LMFDB - Embedded newform 185.2.c.b.36.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [185,2,Mod(36,185)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(185, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("185.36"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 185 = 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	185.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 21x^{10} + 162x^{8} + 574x^{6} + 985x^{4} + 765x^{2} + 196 $ x^12 + 21x^10 + 162x^8 + 574x^6 + 985x^4 + 765*x^2 + 196
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			36.6
Root			$-0.694469i$ of defining polynomial
Character	$\chi$	$=$	185.36
Dual form			185.2.c.b.36.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.694469i q^{2} -2.37730 q^{3} +1.51771 q^{4} +1.00000i q^{5} +1.65096i q^{6} +2.16868 q^{7} -2.44294i q^{8} +2.65157 q^{9} +0.694469 q^{10} +4.35199 q^{11} -3.60806 q^{12} -5.72273i q^{13} -1.50608i q^{14} -2.37730i q^{15} +1.33888 q^{16} +6.00355i q^{17} -1.84143i q^{18} -4.14041i q^{19} +1.51771i q^{20} -5.15560 q^{21} -3.02232i q^{22} +0.165727i q^{23} +5.80761i q^{24} -1.00000 q^{25} -3.97426 q^{26} +0.828325 q^{27} +3.29143 q^{28} +8.05774i q^{29} -1.65096 q^{30} +0.0682170i q^{31} -5.81569i q^{32} -10.3460 q^{33} +4.16928 q^{34} +2.16868i q^{35} +4.02432 q^{36} +(-3.86375 + 4.69802i) q^{37} -2.87539 q^{38} +13.6047i q^{39} +2.44294 q^{40} -8.59751 q^{41} +3.58040i q^{42} +0.445335i q^{43} +6.60506 q^{44} +2.65157i q^{45} +0.115093 q^{46} -6.94655 q^{47} -3.18292 q^{48} -2.29684 q^{49} +0.694469i q^{50} -14.2723i q^{51} -8.68547i q^{52} +4.63281 q^{53} -0.575246i q^{54} +4.35199i q^{55} -5.29795i q^{56} +9.84301i q^{57} +5.59585 q^{58} -9.44099i q^{59} -3.60806i q^{60} +2.38799i q^{61} +0.0473746 q^{62} +5.75039 q^{63} -1.36106 q^{64} +5.72273 q^{65} +7.18497i q^{66} +11.4214 q^{67} +9.11167i q^{68} -0.393984i q^{69} +1.50608 q^{70} -2.32872 q^{71} -6.47763i q^{72} -10.6095 q^{73} +(3.26263 + 2.68326i) q^{74} +2.37730 q^{75} -6.28395i q^{76} +9.43805 q^{77} +9.44802 q^{78} -8.06222i q^{79} +1.33888i q^{80} -9.92389 q^{81} +5.97071i q^{82} -6.59438 q^{83} -7.82472 q^{84} -6.00355 q^{85} +0.309271 q^{86} -19.1557i q^{87} -10.6316i q^{88} +2.34335i q^{89} +1.84143 q^{90} -12.4108i q^{91} +0.251527i q^{92} -0.162173i q^{93} +4.82416i q^{94} +4.14041 q^{95} +13.8257i q^{96} +8.58288i q^{97} +1.59509i q^{98} +11.5396 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{3} - 18 q^{4} - 18 q^{7} + 22 q^{9} - 2 q^{10} + 2 q^{11} - 36 q^{12} + 30 q^{16} - 6 q^{21} - 12 q^{25} - 12 q^{26} + 26 q^{27} + 24 q^{28} - 12 q^{30} - 18 q^{33} + 4 q^{34} - 22 q^{36} + 10 q^{37}+ \cdots - 84 q^{99}+O(q^{100}) $ 12 * q + 2 * q^3 - 18 * q^4 - 18 * q^7 + 22 * q^9 - 2 * q^10 + 2 * q^11 - 36 * q^12 + 30 * q^16 - 6 * q^21 - 12 * q^25 - 12 * q^26 + 26 * q^27 + 24 * q^28 - 12 * q^30 - 18 * q^33 + 4 * q^34 - 22 * q^36 + 10 * q^37 + 12 * q^38 + 6 * q^40 - 10 * q^41 + 44 * q^44 - 24 * q^46 + 2 * q^47 + 60 * q^48 + 30 * q^49 - 6 * q^53 - 24 * q^58 + 44 * q^62 - 16 * q^63 - 126 * q^64 + 20 * q^65 + 16 * q^67 - 28 * q^70 + 42 * q^71 - 46 * q^73 + 50 * q^74 - 2 * q^75 + 30 * q^77 + 132 * q^78 - 12 * q^81 - 62 * q^83 - 84 * q^84 - 12 * q^85 - 64 * q^86 - 26 * q^90 + 44 * q^95 - 84 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$.

$n$	$76$	$112$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	0.694469i		−	0.491064i	−0.969389	−	0.245532i	$-0.921037\pi$
$2$		−	0.694469i		−	0.491064i	0.969389	−	0.245532i	$-0.0789626\pi$
$3$	−2.37730			−1.37254			−0.686268	−	0.727349i	$-0.740752\pi$
$3$	−2.37730			−1.37254			−0.686268	+	0.727349i	$0.740752\pi$
$4$	1.51771			0.758856
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$			1.65096i			0.674003i
$7$	2.16868			0.819682			0.409841	−	0.912157i	$-0.365584\pi$
$7$	2.16868			0.819682			0.409841	+	0.912157i	$0.365584\pi$
$8$		−	2.44294i		−	0.863711i
$9$	2.65157			0.883856
$10$	0.694469			0.219610
$11$	4.35199			1.31217			0.656087	−	0.754686i	$-0.272211\pi$
$11$	4.35199			1.31217			0.656087	+	0.754686i	$0.272211\pi$
$12$	−3.60806			−1.04156
$13$		−	5.72273i		−	1.58720i	−0.608439	−	0.793601i	$-0.708204\pi$
$13$		−	5.72273i		−	1.58720i	0.608439	−	0.793601i	$-0.291796\pi$
$14$		−	1.50608i		−	0.402516i
$15$		−	2.37730i		−	0.613817i
$16$	1.33888			0.334720
$17$			6.00355i			1.45608i	0.685537	+	0.728038i	$0.259568\pi$
$17$			6.00355i			1.45608i	−0.685537	+	0.728038i	$0.740432\pi$
$18$		−	1.84143i		−	0.434030i
$19$		−	4.14041i		−	0.949875i	−0.880019	−	0.474938i	$-0.842471\pi$
$19$		−	4.14041i		−	0.949875i	0.880019	−	0.474938i	$-0.157529\pi$
$20$			1.51771i			0.339371i
$21$	−5.15560			−1.12504
$22$		−	3.02232i		−	0.644361i
$23$			0.165727i			0.0345566i	0.999851	+	0.0172783i	$0.00550012\pi$
$23$			0.165727i			0.0345566i	−0.999851	+	0.0172783i	$0.994500\pi$
$24$			5.80761i			1.18547i
$25$	−1.00000			−0.200000
$26$	−3.97426			−0.779417
$27$	0.828325			0.159411
$28$	3.29143			0.622021
$29$			8.05774i			1.49629i	0.663538	+	0.748143i	$0.269054\pi$
$29$			8.05774i			1.49629i	−0.663538	+	0.748143i	$0.730946\pi$
$30$	−1.65096			−0.301423
$31$			0.0682170i			0.0122521i	0.999981	+	0.00612607i	$0.00195000\pi$
$31$			0.0682170i			0.0122521i	−0.999981	+	0.00612607i	$0.998050\pi$
$32$		−	5.81569i		−	1.02808i
$33$	−10.3460			−1.80101
$34$	4.16928			0.715026
$35$			2.16868i			0.366573i
$36$	4.02432			0.670720
$37$	−3.86375	+	4.69802i	−0.635197	+	0.772350i
$37$	−3.86375	+	4.69802i	−0.635197	+	0.772350i
$38$	−2.87539			−0.466449
$39$			13.6047i			2.17849i
$40$	2.44294			0.386263
$41$	−8.59751			−1.34271			−0.671353	−	0.741138i	$-0.734287\pi$
$41$	−8.59751			−1.34271			−0.671353	+	0.741138i	$0.734287\pi$
$42$			3.58040i			0.552468i
$43$			0.445335i			0.0679129i	0.999423	+	0.0339565i	$0.0108108\pi$
$43$			0.445335i			0.0679129i	−0.999423	+	0.0339565i	$0.989189\pi$
$44$	6.60506			0.995751
$45$			2.65157i			0.395273i
$46$	0.115093			0.0169695
$47$	−6.94655			−1.01326			−0.506629	−	0.862164i	$-0.669109\pi$
$47$	−6.94655			−1.01326			−0.506629	+	0.862164i	$0.669109\pi$
$48$	−3.18292			−0.459415
$49$	−2.29684			−0.328121
$50$			0.694469i			0.0982127i
$51$		−	14.2723i		−	1.99852i
$52$		−	8.68547i		−	1.20446i
$53$	4.63281			0.636365			0.318182	−	0.948030i	$-0.396928\pi$
$53$	4.63281			0.636365			0.318182	+	0.948030i	$0.396928\pi$
$54$		−	0.575246i		−	0.0782811i
$55$			4.35199i			0.586822i
$56$		−	5.29795i		−	0.707968i
$57$			9.84301i			1.30374i
$58$	5.59585			0.734772
$59$		−	9.44099i		−	1.22911i	−0.788873	−	0.614556i	$-0.789335\pi$
$59$		−	9.44099i		−	1.22911i	0.788873	−	0.614556i	$-0.210665\pi$
$60$		−	3.60806i		−	0.465799i
$61$			2.38799i			0.305750i	0.988246	+	0.152875i	$0.0488532\pi$
$61$			2.38799i			0.305750i	−0.988246	+	0.152875i	$0.951147\pi$
$62$	0.0473746			0.00601658
$63$	5.75039			0.724482
$64$	−1.36106			−0.170133
$65$	5.72273			0.709818
$66$			7.18497i			0.884408i
$67$	11.4214			1.39534			0.697671	−	0.716418i	$-0.254220\pi$
$67$	11.4214			1.39534			0.697671	+	0.716418i	$0.254220\pi$
$68$			9.11167i			1.10495i
$69$		−	0.393984i		−	0.0474301i
$70$	1.50608			0.180011
$71$	−2.32872			−0.276368			−0.138184	−	0.990407i	$-0.544126\pi$
$71$	−2.32872			−0.276368			−0.138184	+	0.990407i	$0.544126\pi$
$72$		−	6.47763i		−	0.763396i
$73$	−10.6095			−1.24175			−0.620876	−	0.783909i	$-0.713223\pi$
$73$	−10.6095			−1.24175			−0.620876	+	0.783909i	$0.713223\pi$
$74$	3.26263	+	2.68326i	0.379273	+	0.311922i
$75$	2.37730			0.274507
$76$		−	6.28395i		−	0.720819i
$77$	9.43805			1.07557
$78$	9.44802			1.06978
$79$		−	8.06222i		−	0.907071i	−0.891238	−	0.453535i	$-0.850163\pi$
$79$		−	8.06222i		−	0.907071i	0.891238	−	0.453535i	$-0.149837\pi$
$80$			1.33888i			0.149691i
$81$	−9.92389			−1.10265
$82$			5.97071i			0.659354i
$83$	−6.59438			−0.723827			−0.361914	−	0.932212i	$-0.617876\pi$
$83$	−6.59438			−0.723827			−0.361914	+	0.932212i	$0.617876\pi$
$84$	−7.82472			−0.853747
$85$	−6.00355			−0.651177
$86$	0.309271			0.0333496
$87$		−	19.1557i		−	2.05371i
$88$		−	10.6316i		−	1.13334i
$89$			2.34335i			0.248395i	0.992258	+	0.124197i	$0.0396356\pi$
$89$			2.34335i			0.248395i	−0.992258	+	0.124197i	$0.960364\pi$
$90$	1.84143			0.194104
$91$		−	12.4108i		−	1.30100i
$92$			0.251527i			0.0262235i
$93$		−	0.162173i		−	0.0168165i
$94$			4.82416i			0.497575i
$95$	4.14041			0.424797
$96$			13.8257i			1.41108i
$97$			8.58288i			0.871460i	0.900078	+	0.435730i	$0.143510\pi$
$97$			8.58288i			0.871460i	−0.900078	+	0.435730i	$0.856490\pi$
$98$			1.59509i			0.161128i
$99$	11.5396			1.15977
$100$	−1.51771			−0.151771
$101$	0.976765			0.0971918			0.0485959	−	0.998819i	$-0.484525\pi$
$101$	0.976765			0.0971918			0.0485959	+	0.998819i	$0.484525\pi$
$102$	−9.91165			−0.981399
$103$			19.1838i			1.89023i	0.326732	+	0.945117i	$0.394053\pi$
$103$			19.1838i			1.89023i	−0.326732	+	0.945117i	$0.605947\pi$
$104$	−13.9803			−1.37088
$105$		−	5.15560i		−	0.503135i
$106$		−	3.21734i		−	0.312496i
$107$	−4.92481			−0.476099			−0.238050	−	0.971253i	$-0.576508\pi$
$107$	−4.92481			−0.476099			−0.238050	+	0.971253i	$0.576508\pi$
$108$	1.25716			0.120970
$109$		−	6.66759i		−	0.638640i	−0.947647	−	0.319320i	$-0.896546\pi$
$109$		−	6.66759i		−	0.638640i	0.947647	−	0.319320i	$-0.103454\pi$
$110$	3.02232			0.288167
$111$	9.18531	−	11.1686i	0.871831	−	1.06008i
$112$	2.90359			0.274364
$113$		−	4.69442i		−	0.441614i	−0.975318	−	0.220807i	$-0.929131\pi$
$113$		−	4.69442i		−	0.441614i	0.975318	−	0.220807i	$-0.0708691\pi$
$114$	6.83566			0.640219
$115$	−0.165727			−0.0154542
$116$			12.2293i			1.13547i
$117$		−	15.1742i		−	1.40286i
$118$	−6.55648			−0.603573
$119$			13.0198i			1.19352i
$120$	−5.80761			−0.530160
$121$	7.93978			0.721798
$122$	1.65838			0.150143
$123$	20.4389			1.84291
$124$			0.103534i			0.00929762i
$125$		−	1.00000i		−	0.0894427i
$126$		−	3.99347i		−	0.355767i
$127$	9.18965			0.815450			0.407725	−	0.913105i	$-0.366322\pi$
$127$	9.18965			0.815450			0.407725	+	0.913105i	$0.366322\pi$
$128$		−	10.6862i		−	0.944533i
$129$		−	1.05870i		−	0.0932130i
$130$		−	3.97426i		−	0.348566i
$131$			22.4849i			1.96451i	0.187544	+	0.982256i	$0.439947\pi$
$131$			22.4849i			1.96451i	−0.187544	+	0.982256i	$0.560053\pi$
$132$	−15.7022			−1.36670
$133$		−	8.97921i		−	0.778596i
$134$		−	7.93178i		−	0.685202i
$135$			0.828325i			0.0712909i
$136$	14.6663			1.25763
$137$	8.66881			0.740626			0.370313	−	0.928907i	$-0.379250\pi$
$137$	8.66881			0.740626			0.370313	+	0.928907i	$0.379250\pi$
$138$	−0.273610			−0.0232912
$139$	14.0011			1.18756			0.593779	−	0.804628i	$-0.297635\pi$
$139$	14.0011			1.18756			0.593779	+	0.804628i	$0.297635\pi$
$140$			3.29143i			0.278176i
$141$	16.5141			1.39073
$142$			1.61722i			0.135714i
$143$		−	24.9053i		−	2.08268i
$144$	3.55013			0.295844
$145$	−8.05774			−0.669159
$146$			7.36799i			0.609779i
$147$	5.46030			0.450358
$148$	−5.86407	+	7.13025i	−0.482023	+	0.586103i
$149$	−19.5226			−1.59935			−0.799677	−	0.600430i	$-0.794996\pi$
$149$	−19.5226			−1.59935			−0.799677	+	0.600430i	$0.794996\pi$
$150$		−	1.65096i		−	0.134801i
$151$	−23.2295			−1.89039			−0.945195	−	0.326506i	$-0.894129\pi$
$151$	−23.2295			−1.89039			−0.945195	+	0.326506i	$0.894129\pi$
$152$	−10.1148			−0.820417
$153$			15.9188i			1.28696i
$154$		−	6.55443i		−	0.528171i
$155$	−0.0682170			−0.00547933
$156$			20.6480i			1.65316i
$157$	14.2147			1.13446			0.567229	−	0.823560i	$-0.308016\pi$
$157$	14.2147			1.13446			0.567229	+	0.823560i	$0.308016\pi$
$158$	−5.59896			−0.445429
$159$	−11.0136			−0.873434
$160$	5.81569			0.459771
$161$			0.359409i			0.0283254i
$162$			6.89183i			0.541473i
$163$			10.8566i			0.850354i	0.905110	+	0.425177i	$0.139788\pi$
$163$			10.8566i			0.850354i	−0.905110	+	0.425177i	$0.860212\pi$
$164$	−13.0486			−1.01892
$165$		−	10.3460i		−	0.805434i
$166$			4.57959i			0.355445i
$167$		−	7.41823i		−	0.574040i	−0.957925	−	0.287020i	$-0.907335\pi$
$167$		−	7.41823i		−	0.574040i	0.957925	−	0.287020i	$-0.0926646\pi$
$168$			12.5948i			0.971712i
$169$	−19.7497			−1.51921
$170$			4.16928i			0.319769i
$171$		−	10.9786i		−	0.839553i
$172$			0.675890i			0.0515362i
$173$	−7.71644			−0.586670			−0.293335	−	0.956010i	$-0.594765\pi$
$173$	−7.71644			−0.586670			−0.293335	+	0.956010i	$0.594765\pi$
$174$	−13.3030			−1.00850
$175$	−2.16868			−0.163936
$176$	5.82678			0.439210
$177$			22.4441i			1.68700i
$178$	1.62738			0.121978
$179$		−	3.95371i		−	0.295514i	−0.989024	−	0.147757i	$-0.952795\pi$
$179$		−	3.95371i		−	0.295514i	0.989024	−	0.147757i	$-0.0472054\pi$
$180$			4.02432i			0.299955i
$181$	13.4910			1.00278			0.501390	−	0.865221i	$-0.332822\pi$
$181$	13.4910			1.00278			0.501390	+	0.865221i	$0.332822\pi$
$182$	−8.61889			−0.638874
$183$		−	5.67697i		−	0.419654i
$184$	0.404862			0.0298469
$185$	−4.69802	−	3.86375i	−0.345406	−	0.284069i
$186$	−0.112624			−0.00825798
$187$			26.1274i			1.91062i
$188$	−10.5429			−0.768918
$189$	1.79637			0.130667
$190$		−	2.87539i		−	0.208602i
$191$			3.91989i			0.283633i	0.989893	+	0.141817i	$0.0452943\pi$
$191$			3.91989i			0.283633i	−0.989893	+	0.141817i	$0.954706\pi$
$192$	3.23566			0.233513
$193$			8.40231i			0.604811i	0.953179	+	0.302406i	$0.0977897\pi$
$193$			8.40231i			0.604811i	−0.953179	+	0.302406i	$0.902210\pi$
$194$	5.96054			0.427942
$195$	−13.6047			−0.974251
$196$	−3.48595			−0.248996
$197$	−7.79756			−0.555553			−0.277776	−	0.960646i	$-0.589597\pi$
$197$	−7.79756			−0.555553			−0.277776	+	0.960646i	$0.589597\pi$
$198$		−	8.01389i		−	0.569522i
$199$		−	1.51208i		−	0.107188i	−0.998563	−	0.0535941i	$-0.982932\pi$
$199$		−	1.51208i		−	0.107188i	0.998563	−	0.0535941i	$-0.0170677\pi$
$200$			2.44294i			0.172742i
$201$	−27.1520			−1.91516
$202$		−	0.678333i		−	0.0477273i
$203$			17.4746i			1.22648i
$204$		−	21.6612i		−	1.51659i
$205$		−	8.59751i		−	0.600476i
$206$	13.3225			0.928225
$207$			0.439438i			0.0305430i
$208$		−	7.66205i		−	0.531267i
$209$		−	18.0190i		−	1.24640i
$210$	−3.58040			−0.247071
$211$	−11.6259			−0.800357			−0.400178	−	0.916437i	$-0.631052\pi$
$211$	−11.6259			−0.800357			−0.400178	+	0.916437i	$0.631052\pi$
$212$	7.03127			0.482910
$213$	5.53606			0.379325
$214$			3.42013i			0.233795i
$215$	−0.445335			−0.0303716
$216$		−	2.02355i		−	0.137685i
$217$			0.147941i			0.0100429i
$218$	−4.63044			−0.313613
$219$	25.2221			1.70435
$220$			6.60506i			0.445313i
$221$	34.3568			2.31109
$222$	−7.75626	−	6.37891i	−0.520566	−	0.428124i
$223$	2.59438			0.173733			0.0868663	−	0.996220i	$-0.472315\pi$
$223$	2.59438			0.173733			0.0868663	+	0.996220i	$0.472315\pi$
$224$		−	12.6124i		−	0.842698i
$225$	−2.65157			−0.176771
$226$	−3.26013			−0.216860
$227$		−	2.99424i		−	0.198735i	−0.995051	−	0.0993673i	$-0.968318\pi$
$227$		−	2.99424i		−	0.198735i	0.995051	−	0.0993673i	$-0.0316819\pi$
$228$			14.9389i			0.989350i
$229$	6.89738			0.455792			0.227896	−	0.973686i	$-0.426815\pi$
$229$	6.89738			0.455792			0.227896	+	0.973686i	$0.426815\pi$
$230$			0.115093i			0.00758898i
$231$	−22.4371			−1.47625
$232$	19.6846			1.29236
$233$	23.8710			1.56384			0.781922	−	0.623376i	$-0.214239\pi$
$233$	23.8710			1.56384			0.781922	+	0.623376i	$0.214239\pi$
$234$	−10.5380			−0.688893
$235$		−	6.94655i		−	0.453143i
$236$		−	14.3287i		−	0.932720i
$237$			19.1663i			1.24499i
$238$	9.04182			0.586094
$239$		−	5.31643i		−	0.343892i	−0.985106	−	0.171946i	$-0.944995\pi$
$239$		−	5.31643i		−	0.343892i	0.985106	−	0.171946i	$-0.0550054\pi$
$240$		−	3.18292i		−	0.205457i
$241$		−	13.3776i		−	0.861725i	−0.902418	−	0.430862i	$-0.858209\pi$
$241$		−	13.3776i		−	0.861725i	0.902418	−	0.430862i	$-0.141791\pi$
$242$		−	5.51393i		−	0.354449i
$243$	21.1071			1.35402
$244$			3.62428i			0.232021i
$245$		−	2.29684i		−	0.146740i
$246$		−	14.1942i		−	0.904988i
$247$	−23.6945			−1.50764
$248$	0.166650			0.0105823
$249$	15.6768			0.993479
$250$	−0.694469			−0.0439221
$251$		−	12.4789i		−	0.787660i	−0.919183	−	0.393830i	$-0.871150\pi$
$251$		−	12.4789i		−	0.787660i	0.919183	−	0.393830i	$-0.128850\pi$
$252$	8.72745			0.549778
$253$			0.721243i			0.0453442i
$254$		−	6.38193i		−	0.400438i
$255$	14.2723			0.893764
$256$	−10.1433			−0.633959
$257$		−	20.8290i		−	1.29928i	−0.760243	−	0.649639i	$-0.774920\pi$
$257$		−	20.8290i		−	1.29928i	0.760243	−	0.649639i	$-0.225080\pi$
$258$	−0.735231			−0.0457735
$259$	−8.37922	+	10.1885i	−0.520660	+	0.633082i
$260$	8.68547			0.538650
$261$			21.3657i			1.32250i
$262$	15.6150			0.964701
$263$	−5.45327			−0.336263			−0.168132	−	0.985765i	$-0.553773\pi$
$263$	−5.45327			−0.336263			−0.168132	+	0.985765i	$0.553773\pi$
$264$			25.2747i			1.55555i
$265$			4.63281i			0.284591i
$266$	−6.23578			−0.382340
$267$		−	5.57085i		−	0.340931i
$268$	17.3344			1.05886
$269$	20.0095			1.22000			0.609999	−	0.792402i	$-0.291170\pi$
$269$	20.0095			1.22000			0.609999	+	0.792402i	$0.291170\pi$
$270$	0.575246			0.0350084
$271$	10.1158			0.614491			0.307246	−	0.951630i	$-0.400593\pi$
$271$	10.1158			0.614491			0.307246	+	0.951630i	$0.400593\pi$
$272$			8.03803i			0.487377i
$273$			29.5041i			1.78567i
$274$		−	6.02022i		−	0.363695i
$275$	−4.35199			−0.262435
$276$		−	0.597955i		−	0.0359927i
$277$		−	13.8144i		−	0.830029i	−0.909815	−	0.415014i	$-0.863777\pi$
$277$		−	13.8144i		−	0.830029i	0.909815	−	0.415014i	$-0.136223\pi$
$278$		−	9.72334i		−	0.583167i
$279$			0.180882i			0.0108291i
$280$	5.29795			0.316613
$281$			19.8826i			1.18609i	0.805168	+	0.593047i	$0.202075\pi$
$281$			19.8826i			1.18609i	−0.805168	+	0.593047i	$0.797925\pi$
$282$		−	11.4685i		−	0.682939i
$283$		−	24.9559i		−	1.48348i	−0.670690	−	0.741738i	$-0.734002\pi$
$283$		−	24.9559i		−	1.48348i	0.670690	−	0.741738i	$-0.265998\pi$
$284$	−3.53432			−0.209723
$285$	−9.84301			−0.583050
$286$	−17.2959			−1.02273
$287$	−18.6452			−1.10059
$288$		−	15.4207i		−	0.908674i
$289$	−19.0427			−1.12016
$290$			5.59585i			0.328600i
$291$		−	20.4041i		−	1.19611i
$292$	−16.1022			−0.942312
$293$	5.19503			0.303497			0.151748	−	0.988419i	$-0.451510\pi$
$293$	5.19503			0.303497			0.151748	+	0.988419i	$0.451510\pi$
$294$		−	3.79201i		−	0.221154i
$295$	9.44099			0.549676
$296$	11.4770	+	9.43892i	0.667087	+	0.548626i
$297$	3.60486			0.209175
$298$			13.5578i			0.785385i
$299$	0.948414			0.0548482
$300$	3.60806			0.208312
$301$			0.965787i			0.0556670i
$302$			16.1322i			0.928302i
$303$	−2.32207			−0.133399
$304$		−	5.54351i		−	0.317942i
$305$	−2.38799			−0.136736
$306$	11.0551			0.631980
$307$	−20.7362			−1.18348			−0.591739	−	0.806130i	$-0.701558\pi$
$307$	−20.7362			−1.18348			−0.591739	+	0.806130i	$0.701558\pi$
$308$	14.3242			0.816200
$309$		−	45.6057i		−	2.59442i
$310$			0.0473746i			0.00269070i
$311$			23.7997i			1.34956i	0.738020	+	0.674779i	$0.235761\pi$
$311$			23.7997i			1.34956i	−0.738020	+	0.674779i	$0.764239\pi$
$312$	33.2354			1.88159
$313$			13.7661i			0.778107i	0.921215	+	0.389053i	$0.127198\pi$
$313$			13.7661i			0.778107i	−0.921215	+	0.389053i	$0.872802\pi$
$314$		−	9.87167i		−	0.557091i
$315$			5.75039i			0.323998i
$316$		−	12.2361i		−	0.688336i
$317$	−26.3650			−1.48081			−0.740403	−	0.672164i	$-0.765365\pi$
$317$	−26.3650			−1.48081			−0.740403	+	0.672164i	$0.765365\pi$
$318$			7.64859i			0.428912i
$319$			35.0672i			1.96339i
$320$		−	1.36106i		−	0.0760857i
$321$	11.7078			0.653464
$322$	0.249598			0.0139096
$323$	24.8572			1.38309
$324$	−15.0616			−0.836756
$325$			5.72273i			0.317440i
$326$	7.53957			0.417578
$327$			15.8509i			0.876556i
$328$			21.0032i			1.15971i
$329$	−15.0648			−0.830550
$330$	−7.18497			−0.395519
$331$		−	34.9649i		−	1.92185i	−0.276816	−	0.960923i	$-0.589279\pi$
$331$		−	34.9649i		−	1.92185i	0.276816	−	0.960923i	$-0.410721\pi$
$332$	−10.0084			−0.549281
$333$	−10.2450	+	12.4571i	−0.561423	+	0.682647i
$334$	−5.15173			−0.281890
$335$			11.4214i			0.624016i
$336$	−6.90272			−0.376574
$337$	9.97937			0.543611			0.271805	−	0.962352i	$-0.412379\pi$
$337$	9.97937			0.543611			0.271805	+	0.962352i	$0.412379\pi$
$338$			13.7155i			0.746028i
$339$			11.1601i			0.606131i
$340$	−9.11167			−0.494150
$341$			0.296880i			0.0160769i
$342$	−7.62429			−0.412274
$343$	−20.1618			−1.08864
$344$	1.08793			0.0586571
$345$	0.393984			0.0212114
$346$			5.35883i			0.288092i
$347$		−	14.3875i		−	0.772361i	−0.922423	−	0.386180i	$-0.873794\pi$
$347$		−	14.3875i		−	0.772361i	0.922423	−	0.386180i	$-0.126206\pi$
$348$		−	29.0729i		−	1.55847i
$349$	7.24895			0.388027			0.194014	−	0.980999i	$-0.437849\pi$
$349$	7.24895			0.388027			0.194014	+	0.980999i	$0.437849\pi$
$350$			1.50608i			0.0805033i
$351$		−	4.74029i		−	0.253018i
$352$		−	25.3098i		−	1.34902i
$353$		−	10.8049i		−	0.575085i	−0.957768	−	0.287543i	$-0.907162\pi$
$353$		−	10.8049i		−	0.575085i	0.957768	−	0.287543i	$-0.0928383\pi$
$354$	15.5867			0.828426
$355$		−	2.32872i		−	0.123595i
$356$			3.55653i			0.188496i
$357$		−	30.9519i		−	1.63815i
$358$	−2.74573			−0.145116
$359$	13.1745			0.695323			0.347662	−	0.937620i	$-0.386976\pi$
$359$	13.1745			0.695323			0.347662	+	0.937620i	$0.386976\pi$
$360$	6.47763			0.341401
$361$	1.85701			0.0977371
$362$		−	9.36910i		−	0.492429i
$363$	−18.8753			−0.990694
$364$		−	18.8360i		−	0.987273i
$365$		−	10.6095i		−	0.555328i
$366$	−3.94248			−0.206077
$367$	24.5181			1.27983			0.639917	−	0.768444i	$-0.278969\pi$
$367$	24.5181			1.27983			0.639917	+	0.768444i	$0.278969\pi$
$368$			0.221889i			0.0115668i
$369$	−22.7969			−1.18676
$370$	−2.68326	+	3.26263i	−0.139496	+	0.169616i
$371$	10.0471			0.521617
$372$		−	0.246131i		−	0.0127613i
$373$	−18.8794			−0.977539			−0.488770	−	0.872413i	$-0.662554\pi$
$373$	−18.8794			−0.977539			−0.488770	+	0.872413i	$0.662554\pi$
$374$	18.1447			0.938238
$375$			2.37730i			0.122763i
$376$			16.9700i			0.875162i
$377$	46.1123			2.37491
$378$		−	1.24752i		−	0.0641656i
$379$	−4.90409			−0.251906			−0.125953	−	0.992036i	$-0.540199\pi$
$379$	−4.90409			−0.251906			−0.125953	+	0.992036i	$0.540199\pi$
$380$	6.28395			0.322360
$381$	−21.8466			−1.11923
$382$	2.72224			0.139282
$383$			4.51567i			0.230740i	0.993323	+	0.115370i	$0.0368053\pi$
$383$			4.51567i			0.230740i	−0.993323	+	0.115370i	$0.963195\pi$
$384$			25.4043i			1.29641i
$385$			9.43805i			0.481007i
$386$	5.83514			0.297001
$387$			1.18084i			0.0600253i
$388$			13.0263i			0.661313i
$389$			9.09674i			0.461223i	0.973046	+	0.230612i	$0.0740727\pi$
$389$			9.09674i			0.461223i	−0.973046	+	0.230612i	$0.925927\pi$
$390$			9.44802i			0.478419i
$391$	−0.994954			−0.0503170
$392$			5.61106i			0.283401i
$393$		−	53.4534i		−	2.69636i
$394$			5.41516i			0.272812i
$395$	8.06222			0.405654
$396$	17.5138			0.880101
$397$	−23.4743			−1.17814			−0.589071	−	0.808081i	$-0.700506\pi$
$397$	−23.4743			−1.17814			−0.589071	+	0.808081i	$0.700506\pi$
$398$	−1.05009			−0.0526362
$399$			21.3463i			1.06865i
$400$	−1.33888			−0.0669439
$401$		−	21.4285i		−	1.07009i	−0.844825	−	0.535043i	$-0.820295\pi$
$401$		−	21.4285i		−	1.07009i	0.844825	−	0.535043i	$-0.179705\pi$
$402$			18.8563i			0.940464i
$403$	0.390388			0.0194466
$404$	1.48245			0.0737546
$405$		−	9.92389i		−	0.493122i
$406$	12.1356			0.602279
$407$	−16.8150	+	20.4457i	−0.833488	+	1.01346i
$408$	−34.8663			−1.72614
$409$			22.3741i			1.10633i	0.833072	+	0.553164i	$0.186580\pi$
$409$			22.3741i			1.10633i	−0.833072	+	0.553164i	$0.813420\pi$
$410$	−5.97071			−0.294872
$411$	−20.6084			−1.01654
$412$			29.1155i			1.43442i
$413$		−	20.4745i		−	1.00748i
$414$	0.305176			0.0149986
$415$		−	6.59438i		−	0.323705i
$416$	−33.2817			−1.63177
$417$	−33.2849			−1.62997
$418$	−12.5136			−0.612062
$419$	−3.38447			−0.165342			−0.0826710	−	0.996577i	$-0.526345\pi$
$419$	−3.38447			−0.165342			−0.0826710	+	0.996577i	$0.526345\pi$
$420$		−	7.82472i		−	0.381807i
$421$			38.7578i			1.88894i	0.328597	+	0.944470i	$0.393424\pi$
$421$			38.7578i			1.88894i	−0.328597	+	0.944470i	$0.606576\pi$
$422$			8.07380i			0.393026i
$423$	−18.4193			−0.895575
$424$		−	11.3177i		−	0.549635i
$425$		−	6.00355i		−	0.291215i
$426$		−	3.84462i		−	0.186273i
$427$			5.17877i			0.250618i
$428$	−7.47445			−0.361291
$429$			59.2073i			2.85856i
$430$			0.309271i			0.0149144i
$431$		−	4.50684i		−	0.217087i	−0.994092	−	0.108543i	$-0.965381\pi$
$431$		−	4.50684i		−	0.217087i	0.994092	−	0.108543i	$-0.0346186\pi$
$432$	1.10903			0.0533581
$433$	−5.62353			−0.270250			−0.135125	−	0.990829i	$-0.543144\pi$
$433$	−5.62353			−0.270250			−0.135125	+	0.990829i	$0.543144\pi$
$434$	0.102740			0.00493169
$435$	19.1557			0.918446
$436$		−	10.1195i		−	0.484636i
$437$	0.686179			0.0328244
$438$		−	17.5160i		−	0.836945i
$439$			31.3943i			1.49837i	0.662362	+	0.749184i	$0.269554\pi$
$439$			31.3943i			1.49837i	−0.662362	+	0.749184i	$0.730446\pi$
$440$	10.6316			0.506844
$441$	−6.09024			−0.290012
$442$		−	23.8597i		−	1.13489i
$443$	−25.2783			−1.20101			−0.600504	−	0.799622i	$-0.705033\pi$
$443$	−25.2783			−1.20101			−0.600504	+	0.799622i	$0.705033\pi$
$444$	13.9407	−	16.9508i	0.661594	−	0.804448i
$445$	−2.34335			−0.111085
$446$		−	1.80172i		−	0.0853138i
$447$	46.4112			2.19517
$448$	−2.95170			−0.139455
$449$		−	12.0163i		−	0.567086i	−0.958960	−	0.283543i	$-0.908490\pi$
$449$		−	12.0163i		−	0.567086i	0.958960	−	0.283543i	$-0.0915098\pi$
$450$			1.84143i			0.0868060i
$451$	−37.4163			−1.76186
$452$		−	7.12478i		−	0.335121i
$453$	55.2236			2.59463
$454$	−2.07941			−0.0975913
$455$	12.4108			0.581825
$456$	24.0459			1.12605
$457$			38.7961i			1.81480i	0.420264	+	0.907402i	$0.361937\pi$
$457$			38.7961i			1.81480i	−0.420264	+	0.907402i	$0.638063\pi$
$458$		−	4.79001i		−	0.223823i
$459$			4.97290i			0.232115i
$460$	−0.251527			−0.0117275
$461$			34.7227i			1.61720i	0.588360	+	0.808599i	$0.299774\pi$
$461$			34.7227i			1.61720i	−0.588360	+	0.808599i	$0.700226\pi$
$462$			15.5819i			0.724934i
$463$		−	6.90276i		−	0.320798i	−0.987052	−	0.160399i	$-0.948722\pi$
$463$		−	6.90276i		−	0.320798i	0.987052	−	0.160399i	$-0.0512782\pi$
$464$			10.7883i			0.500836i
$465$	0.162173			0.00752057
$466$		−	16.5777i		−	0.767947i
$467$		−	27.2476i		−	1.26087i	−0.776243	−	0.630434i	$-0.782877\pi$
$467$		−	27.2476i		−	1.26087i	0.776243	−	0.630434i	$-0.217123\pi$
$468$		−	23.0301i		−	1.06457i
$469$	24.7692			1.14374
$470$	−4.82416			−0.222522
$471$	−33.7927			−1.55708
$472$	−23.0638			−1.06160
$473$			1.93809i			0.0891135i
$474$	13.3104			0.611368
$475$			4.14041i			0.189975i
$476$			19.7603i			0.905710i
$477$	12.2842			0.562455
$478$	−3.69210			−0.168873
$479$		−	38.6778i		−	1.76724i	−0.468209	−	0.883618i	$-0.655101\pi$
$479$		−	38.6778i		−	1.76724i	0.468209	−	0.883618i	$-0.344899\pi$
$480$	−13.8257			−0.631052
$481$	26.8855	+	22.1112i	1.22588	+	1.00819i
$482$	−9.29030			−0.423162
$483$		−	0.854424i		−	0.0388776i
$484$	12.0503			0.547741
$485$	−8.58288			−0.389729
$486$		−	14.6582i		−	0.664911i
$487$		−	2.02287i		−	0.0916651i	−0.998949	−	0.0458326i	$-0.985406\pi$
$487$		−	2.02287i		−	0.0916651i	0.998949	−	0.0458326i	$-0.0145941\pi$
$488$	5.83371			0.264080
$489$		−	25.8094i		−	1.16714i
$490$	−1.59509			−0.0720587
$491$	34.4832			1.55621			0.778103	−	0.628137i	$-0.216182\pi$
$491$	34.4832			1.55621			0.778103	+	0.628137i	$0.216182\pi$
$492$	31.0204			1.39851
$493$	−48.3751			−2.17871
$494$			16.4551i			0.740349i
$495$			11.5396i			0.518666i
$496$			0.0913343i			0.00410103i
$497$	−5.05023			−0.226534
$498$		−	10.8871i		−	0.487862i
$499$			8.93562i			0.400013i	0.979795	+	0.200007i	$0.0640964\pi$
$499$			8.93562i			0.400013i	−0.979795	+	0.200007i	$0.935904\pi$
$500$		−	1.51771i		−	0.0678742i
$501$			17.6354i			0.787891i
$502$	−8.66619			−0.386791
$503$			2.50197i			0.111557i	0.998443	+	0.0557786i	$0.0177641\pi$
$503$			2.50197i			0.111557i	−0.998443	+	0.0557786i	$0.982236\pi$
$504$		−	14.0479i		−	0.625742i
$505$			0.976765i			0.0434655i
$506$	0.500881			0.0222669
$507$	46.9510			2.08517
$508$	13.9473			0.618809
$509$	−12.8713			−0.570508			−0.285254	−	0.958452i	$-0.592078\pi$
$509$	−12.8713			−0.570508			−0.285254	+	0.958452i	$0.592078\pi$
$510$		−	9.91165i		−	0.438895i
$511$	−23.0086			−1.01784
$512$		−	14.3281i		−	0.633219i
$513$		−	3.42961i		−	0.151421i
$514$	−14.4651			−0.638028
$515$	−19.1838			−0.845338
$516$		−	1.60680i		−	0.0707353i
$517$	−30.2313			−1.32957
$518$	7.07559	+	5.81911i	0.310884	+	0.255677i
$519$	18.3443			0.805226
$520$		−	13.9803i		−	0.613077i
$521$	21.2718			0.931935			0.465967	−	0.884802i	$-0.345706\pi$
$521$	21.2718			0.931935			0.465967	+	0.884802i	$0.345706\pi$
$522$	14.8378			0.649433
$523$		−	22.9221i		−	1.00231i	−0.865357	−	0.501156i	$-0.832908\pi$
$523$		−	22.9221i		−	1.00231i	0.865357	−	0.501156i	$-0.167092\pi$
$524$			34.1256i			1.49078i
$525$	5.15560			0.225009
$526$			3.78713i			0.165127i
$527$	−0.409545			−0.0178401
$528$	−13.8520			−0.602832
$529$	22.9725			0.998806
$530$	3.21734			0.139752
$531$		−	25.0335i		−	1.08636i
$532$		−	13.6279i		−	0.590843i
$533$			49.2013i			2.13114i
$534$	−3.86878			−0.167419
$535$		−	4.92481i		−	0.212918i
$536$		−	27.9017i		−	1.20517i
$537$			9.39917i			0.405604i
$538$		−	13.8959i		−	0.599097i
$539$	−9.99583			−0.430551
$540$			1.25716i			0.0540996i
$541$		−	27.5498i		−	1.18446i	−0.805770	−	0.592228i	$-0.798248\pi$
$541$		−	27.5498i		−	1.18446i	0.805770	−	0.592228i	$-0.201752\pi$
$542$		−	7.02511i		−	0.301754i
$543$	−32.0722			−1.37635
$544$	34.9148			1.49696
$545$	6.66759			0.285608
$546$	20.4897			0.876878
$547$		−	14.7301i		−	0.629812i	−0.949123	−	0.314906i	$-0.898027\pi$
$547$		−	14.7301i		−	0.629812i	0.949123	−	0.314906i	$-0.101973\pi$
$548$	13.1568			0.562029
$549$			6.33191i			0.270239i
$550$			3.02232i			0.128872i
$551$	33.3624			1.42128
$552$	−0.962481			−0.0409659
$553$		−	17.4843i		−	0.743510i
$554$	−9.59369			−0.407597
$555$	11.1686	+	9.18531i	0.474082	+	0.389895i
$556$	21.2497			0.901187
$557$		−	41.3384i		−	1.75156i	−0.482707	−	0.875782i	$-0.660346\pi$
$557$		−	41.3384i		−	1.75156i	0.482707	−	0.875782i	$-0.339654\pi$
$558$	0.125617			0.00531780
$559$	2.54853			0.107791
$560$			2.90359i			0.122699i
$561$		−	62.1127i		−	2.62240i
$562$	13.8078			0.582448
$563$		−	12.3396i		−	0.520052i	−0.965602	−	0.260026i	$-0.916269\pi$
$563$		−	12.3396i		−	0.520052i	0.965602	−	0.260026i	$-0.0837311\pi$
$564$	25.0636			1.05537
$565$	4.69442			0.197496
$566$	−17.3311			−0.728481
$567$	−21.5217			−0.903826
$568$			5.68892i			0.238702i
$569$			20.3376i			0.852597i	0.904582	+	0.426299i	$0.140183\pi$
$569$			20.3376i			0.852597i	−0.904582	+	0.426299i	$0.859817\pi$
$570$			6.83566i			0.286314i
$571$	2.20913			0.0924493			0.0462246	−	0.998931i	$-0.485281\pi$
$571$	2.20913			0.0924493			0.0462246	+	0.998931i	$0.485281\pi$
$572$		−	37.7990i		−	1.58046i
$573$		−	9.31876i		−	0.389297i
$574$			12.9485i			0.540461i
$575$		−	0.165727i		−	0.00691131i
$576$	−3.60895			−0.150373
$577$			27.2952i			1.13631i	0.822920	+	0.568157i	$0.192344\pi$
$577$			27.2952i			1.13631i	−0.822920	+	0.568157i	$0.807656\pi$
$578$			13.2245i			0.550068i
$579$		−	19.9748i		−	0.830126i
$580$	−12.2293			−0.507796
$581$	−14.3011			−0.593309
$582$	−14.1700			−0.587366
$583$	20.1619			0.835021
$584$			25.9185i			1.07251i
$585$	15.1742			0.627377
$586$		−	3.60779i		−	0.149036i
$587$		−	0.417280i		−	0.0172230i	−0.999963	−	0.00861150i	$-0.997259\pi$
$587$		−	0.417280i		−	0.0172230i	0.999963	−	0.00861150i	$-0.00274116\pi$
$588$	8.28716			0.341757
$589$	0.282447			0.0116380
$590$		−	6.55648i		−	0.269926i
$591$	18.5372			0.762517
$592$	−5.17309	+	6.29008i	−0.212613	+	0.258521i
$593$	2.54532			0.104524			0.0522619	−	0.998633i	$-0.483357\pi$
$593$	2.54532			0.104524			0.0522619	+	0.998633i	$0.483357\pi$
$594$		−	2.50346i		−	0.102718i
$595$	−13.0198			−0.533758
$596$	−29.6297			−1.21368
$597$			3.59466i			0.147120i
$598$		−	0.658644i		−	0.0269340i
$599$	−17.2975			−0.706757			−0.353379	−	0.935480i	$-0.614967\pi$
$599$	−17.2975			−0.706757			−0.353379	+	0.935480i	$0.614967\pi$
$600$		−	5.80761i		−	0.237095i
$601$	−39.3207			−1.60392			−0.801962	−	0.597375i	$-0.796211\pi$
$601$	−39.3207			−1.60392			−0.801962	+	0.597375i	$0.796211\pi$
$602$	0.670709			0.0273361
$603$	30.2845			1.23328
$604$	−35.2557			−1.43453
$605$			7.93978i			0.322798i
$606$			1.61260i			0.0655075i
$607$		−	14.0635i		−	0.570820i	−0.958405	−	0.285410i	$-0.907870\pi$
$607$		−	14.0635i		−	0.570820i	0.958405	−	0.285410i	$-0.0921298\pi$
$608$	−24.0794			−0.976547
$609$		−	41.5425i		−	1.68339i
$610$			1.65838i			0.0671459i
$611$			39.7533i			1.60825i
$612$			24.1602i			0.976619i
$613$	28.9940			1.17105			0.585527	−	0.810653i	$-0.300887\pi$
$613$	28.9940			1.17105			0.585527	+	0.810653i	$0.300887\pi$
$614$			14.4007i			0.581163i
$615$			20.4389i			0.824176i
$616$		−	23.0566i		−	0.928977i
$617$	13.4011			0.539510			0.269755	−	0.962929i	$-0.413057\pi$
$617$	13.4011			0.539510			0.269755	+	0.962929i	$0.413057\pi$
$618$	−31.6717			−1.27402
$619$	42.6050			1.71244			0.856220	−	0.516611i	$-0.172807\pi$
$619$	42.6050			1.71244			0.856220	+	0.516611i	$0.172807\pi$
$620$	−0.103534			−0.00415802
$621$			0.137276i			0.00550870i
$622$	16.5282			0.662719
$623$			5.08197i			0.203605i
$624$			18.2150i			0.729184i
$625$	1.00000			0.0400000
$626$	9.56014			0.382100
$627$			42.8366i			1.71073i
$628$	21.5738			0.860890
$629$	−28.2048	−	23.1962i	−1.12460	−	0.924895i
$630$	3.99347			0.159104
$631$			37.8981i			1.50870i	0.656472	+	0.754350i	$0.272048\pi$
$631$			37.8981i			1.50870i	−0.656472	+	0.754350i	$0.727952\pi$
$632$	−19.6955			−0.783446
$633$	27.6382			1.09852
$634$			18.3097i			0.727170i
$635$			9.18965i			0.364680i
$636$	−16.7155			−0.662811
$637$			13.1442i			0.520793i
$638$	24.3531			0.964147
$639$	−6.17475			−0.244269
$640$	10.6862			0.422408
$641$	−5.17563			−0.204425			−0.102213	−	0.994763i	$-0.532592\pi$
$641$	−5.17563			−0.204425			−0.102213	+	0.994763i	$0.532592\pi$
$642$		−	8.13068i		−	0.320892i
$643$		−	40.7663i		−	1.60767i	−0.594854	−	0.803834i	$-0.702790\pi$
$643$		−	40.7663i		−	1.60767i	0.594854	−	0.803834i	$-0.297210\pi$
$644$			0.545480i			0.0214949i
$645$	1.05870			0.0416861
$646$		−	17.2625i		−	0.679185i
$647$			0.183619i			0.00721883i	0.999993	+	0.00360941i	$0.00114891\pi$
$647$			0.183619i			0.00721883i	−0.999993	+	0.00360941i	$0.998851\pi$
$648$			24.2435i			0.952374i
$649$		−	41.0871i		−	1.61281i
$650$	3.97426			0.155883
$651$		−	0.351700i		−	0.0137842i
$652$			16.4772i			0.645297i
$653$			16.8021i			0.657516i	0.944414	+	0.328758i	$0.106630\pi$
$653$			16.8021i			0.657516i	−0.944414	+	0.328758i	$0.893370\pi$
$654$	11.0080			0.430445
$655$	−22.4849			−0.878557
$656$	−11.5110			−0.449430
$657$	−28.1319			−1.09753
$658$			10.4620i			0.407853i
$659$	21.1834			0.825190			0.412595	−	0.910915i	$-0.364623\pi$
$659$	21.1834			0.825190			0.412595	+	0.910915i	$0.364623\pi$
$660$		−	15.7022i		−	0.611209i
$661$		−	26.3955i		−	1.02666i	−0.858190	−	0.513332i	$-0.828411\pi$
$661$		−	26.3955i		−	1.02666i	0.858190	−	0.513332i	$-0.171589\pi$
$662$	−24.2821			−0.943749
$663$	−81.6764			−3.17205
$664$			16.1097i			0.625177i
$665$	8.97921			0.348199
$666$	8.65109	+	7.11484i	0.335223	+	0.275694i
$667$	−1.33539			−0.0517065
$668$		−	11.2587i		−	0.435614i
$669$	−6.16763			−0.238454
$670$	7.93178			0.306432
$671$			10.3925i			0.401197i
$672$			29.9834i			1.15663i
$673$	44.0680			1.69870			0.849349	−	0.527832i	$-0.176995\pi$
$673$	44.0680			1.69870			0.849349	+	0.527832i	$0.176995\pi$
$674$		−	6.93036i		−	0.266948i
$675$	−0.828325			−0.0318823
$676$	−29.9744			−1.15286
$677$	1.37058			0.0526756			0.0263378	−	0.999653i	$-0.491615\pi$
$677$	1.37058			0.0526756			0.0263378	+	0.999653i	$0.491615\pi$
$678$	7.75031			0.297649
$679$			18.6135i			0.714320i
$680$			14.6663i			0.562428i
$681$			7.11821i			0.272770i
$682$	0.206174			0.00789480
$683$			9.46755i			0.362266i	0.983459	+	0.181133i	$0.0579764\pi$
$683$			9.46755i			0.362266i	−0.983459	+	0.181133i	$0.942024\pi$
$684$		−	16.6623i		−	0.637100i
$685$			8.66881i			0.331218i
$686$			14.0018i			0.534590i
$687$	−16.3972			−0.625591
$688$			0.596249i			0.0227318i
$689$		−	26.5123i		−	1.01004i
$690$		−	0.273610i		−	0.0104161i
$691$	28.7211			1.09260			0.546301	−	0.837589i	$-0.316036\pi$
$691$	28.7211			1.09260			0.546301	+	0.837589i	$0.316036\pi$
$692$	−11.7113			−0.445198
$693$	25.0256			0.950645
$694$	−9.99166			−0.379278
$695$			14.0011i			0.531092i
$696$	−46.7963			−1.77381
$697$		−	51.6157i		−	1.95508i
$698$		−	5.03417i		−	0.190546i
$699$	−56.7487			−2.14643
$700$	−3.29143			−0.124404
$701$		−	17.9577i		−	0.678252i	−0.940741	−	0.339126i	$-0.889869\pi$
$701$		−	17.9577i		−	0.678252i	0.940741	−	0.339126i	$-0.110131\pi$
$702$	−3.29198			−0.124248
$703$	19.4517	+	15.9975i	0.733636	+	0.603358i
$704$	−5.92332			−0.223244
$705$			16.5141i			0.621955i
$706$	−7.50365			−0.282403
$707$	2.11829			0.0796664
$708$			34.0637i			1.28019i
$709$		−	15.3109i		−	0.575012i	−0.957779	−	0.287506i	$-0.907174\pi$
$709$		−	15.3109i		−	0.575012i	0.957779	−	0.287506i	$-0.0928261\pi$
$710$	−1.61722			−0.0606932
$711$		−	21.3775i		−	0.801720i
$712$	5.72467			0.214541
$713$	−0.0113054			−0.000423392
$714$	−21.4952			−0.804436
$715$	24.9053			0.931404
$716$		−	6.00060i		−	0.224253i
$717$			12.6388i			0.472004i
$718$		−	9.14928i		−	0.341448i
$719$	13.6890			0.510514			0.255257	−	0.966873i	$-0.417840\pi$
$719$	13.6890			0.510514			0.255257	+	0.966873i	$0.417840\pi$
$720$			3.55013i			0.132305i
$721$			41.6034i			1.54939i
$722$		−	1.28963i		−	0.0479951i
$723$			31.8025i			1.18275i
$724$	20.4755			0.760966
$725$		−	8.05774i		−	0.299257i
$726$			13.1083i			0.486494i
$727$			11.9352i			0.442651i	0.975200	+	0.221326i	$0.0710383\pi$
$727$			11.9352i			0.442651i	−0.975200	+	0.221326i	$0.928962\pi$
$728$	−30.3188			−1.12369
$729$	−20.4063			−0.755790
$730$	−7.36799			−0.272702
$731$	−2.67359			−0.0988864
$732$		−	8.61601i		−	0.318457i
$733$	−10.0865			−0.372555			−0.186277	−	0.982497i	$-0.559642\pi$
$733$	−10.0865			−0.372555			−0.186277	+	0.982497i	$0.559642\pi$
$734$		−	17.0271i		−	0.628480i
$735$			5.46030i			0.201406i
$736$	0.963820			0.0355269
$737$	49.7056			1.83093
$738$			15.8317i			0.582774i
$739$	11.5583			0.425180			0.212590	−	0.977142i	$-0.431810\pi$
$739$	11.5583			0.425180			0.212590	+	0.977142i	$0.431810\pi$
$740$	−7.13025	−	5.86407i	−0.262113	−	0.215567i
$741$	56.3289			2.06929
$742$		−	6.97737i		−	0.256147i
$743$	4.00230			0.146830			0.0734151	−	0.997301i	$-0.476610\pi$
$743$	4.00230			0.146830			0.0734151	+	0.997301i	$0.476610\pi$
$744$	−0.396178			−0.0145246
$745$		−	19.5226i		−	0.715253i
$746$			13.1112i			0.480034i
$747$	−17.4855			−0.639759
$748$			39.6539i			1.44989i
$749$	−10.6803			−0.390250
$750$	1.65096			0.0602846
$751$	12.6259			0.460724			0.230362	−	0.973105i	$-0.426009\pi$
$751$	12.6259			0.460724			0.230362	+	0.973105i	$0.426009\pi$
$752$	−9.30059			−0.339158
$753$			29.6661i			1.08109i
$754$		−	32.0236i		−	1.16623i
$755$		−	23.2295i		−	0.845408i
$756$	2.72637			0.0991572
$757$			0.686799i			0.0249621i	0.999922	+	0.0124811i	$0.00397295\pi$
$757$			0.686799i			0.0249621i	−0.999922	+	0.0124811i	$0.996027\pi$
$758$			3.40574i			0.123702i
$759$		−	1.71461i		−	0.0622365i
$760$		−	10.1148i		−	0.366902i
$761$	45.5758			1.65212			0.826060	−	0.563582i	$-0.190577\pi$
$761$	45.5758			1.65212			0.826060	+	0.563582i	$0.190577\pi$
$762$			15.1718i			0.549616i
$763$		−	14.4599i		−	0.523482i
$764$			5.94927i			0.215237i
$765$	−15.9188			−0.575547
$766$	3.13599			0.113308
$767$	−54.0283			−1.95085
$768$	24.1138			0.870131
$769$		−	40.5462i		−	1.46213i	−0.682306	−	0.731067i	$-0.739023\pi$
$769$		−	40.5462i		−	1.46213i	0.682306	−	0.731067i	$-0.260977\pi$
$770$	6.55443			0.236205
$771$			49.5169i			1.78331i
$772$			12.7523i			0.458965i
$773$	33.7970			1.21559			0.607797	−	0.794093i	$-0.292054\pi$
$773$	33.7970			1.21559			0.607797	+	0.794093i	$0.292054\pi$
$774$	0.820054			0.0294762
$775$		−	0.0682170i		−	0.00245043i
$776$	20.9675			0.752689
$777$	19.9200	−	24.2211i	0.714624	−	0.868928i
$778$	6.31741			0.226490
$779$			35.5972i			1.27540i
$780$	−20.6480			−0.739317
$781$	−10.1345			−0.362642
$782$			0.690964i			0.0247088i
$783$			6.67443i			0.238525i
$784$	−3.07520			−0.109828
$785$			14.2147i			0.507345i
$786$	−37.1217			−1.32409
$787$	7.98198			0.284527			0.142263	−	0.989829i	$-0.454562\pi$
$787$	7.98198			0.284527			0.142263	+	0.989829i	$0.454562\pi$
$788$	−11.8345			−0.421585
$789$	12.9641			0.461533
$790$		−	5.59896i		−	0.199202i
$791$		−	10.1807i		−	0.361983i
$792$		−	28.1906i		−	1.00171i
$793$	13.6658			0.485287
$794$			16.3022i			0.578543i
$795$		−	11.0136i		−	0.390612i
$796$		−	2.29490i		−	0.0813405i
$797$		−	26.0890i		−	0.924119i	−0.886849	−	0.462060i	$-0.847111\pi$
$797$		−	26.0890i		−	0.924119i	0.886849	−	0.462060i	$-0.152889\pi$
$798$	14.8243			0.524776
$799$		−	41.7040i		−	1.47538i
$800$			5.81569i			0.205616i
$801$			6.21355i			0.219545i
$802$	−14.8814			−0.525481
$803$	−46.1725			−1.62939
$804$	−41.2090			−1.45333
$805$	−0.359409			−0.0126675
$806$		−	0.271112i		−	0.00954953i
$807$	−47.5685			−1.67449
$808$		−	2.38618i		−	0.0839455i
$809$		−	37.3911i		−	1.31460i	−0.753629	−	0.657300i	$-0.771698\pi$
$809$		−	37.3911i		−	1.31460i	0.753629	−	0.657300i	$-0.228302\pi$
$810$	−6.89183			−0.242154
$811$	40.7822			1.43206			0.716029	−	0.698070i	$-0.245958\pi$
$811$	40.7822			1.43206			0.716029	+	0.698070i	$0.245958\pi$
$812$			26.5215i			0.930722i
$813$	−24.0483			−0.843412
$814$	14.1989	+	11.6775i	0.497672	+	0.409296i
$815$	−10.8566			−0.380290
$816$		−	19.1088i		−	0.668943i
$817$	1.84387			0.0645088
$818$	15.5381			0.543278
$819$		−	32.9080i		−	1.14990i
$820$		−	13.0486i		−	0.455675i
$821$	−49.7348			−1.73576			−0.867879	−	0.496776i	$-0.834517\pi$
$821$	−49.7348			−1.73576			−0.867879	+	0.496776i	$0.834517\pi$
$822$			14.3119i			0.499184i
$823$	−6.32881			−0.220608			−0.110304	−	0.993898i	$-0.535183\pi$
$823$	−6.32881			−0.220608			−0.110304	+	0.993898i	$0.535183\pi$
$824$	46.8649			1.63262
$825$	10.3460			0.360201
$826$	−14.2189			−0.494738
$827$		−	24.9486i		−	0.867548i	−0.901022	−	0.433774i	$-0.857182\pi$
$827$		−	24.9486i		−	0.867548i	0.901022	−	0.433774i	$-0.142818\pi$
$828$			0.666940i			0.0231778i
$829$			16.7582i			0.582036i	0.956718	+	0.291018i	$0.0939939\pi$
$829$			16.7582i			0.582036i	−0.956718	+	0.291018i	$0.906006\pi$
$830$	−4.57959			−0.158960
$831$			32.8411i			1.13924i
$832$			7.78900i			0.270035i
$833$		−	13.7892i		−	0.477769i
$834$			23.1153i			0.800418i
$835$	7.41823			0.256718
$836$		−	27.3477i		−	0.945839i
$837$			0.0565059i			0.00195313i
$838$			2.35041i			0.0811935i
$839$	−45.1407			−1.55843			−0.779215	−	0.626756i	$-0.784382\pi$
$839$	−45.1407			−1.55843			−0.779215	+	0.626756i	$0.784382\pi$
$840$	−12.5948			−0.434563
$841$	−35.9272			−1.23887
$842$	26.9161			0.927590
$843$		−	47.2669i		−	1.62796i
$844$	−17.6447			−0.607356
$845$		−	19.7497i		−	0.679410i
$846$			12.7916i			0.439784i
$847$	17.2188			0.591645
$848$	6.20276			0.213004
$849$			59.3278i			2.03612i
$850$	−4.16928			−0.143005
$851$	−0.778591	−	0.640329i	−0.0266898	−	0.0219502i
$852$	8.40215			0.287853
$853$			3.04298i			0.104190i	0.998642	+	0.0520948i	$0.0165898\pi$
$853$			3.04298i			0.104190i	−0.998642	+	0.0520948i	$0.983410\pi$
$854$	3.59649			0.123070
$855$	10.9786			0.375460
$856$			12.0310i			0.411212i
$857$			0.397815i			0.0135891i	0.999977	+	0.00679455i	$0.00216279\pi$
$857$			0.397815i			0.0135891i	−0.999977	+	0.00679455i	$0.997837\pi$
$858$	41.1177			1.40373
$859$			28.4886i			0.972018i	0.873954	+	0.486009i	$0.161548\pi$
$859$			28.4886i			0.972018i	−0.873954	+	0.486009i	$0.838452\pi$
$860$	−0.675890			−0.0230477
$861$	44.3253			1.51060
$862$	−3.12986			−0.106603
$863$	−31.2137			−1.06253			−0.531263	−	0.847207i	$-0.678282\pi$
$863$	−31.2137			−1.06253			−0.531263	+	0.847207i	$0.678282\pi$
$864$		−	4.81729i		−	0.163887i
$865$		−	7.71644i		−	0.262367i
$866$			3.90537i			0.132710i
$867$	45.2702			1.53746
$868$			0.224531i			0.00762109i
$869$		−	35.0867i		−	1.19023i
$870$		−	13.3030i		−	0.451015i
$871$		−	65.3614i		−	2.21469i
$872$	−16.2885			−0.551600
$873$			22.7581i			0.770245i
$874$		−	0.476530i		−	0.0161189i
$875$		−	2.16868i		−	0.0733146i
$876$	38.2799			1.29336
$877$	31.9398			1.07853			0.539266	−	0.842136i	$-0.318702\pi$
$877$	31.9398			1.07853			0.539266	+	0.842136i	$0.318702\pi$
$878$	21.8024			0.735794
$879$	−12.3502			−0.416561
$880$			5.82678i			0.196421i
$881$	20.6857			0.696920			0.348460	−	0.937324i	$-0.386705\pi$
$881$	20.6857			0.696920			0.348460	+	0.937324i	$0.386705\pi$
$882$			4.22948i			0.142414i
$883$		−	30.1761i		−	1.01551i	−0.861502	−	0.507754i	$-0.830476\pi$
$883$		−	30.1761i		−	1.01551i	0.861502	−	0.507754i	$-0.169524\pi$
$884$	52.1437			1.75378
$885$	−22.4441			−0.754450
$886$			17.5550i			0.589771i
$887$	−34.4783			−1.15767			−0.578834	−	0.815445i	$-0.696492\pi$
$887$	−34.4783			−1.15767			−0.578834	+	0.815445i	$0.696492\pi$
$888$	−27.2843	−	22.4392i	−0.915601	−	0.753009i
$889$	19.9294			0.668410
$890$			1.62738i			0.0545500i
$891$	−43.1886			−1.44687
$892$	3.93753			0.131838
$893$			28.7616i			0.962469i
$894$		−	32.2311i		−	1.07797i
$895$	3.95371			0.132158
$896$		−	23.1748i		−	0.774217i
$897$	−2.25467			−0.0752812
$898$	−8.34497			−0.278475
$899$	−0.549676			−0.0183327
$900$	−4.02432			−0.134144
$901$			27.8133i			0.926595i
$902$			25.9844i			0.865187i
$903$		−	2.29597i		−	0.0764050i
$904$	−11.4682			−0.381426
$905$			13.4910i			0.448457i
$906$		−	38.3511i		−	1.27413i
$907$			1.66867i			0.0554073i	0.999616	+	0.0277037i	$0.00881948\pi$
$907$			1.66867i			0.0554073i	−0.999616	+	0.0277037i	$0.991181\pi$
$908$		−	4.54439i		−	0.150811i
$909$	2.58996			0.0859036
$910$		−	8.61889i		−	0.285713i
$911$			53.6779i			1.77843i	0.457492	+	0.889214i	$0.348748\pi$
$911$			53.6779i			1.77843i	−0.457492	+	0.889214i	$0.651252\pi$
$912$			13.1786i			0.436387i
$913$	−28.6986			−0.949787
$914$	26.9427			0.891184
$915$	5.67697			0.187675
$916$	10.4682			0.345880
$917$			48.7624i			1.61028i
$918$	3.45352			0.113983
$919$		−	2.69177i		−	0.0887932i	−0.999014	−	0.0443966i	$-0.985863\pi$
$919$		−	2.69177i		−	0.0887932i	0.999014	−	0.0443966i	$-0.0141365\pi$
$920$			0.404862i			0.0133479i
$921$	49.2963			1.62437
$922$	24.1139			0.794147
$923$			13.3266i			0.438651i
$924$	−34.0531			−1.12026
$925$	3.86375	−	4.69802i	0.127039	−	0.154470i
$926$	−4.79375			−0.157532
$927$			50.8671i			1.67070i
$928$	46.8614			1.53830
$929$	−38.5193			−1.26378			−0.631888	−	0.775060i	$-0.717720\pi$
$929$	−38.5193			−1.26378			−0.631888	+	0.775060i	$0.717720\pi$
$930$		−	0.112624i		−	0.00369308i
$931$			9.50988i			0.311674i
$932$	36.2294			1.18673
$933$		−	56.5791i		−	1.85232i
$934$	−18.9226			−0.619167
$935$	−26.1274			−0.854457
$936$	−37.0698			−1.21166
$937$	56.0419			1.83081			0.915404	−	0.402537i	$-0.131871\pi$
$937$	56.0419			1.83081			0.915404	+	0.402537i	$0.131871\pi$
$938$		−	17.2015i		−	0.561648i
$939$		−	32.7262i		−	1.06798i
$940$		−	10.5429i		−	0.343871i
$941$	−36.5917			−1.19286			−0.596428	−	0.802666i	$-0.703414\pi$
$941$	−36.5917			−1.19286			−0.596428	+	0.802666i	$0.703414\pi$
$942$			23.4680i			0.764627i
$943$		−	1.42484i		−	0.0463993i
$944$		−	12.6403i		−	0.411408i
$945$			1.79637i			0.0584359i
$946$	1.34594			0.0437604
$947$			8.48377i			0.275685i	0.990454	+	0.137843i	$0.0440168\pi$
$947$			8.48377i			0.275685i	−0.990454	+	0.137843i	$0.955983\pi$
$948$			29.0890i			0.944767i
$949$			60.7156i			1.97091i
$950$	2.87539			0.0932898
$951$	62.6776			2.03246
$952$	31.8065			1.03086
$953$	16.3555			0.529807			0.264904	−	0.964275i	$-0.414660\pi$
$953$	16.3555			0.529807			0.264904	+	0.964275i	$0.414660\pi$
$954$		−	8.53100i		−	0.276201i
$955$	−3.91989			−0.126845
$956$		−	8.06882i		−	0.260964i
$957$		−	83.3653i		−	2.69482i
$958$	−26.8606			−0.867825
$959$	18.7998			0.607078
$960$			3.23566i			0.104430i
$961$	30.9953			0.999850
$962$	15.3556	−	18.6712i	0.495083	−	0.601983i
$963$	−13.0585			−0.420803
$964$		−	20.3033i		−	0.653925i
$965$	−8.40231			−0.270480
$966$	−0.593371			−0.0190914
$967$		−	26.0712i		−	0.838393i	−0.907895	−	0.419197i	$-0.862312\pi$
$967$		−	26.0712i		−	0.838393i	0.907895	−	0.419197i	$-0.137688\pi$
$968$		−	19.3964i		−	0.623425i
$969$	−59.0930			−1.89834
$970$			5.96054i			0.191382i
$971$	12.3808			0.397320			0.198660	−	0.980068i	$-0.436341\pi$
$971$	12.3808			0.397320			0.198660	+	0.980068i	$0.436341\pi$
$972$	32.0345			1.02751
$973$	30.3639			0.973421
$974$	−1.40482			−0.0450134
$975$		−	13.6047i		−	0.435698i
$976$			3.19722i			0.102341i
$977$			15.7957i			0.505348i	0.967552	+	0.252674i	$0.0813100\pi$
$977$			15.7957i			0.505348i	−0.967552	+	0.252674i	$0.918690\pi$
$978$	−17.9238			−0.573141
$979$			10.1982i			0.325937i
$980$		−	3.48595i		−	0.111355i
$981$		−	17.6796i		−	0.564466i
$982$		−	23.9475i		−	0.764196i
$983$	26.9238			0.858737			0.429369	−	0.903129i	$-0.358736\pi$
$983$	26.9238			0.858737			0.429369	+	0.903129i	$0.358736\pi$
$984$		−	49.9310i		−	1.59174i
$985$		−	7.79756i		−	0.248451i
$986$			33.5950i			1.06988i
$987$	35.8136			1.13996
$988$	−35.9614			−1.14408
$989$	−0.0738042			−0.00234684
$990$	8.01389			0.254698
$991$			54.2528i			1.72340i	0.507420	+	0.861699i	$0.330599\pi$
$991$			54.2528i			1.72340i	−0.507420	+	0.861699i	$0.669401\pi$
$992$	0.396729			0.0125962
$993$			83.1222i			2.63780i
$994$			3.50723i			0.111243i
$995$	1.51208			0.0479360
$996$	23.7929			0.753908
$997$			13.2613i			0.419989i	0.977703	+	0.209995i	$0.0673446\pi$
$997$			13.2613i			0.419989i	−0.977703	+	0.209995i	$0.932655\pi$
$998$	6.20551			0.196432
$999$	−3.20044	+	3.89149i	−0.101258	+	0.123121i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.c.b.36.6	✓	12
3.2	odd	2		1665.2.e.e.406.7		12
4.3	odd	2		2960.2.p.h.961.10		12
5.2	odd	4		925.2.d.e.924.8		12
5.3	odd	4		925.2.d.f.924.5		12
5.4	even	2		925.2.c.c.776.7		12
37.6	odd	4		6845.2.a.i.1.3		6
37.31	odd	4		6845.2.a.h.1.4		6
37.36	even	2	inner	185.2.c.b.36.7	yes	12
111.110	odd	2		1665.2.e.e.406.6		12
148.147	odd	2		2960.2.p.h.961.9		12
185.73	odd	4		925.2.d.e.924.7		12
185.147	odd	4		925.2.d.f.924.6		12
185.184	even	2		925.2.c.c.776.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.c.b.36.6	✓	12	1.1	even	1	trivial
185.2.c.b.36.7	yes	12	37.36	even	2	inner
925.2.c.c.776.6		12	185.184	even	2
925.2.c.c.776.7		12	5.4	even	2
925.2.d.e.924.7		12	185.73	odd	4
925.2.d.e.924.8		12	5.2	odd	4
925.2.d.f.924.5		12	5.3	odd	4
925.2.d.f.924.6		12	185.147	odd	4
1665.2.e.e.406.6		12	111.110	odd	2
1665.2.e.e.406.7		12	3.2	odd	2
2960.2.p.h.961.9		12	148.147	odd	2
2960.2.p.h.961.10		12	4.3	odd	2
6845.2.a.h.1.4		6	37.31	odd	4
6845.2.a.i.1.3		6	37.6	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.694469i q^{2} -2.37730 q^{3} +1.51771 q^{4} +1.00000i q^{5} +1.65096i q^{6} +2.16868 q^{7} -2.44294i q^{8} +2.65157 q^{9} +0.694469 q^{10} +4.35199 q^{11} -3.60806 q^{12} -5.72273i q^{13} -1.50608i q^{14} -2.37730i q^{15} +1.33888 q^{16} +6.00355i q^{17} -1.84143i q^{18} -4.14041i q^{19} +1.51771i q^{20} -5.15560 q^{21} -3.02232i q^{22} +0.165727i q^{23} +5.80761i q^{24} -1.00000 q^{25} -3.97426 q^{26} +0.828325 q^{27} +3.29143 q^{28} +8.05774i q^{29} -1.65096 q^{30} +0.0682170i q^{31} -5.81569i q^{32} -10.3460 q^{33} +4.16928 q^{34} +2.16868i q^{35} +4.02432 q^{36} +(-3.86375 + 4.69802i) q^{37} -2.87539 q^{38} +13.6047i q^{39} +2.44294 q^{40} -8.59751 q^{41} +3.58040i q^{42} +0.445335i q^{43} +6.60506 q^{44} +2.65157i q^{45} +0.115093 q^{46} -6.94655 q^{47} -3.18292 q^{48} -2.29684 q^{49} +0.694469i q^{50} -14.2723i q^{51} -8.68547i q^{52} +4.63281 q^{53} -0.575246i q^{54} +4.35199i q^{55} -5.29795i q^{56} +9.84301i q^{57} +5.59585 q^{58} -9.44099i q^{59} -3.60806i q^{60} +2.38799i q^{61} +0.0473746 q^{62} +5.75039 q^{63} -1.36106 q^{64} +5.72273 q^{65} +7.18497i q^{66} +11.4214 q^{67} +9.11167i q^{68} -0.393984i q^{69} +1.50608 q^{70} -2.32872 q^{71} -6.47763i q^{72} -10.6095 q^{73} +(3.26263 + 2.68326i) q^{74} +2.37730 q^{75} -6.28395i q^{76} +9.43805 q^{77} +9.44802 q^{78} -8.06222i q^{79} +1.33888i q^{80} -9.92389 q^{81} +5.97071i q^{82} -6.59438 q^{83} -7.82472 q^{84} -6.00355 q^{85} +0.309271 q^{86} -19.1557i q^{87} -10.6316i q^{88} +2.34335i q^{89} +1.84143 q^{90} -12.4108i q^{91} +0.251527i q^{92} -0.162173i q^{93} +4.82416i q^{94} +4.14041 q^{95} +13.8257i q^{96} +8.58288i q^{97} +1.59509i q^{98} +11.5396 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{3} - 18 q^{4} - 18 q^{7} + 22 q^{9} - 2 q^{10} + 2 q^{11} - 36 q^{12} + 30 q^{16} - 6 q^{21} - 12 q^{25} - 12 q^{26} + 26 q^{27} + 24 q^{28} - 12 q^{30} - 18 q^{33} + 4 q^{34} - 22 q^{36} + 10 q^{37}+ \cdots - 84 q^{99}+O(q^{100}) \) 12 * q + 2 * q^3 - 18 * q^4 - 18 * q^7 + 22 * q^9 - 2 * q^10 + 2 * q^11 - 36 * q^12 + 30 * q^16 - 6 * q^21 - 12 * q^25 - 12 * q^26 + 26 * q^27 + 24 * q^28 - 12 * q^30 - 18 * q^33 + 4 * q^34 - 22 * q^36 + 10 * q^37 + 12 * q^38 + 6 * q^40 - 10 * q^41 + 44 * q^44 - 24 * q^46 + 2 * q^47 + 60 * q^48 + 30 * q^49 - 6 * q^53 - 24 * q^58 + 44 * q^62 - 16 * q^63 - 126 * q^64 + 20 * q^65 + 16 * q^67 - 28 * q^70 + 42 * q^71 - 46 * q^73 + 50 * q^74 - 2 * q^75 + 30 * q^77 + 132 * q^78 - 12 * q^81 - 62 * q^83 - 84 * q^84 - 12 * q^85 - 64 * q^86 - 26 * q^90 + 44 * q^95 - 84 * q^99

Introduction

L-functions

Modular forms

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