LMFDB - Embedded newform 1205.2.b.c.724.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1205,2,Mod(724,1205)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1205, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1205.724");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1205 = 5 \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1205.b (of order $2$, degree $1$, 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:	$9.62197344356$
Analytic rank:	$0$
Dimension:	$46$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			724.7
Character	$\chi$	$=$	1205.724
Dual form			1205.2.b.c.724.40

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.92263i q^{2} -0.557567i q^{3} -1.69651 q^{4} +(-2.01334 + 0.972856i) q^{5} -1.07200 q^{6} -0.976687i q^{7} -0.583491i q^{8} +2.68912 q^{9} +O(q^{10})$	\(q-1.92263i q^{2} -0.557567i q^{3} -1.69651 q^{4} +(-2.01334 + 0.972856i) q^{5} -1.07200 q^{6} -0.976687i q^{7} -0.583491i q^{8} +2.68912 q^{9} +(1.87044 + 3.87092i) q^{10} +5.68399 q^{11} +0.945921i q^{12} +0.519007i q^{13} -1.87781 q^{14} +(0.542433 + 1.12257i) q^{15} -4.51487 q^{16} +2.78999i q^{17} -5.17019i q^{18} +2.82159 q^{19} +(3.41567 - 1.65046i) q^{20} -0.544569 q^{21} -10.9282i q^{22} -7.25155i q^{23} -0.325336 q^{24} +(3.10710 - 3.91739i) q^{25} +0.997860 q^{26} -3.17207i q^{27} +1.65696i q^{28} +2.98708 q^{29} +(2.15830 - 1.04290i) q^{30} -4.59370 q^{31} +7.51345i q^{32} -3.16920i q^{33} +5.36412 q^{34} +(0.950176 + 1.96641i) q^{35} -4.56213 q^{36} -9.40071i q^{37} -5.42487i q^{38} +0.289381 q^{39} +(0.567653 + 1.17477i) q^{40} +1.99776 q^{41} +1.04700i q^{42} +5.68341i q^{43} -9.64296 q^{44} +(-5.41412 + 2.61613i) q^{45} -13.9421 q^{46} +1.33825i q^{47} +2.51734i q^{48} +6.04608 q^{49} +(-7.53169 - 5.97381i) q^{50} +1.55561 q^{51} -0.880503i q^{52} -2.40587i q^{53} -6.09872 q^{54} +(-11.4438 + 5.52970i) q^{55} -0.569888 q^{56} -1.57322i q^{57} -5.74306i q^{58} -5.64524 q^{59} +(-0.920245 - 1.90446i) q^{60} -11.4529 q^{61} +8.83199i q^{62} -2.62643i q^{63} +5.41586 q^{64} +(-0.504919 - 1.04494i) q^{65} -6.09321 q^{66} +5.66108i q^{67} -4.73325i q^{68} -4.04323 q^{69} +(3.78067 - 1.82684i) q^{70} -10.9432 q^{71} -1.56908i q^{72} -15.5123i q^{73} -18.0741 q^{74} +(-2.18421 - 1.73242i) q^{75} -4.78686 q^{76} -5.55147i q^{77} -0.556374i q^{78} +15.9163 q^{79} +(9.08998 - 4.39232i) q^{80} +6.29872 q^{81} -3.84096i q^{82} +6.63802i q^{83} +0.923868 q^{84} +(-2.71426 - 5.61720i) q^{85} +10.9271 q^{86} -1.66550i q^{87} -3.31656i q^{88} -13.2676 q^{89} +(5.02985 + 10.4094i) q^{90} +0.506907 q^{91} +12.3024i q^{92} +2.56129i q^{93} +2.57295 q^{94} +(-5.68082 + 2.74500i) q^{95} +4.18925 q^{96} +1.00517i q^{97} -11.6244i q^{98} +15.2849 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9}+O(q^{10}) $ 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9	$ 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9} - 7 q^{10} - 64 q^{11} + 66 q^{14} + 5 q^{15} + 22 q^{16} - 2 q^{20} - 14 q^{21} + 50 q^{24} + 30 q^{25} - 60 q^{26} + 36 q^{29} + 7 q^{30} - 36 q^{31} - 12 q^{34} + 3 q^{35} - 34 q^{36} + 88 q^{39} - 30 q^{40} - 76 q^{41} + 100 q^{44} - 17 q^{45} - 12 q^{46} - 22 q^{49} - 14 q^{50} - 112 q^{51} + 26 q^{54} - 5 q^{55} - 120 q^{56} + 84 q^{59} - 33 q^{60} - 78 q^{61} - 28 q^{64} + 9 q^{65} - 2 q^{66} + 24 q^{69} + 88 q^{70} - 172 q^{71} + 16 q^{74} + 59 q^{75} - 18 q^{76} + 54 q^{79} + 63 q^{80} - 42 q^{81} - 44 q^{84} + 30 q^{85} - 80 q^{86} + 86 q^{89} + 17 q^{90} - 88 q^{91} - 4 q^{94} + q^{95} - 122 q^{96} + 148 q^{99}+O(q^{100}) $ 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9 - 7 * q^10 - 64 * q^11 + 66 * q^14 + 5 * q^15 + 22 * q^16 - 2 * q^20 - 14 * q^21 + 50 * q^24 + 30 * q^25 - 60 * q^26 + 36 * q^29 + 7 * q^30 - 36 * q^31 - 12 * q^34 + 3 * q^35 - 34 * q^36 + 88 * q^39 - 30 * q^40 - 76 * q^41 + 100 * q^44 - 17 * q^45 - 12 * q^46 - 22 * q^49 - 14 * q^50 - 112 * q^51 + 26 * q^54 - 5 * q^55 - 120 * q^56 + 84 * q^59 - 33 * q^60 - 78 * q^61 - 28 * q^64 + 9 * q^65 - 2 * q^66 + 24 * q^69 + 88 * q^70 - 172 * q^71 + 16 * q^74 + 59 * q^75 - 18 * q^76 + 54 * q^79 + 63 * q^80 - 42 * q^81 - 44 * q^84 + 30 * q^85 - 80 * q^86 + 86 * q^89 + 17 * q^90 - 88 * q^91 - 4 * q^94 + q^95 - 122 * q^96 + 148 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1205\mathbb{Z}\right)^\times$.

$n$	$242$	$971$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	1.92263i		−	1.35951i	−0.733441	−	0.679753i	$-0.762087\pi$
$2$		−	1.92263i		−	1.35951i	0.733441	−	0.679753i	$-0.237913\pi$
$3$		−	0.557567i		−	0.321912i	−0.986962	−	0.160956i	$-0.948542\pi$
$3$		−	0.557567i		−	0.321912i	0.986962	−	0.160956i	$-0.0514577\pi$
$4$	−1.69651			−0.848257
$5$	−2.01334	+	0.972856i	−0.900394	+	0.435074i
$5$	−2.01334	+	0.972856i	−0.900394	+	0.435074i
$6$	−1.07200			−0.437641
$7$		−	0.976687i		−	0.369153i	−0.982818	−	0.184576i	$-0.940909\pi$
$7$		−	0.976687i		−	0.369153i	0.982818	−	0.184576i	$-0.0590913\pi$
$8$		−	0.583491i		−	0.206295i
$9$	2.68912			0.896373
$10$	1.87044	+	3.87092i	0.591486	+	1.22409i
$11$	5.68399			1.71379			0.856893	−	0.515494i	$-0.172392\pi$
$11$	5.68399			1.71379			0.856893	+	0.515494i	$0.172392\pi$
$12$			0.945921i			0.273064i
$13$			0.519007i			0.143947i	0.997407	+	0.0719733i	$0.0229296\pi$
$13$			0.519007i			0.143947i	−0.997407	+	0.0719733i	$0.977070\pi$
$14$	−1.87781			−0.501866
$15$	0.542433	+	1.12257i	0.140056	+	0.289847i
$16$	−4.51487			−1.12872
$17$			2.78999i			0.676671i	0.941025	+	0.338336i	$0.109864\pi$
$17$			2.78999i			0.676671i	−0.941025	+	0.338336i	$0.890136\pi$
$18$		−	5.17019i		−	1.21862i
$19$	2.82159			0.647316			0.323658	−	0.946174i	$-0.395087\pi$
$19$	2.82159			0.647316			0.323658	+	0.946174i	$0.395087\pi$
$20$	3.41567	−	1.65046i	0.763766	−	0.369055i
$21$	−0.544569			−0.118835
$22$		−	10.9282i		−	2.32990i
$23$		−	7.25155i		−	1.51205i	−0.654541	−	0.756027i	$-0.727138\pi$
$23$		−	7.25155i		−	1.51205i	0.654541	−	0.756027i	$-0.272862\pi$
$24$	−0.325336			−0.0664089
$25$	3.10710	−	3.91739i	0.621420	−	0.783477i
$26$	0.997860			0.195696
$27$		−	3.17207i		−	0.610464i
$28$			1.65696i			0.313137i
$29$	2.98708			0.554687			0.277344	−	0.960771i	$-0.410546\pi$
$29$	2.98708			0.554687			0.277344	+	0.960771i	$0.410546\pi$
$30$	2.15830	−	1.04290i	0.394049	−	0.190406i
$31$	−4.59370			−0.825052			−0.412526	−	0.910946i	$-0.635353\pi$
$31$	−4.59370			−0.825052			−0.412526	+	0.910946i	$0.635353\pi$
$32$			7.51345i			1.32820i
$33$		−	3.16920i		−	0.551688i
$34$	5.36412			0.919939
$35$	0.950176	+	1.96641i	0.160609	+	0.332383i
$36$	−4.56213			−0.760355
$37$		−	9.40071i		−	1.54547i	−0.634731	−	0.772734i	$-0.718889\pi$
$37$		−	9.40071i		−	1.54547i	0.634731	−	0.772734i	$-0.281111\pi$
$38$		−	5.42487i		−	0.880030i
$39$	0.289381			0.0463381
$40$	0.567653	+	1.17477i	0.0897539	+	0.185747i
$41$	1.99776			0.311998			0.155999	−	0.987757i	$-0.450140\pi$
$41$	1.99776			0.311998			0.155999	+	0.987757i	$0.450140\pi$
$42$			1.04700i			0.161556i
$43$			5.68341i			0.866712i	0.901223	+	0.433356i	$0.142671\pi$
$43$			5.68341i			0.866712i	−0.901223	+	0.433356i	$0.857329\pi$
$44$	−9.64296			−1.45373
$45$	−5.41412	+	2.61613i	−0.807089	+	0.389989i
$46$	−13.9421			−2.05565
$47$			1.33825i			0.195203i	0.995226	+	0.0976016i	$0.0311171\pi$
$47$			1.33825i			0.195203i	−0.995226	+	0.0976016i	$0.968883\pi$
$48$			2.51734i			0.363347i
$49$	6.04608			0.863726
$50$	−7.53169	−	5.97381i	−1.06514	−	0.844825i
$51$	1.55561			0.217828
$52$		−	0.880503i		−	0.122104i
$53$		−	2.40587i		−	0.330471i	−0.986254	−	0.165236i	$-0.947162\pi$
$53$		−	2.40587i		−	0.330471i	0.986254	−	0.165236i	$-0.0528384\pi$
$54$	−6.09872			−0.829930
$55$	−11.4438	+	5.52970i	−1.54308	+	0.745625i
$56$	−0.569888			−0.0761545
$57$		−	1.57322i		−	0.208379i
$58$		−	5.74306i		−	0.754101i
$59$	−5.64524			−0.734947			−0.367474	−	0.930034i	$-0.619777\pi$
$59$	−5.64524			−0.734947			−0.367474	+	0.930034i	$0.619777\pi$
$60$	−0.920245	−	1.90446i	−0.118803	−	0.245865i
$61$	−11.4529			−1.46639			−0.733196	−	0.680017i	$-0.761972\pi$
$61$	−11.4529			−1.46639			−0.733196	+	0.680017i	$0.761972\pi$
$62$			8.83199i			1.12166i
$63$		−	2.62643i		−	0.330899i
$64$	5.41586			0.676982
$65$	−0.504919	−	1.04494i	−0.0626275	−	0.129609i
$66$	−6.09321			−0.750023
$67$			5.66108i			0.691611i	0.938306	+	0.345805i	$0.112394\pi$
$67$			5.66108i			0.691611i	−0.938306	+	0.345805i	$0.887606\pi$
$68$		−	4.73325i		−	0.573991i
$69$	−4.04323			−0.486748
$70$	3.78067	−	1.82684i	0.451877	−	0.218349i
$71$	−10.9432			−1.29872			−0.649360	−	0.760481i	$-0.724963\pi$
$71$	−10.9432			−1.29872			−0.649360	+	0.760481i	$0.724963\pi$
$72$		−	1.56908i		−	0.184918i
$73$		−	15.5123i		−	1.81558i	−0.419427	−	0.907789i	$-0.637769\pi$
$73$		−	15.5123i		−	1.81558i	0.419427	−	0.907789i	$-0.362231\pi$
$74$	−18.0741			−2.10107
$75$	−2.18421	−	1.73242i	−0.252210	−	0.200042i
$76$	−4.78686			−0.549091
$77$		−	5.55147i		−	0.632649i
$78$		−	0.556374i		−	0.0629969i
$79$	15.9163			1.79073			0.895363	−	0.445337i	$-0.146916\pi$
$79$	15.9163			1.79073			0.895363	+	0.445337i	$0.146916\pi$
$80$	9.08998	−	4.39232i	1.01629	−	0.491076i
$81$	6.29872			0.699857
$82$		−	3.84096i		−	0.424163i
$83$			6.63802i			0.728618i	0.931278	+	0.364309i	$0.118695\pi$
$83$			6.63802i			0.728618i	−0.931278	+	0.364309i	$0.881305\pi$
$84$	0.923868			0.100802
$85$	−2.71426	−	5.61720i	−0.294402	−	0.609271i
$86$	10.9271			1.17830
$87$		−	1.66550i		−	0.178560i
$88$		−	3.31656i		−	0.353546i
$89$	−13.2676			−1.40636			−0.703182	−	0.711009i	$-0.748238\pi$
$89$	−13.2676			−1.40636			−0.703182	+	0.711009i	$0.748238\pi$
$90$	5.02985	+	10.4094i	0.530192	+	1.09724i
$91$	0.506907			0.0531383
$92$			12.3024i			1.28261i
$93$			2.56129i			0.265594i
$94$	2.57295			0.265380
$95$	−5.68082	+	2.74500i	−0.582840	+	0.281631i
$96$	4.18925			0.427564
$97$			1.00517i			0.102060i	0.998697	+	0.0510298i	$0.0162504\pi$
$97$			1.00517i			0.102060i	−0.998697	+	0.0510298i	$0.983750\pi$
$98$		−	11.6244i		−	1.17424i
$99$	15.2849			1.53619
$100$	−5.27124	+	6.64590i	−0.527124	+	0.664590i
$101$	−7.10243			−0.706718			−0.353359	−	0.935488i	$-0.614961\pi$
$101$	−7.10243			−0.706718			−0.353359	+	0.935488i	$0.614961\pi$
$102$		−	2.99086i		−	0.296139i
$103$		−	5.52638i		−	0.544531i	−0.962222	−	0.272265i	$-0.912227\pi$
$103$		−	5.52638i		−	0.544531i	0.962222	−	0.272265i	$-0.0877729\pi$
$104$	0.302836			0.0296955
$105$	1.09640	−	0.529787i	0.106998	−	0.0517019i
$106$	−4.62559			−0.449277
$107$			7.01208i			0.677884i	0.940807	+	0.338942i	$0.110069\pi$
$107$			7.01208i			0.677884i	−0.940807	+	0.338942i	$0.889931\pi$
$108$			5.38146i			0.517831i
$109$	7.33345			0.702417			0.351209	−	0.936297i	$-0.385771\pi$
$109$	7.33345			0.702417			0.351209	+	0.936297i	$0.385771\pi$
$110$	10.6316	+	22.0022i	1.01368	+	2.09783i
$111$	−5.24153			−0.497504
$112$			4.40961i			0.416669i
$113$		−	0.394108i		−	0.0370746i	−0.999828	−	0.0185373i	$-0.994099\pi$
$113$		−	0.394108i		−	0.0370746i	0.999828	−	0.0185373i	$-0.00590094\pi$
$114$	−3.02473			−0.283292
$115$	7.05472	+	14.5999i	0.657856	+	1.36144i
$116$	−5.06763			−0.470517
$117$			1.39567i			0.129030i
$118$			10.8537i			0.999165i
$119$	2.72494			0.249795
$120$	0.655012	−	0.316505i	0.0597942	−	0.0288928i
$121$	21.3077			1.93706
$122$			22.0197i			1.99357i
$123$		−	1.11389i		−	0.100436i
$124$	7.79327			0.699857
$125$	−2.44461	+	10.9098i	−0.218652	+	0.975803i
$126$	−5.04965			−0.449859
$127$		−	9.43489i		−	0.837211i	−0.908168	−	0.418605i	$-0.862519\pi$
$127$		−	9.43489i		−	0.837211i	0.908168	−	0.418605i	$-0.137481\pi$
$128$			4.61419i			0.407841i
$129$	3.16888			0.279005
$130$	−2.00903	+	0.970774i	−0.176204	+	0.0851425i
$131$	9.36627			0.818335			0.409167	−	0.912459i	$-0.365819\pi$
$131$	9.36627			0.818335			0.409167	+	0.912459i	$0.365819\pi$
$132$			5.37660i			0.467973i
$133$		−	2.75581i		−	0.238959i
$134$	10.8842			0.940249
$135$	3.08596	+	6.38646i	0.265598	+	0.549659i
$136$	1.62793			0.139594
$137$		−	5.32866i		−	0.455258i	−0.973748	−	0.227629i	$-0.926903\pi$
$137$		−	5.32866i		−	0.455258i	0.973748	−	0.227629i	$-0.0730974\pi$
$138$			7.77364i			0.661736i
$139$	−7.74702			−0.657093			−0.328547	−	0.944488i	$-0.606559\pi$
$139$	−7.74702			−0.657093			−0.328547	+	0.944488i	$0.606559\pi$
$140$	−1.61199	−	3.33604i	−0.136238	−	0.281946i
$141$	0.746162			0.0628382
$142$			21.0398i			1.76562i
$143$			2.95003i			0.246694i
$144$	−12.1410			−1.01175
$145$	−6.01402	+	2.90600i	−0.499437	+	0.241330i
$146$	−29.8245			−2.46829
$147$		−	3.37110i		−	0.278043i
$148$			15.9484i			1.31095i
$149$	19.8084			1.62277			0.811383	−	0.584515i	$-0.198715\pi$
$149$	19.8084			1.62277			0.811383	+	0.584515i	$0.198715\pi$
$150$	−3.33080	+	4.19943i	−0.271959	+	0.342882i
$151$	19.6869			1.60209			0.801047	−	0.598601i	$-0.204276\pi$
$151$	19.6869			1.60209			0.801047	+	0.598601i	$0.204276\pi$
$152$		−	1.64637i		−	0.133538i
$153$			7.50261i			0.606550i
$154$	−10.6734			−0.860090
$155$	9.24869	−	4.46901i	0.742873	−	0.358959i
$156$	−0.490940			−0.0393066
$157$		−	21.5455i		−	1.71952i	−0.510701	−	0.859758i	$-0.670614\pi$
$157$		−	21.5455i		−	1.71952i	0.510701	−	0.859758i	$-0.329386\pi$
$158$		−	30.6012i		−	2.43450i
$159$	−1.34143			−0.106382
$160$	−7.30950	−	15.1271i	−0.577867	−	1.19591i
$161$	−7.08250			−0.558179
$162$		−	12.1101i		−	0.951460i
$163$		−	12.5163i		−	0.980349i	−0.871624	−	0.490175i	$-0.836933\pi$
$163$		−	12.5163i		−	0.980349i	0.871624	−	0.490175i	$-0.163067\pi$
$164$	−3.38923			−0.264654
$165$	3.08318	+	6.38070i	0.240025	+	0.496737i
$166$	12.7625			0.990560
$167$			7.38516i			0.571481i	0.958307	+	0.285740i	$0.0922395\pi$
$167$			7.38516i			0.571481i	−0.958307	+	0.285740i	$0.907761\pi$
$168$			0.317751i			0.0245150i
$169$	12.7306			0.979279
$170$	−10.7998	+	5.21852i	−0.828308	+	0.400242i
$171$	7.58758			0.580237
$172$		−	9.64199i		−	0.735195i
$173$		−	17.6215i		−	1.33974i	−0.742480	−	0.669868i	$-0.766351\pi$
$173$		−	17.6215i		−	1.33974i	0.742480	−	0.669868i	$-0.233649\pi$
$174$	−3.20214			−0.242754
$175$	−3.82606	−	3.03467i	−0.289223	−	0.229399i
$176$	−25.6624			−1.93438
$177$			3.14760i			0.236588i
$178$			25.5088i			1.91196i
$179$	2.22554			0.166345			0.0831723	−	0.996535i	$-0.473495\pi$
$179$	2.22554			0.166345			0.0831723	+	0.996535i	$0.473495\pi$
$180$	9.18513	−	4.43829i	0.684619	−	0.330811i
$181$	−18.6828			−1.38868			−0.694341	−	0.719646i	$-0.744304\pi$
$181$	−18.6828			−1.38868			−0.694341	+	0.719646i	$0.744304\pi$
$182$		−	0.974596i		−	0.0722419i
$183$			6.38576i			0.472049i
$184$	−4.23122			−0.311930
$185$	9.14554	+	18.9269i	0.672393	+	1.39153i
$186$	4.92443			0.361077
$187$			15.8583i			1.15967i
$188$		−	2.27035i		−	0.165583i
$189$	−3.09812			−0.225355
$190$	5.27762	+	10.9221i	0.382879	+	0.792374i
$191$	−13.4719			−0.974793			−0.487396	−	0.873181i	$-0.662053\pi$
$191$	−13.4719			−0.974793			−0.487396	+	0.873181i	$0.662053\pi$
$192$		−	3.01971i		−	0.217928i
$193$			9.23670i			0.664872i	0.943126	+	0.332436i	$0.107871\pi$
$193$			9.23670i			0.664872i	−0.943126	+	0.332436i	$0.892129\pi$
$194$	1.93257			0.138751
$195$	−0.582624	+	0.281526i	−0.0417226	+	0.0201605i
$196$	−10.2573			−0.732662
$197$			25.8626i			1.84263i	0.388816	+	0.921315i	$0.372884\pi$
$197$			25.8626i			1.84263i	−0.388816	+	0.921315i	$0.627116\pi$
$198$		−	29.3873i		−	2.08846i
$199$	−4.26338			−0.302223			−0.151112	−	0.988517i	$-0.548285\pi$
$199$	−4.26338			−0.302223			−0.151112	+	0.988517i	$0.548285\pi$
$200$	−2.28576	−	1.81297i	−0.161628	−	0.128196i
$201$	3.15643			0.222638
$202$			13.6554i			0.960788i
$203$		−	2.91744i		−	0.204764i
$204$	−2.63911			−0.184774
$205$	−4.02218	+	1.94353i	−0.280921	+	0.135742i
$206$	−10.6252			−0.740293
$207$		−	19.5003i		−	1.35536i
$208$		−	2.34325i		−	0.162475i
$209$	16.0379			1.10936
$210$	−1.01859	−	2.10798i	−0.0702891	−	0.145464i
$211$	6.03303			0.415331			0.207665	−	0.978200i	$-0.433413\pi$
$211$	6.03303			0.415331			0.207665	+	0.978200i	$0.433413\pi$
$212$			4.08159i			0.280324i
$213$			6.10158i			0.418073i
$214$	13.4817			0.921587
$215$	−5.52914	−	11.4427i	−0.377084	−	0.780383i
$216$	−1.85087			−0.125936
$217$			4.48660i			0.304570i
$218$		−	14.0995i		−	0.954941i
$219$	−8.64915			−0.584456
$220$	19.4146	−	9.38122i	1.30893	−	0.632482i
$221$	−1.44802			−0.0974046
$222$			10.0775i			0.676360i
$223$			21.1766i			1.41809i	0.705162	+	0.709046i	$0.250874\pi$
$223$			21.1766i			1.41809i	−0.705162	+	0.709046i	$0.749126\pi$
$224$	7.33828			0.490310
$225$	8.35537	−	10.5343i	0.557024	−	0.702288i
$226$	−0.757725			−0.0504031
$227$			3.50318i			0.232514i	0.993219	+	0.116257i	$0.0370897\pi$
$227$			3.50318i			0.232514i	−0.993219	+	0.116257i	$0.962910\pi$
$228$			2.66900i			0.176759i
$229$	19.3330			1.27756			0.638781	−	0.769389i	$-0.279439\pi$
$229$	19.3330			1.27756			0.638781	+	0.769389i	$0.279439\pi$
$230$	28.0702	−	13.5636i	1.85089	−	0.894359i
$231$	−3.09532			−0.203657
$232$		−	1.74294i		−	0.114429i
$233$			23.0684i			1.51126i	0.654997	+	0.755632i	$0.272670\pi$
$233$			23.0684i			1.51126i	−0.654997	+	0.755632i	$0.727330\pi$
$234$	2.68336			0.175417
$235$	−1.30192	−	2.69435i	−0.0849280	−	0.175760i
$236$	9.57722			0.623424
$237$		−	8.87442i		−	0.576456i
$238$		−	5.23906i		−	0.339598i
$239$	3.13382			0.202710			0.101355	−	0.994850i	$-0.467682\pi$
$239$	3.13382			0.202710			0.101355	+	0.994850i	$0.467682\pi$
$240$	−2.44901	−	5.06827i	−0.158083	−	0.327156i
$241$	1.00000			0.0644157
$241$	1.00000			0.0644157
$242$		−	40.9669i		−	2.63345i
$243$		−	13.0282i		−	0.835757i
$244$	19.4300			1.24388
$245$	−12.1728	+	5.88197i	−0.777694	+	0.375785i
$246$	−2.14159			−0.136543
$247$			1.46442i			0.0931790i
$248$			2.68038i			0.170204i
$249$	3.70114			0.234551
$250$	20.9755	+	4.70008i	1.32661	+	0.297259i
$251$	8.51378			0.537385			0.268693	−	0.963226i	$-0.413408\pi$
$251$	8.51378			0.537385			0.268693	+	0.963226i	$0.413408\pi$
$252$			4.45577i			0.280687i
$253$		−	41.2177i		−	2.59134i
$254$	−18.1398			−1.13819
$255$	−3.13197	+	1.51338i	−0.196131	+	0.0947716i
$256$	19.7031			1.23144
$257$			0.300229i			0.0187278i	0.999956	+	0.00936389i	$0.00298066\pi$
$257$			0.300229i			0.0187278i	−0.999956	+	0.00936389i	$0.997019\pi$
$258$		−	6.09260i		−	0.379309i
$259$	−9.18155			−0.570514
$260$	0.856603	+	1.77275i	0.0531242	+	0.109942i
$261$	8.03262			0.497207
$262$		−	18.0079i		−	1.11253i
$263$			15.5157i			0.956740i	0.878158	+	0.478370i	$0.158772\pi$
$263$			15.5157i			0.956740i	−0.878158	+	0.478370i	$0.841228\pi$
$264$	−1.84920			−0.113811
$265$	2.34056	+	4.84383i	0.143780	+	0.297554i
$266$	−5.29840			−0.324866
$267$			7.39759i			0.452725i
$268$		−	9.60410i		−	0.586664i
$269$	28.6731			1.74823			0.874115	−	0.485718i	$-0.161442\pi$
$269$	28.6731			1.74823			0.874115	+	0.485718i	$0.161442\pi$
$270$	12.2788	−	5.93317i	0.747265	−	0.361081i
$271$	−6.01685			−0.365498			−0.182749	−	0.983160i	$-0.558500\pi$
$271$	−6.01685			−0.365498			−0.182749	+	0.983160i	$0.558500\pi$
$272$		−	12.5964i		−	0.763771i
$273$		−	0.282635i		−	0.0171058i
$274$	−10.2451			−0.618927
$275$	17.6607	−	22.2664i	1.06498	−	1.34271i
$276$	6.85940			0.412887
$277$			22.1758i			1.33241i	0.745767	+	0.666207i	$0.232083\pi$
$277$			22.1758i			1.33241i	−0.745767	+	0.666207i	$0.767917\pi$
$278$			14.8947i			0.893322i
$279$	−12.3530			−0.739555
$280$	1.14738	−	0.554419i	0.0685691	−	0.0331329i
$281$	−17.6552			−1.05322			−0.526610	−	0.850107i	$-0.676537\pi$
$281$	−17.6552			−1.05322			−0.526610	+	0.850107i	$0.676537\pi$
$282$		−	1.43460i		−	0.0854289i
$283$		−	3.73383i		−	0.221953i	−0.993823	−	0.110977i	$-0.964602\pi$
$283$		−	3.73383i		−	0.221953i	0.993823	−	0.110977i	$-0.0353979\pi$
$284$	18.5653			1.10165
$285$	1.53052	+	3.16744i	0.0906602	+	0.187623i
$286$	5.67182			0.335382
$287$		−	1.95119i		−	0.115175i
$288$			20.2046i			1.19056i
$289$	9.21597			0.542116
$290$	5.58717	+	11.5627i	0.328090	+	0.678988i
$291$	0.560451			0.0328542
$292$			26.3168i			1.54008i
$293$			30.3941i			1.77564i	0.460190	+	0.887821i	$0.347781\pi$
$293$			30.3941i			1.77564i	−0.460190	+	0.887821i	$0.652219\pi$
$294$	−6.48138			−0.378002
$295$	11.3658	−	5.49200i	0.661742	−	0.319757i
$296$	−5.48523			−0.318823
$297$		−	18.0300i		−	1.04621i
$298$		−	38.0842i		−	2.20616i
$299$	3.76361			0.217655
$300$	3.70554	+	2.93907i	0.213939	+	0.169687i
$301$	5.55091			0.319949
$302$		−	37.8506i		−	2.17806i
$303$			3.96008i			0.227501i
$304$	−12.7391			−0.730637
$305$	23.0586	−	11.1420i	1.32033	−	0.637990i
$306$	14.4248			0.824608
$307$			5.88448i			0.335845i	0.985800	+	0.167923i	$0.0537059\pi$
$307$			5.88448i			0.335845i	−0.985800	+	0.167923i	$0.946294\pi$
$308$			9.41815i			0.536649i
$309$	−3.08133			−0.175291
$310$	−8.59225	−	17.7818i	−0.488007	−	1.00994i
$311$	−8.56865			−0.485883			−0.242942	−	0.970041i	$-0.578112\pi$
$311$	−8.56865			−0.485883			−0.242942	+	0.970041i	$0.578112\pi$
$312$		−	0.168852i		−	0.00955933i
$313$			6.68268i			0.377728i	0.982003	+	0.188864i	$0.0604805\pi$
$313$			6.68268i			0.377728i	−0.982003	+	0.188864i	$0.939520\pi$
$314$	−41.4240			−2.33769
$315$	2.55514	+	5.28790i	0.143966	+	0.297939i
$316$	−27.0023			−1.51900
$317$			18.7500i			1.05311i	0.850142	+	0.526553i	$0.176516\pi$
$317$			18.7500i			1.05311i	−0.850142	+	0.526553i	$0.823484\pi$
$318$			2.57908i			0.144628i
$319$	16.9785			0.950615
$320$	−10.9040	+	5.26885i	−0.609551	+	0.294538i
$321$	3.90971			0.218219
$322$			13.6170i			0.758848i
$323$			7.87219i			0.438020i
$324$	−10.6859			−0.593659
$325$	2.03315	+	1.61261i	0.112779	+	0.0894514i
$326$	−24.0642			−1.33279
$327$		−	4.08889i		−	0.226116i
$328$		−	1.16568i		−	0.0643637i
$329$	1.30705			0.0720598
$330$	12.2677	−	5.92782i	0.675316	−	0.326316i
$331$	−10.1395			−0.557317			−0.278659	−	0.960390i	$-0.589890\pi$
$331$	−10.1395			−0.557317			−0.278659	+	0.960390i	$0.589890\pi$
$332$		−	11.2615i		−	0.618055i
$333$		−	25.2796i		−	1.38531i
$334$	14.1989			0.776932
$335$	−5.50741	−	11.3977i	−0.300902	−	0.622722i
$336$	2.45865			0.134131
$337$		−	22.7996i		−	1.24197i	−0.783822	−	0.620986i	$-0.786732\pi$
$337$		−	22.7996i		−	1.24197i	0.783822	−	0.620986i	$-0.213268\pi$
$338$		−	24.4763i		−	1.33134i
$339$	−0.219742			−0.0119347
$340$	4.60478	+	9.52966i	0.249729	+	0.516819i
$341$	−26.1105			−1.41396
$342$		−	14.5881i		−	0.788835i
$343$		−	12.7419i		−	0.688000i
$344$	3.31622			0.178799
$345$	8.14041	−	3.93348i	0.438265	−	0.211771i
$346$	−33.8796			−1.82138
$347$			33.0431i			1.77385i	0.461916	+	0.886924i	$0.347162\pi$
$347$			33.0431i			1.77385i	−0.461916	+	0.886924i	$0.652838\pi$
$348$			2.82554i			0.151465i
$349$	10.7629			0.576126			0.288063	−	0.957611i	$-0.406989\pi$
$349$	10.7629			0.576126			0.288063	+	0.957611i	$0.406989\pi$
$350$	−5.83454	+	7.35610i	−0.311870	+	0.393200i
$351$	1.64632			0.0878743
$352$			42.7063i			2.27626i
$353$			12.8113i			0.681879i	0.940085	+	0.340940i	$0.110745\pi$
$353$			12.8113i			0.681879i	−0.940085	+	0.340940i	$0.889255\pi$
$354$	6.05167			0.321643
$355$	22.0325	−	10.6462i	1.16936	−	0.565040i
$356$	22.5087			1.19296
$357$		−	1.51934i		−	0.0804120i
$358$		−	4.27889i		−	0.226146i
$359$	−12.7434			−0.672570			−0.336285	−	0.941760i	$-0.609170\pi$
$359$	−12.7434			−0.672570			−0.336285	+	0.941760i	$0.609170\pi$
$360$	1.52649	+	3.15909i	0.0804529	+	0.166499i
$361$	−11.0387			−0.580982
$362$			35.9202i			1.88792i
$363$		−	11.8805i		−	0.623563i
$364$	−0.859975			−0.0450750
$365$	15.0912	+	31.2316i	0.789912	+	1.63474i
$366$	12.2775			0.641753
$367$		−	1.03639i		−	0.0540989i	−0.999634	−	0.0270495i	$-0.991389\pi$
$367$		−	1.03639i		−	0.0540989i	0.999634	−	0.0270495i	$-0.00861116\pi$
$368$			32.7398i			1.70668i
$369$	5.37222			0.279666
$370$	36.3894	−	17.5835i	1.89179	−	0.914123i
$371$	−2.34978			−0.121994
$372$		−	4.34527i		−	0.225292i
$373$		−	14.7553i		−	0.763999i	−0.924163	−	0.381999i	$-0.875236\pi$
$373$		−	14.7553i		−	0.763999i	0.924163	−	0.381999i	$-0.124764\pi$
$374$	30.4896			1.57658
$375$	6.08295	+	1.36303i	0.314122	+	0.0703868i
$376$	0.780855			0.0402695
$377$			1.55032i			0.0798454i
$378$			5.95654i			0.306371i
$379$	−23.1923			−1.19131			−0.595653	−	0.803242i	$-0.703107\pi$
$379$	−23.1923			−1.19131			−0.595653	+	0.803242i	$0.703107\pi$
$380$	9.63759	−	4.65693i	0.494398	−	0.238895i
$381$	−5.26058			−0.269508
$382$			25.9015i			1.32524i
$383$		−	12.7484i		−	0.651415i	−0.945471	−	0.325707i	$-0.894398\pi$
$383$		−	12.7484i		−	0.651415i	0.945471	−	0.325707i	$-0.105602\pi$
$384$	2.57272			0.131289
$385$	5.40079	+	11.1770i	0.275250	+	0.569634i
$386$	17.7588			0.903898
$387$			15.2834i			0.776897i
$388$		−	1.70529i		−	0.0865728i
$389$	−31.6959			−1.60705			−0.803523	−	0.595274i	$-0.797043\pi$
$389$	−31.6959			−1.60705			−0.803523	+	0.595274i	$0.797043\pi$
$390$	0.541272	+	1.12017i	0.0274084	+	0.0567221i
$391$	20.2317			1.02316
$392$		−	3.52784i		−	0.178183i
$393$		−	5.22233i		−	0.263432i
$394$	49.7242			2.50507
$395$	−32.0450	+	15.4843i	−1.61236	+	0.779099i
$396$	−25.9311			−1.30309
$397$		−	18.0796i		−	0.907389i	−0.891157	−	0.453694i	$-0.850106\pi$
$397$		−	18.0796i		−	0.907389i	0.891157	−	0.453694i	$-0.149894\pi$
$398$			8.19692i			0.410874i
$399$	−1.53655			−0.0769236
$400$	−14.0282	+	17.6865i	−0.701408	+	0.884324i
$401$	24.8583			1.24136			0.620682	−	0.784063i	$-0.286856\pi$
$401$	24.8583			1.24136			0.620682	+	0.784063i	$0.286856\pi$
$402$		−	6.06866i		−	0.302677i
$403$		−	2.38416i		−	0.118764i
$404$	12.0494			0.599479
$405$	−12.6815	+	6.12774i	−0.630148	+	0.304490i
$406$	−5.60917			−0.278378
$407$		−	53.4335i		−	2.64860i
$408$		−	0.907683i		−	0.0449370i
$409$	−4.25506			−0.210399			−0.105200	−	0.994451i	$-0.533548\pi$
$409$	−4.25506			−0.210399			−0.105200	+	0.994451i	$0.533548\pi$
$410$	3.73670	+	7.73317i	0.184543	+	0.381914i
$411$	−2.97109			−0.146553
$412$			9.37559i			0.461902i
$413$			5.51363i			0.271308i
$414$	−37.4919			−1.84263
$415$	−6.45784	−	13.3646i	−0.317003	−	0.656043i
$416$	−3.89953			−0.191190
$417$			4.31948i			0.211526i
$418$		−	30.8349i		−	1.50818i
$419$	−16.7521			−0.818396			−0.409198	−	0.912446i	$-0.634191\pi$
$419$	−16.7521			−0.818396			−0.409198	+	0.912446i	$0.634191\pi$
$420$	−1.86006	+	0.898791i	−0.0907618	+	0.0438565i
$421$	20.9251			1.01982			0.509912	−	0.860226i	$-0.329678\pi$
$421$	20.9251			1.01982			0.509912	+	0.860226i	$0.329678\pi$
$422$		−	11.5993i		−	0.564645i
$423$			3.59870i			0.174975i
$424$	−1.40380			−0.0681746
$425$	10.9295	+	8.66878i	0.530157	+	0.420497i
$426$	11.7311			0.568373
$427$			11.1859i			0.541323i
$428$		−	11.8961i		−	0.575020i
$429$	1.64484			0.0794136
$430$	−22.0000	+	10.6305i	−1.06094	+	0.512649i
$431$	−27.7303			−1.33572			−0.667861	−	0.744286i	$-0.732790\pi$
$431$	−27.7303			−1.33572			−0.667861	+	0.744286i	$0.732790\pi$
$432$			14.3215i			0.689042i
$433$			28.0853i			1.34969i	0.737958	+	0.674847i	$0.235790\pi$
$433$			28.0853i			1.34969i	−0.737958	+	0.674847i	$0.764210\pi$
$434$	8.62609			0.414065
$435$	1.62029	+	3.35322i	0.0776870	+	0.160775i
$436$	−12.4413			−0.595831
$437$		−	20.4609i		−	0.978777i
$438$			16.6291i			0.794571i
$439$	10.0542			0.479863			0.239931	−	0.970790i	$-0.422875\pi$
$439$	10.0542			0.479863			0.239931	+	0.970790i	$0.422875\pi$
$440$	3.22653	+	6.67737i	0.153819	+	0.318331i
$441$	16.2586			0.774221
$442$			2.78402i			0.132422i
$443$			4.38230i			0.208209i	0.994566	+	0.104105i	$0.0331977\pi$
$443$			4.38230i			0.208209i	−0.994566	+	0.104105i	$0.966802\pi$
$444$	8.89233			0.422011
$445$	26.7123	−	12.9075i	1.26628	−	0.611874i
$446$	40.7149			1.92791
$447$		−	11.0445i		−	0.522387i
$448$		−	5.28960i		−	0.249910i
$449$	−7.51495			−0.354652			−0.177326	−	0.984152i	$-0.556745\pi$
$449$	−7.51495			−0.354652			−0.177326	+	0.984152i	$0.556745\pi$
$450$	−20.2536	−	16.0643i	−0.954765	−	0.757278i
$451$	11.3552			0.534698
$452$			0.668610i			0.0314488i
$453$		−	10.9768i		−	0.515733i
$454$	6.73533			0.316105
$455$	−1.02058	+	0.493148i	−0.0478454	+	0.0231191i
$456$	−0.917963			−0.0429875
$457$		−	27.0931i		−	1.26736i	−0.773594	−	0.633682i	$-0.781543\pi$
$457$		−	27.0931i		−	1.26736i	0.773594	−	0.633682i	$-0.218457\pi$
$458$		−	37.1703i		−	1.73685i
$459$	8.85003			0.413084
$460$	−11.9684	−	24.7689i	−0.558031	−	1.15486i
$461$	8.28811			0.386016			0.193008	−	0.981197i	$-0.438176\pi$
$461$	8.28811			0.386016			0.193008	+	0.981197i	$0.438176\pi$
$462$			5.95116i			0.276873i
$463$			39.3319i			1.82791i	0.405815	+	0.913955i	$0.366988\pi$
$463$			39.3319i			1.82791i	−0.405815	+	0.913955i	$0.633012\pi$
$464$	−13.4863			−0.626085
$465$	−2.49177	−	5.15677i	−0.115553	−	0.239139i
$466$	44.3521			2.05457
$467$		−	1.62543i		−	0.0752160i	−0.999293	−	0.0376080i	$-0.988026\pi$
$467$		−	1.62543i		−	0.0752160i	0.999293	−	0.0376080i	$-0.0119738\pi$
$468$		−	2.36778i		−	0.109451i
$469$	5.52910			0.255310
$470$	−5.18024	+	2.50312i	−0.238947	+	0.115460i
$471$	−12.0131			−0.553532
$472$			3.29395i			0.151616i
$473$			32.3044i			1.48536i
$474$	−17.0622			−0.783695
$475$	8.76695	−	11.0532i	0.402255	−	0.507158i
$476$	−4.62291			−0.211891
$477$		−	6.46966i		−	0.296225i
$478$		−	6.02518i		−	0.275585i
$479$	−27.2783			−1.24638			−0.623189	−	0.782071i	$-0.714163\pi$
$479$	−27.2783			−1.24638			−0.623189	+	0.782071i	$0.714163\pi$
$480$	−8.43440	+	4.07554i	−0.384976	+	0.186022i
$481$	4.87903			0.222465
$482$		−	1.92263i		−	0.0875735i
$483$			3.94897i			0.179684i
$484$	−36.1488			−1.64313
$485$	−0.977887	−	2.02375i	−0.0444036	−	0.0918940i
$486$	−25.0484			−1.13622
$487$			16.1457i			0.731631i	0.930687	+	0.365815i	$0.119210\pi$
$487$			16.1457i			0.731631i	−0.930687	+	0.365815i	$0.880790\pi$
$488$			6.68266i			0.302510i
$489$	−6.97866			−0.315586
$490$	11.3089	+	23.4039i	0.510882	+	1.05728i
$491$	−13.9774			−0.630791			−0.315395	−	0.948960i	$-0.602137\pi$
$491$	−13.9774			−0.630791			−0.315395	+	0.948960i	$0.602137\pi$
$492$			1.88972i			0.0851953i
$493$			8.33392i			0.375341i
$494$	2.81555			0.126677
$495$	−30.7738	+	14.8700i	−1.38318	+	0.668358i
$496$	20.7399			0.931251
$497$			10.6881i			0.479427i
$498$		−	7.11594i		−	0.318873i
$499$	−13.5580			−0.606937			−0.303469	−	0.952841i	$-0.598145\pi$
$499$	−13.5580			−0.606937			−0.303469	+	0.952841i	$0.598145\pi$
$500$	4.14731	−	18.5086i	0.185474	−	0.827732i
$501$	4.11772			0.183966
$502$		−	16.3689i		−	0.730578i
$503$			28.0739i			1.25175i	0.779923	+	0.625876i	$0.215258\pi$
$503$			28.0739i			1.25175i	−0.779923	+	0.625876i	$0.784742\pi$
$504$	−1.53250			−0.0682629
$505$	14.2996	−	6.90964i	0.636325	−	0.307475i
$506$	−79.2465			−3.52294
$507$		−	7.09818i		−	0.315241i
$508$			16.0064i			0.710170i
$509$	39.5857			1.75460			0.877302	−	0.479939i	$-0.159341\pi$
$509$	39.5857			1.75460			0.877302	+	0.479939i	$0.159341\pi$
$510$	2.90967	+	6.02162i	0.128843	+	0.266642i
$511$	−15.1507			−0.670226
$512$		−	28.6534i		−	1.26632i
$513$		−	8.95026i		−	0.395164i
$514$	0.577230			0.0254605
$515$	5.37638	+	11.1265i	0.236911	+	0.490293i
$516$	−5.37606			−0.236668
$517$			7.60657i			0.334537i
$518$			17.6527i			0.775617i
$519$	−9.82516			−0.431277
$520$	−0.609713	+	0.294616i	−0.0267377	+	0.0129198i
$521$	13.3893			0.586597			0.293299	−	0.956021i	$-0.405247\pi$
$521$	13.3893			0.586597			0.293299	+	0.956021i	$0.405247\pi$
$522$		−	15.4438i		−	0.675955i
$523$			11.5484i			0.504976i	0.967600	+	0.252488i	$0.0812489\pi$
$523$			11.5484i			0.504976i	−0.967600	+	0.252488i	$0.918751\pi$
$524$	−15.8900			−0.694158
$525$	−1.69203	+	2.13329i	−0.0738462	+	0.0931042i
$526$	29.8310			1.30069
$527$		−	12.8164i		−	0.558289i
$528$			14.3085i			0.622699i
$529$	−29.5850			−1.28631
$530$	9.31291	−	4.50004i	0.404527	−	0.195469i
$531$	−15.1807			−0.658787
$532$			4.67526i			0.202698i
$533$			1.03685i			0.0449110i
$534$	14.2228			0.615483
$535$	−6.82175	−	14.1177i	−0.294930	−	0.610363i
$536$	3.30319			0.142676
$537$		−	1.24089i		−	0.0535482i
$538$		−	55.1279i		−	2.37673i
$539$	34.3659			1.48024
$540$	−5.23538	−	10.8347i	−0.225295	−	0.466252i
$541$	−24.7679			−1.06486			−0.532428	−	0.846476i	$-0.678720\pi$
$541$	−24.7679			−1.06486			−0.532428	+	0.846476i	$0.678720\pi$
$542$			11.5682i			0.496897i
$543$			10.4169i			0.447033i
$544$	−20.9624			−0.898757
$545$	−14.7648	+	7.13439i	−0.632453	+	0.305604i
$546$	−0.543403			−0.0232555
$547$		−	34.4650i		−	1.47362i	−0.676102	−	0.736808i	$-0.736332\pi$
$547$		−	34.4650i		−	1.47362i	0.676102	−	0.736808i	$-0.263668\pi$
$548$			9.04015i			0.386176i
$549$	−30.7982			−1.31443
$550$	−42.8100	−	33.9551i	−1.82543	−	1.44785i
$551$	8.42831			0.359058
$552$			2.35919i			0.100414i
$553$		−	15.5453i		−	0.661052i
$554$	42.6359			1.81142
$555$	10.5530	−	5.09925i	0.447950	−	0.216451i
$556$	13.1429			0.557384
$557$			3.13055i			0.132646i	0.997798	+	0.0663228i	$0.0211267\pi$
$557$			3.13055i			0.132646i	−0.997798	+	0.0663228i	$0.978873\pi$
$558$			23.7503i			1.00543i
$559$	−2.94973			−0.124760
$560$	−4.28992	−	8.87806i	−0.181282	−	0.375167i
$561$	8.84204			0.373311
$562$			33.9444i			1.43186i
$563$			41.5012i			1.74907i	0.484966	+	0.874533i	$0.338832\pi$
$563$			41.5012i			1.74907i	−0.484966	+	0.874533i	$0.661168\pi$
$564$	−1.26587			−0.0533029
$565$	0.383411	+	0.793475i	0.0161302	+	0.0333817i
$566$	−7.17878			−0.301747
$567$		−	6.15187i		−	0.258354i
$568$			6.38527i			0.267920i
$569$	−9.52061			−0.399125			−0.199562	−	0.979885i	$-0.563952\pi$
$569$	−9.52061			−0.399125			−0.199562	+	0.979885i	$0.563952\pi$
$570$	6.08982	−	2.94263i	0.255075	−	0.123253i
$571$	−12.5830			−0.526583			−0.263292	−	0.964716i	$-0.584808\pi$
$571$	−12.5830			−0.526583			−0.263292	+	0.964716i	$0.584808\pi$
$572$		−	5.00477i		−	0.209260i
$573$			7.51149i			0.313797i
$574$	−3.75141			−0.156581
$575$	−28.4071	−	22.5313i	−1.18466	−	0.939621i
$576$	14.5639			0.606829
$577$			4.59818i			0.191425i	0.995409	+	0.0957123i	$0.0305129\pi$
$577$			4.59818i			0.191425i	−0.995409	+	0.0957123i	$0.969487\pi$
$578$		−	17.7189i		−	0.737010i
$579$	5.15008			0.214030
$580$	10.2029	−	4.93007i	0.423651	−	0.204710i
$581$	6.48327			0.268971
$582$		−	1.07754i		−	0.0446655i
$583$		−	13.6749i		−	0.566357i
$584$	−9.05130			−0.374545
$585$	−1.35779	−	2.80997i	−0.0561376	−	0.116178i
$586$	58.4366			2.41400
$587$			11.2149i			0.462887i	0.972848	+	0.231443i	$0.0743448\pi$
$587$			11.2149i			0.462887i	−0.972848	+	0.231443i	$0.925655\pi$
$588$			5.71912i			0.235852i
$589$	−12.9615			−0.534070
$590$	−10.5591	−	21.8522i	−0.434711	−	0.899643i
$591$	14.4201			0.593164
$592$			42.4430i			1.74439i
$593$			15.2963i			0.628144i	0.949399	+	0.314072i	$0.101693\pi$
$593$			15.2963i			0.628144i	−0.949399	+	0.314072i	$0.898307\pi$
$594$	−34.6650			−1.42232
$595$	−5.48625	+	2.65098i	−0.224914	+	0.108680i
$596$	−33.6052			−1.37652
$597$			2.37712i			0.0972892i
$598$		−	7.23603i		−	0.295903i
$599$	−26.5049			−1.08296			−0.541480	−	0.840713i	$-0.682136\pi$
$599$	−26.5049			−1.08296			−0.541480	+	0.840713i	$0.682136\pi$
$600$	−1.01085	+	1.27447i	−0.0412678	+	0.0520298i
$601$	−4.30453			−0.175586			−0.0877928	−	0.996139i	$-0.527981\pi$
$601$	−4.30453			−0.175586			−0.0877928	+	0.996139i	$0.527981\pi$
$602$		−	10.6724i		−	0.434973i
$603$			15.2233i			0.619941i
$604$	−33.3991			−1.35899
$605$	−42.8997	+	20.7293i	−1.74412	+	0.842767i
$606$	7.61378			0.309289
$607$			5.46958i			0.222004i	0.993820	+	0.111002i	$0.0354059\pi$
$607$			5.46958i			0.222004i	−0.993820	+	0.111002i	$0.964594\pi$
$608$			21.1998i			0.859767i
$609$	−1.62667			−0.0659160
$610$	−21.4220	−	44.3332i	−0.867351	−	1.79500i
$611$	−0.694559			−0.0280989
$612$		−	12.7283i		−	0.514510i
$613$			34.9065i			1.40986i	0.709277	+	0.704930i	$0.249021\pi$
$613$			34.9065i			1.40986i	−0.709277	+	0.704930i	$0.750979\pi$
$614$	11.3137			0.456584
$615$	1.08365	+	2.24264i	0.0436970	+	0.0904318i
$616$	−3.23924			−0.130513
$617$			24.0459i			0.968052i	0.875054	+	0.484026i	$0.160826\pi$
$617$			24.0459i			0.968052i	−0.875054	+	0.484026i	$0.839174\pi$
$618$			5.92427i			0.238309i
$619$	36.3148			1.45961			0.729807	−	0.683653i	$-0.239610\pi$
$619$	36.3148			1.45961			0.729807	+	0.683653i	$0.239610\pi$
$620$	−15.6905	+	7.58173i	−0.630147	+	0.304490i
$621$	−23.0024			−0.923055
$622$			16.4744i			0.660562i
$623$			12.9583i			0.519164i
$624$	−1.30652			−0.0523026
$625$	−5.69184	−	24.3434i	−0.227673	−	0.973738i
$626$	12.8483			0.513523
$627$		−	8.94218i		−	0.357116i
$628$			36.5522i			1.45859i
$629$	26.2279			1.04577
$630$	10.1667	−	4.91258i	0.405050	−	0.195722i
$631$	−19.2957			−0.768150			−0.384075	−	0.923302i	$-0.625480\pi$
$631$	−19.2957			−0.768150			−0.384075	+	0.923302i	$0.625480\pi$
$632$		−	9.28704i		−	0.369419i
$633$		−	3.36382i		−	0.133700i
$634$	36.0494			1.43171
$635$	9.17879	+	18.9957i	0.364249	+	0.753820i
$636$	2.27576			0.0902397
$637$			3.13796i			0.124330i
$638$		−	32.6435i		−	1.29237i
$639$	−29.4276			−1.16414
$640$	−4.48894	−	9.28995i	−0.177441	−	0.367217i
$641$	−29.0190			−1.14618			−0.573091	−	0.819492i	$-0.694256\pi$
$641$	−29.0190			−1.14618			−0.573091	+	0.819492i	$0.694256\pi$
$642$		−	7.51693i		−	0.296670i
$643$			29.2586i			1.15385i	0.816798	+	0.576924i	$0.195747\pi$
$643$			29.2586i			1.15385i	−0.816798	+	0.576924i	$0.804253\pi$
$644$	12.0156			0.473479
$645$	−6.38005	+	3.08287i	−0.251214	+	0.121388i
$646$	15.1353			0.595491
$647$		−	32.7993i		−	1.28947i	−0.764405	−	0.644736i	$-0.776967\pi$
$647$		−	32.7993i		−	1.28947i	0.764405	−	0.644736i	$-0.223033\pi$
$648$		−	3.67525i		−	0.144377i
$649$	−32.0874			−1.25954
$650$	3.10045	−	3.90900i	0.121610	−	0.153324i
$651$	2.50158			0.0980448
$652$			21.2340i			0.831588i
$653$			15.9479i			0.624092i	0.950067	+	0.312046i	$0.101014\pi$
$653$			15.9479i			0.624092i	−0.950067	+	0.312046i	$0.898986\pi$
$654$	−7.86144			−0.307407
$655$	−18.8575	+	9.11203i	−0.736824	+	0.356037i
$656$	−9.01963			−0.352157
$657$		−	41.7144i		−	1.62743i
$658$		−	2.51297i		−	0.0979658i
$659$	19.1492			0.745947			0.372973	−	0.927842i	$-0.378338\pi$
$659$	19.1492			0.745947			0.372973	+	0.927842i	$0.378338\pi$
$660$	−5.23066	−	10.8249i	−0.203603	−	0.421360i
$661$	−2.28059			−0.0887045			−0.0443523	−	0.999016i	$-0.514122\pi$
$661$	−2.28059			−0.0887045			−0.0443523	+	0.999016i	$0.514122\pi$
$662$			19.4945i			0.757676i
$663$			0.807370i			0.0313557i
$664$	3.87323			0.150310
$665$	2.68100	+	5.54838i	0.103965	+	0.215157i
$666$	−48.6034			−1.88334
$667$		−	21.6610i		−	0.838717i
$668$		−	12.5290i		−	0.484763i
$669$	11.8074			0.456500
$670$	−21.9136	+	10.5887i	−0.846595	+	0.409078i
$671$	−65.0981			−2.51308
$672$		−	4.09159i		−	0.157836i
$673$			24.0503i			0.927073i	0.886078	+	0.463536i	$0.153420\pi$
$673$			24.0503i			0.927073i	−0.886078	+	0.463536i	$0.846580\pi$
$674$	−43.8352			−1.68847
$675$	−12.4262	−	9.85593i	−0.478285	−	0.379355i
$676$	−21.5977			−0.830681
$677$		−	47.6572i		−	1.83161i	−0.401619	−	0.915807i	$-0.631552\pi$
$677$		−	47.6572i		−	1.83161i	0.401619	−	0.915807i	$-0.368448\pi$
$678$			0.422483i			0.0162254i
$679$	0.981737			0.0376756
$680$	−3.27759	+	1.58375i	−0.125690	+	0.0607339i
$681$	1.95326			0.0748491
$682$			50.2009i			1.92229i
$683$			30.1166i			1.15238i	0.817316	+	0.576190i	$0.195461\pi$
$683$			30.1166i			1.15238i	−0.817316	+	0.576190i	$0.804539\pi$
$684$	−12.8724			−0.492190
$685$	5.18402	+	10.7284i	0.198071	+	0.409912i
$686$	−24.4981			−0.935340
$687$		−	10.7795i		−	0.411262i
$688$		−	25.6599i		−	0.978273i
$689$	1.24866			0.0475702
$690$	−7.56264	−	15.6510i	−0.287905	−	0.595824i
$691$	6.81543			0.259271			0.129636	−	0.991562i	$-0.458619\pi$
$691$	6.81543			0.259271			0.129636	+	0.991562i	$0.458619\pi$
$692$			29.8951i			1.13644i
$693$		−	14.9286i		−	0.567090i
$694$	63.5297			2.41156
$695$	15.5974	−	7.53673i	0.591643	−	0.285885i
$696$	−0.971804			−0.0368361
$697$			5.57373i			0.211120i
$698$		−	20.6931i		−	0.783247i
$699$	12.8622			0.486493
$700$	6.49096	+	5.14835i	0.245335	+	0.194589i
$701$	38.7899			1.46507			0.732537	−	0.680727i	$-0.238336\pi$
$701$	38.7899			1.46507			0.732537	+	0.680727i	$0.238336\pi$
$702$		−	3.16528i		−	0.119466i
$703$		−	26.5249i		−	1.00041i
$704$	30.7837			1.16020
$705$	−1.50228	+	0.725909i	−0.0565792	+	0.0273393i
$706$	24.6315			0.927019
$707$			6.93685i			0.260887i
$708$		−	5.33995i		−	0.200687i
$709$	8.72623			0.327720			0.163860	−	0.986484i	$-0.447605\pi$
$709$	8.72623			0.327720			0.163860	+	0.986484i	$0.447605\pi$
$710$	−20.4687	−	42.3603i	−0.768176	−	1.58975i
$711$	42.8009			1.60516
$712$			7.74154i			0.290127i
$713$			33.3114i			1.24752i
$714$	−2.92113			−0.109321
$715$	−2.86995	−	5.93942i	−0.107330	−	0.222122i
$716$	−3.77566			−0.141103
$717$		−	1.74732i		−	0.0652547i
$718$			24.5008i			0.914362i
$719$	22.6803			0.845832			0.422916	−	0.906169i	$-0.361006\pi$
$719$	22.6803			0.845832			0.422916	+	0.906169i	$0.361006\pi$
$720$	24.4440	−	11.8115i	0.910975	−	0.440187i
$721$	−5.39755			−0.201015
$722$			21.2233i			0.789848i
$723$		−	0.557567i		−	0.0207361i
$724$	31.6956			1.17796
$725$	9.28117	−	11.7016i	0.344694	−	0.434585i
$726$	−22.8418			−0.847738
$727$		−	7.41044i		−	0.274838i	−0.990513	−	0.137419i	$-0.956119\pi$
$727$		−	7.41044i		−	0.274838i	0.990513	−	0.137419i	$-0.0438807\pi$
$728$		−	0.295776i		−	0.0109622i
$729$	11.6321			0.430818
$730$	60.0469	−	29.0149i	2.22243	−	1.07389i
$731$	−15.8567			−0.586479
$732$		−	10.8335i		−	0.400419i
$733$			9.84342i			0.363575i	0.983338	+	0.181787i	$0.0581883\pi$
$733$			9.84342i			0.363575i	−0.983338	+	0.181787i	$0.941812\pi$
$734$	−1.99259			−0.0735478
$735$	3.27959	+	6.78718i	0.120970	+	0.250349i
$736$	54.4842			2.00831
$737$			32.1775i			1.18527i
$738$		−	10.3288i		−	0.380208i
$739$	25.0992			0.923289			0.461645	−	0.887065i	$-0.347260\pi$
$739$	25.0992			0.923289			0.461645	+	0.887065i	$0.347260\pi$
$740$	−15.5155	−	32.1097i	−0.570362	−	1.18038i
$741$	0.816514			0.0299954
$742$			4.51776i			0.165852i
$743$		−	45.4541i		−	1.66755i	−0.552106	−	0.833774i	$-0.686176\pi$
$743$		−	45.4541i		−	1.66755i	0.552106	−	0.833774i	$-0.313824\pi$
$744$	1.49449			0.0547908
$745$	−39.8811	+	19.2707i	−1.46113	+	0.706024i
$746$	−28.3690			−1.03866
$747$			17.8504i			0.653113i
$748$		−	26.9038i		−	0.983699i
$749$	6.84861			0.250243
$750$	2.62061	−	11.6953i	0.0956912	−	0.427051i
$751$	0.291173			0.0106251			0.00531253	−	0.999986i	$-0.498309\pi$
$751$	0.291173			0.0106251			0.00531253	+	0.999986i	$0.498309\pi$
$752$		−	6.04200i		−	0.220329i
$753$		−	4.74701i		−	0.172991i
$754$	2.98069			0.108550
$755$	−39.6364	+	19.1525i	−1.44252	+	0.697031i
$756$	5.25600			0.191159
$757$			8.45373i			0.307256i	0.988129	+	0.153628i	$0.0490957\pi$
$757$			8.45373i			0.307256i	−0.988129	+	0.153628i	$0.950904\pi$
$758$			44.5902i			1.61959i
$759$	−22.9817			−0.834181
$760$	1.60168	+	3.31471i	0.0580991	+	0.120237i
$761$	−18.3586			−0.665498			−0.332749	−	0.943015i	$-0.607976\pi$
$761$	−18.3586			−0.665498			−0.332749	+	0.943015i	$0.607976\pi$
$762$			10.1142i			0.366398i
$763$		−	7.16249i		−	0.259299i
$764$	22.8553			0.826875
$765$	−7.29896	−	15.1053i	−0.263894	−	0.546134i
$766$	−24.5106			−0.885602
$767$		−	2.92992i		−	0.105793i
$768$		−	10.9858i		−	0.396416i
$769$	45.6484			1.64612			0.823061	−	0.567953i	$-0.192264\pi$
$769$	45.6484			1.64612			0.823061	+	0.567953i	$0.192264\pi$
$770$	21.4893	−	10.3837i	0.774421	−	0.374203i
$771$	0.167398			0.00602869
$772$		−	15.6702i		−	0.563983i
$773$		−	47.5774i		−	1.71124i	−0.517604	−	0.855620i	$-0.673176\pi$
$773$		−	47.5774i		−	1.71124i	0.517604	−	0.855620i	$-0.326824\pi$
$774$	29.3843			1.05620
$775$	−14.2731	+	17.9953i	−0.512704	+	0.646410i
$776$	0.586509			0.0210544
$777$			5.11933i			0.183655i
$778$			60.9395i			2.18479i
$779$	5.63685			0.201961
$780$	0.988430	−	0.477614i	0.0353915	−	0.0171013i
$781$	−62.2011			−2.22573
$782$		−	38.8982i		−	1.39100i
$783$		−	9.47522i		−	0.338617i
$784$	−27.2973			−0.974902
$785$	20.9606	+	43.3784i	0.748118	+	1.54824i
$786$	−10.0406			−0.358137
$787$		−	48.3487i		−	1.72345i	−0.507378	−	0.861723i	$-0.669385\pi$
$787$		−	48.3487i		−	1.72345i	0.507378	−	0.861723i	$-0.330615\pi$
$788$		−	43.8762i		−	1.56302i
$789$	8.65106			0.307986
$790$	29.7706	+	61.6108i	1.05919	+	2.19201i
$791$	−0.384920			−0.0136862
$792$		−	8.91862i		−	0.316909i
$793$		−	5.94413i		−	0.211082i
$794$	−34.7604			−1.23360
$795$	2.70076	−	1.30502i	0.0957862	−	0.0462843i
$796$	7.23289			0.256363
$797$			26.2387i			0.929422i	0.885463	+	0.464711i	$0.153842\pi$
$797$			26.2387i			0.929422i	−0.885463	+	0.464711i	$0.846158\pi$
$798$			2.95421i			0.104578i
$799$	−3.73369			−0.132088
$800$	29.4331	+	23.3450i	1.04062	+	0.825372i
$801$	−35.6782			−1.26063
$802$		−	47.7933i		−	1.68764i
$803$		−	88.1717i		−	3.11151i
$804$	−5.35493			−0.188854
$805$	14.2595	−	6.89025i	0.502581	−	0.242849i
$806$	−4.58386			−0.161460
$807$		−	15.9872i		−	0.562776i
$808$			4.14421i			0.145793i
$809$	−8.43180			−0.296446			−0.148223	−	0.988954i	$-0.547355\pi$
$809$	−8.43180			−0.296446			−0.148223	+	0.988954i	$0.547355\pi$
$810$	11.7814	+	24.3818i	0.413956	+	0.856690i
$811$	30.9938			1.08834			0.544170	−	0.838975i	$-0.316845\pi$
$811$	30.9938			1.08834			0.544170	+	0.838975i	$0.316845\pi$
$812$			4.94948i			0.173693i
$813$			3.35480i			0.117658i
$814$	−102.733			−3.60079
$815$	12.1765	+	25.1995i	0.426525	+	0.882701i
$816$	−7.02335			−0.245867
$817$			16.0362i			0.561037i
$818$			8.18092i			0.286039i
$819$	1.36313			0.0476317
$820$	6.82368	−	3.29723i	0.238293	−	0.115144i
$821$	30.6989			1.07140			0.535699	−	0.844409i	$-0.320048\pi$
$821$	30.6989			1.07140			0.535699	+	0.844409i	$0.320048\pi$
$822$			5.71231i			0.199240i
$823$		−	20.4776i		−	0.713804i	−0.934142	−	0.356902i	$-0.883833\pi$
$823$		−	20.4776i		−	0.713804i	0.934142	−	0.356902i	$-0.116167\pi$
$824$	−3.22460			−0.112334
$825$	−12.4150	−	9.84704i	−0.432235	−	0.342830i
$826$	10.6007			0.368845
$827$		−	27.5776i		−	0.958967i	−0.877551	−	0.479484i	$-0.840824\pi$
$827$		−	27.5776i		−	0.958967i	0.877551	−	0.479484i	$-0.159176\pi$
$828$			33.0825i			1.14970i
$829$	13.2760			0.461094			0.230547	−	0.973061i	$-0.425948\pi$
$829$	13.2760			0.461094			0.230547	+	0.973061i	$0.425948\pi$
$830$	−25.6952	+	12.4161i	−0.891895	+	0.430968i
$831$	12.3645			0.428919
$832$			2.81087i			0.0974493i
$833$			16.8685i			0.584459i
$834$	8.30478			0.287571
$835$	−7.18470	−	14.8689i	−0.248637	−	0.514558i
$836$	−27.2084			−0.941024
$837$			14.5715i			0.503665i
$838$			32.2082i			1.11261i
$839$	−10.9056			−0.376504			−0.188252	−	0.982121i	$-0.560282\pi$
$839$	−10.9056			−0.376504			−0.188252	+	0.982121i	$0.560282\pi$
$840$	−0.309126	−	0.639742i	−0.0106659	−	0.0220732i
$841$	−20.0773			−0.692322
$842$		−	40.2312i		−	1.38646i
$843$			9.84395i			0.339043i
$844$	−10.2351			−0.352307
$845$	−25.6311	+	12.3851i	−0.881738	+	0.426059i
$846$	6.91898			0.237879
$847$		−	20.8109i		−	0.715073i
$848$			10.8622i			0.373008i
$849$	−2.08186			−0.0714493
$850$	16.6669	−	21.0133i	0.571669	−	0.720751i
$851$	−68.1697			−2.33683
$852$		−	10.3514i		−	0.354634i
$853$			8.12490i			0.278191i	0.990279	+	0.139096i	$0.0444195\pi$
$853$			8.12490i			0.278191i	−0.990279	+	0.139096i	$0.955580\pi$
$854$	21.5063			0.735932
$855$	−15.2764	+	7.38162i	−0.522442	+	0.252446i
$856$	4.09149			0.139844
$857$		−	34.5296i		−	1.17951i	−0.807582	−	0.589755i	$-0.799224\pi$
$857$		−	34.5296i		−	1.17951i	0.807582	−	0.589755i	$-0.200776\pi$
$858$		−	3.16242i		−	0.107963i
$859$	29.8705			1.01917			0.509584	−	0.860421i	$-0.329799\pi$
$859$	29.8705			1.01917			0.509584	+	0.860421i	$0.329799\pi$
$860$	9.38027	+	19.4126i	0.319865	+	0.661965i
$861$	−1.08792			−0.0370761
$862$			53.3152i			1.81592i
$863$		−	13.2136i		−	0.449797i	−0.974382	−	0.224899i	$-0.927795\pi$
$863$		−	13.2136i		−	0.449797i	0.974382	−	0.224899i	$-0.0722051\pi$
$864$	23.8332			0.810820
$865$	17.1432	+	35.4781i	0.582885	+	1.20629i
$866$	53.9977			1.83492
$867$		−	5.13852i		−	0.174513i
$868$		−	7.61159i		−	0.258354i
$869$	90.4682			3.06892
$870$	6.44701	−	3.11522i	0.218574	−	0.105616i
$871$	−2.93814			−0.0995550
$872$		−	4.27901i		−	0.144905i
$873$			2.70302i			0.0914835i
$874$	−39.3387			−1.33065
$875$	10.6555	+	2.38762i	0.360220	+	0.0807162i
$876$	14.6734			0.495769
$877$			30.5723i			1.03235i	0.856482	+	0.516176i	$0.172645\pi$
$877$			30.5723i			1.03235i	−0.856482	+	0.516176i	$0.827355\pi$
$878$		−	19.3306i		−	0.652377i
$879$	16.9467			0.571600
$880$	51.6673	−	24.9659i	1.74170	−	0.841599i
$881$	23.4110			0.788736			0.394368	−	0.918953i	$-0.370964\pi$
$881$	23.4110			0.788736			0.394368	+	0.918953i	$0.370964\pi$
$882$		−	31.2594i		−	1.05256i
$883$			25.5119i			0.858545i	0.903175	+	0.429273i	$0.141230\pi$
$883$			25.5119i			0.858545i	−0.903175	+	0.429273i	$0.858770\pi$
$884$	2.45659			0.0826241
$885$	−3.06216	−	6.33720i	−0.102933	−	0.213023i
$886$	8.42555			0.283062
$887$			6.77343i			0.227430i	0.993513	+	0.113715i	$0.0362750\pi$
$887$			6.77343i			0.227430i	−0.993513	+	0.113715i	$0.963725\pi$
$888$			3.05839i			0.102633i
$889$	−9.21493			−0.309059
$890$	−24.8163	−	51.3579i	−0.831846	−	1.72152i
$891$	35.8018			1.19941
$892$		−	35.9265i		−	1.20291i
$893$			3.77598i			0.126358i
$894$	−21.2345			−0.710188
$895$	−4.48077	+	2.16513i	−0.149776	+	0.0723723i
$896$	4.50662			0.150556
$897$		−	2.09846i		−	0.0700657i
$898$			14.4485i			0.482152i
$899$	−13.7217			−0.457646
$900$	−14.1750	+	17.8716i	−0.472500	+	0.595721i
$901$	6.71234			0.223620
$902$		−	21.8320i		−	0.726925i
$903$		−	3.09501i		−	0.102995i
$904$	−0.229959			−0.00764831
$905$	37.6149	−	18.1757i	1.25036	−	0.604180i
$906$	−21.1043			−0.701142
$907$			55.9625i			1.85821i	0.369822	+	0.929103i	$0.379419\pi$
$907$			55.9625i			1.85821i	−0.369822	+	0.929103i	$0.620581\pi$
$908$		−	5.94320i		−	0.197232i
$909$	−19.0993			−0.633483
$910$	0.948142	+	1.96220i	0.0314306	+	0.0650462i
$911$	−13.0286			−0.431656			−0.215828	−	0.976431i	$-0.569245\pi$
$911$	−13.0286			−0.431656			−0.215828	+	0.976431i	$0.569245\pi$
$912$			7.10290i			0.235200i
$913$			37.7304i			1.24870i
$914$	−52.0901			−1.72299
$915$	−6.21242	−	12.8567i	−0.205376	−	0.425030i
$916$	−32.7987			−1.08370
$917$		−	9.14791i		−	0.302091i
$918$		−	17.0153i		−	0.561590i
$919$	−28.4860			−0.939668			−0.469834	−	0.882755i	$-0.655686\pi$
$919$	−28.4860			−0.939668			−0.469834	+	0.882755i	$0.655686\pi$
$920$	8.51890	−	4.11637i	0.280860	−	0.135713i
$921$	3.28100			0.108112
$922$		−	15.9350i		−	0.524791i
$923$		−	5.67961i		−	0.186947i
$924$	5.25125			0.172754
$925$	−36.8262	−	29.2090i	−1.21084	−	0.960385i
$926$	75.6209			2.48506
$927$		−	14.8611i		−	0.488103i
$928$			22.4433i			0.736737i
$929$	29.8029			0.977801			0.488900	−	0.872340i	$-0.337398\pi$
$929$	29.8029			0.977801			0.488900	+	0.872340i	$0.337398\pi$
$930$	−9.91456	+	4.79076i	−0.325111	+	0.157095i
$931$	17.0595			0.559104
$932$		−	39.1359i		−	1.28194i
$933$			4.77760i			0.156412i
$934$	−3.12511			−0.102257
$935$	−15.4278	−	31.9281i	−0.504543	−	1.04416i
$936$	0.814362			0.0266183
$937$		−	8.54890i		−	0.279281i	−0.990202	−	0.139640i	$-0.955405\pi$
$937$		−	8.54890i		−	0.279281i	0.990202	−	0.139640i	$-0.0445946\pi$
$938$		−	10.6304i		−	0.347096i
$939$	3.72605			0.121595
$940$	2.20873	+	4.57100i	0.0720407	+	0.149090i
$941$	−5.33942			−0.174060			−0.0870300	−	0.996206i	$-0.527738\pi$
$941$	−5.33942			−0.174060			−0.0870300	+	0.996206i	$0.527738\pi$
$942$			23.0967i			0.752531i
$943$		−	14.4869i		−	0.471757i
$944$	25.4875			0.829547
$945$	6.23757	−	3.01402i	0.202908	−	0.0980461i
$946$	62.1096			2.01936
$947$		−	24.4488i		−	0.794481i	−0.917715	−	0.397240i	$-0.869968\pi$
$947$		−	24.4488i		−	0.794481i	0.917715	−	0.397240i	$-0.130032\pi$
$948$			15.0556i			0.488983i
$949$	8.05100			0.261346
$950$	−21.2513	−	16.8556i	−0.689484	−	0.546869i
$951$	10.4544			0.339007
$952$		−	1.58998i		−	0.0515316i
$953$		−	42.1998i		−	1.36699i	−0.729957	−	0.683493i	$-0.760460\pi$
$953$		−	42.1998i		−	1.36699i	0.729957	−	0.683493i	$-0.239540\pi$
$954$	−12.4388			−0.402720
$955$	27.1236	−	13.1062i	0.877698	−	0.424107i
$956$	−5.31657			−0.171950
$957$		−	9.46667i		−	0.306014i
$958$			52.4462i			1.69446i
$959$	−5.20443			−0.168060
$960$	2.93774	+	6.07970i	0.0948151	+	0.196222i
$961$	−9.89795			−0.319289
$962$		−	9.38059i		−	0.302442i
$963$			18.8563i			0.607636i
$964$	−1.69651			−0.0546410
$965$	−8.98598	−	18.5967i	−0.289269	−	0.598647i
$966$	7.59241			0.244282
$967$		−	12.1031i		−	0.389211i	−0.980882	−	0.194605i	$-0.937657\pi$
$967$		−	12.1031i		−	0.389211i	0.980882	−	0.194605i	$-0.0623427\pi$
$968$		−	12.4329i		−	0.399607i
$969$	4.38928			0.141004
$970$	−3.89094	+	1.88012i	−0.124930	+	0.0603669i
$971$	5.26565			0.168983			0.0844913	−	0.996424i	$-0.473073\pi$
$971$	5.26565			0.168983			0.0844913	+	0.996424i	$0.473073\pi$
$972$			22.1025i			0.708937i
$973$			7.56641i			0.242568i
$974$	31.0422			0.994657
$975$	0.899137	−	1.13362i	0.0287954	−	0.0363048i
$976$	51.7083			1.65514
$977$			9.31335i			0.297961i	0.988840	+	0.148980i	$0.0475991\pi$
$977$			9.31335i			0.297961i	−0.988840	+	0.148980i	$0.952401\pi$
$978$			13.4174i			0.429041i
$979$	−75.4130			−2.41021
$980$	20.6514	−	9.97884i	0.659685	−	0.318762i
$981$	19.7205			0.629628
$982$			26.8734i			0.857564i
$983$			27.0262i			0.862003i	0.902351	+	0.431002i	$0.141840\pi$
$983$			27.0262i			0.862003i	−0.902351	+	0.431002i	$0.858160\pi$
$984$	−0.649943			−0.0207194
$985$	−25.1605	−	52.0702i	−0.801682	−	1.65909i
$986$	16.0231			0.510278
$987$		−	0.728767i		−	0.0231969i
$988$		−	2.48441i		−	0.0790397i
$989$	41.2136			1.31052
$990$	28.5896	+	59.1667i	0.908637	+	1.88044i
$991$	−22.7776			−0.723554			−0.361777	−	0.932265i	$-0.617830\pi$
$991$	−22.7776			−0.723554			−0.361777	+	0.932265i	$0.617830\pi$
$992$		−	34.5145i		−	1.09584i
$993$			5.65345i			0.179407i
$994$	20.5493			0.651783
$995$	8.58365	−	4.14766i	0.272120	−	0.131490i
$996$	−6.27904			−0.198959
$997$			24.9695i			0.790791i	0.918511	+	0.395395i	$0.129392\pi$
$997$			24.9695i			0.790791i	−0.918511	+	0.395395i	$0.870608\pi$
$998$			26.0670i			0.825135i
$999$	−29.8197			−0.943453

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.b.c.724.7	✓	46
5.2	odd	4		6025.2.a.p.1.40		46
5.3	odd	4		6025.2.a.p.1.7		46
5.4	even	2	inner	1205.2.b.c.724.40	yes	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.b.c.724.7	✓	46	1.1	even	1	trivial
1205.2.b.c.724.40	yes	46	5.4	even	2	inner
6025.2.a.p.1.7		46	5.3	odd	4
6025.2.a.p.1.40		46	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1205 = 5 \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1205.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.92263i q^{2} -0.557567i q^{3} -1.69651 q^{4} +(-2.01334 + 0.972856i) q^{5} -1.07200 q^{6} -0.976687i q^{7} -0.583491i q^{8} +2.68912 q^{9} +O(q^{10})\)	\(q-1.92263i q^{2} -0.557567i q^{3} -1.69651 q^{4} +(-2.01334 + 0.972856i) q^{5} -1.07200 q^{6} -0.976687i q^{7} -0.583491i q^{8} +2.68912 q^{9} +(1.87044 + 3.87092i) q^{10} +5.68399 q^{11} +0.945921i q^{12} +0.519007i q^{13} -1.87781 q^{14} +(0.542433 + 1.12257i) q^{15} -4.51487 q^{16} +2.78999i q^{17} -5.17019i q^{18} +2.82159 q^{19} +(3.41567 - 1.65046i) q^{20} -0.544569 q^{21} -10.9282i q^{22} -7.25155i q^{23} -0.325336 q^{24} +(3.10710 - 3.91739i) q^{25} +0.997860 q^{26} -3.17207i q^{27} +1.65696i q^{28} +2.98708 q^{29} +(2.15830 - 1.04290i) q^{30} -4.59370 q^{31} +7.51345i q^{32} -3.16920i q^{33} +5.36412 q^{34} +(0.950176 + 1.96641i) q^{35} -4.56213 q^{36} -9.40071i q^{37} -5.42487i q^{38} +0.289381 q^{39} +(0.567653 + 1.17477i) q^{40} +1.99776 q^{41} +1.04700i q^{42} +5.68341i q^{43} -9.64296 q^{44} +(-5.41412 + 2.61613i) q^{45} -13.9421 q^{46} +1.33825i q^{47} +2.51734i q^{48} +6.04608 q^{49} +(-7.53169 - 5.97381i) q^{50} +1.55561 q^{51} -0.880503i q^{52} -2.40587i q^{53} -6.09872 q^{54} +(-11.4438 + 5.52970i) q^{55} -0.569888 q^{56} -1.57322i q^{57} -5.74306i q^{58} -5.64524 q^{59} +(-0.920245 - 1.90446i) q^{60} -11.4529 q^{61} +8.83199i q^{62} -2.62643i q^{63} +5.41586 q^{64} +(-0.504919 - 1.04494i) q^{65} -6.09321 q^{66} +5.66108i q^{67} -4.73325i q^{68} -4.04323 q^{69} +(3.78067 - 1.82684i) q^{70} -10.9432 q^{71} -1.56908i q^{72} -15.5123i q^{73} -18.0741 q^{74} +(-2.18421 - 1.73242i) q^{75} -4.78686 q^{76} -5.55147i q^{77} -0.556374i q^{78} +15.9163 q^{79} +(9.08998 - 4.39232i) q^{80} +6.29872 q^{81} -3.84096i q^{82} +6.63802i q^{83} +0.923868 q^{84} +(-2.71426 - 5.61720i) q^{85} +10.9271 q^{86} -1.66550i q^{87} -3.31656i q^{88} -13.2676 q^{89} +(5.02985 + 10.4094i) q^{90} +0.506907 q^{91} +12.3024i q^{92} +2.56129i q^{93} +2.57295 q^{94} +(-5.68082 + 2.74500i) q^{95} +4.18925 q^{96} +1.00517i q^{97} -11.6244i q^{98} +15.2849 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9}+O(q^{10}) \) 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9	\( 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9} - 7 q^{10} - 64 q^{11} + 66 q^{14} + 5 q^{15} + 22 q^{16} - 2 q^{20} - 14 q^{21} + 50 q^{24} + 30 q^{25} - 60 q^{26} + 36 q^{29} + 7 q^{30} - 36 q^{31} - 12 q^{34} + 3 q^{35} - 34 q^{36} + 88 q^{39} - 30 q^{40} - 76 q^{41} + 100 q^{44} - 17 q^{45} - 12 q^{46} - 22 q^{49} - 14 q^{50} - 112 q^{51} + 26 q^{54} - 5 q^{55} - 120 q^{56} + 84 q^{59} - 33 q^{60} - 78 q^{61} - 28 q^{64} + 9 q^{65} - 2 q^{66} + 24 q^{69} + 88 q^{70} - 172 q^{71} + 16 q^{74} + 59 q^{75} - 18 q^{76} + 54 q^{79} + 63 q^{80} - 42 q^{81} - 44 q^{84} + 30 q^{85} - 80 q^{86} + 86 q^{89} + 17 q^{90} - 88 q^{91} - 4 q^{94} + q^{95} - 122 q^{96} + 148 q^{99}+O(q^{100}) \) 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9 - 7 * q^10 - 64 * q^11 + 66 * q^14 + 5 * q^15 + 22 * q^16 - 2 * q^20 - 14 * q^21 + 50 * q^24 + 30 * q^25 - 60 * q^26 + 36 * q^29 + 7 * q^30 - 36 * q^31 - 12 * q^34 + 3 * q^35 - 34 * q^36 + 88 * q^39 - 30 * q^40 - 76 * q^41 + 100 * q^44 - 17 * q^45 - 12 * q^46 - 22 * q^49 - 14 * q^50 - 112 * q^51 + 26 * q^54 - 5 * q^55 - 120 * q^56 + 84 * q^59 - 33 * q^60 - 78 * q^61 - 28 * q^64 + 9 * q^65 - 2 * q^66 + 24 * q^69 + 88 * q^70 - 172 * q^71 + 16 * q^74 + 59 * q^75 - 18 * q^76 + 54 * q^79 + 63 * q^80 - 42 * q^81 - 44 * q^84 + 30 * q^85 - 80 * q^86 + 86 * q^89 + 17 * q^90 - 88 * q^91 - 4 * q^94 + q^95 - 122 * q^96 + 148 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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