LMFDB - Embedded newform 555.2.g.a.184.10

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			184.10
Character	$\chi$	$=$	555.184
Dual form			555.2.g.a.184.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.72645 q^{2} +1.00000i q^{3} +0.980624 q^{4} +(-1.26006 + 1.84723i) q^{5} -1.72645i q^{6} -2.83159i q^{7} +1.75990 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.72645 q^{2} +1.00000i q^{3} +0.980624 q^{4} +(-1.26006 + 1.84723i) q^{5} -1.72645i q^{6} -2.83159i q^{7} +1.75990 q^{8} -1.00000 q^{9} +(2.17542 - 3.18915i) q^{10} +3.10296 q^{11} +0.980624i q^{12} -5.74396 q^{13} +4.88859i q^{14} +(-1.84723 - 1.26006i) q^{15} -4.99962 q^{16} -4.52624 q^{17} +1.72645 q^{18} -1.75213i q^{19} +(-1.23564 + 1.81144i) q^{20} +2.83159 q^{21} -5.35710 q^{22} +7.13585 q^{23} +1.75990i q^{24} +(-1.82452 - 4.65523i) q^{25} +9.91666 q^{26} -1.00000i q^{27} -2.77672i q^{28} -5.33573i q^{29} +(3.18915 + 2.17542i) q^{30} -4.68047i q^{31} +5.11179 q^{32} +3.10296i q^{33} +7.81433 q^{34} +(5.23059 + 3.56795i) q^{35} -0.980624 q^{36} +(5.81776 + 1.77584i) q^{37} +3.02496i q^{38} -5.74396i q^{39} +(-2.21757 + 3.25094i) q^{40} +1.05237 q^{41} -4.88859 q^{42} +7.15721 q^{43} +3.04284 q^{44} +(1.26006 - 1.84723i) q^{45} -12.3197 q^{46} -9.66478i q^{47} -4.99962i q^{48} -1.01787 q^{49} +(3.14994 + 8.03701i) q^{50} -4.52624i q^{51} -5.63267 q^{52} +7.77708i q^{53} +1.72645i q^{54} +(-3.90990 + 5.73188i) q^{55} -4.98331i q^{56} +1.75213 q^{57} +9.21186i q^{58} +1.06083i q^{59} +(-1.81144 - 1.23564i) q^{60} -8.12616i q^{61} +8.08060i q^{62} +2.83159i q^{63} +1.17400 q^{64} +(7.23771 - 10.6104i) q^{65} -5.35710i q^{66} -12.3955i q^{67} -4.43854 q^{68} +7.13585i q^{69} +(-9.03034 - 6.15989i) q^{70} +3.54659 q^{71} -1.75990 q^{72} -5.95242i q^{73} +(-10.0441 - 3.06590i) q^{74} +(4.65523 - 1.82452i) q^{75} -1.71818i q^{76} -8.78629i q^{77} +9.91666i q^{78} -4.11758i q^{79} +(6.29980 - 9.23546i) q^{80} +1.00000 q^{81} -1.81686 q^{82} +10.8378i q^{83} +2.77672 q^{84} +(5.70332 - 8.36102i) q^{85} -12.3566 q^{86} +5.33573 q^{87} +5.46089 q^{88} -9.50316i q^{89} +(-2.17542 + 3.18915i) q^{90} +16.2645i q^{91} +6.99759 q^{92} +4.68047 q^{93} +16.6857i q^{94} +(3.23659 + 2.20778i) q^{95} +5.11179i q^{96} +2.02461 q^{97} +1.75731 q^{98} -3.10296 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.72645			−1.22078			−0.610392	−	0.792100i	$-0.708988\pi$
$2$	−1.72645			−1.22078			−0.610392	+	0.792100i	$0.708988\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	0.980624			0.490312
$5$	−1.26006	+	1.84723i	−0.563514	+	0.826107i
$5$	−1.26006	+	1.84723i	−0.563514	+	0.826107i
$6$		−	1.72645i		−	0.704820i
$7$		−	2.83159i		−	1.07024i	−0.844777	−	0.535119i	$-0.820267\pi$
$7$		−	2.83159i		−	1.07024i	0.844777	−	0.535119i	$-0.179733\pi$
$8$	1.75990			0.622219
$9$	−1.00000			−0.333333
$10$	2.17542	−	3.18915i	0.687928	−	1.00850i
$11$	3.10296			0.935577			0.467788	−	0.883840i	$-0.345051\pi$
$11$	3.10296			0.935577			0.467788	+	0.883840i	$0.345051\pi$
$12$			0.980624i			0.283082i
$13$	−5.74396			−1.59309			−0.796544	−	0.604580i	$-0.793341\pi$
$13$	−5.74396			−1.59309			−0.796544	+	0.604580i	$0.793341\pi$
$14$			4.88859i			1.30653i
$15$	−1.84723	−	1.26006i	−0.476953	−	0.325345i
$16$	−4.99962			−1.24991
$17$	−4.52624			−1.09778			−0.548888	−	0.835896i	$-0.684949\pi$
$17$	−4.52624			−1.09778			−0.548888	+	0.835896i	$0.684949\pi$
$18$	1.72645			0.406928
$19$		−	1.75213i		−	0.401966i	−0.979595	−	0.200983i	$-0.935586\pi$
$19$		−	1.75213i		−	0.401966i	0.979595	−	0.200983i	$-0.0644136\pi$
$20$	−1.23564	+	1.81144i	−0.276298	+	0.405050i
$21$	2.83159			0.617903
$22$	−5.35710			−1.14214
$23$	7.13585			1.48793			0.743964	−	0.668220i	$-0.232944\pi$
$23$	7.13585			1.48793			0.743964	+	0.668220i	$0.232944\pi$
$24$			1.75990i			0.359238i
$25$	−1.82452	−	4.65523i	−0.364904	−	0.931045i
$26$	9.91666			1.94482
$27$		−	1.00000i		−	0.192450i
$28$		−	2.77672i		−	0.524751i
$29$		−	5.33573i		−	0.990820i	−0.868659	−	0.495410i	$-0.835018\pi$
$29$		−	5.33573i		−	0.990820i	0.868659	−	0.495410i	$-0.164982\pi$
$30$	3.18915	+	2.17542i	0.582256	+	0.397176i
$31$		−	4.68047i		−	0.840638i	−0.907376	−	0.420319i	$-0.861918\pi$
$31$		−	4.68047i		−	0.840638i	0.907376	−	0.420319i	$-0.138082\pi$
$32$	5.11179			0.903646
$33$			3.10296i			0.540156i
$34$	7.81433			1.34015
$35$	5.23059	+	3.56795i	0.884131	+	0.603094i
$36$	−0.980624			−0.163437
$37$	5.81776	+	1.77584i	0.956435	+	0.291946i
$37$	5.81776	+	1.77584i	0.956435	+	0.291946i
$38$			3.02496i			0.490713i
$39$		−	5.74396i		−	0.919770i
$40$	−2.21757	+	3.25094i	−0.350629	+	0.514019i
$41$	1.05237			0.164353			0.0821764	−	0.996618i	$-0.473813\pi$
$41$	1.05237			0.164353			0.0821764	+	0.996618i	$0.473813\pi$
$42$	−4.88859			−0.754325
$43$	7.15721			1.09147			0.545733	−	0.837959i	$-0.316251\pi$
$43$	7.15721			1.09147			0.545733	+	0.837959i	$0.316251\pi$
$44$	3.04284			0.458725
$45$	1.26006	−	1.84723i	0.187838	−	0.275369i
$46$	−12.3197			−1.81644
$47$		−	9.66478i		−	1.40975i	−0.709330	−	0.704876i	$-0.751002\pi$
$47$		−	9.66478i		−	1.40975i	0.709330	−	0.704876i	$-0.248998\pi$
$48$		−	4.99962i		−	0.721634i
$49$	−1.01787			−0.145411
$50$	3.14994	+	8.03701i	0.445469	+	1.13660i
$51$		−	4.52624i		−	0.633801i
$52$	−5.63267			−0.781111
$53$			7.77708i			1.06826i	0.845401	+	0.534132i	$0.179361\pi$
$53$			7.77708i			1.06826i	−0.845401	+	0.534132i	$0.820639\pi$
$54$			1.72645i			0.234940i
$55$	−3.90990	+	5.73188i	−0.527211	+	0.772886i
$56$		−	4.98331i		−	0.665922i
$57$	1.75213			0.232075
$58$			9.21186i			1.20958i
$59$			1.06083i			0.138108i	0.997613	+	0.0690540i	$0.0219981\pi$
$59$			1.06083i			0.138108i	−0.997613	+	0.0690540i	$0.978002\pi$
$60$	−1.81144	−	1.23564i	−0.233856	−	0.159521i
$61$		−	8.12616i		−	1.04045i	−0.854030	−	0.520224i	$-0.825848\pi$
$61$		−	8.12616i		−	1.04045i	0.854030	−	0.520224i	$-0.174152\pi$
$62$			8.08060i			1.02624i
$63$			2.83159i			0.356746i
$64$	1.17400			0.146750
$65$	7.23771	−	10.6104i	0.897728	−	1.31606i
$66$		−	5.35710i		−	0.659413i
$67$		−	12.3955i		−	1.51436i	−0.653209	−	0.757178i	$-0.726578\pi$
$67$		−	12.3955i		−	1.51436i	0.653209	−	0.757178i	$-0.273422\pi$
$68$	−4.43854			−0.538253
$69$			7.13585i			0.859055i
$70$	−9.03034	−	6.15989i	−1.07933	−	0.736248i
$71$	3.54659			0.420903			0.210452	−	0.977604i	$-0.432507\pi$
$71$	3.54659			0.420903			0.210452	+	0.977604i	$0.432507\pi$
$72$	−1.75990			−0.207406
$73$		−	5.95242i		−	0.696678i	−0.937369	−	0.348339i	$-0.886746\pi$
$73$		−	5.95242i		−	0.696678i	0.937369	−	0.348339i	$-0.113254\pi$
$74$	−10.0441	−	3.06590i	−1.16760	−	0.356403i
$75$	4.65523	−	1.82452i	0.537539	−	0.210677i
$76$		−	1.71818i		−	0.197089i
$77$		−	8.78629i		−	1.00129i
$78$			9.91666i			1.12284i
$79$		−	4.11758i		−	0.463264i	−0.972804	−	0.231632i	$-0.925594\pi$
$79$		−	4.11758i		−	0.463264i	0.972804	−	0.231632i	$-0.0744064\pi$
$80$	6.29980	−	9.23546i	0.704340	−	1.03256i
$81$	1.00000			0.111111
$82$	−1.81686			−0.200639
$83$			10.8378i			1.18960i	0.803873	+	0.594801i	$0.202769\pi$
$83$			10.8378i			1.18960i	−0.803873	+	0.594801i	$0.797231\pi$
$84$	2.77672			0.302965
$85$	5.70332	−	8.36102i	0.618612	−	0.906879i
$86$	−12.3566			−1.33244
$87$	5.33573			0.572050
$88$	5.46089			0.582133
$89$		−	9.50316i		−	1.00733i	−0.863898	−	0.503666i	$-0.831984\pi$
$89$		−	9.50316i		−	1.00733i	0.863898	−	0.503666i	$-0.168016\pi$
$90$	−2.17542	+	3.18915i	−0.229309	+	0.336166i
$91$			16.2645i			1.70499i
$92$	6.99759			0.729549
$93$	4.68047			0.485342
$94$			16.6857i			1.72100i
$95$	3.23659	+	2.20778i	0.332067	+	0.226513i
$96$			5.11179i			0.521720i
$97$	2.02461			0.205568			0.102784	−	0.994704i	$-0.467225\pi$
$97$	2.02461			0.205568			0.102784	+	0.994704i	$0.467225\pi$
$98$	1.75731			0.177515
$99$	−3.10296			−0.311859
$100$	−1.78917	−	4.56503i	−0.178917	−	0.456503i
$101$	−17.4683			−1.73816			−0.869082	−	0.494667i	$-0.835290\pi$
$101$	−17.4683			−1.73816			−0.869082	+	0.494667i	$0.835290\pi$
$102$			7.81433i			0.773734i
$103$	−1.05838			−0.104285			−0.0521424	−	0.998640i	$-0.516605\pi$
$103$	−1.05838			−0.104285			−0.0521424	+	0.998640i	$0.516605\pi$
$104$	−10.1088			−0.991249
$105$	−3.56795	+	5.23059i	−0.348197	+	0.510453i
$106$		−	13.4267i		−	1.30412i
$107$			13.2718i			1.28304i	0.767108	+	0.641519i	$0.221695\pi$
$107$			13.2718i			1.28304i	−0.767108	+	0.641519i	$0.778305\pi$
$108$		−	0.980624i		−	0.0943606i
$109$		−	2.62198i		−	0.251141i	−0.992085	−	0.125570i	$-0.959924\pi$
$109$		−	2.62198i		−	0.251141i	0.992085	−	0.125570i	$-0.0400761\pi$
$110$	6.75024	−	9.89579i	0.643610	−	0.943527i
$111$	−1.77584	+	5.81776i	−0.168555	+	0.552198i
$112$			14.1569i			1.33770i
$113$	−10.9824			−1.03314			−0.516571	−	0.856245i	$-0.672792\pi$
$113$	−10.9824			−1.03314			−0.516571	+	0.856245i	$0.672792\pi$
$114$	−3.02496			−0.283314
$115$	−8.99157	+	13.1816i	−0.838468	+	1.22919i
$116$		−	5.23235i		−	0.485811i
$117$	5.74396			0.531030
$118$		−	1.83146i		−	0.168600i
$119$			12.8164i			1.17488i
$120$	−3.25094	−	2.21757i	−0.296769	−	0.202436i
$121$	−1.37165			−0.124696
$122$			14.0294i			1.27016i
$123$			1.05237i			0.0948891i
$124$		−	4.58978i		−	0.412175i
$125$	10.8983	+	2.49553i	0.974771	+	0.223207i
$126$		−	4.88859i		−	0.435510i
$127$		−	18.2336i		−	1.61797i	−0.587827	−	0.808986i	$-0.700017\pi$
$127$		−	18.2336i		−	1.61797i	0.587827	−	0.808986i	$-0.299983\pi$
$128$	−12.2504			−1.08280
$129$			7.15721i			0.630158i
$130$	−12.4955	+	18.3183i	−1.09593	+	1.60663i
$131$		−	15.8974i		−	1.38897i	−0.719509	−	0.694483i	$-0.755633\pi$
$131$		−	15.8974i		−	1.38897i	0.719509	−	0.694483i	$-0.244367\pi$
$132$			3.04284i			0.264845i
$133$	−4.96130			−0.430200
$134$			21.4003i			1.84870i
$135$	1.84723	+	1.26006i	0.158984	+	0.108448i
$136$	−7.96574			−0.683056
$137$			16.7748i			1.43316i	0.697503	+	0.716582i	$0.254294\pi$
$137$			16.7748i			1.43316i	−0.697503	+	0.716582i	$0.745706\pi$
$138$		−	12.3197i		−	1.04872i
$139$	−6.50497			−0.551745			−0.275872	−	0.961194i	$-0.588967\pi$
$139$	−6.50497			−0.551745			−0.275872	+	0.961194i	$0.588967\pi$
$140$	5.12924	+	3.49882i	0.433500	+	0.295704i
$141$	9.66478			0.813921
$142$	−6.12301			−0.513832
$143$	−17.8233			−1.49046
$144$	4.99962			0.416635
$145$	9.85632	+	6.72332i	0.818523	+	0.558341i
$146$			10.2765i			0.850493i
$147$		−	1.01787i		−	0.0839529i
$148$	5.70504	+	1.74143i	0.468951	+	0.143145i
$149$	13.3125			1.09060			0.545301	−	0.838241i	$-0.316416\pi$
$149$	13.3125			1.09060			0.545301	+	0.838241i	$0.316416\pi$
$150$	−8.03701	+	3.14994i	−0.656219	+	0.257192i
$151$	−8.62305			−0.701734			−0.350867	−	0.936425i	$-0.614113\pi$
$151$	−8.62305			−0.701734			−0.350867	+	0.936425i	$0.614113\pi$
$152$		−	3.08357i		−	0.250111i
$153$	4.52624			0.365925
$154$			15.1691i			1.22236i
$155$	8.64591	+	5.89766i	0.694456	+	0.473711i
$156$		−	5.63267i		−	0.450974i
$157$		−	6.42202i		−	0.512533i	−0.966606	−	0.256266i	$-0.917508\pi$
$157$		−	6.42202i		−	0.512533i	0.966606	−	0.256266i	$-0.0824925\pi$
$158$			7.10878i			0.565544i
$159$	−7.77708			−0.616762
$160$	−6.44114	+	9.44266i	−0.509217	+	0.746508i
$161$		−	20.2058i		−	1.59244i
$162$	−1.72645			−0.135643
$163$	14.5026			1.13593			0.567966	−	0.823052i	$-0.307730\pi$
$163$	14.5026			1.13593			0.567966	+	0.823052i	$0.307730\pi$
$164$	1.03198			0.0805841
$165$	−5.73188	−	3.90990i	−0.446226	−	0.304385i
$166$		−	18.7109i		−	1.45225i
$167$	−11.9665			−0.925998			−0.462999	−	0.886359i	$-0.653227\pi$
$167$	−11.9665			−0.925998			−0.462999	+	0.886359i	$0.653227\pi$
$168$	4.98331			0.384470
$169$	19.9931			1.53793
$170$	−9.84649	+	14.4349i	−0.755191	+	1.10710i
$171$			1.75213i			0.133989i
$172$	7.01854			0.535158
$173$			8.25572i			0.627671i	0.949477	+	0.313836i	$0.101614\pi$
$173$			8.25572i			0.627671i	−0.949477	+	0.313836i	$0.898386\pi$
$174$	−9.21186			−0.698350
$175$	−13.1817	+	5.16628i	−0.996440	+	0.390534i
$176$	−15.5136			−1.16938
$177$	−1.06083			−0.0797367
$178$			16.4067i			1.22974i
$179$		−	0.771363i		−	0.0576544i	−0.999584	−	0.0288272i	$-0.990823\pi$
$179$		−	0.771363i		−	0.0576544i	0.999584	−	0.0288272i	$-0.00917725\pi$
$180$	1.23564	−	1.81144i	0.0920992	−	0.135017i
$181$	8.00615			0.595093			0.297546	−	0.954707i	$-0.403832\pi$
$181$	8.00615			0.595093			0.297546	+	0.954707i	$0.403832\pi$
$182$		−	28.0799i		−	2.08142i
$183$	8.12616			0.600703
$184$	12.5584			0.925816
$185$	−10.6111	+	8.50909i	−0.780143	+	0.625601i
$186$	−8.08060			−0.592498
$187$	−14.0447			−1.02705
$188$		−	9.47751i		−	0.691219i
$189$	−2.83159			−0.205968
$190$	−5.58780	−	3.81162i	−0.405382	−	0.276524i
$191$		−	4.30944i		−	0.311820i	−0.987771	−	0.155910i	$-0.950169\pi$
$191$		−	4.30944i		−	0.311820i	0.987771	−	0.155910i	$-0.0498310\pi$
$192$			1.17400i			0.0847262i
$193$	−18.9458			−1.36375			−0.681873	−	0.731471i	$-0.738834\pi$
$193$	−18.9458			−1.36375			−0.681873	+	0.731471i	$0.738834\pi$
$194$	−3.49539			−0.250954
$195$	10.6104	+	7.23771i	0.759828	+	0.518303i
$196$	−0.998152			−0.0712966
$197$		−	16.3631i		−	1.16582i	−0.812535	−	0.582912i	$-0.801913\pi$
$197$		−	16.3631i		−	1.16582i	0.812535	−	0.582912i	$-0.198087\pi$
$198$	5.35710			0.380712
$199$			22.4719i			1.59299i	0.604642	+	0.796497i	$0.293316\pi$
$199$			22.4719i			1.59299i	−0.604642	+	0.796497i	$0.706684\pi$
$200$	−3.21097	−	8.19273i	−0.227050	−	0.579314i
$201$	12.3955			0.874314
$202$	30.1582			2.12192
$203$	−15.1086			−1.06041
$204$		−	4.43854i		−	0.310760i
$205$	−1.32605	+	1.94397i	−0.0926151	+	0.135773i
$206$	1.82723			0.127309
$207$	−7.13585			−0.495976
$208$	28.7177			1.99121
$209$		−	5.43678i		−	0.376070i
$210$	6.15989	−	9.03034i	0.425073	−	0.623153i
$211$	−25.6046			−1.76269			−0.881347	−	0.472469i	$-0.843363\pi$
$211$	−25.6046			−1.76269			−0.881347	+	0.472469i	$0.843363\pi$
$212$			7.62639i			0.523783i
$213$			3.54659i			0.243009i
$214$		−	22.9131i		−	1.56631i
$215$	−9.01849	+	13.2210i	−0.615056	+	0.901666i
$216$		−	1.75990i		−	0.119746i
$217$	−13.2532			−0.899683
$218$			4.52672i			0.306588i
$219$	5.95242			0.402227
$220$	−3.83414	+	5.62082i	−0.258498	+	0.378955i
$221$	25.9986			1.74885
$222$	3.06590	−	10.0441i	0.205770	−	0.674114i
$223$		−	26.0268i		−	1.74288i	−0.490500	−	0.871441i	$-0.663186\pi$
$223$		−	26.0268i		−	1.74288i	0.490500	−	0.871441i	$-0.336814\pi$
$224$		−	14.4745i		−	0.967117i
$225$	1.82452	+	4.65523i	0.121635	+	0.310348i
$226$	18.9606			1.26124
$227$	−0.638999			−0.0424118			−0.0212059	−	0.999775i	$-0.506751\pi$
$227$	−0.638999			−0.0424118			−0.0212059	+	0.999775i	$0.506751\pi$
$228$	1.71818			0.113789
$229$	15.4790			1.02288			0.511441	−	0.859319i	$-0.329112\pi$
$229$	15.4790			1.02288			0.511441	+	0.859319i	$0.329112\pi$
$230$	15.5235	−	22.7573i	1.02359	−	1.50057i
$231$	8.78629			0.578095
$232$		−	9.39035i		−	0.616507i
$233$		−	10.2993i		−	0.674729i	−0.941374	−	0.337365i	$-0.890464\pi$
$233$		−	10.2993i		−	0.674729i	0.941374	−	0.337365i	$-0.109536\pi$
$234$	−9.91666			−0.648272
$235$	17.8531	+	12.1782i	1.16461	+	0.794415i
$236$			1.04027i			0.0677160i
$237$	4.11758			0.267465
$238$		−	22.1269i		−	1.43428i
$239$		−	13.4927i		−	0.872768i	−0.899760	−	0.436384i	$-0.856259\pi$
$239$		−	13.4927i		−	0.872768i	0.899760	−	0.436384i	$-0.143741\pi$
$240$	9.23546	+	6.29980i	0.596146	+	0.406651i
$241$			25.9107i			1.66906i	0.550966	+	0.834528i	$0.314259\pi$
$241$			25.9107i			1.66906i	−0.550966	+	0.834528i	$0.685741\pi$
$242$	2.36809			0.152227
$243$			1.00000i			0.0641500i
$244$		−	7.96871i		−	0.510144i
$245$	1.28258	−	1.88025i	0.0819409	−	0.120125i
$246$		−	1.81686i		−	0.115839i
$247$			10.0642i			0.640368i
$248$		−	8.23716i		−	0.523060i
$249$	−10.8378			−0.686817
$250$	−18.8153	−	4.30841i	−1.18998	−	0.272488i
$251$		−	1.92047i		−	0.121219i	−0.998162	−	0.0606095i	$-0.980696\pi$
$251$		−	1.92047i		−	0.121219i	0.998162	−	0.0606095i	$-0.0193044\pi$
$252$			2.77672i			0.174917i
$253$	22.1422			1.39207
$254$			31.4794i			1.97519i
$255$	8.36102	+	5.70332i	0.523587	+	0.357156i
$256$	18.8018			1.17511
$257$	16.5592			1.03294			0.516468	−	0.856307i	$-0.327247\pi$
$257$	16.5592			1.03294			0.516468	+	0.856307i	$0.327247\pi$
$258$		−	12.3566i		−	0.769286i
$259$	5.02845	−	16.4735i	0.312452	−	1.02361i
$260$	7.09748	−	10.4048i	0.440167	−	0.645281i
$261$			5.33573i			0.330273i
$262$			27.4461i			1.69563i
$263$		−	2.30498i		−	0.142131i	−0.997472	−	0.0710656i	$-0.977360\pi$
$263$		−	2.30498i		−	0.142131i	0.997472	−	0.0710656i	$-0.0226400\pi$
$264$			5.46089i			0.336095i
$265$	−14.3661	−	9.79955i	−0.882500	−	0.601981i
$266$	8.56543			0.525180
$267$	9.50316			0.581584
$268$		−	12.1554i		−	0.742507i
$269$	7.81395			0.476425			0.238212	−	0.971213i	$-0.423439\pi$
$269$	7.81395			0.476425			0.238212	+	0.971213i	$0.423439\pi$
$270$	−3.18915	−	2.17542i	−0.194085	−	0.132392i
$271$	−15.0306			−0.913044			−0.456522	−	0.889712i	$-0.650905\pi$
$271$	−15.0306			−0.913044			−0.456522	+	0.889712i	$0.650905\pi$
$272$	22.6295			1.37212
$273$	−16.2645			−0.984374
$274$		−	28.9607i		−	1.74958i
$275$	−5.66141	−	14.4450i	−0.341396	−	0.871064i
$276$			6.99759i			0.421205i
$277$	3.75230			0.225454			0.112727	−	0.993626i	$-0.464041\pi$
$277$	3.75230			0.225454			0.112727	+	0.993626i	$0.464041\pi$
$278$	11.2305			0.673561
$279$			4.68047i			0.280213i
$280$	9.20531	+	6.27924i	0.550123	+	0.375257i
$281$		−	7.47328i		−	0.445819i	−0.974839	−	0.222909i	$-0.928445\pi$
$281$		−	7.47328i		−	0.445819i	0.974839	−	0.222909i	$-0.0715554\pi$
$282$	−16.6857			−0.993621
$283$	−1.21677			−0.0723293			−0.0361647	−	0.999346i	$-0.511514\pi$
$283$	−1.21677			−0.0723293			−0.0361647	+	0.999346i	$0.511514\pi$
$284$	3.47787			0.206374
$285$	−2.20778	+	3.23659i	−0.130778	+	0.191719i
$286$	30.7710			1.81953
$287$		−	2.97988i		−	0.175897i
$288$	−5.11179			−0.301215
$289$	3.48689			0.205111
$290$	−17.0164	−	11.6075i	−0.999239	−	0.681614i
$291$			2.02461i			0.118685i
$292$		−	5.83708i		−	0.341589i
$293$		−	23.9207i		−	1.39746i	−0.715384	−	0.698731i	$-0.753748\pi$
$293$		−	23.9207i		−	1.39746i	0.715384	−	0.698731i	$-0.246252\pi$
$294$			1.75731i			0.102488i
$295$	−1.95959	−	1.33670i	−0.114092	−	0.0778258i
$296$	10.2387	+	3.12530i	0.595111	+	0.181655i
$297$		−	3.10296i		−	0.180052i
$298$	−22.9833			−1.33139
$299$	−40.9881			−2.37040
$300$	4.56503	−	1.78917i	0.263562	−	0.103298i
$301$		−	20.2663i		−	1.16813i
$302$	14.8873			0.856665
$303$		−	17.4683i		−	1.00353i
$304$			8.75999i			0.502420i
$305$	15.0109	+	10.2394i	0.859521	+	0.586307i
$306$	−7.81433			−0.446715
$307$			24.2455i			1.38376i	0.722012	+	0.691881i	$0.243218\pi$
$307$			24.2455i			1.38376i	−0.722012	+	0.691881i	$0.756782\pi$
$308$		−	8.61605i		−	0.490945i
$309$		−	1.05838i		−	0.0602089i
$310$	−14.9267	−	10.1820i	−0.847781	−	0.578299i
$311$		−	1.30074i		−	0.0737582i	−0.999320	−	0.0368791i	$-0.988258\pi$
$311$		−	1.30074i		−	0.0737582i	0.999320	−	0.0368791i	$-0.0117416\pi$
$312$		−	10.1088i		−	0.572298i
$313$	−9.51454			−0.537794			−0.268897	−	0.963169i	$-0.586659\pi$
$313$	−9.51454			−0.537794			−0.268897	+	0.963169i	$0.586659\pi$
$314$			11.0873i			0.625692i
$315$	−5.23059	−	3.56795i	−0.294710	−	0.201031i
$316$		−	4.03780i		−	0.227144i
$317$		−	29.3063i		−	1.64601i	−0.568036	−	0.823004i	$-0.692297\pi$
$317$		−	29.3063i		−	1.64601i	0.568036	−	0.823004i	$-0.307703\pi$
$318$	13.4267			0.752933
$319$		−	16.5565i		−	0.926989i
$320$	−1.47931	+	2.16865i	−0.0826957	+	0.121231i
$321$	−13.2718			−0.740762
$322$			34.8842i			1.94402i
$323$			7.93057i			0.441268i
$324$	0.980624			0.0544791
$325$	10.4800	+	26.7394i	0.581325	+	1.48324i
$326$	−25.0380			−1.38673
$327$	2.62198			0.144996
$328$	1.85207			0.102263
$329$	−27.3666			−1.50877
$330$	9.89579	+	6.75024i	0.544745	+	0.371588i
$331$			25.7197i			1.41368i	0.707373	+	0.706840i	$0.249880\pi$
$331$			25.7197i			1.41368i	−0.707373	+	0.706840i	$0.750120\pi$
$332$			10.6278i			0.583276i
$333$	−5.81776	−	1.77584i	−0.318812	−	0.0973155i
$334$	20.6596			1.13044
$335$	22.8974	+	15.6191i	1.25102	+	0.853361i
$336$	−14.1569			−0.772320
$337$		−	0.698454i		−	0.0380472i	−0.999819	−	0.0190236i	$-0.993944\pi$
$337$		−	0.698454i		−	0.0380472i	0.999819	−	0.0190236i	$-0.00605577\pi$
$338$	−34.5171			−1.87748
$339$		−	10.9824i		−	0.596484i
$340$	5.59281	−	8.19901i	0.303313	−	0.444654i
$341$		−	14.5233i		−	0.786481i
$342$		−	3.02496i		−	0.163571i
$343$		−	16.9389i		−	0.914615i
$344$	12.5960			0.679130
$345$	−13.1816	−	8.99157i	−0.709671	−	0.484090i
$346$		−	14.2531i		−	0.766250i
$347$	−31.1144			−1.67031			−0.835154	−	0.550017i	$-0.814621\pi$
$347$	−31.1144			−1.67031			−0.835154	+	0.550017i	$0.814621\pi$
$348$	5.23235			0.280483
$349$	4.25162			0.227584			0.113792	−	0.993505i	$-0.463700\pi$
$349$	4.25162			0.227584			0.113792	+	0.993505i	$0.463700\pi$
$350$	22.7575	−	8.91932i	1.21644	−	0.476758i
$351$			5.74396i			0.306590i
$352$	15.8617			0.845430
$353$	−27.3493			−1.45566			−0.727829	−	0.685759i	$-0.759470\pi$
$353$	−27.3493			−1.45566			−0.727829	+	0.685759i	$0.759470\pi$
$354$	1.83146			0.0973412
$355$	−4.46890	+	6.55137i	−0.237185	+	0.347711i
$356$		−	9.31903i		−	0.493907i
$357$	−12.8164			−0.678318
$358$			1.33172i			0.0703835i
$359$	−10.6456			−0.561853			−0.280926	−	0.959729i	$-0.590642\pi$
$359$	−10.6456			−0.561853			−0.280926	+	0.959729i	$0.590642\pi$
$360$	2.21757	−	3.25094i	0.116876	−	0.171340i
$361$	15.9300			0.838423
$362$	−13.8222			−0.726479
$363$		−	1.37165i		−	0.0719932i
$364$			15.9494i			0.835975i
$365$	10.9955	+	7.50038i	0.575530	+	0.392588i
$366$	−14.0294			−0.733328
$367$		−	8.77108i		−	0.457847i	−0.973444	−	0.228923i	$-0.926479\pi$
$367$		−	8.77108i		−	0.457847i	0.973444	−	0.228923i	$-0.0735205\pi$
$368$	−35.6766			−1.85977
$369$	−1.05237			−0.0547843
$370$	18.3195	−	14.6905i	0.952386	−	0.763723i
$371$	22.0215			1.14330
$372$	4.58978			0.237969
$373$			24.2661i			1.25645i	0.778031	+	0.628226i	$0.216219\pi$
$373$			24.2661i			1.25645i	−0.778031	+	0.628226i	$0.783781\pi$
$374$	24.2475			1.25381
$375$	−2.49553	+	10.8983i	−0.128869	+	0.562784i
$376$		−	17.0090i		−	0.877174i
$377$			30.6482i			1.57846i
$378$	4.88859			0.251442
$379$	19.9178			1.02311			0.511554	−	0.859251i	$-0.329070\pi$
$379$	19.9178			1.02311			0.511554	+	0.859251i	$0.329070\pi$
$380$	3.17387	+	2.16500i	0.162816	+	0.111062i
$381$	18.2336			0.934137
$382$			7.44003i			0.380665i
$383$	14.5335			0.742629			0.371314	−	0.928507i	$-0.378907\pi$
$383$	14.5335			0.742629			0.371314	+	0.928507i	$0.378907\pi$
$384$		−	12.2504i		−	0.625153i
$385$	16.2303	+	11.0712i	0.827173	+	0.564241i
$386$	32.7089			1.66484
$387$	−7.15721			−0.363822
$388$	1.98538			0.100793
$389$		−	12.6751i		−	0.642655i	−0.946968	−	0.321328i	$-0.895871\pi$
$389$		−	12.6751i		−	0.642655i	0.946968	−	0.321328i	$-0.104129\pi$
$390$	−18.3183	−	12.4955i	−0.927586	−	0.632736i
$391$	−32.2986			−1.63341
$392$	−1.79136			−0.0904772
$393$	15.8974			0.801920
$394$			28.2501i			1.42322i
$395$	7.60611	+	5.18838i	0.382705	+	0.261055i
$396$	−3.04284			−0.152908
$397$		−	1.78813i		−	0.0897438i	−0.998993	−	0.0448719i	$-0.985712\pi$
$397$		−	1.78813i		−	0.0897438i	0.998993	−	0.0448719i	$-0.0142880\pi$
$398$		−	38.7967i		−	1.94470i
$399$		−	4.96130i		−	0.248376i
$400$	9.12192	+	23.2744i	0.456096	+	1.16372i
$401$			21.1473i			1.05605i	0.849230	+	0.528023i	$0.177066\pi$
$401$			21.1473i			1.05605i	−0.849230	+	0.528023i	$0.822934\pi$
$402$	−21.4003			−1.06735
$403$			26.8845i			1.33921i
$404$	−17.1299			−0.852243
$405$	−1.26006	+	1.84723i	−0.0626127	+	0.0917896i
$406$	26.0842			1.29454
$407$	18.0523	+	5.51036i	0.894818	+	0.273138i
$408$		−	7.96574i		−	0.394363i
$409$		−	18.3669i		−	0.908185i	−0.890954	−	0.454093i	$-0.849963\pi$
$409$		−	18.3669i		−	0.908185i	0.890954	−	0.454093i	$-0.150037\pi$
$410$	2.28935	−	3.35617i	0.113063	−	0.165749i
$411$	−16.7748			−0.827438
$412$	−1.03787			−0.0511321
$413$	3.00382			0.147809
$414$	12.3197			0.605479
$415$	−20.0199	−	13.6562i	−0.982738	−	0.670357i
$416$	−29.3620			−1.43959
$417$		−	6.50497i		−	0.318550i
$418$			9.38633i			0.459100i
$419$	10.4851			0.512229			0.256115	−	0.966646i	$-0.417558\pi$
$419$	10.4851			0.512229			0.256115	+	0.966646i	$0.417558\pi$
$420$	−3.49882	+	5.12924i	−0.170725	+	0.250281i
$421$			28.1137i			1.37018i	0.728460	+	0.685089i	$0.240237\pi$
$421$			28.1137i			1.37018i	−0.728460	+	0.685089i	$0.759763\pi$
$422$	44.2050			2.15187
$423$			9.66478i			0.469918i
$424$			13.6869i			0.664693i
$425$	8.25822	+	21.0707i	0.400583	+	1.02208i
$426$		−	6.12301i		−	0.296661i
$427$	−23.0099			−1.11353
$428$			13.0147i			0.629089i
$429$		−	17.8233i		−	0.860516i
$430$	15.5700	−	22.8254i	0.750850	−	1.10074i
$431$			35.5346i			1.71164i	0.517272	+	0.855821i	$0.326948\pi$
$431$			35.5346i			1.71164i	−0.517272	+	0.855821i	$0.673052\pi$
$432$			4.99962i			0.240545i
$433$		−	12.1596i		−	0.584354i	−0.956364	−	0.292177i	$-0.905620\pi$
$433$		−	12.1596i		−	0.584354i	0.956364	−	0.292177i	$-0.0943797\pi$
$434$	22.8809			1.09832
$435$	−6.72332	+	9.85632i	−0.322358	+	0.472575i
$436$		−	2.57118i		−	0.123137i
$437$		−	12.5029i		−	0.598096i
$438$	−10.2765			−0.491032
$439$		−	32.8046i		−	1.56568i	−0.622226	−	0.782838i	$-0.713771\pi$
$439$		−	32.8046i		−	1.56568i	0.622226	−	0.782838i	$-0.286229\pi$
$440$	−6.88103	+	10.0875i	−0.328040	+	0.480904i
$441$	1.01787			0.0484702
$442$	−44.8852			−2.13497
$443$			28.3513i			1.34701i	0.739183	+	0.673505i	$0.235212\pi$
$443$			28.3513i			1.34701i	−0.739183	+	0.673505i	$0.764788\pi$
$444$	−1.74143	+	5.70504i	−0.0826447	+	0.270749i
$445$	17.5545	+	11.9745i	0.832164	+	0.567646i
$446$			44.9339i			2.12768i
$447$			13.3125i			0.629659i
$448$		−	3.32428i		−	0.157058i
$449$			12.5039i			0.590093i	0.955483	+	0.295047i	$0.0953352\pi$
$449$			12.5039i			0.590093i	−0.955483	+	0.295047i	$0.904665\pi$
$450$	−3.14994	−	8.03701i	−0.148490	−	0.378868i
$451$	3.26546			0.153765
$452$	−10.7696			−0.506562
$453$		−	8.62305i		−	0.405146i
$454$	1.10320			0.0517756
$455$	−30.0443	−	20.4942i	−1.40850	−	0.960783i
$456$	3.08357			0.144401
$457$	34.1220			1.59616			0.798079	−	0.602553i	$-0.205850\pi$
$457$	34.1220			1.59616			0.798079	+	0.602553i	$0.205850\pi$
$458$	−26.7237			−1.24872
$459$			4.52624i			0.211267i
$460$	−8.81735	+	12.9262i	−0.411111	+	0.602685i
$461$			29.5251i			1.37512i	0.726127	+	0.687560i	$0.241318\pi$
$461$			29.5251i			1.37512i	−0.726127	+	0.687560i	$0.758682\pi$
$462$	−15.1691			−0.705729
$463$	−4.74603			−0.220567			−0.110283	−	0.993900i	$-0.535176\pi$
$463$	−4.74603			−0.220567			−0.110283	+	0.993900i	$0.535176\pi$
$464$			26.6767i			1.23843i
$465$	−5.89766	+	8.64591i	−0.273497	+	0.400945i
$466$			17.7812i			0.823698i
$467$	13.0944			0.605937			0.302969	−	0.953001i	$-0.402022\pi$
$467$	13.0944			0.605937			0.302969	+	0.953001i	$0.402022\pi$
$468$	5.63267			0.260370
$469$	−35.0990			−1.62072
$470$	−30.8224	−	21.0250i	−1.42173	−	0.969809i
$471$	6.42202			0.295911
$472$			1.86695i			0.0859334i
$473$	22.2085			1.02115
$474$	−7.10878			−0.326517
$475$	−8.15656	+	3.19680i	−0.374249	+	0.146679i
$476$			12.5681i			0.576059i
$477$		−	7.77708i		−	0.356088i
$478$			23.2944i			1.06546i
$479$			17.1884i			0.785357i	0.919676	+	0.392678i	$0.128451\pi$
$479$			17.1884i			0.785357i	−0.919676	+	0.392678i	$0.871549\pi$
$480$	−9.44266	−	6.44114i	−0.430997	−	0.293997i
$481$	−33.4170	−	10.2004i	−1.52369	−	0.465097i
$482$		−	44.7335i		−	2.03756i
$483$	20.2058			0.919394
$484$	−1.34508			−0.0611399
$485$	−2.55112	+	3.73993i	−0.115841	+	0.169821i
$486$		−	1.72645i		−	0.0783133i
$487$	−33.9489			−1.53837			−0.769185	−	0.639026i	$-0.779338\pi$
$487$	−33.9489			−1.53837			−0.769185	+	0.639026i	$0.779338\pi$
$488$		−	14.3012i		−	0.647386i
$489$			14.5026i			0.655831i
$490$	−2.21430	+	3.24615i	−0.100032	+	0.146646i
$491$	27.9158			1.25982			0.629911	−	0.776668i	$-0.283091\pi$
$491$	27.9158			1.25982			0.629911	+	0.776668i	$0.283091\pi$
$492$			1.03198i			0.0465253i
$493$			24.1508i			1.08770i
$494$		−	17.3753i		−	0.781750i
$495$	3.90990	−	5.73188i	0.175737	−	0.257629i
$496$			23.4006i			1.05072i
$497$		−	10.0425i		−	0.450467i
$498$	18.7109			0.838455
$499$		−	24.1658i		−	1.08181i	−0.841084	−	0.540905i	$-0.818082\pi$
$499$		−	24.1658i		−	1.08181i	0.841084	−	0.540905i	$-0.181918\pi$
$500$	10.6871	+	2.44718i	0.477942	+	0.109441i
$501$		−	11.9665i		−	0.534625i
$502$			3.31559i			0.147982i
$503$	22.8576			1.01917			0.509585	−	0.860420i	$-0.329799\pi$
$503$	22.8576			1.01917			0.509585	+	0.860420i	$0.329799\pi$
$504$			4.98331i			0.221974i
$505$	22.0111	−	32.2680i	0.979480	−	1.43591i
$506$	−38.2274			−1.69942
$507$			19.9931i			0.887925i
$508$		−	17.8803i		−	0.793312i
$509$	12.6838			0.562201			0.281101	−	0.959678i	$-0.409300\pi$
$509$	12.6838			0.562201			0.281101	+	0.959678i	$0.409300\pi$
$510$	−14.4349	−	9.84649i	−0.639186	−	0.436010i
$511$	−16.8548			−0.745611
$512$	−7.95938			−0.351758
$513$	−1.75213			−0.0773584
$514$	−28.5886			−1.26099
$515$	1.33361	−	1.95506i	0.0587660	−	0.0861504i
$516$			7.01854i			0.308974i
$517$		−	29.9894i		−	1.31893i
$518$	−8.68135	+	28.4406i	−0.381437	+	1.24961i
$519$	−8.25572			−0.362386
$520$	12.7376	−	18.6733i	0.558583	−	0.818878i
$521$	−40.6186			−1.77953			−0.889766	−	0.456416i	$-0.849133\pi$
$521$	−40.6186			−1.77953			−0.889766	+	0.456416i	$0.849133\pi$
$522$		−	9.21186i		−	0.403192i
$523$	36.7723			1.60794			0.803971	−	0.594669i	$-0.202717\pi$
$523$	36.7723			1.60794			0.803971	+	0.594669i	$0.202717\pi$
$524$		−	15.5894i		−	0.681027i
$525$	−5.16628	−	13.1817i	−0.225475	−	0.575295i
$526$			3.97943i			0.173511i
$527$			21.1850i			0.922832i
$528$		−	15.5136i		−	0.675144i
$529$	27.9203			1.21393
$530$	24.8022	+	16.9184i	1.07734	+	0.734889i
$531$		−	1.06083i		−	0.0460360i
$532$	−4.86517			−0.210932
$533$	−6.04478			−0.261829
$534$	−16.4067			−0.709988
$535$	−24.5161	−	16.7233i	−1.05993	−	0.723009i
$536$		−	21.8149i		−	0.942260i
$537$	0.771363			0.0332868
$538$	−13.4904			−0.581612
$539$	−3.15842			−0.136043
$540$	1.81144	+	1.23564i	0.0779519	+	0.0531735i
$541$		−	5.89570i		−	0.253476i	−0.991936	−	0.126738i	$-0.959549\pi$
$541$		−	5.89570i		−	0.253476i	0.991936	−	0.126738i	$-0.0404507\pi$
$542$	25.9496			1.11463
$543$			8.00615i			0.343577i
$544$	−23.1372			−0.992001
$545$	4.84341	+	3.30385i	0.207469	+	0.141521i
$546$	28.0799			1.20171
$547$	17.2327			0.736817			0.368408	−	0.929664i	$-0.379903\pi$
$547$	17.2327			0.736817			0.368408	+	0.929664i	$0.379903\pi$
$548$			16.4497i			0.702698i
$549$			8.12616i			0.346816i
$550$	9.77413	+	24.9385i	0.416770	+	1.06338i
$551$	−9.34889			−0.398276
$552$			12.5584i			0.534520i
$553$	−11.6593			−0.495803
$554$	−6.47815			−0.275230
$555$	−8.50909	−	10.6111i	−0.361191	−	0.450416i
$556$	−6.37893			−0.270527
$557$	−9.70885			−0.411377			−0.205689	−	0.978617i	$-0.565943\pi$
$557$	−9.70885			−0.411377			−0.205689	+	0.978617i	$0.565943\pi$
$558$		−	8.08060i		−	0.342079i
$559$	−41.1108			−1.73880
$560$	−26.1510	−	17.8384i	−1.10508	−	0.753811i
$561$		−	14.0447i		−	0.592970i
$562$			12.9022i			0.544248i
$563$	8.01043			0.337600			0.168800	−	0.985650i	$-0.446011\pi$
$563$	8.01043			0.337600			0.168800	+	0.985650i	$0.446011\pi$
$564$	9.47751			0.399075
$565$	13.8385	−	20.2871i	0.582189	−	0.853485i
$566$	2.10069			0.0882984
$567$		−	2.83159i		−	0.118915i
$568$	6.24165			0.261894
$569$		−	9.88027i		−	0.414203i	−0.978320	−	0.207101i	$-0.933597\pi$
$569$		−	9.88027i		−	0.414203i	0.978320	−	0.207101i	$-0.0664030\pi$
$570$	3.81162	−	5.58780i	0.159651	−	0.234047i
$571$	32.7195			1.36927			0.684635	−	0.728886i	$-0.259962\pi$
$571$	32.7195			1.36927			0.684635	+	0.728886i	$0.259962\pi$
$572$	−17.4779			−0.730789
$573$	4.30944			0.180029
$574$			5.14461i			0.214732i
$575$	−13.0195	−	33.2190i	−0.542951	−	1.38533i
$576$	−1.17400			−0.0489167
$577$	−0.370678			−0.0154315			−0.00771576	−	0.999970i	$-0.502456\pi$
$577$	−0.370678			−0.0154315			−0.00771576	+	0.999970i	$0.502456\pi$
$578$	−6.01993			−0.250396
$579$		−	18.9458i		−	0.787359i
$580$	9.66535	+	6.59305i	0.401332	+	0.273761i
$581$	30.6881			1.27316
$582$		−	3.49539i		−	0.144889i
$583$			24.1319i			0.999443i
$584$		−	10.4757i		−	0.433486i
$585$	−7.23771	+	10.6104i	−0.299243	+	0.438687i
$586$			41.2979i			1.70600i
$587$	−4.35439			−0.179725			−0.0898625	−	0.995954i	$-0.528643\pi$
$587$	−4.35439			−0.179725			−0.0898625	+	0.995954i	$0.528643\pi$
$588$		−	0.998152i		−	0.0411631i
$589$	−8.20079			−0.337908
$590$	3.38314	+	2.30775i	0.139282	+	0.0950084i
$591$	16.3631			0.673089
$592$	−29.0866	−	8.87854i	−1.19545	−	0.364906i
$593$			25.6303i			1.05251i	0.850327	+	0.526255i	$0.176404\pi$
$593$			25.6303i			1.05251i	−0.850327	+	0.526255i	$0.823596\pi$
$594$			5.35710i			0.219804i
$595$	−23.6749	−	16.1494i	−0.970577	−	0.662062i
$596$	13.0545			0.534735
$597$	−22.4719			−0.919716
$598$	70.7638			2.89375
$599$	−6.12395			−0.250218			−0.125109	−	0.992143i	$-0.539928\pi$
$599$	−6.12395			−0.250218			−0.125109	+	0.992143i	$0.539928\pi$
$600$	8.19273	−	3.21097i	0.334467	−	0.131087i
$601$	−16.1431			−0.658491			−0.329245	−	0.944244i	$-0.606794\pi$
$601$	−16.1431			−0.658491			−0.329245	+	0.944244i	$0.606794\pi$
$602$			34.9887i			1.42603i
$603$			12.3955i			0.504785i
$604$	−8.45597			−0.344069
$605$	1.72836	−	2.53376i	0.0702678	−	0.103012i
$606$			30.1582i			1.22509i
$607$	12.7960			0.519373			0.259686	−	0.965693i	$-0.416381\pi$
$607$	12.7960			0.519373			0.259686	+	0.965693i	$0.416381\pi$
$608$		−	8.95652i		−	0.363235i
$609$		−	15.1086i		−	0.612230i
$610$	−25.9155	−	17.6778i	−1.04929	−	0.715754i
$611$			55.5141i			2.24586i
$612$	4.43854			0.179418
$613$		−	11.7842i		−	0.475958i	−0.971270	−	0.237979i	$-0.923515\pi$
$613$		−	11.7842i		−	0.475958i	0.971270	−	0.237979i	$-0.0764850\pi$
$614$		−	41.8585i		−	1.68927i
$615$	−1.94397	−	1.32605i	−0.0783885	−	0.0534713i
$616$		−	15.4630i		−	0.623022i
$617$			34.3221i			1.38175i	0.722972	+	0.690877i	$0.242776\pi$
$617$			34.3221i			1.38175i	−0.722972	+	0.690877i	$0.757224\pi$
$618$			1.82723i			0.0735020i
$619$	−22.0099			−0.884652			−0.442326	−	0.896854i	$-0.645847\pi$
$619$	−22.0099			−0.884652			−0.442326	+	0.896854i	$0.645847\pi$
$620$	8.47839	+	5.78338i	0.340500	+	0.232266i
$621$		−	7.13585i		−	0.286352i
$622$			2.24566i			0.0900428i
$623$	−26.9090			−1.07809
$624$			28.7177i			1.14963i
$625$	−18.3423	+	16.9871i	−0.733690	+	0.679484i
$626$	16.4264			0.656530
$627$	5.43678			0.217124
$628$		−	6.29759i		−	0.251301i
$629$	−26.3326	−	8.03789i	−1.04995	−	0.320492i
$630$	9.03034	+	6.15989i	0.359778	+	0.245416i
$631$			13.5444i			0.539194i	0.962973	+	0.269597i	$0.0868905\pi$
$631$			13.5444i			0.539194i	−0.962973	+	0.269597i	$0.913110\pi$
$632$		−	7.24652i		−	0.288251i
$633$		−	25.6046i		−	1.01769i
$634$			50.5959i			2.00942i
$635$	33.6817	+	22.9754i	1.33662	+	0.911750i
$636$	−7.62639			−0.302406
$637$	5.84663			0.231652
$638$			28.5840i			1.13165i
$639$	−3.54659			−0.140301
$640$	15.4362	−	22.6294i	0.610171	−	0.894505i
$641$	−12.9984			−0.513408			−0.256704	−	0.966490i	$-0.582637\pi$
$641$	−12.9984			−0.513408			−0.256704	+	0.966490i	$0.582637\pi$
$642$	22.9131			0.904310
$643$	15.7429			0.620840			0.310420	−	0.950599i	$-0.399530\pi$
$643$	15.7429			0.620840			0.310420	+	0.950599i	$0.399530\pi$
$644$		−	19.8143i		−	0.780791i
$645$	−13.2210	−	9.01849i	−0.520577	−	0.355103i
$646$		−	13.6917i		−	0.538693i
$647$	38.6834			1.52080			0.760400	−	0.649455i	$-0.225003\pi$
$647$	38.6834			1.52080			0.760400	+	0.649455i	$0.225003\pi$
$648$	1.75990			0.0691354
$649$			3.29170i			0.129211i
$650$	−18.0931	−	46.1643i	−0.709671	−	1.81071i
$651$		−	13.2532i		−	0.519432i
$652$	14.2216			0.556961
$653$	30.1694			1.18062			0.590310	−	0.807177i	$-0.299005\pi$
$653$	30.1694			1.18062			0.590310	+	0.807177i	$0.299005\pi$
$654$	−4.52672			−0.177009
$655$	29.3662	+	20.0317i	1.14743	+	0.782702i
$656$	−5.26146			−0.205426
$657$			5.95242i			0.232226i
$658$	47.2471			1.84188
$659$	−10.0529			−0.391604			−0.195802	−	0.980643i	$-0.562731\pi$
$659$	−10.0529			−0.391604			−0.195802	+	0.980643i	$0.562731\pi$
$660$	−5.62082	−	3.83414i	−0.218790	−	0.149244i
$661$		−	6.89136i		−	0.268043i	−0.990978	−	0.134021i	$-0.957211\pi$
$661$		−	6.89136i		−	0.268043i	0.990978	−	0.134021i	$-0.0427891\pi$
$662$		−	44.4037i		−	1.72580i
$663$			25.9986i			1.00970i
$664$			19.0734i			0.740192i
$665$	6.25152	−	9.16467i	0.242423	−	0.355391i
$666$	10.0441	+	3.06590i	0.389200	+	0.118801i
$667$		−	38.0750i		−	1.47427i
$668$	−11.7347			−0.454028
$669$	26.0268			1.00625
$670$	−39.5312	−	26.9655i	−1.52722	−	1.04177i
$671$		−	25.2151i		−	0.973419i
$672$	14.4745			0.558365
$673$		−	47.1290i		−	1.81669i	−0.418221	−	0.908345i	$-0.637346\pi$
$673$		−	47.1290i		−	1.81669i	0.418221	−	0.908345i	$-0.362654\pi$
$674$			1.20585i			0.0464474i
$675$	−4.65523	+	1.82452i	−0.179180	+	0.0702258i
$676$	19.6057			0.754067
$677$		−	48.2084i		−	1.85280i	−0.376540	−	0.926400i	$-0.622886\pi$
$677$		−	48.2084i		−	1.85280i	0.376540	−	0.926400i	$-0.377114\pi$
$678$			18.9606i			0.728178i
$679$		−	5.73286i		−	0.220007i
$680$	10.0373	−	14.7146i	0.384912	−	0.564277i
$681$		−	0.638999i		−	0.0244865i
$682$			25.0737i			0.960123i
$683$	4.20808			0.161018			0.0805089	−	0.996754i	$-0.474345\pi$
$683$	4.20808			0.161018			0.0805089	+	0.996754i	$0.474345\pi$
$684$			1.71818i			0.0656963i
$685$	−30.9868	−	21.1371i	−1.18395	−	0.807608i
$686$			29.2441i			1.11655i
$687$			15.4790i			0.590561i
$688$	−35.7834			−1.36423
$689$		−	44.6712i		−	1.70184i
$690$	22.7573	+	15.5235i	0.866355	+	0.590969i
$691$	−20.2048			−0.768625			−0.384312	−	0.923203i	$-0.625561\pi$
$691$	−20.2048			−0.768625			−0.384312	+	0.923203i	$0.625561\pi$
$692$			8.09576i			0.307755i
$693$			8.78629i			0.333764i
$694$	53.7174			2.03908
$695$	8.19663	−	12.0162i	0.310916	−	0.455800i
$696$	9.39035			0.355940
$697$	−4.76329			−0.180422
$698$	−7.34020			−0.277831
$699$	10.2993			0.389555
$700$	−12.9263	+	5.06618i	−0.488567	+	0.191484i
$701$		−	37.9252i		−	1.43242i	−0.697887	−	0.716208i	$-0.745876\pi$
$701$		−	37.9252i		−	1.43242i	0.697887	−	0.716208i	$-0.254124\pi$
$702$		−	9.91666i		−	0.374280i
$703$	3.11150	−	10.1935i	0.117353	−	0.384454i
$704$	3.64287			0.137296
$705$	−12.1782	+	17.8531i	−0.458656	+	0.672386i
$706$	47.2172			1.77704
$707$			49.4631i			1.86025i
$708$	−1.04027			−0.0390959
$709$			41.6382i			1.56376i	0.623431	+	0.781878i	$0.285738\pi$
$709$			41.6382i			1.56376i	−0.623431	+	0.781878i	$0.714262\pi$
$710$	7.71533	−	11.3106i	0.289551	−	0.424480i
$711$			4.11758i			0.154421i
$712$		−	16.7246i		−	0.626781i
$713$		−	33.3991i		−	1.25081i
$714$	22.1269			0.828080
$715$	22.4583	−	32.9237i	0.839893	−	1.23128i
$716$		−	0.756417i		−	0.0282686i
$717$	13.4927			0.503893
$718$	18.3791			0.685900
$719$	35.2128			1.31322			0.656608	−	0.754232i	$-0.271991\pi$
$719$	35.2128			1.31322			0.656608	+	0.754232i	$0.271991\pi$
$720$	−6.29980	+	9.23546i	−0.234780	+	0.344185i
$721$			2.99688i			0.111610i
$722$	−27.5024			−1.02353
$723$	−25.9107			−0.963630
$724$	7.85103			0.291781
$725$	−24.8390	+	9.73515i	−0.922498	+	0.361554i
$726$			2.36809i			0.0878881i
$727$	1.68097			0.0623438			0.0311719	−	0.999514i	$-0.490076\pi$
$727$	1.68097			0.0623438			0.0311719	+	0.999514i	$0.490076\pi$
$728$			28.6239i			1.06087i
$729$	−1.00000			−0.0370370
$730$	−18.9831	−	12.9490i	−0.702597	−	0.479264i
$731$	−32.3953			−1.19818
$732$	7.96871			0.294532
$733$		−	1.63403i		−	0.0603543i	−0.999545	−	0.0301772i	$-0.990393\pi$
$733$		−	1.63403i		−	0.0603543i	0.999545	−	0.0301772i	$-0.00960715\pi$
$734$			15.1428i			0.558932i
$735$	1.88025	+	1.28258i	0.0693540	+	0.0473086i
$736$	36.4770			1.34456
$737$		−	38.4628i		−	1.41680i
$738$	1.81686			0.0668797
$739$	−12.8264			−0.471825			−0.235913	−	0.971774i	$-0.575808\pi$
$739$	−12.8264			−0.471825			−0.235913	+	0.971774i	$0.575808\pi$
$740$	−10.4055	+	8.34422i	−0.382514	+	0.306740i
$741$	−10.0642			−0.369716
$742$	−38.0189			−1.39572
$743$			47.8420i			1.75515i	0.479436	+	0.877577i	$0.340841\pi$
$743$			47.8420i			1.75515i	−0.479436	+	0.877577i	$0.659159\pi$
$744$	8.23716			0.301989
$745$	−16.7745	+	24.5912i	−0.614569	+	0.900953i
$746$		−	41.8942i		−	1.53386i
$747$		−	10.8378i		−	0.396534i
$748$	−13.7726			−0.503577
$749$	37.5803			1.37316
$750$	4.30841	−	18.8153i	0.157321	−	0.687038i
$751$	3.58403			0.130783			0.0653916	−	0.997860i	$-0.479170\pi$
$751$	3.58403			0.130783			0.0653916	+	0.997860i	$0.479170\pi$
$752$			48.3203i			1.76206i
$753$	1.92047			0.0699859
$754$		−	52.9126i		−	1.92696i
$755$	10.8655	−	15.9288i	0.395437	−	0.579707i
$756$	−2.77672			−0.100988
$757$	41.4380			1.50609			0.753046	−	0.657968i	$-0.228584\pi$
$757$	41.4380			1.50609			0.753046	+	0.657968i	$0.228584\pi$
$758$	−34.3870			−1.24899
$759$			22.1422i			0.803712i
$760$	5.69607	+	3.88547i	0.206618	+	0.140941i
$761$	41.5888			1.50759			0.753797	−	0.657107i	$-0.228220\pi$
$761$	41.5888			1.50759			0.753797	+	0.657107i	$0.228220\pi$
$762$	−31.4794			−1.14038
$763$	−7.42437			−0.268780
$764$		−	4.22594i		−	0.152889i
$765$	−5.70332	+	8.36102i	−0.206204	+	0.302293i
$766$	−25.0914			−0.906589
$767$		−	6.09336i		−	0.220018i
$768$			18.8018i			0.678450i
$769$			4.10288i			0.147954i	0.997260	+	0.0739768i	$0.0235691\pi$
$769$			4.10288i			0.147954i	−0.997260	+	0.0739768i	$0.976431\pi$
$770$	−28.0208	−	19.1139i	−1.00980	−	0.688816i
$771$			16.5592i			0.596365i
$772$	−18.5787			−0.668661
$773$			4.85790i			0.174727i	0.996177	+	0.0873633i	$0.0278441\pi$
$773$			4.85790i			0.174727i	−0.996177	+	0.0873633i	$0.972156\pi$
$774$	12.3566			0.444147
$775$	−21.7887	+	8.53962i	−0.782672	+	0.306752i
$776$	3.56311			0.127908
$777$	16.4735	+	5.02845i	0.590983	+	0.180394i
$778$			21.8830i			0.784543i
$779$		−	1.84389i		−	0.0660642i
$780$	10.4048	+	7.09748i	0.372553	+	0.254130i
$781$	11.0049			0.393787
$782$	55.7619			1.99404
$783$	−5.33573			−0.190683
$784$	5.08899			0.181750
$785$	11.8629	+	8.09210i	0.423407	+	0.288819i
$786$	−27.4461			−0.978971
$787$			21.9443i			0.782229i	0.920342	+	0.391114i	$0.127910\pi$
$787$			21.9443i			0.782229i	−0.920342	+	0.391114i	$0.872090\pi$
$788$		−	16.0461i		−	0.571618i
$789$	2.30498			0.0820595
$790$	−13.1316	−	8.95746i	−0.467200	−	0.318692i
$791$			31.0977i			1.10571i
$792$	−5.46089			−0.194044
$793$			46.6763i			1.65753i
$794$			3.08712i			0.109558i
$795$	9.79955	−	14.3661i	0.347554	−	0.509511i
$796$			22.0365i			0.781064i
$797$	−31.1968			−1.10505			−0.552524	−	0.833497i	$-0.686335\pi$
$797$	−31.1968			−1.10505			−0.552524	+	0.833497i	$0.686335\pi$
$798$			8.56543i			0.303213i
$799$			43.7451i			1.54759i
$800$	−9.32657	−	23.7966i	−0.329744	−	0.841335i
$801$			9.50316i			0.335778i
$802$		−	36.5097i		−	1.28920i
$803$		−	18.4701i		−	0.651796i
$804$	12.1554			0.428687
$805$	37.3247	+	25.4604i	1.31552	+	0.897361i
$806$		−	46.4146i		−	1.63489i
$807$			7.81395i			0.275064i
$808$	−30.7425			−1.08152
$809$			4.54212i			0.159692i	0.996807	+	0.0798462i	$0.0254429\pi$
$809$			4.54212i			0.159692i	−0.996807	+	0.0798462i	$0.974557\pi$
$810$	2.17542	−	3.18915i	0.0764365	−	0.112055i
$811$	35.1815			1.23539			0.617695	−	0.786418i	$-0.288067\pi$
$811$	35.1815			1.23539			0.617695	+	0.786418i	$0.288067\pi$
$812$	−14.8158			−0.519934
$813$		−	15.0306i		−	0.527146i
$814$	−31.1663	−	9.51335i	−1.09238	−	0.333443i
$815$	−18.2741	+	26.7897i	−0.640114	+	0.938401i
$816$			22.6295i			0.792192i
$817$		−	12.5404i		−	0.438732i
$818$			31.7095i			1.10870i
$819$		−	16.2645i		−	0.568328i
$820$	−1.30035	+	1.90631i	−0.0454103	+	0.0665711i
$821$	−16.4336			−0.573536			−0.286768	−	0.958000i	$-0.592581\pi$
$821$	−16.4336			−0.573536			−0.286768	+	0.958000i	$0.592581\pi$
$822$	28.9607			1.01012
$823$		−	22.2165i		−	0.774419i	−0.921992	−	0.387209i	$-0.873439\pi$
$823$		−	22.2165i		−	0.774419i	0.921992	−	0.387209i	$-0.126561\pi$
$824$	−1.86264			−0.0648880
$825$	14.4450	−	5.66141i	0.502909	−	0.197105i
$826$	−5.18595			−0.180442
$827$	−42.9400			−1.49317			−0.746586	−	0.665289i	$-0.768308\pi$
$827$	−42.9400			−1.49317			−0.746586	+	0.665289i	$0.768308\pi$
$828$	−6.99759			−0.243183
$829$		−	21.9652i		−	0.762882i	−0.924393	−	0.381441i	$-0.875428\pi$
$829$		−	21.9652i		−	0.762882i	0.924393	−	0.381441i	$-0.124572\pi$
$830$	34.5633	+	23.5767i	1.19971	+	0.818361i
$831$			3.75230i			0.130166i
$832$	−6.74341			−0.233786
$833$	4.60715			0.159628
$834$			11.2305i			0.388880i
$835$	15.0785	−	22.1049i	0.521813	−	0.764973i
$836$		−	5.33144i		−	0.184392i
$837$	−4.68047			−0.161781
$838$	−18.1019			−0.625321
$839$	−0.225911			−0.00779932			−0.00389966	−	0.999992i	$-0.501241\pi$
$839$	−0.225911			−0.00779932			−0.00389966	+	0.999992i	$0.501241\pi$
$840$	−6.27924	+	9.20531i	−0.216654	+	0.317614i
$841$	0.529978			0.0182751
$842$		−	48.5368i		−	1.67269i
$843$	7.47328			0.257393
$844$	−25.1085			−0.864270
$845$	−25.1924	+	36.9319i	−0.866646	+	1.27050i
$846$		−	16.6857i		−	0.573668i
$847$			3.88395i			0.133454i
$848$		−	38.8825i		−	1.33523i
$849$		−	1.21677i		−	0.0417593i
$850$	−14.2574	−	36.3775i	−0.489025	−	1.24774i
$851$	41.5147	+	12.6721i	1.42311	+	0.434395i
$852$			3.47787i			0.119150i
$853$	−44.7556			−1.53240			−0.766201	−	0.642601i	$-0.777855\pi$
$853$	−44.7556			−1.53240			−0.766201	+	0.642601i	$0.777855\pi$
$854$	39.7254			1.35938
$855$	−3.23659	−	2.20778i	−0.110689	−	0.0755045i
$856$			23.3571i			0.798330i
$857$	−22.4074			−0.765422			−0.382711	−	0.923868i	$-0.625010\pi$
$857$	−22.4074			−0.765422			−0.382711	+	0.923868i	$0.625010\pi$
$858$			30.7710i			1.05050i
$859$		−	46.2169i		−	1.57690i	−0.615099	−	0.788450i	$-0.710884\pi$
$859$		−	46.2169i		−	1.57690i	0.615099	−	0.788450i	$-0.289116\pi$
$860$	−8.84375	+	12.9649i	−0.301569	+	0.442098i
$861$	2.97988			0.101554
$862$		−	61.3487i		−	2.08954i
$863$			16.5381i			0.562964i	0.959566	+	0.281482i	$0.0908260\pi$
$863$			16.5381i			0.562964i	−0.959566	+	0.281482i	$0.909174\pi$
$864$		−	5.11179i		−	0.173907i
$865$	−15.2502	−	10.4027i	−0.518523	−	0.353701i
$866$			20.9930i			0.713370i
$867$			3.48689i			0.118421i
$868$	−12.9964			−0.441125
$869$		−	12.7767i		−	0.433419i
$870$	11.6075	−	17.0164i	0.393530	−	0.576911i
$871$			71.1995i			2.41250i
$872$		−	4.61443i		−	0.156264i
$873$	−2.02461			−0.0685227
$874$			21.5857i			0.730146i
$875$	7.06632	−	30.8594i	0.238885	−	1.04324i
$876$	5.83708			0.197217
$877$			11.4962i			0.388197i	0.980982	+	0.194099i	$0.0621782\pi$
$877$			11.4962i			0.388197i	−0.980982	+	0.194099i	$0.937822\pi$
$878$			56.6354i			1.91135i
$879$	23.9207			0.806826
$880$	19.5480	−	28.6572i	0.658964	−	0.966035i
$881$	−11.1543			−0.375799			−0.187900	−	0.982188i	$-0.560168\pi$
$881$	−11.1543			−0.375799			−0.187900	+	0.982188i	$0.560168\pi$
$882$	−1.75731			−0.0591716
$883$	3.95178			0.132988			0.0664939	−	0.997787i	$-0.478819\pi$
$883$	3.95178			0.132988			0.0664939	+	0.997787i	$0.478819\pi$
$884$	25.4948			0.857484
$885$	1.33670	−	1.95959i	0.0449327	−	0.0658710i
$886$		−	48.9470i		−	1.64441i
$887$			23.8584i			0.801086i	0.916278	+	0.400543i	$0.131179\pi$
$887$			23.8584i			0.801086i	−0.916278	+	0.400543i	$0.868821\pi$
$888$	−3.12530	+	10.2387i	−0.104878	+	0.343588i
$889$	−51.6301			−1.73162
$890$	−30.3070	−	20.6734i	−1.01589	−	0.692973i
$891$	3.10296			0.103953
$892$		−	25.5225i		−	0.854556i
$893$	−16.9339			−0.566673
$894$		−	22.9833i		−	0.768677i
$895$	1.42489	+	0.971960i	0.0476287	+	0.0324890i
$896$			34.6882i			1.15885i
$897$		−	40.9881i		−	1.36855i
$898$		−	21.5873i		−	0.720376i
$899$	−24.9737			−0.832921
$900$	1.78917	+	4.56503i	0.0596389	+	0.152168i
$901$		−	35.2009i		−	1.17271i
$902$	−5.63765			−0.187713
$903$	20.2663			0.674419
$904$	−19.3280			−0.642840
$905$	−10.0882	+	14.7892i	−0.335343	+	0.491610i
$906$			14.8873i			0.494596i
$907$	30.2797			1.00542			0.502710	−	0.864455i	$-0.332336\pi$
$907$	30.2797			1.00542			0.502710	+	0.864455i	$0.332336\pi$
$908$	−0.626617			−0.0207950
$909$	17.4683			0.579388
$910$	51.8700	+	35.3822i	1.71947	+	1.17291i
$911$			2.18038i			0.0722393i	0.999347	+	0.0361196i	$0.0114997\pi$
$911$			2.18038i			0.0722393i	−0.999347	+	0.0361196i	$0.988500\pi$
$912$	−8.75999			−0.290072
$913$			33.6292i			1.11296i
$914$	−58.9098			−1.94856
$915$	−10.2394	+	15.0109i	−0.338504	+	0.496245i
$916$	15.1791			0.501531
$917$	−45.0150			−1.48653
$918$		−	7.81433i		−	0.257911i
$919$			26.1806i			0.863619i	0.901965	+	0.431810i	$0.142125\pi$
$919$			26.1806i			0.863619i	−0.901965	+	0.431810i	$0.857875\pi$
$920$	−15.8243	+	23.1982i	−0.521710	+	0.764823i
$921$	−24.2455			−0.798915
$922$		−	50.9735i		−	1.67872i
$923$	−20.3715			−0.670536
$924$	8.61605			0.283447
$925$	−2.34769	−	30.3231i	−0.0771915	−	0.997016i
$926$	8.19378			0.269264
$927$	1.05838			0.0347616
$928$		−	27.2752i		−	0.895351i
$929$	−41.9296			−1.37567			−0.687833	−	0.725869i	$-0.741438\pi$
$929$	−41.9296			−1.37567			−0.687833	+	0.725869i	$0.741438\pi$
$930$	10.1820	−	14.9267i	0.333881	−	0.489466i
$931$			1.78345i			0.0584501i
$932$		−	10.0997i		−	0.330828i
$933$	1.30074			0.0425843
$934$	−22.6068			−0.739718
$935$	17.6972	−	25.9439i	0.578759	−	0.848456i
$936$	10.1088			0.330416
$937$			23.3404i			0.762497i	0.924473	+	0.381249i	$0.124506\pi$
$937$			23.3404i			0.762497i	−0.924473	+	0.381249i	$0.875494\pi$
$938$	60.5966			1.97855
$939$		−	9.51454i		−	0.310495i
$940$	17.5072	+	11.9422i	0.571020	+	0.389511i
$941$	22.0020			0.717245			0.358623	−	0.933483i	$-0.383246\pi$
$941$	22.0020			0.717245			0.358623	+	0.933483i	$0.383246\pi$
$942$	−11.0873			−0.361243
$943$	7.50956			0.244545
$944$		−	5.30374i		−	0.172622i
$945$	3.56795	−	5.23059i	0.116066	−	0.170151i
$946$	−38.3419			−1.24660
$947$	−18.1765			−0.590658			−0.295329	−	0.955396i	$-0.595429\pi$
$947$	−18.1765			−0.590658			−0.295329	+	0.955396i	$0.595429\pi$
$948$	4.03780			0.131141
$949$			34.1905i			1.10987i
$950$	14.0819	−	5.51910i	0.456876	−	0.179063i
$951$	29.3063			0.950323
$952$			22.5557i			0.731033i
$953$		−	25.5753i		−	0.828465i	−0.910171	−	0.414232i	$-0.864050\pi$
$953$		−	25.5753i		−	0.828465i	0.910171	−	0.414232i	$-0.135950\pi$
$954$			13.4267i			0.434706i
$955$	7.96053	+	5.43014i	0.257597	+	0.175715i
$956$		−	13.2312i		−	0.427929i
$957$	16.5565			0.535197
$958$		−	29.6748i		−	0.958751i
$959$	47.4991			1.53383
$960$	−2.16865	−	1.47931i	−0.0699928	−	0.0477444i
$961$	9.09317			0.293328
$962$	57.6928	+	17.6104i	1.86009	+	0.567782i
$963$		−	13.2718i		−	0.427679i
$964$			25.4087i			0.818358i
$965$	23.8727	−	34.9972i	0.768490	−	1.12660i
$966$	−34.8842			−1.12238
$967$	46.2383			1.48692			0.743461	−	0.668779i	$-0.233183\pi$
$967$	46.2383			1.48692			0.743461	+	0.668779i	$0.233183\pi$
$968$	−2.41397			−0.0775880
$969$	−7.93057			−0.254766
$970$	4.40438	−	6.45679i	0.141416	−	0.207315i
$971$	19.3514			0.621016			0.310508	−	0.950571i	$-0.399501\pi$
$971$	19.3514			0.621016			0.310508	+	0.950571i	$0.399501\pi$
$972$			0.980624i			0.0314535i
$973$			18.4194i			0.590498i
$974$	58.6110			1.87802
$975$	−26.7394	+	10.4800i	−0.856348	+	0.335628i
$976$			40.6277i			1.30046i
$977$	40.2007			1.28613			0.643067	−	0.765810i	$-0.277662\pi$
$977$	40.2007			1.28613			0.643067	+	0.765810i	$0.277662\pi$
$978$		−	25.0380i		−	0.800627i
$979$		−	29.4879i		−	0.942437i
$980$	1.25773	−	1.84382i	0.0401766	−	0.0588986i
$981$			2.62198i			0.0837135i
$982$	−48.1952			−1.53797
$983$		−	41.1878i		−	1.31369i	−0.754028	−	0.656843i	$-0.771891\pi$
$983$		−	41.1878i		−	1.31369i	0.754028	−	0.656843i	$-0.228109\pi$
$984$			1.85207i			0.0590418i
$985$	30.2265	+	20.6184i	0.963095	+	0.656958i
$986$		−	41.6951i		−	1.32784i
$987$		−	27.3666i		−	0.871090i
$988$			9.86917i			0.313980i
$989$	51.0728			1.62402
$990$	−6.75024	+	9.89579i	−0.214537	+	0.314509i
$991$			9.29836i			0.295372i	0.989034	+	0.147686i	$0.0471825\pi$
$991$			9.29836i			0.295372i	−0.989034	+	0.147686i	$0.952817\pi$
$992$		−	23.9256i		−	0.759639i
$993$	−25.7197			−0.816189
$994$			17.3378i			0.549922i
$995$	−41.5109	−	28.3159i	−1.31598	−	0.897674i
$996$	−10.6278			−0.336755
$997$	6.69474			0.212025			0.106012	−	0.994365i	$-0.466192\pi$
$997$	6.69474			0.212025			0.106012	+	0.994365i	$0.466192\pi$
$998$			41.7210i			1.32066i
$999$	1.77584	−	5.81776i	0.0561851	−	0.184066i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	555.2.g.a.184.10	yes	40
3.2	odd	2		1665.2.g.e.739.31		40
5.4	even	2	inner	555.2.g.a.184.31	yes	40
15.14	odd	2		1665.2.g.e.739.10		40
37.36	even	2	inner	555.2.g.a.184.32	yes	40
111.110	odd	2		1665.2.g.e.739.9		40
185.184	even	2	inner	555.2.g.a.184.9	✓	40
555.554	odd	2		1665.2.g.e.739.32		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
555.2.g.a.184.9	✓	40	185.184	even	2	inner
555.2.g.a.184.10	yes	40	1.1	even	1	trivial
555.2.g.a.184.31	yes	40	5.4	even	2	inner
555.2.g.a.184.32	yes	40	37.36	even	2	inner
1665.2.g.e.739.9		40	111.110	odd	2
1665.2.g.e.739.10		40	15.14	odd	2
1665.2.g.e.739.31		40	3.2	odd	2
1665.2.g.e.739.32		40	555.554	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)

\(f(q)\)	\(=\)	\(q-1.72645 q^{2} +1.00000i q^{3} +0.980624 q^{4} +(-1.26006 + 1.84723i) q^{5} -1.72645i q^{6} -2.83159i q^{7} +1.75990 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.72645 q^{2} +1.00000i q^{3} +0.980624 q^{4} +(-1.26006 + 1.84723i) q^{5} -1.72645i q^{6} -2.83159i q^{7} +1.75990 q^{8} -1.00000 q^{9} +(2.17542 - 3.18915i) q^{10} +3.10296 q^{11} +0.980624i q^{12} -5.74396 q^{13} +4.88859i q^{14} +(-1.84723 - 1.26006i) q^{15} -4.99962 q^{16} -4.52624 q^{17} +1.72645 q^{18} -1.75213i q^{19} +(-1.23564 + 1.81144i) q^{20} +2.83159 q^{21} -5.35710 q^{22} +7.13585 q^{23} +1.75990i q^{24} +(-1.82452 - 4.65523i) q^{25} +9.91666 q^{26} -1.00000i q^{27} -2.77672i q^{28} -5.33573i q^{29} +(3.18915 + 2.17542i) q^{30} -4.68047i q^{31} +5.11179 q^{32} +3.10296i q^{33} +7.81433 q^{34} +(5.23059 + 3.56795i) q^{35} -0.980624 q^{36} +(5.81776 + 1.77584i) q^{37} +3.02496i q^{38} -5.74396i q^{39} +(-2.21757 + 3.25094i) q^{40} +1.05237 q^{41} -4.88859 q^{42} +7.15721 q^{43} +3.04284 q^{44} +(1.26006 - 1.84723i) q^{45} -12.3197 q^{46} -9.66478i q^{47} -4.99962i q^{48} -1.01787 q^{49} +(3.14994 + 8.03701i) q^{50} -4.52624i q^{51} -5.63267 q^{52} +7.77708i q^{53} +1.72645i q^{54} +(-3.90990 + 5.73188i) q^{55} -4.98331i q^{56} +1.75213 q^{57} +9.21186i q^{58} +1.06083i q^{59} +(-1.81144 - 1.23564i) q^{60} -8.12616i q^{61} +8.08060i q^{62} +2.83159i q^{63} +1.17400 q^{64} +(7.23771 - 10.6104i) q^{65} -5.35710i q^{66} -12.3955i q^{67} -4.43854 q^{68} +7.13585i q^{69} +(-9.03034 - 6.15989i) q^{70} +3.54659 q^{71} -1.75990 q^{72} -5.95242i q^{73} +(-10.0441 - 3.06590i) q^{74} +(4.65523 - 1.82452i) q^{75} -1.71818i q^{76} -8.78629i q^{77} +9.91666i q^{78} -4.11758i q^{79} +(6.29980 - 9.23546i) q^{80} +1.00000 q^{81} -1.81686 q^{82} +10.8378i q^{83} +2.77672 q^{84} +(5.70332 - 8.36102i) q^{85} -12.3566 q^{86} +5.33573 q^{87} +5.46089 q^{88} -9.50316i q^{89} +(-2.17542 + 3.18915i) q^{90} +16.2645i q^{91} +6.99759 q^{92} +4.68047 q^{93} +16.6857i q^{94} +(3.23659 + 2.20778i) q^{95} +5.11179i q^{96} +2.02461 q^{97} +1.75731 q^{98} -3.10296 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 44 q^{4} - 40 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more