LMFDB - Embedded newform 95.2.r.a.33.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [95,2,Mod(2,95)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(95, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("95.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	95.r (of order $36$, degree $12$, 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:	$0.758578819202$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			33.5
Character	$\chi$	$=$	95.33
Dual form			95.2.r.a.72.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.569347 + 0.265491i) q^{2} +(-1.31808 - 1.88242i) q^{3} +(-1.03190 - 1.22978i) q^{4} +(-1.98334 - 1.03264i) q^{5} +(-0.250682 - 1.42169i) q^{6} +(3.96441 + 1.06226i) q^{7} +(-0.586200 - 2.18773i) q^{8} +(-0.780089 + 2.14328i) q^{9} +O(q^{10})$	\(q+(0.569347 + 0.265491i) q^{2} +(-1.31808 - 1.88242i) q^{3} +(-1.03190 - 1.22978i) q^{4} +(-1.98334 - 1.03264i) q^{5} +(-0.250682 - 1.42169i) q^{6} +(3.96441 + 1.06226i) q^{7} +(-0.586200 - 2.18773i) q^{8} +(-0.780089 + 2.14328i) q^{9} +(-0.855053 - 1.11449i) q^{10} +(-0.537990 + 0.931826i) q^{11} +(-0.954815 + 3.56342i) q^{12} +(3.66401 + 2.56557i) q^{13} +(1.97510 + 1.65731i) q^{14} +(0.670345 + 5.09458i) q^{15} +(-0.310465 + 1.76073i) q^{16} +(2.96843 - 6.36581i) q^{17} +(-1.01316 + 1.01316i) q^{18} +(-4.18557 - 1.21696i) q^{19} +(0.776702 + 3.50466i) q^{20} +(-3.22580 - 8.86282i) q^{21} +(-0.553694 + 0.387701i) q^{22} +(2.54192 + 0.222389i) q^{23} +(-3.34556 + 3.98708i) q^{24} +(2.86730 + 4.09617i) q^{25} +(1.40496 + 2.43346i) q^{26} +(-1.59635 + 0.427740i) q^{27} +(-2.78455 - 5.97149i) q^{28} +(1.20378 + 0.438142i) q^{29} +(-0.970906 + 3.07856i) q^{30} +(-1.05977 + 0.611858i) q^{31} +(-3.24241 + 4.63064i) q^{32} +(2.46320 - 0.215502i) q^{33} +(3.38013 - 2.83626i) q^{34} +(-6.76585 - 6.20065i) q^{35} +(3.44073 - 1.25232i) q^{36} +(4.05617 + 4.05617i) q^{37} +(-2.05995 - 1.80410i) q^{38} -10.2788i q^{39} +(-1.09651 + 4.94435i) q^{40} +(0.471629 + 0.0831609i) q^{41} +(0.516396 - 5.90244i) q^{42} +(0.268395 + 3.06777i) q^{43} +(1.70109 - 0.299948i) q^{44} +(3.76043 - 3.44530i) q^{45} +(1.38819 + 0.801474i) q^{46} +(-0.0736367 + 0.0343374i) q^{47} +(3.72365 - 1.73637i) q^{48} +(8.52599 + 4.92248i) q^{49} +(0.544992 + 3.09338i) q^{50} +(-15.8957 + 2.80285i) q^{51} +(-0.625835 - 7.15333i) q^{52} +(-0.274673 + 3.13952i) q^{53} +(-1.02244 - 0.180283i) q^{54} +(2.02926 - 1.29258i) q^{55} -9.29576i q^{56} +(3.22610 + 9.48304i) q^{57} +(0.569048 + 0.569048i) q^{58} +(-2.18803 + 0.796379i) q^{59} +(5.57347 - 6.08150i) q^{60} +(4.75697 - 3.99157i) q^{61} +(-0.765818 + 0.0670004i) q^{62} +(-5.36932 + 7.66818i) q^{63} +(0.0212756 - 0.0122835i) q^{64} +(-4.61767 - 8.87201i) q^{65} +(1.45963 + 0.531261i) q^{66} +(-3.50265 - 7.51146i) q^{67} +(-10.8917 + 2.91841i) q^{68} +(-2.93183 - 5.07808i) q^{69} +(-2.20590 - 5.32659i) q^{70} +(-7.60594 + 9.06440i) q^{71} +(5.14620 + 0.450234i) q^{72} +(6.93136 - 4.85339i) q^{73} +(1.23249 + 3.38624i) q^{74} +(3.93136 - 10.7965i) q^{75} +(2.82253 + 6.40310i) q^{76} +(-3.12266 + 3.12266i) q^{77} +(2.72893 - 5.85221i) q^{78} +(-1.64543 + 9.33169i) q^{79} +(2.43397 - 3.17154i) q^{80} +(8.15095 + 6.83946i) q^{81} +(0.246442 + 0.172561i) q^{82} +(-0.677110 + 2.52701i) q^{83} +(-7.57056 + 13.1126i) q^{84} +(-12.4610 + 9.56026i) q^{85} +(-0.661656 + 1.81788i) q^{86} +(-0.761921 - 2.84353i) q^{87} +(2.35395 + 0.630739i) q^{88} +(0.522763 + 2.96473i) q^{89} +(3.05568 - 0.963213i) q^{90} +(11.8003 + 14.0631i) q^{91} +(-2.34953 - 3.35548i) q^{92} +(2.54863 + 1.18845i) q^{93} -0.0510411 q^{94} +(7.04474 + 6.73585i) q^{95} +12.9906 q^{96} +(-5.52418 - 2.57597i) q^{97} +(3.54737 + 5.06617i) q^{98} +(-1.57748 - 1.87997i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 12 q^{6} - 18 q^{8}+O(q^{10}) $ 96 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 12 * q^6 - 18 * q^8	$ 96 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 12 q^{6} - 18 q^{8} - 12 q^{10} - 12 q^{11} - 18 q^{12} - 12 q^{13} + 6 q^{15} + 12 q^{16} - 30 q^{17} - 84 q^{20} + 24 q^{21} - 24 q^{22} + 12 q^{25} - 48 q^{26} - 18 q^{27} - 6 q^{30} - 36 q^{31} + 18 q^{32} + 90 q^{33} - 30 q^{35} + 24 q^{36} + 54 q^{38} + 54 q^{40} + 12 q^{41} + 24 q^{42} + 48 q^{43} + 12 q^{45} - 36 q^{46} - 24 q^{47} + 60 q^{48} + 126 q^{50} - 96 q^{51} - 30 q^{53} + 18 q^{55} - 66 q^{57} + 120 q^{58} + 84 q^{60} - 48 q^{61} + 60 q^{62} - 126 q^{63} + 72 q^{65} + 72 q^{66} + 108 q^{67} + 18 q^{68} + 36 q^{70} - 24 q^{71} + 48 q^{72} + 6 q^{73} + 60 q^{76} + 168 q^{77} - 138 q^{78} - 60 q^{80} - 120 q^{81} + 60 q^{82} - 36 q^{85} - 180 q^{86} - 6 q^{87} - 198 q^{88} - 270 q^{90} - 24 q^{91} - 72 q^{92} - 90 q^{93} - 24 q^{95} - 192 q^{96} - 72 q^{97} - 90 q^{98}+O(q^{100}) $ 96 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 12 * q^6 - 18 * q^8 - 12 * q^10 - 12 * q^11 - 18 * q^12 - 12 * q^13 + 6 * q^15 + 12 * q^16 - 30 * q^17 - 84 * q^20 + 24 * q^21 - 24 * q^22 + 12 * q^25 - 48 * q^26 - 18 * q^27 - 6 * q^30 - 36 * q^31 + 18 * q^32 + 90 * q^33 - 30 * q^35 + 24 * q^36 + 54 * q^38 + 54 * q^40 + 12 * q^41 + 24 * q^42 + 48 * q^43 + 12 * q^45 - 36 * q^46 - 24 * q^47 + 60 * q^48 + 126 * q^50 - 96 * q^51 - 30 * q^53 + 18 * q^55 - 66 * q^57 + 120 * q^58 + 84 * q^60 - 48 * q^61 + 60 * q^62 - 126 * q^63 + 72 * q^65 + 72 * q^66 + 108 * q^67 + 18 * q^68 + 36 * q^70 - 24 * q^71 + 48 * q^72 + 6 * q^73 + 60 * q^76 + 168 * q^77 - 138 * q^78 - 60 * q^80 - 120 * q^81 + 60 * q^82 - 36 * q^85 - 180 * q^86 - 6 * q^87 - 198 * q^88 - 270 * q^90 - 24 * q^91 - 72 * q^92 - 90 * q^93 - 24 * q^95 - 192 * q^96 - 72 * q^97 - 90 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.569347	+	0.265491i	0.402589	+	0.187730i	0.613357	−	0.789806i	$-0.289819\pi$
$2$	0.569347	+	0.265491i	0.402589	+	0.187730i	−0.210768	+	0.977536i	$0.567596\pi$
$3$	−1.31808	−	1.88242i	−0.760995	−	1.08681i	−0.993457	−	0.114208i	$-0.963567\pi$
$3$	−1.31808	−	1.88242i	−0.760995	−	1.08681i	0.232462	−	0.972605i	$-0.425322\pi$
$4$	−1.03190	−	1.22978i	−0.515952	−	0.614888i
$5$	−1.98334	−	1.03264i	−0.886978	−	0.461812i
$5$	−1.98334	−	1.03264i	−0.886978	−	0.461812i
$6$	−0.250682	−	1.42169i	−0.102340	−	0.580401i
$7$	3.96441	+	1.06226i	1.49841	+	0.401497i	0.912566	−	0.408929i	$-0.134098\pi$
$7$	3.96441	+	1.06226i	1.49841	+	0.401497i	0.585841	+	0.810426i	$0.300764\pi$
$8$	−0.586200	−	2.18773i	−0.207253	−	0.773479i
$9$	−0.780089	+	2.14328i	−0.260030	+	0.714426i
$10$	−0.855053	−	1.11449i	−0.270391	−	0.352433i
$11$	−0.537990	+	0.931826i	−0.162210	+	0.280956i	−0.935661	−	0.352900i	$-0.885196\pi$
$11$	−0.537990	+	0.931826i	−0.162210	+	0.280956i	0.773451	+	0.633856i	$0.218529\pi$
$12$	−0.954815	+	3.56342i	−0.275631	+	1.02867i
$13$	3.66401	+	2.56557i	1.01621	+	0.711560i	0.958007	−	0.286744i	$-0.0925730\pi$
$13$	3.66401	+	2.56557i	1.01621	+	0.711560i	0.0582062	+	0.998305i	$0.481462\pi$
$14$	1.97510	+	1.65731i	0.527869	+	0.442935i
$15$	0.670345	+	5.09458i	0.173082	+	1.31542i
$16$	−0.310465	+	1.76073i	−0.0776162	+	0.440183i
$17$	2.96843	−	6.36581i	0.719949	−	1.54394i	−0.114851	−	0.993383i	$-0.536639\pi$
$17$	2.96843	−	6.36581i	0.719949	−	1.54394i	0.834800	−	0.550553i	$-0.185583\pi$
$18$	−1.01316	+	1.01316i	−0.238805	+	0.238805i
$19$	−4.18557	−	1.21696i	−0.960236	−	0.279189i
$19$	−4.18557	−	1.21696i	−0.960236	−	0.279189i
$20$	0.776702	+	3.50466i	0.173676	+	0.783665i
$21$	−3.22580	−	8.86282i	−0.703928	−	1.93403i
$22$	−0.553694	+	0.387701i	−0.118048	+	0.0826581i
$23$	2.54192	+	0.222389i	0.530028	+	0.0463714i	0.349029	−	0.937112i	$-0.386511\pi$
$23$	2.54192	+	0.222389i	0.530028	+	0.0463714i	0.180999	+	0.983483i	$0.442067\pi$
$24$	−3.34556	+	3.98708i	−0.682909	+	0.813859i
$25$	2.86730	+	4.09617i	0.573460	+	0.819234i
$26$	1.40496	+	2.43346i	0.275535	+	0.477240i
$27$	−1.59635	+	0.427740i	−0.307217	+	0.0823185i
$28$	−2.78455	−	5.97149i	−0.526231	−	1.12851i
$29$	1.20378	+	0.438142i	0.223537	+	0.0813609i	0.451361	−	0.892342i	$-0.350939\pi$
$29$	1.20378	+	0.438142i	0.223537	+	0.0813609i	−0.227824	+	0.973702i	$0.573161\pi$
$30$	−0.970906	+	3.07856i	−0.177262	+	0.562065i
$31$	−1.05977	+	0.611858i	−0.190340	+	0.109893i	−0.592142	−	0.805834i	$-0.701717\pi$
$31$	−1.05977	+	0.611858i	−0.190340	+	0.109893i	0.401802	+	0.915727i	$0.368384\pi$
$32$	−3.24241	+	4.63064i	−0.573183	+	0.818590i
$33$	2.46320	−	0.215502i	0.428788	−	0.0375141i
$34$	3.38013	−	2.83626i	0.579687	−	0.486415i
$35$	−6.76585	−	6.20065i	−1.14364	−	1.04810i
$36$	3.44073	−	1.25232i	0.573455	−	0.208721i
$37$	4.05617	+	4.05617i	0.666831	+	0.666831i	0.956981	−	0.290150i	$-0.0937054\pi$
$37$	4.05617	+	4.05617i	0.666831	+	0.666831i	−0.290150	+	0.956981i	$0.593705\pi$
$38$	−2.05995	−	1.80410i	−0.334168	−	0.292664i
$39$		−	10.2788i		−	1.64593i
$40$	−1.09651	+	4.94435i	−0.173373	+	0.781771i
$41$	0.471629	+	0.0831609i	0.0736561	+	0.0129876i	0.210355	−	0.977625i	$-0.432538\pi$
$41$	0.471629	+	0.0831609i	0.0736561	+	0.0129876i	−0.136699	+	0.990613i	$0.543649\pi$
$42$	0.516396	−	5.90244i	0.0796817	−	0.910766i
$43$	0.268395	+	3.06777i	0.0409299	+	0.467831i	0.988808	+	0.149197i	$0.0476687\pi$
$43$	0.268395	+	3.06777i	0.0409299	+	0.467831i	−0.947878	+	0.318635i	$0.896776\pi$
$44$	1.70109	−	0.299948i	0.256449	−	0.0452189i
$45$	3.76043	−	3.44530i	0.560571	−	0.513595i
$46$	1.38819	+	0.801474i	0.204678	+	0.118171i
$47$	−0.0736367	+	0.0343374i	−0.0107410	+	0.00500862i	−0.427981	−	0.903788i	$-0.640775\pi$
$47$	−0.0736367	+	0.0343374i	−0.0107410	+	0.00500862i	0.417240	+	0.908796i	$0.362997\pi$
$48$	3.72365	−	1.73637i	0.537462	−	0.250623i
$49$	8.52599	+	4.92248i	1.21800	+	0.703212i
$50$	0.544992	+	3.09338i	0.0770735	+	0.437470i
$51$	−15.8957	+	2.80285i	−2.22585	+	0.392477i
$52$	−0.625835	−	7.15333i	−0.0867878	−	0.991989i
$53$	−0.274673	+	3.13952i	−0.0377292	+	0.431247i	0.953715	+	0.300713i	$0.0972246\pi$
$53$	−0.274673	+	3.13952i	−0.0377292	+	0.431247i	−0.991444	+	0.130534i	$0.958331\pi$
$54$	−1.02244	−	0.180283i	−0.139136	−	0.0245334i
$55$	2.02926	−	1.29258i	0.273626	−	0.174291i
$56$		−	9.29576i		−	1.24220i
$57$	3.22610	+	9.48304i	0.427308	+	1.25606i
$58$	0.569048	+	0.569048i	0.0747197	+	0.0747197i
$59$	−2.18803	+	0.796379i	−0.284858	+	0.103680i	−0.480498	−	0.876996i	$-0.659544\pi$
$59$	−2.18803	+	0.796379i	−0.284858	+	0.103680i	0.195640	+	0.980676i	$0.437322\pi$
$60$	5.57347	−	6.08150i	0.719531	−	0.785118i
$61$	4.75697	−	3.99157i	0.609068	−	0.511068i	−0.285278	−	0.958445i	$-0.592086\pi$
$61$	4.75697	−	3.99157i	0.609068	−	0.511068i	0.894346	+	0.447376i	$0.147642\pi$
$62$	−0.765818	+	0.0670004i	−0.0972590	+	0.00850906i
$63$	−5.36932	+	7.66818i	−0.676470	+	0.966100i
$64$	0.0212756	−	0.0122835i	0.00265945	−	0.00153543i
$65$	−4.61767	−	8.87201i	−0.572752	−	1.10044i
$66$	1.45963	+	0.531261i	0.179668	+	0.0653937i
$67$	−3.50265	−	7.51146i	−0.427917	−	0.917671i	−0.995536	−	0.0943801i	$-0.969913\pi$
$67$	−3.50265	−	7.51146i	−0.427917	−	0.917671i	0.567619	−	0.823291i	$-0.307865\pi$
$68$	−10.8917	+	2.91841i	−1.32081	+	0.353909i
$69$	−2.93183	−	5.07808i	−0.352951	−	0.611329i
$70$	−2.20590	−	5.32659i	−0.263656	−	0.636649i
$71$	−7.60594	+	9.06440i	−0.902659	+	1.07575i	0.0941213	+	0.995561i	$0.469996\pi$
$71$	−7.60594	+	9.06440i	−0.902659	+	1.07575i	−0.996780	+	0.0801859i	$0.974449\pi$
$72$	5.14620	+	0.450234i	0.606485	+	0.0530606i
$73$	6.93136	−	4.85339i	0.811255	−	0.568047i	−0.0926906	−	0.995695i	$-0.529547\pi$
$73$	6.93136	−	4.85339i	0.811255	−	0.568047i	0.903945	+	0.427648i	$0.140658\pi$
$74$	1.23249	+	3.38624i	0.143274	+	0.393643i
$75$	3.93136	−	10.7965i	0.453954	−	1.24668i
$76$	2.82253	+	6.40310i	0.323766	+	0.734486i
$77$	−3.12266	+	3.12266i	−0.355860	+	0.355860i
$78$	2.72893	−	5.85221i	0.308991	−	0.662632i
$79$	−1.64543	+	9.33169i	−0.185125	+	1.04990i	0.740669	+	0.671870i	$0.234509\pi$
$79$	−1.64543	+	9.33169i	−0.185125	+	1.04990i	−0.925794	+	0.378027i	$0.876603\pi$
$80$	2.43397	−	3.17154i	0.272126	−	0.354589i
$81$	8.15095	+	6.83946i	0.905661	+	0.759940i
$82$	0.246442	+	0.172561i	0.0272150	+	0.0190561i
$83$	−0.677110	+	2.52701i	−0.0743224	+	0.277375i	−0.993079	−	0.117450i	$-0.962528\pi$
$83$	−0.677110	+	2.52701i	−0.0743224	+	0.277375i	0.918756	+	0.394825i	$0.129195\pi$
$84$	−7.57056	+	13.1126i	−0.826016	+	1.43070i
$85$	−12.4610	+	9.56026i	−1.35159	+	1.03696i
$86$	−0.661656	+	1.81788i	−0.0713482	+	0.196027i
$87$	−0.761921	−	2.84353i	−0.0816865	−	0.304858i
$88$	2.35395	+	0.630739i	0.250932	+	0.0672370i
$89$	0.522763	+	2.96473i	0.0554127	+	0.314261i	0.999898	−	0.0142930i	$-0.00454975\pi$
$89$	0.522763	+	2.96473i	0.0554127	+	0.314261i	−0.944485	+	0.328554i	$0.893439\pi$
$90$	3.05568	−	0.963213i	0.322097	−	0.101532i
$91$	11.8003	+	14.0631i	1.23701	+	1.47421i
$92$	−2.34953	−	3.35548i	−0.244956	−	0.349833i
$93$	2.54863	+	1.18845i	0.264281	+	0.123236i
$94$	−0.0510411			−0.00526449
$95$	7.04474	+	6.73585i	0.722775	+	0.691083i
$96$	12.9906			1.32584
$97$	−5.52418	−	2.57597i	−0.560896	−	0.261550i	0.121428	−	0.992600i	$-0.461253\pi$
$97$	−5.52418	−	2.57597i	−0.560896	−	0.261550i	−0.682324	+	0.731050i	$0.739030\pi$
$98$	3.54737	+	5.06617i	0.358339	+	0.511760i
$99$	−1.57748	−	1.87997i	−0.158543	−	0.188944i
$100$	2.07859	−	7.75299i	0.207859	−	0.775299i
$101$	−1.25952	−	7.14312i	−0.125327	−	0.710767i	−0.981113	−	0.193436i	$-0.938037\pi$
$101$	−1.25952	−	7.14312i	−0.125327	−	0.710767i	0.855785	−	0.517331i	$-0.173074\pi$
$102$	−9.79431	−	2.62438i	−0.969782	−	0.259852i
$103$	−0.597635	−	2.23040i	−0.0588867	−	0.219768i	0.930212	−	0.367023i	$-0.119623\pi$
$103$	−0.597635	−	2.23040i	−0.0588867	−	0.219768i	−0.989099	+	0.147255i	$0.952956\pi$
$104$	3.46492	−	9.51979i	0.339763	−	0.933493i
$105$	−2.75425	+	20.9091i	−0.268788	+	2.04052i
$106$	−0.989898	+	1.71455i	−0.0961474	+	0.166532i
$107$	−1.85729	+	6.93148i	−0.179551	+	0.670092i	0.816181	+	0.577796i	$0.196087\pi$
$107$	−1.85729	+	6.93148i	−0.179551	+	0.670092i	−0.995732	+	0.0922957i	$0.970580\pi$
$108$	2.17330	+	1.52176i	0.209126	+	0.146432i
$109$	−8.75571	−	7.34691i	−0.838645	−	0.703707i	0.118614	−	0.992940i	$-0.462155\pi$
$109$	−8.75571	−	7.34691i	−0.838645	−	0.703707i	−0.957258	+	0.289234i	$0.906599\pi$
$110$	1.49852	−	0.197175i	0.142878	−	0.0187999i
$111$	2.28904	−	12.9818i	0.217266	−	1.23217i
$112$	−3.10117	+	6.65048i	−0.293033	+	0.628411i
$113$	−11.3216	+	11.3216i	−1.06505	+	1.06505i	−0.0673163	+	0.997732i	$0.521444\pi$
$113$	−11.3216	+	11.3216i	−1.06505	+	1.06505i	−0.997732	+	0.0673163i	$0.978556\pi$
$114$	−0.680887	+	6.25564i	−0.0637709	+	0.585894i
$115$	−4.81186	−	3.06597i	−0.448708	−	0.285903i
$116$	−0.703375	−	1.93251i	−0.0653067	−	0.179429i
$117$	−8.35698	+	5.85162i	−0.772603	+	0.540982i
$118$	−1.45718	−	0.127487i	−0.134144	−	0.0117361i
$119$	18.5302	−	22.0835i	1.69866	−	2.02439i
$120$	10.7526	−	4.45298i	0.981575	−	0.406500i
$121$	4.92113	+	8.52365i	0.447376	+	0.774878i
$122$	3.76809	−	1.00966i	0.341147	−	0.0914100i
$123$	−0.465102	−	0.997415i	−0.0419369	−	0.0899339i
$124$	1.84603	+	0.671899i	0.165778	+	0.0603383i
$125$	−1.45696	−	11.0850i	−0.130314	−	0.991473i
$126$	−5.09283	+	2.94035i	−0.453706	+	0.261947i
$127$	1.71706	−	2.45222i	0.152364	−	0.217599i	−0.735712	−	0.677294i	$-0.763152\pi$
$127$	1.71706	−	2.45222i	0.152364	−	0.217599i	0.888077	+	0.459695i	$0.152041\pi$
$128$	11.2783	−	0.986723i	0.996870	−	0.0872148i
$129$	5.42106	−	4.54881i	0.477298	−	0.400500i
$130$	−0.273620	−	6.27720i	−0.0239981	−	0.550547i
$131$	−5.22798	+	1.90283i	−0.456771	+	0.166251i	−0.560150	−	0.828391i	$-0.689257\pi$
$131$	−5.22798	+	1.90283i	−0.456771	+	0.166251i	0.103379	+	0.994642i	$0.467034\pi$
$132$	−2.80680	−	2.80680i	−0.244301	−	0.244301i
$133$	−15.3006	−	9.27070i	−1.32673	−	0.803871i
$134$		−	5.20655i		−	0.449777i
$135$	3.60780	+	0.800101i	0.310510	+	0.0688617i
$136$	−15.6668	−	2.76247i	−1.34341	−	0.236880i
$137$	0.931724	−	10.6497i	0.0796026	−	0.909862i	−0.846450	−	0.532468i	$-0.821265\pi$
$137$	0.931724	−	10.6497i	0.0796026	−	0.909862i	0.926053	−	0.377394i	$-0.123180\pi$
$138$	−0.321045	−	3.66957i	−0.0273292	−	0.312374i
$139$	−8.61598	+	1.51923i	−0.730798	+	0.128859i	−0.526652	−	0.850081i	$-0.676553\pi$
$139$	−8.61598	+	1.51923i	−0.730798	+	0.128859i	−0.204146	+	0.978940i	$0.565442\pi$
$140$	−0.643695	+	14.7190i	−0.0544021	+	1.24398i
$141$	0.161696	+	0.0933555i	0.0136173	+	0.00786195i
$142$	−6.73693	+	3.14148i	−0.565351	+	0.263627i
$143$	−4.36186	+	2.03397i	−0.364757	+	0.170089i
$144$	−3.53155	−	2.03894i	−0.294296	−	0.169912i
$145$	−1.93507	−	2.11206i	−0.160699	−	0.175397i
$146$	5.23488	−	0.923050i	0.433242	−	0.0763922i
$147$	−1.97179	−	22.5377i	−0.162631	−	1.85888i
$148$	0.802601	−	9.17377i	0.0659734	−	0.754079i
$149$	19.3300	+	3.40840i	1.58358	+	0.279227i	0.895044	−	0.445978i	$-0.147144\pi$
$149$	19.3300	+	3.40840i	1.58358	+	0.279227i	0.688533	+	0.725205i	$0.258255\pi$
$150$	5.10469	−	5.10323i	0.416796	−	0.416677i
$151$		−	12.2312i		−	0.995364i	−0.867360	−	0.497682i	$-0.834185\pi$
$151$		−	12.2312i		−	0.995364i	0.867360	−	0.497682i	$-0.165815\pi$
$152$	−0.208792	+	9.87028i	−0.0169353	+	0.800585i
$153$	11.3281	+	11.3281i	0.915820	+	0.915820i
$154$	−2.60691	+	0.948838i	−0.210071	+	0.0764595i
$155$	2.73371	−	0.119161i	0.219577	−	0.00957127i
$156$	−12.6406	+	10.6068i	−1.01206	+	0.849220i
$157$	−6.07468	+	0.531466i	−0.484812	+	0.0424156i	−0.326942	−	0.945044i	$-0.606018\pi$
$157$	−6.07468	+	0.531466i	−0.484812	+	0.0424156i	−0.157870	+	0.987460i	$0.550463\pi$
$158$	−3.41430	+	4.87612i	−0.271627	+	0.387923i
$159$	6.27193	−	3.62110i	0.497396	−	0.287172i
$160$	11.2126	−	5.83590i	0.886435	−	0.461368i
$161$	9.84099	+	3.58183i	0.775579	+	0.282288i
$162$	2.82490	+	6.05802i	0.221945	+	0.475963i
$163$	20.3932	−	5.46434i	1.59732	−	0.428000i	0.653087	−	0.757283i	$-0.273474\pi$
$163$	20.3932	−	5.46434i	1.59732	−	0.428000i	0.944231	+	0.329283i	$0.106807\pi$
$164$	−0.384407	−	0.665812i	−0.0300171	−	0.0519912i
$165$	−5.10790	−	2.11619i	−0.397650	−	0.164745i
$166$	−1.05641	+	1.25898i	−0.0819931	+	0.0977156i
$167$	9.76628	+	0.854439i	0.755737	+	0.0661184i	0.458511	−	0.888689i	$-0.348383\pi$
$167$	9.76628	+	0.854439i	0.755737	+	0.0661184i	0.297226	+	0.954807i	$0.403938\pi$
$168$	−17.4985	+	12.2526i	−1.35004	+	0.945306i
$169$	2.39657	+	6.58452i	0.184351	+	0.506501i
$170$	−9.63280	+	2.13482i	−0.738802	+	0.163733i
$171$	5.87340	−	8.02151i	0.449150	−	0.613420i
$172$	3.49572	−	3.49572i	0.266546	−	0.266546i
$173$	0.129964	−	0.278709i	0.00988098	−	0.0211898i	−0.901305	−	0.433184i	$-0.857390\pi$
$173$	0.129964	−	0.278709i	0.00988098	−	0.0211898i	0.911186	+	0.411994i	$0.135168\pi$
$174$	0.321133	−	1.82124i	0.0243451	−	0.138068i
$175$	7.01595	+	19.2847i	0.530356	+	1.45779i
$176$	−1.47367	−	1.23656i	−0.111082	−	0.0932089i
$177$	4.38313	+	3.06910i	0.329456	+	0.230688i
$178$	−0.489476	+	1.82675i	−0.0366878	+	0.136921i
$179$	−5.31425	+	9.20455i	−0.397206	+	0.687980i	−0.993380	−	0.114875i	$-0.963353\pi$
$179$	−5.31425	+	9.20455i	−0.397206	+	0.687980i	0.596174	+	0.802855i	$0.296687\pi$
$180$	−8.11735	−	1.06926i	−0.605032	−	0.0796978i
$181$	5.04580	−	13.8632i	0.375052	−	1.03045i	−0.598329	−	0.801251i	$-0.704168\pi$
$181$	5.04580	−	13.8632i	0.375052	−	1.03045i	0.973380	−	0.229195i	$-0.0736095\pi$
$182$	2.98486	+	11.1397i	0.221253	+	0.825727i
$183$	−13.7839	−	3.69338i	−1.01893	−	0.273022i
$184$	−1.00355	−	5.69140i	−0.0739825	−	0.419576i
$185$	−3.85620	−	12.2334i	−0.283514	−	0.899414i
$186$	1.13553	+	1.35328i	0.0832614	+	0.0992270i
$187$	4.33484	+	6.19080i	0.316995	+	0.452716i
$188$	0.118213	+	0.0551238i	0.00862160	+	0.00402032i
$189$	−6.78294			−0.493387
$190$	2.22260	+	5.70535i	0.161244	+	0.413909i
$191$	−11.0634			−0.800520			−0.400260	−	0.916402i	$-0.631080\pi$
$191$	−11.0634			−0.800520			−0.400260	+	0.916402i	$0.631080\pi$
$192$	−0.0511656	−	0.0238589i	−0.00369256	−	0.00172187i
$193$	−7.30316	−	10.4300i	−0.525693	−	0.750767i	0.465231	−	0.885189i	$-0.345971\pi$
$193$	−7.30316	−	10.4300i	−0.525693	−	0.750767i	−0.990924	+	0.134422i	$0.957082\pi$
$194$	−2.46128	−	2.93324i	−0.176710	−	0.210594i
$195$	−10.6143	+	20.3864i	−0.760109	+	1.45990i
$196$	−2.74446	−	15.5646i	−0.196033	−	1.11176i
$197$	−1.28846	−	0.345241i	−0.0917987	−	0.0245974i	0.212627	−	0.977133i	$-0.431798\pi$
$197$	−1.28846	−	0.345241i	−0.0917987	−	0.0245974i	−0.304426	+	0.952536i	$0.598465\pi$
$198$	−0.399020	−	1.48916i	−0.0283571	−	0.105830i
$199$	−4.76029	+	13.0788i	−0.337448	+	0.927131i	0.648668	+	0.761072i	$0.275327\pi$
$199$	−4.76029	+	13.0788i	−0.337448	+	0.927131i	−0.986116	+	0.166059i	$0.946896\pi$
$200$	7.28050	−	8.67405i	0.514809	−	0.613348i
$201$	−9.52292	+	16.4942i	−0.671695	+	1.16341i
$202$	1.17933	−	4.40130i	0.0829771	−	0.309675i
$203$	4.30688	+	3.01571i	0.302283	+	0.211661i
$204$	19.8498	+	16.6559i	1.38976	+	1.16615i
$205$	−0.849527	−	0.651961i	−0.0593335	−	0.0455349i
$206$	0.251890	−	1.42854i	0.0175500	−	0.0995311i
$207$	−2.45957	+	5.27456i	−0.170952	+	0.366608i
$208$	−5.65482	+	5.65482i	−0.392091	+	0.392091i
$209$	3.38579	−	3.24551i	0.234200	−	0.224497i
$210$	−7.11930	+	11.1733i	−0.491278	+	0.771031i
$211$	3.30574	+	9.08245i	0.227577	+	0.625262i	0.999951	−	0.00990600i	$-0.00315323\pi$
$211$	3.30574	+	9.08245i	0.227577	+	0.625262i	−0.772374	+	0.635168i	$0.780931\pi$
$212$	4.14435	−	2.90190i	0.284635	−	0.199303i
$213$	27.0882	+	2.36991i	1.85605	+	0.162384i
$214$	−2.89768	+	3.45333i	−0.198082	+	0.236065i
$215$	2.63559	−	6.36160i	0.179746	−	0.433858i
$216$	1.87156	+	3.24163i	0.127343	+	0.220565i
$217$	−4.85131	+	1.29990i	−0.329328	+	0.0882433i
$218$	−3.03450	−	6.50750i	−0.205522	−	0.440744i
$219$	−18.2722	−	6.65054i	−1.23472	−	0.449402i
$220$	−3.68359	−	1.16172i	−0.248347	−	0.0783231i
$221$	27.2083	−	15.7087i	1.83023	−	1.05668i
$222$	4.74980	−	6.78341i	0.318785	−	0.455273i
$223$	−3.07705	+	0.269207i	−0.206054	+	0.0180274i	−0.189716	−	0.981839i	$-0.560757\pi$
$223$	−3.07705	+	0.269207i	−0.206054	+	0.0180274i	−0.0163388	+	0.999867i	$0.505201\pi$
$224$	−17.7732	+	14.9135i	−1.18752	+	0.996449i
$225$	−11.0160	+	2.95004i	−0.734399	+	0.196669i
$226$	−9.45171	+	3.44014i	−0.628718	+	0.228835i
$227$	20.6198	+	20.6198i	1.36858	+	1.36858i	0.862465	+	0.506117i	$0.168920\pi$
$227$	20.6198	+	20.6198i	1.36858	+	1.36858i	0.506117	+	0.862465i	$0.331080\pi$
$228$	8.33298	−	13.7530i	0.551865	−	0.910813i
$229$			2.06483i			0.136448i	0.997670	+	0.0682240i	$0.0217333\pi$
$229$			2.06483i			0.136448i	−0.997670	+	0.0682240i	$0.978267\pi$
$230$	−1.92563	−	3.02311i	−0.126972	−	0.199338i
$231$	9.99405	+	1.76222i	0.657560	+	0.115946i
$232$	0.252877	−	2.89039i	0.0166022	−	0.189764i
$233$	2.03024	+	23.2058i	0.133006	+	1.52026i	0.710401	+	0.703797i	$0.248514\pi$
$233$	2.03024	+	23.2058i	0.133006	+	1.52026i	−0.577395	+	0.816465i	$0.695931\pi$
$234$	−6.31157	+	1.11290i	−0.412600	+	0.0727526i
$235$	0.181505	+	0.00793765i	0.0118401	+	0.000517795i
$236$	3.23721	+	1.86901i	0.210725	+	0.121662i
$237$	19.7349	−	9.20255i	1.28192	−	0.597770i
$238$	16.4131	−	7.65354i	1.06390	−	0.496105i
$239$	−19.8647	−	11.4689i	−1.28494	−	0.741860i	−0.307192	−	0.951648i	$-0.599389\pi$
$239$	−19.8647	−	11.4689i	−1.28494	−	0.741860i	−0.977747	+	0.209788i	$0.932723\pi$
$240$	−9.17832	−	0.401389i	−0.592458	−	0.0259096i
$241$	−21.9755	+	3.87487i	−1.41557	+	0.249602i	−0.828523	−	0.559954i	$-0.810819\pi$
$241$	−21.9755	+	3.87487i	−1.41557	+	0.249602i	−0.587042	+	0.809557i	$0.699708\pi$
$242$	0.538880	+	6.15943i	0.0346405	+	0.395943i
$243$	1.69897	−	19.4193i	0.108989	−	1.24575i
$244$	−9.81748	−	1.73109i	−0.628500	−	0.110821i
$245$	−11.8268	−	18.5673i	−0.755586	−	1.18622i
$246$		−	0.691355i		−	0.0440792i
$247$	−12.2138	−	15.1973i	−0.777145	−	0.966982i
$248$	1.95981	+	1.95981i	0.124448	+	0.124448i
$249$	5.64937	−	2.05620i	0.358014	−	0.130306i
$250$	2.11345	−	6.69802i	0.133666	−	0.423620i
$251$	−4.92451	+	4.13215i	−0.310832	+	0.260819i	−0.784836	−	0.619704i	$-0.787253\pi$
$251$	−4.92451	+	4.13215i	−0.310832	+	0.260819i	0.474004	+	0.880523i	$0.342808\pi$
$252$	14.9708	−	1.30977i	0.943070	−	0.0825079i
$253$	−1.57476	+	2.24899i	−0.0990041	+	0.141393i
$254$	1.62864	−	0.940297i	0.102190	−	0.0589995i
$255$	34.4210	+	10.8556i	2.15553	+	0.679804i
$256$	6.63706	+	2.41569i	0.414816	+	0.150981i
$257$	1.69094	+	3.62623i	0.105478	+	0.226198i	0.951962	−	0.306216i	$-0.0990629\pi$
$257$	1.69094	+	3.62623i	0.105478	+	0.226198i	−0.846484	+	0.532414i	$0.821285\pi$
$258$	4.29413	−	1.15061i	0.267341	−	0.0716338i
$259$	11.7716	+	20.3891i	0.731453	+	1.26691i
$260$	−6.14559	+	14.8338i	−0.381133	+	0.919952i
$261$	−1.87812	+	2.23826i	−0.116253	+	0.138545i
$262$	−3.48172	−	0.304611i	−0.215101	−	0.0188189i
$263$	3.88769	−	2.72219i	0.239725	−	0.167857i	−0.447540	−	0.894264i	$-0.647700\pi$
$263$	3.88769	−	2.72219i	0.239725	−	0.167857i	0.687265	+	0.726406i	$0.258811\pi$
$264$	−1.91539	−	5.26248i	−0.117884	−	0.323883i
$265$	3.78678	−	5.94311i	0.232620	−	0.365082i
$266$	−6.25007	−	9.34041i	−0.383216	−	0.572697i
$267$	4.89182	−	4.89182i	0.299374	−	0.299374i
$268$	−5.62302	+	12.0586i	−0.343480	+	0.736596i
$269$	−4.24761	+	24.0894i	−0.258981	+	1.46876i	0.526661	+	0.850075i	$0.323444\pi$
$269$	−4.24761	+	24.0894i	−0.258981	+	1.46876i	−0.785643	+	0.618681i	$0.787668\pi$
$270$	1.84167	+	1.41337i	0.112081	+	0.0860152i
$271$	−22.6330	−	18.9913i	−1.37485	−	1.15364i	−0.971073	−	0.238784i	$-0.923251\pi$
$271$	−22.6330	−	18.9913i	−1.37485	−	1.15364i	−0.403781	−	0.914855i	$-0.632304\pi$
$272$	10.2869	+	7.20296i	0.623735	+	0.436744i
$273$	10.9188	−	40.7495i	0.660835	−	2.46627i
$274$	3.35786	−	5.81598i	0.202856	−	0.351356i
$275$	−5.35949	+	0.468125i	−0.323190	+	0.0282290i
$276$	−3.21953	+	8.84560i	−0.193793	+	0.532442i
$277$	2.35176	+	8.77687i	0.141303	+	0.527351i	0.999892	+	0.0146864i	$0.00467499\pi$
$277$	2.35176	+	8.77687i	0.141303	+	0.527351i	−0.858589	+	0.512665i	$0.828658\pi$
$278$	−5.30882	−	1.42249i	−0.318402	−	0.0853155i
$279$	−0.484667	−	2.74868i	−0.0290162	−	0.164559i
$280$	−9.59919	+	18.4367i	−0.573662	+	1.10180i
$281$	−15.5160	−	18.4913i	−0.925610	−	1.10310i	−0.994423	−	0.105469i	$-0.966366\pi$
$281$	−15.5160	−	18.4913i	−0.925610	−	1.10310i	0.0688126	−	0.997630i	$-0.478079\pi$
$282$	0.0672763	+	0.0960806i	0.00400625	+	0.00572151i
$283$	−17.4668	−	8.14489i	−1.03829	−	0.484163i	−0.172732	−	0.984969i	$-0.555259\pi$
$283$	−17.4668	−	8.14489i	−1.03829	−	0.484163i	−0.865560	+	0.500805i	$0.833037\pi$
$284$	18.9958			1.12719
$285$	3.39412	−	22.1395i	0.201050	−	1.31143i
$286$	−3.02341			−0.178778
$287$	1.78139	+	0.830677i	0.105152	+	0.0490333i
$288$	−7.39538	−	10.5617i	−0.435777	−	0.622354i
$289$	−20.7846	−	24.7701i	−1.22262	−	1.45707i
$290$	−0.540994	−	1.71624i	−0.0317683	−	0.100781i
$291$	2.43228	+	13.7941i	0.142583	+	0.808627i
$292$	−13.1211	−	3.51579i	−0.767854	−	0.205746i
$293$	−6.61838	−	24.7001i	−0.386650	−	1.44300i	−0.835549	−	0.549415i	$-0.814850\pi$
$293$	−6.61838	−	24.7001i	−0.386650	−	1.44300i	0.448899	−	0.893582i	$-0.351816\pi$
$294$	4.86091	−	13.3553i	0.283494	−	0.778894i
$295$	5.16200	+	0.679964i	0.300543	+	0.0395890i
$296$	6.49607	−	11.2515i	0.377577	−	0.653982i
$297$	0.460239	−	1.71764i	0.0267058	−	0.0996673i
$298$	10.1006	+	7.07250i	0.585111	+	0.409699i
$299$	8.74307	+	7.33631i	0.505625	+	0.424270i
$300$	−17.3341	+	6.30630i	−1.00079	+	0.364095i
$301$	−2.19475	+	12.4470i	−0.126503	+	0.717435i
$302$	3.24728	−	6.96382i	0.186860	−	0.400723i
$303$	−11.7862	+	11.7862i	−0.677097	+	0.677097i
$304$	3.44221	−	6.99185i	0.197424	−	0.401010i
$305$	−13.5566	+	3.00441i	−0.776247	+	0.172032i
$306$	3.44210	+	9.45709i	0.196772	+	0.540626i
$307$	24.6314	−	17.2471i	1.40579	−	0.984342i	0.408347	−	0.912827i	$-0.366105\pi$
$307$	24.6314	−	17.2471i	1.40579	−	0.984342i	0.997440	−	0.0715151i	$-0.0227834\pi$
$308$	7.06245	+	0.617884i	0.402420	+	0.0352072i
$309$	−3.41082	+	4.06485i	−0.194035	+	0.231241i
$310$	1.58807	+	0.657932i	0.0901962	+	0.0373680i
$311$	−2.79493	−	4.84095i	−0.158486	−	0.274505i	0.775837	−	0.630933i	$-0.217328\pi$
$311$	−2.79493	−	4.84095i	−0.158486	−	0.274505i	−0.934323	+	0.356428i	$0.883994\pi$
$312$	−22.4873	+	6.02544i	−1.27309	+	0.341124i
$313$	9.61280	+	20.6147i	0.543347	+	1.16521i	0.965910	+	0.258878i	$0.0833529\pi$
$313$	9.61280	+	20.6147i	0.543347	+	1.16521i	−0.422563	+	0.906334i	$0.638869\pi$
$314$	−3.59970	−	1.31018i	−0.203143	−	0.0739379i
$315$	18.5677	−	9.66404i	1.04617	−	0.544507i
$316$	13.1738	−	7.60591i	0.741085	−	0.427866i
$317$	8.60655	−	12.2914i	0.483392	−	0.690355i	−0.501178	−	0.865344i	$-0.667100\pi$
$317$	8.60655	−	12.2914i	0.483392	−	0.690355i	0.984570	+	0.174989i	$0.0559888\pi$
$318$	4.53227	−	0.396522i	0.254157	−	0.0222359i
$319$	−1.05590	+	0.886001i	−0.0591188	+	0.0496066i
$320$	−0.0548813	+	0.00239225i	−0.00306796	+	0.000133731i
$321$	15.4960	−	5.64008i	0.864902	−	0.314799i
$322$	4.65200	+	4.65200i	0.259246	+	0.259246i
$323$	−20.1715	+	23.0321i	−1.12237	+	1.28154i
$324$		−	17.0815i		−	0.948973i
$325$	−0.00318783	+	22.3646i	−0.000176829	+	1.24057i
$326$	13.0615	+	2.30310i	0.723411	+	0.127557i
$327$	−2.28920	+	26.1657i	−0.126593	+	1.44697i
$328$	−0.0945355	−	1.08055i	−0.00521985	−	0.0596631i
$329$	−0.328402	+	0.0579061i	−0.0181054	+	0.00319246i
$330$	−2.34634	−	2.56095i	−0.129162	−	0.140975i
$331$	−11.1100	−	6.41437i	−0.610662	−	0.352566i	0.162563	−	0.986698i	$-0.448024\pi$
$331$	−11.1100	−	6.41437i	−0.610662	−	0.352566i	−0.773224	+	0.634132i	$0.781357\pi$
$332$	3.80637	−	1.77494i	0.208902	−	0.0974124i
$333$	−11.8577	+	5.52933i	−0.649797	+	0.303005i
$334$	5.33355	+	3.07933i	0.291839	+	0.168493i
$335$	−0.809696	+	18.5148i	−0.0442384	+	1.01157i
$336$	16.6066	−	2.92818i	0.905962	−	0.159745i
$337$	2.09285	+	23.9213i	0.114005	+	1.30308i	0.810594	+	0.585608i	$0.199144\pi$
$337$	2.09285	+	23.9213i	0.114005	+	1.30308i	−0.696590	+	0.717470i	$0.745300\pi$
$338$	−0.383650	+	4.38514i	−0.0208678	+	0.238520i
$339$	36.2348	+	6.38917i	1.96800	+	0.347012i
$340$	24.6156	+	5.45898i	1.33497	+	0.296055i
$341$		−	1.31669i		−	0.0713029i
$342$	5.47364	−	3.00769i	0.295980	−	0.162637i
$343$	8.25651	+	8.25651i	0.445810	+	0.445810i
$344$	6.55412	−	2.38551i	0.353375	−	0.128618i
$345$	0.570984	+	13.0991i	0.0307408	+	0.705233i
$346$	0.147989	−	0.124178i	0.00795595	−	0.00667583i
$347$	−23.5149	+	2.05728i	−1.26234	+	0.110441i	−0.698602	−	0.715510i	$-0.746194\pi$
$347$	−23.5149	+	2.05728i	−1.26234	+	0.110441i	−0.563742	+	0.825951i	$0.690639\pi$
$348$	−2.71067	+	3.87124i	−0.145307	+	0.207520i
$349$	−18.7277	+	10.8124i	−1.00247	+	0.578777i	−0.908978	−	0.416843i	$-0.863136\pi$
$349$	−18.7277	+	10.8124i	−1.00247	+	0.578777i	−0.0934926	+	0.995620i	$0.529803\pi$
$350$	−1.12541	+	12.8424i	−0.0601555	+	0.686453i
$351$	−6.94642	−	2.52829i	−0.370773	−	0.134950i
$352$	−2.57057	−	5.51260i	−0.137012	−	0.293823i
$353$	−10.9144	+	2.92450i	−0.580914	+	0.155656i	−0.537298	−	0.843393i	$-0.680555\pi$
$353$	−10.9144	+	2.92450i	−0.580914	+	0.155656i	−0.0436169	+	0.999048i	$0.513888\pi$
$354$	1.68070	+	2.91106i	0.0893283	+	0.154721i
$355$	24.4455	−	10.1236i	1.29743	−	0.537305i
$356$	3.10652	−	3.70220i	0.164645	−	0.196216i
$357$	−65.9946	−	5.77378i	−3.49280	−	0.305581i
$358$	−5.46937	+	3.82970i	−0.289065	+	0.202406i
$359$	−1.83322	−	5.03672i	−0.0967534	−	0.265828i	0.881868	−	0.471495i	$-0.156286\pi$
$359$	−1.83322	−	5.03672i	−0.0967534	−	0.265828i	−0.978622	+	0.205668i	$0.934063\pi$
$360$	−9.74175	−	6.20715i	−0.513435	−	0.327146i
$361$	16.0380	+	10.1873i	0.844107	+	0.536176i
$362$	6.55337	−	6.55337i	0.344438	−	0.344438i
$363$	9.55860	−	20.4985i	0.501697	−	1.07589i
$364$	5.11764	−	29.0236i	0.268237	−	1.52125i
$365$	−18.7591	+	2.46832i	−0.981895	+	0.129198i
$366$	−6.86725	−	5.76230i	−0.358957	−	0.301200i
$367$	−4.37757	−	3.06521i	−0.228508	−	0.160003i	0.453716	−	0.891146i	$-0.350098\pi$
$367$	−4.37757	−	3.06521i	−0.228508	−	0.160003i	−0.682224	+	0.731144i	$0.738987\pi$
$368$	−1.18075	+	4.40660i	−0.0615506	+	0.229710i
$369$	−0.546150	+	0.945959i	−0.0284314	+	0.0492447i
$370$	1.05233	−	7.98881i	0.0547078	−	0.415318i
$371$	−4.42391	+	12.1546i	−0.229678	+	0.631035i
$372$	−1.16842	−	4.36061i	−0.0605799	−	0.226087i
$373$	0.178223	+	0.0477546i	0.00922802	+	0.00247264i	0.263430	−	0.964678i	$-0.415146\pi$
$373$	0.178223	+	0.0477546i	0.00922802	+	0.00247264i	−0.254202	+	0.967151i	$0.581813\pi$
$374$	0.824429	+	4.67557i	0.0426302	+	0.241768i
$375$	−18.9462	+	17.3535i	−0.978377	+	0.896133i
$376$	0.118287	+	0.140969i	0.00610017	+	0.00726990i
$377$	3.28660	+	4.69374i	0.169268	+	0.241740i
$378$	−3.86185	−	1.80081i	−0.198632	−	0.0926236i
$379$	25.7959			1.32505			0.662523	−	0.749042i	$-0.269486\pi$
$379$	25.7959			1.32505			0.662523	+	0.749042i	$0.269486\pi$
$380$	1.01408	−	15.6142i	0.0520213	−	0.800992i
$381$	−6.87931			−0.352438
$382$	−6.29891	−	2.93723i	−0.322280	−	0.150282i
$383$	3.81477	+	5.44805i	0.194925	+	0.278382i	0.904702	−	0.426044i	$-0.140093\pi$
$383$	3.81477	+	5.44805i	0.194925	+	0.278382i	−0.709777	+	0.704427i	$0.751204\pi$
$384$	−16.7231	−	19.9299i	−0.853399	−	1.01704i
$385$	9.41788	−	2.96871i	0.479980	−	0.151299i
$386$	−1.38896	−	7.87720i	−0.0706964	−	0.400939i
$387$	−6.78446	−	1.81789i	−0.344874	−	0.0924086i
$388$	2.53257	+	9.45166i	0.128572	+	0.479836i
$389$	4.98646	−	13.7002i	0.252824	−	0.694627i	−0.746741	−	0.665115i	$-0.768382\pi$
$389$	4.98646	−	13.7002i	0.252824	−	0.694627i	0.999564	−	0.0295119i	$-0.00939530\pi$
$390$	−11.4556	+	8.78893i	−0.580079	+	0.445045i
$391$	8.96120	−	15.5213i	0.453187	−	0.784943i
$392$	5.77112	−	21.5381i	0.291485	−	1.08784i
$393$	10.4728	+	7.33315i	0.528284	+	0.369909i
$394$	−0.641920	−	0.538635i	−0.0323395	−	0.0271360i
$395$	12.8998	−	16.8088i	0.649057	−	0.845743i
$396$	−0.684131	+	3.87990i	−0.0343789	+	0.194972i
$397$	−14.1640	+	30.3748i	−0.710870	+	1.52447i	0.134866	+	0.990864i	$0.456940\pi$
$397$	−14.1640	+	30.3748i	−0.710870	+	1.52447i	−0.845736	+	0.533602i	$0.820838\pi$
$398$	−6.18255	+	6.18255i	−0.309903	+	0.309903i
$399$	2.71614	+	41.0216i	0.135977	+	2.05365i
$400$	−8.10245	+	3.77683i	−0.405123	+	0.188842i
$401$	2.21824	+	6.09457i	0.110774	+	0.304348i	0.982676	−	0.185331i	$-0.0593359\pi$
$401$	2.21824	+	6.09457i	0.110774	+	0.304348i	−0.871902	+	0.489680i	$0.837114\pi$
$402$	−9.80089	+	6.86266i	−0.488824	+	0.342278i
$403$	−5.45276	−	0.477055i	−0.271621	−	0.0237638i
$404$	−7.48473	+	8.91995i	−0.372379	+	0.443784i
$405$	−9.10341	−	21.9820i	−0.452352	−	1.09229i
$406$	1.65146	+	2.86042i	0.0819608	+	0.141960i
$407$	−5.96182	+	1.59747i	−0.295517	+	0.0791834i
$408$	15.4499	+	33.1325i	0.764886	+	1.64030i
$409$	−0.257973	−	0.0938944i	−0.0127559	−	0.00464278i	0.335634	−	0.941992i	$-0.391049\pi$
$409$	−0.257973	−	0.0938944i	−0.0127559	−	0.00464278i	−0.348390	+	0.937350i	$0.613272\pi$
$410$	−0.310586	−	0.596733i	−0.0153387	−	0.0294706i
$411$	−21.2752	+	12.2832i	−1.04943	+	0.605887i
$412$	−2.12620	+	3.03652i	−0.104750	+	0.149599i
$413$	−9.52023	+	0.832913i	−0.468460	+	0.0409849i
$414$	−2.80070	+	2.35006i	−0.137647	+	0.115499i
$415$	3.95244	−	4.31271i	0.194017	−	0.211703i
$416$	−23.7604	+	8.64809i	−1.16495	+	0.424008i
$417$	14.2164	+	14.2164i	0.696179	+	0.696179i
$418$	2.78934	−	0.948926i	0.136431	−	0.0464135i
$419$			12.7973i			0.625191i	0.949886	+	0.312596i	$0.101198\pi$
$419$			12.7973i			0.625191i	−0.949886	+	0.312596i	$0.898802\pi$
$420$	28.5557	−	18.1891i	1.39337	−	0.887537i
$421$	26.4301	+	4.66034i	1.28813	+	0.227131i	0.775427	−	0.631437i	$-0.217535\pi$
$421$	26.4301	+	4.66034i	1.28813	+	0.227131i	0.512699	+	0.858569i	$0.328646\pi$
$422$	−0.529193	+	6.04871i	−0.0257607	+	0.294446i
$423$	−0.0161513	−	0.184610i	−0.000785303	−	0.00897606i
$424$	7.02944	−	1.23948i	0.341380	−	0.0601944i
$425$	34.5868	−	6.09350i	1.67771	−	0.295578i
$426$	14.7934	+	8.54097i	0.716743	+	0.413812i
$427$	23.0987	−	10.7711i	1.11782	−	0.521250i
$428$	10.4407	−	4.86859i	0.504671	−	0.235332i
$429$	9.57806	+	5.52990i	0.462433	+	0.266986i
$430$	3.18951	−	2.92223i	0.153812	−	0.140923i
$431$	31.4917	−	5.55284i	1.51690	−	0.267471i	0.647688	−	0.761905i	$-0.275736\pi$
$431$	31.4917	−	5.55284i	1.51690	−	0.267471i	0.869215	+	0.494434i	$0.164625\pi$
$432$	−0.257526	−	2.94354i	−0.0123902	−	0.141621i
$433$	0.350634	−	4.00776i	0.0168504	−	0.192601i	−0.983104	−	0.183048i	$-0.941404\pi$
$433$	0.350634	−	4.00776i	0.0168504	−	0.192601i	0.999954	−	0.00955280i	$-0.00304080\pi$
$434$	−3.10719	−	0.547882i	−0.149150	−	0.0262992i
$435$	−1.42520	+	6.42649i	−0.0683330	+	0.308126i
$436$			18.3489i			0.878752i
$437$	−10.3688	−	4.02424i	−0.496005	−	0.192506i
$438$	−8.63756	−	8.63756i	−0.412719	−	0.412719i
$439$	−17.8434	+	6.49446i	−0.851618	+	0.309964i	−0.730700	−	0.682699i	$-0.760806\pi$
$439$	−17.8434	+	6.49446i	−0.851618	+	0.309964i	−0.120918	+	0.992662i	$0.538584\pi$
$440$	−4.01736	−	3.68176i	−0.191520	−	0.175521i
$441$	−17.2013	+	14.4336i	−0.819109	+	0.687314i
$442$	19.6614	−	1.72015i	0.935200	−	0.0818194i
$443$	17.5894	−	25.1203i	0.835698	−	1.19350i	−0.143309	−	0.989678i	$-0.545774\pi$
$443$	17.5894	−	25.1203i	0.835698	−	1.19350i	0.979008	−	0.203823i	$-0.0653367\pi$
$444$	−18.3267	+	10.5809i	−0.869748	+	0.502150i
$445$	2.02469	−	6.41991i	0.0959797	−	0.304333i
$446$	−1.82338	−	0.663656i	−0.0863395	−	0.0314250i
$447$	−19.0625	−	40.8797i	−0.901626	−	1.93354i
$448$	0.0973935	−	0.0260965i	0.00460141	−	0.00123294i
$449$	−16.3753	−	28.3629i	−0.772800	−	1.33853i	−0.936023	−	0.351940i	$-0.885522\pi$
$449$	−16.3753	−	28.3629i	−0.772800	−	1.33853i	0.163222	−	0.986589i	$-0.447811\pi$
$450$	−7.05512	−	1.24505i	−0.332582	−	0.0586920i
$451$	−0.331223	+	0.394736i	−0.0155967	+	0.0185874i
$452$	25.6059	+	2.24022i	1.20440	+	0.105371i
$453$	−23.0243	+	16.1218i	−1.08177	+	0.757467i
$454$	6.26544	+	17.2142i	0.294052	+	0.807900i
$455$	−8.88197	−	40.0775i	−0.416393	−	1.87886i
$456$	18.8552	−	12.6168i	0.882974	−	0.590836i
$457$	11.3686	−	11.3686i	0.531802	−	0.531802i	−0.389306	−	0.921108i	$-0.627285\pi$
$457$	11.3686	−	11.3686i	0.531802	−	0.531802i	0.921108	+	0.389306i	$0.127285\pi$
$458$	−0.548194	+	1.17561i	−0.0256154	+	0.0549325i
$459$	−2.01573	+	11.4317i	−0.0940860	+	0.533588i
$460$	1.19492	+	9.08130i	0.0557133	+	0.423418i
$461$	−1.02117	−	0.856867i	−0.0475608	−	0.0399083i	0.618697	−	0.785629i	$-0.287661\pi$
$461$	−1.02117	−	0.856867i	−0.0475608	−	0.0399083i	−0.666258	+	0.745721i	$0.732105\pi$
$462$	5.22223	+	3.65664i	0.242960	+	0.170122i
$463$	1.44633	−	5.39777i	0.0672165	−	0.250855i	−0.924139	−	0.382055i	$-0.875216\pi$
$463$	1.44633	−	5.39777i	0.0672165	−	0.250855i	0.991356	+	0.131200i	$0.0418830\pi$
$464$	−1.14518	+	1.98351i	−0.0531638	+	0.0920824i
$465$	−3.82757	−	4.98892i	−0.177499	−	0.231356i
$466$	−5.00501	+	13.7512i	−0.231853	+	0.637010i
$467$	−5.05863	−	18.8791i	−0.234086	−	0.873620i	−0.978559	−	0.205967i	$-0.933966\pi$
$467$	−5.05863	−	18.8791i	−0.234086	−	0.873620i	0.744473	−	0.667652i	$-0.232701\pi$
$468$	15.8198	+	4.23890i	0.731270	+	0.195943i
$469$	−5.90683	−	33.4993i	−0.272752	−	1.54685i
$470$	0.101232	+	0.0527072i	0.00466948	+	0.00243120i
$471$	9.00736	+	10.7346i	0.415037	+	0.494622i
$472$	3.02489	+	4.31999i	0.139232	+	0.198844i
$473$	−3.00302	−	1.40033i	−0.138079	−	0.0643874i
$474$	13.6792			0.628307
$475$	−7.01642	−	20.6342i	−0.321935	−	0.946762i
$476$	−46.2791			−2.12120
$477$	−6.51460	−	3.03781i	−0.298283	−	0.139092i
$478$	−8.26501	−	11.8037i	−0.378033	−	0.539887i
$479$	20.6311	+	24.5872i	0.942660	+	1.12342i	0.992201	+	0.124646i	$0.0397795\pi$
$479$	20.6311	+	24.5872i	0.942660	+	1.12342i	−0.0495416	+	0.998772i	$0.515776\pi$
$480$	−25.7647	−	13.4146i	−1.17599	−	0.612290i
$481$	4.45547	+	25.2682i	0.203152	+	1.15213i
$482$	−13.5404	−	3.62814i	−0.616749	−	0.165257i
$483$	−6.22874	−	23.2460i	−0.283418	−	1.05773i
$484$	5.40405	−	14.8475i	0.245638	−	0.674886i
$485$	8.29629	+	10.8135i	0.376715	+	0.491017i
$486$	6.12296	−	10.6053i	0.277743	−	0.481065i
$487$	2.42659	−	9.05617i	0.109959	−	0.410374i	−0.888901	−	0.458099i	$-0.848530\pi$
$487$	2.42659	−	9.05617i	0.109959	−	0.410374i	0.998861	+	0.0477250i	$0.0151971\pi$
$488$	−11.5210	−	8.06710i	−0.521532	−	0.365180i
$489$	−37.1660	−	31.1860i	−1.68071	−	1.41028i
$490$	−1.80411	−	13.7111i	−0.0815013	−	0.619405i
$491$	−4.43631	+	25.1596i	−0.200208	+	1.13543i	0.704597	+	0.709608i	$0.251128\pi$
$491$	−4.43631	+	25.1596i	−0.200208	+	1.13543i	−0.904805	+	0.425827i	$0.859983\pi$
$492$	−0.746656	+	1.60121i	−0.0336619	+	0.0721881i
$493$	6.36247	−	6.36247i	0.286551	−	0.286551i
$494$	−2.91913	−	11.8952i	−0.131338	−	0.535190i
$495$	1.18735	+	5.35760i	0.0533674	+	0.240806i
$496$	−0.748297	−	2.05593i	−0.0335995	−	0.0923139i
$497$	−39.7818	+	27.8555i	−1.78446	+	1.24949i
$498$	3.76235	+	0.329163i	0.168595	+	0.0147501i
$499$	23.8013	−	28.3653i	1.06549	−	1.26980i	0.104116	−	0.994565i	$-0.466799\pi$
$499$	23.8013	−	28.3653i	1.06549	−	1.26980i	0.961376	−	0.275239i	$-0.0887568\pi$
$500$	−12.1286	+	13.2304i	−0.542409	+	0.591681i
$501$	−11.2643	−	19.5104i	−0.503254	−	0.871661i
$502$	−3.90080	+	1.04522i	−0.174101	+	0.0466503i
$503$	−2.63742	−	5.65596i	−0.117597	−	0.252187i	0.838695	−	0.544601i	$-0.183319\pi$
$503$	−2.63742	−	5.65596i	−0.117597	−	0.252187i	−0.956292	+	0.292415i	$0.905541\pi$
$504$	19.9234	+	7.25152i	0.887458	+	0.323008i
$505$	−4.87822	+	15.4679i	−0.217078	+	0.688312i
$506$	−1.49367	+	0.862369i	−0.0664016	+	0.0383370i
$507$	9.23593	−	13.1903i	0.410182	−	0.585800i
$508$	−4.78752	+	0.418854i	−0.212412	+	0.0185836i
$509$	−3.84230	+	3.22407i	−0.170307	+	0.142904i	−0.723957	−	0.689845i	$-0.757679\pi$
$509$	−3.84230	+	3.22407i	−0.170307	+	0.142904i	0.553651	+	0.832749i	$0.313234\pi$
$510$	16.7154	+	15.3191i	0.740172	+	0.678340i
$511$	32.6343	−	11.8779i	1.44366	−	0.525449i
$512$	−12.8734	−	12.8734i	−0.568929	−	0.568929i
$513$	7.20216	+	0.152352i	0.317983	+	0.00672650i
$514$			2.51351i			0.110866i
$515$	−1.11790	+	5.04080i	−0.0492604	+	0.222124i
$516$	−11.1880	−	1.97275i	−0.492526	−	0.0868456i
$517$	0.00761937	−	0.0870898i	0.000335099	−	0.00383020i
$518$	1.28903	+	14.7337i	0.0566368	+	0.647362i
$519$	−0.695949	+	0.122715i	−0.0305488	+	0.00538657i
$520$	−16.7027	+	15.3030i	−0.732461	+	0.671080i
$521$	37.5008	+	21.6511i	1.64294	+	0.948551i	0.979782	+	0.200070i	$0.0641171\pi$
$521$	37.5008	+	21.6511i	1.64294	+	0.948551i	0.663157	+	0.748480i	$0.269216\pi$
$522$	−1.66354	+	0.775720i	−0.0728110	+	0.0339523i
$523$	29.1832	−	13.6084i	1.27609	−	0.595052i	0.337905	−	0.941180i	$-0.390282\pi$
$523$	29.1832	−	13.6084i	1.27609	−	0.595052i	0.938187	+	0.346129i	$0.112504\pi$
$524$	7.73484	+	4.46571i	0.337898	+	0.195085i
$525$	27.0543	−	38.6258i	1.18075	−	1.68577i
$526$	2.93616	−	0.517724i	0.128023	−	0.0225738i
$527$	0.749125	+	8.56254i	0.0326324	+	0.372990i
$528$	−0.385295	+	4.40394i	−0.0167678	+	0.191657i
$529$	−16.2387	−	2.86331i	−0.706029	−	0.124492i
$530$	3.73383	−	2.37834i	0.162187	−	0.103308i
$531$		−	5.31081i		−	0.230470i
$532$	4.38789	+	28.3828i	0.190239	+	1.23055i
$533$	1.51470	+	1.51470i	0.0656089	+	0.0656089i
$534$	4.08387	−	1.48641i	0.176727	−	0.0643232i
$535$	10.8414	−	11.8296i	0.468714	−	0.511438i
$536$	−14.3798	+	12.0661i	−0.621112	+	0.521175i
$537$	24.3314	−	2.12872i	1.04998	−	0.0918611i
$538$	−8.81387	+	12.5875i	−0.379993	+	0.542686i
$539$	−9.17379	+	5.29649i	−0.395143	+	0.228136i
$540$	−2.73897	−	5.26242i	−0.117866	−	0.226458i
$541$	−28.5358	−	10.3862i	−1.22685	−	0.446537i	−0.354332	−	0.935120i	$-0.615292\pi$
$541$	−28.5358	−	10.3862i	−1.22685	−	0.446537i	−0.872517	+	0.488583i	$0.837514\pi$
$542$	−7.84398	−	16.8215i	−0.336928	−	0.722544i
$543$	−32.7472	+	8.77457i	−1.40531	+	0.376553i
$544$	19.8529	+	34.3863i	0.851188	+	1.47430i
$545$	9.77884	+	23.6130i	0.418879	+	1.01147i
$546$	17.0352	−	20.3017i	0.729038	−	0.868834i
$547$	−1.71989	−	0.150471i	−0.0735373	−	0.00643368i	0.0503277	−	0.998733i	$-0.483973\pi$
$547$	−1.71989	−	0.150471i	−0.0735373	−	0.00643368i	−0.123865	+	0.992299i	$0.539529\pi$
$548$	−14.0581	+	9.84362i	−0.600534	+	0.420499i
$549$	4.84419	+	13.3093i	0.206745	+	0.568027i
$550$	−3.17569	−	1.15637i	−0.135412	−	0.0493078i
$551$	−4.50533	−	3.29883i	−0.191933	−	0.140535i
$552$	−9.39083	+	9.39083i	−0.399700	+	0.399700i
$553$	−16.4359	+	35.2468i	−0.698923	+	1.49885i
$554$	−0.991214	+	5.62145i	−0.0421127	+	0.238833i
$555$	−17.9455	+	23.3835i	−0.761743	+	0.992576i
$556$	10.7592	+	9.02802i	0.456291	+	0.382873i
$557$	−5.22551	−	3.65894i	−0.221412	−	0.155034i	0.457608	−	0.889154i	$-0.348706\pi$
$557$	−5.22551	−	3.65894i	−0.221412	−	0.155034i	−0.679020	+	0.734120i	$0.737595\pi$
$558$	0.453806	−	1.69363i	0.0192111	−	0.0716970i
$559$	−6.88718	+	11.9289i	−0.291296	+	0.504540i
$560$	13.0182	−	9.98778i	0.550121	−	0.422061i
$561$	5.93998	−	16.3200i	0.250786	−	0.689029i
$562$	−3.92474	−	14.6473i	−0.165555	−	0.617861i
$563$	5.00209	+	1.34031i	0.210813	+	0.0564872i	0.362680	−	0.931914i	$-0.381862\pi$
$563$	5.00209	+	1.34031i	0.210813	+	0.0564872i	−0.151867	+	0.988401i	$0.548529\pi$
$564$	−0.0520490	−	0.295184i	−0.00219166	−	0.0124295i
$565$	34.1458	−	10.7635i	1.43653	−	0.452822i
$566$	−7.78226	−	9.27453i	−0.327113	−	0.389838i
$567$	25.0484	+	35.7729i	1.05194	+	1.50232i
$568$	24.2891	+	11.3262i	1.01915	+	0.475236i
$569$	−5.57682			−0.233793			−0.116896	−	0.993144i	$-0.537295\pi$
$569$	−5.57682			−0.233793			−0.116896	+	0.993144i	$0.537295\pi$
$570$	7.81027	−	11.7040i	0.327136	−	0.490225i
$571$	−1.69061			−0.0707500			−0.0353750	−	0.999374i	$-0.511263\pi$
$571$	−1.69061			−0.0707500			−0.0353750	+	0.999374i	$0.511263\pi$
$572$	7.00235	+	3.26525i	0.292783	+	0.136527i
$573$	14.5825	+	20.8259i	0.609191	+	0.870016i
$574$	0.793694	+	0.945887i	0.0331281	+	0.0394806i
$575$	6.37751	+	11.0498i	0.265960	+	0.460809i
$576$	0.00973003	+	0.0551817i	0.000405418	+	0.00229924i
$577$	−2.95493	−	0.791771i	−0.123015	−	0.0329619i	0.196786	−	0.980446i	$-0.436950\pi$
$577$	−2.95493	−	0.791771i	−0.123015	−	0.0329619i	−0.319801	+	0.947485i	$0.603616\pi$
$578$	−5.25741	−	19.6209i	−0.218679	−	0.816122i
$579$	−10.0074	+	27.4952i	−0.415894	+	1.14266i
$580$	−0.600555	+	4.55916i	−0.0249367	+	0.189309i
$581$	−5.36868	+	9.29883i	−0.222731	+	0.385781i
$582$	−2.27741	+	8.49940i	−0.0944016	+	0.352312i
$583$	−2.77772	−	1.94498i	−0.115041	−	0.0805528i
$584$	−14.6811	−	12.3189i	−0.607507	−	0.509759i
$585$	22.6174	−	2.97600i	0.935114	−	0.123042i
$586$	2.78950	−	15.8201i	0.115233	−	0.653521i
$587$	−4.25705	+	9.12928i	−0.175707	+	0.376806i	−0.974363	−	0.224983i	$-0.927767\pi$
$587$	−4.25705	+	9.12928i	−0.175707	+	0.376806i	0.798655	+	0.601789i	$0.205545\pi$
$588$	−25.6816	+	25.6816i	−1.05909	+	1.05909i
$589$	5.18034	−	1.27128i	0.213452	−	0.0523822i
$590$	2.75844	+	1.75760i	0.113563	+	0.0723592i
$591$	1.04840	+	2.88047i	0.0431256	+	0.118487i
$592$	−8.40113	+	5.88254i	−0.345284	+	0.241771i
$593$	44.2356	+	3.87012i	1.81654	+	0.158927i	0.944071	−	0.329743i	$-0.106962\pi$
$593$	44.2356	+	3.87012i	1.81654	+	0.158927i	0.872469	+	0.488669i	$0.162518\pi$
$594$	0.718052	−	0.855741i	0.0294620	−	0.0351115i
$595$	−59.5561	+	24.6640i	−2.44156	+	1.01112i
$596$	−15.7552	−	27.2887i	−0.645357	−	1.11779i
$597$	30.8942	−	8.27807i	1.26441	−	0.338799i
$598$	3.03012	+	6.49811i	0.123911	+	0.265727i
$599$	7.99745	+	2.91083i	0.326767	+	0.118933i	0.500194	−	0.865913i	$-0.333262\pi$
$599$	7.99745	+	2.91083i	0.326767	+	0.118933i	−0.173427	+	0.984847i	$0.555484\pi$
$600$	−25.9244	−	2.27182i	−1.05836	−	0.0927466i
$601$	−22.6674	+	13.0870i	−0.924623	+	0.533831i	−0.885107	−	0.465388i	$-0.845915\pi$
$601$	−22.6674	+	13.0870i	−0.924623	+	0.533831i	−0.0395160	+	0.999219i	$0.512582\pi$
$602$	−4.55414	+	6.50399i	−0.185613	+	0.265083i
$603$	18.8315	−	1.64755i	0.766880	−	0.0670933i
$604$	−15.0417	+	12.6215i	−0.612038	+	0.513561i
$605$	−0.958408	−	21.9871i	−0.0389648	−	0.893903i
$606$	−9.83953	+	3.58130i	−0.399704	+	0.145480i
$607$	−19.3430	−	19.3430i	−0.785108	−	0.785108i	0.195579	−	0.980688i	$-0.437341\pi$
$607$	−19.3430	−	19.3430i	−0.785108	−	0.785108i	−0.980688	+	0.195579i	$0.937341\pi$
$608$	19.2066	−	15.4360i	0.778932	−	0.626013i
$609$		−	12.0823i		−	0.489599i
$610$	−8.51603	−	1.88860i	−0.344804	−	0.0764670i
$611$	−0.357900	−	0.0631075i	−0.0144791	−	0.00255306i
$612$	2.24150	−	25.6205i	0.0906073	−	1.03565i
$613$	−1.02321	−	11.6953i	−0.0413270	−	0.472370i	−0.988455	−	0.151514i	$-0.951585\pi$
$613$	−1.02321	−	11.6953i	−0.0413270	−	0.472370i	0.947128	−	0.320856i	$-0.103970\pi$
$614$	18.6027	−	3.28016i	0.750745	−	0.132377i
$615$	−0.107516	+	2.45850i	−0.00433546	+	0.0991363i
$616$	8.66202	+	5.00102i	0.349003	+	0.201497i
$617$	−39.2926	+	18.3224i	−1.58186	+	0.737633i	−0.997280	−	0.0737036i	$-0.976518\pi$
$617$	−39.2926	+	18.3224i	−1.58186	+	0.737633i	−0.584579	+	0.811337i	$0.698740\pi$
$618$	−3.02112	+	1.40877i	−0.121527	+	0.0566691i
$619$	8.25420	+	4.76557i	0.331764	+	0.191544i	0.656624	−	0.754218i	$-0.271984\pi$
$619$	8.25420	+	4.76557i	0.331764	+	0.191544i	−0.324860	+	0.945762i	$0.605317\pi$
$620$	−2.96747	−	3.23889i	−0.119177	−	0.130077i
$621$	−4.15291	+	0.732271i	−0.166651	+	0.0293850i
$622$	−0.306054	−	3.49821i	−0.0122716	−	0.140265i
$623$	−1.07688	+	12.3087i	−0.0431441	+	0.493139i
$624$	18.0982	+	3.19121i	0.724510	+	0.127751i
$625$	−8.55720	+	23.4899i	−0.342288	+	0.939595i
$626$			14.2890i			0.571104i
$627$	−10.5721	−	2.09561i	−0.422211	−	0.0836906i
$628$	6.92208	+	6.92208i	0.276221	+	0.276221i
$629$	37.8613	−	13.7804i	1.50963	−	0.549460i
$630$	13.1372	−	0.572643i	0.523397	−	0.0228146i
$631$	13.5550	−	11.3740i	0.539614	−	0.452790i	−0.331792	−	0.943353i	$-0.607653\pi$
$631$	13.5550	−	11.3740i	0.539614	−	0.452790i	0.871406	+	0.490563i	$0.163209\pi$
$632$	21.3798	−	1.87049i	0.850441	−	0.0744040i
$633$	12.7397	−	18.1942i	0.506358	−	0.723154i
$634$	8.16337	−	4.71313i	0.324209	−	0.187182i
$635$	−5.93778	+	3.09047i	−0.235634	+	0.122642i
$636$	−10.9252	−	3.97644i	−0.433211	−	0.157676i
$637$	18.6103	+	39.9100i	0.737369	+	1.58129i
$638$	−0.836396	+	0.224112i	−0.0331132	+	0.00887266i
$639$	−13.4942	−	23.3727i	−0.533823	−	0.924609i
$640$	−23.3877	−	9.68944i	−0.924478	−	0.383009i
$641$	9.35413	−	11.1478i	0.369466	−	0.440312i	−0.548994	−	0.835826i	$-0.684989\pi$
$641$	9.35413	−	11.1478i	0.369466	−	0.440312i	0.918460	+	0.395514i	$0.129433\pi$
$642$	10.3200	+	0.902881i	0.407297	+	0.0356339i
$643$	−29.9336	+	20.9597i	−1.18047	+	0.826571i	−0.987958	−	0.154724i	$-0.950551\pi$
$643$	−29.9336	+	20.9597i	−1.18047	+	0.826571i	−0.192509	+	0.981295i	$0.561662\pi$
$644$	−5.75012	−	15.7983i	−0.226587	−	0.622541i
$645$	−15.4491	+	3.42383i	−0.608308	+	0.134813i
$646$	−17.5994	+	7.75791i	−0.692438	+	0.305231i
$647$	18.2758	−	18.2758i	0.718495	−	0.718495i	−0.249802	−	0.968297i	$-0.580366\pi$
$647$	18.2758	−	18.2758i	0.718495	−	0.718495i	0.968297	+	0.249802i	$0.0803655\pi$
$648$	10.1848	−	21.8414i	0.400096	−	0.858009i
$649$	0.435053	−	2.46731i	0.0170773	−	0.0968504i
$650$	−5.93942	+	12.7324i	−0.232963	+	0.499406i
$651$	8.84139	+	7.41880i	0.346521	+	0.290766i
$652$	−27.7637	−	19.4404i	−1.08731	−	0.761344i
$653$	−1.49851	+	5.59253i	−0.0586414	+	0.218853i	−0.989028	−	0.147727i	$-0.952804\pi$
$653$	−1.49851	+	5.59253i	−0.0586414	+	0.218853i	0.930387	+	0.366579i	$0.119471\pi$
$654$	−8.25011	+	14.2896i	−0.322605	+	0.558768i
$655$	12.3338	+	1.62467i	0.481923	+	0.0634812i
$656$	−0.292848	+	0.804594i	−0.0114338	+	0.0314141i
$657$	4.99509	+	18.6419i	0.194877	+	0.727290i
$658$	−0.202348	−	0.0542190i	−0.00788834	−	0.00211368i
$659$	−3.00203	−	17.0253i	−0.116942	−	0.663213i	−0.985770	−	0.168099i	$-0.946237\pi$
$659$	−3.00203	−	17.0253i	−0.116942	−	0.663213i	0.868828	−	0.495114i	$-0.164874\pi$
$660$	2.66843	+	8.46528i	0.103869	+	0.329511i
$661$	−25.0124	−	29.8086i	−0.972870	−	1.15942i	−0.987194	−	0.159524i	$-0.949004\pi$
$661$	−25.0124	−	29.8086i	−0.972870	−	1.15942i	0.0143240	−	0.999897i	$-0.495440\pi$
$662$	−4.62250	−	6.60161i	−0.179658	−	0.256579i
$663$	−65.4330	−	30.5119i	−2.54121	−	1.18498i
$664$	5.92533			0.229947
$665$	20.7730	+	34.1870i	0.805544	+	1.32572i
$666$	−8.21912			−0.318484
$667$	2.96249	+	1.38143i	0.114708	+	0.0534892i
$668$	−9.02710	−	12.8920i	−0.349269	−	0.498808i
$669$	4.56256	+	5.43745i	0.176399	+	0.210224i
$670$	−5.37651	+	10.3264i	−0.207713	+	0.398943i
$671$	1.16025	+	6.58009i	0.0447909	+	0.254022i
$672$	51.4999	+	13.7994i	1.98665	+	0.532322i
$673$	−11.1589	−	41.6457i	−0.430145	−	1.60532i	−0.752425	−	0.658678i	$-0.771116\pi$
$673$	−11.1589	−	41.6457i	−0.430145	−	1.60532i	0.322280	−	0.946644i	$-0.395551\pi$
$674$	−5.15934	+	14.1752i	−0.198730	+	0.546007i
$675$	−6.32929	−	5.31245i	−0.243615	−	0.204476i
$676$	5.62445	−	9.74184i	0.216325	−	0.374686i
$677$	6.92599	−	25.8481i	0.266187	−	0.993425i	−0.695332	−	0.718689i	$-0.744743\pi$
$677$	6.92599	−	25.8481i	0.266187	−	0.993425i	0.961520	−	0.274736i	$-0.0885906\pi$
$678$	18.9339	+	13.2577i	0.727152	+	0.509157i
$679$	−19.1638	−	16.0803i	−0.735439	−	0.617106i
$680$	28.2199	+	21.6571i	1.08218	+	0.830512i
$681$	11.6364	−	65.9935i	0.445909	−	2.52888i
$682$	0.349570	−	0.749655i	0.0133857	−	0.0287058i
$683$	−4.04665	+	4.04665i	−0.154841	+	0.154841i	−0.780276	−	0.625435i	$-0.784921\pi$
$683$	−4.04665	+	4.04665i	−0.154841	+	0.154841i	0.625435	+	0.780276i	$0.284921\pi$
$684$	−15.9255	+	1.05446i	−0.608925	+	0.0403184i
$685$	−12.8452	+	20.1598i	−0.490791	+	0.770266i
$686$	2.50879	+	6.89285i	0.0957861	+	0.263170i
$687$	3.88688	−	2.72162i	0.148294	−	0.103836i
$688$	−5.48486	−	0.479863i	−0.209108	−	0.0182946i
$689$	−9.06106	+	10.7985i	−0.345199	+	0.411392i
$690$	−3.15261	+	7.60953i	−0.120018	+	0.289690i
$691$	6.33959	+	10.9805i	0.241169	+	0.417717i	0.961048	−	0.276383i	$-0.0891358\pi$
$691$	6.33959	+	10.9805i	0.241169	+	0.417717i	−0.719878	+	0.694100i	$0.755802\pi$
$692$	−0.476860	+	0.127774i	−0.0181275	+	0.00485725i
$693$	−4.25677	−	9.12867i	−0.161701	−	0.346769i
$694$	−13.9343	−	5.07167i	−0.528939	−	0.192518i
$695$	18.6573	+	5.88407i	0.707710	+	0.223196i
$696$	−5.77423	+	3.33375i	−0.218872	+	0.126366i
$697$	1.92938	−	2.75544i	0.0730806	−	0.104370i
$698$	−13.5332	+	1.18400i	−0.512238	+	0.0448150i
$699$	41.0069	−	34.4089i	1.55102	−	1.30146i
$700$	16.4761	−	28.5280i	0.622738	−	1.07826i
$701$	31.1758	−	11.3471i	1.17749	−	0.428572i	0.322177	−	0.946679i	$-0.395585\pi$
$701$	31.1758	−	11.3471i	1.17749	−	0.428572i	0.855316	+	0.518107i	$0.173363\pi$
$702$	−3.28368	−	3.28368i	−0.123935	−	0.123935i
$703$	−12.0412	−	21.9136i	−0.454143	−	0.826487i
$704$			0.0264335i			0.000996251i
$705$	−0.224297	−	0.352131i	−0.00844750	−	0.0132620i
$706$	−6.99050	−	1.23261i	−0.263091	−	0.0463900i
$707$	2.59458	−	29.6562i	0.0975793	−	1.11534i
$708$	−0.748665	−	8.55728i	−0.0281366	−	0.321602i
$709$	35.4856	−	6.25707i	1.33269	−	0.234989i	0.538484	−	0.842636i	$-0.318997\pi$
$709$	35.4856	−	6.25707i	1.33269	−	0.234989i	0.794207	+	0.607647i	$0.207886\pi$
$710$	16.6057	+	0.726205i	0.623200	+	0.0272540i
$711$	−18.7168	−	10.8062i	−0.701936	−	0.405263i
$712$	6.17959	−	2.88159i	0.231590	−	0.107992i
$713$	−2.82992	+	1.31961i	−0.105981	+	0.0494199i
$714$	−36.0409	−	20.8082i	−1.34880	−	0.778729i
$715$	10.7514	+	0.470185i	0.402081	+	0.0175839i
$716$	16.8033	−	2.96288i	0.627970	−	0.110728i
$717$	4.59407	+	52.5105i	0.171569	+	1.96104i
$718$	0.293467	−	3.35434i	0.0109521	−	0.125183i
$719$	−42.9840	−	7.57923i	−1.60303	−	0.282658i	−0.700620	−	0.713534i	$-0.747093\pi$
$719$	−42.9840	−	7.57923i	−1.60303	−	0.282658i	−0.902411	+	0.430877i	$0.858204\pi$
$720$	4.89878	+	7.69075i	0.182567	+	0.286617i
$721$		−	9.47709i		−	0.352945i
$722$	6.42655	+	10.0581i	0.239172	+	0.374323i
$723$	36.2596	+	36.2596i	1.34851	+	1.34851i
$724$	−22.2555	+	8.10033i	−0.827118	+	0.301046i
$725$	1.65691	+	6.18719i	0.0615360	+	0.229786i
$726$	10.8843	−	9.13303i	0.403955	−	0.338959i
$727$	5.92971	−	0.518782i	0.219921	−	0.0192406i	0.0233372	−	0.999728i	$-0.492571\pi$
$727$	5.92971	−	0.518782i	0.219921	−	0.0192406i	0.196584	+	0.980487i	$0.437015\pi$
$728$	23.8489	−	34.0597i	0.883898	−	1.26234i
$729$	−11.1503	+	6.43763i	−0.412974	+	0.238431i
$730$	−11.3357	−	3.57503i	−0.419555	−	0.132318i
$731$	20.3256	+	7.39791i	0.751769	+	0.273621i
$732$	9.68162	+	20.7623i	0.357843	+	0.767396i
$733$	25.1828	−	6.74771i	0.930148	−	0.249232i	0.238230	−	0.971209i	$-0.423433\pi$
$733$	25.1828	−	6.74771i	0.930148	−	0.249232i	0.691918	+	0.721976i	$0.256766\pi$
$734$	−1.67857	−	2.90737i	−0.0619573	−	0.107313i
$735$	−19.3626	+	46.7361i	−0.714202	+	1.72389i
$736$	−9.27176	+	11.0497i	−0.341762	+	0.407296i
$737$	8.88377	+	0.777229i	0.327238	+	0.0286296i
$738$	−0.562092	+	0.393581i	−0.0206909	+	0.0144879i
$739$	1.90370	+	5.23037i	0.0700287	+	0.192402i	0.969770	−	0.244022i	$-0.0784669\pi$
$739$	1.90370	+	5.23037i	0.0700287	+	0.192402i	−0.899741	+	0.436424i	$0.856245\pi$
$740$	−11.0651	+	17.3659i	−0.406760	+	0.638384i
$741$	−12.5089	+	43.0227i	−0.459526	+	1.58048i
$742$	−5.74567	+	5.74567i	−0.210930	+	0.210930i
$743$	17.9941	−	38.5885i	0.660140	−	1.41567i	−0.235934	−	0.971769i	$-0.575815\pi$
$743$	17.9941	−	38.5885i	0.660140	−	1.41567i	0.896074	−	0.443905i	$-0.146407\pi$
$744$	1.10599	−	6.27238i	0.0405476	−	0.229957i
$745$	−34.8184	−	26.7210i	−1.27565	−	0.978983i
$746$	0.0887921	+	0.0745054i	0.00325091	+	0.00272784i
$747$	−4.88787	−	3.42253i	−0.178838	−	0.125224i
$748$	3.14015	−	11.7192i	0.114815	−	0.428496i
$749$	−14.7261	+	25.5063i	−0.538080	+	0.931981i
$750$	−15.3942	+	4.85014i	−0.562115	+	0.177102i
$751$	−8.34465	+	22.9267i	−0.304501	+	0.836609i	0.689203	+	0.724568i	$0.257961\pi$
$751$	−8.34465	+	22.9267i	−0.304501	+	0.836609i	−0.993704	+	0.112040i	$0.964261\pi$
$752$	−0.0375973	−	0.140315i	−0.00137103	−	0.00511677i
$753$	14.2693	+	3.82346i	0.520004	+	0.139335i
$754$	0.625067	+	3.54493i	0.0227636	+	0.129099i
$755$	−12.6305	+	24.2587i	−0.459671	+	0.882866i
$756$	6.99935	+	8.34150i	0.254564	+	0.303378i
$757$	7.41731	+	10.5930i	0.269587	+	0.385010i	0.931004	−	0.365008i	$-0.118934\pi$
$757$	7.41731	+	10.5930i	0.269587	+	0.385010i	−0.661418	+	0.750018i	$0.730045\pi$
$758$	14.6868	+	6.84857i	0.533449	+	0.248751i
$759$	6.30918			0.229009
$760$	10.6066	−	19.3605i	0.384741	−	0.702280i
$761$	19.7890			0.717350			0.358675	−	0.933462i	$-0.383229\pi$
$761$	19.7890			0.717350			0.358675	+	0.933462i	$0.383229\pi$
$762$	−3.91672	−	1.82639i	−0.141888	−	0.0661633i
$763$	−26.9069	−	38.4270i	−0.974095	−	1.39115i
$764$	11.4164	+	13.6055i	0.413030	+	0.492230i
$765$	−10.7696	−	34.1653i	−0.389375	−	1.23525i
$766$	0.725518	+	4.11462i	0.0262140	+	0.148667i
$767$	−10.0601	−	2.69561i	−0.363251	−	0.0973327i
$768$	−4.20085	−	15.6778i	−0.151585	−	0.565723i
$769$	−5.86652	+	16.1181i	−0.211552	+	0.581235i	−0.999400	−	0.0346351i	$-0.988973\pi$
$769$	−5.86652	+	16.1181i	−0.211552	+	0.581235i	0.787848	+	0.615870i	$0.211195\pi$
$770$	6.15021	+	0.810136i	0.221638	+	0.0291953i
$771$	4.59727	−	7.96271i	0.165567	−	0.286770i
$772$	−5.29039	+	19.7440i	−0.190405	+	0.710602i
$773$	−40.7330	−	28.5215i	−1.46506	−	1.02585i	−0.989239	−	0.146308i	$-0.953261\pi$
$773$	−40.7330	−	28.5215i	−1.46506	−	1.02585i	−0.475824	−	0.879541i	$-0.657850\pi$
$774$	−3.38008	−	2.83622i	−0.121494	−	0.101946i
$775$	−5.54494	−	2.58661i	−0.199180	−	0.0929139i
$776$	−2.39724	+	13.5954i	−0.0860561	+	0.488048i
$777$	22.8647	−	49.0335i	0.820267	−	1.75907i
$778$	6.47630	−	6.47630i	0.232187	−	0.232187i
$779$	−1.87283	−	0.922029i	−0.0671012	−	0.0330351i
$780$	36.0237	−	7.98357i	1.28986	−	0.285858i
$781$	−4.35453	−	11.9640i	−0.155817	−	0.428104i
$782$	9.22278	−	6.45786i	0.329806	−	0.230933i
$783$	−2.10907	−	0.184519i	−0.0753719	−	0.00659419i
$784$	−11.3142	+	13.4837i	−0.404078	+	0.481562i
$785$	12.5970	+	5.21890i	0.449606	+	0.186270i
$786$	4.01579	+	6.95555i	0.143238	+	0.248096i
$787$	−14.1149	+	3.78207i	−0.503142	+	0.134816i	−0.501458	−	0.865182i	$-0.667203\pi$
$787$	−14.1149	+	3.78207i	−0.503142	+	0.134816i	−0.00168396	+	0.999999i	$0.500536\pi$
$788$	0.904995	+	1.94077i	0.0322391	+	0.0691370i
$789$	−10.2486	−	3.73018i	−0.364859	−	0.132798i
$790$	11.8070	−	6.14527i	0.420075	−	0.218639i
$791$	−56.9101	+	32.8570i	−2.02349	+	1.16826i
$792$	−3.18814	+	4.55314i	−0.113286	+	0.161789i
$793$	27.6702	−	2.42083i	0.982598	−	0.0859662i
$794$	−16.1284	+	13.5334i	−0.572377	+	0.480281i
$795$	−16.1787	+	0.705221i	−0.573799	+	0.0250116i
$796$	20.9962	−	7.64198i	0.744189	−	0.270863i
$797$	25.0687	+	25.0687i	0.887980	+	0.887980i	0.994329	−	0.106349i	$-0.0339159\pi$
$797$	25.0687	+	25.0687i	0.887980	+	0.887980i	−0.106349	+	0.994329i	$0.533916\pi$
$798$	−9.34444	+	24.0766i	−0.330789	+	0.852304i
$799$			0.570685i			0.0201894i
$800$	−28.2649	−	0.00402884i	−0.999313	−	0.000142441i
$801$	−6.76205	−	1.19233i	−0.238925	−	0.0421290i
$802$	−0.355103	+	4.05885i	−0.0125391	+	0.143323i
$803$	0.793513	+	9.06990i	0.0280025	+	0.320070i
$804$	30.1109	−	5.30936i	1.06193	−	0.187247i
$805$	−15.8193	−	17.2662i	−0.557558	−	0.608555i
$806$	−2.97786	−	1.71927i	−0.104891	−	0.0605586i
$807$	50.9449	−	23.7560i	1.79335	−	0.836251i
$808$	−14.8889	+	6.94280i	−0.523789	+	0.244247i
$809$	23.6634	+	13.6621i	0.831962	+	0.480334i	0.854524	−	0.519412i	$-0.173849\pi$
$809$	23.6634	+	13.6621i	0.831962	+	0.480334i	−0.0225618	+	0.999745i	$0.507182\pi$
$810$	0.653023	−	14.9323i	0.0229449	−	0.524666i
$811$	−24.8711	+	4.38545i	−0.873343	+	0.153994i	−0.592316	−	0.805706i	$-0.701786\pi$
$811$	−24.8711	+	4.38545i	−0.873343	+	0.153994i	−0.281027	+	0.959700i	$0.590675\pi$
$812$	−0.735641	−	8.40842i	−0.0258159	−	0.295078i
$813$	−5.91745	+	67.6367i	−0.207534	+	2.37212i
$814$	−3.81846	−	0.673297i	−0.133837	−	0.0235991i
$815$	−46.0894	−	10.2212i	−1.61444	−	0.358034i
$816$		−	28.8583i		−	1.01024i
$817$	2.60996	−	13.1670i	0.0913111	−	0.460655i
$818$	−0.121948	−	0.121948i	−0.00426381	−	0.00426381i
$819$	−39.3465	+	14.3209i	−1.37488	+	0.500414i
$820$	0.0748646	+	1.71749i	0.00261438	+	0.0599773i
$821$	22.1402	−	18.5778i	0.772698	−	0.648370i	−0.168700	−	0.985667i	$-0.553957\pi$
$821$	22.1402	−	18.5778i	0.772698	−	0.648370i	0.941398	+	0.337297i	$0.109513\pi$
$822$	−15.3740	+	1.34505i	−0.536231	+	0.0469141i
$823$	−19.1177	+	27.3028i	−0.666400	+	0.951717i	0.333560	+	0.942729i	$0.391750\pi$
$823$	−19.1177	+	27.3028i	−0.666400	+	0.951717i	−0.999960	+	0.00898856i	$0.997139\pi$
$824$	−4.52919	+	2.61493i	−0.157782	+	0.0910953i
$825$	7.94546	+	9.47177i	0.276625	+	0.329765i
$826$	−5.64145	−	2.05332i	−0.196291	−	0.0714441i
$827$	−11.0111	−	23.6133i	−0.382893	−	0.821116i	−0.999429	−	0.0337895i	$-0.989242\pi$
$827$	−11.0111	−	23.6133i	−0.382893	−	0.821116i	0.616536	−	0.787326i	$-0.288535\pi$
$828$	9.02458	−	2.41813i	0.313626	−	0.0840357i
$829$	9.71454	+	16.8261i	0.337400	+	0.584394i	0.983943	−	0.178484i	$-0.0571192\pi$
$829$	9.71454	+	16.8261i	0.337400	+	0.584394i	−0.646543	+	0.762878i	$0.723786\pi$
$830$	3.39529	−	1.40609i	0.117852	−	0.0488062i
$831$	13.4219	−	15.9956i	0.465601	−	0.554882i
$832$	0.109468	+	0.00957722i	0.00379512	+	0.000332030i
$833$	56.6443	−	39.6628i	1.96261	−	1.37423i
$834$	4.31973	+	11.8684i	0.149580	+	0.410968i
$835$	−18.4875	−	11.7797i	−0.639788	−	0.407654i
$836$	−7.48506	−	0.814702i	−0.258876	−	0.0281771i
$837$	1.43004	−	1.43004i	0.0494295	−	0.0494295i
$838$	−3.39758	+	7.28613i	−0.117367	+	0.251695i
$839$	−2.26649	+	12.8539i	−0.0782479	+	0.443766i	0.920363	+	0.391066i	$0.127894\pi$
$839$	−2.26649	+	12.8539i	−0.0782479	+	0.443766i	−0.998610	+	0.0526996i	$0.983217\pi$
$840$	47.3580	−	6.23137i	1.63401	−	0.215003i
$841$	−20.9582	−	17.5860i	−0.722695	−	0.606413i
$842$	13.8106	+	9.67031i	0.475946	+	0.333261i
$843$	−14.3569	+	53.5807i	−0.494478	+	1.84542i
$844$	7.75817	−	13.4375i	0.267047	−	0.462539i
$845$	2.04624	−	15.5342i	0.0703927	−	0.534391i
$846$	0.0398166	−	0.109395i	0.00136892	−	0.00376109i
$847$	10.4551	+	39.0188i	0.359240	+	1.34070i
$848$	−5.44258	−	1.45834i	−0.186899	−	0.0500795i
$849$	7.69056	+	43.6154i	0.263939	+	1.49688i
$850$	21.3097	+	5.71316i	0.730915	+	0.195960i
$851$	9.40843	+	11.2125i	0.322517	+	0.384360i
$852$	−25.0380	−	35.7580i	−0.857788	−	1.22505i
$853$	3.78010	+	1.76269i	0.129428	+	0.0603533i	0.486254	−	0.873818i	$-0.338363\pi$
$853$	3.78010	+	1.76269i	0.129428	+	0.0603533i	−0.356825	+	0.934171i	$0.616141\pi$
$854$	16.0108			0.547878
$855$	−19.9323	+	9.84428i	−0.681671	+	0.336667i
$856$	16.2529			0.555514
$857$	−7.32753	−	3.41688i	−0.250304	−	0.116719i	0.293418	−	0.955984i	$-0.405207\pi$
$857$	−7.32753	−	3.41688i	−0.250304	−	0.116719i	−0.543721	+	0.839266i	$0.682985\pi$
$858$	3.98510	+	5.69132i	0.136049	+	0.194298i
$859$	−2.51313	−	2.99503i	−0.0857467	−	0.102189i	0.721465	−	0.692451i	$-0.243469\pi$
$859$	−2.51313	−	2.99503i	−0.0857467	−	0.102189i	−0.807212	+	0.590262i	$0.799025\pi$
$860$	−10.5430	+	3.32338i	−0.359514	+	0.113326i
$861$	−0.784342	−	4.44822i	−0.0267303	−	0.151595i
$862$	19.4039	+	5.19927i	0.660901	+	0.177088i
$863$	13.7144	+	51.1830i	0.466845	+	1.74229i	0.650699	+	0.759336i	$0.274476\pi$
$863$	13.7144	+	51.1830i	0.466845	+	1.74229i	−0.183854	+	0.982954i	$0.558857\pi$
$864$	3.19530	−	8.77901i	0.108706	−	0.298668i
$865$	−0.545570	+	0.418569i	−0.0185499	+	0.0142318i
$866$	1.26366	−	2.18872i	0.0429408	−	0.0743756i
$867$	−19.2319	+	71.7743i	−0.653148	+	2.43758i
$868$	6.60468	+	4.62465i	0.224178	+	0.156971i
$869$	−7.81029	−	6.55361i	−0.264946	−	0.222316i
$870$	−2.51760	+	3.28052i	−0.0853548	+	0.111220i
$871$	6.43741	−	36.5084i	0.218123	−	1.23704i
$872$	−10.9405	+	23.4619i	−0.370491	+	0.794520i
$873$	9.83038	−	9.83038i	0.332708	−	0.332708i
$874$	−4.83502	−	5.04400i	−0.163547	−	0.170616i
$875$	5.99919	−	45.4932i	0.202810	−	1.53795i
$876$	10.6765	+	29.3334i	0.360725	+	0.991085i
$877$	12.6977	−	8.89105i	0.428772	−	0.300229i	−0.339198	−	0.940715i	$-0.610156\pi$
$877$	12.6977	−	8.89105i	0.428772	−	0.300229i	0.767970	+	0.640486i	$0.221267\pi$
$878$	−11.8833	−	1.03965i	−0.401042	−	0.0350866i
$879$	−37.7724	+	45.0154i	−1.27403	+	1.51833i
$880$	1.64587	+	3.97429i	0.0554823	+	0.133973i
$881$	17.5503	+	30.3981i	0.591286	+	1.02414i	0.994060	+	0.108837i	$0.0347128\pi$
$881$	17.5503	+	30.3981i	0.591286	+	1.02414i	−0.402774	+	0.915300i	$0.631954\pi$
$882$	−13.6255	+	3.65094i	−0.458794	+	0.122933i
$883$	19.6634	+	42.1682i	0.661725	+	1.41907i	0.894734	+	0.446600i	$0.147365\pi$
$883$	19.6634	+	42.1682i	0.661725	+	1.41907i	−0.233009	+	0.972475i	$0.574857\pi$
$884$	−47.3945	−	17.2502i	−1.59405	−	0.580187i
$885$	−5.52396	−	10.6133i	−0.185686	−	0.356761i
$886$	16.6837	−	9.63233i	0.560499	−	0.323604i
$887$	−17.3537	+	24.7837i	−0.582680	+	0.832154i	−0.996953	−	0.0779990i	$-0.975147\pi$
$887$	−17.3537	+	24.7837i	−0.582680	+	0.832154i	0.414273	+	0.910153i	$0.364036\pi$
$888$	−29.7424	+	2.60212i	−0.998090	+	0.0873216i
$889$	9.41202	−	7.89763i	0.315669	−	0.264878i
$890$	2.85718	−	3.11762i	0.0957729	−	0.104503i
$891$	−10.7583	+	3.91570i	−0.360417	+	0.131181i
$892$	3.50629	+	3.50629i	0.117399	+	0.117399i
$893$	0.349999	−	0.0541087i	0.0117123	−	0.00181068i
$894$		−	28.3356i		−	0.947685i
$895$	20.0450	−	12.7681i	0.670030	−	0.426789i
$896$	45.7600	+	8.06872i	1.52873	+	0.269557i
$897$	2.28590	−	26.1280i	0.0763240	−	0.872387i
$898$	−1.79315	−	20.4958i	−0.0598383	−	0.683955i
$899$	−1.54381	+	0.272216i	−0.0514890	+	0.00907891i
$900$	14.9953	+	10.5030i	0.499844	+	0.350101i
$901$	19.1703	+	11.0680i	0.638654	+	0.368727i
$902$	−0.293380	+	0.136805i	−0.00976848	+	0.00455512i
$903$	26.3233	−	12.2748i	0.875986	−	0.408479i
$904$	31.4054	+	18.1319i	1.04453	+	0.603058i
$905$	−24.3233	+	22.2850i	−0.808535	+	0.740780i
$906$	−17.3890	+	3.06615i	−0.577710	+	0.101866i
$907$	−4.78506	−	54.6935i	−0.158885	−	1.81607i	−0.489174	−	0.872186i	$-0.662702\pi$
$907$	−4.78506	−	54.6935i	−0.158885	−	1.81607i	0.330288	−	0.943880i	$-0.392854\pi$
$908$	4.08006	−	46.6353i	0.135402	−	1.54765i
$909$	16.2922	+	2.87276i	0.540379	+	0.0952834i
$910$	5.58328	−	25.1761i	0.185084	−	0.834578i
$911$			21.0691i			0.698050i	0.937113	+	0.349025i	$0.113487\pi$
$911$			21.0691i			0.698050i	−0.937113	+	0.349025i	$0.886513\pi$
$912$	−17.6987	+	2.73616i	−0.586062	+	0.0906033i
$913$	−1.99045	−	1.99045i	−0.0658744	−	0.0658744i
$914$	9.49096	−	3.45443i	0.313933	−	0.114262i
$915$	23.5242	+	21.5590i	0.777686	+	0.712720i
$916$	2.53928	−	2.13071i	0.0839003	−	0.0704007i
$917$	−22.7472	+	1.99012i	−0.751178	+	0.0657196i
$918$	−4.18267	+	5.97347i	−0.138049	+	0.197154i
$919$	42.9667	−	24.8068i	1.41734	−	0.818302i	0.421276	−	0.906933i	$-0.361583\pi$
$919$	42.9667	−	24.8068i	1.41734	−	0.818302i	0.996065	+	0.0886309i	$0.0282492\pi$
$920$	−3.88681	+	12.3243i	−0.128144	+	0.406320i
$921$	−64.9323	−	23.6334i	−2.13959	−	0.778748i
$922$	−0.353912	−	0.758967i	−0.0116555	−	0.0249952i
$923$	−51.1235	+	13.6985i	−1.68275	+	0.450892i
$924$	−8.14577	−	14.1089i	−0.267976	−	0.464148i
$925$	−4.98451	+	28.2450i	−0.163890	+	0.928691i
$926$	2.25652	−	2.68921i	0.0741538	−	0.0883731i
$927$	5.24659	+	0.459017i	0.172321	+	0.0150761i
$928$	−5.93204	+	4.15366i	−0.194729	+	0.136351i
$929$	−7.44981	−	20.4682i	−0.244420	−	0.671539i	−0.999867	−	0.0163287i	$-0.994802\pi$
$929$	−7.44981	−	20.4682i	−0.244420	−	0.671539i	0.755446	−	0.655210i	$-0.227420\pi$
$930$	−0.854702	−	3.85661i	−0.0280268	−	0.126463i
$931$	−29.6957	−	30.9792i	−0.973237	−	1.01530i
$932$	26.4429	−	26.4429i	0.866166	−	0.866166i
$933$	−5.42875	+	11.6420i	−0.177729	+	0.381141i
$934$	2.13210	−	12.0918i	0.0697646	−	0.395655i
$935$	−2.20460	−	16.7548i	−0.0720981	−	0.547941i
$936$	17.7006	+	14.8526i	0.578563	+	0.485472i
$937$	−11.5030	−	8.05445i	−0.375785	−	0.263127i	0.370391	−	0.928876i	$-0.379224\pi$
$937$	−11.5030	−	8.05445i	−0.375785	−	0.263127i	−0.746176	+	0.665748i	$0.768112\pi$
$938$	5.53072	−	20.6409i	0.180584	−	0.673950i
$939$	26.1350	−	45.2672i	0.852884	−	1.47724i
$940$	−0.177534	−	0.231402i	−0.00579054	−	0.00754749i
$941$	−13.7668	+	37.8240i	−0.448785	+	1.23303i	0.484785	+	0.874633i	$0.338898\pi$
$941$	−13.7668	+	37.8240i	−0.448785	+	1.23303i	−0.933570	+	0.358394i	$0.883324\pi$
$942$	2.27839	+	8.50306i	0.0742339	+	0.277045i
$943$	1.18035	+	0.316274i	0.0384375	+	0.0102993i
$944$	−0.722904	−	4.09979i	−0.0235285	−	0.133437i
$945$	13.4529	+	7.00436i	0.437623	+	0.227852i
$946$	−1.33799	−	1.59455i	−0.0435017	−	0.0518433i
$947$	−3.92013	−	5.59853i	−0.127387	−	0.181928i	0.750392	−	0.660993i	$-0.229865\pi$
$947$	−3.92013	−	5.59853i	−0.127387	−	0.181928i	−0.877779	+	0.479065i	$0.840976\pi$
$948$	−31.6816	−	14.7734i	−1.02897	−	0.479818i
$949$	37.8483			1.22861
$950$	1.48341	−	13.6108i	0.0481283	−	0.441593i
$951$	−34.4817			−1.11815
$952$	−59.1750	−	27.5938i	−1.91787	−	0.894319i
$953$	−12.2930	−	17.5563i	−0.398211	−	0.568704i	0.569109	−	0.822262i	$-0.307288\pi$
$953$	−12.2930	−	17.5563i	−0.398211	−	0.568704i	−0.967320	+	0.253558i	$0.918399\pi$
$954$	−2.90256	−	3.45913i	−0.0939738	−	0.111994i
$955$	21.9425	+	11.4245i	0.710043	+	0.369690i
$956$	6.39430	+	36.2639i	0.206807	+	1.17286i
$957$	3.05958	+	0.819812i	0.0989022	+	0.0265008i
$958$	5.21858	+	19.4760i	0.168605	+	0.629242i
$959$	15.0065	−	41.2299i	0.484584	−	1.33138i
$960$	0.0768412	+	0.100156i	0.00248004	+	0.00323253i
$961$	−14.7513	+	25.5499i	−0.475847	+	0.824191i
$962$	−4.17177	+	15.5693i	−0.134503	+	0.501974i
$963$	−13.4072	−	9.38786i	−0.432043	−	0.302519i
$964$	27.4418	+	23.0264i	0.883842	+	0.741631i
$965$	3.71421	+	28.2278i	0.119565	+	0.908685i
$966$	2.62528	−	14.8887i	0.0844670	−	0.479036i
$967$	9.53625	−	20.4505i	0.306665	−	0.657645i	−0.691220	−	0.722644i	$-0.742927\pi$
$967$	9.53625	−	20.4505i	0.306665	−	0.657645i	0.997885	+	0.0649988i	$0.0207044\pi$
$968$	15.7627	−	15.7627i	0.506631	−	0.506631i
$969$	69.9437	+	7.61293i	2.24691	+	0.244563i
$970$	1.85257	+	8.35924i	0.0594826	+	0.268399i
$971$	−12.7036	−	34.9029i	−0.407679	−	1.12009i	−0.958407	−	0.285404i	$-0.907872\pi$
$971$	−12.7036	−	34.9029i	−0.407679	−	1.12009i	0.550729	−	0.834684i	$-0.314350\pi$
$972$	−25.6346	+	17.9495i	−0.822230	+	0.575732i
$973$	−35.7711	−	3.12957i	−1.14677	−	0.100329i
$974$	3.78590	−	4.51186i	0.121308	−	0.144569i
$975$	42.1038	−	29.4724i	1.34840	−	0.943873i
$976$	5.55122	+	9.61499i	0.177690	+	0.307768i
$977$	−29.9054	+	8.01314i	−0.956760	+	0.256363i	−0.703228	−	0.710964i	$-0.748259\pi$
$977$	−29.9054	+	8.01314i	−0.956760	+	0.256363i	−0.253531	+	0.967327i	$0.581592\pi$
$978$	−12.8808	−	27.6229i	−0.411882	−	0.883283i
$979$	−3.04386	−	1.10787i	−0.0972821	−	0.0354078i
$980$	−10.6295	+	33.7040i	−0.339546	+	1.07663i
$981$	22.5767	−	13.0347i	0.720819	−	0.416165i
$982$	−9.20543	+	13.1467i	−0.293757	+	0.419528i
$983$	45.2705	−	3.96066i	1.44391	−	0.126325i	0.661898	−	0.749594i	$-0.269751\pi$
$983$	45.2705	−	3.96066i	1.44391	−	0.126325i	0.782008	+	0.623269i	$0.214196\pi$
$984$	−1.90943	+	1.60220i	−0.0608704	+	0.0510763i
$985$	2.19894	+	2.01525i	0.0700640	+	0.0642111i
$986$	5.31163	−	1.93328i	0.169157	−	0.0615680i
$987$	0.541863	+	0.541863i	0.0172477	+	0.0172477i
$988$	−6.08583	+	30.7024i	−0.193616	+	0.976774i
$989$			7.85773i			0.249861i
$990$	−0.746379	+	3.36556i	−0.0237215	+	0.106965i
$991$	−8.77644	−	1.54752i	−0.278793	−	0.0491587i	0.0325034	−	0.999472i	$-0.489652\pi$
$991$	−8.77644	−	1.54752i	−0.278793	−	0.0491587i	−0.311296	+	0.950313i	$0.600763\pi$
$992$	0.602911	−	6.89130i	0.0191424	−	0.218799i
$993$	2.56940	+	29.3683i	0.0815374	+	0.931976i
$994$	−30.0450	+	5.29775i	−0.952971	+	0.168034i
$995$	22.9470	−	21.0240i	0.727469	−	0.666507i
$996$	−8.35827	−	4.82565i	−0.264842	−	0.152907i
$997$	−25.7216	+	11.9942i	−0.814612	+	0.379860i	−0.784841	−	0.619697i	$-0.787255\pi$
$997$	−25.7216	+	11.9942i	−0.814612	+	0.379860i	−0.0297706	+	0.999557i	$0.509478\pi$
$998$	21.0819	−	9.83065i	0.667336	−	0.311184i
$999$	−8.21004	−	4.74007i	−0.259754	−	0.149969i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.2.r.a.33.5	✓	96
3.2	odd	2		855.2.dl.a.793.4		96
5.2	odd	4	inner	95.2.r.a.52.4	yes	96
5.3	odd	4		475.2.bb.b.432.5		96
5.4	even	2		475.2.bb.b.318.4		96
15.2	even	4		855.2.dl.a.622.5		96
19.15	odd	18	inner	95.2.r.a.53.4	yes	96
57.53	even	18		855.2.dl.a.433.5		96
95.34	odd	18		475.2.bb.b.243.5		96
95.53	even	36		475.2.bb.b.357.4		96
95.72	even	36	inner	95.2.r.a.72.5	yes	96
285.167	odd	36		855.2.dl.a.262.4		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.r.a.33.5	✓	96	1.1	even	1	trivial
95.2.r.a.52.4	yes	96	5.2	odd	4	inner
95.2.r.a.53.4	yes	96	19.15	odd	18	inner
95.2.r.a.72.5	yes	96	95.72	even	36	inner
475.2.bb.b.243.5		96	95.34	odd	18
475.2.bb.b.318.4		96	5.4	even	2
475.2.bb.b.357.4		96	95.53	even	36
475.2.bb.b.432.5		96	5.3	odd	4
855.2.dl.a.262.4		96	285.167	odd	36
855.2.dl.a.433.5		96	57.53	even	18
855.2.dl.a.622.5		96	15.2	even	4
855.2.dl.a.793.4		96	3.2	odd	2

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:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	95.r (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.569347 + 0.265491i) q^{2} +(-1.31808 - 1.88242i) q^{3} +(-1.03190 - 1.22978i) q^{4} +(-1.98334 - 1.03264i) q^{5} +(-0.250682 - 1.42169i) q^{6} +(3.96441 + 1.06226i) q^{7} +(-0.586200 - 2.18773i) q^{8} +(-0.780089 + 2.14328i) q^{9} +O(q^{10})\)	\(q+(0.569347 + 0.265491i) q^{2} +(-1.31808 - 1.88242i) q^{3} +(-1.03190 - 1.22978i) q^{4} +(-1.98334 - 1.03264i) q^{5} +(-0.250682 - 1.42169i) q^{6} +(3.96441 + 1.06226i) q^{7} +(-0.586200 - 2.18773i) q^{8} +(-0.780089 + 2.14328i) q^{9} +(-0.855053 - 1.11449i) q^{10} +(-0.537990 + 0.931826i) q^{11} +(-0.954815 + 3.56342i) q^{12} +(3.66401 + 2.56557i) q^{13} +(1.97510 + 1.65731i) q^{14} +(0.670345 + 5.09458i) q^{15} +(-0.310465 + 1.76073i) q^{16} +(2.96843 - 6.36581i) q^{17} +(-1.01316 + 1.01316i) q^{18} +(-4.18557 - 1.21696i) q^{19} +(0.776702 + 3.50466i) q^{20} +(-3.22580 - 8.86282i) q^{21} +(-0.553694 + 0.387701i) q^{22} +(2.54192 + 0.222389i) q^{23} +(-3.34556 + 3.98708i) q^{24} +(2.86730 + 4.09617i) q^{25} +(1.40496 + 2.43346i) q^{26} +(-1.59635 + 0.427740i) q^{27} +(-2.78455 - 5.97149i) q^{28} +(1.20378 + 0.438142i) q^{29} +(-0.970906 + 3.07856i) q^{30} +(-1.05977 + 0.611858i) q^{31} +(-3.24241 + 4.63064i) q^{32} +(2.46320 - 0.215502i) q^{33} +(3.38013 - 2.83626i) q^{34} +(-6.76585 - 6.20065i) q^{35} +(3.44073 - 1.25232i) q^{36} +(4.05617 + 4.05617i) q^{37} +(-2.05995 - 1.80410i) q^{38} -10.2788i q^{39} +(-1.09651 + 4.94435i) q^{40} +(0.471629 + 0.0831609i) q^{41} +(0.516396 - 5.90244i) q^{42} +(0.268395 + 3.06777i) q^{43} +(1.70109 - 0.299948i) q^{44} +(3.76043 - 3.44530i) q^{45} +(1.38819 + 0.801474i) q^{46} +(-0.0736367 + 0.0343374i) q^{47} +(3.72365 - 1.73637i) q^{48} +(8.52599 + 4.92248i) q^{49} +(0.544992 + 3.09338i) q^{50} +(-15.8957 + 2.80285i) q^{51} +(-0.625835 - 7.15333i) q^{52} +(-0.274673 + 3.13952i) q^{53} +(-1.02244 - 0.180283i) q^{54} +(2.02926 - 1.29258i) q^{55} -9.29576i q^{56} +(3.22610 + 9.48304i) q^{57} +(0.569048 + 0.569048i) q^{58} +(-2.18803 + 0.796379i) q^{59} +(5.57347 - 6.08150i) q^{60} +(4.75697 - 3.99157i) q^{61} +(-0.765818 + 0.0670004i) q^{62} +(-5.36932 + 7.66818i) q^{63} +(0.0212756 - 0.0122835i) q^{64} +(-4.61767 - 8.87201i) q^{65} +(1.45963 + 0.531261i) q^{66} +(-3.50265 - 7.51146i) q^{67} +(-10.8917 + 2.91841i) q^{68} +(-2.93183 - 5.07808i) q^{69} +(-2.20590 - 5.32659i) q^{70} +(-7.60594 + 9.06440i) q^{71} +(5.14620 + 0.450234i) q^{72} +(6.93136 - 4.85339i) q^{73} +(1.23249 + 3.38624i) q^{74} +(3.93136 - 10.7965i) q^{75} +(2.82253 + 6.40310i) q^{76} +(-3.12266 + 3.12266i) q^{77} +(2.72893 - 5.85221i) q^{78} +(-1.64543 + 9.33169i) q^{79} +(2.43397 - 3.17154i) q^{80} +(8.15095 + 6.83946i) q^{81} +(0.246442 + 0.172561i) q^{82} +(-0.677110 + 2.52701i) q^{83} +(-7.57056 + 13.1126i) q^{84} +(-12.4610 + 9.56026i) q^{85} +(-0.661656 + 1.81788i) q^{86} +(-0.761921 - 2.84353i) q^{87} +(2.35395 + 0.630739i) q^{88} +(0.522763 + 2.96473i) q^{89} +(3.05568 - 0.963213i) q^{90} +(11.8003 + 14.0631i) q^{91} +(-2.34953 - 3.35548i) q^{92} +(2.54863 + 1.18845i) q^{93} -0.0510411 q^{94} +(7.04474 + 6.73585i) q^{95} +12.9906 q^{96} +(-5.52418 - 2.57597i) q^{97} +(3.54737 + 5.06617i) q^{98} +(-1.57748 - 1.87997i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 12 q^{6} - 18 q^{8}+O(q^{10}) \) 96 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 12 * q^6 - 18 * q^8	\( 96 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 12 q^{6} - 18 q^{8} - 12 q^{10} - 12 q^{11} - 18 q^{12} - 12 q^{13} + 6 q^{15} + 12 q^{16} - 30 q^{17} - 84 q^{20} + 24 q^{21} - 24 q^{22} + 12 q^{25} - 48 q^{26} - 18 q^{27} - 6 q^{30} - 36 q^{31} + 18 q^{32} + 90 q^{33} - 30 q^{35} + 24 q^{36} + 54 q^{38} + 54 q^{40} + 12 q^{41} + 24 q^{42} + 48 q^{43} + 12 q^{45} - 36 q^{46} - 24 q^{47} + 60 q^{48} + 126 q^{50} - 96 q^{51} - 30 q^{53} + 18 q^{55} - 66 q^{57} + 120 q^{58} + 84 q^{60} - 48 q^{61} + 60 q^{62} - 126 q^{63} + 72 q^{65} + 72 q^{66} + 108 q^{67} + 18 q^{68} + 36 q^{70} - 24 q^{71} + 48 q^{72} + 6 q^{73} + 60 q^{76} + 168 q^{77} - 138 q^{78} - 60 q^{80} - 120 q^{81} + 60 q^{82} - 36 q^{85} - 180 q^{86} - 6 q^{87} - 198 q^{88} - 270 q^{90} - 24 q^{91} - 72 q^{92} - 90 q^{93} - 24 q^{95} - 192 q^{96} - 72 q^{97} - 90 q^{98}+O(q^{100}) \) 96 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 12 * q^6 - 18 * q^8 - 12 * q^10 - 12 * q^11 - 18 * q^12 - 12 * q^13 + 6 * q^15 + 12 * q^16 - 30 * q^17 - 84 * q^20 + 24 * q^21 - 24 * q^22 + 12 * q^25 - 48 * q^26 - 18 * q^27 - 6 * q^30 - 36 * q^31 + 18 * q^32 + 90 * q^33 - 30 * q^35 + 24 * q^36 + 54 * q^38 + 54 * q^40 + 12 * q^41 + 24 * q^42 + 48 * q^43 + 12 * q^45 - 36 * q^46 - 24 * q^47 + 60 * q^48 + 126 * q^50 - 96 * q^51 - 30 * q^53 + 18 * q^55 - 66 * q^57 + 120 * q^58 + 84 * q^60 - 48 * q^61 + 60 * q^62 - 126 * q^63 + 72 * q^65 + 72 * q^66 + 108 * q^67 + 18 * q^68 + 36 * q^70 - 24 * q^71 + 48 * q^72 + 6 * q^73 + 60 * q^76 + 168 * q^77 - 138 * q^78 - 60 * q^80 - 120 * q^81 + 60 * q^82 - 36 * q^85 - 180 * q^86 - 6 * q^87 - 198 * q^88 - 270 * q^90 - 24 * q^91 - 72 * q^92 - 90 * q^93 - 24 * q^95 - 192 * q^96 - 72 * q^97 - 90 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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