LMFDB - Embedded newform 891.2.n.h.676.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(136,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("891.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.n (of order $15$, degree $8$, not 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:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 297)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			676.2
Character	$\chi$	$=$	891.676
Dual form			891.2.n.h.460.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.837031 + 0.929617i) q^{2} +(0.0454900 + 0.432808i) q^{4} +(1.09829 + 1.21977i) q^{5} +(-2.68603 - 1.19590i) q^{7} +(-2.46446 - 1.79053i) q^{8} -2.05323 q^{10} +(3.01716 - 1.37722i) q^{11} +(-3.53897 - 0.752232i) q^{13} +(3.36001 - 1.49597i) q^{14} +(2.87597 - 0.611307i) q^{16} +(1.98276 - 6.10230i) q^{17} +(-5.02334 - 3.64967i) q^{19} +(-0.477967 + 0.530836i) q^{20} +(-1.24518 + 3.95758i) q^{22} +(-0.195223 + 0.338136i) q^{23} +(0.241033 - 2.29328i) q^{25} +(3.66151 - 2.66025i) q^{26} +(0.395406 - 1.21694i) q^{28} +(4.84087 + 2.15530i) q^{29} +(3.32795 + 0.707377i) q^{31} +(1.20724 - 2.09100i) q^{32} +(4.01317 + 6.95102i) q^{34} +(-1.49131 - 4.58979i) q^{35} +(-2.61803 + 1.90211i) q^{37} +(7.59748 - 1.61489i) q^{38} +(-0.522642 - 4.97261i) q^{40} +(-7.14942 + 3.18313i) q^{41} +(-0.325465 - 0.563722i) q^{43} +(0.733321 + 1.24320i) q^{44} +(-0.150930 - 0.464513i) q^{46} +(1.40230 - 13.3420i) q^{47} +(1.10066 + 1.22241i) q^{49} +(1.93012 + 2.14361i) q^{50} +(0.164584 - 1.56591i) q^{52} +(1.48983 + 4.58522i) q^{53} +(4.99362 + 2.16768i) q^{55} +(4.47831 + 7.75666i) q^{56} +(-6.05556 + 2.69611i) q^{58} +(0.205423 + 1.95447i) q^{59} +(-11.1789 + 2.37615i) q^{61} +(-3.44318 + 2.50162i) q^{62} +(2.75049 + 8.46514i) q^{64} +(-2.96926 - 5.14292i) q^{65} +(-0.427051 + 0.739674i) q^{67} +(2.73132 + 0.580560i) q^{68} +(5.51502 + 2.45545i) q^{70} +(0.340470 - 1.04786i) q^{71} +(2.52131 - 1.83184i) q^{73} +(0.423139 - 4.02590i) q^{74} +(1.35109 - 2.34016i) q^{76} +(-9.75119 + 0.0910248i) q^{77} +(1.10740 - 1.22989i) q^{79} +(3.90431 + 2.83665i) q^{80} +(3.02520 - 9.31060i) q^{82} +(12.6550 - 2.68990i) q^{83} +(9.62108 - 4.28358i) q^{85} +(0.796469 + 0.169295i) q^{86} +(-9.90162 - 2.00824i) q^{88} +5.92297 q^{89} +(8.60618 + 6.25276i) q^{91} +(-0.155229 - 0.0691123i) q^{92} +(11.2292 + 12.4713i) q^{94} +(-1.06531 - 10.1357i) q^{95} +(12.4739 - 13.8536i) q^{97} -2.05766 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 10 q^{4} + 24 q^{10} + 10 q^{16} - 4 q^{19} + 36 q^{22} - 32 q^{25} + 84 q^{28} + 26 q^{31} + 48 q^{34} - 48 q^{37} + 20 q^{40} - 24 q^{43} - 32 q^{46} - 24 q^{49} + 40 q^{52} - 32 q^{55} - 106 q^{58}+ \cdots - 72 q^{97}+O(q^{100}) $ 32 * q + 10 * q^4 + 24 * q^10 + 10 * q^16 - 4 * q^19 + 36 * q^22 - 32 * q^25 + 84 * q^28 + 26 * q^31 + 48 * q^34 - 48 * q^37 + 20 * q^40 - 24 * q^43 - 32 * q^46 - 24 * q^49 + 40 * q^52 - 32 * q^55 - 106 * q^58 + 6 * q^61 + 124 * q^64 + 40 * q^67 + 58 * q^70 - 60 * q^76 - 64 * q^79 - 168 * q^82 + 18 * q^85 - 80 * q^88 - 20 * q^91 - 90 * q^94 - 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.837031	+	0.929617i	−0.591870	+	0.657338i	−0.962449	−	0.271463i	$-0.912493\pi$
$2$	−0.837031	+	0.929617i	−0.591870	+	0.657338i	0.370579	+	0.928801i	$0.379159\pi$
$3$		0			0
$3$		0			0
$4$	0.0454900	+	0.432808i	0.0227450	+	0.216404i
$5$	1.09829	+	1.21977i	0.491170	+	0.545500i	0.936868	−	0.349684i	$-0.113711\pi$
$5$	1.09829	+	1.21977i	0.491170	+	0.545500i	−0.445697	+	0.895184i	$0.647044\pi$
$6$		0			0
$7$	−2.68603	−	1.19590i	−1.01522	−	0.452006i	−0.169444	−	0.985540i	$-0.554197\pi$
$7$	−2.68603	−	1.19590i	−1.01522	−	0.452006i	−0.845779	+	0.533533i	$0.820864\pi$
$8$	−2.46446	−	1.79053i	−0.871317	−	0.633049i
$9$		0			0
$10$	−2.05323			−0.649287
$11$	3.01716	−	1.37722i	0.909709	−	0.415246i
$11$	3.01716	−	1.37722i	0.909709	−	0.415246i
$12$		0			0
$13$	−3.53897	−	0.752232i	−0.981534	−	0.208631i	−0.310918	−	0.950437i	$-0.600637\pi$
$13$	−3.53897	−	0.752232i	−0.981534	−	0.208631i	−0.670616	+	0.741805i	$0.733970\pi$
$14$	3.36001	−	1.49597i	0.898001	−	0.399816i
$15$		0			0
$16$	2.87597	−	0.611307i	0.718993	−	0.152827i
$17$	1.98276	−	6.10230i	0.480889	−	1.48003i	−0.356958	−	0.934121i	$-0.616186\pi$
$17$	1.98276	−	6.10230i	0.480889	−	1.48003i	0.837847	−	0.545905i	$-0.183814\pi$
$18$		0			0
$19$	−5.02334	−	3.64967i	−1.15243	−	0.837291i	−0.163630	−	0.986522i	$-0.552320\pi$
$19$	−5.02334	−	3.64967i	−1.15243	−	0.837291i	−0.988802	+	0.149230i	$0.952320\pi$
$20$	−0.477967	+	0.530836i	−0.106877	+	0.118699i
$21$		0			0
$22$	−1.24518	+	3.95758i	−0.265472	+	0.843758i
$23$	−0.195223	+	0.338136i	−0.0407068	+	0.0705063i	−0.885661	−	0.464332i	$-0.846294\pi$
$23$	−0.195223	+	0.338136i	−0.0407068	+	0.0705063i	0.844954	+	0.534839i	$0.179628\pi$
$24$		0			0
$25$	0.241033	−	2.29328i	0.0482066	−	0.458655i
$26$	3.66151	−	2.66025i	0.718082	−	0.521717i
$27$		0			0
$28$	0.395406	−	1.21694i	0.0747248	−	0.229979i
$29$	4.84087	+	2.15530i	0.898927	+	0.400228i	0.803567	−	0.595215i	$-0.202933\pi$
$29$	4.84087	+	2.15530i	0.898927	+	0.400228i	0.0953605	+	0.995443i	$0.469600\pi$
$30$		0			0
$31$	3.32795	+	0.707377i	0.597717	+	0.127049i	0.496828	−	0.867849i	$-0.334498\pi$
$31$	3.32795	+	0.707377i	0.597717	+	0.127049i	0.100889	+	0.994898i	$0.467831\pi$
$32$	1.20724	−	2.09100i	0.213412	−	0.369641i
$33$		0			0
$34$	4.01317	+	6.95102i	0.688253	+	1.19209i
$35$	−1.49131	−	4.58979i	−0.252078	−	0.775816i
$36$		0			0
$37$	−2.61803	+	1.90211i	−0.430402	+	0.312705i	−0.781810	−	0.623517i	$-0.785703\pi$
$37$	−2.61803	+	1.90211i	−0.430402	+	0.312705i	0.351408	+	0.936223i	$0.385703\pi$
$38$	7.59748	−	1.61489i	1.23247	−	0.261970i
$39$		0			0
$40$	−0.522642	−	4.97261i	−0.0826370	−	0.786239i
$41$	−7.14942	+	3.18313i	−1.11655	+	0.497121i	−0.880227	−	0.474553i	$-0.842610\pi$
$41$	−7.14942	+	3.18313i	−1.11655	+	0.497121i	−0.236325	+	0.971674i	$0.575943\pi$
$42$		0			0
$43$	−0.325465	−	0.563722i	−0.0496329	−	0.0859667i	0.840142	−	0.542367i	$-0.182472\pi$
$43$	−0.325465	−	0.563722i	−0.0496329	−	0.0859667i	−0.889775	+	0.456400i	$0.849138\pi$
$44$	0.733321	+	1.24320i	0.110552	+	0.187420i
$45$		0			0
$46$	−0.150930	−	0.464513i	−0.0222533	−	0.0684888i
$47$	1.40230	−	13.3420i	0.204547	−	1.94613i	−0.103191	−	0.994662i	$-0.532905\pi$
$47$	1.40230	−	13.3420i	0.204547	−	1.94613i	0.307738	−	0.951471i	$-0.400428\pi$
$48$		0			0
$49$	1.10066	+	1.22241i	0.157238	+	0.174630i
$50$	1.93012	+	2.14361i	0.272960	+	0.303152i
$51$		0			0
$52$	0.164584	−	1.56591i	0.0228237	−	0.217153i
$53$	1.48983	+	4.58522i	0.204644	+	0.629828i	0.999728	+	0.0233292i	$0.00742659\pi$
$53$	1.48983	+	4.58522i	0.204644	+	0.629828i	−0.795084	+	0.606499i	$0.792573\pi$
$54$		0			0
$55$	4.99362	+	2.16768i	0.673339	+	0.292290i
$56$	4.47831	+	7.75666i	0.598439	+	1.03653i
$57$		0			0
$58$	−6.05556	+	2.69611i	−0.795134	+	0.354016i
$59$	0.205423	+	1.95447i	0.0267438	+	0.254450i	0.999723	+	0.0235554i	$0.00749861\pi$
$59$	0.205423	+	1.95447i	0.0267438	+	0.254450i	−0.972979	+	0.230895i	$0.925835\pi$
$60$		0			0
$61$	−11.1789	+	2.37615i	−1.43131	+	0.304235i	−0.857386	−	0.514673i	$-0.827913\pi$
$61$	−11.1789	+	2.37615i	−1.43131	+	0.304235i	−0.573925	+	0.818908i	$0.694580\pi$
$62$	−3.44318	+	2.50162i	−0.437285	+	0.317706i
$63$		0			0
$64$	2.75049	+	8.46514i	0.343811	+	1.05814i
$65$	−2.96926	−	5.14292i	−0.368292	−	0.637900i
$66$		0			0
$67$	−0.427051	+	0.739674i	−0.0521726	+	0.0903656i	−0.890932	−	0.454136i	$-0.849948\pi$
$67$	−0.427051	+	0.739674i	−0.0521726	+	0.0903656i	0.838760	+	0.544502i	$0.183281\pi$
$68$	2.73132	+	0.580560i	0.331221	+	0.0704033i
$69$		0			0
$70$	5.51502	+	2.45545i	0.659171	+	0.293482i
$71$	0.340470	−	1.04786i	0.0404064	−	0.124358i	−0.928819	−	0.370535i	$-0.879174\pi$
$71$	0.340470	−	1.04786i	0.0404064	−	0.124358i	0.969225	+	0.246177i	$0.0791744\pi$
$72$		0			0
$73$	2.52131	−	1.83184i	0.295097	−	0.214401i	−0.430378	−	0.902649i	$-0.641620\pi$
$73$	2.52131	−	1.83184i	0.295097	−	0.214401i	0.725476	+	0.688248i	$0.241620\pi$
$74$	0.423139	−	4.02590i	0.0491889	−	0.468001i
$75$		0			0
$76$	1.35109	−	2.34016i	0.154981	−	0.268435i
$77$	−9.75119	+	0.0910248i	−1.11125	+	0.0103732i
$78$		0			0
$79$	1.10740	−	1.22989i	0.124592	−	0.138373i	−0.677621	−	0.735411i	$-0.736989\pi$
$79$	1.10740	−	1.22989i	0.124592	−	0.138373i	0.802213	+	0.597038i	$0.203656\pi$
$80$	3.90431	+	2.83665i	0.436515	+	0.317147i
$81$		0			0
$82$	3.02520	−	9.31060i	0.334077	−	1.02818i
$83$	12.6550	−	2.68990i	1.38906	−	0.295255i	0.548130	−	0.836393i	$-0.315340\pi$
$83$	12.6550	−	2.68990i	1.38906	−	0.295255i	0.840934	+	0.541138i	$0.182006\pi$
$84$		0			0
$85$	9.62108	−	4.28358i	1.04355	−	0.464619i
$86$	0.796469	+	0.169295i	0.0858855	+	0.0182555i
$87$		0			0
$88$	−9.90162	−	2.00824i	−1.05552	−	0.214079i
$89$	5.92297			0.627834			0.313917	−	0.949451i	$-0.398359\pi$
$89$	5.92297			0.627834			0.313917	+	0.949451i	$0.398359\pi$
$90$		0			0
$91$	8.60618	+	6.25276i	0.902173	+	0.655467i
$92$	−0.155229	−	0.0691123i	−0.0161837	−	0.00720546i
$93$		0			0
$94$	11.2292	+	12.4713i	1.15820	+	1.28631i
$95$	−1.06531	−	10.1357i	−0.109298	−	1.03990i
$96$		0			0
$97$	12.4739	−	13.8536i	1.26653	−	1.40662i	0.393226	−	0.919442i	$-0.371359\pi$
$97$	12.4739	−	13.8536i	1.26653	−	1.40662i	0.873302	−	0.487180i	$-0.161974\pi$
$98$	−2.05766			−0.207855
$99$		0			0
$100$	1.00351			0.100351
$101$	−1.21199	+	1.34605i	−0.120597	+	0.133937i	−0.800420	−	0.599440i	$-0.795390\pi$
$101$	−1.21199	+	1.34605i	−0.120597	+	0.133937i	0.679823	+	0.733377i	$0.262057\pi$
$102$		0			0
$103$	−1.69190	−	16.0974i	−0.166708	−	1.58612i	−0.683462	−	0.729986i	$-0.739527\pi$
$103$	−1.69190	−	16.0974i	−0.166708	−	1.58612i	0.516754	−	0.856134i	$-0.327140\pi$
$104$	7.37475	+	8.19049i	0.723154	+	0.803144i
$105$		0			0
$106$	−5.50953	−	2.45300i	−0.535133	−	0.238256i
$107$	−8.63171	−	6.27130i	−0.834459	−	0.606270i	0.0863585	−	0.996264i	$-0.472477\pi$
$107$	−8.63171	−	6.27130i	−0.834459	−	0.606270i	−0.920817	+	0.389994i	$0.872477\pi$
$108$		0			0
$109$	3.37595			0.323357			0.161679	−	0.986843i	$-0.448309\pi$
$109$	3.37595			0.323357			0.161679	+	0.986843i	$0.448309\pi$
$110$	−6.19492	+	2.82774i	−0.590662	+	0.269614i
$111$		0			0
$112$	−8.45600	−	1.79738i	−0.799017	−	0.169836i
$113$	−12.6124	+	5.61539i	−1.18647	+	0.528251i	−0.902545	−	0.430595i	$-0.858304\pi$
$113$	−12.6124	+	5.61539i	−1.18647	+	0.528251i	−0.283926	+	0.958846i	$0.591637\pi$
$114$		0			0
$115$	−0.626862	+	0.133244i	−0.0584552	+	0.0124250i
$116$	−0.712618	+	2.19321i	−0.0661649	+	0.203635i
$117$		0			0
$118$	−1.98885	−	1.44499i	−0.183089	−	0.133022i
$119$	−12.6235	+	14.0198i	−1.15719	+	1.28519i
$120$		0			0
$121$	7.20655	−	8.31057i	0.655141	−	0.755507i
$122$	7.14817	−	12.3810i	0.647165	−	1.12092i
$123$		0			0
$124$	−0.154770	+	1.47254i	−0.0138988	+	0.132238i
$125$	9.70148	−	7.04854i	0.867727	−	0.630440i
$126$		0			0
$127$	0.297703	−	0.916236i	0.0264169	−	0.0813028i	−0.936979	−	0.349386i	$-0.886390\pi$
$127$	0.297703	−	0.916236i	0.0264169	−	0.0813028i	0.963396	+	0.268083i	$0.0863902\pi$
$128$	−5.76011	−	2.56456i	−0.509126	−	0.226678i
$129$		0			0
$130$	7.26631	+	1.54450i	0.637297	+	0.135462i
$131$	5.14336	−	8.90855i	0.449377	−	0.778344i	−0.548968	−	0.835843i	$-0.684979\pi$
$131$	5.14336	−	8.90855i	0.449377	−	0.778344i	0.998346	+	0.0574991i	$0.0183126\pi$
$132$		0			0
$133$	9.12820	+	15.8105i	0.791515	+	1.37094i
$134$	−0.330159	−	1.01612i	−0.0285214	−	0.0877797i
$135$		0			0
$136$	−15.8128	+	11.4887i	−1.35594	+	0.985145i
$137$	−18.8427	+	4.00515i	−1.60984	+	0.342183i	−0.923053	−	0.384672i	$-0.874314\pi$
$137$	−18.8427	+	4.00515i	−1.60984	+	0.342183i	−0.686791	+	0.726855i	$0.740981\pi$
$138$		0			0
$139$	−0.591700	−	5.62965i	−0.0501874	−	0.477501i	−0.990532	−	0.137279i	$-0.956164\pi$
$139$	−0.591700	−	5.62965i	−0.0501874	−	0.477501i	0.940345	−	0.340222i	$-0.110502\pi$
$140$	1.91866	−	0.854242i	0.162156	−	0.0721966i
$141$		0			0
$142$	0.689124	+	1.19360i	0.0578300	+	0.100165i
$143$	−11.7136	+	2.60432i	−0.979544	+	0.217784i
$144$		0			0
$145$	2.68771	+	8.27191i	0.223202	+	0.686945i
$146$	−0.407506	+	3.87716i	−0.0337255	+	0.320876i
$147$		0			0
$148$	−0.942344	−	1.04658i	−0.0774602	−	0.0860283i
$149$	5.30029	+	5.88657i	0.434217	+	0.482246i	0.920048	−	0.391806i	$-0.128150\pi$
$149$	5.30029	+	5.88657i	0.434217	+	0.482246i	−0.485831	+	0.874053i	$0.661483\pi$
$150$		0			0
$151$	−1.75031	+	16.6531i	−0.142438	+	1.35521i	0.656741	+	0.754116i	$0.271934\pi$
$151$	−1.75031	+	16.6531i	−0.142438	+	1.35521i	−0.799179	+	0.601093i	$0.794732\pi$
$152$	5.84495	+	17.9889i	0.474088	+	1.45909i
$153$		0			0
$154$	8.07743	−	9.14106i	0.650898	−	0.736608i
$155$	2.79221	+	4.83625i	0.224276	+	0.388457i
$156$		0			0
$157$	−12.1006	+	5.38755i	−0.965736	+	0.429973i	−0.828144	−	0.560515i	$-0.810603\pi$
$157$	−12.1006	+	5.38755i	−0.965736	+	0.429973i	−0.137592	+	0.990489i	$0.543936\pi$
$158$	0.216400	+	2.05891i	0.0172159	+	0.163798i
$159$		0			0
$160$	3.87645	−	0.823966i	0.306461	−	0.0651402i
$161$	0.928751	−	0.674777i	0.0731958	−	0.0531799i
$162$		0			0
$163$	−4.12803	−	12.7048i	−0.323333	−	0.995115i	−0.972188	−	0.234203i	$-0.924752\pi$
$163$	−4.12803	−	12.7048i	−0.323333	−	0.995115i	0.648855	−	0.760912i	$-0.275248\pi$
$164$	−1.70291	−	2.94953i	−0.132975	−	0.230319i
$165$		0			0
$166$	−8.09203	+	14.0158i	−0.628063	+	1.08784i
$167$	5.27626	+	1.12150i	0.408289	+	0.0867846i	0.407478	−	0.913215i	$-0.366408\pi$
$167$	5.27626	+	1.12150i	0.408289	+	0.0867846i	0.000811561		1.00000i	$0.499742\pi$
$168$		0			0
$169$	0.0823743	+	0.0366754i	0.00633649	+	0.00282119i
$170$	−4.07105	+	12.5294i	−0.312235	+	0.960961i
$171$		0			0
$172$	0.229178	−	0.166507i	0.0174746	−	0.0126961i
$173$	−0.671193	+	6.38597i	−0.0510298	+	0.485516i	0.938924	+	0.344125i	$0.111824\pi$
$173$	−0.671193	+	6.38597i	−0.0510298	+	0.485516i	−0.989954	+	0.141392i	$0.954842\pi$
$174$		0			0
$175$	−3.38994	+	5.87155i	−0.256255	+	0.443848i
$176$	7.83538	−	5.80525i	0.590614	−	0.437587i
$177$		0			0
$178$	−4.95771	+	5.50609i	−0.371596	+	0.412699i
$179$	−16.0419	−	11.6551i	−1.19903	−	0.871144i	−0.204839	−	0.978796i	$-0.565667\pi$
$179$	−16.0419	−	11.6551i	−1.19903	−	0.871144i	−0.994189	+	0.107651i	$0.965667\pi$
$180$		0			0
$181$	−2.22263	+	6.84054i	−0.165207	+	0.508454i	−0.999051	−	0.0435452i	$-0.986135\pi$
$181$	−2.22263	+	6.84054i	−0.165207	+	0.508454i	0.833845	+	0.551999i	$0.186135\pi$
$182$	−13.0163	+	2.76670i	−0.964833	+	0.205082i
$183$		0			0
$184$	1.08656	−	0.483769i	0.0801025	−	0.0356640i
$185$	−5.19551	−	1.10434i	−0.381982	−	0.0811927i
$186$		0			0
$187$	−2.42188	−	21.1423i	−0.177106	−	1.54608i
$188$	5.83832			0.425803
$189$		0			0
$190$	10.3140	+	7.49359i	0.748260	+	0.543643i
$191$	2.37709	+	1.05835i	0.172000	+	0.0765795i	0.490931	−	0.871199i	$-0.336657\pi$
$191$	2.37709	+	1.05835i	0.172000	+	0.0765795i	−0.318930	+	0.947778i	$0.603324\pi$
$192$		0			0
$193$	16.8704	+	18.7364i	1.21436	+	1.34868i	0.919477	+	0.393144i	$0.128613\pi$
$193$	16.8704	+	18.7364i	1.21436	+	1.34868i	0.294879	+	0.955535i	$0.404721\pi$
$194$	2.43756	+	23.1918i	0.175006	+	1.66507i
$195$		0			0
$196$	−0.479000	+	0.531983i	−0.0342143	+	0.0379988i
$197$	−21.2052			−1.51081			−0.755403	−	0.655260i	$-0.772559\pi$
$197$	−21.2052			−1.51081			−0.755403	+	0.655260i	$0.772559\pi$
$198$		0			0
$199$	−23.5761			−1.67126			−0.835632	−	0.549289i	$-0.814898\pi$
$199$	−23.5761			−1.67126			−0.835632	+	0.549289i	$0.814898\pi$
$200$	−4.70020	+	5.22010i	−0.332354	+	0.369117i
$201$		0			0
$202$	−0.236839	−	2.25337i	−0.0166639	−	0.158547i
$203$	−10.4252	−	11.5784i	−0.731706	−	0.812642i
$204$		0			0
$205$	−11.7348	−	5.22469i	−0.819597	−	0.364908i
$206$	16.3805	+	11.9012i	1.14129	+	0.829193i
$207$		0			0
$208$	−10.6378			−0.737601
$209$	−20.1826	−	4.09343i	−1.39606	−	0.283148i
$210$		0			0
$211$	−26.5539	−	5.64420i	−1.82804	−	0.388563i	−0.839982	−	0.542614i	$-0.817435\pi$
$211$	−26.5539	−	5.64420i	−1.82804	−	0.388563i	−0.988063	+	0.154051i	$0.950768\pi$
$212$	−1.91675	+	0.853391i	−0.131643	+	0.0586111i
$213$		0			0
$214$	13.0549	−	2.77491i	0.892416	−	0.189689i
$215$	0.330159	−	1.01612i	0.0225166	−	0.0692991i
$216$		0			0
$217$	−8.09301	−	5.87992i	−0.549389	−	0.399155i
$218$	−2.82578	+	3.13834i	−0.191386	+	0.212555i
$219$		0			0
$220$	−0.711029	+	2.25988i	−0.0479376	+	0.152361i
$221$	−11.6073	+	20.1044i	−0.780789	+	1.35237i
$222$		0			0
$223$	0.694950	−	6.61201i	0.0465373	−	0.442773i	−0.946299	−	0.323292i	$-0.895210\pi$
$223$	0.694950	−	6.61201i	0.0465373	−	0.442773i	0.992837	−	0.119481i	$-0.0381230\pi$
$224$	−5.74331	+	4.17276i	−0.383741	+	0.278804i
$225$		0			0
$226$	5.33678	−	16.4249i	0.354997	−	1.09257i
$227$	9.70914	+	4.32279i	0.644418	+	0.286913i	0.702807	−	0.711381i	$-0.251930\pi$
$227$	9.70914	+	4.32279i	0.644418	+	0.286913i	−0.0583891	+	0.998294i	$0.518596\pi$
$228$		0			0
$229$	−4.14958	−	0.882021i	−0.274212	−	0.0582856i	0.0687530	−	0.997634i	$-0.478098\pi$
$229$	−4.14958	−	0.882021i	−0.274212	−	0.0582856i	−0.342965	+	0.939348i	$0.611431\pi$
$230$	0.400837	−	0.694271i	0.0264304	−	0.0457788i
$231$		0			0
$232$	−8.07100	−	13.9794i	−0.529887	−	0.917791i
$233$	5.26466	+	16.2029i	0.344899	+	1.06149i	0.961638	+	0.274322i	$0.0884535\pi$
$233$	5.26466	+	16.2029i	0.344899	+	1.06149i	−0.616739	+	0.787168i	$0.711546\pi$
$234$		0			0
$235$	17.8144	−	12.9429i	1.16208	−	0.844302i
$236$	−0.836565	+	0.177817i	−0.0544557	+	0.0115749i
$237$		0			0
$238$	−2.46679	−	23.4700i	−0.159898	−	1.52133i
$239$	15.0180	−	6.68646i	0.971436	−	0.432511i	0.141235	−	0.989976i	$-0.454893\pi$
$239$	15.0180	−	6.68646i	0.971436	−	0.432511i	0.830200	+	0.557465i	$0.188226\pi$
$240$		0			0
$241$	1.56137	+	2.70437i	0.100577	+	0.174204i	0.911922	−	0.410363i	$-0.134598\pi$
$241$	1.56137	+	2.70437i	0.100577	+	0.174204i	−0.811346	+	0.584566i	$0.801265\pi$
$242$	1.69354	+	13.6555i	0.108865	+	0.877811i
$243$		0			0
$244$	−1.53694	−	4.73023i	−0.0983927	−	0.302822i
$245$	−0.282218	+	2.68512i	−0.0180302	+	0.171546i
$246$		0			0
$247$	15.0321	+	16.6948i	0.956467	+	1.06226i
$248$	−6.93501	−	7.70210i	−0.440373	−	0.489084i
$249$		0			0
$250$	−1.56800	+	14.9185i	−0.0991689	+	0.943529i
$251$	3.20271	+	9.85694i	0.202154	+	0.622165i	0.999818	+	0.0190635i	$0.00606848\pi$
$251$	3.20271	+	9.85694i	0.202154	+	0.622165i	−0.797665	+	0.603101i	$0.793932\pi$
$252$		0			0
$253$	−0.123333	+	1.28908i	−0.00775390	+	0.0810436i
$254$	0.602562	+	1.04367i	0.0378081	+	0.0654855i
$255$		0			0
$256$	−9.05708	+	4.03247i	−0.566068	+	0.252030i
$257$	−1.77898	−	16.9259i	−0.110970	−	1.05581i	−0.898332	−	0.439318i	$-0.855220\pi$
$257$	−1.77898	−	16.9259i	−0.110970	−	1.05581i	0.787362	−	0.616491i	$-0.211446\pi$
$258$		0			0
$259$	9.30684	−	1.97823i	0.578299	−	0.122921i
$260$	2.09082	−	1.51907i	0.129667	−	0.0942089i
$261$		0			0
$262$	3.97639	+	12.2381i	0.245662	+	0.756071i
$263$	−6.58321	−	11.4025i	−0.405938	−	0.703105i	0.588492	−	0.808503i	$-0.299722\pi$
$263$	−6.58321	−	11.4025i	−0.405938	−	0.703105i	−0.994430	+	0.105398i	$0.966388\pi$
$264$		0			0
$265$	−3.95667	+	6.85316i	−0.243056	+	0.420986i
$266$	−22.3383	−	4.74815i	−1.36965	−	0.291128i
$267$		0			0
$268$	−0.339563	−	0.151183i	−0.0207421	−	0.00923499i
$269$	2.84018	−	8.74119i	0.173169	−	0.532960i	−0.826376	−	0.563119i	$-0.809601\pi$
$269$	2.84018	−	8.74119i	0.173169	−	0.532960i	0.999545	+	0.0301591i	$0.00960140\pi$
$270$		0			0
$271$	6.17656	−	4.48753i	0.375199	−	0.272598i	−0.384164	−	0.923265i	$-0.625510\pi$
$271$	6.17656	−	4.48753i	0.375199	−	0.272598i	0.759364	+	0.650667i	$0.225510\pi$
$272$	1.97198	−	18.7621i	0.119569	−	1.13762i
$273$		0			0
$274$	12.0487	−	20.8690i	0.727889	−	1.26074i
$275$	−2.43110	−	7.25114i	−0.146601	−	0.437260i
$276$		0			0
$277$	0.497566	−	0.552604i	0.0298959	−	0.0332027i	−0.728011	−	0.685565i	$-0.759555\pi$
$277$	0.497566	−	0.552604i	0.0298959	−	0.0332027i	0.757907	+	0.652362i	$0.226222\pi$
$278$	5.72869	+	4.16214i	0.343584	+	0.249628i
$279$		0			0
$280$	−4.54290	+	13.9816i	−0.271490	+	0.835560i
$281$	24.2852	−	5.16198i	1.44873	−	0.307938i	0.584650	−	0.811286i	$-0.301232\pi$
$281$	24.2852	−	5.16198i	1.44873	−	0.307938i	0.864084	+	0.503348i	$0.167898\pi$
$282$		0			0
$283$	−14.9028	+	6.63515i	−0.885879	+	0.394419i	−0.798669	−	0.601771i	$-0.794462\pi$
$283$	−14.9028	+	6.63515i	−0.885879	+	0.394419i	−0.0872105	+	0.996190i	$0.527795\pi$
$284$	0.469010	+	0.0996912i	0.0278306	+	0.00591559i
$285$		0			0
$286$	7.38366	−	13.0691i	0.436605	−	0.772792i
$287$	23.0102			1.35825
$288$		0			0
$289$	−19.5535	−	14.2064i	−1.15020	−	0.835672i
$290$	−9.93940	−	4.42531i	−0.583662	−	0.259863i
$291$		0			0
$292$	0.907530	+	1.00791i	0.0531092	+	0.0589837i
$293$	0.597029	+	5.68036i	0.0348788	+	0.331850i	0.998022	+	0.0628616i	$0.0200227\pi$
$293$	0.597029	+	5.68036i	0.0348788	+	0.331850i	−0.963143	+	0.268988i	$0.913311\pi$
$294$		0			0
$295$	−2.15840	+	2.39714i	−0.125667	+	0.139567i
$296$	9.85783			0.572975
$297$		0			0
$298$	−9.90876			−0.573999
$299$	0.945246	−	1.04980i	0.0546650	−	0.0607116i
$300$		0			0
$301$	0.200055	+	1.90339i	0.0115310	+	0.109710i
$302$	−14.0159	−	15.5663i	−0.806526	−	0.895738i
$303$		0			0
$304$	−16.6780	−	7.42555i	−0.956552	−	0.425884i
$305$	−15.1760	−	11.0260i	−0.868978	−	0.631349i
$306$		0			0
$307$	−1.48842			−0.0849485			−0.0424743	−	0.999098i	$-0.513524\pi$
$307$	−1.48842			−0.0849485			−0.0424743	+	0.999098i	$0.513524\pi$
$308$	−0.482978	−	4.21625i	−0.0275202	−	0.240243i
$309$		0			0
$310$	−6.83303	−	1.45241i	−0.388090	−	0.0824911i
$311$	27.0996	−	12.0655i	1.53668	−	0.684174i	0.548314	−	0.836273i	$-0.315270\pi$
$311$	27.0996	−	12.0655i	1.53668	−	0.684174i	0.988365	+	0.152099i	$0.0486032\pi$
$312$		0			0
$313$	−18.2082	+	3.87028i	−1.02919	+	0.218761i	−0.691409	−	0.722464i	$-0.743010\pi$
$313$	−18.2082	+	3.87028i	−1.02919	+	0.218761i	−0.337781	+	0.941225i	$0.609676\pi$
$314$	5.12025	−	15.7585i	0.288952	−	0.889304i
$315$		0			0
$316$	0.582681	+	0.423343i	0.0327784	+	0.0238149i
$317$	−3.12498	+	3.47064i	−0.175516	+	0.194931i	−0.824484	−	0.565885i	$-0.808534\pi$
$317$	−3.12498	+	3.47064i	−0.175516	+	0.194931i	0.648967	+	0.760816i	$0.275201\pi$
$318$		0			0
$319$	17.5740	−	0.164049i	0.983956	−	0.00918497i
$320$	−7.30473	+	12.6522i	−0.408347	+	0.707278i
$321$		0			0
$322$	−0.150109	+	1.42819i	−0.00836525	+	0.0795900i
$323$	−32.2314	+	23.4175i	−1.79341	+	1.30299i
$324$		0			0
$325$	−2.57808	+	7.93452i	−0.143006	+	0.440128i
$326$	15.2659	+	6.79680i	0.845498	+	0.376440i
$327$		0			0
$328$	23.3189	+	4.95659i	1.28757	+	0.273682i
$329$	−19.7223	+	34.1600i	−1.08733	+	1.88330i
$330$		0			0
$331$	12.7376	+	22.0621i	0.700119	+	1.21264i	0.968424	+	0.249308i	$0.0802033\pi$
$331$	12.7376	+	22.0621i	0.700119	+	1.21264i	−0.268305	+	0.963334i	$0.586463\pi$
$332$	1.73988	+	5.35481i	0.0954885	+	0.293883i
$333$		0			0
$334$	−5.45896	+	3.96617i	−0.298701	+	0.217019i
$335$	−1.37126	+	0.291471i	−0.0749200	+	0.0159247i
$336$		0			0
$337$	−2.74840	−	26.1493i	−0.149715	−	1.42444i	−0.768986	−	0.639266i	$-0.779238\pi$
$337$	−2.74840	−	26.1493i	−0.149715	−	1.42444i	0.619271	−	0.785178i	$-0.287428\pi$
$338$	−0.103044	+	0.0458781i	−0.00560485	+	0.00249544i
$339$		0			0
$340$	2.29163	+	3.96922i	0.124281	+	0.215261i
$341$	11.0152	−	2.44903i	0.596505	−	0.132622i
$342$		0			0
$343$	4.86552	+	14.9745i	0.262713	+	0.808548i
$344$	−0.207268	+	1.97202i	−0.0111751	+	0.106324i
$345$		0			0
$346$	−5.37470	−	5.96921i	−0.288946	−	0.320907i
$347$	−7.47577	−	8.30268i	−0.401320	−	0.445711i	0.508282	−	0.861190i	$-0.330281\pi$
$347$	−7.47577	−	8.30268i	−0.401320	−	0.445711i	−0.909603	+	0.415479i	$0.863614\pi$
$348$		0			0
$349$	−0.763710	+	7.26621i	−0.0408805	+	0.388952i	0.954882	+	0.296986i	$0.0959815\pi$
$349$	−0.763710	+	7.26621i	−0.0408805	+	0.388952i	−0.995762	+	0.0919653i	$0.970685\pi$
$350$	−2.62081	−	8.06602i	−0.140088	−	0.431147i
$351$		0			0
$352$	0.762681	−	7.97153i	0.0406510	−	0.424884i
$353$	10.0286	+	17.3700i	0.533768	+	0.924513i	0.999222	+	0.0394411i	$0.0125578\pi$
$353$	10.0286	+	17.3700i	0.533768	+	0.924513i	−0.465454	+	0.885072i	$0.654109\pi$
$354$		0			0
$355$	1.65209	−	0.735558i	0.0876838	−	0.0390393i
$356$	0.269436	+	2.56351i	0.0142801	+	0.135866i
$357$		0			0
$358$	24.2624	−	5.15712i	1.28231	−	0.272562i
$359$	22.4760	−	16.3297i	1.18624	−	0.861851i	0.193375	−	0.981125i	$-0.438057\pi$
$359$	22.4760	−	16.3297i	1.18624	−	0.861851i	0.992861	+	0.119274i	$0.0380567\pi$
$360$		0			0
$361$	6.04252	+	18.5970i	0.318027	+	0.978788i
$362$	−4.49868	−	7.79194i	−0.236445	−	0.409535i
$363$		0			0
$364$	−2.31475	+	4.00926i	−0.121326	+	0.210143i
$365$	5.00357	+	1.06354i	0.261899	+	0.0556683i
$366$		0			0
$367$	25.6866	+	11.4364i	1.34083	+	0.596977i	0.946712	−	0.322082i	$-0.104383\pi$
$367$	25.6866	+	11.4364i	1.34083	+	0.596977i	0.394120	+	0.919059i	$0.371049\pi$
$368$	−0.354751	+	1.09181i	−0.0184927	+	0.0569147i
$369$		0			0
$370$	5.37542	−	3.90547i	0.279455	−	0.203036i
$371$	1.48173	−	14.0977i	0.0769275	−	0.731916i
$372$		0			0
$373$	−13.1644	+	22.8014i	−0.681625	+	1.18061i	0.292859	+	0.956156i	$0.405393\pi$
$373$	−13.1644	+	22.8014i	−0.681625	+	1.18061i	−0.974485	+	0.224454i	$0.927940\pi$
$374$	21.6815	+	15.4454i	1.12112	+	0.798660i
$375$		0			0
$376$	−27.3452	+	30.3700i	−1.41022	+	1.56621i
$377$	−15.5104	−	11.2690i	−0.798828	−	0.580382i
$378$		0			0
$379$	1.83772	−	5.65591i	0.0943972	−	0.290525i	−0.892699	−	0.450654i	$-0.851191\pi$
$379$	1.83772	−	5.65591i	0.0943972	−	0.290525i	0.987096	+	0.160129i	$0.0511910\pi$
$380$	4.33837	−	0.922149i	0.222554	−	0.0473052i
$381$		0			0
$382$	−2.97356	+	1.32391i	−0.152141	+	0.0677374i
$383$	13.0924	+	2.78287i	0.668988	+	0.142198i	0.529871	−	0.848078i	$-0.322240\pi$
$383$	13.0924	+	2.78287i	0.668988	+	0.142198i	0.139117	+	0.990276i	$0.455574\pi$
$384$		0			0
$385$	−10.8207	−	11.7943i	−0.551472	−	0.601093i
$386$	−31.5387			−1.60528
$387$		0			0
$388$	6.56339	+	4.76858i	0.333206	+	0.242088i
$389$	17.7721	+	7.91265i	0.901081	+	0.401187i	0.804372	−	0.594125i	$-0.202502\pi$
$389$	17.7721	+	7.91265i	0.901081	+	0.401187i	0.0967089	+	0.995313i	$0.469168\pi$
$390$		0			0
$391$	1.67633	+	1.86175i	0.0847757	+	0.0941529i
$392$	−0.523771	−	4.98335i	−0.0264544	−	0.251697i
$393$		0			0
$394$	17.7494	−	19.7127i	0.894201	−	0.993111i
$395$	2.71643			0.136678
$396$		0			0
$397$	22.4919			1.12884			0.564419	−	0.825489i	$-0.309100\pi$
$397$	22.4919			1.12884			0.564419	+	0.825489i	$0.309100\pi$
$398$	19.7339	−	21.9167i	0.989171	−	1.09859i
$399$		0			0
$400$	−0.708691	−	6.74274i	−0.0354345	−	0.337137i
$401$	3.52521	+	3.91514i	0.176040	+	0.195513i	0.824707	−	0.565560i	$-0.191340\pi$
$401$	3.52521	+	3.91514i	0.176040	+	0.195513i	−0.648667	+	0.761072i	$0.724673\pi$
$402$		0			0
$403$	−11.2454	−	5.00678i	−0.560173	−	0.249405i
$404$	−0.637714	−	0.463327i	−0.0317275	−	0.0230514i
$405$		0			0
$406$	19.4897			0.967256
$407$	−5.27942	+	9.34458i	−0.261691	+	0.463194i
$408$		0			0
$409$	−11.1474	−	2.36945i	−0.551202	−	0.117162i	−0.0761127	−	0.997099i	$-0.524251\pi$
$409$	−11.1474	−	2.36945i	−0.551202	−	0.117162i	−0.475089	+	0.879938i	$0.657584\pi$
$410$	14.6794	−	6.53568i	0.724963	−	0.322774i
$411$		0			0
$412$	6.89010	−	1.46454i	0.339451	−	0.0721525i
$413$	1.78557	−	5.49542i	0.0878622	−	0.270412i
$414$		0			0
$415$	17.1799	+	12.4819i	0.843328	+	0.612714i
$416$	−5.84531	+	6.49187i	−0.286590	+	0.318290i
$417$		0			0
$418$	20.6988	−	15.3358i	1.01241	−	0.750097i
$419$	7.82991	−	13.5618i	0.382516	−	0.662537i	−0.608905	−	0.793243i	$-0.708391\pi$
$419$	7.82991	−	13.5618i	0.382516	−	0.662537i	0.991421	+	0.130706i	$0.0417244\pi$
$420$		0			0
$421$	−2.69933	+	25.6824i	−0.131557	+	1.25168i	0.707136	+	0.707078i	$0.249987\pi$
$421$	−2.69933	+	25.6824i	−0.131557	+	1.25168i	−0.838693	+	0.544605i	$0.816680\pi$
$422$	27.4734	−	19.9606i	1.33738	−	0.971665i
$423$		0			0
$424$	4.53837	−	13.9677i	0.220403	−	0.678330i
$425$	−13.5163	−	6.01787i	−0.655639	−	0.291909i
$426$		0			0
$427$	32.8685	+	6.98641i	1.59062	+	0.338096i
$428$	2.32161	−	4.02115i	0.112219	−	0.194370i
$429$		0			0
$430$	0.668253	+	1.15745i	0.0322260	+	0.0558171i
$431$	−2.82734	−	8.70166i	−0.136188	−	0.419144i	0.859585	−	0.510993i	$-0.170722\pi$
$431$	−2.82734	−	8.70166i	−0.136188	−	0.419144i	−0.995773	+	0.0918491i	$0.970722\pi$
$432$		0			0
$433$	10.9105	−	7.92694i	0.524325	−	0.380945i	−0.293906	−	0.955834i	$-0.594955\pi$
$433$	10.9105	−	7.92694i	0.524325	−	0.380945i	0.818231	+	0.574890i	$0.194955\pi$
$434$	12.2402	−	2.60173i	0.587547	−	0.124887i
$435$		0			0
$436$	0.153572	+	1.46114i	0.00735476	+	0.0699759i
$437$	2.21476	−	0.986074i	0.105946	−	0.0471703i
$438$		0			0
$439$	−15.0834	−	26.1251i	−0.719889	−	1.24688i	−0.961043	−	0.276398i	$-0.910859\pi$
$439$	−15.0834	−	26.1251i	−0.719889	−	1.24688i	0.241154	−	0.970487i	$-0.422474\pi$
$440$	−8.42525	−	14.2834i	−0.401658	−	0.680934i
$441$		0			0
$442$	−8.97373	−	27.6183i	−0.426837	−	1.31367i
$443$	0.00542516	−	0.0516169i	0.000257757	−	0.00245239i	−0.994392	−	0.105755i	$-0.966274\pi$
$443$	0.00542516	−	0.0516169i	0.000257757	−	0.00245239i	0.994650	+	0.103302i	$0.0329409\pi$
$444$		0			0
$445$	6.50514	+	7.22469i	0.308373	+	0.342483i
$446$	5.56494	+	6.18049i	0.263507	+	0.292655i
$447$		0			0
$448$	2.73554	−	26.0269i	0.129242	−	1.22966i
$449$	−9.77373	−	30.0804i	−0.461251	−	1.41958i	−0.863637	−	0.504114i	$-0.831819\pi$
$449$	−9.77373	−	30.0804i	−0.461251	−	1.41958i	0.402387	−	0.915470i	$-0.368181\pi$
$450$		0			0
$451$	−17.1871	+	19.4503i	−0.809310	+	0.915879i
$452$	−3.00412	−	5.20329i	−0.141302	−	0.244742i
$453$		0			0
$454$	−12.1454	+	5.40747i	−0.570011	+	0.253785i
$455$	1.82513	+	17.3650i	0.0855634	+	0.814082i
$456$		0			0
$457$	14.5363	−	3.08978i	0.679977	−	0.144534i	0.145040	−	0.989426i	$-0.453669\pi$
$457$	14.5363	−	3.08978i	0.679977	−	0.144534i	0.534937	+	0.844892i	$0.320335\pi$
$458$	4.29327	−	3.11924i	0.200611	−	0.145753i
$459$		0			0
$460$	−0.0861849	−	0.265250i	−0.00401839	−	0.0123673i
$461$	3.20407	+	5.54962i	0.149229	+	0.258471i	0.930943	−	0.365166i	$-0.118988\pi$
$461$	3.20407	+	5.54962i	0.149229	+	0.258471i	−0.781714	+	0.623637i	$0.785654\pi$
$462$		0			0
$463$	−6.57285	+	11.3845i	−0.305466	+	0.529083i	−0.977365	−	0.211560i	$-0.932146\pi$
$463$	−6.57285	+	11.3845i	−0.305466	+	0.529083i	0.671899	+	0.740643i	$0.265479\pi$
$464$	15.2398	+	3.23931i	0.707488	+	0.150381i
$465$		0			0
$466$	−19.4692	−	8.66825i	−0.901894	−	0.401549i
$467$	3.71967	−	11.4480i	0.172126	−	0.529749i	−0.827365	−	0.561665i	$-0.810161\pi$
$467$	3.71967	−	11.4480i	0.172126	−	0.529749i	0.999491	+	0.0319163i	$0.0101610\pi$
$468$		0			0
$469$	2.03164	−	1.47608i	0.0938126	−	0.0681589i
$470$	−2.87924	+	27.3942i	−0.132810	+	1.26360i
$471$		0			0
$472$	2.99328	−	5.18452i	0.137777	−	0.238637i
$473$	−1.75835	−	1.25260i	−0.0808489	−	0.0575948i
$474$		0			0
$475$	−9.58049	+	10.6402i	−0.439583	+	0.488206i
$476$	−6.64211	−	4.82578i	−0.304441	−	0.221189i
$477$		0			0
$478$	−6.35471	+	19.5578i	−0.290658	+	0.894552i
$479$	10.1832	−	2.16450i	0.465281	−	0.0988986i	0.0306949	−	0.999529i	$-0.490228\pi$
$479$	10.1832	−	2.16450i	0.465281	−	0.0988986i	0.434586	+	0.900630i	$0.356895\pi$
$480$		0			0
$481$	10.6960	−	4.76216i	0.487695	−	0.217136i
$482$	−3.82094	−	0.812165i	−0.174039	−	0.0369931i
$483$		0			0
$484$	3.92471	+	2.74101i	0.178396	+	0.124591i
$485$	30.5982			1.38939
$486$		0			0
$487$	−13.3271	−	9.68267i	−0.603907	−	0.438764i	0.243357	−	0.969937i	$-0.421751\pi$
$487$	−13.3271	−	9.68267i	−0.603907	−	0.438764i	−0.847263	+	0.531173i	$0.821751\pi$
$488$	31.8045	+	14.1603i	1.43972	+	0.641005i
$489$		0			0
$490$	−2.25991	−	2.50988i	−0.102092	−	0.113385i
$491$	−1.72041	−	16.3686i	−0.0776410	−	0.738705i	−0.962212	−	0.272300i	$-0.912216\pi$
$491$	−1.72041	−	16.3686i	−0.0776410	−	0.738705i	0.884571	−	0.466405i	$-0.154451\pi$
$492$		0			0
$493$	22.7505	−	25.2670i	1.02463	−	1.13797i
$494$	−28.1020			−1.26437
$495$		0			0
$496$	10.0035			0.449171
$497$	−2.16765	+	2.40741i	−0.0972322	+	0.107987i
$498$		0			0
$499$	2.11277	+	20.1016i	0.0945805	+	0.899873i	0.934212	+	0.356717i	$0.116104\pi$
$499$	2.11277	+	20.1016i	0.0945805	+	0.899873i	−0.839632	+	0.543156i	$0.817229\pi$
$500$	3.49198	+	3.87824i	0.156166	+	0.173440i
$501$		0			0
$502$	−11.8440	−	5.27327i	−0.528621	−	0.235357i
$503$	19.6309	+	14.2627i	0.875299	+	0.635942i	0.932004	−	0.362449i	$-0.118059\pi$
$503$	19.6309	+	14.2627i	0.875299	+	0.635942i	−0.0567046	+	0.998391i	$0.518059\pi$
$504$		0			0
$505$	−2.97299			−0.132296
$506$	−1.09511	−	1.19365i	−0.0486838	−	0.0530642i
$507$		0			0
$508$	0.410097	+	0.0871687i	0.0181951	+	0.00386749i
$509$	−23.3821	+	10.4104i	−1.03639	+	0.461433i	−0.853167	−	0.521638i	$-0.825321\pi$
$509$	−23.3821	+	10.4104i	−1.03639	+	0.461433i	−0.183228	+	0.983071i	$0.558655\pi$
$510$		0			0
$511$	−8.96301	+	1.90515i	−0.396500	+	0.0842787i
$512$	7.72924	−	23.7882i	0.341587	−	1.05130i
$513$		0			0
$514$	17.2237	+	12.5137i	0.759703	+	0.551957i
$515$	17.7770	−	19.7433i	0.783346	−	0.869994i
$516$		0			0
$517$	−14.1439	−	42.1863i	−0.622046	−	1.85535i
$518$	−5.95112	+	10.3076i	−0.261477	+	0.452892i
$519$		0			0
$520$	−1.89094	+	17.9911i	−0.0829231	+	0.788961i
$521$	−19.4725	+	14.1476i	−0.853105	+	0.619817i	−0.926000	−	0.377522i	$-0.876776\pi$
$521$	−19.4725	+	14.1476i	−0.853105	+	0.619817i	0.0728952	+	0.997340i	$0.476776\pi$
$522$		0			0
$523$	−4.79382	+	14.7539i	−0.209619	+	0.645141i	0.789873	+	0.613271i	$0.210146\pi$
$523$	−4.79382	+	14.7539i	−0.209619	+	0.645141i	−0.999492	+	0.0318707i	$0.989854\pi$
$524$	4.08967	+	1.82084i	0.178658	+	0.0795436i
$525$		0			0
$526$	16.1103	+	3.42434i	0.702441	+	0.149308i
$527$	10.9151	−	18.9056i	0.475471	−	0.823540i
$528$		0			0
$529$	11.4238	+	19.7866i	0.496686	+	0.860285i
$530$	−3.05895	−	9.41449i	−0.132872	−	0.408939i
$531$		0			0
$532$	−6.42767	+	4.66998i	−0.278675	+	0.202469i
$533$	27.6960	−	5.88698i	1.19965	−	0.254993i
$534$		0			0
$535$	−1.83054	−	17.4165i	−0.0791413	−	0.752979i
$536$	2.37686	−	1.05825i	0.102665	−	0.0457093i
$537$		0			0
$538$	5.74863	+	9.95692i	0.247841	+	0.429273i
$539$	5.00440	+	2.17236i	0.215555	+	0.0935702i
$540$		0			0
$541$	−3.39223	−	10.4402i	−0.145844	−	0.448860i	0.851275	−	0.524720i	$-0.175830\pi$
$541$	−3.39223	−	10.4402i	−0.145844	−	0.448860i	−0.997119	+	0.0758596i	$0.975830\pi$
$542$	−0.998284	+	9.49804i	−0.0428800	+	0.407976i
$543$		0			0
$544$	−10.3663	−	11.5129i	−0.444450	−	0.493612i
$545$	3.70777	+	4.11790i	0.158824	+	0.176391i
$546$		0			0
$547$	−0.880679	+	8.37910i	−0.0376551	+	0.358264i	0.959429	+	0.281951i	$0.0909816\pi$
$547$	−0.880679	+	8.37910i	−0.0376551	+	0.358264i	−0.997084	+	0.0763134i	$0.975685\pi$
$548$	−2.59062	−	7.97310i	−0.110666	−	0.340594i
$549$		0			0
$550$	8.77569	+	3.80944i	0.374197	+	0.162435i
$551$	−16.4512	−	28.4944i	−0.700846	−	1.21390i
$552$		0			0
$553$	−4.44532	+	1.97918i	−0.189034	+	0.0841634i
$554$	0.0972311	+	0.925092i	0.00413095	+	0.0393034i
$555$		0			0
$556$	2.40964	−	0.512185i	0.102192	−	0.0217215i
$557$	19.9867	−	14.5212i	0.846864	−	0.615283i	−0.0774156	−	0.996999i	$-0.524667\pi$
$557$	19.9867	−	14.5212i	0.846864	−	0.615283i	0.924280	+	0.381716i	$0.124667\pi$
$558$		0			0
$559$	0.727761	+	2.23982i	0.0307810	+	0.0947343i
$560$	−7.09475	−	12.2885i	−0.299808	−	0.519282i
$561$		0			0
$562$	−15.5288	+	26.8967i	−0.655043	+	1.13457i
$563$	4.20657	+	0.894134i	0.177286	+	0.0376832i	0.295699	−	0.955281i	$-0.404447\pi$
$563$	4.20657	+	0.894134i	0.177286	+	0.0376832i	−0.118413	+	0.992964i	$0.537781\pi$
$564$		0			0
$565$	−20.7015	−	9.21692i	−0.870921	−	0.387759i
$566$	6.30595	−	19.4077i	0.265059	−	0.815767i
$567$		0			0
$568$	−2.71530	+	1.97278i	−0.113932	+	0.0827762i
$569$	−0.823877	+	7.83867i	−0.0345387	+	0.328614i	0.963586	+	0.267399i	$0.0861642\pi$
$569$	−0.823877	+	7.83867i	−0.0345387	+	0.328614i	−0.998125	+	0.0612150i	$0.980502\pi$
$570$		0			0
$571$	11.5035	−	19.9247i	0.481407	−	0.833821i	−0.518365	−	0.855159i	$-0.673459\pi$
$571$	11.5035	−	19.9247i	0.481407	−	0.833821i	0.999772	+	0.0213379i	$0.00679257\pi$
$572$	−1.66002	−	4.95129i	−0.0694091	−	0.207024i
$573$		0			0
$574$	−19.2603	+	21.3907i	−0.803908	+	0.892831i
$575$	0.728385	+	0.529202i	0.0303757	+	0.0220693i
$576$		0			0
$577$	7.80507	−	24.0215i	0.324929	−	1.00003i	−0.646543	−	0.762877i	$-0.723786\pi$
$577$	7.80507	−	24.0215i	0.324929	−	1.00003i	0.971472	−	0.237152i	$-0.0762140\pi$
$578$	29.5734	−	6.28602i	1.23009	−	0.261464i
$579$		0			0
$580$	−3.45789	+	1.53955i	−0.143581	+	0.0639264i
$581$	−37.2085	−	7.90890i	−1.54367	−	0.328117i
$582$		0			0
$583$	10.8099	+	11.7825i	0.447700	+	0.487983i
$584$	−9.49365			−0.392850
$585$		0			0
$586$	−5.78029	−	4.19962i	−0.238781	−	0.173485i
$587$	−21.2632	−	9.46697i	−0.877625	−	0.390744i	−0.0820707	−	0.996627i	$-0.526153\pi$
$587$	−21.2632	−	9.46697i	−0.877625	−	0.390744i	−0.795554	+	0.605883i	$0.792820\pi$
$588$		0			0
$589$	−14.1357	−	15.6993i	−0.582452	−	0.646879i
$590$	−0.421780	−	4.01296i	−0.0173644	−	0.165211i
$591$		0			0
$592$	−6.36662	+	7.07085i	−0.261666	+	0.290610i
$593$	17.1253			0.703251			0.351626	−	0.936141i	$-0.385629\pi$
$593$	17.1253			0.703251			0.351626	+	0.936141i	$0.385629\pi$
$594$		0			0
$595$	−30.9652			−1.26945
$596$	−2.30664	+	2.56179i	−0.0944838	+	0.104935i
$597$		0			0
$598$	0.184714	+	1.75743i	0.00755350	+	0.0718668i
$599$	28.5945	+	31.7574i	1.16834	+	1.29757i	0.946579	+	0.322471i	$0.104514\pi$
$599$	28.5945	+	31.7574i	1.16834	+	1.29757i	0.221760	+	0.975101i	$0.428820\pi$
$600$		0			0
$601$	11.6994	+	5.20890i	0.477227	+	0.212475i	0.631231	−	0.775595i	$-0.282550\pi$
$601$	11.6994	+	5.20890i	0.477227	+	0.212475i	−0.154003	+	0.988070i	$0.549217\pi$
$602$	−1.93688	−	1.40722i	−0.0789413	−	0.0573542i
$603$		0			0
$604$	−7.28721			−0.296512
$605$	18.0519	−	0.337049i	0.733915	−	0.0137030i
$606$		0			0
$607$	−11.1903	−	2.37858i	−0.454202	−	0.0965436i	−0.0248706	−	0.999691i	$-0.507917\pi$
$607$	−11.1903	−	2.37858i	−0.454202	−	0.0965436i	−0.429331	+	0.903147i	$0.641251\pi$
$608$	−13.6958	+	6.09778i	−0.555440	+	0.247298i
$609$		0			0
$610$	22.9528	−	4.87877i	0.929332	−	0.197536i
$611$	−14.9990	+	46.1621i	−0.606794	+	1.86752i
$612$		0			0
$613$	−15.2464	−	11.0772i	−0.615796	−	0.447402i	0.235654	−	0.971837i	$-0.424277\pi$
$613$	−15.2464	−	11.0772i	−0.615796	−	0.447402i	−0.851451	+	0.524435i	$0.824277\pi$
$614$	1.24585	−	1.38366i	0.0502785	−	0.0558399i
$615$		0			0
$616$	24.1944	+	17.2355i	0.974820	+	0.694439i
$617$	7.65992	−	13.2674i	0.308377	−	0.534124i	−0.669631	−	0.742694i	$-0.733548\pi$
$617$	7.65992	−	13.2674i	0.308377	−	0.534124i	0.978007	+	0.208570i	$0.0668809\pi$
$618$		0			0
$619$	0.231919	−	2.20656i	0.00932160	−	0.0886891i	−0.988872	−	0.148769i	$-0.952469\pi$
$619$	0.231919	−	2.20656i	0.00932160	−	0.0886891i	0.998194	+	0.0600799i	$0.0191356\pi$
$620$	−1.96615	+	1.42849i	−0.0789626	+	0.0573697i
$621$		0			0
$622$	−11.4669	+	35.2915i	−0.459781	+	1.41506i
$623$	−15.9093	−	7.08326i	−0.637391	−	0.283785i
$624$		0			0
$625$	7.97509	+	1.69516i	0.319003	+	0.0678063i
$626$	11.6430	−	20.1662i	0.465346	−	0.806004i
$627$		0			0
$628$	−2.88223	−	4.99218i	−0.115014	−	0.199209i
$629$	6.41634	+	19.7475i	0.255836	+	0.787383i
$630$		0			0
$631$	10.0626	−	7.31089i	0.400585	−	0.291042i	−0.369194	−	0.929352i	$-0.620366\pi$
$631$	10.0626	−	7.31089i	0.400585	−	0.291042i	0.769779	+	0.638310i	$0.220366\pi$
$632$	−4.93129	+	1.04818i	−0.196156	+	0.0416943i
$633$		0			0
$634$	−0.610663	−	5.81007i	−0.0242525	−	0.230747i
$635$	1.44457	−	0.643162i	0.0573258	−	0.0255231i
$636$		0			0
$637$	−2.97568	−	5.15403i	−0.117901	−	0.204210i
$638$	−14.5575	+	16.4744i	−0.576336	+	0.652228i
$639$		0			0
$640$	−3.19808	−	9.84267i	−0.126415	−	0.389066i
$641$	2.57845	−	24.5323i	0.101843	−	0.968968i	−0.817611	−	0.575771i	$-0.804702\pi$
$641$	2.57845	−	24.5323i	0.101843	−	0.968968i	0.919454	−	0.393198i	$-0.128631\pi$
$642$		0			0
$643$	11.4352	+	12.7001i	0.450960	+	0.500842i	0.925161	−	0.379575i	$-0.123930\pi$
$643$	11.4352	+	12.7001i	0.450960	+	0.500842i	−0.474201	+	0.880417i	$0.657263\pi$
$644$	0.334298	+	0.371275i	0.0131732	+	0.0146303i
$645$		0			0
$646$	5.20939	−	49.5641i	0.204961	−	1.95007i
$647$	12.2195	+	37.6077i	0.480398	+	1.47851i	0.838537	+	0.544844i	$0.183411\pi$
$647$	12.2195	+	37.6077i	0.480398	+	1.47851i	−0.358139	+	0.933668i	$0.616589\pi$
$648$		0			0
$649$	3.31152	+	5.61404i	0.129988	+	0.220370i
$650$	−5.21813	−	9.03807i	−0.204672	−	0.354502i
$651$		0			0
$652$	5.31095	−	2.36459i	0.207993	−	0.0926044i
$653$	3.02265	+	28.7586i	0.118285	+	1.12541i	0.879165	+	0.476517i	$0.158101\pi$
$653$	3.02265	+	28.7586i	0.118285	+	1.12541i	−0.760880	+	0.648893i	$0.775232\pi$
$654$		0			0
$655$	16.5153	−	3.51044i	0.645307	−	0.137164i
$656$	−18.6157	+	13.5251i	−0.726820	+	0.528066i
$657$		0			0
$658$	−15.2476	−	46.9272i	−0.594412	−	1.82941i
$659$	12.2344	+	21.1906i	0.476585	+	0.825470i	0.999640	−	0.0268290i	$-0.00854098\pi$
$659$	12.2344	+	21.1906i	0.476585	+	0.825470i	−0.523055	+	0.852299i	$0.675208\pi$
$660$		0			0
$661$	−14.9366	+	25.8710i	−0.580967	+	1.00626i	0.414398	+	0.910096i	$0.363992\pi$
$661$	−14.9366	+	25.8710i	−0.580967	+	1.00626i	−0.995365	+	0.0961687i	$0.969341\pi$
$662$	−31.1710	−	6.62561i	−1.21150	−	0.257511i
$663$		0			0
$664$	−36.0040	−	16.0300i	−1.39723	−	0.622085i
$665$	−9.25985	+	28.4989i	−0.359081	+	1.10514i
$666$		0			0
$667$	−1.67383	+	1.21611i	−0.0648111	+	0.0470880i
$668$	−0.245379	+	2.33463i	−0.00949400	+	0.0903294i
$669$		0			0
$670$	0.876832	−	1.51872i	0.0338750	−	0.0586732i
$671$	−30.4561	+	22.5650i	−1.17574	+	0.871112i
$672$		0			0
$673$	17.5924	−	19.5383i	0.678136	−	0.753146i	−0.301601	−	0.953434i	$-0.597521\pi$
$673$	17.5924	−	19.5383i	0.678136	−	0.753146i	0.979737	+	0.200288i	$0.0641878\pi$
$674$	26.6093	+	19.3328i	1.02495	+	0.744672i
$675$		0			0
$676$	−0.0121262	+	0.0373206i	−0.000466393	+	0.00143541i
$677$	−42.7807	+	9.09332i	−1.64420	+	0.349485i	−0.934759	−	0.355283i	$-0.884384\pi$
$677$	−42.7807	+	9.09332i	−1.64420	+	0.349485i	−0.709438	+	0.704768i	$0.751051\pi$
$678$		0			0
$679$	−50.0726	+	22.2938i	−1.92161	+	0.855556i
$680$	−31.3806	−	6.67016i	−1.20339	−	0.255789i
$681$		0			0
$682$	−6.94338	+	12.2898i	−0.265876	+	0.470601i
$683$	−14.0939			−0.539288			−0.269644	−	0.962960i	$-0.586906\pi$
$683$	−14.0939			−0.539288			−0.269644	+	0.962960i	$0.586906\pi$
$684$		0			0
$685$	−25.5802	−	18.5851i	−0.977368	−	0.710100i
$686$	−17.9932	−	8.01107i	−0.686982	−	0.305864i
$687$		0			0
$688$	−1.28063	−	1.42229i	−0.0488237	−	0.0542243i
$689$	−1.82331	−	17.3477i	−0.0694626	−	0.660893i
$690$		0			0
$691$	−3.93027	+	4.36500i	−0.149514	+	0.166053i	−0.813250	−	0.581915i	$-0.802304\pi$
$691$	−3.93027	+	4.36500i	−0.149514	+	0.166053i	0.663735	+	0.747968i	$0.268970\pi$
$692$	−2.79443			−0.106228
$693$		0			0
$694$	13.9758			0.530513
$695$	6.21705	−	6.90473i	0.235826	−	0.261911i
$696$		0			0
$697$	5.24883	+	49.9393i	0.198814	+	1.89159i
$698$	−6.11555	−	6.79200i	−0.231477	−	0.257081i
$699$		0			0
$700$	−2.69546	−	1.20010i	−0.101879	−	0.0453594i
$701$	0.165822	+	0.120477i	0.00626302	+	0.00455035i	0.590912	−	0.806736i	$-0.298768\pi$
$701$	0.165822	+	0.120477i	0.00626302	+	0.00455035i	−0.584649	+	0.811286i	$0.698768\pi$
$702$		0			0
$703$	20.0934			0.757835
$704$	19.9570	+	21.7527i	0.752158	+	0.819836i
$705$		0			0
$706$	−24.5417	−	5.21650i	−0.923639	−	0.196326i
$707$	4.86517	−	2.16611i	0.182974	−	0.0814651i
$708$		0			0
$709$	37.4863	−	7.96795i	1.40783	−	0.299243i	0.559550	−	0.828797i	$-0.310974\pi$
$709$	37.4863	−	7.96795i	1.40783	−	0.299243i	0.848276	+	0.529554i	$0.177641\pi$
$710$	−0.699063	+	2.15149i	−0.0262354	+	0.0807441i
$711$		0			0
$712$	−14.5969	−	10.6053i	−0.547042	−	0.397449i
$713$	−0.888883	+	0.987204i	−0.0332889	+	0.0369711i
$714$		0			0
$715$	−16.0417	−	11.4277i	−0.599924	−	0.427372i
$716$	4.31468	−	7.47325i	0.161247	−	0.279289i
$717$		0			0
$718$	−3.63267	+	34.5625i	−0.135570	+	1.28986i
$719$	32.0818	−	23.3088i	1.19645	−	0.869270i	0.202517	−	0.979279i	$-0.435088\pi$
$719$	32.0818	−	23.3088i	1.19645	−	0.869270i	0.993931	+	0.110009i	$0.0350878\pi$
$720$		0			0
$721$	−14.7063	+	45.2613i	−0.547691	+	1.68562i
$722$	−22.3458	−	9.94900i	−0.831625	−	0.370264i
$723$		0			0
$724$	−3.06175	−	0.650795i	−0.113789	−	0.0241866i
$725$	6.10949	−	10.5820i	0.226901	−	0.393004i
$726$		0			0
$727$	6.09749	+	10.5612i	0.226144	+	0.391692i	0.956662	−	0.291201i	$-0.0940548\pi$
$727$	6.09749	+	10.5612i	0.226144	+	0.391692i	−0.730518	+	0.682893i	$0.760722\pi$
$728$	−10.0138	−	30.8193i	−0.371136	−	1.14224i
$729$		0			0
$730$	−5.17683	+	3.76119i	−0.191603	+	0.139208i
$731$	−4.08532	+	0.868361i	−0.151101	+	0.0321175i
$732$		0			0
$733$	−1.57840	−	15.0175i	−0.0582997	−	0.554684i	−0.984218	−	0.176961i	$-0.943374\pi$
$733$	−1.57840	−	15.0175i	−0.0582997	−	0.554684i	0.925918	−	0.377724i	$-0.123293\pi$
$734$	−32.1320	+	14.3061i	−1.18601	+	0.528047i
$735$		0			0
$736$	0.471363	+	0.816424i	0.0173747	+	0.0300938i
$737$	−0.269792	+	2.81986i	−0.00993791	+	0.103871i
$738$		0			0
$739$	−5.34127	−	16.4387i	−0.196482	−	0.604709i	−0.999956	−	0.00936931i	$-0.997018\pi$
$739$	−5.34127	−	16.4387i	−0.196482	−	0.604709i	0.803474	−	0.595339i	$-0.202982\pi$
$740$	0.241624	−	2.29890i	0.00888226	−	0.0845091i
$741$		0			0
$742$	11.8652	+	13.1777i	0.435586	+	0.483767i
$743$	13.0653	+	14.5105i	0.479319	+	0.532338i	0.933503	−	0.358570i	$-0.116736\pi$
$743$	13.0653	+	14.5105i	0.479319	+	0.532338i	−0.454183	+	0.890908i	$0.650069\pi$
$744$		0			0
$745$	−1.35903	+	12.9303i	−0.0497911	+	0.473730i
$746$	−10.1775	−	31.3233i	−0.372626	−	1.14683i
$747$		0			0
$748$	9.04040	−	2.00997i	0.330550	−	0.0734919i
$749$	15.6852	+	27.1675i	0.573124	+	0.992680i
$750$		0			0
$751$	33.0580	−	14.7184i	1.20630	−	0.537081i	0.297668	−	0.954670i	$-0.403791\pi$
$751$	33.0580	−	14.7184i	1.20630	−	0.537081i	0.908636	+	0.417588i	$0.137125\pi$
$752$	−4.12308	−	39.2285i	−0.150353	−	1.43052i
$753$		0			0
$754$	23.4585	−	4.98627i	0.854310	−	0.181589i
$755$	−22.2354	+	16.1549i	−0.809228	+	0.587938i
$756$		0			0
$757$	−8.14836	−	25.0781i	−0.296157	−	0.911479i	−0.982830	−	0.184512i	$-0.940930\pi$
$757$	−8.14836	−	25.0781i	−0.296157	−	0.911479i	0.686673	−	0.726967i	$-0.259070\pi$
$758$	3.71961	+	6.44255i	0.135102	+	0.234004i
$759$		0			0
$760$	−15.5230	+	26.8866i	−0.563077	+	0.975278i
$761$	8.27181	+	1.75823i	0.299853	+	0.0637357i	0.355381	−	0.934721i	$-0.384351\pi$
$761$	8.27181	+	1.75823i	0.299853	+	0.0637357i	−0.0555285	+	0.998457i	$0.517684\pi$
$762$		0			0
$763$	−9.06790	−	4.03729i	−0.328280	−	0.146160i
$764$	−0.349929	+	1.07697i	−0.0126600	+	0.0389634i
$765$		0			0
$766$	−13.5457	+	9.84153i	−0.489426	+	0.355589i
$767$	0.743227	−	7.07133i	0.0268364	−	0.255331i
$768$		0			0
$769$	−2.53050	+	4.38295i	−0.0912520	+	0.158053i	−0.908038	−	0.418887i	$-0.862420\pi$
$769$	−2.53050	+	4.38295i	−0.0912520	+	0.158053i	0.816786	+	0.576940i	$0.195754\pi$
$770$	20.0214	−	0.186895i	0.721521	−	0.00673521i
$771$		0			0
$772$	−7.34185	+	8.15395i	−0.264239	+	0.293467i
$773$	21.8296	+	15.8601i	0.785156	+	0.570449i	0.906522	−	0.422159i	$-0.138727\pi$
$773$	21.8296	+	15.8601i	0.785156	+	0.570449i	−0.121366	+	0.992608i	$0.538727\pi$
$774$		0			0
$775$	2.42436	−	7.46140i	0.0870854	−	0.268021i
$776$	−55.5466	+	11.8068i	−1.99401	+	0.423840i
$777$		0			0
$778$	−22.2315	+	9.89811i	−0.797039	+	0.354865i
$779$	47.5313	+	10.1031i	1.70299	+	0.361981i
$780$		0			0
$781$	−0.415875	−	3.63047i	−0.0148812	−	0.129908i
$782$	−3.13386			−0.112066
$783$		0			0
$784$	3.91274	+	2.84277i	0.139741	+	0.101528i
$785$	−19.8616	−	8.84296i	−0.708892	−	0.315619i
$786$		0			0
$787$	10.1958	+	11.3236i	0.363442	+	0.403643i	0.896936	−	0.442161i	$-0.145788\pi$
$787$	10.1958	+	11.3236i	0.363442	+	0.403643i	−0.533494	+	0.845804i	$0.679121\pi$
$788$	−0.964623	−	9.17777i	−0.0343633	−	0.326945i
$789$		0			0
$790$	−2.27374	+	2.52524i	−0.0808959	+	0.0898440i
$791$	40.5926			1.44331
$792$		0			0
$793$	41.3492			1.46835
$794$	−18.8264	+	20.9089i	−0.668125	+	0.742028i
$795$		0			0
$796$	−1.07248	−	10.2039i	−0.0380129	−	0.361668i
$797$	−6.64856	−	7.38398i	−0.235504	−	0.261554i	0.613795	−	0.789465i	$-0.289642\pi$
$797$	−6.64856	−	7.38398i	−0.235504	−	0.261554i	−0.849300	+	0.527911i	$0.822975\pi$
$798$		0			0
$799$	−78.6366	−	35.0113i	−2.78196	−	1.23861i
$800$	−4.50426	−	3.27254i	−0.159250	−	0.115702i
$801$		0			0
$802$	−6.59029			−0.232711
$803$	5.08437	−	8.99936i	0.179424	−	0.317581i
$804$		0			0
$805$	1.84311	+	0.391766i	0.0649613	+	0.0138079i
$806$	14.0671	−	6.26309i	0.495494	−	0.220608i
$807$		0			0
$808$	5.39704	−	1.14718i	0.189867	−	0.0403575i
$809$	−11.4547	+	35.2540i	−0.402727	+	1.23947i	0.520052	+	0.854135i	$0.325913\pi$
$809$	−11.4547	+	35.2540i	−0.402727	+	1.23947i	−0.922778	+	0.385331i	$0.874087\pi$
$810$		0			0
$811$	34.3539	+	24.9596i	1.20633	+	0.876449i	0.994892	−	0.100943i	$-0.0321860\pi$
$811$	34.3539	+	24.9596i	1.20633	+	0.876449i	0.211436	+	0.977392i	$0.432186\pi$
$812$	4.53697	−	5.03881i	0.159216	−	0.176828i
$813$		0			0
$814$	−4.26785	−	12.7295i	−0.149588	−	0.446170i
$815$	10.9632	−	18.9888i	0.384024	−	0.665149i
$816$		0			0
$817$	−0.422477	+	4.01960i	−0.0147806	+	0.140628i
$818$	11.5334	−	8.37948i	0.403255	−	0.292982i
$819$		0			0
$820$	1.72747	−	5.31660i	0.0603258	−	0.185664i
$821$	7.00012	+	3.11665i	0.244306	+	0.108772i	0.525237	−	0.850956i	$-0.323977\pi$
$821$	7.00012	+	3.11665i	0.244306	+	0.108772i	−0.280931	+	0.959728i	$0.590643\pi$
$822$		0			0
$823$	−3.62929	−	0.771430i	−0.126509	−	0.0268904i	0.144222	−	0.989545i	$-0.453932\pi$
$823$	−3.62929	−	0.771430i	−0.126509	−	0.0268904i	−0.270731	+	0.962655i	$0.587265\pi$
$824$	−24.6532	+	42.7007i	−0.858836	+	1.48755i
$825$		0			0
$826$	3.61406	+	6.25973i	0.125749	+	0.217804i
$827$	1.30500	+	4.01636i	0.0453791	+	0.139663i	0.971179	−	0.238352i	$-0.0766070\pi$
$827$	1.30500	+	4.01636i	0.0453791	+	0.139663i	−0.925800	+	0.378014i	$0.876607\pi$
$828$		0			0
$829$	21.2154	−	15.4139i	0.736840	−	0.535346i	−0.154880	−	0.987933i	$-0.549499\pi$
$829$	21.2154	−	15.4139i	0.736840	−	0.535346i	0.891720	+	0.452588i	$0.149499\pi$
$830$	−25.9835	+	5.52297i	−0.901901	+	0.191705i
$831$		0			0
$832$	−3.36616	−	32.0269i	−0.116701	−	1.11033i
$833$	9.64186	−	4.29283i	0.334071	−	0.148738i
$834$		0			0
$835$	4.42689	+	7.66759i	0.153199	+	0.265348i
$836$	0.853561	−	8.92141i	0.0295210	−	0.308553i
$837$		0			0
$838$	6.05340	+	18.6305i	0.209111	+	0.643578i
$839$	1.71144	−	16.2833i	0.0590855	−	0.562161i	−0.924432	−	0.381347i	$-0.875460\pi$
$839$	1.71144	−	16.2833i	0.0590855	−	0.562161i	0.983517	−	0.180814i	$-0.0578731\pi$
$840$		0			0
$841$	−0.616043	−	0.684185i	−0.0212429	−	0.0235926i
$842$	−21.6154	−	24.0063i	−0.744914	−	0.827311i
$843$		0			0
$844$	1.23492	−	11.7495i	0.0425077	−	0.404434i
$845$	0.0457352	+	0.140758i	0.00157334	+	0.00484224i
$846$		0			0
$847$	−29.2956	+	13.7041i	−1.00661	+	0.470880i
$848$	7.08768	+	12.2762i	0.243392	+	0.421567i
$849$		0			0
$850$	16.9079	−	7.52789i	0.579936	−	0.258204i
$851$	−0.132073	−	1.25659i	−0.00452740	−	0.0430753i
$852$		0			0
$853$	−40.8195	+	8.67644i	−1.39763	+	0.297076i	−0.844293	−	0.535881i	$-0.819980\pi$
$853$	−40.8195	+	8.67644i	−1.39763	+	0.297076i	−0.553338	+	0.832957i	$0.686646\pi$
$854$	−34.0066	+	24.7072i	−1.16368	+	0.845464i
$855$		0			0
$856$	10.0435	+	30.9107i	0.343280	+	1.05651i
$857$	22.1267	+	38.3246i	0.755834	+	1.30914i	0.944959	+	0.327190i	$0.106102\pi$
$857$	22.1267	+	38.3246i	0.755834	+	1.30914i	−0.189124	+	0.981953i	$0.560565\pi$
$858$		0			0
$859$	11.2862	−	19.5482i	0.385080	−	0.666978i	−0.606701	−	0.794930i	$-0.707507\pi$
$859$	11.2862	−	19.5482i	0.385080	−	0.666978i	0.991780	+	0.127953i	$0.0408406\pi$
$860$	0.454805	+	0.0966719i	0.0155087	+	0.00329648i
$861$		0			0
$862$	10.4558	+	4.65521i	0.356125	+	0.158557i
$863$	−0.793169	+	2.44112i	−0.0269998	+	0.0830968i	−0.963648	−	0.267174i	$-0.913910\pi$
$863$	−0.793169	+	2.44112i	−0.0269998	+	0.0830968i	0.936649	+	0.350270i	$0.113910\pi$
$864$		0			0
$865$	−8.52661	+	6.19495i	−0.289914	+	0.210635i
$866$	−1.76341	+	16.7777i	−0.0599229	+	0.570129i
$867$		0			0
$868$	2.17672	−	3.77020i	0.0738829	−	0.127969i
$869$	1.64737	−	5.23590i	0.0558833	−	0.177616i
$870$		0			0
$871$	2.06773	−	2.29644i	0.0700623	−	0.0778120i
$872$	−8.31989	−	6.04475i	−0.281747	−	0.204701i
$873$		0			0
$874$	−0.937150	+	2.88425i	−0.0316996	+	0.0975612i
$875$	−34.4878	+	7.33060i	−1.16590	+	0.247820i
$876$		0			0
$877$	49.1400	−	21.8785i	1.65934	−	0.738786i	0.659424	−	0.751771i	$-0.270800\pi$
$877$	49.1400	−	21.8785i	1.65934	−	0.738786i	0.999916	+	0.0129855i	$0.00413354\pi$
$878$	36.9116	+	7.84580i	1.24571	+	0.264783i
$879$		0			0
$880$	15.6866	+	3.18155i	0.528796	+	0.107250i
$881$	−42.7815			−1.44134			−0.720672	−	0.693276i	$-0.756167\pi$
$881$	−42.7815			−1.44134			−0.720672	+	0.693276i	$0.756167\pi$
$882$		0			0
$883$	−2.00195	−	1.45450i	−0.0673711	−	0.0489479i	0.553590	−	0.832789i	$-0.313257\pi$
$883$	−2.00195	−	1.45450i	−0.0673711	−	0.0489479i	−0.620961	+	0.783841i	$0.713257\pi$
$884$	−9.22935	−	4.10917i	−0.310417	−	0.138206i
$885$		0			0
$886$	0.0434429	+	0.0482483i	0.00145949	+	0.00162093i
$887$	0.220080	+	2.09392i	0.00738957	+	0.0703070i	0.997595	−	0.0693096i	$-0.0220796\pi$
$887$	0.220080	+	2.09392i	0.00738957	+	0.0703070i	−0.990206	+	0.139617i	$0.955413\pi$
$888$		0			0
$889$	−1.89536	+	2.10501i	−0.0635684	+	0.0705999i
$890$	−12.1612			−0.407644
$891$		0			0
$892$	2.89334			0.0968763
$893$	−55.7382	+	61.9035i	−1.86521	+	2.07152i
$894$		0			0
$895$	−3.40204	−	32.3682i	−0.113718	−	1.08195i
$896$	12.4049	+	13.7770i	0.414417	+	0.460257i
$897$		0			0
$898$	36.1442	+	16.0924i	1.20615	+	0.537011i
$899$	14.5856	+	10.5970i	0.486456	+	0.353431i
$900$		0			0
$901$	30.9344			1.03057
$902$	−3.69519	−	32.2579i	−0.123036	−	1.07407i
$903$		0			0
$904$	41.1372	+	8.74398i	1.36820	+	0.290820i
$905$	−10.7850	+	4.80180i	−0.358506	+	0.159617i
$906$		0			0
$907$	13.3495	−	2.83753i	0.443264	−	0.0942186i	0.0191276	−	0.999817i	$-0.493911\pi$
$907$	13.3495	−	2.83753i	0.443264	−	0.0942186i	0.424136	+	0.905598i	$0.360578\pi$
$908$	−1.42927	+	4.39884i	−0.0474319	+	0.145980i
$909$		0			0
$910$	−17.6704	−	12.8383i	−0.585769	−	0.425586i
$911$	−5.06855	+	5.62920i	−0.167929	+	0.186504i	−0.821235	−	0.570590i	$-0.806715\pi$
$911$	−5.06855	+	5.62920i	−0.167929	+	0.186504i	0.653307	+	0.757094i	$0.273381\pi$
$912$		0			0
$913$	34.4776	−	25.5445i	1.14104	−	0.845399i
$914$	−9.29498	+	16.0994i	−0.307451	+	0.532520i
$915$		0			0
$916$	0.192981	−	1.83610i	0.00637629	−	0.0606663i
$917$	−24.4689	+	17.7777i	−0.808034	+	0.587071i
$918$		0			0
$919$	−5.16917	+	15.9091i	−0.170515	+	0.524792i	−0.999400	−	0.0346269i	$-0.988976\pi$
$919$	−5.16917	+	15.9091i	−0.170515	+	0.524792i	0.828885	+	0.559419i	$0.188976\pi$
$920$	1.78345	+	0.794044i	0.0587987	+	0.0261789i
$921$		0			0
$922$	−7.84092	−	1.66664i	−0.258227	−	0.0548879i
$923$	−1.99315	+	3.45224i	−0.0656053	+	0.113632i
$924$		0			0
$925$	3.73104	+	6.46234i	0.122676	+	0.212481i
$926$	−5.08155	−	15.6394i	−0.166990	−	0.513943i
$927$		0			0
$928$	10.3508	−	7.52032i	0.339783	−	0.246866i
$929$	−20.1775	+	4.28886i	−0.662003	+	0.140713i	−0.526647	−	0.850084i	$-0.676551\pi$
$929$	−20.1775	+	4.28886i	−0.662003	+	0.140713i	−0.135356	+	0.990797i	$0.543218\pi$
$930$		0			0
$931$	−1.06761	−	10.1576i	−0.0349895	−	0.332903i
$932$	−6.77328	+	3.01566i	−0.221866	+	0.0987811i
$933$		0			0
$934$	7.52874	+	13.0402i	0.246348	+	0.426687i
$935$	23.1290	−	26.1746i	0.756398	−	0.856000i
$936$		0			0
$937$	−9.60247	−	29.5534i	−0.313699	−	0.965466i	−0.976287	−	0.216482i	$-0.930542\pi$
$937$	−9.60247	−	29.5534i	−0.313699	−	0.965466i	0.662588	−	0.748984i	$-0.269458\pi$
$938$	−0.328364	+	3.12417i	−0.0107215	+	0.102008i
$939$		0			0
$940$	6.41217	+	7.12144i	0.209142	+	0.232276i
$941$	10.5681	+	11.7371i	0.344511	+	0.382618i	0.890354	−	0.455270i	$-0.150457\pi$
$941$	10.5681	+	11.7371i	0.344511	+	0.382618i	−0.545843	+	0.837888i	$0.683790\pi$
$942$		0			0
$943$	0.319401	−	3.03890i	0.0104011	−	0.0989602i
$944$	1.78557	+	5.49542i	0.0581154	+	0.178861i
$945$		0			0
$946$	2.63623	−	0.586120i	0.0857113	−	0.0190564i
$947$	−26.3537	−	45.6460i	−0.856381	−	1.48329i	−0.875358	−	0.483475i	$-0.839374\pi$
$947$	−26.3537	−	45.6460i	−0.856381	−	1.48329i	0.0189774	−	0.999820i	$-0.493959\pi$
$948$		0			0
$949$	−10.3008	+	4.58622i	−0.334379	+	0.148875i
$950$	−1.87215	−	17.8124i	−0.0607407	−	0.577909i
$951$		0			0
$952$	56.2129	−	11.9484i	1.82187	−	0.387250i
$953$	−38.4078	+	27.9049i	−1.24415	+	0.903928i	−0.997868	−	0.0652707i	$-0.979209\pi$
$953$	−38.4078	+	27.9049i	−1.24415	+	0.903928i	−0.246282	+	0.969198i	$0.579209\pi$
$954$		0			0
$955$	1.31979	+	4.06190i	0.0427074	+	0.131440i
$956$	3.57712	+	6.19576i	0.115692	+	0.200385i
$957$		0			0
$958$	−6.51147	+	11.2782i	−0.210376	+	0.364382i
$959$	55.4019	+	11.7760i	1.78902	+	0.380268i
$960$		0			0
$961$	−17.7451	−	7.90061i	−0.572421	−	0.254858i
$962$	−4.52588	+	13.9292i	−0.145920	+	0.449096i
$963$		0			0
$964$	−1.09945	+	0.798794i	−0.0354108	+	0.0257274i
$965$	−4.32568	+	41.1561i	−0.139249	+	1.32486i
$966$		0			0
$967$	−6.56700	+	11.3744i	−0.211180	+	0.365775i	−0.952084	−	0.305836i	$-0.901064\pi$
$967$	−6.56700	+	11.3744i	−0.211180	+	0.365775i	0.740904	+	0.671611i	$0.234397\pi$
$968$	−32.6406	+	7.57748i	−1.04911	+	0.243550i
$969$		0			0
$970$	−25.6116	+	28.4446i	−0.822340	+	0.913301i
$971$	26.8860	+	19.5338i	0.862814	+	0.626871i	0.928649	−	0.370960i	$-0.120971\pi$
$971$	26.8860	+	19.5338i	0.862814	+	0.626871i	−0.0658353	+	0.997831i	$0.520971\pi$
$972$		0			0
$973$	−5.14316	+	15.8290i	−0.164882	+	0.507455i
$974$	20.1563	−	4.28436i	0.645850	−	0.137280i
$975$		0			0
$976$	−30.6977	+	13.6675i	−0.982608	+	0.437485i
$977$	15.0505	+	3.19908i	0.481507	+	0.102348i	0.442269	−	0.896882i	$-0.354174\pi$
$977$	15.0505	+	3.19908i	0.481507	+	0.102348i	0.0392382	+	0.999230i	$0.487507\pi$
$978$		0			0
$979$	17.8706	−	8.15721i	0.571146	−	0.260706i
$980$	−1.17498			−0.0375334
$981$		0			0
$982$	16.6566	+	12.1017i	0.531532	+	0.386181i
$983$	−35.2182	−	15.6802i	−1.12329	−	0.500120i	−0.240856	−	0.970561i	$-0.577428\pi$
$983$	−35.2182	−	15.6802i	−1.12329	−	0.500120i	−0.882431	+	0.470441i	$0.844095\pi$
$984$		0			0
$985$	−23.2894	−	25.8655i	−0.742063	−	0.824145i
$986$	4.44576	+	42.2986i	0.141582	+	1.34706i
$987$		0			0
$988$	−6.54183	+	7.26544i	−0.208123	+	0.231144i
$989$	0.254153			0.00808160
$990$		0			0
$991$	10.3606			0.329114			0.164557	−	0.986368i	$-0.447381\pi$
$991$	10.3606			0.329114			0.164557	+	0.986368i	$0.447381\pi$
$992$	5.49676	−	6.10477i	0.174522	−	0.193827i
$993$		0			0
$994$	−0.423587	−	4.03016i	−0.0134354	−	0.127829i
$995$	−25.8934	−	28.7575i	−0.820876	−	0.911675i
$996$		0			0
$997$	−4.17048	−	1.85682i	−0.132080	−	0.0588060i	0.339632	−	0.940558i	$-0.389697\pi$
$997$	−4.17048	−	1.85682i	−0.132080	−	0.0588060i	−0.471713	+	0.881752i	$0.656364\pi$
$998$	−20.4553	−	14.8616i	−0.647500	−	0.470437i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.n.h.676.2		32
3.2	odd	2	inner	891.2.n.h.676.3		32
9.2	odd	6	inner	891.2.n.h.379.2		32
9.4	even	3		297.2.f.b.82.2	✓	16
9.5	odd	6		297.2.f.b.82.3	yes	16
9.7	even	3	inner	891.2.n.h.379.3		32
11.9	even	5	inner	891.2.n.h.757.3		32
33.20	odd	10	inner	891.2.n.h.757.2		32
99.14	odd	30		3267.2.a.bj.1.6		8
99.20	odd	30	inner	891.2.n.h.460.3		32
99.31	even	15		297.2.f.b.163.2	yes	16
99.41	even	30		3267.2.a.bi.1.3		8
99.58	even	15		3267.2.a.bj.1.3		8
99.85	odd	30		3267.2.a.bi.1.6		8
99.86	odd	30		297.2.f.b.163.3	yes	16
99.97	even	15	inner	891.2.n.h.460.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.f.b.82.2	✓	16	9.4	even	3
297.2.f.b.82.3	yes	16	9.5	odd	6
297.2.f.b.163.2	yes	16	99.31	even	15
297.2.f.b.163.3	yes	16	99.86	odd	30
891.2.n.h.379.2		32	9.2	odd	6	inner
891.2.n.h.379.3		32	9.7	even	3	inner
891.2.n.h.460.2		32	99.97	even	15	inner
891.2.n.h.460.3		32	99.20	odd	30	inner
891.2.n.h.676.2		32	1.1	even	1	trivial
891.2.n.h.676.3		32	3.2	odd	2	inner
891.2.n.h.757.2		32	33.20	odd	10	inner
891.2.n.h.757.3		32	11.9	even	5	inner
3267.2.a.bi.1.3		8	99.41	even	30
3267.2.a.bi.1.6		8	99.85	odd	30
3267.2.a.bj.1.3		8	99.58	even	15
3267.2.a.bj.1.6		8	99.14	odd	30

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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.837031 + 0.929617i) q^{2} +(0.0454900 + 0.432808i) q^{4} +(1.09829 + 1.21977i) q^{5} +(-2.68603 - 1.19590i) q^{7} +(-2.46446 - 1.79053i) q^{8} -2.05323 q^{10} +(3.01716 - 1.37722i) q^{11} +(-3.53897 - 0.752232i) q^{13} +(3.36001 - 1.49597i) q^{14} +(2.87597 - 0.611307i) q^{16} +(1.98276 - 6.10230i) q^{17} +(-5.02334 - 3.64967i) q^{19} +(-0.477967 + 0.530836i) q^{20} +(-1.24518 + 3.95758i) q^{22} +(-0.195223 + 0.338136i) q^{23} +(0.241033 - 2.29328i) q^{25} +(3.66151 - 2.66025i) q^{26} +(0.395406 - 1.21694i) q^{28} +(4.84087 + 2.15530i) q^{29} +(3.32795 + 0.707377i) q^{31} +(1.20724 - 2.09100i) q^{32} +(4.01317 + 6.95102i) q^{34} +(-1.49131 - 4.58979i) q^{35} +(-2.61803 + 1.90211i) q^{37} +(7.59748 - 1.61489i) q^{38} +(-0.522642 - 4.97261i) q^{40} +(-7.14942 + 3.18313i) q^{41} +(-0.325465 - 0.563722i) q^{43} +(0.733321 + 1.24320i) q^{44} +(-0.150930 - 0.464513i) q^{46} +(1.40230 - 13.3420i) q^{47} +(1.10066 + 1.22241i) q^{49} +(1.93012 + 2.14361i) q^{50} +(0.164584 - 1.56591i) q^{52} +(1.48983 + 4.58522i) q^{53} +(4.99362 + 2.16768i) q^{55} +(4.47831 + 7.75666i) q^{56} +(-6.05556 + 2.69611i) q^{58} +(0.205423 + 1.95447i) q^{59} +(-11.1789 + 2.37615i) q^{61} +(-3.44318 + 2.50162i) q^{62} +(2.75049 + 8.46514i) q^{64} +(-2.96926 - 5.14292i) q^{65} +(-0.427051 + 0.739674i) q^{67} +(2.73132 + 0.580560i) q^{68} +(5.51502 + 2.45545i) q^{70} +(0.340470 - 1.04786i) q^{71} +(2.52131 - 1.83184i) q^{73} +(0.423139 - 4.02590i) q^{74} +(1.35109 - 2.34016i) q^{76} +(-9.75119 + 0.0910248i) q^{77} +(1.10740 - 1.22989i) q^{79} +(3.90431 + 2.83665i) q^{80} +(3.02520 - 9.31060i) q^{82} +(12.6550 - 2.68990i) q^{83} +(9.62108 - 4.28358i) q^{85} +(0.796469 + 0.169295i) q^{86} +(-9.90162 - 2.00824i) q^{88} +5.92297 q^{89} +(8.60618 + 6.25276i) q^{91} +(-0.155229 - 0.0691123i) q^{92} +(11.2292 + 12.4713i) q^{94} +(-1.06531 - 10.1357i) q^{95} +(12.4739 - 13.8536i) q^{97} -2.05766 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 10 q^{4} + 24 q^{10} + 10 q^{16} - 4 q^{19} + 36 q^{22} - 32 q^{25} + 84 q^{28} + 26 q^{31} + 48 q^{34} - 48 q^{37} + 20 q^{40} - 24 q^{43} - 32 q^{46} - 24 q^{49} + 40 q^{52} - 32 q^{55} - 106 q^{58}+ \cdots - 72 q^{97}+O(q^{100}) \) 32 * q + 10 * q^4 + 24 * q^10 + 10 * q^16 - 4 * q^19 + 36 * q^22 - 32 * q^25 + 84 * q^28 + 26 * q^31 + 48 * q^34 - 48 * q^37 + 20 * q^40 - 24 * q^43 - 32 * q^46 - 24 * q^49 + 40 * q^52 - 32 * q^55 - 106 * q^58 + 6 * q^61 + 124 * q^64 + 40 * q^67 + 58 * q^70 - 60 * q^76 - 64 * q^79 - 168 * q^82 + 18 * q^85 - 80 * q^88 - 20 * q^91 - 90 * q^94 - 72 * q^97

Introduction

L-functions

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