LMFDB - Embedded newform 261.2.k.d.190.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,2,Mod(82,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("261.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.k (of order $7$, degree $6$, 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:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			190.1
Character	$\chi$	$=$	261.190
Dual form			261.2.k.d.136.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.95622 - 0.942065i) q^{2} +(1.69232 + 2.12210i) q^{4} +(-0.656754 - 0.316276i) q^{5} +(0.363311 - 0.455578i) q^{7} +(-0.345098 - 1.51197i) q^{8} +O(q^{10})$	\(q+(-1.95622 - 0.942065i) q^{2} +(1.69232 + 2.12210i) q^{4} +(-0.656754 - 0.316276i) q^{5} +(0.363311 - 0.455578i) q^{7} +(-0.345098 - 1.51197i) q^{8} +(0.986801 + 1.23741i) q^{10} +(0.764678 - 3.35027i) q^{11} +(0.164815 - 0.722101i) q^{13} +(-1.13990 + 0.548947i) q^{14} +(0.458675 - 2.00959i) q^{16} +1.15663 q^{17} +(-2.86344 - 3.59065i) q^{19} +(-0.440268 - 1.92894i) q^{20} +(-4.65205 + 5.83349i) q^{22} +(1.69884 - 0.818120i) q^{23} +(-2.78615 - 3.49373i) q^{25} +(-1.00268 + 1.25732i) q^{26} +1.58162 q^{28} +(-3.01914 - 4.45923i) q^{29} +(-5.25634 - 2.53132i) q^{31} +(-4.72432 + 5.92410i) q^{32} +(-2.26262 - 1.08962i) q^{34} +(-0.382694 + 0.184296i) q^{35} +(-0.448168 - 1.96355i) q^{37} +(2.21890 + 9.72164i) q^{38} +(-0.251557 + 1.10214i) q^{40} -4.49970 q^{41} +(6.97984 - 3.36131i) q^{43} +(8.40371 - 4.04701i) q^{44} -4.09403 q^{46} +(1.04716 - 4.58793i) q^{47} +(1.48209 + 6.49346i) q^{49} +(2.15901 + 9.45923i) q^{50} +(1.81129 - 0.872273i) q^{52} +(8.32592 + 4.00955i) q^{53} +(-1.56182 + 1.95846i) q^{55} +(-0.814200 - 0.392098i) q^{56} +(1.70522 + 11.5675i) q^{58} +7.16705 q^{59} +(7.83850 - 9.82917i) q^{61} +(7.89787 + 9.90362i) q^{62} +(11.1084 - 5.34953i) q^{64} +(-0.336626 + 0.422116i) q^{65} +(3.26496 + 14.3047i) q^{67} +(1.95739 + 2.45449i) q^{68} +0.922252 q^{70} +(2.26207 - 9.91077i) q^{71} +(-4.90782 + 2.36348i) q^{73} +(-0.973079 + 4.26334i) q^{74} +(2.77386 - 12.1531i) q^{76} +(-1.24849 - 1.56556i) q^{77} +(1.56435 + 6.85386i) q^{79} +(-0.936820 + 1.17474i) q^{80} +(8.80240 + 4.23901i) q^{82} +(7.17629 + 8.99878i) q^{83} +(-0.759622 - 0.365815i) q^{85} -16.8207 q^{86} -5.32942 q^{88} +(-13.9703 - 6.72773i) q^{89} +(-0.269094 - 0.337434i) q^{91} +(4.61112 + 2.22060i) q^{92} +(-6.37060 + 7.98848i) q^{94} +(0.744943 + 3.26381i) q^{95} +(3.05509 + 3.83096i) q^{97} +(3.21797 - 14.0989i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{4}+O(q^{10}) $ 24 * q + 2 * q^4	$ 24 q + 2 q^{4} - 4 q^{10} + 18 q^{13} - 22 q^{16} - 40 q^{22} + 18 q^{25} - 24 q^{28} - 28 q^{31} - 50 q^{34} - 40 q^{37} + 30 q^{43} + 40 q^{46} + 36 q^{49} - 52 q^{52} + 10 q^{55} + 54 q^{58} + 64 q^{61} + 20 q^{64} - 24 q^{67} + 120 q^{70} - 76 q^{73} + 126 q^{76} + 10 q^{79} - 10 q^{82} + 62 q^{85} - 20 q^{88} + 82 q^{91} - 36 q^{94} - 60 q^{97}+O(q^{100}) $ 24 * q + 2 * q^4 - 4 * q^10 + 18 * q^13 - 22 * q^16 - 40 * q^22 + 18 * q^25 - 24 * q^28 - 28 * q^31 - 50 * q^34 - 40 * q^37 + 30 * q^43 + 40 * q^46 + 36 * q^49 - 52 * q^52 + 10 * q^55 + 54 * q^58 + 64 * q^61 + 20 * q^64 - 24 * q^67 + 120 * q^70 - 76 * q^73 + 126 * q^76 + 10 * q^79 - 10 * q^82 + 62 * q^85 - 20 * q^88 + 82 * q^91 - 36 * q^94 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{1}{7}\right)$	$1$

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 $

$2$	−1.95622	−	0.942065i	−1.38325	−	0.666140i	−0.413564	−	0.910475i	$-0.635716\pi$
$2$	−1.95622	−	0.942065i	−1.38325	−	0.666140i	−0.969691	+	0.244335i	$0.921430\pi$
$3$		0			0
$3$		0			0
$4$	1.69232	+	2.12210i	0.846161	+	1.06105i
$5$	−0.656754	−	0.316276i	−0.293709	−	0.141443i	0.281227	−	0.959641i	$-0.409259\pi$
$5$	−0.656754	−	0.316276i	−0.293709	−	0.141443i	−0.574936	+	0.818198i	$0.694973\pi$
$6$		0			0
$7$	0.363311	−	0.455578i	0.137319	−	0.172192i	−0.708417	−	0.705794i	$-0.750590\pi$
$7$	0.363311	−	0.455578i	0.137319	−	0.172192i	0.845736	+	0.533602i	$0.179162\pi$
$8$	−0.345098	−	1.51197i	−0.122011	−	0.534564i
$9$		0			0
$10$	0.986801	+	1.23741i	0.312054	+	0.391303i
$11$	0.764678	−	3.35027i	0.230559	−	1.01015i	−0.718619	−	0.695404i	$-0.755225\pi$
$11$	0.764678	−	3.35027i	0.230559	−	1.01015i	0.949178	−	0.314741i	$-0.101918\pi$
$12$		0			0
$13$	0.164815	−	0.722101i	0.0457114	−	0.200275i	−0.946916	−	0.321481i	$-0.895819\pi$
$13$	0.164815	−	0.722101i	0.0457114	−	0.200275i	0.992627	+	0.121207i	$0.0386764\pi$
$14$	−1.13990	+	0.548947i	−0.304651	+	0.146712i
$15$		0			0
$16$	0.458675	−	2.00959i	0.114669	−	0.502397i
$17$	1.15663			0.280524			0.140262	−	0.990114i	$-0.455205\pi$
$17$	1.15663			0.280524			0.140262	+	0.990114i	$0.455205\pi$
$18$		0			0
$19$	−2.86344	−	3.59065i	−0.656919	−	0.823751i	0.336085	−	0.941832i	$-0.390897\pi$
$19$	−2.86344	−	3.59065i	−0.656919	−	0.823751i	−0.993004	+	0.118081i	$0.962326\pi$
$20$	−0.440268	−	1.92894i	−0.0984470	−	0.431324i
$21$		0			0
$22$	−4.65205	+	5.83349i	−0.991820	+	1.24370i
$23$	1.69884	−	0.818120i	0.354233	−	0.170590i	−0.248301	−	0.968683i	$-0.579872\pi$
$23$	1.69884	−	0.818120i	0.354233	−	0.170590i	0.602534	+	0.798093i	$0.294158\pi$
$24$		0			0
$25$	−2.78615	−	3.49373i	−0.557231	−	0.698745i
$26$	−1.00268	+	1.25732i	−0.196642	+	0.246581i
$27$		0			0
$28$	1.58162			0.298899
$29$	−3.01914	−	4.45923i	−0.560641	−	0.828059i
$29$	−3.01914	−	4.45923i	−0.560641	−	0.828059i
$30$		0			0
$31$	−5.25634	−	2.53132i	−0.944066	−	0.454638i	−0.102464	−	0.994737i	$-0.532673\pi$
$31$	−5.25634	−	2.53132i	−0.944066	−	0.454638i	−0.841602	+	0.540099i	$0.818387\pi$
$32$	−4.72432	+	5.92410i	−0.835149	+	1.04724i
$33$		0			0
$34$	−2.26262	−	1.08962i	−0.388037	−	0.186869i
$35$	−0.382694	+	0.184296i	−0.0646872	+	0.0311517i
$36$		0			0
$37$	−0.448168	−	1.96355i	−0.0736784	−	0.322806i	0.924635	−	0.380853i	$-0.124370\pi$
$37$	−0.448168	−	1.96355i	−0.0736784	−	0.322806i	−0.998314	+	0.0580473i	$0.981513\pi$
$38$	2.21890	+	9.72164i	0.359953	+	1.57706i
$39$		0			0
$40$	−0.251557	+	1.10214i	−0.0397746	+	0.174264i
$41$	−4.49970			−0.702736			−0.351368	−	0.936238i	$-0.614283\pi$
$41$	−4.49970			−0.702736			−0.351368	+	0.936238i	$0.614283\pi$
$42$		0			0
$43$	6.97984	−	3.36131i	1.06442	−	0.512595i	0.182113	−	0.983278i	$-0.441706\pi$
$43$	6.97984	−	3.36131i	1.06442	−	0.512595i	0.882303	+	0.470682i	$0.155992\pi$
$44$	8.40371	−	4.04701i	1.26691	−	0.610110i
$45$		0			0
$46$	−4.09403			−0.603632
$47$	1.04716	−	4.58793i	0.152745	−	0.669218i	−0.839336	−	0.543613i	$-0.817056\pi$
$47$	1.04716	−	4.58793i	0.152745	−	0.669218i	0.992080	−	0.125604i	$-0.0400870\pi$
$48$		0			0
$49$	1.48209	+	6.49346i	0.211727	+	0.927637i
$50$	2.15901	+	9.45923i	0.305330	+	1.33774i
$51$		0			0
$52$	1.81129	−	0.872273i	0.251181	−	0.120963i
$53$	8.32592	+	4.00955i	1.14365	+	0.550755i	0.907121	−	0.420869i	$-0.138275\pi$
$53$	8.32592	+	4.00955i	1.14365	+	0.550755i	0.236532	+	0.971624i	$0.423989\pi$
$54$		0			0
$55$	−1.56182	+	1.95846i	−0.210595	+	0.264078i
$56$	−0.814200	−	0.392098i	−0.108802	−	0.0523963i
$57$		0			0
$58$	1.70522	+	11.5675i	0.223906	+	1.51888i
$59$	7.16705			0.933070			0.466535	−	0.884503i	$-0.345502\pi$
$59$	7.16705			0.933070			0.466535	+	0.884503i	$0.345502\pi$
$60$		0			0
$61$	7.83850	−	9.82917i	1.00362	−	1.25850i	0.0377959	−	0.999285i	$-0.487966\pi$
$61$	7.83850	−	9.82917i	1.00362	−	1.25850i	0.965821	−	0.259210i	$-0.0834622\pi$
$62$	7.89787	+	9.90362i	1.00303	+	1.25776i
$63$		0			0
$64$	11.1084	−	5.34953i	1.38855	−	0.668691i
$65$	−0.336626	+	0.422116i	−0.0417533	+	0.0523570i
$66$		0			0
$67$	3.26496	+	14.3047i	0.398878	+	1.74760i	0.631826	+	0.775110i	$0.282306\pi$
$67$	3.26496	+	14.3047i	0.398878	+	1.74760i	−0.232948	+	0.972489i	$0.574837\pi$
$68$	1.95739	+	2.45449i	0.237369	+	0.297651i
$69$		0			0
$70$	0.922252			0.110230
$71$	2.26207	−	9.91077i	0.268458	−	1.17619i	−0.643349	−	0.765573i	$-0.722456\pi$
$71$	2.26207	−	9.91077i	0.268458	−	1.17619i	0.911807	−	0.410619i	$-0.134687\pi$
$72$		0			0
$73$	−4.90782	+	2.36348i	−0.574417	+	0.276625i	−0.698456	−	0.715653i	$-0.746129\pi$
$73$	−4.90782	+	2.36348i	−0.574417	+	0.276625i	0.124039	+	0.992277i	$0.460415\pi$
$74$	−0.973079	+	4.26334i	−0.113118	+	0.495603i
$75$		0			0
$76$	2.77386	−	12.1531i	0.318183	−	1.39405i
$77$	−1.24849	−	1.56556i	−0.142279	−	0.178412i
$78$		0			0
$79$	1.56435	+	6.85386i	0.176003	+	0.771120i	0.983450	+	0.181180i	$0.0579915\pi$
$79$	1.56435	+	6.85386i	0.176003	+	0.771120i	−0.807447	+	0.589940i	$0.799151\pi$
$80$	−0.936820	+	1.17474i	−0.104740	+	0.131339i
$81$		0			0
$82$	8.80240	+	4.23901i	0.972062	+	0.468121i
$83$	7.17629	+	8.99878i	0.787700	+	0.987745i	0.999945	+	0.0105282i	$0.00335130\pi$
$83$	7.17629	+	8.99878i	0.787700	+	0.987745i	−0.212244	+	0.977217i	$0.568077\pi$
$84$		0			0
$85$	−0.759622	−	0.365815i	−0.0823926	−	0.0396782i
$86$	−16.8207			−1.81382
$87$		0			0
$88$	−5.32942			−0.568118
$89$	−13.9703	−	6.72773i	−1.48085	−	0.713138i	−0.493212	−	0.869909i	$-0.664177\pi$
$89$	−13.9703	−	6.72773i	−1.48085	−	0.713138i	−0.987635	+	0.156771i	$0.949892\pi$
$90$		0			0
$91$	−0.269094	−	0.337434i	−0.0282087	−	0.0353726i
$92$	4.61112	+	2.22060i	0.480743	+	0.231514i
$93$		0			0
$94$	−6.37060	+	7.98848i	−0.657078	+	0.823949i
$95$	0.744943	+	3.26381i	0.0764296	+	0.334860i
$96$		0			0
$97$	3.05509	+	3.83096i	0.310197	+	0.388975i	0.912353	−	0.409403i	$-0.134263\pi$
$97$	3.05509	+	3.83096i	0.310197	+	0.388975i	−0.602157	+	0.798378i	$0.705692\pi$
$98$	3.21797	−	14.0989i	0.325064	−	1.42420i
$99$		0			0
$100$	2.69898	−	11.8250i	0.269898	−	1.18250i
$101$	−11.3965	+	5.48829i	−1.13400	+	0.546105i	−0.904190	−	0.427131i	$-0.859524\pi$
$101$	−11.3965	+	5.48829i	−1.13400	+	0.546105i	−0.229809	+	0.973236i	$0.573810\pi$
$102$		0			0
$103$	1.13244	−	4.96154i	0.111582	−	0.488875i	−0.887996	−	0.459851i	$-0.847903\pi$
$103$	1.13244	−	4.96154i	0.111582	−	0.488875i	0.999579	−	0.0290241i	$-0.00923996\pi$
$104$	−1.14868			−0.112637
$105$		0			0
$106$	−12.5101	−	15.6871i	−1.21508	−	1.52367i
$107$	−3.06973	−	13.4494i	−0.296762	−	1.30020i	−0.874917	−	0.484273i	$-0.839084\pi$
$107$	−3.06973	−	13.4494i	−0.296762	−	1.30020i	0.578155	−	0.815927i	$-0.303773\pi$
$108$		0			0
$109$	−8.99364	+	11.2777i	−0.861434	+	1.08020i	0.134571	+	0.990904i	$0.457035\pi$
$109$	−8.99364	+	11.2777i	−0.861434	+	1.08020i	−0.996005	+	0.0893003i	$0.971537\pi$
$110$	4.90024	−	2.35983i	0.467220	−	0.225001i
$111$		0			0
$112$	−0.748881	−	0.939067i	−0.0707626	−	0.0887335i
$113$	−1.32941	+	1.66703i	−0.125061	+	0.156821i	−0.840420	−	0.541936i	$-0.817692\pi$
$113$	−1.32941	+	1.66703i	−0.125061	+	0.156821i	0.715359	+	0.698757i	$0.246263\pi$
$114$		0			0
$115$	−1.37447			−0.128170
$116$	4.35359	−	13.9534i	0.404221	−	1.29554i
$117$		0			0
$118$	−14.0203	−	6.75183i	−1.29067	−	0.621556i
$119$	0.420217	−	0.526936i	0.0385213	−	0.0483041i
$120$		0			0
$121$	−0.728936	−	0.351037i	−0.0662669	−	0.0319125i
$122$	−24.5935	+	11.8436i	−2.22659	+	1.07227i
$123$		0			0
$124$	−3.52369	−	15.4383i	−0.316437	−	1.38640i
$125$	1.53586	+	6.72904i	0.137371	+	0.601864i
$126$		0			0
$127$	−0.822699	+	3.60448i	−0.0730028	+	0.319846i	−0.998223	−	0.0595837i	$-0.981023\pi$
$127$	−0.822699	+	3.60448i	−0.0730028	+	0.319846i	0.925221	+	0.379430i	$0.123880\pi$
$128$	−11.6156			−1.02669
$129$		0			0
$130$	1.05617	−	0.508627i	0.0926326	−	0.0446095i
$131$	16.3663	−	7.88161i	1.42993	−	0.688620i	0.450948	−	0.892550i	$-0.351086\pi$
$131$	16.3663	−	7.88161i	1.42993	−	0.688620i	0.978985	+	0.203930i	$0.0653716\pi$
$132$		0			0
$133$	−2.67614			−0.232051
$134$	7.08900	−	31.0589i	0.612396	−	2.68308i
$135$		0			0
$136$	−0.399152	−	1.74880i	−0.0342270	−	0.149958i
$137$	1.72140	+	7.54195i	0.147069	+	0.644352i	0.993691	+	0.112156i	$0.0357758\pi$
$137$	1.72140	+	7.54195i	0.147069	+	0.644352i	−0.846621	+	0.532196i	$0.821367\pi$
$138$		0			0
$139$	−3.74500	+	1.80350i	−0.317647	+	0.152971i	−0.585913	−	0.810374i	$-0.699264\pi$
$139$	−3.74500	+	1.80350i	−0.317647	+	0.152971i	0.268266	+	0.963345i	$0.413550\pi$
$140$	−1.03874	−	0.500230i	−0.0877893	−	0.0422771i
$141$		0			0
$142$	−13.7617	+	17.2566i	−1.15485	+	1.44814i
$143$	−2.29321	−	1.10435i	−0.191767	−	0.0923504i
$144$		0			0
$145$	0.572486	+	3.88350i	0.0475424	+	0.322507i
$146$	11.8273			0.978836
$147$		0			0
$148$	3.40842	−	4.27402i	0.280170	−	0.351322i
$149$	2.61777	+	3.28258i	0.214456	+	0.268919i	0.877411	−	0.479740i	$-0.159269\pi$
$149$	2.61777	+	3.28258i	0.214456	+	0.268919i	−0.662954	+	0.748660i	$0.730698\pi$
$150$		0			0
$151$	8.16525	−	3.93218i	0.664479	−	0.319996i	−0.0710666	−	0.997472i	$-0.522640\pi$
$151$	8.16525	−	3.93218i	0.664479	−	0.319996i	0.735545	+	0.677475i	$0.236926\pi$
$152$	−4.44080	+	5.56858i	−0.360196	+	0.451672i
$153$		0			0
$154$	0.967465	+	4.23874i	0.0779606	+	0.341568i
$155$	2.65152	+	3.32491i	0.212976	+	0.267063i
$156$		0			0
$157$	4.26604			0.340467			0.170234	−	0.985404i	$-0.445548\pi$
$157$	4.26604			0.340467			0.170234	+	0.985404i	$0.445548\pi$
$158$	3.39657	−	14.8814i	0.270217	−	1.18390i
$159$		0			0
$160$	4.97637	−	2.39649i	0.393416	−	0.189459i
$161$	0.244492	−	1.07119i	0.0192686	−	0.0844214i
$162$		0			0
$163$	0.528272	−	2.31451i	0.0413775	−	0.181287i	−0.950016	−	0.312200i	$-0.898934\pi$
$163$	0.528272	−	2.31451i	0.0413775	−	0.181287i	0.991394	+	0.130914i	$0.0417911\pi$
$164$	−7.61495	−	9.54884i	−0.594627	−	0.745639i
$165$		0			0
$166$	−5.56095	−	24.3641i	−0.431613	−	1.89102i
$167$	−7.17067	+	8.99173i	−0.554883	+	0.695801i	−0.977603	−	0.210459i	$-0.932504\pi$
$167$	−7.17067	+	8.99173i	−0.554883	+	0.695801i	0.422720	+	0.906260i	$0.361075\pi$
$168$		0			0
$169$	11.2183	+	5.40246i	0.862948	+	0.415574i
$170$	1.14137	+	1.43123i	0.0875387	+	0.109770i
$171$		0			0
$172$	18.9452	+	9.12352i	1.44456	+	0.695662i
$173$	−23.2286			−1.76604			−0.883018	−	0.469339i	$-0.844492\pi$
$173$	−23.2286			−1.76604			−0.883018	+	0.469339i	$0.844492\pi$
$174$		0			0
$175$	−2.60391			−0.196837
$176$	−6.38192	−	3.07337i	−0.481056	−	0.231664i
$177$		0			0
$178$	20.9910	+	26.3218i	1.57334	+	1.97290i
$179$	14.5741	+	7.01853i	1.08932	+	0.524590i	0.890286	−	0.455402i	$-0.150505\pi$
$179$	14.5741	+	7.01853i	1.08932	+	0.524590i	0.199036	+	0.979992i	$0.436219\pi$
$180$		0			0
$181$	−3.43541	+	4.30787i	−0.255352	+	0.320201i	−0.892939	−	0.450177i	$-0.851361\pi$
$181$	−3.43541	+	4.30787i	−0.255352	+	0.320201i	0.637588	+	0.770378i	$0.279932\pi$
$182$	0.208523	+	0.913598i	0.0154567	+	0.0677204i
$183$		0			0
$184$	−1.82324	−	2.28628i	−0.134411	−	0.168546i
$185$	−0.326688	+	1.43132i	−0.0240186	+	0.105232i
$186$		0			0
$187$	0.884451	−	3.87503i	0.0646774	−	0.283370i
$188$	11.5082	−	5.54205i	0.839321	−	0.404196i
$189$		0			0
$190$	1.61745	−	7.08651i	0.117342	−	0.514109i
$191$	1.95100			0.141169			0.0705846	−	0.997506i	$-0.477514\pi$
$191$	1.95100			0.141169			0.0705846	+	0.997506i	$0.477514\pi$
$192$		0			0
$193$	−3.14384	−	3.94225i	−0.226299	−	0.283769i	0.655700	−	0.755022i	$-0.272374\pi$
$193$	−3.14384	−	3.94225i	−0.226299	−	0.283769i	−0.881999	+	0.471252i	$0.843802\pi$
$194$	−2.36740	−	10.3723i	−0.169970	−	0.744686i
$195$		0			0
$196$	−11.2716	+	14.1342i	−0.805117	+	1.00958i
$197$	−13.0631	+	6.29084i	−0.930704	+	0.448204i	−0.836881	−	0.547385i	$-0.815623\pi$
$197$	−13.0631	+	6.29084i	−0.930704	+	0.448204i	−0.0938235	+	0.995589i	$0.529909\pi$
$198$		0			0
$199$	4.11392	+	5.15869i	0.291628	+	0.365690i	0.905964	−	0.423355i	$-0.139148\pi$
$199$	4.11392	+	5.15869i	0.291628	+	0.365690i	−0.614336	+	0.789044i	$0.710576\pi$
$200$	−4.32093	+	5.41827i	−0.305536	+	0.383130i
$201$		0			0
$202$	27.4644			1.93239
$203$	−3.12842	−	0.244634i	−0.219572	−	0.0171699i
$204$		0			0
$205$	2.95520	+	1.42315i	0.206400	+	0.0993970i
$206$	−6.88939	+	8.63902i	−0.480006	+	0.601909i
$207$		0			0
$208$	−1.37553	−	0.662419i	−0.0953757	−	0.0459305i
$209$	−14.2193	+	6.84763i	−0.983567	+	0.473661i
$210$		0			0
$211$	−2.35621	−	10.3233i	−0.162209	−	0.710682i	−0.988968	−	0.148127i	$-0.952676\pi$
$211$	−2.35621	−	10.3233i	−0.162209	−	0.710682i	0.826760	−	0.562555i	$-0.190182\pi$
$212$	5.58145	+	24.4539i	0.383336	+	1.67950i
$213$		0			0
$214$	−6.66512	+	29.2018i	−0.455618	+	1.99619i
$215$	−5.64714			−0.385132
$216$		0			0
$217$	−3.06290	+	1.47501i	−0.207923	+	0.100130i
$218$	28.2178	−	13.5890i	1.91115	−	0.920362i
$219$		0			0
$220$	−6.79914			−0.458398
$221$	0.190630	−	0.835205i	0.0128232	−	0.0561820i
$222$		0			0
$223$	−2.10703	−	9.23148i	−0.141097	−	0.618186i	−0.995181	−	0.0980514i	$-0.968739\pi$
$223$	−2.10703	−	9.23148i	−0.141097	−	0.618186i	0.854085	−	0.520134i	$-0.174118\pi$
$224$	0.982494	+	4.30459i	0.0656456	+	0.287612i
$225$		0			0
$226$	4.17107	−	2.00868i	0.277455	−	0.133615i
$227$	20.7189	+	9.97770i	1.37516	+	0.662243i	0.967962	−	0.251095i	$-0.0807908\pi$
$227$	20.7189	+	9.97770i	1.37516	+	0.662243i	0.407200	+	0.913339i	$0.366505\pi$
$228$		0			0
$229$	8.54164	−	10.7109i	0.564448	−	0.707795i	−0.414925	−	0.909855i	$-0.636192\pi$
$229$	8.54164	−	10.7109i	0.564448	−	0.707795i	0.979373	+	0.202060i	$0.0647637\pi$
$230$	2.68877	+	1.29484i	0.177292	+	0.0853794i
$231$		0			0
$232$	−5.70035	+	6.10374i	−0.374246	+	0.400730i
$233$	5.75529			0.377041			0.188521	−	0.982069i	$-0.439631\pi$
$233$	5.75529			0.377041			0.188521	+	0.982069i	$0.439631\pi$
$234$		0			0
$235$	−2.13878	+	2.68194i	−0.139519	+	0.174951i
$236$	12.1290	+	15.2092i	0.789528	+	0.990036i
$237$		0			0
$238$	−1.31844	+	0.634929i	−0.0854620	+	0.0411563i
$239$	12.7700	−	16.0131i	0.826022	−	1.03580i	−0.172685	−	0.984977i	$-0.555244\pi$
$239$	12.7700	−	16.0131i	0.826022	−	1.03580i	0.998708	−	0.0508224i	$-0.0161842\pi$
$240$		0			0
$241$	−3.16611	−	13.8716i	−0.203947	−	0.893550i	−0.968505	−	0.248995i	$-0.919900\pi$
$241$	−3.16611	−	13.8716i	−0.203947	−	0.893550i	0.764558	−	0.644555i	$-0.222957\pi$
$242$	1.09526	+	1.37341i	0.0704059	+	0.0882862i
$243$		0			0
$244$	34.1238			2.18455
$245$	1.08036	−	4.73336i	0.0690215	−	0.302403i
$246$		0			0
$247$	−3.06475	+	1.47591i	−0.195005	+	0.0939096i
$248$	−2.01334	+	8.82100i	−0.127847	+	0.560134i
$249$		0			0
$250$	3.33472	−	14.6103i	0.210906	−	0.924039i
$251$	15.3990	+	19.3098i	0.971977	+	1.21882i	0.975763	+	0.218828i	$0.0702233\pi$
$251$	15.3990	+	19.3098i	0.971977	+	1.21882i	−0.00378637	+	0.999993i	$0.501205\pi$
$252$		0			0
$253$	−1.44186	−	6.31718i	−0.0906487	−	0.397158i
$254$	5.00503	−	6.27612i	0.314044	−	0.393798i
$255$		0			0
$256$	0.505894	+	0.243626i	0.0316184	+	0.0152266i
$257$	17.4836	+	21.9238i	1.09060	+	1.36757i	0.924378	+	0.381479i	$0.124585\pi$
$257$	17.4836	+	21.9238i	1.09060	+	1.36757i	0.166221	+	0.986089i	$0.446844\pi$
$258$		0			0
$259$	−1.05738	−	0.509205i	−0.0657021	−	0.0316405i
$260$	−1.46545			−0.0908836
$261$		0			0
$262$	−39.4411			−2.43668
$263$	−22.2136	−	10.6975i	−1.36975	−	0.659638i	−0.402964	−	0.915216i	$-0.632020\pi$
$263$	−22.2136	−	10.6975i	−1.36975	−	0.659638i	−0.966788	+	0.255578i	$0.917734\pi$
$264$		0			0
$265$	−4.19996	−	5.26658i	−0.258001	−	0.323523i
$266$	5.23511	+	2.52110i	0.320985	+	0.154578i
$267$		0			0
$268$	−24.8307	+	31.1368i	−1.51678	+	1.90198i
$269$	3.27265	+	14.3384i	0.199537	+	0.874228i	0.971213	+	0.238212i	$0.0765615\pi$
$269$	3.27265	+	14.3384i	0.199537	+	0.874228i	−0.771676	+	0.636016i	$0.780581\pi$
$270$		0			0
$271$	−11.4531	−	14.3618i	−0.695728	−	0.872415i	0.300968	−	0.953634i	$-0.402690\pi$
$271$	−11.4531	−	14.3618i	−0.695728	−	0.872415i	−0.996696	+	0.0812189i	$0.974119\pi$
$272$	0.530518	−	2.32435i	0.0321674	−	0.140934i
$273$		0			0
$274$	3.73757	−	16.3754i	0.225795	−	0.989272i
$275$	−13.8354	+	6.66280i	−0.834309	+	0.401782i
$276$		0			0
$277$	−4.37894	+	19.1854i	−0.263105	+	1.15274i	0.654757	+	0.755839i	$0.272771\pi$
$277$	−4.37894	+	19.1854i	−0.263105	+	1.15274i	−0.917862	+	0.396899i	$0.870086\pi$
$278$	9.02505			0.541287
$279$		0			0
$280$	0.410718	+	0.515024i	0.0245451	+	0.0307786i
$281$	−1.71047	−	7.49407i	−0.102038	−	0.447059i	−0.999976	−	0.00693619i	$-0.997792\pi$
$281$	−1.71047	−	7.49407i	−0.102038	−	0.447059i	0.897938	−	0.440123i	$-0.145065\pi$
$282$		0			0
$283$	11.3286	−	14.2057i	0.673417	−	0.844438i	−0.321312	−	0.946973i	$-0.604124\pi$
$283$	11.3286	−	14.2057i	0.673417	−	0.844438i	0.994729	+	0.102535i	$0.0326953\pi$
$284$	24.8598	−	11.9719i	1.47516	−	0.710399i
$285$		0			0
$286$	3.44564	+	4.32070i	0.203745	+	0.255488i
$287$	−1.63479	+	2.04997i	−0.0964988	+	0.121006i
$288$		0			0
$289$	−15.6622			−0.921306
$290$	2.53860	−	8.13629i	0.149072	−	0.477780i
$291$		0			0
$292$	−13.3212	−	6.41514i	−0.779563	−	0.375418i
$293$	−1.05192	+	1.31907i	−0.0614538	+	0.0770606i	−0.811608	−	0.584202i	$-0.801408\pi$
$293$	−1.05192	+	1.31907i	−0.0614538	+	0.0770606i	0.750155	+	0.661263i	$0.229979\pi$
$294$		0			0
$295$	−4.70699	−	2.26677i	−0.274051	−	0.131976i
$296$	−2.81418	+	1.35524i	−0.163571	+	0.0787716i
$297$		0			0
$298$	−2.02853	−	8.88755i	−0.117509	−	0.514842i
$299$	−0.310771	−	1.36157i	−0.0179723	−	0.0787419i
$300$		0			0
$301$	1.00451	−	4.40106i	0.0578992	−	0.253673i
$302$	−19.6774			−1.13231
$303$		0			0
$304$	−8.52910	+	4.10740i	−0.489178	+	0.235576i
$305$	−8.25669	+	3.97621i	−0.472777	+	0.227677i
$306$		0			0
$307$	−9.11651			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$307$	−9.11651			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$308$	1.20943	−	5.29887i	0.0689138	−	0.301931i
$309$		0			0
$310$	−2.05468	−	9.00215i	−0.116698	−	0.511288i
$311$	1.78034	+	7.80016i	0.100954	+	0.442306i	0.999990	+	0.00443301i	$0.00141108\pi$
$311$	1.78034	+	7.80016i	0.100954	+	0.442306i	−0.899037	+	0.437873i	$0.855732\pi$
$312$		0			0
$313$	21.2677	−	10.2420i	1.20212	−	0.578912i	0.277844	−	0.960626i	$-0.410380\pi$
$313$	21.2677	−	10.2420i	1.20212	−	0.578912i	0.924281	+	0.381714i	$0.124666\pi$
$314$	−8.34531	−	4.01889i	−0.470953	−	0.226799i
$315$		0			0
$316$	−11.8972	+	14.9187i	−0.669271	+	0.839240i
$317$	−8.08322	−	3.89267i	−0.453999	−	0.218634i	0.192887	−	0.981221i	$-0.438215\pi$
$317$	−8.08322	−	3.89267i	−0.453999	−	0.218634i	−0.646886	+	0.762587i	$0.723929\pi$
$318$		0			0
$319$	−17.2483	+	6.70508i	−0.965721	+	0.375412i
$320$	−8.98742			−0.502412
$321$		0			0
$322$	−1.48741	+	1.86515i	−0.0828899	+	0.103941i
$323$	−3.31195	−	4.15305i	−0.184282	−	0.231082i
$324$		0			0
$325$	−2.98202	+	1.43607i	−0.165413	+	0.0796587i
$326$	−3.21384	+	4.03002i	−0.177998	+	0.223202i
$327$		0			0
$328$	1.55284	+	6.80344i	0.0857412	+	0.375657i
$329$	−1.70971	−	2.14391i	−0.0942594	−	0.118198i
$330$		0			0
$331$	16.0584			0.882647			0.441323	−	0.897348i	$-0.354509\pi$
$331$	16.0584			0.882647			0.441323	+	0.897348i	$0.354509\pi$
$332$	−6.95177	+	30.4577i	−0.381528	+	1.67158i
$333$		0			0
$334$	22.4982	−	10.8346i	1.23105	−	0.592840i
$335$	2.37996	−	10.4273i	0.130031	−	0.569705i
$336$		0			0
$337$	7.16282	−	31.3824i	0.390184	−	1.70951i	−0.273824	−	0.961780i	$-0.588289\pi$
$337$	7.16282	−	31.3824i	0.390184	−	1.70951i	0.664007	−	0.747726i	$-0.268854\pi$
$338$	−16.8560	−	21.1368i	−0.916847	−	1.14969i
$339$		0			0
$340$	−0.509228	−	2.23107i	−0.0276168	−	0.120997i
$341$	−12.5000	+	15.6745i	−0.676913	+	0.848823i
$342$		0			0
$343$	7.17174	+	3.45373i	0.387237	+	0.186484i
$344$	−7.49095	−	9.39335i	−0.403885	−	0.506456i
$345$		0			0
$346$	45.4402	+	21.8828i	2.44288	+	1.17643i
$347$	14.5306			0.780041			0.390021	−	0.920806i	$-0.372468\pi$
$347$	14.5306			0.780041			0.390021	+	0.920806i	$0.372468\pi$
$348$		0			0
$349$	−30.7682			−1.64699			−0.823493	−	0.567326i	$-0.807978\pi$
$349$	−30.7682			−1.64699			−0.823493	+	0.567326i	$0.807978\pi$
$350$	5.09381	+	2.45305i	0.272275	+	0.131121i
$351$		0			0
$352$	16.2348	+	20.3578i	0.865317	+	1.08507i
$353$	−23.0334	−	11.0923i	−1.22594	−	0.590382i	−0.294981	−	0.955503i	$-0.595313\pi$
$353$	−23.0334	−	11.0923i	−1.22594	−	0.590382i	−0.930960	+	0.365121i	$0.881028\pi$
$354$		0			0
$355$	−4.62016	+	5.79350i	−0.245213	+	0.307487i
$356$	−9.36526	−	41.0319i	−0.496358	−	2.17469i
$357$		0			0
$358$	−21.8983	−	27.4596i	−1.15736	−	1.45128i
$359$	4.01713	−	17.6002i	0.212016	−	0.928904i	−0.751178	−	0.660099i	$-0.770514\pi$
$359$	4.01713	−	17.6002i	0.212016	−	0.928904i	0.963195	−	0.268805i	$-0.0866286\pi$
$360$		0			0
$361$	−0.465527	+	2.03961i	−0.0245014	+	0.107348i
$362$	10.7787	−	5.19075i	0.566516	−	0.272820i
$363$		0			0
$364$	0.260675	−	1.14209i	0.0136631	−	0.0598619i
$365$	3.97075			0.207838
$366$		0			0
$367$	19.9431	+	25.0078i	1.04102	+	1.30540i	0.950911	+	0.309465i	$0.100150\pi$
$367$	19.9431	+	25.0078i	1.04102	+	1.30540i	0.0901087	+	0.995932i	$0.471279\pi$
$368$	−0.864865	−	3.78922i	−0.0450842	−	0.197527i
$369$		0			0
$370$	1.98747	−	2.49220i	0.103323	−	0.129563i
$371$	4.85157	−	2.33639i	0.251881	−	0.121299i
$372$		0			0
$373$	18.6354	+	23.3680i	0.964903	+	1.20995i	0.977694	+	0.210032i	$0.0673570\pi$
$373$	18.6354	+	23.3680i	0.964903	+	1.20995i	−0.0127909	+	0.999918i	$0.504072\pi$
$374$	−5.38071	+	6.74719i	−0.278230	+	0.348889i
$375$		0			0
$376$	−7.29820			−0.376376
$377$	−3.71762	+	1.44518i	−0.191467	+	0.0744306i
$378$		0			0
$379$	20.9313	+	10.0800i	1.07517	+	0.517773i	0.885769	−	0.464127i	$-0.153632\pi$
$379$	20.9313	+	10.0800i	1.07517	+	0.517773i	0.189399	+	0.981900i	$0.439346\pi$
$380$	−5.66546	+	7.10426i	−0.290632	+	0.364441i
$381$		0			0
$382$	−3.81658	−	1.83797i	−0.195273	−	0.0940386i
$383$	6.70827	−	3.23053i	0.342777	−	0.165072i	−0.254573	−	0.967054i	$-0.581935\pi$
$383$	6.70827	−	3.23053i	0.342777	−	0.165072i	0.597349	+	0.801981i	$0.296221\pi$
$384$		0			0
$385$	0.324804	+	1.42306i	0.0165535	+	0.0725257i
$386$	2.43618	+	10.6736i	0.123998	+	0.543272i
$387$		0			0
$388$	−2.95950	+	12.9664i	−0.150246	+	0.658270i
$389$	19.2548			0.976256			0.488128	−	0.872772i	$-0.337680\pi$
$389$	19.2548			0.976256			0.488128	+	0.872772i	$0.337680\pi$
$390$		0			0
$391$	1.96494	−	0.946263i	0.0993711	−	0.0478546i
$392$	9.30648	−	4.48177i	0.470048	−	0.226363i
$393$		0			0
$394$	31.4806			1.58597
$395$	1.14032	−	4.99607i	0.0573757	−	0.251379i
$396$		0			0
$397$	−3.20540	−	14.0438i	−0.160874	−	0.704836i	−0.989440	−	0.144944i	$-0.953700\pi$
$397$	−3.20540	−	14.0438i	−0.160874	−	0.704836i	0.828566	−	0.559892i	$-0.189157\pi$
$398$	−3.18790	−	13.9671i	−0.159795	−	0.700107i
$399$		0			0
$400$	−8.29888	+	3.99653i	−0.414944	+	0.199827i
$401$	19.9736	+	9.61876i	0.997432	+	0.480338i	0.860066	−	0.510182i	$-0.170422\pi$
$401$	19.9736	+	9.61876i	0.997432	+	0.480338i	0.137366	+	0.990520i	$0.456136\pi$
$402$		0			0
$403$	−2.69419	+	3.37841i	−0.134207	+	0.168290i
$404$	−30.9333	−	14.8967i	−1.53899	−	0.741139i
$405$		0			0
$406$	5.88940	+	3.42573i	0.292286	+	0.170016i
$407$	−6.92114			−0.343068
$408$		0			0
$409$	−20.2742	+	25.4231i	−1.00250	+	1.25709i	−0.0362844	+	0.999342i	$0.511552\pi$
$409$	−20.2742	+	25.4231i	−1.00250	+	1.25709i	−0.966212	+	0.257749i	$0.917019\pi$
$410$	−4.44031	−	5.56797i	−0.219291	−	0.274983i
$411$		0			0
$412$	12.4454	−	5.99337i	0.613139	−	0.295272i
$413$	2.60387	−	3.26515i	0.128128	−	0.160667i
$414$		0			0
$415$	−1.86696	−	8.17967i	−0.0916453	−	0.401524i
$416$	3.49917	+	4.38782i	0.171561	+	0.215130i
$417$		0			0
$418$	34.2669			1.67605
$419$	4.90678	−	21.4980i	0.239712	−	1.05025i	−0.701563	−	0.712607i	$-0.747514\pi$
$419$	4.90678	−	21.4980i	0.239712	−	1.05025i	0.941275	−	0.337640i	$-0.109629\pi$
$420$		0			0
$421$	11.1399	−	5.36467i	0.542923	−	0.261458i	−0.142259	−	0.989829i	$-0.545437\pi$
$421$	11.1399	−	5.36467i	0.542923	−	0.261458i	0.685183	+	0.728371i	$0.259722\pi$
$422$	−5.11590	+	22.4142i	−0.249038	+	1.09111i
$423$		0			0
$424$	3.18908	−	13.9723i	0.154875	−	0.678554i
$425$	−3.22255	−	4.04095i	−0.156317	−	0.196015i
$426$		0			0
$427$	−1.63014	−	7.14209i	−0.0788878	−	0.345630i
$428$	23.3460	−	29.2750i	1.12847	−	1.41506i
$429$		0			0
$430$	11.0470	+	5.31997i	0.532735	+	0.256552i
$431$	−12.3223	−	15.4516i	−0.593543	−	0.744279i	0.390813	−	0.920470i	$-0.372194\pi$
$431$	−12.3223	−	15.4516i	−0.593543	−	0.744279i	−0.984356	+	0.176191i	$0.943622\pi$
$432$		0			0
$433$	8.79038	+	4.23322i	0.422439	+	0.203436i	0.633011	−	0.774142i	$-0.281819\pi$
$433$	8.79038	+	4.23322i	0.422439	+	0.203436i	−0.210573	+	0.977578i	$0.567533\pi$
$434$	7.38125			0.354312
$435$		0			0
$436$	−39.1525			−1.87507
$437$	−7.80212	−	3.75730i	−0.373226	−	0.179736i
$438$		0			0
$439$	−0.963450	−	1.20813i	−0.0459830	−	0.0576608i	0.758308	−	0.651896i	$-0.226026\pi$
$439$	−0.963450	−	1.20813i	−0.0459830	−	0.0576608i	−0.804291	+	0.594235i	$0.797455\pi$
$440$	3.50011	+	1.68557i	0.166861	+	0.0803562i
$441$		0			0
$442$	−1.15973	+	1.45426i	−0.0551628	+	0.0691720i
$443$	5.46851	+	23.9591i	0.259817	+	1.13833i	0.921448	+	0.388502i	$0.127007\pi$
$443$	5.46851	+	23.9591i	0.259817	+	1.13833i	−0.661631	+	0.749829i	$0.730136\pi$
$444$		0			0
$445$	7.04722	+	8.83693i	0.334070	+	0.418911i
$446$	−4.57485	+	20.0437i	−0.216626	+	0.949099i
$447$		0			0
$448$	1.59868	−	7.00429i	0.0755307	−	0.330922i
$449$	−10.3337	+	4.97643i	−0.487676	+	0.234852i	−0.661529	−	0.749919i	$-0.730092\pi$
$449$	−10.3337	+	4.97643i	−0.487676	+	0.234852i	0.173854	+	0.984772i	$0.444378\pi$
$450$		0			0
$451$	−3.44082	+	15.0752i	−0.162022	+	0.709865i
$452$	−5.78740			−0.272217
$453$		0			0
$454$	−31.1311	−	39.0371i	−1.46105	−	1.83210i
$455$	0.0700066	+	0.306719i	0.00328196	+	0.0143792i
$456$		0			0
$457$	9.49235	−	11.9030i	0.444033	−	0.556800i	−0.508568	−	0.861022i	$-0.669825\pi$
$457$	9.49235	−	11.9030i	0.444033	−	0.556800i	0.952601	+	0.304222i	$0.0983963\pi$
$458$	−26.7997	+	12.9060i	−1.25227	+	0.603059i
$459$		0			0
$460$	−2.32605	−	2.91678i	−0.108453	−	0.135995i
$461$	22.2256	−	27.8700i	1.03515	−	1.29804i	0.0816432	−	0.996662i	$-0.473983\pi$
$461$	22.2256	−	27.8700i	1.03515	−	1.29804i	0.953506	−	0.301374i	$-0.0974454\pi$
$462$		0			0
$463$	−5.80117			−0.269603			−0.134802	−	0.990873i	$-0.543040\pi$
$463$	−5.80117			−0.269603			−0.134802	+	0.990873i	$0.543040\pi$
$464$	−10.3460	+	4.02189i	−0.480302	+	0.186712i
$465$		0			0
$466$	−11.2586	−	5.42185i	−0.521544	−	0.251162i
$467$	−7.37088	+	9.24279i	−0.341084	+	0.427705i	−0.922557	−	0.385860i	$-0.873905\pi$
$467$	−7.37088	+	9.24279i	−0.341084	+	0.427705i	0.581474	+	0.813565i	$0.302476\pi$
$468$		0			0
$469$	7.70311	+	3.70962i	0.355696	+	0.171294i
$470$	6.71048	−	3.23160i	0.309532	−	0.149063i
$471$		0			0
$472$	−2.47334	−	10.8364i	−0.113845	−	0.498786i
$473$	−5.92399	−	25.9547i	−0.272385	−	1.19340i
$474$		0			0
$475$	−4.56674	+	20.0082i	−0.209536	+	0.918039i
$476$	1.82936			0.0838484
$477$		0			0
$478$	−40.0662	+	19.2949i	−1.83259	+	0.882528i
$479$	−34.6814	+	16.7017i	−1.58464	+	0.763120i	−0.998878	−	0.0473659i	$-0.984917\pi$
$479$	−34.6814	+	16.7017i	−1.58464	+	0.763120i	−0.585758	+	0.810486i	$0.699203\pi$
$480$		0			0
$481$	−1.49175			−0.0680179
$482$	−6.87437	+	30.1186i	−0.313119	+	1.37186i
$483$		0			0
$484$	−0.488657	−	2.14095i	−0.0222117	−	0.0973158i
$485$	−0.794800	−	3.48224i	−0.0360900	−	0.158121i
$486$		0			0
$487$	5.48212	−	2.64005i	0.248418	−	0.119632i	−0.305532	−	0.952182i	$-0.598834\pi$
$487$	5.48212	−	2.64005i	0.248418	−	0.119632i	0.553950	+	0.832550i	$0.313120\pi$
$488$	−17.5665	−	8.45958i	−0.795198	−	0.382947i
$489$		0			0
$490$	−6.57254	+	8.24171i	−0.296917	+	0.372322i
$491$	31.4404	+	15.1409i	1.41888	+	0.683298i	0.976894	−	0.213722i	$-0.0685588\pi$
$491$	31.4404	+	15.1409i	1.41888	+	0.683298i	0.441989	+	0.897021i	$0.354273\pi$
$492$		0			0
$493$	−3.49204	−	5.15769i	−0.157273	−	0.232291i
$494$	7.38571			0.332299
$495$		0			0
$496$	−7.49785	+	9.40201i	−0.336663	+	0.422163i
$497$	−3.69329	−	4.63124i	−0.165667	−	0.207740i
$498$		0			0
$499$	−17.6476	+	8.49865i	−0.790016	+	0.380452i	−0.784969	−	0.619535i	$-0.787321\pi$
$499$	−17.6476	+	8.49865i	−0.790016	+	0.380452i	−0.00504766	+	0.999987i	$0.501607\pi$
$500$	−11.6806	+	14.6470i	−0.522370	+	0.655032i
$501$		0			0
$502$	−11.9328	−	52.2809i	−0.532586	−	2.33341i
$503$	−15.5304	−	19.4746i	−0.692468	−	0.868328i	0.303968	−	0.952682i	$-0.401689\pi$
$503$	−15.5304	−	19.4746i	−0.692468	−	0.868328i	−0.996436	+	0.0843547i	$0.973117\pi$
$504$		0			0
$505$	9.22054			0.410309
$506$	−3.13061	+	13.7161i	−0.139173	+	0.609755i
$507$		0			0
$508$	−9.04136	+	4.35409i	−0.401145	+	0.193181i
$509$	6.53837	−	28.6465i	0.289808	−	1.26973i	−0.594981	−	0.803740i	$-0.702840\pi$
$509$	6.53837	−	28.6465i	0.289808	−	1.26973i	0.884789	−	0.465992i	$-0.154302\pi$
$510$		0			0
$511$	−0.706317	+	3.09458i	−0.0312456	+	0.136896i
$512$	13.7243	+	17.2098i	0.606535	+	0.760571i
$513$		0			0
$514$	−13.5482	−	59.3584i	−0.597584	−	2.61819i
$515$	−2.31295	+	2.90035i	−0.101921	+	0.127805i
$516$		0			0
$517$	−14.5701	−	7.01657i	−0.640790	−	0.308588i
$518$	1.58875	+	1.99223i	0.0698058	+	0.0875337i
$519$		0			0
$520$	0.754397	+	0.363299i	0.0330825	+	0.0159317i
$521$	4.35598			0.190839			0.0954195	−	0.995437i	$-0.469581\pi$
$521$	4.35598			0.190839			0.0954195	+	0.995437i	$0.469581\pi$
$522$		0			0
$523$	−17.6527			−0.771897			−0.385948	−	0.922520i	$-0.626126\pi$
$523$	−17.6527			−0.771897			−0.385948	+	0.922520i	$0.626126\pi$
$524$	44.4227	+	21.3929i	1.94062	+	0.934551i
$525$		0			0
$526$	33.3770	+	41.8534i	1.45530	+	1.82489i
$527$	−6.07964	−	2.92780i	−0.264833	−	0.127537i
$528$		0			0
$529$	−12.1235	+	15.2024i	−0.527109	+	0.660974i
$530$	3.25457	+	14.2592i	0.141370	+	0.619380i
$531$		0			0
$532$	−4.52889	−	5.67905i	−0.196352	−	0.246218i
$533$	−0.741618	+	3.24924i	−0.0321230	+	0.140740i
$534$		0			0
$535$	−2.23766	+	9.80381i	−0.0967423	+	0.423856i
$536$	20.5016	−	9.87307i	0.885536	−	0.426452i
$537$		0			0
$538$	7.10570	−	31.1321i	0.306348	−	1.34220i
$539$	22.8882			0.985864
$540$		0			0
$541$	13.4878	+	16.9131i	0.579885	+	0.727153i	0.982093	−	0.188395i	$-0.0603286\pi$
$541$	13.4878	+	16.9131i	0.579885	+	0.727153i	−0.402208	+	0.915548i	$0.631757\pi$
$542$	8.87509	+	38.8843i	0.381218	+	1.67023i
$543$		0			0
$544$	−5.46429	+	6.85201i	−0.234280	+	0.293777i
$545$	9.47346	−	4.56218i	0.405798	−	0.195422i
$546$		0			0
$547$	−16.1916	−	20.3036i	−0.692302	−	0.868119i	0.304120	−	0.952634i	$-0.401637\pi$
$547$	−16.1916	−	20.3036i	−0.692302	−	0.868119i	−0.996422	+	0.0845145i	$0.973066\pi$
$548$	−13.0916	+	16.4164i	−0.559247	+	0.701274i
$549$		0			0
$550$	33.3419			1.42170
$551$	−7.36638	+	23.6095i	−0.313818	+	1.00580i
$552$		0			0
$553$	3.69081	+	1.77740i	0.156949	+	0.0755828i
$554$	26.6400	−	33.4056i	1.13183	−	1.41927i
$555$		0			0
$556$	−10.1650	−	4.89519i	−0.431090	−	0.207602i
$557$	31.2446	−	15.0466i	1.32388	−	0.637546i	0.367594	−	0.929986i	$-0.380182\pi$
$557$	31.2446	−	15.0466i	1.32388	−	0.637546i	0.956284	+	0.292441i	$0.0944674\pi$
$558$		0			0
$559$	−1.27683	−	5.59414i	−0.0540040	−	0.236607i
$560$	0.194826	+	0.853589i	0.00823291	+	0.0360707i
$561$		0			0
$562$	−3.71384	+	16.2714i	−0.156659	+	0.686368i
$563$	12.3193			0.519196			0.259598	−	0.965717i	$-0.416410\pi$
$563$	12.3193			0.519196			0.259598	+	0.965717i	$0.416410\pi$
$564$		0			0
$565$	1.40034	−	0.674367i	0.0589127	−	0.0283708i
$566$	−35.5439	+	17.1170i	−1.49402	+	0.719483i
$567$		0			0
$568$	−15.7655			−0.661504
$569$	−4.05169	+	17.7516i	−0.169856	+	0.744187i	0.816200	+	0.577770i	$0.196077\pi$
$569$	−4.05169	+	17.7516i	−0.169856	+	0.744187i	−0.986055	+	0.166417i	$0.946780\pi$
$570$		0			0
$571$	0.0453605	+	0.198737i	0.00189828	+	0.00831690i	0.975868	−	0.218360i	$-0.0700709\pi$
$571$	0.0453605	+	0.198737i	0.00189828	+	0.00831690i	−0.973970	+	0.226677i	$0.927214\pi$
$572$	−1.53730	−	6.73534i	−0.0642776	−	0.281619i
$573$		0			0
$574$	5.12921	−	2.47010i	0.214089	−	0.103100i
$575$	−7.59152	−	3.65589i	−0.316588	−	0.152461i
$576$		0			0
$577$	1.06414	−	1.33439i	0.0443008	−	0.0555514i	−0.759188	−	0.650872i	$-0.774403\pi$
$577$	1.06414	−	1.33439i	0.0443008	−	0.0555514i	0.803488	+	0.595321i	$0.202975\pi$
$578$	30.6387	+	14.7548i	1.27440	+	0.613719i
$579$		0			0
$580$	−7.27237	+	7.78701i	−0.301969	+	0.323338i
$581$	6.70687			0.278248
$582$		0			0
$583$	19.7997	−	24.8281i	0.820022	−	1.02827i
$584$	5.26721	+	6.60487i	0.217959	+	0.273311i
$585$		0			0
$586$	3.30043	−	1.58940i	0.136339	−	0.0656576i
$587$	12.4024	−	15.5522i	0.511903	−	0.641906i	−0.456965	−	0.889485i	$-0.651063\pi$
$587$	12.4024	−	15.5522i	0.511903	−	0.641906i	0.968868	+	0.247579i	$0.0796348\pi$
$588$		0			0
$589$	5.96216	+	26.1219i	0.245667	+	1.07634i
$590$	7.07245	+	8.86857i	0.291168	+	0.365113i
$591$		0			0
$592$	−4.15149			−0.170625
$593$	−2.51750	+	11.0299i	−0.103381	+	0.452943i	0.896568	+	0.442906i	$0.146052\pi$
$593$	−2.51750	+	11.0299i	−0.103381	+	0.452943i	−0.999950	+	0.0100378i	$0.996805\pi$
$594$		0			0
$595$	−0.442636	+	0.213162i	−0.0181463	+	0.00873881i
$596$	−2.53587	+	11.1104i	−0.103873	+	0.455098i
$597$		0			0
$598$	−0.674757	+	2.95630i	−0.0275929	+	0.120892i
$599$	−4.03707	−	5.06233i	−0.164950	−	0.206841i	0.692486	−	0.721431i	$-0.256515\pi$
$599$	−4.03707	−	5.06233i	−0.164950	−	0.206841i	−0.857436	+	0.514590i	$0.827944\pi$
$600$		0			0
$601$	6.00009	+	26.2881i	0.244749	+	1.07231i	0.936635	+	0.350307i	$0.113923\pi$
$601$	6.00009	+	26.2881i	0.244749	+	1.07231i	−0.691886	+	0.722007i	$0.743220\pi$
$602$	−6.11113	+	7.66312i	−0.249071	+	0.312325i
$603$		0			0
$604$	22.1627	+	10.6730i	0.901789	+	0.434278i
$605$	0.367707	+	0.461090i	0.0149494	+	0.0187460i
$606$		0			0
$607$	34.2517	+	16.4947i	1.39023	+	0.669501i	0.971155	−	0.238449i	$-0.0766391\pi$
$607$	34.2517	+	16.4947i	1.39023	+	0.669501i	0.419078	+	0.907950i	$0.362353\pi$
$608$	34.7992			1.41129
$609$		0			0
$610$	19.8977			0.805636
$611$	−3.14036	−	1.51232i	−0.127045	−	0.0611818i
$612$		0			0
$613$	−10.4013	−	13.0429i	−0.420106	−	0.526796i	0.526074	−	0.850439i	$-0.323664\pi$
$613$	−10.4013	−	13.0429i	−0.420106	−	0.526796i	−0.946179	+	0.323643i	$0.895092\pi$
$614$	17.8339	+	8.58834i	0.719716	+	0.346597i
$615$		0			0
$616$	−1.93624	+	2.42796i	−0.0780132	+	0.0978254i
$617$	4.28736	+	18.7841i	0.172603	+	0.756221i	0.984921	+	0.173007i	$0.0553482\pi$
$617$	4.28736	+	18.7841i	0.172603	+	0.756221i	−0.812318	+	0.583215i	$0.801795\pi$
$618$		0			0
$619$	−17.4925	−	21.9349i	−0.703082	−	0.881637i	0.294168	−	0.955754i	$-0.404958\pi$
$619$	−17.4925	−	21.9349i	−0.703082	−	0.881637i	−0.997250	+	0.0741170i	$0.976386\pi$
$620$	−2.56857	+	11.2536i	−0.103156	+	0.451956i
$621$		0			0
$622$	3.86553	−	16.9360i	0.154994	−	0.679072i
$623$	−8.14057	+	3.92029i	−0.326145	+	0.157063i
$624$		0			0
$625$	−3.85228	+	16.8779i	−0.154091	+	0.675118i
$626$	−51.2530			−2.04848
$627$		0			0
$628$	7.21952	+	9.05299i	0.288090	+	0.361254i
$629$	−0.518365	−	2.27111i	−0.0206686	−	0.0905550i
$630$		0			0
$631$	−2.56514	+	3.21658i	−0.102117	+	0.128050i	−0.830264	−	0.557371i	$-0.811810\pi$
$631$	−2.56514	+	3.21658i	−0.102117	+	0.128050i	0.728147	+	0.685421i	$0.240382\pi$
$632$	9.82301	−	4.73051i	0.390738	−	0.188170i
$633$		0			0
$634$	12.1454	+	15.2298i	0.482355	+	0.604854i
$635$	1.68032	−	2.10706i	0.0666816	−	0.0836160i
$636$		0			0
$637$	4.93321			0.195461
$638$	40.0581	+	3.13244i	1.58591	+	0.124014i
$639$		0			0
$640$	7.62861	+	3.67375i	0.301547	+	0.145218i
$641$	15.8142	−	19.8304i	0.624625	−	0.783254i	−0.364362	−	0.931257i	$-0.618713\pi$
$641$	15.8142	−	19.8304i	0.624625	−	0.783254i	0.988987	+	0.148003i	$0.0472845\pi$
$642$		0			0
$643$	28.4535	+	13.7025i	1.12210	+	0.540374i	0.900540	−	0.434774i	$-0.143172\pi$
$643$	28.4535	+	13.7025i	1.12210	+	0.540374i	0.221557	+	0.975147i	$0.428886\pi$
$644$	2.68693	−	1.29396i	0.105880	−	0.0509891i
$645$		0			0
$646$	2.56645	+	11.2444i	0.100976	+	0.442403i
$647$	−9.25329	−	40.5413i	−0.363784	−	1.59384i	−0.743497	−	0.668739i	$-0.766834\pi$
$647$	−9.25329	−	40.5413i	−0.363784	−	1.59384i	0.379713	−	0.925104i	$-0.376023\pi$
$648$		0			0
$649$	5.48048	−	24.0116i	0.215128	−	0.942537i
$650$	7.18636			0.281872
$651$		0			0
$652$	5.80564	−	2.79585i	0.227367	−	0.109494i
$653$	−10.2235	+	4.92339i	−0.400077	+	0.192667i	−0.623093	−	0.782148i	$-0.714124\pi$
$653$	−10.2235	+	4.92339i	−0.400077	+	0.192667i	0.223016	+	0.974815i	$0.428410\pi$
$654$		0			0
$655$	−13.2414			−0.517385
$656$	−2.06390	+	9.04254i	−0.0805818	+	0.353052i
$657$		0			0
$658$	1.32486	+	5.80461i	0.0516486	+	0.226287i
$659$	1.60215	+	7.01947i	0.0624108	+	0.273440i	0.996499	−	0.0836022i	$-0.0266425\pi$
$659$	1.60215	+	7.01947i	0.0624108	+	0.273440i	−0.934088	+	0.357042i	$0.883785\pi$
$660$		0			0
$661$	−6.38520	+	3.07495i	−0.248355	+	0.119602i	−0.553921	−	0.832570i	$-0.686869\pi$
$661$	−6.38520	+	3.07495i	−0.248355	+	0.119602i	0.305565	+	0.952171i	$0.401155\pi$
$662$	−31.4136	−	15.1280i	−1.22093	−	0.587967i
$663$		0			0
$664$	11.1294	−	13.9558i	0.431905	−	0.541591i
$665$	1.75757	+	0.846399i	0.0681555	+	0.0328219i
$666$		0			0
$667$	−8.77724	−	5.10552i	−0.339856	−	0.197686i
$668$	−31.2165			−1.20780
$669$		0			0
$670$	−14.4789	+	18.1560i	−0.559370	+	0.701427i
$671$	−26.9365	−	33.7772i	−1.03987	−	1.30396i
$672$		0			0
$673$	18.1120	−	8.72228i	0.698166	−	0.336219i	−0.0509096	−	0.998703i	$-0.516212\pi$
$673$	18.1120	−	8.72228i	0.698166	−	0.336219i	0.749076	+	0.662484i	$0.230498\pi$
$674$	−43.5762	+	54.6429i	−1.67849	+	2.10476i
$675$		0			0
$676$	7.52043	+	32.9492i	0.289247	+	1.26728i
$677$	−4.87159	−	6.10878i	−0.187231	−	0.234780i	0.679353	−	0.733812i	$-0.262260\pi$
$677$	−4.87159	−	6.10878i	−0.187231	−	0.234780i	−0.866584	+	0.499032i	$0.833689\pi$
$678$		0			0
$679$	2.85525			0.109574
$680$	−0.290958	+	1.27477i	−0.0111577	+	0.0488853i
$681$		0			0
$682$	39.2191	−	18.8869i	1.50178	−	0.723219i
$683$	−1.15607	+	5.06508i	−0.0442359	+	0.193810i	−0.992218	−	0.124514i	$-0.960263\pi$
$683$	−1.15607	+	5.06508i	−0.0442359	+	0.193810i	0.947982	+	0.318324i	$0.103120\pi$
$684$		0			0
$685$	1.25480	−	5.49764i	0.0479435	−	0.210054i
$686$	−10.7758	−	13.5125i	−0.411424	−	0.515909i
$687$		0			0
$688$	−3.55337	−	15.5683i	−0.135471	−	0.593537i
$689$	4.26754	−	5.35133i	0.162580	−	0.203869i
$690$		0			0
$691$	24.3969	+	11.7489i	0.928102	+	0.446950i	0.835957	−	0.548795i	$-0.184913\pi$
$691$	24.3969	+	11.7489i	0.928102	+	0.446950i	0.0921449	+	0.995746i	$0.470628\pi$
$692$	−39.3102	−	49.2935i	−1.49435	−	1.87386i
$693$		0			0
$694$	−28.4249	−	13.6887i	−1.07900	−	0.519617i
$695$	3.02995			0.114932
$696$		0			0
$697$	−5.20450			−0.197134
$698$	60.1894	+	28.9857i	2.27820	+	1.09712i
$699$		0			0
$700$	−4.40665	−	5.52576i	−0.166556	−	0.208854i
$701$	−15.9999	−	7.70515i	−0.604309	−	0.291020i	0.106602	−	0.994302i	$-0.466003\pi$
$701$	−15.9999	−	7.70515i	−0.604309	−	0.291020i	−0.710911	+	0.703282i	$0.751717\pi$
$702$		0			0
$703$	−5.76712	+	7.23174i	−0.217511	+	0.272750i
$704$	−9.42802	−	41.3069i	−0.355332	−	1.55681i
$705$		0			0
$706$	34.6086	+	43.3978i	1.30251	+	1.63330i
$707$	−1.64015	+	7.18597i	−0.0616842	+	0.270256i
$708$		0			0
$709$	2.06006	−	9.02570i	0.0773671	−	0.338967i	−0.921400	−	0.388616i	$-0.872953\pi$
$709$	2.06006	−	9.02570i	0.0773671	−	0.338967i	0.998767	+	0.0496491i	$0.0158103\pi$
$710$	14.4959	−	6.98085i	0.544021	−	0.261987i
$711$		0			0
$712$	−5.35104	+	23.4444i	−0.200539	+	0.878618i
$713$	−11.0006			−0.411976
$714$		0			0
$715$	1.15679	+	1.45057i	0.0432616	+	0.0542483i
$716$	9.77007	+	42.8055i	0.365125	+	1.59972i
$717$		0			0
$718$	−24.4389	+	30.6455i	−0.912053	+	1.14368i
$719$	−42.9112	+	20.6649i	−1.60032	+	0.770672i	−0.999586	−	0.0287792i	$-0.990838\pi$
$719$	−42.9112	+	20.6649i	−1.60032	+	0.770672i	−0.600731	+	0.799451i	$0.705124\pi$
$720$		0			0
$721$	−1.84894	−	2.31850i	−0.0688581	−	0.0863453i
$722$	2.83211	−	3.55136i	0.105400	−	0.132168i
$723$		0			0
$724$	−14.9556			−0.555819
$725$	−7.16754	+	22.9722i	−0.266196	+	0.853165i
$726$		0			0
$727$	−42.8986	−	20.6589i	−1.59102	−	0.766196i	−0.591818	−	0.806072i	$-0.701590\pi$
$727$	−42.8986	−	20.6589i	−1.59102	−	0.766196i	−0.999205	+	0.0398756i	$0.987304\pi$
$728$	−0.417327	+	0.523311i	−0.0154672	+	0.0193952i
$729$		0			0
$730$	−7.76764	−	3.74070i	−0.287493	−	0.138449i
$731$	8.07310	−	3.88780i	0.298594	−	0.143795i
$732$		0			0
$733$	−7.54693	−	33.0652i	−0.278752	−	1.22129i	−0.899373	−	0.437182i	$-0.855977\pi$
$733$	−7.54693	−	33.0652i	−0.278752	−	1.22129i	0.620621	−	0.784111i	$-0.286881\pi$
$734$	−15.4540	−	67.7084i	−0.570417	−	2.49916i
$735$		0			0
$736$	−3.17924	+	13.9292i	−0.117188	+	0.513436i
$737$	50.4213			1.85729
$738$		0			0
$739$	33.6689	−	16.2141i	1.23853	−	0.596445i	0.304118	−	0.952635i	$-0.401638\pi$
$739$	33.6689	−	16.2141i	1.23853	−	0.596445i	0.934414	+	0.356189i	$0.115924\pi$
$740$	−3.59026	+	1.72898i	−0.131981	+	0.0635586i
$741$		0			0
$742$	−11.6917			−0.429218
$743$	−8.00088	+	35.0541i	−0.293524	+	1.28601i	0.586060	+	0.810267i	$0.300678\pi$
$743$	−8.00088	+	35.0541i	−0.293524	+	1.28601i	−0.879584	+	0.475744i	$0.842179\pi$
$744$		0			0
$745$	−0.681030	−	2.98379i	−0.0249510	−	0.109317i
$746$	−14.4407	−	63.2687i	−0.528710	−	2.31643i
$747$		0			0
$748$	9.72000	−	4.68090i	0.355398	−	0.171151i
$749$	−7.24251	−	3.48781i	−0.264635	−	0.127442i
$750$		0			0
$751$	8.11321	−	10.1736i	0.296055	−	0.371241i	−0.611450	−	0.791283i	$-0.709413\pi$
$751$	8.11321	−	10.1736i	0.296055	−	0.371241i	0.907505	+	0.420042i	$0.137985\pi$
$752$	−8.73952	−	4.20873i	−0.318698	−	0.153477i
$753$		0			0
$754$	8.63392	+	0.675150i	0.314429	+	0.0245875i
$755$	−6.60621			−0.240425
$756$		0			0
$757$	31.0080	−	38.8828i	1.12701	−	1.41322i	0.228896	−	0.973451i	$-0.426488\pi$
$757$	31.0080	−	38.8828i	1.12701	−	1.41322i	0.898110	−	0.439770i	$-0.144940\pi$
$758$	−31.4501	−	39.4372i	−1.14232	−	1.43242i
$759$		0			0
$760$	4.67772	−	2.25267i	0.169679	−	0.0817129i
$761$	32.2041	−	40.3827i	1.16740	−	1.46387i	0.308871	−	0.951104i	$-0.400049\pi$
$761$	32.2041	−	40.3827i	1.16740	−	1.46387i	0.858528	−	0.512767i	$-0.171380\pi$
$762$		0			0
$763$	1.87037	+	8.19460i	0.0677118	+	0.296665i
$764$	3.30172	+	4.14022i	0.119452	+	0.149788i
$765$		0			0
$766$	−16.1662			−0.584109
$767$	1.18124	−	5.17534i	0.0426520	−	0.186871i
$768$		0			0
$769$	−42.4112	+	20.4242i	−1.52939	+	0.736514i	−0.994132	−	0.108176i	$-0.965499\pi$
$769$	−42.4112	+	20.4242i	−1.52939	+	0.736514i	−0.535256	+	0.844690i	$0.679785\pi$
$770$	0.705226	−	3.08980i	0.0254146	−	0.111349i
$771$		0			0
$772$	3.04548	−	13.3431i	0.109609	−	0.480229i
$773$	31.3906	+	39.3626i	1.12904	+	1.41578i	0.896419	+	0.443209i	$0.146160\pi$
$773$	31.3906	+	39.3626i	1.12904	+	1.41578i	0.232624	+	0.972567i	$0.425269\pi$
$774$		0			0
$775$	5.80123	+	25.4168i	0.208386	+	0.913000i
$776$	4.73800	−	5.94127i	0.170084	−	0.213279i
$777$		0			0
$778$	−37.6665	−	18.1393i	−1.35041	−	0.650324i
$779$	12.8847	+	16.1568i	0.461641	+	0.578879i
$780$		0			0
$781$	−31.4740	−	15.1571i	−1.12623	−	0.542363i
$782$	−4.73528			−0.169333
$783$		0			0
$784$	13.7290			0.490320
$785$	−2.80174	−	1.34925i	−0.0999984	−	0.0481567i
$786$		0			0
$787$	−27.5512	−	34.5481i	−0.982093	−	1.23151i	−0.972823	−	0.231549i	$-0.925621\pi$
$787$	−27.5512	−	34.5481i	−0.982093	−	1.23151i	−0.00927023	−	0.999957i	$-0.502951\pi$
$788$	−35.4567	−	17.0751i	−1.26309	−	0.608273i
$789$		0			0
$790$	−6.93733	+	8.69914i	−0.246819	+	0.309501i
$791$	0.276472	+	1.21130i	0.00983020	+	0.0430689i
$792$		0			0
$793$	−5.80575	−	7.28018i	−0.206168	−	0.258527i
$794$	−6.95968	+	30.4923i	−0.246990	+	1.08213i
$795$		0			0
$796$	−3.98520	+	17.4603i	−0.141252	+	0.618865i
$797$	2.66606	−	1.28391i	0.0944366	−	0.0454783i	−0.386069	−	0.922470i	$-0.626167\pi$
$797$	2.66606	−	1.28391i	0.0944366	−	0.0454783i	0.480506	+	0.876992i	$0.340453\pi$
$798$		0			0
$799$	1.21118	−	5.30654i	0.0428486	−	0.187732i
$800$	33.8599			1.19713
$801$		0			0
$802$	−30.0111	−	37.6328i	−1.05973	−	1.32886i
$803$	4.16541	+	18.2499i	0.146994	+	0.644023i
$804$		0			0
$805$	−0.499362	+	0.626180i	−0.0176002	+	0.0220699i
$806$	8.45310	−	4.07080i	0.297748	−	0.143388i
$807$		0			0
$808$	12.2311	+	15.3373i	0.430288	+	0.539564i
$809$	22.5192	−	28.2381i	0.791732	−	0.992800i	−0.208160	−	0.978095i	$-0.566748\pi$
$809$	22.5192	−	28.2381i	0.791732	−	0.992800i	0.999892	−	0.0147054i	$-0.00468105\pi$
$810$		0			0
$811$	−27.4911			−0.965345			−0.482672	−	0.875801i	$-0.660334\pi$
$811$	−27.4911			−0.965345			−0.482672	+	0.875801i	$0.660334\pi$
$812$	−4.77515	−	7.05283i	−0.167575	−	0.247506i
$813$		0			0
$814$	13.5393	+	6.52016i	0.474551	+	0.228532i
$815$	−1.07897	+	1.35299i	−0.0377947	+	0.0473930i
$816$		0			0
$817$	−32.0557	−	15.4372i	−1.12149	−	0.540079i
$818$	63.6110	−	30.6334i	2.22411	−	1.07107i
$819$		0			0
$820$	1.98108	+	8.67966i	0.0691822	+	0.303107i
$821$	−5.80920	−	25.4518i	−0.202743	−	0.888274i	−0.969258	−	0.246047i	$-0.920868\pi$
$821$	−5.80920	−	25.4518i	−0.202743	−	0.888274i	0.766515	−	0.642226i	$-0.221989\pi$
$822$		0			0
$823$	8.59118	−	37.6404i	0.299470	−	1.31206i	−0.571450	−	0.820637i	$-0.693619\pi$
$823$	8.59118	−	37.6404i	0.299470	−	1.31206i	0.870920	−	0.491425i	$-0.163524\pi$
$824$	−7.89252			−0.274949
$825$		0			0
$826$	−8.16972	+	3.93433i	−0.284261	+	0.136893i
$827$	−39.4583	+	19.0021i	−1.37210	+	0.660769i	−0.967300	−	0.253636i	$-0.918373\pi$
$827$	−39.4583	+	19.0021i	−1.37210	+	0.660769i	−0.404801	+	0.914405i	$0.632659\pi$
$828$		0			0
$829$	−1.01710			−0.0353255			−0.0176627	−	0.999844i	$-0.505623\pi$
$829$	−1.01710			−0.0353255			−0.0176627	+	0.999844i	$0.505623\pi$
$830$	−4.05361	+	17.7600i	−0.140703	+	0.616459i
$831$		0			0
$832$	−2.03207	−	8.90308i	−0.0704493	−	0.308659i
$833$	1.71423	+	7.51054i	0.0593946	+	0.260225i
$834$		0			0
$835$	7.55323	−	3.63745i	0.261390	−	0.125879i
$836$	−38.5950	−	18.5863i	−1.33483	−	0.642822i
$837$		0			0
$838$	−29.8513	+	37.4323i	−1.03120	+	1.29308i
$839$	−12.5712	−	6.05397i	−0.434006	−	0.209006i	0.204108	−	0.978948i	$-0.434571\pi$
$839$	−12.5712	−	6.05397i	−0.434006	−	0.209006i	−0.638114	+	0.769942i	$0.720285\pi$
$840$		0			0
$841$	−10.7695	+	26.9261i	−0.371363	+	0.928488i
$842$	−26.8459			−0.925169
$843$		0			0
$844$	17.9195	−	22.4704i	0.616816	−	0.773463i
$845$	−5.65901	−	7.09618i	−0.194676	−	0.244116i
$846$		0			0
$847$	−0.424756	+	0.204551i	−0.0145948	+	0.00702847i
$848$	11.8764	−	14.8926i	0.407838	−	0.511413i
$849$		0			0
$850$	2.49718	+	10.9408i	0.0856524	+	0.375268i
$851$	−2.36779	−	2.96911i	−0.0811667	−	0.101780i
$852$		0			0
$853$	−34.3835			−1.17727			−0.588634	−	0.808400i	$-0.700334\pi$
$853$	−34.3835			−1.17727			−0.588634	+	0.808400i	$0.700334\pi$
$854$	−3.53941	+	15.5072i	−0.121116	+	0.530645i
$855$		0			0
$856$	−19.2758	+	9.28271i	−0.658832	+	0.317277i
$857$	9.24345	−	40.4982i	0.315750	−	1.38339i	−0.529177	−	0.848511i	$-0.677499\pi$
$857$	9.24345	−	40.4982i	0.315750	−	1.38339i	0.844927	−	0.534881i	$-0.179644\pi$
$858$		0			0
$859$	−0.465253	+	2.03841i	−0.0158742	+	0.0695495i	−0.982245	−	0.187605i	$-0.939928\pi$
$859$	−0.465253	+	2.03841i	−0.0158742	+	0.0695495i	0.966370	+	0.257154i	$0.0827848\pi$
$860$	−9.55677	−	11.9838i	−0.325883	−	0.408645i
$861$		0			0
$862$	9.54860	+	41.8351i	0.325227	+	1.42491i
$863$	−26.1105	+	32.7416i	−0.888813	+	1.11454i	0.103966	+	0.994581i	$0.466847\pi$
$863$	−26.1105	+	32.7416i	−0.888813	+	1.11454i	−0.992779	+	0.119956i	$0.961725\pi$
$864$		0			0
$865$	15.2555	+	7.34664i	0.518701	+	0.249793i
$866$	−13.2079	−	16.5622i	−0.448823	−	0.562807i
$867$		0			0
$868$	−8.31354	−	4.00359i	−0.282180	−	0.135891i
$869$	24.1585			0.819522
$870$		0			0
$871$	10.8676			0.368233
$872$	20.1552	+	9.70625i	0.682542	+	0.328695i
$873$		0			0
$874$	11.7230	+	14.7002i	0.396537	+	0.497242i
$875$	3.62360	+	1.74503i	0.122500	+	0.0589929i
$876$		0			0
$877$	23.2491	−	29.1535i	0.785067	−	0.984443i	−0.214902	−	0.976636i	$-0.568943\pi$
$877$	23.2491	−	29.1535i	0.785067	−	0.984443i	0.999970	−	0.00780752i	$-0.00248524\pi$
$878$	0.746583	+	3.27099i	0.0251960	+	0.110391i
$879$		0			0
$880$	3.21932	+	4.03690i	0.108523	+	0.136084i
$881$	−7.43202	+	32.5618i	−0.250391	+	1.09703i	0.680790	+	0.732478i	$0.261636\pi$
$881$	−7.43202	+	32.5618i	−0.250391	+	1.09703i	−0.931181	+	0.364556i	$0.881221\pi$
$882$		0			0
$883$	2.17178	−	9.51521i	0.0730864	−	0.320212i	−0.925148	−	0.379606i	$-0.876060\pi$
$883$	2.17178	−	9.51521i	0.0730864	−	0.320212i	0.998235	+	0.0593937i	$0.0189167\pi$
$884$	2.09500	−	1.00890i	0.0704625	−	0.0339329i
$885$		0			0
$886$	11.8734	−	52.0209i	0.398896	−	1.74768i
$887$	−45.2538			−1.51948			−0.759738	−	0.650230i	$-0.774673\pi$
$887$	−45.2538			−1.51948			−0.759738	+	0.650230i	$0.774673\pi$
$888$		0			0
$889$	1.34323	+	1.68435i	0.0450504	+	0.0564914i
$890$	−5.46093	−	23.9259i	−0.183051	−	0.801998i
$891$		0			0
$892$	16.0244	−	20.0940i	0.536537	−	0.672796i
$893$	−19.4721	+	9.37728i	−0.651609	+	0.313799i
$894$		0			0
$895$	−7.35183	−	9.21890i	−0.245744	−	0.308154i
$896$	−4.22009	+	5.29183i	−0.140983	+	0.176788i
$897$		0			0
$898$	24.9030			0.831025
$899$	4.58190	+	31.0816i	0.152815	+	1.03663i
$900$		0			0
$901$	9.63003	+	4.63758i	0.320823	+	0.154500i
$902$	20.9328	−	26.2490i	0.696987	−	0.873995i
$903$		0			0
$904$	2.97928	+	1.43475i	0.0990895	+	0.0477190i
$905$	3.61869	−	1.74267i	0.120289	−	0.0579283i
$906$		0			0
$907$	4.41247	+	19.3323i	0.146514	+	0.641918i	0.993838	+	0.110842i	$0.0353549\pi$
$907$	4.41247	+	19.3323i	0.146514	+	0.641918i	−0.847324	+	0.531076i	$0.821788\pi$
$908$	13.8893	+	60.8532i	0.460934	+	2.01948i
$909$		0			0
$910$	0.152001	−	0.665960i	0.00503878	−	0.0220763i
$911$	1.97635			0.0654794			0.0327397	−	0.999464i	$-0.489577\pi$
$911$	1.97635			0.0654794			0.0327397	+	0.999464i	$0.489577\pi$
$912$		0			0
$913$	35.6359	−	17.1614i	1.17938	−	0.567958i
$914$	−29.7825	+	14.3425i	−0.985119	+	0.474408i
$915$		0			0
$916$	37.1848			1.22862
$917$	2.35539	−	10.3196i	0.0777817	−	0.340784i
$918$		0			0
$919$	4.39568	+	19.2587i	0.145000	+	0.635287i	0.994231	+	0.107264i	$0.0342091\pi$
$919$	4.39568	+	19.2587i	0.145000	+	0.635287i	−0.849231	+	0.528022i	$0.822934\pi$
$920$	0.474328	+	2.07817i	0.0156381	+	0.0685152i
$921$		0			0
$922$	−69.7335	+	33.5819i	−2.29655	+	1.10596i
$923$	−6.78376	−	3.26688i	−0.223290	−	0.107531i
$924$		0			0
$925$	−5.61145	+	7.03654i	−0.184503	+	0.231360i
$926$	11.3484	+	5.46508i	0.372930	+	0.179594i
$927$		0			0
$928$	40.6804	+	3.18110i	1.33540	+	0.104425i
$929$	−21.3652			−0.700970			−0.350485	−	0.936568i	$-0.613983\pi$
$929$	−21.3652			−0.700970			−0.350485	+	0.936568i	$0.613983\pi$
$930$		0			0
$931$	19.0718	−	23.9153i	0.625054	−	0.783793i
$932$	9.73980	+	12.2133i	0.319038	+	0.400061i
$933$		0			0
$934$	23.1264	−	11.1371i	0.756717	−	0.364416i
$935$	−1.80645	+	2.26521i	−0.0590771	+	0.0740803i
$936$		0			0
$937$	6.83507	+	29.9464i	0.223292	+	0.978307i	0.954981	+	0.296668i	$0.0958753\pi$
$937$	6.83507	+	29.9464i	0.223292	+	0.978307i	−0.731689	+	0.681639i	$0.761268\pi$
$938$	−11.5743	−	14.5137i	−0.377913	−	0.473888i
$939$		0			0
$940$	−9.31087			−0.303687
$941$	−4.69712	+	20.5794i	−0.153122	+	0.670870i	0.838845	+	0.544370i	$0.183231\pi$
$941$	−4.69712	+	20.5794i	−0.153122	+	0.670870i	−0.991967	+	0.126499i	$0.959626\pi$
$942$		0			0
$943$	−7.64429	+	3.68130i	−0.248932	+	0.119879i
$944$	3.28735	−	14.4028i	0.106994	−	0.468771i
$945$		0			0
$946$	−12.8624	+	56.3538i	−0.418192	+	1.83222i
$947$	18.6461	+	23.3815i	0.605918	+	0.759797i	0.986287	−	0.165038i	$-0.0527746\pi$
$947$	18.6461	+	23.3815i	0.605918	+	0.759797i	−0.380369	+	0.924835i	$0.624203\pi$
$948$		0			0
$949$	0.897792	+	3.93348i	0.0291436	+	0.127686i
$950$	27.7825	−	34.8382i	0.901385	−	1.13030i
$951$		0			0
$952$	−0.941730	−	0.453513i	−0.0305216	−	0.0146984i
$953$	2.49000	+	3.12236i	0.0806591	+	0.101143i	0.820524	−	0.571612i	$-0.193682\pi$
$953$	2.49000	+	3.12236i	0.0806591	+	0.101143i	−0.739865	+	0.672756i	$0.765110\pi$
$954$		0			0
$955$	−1.28133	−	0.617054i	−0.0414627	−	0.0199674i
$956$	55.5924			1.79799
$957$		0			0
$958$	83.5785			2.70030
$959$	4.06135	+	1.95584i	0.131148	+	0.0631574i
$960$		0			0
$961$	1.89331	+	2.37414i	0.0610746	+	0.0765852i
$962$	2.91818	+	1.40532i	0.0940861	+	0.0453095i
$963$		0			0
$964$	24.0790	−	30.1941i	0.775531	−	0.972485i
$965$	0.817890	+	3.58341i	0.0263288	+	0.115354i
$966$		0			0
$967$	25.3598	+	31.8001i	0.815515	+	1.02262i	0.999214	+	0.0396408i	$0.0126214\pi$
$967$	25.3598	+	31.8001i	0.815515	+	1.02262i	−0.183699	+	0.982983i	$0.558807\pi$
$968$	−0.279205	+	1.22328i	−0.00897398	+	0.0393176i
$969$		0			0
$970$	−1.72570	+	7.56078i	−0.0554089	+	0.242762i
$971$	−16.2388	+	7.82019i	−0.521127	+	0.250962i	−0.675907	−	0.736987i	$-0.736248\pi$
$971$	−16.2388	+	7.82019i	−0.521127	+	0.250962i	0.154779	+	0.987949i	$0.450533\pi$
$972$		0			0
$973$	−0.538968	+	2.36137i	−0.0172785	+	0.0757021i
$974$	−13.2113			−0.423318
$975$		0			0
$976$	−16.1572	−	20.2605i	−0.517180	−	0.648524i
$977$	12.6581	+	55.4590i	0.404970	+	1.77429i	0.606785	+	0.794866i	$0.292459\pi$
$977$	12.6581	+	55.4590i	0.404970	+	1.77429i	−0.201815	+	0.979424i	$0.564684\pi$
$978$		0			0
$979$	−33.2225	+	41.6597i	−1.06180	+	1.33145i
$980$	11.8730	−	5.71773i	0.379269	−	0.182646i
$981$		0			0
$982$	−47.2405	−	59.2377i	−1.50750	−	1.89035i
$983$	−10.2217	+	12.8177i	−0.326023	+	0.408820i	−0.917648	−	0.397393i	$-0.869915\pi$
$983$	−10.2217	+	12.8177i	−0.326023	+	0.408820i	0.591626	+	0.806213i	$0.298486\pi$
$984$		0			0
$985$	10.5689			0.336752
$986$	1.97231	+	13.3793i	0.0628111	+	0.426083i
$987$		0			0
$988$	−8.31857	−	4.00601i	−0.264649	−	0.127448i
$989$	9.10769	−	11.4207i	0.289608	−	0.363157i
$990$		0			0
$991$	28.8424	+	13.8898i	0.916209	+	0.441223i	0.831716	−	0.555201i	$-0.187359\pi$
$991$	28.8424	+	13.8898i	0.916209	+	0.441223i	0.0844931	+	0.996424i	$0.473073\pi$
$992$	39.8284	−	19.1803i	1.26455	−	0.608976i
$993$		0			0
$994$	2.86195	+	12.5390i	0.0907756	+	0.397714i
$995$	−1.07026	−	4.68912i	−0.0339296	−	0.148655i
$996$		0			0
$997$	−9.28403	+	40.6760i	−0.294028	+	1.28822i	0.584837	+	0.811151i	$0.301159\pi$
$997$	−9.28403	+	40.6760i	−0.294028	+	1.28822i	−0.878865	+	0.477071i	$0.841699\pi$
$998$	42.5289			1.34623
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.k.d.190.1	yes	24
3.2	odd	2	inner	261.2.k.d.190.4	yes	24
29.7	even	7		7569.2.a.bq.1.11		12
29.20	even	7	inner	261.2.k.d.136.1	✓	24
29.22	even	14		7569.2.a.br.1.2		12
87.20	odd	14	inner	261.2.k.d.136.4	yes	24
87.65	odd	14		7569.2.a.bq.1.2		12
87.80	odd	14		7569.2.a.br.1.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.k.d.136.1	✓	24	29.20	even	7	inner
261.2.k.d.136.4	yes	24	87.20	odd	14	inner
261.2.k.d.190.1	yes	24	1.1	even	1	trivial
261.2.k.d.190.4	yes	24	3.2	odd	2	inner
7569.2.a.bq.1.2		12	87.65	odd	14
7569.2.a.bq.1.11		12	29.7	even	7
7569.2.a.br.1.2		12	29.22	even	14
7569.2.a.br.1.11		12	87.80	odd	14

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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.k (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.95622 - 0.942065i) q^{2} +(1.69232 + 2.12210i) q^{4} +(-0.656754 - 0.316276i) q^{5} +(0.363311 - 0.455578i) q^{7} +(-0.345098 - 1.51197i) q^{8} +O(q^{10})\)	\(q+(-1.95622 - 0.942065i) q^{2} +(1.69232 + 2.12210i) q^{4} +(-0.656754 - 0.316276i) q^{5} +(0.363311 - 0.455578i) q^{7} +(-0.345098 - 1.51197i) q^{8} +(0.986801 + 1.23741i) q^{10} +(0.764678 - 3.35027i) q^{11} +(0.164815 - 0.722101i) q^{13} +(-1.13990 + 0.548947i) q^{14} +(0.458675 - 2.00959i) q^{16} +1.15663 q^{17} +(-2.86344 - 3.59065i) q^{19} +(-0.440268 - 1.92894i) q^{20} +(-4.65205 + 5.83349i) q^{22} +(1.69884 - 0.818120i) q^{23} +(-2.78615 - 3.49373i) q^{25} +(-1.00268 + 1.25732i) q^{26} +1.58162 q^{28} +(-3.01914 - 4.45923i) q^{29} +(-5.25634 - 2.53132i) q^{31} +(-4.72432 + 5.92410i) q^{32} +(-2.26262 - 1.08962i) q^{34} +(-0.382694 + 0.184296i) q^{35} +(-0.448168 - 1.96355i) q^{37} +(2.21890 + 9.72164i) q^{38} +(-0.251557 + 1.10214i) q^{40} -4.49970 q^{41} +(6.97984 - 3.36131i) q^{43} +(8.40371 - 4.04701i) q^{44} -4.09403 q^{46} +(1.04716 - 4.58793i) q^{47} +(1.48209 + 6.49346i) q^{49} +(2.15901 + 9.45923i) q^{50} +(1.81129 - 0.872273i) q^{52} +(8.32592 + 4.00955i) q^{53} +(-1.56182 + 1.95846i) q^{55} +(-0.814200 - 0.392098i) q^{56} +(1.70522 + 11.5675i) q^{58} +7.16705 q^{59} +(7.83850 - 9.82917i) q^{61} +(7.89787 + 9.90362i) q^{62} +(11.1084 - 5.34953i) q^{64} +(-0.336626 + 0.422116i) q^{65} +(3.26496 + 14.3047i) q^{67} +(1.95739 + 2.45449i) q^{68} +0.922252 q^{70} +(2.26207 - 9.91077i) q^{71} +(-4.90782 + 2.36348i) q^{73} +(-0.973079 + 4.26334i) q^{74} +(2.77386 - 12.1531i) q^{76} +(-1.24849 - 1.56556i) q^{77} +(1.56435 + 6.85386i) q^{79} +(-0.936820 + 1.17474i) q^{80} +(8.80240 + 4.23901i) q^{82} +(7.17629 + 8.99878i) q^{83} +(-0.759622 - 0.365815i) q^{85} -16.8207 q^{86} -5.32942 q^{88} +(-13.9703 - 6.72773i) q^{89} +(-0.269094 - 0.337434i) q^{91} +(4.61112 + 2.22060i) q^{92} +(-6.37060 + 7.98848i) q^{94} +(0.744943 + 3.26381i) q^{95} +(3.05509 + 3.83096i) q^{97} +(3.21797 - 14.0989i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{4}+O(q^{10}) \) 24 * q + 2 * q^4	\( 24 q + 2 q^{4} - 4 q^{10} + 18 q^{13} - 22 q^{16} - 40 q^{22} + 18 q^{25} - 24 q^{28} - 28 q^{31} - 50 q^{34} - 40 q^{37} + 30 q^{43} + 40 q^{46} + 36 q^{49} - 52 q^{52} + 10 q^{55} + 54 q^{58} + 64 q^{61} + 20 q^{64} - 24 q^{67} + 120 q^{70} - 76 q^{73} + 126 q^{76} + 10 q^{79} - 10 q^{82} + 62 q^{85} - 20 q^{88} + 82 q^{91} - 36 q^{94} - 60 q^{97}+O(q^{100}) \) 24 * q + 2 * q^4 - 4 * q^10 + 18 * q^13 - 22 * q^16 - 40 * q^22 + 18 * q^25 - 24 * q^28 - 28 * q^31 - 50 * q^34 - 40 * q^37 + 30 * q^43 + 40 * q^46 + 36 * q^49 - 52 * q^52 + 10 * q^55 + 54 * q^58 + 64 * q^61 + 20 * q^64 - 24 * q^67 + 120 * q^70 - 76 * q^73 + 126 * q^76 + 10 * q^79 - 10 * q^82 + 62 * q^85 - 20 * q^88 + 82 * q^91 - 36 * q^94 - 60 * q^97

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