} +(0.0982545 + 0.0982545i) q^{38} +(-1.03256 - 0.276674i) q^{39} +(0.642592 + 2.14175i) q^{40} +(-6.11196 - 3.52874i) q^{41} +(2.08851 + 1.20580i) q^{42} +8.52588 q^{43} +(0.947314 + 0.546932i) q^{44} +(-4.10537 - 3.86858i) 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} +(4.47084 + 2.23865i) q^{50} +(-4.80728 - 4.80728i) q^{51} +(-0.227440 - 0.393937i) q^{52} +(-2.03337 + 7.58864i) q^{53} +(0.290312 - 1.08346i) q^{54} +(2.34278 - 0.702908i) q^{55} +(0.265598 + 0.991227i) q^{56} +(-0.163272 - 0.282796i) q^{57} +(-1.75559 - 0.470410i) q^{58} +(-0.934291 + 3.48682i) q^{59} +(-0.155976 - 5.25254i) q^{60} +(4.90553 - 1.31443i) q^{61} +(-0.291337 + 1.08729i) q^{62} +(-1.83054 - 1.83054i) q^{63} +1.00000 q^{64} +(-0.989863 - 0.233977i) q^{65} +(-1.81771 - 1.81771i) q^{66} +(12.3464 - 3.30819i) q^{67} -2.89294i q^{68} +(-0.237550 - 0.886550i) q^{69} +(2.02040 + 1.08783i) q^{70} +(3.63611 - 6.29793i) q^{71} +(-2.18472 + 1.26135i) 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} +(1.08427 - 0.290529i) q^{77} +(0.276674 + 1.03256i) q^{78} +(-4.98605 + 1.33601i) q^{79} +(1.53351 - 1.62737i) q^{80} +(-5.10205 + 8.83700i) q^{81} +7.05749i q^{82} +(1.08371 - 4.04446i) q^{83} -2.41160i q^{84} +(-4.70789 - 4.43635i) q^{85} +(-4.26294 - 7.38363i) q^{86} +(3.69902 + 2.13563i) q^{87} -1.09386i q^{88} +(-13.3347 - 3.57303i) q^{89} +(-1.29760 + 5.48965i) q^{90} +(-0.450888 - 0.120815i) q^{91} +(0.195278 - 0.338232i) q^{92} +(1.32265 - 2.29090i) q^{93} +(-9.14429 - 2.45020i) q^{94} +(-0.163272 - 0.264351i) q^{95} +(-2.26997 - 0.608236i) q^{96} +11.8906i q^{97} +(-5.15019 - 2.97346i) q^{98} +(1.37974 + 2.38979i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 6 q^{4} + 2 q^{5} + 6 q^{6} - 4 q^{7} + 12 q^{8} + 18 q^{9} - 4 q^{10} - 6 q^{12} + 8 q^{14} - 10 q^{15} - 6 q^{16} - 12 q^{17} - 18 q^{18} - 8 q^{19} + 2 q^{20} + 54 q^{21} - 6 q^{22}+ \cdots + 28 q^{99}+O(q^{100}) $ 12 * q - 6 * q^2 - 6 * q^4 + 2 * q^5 + 6 * q^6 - 4 * q^7 + 12 * q^8 + 18 * q^9 - 4 * q^10 - 6 * q^12 + 8 * q^14 - 10 * q^15 - 6 * q^16 - 12 * q^17 - 18 * q^18 - 8 * q^19 + 2 * q^20 + 54 * q^21 - 6 * q^22 - 4 * q^23 - 14 * q^25 + 18 * q^27 - 4 * q^28 + 4 * q^29 - 4 * q^30 - 2 * q^31 - 6 * q^32 + 20 * q^33 + 12 * q^34 + 6 * q^35 + 14 * q^37 + 16 * q^38 - 30 * q^39 + 2 * q^40 + 12 * q^41 - 54 * q^42 + 44 * q^43 + 6 * q^44 - 60 * q^45 + 2 * q^46 - 28 * q^47 + 6 * q^48 + 24 * q^49 + 10 * q^50 - 8 * q^51 + 8 * q^53 - 18 * q^54 - 4 * q^56 - 28 * q^57 - 14 * q^58 + 14 * q^60 + 24 * q^61 - 14 * q^62 + 8 * q^63 + 12 * q^64 - 10 * q^65 + 8 * q^66 + 18 * q^67 - 40 * q^69 - 30 * q^70 + 18 * q^72 - 28 * q^73 + 38 * q^74 - 30 * q^75 - 8 * q^76 + 10 * q^77 + 48 * q^78 - 56 * q^79 - 4 * q^80 + 4 * q^81 + 14 * q^83 - 28 * q^85 - 22 * q^86 + 18 * q^87 - 2 * q^89 + 18 * q^90 + 38 * q^91 + 2 * q^92 - 16 * q^94 - 28 * q^95 - 6 * q^96 - 24 * q^98 + 28 * q^99

Character values

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

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.608236	+	2.26997i	0.351165	+	1.31057i	0.885242	+	0.465130i	$0.153992\pi$
$3$	0.608236	+	2.26997i	0.351165	+	1.31057i	−0.534077	+	0.845436i	$0.679341\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.642592	+	2.14175i	0.287376	+	0.957818i
$5$	0.642592	+	2.14175i	0.287376	+	0.957818i
$6$	1.66173	−	1.66173i	0.678399	−	0.678399i
$7$	0.265598	+	0.991227i	0.100387	+	0.374649i	0.997781	−	0.0665810i	$-0.0212091\pi$
$7$	0.265598	+	0.991227i	0.100387	+	0.374649i	−0.897394	+	0.441230i	$0.854542\pi$
$8$	1.00000			0.353553
$9$	−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	$-0.0527321\pi$
$12$	−2.26997	−	0.608236i	−0.655283	−	0.175583i
$13$	−0.227440	+	0.393937i	−0.0630804	+	0.109258i	−0.895841	−	0.444375i	$-0.853426\pi$
$13$	−0.227440	+	0.393937i	−0.0630804	+	0.109258i	0.832760	+	0.553633i	$0.186759\pi$
$14$	0.725629	−	0.725629i	0.193932	−	0.193932i
$15$	−4.47084	+	2.76135i	−1.15437	+	0.712977i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.50536	+	1.44647i	−0.607638	+	0.350820i	−0.772040	−	0.635573i	$-0.780764\pi$
$17$	−2.50536	+	1.44647i	−0.607638	+	0.350820i	0.164403	+	0.986393i	$0.447430\pi$
$18$	2.18472	+	1.26135i	0.514943	+	0.297303i
$19$	−0.134218	+	0.0359636i	−0.0307917	+	0.00825062i	−0.274182	−	0.961678i	$-0.588407\pi$
$19$	−0.134218	+	0.0359636i	−0.0307917	+	0.00825062i	0.243390	+	0.969928i	$0.421740\pi$
$20$	−2.17610	−	0.514372i	−0.486591	−	0.115017i
$21$	−2.08851	+	1.20580i	−0.455749	+	0.263127i
$22$	−0.947314	+	0.546932i	−0.201968	+	0.116606i
$23$	−0.390557			−0.0814367			−0.0407183	−	0.999171i	$-0.512965\pi$
$23$	−0.390557			−0.0814367			−0.0407183	+	0.999171i	$0.512965\pi$
$24$	0.608236	+	2.26997i	0.124156	+	0.463355i
$25$	−4.17415	+	2.75254i	−0.834830	+	0.550508i
$26$	0.454879			0.0892091
$27$	0.793148	+	0.793148i	0.152641	+	0.152641i
$28$	−0.991227	−	0.265598i	−0.187324	−	0.0501934i
$29$	1.28518	−	1.28518i	0.238653	−	0.238653i	−0.577639	−	0.816292i	$-0.696026\pi$
$29$	1.28518	−	1.28518i	0.238653	−	0.238653i	0.816292	+	0.577639i	$0.196026\pi$
$30$	4.62682	+	2.49119i	0.844738	+	0.454827i
$31$	−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	$0.782232\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	2.48303	−	0.665327i	0.432241	−	0.115819i
$34$	2.50536	+	1.44647i	0.429665	+	0.248067i
$35$	−1.95228	+	1.20580i	−0.329996	+	0.203817i
$36$		−	2.52270i		−	0.420450i
$37$	1.64941	+	5.85486i	0.271162	+	0.962534i
$37$	1.64941	+	5.85486i	0.271162	+	0.962534i
$38$	0.0982545	+	0.0982545i	0.0159390	+	0.0159390i
$39$	−1.03256	−	0.276674i	−0.165342	−	0.0443032i
$40$	0.642592	+	2.14175i	0.101603	+	0.338640i
$41$	−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	$0.852457\pi$
$42$	2.08851	+	1.20580i	0.322263	+	0.186059i
$43$	8.52588			1.30018			0.650092	−	0.759855i	$-0.274730\pi$
$43$	8.52588			1.30018			0.650092	+	0.759855i	$0.274730\pi$
$44$	0.947314	+	0.546932i	0.142813	+	0.0824531i
$45$	−4.10537	−	3.86858i	−0.611993	−	0.576694i
$46$	0.195278	+	0.338232i	0.0287922	+	0.0498696i
$47$	6.69408	−	6.69408i	0.976432	−	0.976432i	−0.0232961	−	0.999729i	$-0.507416\pi$
$47$	6.69408	−	6.69408i	0.976432	−	0.976432i	0.999729	+	0.0232961i	$0.00741606\pi$
$48$	1.66173	−	1.66173i	0.239850	−	0.239850i
$49$	5.15019	−	2.97346i	0.735741	−	0.424780i
$50$	4.47084	+	2.23865i	0.632273	+	0.316593i
$51$	−4.80728	−	4.80728i	−0.673154	−	0.673154i
$52$	−0.227440	−	0.393937i	−0.0315402	−	0.0546292i
$53$	−2.03337	+	7.58864i	−0.279305	+	1.04238i	0.673597	+	0.739099i	$0.264749\pi$
$53$	−2.03337	+	7.58864i	−0.279305	+	1.04238i	−0.952901	+	0.303280i	$0.901918\pi$
$54$	0.290312	−	1.08346i	0.0395065	−	0.147440i
$55$	2.34278	−	0.702908i	0.315900	−	0.0947801i
$56$	0.265598	+	0.991227i	0.0354921	+	0.132458i
$57$	−0.163272	−	0.282796i	−0.0216260	−	0.0374573i
$58$	−1.75559	−	0.470410i	−0.230521	−	0.0617679i
$59$	−0.934291	+	3.48682i	−0.121634	+	0.453946i	−0.999697	−	0.0245994i	$-0.992169\pi$
$59$	−0.934291	+	3.48682i	−0.121634	+	0.453946i	0.878063	+	0.478545i	$0.158836\pi$
$60$	−0.155976	−	5.25254i	−0.0201365	−	0.678100i
$61$	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	$0.311261\pi$
$62$	−0.291337	+	1.08729i	−0.0369999	+	0.138085i
$63$	−1.83054	−	1.83054i	−0.230627	−	0.230627i
$64$	1.00000			0.125000
$65$	−0.989863	−	0.233977i	−0.122777	−	0.0290213i
$66$	−1.81771	−	1.81771i	−0.223744	−	0.223744i
$67$	12.3464	−	3.30819i	1.50835	−	0.404160i	0.592461	−	0.805599i	$-0.298156\pi$
$67$	12.3464	−	3.30819i	1.50835	−	0.404160i	0.915886	+	0.401439i	$0.131490\pi$
$68$		−	2.89294i		−	0.350820i
$69$	−0.237550	−	0.886550i	−0.0285977	−	0.106728i
$70$	2.02040	+	1.08783i	0.241483	+	0.130020i
$71$	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	$0.0246417\pi$
$72$	−2.18472	+	1.26135i	−0.257472	+	0.148651i
$73$	1.40473	−	1.40473i	0.164411	−	0.164411i	−0.620107	−	0.784518i	$-0.712911\pi$
$73$	1.40473	−	1.40473i	0.164411	−	0.164411i	0.784518	+	0.620107i	$0.212911\pi$
$74$	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
$77$	1.08427	−	0.290529i	0.123564	−	0.0331088i
$78$	0.276674	+	1.03256i	0.0313271	+	0.116914i
$79$	−4.98605	+	1.33601i	−0.560975	+	0.150313i	−0.528154	−	0.849149i	$-0.677116\pi$
$79$	−4.98605	+	1.33601i	−0.560975	+	0.150313i	−0.0328206	+	0.999461i	$0.510449\pi$
$80$	1.53351	−	1.62737i	0.171452	−	0.181946i
$81$	−5.10205	+	8.83700i	−0.566894	+	0.981889i
$82$			7.05749i			0.779369i
$83$	1.08371	−	4.04446i	0.118953	−	0.443938i	−0.880599	−	0.473861i	$-0.842860\pi$
$83$	1.08371	−	4.04446i	0.118953	−	0.443938i	0.999552	+	0.0299237i	$0.00952644\pi$
$84$		−	2.41160i		−	0.263127i
$85$	−4.70789	−	4.43635i	−0.510642	−	0.481189i
$86$	−4.26294	−	7.38363i	−0.459685	−	0.796197i
$87$	3.69902	+	2.13563i	0.396577	+	0.228964i
$88$		−	1.09386i		−	0.116606i
$89$	−13.3347	−	3.57303i	−1.41348	−	0.378741i	−0.530314	−	0.847801i	$-0.677926\pi$
$89$	−13.3347	−	3.57303i	−1.41348	−	0.378741i	−0.883166	+	0.469061i	$0.844593\pi$
$90$	−1.29760	+	5.48965i	−0.136780	+	0.578660i
$91$	−0.450888	−	0.120815i	−0.0472660	−	0.0126649i
$92$	0.195278	−	0.338232i	0.0203592	−	0.0352631i
$93$	1.32265	−	2.29090i	0.137153	−	0.237555i
$94$	−9.14429	−	2.45020i	−0.943161	−	0.252719i
$95$	−0.163272	−	0.264351i	−0.0167514	−	0.0271219i
$96$	−2.26997	−	0.608236i	−0.231677	−	0.0620778i
$97$			11.8906i			1.20731i	0.797245	+	0.603656i	$0.206290\pi$
$97$			11.8906i			1.20731i	−0.797245	+	0.603656i	$0.793710\pi$
$98$	−5.15019	−	2.97346i	−0.520248	−	0.300365i
$99$	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	$-0.0417598\pi$
$102$	−1.75959	+	6.56687i	−0.174225	+	0.650217i
$103$		−	6.18963i		−	0.609882i	−0.952371	−	0.304941i	$-0.901363\pi$
$103$		−	6.18963i		−	0.609882i	0.952371	−	0.304941i	$-0.0986368\pi$
$104$	−0.227440	+	0.393937i	−0.0223023	+	0.0386287i
$105$	−3.92457	−	3.69821i	−0.382999	−	0.360908i
$106$	7.58864	−	2.03337i	0.737074	−	0.197498i
$107$	−1.98266	−	7.39938i	−0.191671	−	0.715325i	−0.993104	−	0.117240i	$-0.962595\pi$
$107$	−1.98266	−	7.39938i	−0.191671	−	0.715325i	0.801433	−	0.598085i	$-0.204071\pi$
$108$	−1.08346	+	0.290312i	−0.104256	+	0.0279353i
$109$	0.145164	−	0.541758i	0.0139041	−	0.0518910i	−0.958625	−	0.284671i	$-0.908116\pi$
$109$	0.145164	−	0.541758i	0.0139041	−	0.0518910i	0.972529	+	0.232780i	$0.0747823\pi$
$110$	−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
$113$	4.31602	−	2.49186i	0.406017	−	0.234414i	−0.283060	−	0.959102i	$-0.591349\pi$
$113$	4.31602	−	2.49186i	0.406017	−	0.234414i	0.689077	+	0.724688i	$0.258016\pi$
$114$	−0.163272	+	0.282796i	−0.0152919	+	0.0264863i
$115$	−0.250969	−	0.836473i	−0.0234029	−	0.0780015i
$116$	0.470410	+	1.75559i	0.0436765	+	0.163003i
$117$		−	1.14752i		−	0.106088i
$118$	3.48682	−	0.934291i	0.320988	−	0.0860085i
$119$	−2.09920	−	2.09920i	−0.192433	−	0.192433i
$120$	−4.47084	+	2.76135i	−0.408130	+	0.252075i
$121$	9.80346			0.891224
$122$	−3.59110	−	3.59110i	−0.325123	−	0.325123i
$123$	4.29262	−	16.0203i	0.387052	−	1.44450i
$124$	1.08729	−	0.291337i	0.0976412	−	0.0261629i
$125$	−8.57751	−	7.17121i	−0.767196	−	0.641413i
$126$	−0.670025	+	2.50057i	−0.0596905	+	0.222768i
$127$	20.3452	+	5.45148i	1.80535	+	0.483741i	0.994792	−	0.101924i	$-0.0324999\pi$
$127$	20.3452	+	5.45148i	1.80535	+	0.483741i	0.810553	+	0.585665i	$0.199167\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	5.18575	+	19.3535i	0.456579	+	1.70398i
$130$	0.292302	+	0.974235i	0.0256366	+	0.0854461i
$131$	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	$-0.210012\pi$
$132$	−0.665327	+	2.48303i	−0.0579093	+	0.216120i
$133$	−0.0712962	−	0.123489i	−0.00618217	−	0.0107078i
$134$	−9.03816	−	9.03816i	−0.780778	−	0.780778i
$135$	−1.18905	+	2.20839i	−0.102337	+	0.190068i
$136$	−2.50536	+	1.44647i	−0.214832	+	0.124034i
$137$	−11.0845	+	11.0845i	−0.947009	+	0.947009i	−0.998665	−	0.0516564i	$-0.983550\pi$
$137$	−11.0845	+	11.0845i	−0.947009	+	0.947009i	0.0516564	+	0.998665i	$0.483550\pi$
$138$	−0.649000	+	0.649000i	−0.0552465	+	0.0552465i
$139$	−6.67857	−	11.5676i	−0.566469	−	0.981152i	−0.996911	−	0.0785346i	$-0.974976\pi$
$139$	−6.67857	−	11.5676i	−0.566469	−	0.981152i	0.430443	−	0.902618i	$-0.358357\pi$
$140$	−0.0681103	−	2.29363i	−0.00575637	−	0.193847i
$141$	19.2669	+	11.1238i	1.62257	+	0.936790i
$142$	−7.27222			−0.610271
$143$	0.430913	+	0.248788i	0.0360348	+	0.0208047i
$144$	2.18472	+	1.26135i	0.182060	+	0.105112i
$145$	3.57839	+	1.92669i	0.297169	+	0.160003i
$146$	−1.91889	−	0.514166i	−0.158809	−	0.0425527i
$147$	9.88219	+	9.88219i	0.815069	+	0.815069i
$148$	−5.89517	−	1.49900i	−0.484580	−	0.123217i
$149$		−	2.61183i		−	0.213969i	−0.994261	−	0.106985i	$-0.965880\pi$
$149$		−	2.61183i		−	0.213969i	0.994261	−	0.106985i	$-0.0341196\pi$
$150$	−2.36234	+	11.5103i	−0.192884	+	0.939811i
$151$	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	$0.303735\pi$
$152$	−0.134218	+	0.0359636i	−0.0108865	+	0.00291704i
$153$	3.64900	−	6.32025i	0.295004	−	0.510962i
$154$	−0.793739	−	0.793739i	−0.0639613	−	0.0639613i
$155$	1.19325	−	2.21619i	0.0958441	−	0.178009i
$156$	0.755886	−	0.755886i	0.0605194	−	0.0605194i
$157$	3.09826	+	0.830175i	0.247268	+	0.0662552i	0.380324	−	0.924853i	$-0.375812\pi$
$157$	3.09826	+	0.830175i	0.247268	+	0.0662552i	−0.133056	+	0.991108i	$0.542479\pi$
$158$	3.65004	+	3.65004i	0.290382	+	0.290382i
$159$	−18.4627			−1.46419
$160$	−2.17610	−	0.514372i	−0.172036	−	0.0406647i
$161$	−0.103731	−	0.387130i	−0.00817517	−	0.0305101i
$162$	10.2041			0.801709
$163$	−17.3556	+	10.0203i	−1.35940	+	0.784847i	−0.989542	−	0.144243i	$-0.953925\pi$
$163$	−17.3556	+	10.0203i	−1.35940	+	0.784847i	−0.369853	+	0.929090i	$0.620592\pi$
$164$	6.11196	−	3.52874i	0.477264	−	0.275549i
$165$	3.02054	+	4.89049i	0.235149	+	0.380724i
$166$	−4.04446	+	1.08371i	−0.313911	+	0.0841123i
$167$	4.22666	+	2.44027i	0.327069	+	0.188833i	0.654539	−	0.756028i	$-0.272863\pi$
$167$	4.22666	+	2.44027i	0.327069	+	0.188833i	−0.327470	+	0.944862i	$0.606196\pi$
$168$	−2.08851	+	1.20580i	−0.161132	+	0.0930294i
$169$	6.39654	+	11.0791i	0.492042	+	0.852241i
$170$	−1.48804	+	6.29532i	−0.114128	+	0.482829i
$171$	0.247866	−	0.247866i	0.0189548	−	0.0189548i
$172$	−4.26294	+	7.38363i	−0.325046	+	0.562997i
$173$	15.4323	+	4.13508i	1.17330	+	0.314384i	0.792265	−	0.610177i	$-0.208902\pi$
$173$	15.4323	+	4.13508i	1.17330	+	0.314384i	0.381033	+	0.924561i	$0.375568\pi$
$174$		−	4.27126i		−	0.323803i
$175$	−3.83704	−	3.40646i	−0.290053	−	0.257504i
$176$	−0.947314	+	0.546932i	−0.0714065	+	0.0412265i
$177$	−8.48324			−0.637639
$178$	3.57303	+	13.3347i	0.267810	+	0.999481i
$179$	−8.92638	+	8.92638i	−0.667189	+	0.667189i	−0.957064	−	0.289875i	$-0.906386\pi$
$179$	−8.92638	+	8.92638i	−0.667189	+	0.667189i	0.289875	+	0.957064i	$0.406386\pi$
$180$	5.40298	−	1.62107i	0.402714	−	0.120827i
$181$	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	$-0.0565550\pi$
$182$	0.120815	+	0.450888i	0.00895542	+	0.0334221i
$183$	5.96744	+	10.3359i	0.441126	+	0.764052i
$184$	−0.390557			−0.0287922
$185$	−11.4797	+	7.29491i	−0.844007	+	0.536333i
$186$	−2.64530			−0.193963
$187$	1.58224	+	2.74052i	0.115705	+	0.200406i
$188$	2.45020	+	9.14429i	0.178700	+	0.666916i
$189$	−0.575531	+	0.996849i	−0.0418637	+	0.0725101i
$190$	−0.147299	+	0.273574i	−0.0106862	+	0.0198471i
$191$	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	$0.126379\pi$
$192$	0.608236	+	2.26997i	0.0438956	+	0.163821i
$193$	5.47453			0.394065			0.197033	−	0.980397i	$-0.436870\pi$
$193$	5.47453			0.394065			0.197033	+	0.980397i	$0.436870\pi$
$194$	10.2976	−	5.94532i	0.739325	−	0.426849i
$195$	−0.0709504	−	2.38927i	−0.00508086	−	0.171099i
$196$			5.94693i			0.424780i
$197$	−5.41467	−	1.45086i	−0.385779	−	0.103369i	0.0607164	−	0.998155i	$-0.480661\pi$
$197$	−5.41467	−	1.45086i	−0.385779	−	0.103369i	−0.446496	+	0.894786i	$0.647328\pi$
$198$	1.37974	−	2.38979i	0.0980541	−	0.169835i
$199$	−10.8649	+	10.8649i	−0.770191	+	0.770191i	−0.978140	−	0.207948i	$-0.933321\pi$
$199$	−10.8649	+	10.8649i	−0.770191	+	0.770191i	0.207948	+	0.978140i	$0.433321\pi$
$200$	−4.17415	+	2.75254i	−0.295157	+	0.194634i
$201$	15.0190	+	26.0136i	1.05936	+	1.83486i
$202$	−2.27711	+	1.31469i	−0.160217	+	0.0925011i
$203$	1.61525	+	0.932566i	0.113368	+	0.0654533i
$204$	6.56687	−	1.75959i	0.459773	−	0.123196i
$205$	3.63017	−	15.3578i	0.253542	−	1.07264i
$206$	−5.36037	+	3.09481i	−0.373475	+	0.215626i
$207$	0.853257	−	0.492628i	0.0593054	−	0.0342400i
$208$	0.454879			0.0315402
$209$	0.0393393	+	0.146816i	0.00272116	+	0.0101555i
$210$	−1.24046	+	5.24788i	−0.0855997	+	0.362138i
$211$	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
$213$	16.5077	+	4.42322i	1.13109	+	0.303074i
$214$	−5.41672	+	5.41672i	−0.370280	+	0.370280i
$215$	5.47867	+	18.2603i	0.373642	+	1.24534i
$216$	0.793148	+	0.793148i	0.0539669	+	0.0539669i
$217$	0.577563	−	1.00037i	0.0392075	−	0.0679094i
$218$	−0.541758	+	0.145164i	−0.0366925	+	0.00983172i
$219$	4.04309	+	2.33428i	0.273207	+	0.157736i
$220$	−0.562653	+	2.38036i	−0.0379340	+	0.160484i
$221$		−	1.31594i		−	0.0885194i
$222$	12.4701	+	6.98833i	0.836938	+	0.469026i
$223$	−13.3465	−	13.3465i	−0.893748	−	0.893748i	0.101126	−	0.994874i	$-0.467756\pi$
$223$	−13.3465	−	13.3465i	−0.893748	−	0.893748i	−0.994874	+	0.101126i	$0.967756\pi$
$224$	−0.991227	−	0.265598i	−0.0662291	−	0.0177460i
$225$	5.64744	−	11.2786i	0.376496	−	0.751906i
$226$	−4.31602	−	2.49186i	−0.287098	−	0.165756i
$227$	−8.86763	−	5.11973i	−0.588565	−	0.339808i	0.175965	−	0.984396i	$-0.443696\pi$
$227$	−8.86763	−	5.11973i	−0.588565	−	0.339808i	−0.764530	+	0.644588i	$0.777029\pi$
$228$	0.326545			0.0216260
$229$	0.542093	+	0.312978i	0.0358225	+	0.0206822i	0.517804	−	0.855499i	$-0.326750\pi$
$229$	0.542093	+	0.312978i	0.0358225	+	0.0206822i	−0.481982	+	0.876181i	$0.660083\pi$
$230$	−0.598923	+	0.635582i	−0.0394918	+	0.0419090i
$231$	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	$-0.816737\pi$
$233$	−4.49284	+	4.49284i	−0.294335	+	0.294335i	0.544455	+	0.838790i	$0.316737\pi$
$234$	−0.993783	+	0.573761i	−0.0649657	+	0.0375079i
$235$	18.6386	+	10.0355i	1.21585	+	0.654641i
$236$	−2.55253	−	2.55253i	−0.166156	−	0.166156i
$237$	−6.06539	−	10.5056i	−0.393989	−	0.682410i
$238$	−0.768359	+	2.86756i	−0.0498053	+	0.185876i
$239$	4.58065	−	17.0952i	0.296298	−	1.10580i	−0.643884	−	0.765123i	$-0.722678\pi$
$239$	4.58065	−	17.0952i	0.296298	−	1.10580i	0.940181	−	0.340674i	$-0.110655\pi$
$240$	4.62682	+	2.49119i	0.298660	+	0.160806i
$241$	−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	$0.954056\pi$
$242$	−4.90173	−	8.49005i	−0.315095	−	0.545761i
$243$	−19.9126	−	5.33555i	−1.27739	−	0.342276i
$244$	−1.31443	+	4.90553i	−0.0841480	+	0.314045i
$245$	9.67787	+	9.11967i	0.618297	+	0.582635i
$246$	−16.0203	+	4.29262i	−1.02141	+	0.273687i
$247$	0.0163591	−	0.0610530i	0.00104090	−	0.00388471i
$248$	−0.795949	−	0.795949i	−0.0505428	−	0.0505428i
$249$	9.83995			0.623581
$250$	−1.92169	+	11.0140i	−0.121539	+	0.696583i
$251$	−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	$0.999718\pi$
$252$	2.50057	−	0.670025i	0.157521	−	0.0422076i
$253$			0.427216i			0.0268588i
$254$	−5.45148	−	20.3452i	−0.342056	−	1.27657i
$255$	7.20685	−	13.3851i	0.451310	−	0.838207i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−18.9356	+	10.9325i	−1.18117	+	0.681949i	−0.956285	−	0.292436i	$-0.905534\pi$
$257$	−18.9356	+	10.9325i	−1.18117	+	0.681949i	−0.224886	+	0.974385i	$0.572201\pi$
$258$	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
$262$	−17.6126	+	4.71929i	−1.08811	+	0.291559i
$263$	−2.22756	−	8.31336i	−0.137357	−	0.512624i	−0.999977	−	0.00677111i	$-0.997845\pi$
$263$	−2.22756	−	8.31336i	−0.137357	−	0.512624i	0.862620	−	0.505852i	$-0.168822\pi$
$264$	2.48303	−	0.665327i	0.152820	−	0.0409480i
$265$	−17.5596	+	0.521439i	−1.07868	+	0.0320317i
$266$	−0.0712962	+	0.123489i	−0.00437145	+	0.00757158i
$267$		−	32.4427i		−	1.98546i
$268$	−3.30819	+	12.3464i	−0.202080	+	0.754173i
$269$			5.72668i			0.349162i	0.984643	+	0.174581i	$0.0558570\pi$
$269$			5.72668i			0.349162i	−0.984643	+	0.174581i	$0.944143\pi$
$270$	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	$0.769044\pi$
$272$	2.50536	+	1.44647i	0.151909	+	0.0877050i
$273$		−	1.09699i		−	0.0663926i
$274$	15.1416	+	4.05719i	0.914740	+	0.245104i
$275$	3.01090	+	4.56595i	0.181564	+	0.275337i
$276$	0.886550	+	0.237550i	0.0533641	+	0.0142989i
$277$	−4.44783	+	7.70387i	−0.267244	+	0.462881i	−0.968149	−	0.250374i	$-0.919446\pi$
$277$	−4.44783	+	7.70387i	−0.267244	+	0.462881i	0.700905	+	0.713255i	$0.252780\pi$
$278$	−6.67857	+	11.5676i	−0.400554	+	0.693780i
$279$	2.74289	+	0.734956i	0.164213	+	0.0440007i
$280$	−1.95228	+	1.20580i	−0.116671	+	0.0720603i
$281$	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	$0.567667\pi$
$282$		−	22.2475i		−	1.32482i
$283$	−28.2496	−	16.3099i	−1.67926	−	0.969522i	−0.962133	−	0.272582i	$-0.912122\pi$
$283$	−28.2496	−	16.3099i	−1.67926	−	0.969522i	−0.717129	−	0.696940i	$-0.754544\pi$
$284$	3.63611	+	6.29793i	0.215763	+	0.373713i
$285$	0.500760	−	0.531411i	0.0296625	−	0.0314781i
$286$		−	0.497576i		−	0.0294223i
$287$	1.87446	−	6.99557i	0.110646	−	0.412936i
$288$		−	2.52270i		−	0.148651i
$289$	−4.31546	+	7.47460i	−0.253851	+	0.439682i
$290$	−0.120632	−	4.06232i	−0.00708378	−	0.238548i
$291$	−26.9914	+	7.23232i	−1.58226	+	0.423966i
$292$	0.514166	+	1.91889i	0.0300893	+	0.112295i
$293$	−23.1842	+	6.21218i	−1.35443	+	0.362919i	−0.861769	−	0.507300i	$-0.830643\pi$
$293$	−23.1842	+	6.21218i	−1.35443	+	0.362919i	−0.492664	+	0.870220i	$0.663977\pi$
$294$	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
$298$	−2.26191	+	1.30592i	−0.131029	+	0.0756496i
$299$	0.0888280	−	0.153855i	0.00513706	−	0.00889764i
$300$	11.1494	−	3.70930i	0.643709	−	0.214157i
$301$	2.26446	+	8.45108i	0.130521	+	0.487112i
$302$		−	22.3328i		−	1.28511i
$303$	5.96860	−	1.59928i	0.342887	−	0.0918763i
$304$	0.0982545	+	0.0982545i	0.00563528	+	0.00563528i
$305$	5.96744	+	9.66176i	0.341695	+	0.553231i
$306$	−7.29800			−0.417199
$307$	−14.2681	−	14.2681i	−0.814321	−	0.814321i	0.170957	−	0.985278i	$-0.445314\pi$
$307$	−14.2681	−	14.2681i	−0.814321	−	0.814321i	−0.985278	+	0.170957i	$0.945314\pi$
$308$	−0.290529	+	1.08427i	−0.0165544	+	0.0617819i
$309$	14.0502	−	3.76475i	0.799291	−	0.214169i
$310$	−2.51590	+	0.0747108i	−0.142894	+	0.00424329i
$311$	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	$0.0141930\pi$
$312$	−1.03256	−	0.276674i	−0.0584572	−	0.0156636i
$313$	−16.2812	−	28.1999i	−0.920270	−	1.59395i	−0.798997	−	0.601335i	$-0.794636\pi$
$313$	−16.2812	−	28.1999i	−0.920270	−	1.59395i	−0.121273	−	0.992619i	$-0.538698\pi$
$314$	−0.830175	−	3.09826i	−0.0468495	−	0.174845i
$315$	2.74426	−	5.09685i	0.154622	−	0.287175i
$316$	1.33601	−	4.98605i	0.0751564	−	0.280487i
$317$	6.76893	−	25.2620i	0.380181	−	1.41885i	−0.465444	−	0.885077i	$-0.654106\pi$
$317$	6.76893	−	25.2620i	0.380181	−	1.41885i	0.845625	−	0.533777i	$-0.179228\pi$
$318$	9.23136	+	15.9892i	0.517669	+	0.896629i
$319$	−1.40582	−	1.40582i	−0.0787106	−	0.0787106i
$320$	0.642592	+	2.14175i	0.0359220	+	0.119727i
$321$	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
$325$	−0.134959	−	2.27039i	−0.00748620	−	0.125938i
$326$	17.3556	+	10.0203i	0.961238	+	0.554971i
$327$	1.31807			0.0728892
$328$	−6.11196	−	3.52874i	−0.337477	−	0.194842i
$329$	8.41330	+	4.85742i	0.463840	+	0.267798i
$330$	2.72502	−	5.06111i	0.150008	−	0.278605i
$331$	−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
$333$	−10.9885	−	10.7108i	−0.602168	−	0.586946i
$334$		−	4.88053i		−	0.267051i
$335$	15.0190	+	24.3169i	0.820575	+	1.32858i
$336$	2.08851	+	1.20580i	0.113937	+	0.0657817i
$337$	−21.2283	+	5.68810i	−1.15638	+	0.309851i	−0.785519	−	0.618838i	$-0.787604\pi$
$337$	−21.2283	+	5.68810i	−1.15638	+	0.309851i	−0.370860	+	0.928689i	$0.620937\pi$
$338$	6.39654	−	11.0791i	0.347926	−	0.602626i
$339$	8.28159	+	8.28159i	0.449794	+	0.449794i
$340$	6.19593	−	1.85898i	0.336022	−	0.100817i
$341$	−0.870660	+	0.870660i	−0.0471489	+	0.0471489i
$342$	−0.338592	−	0.0907254i	−0.0183089	−	0.00490587i
$343$	9.39466	+	9.39466i	0.507264	+	0.507264i
$344$	8.52588			0.459685
$345$	1.74612	−	1.07846i	0.0940078	−	0.0580625i
$346$	−4.13508	−	15.4323i	−0.222303	−	0.829647i
$347$	12.3387			0.662377			0.331189	−	0.943565i	$-0.392550\pi$
$347$	12.3387			0.662377			0.331189	+	0.943565i	$0.392550\pi$
$348$	−3.69902	+	2.13563i	−0.198288	+	0.114482i
$349$	19.7732	−	11.4160i	1.05843	−	0.611087i	0.133435	−	0.991058i	$-0.457399\pi$
$349$	19.7732	−	11.4160i	1.05843	−	0.611087i	0.924999	+	0.379971i	$0.124066\pi$
$350$	−1.03156	+	5.02620i	−0.0551393	+	0.268662i
$351$	−0.492844	+	0.132057i	−0.0263061	+	0.00704869i
$352$	0.947314	+	0.546932i	0.0504920	+	0.0291516i
$353$	−14.7854	+	8.53634i	−0.786946	+	0.454343i	−0.838886	−	0.544307i	$-0.816793\pi$
$353$	−14.7854	+	8.53634i	−0.786946	+	0.454343i	0.0519405	+	0.998650i	$0.483459\pi$
$354$	4.24162	+	7.34670i	0.225439	+	0.390473i
$355$	15.8251	+	3.74062i	0.839909	+	0.198532i
$356$	9.76171	−	9.76171i	0.517369	−	0.517369i
$357$	3.48830	−	6.04191i	0.184620	−	0.319772i
$358$	12.1937	+	3.26728i	0.644455	+	0.172681i
$359$			20.3975i			1.07654i	0.842773	+	0.538269i	$0.180922\pi$
$359$			20.3975i			1.07654i	−0.842773	+	0.538269i	$0.819078\pi$
$360$	−4.10537	−	3.86858i	−0.216372	−	0.203892i
$361$	−16.4378	+	9.49035i	−0.865145	+	0.499492i
$362$	−17.3603			−0.912436
$363$	5.96281	+	22.2535i	0.312967	+	1.16801i
$364$	0.330073	−	0.330073i	0.0173005	−	0.0173005i
$365$	3.91123	+	2.10590i	0.204723	+	0.110228i
$366$	5.96744	−	10.3359i	0.311923	−	0.540267i
$367$	3.45216	+	12.8836i	0.180201	+	0.672521i	0.995607	+	0.0936308i	$0.0298473\pi$
$367$	3.45216	+	12.8836i	0.180201	+	0.672521i	−0.815406	+	0.578890i	$0.803486\pi$
$368$	0.195278	+	0.338232i	0.0101796	+	0.0176316i
$369$	17.8039			0.926834
$370$	12.0574	+	6.29428i	0.626837	+	0.327224i
$371$	−8.06212			−0.418565
$372$	1.32265	+	2.29090i	0.0685763	+	0.118778i
$373$	−4.51612	−	16.8544i	−0.233836	−	0.872688i	−0.978670	−	0.205438i	$-0.934138\pi$
$373$	−4.51612	−	16.8544i	−0.233836	−	0.872688i	0.744834	−	0.667250i	$-0.232529\pi$
$374$	1.58224	−	2.74052i	0.0818156	−	0.141709i
$375$	11.0613	−	23.8325i	0.571201	−	1.23070i
$376$	6.69408	−	6.69408i	0.345221	−	0.345221i
$377$	0.213980	+	0.798583i	0.0110205	+	0.0411291i
$378$	1.15106			0.0592043
$379$	21.7843	−	12.5772i	1.11898	−	0.646045i	0.177842	−	0.984059i	$-0.443089\pi$
$379$	21.7843	−	12.5772i	1.11898	−	0.646045i	0.941141	+	0.338014i	$0.109755\pi$
$380$	0.310571	−	0.00922254i	0.0159320	−	0.000473106i
$381$			49.4987i			2.53590i
$382$	−10.1102	−	2.70902i	−0.517284	−	0.138606i
$383$	−5.36863	+	9.29874i	−0.274324	+	0.475143i	−0.969964	−	0.243247i	$-0.921787\pi$
$383$	−5.36863	+	9.29874i	−0.274324	+	0.475143i	0.695640	+	0.718390i	$0.255121\pi$
$384$	1.66173	−	1.66173i	0.0847998	−	0.0847998i
$385$	1.31898	+	2.13553i	0.0672215	+	0.108837i
$386$	−2.73726	−	4.74108i	−0.139323	−	0.241315i
$387$	−18.6267	+	10.7541i	−0.946847	+	0.546662i
$388$	−10.2976	−	5.94532i	−0.522782	−	0.301828i
$389$	29.4549	−	7.89241i	1.49342	−	0.400161i	0.582531	−	0.812808i	$-0.302062\pi$
$389$	29.4549	−	7.89241i	1.49342	−	0.400161i	0.910891	+	0.412647i	$0.135396\pi$
$390$	−2.03369	+	1.25608i	−0.102980	+	0.0636041i
$391$	0.978483	−	0.564927i	0.0494840	−	0.0285696i
$392$	5.15019	−	2.97346i	0.260124	−	0.150183i
$393$	42.8505			2.16152
$394$	1.45086	+	5.41467i	0.0730931	+	0.272787i
$395$	−6.06539	−	9.82035i	−0.305183	−	0.494115i
$396$	−2.75949			−0.138669
$397$	14.1042	+	14.1042i	0.707867	+	0.707867i	0.966086	−	0.258219i	$-0.0831356\pi$
$397$	14.1042	+	14.1042i	0.707867	+	0.707867i	−0.258219	+	0.966086i	$0.583136\pi$
$398$	14.8417	+	3.97682i	0.743948	+	0.199340i
$399$	0.236950	−	0.236950i	0.0118624	−	0.0118624i
$400$	4.47084	+	2.23865i	0.223542	+	0.111933i
$401$	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	$0.640269\pi$
$402$	15.0190	−	26.0136i	0.749079	−	1.29744i
$403$	0.494584	−	0.132523i	0.0246370	−	0.00660146i
$404$	2.27711	+	1.31469i	0.113290	+	0.0654082i
$405$	−22.2051	−	5.24870i	−1.10338	−	0.260810i
$406$		−	1.86513i		−	0.0925650i
$407$	6.40442	−	1.80423i	0.317456	−	0.0894325i
$408$	−4.80728	−	4.80728i	−0.237996	−	0.237996i
$409$	−26.7076	−	7.15628i	−1.32061	−	0.353855i	−0.471401	−	0.881919i	$-0.656251\pi$
$409$	−26.7076	−	7.15628i	−1.32061	−	0.353855i	−0.849205	+	0.528064i	$0.822918\pi$
$410$	−15.1153	+	4.53509i	−0.746494	+	0.223972i
$411$	−31.9033	−	18.4194i	−1.57367	−	0.908561i
$412$	5.36037	+	3.09481i	0.264087	+	0.152471i
$413$	−3.70438			−0.182281
$414$	−0.853257	−	0.492628i	−0.0419353	−	0.0242113i
$415$	9.35860	−	0.277908i	0.459396	−	0.0136420i
$416$	−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	−0.517782	−	0.855513i	$-0.673242\pi$
$419$	−0.732348	+	0.422822i	−0.0357776	+	0.0206562i	0.482005	+	0.876169i	$0.339909\pi$
$420$	5.16503	−	1.54967i	0.252028	−	0.0756164i
$421$	−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	$0.805236\pi$
$422$	−2.30813	−	3.99779i	−0.112358	−	0.194609i
$423$	−6.18112	+	23.0683i	−0.300537	+	1.12162i
$424$	−2.03337	+	7.58864i	−0.0987491	+	0.368537i
$425$	6.47627	−	12.9339i	0.314145	−	0.627384i
$426$	−4.42322	−	16.5077i	−0.214306	−	0.799800i
$427$	2.60580	+	4.51339i	0.126104	+	0.218418i
$428$	7.39938	+	1.98266i	0.357663	+	0.0958354i
$429$	−0.302643	+	1.12948i	−0.0146118	+	0.0545318i
$430$	13.0745	−	13.8748i	0.630510	−	0.669102i
$431$	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	$0.291571\pi$
$432$	0.290312	−	1.08346i	0.0139677	−	0.0521280i
$433$	−19.2276	−	19.2276i	−0.924022	−	0.924022i	0.0732891	−	0.997311i	$-0.476650\pi$
$433$	−19.2276	−	19.2276i	−0.924022	−	0.924022i	−0.997311	+	0.0732891i	$0.976650\pi$
$434$	−1.15513			−0.0554478
$435$	−2.19702	+	9.29470i	−0.105339	+	0.445647i
$436$	0.396594	+	0.396594i	0.0189934	+	0.0189934i
$437$	0.0524198	−	0.0140458i	0.00250758	−	0.000671903i
$438$		−	4.66856i		−	0.223072i
$439$	0.975860	+	3.64196i	0.0465752	+	0.173821i	0.985296	−	0.170859i	$-0.0546542\pi$
$439$	0.975860	+	3.64196i	0.0465752	+	0.173821i	−0.938720	+	0.344680i	$0.887987\pi$
$440$	2.34278	−	0.702908i	0.111688	−	0.0335098i
$441$	−7.50115	+	12.9924i	−0.357198	+	0.618684i
$442$	−1.13963	+	0.657968i	−0.0542068	+	0.0312963i
$443$	−16.0819	+	16.0819i	−0.764074	+	0.764074i	−0.977056	−	0.212982i	$-0.931682\pi$
$443$	−16.0819	+	16.0819i	−0.764074	+	0.764074i	0.212982	+	0.977056i	$0.431682\pi$
$444$	−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
$447$	5.92877	−	1.58861i	0.280421	−	0.0751386i
$448$	0.265598	+	0.991227i	0.0125483	+	0.0468311i
$449$	3.02946	−	0.811742i	0.142969	−	0.0383085i	−0.186625	−	0.982431i	$-0.559755\pi$
$449$	3.02946	−	0.811742i	0.142969	−	0.0383085i	0.329594	+	0.944123i	$0.393088\pi$
$450$	−12.5913	+	0.748466i	−0.593558	+	0.0352830i
$451$	−3.85996	+	6.68566i	−0.181759	+	0.314815i
$452$			4.98372i			0.234414i
$453$	−13.5836	+	50.6948i	−0.638215	+	2.38185i
$454$			10.2395i			0.480562i
$455$	−0.0309819	−	1.04332i	−0.00145246	−	0.0489118i
$456$	−0.163272	−	0.282796i	−0.00764593	−	0.0132431i
$457$	−31.9599	−	18.4520i	−1.49502	−	0.863150i	−0.495036	−	0.868872i	$-0.664845\pi$
$457$	−31.9599	−	18.4520i	−1.49502	−	0.863150i	−0.999984	+	0.00572214i	$0.998179\pi$
$458$		−	0.625956i		−	0.0292490i
$459$	−3.13438	−	0.839855i	−0.146300	−	0.0392011i
$460$	0.849891	+	0.200891i	0.0396264	+	0.00936660i
$461$	−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	$0.777743\pi$
$462$	1.31898	−	2.28454i	0.0613645	−	0.106286i
$463$	−0.812285	+	1.40692i	−0.0377501	+	0.0653850i	−0.884283	−	0.466951i	$-0.845352\pi$
$463$	−0.812285	+	1.40692i	−0.0377501	+	0.0653850i	0.846533	+	0.532336i	$0.178686\pi$
$464$	−1.75559	−	0.470410i	−0.0815014	−	0.0218382i
$465$	5.75645	+	1.36067i	0.266949	+	0.0630996i
$466$	6.13733	+	1.64449i	0.284306	+	0.0761796i
$467$			30.6174i			1.41680i	0.705810	+	0.708401i	$0.250583\pi$
$467$			30.6174i			1.41680i	−0.705810	+	0.708401i	$0.749417\pi$
$468$	0.993783	+	0.573761i	0.0459377	+	0.0265221i
$469$	6.55834	+	11.3594i	0.302836	+	0.524528i
$470$	−0.628332	−	21.1592i	−0.0289828	−	0.976002i
$471$			7.53788i			0.347327i
$472$	−0.934291	+	3.48682i	−0.0430042	+	0.160494i
$473$		−	9.32615i		−	0.428817i
$474$	−6.06539	+	10.5056i	−0.278593	+	0.482537i
$475$	0.461255	−	0.519558i	0.0211638	−	0.0238390i
$476$	2.86756	−	0.768359i	0.131434	−	0.0352177i
$477$	−5.12958	−	19.1438i	−0.234867	−	0.876536i
$478$	−17.0952	+	4.58065i	−0.781917	+	0.209514i
$479$	1.07888	−	4.02643i	0.0492952	−	0.183972i	−0.936888	−	0.349629i	$-0.886308\pi$
$479$	1.07888	−	4.02643i	0.0492952	−	0.183972i	0.986183	+	0.165657i	$0.0529743\pi$
$480$	−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
$483$	0.815680	−	0.470933i	0.0371147	−	0.0214282i
$484$	−4.90173	+	8.49005i	−0.222806	+	0.385911i
$485$	−25.4667	+	7.64084i	−1.15639	+	0.346953i
$486$	5.33555	+	19.9126i	0.242026	+	0.903252i
$487$		−	8.40797i		−	0.381002i	−0.981687	−	0.190501i	$-0.938989\pi$
$487$		−	8.40797i		−	0.381002i	0.981687	−	0.190501i	$-0.0610112\pi$
$488$	4.90553	−	1.31443i	0.222063	−	0.0595016i
$489$	−33.3019	−	33.3019i	−1.50597	−	1.50597i
$490$	3.05893	−	12.9411i	0.138188	−	0.584620i
$491$	−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
$493$	−1.36087	+	5.07882i	−0.0612903	+	0.228739i
$494$	−0.0610530	+	0.0163591i	−0.00274690	+	0.000736031i
$495$	−4.23170	+	4.49072i	−0.190201	+	0.201843i
$496$	−0.291337	+	1.08729i	−0.0130814	+	0.0488206i
$497$	7.20842	+	1.93149i	0.323342	+	0.0866392i
$498$	−4.91997	−	8.52165i	−0.220469	−	0.381864i
$499$	3.97714	+	14.8429i	0.178041	+	0.664459i	0.996014	+	0.0892013i	$0.0284315\pi$
$499$	3.97714	+	14.8429i	0.178041	+	0.664459i	−0.817972	+	0.575257i	$0.804902\pi$
$500$	10.4992	−	3.84274i	0.469539	−	0.171853i
$501$	−2.96851	+	11.0786i	−0.132623	+	0.494957i
$502$	−5.79379	+	21.6227i	−0.258589	+	0.965068i
$503$	16.2062	+	28.0700i	0.722600	+	1.25158i	0.959954	+	0.280156i	$0.0903862\pi$
$503$	16.2062	+	28.0700i	0.722600	+	1.25158i	−0.237355	+	0.971423i	$0.576280\pi$
$504$	−1.83054	−	1.83054i	−0.0815388	−	0.0815388i
$505$	5.63146	−	1.68962i	0.250597	−	0.0751870i
$506$	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	$-0.895820\pi$
$509$	−16.9629	−	29.3806i	−0.751867	−	1.30227i	0.195050	−	0.980793i	$-0.437513\pi$
$510$	−15.1953	+	0.451230i	−0.672857	+	0.0199808i
$511$	1.76550	+	1.01931i	0.0781010	+	0.0450916i
$512$	1.00000			0.0441942
$513$	−0.134979	−	0.0779304i	−0.00595949	−	0.00344071i
$514$	18.9356	+	10.9325i	0.835214	+	0.482211i
$515$	13.2566	−	3.97741i	0.584156	−	0.175265i
$516$	−19.3535	−	5.18575i	−0.851989	−	0.228290i
$517$	−7.32242	−	7.32242i	−0.322039	−	0.322039i
$518$	5.44532	+	3.05160i	0.239254	+	0.134079i
$519$			37.5460i			1.64809i
$520$	−0.989863	−	0.233977i	−0.0434084	−	0.0102606i
$521$	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	$0.612989\pi$
$522$	4.42883	−	1.18670i	0.193845	−	0.0519406i
$523$	6.03193	−	10.4476i	0.263758	−	0.456842i	−0.703479	−	0.710716i	$-0.748371\pi$
$523$	6.03193	−	10.4476i	0.263758	−	0.456842i	0.967237	+	0.253873i	$0.0817046\pi$
$524$	12.8933	+	12.8933i	0.563248	+	0.563248i
$525$	5.39873	−	10.7819i	0.235620	−	0.470560i
$526$	−6.08580	+	6.08580i	−0.265354	+	0.265354i
$527$	3.14545	+	0.842820i	0.137018	+	0.0367138i
$528$	−1.81771	−	1.81771i	−0.0791055	−	0.0791055i
$529$	−22.8475			−0.993368
$530$	9.23136	+	14.9463i	0.400985	+	0.649226i
$531$	−2.35693	−	8.79620i	−0.102282	−	0.381722i
$532$	0.142592			0.00618217
$533$	2.78020	−	1.60515i	0.120424	−	0.0695268i
$534$	−28.0962	+	16.2213i	−1.21584	+	0.701965i
$535$	14.5736	−	9.00114i	0.630070	−	0.389153i
$536$	12.3464	−	3.30819i	0.533281	−	0.142892i
$537$	−25.6919	−	14.8332i	−1.10869	−	0.640102i
$538$	4.95945	−	2.86334i	0.213817	−	0.123447i
$539$	−3.25256	−	5.63361i	−0.140098	−	0.242657i
$540$	−1.31800	−	2.13395i	−0.0567176	−	0.0918304i
$541$	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	$0.00625705\pi$
$542$	3.30228	−	5.71972i	0.141845	−	0.245683i
$543$	39.4073	+	10.5591i	1.69113	+	0.453136i
$544$		−	2.89294i		−	0.124034i
$545$	1.25359	−	0.0372259i	0.0536978	−	0.00159458i
$546$	−0.950017	+	0.548493i	−0.0406570	+	0.0234733i
$547$	32.5413			1.39137			0.695683	−	0.718349i	$-0.255102\pi$
$547$	32.5413			1.39137			0.695683	+	0.718349i	$0.255102\pi$
$548$	−4.05719	−	15.1416i	−0.173315	−	0.646819i
$549$	−9.05926	+	9.05926i	−0.386640	+	0.386640i
$550$	2.44878	−	4.89049i	0.104416	−	0.208531i
$551$	−0.126275	+	0.218715i	−0.00537950	+	0.00931757i
$552$	−0.237550	−	0.886550i	−0.0101108	−	0.0377341i
$553$	−2.64858	−	4.58747i	−0.112629	−	0.195079i
$554$	8.89566			0.377940
$555$	−23.5416	−	21.6216i	−0.999285	−	0.917785i
$556$	13.3571			0.566469
$557$	−2.04900	−	3.54898i	−0.0868190	−	0.150375i	0.819346	−	0.573300i	$-0.194337\pi$
$557$	−2.04900	−	3.54898i	−0.0868190	−	0.150375i	−0.906165	+	0.422925i	$0.861004\pi$
$558$	−0.734956	−	2.74289i	−0.0311132	−	0.116116i
$559$	−1.93912	+	3.35866i	−0.0820162	+	0.142056i
$560$	2.02040	+	1.08783i	0.0853773	+	0.0459692i
$561$	−5.25851	+	5.25851i	−0.222014	+	0.222014i
$562$	−0.426903	−	1.59322i	−0.0180078	−	0.0672061i
$563$	38.2228			1.61090			0.805449	−	0.592665i	$-0.201924\pi$
$563$	38.2228			1.61090			0.805449	+	0.592665i	$0.201924\pi$
$564$	−19.2669	+	11.1238i	−0.811284	+	0.468395i
$565$	8.11037	+	7.64258i	0.341206	+	0.321526i
$566$			32.6198i			1.37111i
$567$	−10.1146	−	2.71019i	−0.424772	−	0.113817i
$568$	3.63611	−	6.29793i	0.152568	−	0.264255i
$569$	−5.18626	+	5.18626i	−0.217420	+	0.217420i	−0.807410	−	0.589991i	$-0.799131\pi$
$569$	−5.18626	+	5.18626i	−0.217420	+	0.217420i	0.589991	+	0.807410i	$0.299131\pi$
$570$	−0.710595	−	0.167965i	−0.0297636	−	0.00703530i
$571$	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	$0.814192\pi$
$572$	−0.430913	+	0.248788i	−0.0180174	+	0.0104023i
$573$	21.3021	+	12.2988i	0.889909	+	0.513789i
$574$	−6.99557	+	1.87446i	−0.291990	+	0.0782384i
$575$	1.63024	−	1.07502i	0.0679858	−	0.0448315i
$576$	−2.18472	+	1.26135i	−0.0910300	+	0.0525562i
$577$	28.7785	−	16.6152i	1.19806	−	0.691702i	0.237940	−	0.971280i	$-0.423528\pi$
$577$	28.7785	−	16.6152i	1.19806	−	0.691702i	0.960123	+	0.279578i	$0.0901946\pi$
$578$	8.63093			0.358999
$579$	3.32980	+	12.4270i	0.138382	+	0.516448i
$580$	−3.45776	+	2.13563i	−0.143575	+	0.0886772i
$581$	4.29681			0.178262
$582$	19.7591	+	19.7591i	0.819039	+	0.819039i
$583$	8.30094	+	2.22423i	0.343790	+	0.0921182i
$584$	1.40473	−	1.40473i	0.0581280	−	0.0581280i
$585$	2.45770	−	0.737389i	0.101613	−	0.0304873i
$586$	16.9720	+	16.9720i	0.701106	+	0.701106i
$587$	−2.92762	+	5.07079i	−0.120836	+	0.209294i	−0.920098	−	0.391689i	$-0.871891\pi$
$587$	−2.92762	+	5.07079i	−0.120836	+	0.209294i	0.799262	+	0.600983i	$0.205224\pi$
$588$	−13.4993	+	3.61713i	−0.556703	+	0.149168i
$589$	0.135456	+	0.0782055i	0.00558136	+	0.00322240i
$590$	4.24162	+	6.86752i	0.174625	+	0.282731i
$591$		−	13.1736i		−	0.541889i
$592$	4.24575	−	4.35587i	0.174499	−	0.179025i
$593$	−6.25765	−	6.25765i	−0.256971	−	0.256971i	0.566850	−	0.823821i	$-0.308162\pi$
$593$	−6.25765	−	6.25765i	−0.256971	−	0.256971i	−0.823821	+	0.566850i	$0.808162\pi$
$594$	−1.18516	−	0.317562i	−0.0486277	−	0.0130297i
$595$	3.14702	−	5.84487i	0.129015	−	0.239616i
$596$	2.26191	+	1.30592i	0.0926515	+	0.0534924i
$597$	−31.2713	−	18.0545i	−1.27985	−	0.738922i
$598$	−0.177656			−0.00726489
$599$	−10.8652	−	6.27302i	−0.443940	−	0.256309i	0.261328	−	0.965250i	$-0.415840\pi$
$599$	−10.8652	−	6.27302i	−0.443940	−	0.256309i	−0.705267	+	0.708941i	$0.749173\pi$
$600$	−8.78704	−	7.80099i	−0.358729	−	0.318474i
$601$	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
$605$	6.29963	+	20.9965i	0.256116	+	0.853630i
$606$	−4.36932	−	4.36932i	−0.177491	−	0.177491i
$607$	0.390284	+	0.675992i	0.0158412	+	0.0274377i	0.873837	−	0.486218i	$-0.161624\pi$
$607$	0.390284	+	0.675992i	0.0158412	+	0.0274377i	−0.857996	+	0.513656i	$0.828291\pi$
$608$	0.0359636	−	0.134218i	0.00145852	−	0.00544326i
$609$	−1.13444	+	4.23379i	−0.0459698	+	0.171562i
$610$	5.38361	−	9.99884i	0.217976	−	0.404841i
$611$	1.11455	+	4.15955i	0.0450897	+	0.168277i
$612$	3.64900	+	6.32025i	0.147502	+	0.255481i
$613$	−20.8106	−	5.57619i	−0.840533	−	0.225220i	−0.187229	−	0.982316i	$-0.559951\pi$
$613$	−20.8106	−	5.57619i	−0.840533	−	0.225220i	−0.653304	+	0.757096i	$0.726617\pi$
$614$	−5.22247	+	19.4905i	−0.210762	+	0.786574i
$615$	37.0697	−	1.10080i	1.49480	−	0.0443886i
$616$	1.08427	−	0.290529i	0.0436864	−	0.0117057i
$617$	6.21897	−	23.2095i	0.250366	−	0.934380i	−0.720243	−	0.693722i	$-0.755970\pi$
$617$	6.21897	−	23.2095i	0.250366	−	0.934380i	0.970610	−	0.240659i	$-0.0773635\pi$
$618$	−10.2855	−	10.2855i	−0.413743	−	0.413743i
$619$	6.63573			0.266713			0.133356	−	0.991068i	$-0.457425\pi$
$619$	6.63573			0.266713			0.133356	+	0.991068i	$0.457425\pi$
$620$	1.32265	+	2.14148i	0.0531190	+	0.0860039i
$621$	−0.309769	−	0.309769i	−0.0124306	−	0.0124306i
$622$	−7.34201	+	1.96729i	−0.294388	+	0.0788810i
$623$		−	14.1667i		−	0.567579i
$624$	0.276674	+	1.03256i	0.0110758	+	0.0413355i
$625$	9.84707	−	22.9790i	0.393883	−	0.919161i
$626$	−16.2812	+	28.1999i	−0.650729	+	1.12710i
$627$	−0.309341	+	0.178598i	−0.0123539	+	0.00713251i
$628$	−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	$0.153110\pi$
$632$	−4.98605	+	1.33601i	−0.198335	+	0.0531436i
$633$	2.80777	+	10.4787i	0.111599	+	0.416492i
$634$	−25.2620	+	6.76893i	−1.00328	+	0.268828i
$635$	1.39798	+	47.0773i	0.0554772	+	1.86821i
$636$	9.23136	−	15.9892i	0.366047	−	0.634012i
$637$			2.70513i			0.107181i
$638$	−0.514565	+	1.92038i	−0.0203718	+	0.0760286i
$639$			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	$0.516456\pi$
$642$	−15.5904	−	9.00114i	−0.615305	−	0.355246i
$643$			18.2603i			0.720117i	0.932930	+	0.360058i	$0.117243\pi$
$643$			18.2603i			0.720117i	−0.932930	+	0.360058i	$0.882757\pi$
$644$	0.387130	+	0.103731i	0.0152551	+	0.00408758i
$645$	−38.1179	+	23.5429i	−1.50089	+	0.927002i
$646$	−0.388284	−	0.104040i	−0.0152768	−	0.00409342i
$647$	6.92548	−	11.9953i	0.272269	−	0.471583i	−0.697174	−	0.716902i	$-0.745559\pi$
$647$	6.92548	−	11.9953i	0.272269	−	0.471583i	0.969442	+	0.245319i	$0.0788927\pi$
$648$	−5.10205	+	8.83700i	−0.200427	+	0.347150i
$649$	3.81411	+	1.02199i	0.149717	+	0.0401165i
$650$	−1.89873	+	1.25207i	−0.0744745	+	0.0491103i
$651$	2.62210	+	0.702589i	0.102768	+	0.0275366i
$652$		−	20.0405i		−	0.784847i
$653$	−1.44486	−	0.834191i	−0.0565418	−	0.0326444i	0.471463	−	0.881886i	$-0.343726\pi$
$653$	−1.44486	−	0.834191i	−0.0565418	−	0.0326444i	−0.528004	+	0.849242i	$0.677060\pi$
$654$	−0.659033	−	1.14148i	−0.0257702	−	0.0446353i
$655$	40.7544	−	1.21022i	1.59241	−	0.0472872i
$656$			7.05749i			0.275549i
$657$	−1.29708	+	4.84079i	−0.0506041	+	0.188857i
$658$		−	9.71484i		−	0.378724i
$659$	−4.01747	+	6.95846i	−0.156498	+	0.271063i	−0.933604	−	0.358307i	$-0.883354\pi$
$659$	−4.01747	+	6.95846i	−0.156498	+	0.271063i	0.777105	+	0.629371i	$0.216687\pi$
$660$	−5.74556	+	0.170617i	−0.223646	+	0.00664126i
$661$	−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	$0.603790\pi$
$662$	4.54843	+	16.9750i	0.176780	+	0.659751i
$663$	2.98713	−	0.800399i	0.116010	−	0.0310849i
$664$	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
$668$	−4.22666	+	2.44027i	−0.163535	+	0.0944167i
$669$	22.1783	−	38.4139i	0.857463	−	1.48517i
$670$	13.5496	−	25.1653i	0.523466	−	0.972220i
$671$	−1.43781	−	5.36599i	−0.0555061	−	0.207152i
$672$		−	2.41160i		−	0.0930294i
$673$	42.8128	−	11.4717i	1.65031	−	0.442200i	0.690613	−	0.723224i	$-0.257341\pi$
$673$	42.8128	−	11.4717i	1.65031	−	0.442200i	0.959701	+	0.281024i	$0.0906740\pi$
$674$	15.5402	+	15.5402i	0.598586	+	0.598586i
$675$	−5.49389	−	1.12755i	−0.211460	−	0.0433994i
$676$	−12.7931			−0.492042
$677$	36.0280	+	36.0280i	1.38467	+	1.38467i	0.836118	+	0.548549i	$0.184820\pi$
$677$	36.0280	+	36.0280i	1.38467	+	1.38467i	0.548549	+	0.836118i	$0.315180\pi$
$678$	3.03127	−	11.3129i	0.116415	−	0.434468i
$679$	−11.7863	+	3.15814i	−0.452318	+	0.121198i
$680$	−4.70789	−	4.43635i	−0.180539	−	0.170126i
$681$	6.22800	−	23.2432i	0.238658	−	0.890682i
$682$	1.18934	+	0.318684i	0.0455423	+	0.0122030i
$683$	−20.5569	−	35.6056i	−0.786588	−	1.36241i	−0.928046	−	0.372467i	$-0.878512\pi$
$683$	−20.5569	−	35.6056i	−0.786588	−	1.36241i	0.141457	−	0.989944i	$-0.454821\pi$
$684$	0.0907254	+	0.338592i	0.00346897	+	0.0129464i
$685$	−30.8629	−	16.6173i	−1.17921	−	0.634914i
$686$	3.43868	−	12.8333i	0.131290	−	0.489979i
$687$	−0.380729	+	1.42090i	−0.0145257	+	0.0542106i
$688$	−4.26294	−	7.38363i	−0.162523	−	0.281498i
$689$	−2.52698	−	2.52698i	−0.0962701	−	0.0962701i
$690$	−1.80703	−	0.972951i	−0.0687926	−	0.0370396i
$691$	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
$695$	20.4833	−	21.7371i	0.776976	−	0.824533i
$696$	3.69902	+	2.13563i	0.140211	+	0.0809509i
$697$	20.4169			0.773343
$698$	−19.7732	−	11.4160i	−0.748425	−	0.432104i
$699$	−12.9313	−	7.46588i	−0.489106	−	0.282386i
$700$	4.86860	−	1.61974i	0.184016	−	0.0612205i
$701$	−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
$703$	−0.431943	−	0.726510i	−0.0162911	−	0.0274008i
$704$		−	1.09386i		−	0.0412265i
$705$	−11.4435	+	48.4129i	−0.430987	+	1.82334i
$706$	14.7854	+	8.53634i	0.556455	+	0.321269i
$707$	2.60631	−	0.698358i	0.0980203	−	0.0262645i
$708$	4.24162	−	7.34670i	0.159410	−	0.276106i
$709$	1.37574	+	1.37574i	0.0516669	+	0.0516669i	0.732468	−	0.680801i	$-0.238368\pi$
$709$	1.37574	+	1.37574i	0.0516669	+	0.0516669i	−0.680801	+	0.732468i	$0.738368\pi$
$710$	−4.67307	−	15.5752i	−0.175377	−	0.584529i
$711$	9.20796	−	9.20796i	0.345325	−	0.345325i
$712$	−13.3347	−	3.57303i	−0.499741	−	0.133905i
$713$	0.310863	+	0.310863i	0.0116419	+	0.0116419i
$714$	−6.97660			−0.261093
$715$	−0.255939	+	1.08278i	−0.00957157	+	0.0404935i
$716$	−3.26728	−	12.1937i	−0.122104	−	0.455699i
$717$	41.5917			1.55327
$718$	17.6647	−	10.1987i	0.659243	−	0.380614i
$719$	32.0917	−	18.5282i	1.19682	−	0.690984i	0.236975	−	0.971516i	$-0.423844\pi$
$719$	32.0917	−	18.5282i	1.19682	−	0.690984i	0.959845	+	0.280532i	$0.0905107\pi$
$720$	−1.29760	+	5.48965i	−0.0483589	+	0.204587i
$721$	6.13533	−	1.64396i	0.228491	−	0.0612241i
$722$	16.4378	+	9.49035i	0.611750	+	0.353194i
$723$	7.40531	−	4.27546i	0.275406	−	0.159006i
$724$	8.68014	+	15.0344i	0.322595	+	0.558751i
$725$	−1.82703	+	8.90207i	−0.0678543	+	0.330615i
$726$	16.2907	−	16.2907i	0.604605	−	0.604605i
$727$	−4.06077	+	7.03346i	−0.150606	+	0.260856i	−0.931450	−	0.363869i	$-0.881456\pi$
$727$	−4.06077	+	7.03346i	−0.150606	+	0.260856i	0.780845	+	0.624725i	$0.214789\pi$
$728$	−0.450888	−	0.120815i	−0.0167110	−	0.00447771i
$729$		−	17.8338i		−	0.660512i
$730$	−0.131853	−	4.44018i	−0.00488010	−	0.164338i
$731$	−21.3604	+	12.3324i	−0.790042	+	0.456131i
$732$	−11.9349			−0.441126
$733$	−12.9773	−	48.4318i	−0.479326	−	1.78887i	−0.604353	−	0.796717i	$-0.706568\pi$
$733$	−12.9773	−	48.4318i	−0.479326	−	1.78887i	0.125027	−	0.992153i	$-0.460098\pi$
$734$	9.43149	−	9.43149i	0.348122	−	0.348122i
$735$	−14.8149	+	27.5154i	−0.546457	+	1.01492i
$736$	0.195278	−	0.338232i	0.00719805	−	0.0124674i
$737$	−3.61871	−	13.5052i	−0.133297	−	0.497471i
$738$	−8.90195	−	15.4186i	−0.327685	−	0.567568i
$739$	12.7958			0.470701			0.235351	−	0.971911i	$-0.424376\pi$
$739$	12.7958			0.470701			0.235351	+	0.971911i	$0.424376\pi$
$740$	−0.577715	−	13.5892i	−0.0212372	−	0.499549i
$741$	0.148538			0.00545670
$742$	4.03106	+	6.98200i	0.147985	+	0.256317i
$743$	12.4148	+	46.3327i	0.455455	+	1.69978i	0.686746	+	0.726897i	$0.259038\pi$
$743$	12.4148	+	46.3327i	0.455455	+	1.69978i	−0.231291	+	0.972885i	$0.574295\pi$
$744$	1.32265	−	2.29090i	0.0484908	−	0.0839885i
$745$	5.59388	−	1.67834i	0.204944	−	0.0614897i
$746$	−12.3383	+	12.3383i	−0.451737	+	0.451737i
$747$	2.73387	+	10.2030i	0.100027	+	0.373307i
$748$	−3.16448			−0.115705
$749$	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	$-0.0510722\pi$
$752$	−9.14429	−	2.45020i	−0.333458	−	0.0893498i
$753$	26.3034	−	45.5588i	0.958549	−	1.66026i
$754$	0.584603	−	0.584603i	0.0212900	−	0.0212900i
$755$	−11.4874	+	48.5986i	−0.418069	+	1.76868i
$756$	−0.575531	−	0.996849i	−0.0209319	−	0.0362551i
$757$	−42.8500	+	24.7395i	−1.55741	+	0.899172i	−0.559908	+	0.828555i	$0.689163\pi$
$757$	−42.8500	+	24.7395i	−1.55741	+	0.899172i	−0.997504	+	0.0706169i	$0.977503\pi$
$758$	−21.7843	−	12.5772i	−0.791240	−	0.456823i
$759$	−0.969765	+	0.259848i	−0.0352003	+	0.00943188i
$760$	−0.163272	−	0.264351i	−0.00592251	−	0.00958902i
$761$	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	$0.312367\pi$
$762$	42.8672	−	24.7494i	1.55291	−	0.896575i
$763$	0.575560			0.0208367
$764$	2.70902	+	10.1102i	0.0980090	+	0.365775i
$765$	15.8812	+	3.75389i	0.574186	+	0.135722i
$766$	10.7373			0.387953
$767$	−1.16109	−	1.16109i	−0.0419246	−	0.0419246i
$768$	−2.26997	−	0.608236i	−0.0819104	−	0.0219478i
$769$	36.4223	−	36.4223i	1.31342	−	1.31342i	0.394543	−	0.918877i	$-0.370903\pi$
$769$	36.4223	−	36.4223i	1.31342	−	1.31342i	0.918877	−	0.394543i	$-0.129097\pi$
$770$	1.18994	−	2.21004i	0.0428823	−	0.0796442i
$771$	−36.3337	−	36.3337i	−1.30852	−	1.30852i
$772$	−2.73726	+	4.74108i	−0.0985163	+	0.170635i
$773$	20.9607	−	5.61641i	0.753905	−	0.202008i	0.138656	−	0.990341i	$-0.455722\pi$
$773$	20.9607	−	5.61641i	0.753905	−	0.202008i	0.615250	+	0.788332i	$0.289055\pi$
$774$	18.6267	+	10.7541i	0.669522	+	0.386549i
$775$	5.51329	+	1.13153i	0.198043	+	0.0406458i
$776$			11.8906i			0.426849i
$777$	−10.5046	−	10.2391i	−0.376850	−	0.367324i
$778$	−21.5625	−	21.5625i	−0.773052	−	0.773052i
$779$	0.947243	+	0.253813i	0.0339385	+	0.00909379i
$780$	2.10464	+	1.13319i	0.0753583	+	0.0405747i
$781$	−6.88907	−	3.97741i	−0.246510	−	0.142323i
$782$	−0.978483	−	0.564927i	−0.0349905	−	0.0202018i
$783$	2.03868			0.0728566
$784$	−5.15019	−	2.97346i	−0.183935	−	0.106195i
$785$	0.212891	+	7.16914i	0.00759840	+	0.255878i
$786$	−21.4253	−	37.1097i	−0.764214	−	1.32366i
$787$	−19.1328	+	19.1328i	−0.682009	+	0.682009i	−0.960453	−	0.278443i	$-0.910182\pi$
$787$	−19.1328	+	19.1328i	−0.682009	+	0.682009i	0.278443	+	0.960453i	$0.410182\pi$
$788$	3.96381	−	3.96381i	0.141205	−	0.141205i
$789$	17.5162	−	10.1130i	0.623592	−	0.360031i
$790$	−5.47198	+	10.1630i	−0.194684	+	0.361582i
$791$	3.61633	+	3.61633i	0.128582	+	0.128582i
$792$	1.37974	+	2.38979i	0.0490271	+	0.0849174i
$793$	−0.597908	+	2.23142i	−0.0212323	+	0.0792402i
$794$	5.16248	−	19.2666i	0.183210	−	0.683747i
$795$	−11.8640	−	39.5425i	−0.420773	−	1.40243i
$796$	−3.97682	−	14.8417i	−0.140955	−	0.526050i
$797$	27.7366	+	48.0413i	0.982482	+	1.70171i	0.652632	+	0.757675i	$0.273665\pi$
$797$	27.7366	+	48.0413i	0.982482	+	1.70171i	0.329850	+	0.944033i	$0.393002\pi$
$798$	−0.323680	−	0.0867298i	−0.0114582	−	0.00307020i
$799$	−7.08828	+	26.4538i	−0.250765	+	0.935869i
$800$	−0.296693	−	4.99119i	−0.0104897	−	0.176465i
$801$	33.6395	−	9.01368i	1.18859	−	0.318483i
$802$	3.50302	−	13.0735i	0.123696	−	0.461640i
$803$	−1.53658	−	1.53658i	−0.0542247	−	0.0542247i
$804$	−30.0380			−1.05936
$805$	0.762478	−	0.470933i	0.0268738	−	0.0165982i
$806$	−0.362060	−	0.362060i	−0.0127530	−	0.0127530i
$807$	−12.9994	+	3.48317i	−0.457599	+	0.122613i
$808$		−	2.62938i		−	0.0925011i
$809$	5.75814	+	21.4897i	0.202445	+	0.755537i	0.990213	+	0.139564i	$0.0445701\pi$
$809$	5.75814	+	21.4897i	0.202445	+	0.755537i	−0.787768	+	0.615973i	$0.788763\pi$
$810$	6.55707	+	21.8546i	0.230392	+	0.767891i
$811$	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	$-0.0560870\pi$
$812$	−1.61525	+	0.932566i	−0.0566842	+	0.0327267i
$813$	−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
$817$	−1.14433	+	0.306622i	−0.0400350	+	0.0107273i
$818$	7.15628	+	26.7076i	0.250213	+	0.933809i
$819$	1.13746	−	0.304780i	0.0397459	−	0.0106499i
$820$	11.4852	+	10.8227i	0.401080	+	0.377946i
$821$	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	$-0.103502\pi$
$822$			36.8387i			1.28490i
$823$	−9.17050	+	34.2248i	−0.319663	+	1.19300i	0.599905	+	0.800071i	$0.295205\pi$
$823$	−9.17050	+	34.2248i	−0.319663	+	1.19300i	−0.919569	+	0.392929i	$0.871462\pi$
$824$		−	6.18963i		−	0.215626i
$825$	−8.53322	+	9.61182i	−0.297089	+	0.334641i
$826$	1.85219	+	3.20809i	0.0644459	+	0.111624i
$827$	−31.6761	−	18.2882i	−1.10149	−	0.635943i	−0.164875	−	0.986315i	$-0.552722\pi$
$827$	−31.6761	−	18.2882i	−1.10149	−	0.635943i	−0.936611	+	0.350372i	$0.886055\pi$
$828$			0.985256i			0.0342400i
$829$	19.8506	+	5.31896i	0.689440	+	0.184735i	0.586496	−	0.809952i	$-0.300507\pi$
$829$	19.8506	+	5.31896i	0.689440	+	0.184735i	0.102944	+	0.994687i	$0.467174\pi$
$830$	−4.91997	−	7.96583i	−0.170775	−	0.276498i
$831$	−20.1929	−	5.41066i	−0.700482	−	0.187694i
$832$	−0.227440	+	0.393937i	−0.00788505	+	0.0136573i
$833$	−8.60204	+	14.8992i	−0.298043	+	0.516225i
$834$	−30.3202	−	8.12428i	−1.04990	−	0.281321i
$835$	−2.51041	+	10.6205i	−0.0868762	+	0.367539i
$836$	−0.146816	−	0.0393393i	−0.00507775	−	0.00136058i
$837$		−	1.26261i		−	0.0436422i
$838$	0.732348	+	0.422822i	0.0252986	+	0.0146061i
$839$	−23.8810	−	41.3632i	−0.824465	−	1.42802i	−0.902328	−	0.431051i	$-0.858143\pi$
$839$	−23.8810	−	41.3632i	−0.824465	−	1.42802i	0.0778627	−	0.996964i	$-0.475190\pi$
$840$	−3.92457	−	3.69821i	−0.135411	−	0.127600i
$841$			25.6966i			0.886090i
$842$	−1.83382	+	6.84391i	−0.0631976	+	0.235857i
$843$			3.87622i			0.133504i
$844$	−2.30813	+	3.99779i	−0.0794489	+	0.137610i
$845$	−19.6183	+	20.8191i	−0.674891	+	0.716200i
$846$	23.0683	−	6.18112i	0.793104	−	0.212511i
$847$	2.60378	+	9.71746i	0.0894671	+	0.333896i
$848$	7.58864	−	2.03337i	0.260595	−	0.0698262i
$849$	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
$853$	−8.69210	+	5.01838i	−0.297612	+	0.171826i	−0.641369	−	0.767232i	$-0.721633\pi$
$853$	−8.69210	+	5.01838i	−0.297612	+	0.171826i	0.343758	+	0.939058i	$0.388300\pi$
$854$	2.60580	−	4.51339i	0.0891688	−	0.154445i
$855$	0.690144	+	0.371590i	0.0236024	+	0.0127081i
$856$	−1.98266	−	7.39938i	−0.0677659	−	0.252906i
$857$			12.1187i			0.413968i	0.978344	+	0.206984i	$0.0663648\pi$
$857$			12.1187i			0.413968i	−0.978344	+	0.206984i	$0.933635\pi$
$858$	1.12948	−	0.302643i	0.0385598	−	0.0103321i
$859$	−4.37193	−	4.37193i	−0.149168	−	0.149168i	0.628578	−	0.777746i	$-0.283637\pi$
$859$	−4.37193	−	4.37193i	−0.149168	−	0.149168i	−0.777746	+	0.628578i	$0.783637\pi$
$860$	−18.5532	−	4.38547i	−0.632659	−	0.149543i
$861$	17.0198			0.580034
$862$	−11.2437	−	11.2437i	−0.382961	−	0.382961i
$863$	8.65353	−	32.2954i	0.294570	−	1.09935i	−0.646989	−	0.762499i	$-0.723972\pi$
$863$	8.65353	−	32.2954i	0.294570	−	1.09935i	0.941559	−	0.336849i	$-0.109361\pi$
$864$	−1.08346	+	0.290312i	−0.0368601	+	0.00987663i
$865$	1.06040	+	35.7093i	0.0360548	+	1.21415i
$866$	−7.03781	+	26.2655i	−0.239154	+	0.892536i
$867$	−19.5919	−	5.24964i	−0.665376	−	0.178287i
$868$	0.577563	+	1.00037i	0.0196038	+	0.0339547i
$869$	1.46141	+	5.45406i	0.0495750	+	0.185016i
$870$	9.14795	−	2.74468i	0.310145	−	0.0930533i
$871$	−1.50483	+	5.61610i	−0.0509892	+	0.190294i
$872$	0.145164	−	0.541758i	0.00491586	−	0.0183462i
$873$	−14.9983	−	25.9777i	−0.507614	−	0.879213i
$874$	−0.0383739	−	0.0383739i	−0.00129802	−	0.00129802i
$875$	4.83012	−	10.4069i	0.163288	−	0.351818i
$876$	−4.04309	+	2.33428i	−0.136603	+	0.0788679i
$877$	8.44407	−	8.44407i	0.285136	−	0.285136i	−0.550017	−	0.835153i	$-0.685379\pi$
$877$	8.44407	−	8.44407i	0.285136	−	0.285136i	0.835153	+	0.550017i	$0.185379\pi$
$878$	2.66610	−	2.66610i	0.0899765	−	0.0899765i
$879$	−28.2029	−	48.8488i	−0.951259	−	1.64763i
$880$	−1.78013	−	1.67745i	−0.0600080	−	0.0565469i
$881$	−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	$0.829620\pi$
$882$	15.0023			0.505154
$883$	12.0749	+	6.97147i	0.406354	+	0.234609i	0.689222	−	0.724550i	$-0.257953\pi$
$883$	12.0749	+	6.97147i	0.406354	+	0.234609i	−0.282868	+	0.959159i	$0.591286\pi$
$884$	1.13963	+	0.657968i	0.0383300	+	0.0221299i
$885$	−5.45126	−	18.1689i	−0.183242	−	0.610742i
$886$	21.9683	+	5.88638i	0.738038	+	0.197757i
$887$	13.4845	+	13.4845i	0.452766	+	0.452766i	0.896272	−	0.443506i	$-0.146265\pi$
$887$	13.4845	+	13.4845i	0.452766	+	0.452766i	−0.443506	+	0.896272i	$0.646265\pi$
$888$	−12.2871	+	7.30525i	−0.412328	+	0.245148i
$889$			21.6146i			0.724931i
$890$	−26.2636	+	16.2213i	−0.880359	+	0.543740i
$891$	9.66648	+	5.58094i	0.323839	+	0.186969i
$892$	18.2317	−	4.88516i	0.610441	−	0.163567i
$893$	−0.657724	+	1.13921i	−0.0220099	+	0.0381222i
$894$	−4.34016	−	4.34016i	−0.145157	−	0.145157i
$895$	−24.8541	−	13.3820i	−0.830780	−	0.447311i
$896$	0.725629	−	0.725629i	0.0242415	−	0.0242415i
$897$	0.403273	+	0.108057i	0.0134649	+	0.00360791i
$898$	−2.21772	−	2.21772i	−0.0740063	−	0.0740063i
$899$	−2.04588			−0.0682340
$900$	6.94382	+	10.5301i	0.231461	+	0.351004i
$901$	−5.88241	−	21.9534i	−0.195971	−	0.731375i
$902$	7.71993			0.257046
$903$	−17.8064	+	10.2805i	−0.592558	+	0.342114i
$904$	4.31602	−	2.49186i	0.143549	−	0.0828780i
$905$	37.7778	+	8.92964i	1.25577	+	0.296831i
$906$	50.6948	−	13.5836i	1.68422	−	0.451286i
$907$	−6.14368	−	3.54706i	−0.203998	−	0.117778i	0.394521	−	0.918887i	$-0.370910\pi$
$907$	−6.14368	−	3.54706i	−0.203998	−	0.117778i	−0.598519	+	0.801109i	$0.704244\pi$
$908$	8.86763	−	5.11973i	0.294283	−	0.169904i
$909$	3.31656	+	5.74445i	0.110003	+	0.190531i
$910$	−0.888054	+	0.548493i	−0.0294387	+	0.0181824i
$911$	−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	$0.252195\pi$
$912$	−0.163272	+	0.282796i	−0.00540649	+	0.00936432i
$913$	−4.42409	−	1.18543i	−0.146416	−	0.0392321i
$914$			36.9041i			1.22068i
$915$	−18.3023	+	19.4225i	−0.605054	+	0.642089i
$916$	−0.542093	+	0.312978i	−0.0179113	+	0.0103411i
$917$	18.7116			0.617910
$918$	0.839855	+	3.13438i	0.0277194	+	0.103450i
$919$	−17.6615	+	17.6615i	−0.582600	+	0.582600i	−0.935617	−	0.353017i	$-0.885156\pi$
$919$	−17.6615	+	17.6615i	−0.582600	+	0.582600i	0.353017	+	0.935617i	$0.385156\pi$
$920$	−0.250969	−	0.836473i	−0.00827419	−	0.0275777i
$921$	23.7097	−	41.0664i	0.781260	−	1.35318i
$922$	6.37384	+	23.7875i	0.209911	+	0.783399i
$923$	1.65399	+	2.86480i	0.0544417	+	0.0942959i
$924$	−2.63796			−0.0867825
$925$	−23.0006	−	19.8990i	−0.756256	−	0.654275i
$926$	1.62457			0.0533867
$927$	7.80728	+	13.5226i	0.256425	+	0.444141i
$928$	0.470410	+	1.75559i	0.0154420	+	0.0576302i
$929$	17.4188	−	30.1703i	0.571492	−	0.989854i	−0.424921	−	0.905231i	$-0.639698\pi$
$929$	17.4188	−	30.1703i	0.571492	−	0.989854i	0.996413	−	0.0846232i	$-0.0269687\pi$
$930$	−1.69985	−	5.66557i	−0.0557403	−	0.185781i
$931$	−0.584312	+	0.584312i	−0.0191501	+	0.0191501i
$932$	−1.64449	−	6.13733i	−0.0538671	−	0.201035i
$933$	17.8627			0.584798
$934$	26.5154	−	15.3087i	0.867611	−	0.500915i
$935$	−4.85276	+	5.14979i	−0.158702	+	0.168416i
$936$		−	1.14752i		−	0.0375079i
$937$	−32.1374	−	8.61118i	−1.04988	−	0.281315i	−0.307679	−	0.951490i	$-0.599552\pi$
$937$	−32.1374	−	8.61118i	−1.04988	−	0.281315i	−0.742203	+	0.670175i	$0.766219\pi$
$938$	6.55834	−	11.3594i	0.214138	−	0.370897i
$939$	54.1101	−	54.1101i	1.76581	−	1.76581i
$940$	−18.0103	+	11.1238i	−0.587430	+	0.362817i
$941$	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	$0.777707\pi$
$942$	6.52799	−	3.76894i	0.212694	−	0.122799i
$943$	2.38707	+	1.37817i	0.0777336	+	0.0448795i
$944$	3.48682	−	0.934291i	0.113486	−	0.0304086i
$945$	−2.50483	−	0.592074i	−0.0814821	−	0.0192602i
$946$	−8.07669	+	4.66308i	−0.262596	+	0.151610i
$947$	−20.5826	+	11.8834i	−0.668846	+	0.386158i	−0.795639	−	0.605771i	$-0.792865\pi$
$947$	−20.5826	+	11.8834i	−0.668846	+	0.386158i	0.126793	+	0.991929i	$0.459531\pi$
$948$	12.1308			0.393989
$949$	0.233883	+	0.872864i	0.00759217	+	0.0283344i
$950$	−0.680578	−	0.139680i	−0.0220809	−	0.00453181i
$951$	61.4609			1.99301
$952$	−2.09920	−	2.09920i	−0.0680353	−	0.0680353i
$953$	47.8057	+	12.8095i	1.54858	+	0.414941i	0.929026	−	0.370014i	$-0.120647\pi$
$953$	47.8057	+	12.8095i	1.54858	+	0.414941i	0.619553	+	0.784955i	$0.287314\pi$
$954$	−14.0143	+	14.0143i	−0.453728	+	0.453728i
$955$	20.6074	+	11.0955i	0.666840	+	0.359043i
$956$	12.5146	+	12.5146i	0.404750	+	0.404750i
$957$	2.33609	−	4.04622i	0.0755150	−	0.130796i
$958$	−4.02643	+	1.07888i	−0.130088	+	0.0348570i
$959$	−13.9312	−	8.04319i	−0.449863	−	0.259728i
$960$	−4.47084	+	2.76135i	−0.144296	+	0.0891221i
$961$		−	29.7329i		−	0.959127i
$962$	0.750284	+	2.66326i	0.0241901	+	0.0858668i
$963$	13.6648	+	13.6648i	0.440341	+	0.440341i
$964$	3.51464	+	0.941745i	0.113199	+	0.0303316i
$965$	3.51789	+	11.7251i	0.113245	+	0.377443i
$966$	−0.815680	−	0.470933i	−0.0262441	−	0.0151520i
$967$	−47.6596	−	27.5163i	−1.53263	−	0.884863i	−0.999239	−	0.0389927i	$-0.987585\pi$
$967$	−47.6596	−	27.5163i	−1.53263	−	0.884863i	−0.533388	−	0.845870i	$-0.679082\pi$
$968$	9.80346			0.315095
$969$	0.818111	+	0.472337i	0.0262815	+	0.0151736i
$970$	19.3505	+	18.2344i	0.621308	+	0.585472i
$971$	−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
$975$	5.07162	−	1.68728i	0.162422	−	0.0540363i
$976$	−3.59110	−	3.59110i	−0.114948	−	0.114948i
$977$	8.53326	+	14.7800i	0.273003	+	0.472855i	0.969629	−	0.244579i	$-0.0786497\pi$
$977$	8.53326	+	14.7800i	0.273003	+	0.472855i	−0.696626	+	0.717434i	$0.745316\pi$
$978$	−12.1894	+	45.4913i	−0.389773	+	1.45465i
$979$	−3.90841	+	14.5864i	−0.124913	+	0.466183i
$980$	−12.7368	+	3.82145i	−0.406862	+	0.122072i
$981$	0.366204	+	1.36669i	0.0116920	+	0.0436351i
$982$	5.44899	+	9.43792i	0.173884	+	0.301176i
$983$	−25.8979	−	6.93932i	−0.826014	−	0.221330i	−0.179040	−	0.983842i	$-0.557299\pi$
$983$	−25.8979	−	6.93932i	−0.826014	−	0.221330i	−0.646974	+	0.762512i	$0.723966\pi$
$984$	4.29262	−	16.0203i	0.136844	−	0.510707i
$985$	−0.372059	−	12.5292i	−0.0118548	−	0.399212i
$986$	5.07882	−	1.36087i	0.161743	−	0.0433388i
$987$	−5.90891	+	22.0524i	−0.188083	+	0.701934i
$988$	0.0446939	+	0.0446939i	0.00142190	+	0.00142190i
$989$	−3.32984			−0.105883
$990$	6.00493	+	1.41940i	0.190849	+	0.0451116i
$991$	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	$0.591015\pi$
$992$	1.08729	−	0.291337i	0.0345214	−	0.00924997i
$993$		−	41.2991i		−	1.31059i
$994$	−1.93149	−	7.20842i	−0.0612632	−	0.228637i
$995$	−30.2515	−	16.2881i	−0.959037	−	0.516369i
$996$	−4.91997	+	8.52165i	−0.155895	+	0.270019i
$997$	6.93928	−	4.00639i	0.219769	−	0.126884i	−0.386074	−	0.922468i	$-0.626169\pi$
$997$	6.93928	−	4.00639i	0.219769	−	0.126884i	0.605843	+	0.795584i	$0.292836\pi$
$998$	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.q.d.103.3	yes	12
5.2	odd	4		370.2.r.d.177.3	yes	12
37.23	odd	12		370.2.r.d.23.3	yes	12
185.97	even	12	inner	370.2.q.d.97.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.q.d.97.3	✓	12	185.97	even	12	inner
370.2.q.d.103.3	yes	12	1.1	even	1	trivial
370.2.r.d.23.3	yes	12	37.23	odd	12
370.2.r.d.177.3	yes	12	5.2	odd	4

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.q (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.608236 + 2.26997i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.642592 + 2.14175i) q^{5} +(1.66173 - 1.66173i) q^{6} +(0.265598 + 0.991227i) q^{7} +1.00000 q^{8} +(-2.18472 + 1.26135i) q^{9} +(1.53351 - 1.62737i) q^{10} -1.09386i q^{11} +(-2.26997 - 0.608236i) q^{12} +(-0.227440 + 0.393937i) q^{13} +(0.725629 - 0.725629i) q^{14} +(-4.47084 + 2.76135i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.50536 + 1.44647i) q^{17} +(2.18472 + 1.26135i) q^{18} +(-0.134218 + 0.0359636i) q^{19} +(-2.17610 - 0.514372i) q^{20} +(-2.08851 + 1.20580i) q^{21} +(-0.947314 + 0.546932i) q^{22} -0.390557 q^{23} +(0.608236 + 2.26997i) q^{24} +(-4.17415 + 2.75254i) q^{25} +0.454879 q^{26} +(0.793148 + 0.793148i) q^{27} +(-0.991227 - 0.265598i) q^{28} +(1.28518 - 1.28518i) q^{29} +(4.62682 + 2.49119i) q^{30} +(-0.795949 - 0.795949i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.48303 - 0.665327i) q^{33} +(2.50536 + 1.44647i) q^{34} +(-1.95228 + 1.20580i) q^{35} -2.52270i q^{36} +(1.64941 + 5.85486i) q^{37} +(0.0982545 + 0.0982545i) q^{38} +(-1.03256 - 0.276674i) q^{39} +(0.642592 + 2.14175i) q^{40} +(-6.11196 - 3.52874i) q^{41} +(2.08851 + 1.20580i) q^{42} +8.52588 q^{43} +(0.947314 + 0.546932i) q^{44} +(-4.10537 - 3.86858i) 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} +(4.47084 + 2.23865i) q^{50} +(-4.80728 - 4.80728i) q^{51} +(-0.227440 - 0.393937i) q^{52} +(-2.03337 + 7.58864i) q^{53} +(0.290312 - 1.08346i) q^{54} +(2.34278 - 0.702908i) q^{55} +(0.265598 + 0.991227i) q^{56} +(-0.163272 - 0.282796i) q^{57} +(-1.75559 - 0.470410i) q^{58} +(-0.934291 + 3.48682i) q^{59} +(-0.155976 - 5.25254i) q^{60} +(4.90553 - 1.31443i) q^{61} +(-0.291337 + 1.08729i) q^{62} +(-1.83054 - 1.83054i) q^{63} +1.00000 q^{64} +(-0.989863 - 0.233977i) q^{65} +(-1.81771 - 1.81771i) q^{66} +(12.3464 - 3.30819i) q^{67} -2.89294i q^{68} +(-0.237550 - 0.886550i) q^{69} +(2.02040 + 1.08783i) q^{70} +(3.63611 - 6.29793i) q^{71} +(-2.18472 + 1.26135i) 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} +(1.08427 - 0.290529i) q^{77} +(0.276674 + 1.03256i) q^{78} +(-4.98605 + 1.33601i) q^{79} +(1.53351 - 1.62737i) q^{80} +(-5.10205 + 8.83700i) q^{81} +7.05749i q^{82} +(1.08371 - 4.04446i) q^{83} -2.41160i q^{84} +(-4.70789 - 4.43635i) q^{85} +(-4.26294 - 7.38363i) q^{86} +(3.69902 + 2.13563i) q^{87} -1.09386i q^{88} +(-13.3347 - 3.57303i) q^{89} +(-1.29760 + 5.48965i) q^{90} +(-0.450888 - 0.120815i) q^{91} +(0.195278 - 0.338232i) q^{92} +(1.32265 - 2.29090i) q^{93} +(-9.14429 - 2.45020i) q^{94} +(-0.163272 - 0.264351i) q^{95} +(-2.26997 - 0.608236i) q^{96} +11.8906i q^{97} +(-5.15019 - 2.97346i) q^{98} +(1.37974 + 2.38979i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{4} + 2 q^{5} + 6 q^{6} - 4 q^{7} + 12 q^{8} + 18 q^{9} - 4 q^{10} - 6 q^{12} + 8 q^{14} - 10 q^{15} - 6 q^{16} - 12 q^{17} - 18 q^{18} - 8 q^{19} + 2 q^{20} + 54 q^{21} - 6 q^{22}+ \cdots + 28 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^4 + 2 * q^5 + 6 * q^6 - 4 * q^7 + 12 * q^8 + 18 * q^9 - 4 * q^10 - 6 * q^12 + 8 * q^14 - 10 * q^15 - 6 * q^16 - 12 * q^17 - 18 * q^18 - 8 * q^19 + 2 * q^20 + 54 * q^21 - 6 * q^22 - 4 * q^23 - 14 * q^25 + 18 * q^27 - 4 * q^28 + 4 * q^29 - 4 * q^30 - 2 * q^31 - 6 * q^32 + 20 * q^33 + 12 * q^34 + 6 * q^35 + 14 * q^37 + 16 * q^38 - 30 * q^39 + 2 * q^40 + 12 * q^41 - 54 * q^42 + 44 * q^43 + 6 * q^44 - 60 * q^45 + 2 * q^46 - 28 * q^47 + 6 * q^48 + 24 * q^49 + 10 * q^50 - 8 * q^51 + 8 * q^53 - 18 * q^54 - 4 * q^56 - 28 * q^57 - 14 * q^58 + 14 * q^60 + 24 * q^61 - 14 * q^62 + 8 * q^63 + 12 * q^64 - 10 * q^65 + 8 * q^66 + 18 * q^67 - 40 * q^69 - 30 * q^70 + 18 * q^72 - 28 * q^73 + 38 * q^74 - 30 * q^75 - 8 * q^76 + 10 * q^77 + 48 * q^78 - 56 * q^79 - 4 * q^80 + 4 * q^81 + 14 * q^83 - 28 * q^85 - 22 * q^86 + 18 * q^87 - 2 * q^89 + 18 * q^90 + 38 * q^91 + 2 * q^92 - 16 * q^94 - 28 * q^95 - 6 * q^96 - 24 * q^98 + 28 * q^99

Introduction

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