LMFDB - Embedded newform 440.2.r.h.67.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [440,2,Mod(67,440)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(440, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("440.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 440 = 2^{3} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	440.r (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.51341768894$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			67.10
Character	$\chi$	$=$	440.67
Dual form			440.2.r.h.243.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.566038 + 1.29599i) q^{2} +(0.112791 - 0.112791i) q^{3} +(-1.35920 - 1.46716i) q^{4} +(-1.73275 - 1.41336i) q^{5} +(0.0823324 + 0.210020i) q^{6} +(-0.285323 + 0.285323i) q^{7} +(2.67080 - 0.931047i) q^{8} +2.97456i q^{9} +O(q^{10})$	\(q+(-0.566038 + 1.29599i) q^{2} +(0.112791 - 0.112791i) q^{3} +(-1.35920 - 1.46716i) q^{4} +(-1.73275 - 1.41336i) q^{5} +(0.0823324 + 0.210020i) q^{6} +(-0.285323 + 0.285323i) q^{7} +(2.67080 - 0.931047i) q^{8} +2.97456i q^{9} +(2.81251 - 1.44561i) q^{10} +1.00000 q^{11} +(-0.318788 - 0.0121771i) q^{12} +(1.87092 + 1.87092i) q^{13} +(-0.208273 - 0.531280i) q^{14} +(-0.354852 + 0.0360235i) q^{15} +(-0.305140 + 3.98834i) q^{16} +(0.874816 + 0.874816i) q^{17} +(-3.85501 - 1.68371i) q^{18} +2.21601i q^{19} +(0.281517 + 4.46327i) q^{20} +0.0643636i q^{21} +(-0.566038 + 1.29599i) q^{22} +(5.75409 + 5.75409i) q^{23} +(0.196228 - 0.406255i) q^{24} +(1.00481 + 4.89799i) q^{25} +(-3.48371 + 1.36569i) q^{26} +(0.673875 + 0.673875i) q^{27} +(0.806427 + 0.0308040i) q^{28} -0.286512 q^{29} +(0.154174 - 0.480277i) q^{30} +5.05784i q^{31} +(-4.99615 - 2.65301i) q^{32} +(0.112791 - 0.112791i) q^{33} +(-1.62894 + 0.638578i) q^{34} +(0.897656 - 0.0911274i) q^{35} +(4.36416 - 4.04302i) q^{36} +(1.72593 - 1.72593i) q^{37} +(-2.87194 - 1.25435i) q^{38} +0.422045 q^{39} +(-5.94372 - 2.16153i) q^{40} -9.62451 q^{41} +(-0.0834149 - 0.0364323i) q^{42} +(6.70865 - 6.70865i) q^{43} +(-1.35920 - 1.46716i) q^{44} +(4.20413 - 5.15415i) q^{45} +(-10.7143 + 4.20024i) q^{46} +(4.74379 - 4.74379i) q^{47} +(0.415432 + 0.484266i) q^{48} +6.83718i q^{49} +(-6.91654 - 1.47022i) q^{50} +0.197343 q^{51} +(0.201988 - 5.28789i) q^{52} +(-3.51588 - 3.51588i) q^{53} +(-1.25478 + 0.491900i) q^{54} +(-1.73275 - 1.41336i) q^{55} +(-0.496390 + 1.02769i) q^{56} +(0.249946 + 0.249946i) q^{57} +(0.162177 - 0.371318i) q^{58} +0.559395i q^{59} +(0.535168 + 0.471663i) q^{60} +11.2560i q^{61} +(-6.55493 - 2.86293i) q^{62} +(-0.848709 - 0.848709i) q^{63} +(6.26630 - 4.97328i) q^{64} +(-0.597540 - 5.88610i) q^{65} +(0.0823324 + 0.210020i) q^{66} +(0.230669 + 0.230669i) q^{67} +(0.0944468 - 2.47255i) q^{68} +1.29802 q^{69} +(-0.390007 + 1.21494i) q^{70} -13.2381i q^{71} +(2.76945 + 7.94443i) q^{72} +(-7.63762 + 7.63762i) q^{73} +(1.25985 + 3.21374i) q^{74} +(0.665783 + 0.439115i) q^{75} +(3.25125 - 3.01200i) q^{76} +(-0.285323 + 0.285323i) q^{77} +(-0.238893 + 0.546967i) q^{78} +5.08654 q^{79} +(6.16570 - 6.47951i) q^{80} -8.77166 q^{81} +(5.44784 - 12.4733i) q^{82} +(4.77497 - 4.77497i) q^{83} +(0.0944320 - 0.0874832i) q^{84} +(-0.279402 - 2.75227i) q^{85} +(4.89702 + 12.4917i) q^{86} +(-0.0323160 + 0.0323160i) q^{87} +(2.67080 - 0.931047i) q^{88} +13.8064i q^{89} +(4.30005 + 8.36597i) q^{90} -1.06763 q^{91} +(0.621223 - 16.2632i) q^{92} +(0.570478 + 0.570478i) q^{93} +(3.46276 + 8.83310i) q^{94} +(3.13202 - 3.83978i) q^{95} +(-0.862756 + 0.264284i) q^{96} +(4.19838 + 4.19838i) q^{97} +(-8.86095 - 3.87010i) q^{98} +2.97456i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{2} + 4 q^{3} - 4 q^{6} - 26 q^{8}+O(q^{10}) $ 56 * q + 4 * q^2 + 4 * q^3 - 4 * q^6 - 26 * q^8	$ 56 q + 4 q^{2} + 4 q^{3} - 4 q^{6} - 26 q^{8} - 10 q^{10} + 56 q^{11} + 8 q^{12} + 8 q^{16} + 12 q^{17} + 12 q^{18} - 24 q^{20} + 4 q^{22} - 16 q^{25} + 40 q^{27} + 32 q^{28} + 18 q^{30} + 14 q^{32} + 4 q^{33} - 24 q^{35} + 44 q^{36} - 56 q^{38} + 42 q^{40} - 8 q^{41} + 16 q^{42} - 16 q^{43} - 16 q^{46} - 96 q^{48} - 22 q^{50} - 32 q^{51} - 76 q^{52} - 40 q^{56} + 16 q^{57} - 64 q^{60} + 4 q^{62} - 52 q^{65} - 4 q^{66} + 52 q^{67} + 8 q^{68} + 8 q^{70} + 50 q^{72} - 36 q^{73} + 52 q^{75} + 68 q^{76} - 20 q^{78} + 68 q^{80} - 96 q^{81} - 36 q^{82} - 16 q^{83} + 52 q^{86} - 26 q^{88} - 112 q^{90} - 48 q^{91} - 32 q^{92} - 88 q^{96} - 16 q^{97} + 76 q^{98}+O(q^{100}) $ 56 * q + 4 * q^2 + 4 * q^3 - 4 * q^6 - 26 * q^8 - 10 * q^10 + 56 * q^11 + 8 * q^12 + 8 * q^16 + 12 * q^17 + 12 * q^18 - 24 * q^20 + 4 * q^22 - 16 * q^25 + 40 * q^27 + 32 * q^28 + 18 * q^30 + 14 * q^32 + 4 * q^33 - 24 * q^35 + 44 * q^36 - 56 * q^38 + 42 * q^40 - 8 * q^41 + 16 * q^42 - 16 * q^43 - 16 * q^46 - 96 * q^48 - 22 * q^50 - 32 * q^51 - 76 * q^52 - 40 * q^56 + 16 * q^57 - 64 * q^60 + 4 * q^62 - 52 * q^65 - 4 * q^66 + 52 * q^67 + 8 * q^68 + 8 * q^70 + 50 * q^72 - 36 * q^73 + 52 * q^75 + 68 * q^76 - 20 * q^78 + 68 * q^80 - 96 * q^81 - 36 * q^82 - 16 * q^83 + 52 * q^86 - 26 * q^88 - 112 * q^90 - 48 * q^91 - 32 * q^92 - 88 * q^96 - 16 * q^97 + 76 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/440\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$221$	$321$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.566038	+	1.29599i	−0.400249	+	0.916406i
$2$	−0.566038	+	1.29599i	−0.400249	+	0.916406i
$3$	0.112791	−	0.112791i	0.0651198	−	0.0651198i	−0.673797	−	0.738917i	$-0.735338\pi$
$3$	0.112791	−	0.112791i	0.0651198	−	0.0651198i	0.738917	+	0.673797i	$0.235338\pi$
$4$	−1.35920	−	1.46716i	−0.679601	−	0.733582i
$5$	−1.73275	−	1.41336i	−0.774907	−	0.632075i
$5$	−1.73275	−	1.41336i	−0.774907	−	0.632075i
$6$	0.0823324	+	0.210020i	0.0336121	+	0.0857404i
$7$	−0.285323	+	0.285323i	−0.107842	+	0.107842i	−0.758969	−	0.651127i	$-0.774297\pi$
$7$	−0.285323	+	0.285323i	−0.107842	+	0.107842i	0.651127	+	0.758969i	$0.274297\pi$
$8$	2.67080	−	0.931047i	0.944269	−	0.329175i
$9$			2.97456i			0.991519i
$10$	2.81251	−	1.44561i	0.889393	−	0.457143i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$	−0.318788	−	0.0121771i	−0.0920263	−	0.00351523i
$13$	1.87092	+	1.87092i	0.518899	+	0.518899i	0.917238	−	0.398339i	$-0.130413\pi$
$13$	1.87092	+	1.87092i	0.518899	+	0.518899i	−0.398339	+	0.917238i	$0.630413\pi$
$14$	−0.208273	−	0.531280i	−0.0556633	−	0.141991i
$15$	−0.354852	+	0.0360235i	−0.0916225	+	0.00930124i
$16$	−0.305140	+	3.98834i	−0.0762849	+	0.997086i
$17$	0.874816	+	0.874816i	0.212174	+	0.212174i	0.805190	−	0.593016i	$-0.202063\pi$
$17$	0.874816	+	0.874816i	0.212174	+	0.212174i	−0.593016	+	0.805190i	$0.702063\pi$
$18$	−3.85501	−	1.68371i	−0.908634	−	0.396855i
$19$			2.21601i			0.508387i	0.967153	+	0.254194i	$0.0818101\pi$
$19$			2.21601i			0.508387i	−0.967153	+	0.254194i	$0.918190\pi$
$20$	0.281517	+	4.46327i	0.0629492	+	0.998017i
$21$			0.0643636i			0.0140453i
$22$	−0.566038	+	1.29599i	−0.120680	+	0.276307i
$23$	5.75409	+	5.75409i	1.19981	+	1.19981i	0.974223	+	0.225588i	$0.0724304\pi$
$23$	5.75409	+	5.75409i	1.19981	+	1.19981i	0.225588	+	0.974223i	$0.427570\pi$
$24$	0.196228	−	0.406255i	0.0400548	−	0.0829265i
$25$	1.00481	+	4.89799i	0.200963	+	0.979599i
$26$	−3.48371	+	1.36569i	−0.683211	+	0.267833i
$27$	0.673875	+	0.673875i	0.129687	+	0.129687i
$28$	0.806427	+	0.0308040i	0.152400	+	0.00582141i
$29$	−0.286512			−0.0532040			−0.0266020	−	0.999646i	$-0.508469\pi$
$29$	−0.286512			−0.0532040			−0.0266020	+	0.999646i	$0.508469\pi$
$30$	0.154174	−	0.480277i	0.0281481	−	0.0876862i
$31$			5.05784i			0.908415i	0.890896	+	0.454208i	$0.150078\pi$
$31$			5.05784i			0.908415i	−0.890896	+	0.454208i	$0.849922\pi$
$32$	−4.99615	−	2.65301i	−0.883203	−	0.468991i
$33$	0.112791	−	0.112791i	0.0196344	−	0.0196344i
$34$	−1.62894	+	0.638578i	−0.279360	+	0.109515i
$35$	0.897656	−	0.0911274i	0.151732	−	0.0154033i
$36$	4.36416	−	4.04302i	0.727360	−	0.673837i
$37$	1.72593	−	1.72593i	0.283741	−	0.283741i	−0.550858	−	0.834599i	$-0.685699\pi$
$37$	1.72593	−	1.72593i	0.283741	−	0.283741i	0.834599	+	0.550858i	$0.185699\pi$
$38$	−2.87194	−	1.25435i	−0.465889	−	0.203482i
$39$	0.422045			0.0675812
$40$	−5.94372	−	2.16153i	−0.939784	−	0.341768i
$41$	−9.62451			−1.50310			−0.751548	−	0.659679i	$-0.770692\pi$
$41$	−9.62451			−1.50310			−0.751548	+	0.659679i	$0.770692\pi$
$42$	−0.0834149	−	0.0364323i	−0.0128712	−	0.00562162i
$43$	6.70865	−	6.70865i	1.02306	−	1.02306i	0.0233315	−	0.999728i	$-0.492573\pi$
$43$	6.70865	−	6.70865i	1.02306	−	1.02306i	0.999728	−	0.0233315i	$-0.00742732\pi$
$44$	−1.35920	−	1.46716i	−0.204907	−	0.221183i
$45$	4.20413	−	5.15415i	0.626714	−	0.768335i
$46$	−10.7143	+	4.20024i	−1.57974	+	0.619291i
$47$	4.74379	−	4.74379i	0.691954	−	0.691954i	−0.270708	−	0.962662i	$-0.587258\pi$
$47$	4.74379	−	4.74379i	0.691954	−	0.691954i	0.962662	+	0.270708i	$0.0872578\pi$
$48$	0.415432	+	0.484266i	0.0599624	+	0.0698978i
$49$			6.83718i			0.976740i
$50$	−6.91654	−	1.47022i	−0.978146	−	0.207920i
$51$	0.197343			0.0276335
$52$	0.201988	−	5.28789i	0.0280106	−	0.733299i
$53$	−3.51588	−	3.51588i	−0.482944	−	0.482944i	0.423127	−	0.906070i	$-0.360932\pi$
$53$	−3.51588	−	3.51588i	−0.482944	−	0.482944i	−0.906070	+	0.423127i	$0.860932\pi$
$54$	−1.25478	+	0.491900i	−0.170754	+	0.0669391i
$55$	−1.73275	−	1.41336i	−0.233643	−	0.190578i
$56$	−0.496390	+	1.02769i	−0.0663329	+	0.137331i
$57$	0.249946	+	0.249946i	0.0331061	+	0.0331061i
$58$	0.162177	−	0.371318i	0.0212949	−	0.0487565i
$59$			0.559395i			0.0728271i	0.999337	+	0.0364135i	$0.0115934\pi$
$59$			0.559395i			0.0728271i	−0.999337	+	0.0364135i	$0.988407\pi$
$60$	0.535168	+	0.471663i	0.0690899	+	0.0608915i
$61$			11.2560i			1.44118i	0.693360	+	0.720591i	$0.256130\pi$
$61$			11.2560i			1.44118i	−0.693360	+	0.720591i	$0.743870\pi$
$62$	−6.55493	−	2.86293i	−0.832477	−	0.363593i
$63$	−0.848709	−	0.848709i	−0.106927	−	0.106927i
$64$	6.26630	−	4.97328i	0.783288	−	0.621659i
$65$	−0.597540	−	5.88610i	−0.0741157	−	0.730081i
$66$	0.0823324	+	0.210020i	0.0101344	+	0.0258517i
$67$	0.230669	+	0.230669i	0.0281807	+	0.0281807i	0.721057	−	0.692876i	$-0.243657\pi$
$67$	0.230669	+	0.230669i	0.0281807	+	0.0281807i	−0.692876	+	0.721057i	$0.743657\pi$
$68$	0.0944468	−	2.47255i	0.0114534	−	0.299841i
$69$	1.29802			0.156263
$70$	−0.390007	+	1.21494i	−0.0466148	+	0.145213i
$71$		−	13.2381i		−	1.57107i	−0.618817	−	0.785535i	$-0.712388\pi$
$71$		−	13.2381i		−	1.57107i	0.618817	−	0.785535i	$-0.287612\pi$
$72$	2.76945	+	7.94443i	0.326383	+	0.936260i
$73$	−7.63762	+	7.63762i	−0.893916	+	0.893916i	−0.994889	−	0.100973i	$-0.967804\pi$
$73$	−7.63762	+	7.63762i	−0.893916	+	0.893916i	0.100973	+	0.994889i	$0.467804\pi$
$74$	1.25985	+	3.21374i	0.146455	+	0.373589i
$75$	0.665783	+	0.439115i	0.0768780	+	0.0507047i
$76$	3.25125	−	3.01200i	0.372944	−	0.345501i
$77$	−0.285323	+	0.285323i	−0.0325156	+	0.0325156i
$78$	−0.238893	+	0.546967i	−0.0270493	+	0.0619319i
$79$	5.08654			0.572281			0.286140	−	0.958188i	$-0.407628\pi$
$79$	5.08654			0.572281			0.286140	+	0.958188i	$0.407628\pi$
$80$	6.16570	−	6.47951i	0.689347	−	0.724432i
$81$	−8.77166			−0.974628
$82$	5.44784	−	12.4733i	0.601613	−	1.37745i
$83$	4.77497	−	4.77497i	0.524121	−	0.524121i	−0.394692	−	0.918813i	$-0.629149\pi$
$83$	4.77497	−	4.77497i	0.524121	−	0.524121i	0.918813	+	0.394692i	$0.129149\pi$
$84$	0.0944320	−	0.0874832i	0.0103034	−	0.00954520i
$85$	−0.279402	−	2.75227i	−0.0303054	−	0.298525i
$86$	4.89702	+	12.4917i	0.528059	+	1.34702i
$87$	−0.0323160	+	0.0323160i	−0.00346463	+	0.00346463i
$88$	2.67080	−	0.931047i	0.284708	−	0.0992500i
$89$			13.8064i			1.46348i	0.681584	+	0.731740i	$0.261291\pi$
$89$			13.8064i			1.46348i	−0.681584	+	0.731740i	$0.738709\pi$
$90$	4.30005	+	8.36597i	0.453265	+	0.881850i
$91$	−1.06763			−0.111918
$92$	0.621223	−	16.2632i	0.0647669	−	1.69555i
$93$	0.570478	+	0.570478i	0.0591559	+	0.0591559i
$94$	3.46276	+	8.83310i	0.357157	+	0.911065i
$95$	3.13202	−	3.83978i	0.321339	−	0.393953i
$96$	−0.862756	+	0.264284i	−0.0880547	+	0.0269734i
$97$	4.19838	+	4.19838i	0.426281	+	0.426281i	0.887360	−	0.461078i	$-0.152537\pi$
$97$	4.19838	+	4.19838i	0.426281	+	0.426281i	−0.461078	+	0.887360i	$0.652537\pi$
$98$	−8.86095	−	3.87010i	−0.895091	−	0.390940i
$99$			2.97456i			0.298954i
$100$	5.82041	−	8.13159i	0.582041	−	0.813159i
$101$		−	6.77398i		−	0.674037i	−0.941498	−	0.337018i	$-0.890582\pi$
$101$		−	6.77398i		−	0.674037i	0.941498	−	0.337018i	$-0.109418\pi$
$102$	−0.111703	+	0.255755i	−0.0110603	+	0.0253235i
$103$	7.36710	+	7.36710i	0.725902	+	0.725902i	0.969801	−	0.243899i	$-0.0784266\pi$
$103$	7.36710	+	7.36710i	0.725902	+	0.725902i	−0.243899	+	0.969801i	$0.578427\pi$
$104$	6.73875	+	3.25492i	0.660789	+	0.319172i
$105$	0.0909691	−	0.111526i	0.00887768	−	0.0108838i
$106$	6.54669	−	2.56644i	0.635870	−	0.249275i
$107$	−6.62082	−	6.62082i	−0.640058	−	0.640058i	0.310511	−	0.950570i	$-0.399500\pi$
$107$	−6.62082	−	6.62082i	−0.640058	−	0.640058i	−0.950570	+	0.310511i	$0.899500\pi$
$108$	0.0727529	−	1.90462i	0.00700065	−	0.183272i
$109$	−0.586745			−0.0562000			−0.0281000	−	0.999605i	$-0.508946\pi$
$109$	−0.586745			−0.0562000			−0.0281000	+	0.999605i	$0.508946\pi$
$110$	2.81251	−	1.44561i	0.268162	−	0.137834i
$111$		−	0.389338i		−	0.0369544i
$112$	−1.05090	−	1.22503i	−0.0993009	−	0.115754i
$113$	9.93714	−	9.93714i	0.934807	−	0.934807i	−0.0631940	−	0.998001i	$-0.520129\pi$
$113$	9.93714	−	9.93714i	0.934807	−	0.934807i	0.998001	+	0.0631940i	$0.0201287\pi$
$114$	−0.465407	+	0.182449i	−0.0435893	+	0.0170879i
$115$	−1.83776	−	18.1030i	−0.171372	−	1.68811i
$116$	0.389428	+	0.420360i	0.0361575	+	0.0390295i
$117$	−5.56515	+	5.56515i	−0.514498	+	0.514498i
$118$	−0.724973	−	0.316639i	−0.0667392	−	0.0291490i
$119$	−0.499210			−0.0457625
$120$	−0.914198	+	0.426596i	−0.0834545	+	0.0389427i
$121$	1.00000			0.0909091
$122$	−14.5877	−	6.37132i	−1.32071	−	0.576832i
$123$	−1.08556	+	1.08556i	−0.0978813	+	0.0978813i
$124$	7.42068	−	6.87463i	0.666397	−	0.617360i
$125$	5.18155	−	9.90714i	0.463452	−	0.886122i
$126$	1.58032	−	0.619520i	0.140786	−	0.0551913i
$127$	−7.88037	+	7.88037i	−0.699270	+	0.699270i	−0.964253	−	0.264983i	$-0.914634\pi$
$127$	−7.88037	+	7.88037i	−0.699270	+	0.699270i	0.264983	+	0.964253i	$0.414634\pi$
$128$	2.89837	+	10.9362i	0.256182	+	0.966628i
$129$		−	1.51335i		−	0.133243i
$130$	7.96659	+	2.55735i	0.698716	+	0.224295i
$131$	14.9948			1.31010			0.655050	−	0.755586i	$-0.272648\pi$
$131$	14.9948			1.31010			0.655050	+	0.755586i	$0.272648\pi$
$132$	−0.318788	−	0.0121771i	−0.0277470	−	0.00105988i
$133$	−0.632278	−	0.632278i	−0.0548255	−	0.0548255i
$134$	−0.429513	+	0.168378i	−0.0371043	+	0.0145457i
$135$	−0.215225	−	2.12008i	−0.0185236	−	0.182468i
$136$	3.15095	+	1.52196i	0.270192	+	0.130507i
$137$	−7.51178	−	7.51178i	−0.641775	−	0.641775i	0.309217	−	0.950992i	$-0.399933\pi$
$137$	−7.51178	−	7.51178i	−0.641775	−	0.641775i	−0.950992	+	0.309217i	$0.899933\pi$
$138$	−0.734728	+	1.68222i	−0.0625442	+	0.143200i
$139$			4.43730i			0.376367i	0.982134	+	0.188184i	$0.0602600\pi$
$139$			4.43730i			0.376367i	−0.982134	+	0.188184i	$0.939740\pi$
$140$	−1.35380	−	1.19315i	−0.114417	−	0.100839i
$141$		−	1.07011i		−	0.0901198i
$142$	17.1565	+	7.49325i	1.43974	+	0.628820i
$143$	1.87092	+	1.87092i	0.156454	+	0.156454i
$144$	−11.8636	−	0.907656i	−0.988630	−	0.0756380i
$145$	0.496453	+	0.404945i	0.0412282	+	0.0336289i
$146$	−5.57513	−	14.2215i	−0.461401	−	1.17698i
$147$	0.771172	+	0.771172i	0.0636052	+	0.0636052i
$148$	−4.87811	−	0.186335i	−0.400978	−	0.0153166i
$149$	−20.7027			−1.69603			−0.848015	−	0.529972i	$-0.822202\pi$
$149$	−20.7027			−1.69603			−0.848015	+	0.529972i	$0.822202\pi$
$150$	−0.945949	+	0.614295i	−0.0772364	+	0.0501570i
$151$		−	4.41346i		−	0.359162i	−0.983743	−	0.179581i	$-0.942526\pi$
$151$		−	4.41346i		−	0.359162i	0.983743	−	0.179581i	$-0.0574743\pi$
$152$	2.06321	+	5.91851i	0.167348	+	0.480054i
$153$	−2.60219	+	2.60219i	−0.210375	+	0.210375i
$154$	−0.208273	−	0.531280i	−0.0167831	−	0.0428118i
$155$	7.14856	−	8.76395i	0.574186	−	0.703938i
$156$	−0.573644	−	0.619209i	−0.0459283	−	0.0495764i
$157$	7.54451	−	7.54451i	0.602117	−	0.602117i	−0.338757	−	0.940874i	$-0.610006\pi$
$157$	7.54451	−	7.54451i	0.602117	−	0.602117i	0.940874	+	0.338757i	$0.110006\pi$
$158$	−2.87918	+	6.59213i	−0.229055	+	0.524442i
$159$	−0.793119			−0.0628984
$160$	4.90739	+	11.6584i	0.387963	+	0.921675i
$161$	−3.28355			−0.258780
$162$	4.96509	−	11.3680i	0.390094	−	0.893156i
$163$	4.97221	−	4.97221i	0.389454	−	0.389454i	−0.485039	−	0.874493i	$-0.661195\pi$
$163$	4.97221	−	4.97221i	0.389454	−	0.389454i	0.874493	+	0.485039i	$0.161195\pi$
$164$	13.0817	+	14.1207i	1.02151	+	1.10264i
$165$	−0.354852	+	0.0360235i	−0.0276252	+	0.00280443i
$166$	3.48552	+	8.89115i	0.270529	+	0.690087i
$167$	−14.4847	+	14.4847i	−1.12086	+	1.12086i	−0.129248	+	0.991612i	$0.541256\pi$
$167$	−14.4847	+	14.4847i	−1.12086	+	1.12086i	−0.991612	+	0.129248i	$0.958744\pi$
$168$	0.0599256	+	0.171902i	0.00462336	+	0.0132625i
$169$		−	5.99934i		−	0.461488i
$170$	3.72507	+	1.19578i	0.285700	+	0.0917125i
$171$	−6.59164			−0.504076
$172$	−18.9611	−	0.724278i	−1.44577	−	0.0552257i
$173$	−8.49105	−	8.49105i	−0.645562	−	0.645562i	0.306355	−	0.951917i	$-0.400891\pi$
$173$	−8.49105	−	8.49105i	−0.645562	−	0.645562i	−0.951917	+	0.306355i	$0.900891\pi$
$174$	−0.0235892	−	0.0601734i	−0.00178830	−	0.00456173i
$175$	−1.68421	−	1.11081i	−0.127314	−	0.0839696i
$176$	−0.305140	+	3.98834i	−0.0230008	+	0.300633i
$177$	0.0630947	+	0.0630947i	0.00474249	+	0.00474249i
$178$	−17.8931	−	7.81497i	−1.34114	−	0.585757i
$179$			2.34258i			0.175093i	0.996160	+	0.0875463i	$0.0279026\pi$
$179$			2.34258i			0.175093i	−0.996160	+	0.0875463i	$0.972097\pi$
$180$	−13.2762	+	0.837389i	−0.989552	+	0.0624153i
$181$			11.9620i			0.889131i	0.895746	+	0.444565i	$0.146642\pi$
$181$			11.9620i			0.889131i	−0.895746	+	0.444565i	$0.853358\pi$
$182$	0.604319	−	1.38364i	0.0447951	−	0.102562i
$183$	1.26957	+	1.26957i	0.0938496	+	0.0938496i
$184$	20.7253	+	10.0107i	1.52789	+	0.737997i
$185$	−5.42996	+	0.551233i	−0.399219	+	0.0405275i
$186$	−1.06225	+	0.416424i	−0.0778879	+	0.0305337i
$187$	0.874816	+	0.874816i	0.0639729	+	0.0639729i
$188$	−13.4077	−	0.512149i	−0.977857	−	0.0373523i
$189$	−0.384544			−0.0279715
$190$	3.20349	+	6.23255i	0.232405	+	0.452156i
$191$		−	2.70454i		−	0.195694i	−0.995201	−	0.0978470i	$-0.968804\pi$
$191$		−	2.70454i		−	0.195694i	0.995201	−	0.0978470i	$-0.0311956\pi$
$192$	0.145842	−	1.26772i	0.0105252	−	0.0914899i
$193$	10.1236	−	10.1236i	0.728713	−	0.728713i	−0.241650	−	0.970363i	$-0.577689\pi$
$193$	10.1236	−	10.1236i	0.728713	−	0.728713i	0.970363	+	0.241650i	$0.0776887\pi$
$194$	−7.81753	+	3.06464i	−0.561266	+	0.220028i
$195$	−0.731296	−	0.596502i	−0.0523692	−	0.0427164i
$196$	10.0313	−	9.29311i	0.716519	−	0.663794i
$197$	−6.89542	+	6.89542i	−0.491278	+	0.491278i	−0.908709	−	0.417431i	$-0.862931\pi$
$197$	−6.89542	+	6.89542i	−0.491278	+	0.491278i	0.417431	+	0.908709i	$0.362931\pi$
$198$	−3.85501	−	1.68371i	−0.273963	−	0.119656i
$199$	14.3829			1.01958			0.509790	−	0.860299i	$-0.329723\pi$
$199$	14.3829			1.01958			0.509790	+	0.860299i	$0.329723\pi$
$200$	7.24392	+	12.1460i	0.512222	+	0.858853i
$201$	0.0520347			0.00367024
$202$	8.77904	+	3.83433i	0.617691	+	0.269783i
$203$	0.0817485	−	0.0817485i	0.00573762	−	0.00573762i
$204$	−0.268228	−	0.289534i	−0.0187797	−	0.0202714i
$205$	16.6768	+	13.6029i	1.16476	+	0.950069i
$206$	−13.7178	+	5.37766i	−0.955762	+	0.374679i
$207$	−17.1159	+	17.1159i	−1.18964	+	1.18964i
$208$	−8.03275	+	6.89097i	−0.556971	+	0.477803i
$209$			2.21601i			0.153285i
$210$	0.0930448	+	0.181023i	0.00642070	+	0.0124918i
$211$	−27.2069			−1.87300			−0.936498	−	0.350672i	$-0.885953\pi$
$211$	−27.2069			−1.87300			−0.936498	+	0.350672i	$0.885953\pi$
$212$	−0.379581	+	9.93717i	−0.0260697	+	0.682488i
$213$	−1.49313	−	1.49313i	−0.102308	−	0.102308i
$214$	12.3282	−	4.83291i	0.842736	−	0.330371i
$215$	−21.1061	+	2.14263i	−1.43943	+	0.146126i
$216$	2.42719	+	1.17237i	0.165150	+	0.0797699i
$217$	−1.44312	−	1.44312i	−0.0979652	−	0.0979652i
$218$	0.332120	−	0.760418i	0.0224940	−	0.0515020i
$219$			1.72291i			0.116423i
$220$	0.281517	+	4.46327i	0.0189799	+	0.300913i
$221$			3.27342i			0.220194i
$222$	0.504580	+	0.220380i	0.0338652	+	0.0147910i
$223$	5.54613	+	5.54613i	0.371396	+	0.371396i	0.867986	−	0.496589i	$-0.165415\pi$
$223$	5.54613	+	5.54613i	0.371396	+	0.371396i	−0.496589	+	0.867986i	$0.665415\pi$
$224$	2.18248	−	0.668550i	0.145823	−	0.0446694i
$225$	−14.5694	+	2.98888i	−0.971291	+	0.199259i
$226$	7.25368	+	18.5033i	0.482507	+	1.23082i
$227$	8.54163	+	8.54163i	0.566928	+	0.566928i	0.931267	−	0.364339i	$-0.118705\pi$
$227$	8.54163	+	8.54163i	0.566928	+	0.566928i	−0.364339	+	0.931267i	$0.618705\pi$
$228$	0.0269846	−	0.706438i	0.00178710	−	0.0467850i
$229$	−23.9016			−1.57946			−0.789732	−	0.613452i	$-0.789780\pi$
$229$	−23.9016			−1.57946			−0.789732	+	0.613452i	$0.789780\pi$
$230$	24.5016	+	7.86525i	1.61559	+	0.518619i
$231$			0.0643636i			0.00423482i
$232$	−0.765216	+	0.266756i	−0.0502389	+	0.0175134i
$233$	19.8215	−	19.8215i	1.29855	−	1.29855i	0.369195	−	0.929352i	$-0.379633\pi$
$233$	19.8215	−	19.8215i	1.29855	−	1.29855i	0.929352	−	0.369195i	$-0.120367\pi$
$234$	−4.06231	−	10.3625i	−0.265562	−	0.677417i
$235$	−14.9245	+	1.51509i	−0.973566	+	0.0988335i
$236$	0.820725	−	0.760331i	0.0534246	−	0.0494933i
$237$	0.573715	−	0.573715i	0.0372668	−	0.0372668i
$238$	0.282572	−	0.646973i	0.0183164	−	0.0419371i
$239$	−0.380215			−0.0245941			−0.0122970	−	0.999924i	$-0.503914\pi$
$239$	−0.380215			−0.0245941			−0.0122970	+	0.999924i	$0.503914\pi$
$240$	−0.0353947	−	1.42627i	−0.00228472	−	0.0920650i
$241$	−8.37058			−0.539196			−0.269598	−	0.962973i	$-0.586891\pi$
$241$	−8.37058			−0.539196			−0.269598	+	0.962973i	$0.586891\pi$
$242$	−0.566038	+	1.29599i	−0.0363863	+	0.0833097i
$243$	−3.01099	+	3.01099i	−0.193155	+	0.193155i
$244$	16.5144	−	15.2992i	1.05723	−	0.979429i
$245$	9.66341	−	11.8471i	0.617373	−	0.756883i
$246$	−0.792409	−	2.02134i	−0.0505221	−	0.128876i
$247$	−4.14597	+	4.14597i	−0.263802	+	0.263802i
$248$	4.70909	+	13.5085i	0.299028	+	0.857788i
$249$		−	1.07715i		−	0.0682614i
$250$	9.90665	+	12.3231i	0.626551	+	0.779380i
$251$	6.01170			0.379455			0.189728	−	0.981837i	$-0.439240\pi$
$251$	6.01170			0.379455			0.189728	+	0.981837i	$0.439240\pi$
$252$	−0.0916282	+	2.39876i	−0.00577203	+	0.151108i
$253$	5.75409	+	5.75409i	0.361757	+	0.361757i
$254$	−5.75232	−	14.6735i	−0.360933	−	0.920697i
$255$	−0.341944	−	0.278917i	−0.0214134	−	0.0174664i
$256$	−15.8138	−	2.43400i	−0.988361	−	0.152125i
$257$	10.3420	+	10.3420i	0.645119	+	0.645119i	0.951809	−	0.306691i	$-0.0992217\pi$
$257$	10.3420	+	10.3420i	0.645119	+	0.645119i	−0.306691	+	0.951809i	$0.599222\pi$
$258$	1.96129	+	0.856613i	0.122105	+	0.0533304i
$259$			0.984895i			0.0611984i
$260$	−7.82370	+	8.87709i	−0.485205	+	0.550534i
$261$		−	0.852247i		−	0.0527527i
$262$	−8.48761	+	19.4331i	−0.524366	+	1.20058i
$263$	−3.12972	−	3.12972i	−0.192987	−	0.192987i	0.603998	−	0.796986i	$-0.293573\pi$
$263$	−3.12972	−	3.12972i	−0.192987	−	0.192987i	−0.796986	+	0.603998i	$0.793573\pi$
$264$	0.196228	−	0.406255i	0.0120770	−	0.0250033i
$265$	1.12291	+	11.0613i	0.0689801	+	0.679493i
$266$	1.17732	−	0.461535i	0.0721862	−	0.0282985i
$267$	1.55724	+	1.55724i	0.0953016	+	0.0953016i
$268$	0.0249034	−	0.651955i	0.00152122	−	0.0398245i
$269$	−11.4887			−0.700481			−0.350241	−	0.936660i	$-0.613900\pi$
$269$	−11.4887			−0.700481			−0.350241	+	0.936660i	$0.613900\pi$
$270$	2.86944	+	0.921119i	0.174629	+	0.0560575i
$271$		−	16.0654i		−	0.975906i	−0.872870	−	0.487953i	$-0.837744\pi$
$271$		−	16.0654i		−	0.975906i	0.872870	−	0.487953i	$-0.162256\pi$
$272$	−3.75601	+	3.22213i	−0.227742	+	0.195370i
$273$	−0.120419	+	0.120419i	−0.00728809	+	0.00728809i
$274$	13.9872	−	5.48327i	0.844996	−	0.331256i
$275$	1.00481	+	4.89799i	0.0605926	+	0.295360i
$276$	−1.76427	−	1.90441i	−0.106197	−	0.114632i
$277$	−7.55739	+	7.55739i	−0.454080	+	0.454080i	−0.896706	−	0.442626i	$-0.854047\pi$
$277$	−7.55739	+	7.55739i	−0.454080	+	0.454080i	0.442626	+	0.896706i	$0.354047\pi$
$278$	−5.75072	−	2.51168i	−0.344905	−	0.150641i
$279$	−15.0448			−0.900711
$280$	2.31261	−	1.07914i	0.138205	−	0.0644911i
$281$	5.50501			0.328401			0.164201	−	0.986427i	$-0.447496\pi$
$281$	5.50501			0.328401			0.164201	+	0.986427i	$0.447496\pi$
$282$	1.38686	+	0.605725i	0.0825864	+	0.0360704i
$283$	2.43572	−	2.43572i	0.144788	−	0.144788i	−0.630997	−	0.775785i	$-0.717354\pi$
$283$	2.43572	−	2.43572i	0.144788	−	0.144788i	0.775785	+	0.630997i	$0.217354\pi$
$284$	−19.4224	+	17.9932i	−1.15251	+	1.06770i
$285$	−0.0798285	−	0.786356i	−0.00472863	−	0.0465797i
$286$	−3.48371	+	1.36569i	−0.205996	+	0.0807548i
$287$	2.74609	−	2.74609i	0.162097	−	0.162097i
$288$	7.89154	−	14.8613i	0.465013	−	0.875712i
$289$		−	15.4694i		−	0.909964i
$290$	−0.805818	+	0.414185i	−0.0473193	+	0.0243218i
$291$	0.947079			0.0555187
$292$	21.5867	+	0.824572i	1.26327	+	0.0482544i
$293$	4.85259	+	4.85259i	0.283491	+	0.283491i	0.834500	−	0.551008i	$-0.185757\pi$
$293$	4.85259	+	4.85259i	0.283491	+	0.283491i	−0.551008	+	0.834500i	$0.685757\pi$
$294$	−1.43595	+	0.562922i	−0.0837461	+	0.0328303i
$295$	0.790628	−	0.969290i	0.0460322	−	0.0564342i
$296$	3.00268	−	6.21653i	0.174528	−	0.361329i
$297$	0.673875	+	0.673875i	0.0391022	+	0.0391022i
$298$	11.7185	−	26.8306i	0.678835	−	1.55425i
$299$			21.5308i			1.24516i
$300$	−0.260680	−	1.57366i	−0.0150503	−	0.0908552i
$301$			3.82826i			0.220657i
$302$	5.71982	+	2.49819i	0.329139	+	0.143754i
$303$	−0.764044	−	0.764044i	−0.0438932	−	0.0438932i
$304$	−8.83821	−	0.676193i	−0.506906	−	0.0387823i
$305$	15.9088	−	19.5038i	0.910935	−	1.11678i
$306$	−1.89949	−	4.84536i	−0.108586	−	0.276991i
$307$	−17.1436	−	17.1436i	−0.978435	−	0.978435i	0.0213373	−	0.999772i	$-0.493208\pi$
$307$	−17.1436	−	17.1436i	−0.978435	−	0.978435i	−0.999772	+	0.0213373i	$0.993208\pi$
$308$	0.806427	+	0.0308040i	0.0459504	+	0.00175522i
$309$	1.66188			0.0945412
$310$	7.31167	+	14.2252i	0.415275	+	0.807939i
$311$		−	31.0090i		−	1.75836i	−0.476490	−	0.879180i	$-0.658091\pi$
$311$		−	31.0090i		−	1.75836i	0.476490	−	0.879180i	$-0.341909\pi$
$312$	1.12719	−	0.392944i	0.0638148	−	0.0222460i
$313$	12.2736	−	12.2736i	0.693743	−	0.693743i	−0.269311	−	0.963053i	$-0.586796\pi$
$313$	12.2736	−	12.2736i	0.693743	−	0.693743i	0.963053	+	0.269311i	$0.0867958\pi$
$314$	5.50716	+	14.0481i	0.310787	+	0.792781i
$315$	0.271064	+	2.67013i	0.0152727	+	0.150445i
$316$	−6.91364	−	7.46279i	−0.388922	−	0.419815i
$317$	3.97766	−	3.97766i	0.223408	−	0.223408i	−0.586524	−	0.809932i	$-0.699504\pi$
$317$	3.97766	−	3.97766i	0.223408	−	0.223408i	0.809932	+	0.586524i	$0.199504\pi$
$318$	0.448935	−	1.02788i	0.0251750	−	0.0576405i
$319$	−0.286512			−0.0160416
$320$	−17.8869	−	0.239132i	−0.999911	−	0.0133679i
$321$	−1.49354			−0.0833610
$322$	1.85861	−	4.25546i	0.103576	−	0.237147i
$323$	−1.93860	+	1.93860i	−0.107867	+	0.107867i
$324$	11.9225	+	12.8695i	0.662358	+	0.714970i
$325$	−7.28381	+	11.0437i	−0.404033	+	0.612592i
$326$	3.62950	+	9.25842i	0.201019	+	0.512776i
$327$	−0.0661795	+	0.0661795i	−0.00365973	+	0.00365973i
$328$	−25.7051	+	8.96087i	−1.41933	+	0.494781i
$329$			2.70703i			0.149243i
$330$	0.154174	−	0.480277i	0.00848698	−	0.0264384i
$331$	19.7904			1.08778			0.543889	−	0.839157i	$-0.316951\pi$
$331$	19.7904			1.08778			0.543889	+	0.839157i	$0.316951\pi$
$332$	−13.4958	−	0.515515i	−0.740679	−	0.0282926i
$333$	5.13388	+	5.13388i	0.281335	+	0.281335i
$334$	−10.5732	−	26.9710i	−0.578540	−	1.47579i
$335$	−0.0736718	−	0.725709i	−0.00402512	−	0.0396497i
$336$	−0.256704	−	0.0196399i	−0.0140044	−	0.00107144i
$337$	20.1648	+	20.1648i	1.09845	+	1.09845i	0.994593	+	0.103853i	$0.0331173\pi$
$337$	20.1648	+	20.1648i	1.09845	+	1.09845i	0.103853	+	0.994593i	$0.466883\pi$
$338$	7.77512	+	3.39586i	0.422911	+	0.184710i
$339$		−	2.24164i		−	0.121749i
$340$	−3.65826	+	4.15081i	−0.198397	+	0.225109i
$341$			5.05784i			0.273897i
$342$	3.73112	−	8.54273i	0.201756	−	0.461938i
$343$	−3.94806	−	3.94806i	−0.213175	−	0.213175i
$344$	11.6714	−	24.1635i	0.629278	−	1.30281i
$345$	−2.24914	−	1.83457i	−0.121089	−	0.0987699i
$346$	15.8106	−	6.19809i	0.849983	−	0.333211i
$347$	−0.0236426	−	0.0236426i	−0.00126920	−	0.00126920i	0.706472	−	0.707741i	$-0.250286\pi$
$347$	−0.0236426	−	0.0236426i	−0.00126920	−	0.00126920i	−0.707741	+	0.706472i	$0.750286\pi$
$348$	0.0913367	+	0.00348889i	0.00489616	+	0.000187024i
$349$	19.3949			1.03819			0.519093	−	0.854718i	$-0.326270\pi$
$349$	19.3949			1.03819			0.519093	+	0.854718i	$0.326270\pi$
$350$	2.39293	−	1.55396i	0.127908	−	0.0830626i
$351$			2.52153i			0.134589i
$352$	−4.99615	−	2.65301i	−0.266296	−	0.141406i
$353$	−15.7826	+	15.7826i	−0.840021	+	0.840021i	−0.988861	−	0.148840i	$-0.952446\pi$
$353$	−15.7826	+	15.7826i	−0.840021	+	0.840021i	0.148840	+	0.988861i	$0.452446\pi$
$354$	−0.117484	+	0.0460564i	−0.00624422	+	0.00244787i
$355$	−18.7102	+	22.9382i	−0.993034	+	1.21743i
$356$	20.2563	−	18.7657i	1.07358	−	0.994582i
$357$	−0.0563063	+	0.0563063i	−0.00298005	+	0.00298005i
$358$	−3.03597	−	1.32599i	−0.160456	−	0.0700807i
$359$	23.3205			1.23081			0.615403	−	0.788212i	$-0.288993\pi$
$359$	23.3205			1.23081			0.615403	+	0.788212i	$0.288993\pi$
$360$	6.42960	−	17.6799i	0.338870	−	0.931814i
$361$	14.0893			0.741542
$362$	−15.5027	−	6.77096i	−0.814805	−	0.355874i
$363$	0.112791	−	0.112791i	0.00591999	−	0.00591999i
$364$	1.45113	+	1.56639i	0.0760596	+	0.0821011i
$365$	24.0288	−	2.43933i	1.25772	−	0.127680i
$366$	−2.36399	+	0.926733i	−0.123568	+	0.0484411i
$367$	20.4270	−	20.4270i	1.06628	−	1.06628i	0.0686386	−	0.997642i	$-0.478134\pi$
$367$	20.4270	−	20.4270i	1.06628	−	1.06628i	0.997642	−	0.0686386i	$-0.0218655\pi$
$368$	−24.7051	+	21.1935i	−1.28784	+	1.10479i
$369$		−	28.6286i		−	1.49035i
$370$	2.35917	−	7.34922i	0.122647	−	0.382068i
$371$	2.00632			0.104163
$372$	0.0615899	−	1.61238i	0.00319329	−	0.0835980i
$373$	−6.27550	−	6.27550i	−0.324933	−	0.324933i	0.525723	−	0.850656i	$-0.323795\pi$
$373$	−6.27550	−	6.27550i	−0.324933	−	0.324933i	−0.850656	+	0.525723i	$0.823795\pi$
$374$	−1.62894	+	0.638578i	−0.0842303	+	0.0330201i
$375$	−0.533004	−	1.70187i	−0.0275242	−	0.0878841i
$376$	8.25301	−	17.0864i	0.425616	−	0.881164i
$377$	−0.536040	−	0.536040i	−0.0276075	−	0.0276075i
$378$	0.217667	−	0.498367i	0.0111956	−	0.0256332i
$379$		−	15.5024i		−	0.796303i	−0.917320	−	0.398152i	$-0.869652\pi$
$379$		−	15.5024i		−	0.796303i	0.917320	−	0.398152i	$-0.130348\pi$
$380$	−9.89064	+	0.623845i	−0.507379	+	0.0320026i
$381$			1.77767i			0.0910727i
$382$	3.50507	+	1.53087i	0.179335	+	0.0783264i
$383$	11.5795	+	11.5795i	0.591683	+	0.591683i	0.938086	−	0.346403i	$-0.112597\pi$
$383$	11.5795	+	11.5795i	0.591683	+	0.591683i	−0.346403	+	0.938086i	$0.612597\pi$
$384$	1.56041	+	0.906588i	0.0796292	+	0.0462641i
$385$	0.897656	−	0.0911274i	0.0457488	−	0.00464428i
$386$	7.38979	+	18.8505i	0.376130	+	0.959464i
$387$	19.9553	+	19.9553i	1.01438	+	1.01438i
$388$	0.453265	−	11.8662i	0.0230111	−	0.602413i
$389$	4.61369			0.233923			0.116962	−	0.993136i	$-0.462685\pi$
$389$	4.61369			0.233923			0.116962	+	0.993136i	$0.462685\pi$
$390$	1.18700	−	0.610113i	0.0601063	−	0.0308942i
$391$			10.0675i			0.509138i
$392$	6.36574	+	18.2607i	0.321518	+	0.922305i
$393$	1.69127	−	1.69127i	0.0853135	−	0.0853135i
$394$	−5.03335	−	12.8395i	−0.253577	−	0.646844i
$395$	−8.81368	−	7.18913i	−0.443464	−	0.361724i
$396$	4.36416	−	4.04302i	0.219307	−	0.203170i
$397$	21.5191	−	21.5191i	1.08001	−	1.08001i	0.0835054	−	0.996507i	$-0.473388\pi$
$397$	21.5191	−	21.5191i	1.08001	−	1.08001i	0.996507	−	0.0835054i	$-0.0266116\pi$
$398$	−8.14130	+	18.6402i	−0.408086	+	0.934350i
$399$	−0.142630			−0.00714045
$400$	−19.8415	+	2.51297i	−0.992075	+	0.125649i
$401$	−11.8594			−0.592230			−0.296115	−	0.955152i	$-0.595691\pi$
$401$	−11.8594			−0.592230			−0.296115	+	0.955152i	$0.595691\pi$
$402$	−0.0294536	+	0.0674367i	−0.00146901	+	0.00336343i
$403$	−9.46280	+	9.46280i	−0.471376	+	0.471376i
$404$	−9.93854	+	9.20721i	−0.494461	+	0.458076i
$405$	15.1990	+	12.3975i	0.755247	+	0.616038i
$406$	0.0596728	+	0.152218i	0.00296151	+	0.00755447i
$407$	1.72593	−	1.72593i	0.0855512	−	0.0855512i
$408$	0.527062	−	0.183735i	0.0260934	−	0.00909625i
$409$		−	20.3192i		−	1.00472i	−0.864659	−	0.502360i	$-0.832465\pi$
$409$		−	20.3192i		−	1.00472i	0.864659	−	0.502360i	$-0.167535\pi$
$410$	−27.0690	+	13.9133i	−1.33684	+	0.687129i
$411$	−1.69452			−0.0835845
$412$	0.795366	−	20.8221i	0.0391849	−	1.02583i
$413$	−0.159608	−	0.159608i	−0.00785381	−	0.00785381i
$414$	−12.4938	−	31.8703i	−0.614039	−	1.56634i
$415$	−15.0226	+	1.52505i	−0.737429	+	0.0748616i
$416$	−4.38381	−	14.3109i	−0.214934	−	0.701652i
$417$	0.500487	+	0.500487i	0.0245090	+	0.0245090i
$418$	−2.87194	−	1.25435i	−0.140471	−	0.0613520i
$419$			33.1628i			1.62011i	0.586355	+	0.810054i	$0.300562\pi$
$419$			33.1628i			1.62011i	−0.586355	+	0.810054i	$0.699438\pi$
$420$	−0.287272	+	0.0181195i	−0.0140174	+	0.000884140i
$421$			22.8238i			1.11236i	0.831061	+	0.556181i	$0.187734\pi$
$421$			22.8238i			1.11236i	−0.831061	+	0.556181i	$0.812266\pi$
$422$	15.4001	−	35.2599i	0.749666	−	1.71643i
$423$	14.1107	+	14.1107i	0.686085	+	0.686085i
$424$	−12.6637	−	6.11675i	−0.615002	−	0.297056i
$425$	−3.40582	+	5.16387i	−0.165206	+	0.250485i
$426$	2.78026	−	1.08992i	0.134704	−	0.0528069i
$427$	−3.21159	−	3.21159i	−0.155420	−	0.155420i
$428$	−0.714796	+	18.7128i	−0.0345510	+	0.904520i
$429$	0.422045			0.0203765
$430$	9.17003	−	28.5662i	0.442218	−	1.37759i
$431$		−	39.6181i		−	1.90833i	−0.299274	−	0.954167i	$-0.596744\pi$
$431$		−	39.6181i		−	1.90833i	0.299274	−	0.954167i	$-0.403256\pi$
$432$	−2.89327	+	2.48202i	−0.139203	+	0.119416i
$433$	2.35945	−	2.35945i	0.113388	−	0.113388i	−0.648136	−	0.761524i	$-0.724451\pi$
$433$	2.35945	−	2.35945i	0.113388	−	0.113388i	0.761524	+	0.648136i	$0.224451\pi$
$434$	2.68713	−	1.05341i	0.128986	−	0.0505654i
$435$	0.101669	−	0.0103212i	0.00487468	−	0.000494863i
$436$	0.797505	+	0.860851i	0.0381935	+	0.0412273i
$437$	−12.7511	+	12.7511i	−0.609969	+	0.609969i
$438$	−2.23288	−	0.975232i	−0.106691	−	0.0465984i
$439$	−8.44908			−0.403253			−0.201626	−	0.979463i	$-0.564623\pi$
$439$	−8.44908			−0.403253			−0.201626	+	0.979463i	$0.564623\pi$
$440$	−5.94372	−	2.16153i	−0.283356	−	0.103047i
$441$	−20.3376			−0.968456
$442$	−4.24233	−	1.85288i	−0.201787	−	0.0881324i
$443$	−29.5580	+	29.5580i	−1.40434	+	1.40434i	−0.618774	+	0.785569i	$0.712370\pi$
$443$	−29.5580	+	29.5580i	−1.40434	+	1.40434i	−0.785569	+	0.618774i	$0.787630\pi$
$444$	−0.571223	+	0.529190i	−0.0271091	+	0.0251142i
$445$	19.5135	−	23.9230i	0.925029	−	1.13406i
$446$	−10.3271	+	4.04843i	−0.489001	+	0.191699i
$447$	−2.33507	+	2.33507i	−0.110445	+	0.110445i
$448$	−0.368930	+	3.20691i	−0.0174303	+	0.151512i
$449$		−	1.46179i		−	0.0689863i	−0.999405	−	0.0344931i	$-0.989018\pi$
$449$		−	1.46179i		−	0.0689863i	0.999405	−	0.0344931i	$-0.0109817\pi$
$450$	4.37324	−	20.5736i	0.206157	−	0.969850i
$451$	−9.62451			−0.453200
$452$	−28.0860	−	1.07283i	−1.32105	−	0.0504618i
$453$	−0.497798	−	0.497798i	−0.0233886	−	0.0233886i
$454$	−15.9048	+	6.23502i	−0.746449	+	0.292624i
$455$	1.84993	+	1.50895i	0.0867261	+	0.0707406i
$456$	0.900265	+	0.434842i	0.0421588	+	0.0203634i
$457$	−6.30888	−	6.30888i	−0.295117	−	0.295117i	0.543981	−	0.839098i	$-0.316916\pi$
$457$	−6.30888	−	6.30888i	−0.295117	−	0.295117i	−0.839098	+	0.543981i	$0.816916\pi$
$458$	13.5292	−	30.9764i	0.632179	−	1.44743i
$459$			1.17903i			0.0550326i
$460$	−24.0622	+	27.3019i	−1.12190	+	1.27296i
$461$		−	15.2314i		−	0.709398i	−0.934981	−	0.354699i	$-0.884583\pi$
$461$		−	15.2314i		−	0.709398i	0.934981	−	0.354699i	$-0.115417\pi$
$462$	−0.0834149	−	0.0364323i	−0.00388081	−	0.00169498i
$463$	13.1028	+	13.1028i	0.608940	+	0.608940i	0.942669	−	0.333729i	$-0.108307\pi$
$463$	13.1028	+	13.1028i	0.608940	+	0.608940i	−0.333729	+	0.942669i	$0.608307\pi$
$464$	0.0874263	−	1.14271i	0.00405866	−	0.0530489i
$465$	−0.182201	−	1.79479i	−0.00844938	−	0.0832312i
$466$	14.4688	+	36.9082i	0.670254	+	1.70974i
$467$	14.7934	+	14.7934i	0.684556	+	0.684556i	0.961023	−	0.276467i	$-0.0891636\pi$
$467$	14.7934	+	14.7934i	0.684556	+	0.684556i	−0.276467	+	0.961023i	$0.589164\pi$
$468$	15.7291	+	0.600824i	0.727080	+	0.0277731i
$469$	−0.131630			−0.00607812
$470$	6.48428	−	20.1997i	0.299098	−	0.931740i
$471$		−	1.70190i		−	0.0784195i
$472$	0.520824	+	1.49403i	0.0239728	+	0.0687683i
$473$	6.70865	−	6.70865i	0.308464	−	0.308464i
$474$	0.418787	+	1.06828i	0.0192355	+	0.0490676i
$475$	−10.8540	+	2.22668i	−0.498016	+	0.102167i
$476$	0.678527	+	0.732423i	0.0311003	+	0.0335706i
$477$	10.4582	−	10.4582i	0.478848	−	0.478848i
$478$	0.215216	−	0.492757i	0.00984376	−	0.0225382i
$479$	−19.6828			−0.899329			−0.449664	−	0.893198i	$-0.648456\pi$
$479$	−19.6828			−0.899329			−0.449664	+	0.893198i	$0.648456\pi$
$480$	1.86847	+	0.761449i	0.0852834	+	0.0347552i
$481$	6.45814			0.294466
$482$	4.73807	−	10.8482i	0.215813	−	0.494123i
$483$	−0.370354	+	0.370354i	−0.0168517	+	0.0168517i
$484$	−1.35920	−	1.46716i	−0.0617819	−	0.0666893i
$485$	−1.34089	−	13.2086i	−0.0608869	−	0.599770i
$486$	−2.19789	−	5.60656i	−0.0996983	−	0.254319i
$487$	13.4743	−	13.4743i	0.610578	−	0.610578i	−0.332519	−	0.943097i	$-0.607898\pi$
$487$	13.4743	−	13.4743i	0.610578	−	0.610578i	0.943097	+	0.332519i	$0.107898\pi$
$488$	10.4799	+	30.0625i	0.474401	+	1.36086i
$489$		−	1.12164i		−	0.0507223i
$490$	9.88391	+	19.2296i	0.446509	+	0.868706i
$491$	24.7812			1.11836			0.559180	−	0.829046i	$-0.311116\pi$
$491$	24.7812			1.11836			0.559180	+	0.829046i	$0.311116\pi$
$492$	3.06818	+	0.117199i	0.138324	+	0.00528373i
$493$	−0.250646	−	0.250646i	−0.0112885	−	0.0112885i
$494$	−3.02638	−	7.71993i	−0.136163	−	0.347336i
$495$	4.20413	−	5.15415i	0.188961	−	0.231662i
$496$	−20.1724	−	1.54335i	−0.905768	−	0.0692984i
$497$	3.77712	+	3.77712i	0.169427	+	0.169427i
$498$	1.39598	+	0.609706i	0.0625552	+	0.0273216i
$499$		−	19.5522i		−	0.875275i	−0.899151	−	0.437638i	$-0.855815\pi$
$499$		−	19.5522i		−	0.875275i	0.899151	−	0.437638i	$-0.144185\pi$
$500$	−21.5782	+	5.86363i	−0.965006	+	0.262229i
$501$			3.26749i			0.145981i
$502$	−3.40285	+	7.79113i	−0.151877	+	0.347735i
$503$	4.55657	+	4.55657i	0.203167	+	0.203167i	0.801356	−	0.598188i	$-0.204112\pi$
$503$	4.55657	+	4.55657i	0.203167	+	0.203167i	−0.598188	+	0.801356i	$0.704112\pi$
$504$	−3.05692	−	1.47654i	−0.136166	−	0.0657703i
$505$	−9.57409	+	11.7376i	−0.426042	+	0.522316i
$506$	−10.7143	+	4.20024i	−0.476309	+	0.186723i
$507$	−0.676671	−	0.676671i	−0.0300520	−	0.0300520i
$508$	22.2728	+	0.850779i	0.988196	+	0.0377472i
$509$	34.0303			1.50836			0.754182	−	0.656665i	$-0.228034\pi$
$509$	34.0303			1.50836			0.754182	+	0.656665i	$0.228034\pi$
$510$	0.555028	−	0.285281i	0.0245770	−	0.0126324i
$511$		−	4.35838i		−	0.192803i
$512$	12.1057	−	19.1168i	0.534999	−	0.844852i
$513$	−1.49331	+	1.49331i	−0.0659314	+	0.0659314i
$514$	−19.2572	+	7.54924i	−0.849399	+	0.332983i
$515$	−2.35293	−	23.1777i	−0.103682	−	1.02133i
$516$	−2.22033	+	2.05695i	−0.0977446	+	0.0905520i
$517$	4.74379	−	4.74379i	0.208632	−	0.208632i
$518$	−1.27642	−	0.557488i	−0.0560826	−	0.0244946i
$519$	−1.91542			−0.0840778
$520$	−7.07615	−	15.1642i	−0.310310	−	0.664996i
$521$	34.1502			1.49615			0.748074	−	0.663615i	$-0.230979\pi$
$521$	34.1502			1.49615			0.748074	+	0.663615i	$0.230979\pi$
$522$	1.10451	+	0.482404i	0.0483429	+	0.0211142i
$523$	−25.6693	+	25.6693i	−1.12244	+	1.12244i	−0.131065	+	0.991374i	$0.541840\pi$
$523$	−25.6693	+	25.6693i	−1.12244	+	1.12244i	−0.991374	+	0.131065i	$0.958160\pi$
$524$	−20.3809	−	21.9998i	−0.890345	−	0.961065i
$525$	−0.315253	+	0.0646735i	−0.0137588	+	0.00282258i
$526$	5.82765	−	2.28456i	0.254098	−	0.0996116i
$527$	−4.42468	+	4.42468i	−0.192742	+	0.192742i
$528$	0.415432	+	0.484266i	0.0180794	+	0.0210750i
$529$			43.2191i			1.87909i
$530$	−14.9711	−	4.80585i	−0.650301	−	0.208753i
$531$	−1.66395			−0.0722094
$532$	−0.0682619	+	1.78705i	−0.00295953	+	0.0774784i
$533$	−18.0066	−	18.0066i	−0.779955	−	0.779955i
$534$	−2.89963	+	1.13672i	−0.125479	+	0.0491906i
$535$	2.11458	+	20.8298i	0.0914212	+	0.900551i
$536$	0.830833	+	0.401306i	0.0358865	+	0.0173338i
$537$	0.264222	+	0.264222i	0.0114020	+	0.0114020i
$538$	6.50307	−	14.8893i	0.280367	−	0.641925i
$539$			6.83718i			0.294498i
$540$	−2.81798	+	3.19739i	−0.121266	+	0.137594i
$541$			19.8518i			0.853495i	0.904371	+	0.426747i	$0.140341\pi$
$541$			19.8518i			0.853495i	−0.904371	+	0.426747i	$0.859659\pi$
$542$	20.8207	+	9.09365i	0.894326	+	0.390606i
$543$	1.34921	+	1.34921i	0.0579001	+	0.0579001i
$544$	−2.04981	−	6.69161i	−0.0878851	−	0.286901i
$545$	1.01668	+	0.829283i	0.0435498	+	0.0355226i
$546$	−0.0879006	−	0.224224i	−0.00376180	−	0.00959590i
$547$	−15.2940	−	15.2940i	−0.653924	−	0.653924i	0.300011	−	0.953936i	$-0.403010\pi$
$547$	−15.2940	−	15.2940i	−0.653924	−	0.653924i	−0.953936	+	0.300011i	$0.903010\pi$
$548$	−0.810986	+	21.2310i	−0.0346436	+	0.906945i
$549$	−33.4816			−1.42896
$550$	−6.91654	−	1.47022i	−0.294922	−	0.0626903i
$551$		−	0.634914i		−	0.0270482i
$552$	3.46674	−	1.20852i	0.147554	−	0.0514379i
$553$	−1.45131	+	1.45131i	−0.0617158	+	0.0617158i
$554$	−5.51657	−	14.0721i	−0.234376	−	0.597867i
$555$	−0.550276	+	0.674624i	−0.0233579	+	0.0286362i
$556$	6.51025	−	6.03119i	0.276096	−	0.255779i
$557$	25.5799	−	25.5799i	1.08386	−	1.08386i	0.0877095	−	0.996146i	$-0.472045\pi$
$557$	25.5799	−	25.5799i	1.08386	−	1.08386i	0.996146	−	0.0877095i	$-0.0279547\pi$
$558$	8.51595	−	19.4980i	0.360509	−	0.825417i
$559$	25.1026			1.06173
$560$	0.0895366	+	3.60797i	0.00378361	+	0.152465i
$561$	0.197343			0.00833181
$562$	−3.11604	+	7.13446i	−0.131442	+	0.300949i
$563$	−16.5125	+	16.5125i	−0.695920	+	0.695920i	−0.963528	−	0.267608i	$-0.913767\pi$
$563$	−16.5125	+	16.5125i	−0.695920	+	0.695920i	0.267608	+	0.963528i	$0.413767\pi$
$564$	−1.57003	+	1.45450i	−0.0661103	+	0.0612455i
$565$	−31.2633	+	3.17376i	−1.31526	+	0.133521i
$566$	1.77797	+	4.53539i	0.0747336	+	0.190637i
$567$	2.50275	−	2.50275i	0.105106	−	0.105106i
$568$	−12.3253	−	35.3562i	−0.517157	−	1.48351i
$569$		−	10.1557i		−	0.425749i	−0.977080	−	0.212875i	$-0.931717\pi$
$569$		−	10.1557i		−	0.425749i	0.977080	−	0.212875i	$-0.0682826\pi$
$570$	1.06430	+	0.341650i	0.0445786	+	0.0143101i
$571$	−24.3864			−1.02054			−0.510271	−	0.860014i	$-0.670455\pi$
$571$	−24.3864			−1.02054			−0.510271	+	0.860014i	$0.670455\pi$
$572$	0.201988	−	5.28789i	0.00844553	−	0.221098i
$573$	−0.305048	−	0.305048i	−0.0127436	−	0.0127436i
$574$	2.00453	+	5.11331i	0.0836673	+	0.213425i
$575$	−22.4017	+	33.9653i	−0.934216	+	1.41645i
$576$	14.7933	+	18.6395i	0.616387	+	0.776644i
$577$	3.60418	+	3.60418i	0.150044	+	0.150044i	0.778138	−	0.628094i	$-0.216165\pi$
$577$	3.60418	+	3.60418i	0.150044	+	0.150044i	−0.628094	+	0.778138i	$0.716165\pi$
$578$	20.0482	+	8.75626i	0.833897	+	0.364213i
$579$		−	2.28370i		−	0.0949073i
$580$	−0.0806581	−	1.27878i	−0.00334915	−	0.0530985i
$581$			2.72482i			0.113044i
$582$	−0.536083	+	1.22741i	−0.0222213	+	0.0508777i
$583$	−3.51588	−	3.51588i	−0.145613	−	0.145613i
$584$	−13.2875	+	27.5095i	−0.549842	+	1.13835i
$585$	17.5086	−	1.77742i	0.723889	−	0.0734871i
$586$	−9.03568	+	3.54218i	−0.373260	+	0.146326i
$587$	20.0053	+	20.0053i	0.825708	+	0.825708i	0.986920	−	0.161212i	$-0.0515402\pi$
$587$	20.0053	+	20.0053i	0.825708	+	0.825708i	−0.161212	+	0.986920i	$0.551540\pi$
$588$	0.0832572	−	2.17961i	0.00343347	−	0.0898857i
$589$	−11.2082			−0.461827
$590$	0.808668	+	1.57330i	0.0332923	+	0.0647719i
$591$			1.55548i			0.0639839i
$592$	6.35695	+	7.41025i	0.261269	+	0.304560i
$593$	−7.88763	+	7.88763i	−0.323906	+	0.323906i	−0.850264	−	0.526357i	$-0.823557\pi$
$593$	−7.88763	+	7.88763i	−0.323906	+	0.323906i	0.526357	+	0.850264i	$0.323557\pi$
$594$	−1.25478	+	0.491900i	−0.0514842	+	0.0201829i
$595$	0.865004	+	0.705565i	0.0354617	+	0.0289253i
$596$	28.1391	+	30.3742i	1.15262	+	1.24418i
$597$	1.62227	−	1.62227i	0.0663949	−	0.0663949i
$598$	−27.9039	−	12.1873i	−1.14107	−	0.498375i
$599$	−24.7820			−1.01256			−0.506282	−	0.862368i	$-0.668980\pi$
$599$	−24.7820			−1.01256			−0.506282	+	0.862368i	$0.668980\pi$
$600$	2.18701	+	0.552911i	0.0892842	+	0.0225725i
$601$	19.3917			0.791002			0.395501	−	0.918465i	$-0.370571\pi$
$601$	19.3917			0.791002			0.395501	+	0.918465i	$0.370571\pi$
$602$	−4.96140	−	2.16694i	−0.202212	−	0.0883179i
$603$	−0.686138	+	0.686138i	−0.0279417	+	0.0279417i
$604$	−6.47527	+	5.99878i	−0.263475	+	0.244087i
$605$	−1.73275	−	1.41336i	−0.0704461	−	0.0574613i
$606$	1.42267	−	0.557718i	0.0577922	−	0.0226558i
$607$	−13.7299	+	13.7299i	−0.557278	+	0.557278i	−0.928531	−	0.371254i	$-0.878928\pi$
$607$	−13.7299	+	13.7299i	−0.557278	+	0.557278i	0.371254	+	0.928531i	$0.378928\pi$
$608$	5.87910	−	11.0715i	0.238429	−	0.449009i
$609$		−	0.0184410i		−	0.000747265i
$610$	16.2718	+	31.6576i	0.658826	+	1.28178i
$611$	17.7505			0.718108
$612$	7.35474	+	0.280937i	0.297298	+	0.0113562i
$613$	−9.51670	−	9.51670i	−0.384376	−	0.384376i	0.488300	−	0.872676i	$-0.337617\pi$
$613$	−9.51670	−	9.51670i	−0.384376	−	0.384376i	−0.872676	+	0.488300i	$0.837617\pi$
$614$	31.9219	−	12.5141i	1.28826	−	0.505026i
$615$	3.41528	−	0.346709i	0.137717	−	0.0139806i
$616$	−0.496390	+	1.02769i	−0.0200001	+	0.0414067i
$617$	4.95100	+	4.95100i	0.199320	+	0.199320i	0.799708	−	0.600389i	$-0.204987\pi$
$617$	4.95100	+	4.95100i	0.199320	+	0.199320i	−0.600389	+	0.799708i	$0.704987\pi$
$618$	−0.940689	+	2.15379i	−0.0378400	+	0.0866381i
$619$			6.58188i			0.264548i	0.991213	+	0.132274i	$0.0422279\pi$
$619$			6.58188i			0.264548i	−0.991213	+	0.132274i	$0.957772\pi$
$620$	−22.5745	+	1.42387i	−0.906614	+	0.0571840i
$621$			7.75508i			0.311201i
$622$	40.1875	+	17.5523i	1.61137	+	0.703782i
$623$	−3.93929	−	3.93929i	−0.157824	−	0.157824i
$624$	−0.128783	+	1.68326i	−0.00515543	+	0.0673843i
$625$	−22.9807	+	9.84315i	−0.919228	+	0.393726i
$626$	8.95916	+	22.8538i	0.358080	+	0.913420i
$627$	0.249946	+	0.249946i	0.00998187	+	0.00998187i
$628$	−21.3235	−	0.814519i	−0.850902	−	0.0325029i
$629$	3.01974			0.120405
$630$	−3.61390	−	1.16010i	−0.143981	−	0.0462194i
$631$			4.05272i			0.161336i	0.996741	+	0.0806681i	$0.0257054\pi$
$631$			4.05272i			0.161336i	−0.996741	+	0.0806681i	$0.974295\pi$
$632$	13.5851	−	4.73581i	0.540387	−	0.188380i
$633$	−3.06868	+	3.06868i	−0.121969	+	0.121969i
$634$	2.90352	+	7.40654i	0.115314	+	0.294151i
$635$	24.7925	−	2.51686i	0.983860	−	0.0998785i
$636$	1.07801	+	1.16364i	0.0427458	+	0.0461411i
$637$	−12.7918	+	12.7918i	−0.506829	+	0.506829i
$638$	0.162177	−	0.371318i	0.00642064	−	0.0147006i
$639$	39.3774			1.55775
$640$	10.4346	−	23.0460i	0.412464	−	0.910974i
$641$	4.69381			0.185394			0.0926972	−	0.995694i	$-0.470451\pi$
$641$	4.69381			0.185394			0.0926972	+	0.995694i	$0.470451\pi$
$642$	0.845398	−	1.93561i	0.0333652	−	0.0763925i
$643$	29.8290	−	29.8290i	1.17634	−	1.17634i	0.195673	−	0.980669i	$-0.437311\pi$
$643$	29.8290	−	29.8290i	1.17634	−	1.17634i	0.980669	−	0.195673i	$-0.0626892\pi$
$644$	4.46300	+	4.81750i	0.175867	+	0.189836i
$645$	−2.13891	+	2.62225i	−0.0842195	+	0.103251i
$646$	−1.41509	−	3.60974i	−0.0556761	−	0.142023i
$647$	6.12198	−	6.12198i	0.240680	−	0.240680i	−0.576452	−	0.817131i	$-0.695563\pi$
$647$	6.12198	−	6.12198i	0.240680	−	0.240680i	0.817131	+	0.576452i	$0.195563\pi$
$648$	−23.4273	+	8.16683i	−0.920311	+	0.320823i
$649$			0.559395i			0.0219582i
$650$	−10.1896	−	15.6909i	−0.399669	−	0.615448i
$651$	−0.325541			−0.0127590
$652$	−14.0533	−	0.536809i	−0.550369	−	0.0210231i
$653$	31.8906	+	31.8906i	1.24798	+	1.24798i	0.956612	+	0.291364i	$0.0941091\pi$
$653$	31.8906	+	31.8906i	1.24798	+	1.24798i	0.291364	+	0.956612i	$0.405891\pi$
$654$	−0.0483081	−	0.123228i	−0.00188900	−	0.00481861i
$655$	−25.9821	−	21.1931i	−1.01521	−	0.828081i
$656$	2.93682	−	38.3859i	0.114664	−	1.49872i
$657$	−22.7185	−	22.7185i	−0.886335	−	0.886335i
$658$	−3.50829	−	1.53228i	−0.136767	−	0.0597345i
$659$		−	49.3027i		−	1.92056i	−0.279038	−	0.960280i	$-0.590016\pi$
$659$		−	49.3027i		−	1.92056i	0.279038	−	0.960280i	$-0.409984\pi$
$660$	0.535168	+	0.471663i	0.0208314	+	0.0183595i
$661$			29.6533i			1.15338i	0.816964	+	0.576689i	$0.195656\pi$
$661$			29.6533i			1.15338i	−0.816964	+	0.576689i	$0.804344\pi$
$662$	−11.2021	+	25.6482i	−0.435382	+	0.996847i
$663$	0.369211	+	0.369211i	0.0143390	+	0.0143390i
$664$	8.30725	−	17.1987i	0.322384	−	0.667439i
$665$	0.201939	+	1.98921i	0.00783086	+	0.0771384i
$666$	−9.55944	+	3.74751i	−0.370421	+	0.145213i
$667$	−1.64862	−	1.64862i	−0.0638347	−	0.0638347i
$668$	40.9391	+	1.56380i	1.58398	+	0.0605051i
$669$	1.25110			0.0483705
$670$	0.982216	+	0.315301i	0.0379463	+	0.0121811i
$671$			11.2560i			0.434533i
$672$	0.170758	−	0.321570i	0.00658712	−	0.0124048i
$673$	27.1144	−	27.1144i	1.04518	−	1.04518i	0.0462547	−	0.998930i	$-0.485271\pi$
$673$	27.1144	−	27.1144i	1.04518	−	1.04518i	0.998930	−	0.0462547i	$-0.0147286\pi$
$674$	−37.5475	+	14.7194i	−1.44628	+	0.566971i
$675$	−2.62352	+	3.97776i	−0.100979	+	0.153104i
$676$	−8.80202	+	8.15432i	−0.338539	+	0.313628i
$677$	12.6211	−	12.6211i	0.485067	−	0.485067i	−0.421678	−	0.906745i	$-0.638559\pi$
$677$	12.6211	−	12.6211i	0.485067	−	0.485067i	0.906745	+	0.421678i	$0.138559\pi$
$678$	2.90515	+	1.26885i	0.111572	+	0.0487300i
$679$	−2.39579			−0.0919420
$680$	−3.30872	−	7.09061i	−0.126883	−	0.271912i
$681$	1.92684			0.0738365
$682$	−6.55493	−	2.86293i	−0.251001	−	0.109627i
$683$	34.3377	−	34.3377i	1.31390	−	1.31390i	0.395379	−	0.918518i	$-0.370613\pi$
$683$	34.3377	−	34.3377i	1.31390	−	1.31390i	0.918518	−	0.395379i	$-0.129387\pi$
$684$	8.95938	+	9.67102i	0.342570	+	0.369781i
$685$	2.39914	+	23.6329i	0.0916663	+	0.902965i
$686$	7.35142	−	2.88191i	0.280679	−	0.110032i
$687$	−2.69589	+	2.69589i	−0.102854	+	0.102854i
$688$	24.7093	+	28.8035i	0.942034	+	1.09812i
$689$		−	13.1558i		−	0.501198i
$690$	3.65069	−	1.87643i	0.138979	−	0.0714345i
$691$	33.5300			1.27554			0.637770	−	0.770227i	$-0.279857\pi$
$691$	33.5300			1.27554			0.637770	+	0.770227i	$0.279857\pi$
$692$	−0.916709	+	23.9988i	−0.0348481	+	0.912298i
$693$	−0.848709	−	0.848709i	−0.0322398	−	0.0322398i
$694$	0.0440233	−	0.0172581i	0.00167110	−	0.000655108i
$695$	6.27152	−	7.68872i	0.237892	−	0.291650i
$696$	−0.0562216	+	0.116397i	−0.00213108	+	0.00441202i
$697$	−8.41968	−	8.41968i	−0.318918	−	0.318918i
$698$	−10.9783	+	25.1357i	−0.415533	+	0.951399i
$699$		−	4.47136i		−	0.169122i
$700$	0.659432	+	3.98083i	0.0249242	+	0.150461i
$701$			35.7084i			1.34869i	0.738418	+	0.674343i	$0.235573\pi$
$701$			35.7084i			1.34869i	−0.738418	+	0.674343i	$0.764427\pi$
$702$	−3.26789	−	1.42728i	−0.123338	−	0.0538693i
$703$	3.82468	+	3.82468i	0.144250	+	0.144250i
$704$	6.26630	−	4.97328i	0.236170	−	0.187437i
$705$	−1.51246	+	1.85423i	−0.0569625	+	0.0698345i
$706$	−11.5206	−	29.3876i	−0.433583	−	1.10602i
$707$	1.93277	+	1.93277i	0.0726894	+	0.0726894i
$708$	0.00681182	−	0.178329i	0.000256004	−	0.00670200i
$709$	−39.0549			−1.46674			−0.733369	−	0.679831i	$-0.762053\pi$
$709$	−39.0549			−1.46674			−0.733369	+	0.679831i	$0.762053\pi$
$710$	−19.1371	−	37.2322i	−0.718203	−	1.39730i
$711$			15.1302i			0.567427i
$712$	12.8544	+	36.8742i	0.481741	+	1.38192i
$713$	−29.1033	+	29.1033i	−1.08993	+	1.08993i
$714$	−0.0411012	−	0.104844i	−0.00153817	−	0.00392370i
$715$	−0.597540	−	5.88610i	−0.0223467	−	0.220128i
$716$	3.43695	−	3.18404i	0.128445	−	0.118993i
$717$	−0.0428848	+	0.0428848i	−0.00160156	+	0.00160156i
$718$	−13.2003	+	30.2232i	−0.492630	+	1.12792i
$719$	−16.9352			−0.631577			−0.315789	−	0.948830i	$-0.602269\pi$
$719$	−16.9352			−0.631577			−0.315789	+	0.948830i	$0.602269\pi$
$720$	19.2737	+	18.3402i	0.718288	+	0.683500i
$721$	−4.20400			−0.156565
$722$	−7.97508	+	18.2597i	−0.296802	+	0.679554i
$723$	−0.944125	+	0.944125i	−0.0351124	+	0.0351124i
$724$	17.5503	−	16.2588i	0.652250	−	0.604254i
$725$	−0.287892	−	1.40333i	−0.0106920	−	0.0521186i
$726$	0.0823324	+	0.210020i	0.00305564	+	0.00779458i
$727$	10.5645	−	10.5645i	0.391816	−	0.391816i	−0.483519	−	0.875334i	$-0.660641\pi$
$727$	10.5645	−	10.5645i	0.391816	−	0.391816i	0.875334	+	0.483519i	$0.160641\pi$
$728$	−2.85142	+	0.994014i	−0.105681	+	0.0368406i
$729$		−	25.6357i		−	0.949472i
$730$	−10.4398	+	32.5219i	−0.386396	+	1.20369i
$731$	11.7377			0.434133
$732$	0.137066	−	3.58828i	0.00506609	−	0.132627i
$733$	−26.7709	−	26.7709i	−0.988806	−	0.988806i	0.0111318	−	0.999938i	$-0.496457\pi$
$733$	−26.7709	−	26.7709i	−0.988806	−	0.988806i	−0.999938	+	0.0111318i	$0.996457\pi$
$734$	14.9108	+	38.0357i	0.550368	+	1.40392i
$735$	−0.246299	−	2.42619i	−0.00908489	−	0.0894913i
$736$	−13.4826	−	44.0140i	−0.496976	−	1.62238i
$737$	0.230669	+	0.230669i	0.00849680	+	0.00849680i
$738$	37.1026	+	16.2049i	1.36576	+	0.596511i
$739$			32.3664i			1.19062i	0.803497	+	0.595308i	$0.202970\pi$
$739$			32.3664i			1.19062i	−0.803497	+	0.595308i	$0.797030\pi$
$740$	8.18917	+	7.21741i	0.301040	+	0.265317i
$741$			0.935255i			0.0343574i
$742$	−1.13565	+	2.60018i	−0.0416912	+	0.0954557i
$743$	−7.97591	−	7.97591i	−0.292608	−	0.292608i	0.545502	−	0.838110i	$-0.316339\pi$
$743$	−7.97591	−	7.97591i	−0.292608	−	0.292608i	−0.838110	+	0.545502i	$0.816339\pi$
$744$	2.05477	+	0.992489i	0.0753317	+	0.0363864i
$745$	35.8725	+	29.2604i	1.31427	+	1.07202i
$746$	11.6852	−	4.58084i	0.427825	−	0.167716i
$747$	14.2034	+	14.2034i	0.519676	+	0.519676i
$748$	0.0944468	−	2.47255i	0.00345332	−	0.0904054i
$749$	3.77814			0.138050
$750$	2.50731	+	0.272552i	0.0915540	+	0.00995218i
$751$			4.90471i			0.178975i	0.995988	+	0.0894877i	$0.0285230\pi$
$751$			4.90471i			0.178975i	−0.995988	+	0.0894877i	$0.971477\pi$
$752$	17.4724	+	20.3674i	0.637152	+	0.742723i
$753$	0.678065	−	0.678065i	0.0247101	−	0.0247101i
$754$	0.998124	−	0.391286i	0.0363495	−	0.0142498i
$755$	−6.23782	+	7.64740i	−0.227017	+	0.278318i
$756$	0.522673	+	0.564189i	0.0190094	+	0.0205194i
$757$	−7.42934	+	7.42934i	−0.270024	+	0.270024i	−0.829110	−	0.559086i	$-0.811152\pi$
$757$	−7.42934	+	7.42934i	−0.270024	+	0.270024i	0.559086	+	0.829110i	$0.311152\pi$
$758$	20.0910	+	8.77493i	0.729737	+	0.318720i
$759$	1.29802			0.0471151
$760$	4.78998	−	13.1713i	0.173751	−	0.477774i
$761$	4.50429			0.163280			0.0816402	−	0.996662i	$-0.473984\pi$
$761$	4.50429			0.163280			0.0816402	+	0.996662i	$0.473984\pi$
$762$	−2.30385	−	1.00623i	−0.0834596	−	0.0364518i
$763$	0.167412	−	0.167412i	0.00606071	−	0.00606071i
$764$	−3.96801	+	3.67602i	−0.143558	+	0.132994i
$765$	8.18677	−	0.831096i	0.295993	−	0.0300484i
$766$	−21.5614	+	8.45251i	−0.779043	+	0.305402i
$767$	−1.04658	+	1.04658i	−0.0377899	+	0.0377899i
$768$	−2.05818	+	1.50912i	−0.0742683	+	0.0544556i
$769$			27.7960i			1.00235i	0.865346	+	0.501175i	$0.167099\pi$
$769$			27.7960i			1.00235i	−0.865346	+	0.501175i	$0.832901\pi$
$770$	−0.390007	+	1.21494i	−0.0140549	+	0.0437834i
$771$	2.33298			0.0840201
$772$	−28.6130	−	1.09296i	−1.02980	−	0.0393366i
$773$	−26.7682	−	26.7682i	−0.962784	−	0.962784i	0.0365482	−	0.999332i	$-0.488364\pi$
$773$	−26.7682	−	26.7682i	−0.962784	−	0.962784i	−0.999332	+	0.0365482i	$0.988364\pi$
$774$	−37.1573	+	14.5665i	−1.33559	+	0.523581i
$775$	−24.7733	+	5.08219i	−0.889882	+	0.182558i
$776$	15.1219	+	7.30413i	0.542845	+	0.262203i
$777$	0.111087	+	0.111087i	0.00398523	+	0.00398523i
$778$	−2.61152	+	5.97931i	−0.0936276	+	0.214369i
$779$		−	21.3280i		−	0.764155i
$780$	0.118813	+	1.88370i	0.00425418	+	0.0674472i
$781$		−	13.2381i		−	0.473695i
$782$	−13.0475	−	5.69861i	−0.466577	−	0.203782i
$783$	−0.193074	−	0.193074i	−0.00689988	−	0.00689988i
$784$	−27.2690	−	2.08630i	−0.973894	−	0.0745106i
$785$	−23.7358	+	2.40959i	−0.847168	+	0.0860020i
$786$	1.23456	+	3.14921i	0.0440352	+	0.112328i
$787$	−35.7033	−	35.7033i	−1.27268	−	1.27268i	−0.944674	−	0.328009i	$-0.893622\pi$
$787$	−35.7033	−	35.7033i	−1.27268	−	1.27268i	−0.328009	−	0.944674i	$-0.606378\pi$
$788$	19.4890	+	0.744442i	0.694266	+	0.0265197i
$789$	−0.706009			−0.0251346
$790$	14.3059	−	7.35316i	0.508983	−	0.261614i
$791$			5.67058i			0.201623i
$792$	2.76945	+	7.94443i	0.0984082	+	0.282293i
$793$	−21.0590	+	21.0590i	−0.747828	+	0.747828i
$794$	15.7080	+	40.0693i	0.557456	+	1.42200i
$795$	1.37427	+	1.12096i	0.0487404	+	0.0397565i
$796$	−19.5493	−	21.1021i	−0.692908	−	0.747946i
$797$	−13.4162	+	13.4162i	−0.475227	+	0.475227i	−0.903601	−	0.428374i	$-0.859086\pi$
$797$	−13.4162	+	13.4162i	−0.475227	+	0.475227i	0.428374	+	0.903601i	$0.359086\pi$
$798$	0.0807342	−	0.184848i	0.00285796	−	0.00654355i
$799$	8.29990			0.293629
$800$	7.97424	−	27.1369i	0.281932	−	0.959434i
$801$	−41.0680			−1.45107
$802$	6.71287	−	15.3697i	0.237040	−	0.542723i
$803$	−7.63762	+	7.63762i	−0.269526	+	0.269526i
$804$	−0.0707257	−	0.0763434i	−0.00249430	−	0.00269242i
$805$	5.68955	+	4.64084i	0.200530	+	0.163568i
$806$	−6.90743	−	17.6200i	−0.243304	−	0.620639i
$807$	−1.29583	+	1.29583i	−0.0456152	+	0.0456152i
$808$	−6.30690	−	18.0919i	−0.221876	−	0.636472i
$809$		−	51.6080i		−	1.81444i	−0.420657	−	0.907220i	$-0.638200\pi$
$809$		−	51.6080i		−	1.81444i	0.420657	−	0.907220i	$-0.361800\pi$
$810$	−24.6704	+	12.6804i	−0.866828	+	0.445544i
$811$	−15.4898			−0.543921			−0.271961	−	0.962308i	$-0.587672\pi$
$811$	−15.4898			−0.543921			−0.271961	+	0.962308i	$0.587672\pi$
$812$	−0.231051	−	0.00882572i	−0.00810830	−	0.000309722i
$813$	−1.81203	−	1.81203i	−0.0635508	−	0.0635508i
$814$	1.25985	+	3.21374i	0.0441578	+	0.112641i
$815$	−15.6431	+	1.58804i	−0.547954	+	0.0556267i
$816$	−0.0602171	+	0.787070i	−0.00210802	+	0.0275530i
$817$	14.8664	+	14.8664i	0.520110	+	0.520110i
$818$	26.3336	+	11.5014i	0.920732	+	0.402138i
$819$		−	3.17573i		−	0.110969i
$820$	−2.70947	−	42.9567i	−0.0946186	−	1.50011i
$821$		−	39.7866i		−	1.38856i	−0.719703	−	0.694282i	$-0.755722\pi$
$821$		−	39.7866i		−	1.38856i	0.719703	−	0.694282i	$-0.244278\pi$
$822$	0.959163	−	2.19609i	0.0334546	−	0.0765974i
$823$	−27.1122	−	27.1122i	−0.945071	−	0.945071i	0.0534972	−	0.998568i	$-0.482963\pi$
$823$	−27.1122	−	27.1122i	−0.945071	−	0.945071i	−0.998568	+	0.0534972i	$0.982963\pi$
$824$	26.5351	+	12.8169i	0.924395	+	0.446498i
$825$	0.665783	+	0.439115i	0.0231796	+	0.0152880i
$826$	0.297196	−	0.116507i	0.0103408	−	0.00405380i
$827$	−21.6527	−	21.6527i	−0.752938	−	0.752938i	0.222088	−	0.975027i	$-0.428713\pi$
$827$	−21.6527	−	21.6527i	−0.752938	−	0.752938i	−0.975027	+	0.222088i	$0.928713\pi$
$828$	48.3757	+	1.84786i	1.68117	+	0.0642176i
$829$	−29.3601			−1.01972			−0.509859	−	0.860258i	$-0.670302\pi$
$829$	−29.3601			−1.01972			−0.509859	+	0.860258i	$0.670302\pi$
$830$	6.52690	−	20.3324i	0.226552	−	0.705748i
$831$			1.70481i			0.0591392i
$832$	21.0283	+	2.41914i	0.729025	+	0.0838687i
$833$	−5.98128	+	5.98128i	−0.207239	+	0.207239i
$834$	−0.931923	+	0.365334i	−0.0322699	+	0.0126505i
$835$	45.5705	−	4.62618i	1.57703	−	0.160095i
$836$	3.25125	−	3.01200i	0.112447	−	0.104172i
$837$	−3.40836	+	3.40836i	−0.117810	+	0.117810i
$838$	−42.9788	−	18.7714i	−1.48468	−	0.648447i
$839$	−2.46543			−0.0851162			−0.0425581	−	0.999094i	$-0.513551\pi$
$839$	−2.46543			−0.0851162			−0.0425581	+	0.999094i	$0.513551\pi$
$840$	0.139124	−	0.382559i	0.00480024	−	0.0131995i
$841$	−28.9179			−0.997169
$842$	−29.5795	−	12.9191i	−1.01938	−	0.445222i
$843$	0.620915	−	0.620915i	0.0213854	−	0.0213854i
$844$	36.9796	+	39.9169i	1.27289	+	1.37400i
$845$	−8.47925	+	10.3953i	−0.291695	+	0.357610i
$846$	−26.2745	+	10.3002i	−0.903338	+	0.354128i
$847$	−0.285323	+	0.285323i	−0.00980381	+	0.00980381i
$848$	15.0954	−	12.9497i	0.518378	−	0.444695i
$849$		−	0.549454i		−	0.0188572i
$850$	−4.76453	−	7.33687i	−0.163422	−	0.251652i
$851$	19.8623			0.680872
$852$	−0.161202	+	4.22014i	−0.00552267	+	0.144580i
$853$	−9.44415	−	9.44415i	−0.323362	−	0.323362i	0.526694	−	0.850055i	$-0.323432\pi$
$853$	−9.44415	−	9.44415i	−0.323362	−	0.323362i	−0.850055	+	0.526694i	$0.823432\pi$
$854$	5.98009	−	2.34432i	0.204634	−	0.0802211i
$855$	11.4216	+	9.31638i	0.390612	+	0.318614i
$856$	−23.8471	−	11.5186i	−0.815078	−	0.393696i
$857$	−27.4771	−	27.4771i	−0.938600	−	0.938600i	0.0596213	−	0.998221i	$-0.481011\pi$
$857$	−27.4771	−	27.4771i	−0.938600	−	0.938600i	−0.998221	+	0.0596213i	$0.981011\pi$
$858$	−0.238893	+	0.546967i	−0.00815568	+	0.0186732i
$859$		−	42.5632i		−	1.45224i	−0.687569	−	0.726119i	$-0.741322\pi$
$859$		−	42.5632i		−	1.45224i	0.687569	−	0.726119i	$-0.258678\pi$
$860$	31.8311	+	28.0539i	1.08543	+	0.956630i
$861$		−	0.619468i		−	0.0211114i
$862$	51.3448	+	22.4253i	1.74881	+	0.763810i
$863$	31.7594	+	31.7594i	1.08110	+	1.08110i	0.996407	+	0.0846967i	$0.0269921\pi$
$863$	31.7594	+	31.7594i	1.08110	+	1.08110i	0.0846967	+	0.996407i	$0.473008\pi$
$864$	−1.57898	−	5.15458i	−0.0537181	−	0.175363i
$865$	2.71190	+	26.7137i	0.0922073	+	0.908295i
$866$	1.72229	+	4.39337i	0.0585259	+	0.149293i
$867$	−1.74481	−	1.74481i	−0.0592567	−	0.0592567i
$868$	−0.155802	+	4.07878i	−0.00528825	+	0.138443i
$869$	5.08654			0.172549
$870$	−0.0441726	+	0.137605i	−0.00149759	+	0.00466526i
$871$			0.863124i			0.0292459i
$872$	−1.56708	+	0.546287i	−0.0530679	+	0.0184996i
$873$	−12.4883	+	12.4883i	−0.422666	+	0.422666i
$874$	−9.30776	−	23.7430i	−0.314840	−	0.803119i
$875$	1.34832	+	4.30515i	0.0455815	+	0.145541i
$876$	2.52779	−	2.34178i	0.0854061	−	0.0791214i
$877$	10.1429	−	10.1429i	0.342502	−	0.342502i	−0.514805	−	0.857307i	$-0.672136\pi$
$877$	10.1429	−	10.1429i	0.342502	−	0.342502i	0.857307	+	0.514805i	$0.172136\pi$
$878$	4.78250	−	10.9500i	0.161402	−	0.369543i
$879$	1.09466			0.0369218
$880$	6.16570	−	6.47951i	0.207846	−	0.218424i
$881$	−31.7447			−1.06951			−0.534753	−	0.845008i	$-0.679595\pi$
$881$	−31.7447			−1.06951			−0.534753	+	0.845008i	$0.679595\pi$
$882$	11.5118	−	26.3574i	0.387624	−	0.887499i
$883$	−25.9174	+	25.9174i	−0.872189	+	0.872189i	−0.992711	−	0.120522i	$-0.961543\pi$
$883$	−25.9174	+	25.9174i	−0.872189	+	0.872189i	0.120522	+	0.992711i	$0.461543\pi$
$884$	4.80264	−	4.44923i	0.161530	−	0.149644i
$885$	−0.0201514	−	0.198503i	−0.000677382	−	0.00667259i
$886$	−21.5760	−	55.0379i	−0.724861	−	1.84904i
$887$	6.16127	−	6.16127i	0.206875	−	0.206875i	−0.596063	−	0.802938i	$-0.703269\pi$
$887$	6.16127	−	6.16127i	0.206875	−	0.206875i	0.802938	+	0.596063i	$0.203269\pi$
$888$	−0.362493	−	1.03984i	−0.0121645	−	0.0348949i
$889$		−	4.49690i		−	0.150821i
$890$	19.9587	+	38.8307i	0.669019	+	1.30161i
$891$	−8.77166			−0.293862
$892$	0.598770	−	15.6754i	0.0200483	−	0.524851i
$893$	10.5123	+	10.5123i	0.351780	+	0.351780i
$894$	−1.70450	−	4.34798i	−0.0570071	−	0.145418i
$895$	3.31091	−	4.05910i	0.110672	−	0.135681i
$896$	−3.94731	−	2.29336i	−0.131870	−	0.0766159i
$897$	2.42848	+	2.42848i	0.0810847	+	0.0810847i
$898$	1.89447	+	0.827430i	0.0632194	+	0.0276117i
$899$		−	1.44913i		−	0.0483313i
$900$	24.1879	+	17.3132i	0.806263	+	0.577105i
$901$		−	6.15150i		−	0.204936i
$902$	5.44784	−	12.4733i	0.181393	−	0.415316i
$903$	0.431793	+	0.431793i	0.0143692	+	0.0143692i
$904$	17.2881	−	35.7920i	0.574994	−	1.19042i
$905$	16.9067	−	20.7272i	0.561997	−	0.688994i
$906$	0.926916	−	0.363371i	0.0307947	−	0.0120722i
$907$	−30.9814	−	30.9814i	−1.02872	−	1.02872i	−0.999575	−	0.0291446i	$-0.990722\pi$
$907$	−30.9814	−	30.9814i	−1.02872	−	1.02872i	−0.0291446	−	0.999575i	$-0.509278\pi$
$908$	0.922170	−	24.1418i	0.0306033	−	0.801173i
$909$	20.1496			0.668320
$910$	−3.00272	+	1.54338i	−0.0995392	+	0.0511625i
$911$		−	37.6883i		−	1.24867i	−0.781158	−	0.624334i	$-0.785370\pi$
$911$		−	37.6883i		−	1.24867i	0.781158	−	0.624334i	$-0.214630\pi$
$912$	−1.07314	+	0.920601i	−0.0355351	+	0.0304841i
$913$	4.77497	−	4.77497i	0.158029	−	0.158029i
$914$	11.7473	−	4.60520i	0.388567	−	0.152327i
$915$	−0.405481	−	3.99422i	−0.0134048	−	0.132045i
$916$	32.4871	+	35.0676i	1.07341	+	1.15867i
$917$	−4.27835	+	4.27835i	−0.141284	+	0.141284i
$918$	−1.52802	−	0.667378i	−0.0504322	−	0.0220268i
$919$	54.9560			1.81283			0.906416	−	0.422387i	$-0.138808\pi$
$919$	54.9560			1.81283			0.906416	+	0.422387i	$0.138808\pi$
$920$	−21.7630	−	46.6384i	−0.717506	−	1.53762i
$921$	−3.86728			−0.127431
$922$	19.7398	+	8.62156i	0.650096	+	0.283936i
$923$	24.7673	−	24.7673i	0.815226	−	0.815226i
$924$	0.0944320	−	0.0874832i	0.00310658	−	0.00287798i
$925$	10.1878	+	6.71936i	0.334974	+	0.220931i
$926$	−24.3979	+	9.56449i	−0.801764	+	0.314309i
$927$	−21.9138	+	21.9138i	−0.719745	+	0.719745i
$928$	1.43146	+	0.760121i	0.0469899	+	0.0249522i
$929$			22.8701i			0.750343i	0.926955	+	0.375171i	$0.122416\pi$
$929$			22.8701i			0.750343i	−0.926955	+	0.375171i	$0.877584\pi$
$930$	2.42917	+	0.779785i	0.0796555	+	0.0255702i
$931$	−15.1513			−0.496562
$932$	−56.0227	−	2.13996i	−1.83508	−	0.0700968i
$933$	−3.49753	−	3.49753i	−0.114504	−	0.114504i
$934$	−27.5458	+	10.7985i	−0.901325	+	0.353339i
$935$	−0.279402	−	2.75227i	−0.00913742	−	0.0900087i
$936$	−9.68195	+	20.0448i	−0.316465	+	0.655184i
$937$	−12.1780	−	12.1780i	−0.397839	−	0.397839i	0.479631	−	0.877470i	$-0.340770\pi$
$937$	−12.1780	−	12.1780i	−0.397839	−	0.397839i	−0.877470	+	0.479631i	$0.840770\pi$
$938$	0.0745077	−	0.170592i	0.00243276	−	0.00557003i
$939$		−	2.76869i		−	0.0903528i
$940$	22.5083	+	19.8374i	0.734139	+	0.647023i
$941$			1.63679i			0.0533578i	0.999644	+	0.0266789i	$0.00849317\pi$
$941$			1.63679i			0.0533578i	−0.999644	+	0.0266789i	$0.991507\pi$
$942$	2.20566	+	0.963342i	0.0718642	+	0.0313874i
$943$	−55.3803	−	55.3803i	−1.80343	−	1.80343i
$944$	−2.23106	−	0.170694i	−0.0726149	−	0.00555561i
$945$	0.666317	+	0.543500i	0.0216753	+	0.0176801i
$946$	4.89702	+	12.4917i	0.159216	+	0.406141i
$947$	−20.6519	−	20.6519i	−0.671097	−	0.671097i	0.286872	−	0.957969i	$-0.407385\pi$
$947$	−20.6519	−	20.6519i	−0.671097	−	0.671097i	−0.957969	+	0.286872i	$0.907385\pi$
$948$	−1.62153	−	0.0619394i	−0.0526648	−	0.00201170i
$949$	−28.5787			−0.927704
$950$	3.25801	−	15.3271i	0.105704	−	0.497277i
$951$		−	0.897288i		−	0.0290966i
$952$	−1.33329	+	0.464788i	−0.0432121	+	0.0150639i
$953$	−24.9911	+	24.9911i	−0.809542	+	0.809542i	−0.984564	−	0.175023i	$-0.944000\pi$
$953$	−24.9911	+	24.9911i	−0.809542	+	0.809542i	0.175023	+	0.984564i	$0.444000\pi$
$954$	7.63402	+	19.4735i	0.247161	+	0.630477i
$955$	−3.82250	+	4.68629i	−0.123693	+	0.151645i
$956$	0.516789	+	0.557838i	0.0167142	+	0.0180418i
$957$	−0.0323160	+	0.0323160i	−0.00104463	+	0.00104463i
$958$	11.1412	−	25.5088i	0.359956	−	0.824151i
$959$	4.28656			0.138420
$960$	−2.04446	+	1.99051i	−0.0659845	+	0.0642435i
$961$	5.41824			0.174782
$962$	−3.65555	+	8.36972i	−0.117860	+	0.269850i
$963$	19.6940	−	19.6940i	0.634630	−	0.634630i
$964$	11.3773	+	12.2810i	0.366438	+	0.395545i
$965$	−31.8499	+	3.23331i	−1.02529	+	0.104084i
$966$	−0.270342	−	0.689611i	−0.00869812	−	0.0221879i
$967$	−6.48045	+	6.48045i	−0.208397	+	0.208397i	−0.803586	−	0.595189i	$-0.797077\pi$
$967$	−6.48045	+	6.48045i	−0.208397	+	0.208397i	0.595189	+	0.803586i	$0.297077\pi$
$968$	2.67080	−	0.931047i	0.0858426	−	0.0299250i
$969$			0.437313i			0.0140485i
$970$	17.8772	+	5.73876i	0.574003	+	0.184260i
$971$	21.2930			0.683325			0.341662	−	0.939823i	$-0.389010\pi$
$971$	21.2930			0.683325			0.341662	+	0.939823i	$0.389010\pi$
$972$	8.51016	+	0.325072i	0.272963	+	0.0104267i
$973$	−1.26606	−	1.26606i	−0.0405881	−	0.0405881i
$974$	9.83564	+	25.0895i	0.315154	+	0.803921i
$975$	0.424077	+	2.06717i	0.0135813	+	0.0662025i
$976$	−44.8928	−	3.43465i	−1.43698	−	0.109941i
$977$	12.3197	+	12.3197i	0.394143	+	0.394143i	0.876161	−	0.482018i	$-0.160096\pi$
$977$	12.3197	+	12.3197i	0.394143	+	0.394143i	−0.482018	+	0.876161i	$0.660096\pi$
$978$	1.45364	+	0.634891i	0.0464822	+	0.0203016i
$979$			13.8064i			0.441256i
$980$	−30.5162	+	1.92478i	−0.974803	+	0.0614850i
$981$		−	1.74531i		−	0.0557233i
$982$	−14.0271	+	32.1163i	−0.447623	+	1.02487i
$983$	9.97291	+	9.97291i	0.318087	+	0.318087i	0.848032	−	0.529945i	$-0.177788\pi$
$983$	9.97291	+	9.97291i	0.318087	+	0.318087i	−0.529945	+	0.848032i	$0.677788\pi$
$984$	−1.88860	+	3.91001i	−0.0602062	+	0.124646i
$985$	21.6937	−	2.20228i	0.691219	−	0.0701705i
$986$	0.466710	−	0.182960i	0.0148631	−	0.00582664i
$987$	0.305328	+	0.305328i	0.00971869	+	0.00971869i
$988$	11.7180	+	0.447606i	0.372800	+	0.0142403i
$989$	77.2044			2.45496
$990$	4.30005	+	8.36597i	0.136665	+	0.265888i
$991$			10.2604i			0.325932i	0.986632	+	0.162966i	$0.0521061\pi$
$991$			10.2604i			0.325932i	−0.986632	+	0.162966i	$0.947894\pi$
$992$	13.4185	−	25.2697i	0.426039	−	0.802315i
$993$	2.23217	−	2.23217i	0.0708359	−	0.0708359i
$994$	−7.03313	+	2.75713i	−0.223077	+	0.0874510i
$995$	−24.9220	−	20.3283i	−0.790080	−	0.644451i
$996$	−1.58035	+	1.46406i	−0.0500753	+	0.0463905i
$997$	−1.24824	+	1.24824i	−0.0395321	+	0.0395321i	−0.726597	−	0.687064i	$-0.758899\pi$
$997$	−1.24824	+	1.24824i	−0.0395321	+	0.0395321i	0.687064	+	0.726597i	$0.258899\pi$
$998$	25.3395	+	11.0673i	0.802108	+	0.350328i
$999$	2.32612			0.0735953

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	440.2.r.h.67.10	✓	56
5.3	odd	4	inner	440.2.r.h.243.26	yes	56
8.3	odd	2	inner	440.2.r.h.67.26	yes	56
40.3	even	4	inner	440.2.r.h.243.10	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
440.2.r.h.67.10	✓	56	1.1	even	1	trivial
440.2.r.h.67.26	yes	56	8.3	odd	2	inner
440.2.r.h.243.10	yes	56	40.3	even	4	inner
440.2.r.h.243.26	yes	56	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	440.r (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.566038 + 1.29599i) q^{2} +(0.112791 - 0.112791i) q^{3} +(-1.35920 - 1.46716i) q^{4} +(-1.73275 - 1.41336i) q^{5} +(0.0823324 + 0.210020i) q^{6} +(-0.285323 + 0.285323i) q^{7} +(2.67080 - 0.931047i) q^{8} +2.97456i q^{9} +O(q^{10})\)	\(q+(-0.566038 + 1.29599i) q^{2} +(0.112791 - 0.112791i) q^{3} +(-1.35920 - 1.46716i) q^{4} +(-1.73275 - 1.41336i) q^{5} +(0.0823324 + 0.210020i) q^{6} +(-0.285323 + 0.285323i) q^{7} +(2.67080 - 0.931047i) q^{8} +2.97456i q^{9} +(2.81251 - 1.44561i) q^{10} +1.00000 q^{11} +(-0.318788 - 0.0121771i) q^{12} +(1.87092 + 1.87092i) q^{13} +(-0.208273 - 0.531280i) q^{14} +(-0.354852 + 0.0360235i) q^{15} +(-0.305140 + 3.98834i) q^{16} +(0.874816 + 0.874816i) q^{17} +(-3.85501 - 1.68371i) q^{18} +2.21601i q^{19} +(0.281517 + 4.46327i) q^{20} +0.0643636i q^{21} +(-0.566038 + 1.29599i) q^{22} +(5.75409 + 5.75409i) q^{23} +(0.196228 - 0.406255i) q^{24} +(1.00481 + 4.89799i) q^{25} +(-3.48371 + 1.36569i) q^{26} +(0.673875 + 0.673875i) q^{27} +(0.806427 + 0.0308040i) q^{28} -0.286512 q^{29} +(0.154174 - 0.480277i) q^{30} +5.05784i q^{31} +(-4.99615 - 2.65301i) q^{32} +(0.112791 - 0.112791i) q^{33} +(-1.62894 + 0.638578i) q^{34} +(0.897656 - 0.0911274i) q^{35} +(4.36416 - 4.04302i) q^{36} +(1.72593 - 1.72593i) q^{37} +(-2.87194 - 1.25435i) q^{38} +0.422045 q^{39} +(-5.94372 - 2.16153i) q^{40} -9.62451 q^{41} +(-0.0834149 - 0.0364323i) q^{42} +(6.70865 - 6.70865i) q^{43} +(-1.35920 - 1.46716i) q^{44} +(4.20413 - 5.15415i) q^{45} +(-10.7143 + 4.20024i) q^{46} +(4.74379 - 4.74379i) q^{47} +(0.415432 + 0.484266i) q^{48} +6.83718i q^{49} +(-6.91654 - 1.47022i) q^{50} +0.197343 q^{51} +(0.201988 - 5.28789i) q^{52} +(-3.51588 - 3.51588i) q^{53} +(-1.25478 + 0.491900i) q^{54} +(-1.73275 - 1.41336i) q^{55} +(-0.496390 + 1.02769i) q^{56} +(0.249946 + 0.249946i) q^{57} +(0.162177 - 0.371318i) q^{58} +0.559395i q^{59} +(0.535168 + 0.471663i) q^{60} +11.2560i q^{61} +(-6.55493 - 2.86293i) q^{62} +(-0.848709 - 0.848709i) q^{63} +(6.26630 - 4.97328i) q^{64} +(-0.597540 - 5.88610i) q^{65} +(0.0823324 + 0.210020i) q^{66} +(0.230669 + 0.230669i) q^{67} +(0.0944468 - 2.47255i) q^{68} +1.29802 q^{69} +(-0.390007 + 1.21494i) q^{70} -13.2381i q^{71} +(2.76945 + 7.94443i) q^{72} +(-7.63762 + 7.63762i) q^{73} +(1.25985 + 3.21374i) q^{74} +(0.665783 + 0.439115i) q^{75} +(3.25125 - 3.01200i) q^{76} +(-0.285323 + 0.285323i) q^{77} +(-0.238893 + 0.546967i) q^{78} +5.08654 q^{79} +(6.16570 - 6.47951i) q^{80} -8.77166 q^{81} +(5.44784 - 12.4733i) q^{82} +(4.77497 - 4.77497i) q^{83} +(0.0944320 - 0.0874832i) q^{84} +(-0.279402 - 2.75227i) q^{85} +(4.89702 + 12.4917i) q^{86} +(-0.0323160 + 0.0323160i) q^{87} +(2.67080 - 0.931047i) q^{88} +13.8064i q^{89} +(4.30005 + 8.36597i) q^{90} -1.06763 q^{91} +(0.621223 - 16.2632i) q^{92} +(0.570478 + 0.570478i) q^{93} +(3.46276 + 8.83310i) q^{94} +(3.13202 - 3.83978i) q^{95} +(-0.862756 + 0.264284i) q^{96} +(4.19838 + 4.19838i) q^{97} +(-8.86095 - 3.87010i) q^{98} +2.97456i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{2} + 4 q^{3} - 4 q^{6} - 26 q^{8}+O(q^{10}) \) 56 * q + 4 * q^2 + 4 * q^3 - 4 * q^6 - 26 * q^8	\( 56 q + 4 q^{2} + 4 q^{3} - 4 q^{6} - 26 q^{8} - 10 q^{10} + 56 q^{11} + 8 q^{12} + 8 q^{16} + 12 q^{17} + 12 q^{18} - 24 q^{20} + 4 q^{22} - 16 q^{25} + 40 q^{27} + 32 q^{28} + 18 q^{30} + 14 q^{32} + 4 q^{33} - 24 q^{35} + 44 q^{36} - 56 q^{38} + 42 q^{40} - 8 q^{41} + 16 q^{42} - 16 q^{43} - 16 q^{46} - 96 q^{48} - 22 q^{50} - 32 q^{51} - 76 q^{52} - 40 q^{56} + 16 q^{57} - 64 q^{60} + 4 q^{62} - 52 q^{65} - 4 q^{66} + 52 q^{67} + 8 q^{68} + 8 q^{70} + 50 q^{72} - 36 q^{73} + 52 q^{75} + 68 q^{76} - 20 q^{78} + 68 q^{80} - 96 q^{81} - 36 q^{82} - 16 q^{83} + 52 q^{86} - 26 q^{88} - 112 q^{90} - 48 q^{91} - 32 q^{92} - 88 q^{96} - 16 q^{97} + 76 q^{98}+O(q^{100}) \) 56 * q + 4 * q^2 + 4 * q^3 - 4 * q^6 - 26 * q^8 - 10 * q^10 + 56 * q^11 + 8 * q^12 + 8 * q^16 + 12 * q^17 + 12 * q^18 - 24 * q^20 + 4 * q^22 - 16 * q^25 + 40 * q^27 + 32 * q^28 + 18 * q^30 + 14 * q^32 + 4 * q^33 - 24 * q^35 + 44 * q^36 - 56 * q^38 + 42 * q^40 - 8 * q^41 + 16 * q^42 - 16 * q^43 - 16 * q^46 - 96 * q^48 - 22 * q^50 - 32 * q^51 - 76 * q^52 - 40 * q^56 + 16 * q^57 - 64 * q^60 + 4 * q^62 - 52 * q^65 - 4 * q^66 + 52 * q^67 + 8 * q^68 + 8 * q^70 + 50 * q^72 - 36 * q^73 + 52 * q^75 + 68 * q^76 - 20 * q^78 + 68 * q^80 - 96 * q^81 - 36 * q^82 - 16 * q^83 + 52 * q^86 - 26 * q^88 - 112 * q^90 - 48 * q^91 - 32 * q^92 - 88 * q^96 - 16 * q^97 + 76 * q^98

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