LMFDB - Embedded newform 555.2.g.a.184.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [555,2,Mod(184,555)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(555, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("555.184");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 555 = 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	555.g (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:	$4.43169731218$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			184.8
Character	$\chi$	$=$	555.184
Dual form			555.2.g.a.184.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.81177 q^{2} +1.00000i q^{3} +1.28250 q^{4} +(-2.16949 + 0.541568i) q^{5} -1.81177i q^{6} +4.65490i q^{7} +1.29994 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.81177 q^{2} +1.00000i q^{3} +1.28250 q^{4} +(-2.16949 + 0.541568i) q^{5} -1.81177i q^{6} +4.65490i q^{7} +1.29994 q^{8} -1.00000 q^{9} +(3.93062 - 0.981196i) q^{10} +4.78039 q^{11} +1.28250i q^{12} +5.66185 q^{13} -8.43359i q^{14} +(-0.541568 - 2.16949i) q^{15} -4.92019 q^{16} -1.75858 q^{17} +1.81177 q^{18} +4.16013i q^{19} +(-2.78238 + 0.694563i) q^{20} -4.65490 q^{21} -8.66096 q^{22} -5.64038 q^{23} +1.29994i q^{24} +(4.41341 - 2.34986i) q^{25} -10.2580 q^{26} -1.00000i q^{27} +5.96992i q^{28} -0.922027i q^{29} +(0.981196 + 3.93062i) q^{30} +6.40502i q^{31} +6.31437 q^{32} +4.78039i q^{33} +3.18614 q^{34} +(-2.52094 - 10.0988i) q^{35} -1.28250 q^{36} +(-4.14887 + 4.44824i) q^{37} -7.53719i q^{38} +5.66185i q^{39} +(-2.82021 + 0.704005i) q^{40} -0.323318 q^{41} +8.43359 q^{42} +2.09855 q^{43} +6.13087 q^{44} +(2.16949 - 0.541568i) q^{45} +10.2191 q^{46} +1.02660i q^{47} -4.92019i q^{48} -14.6681 q^{49} +(-7.99607 + 4.25740i) q^{50} -1.75858i q^{51} +7.26134 q^{52} -10.1994i q^{53} +1.81177i q^{54} +(-10.3710 + 2.58891i) q^{55} +6.05108i q^{56} -4.16013 q^{57} +1.67050i q^{58} +14.2998i q^{59} +(-0.694563 - 2.78238i) q^{60} -7.21886i q^{61} -11.6044i q^{62} -4.65490i q^{63} -1.59979 q^{64} +(-12.2834 + 3.06628i) q^{65} -8.66096i q^{66} +4.18794i q^{67} -2.25538 q^{68} -5.64038i q^{69} +(4.56737 + 18.2966i) q^{70} -12.3319 q^{71} -1.29994 q^{72} -13.7935i q^{73} +(7.51679 - 8.05919i) q^{74} +(2.34986 + 4.41341i) q^{75} +5.33538i q^{76} +22.2522i q^{77} -10.2580i q^{78} -2.74395i q^{79} +(10.6743 - 2.66462i) q^{80} +1.00000 q^{81} +0.585778 q^{82} +9.59951i q^{83} -5.96992 q^{84} +(3.81523 - 0.952391i) q^{85} -3.80208 q^{86} +0.922027 q^{87} +6.21421 q^{88} +1.00437i q^{89} +(-3.93062 + 0.981196i) q^{90} +26.3553i q^{91} -7.23381 q^{92} -6.40502 q^{93} -1.85995i q^{94} +(-2.25299 - 9.02537i) q^{95} +6.31437i q^{96} +3.50566 q^{97} +26.5751 q^{98} -4.78039 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 44 q^{4} - 40 q^{9}+O(q^{10}) $ 40 * q + 44 * q^4 - 40 * q^9	$ 40 q + 44 q^{4} - 40 q^{9} + 4 q^{10} + 8 q^{11} + 52 q^{16} - 16 q^{21} + 8 q^{25} - 16 q^{26} + 16 q^{30} - 32 q^{34} - 44 q^{36} - 28 q^{40} + 8 q^{41} + 16 q^{44} - 8 q^{46} - 24 q^{49} + 92 q^{64} - 48 q^{65} - 56 q^{70} + 24 q^{71} - 68 q^{74} + 8 q^{75} + 40 q^{81} - 16 q^{84} - 64 q^{85} + 80 q^{86} - 4 q^{90} + 32 q^{95} - 8 q^{99}+O(q^{100}) $ 40 * q + 44 * q^4 - 40 * q^9 + 4 * q^10 + 8 * q^11 + 52 * q^16 - 16 * q^21 + 8 * q^25 - 16 * q^26 + 16 * q^30 - 32 * q^34 - 44 * q^36 - 28 * q^40 + 8 * q^41 + 16 * q^44 - 8 * q^46 - 24 * q^49 + 92 * q^64 - 48 * q^65 - 56 * q^70 + 24 * q^71 - 68 * q^74 + 8 * q^75 + 40 * q^81 - 16 * q^84 - 64 * q^85 + 80 * q^86 - 4 * q^90 + 32 * q^95 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/555\mathbb{Z}\right)^\times$.

$n$	$76$	$112$	$371$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−1.81177			−1.28111			−0.640557	−	0.767911i	$-0.721296\pi$
$2$	−1.81177			−1.28111			−0.640557	+	0.767911i	$0.721296\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.28250			0.641251
$5$	−2.16949	+	0.541568i	−0.970227	+	0.242197i
$5$	−2.16949	+	0.541568i	−0.970227	+	0.242197i
$6$		−	1.81177i		−	0.739651i
$7$			4.65490i			1.75939i	0.475543	+	0.879693i	$0.342252\pi$
$7$			4.65490i			1.75939i	−0.475543	+	0.879693i	$0.657748\pi$
$8$	1.29994			0.459598
$9$	−1.00000			−0.333333
$10$	3.93062	−	0.981196i	1.24297	−	0.310281i
$11$	4.78039			1.44134			0.720671	−	0.693277i	$-0.243834\pi$
$11$	4.78039			1.44134			0.720671	+	0.693277i	$0.243834\pi$
$12$			1.28250i			0.370227i
$13$	5.66185			1.57032			0.785158	−	0.619296i	$-0.212582\pi$
$13$	5.66185			1.57032			0.785158	+	0.619296i	$0.212582\pi$
$14$		−	8.43359i		−	2.25397i
$15$	−0.541568	−	2.16949i	−0.139832	−	0.560161i
$16$	−4.92019			−1.23005
$17$	−1.75858			−0.426518			−0.213259	−	0.976996i	$-0.568408\pi$
$17$	−1.75858			−0.426518			−0.213259	+	0.976996i	$0.568408\pi$
$18$	1.81177			0.427038
$19$			4.16013i			0.954399i	0.878795	+	0.477199i	$0.158348\pi$
$19$			4.16013i			0.954399i	−0.878795	+	0.477199i	$0.841652\pi$
$20$	−2.78238	+	0.694563i	−0.622160	+	0.155309i
$21$	−4.65490			−1.01578
$22$	−8.66096			−1.84652
$23$	−5.64038			−1.17610			−0.588051	−	0.808824i	$-0.700104\pi$
$23$	−5.64038			−1.17610			−0.588051	+	0.808824i	$0.700104\pi$
$24$			1.29994i			0.265349i
$25$	4.41341	−	2.34986i	0.882681	−	0.469972i
$26$	−10.2580			−2.01175
$27$		−	1.00000i		−	0.192450i
$28$			5.96992i			1.12821i
$29$		−	0.922027i		−	0.171216i	−0.996329	−	0.0856081i	$-0.972717\pi$
$29$		−	0.922027i		−	0.171216i	0.996329	−	0.0856081i	$-0.0272833\pi$
$30$	0.981196	+	3.93062i	0.179141	+	0.717630i
$31$			6.40502i			1.15038i	0.818021	+	0.575188i	$0.195071\pi$
$31$			6.40502i			1.15038i	−0.818021	+	0.575188i	$0.804929\pi$
$32$	6.31437			1.11623
$33$			4.78039i			0.832159i
$34$	3.18614			0.546418
$35$	−2.52094	−	10.0988i	−0.426117	−	1.70700i
$36$	−1.28250			−0.213750
$37$	−4.14887	+	4.44824i	−0.682070	+	0.731287i
$37$	−4.14887	+	4.44824i	−0.682070	+	0.731287i
$38$		−	7.53719i		−	1.22269i
$39$			5.66185i			0.906622i
$40$	−2.82021	+	0.704005i	−0.445914	+	0.111313i
$41$	−0.323318			−0.0504938			−0.0252469	−	0.999681i	$-0.508037\pi$
$41$	−0.323318			−0.0504938			−0.0252469	+	0.999681i	$0.508037\pi$
$42$	8.43359			1.30133
$43$	2.09855			0.320026			0.160013	−	0.987115i	$-0.448846\pi$
$43$	2.09855			0.320026			0.160013	+	0.987115i	$0.448846\pi$
$44$	6.13087			0.924263
$45$	2.16949	−	0.541568i	0.323409	−	0.0807322i
$46$	10.2191			1.50672
$47$			1.02660i			0.149744i	0.997193	+	0.0748722i	$0.0238549\pi$
$47$			1.02660i			0.149744i	−0.997193	+	0.0748722i	$0.976145\pi$
$48$		−	4.92019i		−	0.710169i
$49$	−14.6681			−2.09544
$50$	−7.99607	+	4.25740i	−1.13082	+	0.602087i
$51$		−	1.75858i		−	0.246250i
$52$	7.26134			1.00697
$53$		−	10.1994i		−	1.40100i	−0.713654	−	0.700498i	$-0.752961\pi$
$53$		−	10.1994i		−	1.40100i	0.713654	−	0.700498i	$-0.247039\pi$
$54$			1.81177i			0.246550i
$55$	−10.3710	+	2.58891i	−1.39843	+	0.349088i
$56$			6.05108i			0.808609i
$57$	−4.16013			−0.551022
$58$			1.67050i			0.219347i
$59$			14.2998i			1.86168i	0.365430	+	0.930839i	$0.380922\pi$
$59$			14.2998i			1.86168i	−0.365430	+	0.930839i	$0.619078\pi$
$60$	−0.694563	−	2.78238i	−0.0896677	−	0.359204i
$61$		−	7.21886i		−	0.924280i	−0.886807	−	0.462140i	$-0.847082\pi$
$61$		−	7.21886i		−	0.924280i	0.886807	−	0.462140i	$-0.152918\pi$
$62$		−	11.6044i		−	1.47376i
$63$		−	4.65490i		−	0.586462i
$64$	−1.59979			−0.199973
$65$	−12.2834	+	3.06628i	−1.52356	+	0.380325i
$66$		−	8.66096i		−	1.06609i
$67$			4.18794i			0.511639i	0.966725	+	0.255819i	$0.0823452\pi$
$67$			4.18794i			0.511639i	−0.966725	+	0.255819i	$0.917655\pi$
$68$	−2.25538			−0.273505
$69$		−	5.64038i		−	0.679022i
$70$	4.56737	+	18.2966i	0.545905	+	2.18686i
$71$	−12.3319			−1.46352			−0.731762	−	0.681560i	$-0.761302\pi$
$71$	−12.3319			−1.46352			−0.731762	+	0.681560i	$0.761302\pi$
$72$	−1.29994			−0.153199
$73$		−	13.7935i		−	1.61441i	−0.590269	−	0.807206i	$-0.700978\pi$
$73$		−	13.7935i		−	1.61441i	0.590269	−	0.807206i	$-0.299022\pi$
$74$	7.51679	−	8.05919i	0.873809	−	0.936861i
$75$	2.34986	+	4.41341i	0.271338	+	0.509616i
$76$			5.33538i			0.612010i
$77$			22.2522i			2.53588i
$78$		−	10.2580i		−	1.16149i
$79$		−	2.74395i		−	0.308719i	−0.988015	−	0.154359i	$-0.950669\pi$
$79$		−	2.74395i		−	0.308719i	0.988015	−	0.154359i	$-0.0493314\pi$
$80$	10.6743	−	2.66462i	1.19343	−	0.297914i
$81$	1.00000			0.111111
$82$	0.585778			0.0646883
$83$			9.59951i			1.05368i	0.849964	+	0.526841i	$0.176624\pi$
$83$			9.59951i			1.05368i	−0.849964	+	0.526841i	$0.823376\pi$
$84$	−5.96992			−0.651371
$85$	3.81523	−	0.952391i	0.413820	−	0.103301i
$86$	−3.80208			−0.409989
$87$	0.922027			0.0988517
$88$	6.21421			0.662437
$89$			1.00437i			0.106463i	0.998582	+	0.0532313i	$0.0169521\pi$
$89$			1.00437i			0.106463i	−0.998582	+	0.0532313i	$0.983048\pi$
$90$	−3.93062	+	0.981196i	−0.414324	+	0.103427i
$91$			26.3553i			2.76279i
$92$	−7.23381			−0.754177
$93$	−6.40502			−0.664170
$94$		−	1.85995i		−	0.191840i
$95$	−2.25299	−	9.02537i	−0.231152	−	0.925984i
$96$			6.31437i			0.644458i
$97$	3.50566			0.355946			0.177973	−	0.984035i	$-0.443046\pi$
$97$	3.50566			0.355946			0.177973	+	0.984035i	$0.443046\pi$
$98$	26.5751			2.68449
$99$	−4.78039			−0.480447
$100$	5.66021	−	3.01370i	0.566021	−	0.301370i
$101$	−2.63853			−0.262543			−0.131272	−	0.991346i	$-0.541906\pi$
$101$	−2.63853			−0.262543			−0.131272	+	0.991346i	$0.541906\pi$
$102$			3.18614i			0.315475i
$103$	−7.93951			−0.782303			−0.391152	−	0.920326i	$-0.627923\pi$
$103$	−7.93951			−0.782303			−0.391152	+	0.920326i	$0.627923\pi$
$104$	7.36006			0.721713
$105$	10.0988	−	2.52094i	0.985539	−	0.246019i
$106$			18.4790i			1.79484i
$107$		−	18.5702i		−	1.79525i	−0.440761	−	0.897625i	$-0.645291\pi$
$107$		−	18.5702i		−	1.79525i	0.440761	−	0.897625i	$-0.354709\pi$
$108$		−	1.28250i		−	0.123409i
$109$		−	11.2783i		−	1.08027i	−0.841580	−	0.540133i	$-0.818374\pi$
$109$		−	11.2783i		−	1.08027i	0.841580	−	0.540133i	$-0.181626\pi$
$110$	18.7899	−	4.69050i	1.79155	−	0.447222i
$111$	−4.44824	−	4.14887i	−0.422209	−	0.393793i
$112$		−	22.9030i		−	2.16413i
$113$	9.91685			0.932898			0.466449	−	0.884548i	$-0.345533\pi$
$113$	9.91685			0.932898			0.466449	+	0.884548i	$0.345533\pi$
$114$	7.53719			0.705922
$115$	12.2368	−	3.05465i	1.14109	−	0.284848i
$116$		−	1.18250i		−	0.109793i
$117$	−5.66185			−0.523439
$118$		−	25.9080i		−	2.38502i
$119$		−	8.18601i		−	0.750410i
$120$	−0.704005	−	2.82021i	−0.0642666	−	0.257449i
$121$	11.8521			1.07747
$122$			13.0789i			1.18411i
$123$		−	0.323318i		−	0.0291526i
$124$			8.21446i			0.737680i
$125$	−8.30225	+	7.48817i	−0.742576	+	0.669762i
$126$			8.43359i			0.751324i
$127$			0.805208i			0.0714507i	0.999362	+	0.0357253i	$0.0113742\pi$
$127$			0.805208i			0.0714507i	−0.999362	+	0.0357253i	$0.988626\pi$
$128$	−9.73030			−0.860045
$129$			2.09855i			0.184767i
$130$	22.2546	−	5.55539i	1.95186	−	0.487240i
$131$			0.0441248i			0.00385520i	0.999998	+	0.00192760i	$0.000613574\pi$
$131$			0.0441248i			0.00385520i	−0.999998	+	0.00192760i	$0.999386\pi$
$132$			6.13087i			0.533623i
$133$	−19.3650			−1.67915
$134$		−	7.58758i		−	0.655467i
$135$	0.541568	+	2.16949i	0.0466108	+	0.186720i
$136$	−2.28605			−0.196027
$137$			16.8763i			1.44184i	0.693017	+	0.720921i	$0.256281\pi$
$137$			16.8763i			1.44184i	−0.693017	+	0.720921i	$0.743719\pi$
$138$			10.2191i			0.869905i
$139$	11.4850			0.974146			0.487073	−	0.873361i	$-0.338065\pi$
$139$	11.4850			0.974146			0.487073	+	0.873361i	$0.338065\pi$
$140$	−3.23312	−	12.9517i	−0.273248	−	1.09462i
$141$	−1.02660			−0.0864550
$142$	22.3425			1.87494
$143$	27.0659			2.26336
$144$	4.92019			0.410016
$145$	0.499341	+	2.00033i	0.0414680	+	0.166119i
$146$			24.9907i			2.06825i
$147$		−	14.6681i		−	1.20980i
$148$	−5.32094	+	5.70489i	−0.437378	+	0.468939i
$149$	6.73600			0.551835			0.275918	−	0.961181i	$-0.411018\pi$
$149$	6.73600			0.551835			0.275918	+	0.961181i	$0.411018\pi$
$150$	−4.25740	−	7.99607i	−0.347615	−	0.652876i
$151$	−11.9827			−0.975136			−0.487568	−	0.873085i	$-0.662116\pi$
$151$	−11.9827			−0.975136			−0.487568	+	0.873085i	$0.662116\pi$
$152$			5.40791i			0.438639i
$153$	1.75858			0.142173
$154$		−	40.3159i		−	3.24874i
$155$	−3.46876	−	13.8957i	−0.278617	−	1.11613i
$156$			7.26134i			0.581373i
$157$		−	3.67659i		−	0.293424i	−0.989179	−	0.146712i	$-0.953131\pi$
$157$		−	3.67659i		−	0.293424i	0.989179	−	0.146712i	$-0.0468690\pi$
$158$			4.97141i			0.395504i
$159$	10.1994			0.808866
$160$	−13.6990	+	3.41966i	−1.08300	+	0.270348i
$161$		−	26.2554i		−	2.06921i
$162$	−1.81177			−0.142346
$163$	12.8387			1.00560			0.502802	−	0.864402i	$-0.332303\pi$
$163$	12.8387			1.00560			0.502802	+	0.864402i	$0.332303\pi$
$164$	−0.414657			−0.0323792
$165$	−2.58891	−	10.3710i	−0.201546	−	0.807384i
$166$		−	17.3921i		−	1.34989i
$167$	8.01894			0.620524			0.310262	−	0.950651i	$-0.399583\pi$
$167$	8.01894			0.620524			0.310262	+	0.950651i	$0.399583\pi$
$168$	−6.05108			−0.466851
$169$	19.0566			1.46589
$170$	−6.91231	+	1.72551i	−0.530150	+	0.132341i
$171$		−	4.16013i		−	0.318133i
$172$	2.69140			0.205217
$173$			25.0618i			1.90541i	0.303894	+	0.952706i	$0.401713\pi$
$173$			25.0618i			1.90541i	−0.303894	+	0.952706i	$0.598287\pi$
$174$	−1.67050			−0.126640
$175$	10.9383	+	20.5440i	0.826861	+	1.55298i
$176$	−23.5204			−1.77292
$177$	−14.2998			−1.07484
$178$		−	1.81968i		−	0.136391i
$179$		−	1.19334i		−	0.0891943i	−0.999005	−	0.0445971i	$-0.985800\pi$
$179$		−	1.19334i		−	0.0891943i	0.999005	−	0.0445971i	$-0.0142004\pi$
$180$	2.78238	−	0.694563i	0.207387	−	0.0517697i
$181$	−3.25723			−0.242108			−0.121054	−	0.992646i	$-0.538627\pi$
$181$	−3.25723			−0.242108			−0.121054	+	0.992646i	$0.538627\pi$
$182$		−	47.7497i		−	3.53945i
$183$	7.21886			0.533633
$184$	−7.33215			−0.540533
$185$	6.59192	−	11.8973i	0.484647	−	0.874710i
$186$	11.6044			0.850877
$187$	−8.40670			−0.614759
$188$			1.31661i			0.0960238i
$189$	4.65490			0.338594
$190$	4.08190	+	16.3519i	0.296132	+	1.18629i
$191$		−	6.61164i		−	0.478401i	−0.970970	−	0.239201i	$-0.923115\pi$
$191$		−	6.61164i		−	0.478401i	0.970970	−	0.239201i	$-0.0768854\pi$
$192$		−	1.59979i		−	0.115455i
$193$	11.4135			0.821562			0.410781	−	0.911734i	$-0.365256\pi$
$193$	11.4135			0.821562			0.410781	+	0.911734i	$0.365256\pi$
$194$	−6.35144			−0.456007
$195$	−3.06628	−	12.2834i	−0.219581	−	0.879629i
$196$	−18.8118			−1.34370
$197$			15.3939i			1.09677i	0.836226	+	0.548385i	$0.184757\pi$
$197$			15.3939i			1.09677i	−0.836226	+	0.548385i	$0.815243\pi$
$198$	8.66096			0.615508
$199$			1.41076i			0.100006i	0.998749	+	0.0500030i	$0.0159231\pi$
$199$			1.41076i			0.100006i	−0.998749	+	0.0500030i	$0.984077\pi$
$200$	5.73716	−	3.05467i	0.405678	−	0.215998i
$201$	−4.18794			−0.295395
$202$	4.78040			0.336348
$203$	4.29194			0.301235
$204$		−	2.25538i		−	0.157908i
$205$	0.701437	−	0.175099i	0.0489905	−	0.0122294i
$206$	14.3846			1.00222
$207$	5.64038			0.392034
$208$	−27.8574			−1.93156
$209$			19.8870i			1.37562i
$210$	−18.2966	+	4.56737i	−1.26259	+	0.315178i
$211$	11.3947			0.784445			0.392222	−	0.919870i	$-0.371706\pi$
$211$	11.3947			0.784445			0.392222	+	0.919870i	$0.371706\pi$
$212$		−	13.0808i		−	0.898391i
$213$		−	12.3319i		−	0.844966i
$214$			33.6449i			2.29992i
$215$	−4.55279	+	1.13651i	−0.310498	+	0.0775092i
$216$		−	1.29994i		−	0.0884496i
$217$	−29.8147			−2.02395
$218$			20.4337i			1.38394i
$219$	13.7935			0.932082
$220$	−13.3009	+	3.32028i	−0.896745	+	0.223853i
$221$	−9.95682			−0.669768
$222$	8.05919	+	7.51679i	0.540897	+	0.504494i
$223$			7.25610i			0.485904i	0.970038	+	0.242952i	$0.0781158\pi$
$223$			7.25610i			0.485904i	−0.970038	+	0.242952i	$0.921884\pi$
$224$			29.3927i			1.96388i
$225$	−4.41341	+	2.34986i	−0.294227	+	0.156657i
$226$	−17.9670			−1.19515
$227$	5.15024			0.341833			0.170917	−	0.985285i	$-0.445327\pi$
$227$	5.15024			0.341833			0.170917	+	0.985285i	$0.445327\pi$
$228$	−5.33538			−0.353344
$229$	−18.0742			−1.19438			−0.597189	−	0.802101i	$-0.703716\pi$
$229$	−18.0742			−1.19438			−0.597189	+	0.802101i	$0.703716\pi$
$230$	−22.1702	+	5.53432i	−1.46186	+	0.364922i
$231$	−22.2522			−1.46409
$232$		−	1.19858i		−	0.0786906i
$233$			13.6039i			0.891223i	0.895226	+	0.445612i	$0.147014\pi$
$233$			13.6039i			0.891223i	−0.895226	+	0.445612i	$0.852986\pi$
$234$	10.2580			0.670584
$235$	−0.555972	−	2.22719i	−0.0362676	−	0.145286i
$236$			18.3396i			1.19380i
$237$	2.74395			0.178239
$238$			14.8311i			0.961360i
$239$			7.08497i			0.458289i	0.973392	+	0.229144i	$0.0735928\pi$
$239$			7.08497i			0.458289i	−0.973392	+	0.229144i	$0.926407\pi$
$240$	2.66462	+	10.6743i	0.172001	+	0.689025i
$241$			6.91419i			0.445382i	0.974889	+	0.222691i	$0.0714842\pi$
$241$			6.91419i			0.445382i	−0.974889	+	0.222691i	$0.928516\pi$
$242$	−21.4733			−1.38036
$243$			1.00000i			0.0641500i
$244$		−	9.25821i		−	0.592696i
$245$	31.8222	−	7.94375i	2.03305	−	0.507508i
$246$			0.585778i			0.0373478i
$247$			23.5540i			1.49871i
$248$			8.32613i			0.528710i
$249$	−9.59951			−0.608344
$250$	15.0418	−	13.5668i	0.951324	−	0.858041i
$251$		−	6.46298i		−	0.407939i	−0.978977	−	0.203970i	$-0.934616\pi$
$251$		−	6.46298i		−	0.407939i	0.978977	−	0.203970i	$-0.0653844\pi$
$252$		−	5.96992i		−	0.376069i
$253$	−26.9632			−1.69516
$254$		−	1.45885i		−	0.0915364i
$255$	0.952391	+	3.81523i	0.0596411	+	0.238919i
$256$	20.8286			1.30179
$257$	−9.14900			−0.570699			−0.285349	−	0.958424i	$-0.592110\pi$
$257$	−9.14900			−0.570699			−0.285349	+	0.958424i	$0.592110\pi$
$258$		−	3.80208i		−	0.236707i
$259$	−20.7061	−	19.3126i	−1.28662	−	1.20002i
$260$	−15.7534	+	3.93251i	−0.976987	+	0.243884i
$261$			0.922027i			0.0570721i
$262$		−	0.0799438i		−	0.00493895i
$263$			17.7044i			1.09170i	0.837883	+	0.545849i	$0.183793\pi$
$263$			17.7044i			1.09170i	−0.837883	+	0.545849i	$0.816207\pi$
$264$			6.21421i			0.382458i
$265$	5.52368	+	22.1276i	0.339317	+	1.35929i
$266$	35.0848			2.15119
$267$	−1.00437			−0.0614662
$268$			5.37105i			0.328089i
$269$	2.87815			0.175484			0.0877418	−	0.996143i	$-0.472035\pi$
$269$	2.87815			0.175484			0.0877418	+	0.996143i	$0.472035\pi$
$270$	−0.981196	−	3.93062i	−0.0597137	−	0.239210i
$271$	26.7670			1.62598			0.812989	−	0.582279i	$-0.197839\pi$
$271$	26.7670			1.62598			0.812989	+	0.582279i	$0.197839\pi$
$272$	8.65255			0.524638
$273$	−26.3553			−1.59510
$274$		−	30.5760i		−	1.84716i
$275$	21.0978	−	11.2332i	1.27225	−	0.677390i
$276$		−	7.23381i		−	0.435424i
$277$	−21.3841			−1.28485			−0.642424	−	0.766349i	$-0.722071\pi$
$277$	−21.3841			−1.28485			−0.642424	+	0.766349i	$0.722071\pi$
$278$	−20.8082			−1.24799
$279$		−	6.40502i		−	0.383459i
$280$	−3.27707	−	13.1278i	−0.195842	−	0.784535i
$281$		−	3.35241i		−	0.199988i	−0.994988	−	0.0999940i	$-0.968118\pi$
$281$		−	3.35241i		−	0.199988i	0.994988	−	0.0999940i	$-0.0318824\pi$
$282$	1.85995			0.110759
$283$	−2.13042			−0.126640			−0.0633201	−	0.997993i	$-0.520169\pi$
$283$	−2.13042			−0.126640			−0.0633201	+	0.997993i	$0.520169\pi$
$284$	−15.8157			−0.938487
$285$	9.02537	−	2.25299i	0.534617	−	0.133456i
$286$	−49.0371			−2.89962
$287$		−	1.50501i		−	0.0888381i
$288$	−6.31437			−0.372078
$289$	−13.9074			−0.818082
$290$	−0.904690	−	3.62414i	−0.0531252	−	0.212817i
$291$			3.50566i			0.205505i
$292$		−	17.6903i		−	1.03524i
$293$		−	13.5524i		−	0.791739i	−0.918307	−	0.395869i	$-0.870443\pi$
$293$		−	13.5524i		−	0.791739i	0.918307	−	0.395869i	$-0.129557\pi$
$294$			26.5751i			1.54989i
$295$	−7.74433	−	31.0234i	−0.450892	−	1.80625i
$296$	−5.39327	+	5.78244i	−0.313478	+	0.336098i
$297$		−	4.78039i		−	0.277386i
$298$	−12.2041			−0.706963
$299$	−31.9350			−1.84685
$300$	3.01370	+	5.66021i	0.173996	+	0.326792i
$301$			9.76853i			0.563049i
$302$	21.7098			1.24926
$303$		−	2.63853i		−	0.151579i
$304$		−	20.4686i		−	1.17396i
$305$	3.90951	+	15.6613i	0.223858	+	0.896762i
$306$	−3.18614			−0.182139
$307$		−	9.80848i		−	0.559800i	−0.960029	−	0.279900i	$-0.909699\pi$
$307$		−	9.80848i		−	0.559800i	0.960029	−	0.279900i	$-0.0903013\pi$
$308$			28.5385i			1.62613i
$309$		−	7.93951i		−	0.451663i
$310$	6.28458	+	25.1757i	0.356940	+	1.42988i
$311$		−	9.11019i		−	0.516592i	−0.966066	−	0.258296i	$-0.916839\pi$
$311$		−	9.11019i		−	0.516592i	0.966066	−	0.258296i	$-0.0831609\pi$
$312$			7.36006i			0.416681i
$313$	31.8348			1.79941			0.899705	−	0.436499i	$-0.143782\pi$
$313$	31.8348			1.79941			0.899705	+	0.436499i	$0.143782\pi$
$314$			6.66112i			0.375909i
$315$	2.52094	+	10.0988i	0.142039	+	0.569001i
$316$		−	3.51913i		−	0.197966i
$317$		−	12.6429i		−	0.710096i	−0.934848	−	0.355048i	$-0.884465\pi$
$317$		−	12.6429i		−	0.710096i	0.934848	−	0.355048i	$-0.115535\pi$
$318$	−18.4790			−1.03625
$319$		−	4.40765i		−	0.246781i
$320$	3.47073	−	0.866394i	0.194020	−	0.0484329i
$321$	18.5702			1.03649
$322$			47.5687i			2.65090i
$323$		−	7.31592i		−	0.407069i
$324$	1.28250			0.0712502
$325$	24.9881	−	13.3046i	1.38609	−	0.738004i
$326$	−23.2607			−1.28829
$327$	11.2783			0.623692
$328$	−0.420294			−0.0232068
$329$	−4.77870			−0.263458
$330$	4.69050	+	18.7899i	0.258204	+	1.03435i
$331$		−	11.2837i		−	0.620210i	−0.950702	−	0.310105i	$-0.899636\pi$
$331$		−	11.2837i		−	0.620210i	0.950702	−	0.310105i	$-0.100364\pi$
$332$			12.3114i			0.675676i
$333$	4.14887	−	4.44824i	0.227357	−	0.243762i
$334$	−14.5285			−0.794962
$335$	−2.26806	−	9.08572i	−0.123917	−	0.496406i
$336$	22.9030			1.24946
$337$			6.53576i			0.356025i	0.984028	+	0.178013i	$0.0569668\pi$
$337$			6.53576i			0.356025i	−0.984028	+	0.178013i	$0.943033\pi$
$338$	−34.5261			−1.87797
$339$			9.91685i			0.538609i
$340$	4.89304	−	1.22144i	0.265362	−	0.0662421i
$341$			30.6185i			1.65809i
$342$			7.53719i			0.407564i
$343$		−	35.6940i		−	1.92729i
$344$	2.72798			0.147083
$345$	3.05465	+	12.2368i	0.164457	+	0.658806i
$346$		−	45.4061i		−	2.44105i
$347$	−9.70473			−0.520977			−0.260489	−	0.965477i	$-0.583884\pi$
$347$	−9.70473			−0.520977			−0.260489	+	0.965477i	$0.583884\pi$
$348$	1.18250			0.0633888
$349$	13.4098			0.717810			0.358905	−	0.933374i	$-0.383150\pi$
$349$	13.4098			0.717810			0.358905	+	0.933374i	$0.383150\pi$
$350$	−19.8177	−	37.2209i	−1.05930	−	1.98954i
$351$		−	5.66185i		−	0.302207i
$352$	30.1852			1.60887
$353$	−11.7205			−0.623817			−0.311909	−	0.950112i	$-0.600968\pi$
$353$	−11.7205			−0.623817			−0.311909	+	0.950112i	$0.600968\pi$
$354$	25.9080			1.37699
$355$	26.7539	−	6.67855i	1.41995	−	0.354461i
$356$			1.28810i			0.0682693i
$357$	8.18601			0.433249
$358$			2.16205i			0.114268i
$359$	12.2775			0.647981			0.323990	−	0.946060i	$-0.394975\pi$
$359$	12.2775			0.647981			0.323990	+	0.946060i	$0.394975\pi$
$360$	2.82021	−	0.704005i	0.148638	−	0.0371043i
$361$	1.69334			0.0891230
$362$	5.90135			0.310168
$363$			11.8521i			0.622076i
$364$			33.8008i			1.77164i
$365$	7.47015	+	29.9250i	0.391005	+	1.56635i
$366$	−13.0789			−0.683645
$367$		−	34.3685i		−	1.79402i	−0.442007	−	0.897012i	$-0.645733\pi$
$367$		−	34.3685i		−	1.79402i	0.442007	−	0.897012i	$-0.354267\pi$
$368$	27.7518			1.44666
$369$	0.323318			0.0168313
$370$	−11.9430	+	21.5552i	−0.620888	+	1.12060i
$371$	47.4772			2.46489
$372$	−8.21446			−0.425900
$373$			34.9216i			1.80817i	0.427350	+	0.904086i	$0.359447\pi$
$373$			34.9216i			1.80817i	−0.427350	+	0.904086i	$0.640553\pi$
$374$	15.2310			0.787576
$375$	−7.48817	−	8.30225i	−0.386687	−	0.428726i
$376$			1.33451i			0.0688222i
$377$		−	5.22038i		−	0.268863i
$378$	−8.43359			−0.433777
$379$	−15.2319			−0.782411			−0.391206	−	0.920303i	$-0.627942\pi$
$379$	−15.2319			−0.782411			−0.391206	+	0.920303i	$0.627942\pi$
$380$	−2.88947	−	11.5751i	−0.148227	−	0.593788i
$381$	−0.805208			−0.0412521
$382$			11.9788i			0.612886i
$383$	23.0449			1.17754			0.588769	−	0.808301i	$-0.299613\pi$
$383$	23.0449			1.17754			0.588769	+	0.808301i	$0.299613\pi$
$384$		−	9.73030i		−	0.496547i
$385$	−12.0511	−	48.2761i	−0.614181	−	2.46038i
$386$	−20.6786			−1.05251
$387$	−2.09855			−0.106675
$388$	4.49602			0.228251
$389$			17.8656i			0.905821i	0.891556	+	0.452911i	$0.149614\pi$
$389$			17.8656i			0.905821i	−0.891556	+	0.452911i	$0.850386\pi$
$390$	5.55539	+	22.2546i	0.281308	+	1.12690i
$391$	9.91907			0.501629
$392$	−19.0676			−0.963057
$393$	−0.0441248			−0.00222580
$394$		−	27.8902i		−	1.40509i
$395$	1.48604	+	5.95299i	0.0747707	+	0.299527i
$396$	−6.13087			−0.308088
$397$		−	13.0013i		−	0.652514i	−0.945281	−	0.326257i	$-0.894212\pi$
$397$		−	13.0013i		−	0.652514i	0.945281	−	0.326257i	$-0.105788\pi$
$398$		−	2.55597i		−	0.128119i
$399$		−	19.3650i		−	0.969461i
$400$	−21.7148	+	11.5618i	−1.08574	+	0.578088i
$401$		−	5.46894i		−	0.273106i	−0.990633	−	0.136553i	$-0.956398\pi$
$401$		−	5.46894i		−	0.273106i	0.990633	−	0.136553i	$-0.0436023\pi$
$402$	7.58758			0.378434
$403$			36.2643i			1.80645i
$404$	−3.38392			−0.168356
$405$	−2.16949	+	0.541568i	−0.107803	+	0.0269107i
$406$	−7.77600			−0.385916
$407$	−19.8332	+	21.2644i	−0.983096	+	1.05403i
$408$		−	2.28605i		−	0.113176i
$409$		−	7.48986i		−	0.370350i	−0.982706	−	0.185175i	$-0.940715\pi$
$409$		−	7.48986i		−	0.370350i	0.982706	−	0.185175i	$-0.0592852\pi$
$410$	−1.27084	+	0.317239i	−0.0627624	+	0.0156673i
$411$	−16.8763			−0.832448
$412$	−10.1824			−0.501653
$413$	−66.5642			−3.27541
$414$	−10.2191			−0.502240
$415$	−5.19879	−	20.8261i	−0.255199	−	1.02231i
$416$	35.7510			1.75284
$417$			11.4850i			0.562423i
$418$		−	36.0307i		−	1.76232i
$419$	9.44368			0.461354			0.230677	−	0.973030i	$-0.425906\pi$
$419$	9.44368			0.461354			0.230677	+	0.973030i	$0.425906\pi$
$420$	12.9517	−	3.23312i	0.631978	−	0.157760i
$421$			35.8879i			1.74907i	0.484962	+	0.874535i	$0.338834\pi$
$421$			35.8879i			1.74907i	−0.484962	+	0.874535i	$0.661166\pi$
$422$	−20.6446			−1.00496
$423$		−	1.02660i		−	0.0499148i
$424$		−	13.2586i		−	0.643895i
$425$	−7.76133	+	4.13241i	−0.376480	+	0.200452i
$426$			22.3425i			1.08250i
$427$	33.6030			1.62617
$428$		−	23.8163i		−	1.15121i
$429$			27.0659i			1.30675i
$430$	8.24860	−	2.05909i	0.397783	−	0.0992981i
$431$		−	26.6887i		−	1.28555i	−0.766055	−	0.642775i	$-0.777783\pi$
$431$		−	26.6887i		−	1.28555i	0.766055	−	0.642775i	$-0.222217\pi$
$432$			4.92019i			0.236723i
$433$		−	10.3216i		−	0.496025i	−0.968757	−	0.248012i	$-0.920223\pi$
$433$		−	10.3216i		−	0.496025i	0.968757	−	0.248012i	$-0.0797774\pi$
$434$	54.0173			2.59291
$435$	−2.00033	+	0.499341i	−0.0959086	+	0.0239416i
$436$		−	14.4645i		−	0.692722i
$437$		−	23.4647i		−	1.12247i
$438$	−24.9907			−1.19410
$439$			25.4796i			1.21607i	0.793909	+	0.608037i	$0.208043\pi$
$439$			25.4796i			1.21607i	−0.793909	+	0.608037i	$0.791957\pi$
$440$	−13.4817	+	3.36542i	−0.642715	+	0.160440i
$441$	14.6681			0.698479
$442$	18.0395			0.858049
$443$		−	2.70684i		−	0.128606i	−0.997930	−	0.0643028i	$-0.979518\pi$
$443$		−	2.70684i		−	0.128606i	0.997930	−	0.0643028i	$-0.0204824\pi$
$444$	−5.70489	−	5.32094i	−0.270742	−	0.252520i
$445$	−0.543933	−	2.17897i	−0.0257849	−	0.103293i
$446$		−	13.1464i		−	0.622499i
$447$			6.73600i			0.318602i
$448$		−	7.44684i		−	0.351830i
$449$		−	18.2097i		−	0.859369i	−0.902979	−	0.429684i	$-0.858625\pi$
$449$		−	18.2097i		−	0.859369i	0.902979	−	0.429684i	$-0.141375\pi$
$450$	7.99607	−	4.25740i	0.376938	−	0.200696i
$451$	−1.54559			−0.0727789
$452$	12.7184			0.598222
$453$		−	11.9827i		−	0.562995i
$454$	−9.33104			−0.437927
$455$	−14.2732	−	57.1777i	−0.669139	−	2.68053i
$456$	−5.40791			−0.253249
$457$	39.6572			1.85509			0.927543	−	0.373717i	$-0.121917\pi$
$457$	39.6572			1.85509			0.927543	+	0.373717i	$0.121917\pi$
$458$	32.7463			1.53013
$459$			1.75858i			0.0820835i
$460$	15.6937	−	3.91760i	0.731723	−	0.182659i
$461$		−	3.22951i		−	0.150413i	−0.997168	−	0.0752066i	$-0.976038\pi$
$461$		−	3.22951i		−	0.150413i	0.997168	−	0.0752066i	$-0.0239616\pi$
$462$	40.3159			1.87566
$463$	−24.9177			−1.15802			−0.579012	−	0.815319i	$-0.696562\pi$
$463$	−24.9177			−1.15802			−0.579012	+	0.815319i	$0.696562\pi$
$464$			4.53655i			0.210604i
$465$	13.8957	−	3.46876i	0.644395	−	0.160860i
$466$		−	24.6472i		−	1.14176i
$467$	12.4391			0.575613			0.287806	−	0.957689i	$-0.407074\pi$
$467$	12.4391			0.575613			0.287806	+	0.957689i	$0.407074\pi$
$468$	−7.26134			−0.335656
$469$	−19.4944			−0.900169
$470$	1.00729	+	4.03516i	0.0464629	+	0.186128i
$471$	3.67659			0.169408
$472$			18.5889i			0.855623i
$473$	10.0319			0.461267
$474$	−4.97141			−0.228344
$475$	9.77571	+	18.3603i	0.448540	+	0.842430i
$476$		−	10.4986i		−	0.481201i
$477$			10.1994i			0.466999i
$478$		−	12.8363i		−	0.587120i
$479$			37.4103i			1.70932i	0.519188	+	0.854660i	$0.326234\pi$
$479$			37.4103i			1.70932i	−0.519188	+	0.854660i	$0.673766\pi$
$480$	−3.41966	−	13.6990i	−0.156086	−	0.625270i
$481$	−23.4903	+	25.1853i	−1.07107	+	1.14835i
$482$		−	12.5269i		−	0.570585i
$483$	26.2554			1.19466
$484$	15.2004			0.690928
$485$	−7.60550	+	1.89855i	−0.345348	+	0.0862089i
$486$		−	1.81177i		−	0.0821835i
$487$	1.77283			0.0803346			0.0401673	−	0.999193i	$-0.487211\pi$
$487$	1.77283			0.0803346			0.0401673	+	0.999193i	$0.487211\pi$
$488$		−	9.38407i		−	0.424797i
$489$			12.8387i			0.580586i
$490$	−57.6545	+	14.3922i	−2.60457	+	0.650175i
$491$	14.3636			0.648218			0.324109	−	0.946020i	$-0.394935\pi$
$491$	14.3636			0.648218			0.324109	+	0.946020i	$0.394935\pi$
$492$		−	0.414657i		−	0.0186942i
$493$			1.62146i			0.0730268i
$494$		−	42.6744i		−	1.92001i
$495$	10.3710	−	2.58891i	0.466143	−	0.116363i
$496$		−	31.5139i		−	1.41502i
$497$		−	57.4036i		−	2.57490i
$498$	17.3921			0.779358
$499$			36.3117i			1.62554i	0.582588	+	0.812768i	$0.302040\pi$
$499$			36.3117i			1.62554i	−0.582588	+	0.812768i	$0.697960\pi$
$500$	−10.6477	+	9.60359i	−0.476178	+	0.429486i
$501$			8.01894i			0.358260i
$502$			11.7094i			0.522617i
$503$	28.5348			1.27230			0.636151	−	0.771564i	$-0.280525\pi$
$503$	28.5348			1.27230			0.636151	+	0.771564i	$0.280525\pi$
$504$		−	6.05108i		−	0.269536i
$505$	5.72427	−	1.42894i	0.254726	−	0.0635871i
$506$	48.8511			2.17170
$507$			19.0566i			0.846332i
$508$			1.03268i			0.0458179i
$509$	−15.9477			−0.706870			−0.353435	−	0.935459i	$-0.614986\pi$
$509$	−15.9477			−0.706870			−0.353435	+	0.935459i	$0.614986\pi$
$510$	−1.72551	−	6.91231i	−0.0764070	−	0.306082i
$511$	64.2075			2.84037
$512$	−18.2760			−0.807694
$513$	4.16013			0.183674
$514$	16.5759			0.731130
$515$	17.2247	−	4.29979i	0.759012	−	0.189471i
$516$			2.69140i			0.118482i
$517$			4.90753i			0.215833i
$518$	37.5147	+	34.9899i	1.64830	+	1.53737i
$519$	−25.0618			−1.10009
$520$	−15.9676	+	3.98598i	−0.700226	+	0.174797i
$521$	−3.85259			−0.168785			−0.0843925	−	0.996433i	$-0.526895\pi$
$521$	−3.85259			−0.168785			−0.0843925	+	0.996433i	$0.526895\pi$
$522$		−	1.67050i		−	0.0731158i
$523$	−22.8750			−1.00025			−0.500126	−	0.865952i	$-0.666713\pi$
$523$	−22.8750			−1.00025			−0.500126	+	0.865952i	$0.666713\pi$
$524$			0.0565901i			0.00247215i
$525$	−20.5440	+	10.9383i	−0.896611	+	0.477389i
$526$		−	32.0762i		−	1.39859i
$527$		−	11.2637i		−	0.490656i
$528$		−	23.5204i		−	1.02360i
$529$	8.81392			0.383214
$530$	−10.0076	−	40.0900i	−0.434703	−	1.74140i
$531$		−	14.2998i		−	0.620559i
$532$	−24.8356			−1.07676
$533$	−1.83058			−0.0792912
$534$	1.81968			0.0787452
$535$	10.0570	+	40.2879i	0.434804	+	1.74180i
$536$			5.44407i			0.235148i
$537$	1.19334			0.0514964
$538$	−5.21453			−0.224814
$539$	−70.1190			−3.02024
$540$	0.694563	+	2.78238i	0.0298892	+	0.119735i
$541$		−	17.2598i		−	0.742056i	−0.928622	−	0.371028i	$-0.879005\pi$
$541$		−	17.2598i		−	0.742056i	0.928622	−	0.371028i	$-0.120995\pi$
$542$	−48.4955			−2.08306
$543$		−	3.25723i		−	0.139781i
$544$	−11.1043			−0.476094
$545$	6.10797	+	24.4682i	0.261637	+	1.04810i
$546$	47.7497			2.04350
$547$	−13.2745			−0.567576			−0.283788	−	0.958887i	$-0.591591\pi$
$547$	−13.2745			−0.567576			−0.283788	+	0.958887i	$0.591591\pi$
$548$			21.6439i			0.924583i
$549$			7.21886i			0.308093i
$550$	−38.2243	+	20.3520i	−1.62989	+	0.867813i
$551$	3.83575			0.163409
$552$		−	7.33215i		−	0.312077i
$553$	12.7728			0.543155
$554$	38.7431			1.64604
$555$	11.8973	+	6.59192i	0.505014	+	0.279811i
$556$	14.7296			0.624672
$557$	3.11593			0.132026			0.0660131	−	0.997819i	$-0.478972\pi$
$557$	3.11593			0.132026			0.0660131	+	0.997819i	$0.478972\pi$
$558$			11.6044i			0.491254i
$559$	11.8817			0.502541
$560$	12.4035	+	49.6879i	0.524145	+	2.09970i
$561$		−	8.40670i		−	0.354931i
$562$			6.07379i			0.256207i
$563$	35.7440			1.50643			0.753214	−	0.657775i	$-0.228502\pi$
$563$	35.7440			1.50643			0.753214	+	0.657775i	$0.228502\pi$
$564$	−1.31661			−0.0554394
$565$	−21.5145	+	5.37065i	−0.905123	+	0.225945i
$566$	3.85982			0.162241
$567$			4.65490i			0.195487i
$568$	−16.0307			−0.672632
$569$		−	17.5110i		−	0.734098i	−0.930202	−	0.367049i	$-0.880368\pi$
$569$		−	17.5110i		−	0.734098i	0.930202	−	0.367049i	$-0.119632\pi$
$570$	−16.3519	+	4.08190i	−0.684905	+	0.170972i
$571$	0.508897			0.0212967			0.0106483	−	0.999943i	$-0.496610\pi$
$571$	0.508897			0.0212967			0.0106483	+	0.999943i	$0.496610\pi$
$572$	34.7121			1.45138
$573$	6.61164			0.276205
$574$			2.72673i			0.113812i
$575$	−24.8933	+	13.2541i	−1.03812	+	0.552734i
$576$	1.59979			0.0666578
$577$	46.8022			1.94840			0.974200	−	0.225686i	$-0.0724622\pi$
$577$	46.8022			1.94840			0.974200	+	0.225686i	$0.0724622\pi$
$578$	25.1970			1.04806
$579$			11.4135i			0.474329i
$580$	0.640406	+	2.56543i	0.0265914	+	0.106524i
$581$	−44.6847			−1.85383
$582$		−	6.35144i		−	0.263276i
$583$		−	48.7572i		−	2.01932i
$584$		−	17.9308i		−	0.741980i
$585$	12.2834	−	3.06628i	0.507854	−	0.126775i
$586$			24.5538i			1.01431i
$587$	−38.1443			−1.57438			−0.787192	−	0.616708i	$-0.788466\pi$
$587$	−38.1443			−1.57438			−0.787192	+	0.616708i	$0.788466\pi$
$588$		−	18.8118i		−	0.775786i
$589$	−26.6457			−1.09792
$590$	14.0309	+	56.2071i	0.577644	+	2.31401i
$591$	−15.3939			−0.633220
$592$	20.4132	−	21.8862i	0.838979	−	0.899518i
$593$		−	39.4240i		−	1.61895i	−0.587156	−	0.809474i	$-0.699752\pi$
$593$		−	39.4240i		−	1.61895i	0.587156	−	0.809474i	$-0.300248\pi$
$594$			8.66096i			0.355363i
$595$	4.43328	+	17.7595i	0.181747	+	0.728068i
$596$	8.63895			0.353865
$597$	−1.41076			−0.0577385
$598$	57.8588			2.36602
$599$	3.14044			0.128315			0.0641574	−	0.997940i	$-0.479564\pi$
$599$	3.14044			0.128315			0.0641574	+	0.997940i	$0.479564\pi$
$600$	3.05467	+	5.73716i	0.124706	+	0.234218i
$601$	28.4408			1.16012			0.580062	−	0.814573i	$-0.303028\pi$
$601$	28.4408			1.16012			0.580062	+	0.814573i	$0.303028\pi$
$602$		−	17.6983i		−	0.721329i
$603$		−	4.18794i		−	0.170546i
$604$	−15.3678			−0.625307
$605$	−25.7132	+	6.41875i	−1.04539	+	0.260959i
$606$			4.78040i			0.194190i
$607$	20.4200			0.828822			0.414411	−	0.910090i	$-0.363988\pi$
$607$	20.4200			0.828822			0.414411	+	0.910090i	$0.363988\pi$
$608$			26.2686i			1.06533i
$609$			4.29194i			0.173918i
$610$	−7.08312	−	28.3746i	−0.286787	−	1.14885i
$611$			5.81243i			0.235146i
$612$	2.25538			0.0911685
$613$			17.6593i			0.713252i	0.934247	+	0.356626i	$0.116073\pi$
$613$			17.6593i			0.713252i	−0.934247	+	0.356626i	$0.883927\pi$
$614$			17.7707i			0.717167i
$615$	0.175099	+	0.701437i	0.00706067	+	0.0282847i
$616$			28.9265i			1.16548i
$617$			39.7788i			1.60143i	0.599043	+	0.800717i	$0.295548\pi$
$617$			39.7788i			1.60143i	−0.599043	+	0.800717i	$0.704452\pi$
$618$			14.3846i			0.578632i
$619$	12.0632			0.484860			0.242430	−	0.970169i	$-0.422055\pi$
$619$	12.0632			0.484860			0.242430	+	0.970169i	$0.422055\pi$
$620$	−4.44869	−	17.8212i	−0.178664	−	0.715717i
$621$			5.64038i			0.226341i
$622$			16.5056i			0.661812i
$623$	−4.67522			−0.187309
$624$		−	27.8574i		−	1.11519i
$625$	13.9563	−	20.7418i	0.558253	−	0.829671i
$626$	−57.6773			−2.30525
$627$	−19.8870			−0.794212
$628$		−	4.71523i		−	0.188158i
$629$	7.29612	−	7.82259i	0.290915	−	0.311907i
$630$	−4.56737	−	18.2966i	−0.181968	−	0.728955i
$631$			24.0166i			0.956087i	0.878336	+	0.478043i	$0.158654\pi$
$631$			24.0166i			0.956087i	−0.878336	+	0.478043i	$0.841346\pi$
$632$		−	3.56697i		−	0.141886i
$633$			11.3947i			0.452899i
$634$			22.9060i			0.909714i
$635$	−0.436075	−	1.74689i	−0.0173051	−	0.0693234i
$636$	13.0808			0.518686
$637$	−83.0484			−3.29050
$638$			7.98564i			0.316155i
$639$	12.3319			0.487841
$640$	21.1098	−	5.26962i	0.834439	−	0.208300i
$641$	−16.5692			−0.654444			−0.327222	−	0.944947i	$-0.606112\pi$
$641$	−16.5692			−0.654444			−0.327222	+	0.944947i	$0.606112\pi$
$642$	−33.6449			−1.32786
$643$	31.7409			1.25174			0.625869	−	0.779928i	$-0.284745\pi$
$643$	31.7409			1.25174			0.625869	+	0.779928i	$0.284745\pi$
$644$		−	33.6726i		−	1.32689i
$645$	−1.13651	−	4.55279i	−0.0447500	−	0.179266i
$646$			13.2547i			0.521501i
$647$	42.2257			1.66007			0.830033	−	0.557715i	$-0.188322\pi$
$647$	42.2257			1.66007			0.830033	+	0.557715i	$0.188322\pi$
$648$	1.29994			0.0510664
$649$			68.3587i			2.68332i
$650$	−45.2726	+	24.1048i	−1.77574	+	0.945467i
$651$		−	29.8147i		−	1.16853i
$652$	16.4657			0.644845
$653$	23.2076			0.908183			0.454092	−	0.890955i	$-0.349964\pi$
$653$	23.2076			0.908183			0.454092	+	0.890955i	$0.349964\pi$
$654$	−20.4337			−0.799020
$655$	−0.0238966	−	0.0957284i	−0.000933716	−	0.00374042i
$656$	1.59079			0.0621098
$657$			13.7935i			0.538138i
$658$	8.65789			0.337520
$659$	−30.0028			−1.16874			−0.584371	−	0.811487i	$-0.698659\pi$
$659$	−30.0028			−1.16874			−0.584371	+	0.811487i	$0.698659\pi$
$660$	−3.32028	−	13.3009i	−0.129242	−	0.517736i
$661$		−	37.6589i		−	1.46476i	−0.680895	−	0.732381i	$-0.738409\pi$
$661$		−	37.6589i		−	1.46476i	0.680895	−	0.732381i	$-0.261591\pi$
$662$			20.4435i			0.794559i
$663$		−	9.95682i		−	0.386691i
$664$			12.4788i			0.484270i
$665$	42.0122	−	10.4874i	1.62916	−	0.406686i
$666$	−7.51679	+	8.05919i	−0.291270	+	0.312287i
$667$			5.20059i			0.201368i
$668$	10.2843			0.397912
$669$	−7.25610			−0.280537
$670$	4.10919	+	16.4612i	0.158752	+	0.635952i
$671$		−	34.5090i		−	1.33220i
$672$	−29.3927			−1.13385
$673$		−	11.3191i		−	0.436320i	−0.975913	−	0.218160i	$-0.929995\pi$
$673$		−	11.3191i		−	0.436320i	0.975913	−	0.218160i	$-0.0700055\pi$
$674$		−	11.8413i		−	0.456109i
$675$	−2.34986	−	4.41341i	−0.0904461	−	0.169872i
$676$	24.4401			0.940005
$677$			2.75270i			0.105795i	0.998600	+	0.0528974i	$0.0168456\pi$
$677$			2.75270i			0.105795i	−0.998600	+	0.0528974i	$0.983154\pi$
$678$		−	17.9670i		−	0.690019i
$679$			16.3185i			0.626246i
$680$	4.95956	−	1.23805i	0.190191	−	0.0474770i
$681$			5.15024i			0.197358i
$682$		−	55.4736i		−	2.12419i
$683$	−18.7867			−0.718854			−0.359427	−	0.933173i	$-0.617028\pi$
$683$	−18.7867			−0.718854			−0.359427	+	0.933173i	$0.617028\pi$
$684$		−	5.33538i		−	0.204003i
$685$	−9.13968	−	36.6131i	−0.349209	−	1.39891i
$686$			64.6692i			2.46908i
$687$		−	18.0742i		−	0.689574i
$688$	−10.3253			−0.393647
$689$		−	57.7476i		−	2.20001i
$690$	−5.53432	−	22.1702i	−0.210688	−	0.844005i
$691$	−34.8835			−1.32703			−0.663516	−	0.748162i	$-0.730937\pi$
$691$	−34.8835			−1.32703			−0.663516	+	0.748162i	$0.730937\pi$
$692$			32.1418i			1.22185i
$693$		−	22.2522i		−	0.845292i
$694$	17.5827			0.667431
$695$	−24.9167	+	6.21992i	−0.945143	+	0.235935i
$696$	1.19858			0.0454320
$697$	0.568581			0.0215365
$698$	−24.2954			−0.919596
$699$	−13.6039			−0.514548
$700$	14.0285	+	26.3477i	0.530226	+	0.995848i
$701$		−	26.5403i		−	1.00241i	−0.865328	−	0.501207i	$-0.832890\pi$
$701$		−	26.5403i		−	1.00241i	0.865328	−	0.501207i	$-0.167110\pi$
$702$			10.2580i			0.387162i
$703$	−18.5053	−	17.2598i	−0.697939	−	0.650967i
$704$	−7.64761			−0.288230
$705$	2.22719	−	0.555972i	0.0838810	−	0.0209391i
$706$	21.2348			0.799180
$707$		−	12.2821i		−	0.461914i
$708$	−18.3396			−0.689243
$709$		−	31.2654i		−	1.17420i	−0.809516	−	0.587098i	$-0.800270\pi$
$709$		−	31.2654i		−	1.17420i	0.809516	−	0.587098i	$-0.199730\pi$
$710$	−48.4719	+	12.1000i	−1.81912	+	0.454104i
$711$			2.74395i			0.102906i
$712$			1.30561i			0.0489300i
$713$		−	36.1268i		−	1.35296i
$714$	−14.8311			−0.555042
$715$	−58.7192	+	14.6580i	−2.19598	+	0.548179i
$716$		−	1.53046i		−	0.0571960i
$717$	−7.08497			−0.264593
$718$	−22.2440			−0.830137
$719$	−7.57894			−0.282647			−0.141323	−	0.989963i	$-0.545136\pi$
$719$	−7.57894			−0.282647			−0.141323	+	0.989963i	$0.545136\pi$
$720$	−10.6743	+	2.66462i	−0.397809	+	0.0993045i
$721$		−	36.9576i		−	1.37637i
$722$	−3.06793			−0.114177
$723$	−6.91419			−0.257142
$724$	−4.17741			−0.155252
$725$	−2.16663	−	4.06928i	−0.0804668	−	0.151129i
$726$		−	21.4733i		−	0.796950i
$727$	3.17071			0.117595			0.0587975	−	0.998270i	$-0.481273\pi$
$727$	3.17071			0.117595			0.0587975	+	0.998270i	$0.481273\pi$
$728$			34.2603i			1.26977i
$729$	−1.00000			−0.0370370
$730$	−13.5342	−	54.2172i	−0.500922	−	2.00667i
$731$	−3.69047			−0.136497
$732$	9.25821			0.342193
$733$			47.2860i			1.74655i	0.487228	+	0.873275i	$0.338008\pi$
$733$			47.2860i			1.74655i	−0.487228	+	0.873275i	$0.661992\pi$
$734$			62.2678i			2.29835i
$735$	7.94375	+	31.8222i	0.293010	+	1.17378i
$736$	−35.6155			−1.31280
$737$			20.0200i			0.737446i
$738$	−0.585778			−0.0215628
$739$	27.6645			1.01766			0.508828	−	0.860868i	$-0.330079\pi$
$739$	27.6645			1.01766			0.508828	+	0.860868i	$0.330079\pi$
$740$	8.45415	−	15.2584i	0.310781	−	0.560909i
$741$	−23.5540			−0.865279
$742$	−86.0176			−3.15781
$743$		−	3.52766i		−	0.129417i	−0.997904	−	0.0647087i	$-0.979388\pi$
$743$		−	3.52766i		−	0.129417i	0.997904	−	0.0647087i	$-0.0206118\pi$
$744$	−8.32613			−0.305251
$745$	−14.6137	+	3.64801i	−0.535405	+	0.133653i
$746$		−	63.2699i		−	2.31647i
$747$		−	9.59951i		−	0.351228i
$748$	−10.7816			−0.394215
$749$	86.4424			3.15853
$750$	13.5668	+	15.0418i	0.495390	+	0.549247i
$751$	16.2203			0.591887			0.295944	−	0.955205i	$-0.404366\pi$
$751$	16.2203			0.591887			0.295944	+	0.955205i	$0.404366\pi$
$752$		−	5.05105i		−	0.184193i
$753$	6.46298			0.235524
$754$			9.45812i			0.344445i
$755$	25.9963	−	6.48944i	0.946104	−	0.236175i
$756$	5.96992			0.217124
$757$	−8.94633			−0.325160			−0.162580	−	0.986695i	$-0.551982\pi$
$757$	−8.94633			−0.325160			−0.162580	+	0.986695i	$0.551982\pi$
$758$	27.5967			1.00236
$759$		−	26.9632i		−	0.978704i
$760$	−2.92875	−	11.7324i	−0.106237	−	0.425580i
$761$	−10.0040			−0.362644			−0.181322	−	0.983424i	$-0.558038\pi$
$761$	−10.0040			−0.362644			−0.181322	+	0.983424i	$0.558038\pi$
$762$	1.45885			0.0528486
$763$	52.4993			1.90060
$764$		−	8.47944i		−	0.306775i
$765$	−3.81523	+	0.952391i	−0.137940	+	0.0344338i
$766$	−41.7520			−1.50856
$767$			80.9635i			2.92342i
$768$			20.8286i			0.751588i
$769$			13.3815i			0.482549i	0.970457	+	0.241274i	$0.0775654\pi$
$769$			13.3815i			0.482549i	−0.970457	+	0.241274i	$0.922435\pi$
$770$	21.8338	+	87.4650i	0.786835	+	3.15202i
$771$		−	9.14900i		−	0.329493i
$772$	14.6379			0.526828
$773$			34.7422i			1.24959i	0.780789	+	0.624795i	$0.214817\pi$
$773$			34.7422i			1.24959i	−0.780789	+	0.624795i	$0.785183\pi$
$774$	3.80208			0.136663
$775$	15.0509	+	28.2680i	0.540644	+	1.01542i
$776$	4.55714			0.163592
$777$	19.3126	−	20.7061i	0.692834	−	0.742828i
$778$		−	32.3683i		−	1.16046i
$779$		−	1.34505i		−	0.0481912i
$780$	−3.93251	−	15.7534i	−0.140807	−	0.564064i
$781$	−58.9512			−2.10944
$782$	−17.9710			−0.642643
$783$	−0.922027			−0.0329506
$784$	72.1696			2.57749
$785$	1.99112	+	7.97634i	0.0710663	+	0.284688i
$786$	0.0799438			0.00285150
$787$		−	24.9565i		−	0.889604i	−0.895629	−	0.444802i	$-0.853274\pi$
$787$		−	24.9565i		−	0.889604i	0.895629	−	0.444802i	$-0.146726\pi$
$788$			19.7427i			0.703305i
$789$	−17.7044			−0.630292
$790$	−2.69236	−	10.7854i	−0.0957897	−	0.383728i
$791$			46.1619i			1.64133i
$792$	−6.21421			−0.220812
$793$		−	40.8721i		−	1.45141i
$794$			23.5553i			0.835945i
$795$	−22.1276	+	5.52368i	−0.784784	+	0.195905i
$796$			1.80930i			0.0641290i
$797$	29.5002			1.04495			0.522475	−	0.852654i	$-0.325009\pi$
$797$	29.5002			1.04495			0.522475	+	0.852654i	$0.325009\pi$
$798$			35.0848i			1.24199i
$799$		−	1.80535i		−	0.0638687i
$800$	27.8679	−	14.8379i	0.985279	−	0.524598i
$801$		−	1.00437i		−	0.0354875i
$802$			9.90844i			0.349879i
$803$		−	65.9386i		−	2.32692i
$804$	−5.37105			−0.189422
$805$	14.2191	+	56.9609i	0.501157	+	2.00761i
$806$		−	65.7025i		−	2.31427i
$807$			2.87815i			0.101316i
$808$	−3.42992			−0.120664
$809$			17.1501i			0.602965i	0.953472	+	0.301483i	$0.0974815\pi$
$809$			17.1501i			0.602965i	−0.953472	+	0.301483i	$0.902518\pi$
$810$	3.93062	−	0.981196i	0.138108	−	0.0344757i
$811$	41.7209			1.46502			0.732509	−	0.680757i	$-0.238349\pi$
$811$	41.7209			1.46502			0.732509	+	0.680757i	$0.238349\pi$
$812$	5.50443			0.193168
$813$			26.7670i			0.938759i
$814$	35.9332	−	38.5261i	1.25946	−	1.35034i
$815$	−27.8535	+	6.95303i	−0.975664	+	0.243554i
$816$			8.65255i			0.302900i
$817$			8.73023i			0.305432i
$818$			13.5699i			0.474460i
$819$		−	26.3553i		−	0.920930i
$820$	0.899595	−	0.224565i	0.0314152	−	0.00784215i
$821$	32.1714			1.12279			0.561395	−	0.827548i	$-0.310265\pi$
$821$	32.1714			1.12279			0.561395	+	0.827548i	$0.310265\pi$
$822$	30.5760			1.06646
$823$		−	35.0519i		−	1.22183i	−0.791695	−	0.610916i	$-0.790801\pi$
$823$		−	35.0519i		−	1.22183i	0.791695	−	0.610916i	$-0.209199\pi$
$824$	−10.3209			−0.359545
$825$	11.2332	+	21.0978i	0.391091	+	0.734532i
$826$	120.599			4.19617
$827$	17.5469			0.610165			0.305083	−	0.952326i	$-0.401316\pi$
$827$	17.5469			0.610165			0.305083	+	0.952326i	$0.401316\pi$
$828$	7.23381			0.251392
$829$			41.2013i			1.43098i	0.698623	+	0.715490i	$0.253797\pi$
$829$			41.2013i			1.43098i	−0.698623	+	0.715490i	$0.746203\pi$
$830$	9.41900	+	37.7320i	0.326938	+	1.30970i
$831$		−	21.3841i		−	0.741807i
$832$	−9.05776			−0.314021
$833$	25.7949			0.893742
$834$		−	20.8082i		−	0.720528i
$835$	−17.3970	+	4.34280i	−0.602049	+	0.150289i
$836$			25.5052i			0.882115i
$837$	6.40502			0.221390
$838$	−17.1097			−0.591046
$839$	33.1179			1.14336			0.571679	−	0.820478i	$-0.306292\pi$
$839$	33.1179			1.14336			0.571679	+	0.820478i	$0.306292\pi$
$840$	13.1278	−	3.27707i	0.452951	−	0.113070i
$841$	28.1499			0.970685
$842$		−	65.0206i		−	2.24076i
$843$	3.35241			0.115463
$844$	14.6138			0.503026
$845$	−41.3431	+	10.3204i	−1.42225	+	0.355034i
$846$			1.85995i			0.0639465i
$847$			55.1705i			1.89568i
$848$			50.1831i			1.72329i
$849$		−	2.13042i		−	0.0731158i
$850$	14.0617	−	7.48698i	0.482313	−	0.256801i
$851$	23.4012	−	25.0898i	0.802183	−	0.860067i
$852$		−	15.8157i		−	0.541836i
$853$	−38.7440			−1.32657			−0.663285	−	0.748367i	$-0.730838\pi$
$853$	−38.7440			−1.32657			−0.663285	+	0.748367i	$0.730838\pi$
$854$	−60.8809			−2.08330
$855$	2.25299	+	9.02537i	0.0770508	+	0.308661i
$856$		−	24.1401i		−	0.825092i
$857$	21.3340			0.728755			0.364377	−	0.931251i	$-0.381282\pi$
$857$	21.3340			0.728755			0.364377	+	0.931251i	$0.381282\pi$
$858$		−	49.0371i		−	1.67410i
$859$		−	1.49935i		−	0.0511573i	−0.999673	−	0.0255786i	$-0.991857\pi$
$859$		−	1.49935i		−	0.0511573i	0.999673	−	0.0255786i	$-0.00814282\pi$
$860$	−5.83897	+	1.45757i	−0.199107	+	0.0497029i
$861$	1.50501			0.0512907
$862$			48.3537i			1.64693i
$863$		−	15.8730i		−	0.540324i	−0.962815	−	0.270162i	$-0.912923\pi$
$863$		−	15.8730i		−	0.540324i	0.962815	−	0.270162i	$-0.0870772\pi$
$864$		−	6.31437i		−	0.214819i
$865$	−13.5727	−	54.3714i	−0.461484	−	1.84868i
$866$			18.7004i			0.635464i
$867$		−	13.9074i		−	0.472320i
$868$	−38.2374			−1.29786
$869$		−	13.1172i		−	0.444969i
$870$	3.62414	−	0.904690i	0.122870	−	0.0306719i
$871$			23.7115i			0.803434i
$872$		−	14.6611i		−	0.496488i
$873$	−3.50566			−0.118649
$874$			42.5126i			1.43801i
$875$	−34.8566	−	38.6461i	−1.17837	−	1.30648i
$876$	17.6903			0.597699
$877$			15.2265i			0.514161i	0.966390	+	0.257081i	$0.0827606\pi$
$877$			15.2265i			0.514161i	−0.966390	+	0.257081i	$0.917239\pi$
$878$		−	46.1631i		−	1.55793i
$879$	13.5524			0.457111
$880$	51.0275	−	12.7379i	1.72014	−	0.429395i
$881$	−33.8947			−1.14194			−0.570971	−	0.820970i	$-0.693433\pi$
$881$	−33.8947			−1.14194			−0.570971	+	0.820970i	$0.693433\pi$
$882$	−26.5751			−0.894830
$883$	−17.8486			−0.600653			−0.300326	−	0.953837i	$-0.597096\pi$
$883$	−17.8486			−0.600653			−0.300326	+	0.953837i	$0.597096\pi$
$884$	−12.7697			−0.429490
$885$	31.0234	−	7.74433i	1.04284	−	0.260323i
$886$			4.90416i			0.164758i
$887$		−	7.44248i		−	0.249894i	−0.992163	−	0.124947i	$-0.960124\pi$
$887$		−	7.44248i		−	0.249894i	0.992163	−	0.124947i	$-0.0398761\pi$
$888$	−5.78244	−	5.39327i	−0.194046	−	0.180986i
$889$	−3.74816			−0.125709
$890$	0.985480	+	3.94778i	0.0330334	+	0.132330i
$891$	4.78039			0.160149
$892$			9.30597i			0.311587i
$893$	−4.27077			−0.142916
$894$		−	12.2041i		−	0.408165i
$895$	0.646274	+	2.58894i	0.0216026	+	0.0865387i
$896$		−	45.2935i		−	1.51315i
$897$		−	31.9350i		−	1.06628i
$898$			32.9917i			1.10095i
$899$	5.90560			0.196963
$900$	−5.66021	+	3.01370i	−0.188674	+	0.100457i
$901$			17.9365i			0.597551i
$902$	2.80025			0.0932380
$903$	−9.76853			−0.325076
$904$	12.8913			0.428758
$905$	7.06654	−	1.76401i	0.234900	−	0.0586378i
$906$			21.7098i			0.721261i
$907$	−41.1035			−1.36482			−0.682410	−	0.730970i	$-0.739068\pi$
$907$	−41.1035			−1.36482			−0.682410	+	0.730970i	$0.739068\pi$
$908$	6.60520			0.219201
$909$	2.63853			0.0875144
$910$	25.8598	+	103.593i	0.857242	+	3.43407i
$911$			42.7802i			1.41737i	0.705525	+	0.708685i	$0.250711\pi$
$911$			42.7802i			1.41737i	−0.705525	+	0.708685i	$0.749289\pi$
$912$	20.4686			0.677784
$913$			45.8894i			1.51872i
$914$	−71.8496			−2.37658
$915$	−15.6613	+	3.90951i	−0.517746	+	0.129244i
$916$	−23.1802			−0.765896
$917$	−0.205396			−0.00678278
$918$		−	3.18614i		−	0.105158i
$919$			4.35973i			0.143814i	0.997411	+	0.0719070i	$0.0229085\pi$
$919$			4.35973i			0.143814i	−0.997411	+	0.0719070i	$0.977092\pi$
$920$	15.9071	−	3.97086i	0.524440	−	0.130915i
$921$	9.80848			0.323201
$922$			5.85112i			0.192696i
$923$	−69.8212			−2.29819
$924$	−28.5385			−0.938849
$925$	−7.85791	+	29.3812i	−0.258366	+	0.966047i
$926$	45.1451			1.48356
$927$	7.93951			0.260768
$928$		−	5.82202i		−	0.191117i
$929$	12.6061			0.413593			0.206796	−	0.978384i	$-0.433696\pi$
$929$	12.6061			0.413593			0.206796	+	0.978384i	$0.433696\pi$
$930$	−25.1757	+	6.28458i	−0.825544	+	0.206080i
$931$		−	61.0210i		−	1.99988i
$932$			17.4471i			0.571498i
$933$	9.11019			0.298254
$934$	−22.5368			−0.737425
$935$	18.2383	−	4.55280i	0.596456	−	0.148893i
$936$	−7.36006			−0.240571
$937$			9.93947i			0.324708i	0.986733	+	0.162354i	$0.0519087\pi$
$937$			9.93947i			0.324708i	−0.986733	+	0.162354i	$0.948091\pi$
$938$	35.3194			1.15322
$939$			31.8348i			1.03889i
$940$	−0.713035	−	2.85638i	−0.0232567	−	0.0931649i
$941$	3.32374			0.108351			0.0541753	−	0.998531i	$-0.482747\pi$
$941$	3.32374			0.108351			0.0541753	+	0.998531i	$0.482747\pi$
$942$	−6.66112			−0.217031
$943$	1.82364			0.0593858
$944$		−	70.3579i		−	2.28995i
$945$	−10.0988	+	2.52094i	−0.328513	+	0.0820063i
$946$	−18.1755			−0.590935
$947$	−30.0074			−0.975109			−0.487554	−	0.873093i	$-0.662111\pi$
$947$	−30.0074			−0.975109			−0.487554	+	0.873093i	$0.662111\pi$
$948$	3.51913			0.114296
$949$		−	78.0970i		−	2.53514i
$950$	−17.7113	−	33.2647i	−0.574631	−	1.07925i
$951$	12.6429			0.409974
$952$		−	10.6413i		−	0.344887i
$953$		−	13.1640i		−	0.426424i	−0.977006	−	0.213212i	$-0.931608\pi$
$953$		−	13.1640i		−	0.426424i	0.977006	−	0.213212i	$-0.0683924\pi$
$954$		−	18.4790i		−	0.598279i
$955$	3.58065	+	14.3439i	0.115867	+	0.464158i
$956$			9.08649i			0.293878i
$957$	4.40765			0.142479
$958$		−	67.7788i		−	2.18983i
$959$	−78.5575			−2.53675
$960$	0.866394	+	3.47073i	0.0279628	+	0.112017i
$961$	−10.0243			−0.323364
$962$	42.5590	−	45.6299i	1.37216	−	1.47117i
$963$			18.5702i			0.598416i
$964$			8.86747i			0.285602i
$965$	−24.7615	+	6.18120i	−0.797102	+	0.198980i
$966$	−47.5687			−1.53050
$967$	32.1267			1.03312			0.516562	−	0.856250i	$-0.327212\pi$
$967$	32.1267			1.03312			0.516562	+	0.856250i	$0.327212\pi$
$968$	15.4071			0.495201
$969$	7.31592			0.235021
$970$	13.7794	−	3.43974i	0.442430	−	0.110443i
$971$	42.1872			1.35385			0.676925	−	0.736052i	$-0.263312\pi$
$971$	42.1872			1.35385			0.676925	+	0.736052i	$0.263312\pi$
$972$			1.28250i			0.0411363i
$973$			53.4615i			1.71390i
$974$	−3.21195			−0.102918
$975$	13.3046	+	24.9881i	0.426087	+	0.800259i
$976$			35.5182i			1.13691i
$977$	−43.5431			−1.39307			−0.696534	−	0.717524i	$-0.745276\pi$
$977$	−43.5431			−1.39307			−0.696534	+	0.717524i	$0.745276\pi$
$978$		−	23.2607i		−	0.743796i
$979$			4.80126i			0.153449i
$980$	40.8121	−	10.1879i	1.30370	−	0.325440i
$981$			11.2783i			0.360089i
$982$	−26.0234			−0.830441
$983$			30.6447i			0.977413i	0.872448	+	0.488707i	$0.162531\pi$
$983$			30.6447i			0.977413i	−0.872448	+	0.488707i	$0.837469\pi$
$984$		−	0.420294i		−	0.0133985i
$985$	−8.33685	−	33.3970i	−0.265634	−	1.06412i
$986$		−	2.93771i		−	0.0935557i
$987$		−	4.77870i		−	0.152108i
$988$			30.2081i			0.961048i
$989$	−11.8366			−0.376383
$990$	−18.7899	+	4.69050i	−0.597182	+	0.149074i
$991$		−	11.6501i		−	0.370077i	−0.982731	−	0.185039i	$-0.940759\pi$
$991$		−	11.6501i		−	0.370077i	0.982731	−	0.185039i	$-0.0592410\pi$
$992$			40.4437i			1.28409i
$993$	11.2837			0.358078
$994$			104.002i			3.29874i
$995$	−0.764022	−	3.06063i	−0.0242211	−	0.0970285i
$996$	−12.3114			−0.390102
$997$	−17.1479			−0.543080			−0.271540	−	0.962427i	$-0.587533\pi$
$997$	−17.1479			−0.543080			−0.271540	+	0.962427i	$0.587533\pi$
$998$		−	65.7884i		−	2.08250i
$999$	4.44824	+	4.14887i	0.140736	+	0.131264i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	555.2.g.a.184.8	yes	40
3.2	odd	2		1665.2.g.e.739.34		40
5.4	even	2	inner	555.2.g.a.184.33	yes	40
15.14	odd	2		1665.2.g.e.739.7		40
37.36	even	2	inner	555.2.g.a.184.34	yes	40
111.110	odd	2		1665.2.g.e.739.8		40
185.184	even	2	inner	555.2.g.a.184.7	✓	40
555.554	odd	2		1665.2.g.e.739.33		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
555.2.g.a.184.7	✓	40	185.184	even	2	inner
555.2.g.a.184.8	yes	40	1.1	even	1	trivial
555.2.g.a.184.33	yes	40	5.4	even	2	inner
555.2.g.a.184.34	yes	40	37.36	even	2	inner
1665.2.g.e.739.7		40	15.14	odd	2
1665.2.g.e.739.8		40	111.110	odd	2
1665.2.g.e.739.33		40	555.554	odd	2
1665.2.g.e.739.34		40	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 555 = 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	555.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.81177 q^{2} +1.00000i q^{3} +1.28250 q^{4} +(-2.16949 + 0.541568i) q^{5} -1.81177i q^{6} +4.65490i q^{7} +1.29994 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.81177 q^{2} +1.00000i q^{3} +1.28250 q^{4} +(-2.16949 + 0.541568i) q^{5} -1.81177i q^{6} +4.65490i q^{7} +1.29994 q^{8} -1.00000 q^{9} +(3.93062 - 0.981196i) q^{10} +4.78039 q^{11} +1.28250i q^{12} +5.66185 q^{13} -8.43359i q^{14} +(-0.541568 - 2.16949i) q^{15} -4.92019 q^{16} -1.75858 q^{17} +1.81177 q^{18} +4.16013i q^{19} +(-2.78238 + 0.694563i) q^{20} -4.65490 q^{21} -8.66096 q^{22} -5.64038 q^{23} +1.29994i q^{24} +(4.41341 - 2.34986i) q^{25} -10.2580 q^{26} -1.00000i q^{27} +5.96992i q^{28} -0.922027i q^{29} +(0.981196 + 3.93062i) q^{30} +6.40502i q^{31} +6.31437 q^{32} +4.78039i q^{33} +3.18614 q^{34} +(-2.52094 - 10.0988i) q^{35} -1.28250 q^{36} +(-4.14887 + 4.44824i) q^{37} -7.53719i q^{38} +5.66185i q^{39} +(-2.82021 + 0.704005i) q^{40} -0.323318 q^{41} +8.43359 q^{42} +2.09855 q^{43} +6.13087 q^{44} +(2.16949 - 0.541568i) q^{45} +10.2191 q^{46} +1.02660i q^{47} -4.92019i q^{48} -14.6681 q^{49} +(-7.99607 + 4.25740i) q^{50} -1.75858i q^{51} +7.26134 q^{52} -10.1994i q^{53} +1.81177i q^{54} +(-10.3710 + 2.58891i) q^{55} +6.05108i q^{56} -4.16013 q^{57} +1.67050i q^{58} +14.2998i q^{59} +(-0.694563 - 2.78238i) q^{60} -7.21886i q^{61} -11.6044i q^{62} -4.65490i q^{63} -1.59979 q^{64} +(-12.2834 + 3.06628i) q^{65} -8.66096i q^{66} +4.18794i q^{67} -2.25538 q^{68} -5.64038i q^{69} +(4.56737 + 18.2966i) q^{70} -12.3319 q^{71} -1.29994 q^{72} -13.7935i q^{73} +(7.51679 - 8.05919i) q^{74} +(2.34986 + 4.41341i) q^{75} +5.33538i q^{76} +22.2522i q^{77} -10.2580i q^{78} -2.74395i q^{79} +(10.6743 - 2.66462i) q^{80} +1.00000 q^{81} +0.585778 q^{82} +9.59951i q^{83} -5.96992 q^{84} +(3.81523 - 0.952391i) q^{85} -3.80208 q^{86} +0.922027 q^{87} +6.21421 q^{88} +1.00437i q^{89} +(-3.93062 + 0.981196i) q^{90} +26.3553i q^{91} -7.23381 q^{92} -6.40502 q^{93} -1.85995i q^{94} +(-2.25299 - 9.02537i) q^{95} +6.31437i q^{96} +3.50566 q^{97} +26.5751 q^{98} -4.78039 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 44 q^{4} - 40 q^{9}+O(q^{10}) \) 40 * q + 44 * q^4 - 40 * q^9	\( 40 q + 44 q^{4} - 40 q^{9} + 4 q^{10} + 8 q^{11} + 52 q^{16} - 16 q^{21} + 8 q^{25} - 16 q^{26} + 16 q^{30} - 32 q^{34} - 44 q^{36} - 28 q^{40} + 8 q^{41} + 16 q^{44} - 8 q^{46} - 24 q^{49} + 92 q^{64} - 48 q^{65} - 56 q^{70} + 24 q^{71} - 68 q^{74} + 8 q^{75} + 40 q^{81} - 16 q^{84} - 64 q^{85} + 80 q^{86} - 4 q^{90} + 32 q^{95} - 8 q^{99}+O(q^{100}) \) 40 * q + 44 * q^4 - 40 * q^9 + 4 * q^10 + 8 * q^11 + 52 * q^16 - 16 * q^21 + 8 * q^25 - 16 * q^26 + 16 * q^30 - 32 * q^34 - 44 * q^36 - 28 * q^40 + 8 * q^41 + 16 * q^44 - 8 * q^46 - 24 * q^49 + 92 * q^64 - 48 * q^65 - 56 * q^70 + 24 * q^71 - 68 * q^74 + 8 * q^75 + 40 * q^81 - 16 * q^84 - 64 * q^85 + 80 * q^86 - 4 * q^90 + 32 * q^95 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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