LMFDB - Embedded newform 495.2.n.f.91.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(91,495)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("495.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.n (of order $5$, degree $4$, 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:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 $ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.2
Root			$-0.762262 - 2.34600i$ of defining polynomial
Character	$\chi$	$=$	495.91
Dual form			495.2.n.f.136.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.04238 - 1.48388i) q^{2} +(1.35140 - 4.15918i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.646930 - 1.99105i) q^{7} +(-1.85140 - 5.69802i) q^{8} +O(q^{10})$	\(q+(2.04238 - 1.48388i) q^{2} +(1.35140 - 4.15918i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.646930 - 1.99105i) q^{7} +(-1.85140 - 5.69802i) q^{8} +2.52452 q^{10} +(1.64693 + 2.87882i) q^{11} +(-1.04238 + 0.757336i) q^{13} +(-1.63319 - 5.02644i) q^{14} +(-5.16042 - 3.74926i) q^{16} +(-2.41998 - 1.75822i) q^{17} +(0.664789 + 2.04601i) q^{19} +(3.53801 - 2.57052i) q^{20} +(7.63548 + 3.43582i) q^{22} -8.77882 q^{23} +(0.309017 + 0.951057i) q^{25} +(-1.00515 + 3.09354i) q^{26} +(-7.40686 - 5.38140i) q^{28} +(0.189313 - 0.582646i) q^{29} +(2.94887 - 2.14248i) q^{31} -4.12048 q^{32} -7.55150 q^{34} +(1.69369 - 1.23053i) q^{35} +(-0.578100 + 1.77921i) q^{37} +(4.39378 + 3.19227i) q^{38} +(1.85140 - 5.69802i) q^{40} +(1.57810 + 4.85689i) q^{41} +5.17287 q^{43} +(14.1992 - 2.95944i) q^{44} +(-17.9297 + 13.0267i) q^{46} +(2.25789 + 6.94907i) q^{47} +(2.11737 + 1.53836i) q^{49} +(2.04238 + 1.48388i) q^{50} +(1.74122 + 5.35892i) q^{52} +(-2.38030 + 1.72939i) q^{53} +(-0.359735 + 3.29706i) q^{55} -12.5428 q^{56} +(-0.477925 - 1.47090i) q^{58} +(2.00682 - 6.17636i) q^{59} +(0.406490 + 0.295332i) q^{61} +(2.84355 - 8.75154i) q^{62} +(1.90523 - 1.38423i) q^{64} -1.28846 q^{65} -7.80964 q^{67} +(-10.5831 + 7.68907i) q^{68} +(1.63319 - 5.02644i) q^{70} +(-9.14526 - 6.64442i) q^{71} +(-3.43539 + 10.5730i) q^{73} +(1.45943 + 4.49166i) q^{74} +9.40812 q^{76} +(6.79732 - 1.41672i) q^{77} +(-4.33558 + 3.14998i) q^{79} +(-1.97110 - 6.06643i) q^{80} +(10.4301 + 7.57793i) q^{82} +(8.77408 + 6.37474i) q^{83} +(-0.924349 - 2.84485i) q^{85} +(10.5650 - 7.67591i) q^{86} +(13.3545 - 14.7141i) q^{88} +4.32336 q^{89} +(0.833541 + 2.56538i) q^{91} +(-11.8637 + 36.5127i) q^{92} +(14.9230 + 10.8422i) q^{94} +(-0.664789 + 2.04601i) q^{95} +(0.284493 - 0.206696i) q^{97} +6.60723 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 6 q^{4} + 2 q^{5} - 3 q^{7} + 2 q^{8}+O(q^{10}) $ 8 * q + 4 * q^2 - 6 * q^4 + 2 * q^5 - 3 * q^7 + 2 * q^8	$ 8 q + 4 q^{2} - 6 q^{4} + 2 q^{5} - 3 q^{7} + 2 q^{8} + 6 q^{10} + 5 q^{11} + 4 q^{13} - 16 q^{14} - 20 q^{16} - q^{17} - q^{19} + q^{20} + 33 q^{22} + 18 q^{23} - 2 q^{25} + 14 q^{26} + 4 q^{28} - 19 q^{29} + 6 q^{31} - 12 q^{32} - 20 q^{34} + 8 q^{35} + 4 q^{37} + 6 q^{38} - 2 q^{40} + 4 q^{41} + 42 q^{43} + 28 q^{44} - 41 q^{46} - 4 q^{47} - 15 q^{49} + 4 q^{50} - 26 q^{52} - 3 q^{53} + 5 q^{55} - 30 q^{56} - 6 q^{58} + 19 q^{59} - 2 q^{61} + 38 q^{62} + 6 q^{64} - 14 q^{65} - 2 q^{67} - 35 q^{68} + 16 q^{70} - 40 q^{71} - 23 q^{73} - 48 q^{74} + 16 q^{76} + 28 q^{77} + 17 q^{79} - 15 q^{80} + 2 q^{82} + 25 q^{83} - 4 q^{85} + 31 q^{86} + 22 q^{88} - 12 q^{91} - 81 q^{92} + 33 q^{94} + q^{95} + 12 q^{97} + 84 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 - 6 * q^4 + 2 * q^5 - 3 * q^7 + 2 * q^8 + 6 * q^10 + 5 * q^11 + 4 * q^13 - 16 * q^14 - 20 * q^16 - q^17 - q^19 + q^20 + 33 * q^22 + 18 * q^23 - 2 * q^25 + 14 * q^26 + 4 * q^28 - 19 * q^29 + 6 * q^31 - 12 * q^32 - 20 * q^34 + 8 * q^35 + 4 * q^37 + 6 * q^38 - 2 * q^40 + 4 * q^41 + 42 * q^43 + 28 * q^44 - 41 * q^46 - 4 * q^47 - 15 * q^49 + 4 * q^50 - 26 * q^52 - 3 * q^53 + 5 * q^55 - 30 * q^56 - 6 * q^58 + 19 * q^59 - 2 * q^61 + 38 * q^62 + 6 * q^64 - 14 * q^65 - 2 * q^67 - 35 * q^68 + 16 * q^70 - 40 * q^71 - 23 * q^73 - 48 * q^74 + 16 * q^76 + 28 * q^77 + 17 * q^79 - 15 * q^80 + 2 * q^82 + 25 * q^83 - 4 * q^85 + 31 * q^86 + 22 * q^88 - 12 * q^91 - 81 * q^92 + 33 * q^94 + q^95 + 12 * q^97 + 84 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	2.04238	−	1.48388i	1.44418	−	1.04926i	0.457035	−	0.889449i	$-0.348911\pi$
$2$	2.04238	−	1.48388i	1.44418	−	1.04926i	0.987148	−	0.159812i	$-0.0510887\pi$
$3$		0			0
$3$		0			0
$4$	1.35140	−	4.15918i	0.675700	−	2.07959i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$		0			0
$7$	0.646930	−	1.99105i	0.244517	−	0.752545i	−0.751199	−	0.660076i	$-0.770524\pi$
$7$	0.646930	−	1.99105i	0.244517	−	0.752545i	0.995716	−	0.0924689i	$-0.0294759\pi$
$8$	−1.85140	−	5.69802i	−0.654569	−	2.01456i
$9$		0			0
$10$	2.52452			0.798325
$11$	1.64693	+	2.87882i	0.496568	+	0.867998i
$11$	1.64693	+	2.87882i	0.496568	+	0.867998i
$12$		0			0
$13$	−1.04238	+	0.757336i	−0.289105	+	0.210047i	−0.722879	−	0.690975i	$-0.757182\pi$
$13$	−1.04238	+	0.757336i	−0.289105	+	0.210047i	0.433774	+	0.901022i	$0.357182\pi$
$14$	−1.63319	−	5.02644i	−0.436489	−	1.34337i
$15$		0			0
$16$	−5.16042	−	3.74926i	−1.29010	−	0.937316i
$17$	−2.41998	−	1.75822i	−0.586931	−	0.426430i	0.254285	−	0.967129i	$-0.418160\pi$
$17$	−2.41998	−	1.75822i	−0.586931	−	0.426430i	−0.841216	+	0.540699i	$0.818160\pi$
$18$		0			0
$19$	0.664789	+	2.04601i	0.152513	+	0.469387i	0.997900	−	0.0647668i	$-0.0206304\pi$
$19$	0.664789	+	2.04601i	0.152513	+	0.469387i	−0.845387	+	0.534154i	$0.820630\pi$
$20$	3.53801	−	2.57052i	0.791123	−	0.574785i
$21$		0			0
$22$	7.63548	+	3.43582i	1.62789	+	0.732518i
$23$	−8.77882			−1.83051			−0.915255	−	0.402874i	$-0.868011\pi$
$23$	−8.77882			−1.83051			−0.915255	+	0.402874i	$0.868011\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	−1.00515	+	3.09354i	−0.197126	+	0.606693i
$27$		0			0
$28$	−7.40686	−	5.38140i	−1.39977	−	1.01699i
$29$	0.189313	−	0.582646i	0.0351545	−	0.108195i	−0.931939	−	0.362614i	$-0.881884\pi$
$29$	0.189313	−	0.582646i	0.0351545	−	0.108195i	0.967094	+	0.254419i	$0.0818844\pi$
$30$		0			0
$31$	2.94887	−	2.14248i	0.529633	−	0.384801i	−0.290587	−	0.956848i	$-0.593851\pi$
$31$	2.94887	−	2.14248i	0.529633	−	0.384801i	0.820221	+	0.572047i	$0.193851\pi$
$32$	−4.12048			−0.728405
$33$		0			0
$34$	−7.55150			−1.29507
$35$	1.69369	−	1.23053i	0.286285	−	0.207998i
$36$		0			0
$37$	−0.578100	+	1.77921i	−0.0950391	+	0.292500i	−0.987264	−	0.159091i	$-0.949144\pi$
$37$	−0.578100	+	1.77921i	−0.0950391	+	0.292500i	0.892225	+	0.451592i	$0.149144\pi$
$38$	4.39378	+	3.19227i	0.712766	+	0.517855i
$39$		0			0
$40$	1.85140	−	5.69802i	0.292732	−	0.900937i
$41$	1.57810	+	4.85689i	0.246458	+	0.758519i	0.995393	+	0.0958763i	$0.0305653\pi$
$41$	1.57810	+	4.85689i	0.246458	+	0.758519i	−0.748935	+	0.662643i	$0.769435\pi$
$42$		0			0
$43$	5.17287			0.788856			0.394428	−	0.918927i	$-0.370943\pi$
$43$	5.17287			0.788856			0.394428	+	0.918927i	$0.370943\pi$
$44$	14.1992	−	2.95944i	2.14061	−	0.446152i
$45$		0			0
$46$	−17.9297	+	13.0267i	−2.64359	+	1.92068i
$47$	2.25789	+	6.94907i	0.329347	+	1.01363i	0.969440	+	0.245329i	$0.0788959\pi$
$47$	2.25789	+	6.94907i	0.329347	+	1.01363i	−0.640093	+	0.768298i	$0.721104\pi$
$48$		0			0
$49$	2.11737	+	1.53836i	0.302482	+	0.219766i
$50$	2.04238	+	1.48388i	0.288837	+	0.209852i
$51$		0			0
$52$	1.74122	+	5.35892i	0.241464	+	0.743149i
$53$	−2.38030	+	1.72939i	−0.326959	+	0.237549i	−0.739139	−	0.673553i	$-0.764767\pi$
$53$	−2.38030	+	1.72939i	−0.326959	+	0.237549i	0.412180	+	0.911102i	$0.364767\pi$
$54$		0			0
$55$	−0.359735	+	3.29706i	−0.0485067	+	0.444575i
$56$	−12.5428			−1.67610
$57$		0			0
$58$	−0.477925	−	1.47090i	−0.0627547	−	0.193139i
$59$	2.00682	−	6.17636i	0.261266	−	0.804094i	−0.731264	−	0.682094i	$-0.761069\pi$
$59$	2.00682	−	6.17636i	0.261266	−	0.804094i	0.992530	−	0.121999i	$-0.0389306\pi$
$60$		0			0
$61$	0.406490	+	0.295332i	0.0520457	+	0.0378134i	0.613504	−	0.789692i	$-0.289759\pi$
$61$	0.406490	+	0.295332i	0.0520457	+	0.0378134i	−0.561458	+	0.827505i	$0.689759\pi$
$62$	2.84355	−	8.75154i	0.361131	−	1.11145i
$63$		0			0
$64$	1.90523	−	1.38423i	0.238154	−	0.173029i
$65$	−1.28846			−0.159813
$66$		0			0
$67$	−7.80964			−0.954099			−0.477050	−	0.878876i	$-0.658294\pi$
$67$	−7.80964			−0.954099			−0.477050	+	0.878876i	$0.658294\pi$
$68$	−10.5831	+	7.68907i	−1.28339	+	0.932437i
$69$		0			0
$70$	1.63319	−	5.02644i	0.195204	−	0.600775i
$71$	−9.14526	−	6.64442i	−1.08534	−	0.788548i	−0.106736	−	0.994287i	$-0.534040\pi$
$71$	−9.14526	−	6.64442i	−1.08534	−	0.788548i	−0.978607	+	0.205740i	$0.934040\pi$
$72$		0			0
$73$	−3.43539	+	10.5730i	−0.402082	+	1.23748i	0.521226	+	0.853419i	$0.325475\pi$
$73$	−3.43539	+	10.5730i	−0.402082	+	1.23748i	−0.923308	+	0.384061i	$0.874525\pi$
$74$	1.45943	+	4.49166i	0.169655	+	0.522145i
$75$		0			0
$76$	9.40812			1.07919
$77$	6.79732	−	1.41672i	0.774626	−	0.161450i
$78$		0			0
$79$	−4.33558	+	3.14998i	−0.487791	+	0.354401i	−0.804334	−	0.594177i	$-0.797478\pi$
$79$	−4.33558	+	3.14998i	−0.487791	+	0.354401i	0.316543	+	0.948578i	$0.397478\pi$
$80$	−1.97110	−	6.06643i	−0.220376	−	0.678248i
$81$		0			0
$82$	10.4301	+	7.57793i	1.15181	+	0.836842i
$83$	8.77408	+	6.37474i	0.963080	+	0.699719i	0.953864	−	0.300239i	$-0.0970664\pi$
$83$	8.77408	+	6.37474i	0.963080	+	0.699719i	0.00921619	+	0.999958i	$0.497066\pi$
$84$		0			0
$85$	−0.924349	−	2.84485i	−0.100260	−	0.308568i
$86$	10.5650	−	7.67591i	1.13925	−	0.827715i
$87$		0			0
$88$	13.3545	−	14.7141i	1.42359	−	1.56853i
$89$	4.32336			0.458275			0.229137	−	0.973394i	$-0.426409\pi$
$89$	4.32336			0.458275			0.229137	+	0.973394i	$0.426409\pi$
$90$		0			0
$91$	0.833541	+	2.56538i	0.0873788	+	0.268924i
$92$	−11.8637	+	36.5127i	−1.23688	+	3.80671i
$93$		0			0
$94$	14.9230	+	10.8422i	1.53920	+	1.11829i
$95$	−0.664789	+	2.04601i	−0.0682059	+	0.209916i
$96$		0			0
$97$	0.284493	−	0.206696i	0.0288859	−	0.0209868i	−0.573249	−	0.819381i	$-0.694317\pi$
$97$	0.284493	−	0.206696i	0.0288859	−	0.0209868i	0.602135	+	0.798395i	$0.294317\pi$
$98$	6.60723			0.667431
$99$		0			0
$100$	4.37322			0.437322
$101$	−12.7011	+	9.22791i	−1.26381	+	0.918211i	−0.998938	−	0.0460722i	$-0.985330\pi$
$101$	−12.7011	+	9.22791i	−1.26381	+	0.918211i	−0.264872	+	0.964284i	$0.585330\pi$
$102$		0			0
$103$	2.06420	−	6.35297i	0.203392	−	0.625977i	−0.796383	−	0.604792i	$-0.793256\pi$
$103$	2.06420	−	6.35297i	0.203392	−	0.625977i	0.999776	−	0.0211846i	$-0.00674378\pi$
$104$	6.24518	+	4.53739i	0.612391	+	0.444928i
$105$		0			0
$106$	−2.29528	+	7.06414i	−0.222937	+	0.686130i
$107$	−4.82313	−	14.8441i	−0.466269	−	1.43503i	−0.857379	−	0.514685i	$-0.827909\pi$
$107$	−4.82313	−	14.8441i	−0.466269	−	1.43503i	0.391110	−	0.920344i	$-0.372091\pi$
$108$		0			0
$109$	11.5070			1.10217			0.551087	−	0.834448i	$-0.314213\pi$
$109$	11.5070			1.10217			0.551087	+	0.834448i	$0.314213\pi$
$110$	4.15771	+	7.26766i	0.396423	+	0.692944i
$111$		0			0
$112$	−10.8034	+	7.84912i	−1.02082	+	0.741672i
$113$	−2.79606	−	8.60538i	−0.263031	−	0.809526i	−0.992140	−	0.125129i	$-0.960066\pi$
$113$	−2.79606	−	8.60538i	−0.263031	−	0.809526i	0.729110	−	0.684397i	$-0.239934\pi$
$114$		0			0
$115$	−7.10222	−	5.16006i	−0.662285	−	0.481178i
$116$	−2.16749	−	1.57477i	−0.201246	−	0.146214i
$117$		0			0
$118$	−5.06627	−	15.5924i	−0.466388	−	1.43539i
$119$	−5.06625	+	3.68084i	−0.464422	+	0.337422i
$120$		0			0
$121$	−5.57524	+	9.48244i	−0.506840	+	0.862040i
$122$	1.26845			0.114840
$123$		0			0
$124$	−4.92586	−	15.1602i	−0.442356	−	1.36143i
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$		0			0
$127$	−15.2371	−	11.0704i	−1.35207	−	0.982339i	−0.998905	−	0.0467796i	$-0.985104\pi$
$127$	−15.2371	−	11.0704i	−1.35207	−	0.982339i	−0.353169	−	0.935560i	$-0.614896\pi$
$128$	4.38378	−	13.4919i	0.387475	−	1.19252i
$129$		0			0
$130$	−2.63152	+	1.91191i	−0.230800	+	0.167686i
$131$	20.0997			1.75612			0.878058	−	0.478555i	$-0.158839\pi$
$131$	20.0997			1.75612			0.878058	+	0.478555i	$0.158839\pi$
$132$		0			0
$133$	4.50377			0.390527
$134$	−15.9503	+	11.5886i	−1.37789	+	1.00110i
$135$		0			0
$136$	−5.53801	+	17.0442i	−0.474881	+	1.46153i
$137$	−14.5390	−	10.5632i	−1.24215	−	0.902478i	−0.244414	−	0.969671i	$-0.578596\pi$
$137$	−14.5390	−	10.5632i	−1.24215	−	0.902478i	−0.997740	+	0.0671930i	$0.978596\pi$
$138$		0			0
$139$	5.21098	−	16.0377i	0.441989	−	1.36030i	−0.443762	−	0.896145i	$-0.646357\pi$
$139$	5.21098	−	16.0377i	0.441989	−	1.36030i	0.885752	−	0.464159i	$-0.153643\pi$
$140$	−2.82917	−	8.70729i	−0.239108	−	0.735900i
$141$		0			0
$142$	−28.5376			−2.39482
$143$	−3.89697	−	1.75356i	−0.325881	−	0.146640i
$144$		0			0
$145$	0.495628	−	0.360095i	0.0411597	−	0.0299042i
$146$	8.67272	+	26.6919i	0.717759	+	2.20904i
$147$		0			0
$148$	6.61881	+	4.80885i	0.544063	+	0.395285i
$149$	1.88797	+	1.37169i	0.154669	+	0.112373i	0.662428	−	0.749126i	$-0.269526\pi$
$149$	1.88797	+	1.37169i	0.154669	+	0.112373i	−0.507759	+	0.861499i	$0.669526\pi$
$150$		0			0
$151$	−1.21718	−	3.74609i	−0.0990525	−	0.304852i	0.889236	−	0.457448i	$-0.151237\pi$
$151$	−1.21718	−	3.74609i	−0.0990525	−	0.304852i	−0.988289	+	0.152596i	$0.951237\pi$
$152$	10.4274	−	7.57597i	0.845776	−	0.614492i
$153$		0			0
$154$	11.7805	−	12.9799i	0.949299	−	1.04595i
$155$	3.64501			0.292774
$156$		0			0
$157$	−1.50834	−	4.64218i	−0.120378	−	0.370486i	0.872652	−	0.488342i	$-0.162398\pi$
$157$	−1.50834	−	4.64218i	−0.120378	−	0.370486i	−0.993031	+	0.117856i	$0.962398\pi$
$158$	−4.18073	+	12.8669i	−0.332601	+	1.02364i
$159$		0			0
$160$	−3.33354	−	2.42196i	−0.263540	−	0.191473i
$161$	−5.67928	+	17.4790i	−0.447590	+	1.37754i
$162$		0			0
$163$	5.69202	−	4.13549i	0.445833	−	0.323917i	−0.342115	−	0.939658i	$-0.611143\pi$
$163$	5.69202	−	4.13549i	0.445833	−	0.323917i	0.787948	+	0.615741i	$0.211143\pi$
$164$	22.3333			1.74394
$165$		0			0
$166$	27.3794			2.12505
$167$	8.67223	−	6.30075i	0.671078	−	0.487566i	−0.199308	−	0.979937i	$-0.563869\pi$
$167$	8.67223	−	6.30075i	0.671078	−	0.487566i	0.870386	+	0.492370i	$0.163869\pi$
$168$		0			0
$169$	−3.50422	+	10.7849i	−0.269555	+	0.829605i
$170$	−6.10929	−	4.43866i	−0.468561	−	0.340430i
$171$		0			0
$172$	6.99062	−	21.5149i	0.533030	−	1.64050i
$173$	−2.59940	−	8.00012i	−0.197628	−	0.608238i	−0.999936	−	0.0113267i	$-0.996395\pi$
$173$	−2.59940	−	8.00012i	−0.197628	−	0.608238i	0.802307	−	0.596911i	$-0.203605\pi$
$174$		0			0
$175$	2.09351			0.158254
$176$	2.29462	−	21.0307i	0.172963	−	1.58525i
$177$		0			0
$178$	8.82995	−	6.41533i	0.661833	−	0.480850i
$179$	−6.50062	−	20.0069i	−0.485879	−	1.49538i	−0.830703	−	0.556716i	$-0.812061\pi$
$179$	−6.50062	−	20.0069i	−0.485879	−	1.49538i	0.344824	−	0.938667i	$-0.387939\pi$
$180$		0			0
$181$	1.41020	+	1.02457i	0.104819	+	0.0761557i	0.638960	−	0.769240i	$-0.279365\pi$
$181$	1.41020	+	1.02457i	0.104819	+	0.0761557i	−0.534141	+	0.845395i	$0.679365\pi$
$182$	5.50911	+	4.00261i	0.408363	+	0.296693i
$183$		0			0
$184$	16.2531	+	50.0219i	1.19820	+	3.68767i
$185$	−1.51349	+	1.09961i	−0.111274	+	0.0808451i
$186$		0			0
$187$	1.07606	−	9.86234i	0.0786893	−	0.721206i
$188$	31.9538			2.33047
$189$		0			0
$190$	1.67828	+	5.16520i	0.121755	+	0.374723i
$191$	−0.00771200	+	0.0237351i	−0.000558021	+	0.00171741i	−0.951335	−	0.308158i	$-0.900287\pi$
$191$	−0.00771200	+	0.0237351i	−0.000558021	+	0.00171741i	0.950777	+	0.309876i	$0.100287\pi$
$192$		0			0
$193$	−1.17894	−	0.856548i	−0.0848618	−	0.0616557i	0.544545	−	0.838731i	$-0.316702\pi$
$193$	−1.17894	−	0.856548i	−0.0848618	−	0.0616557i	−0.629407	+	0.777076i	$0.716702\pi$
$194$	0.274331	−	0.844306i	0.0196959	−	0.0606176i
$195$		0			0
$196$	9.25974	−	6.72759i	0.661410	−	0.480542i
$197$	−22.7027			−1.61750			−0.808751	−	0.588151i	$-0.799856\pi$
$197$	−22.7027			−1.61750			−0.808751	+	0.588151i	$0.799856\pi$
$198$		0			0
$199$	−6.62834			−0.469870			−0.234935	−	0.972011i	$-0.575488\pi$
$199$	−6.62834			−0.469870			−0.234935	+	0.972011i	$0.575488\pi$
$200$	4.84703	−	3.52157i	0.342737	−	0.249013i
$201$		0			0
$202$	−12.2475	+	37.6939i	−0.861729	+	2.65213i
$203$	−1.03760	−	0.753862i	−0.0728254	−	0.0529107i
$204$		0			0
$205$	−1.57810	+	4.85689i	−0.110219	+	0.339220i
$206$	−5.21114	−	16.0382i	−0.363077	−	1.11744i
$207$		0			0
$208$	8.21858			0.569856
$209$	−4.79524	+	5.28345i	−0.331694	+	0.365464i
$210$		0			0
$211$	−4.57709	+	3.32545i	−0.315100	+	0.228934i	−0.734082	−	0.679061i	$-0.762387\pi$
$211$	−4.57709	+	3.32545i	−0.315100	+	0.228934i	0.418982	+	0.907995i	$0.362387\pi$
$212$	3.97610	+	12.2372i	0.273080	+	0.840453i
$213$		0			0
$214$	−31.8774	−	23.1603i	−2.17910	−	1.58321i
$215$	4.18494	+	3.04054i	0.285411	+	0.207363i
$216$		0			0
$217$	−2.35807	−	7.25738i	−0.160076	−	0.492663i
$218$	23.5018	−	17.0750i	1.59174	−	1.15647i
$219$		0			0
$220$	13.2269	+	5.95185i	0.891758	+	0.401273i
$221$	3.85410			0.259255
$222$		0			0
$223$	2.43642	+	7.49852i	0.163155	+	0.502138i	0.998896	−	0.0469856i	$-0.0149615\pi$
$223$	2.43642	+	7.49852i	0.163155	+	0.502138i	−0.835741	+	0.549124i	$0.814961\pi$
$224$	−2.66566	+	8.20407i	−0.178107	+	0.548158i
$225$		0			0
$226$	−18.4800	−	13.4265i	−1.22927	−	0.893116i
$227$	3.46451	−	10.6627i	0.229948	−	0.707706i	−0.767804	−	0.640685i	$-0.778650\pi$
$227$	3.46451	−	10.6627i	0.229948	−	0.707706i	0.997752	−	0.0670213i	$-0.0213495\pi$
$228$		0			0
$229$	−21.8360	+	15.8647i	−1.44296	+	1.04837i	−0.455547	+	0.890212i	$0.650556\pi$
$229$	−21.8360	+	15.8647i	−1.44296	+	1.04837i	−0.987413	+	0.158160i	$0.949444\pi$
$230$	−22.1623			−1.46134
$231$		0			0
$232$	−3.67042			−0.240975
$233$	−8.77845	+	6.37792i	−0.575095	+	0.417831i	−0.836953	−	0.547275i	$-0.815665\pi$
$233$	−8.77845	+	6.37792i	−0.575095	+	0.417831i	0.261857	+	0.965107i	$0.415665\pi$
$234$		0			0
$235$	−2.25789	+	6.94907i	−0.147289	+	0.453307i
$236$	−22.9766	−	16.6935i	−1.49565	−	1.08665i
$237$		0			0
$238$	−4.88529	+	15.0354i	−0.316666	+	0.974599i
$239$	3.54327	+	10.9051i	0.229195	+	0.705391i	0.997839	+	0.0657129i	$0.0209322\pi$
$239$	3.54327	+	10.9051i	0.229195	+	0.705391i	−0.768643	+	0.639678i	$0.779068\pi$
$240$		0			0
$241$	12.7542			0.821572			0.410786	−	0.911732i	$-0.365254\pi$
$241$	12.7542			0.821572			0.410786	+	0.911732i	$0.365254\pi$
$242$	2.68401	+	27.6398i	0.172534	+	1.77675i
$243$		0			0
$244$	1.77767	−	1.29155i	0.113804	−	0.0826833i
$245$	0.808764	+	2.48912i	0.0516701	+	0.159024i
$246$		0			0
$247$	−2.24248	−	1.62926i	−0.142686	−	0.103667i
$248$	−17.6675	−	12.8362i	−1.12188	−	0.815097i
$249$		0			0
$250$	0.780121	+	2.40097i	0.0493392	+	0.151850i
$251$	−9.87130	+	7.17192i	−0.623071	+	0.452687i	−0.853993	−	0.520285i	$-0.825826\pi$
$251$	−9.87130	+	7.17192i	−0.623071	+	0.452687i	0.230922	+	0.972972i	$0.425826\pi$
$252$		0			0
$253$	−14.4581	−	25.2727i	−0.908973	−	1.58888i
$254$	−47.5471			−2.98337
$255$		0			0
$256$	−9.61149	−	29.5811i	−0.600718	−	1.84882i
$257$	1.82198	−	5.60747i	0.113652	−	0.349784i	−0.878012	−	0.478639i	$-0.841130\pi$
$257$	1.82198	−	5.60747i	0.113652	−	0.349784i	0.991663	+	0.128855i	$0.0411302\pi$
$258$		0			0
$259$	3.16850	+	2.30205i	0.196881	+	0.143042i
$260$	−1.74122	+	5.35892i	−0.107986	+	0.332346i
$261$		0			0
$262$	41.0512	−	29.8254i	2.53615	−	1.84262i
$263$	21.7305			1.33996			0.669980	−	0.742379i	$-0.266302\pi$
$263$	21.7305			1.33996			0.669980	+	0.742379i	$0.266302\pi$
$264$		0			0
$265$	−2.94221			−0.180738
$266$	9.19843	−	6.68305i	0.563992	−	0.409764i
$267$		0			0
$268$	−10.5539	+	32.4817i	−0.644685	+	1.98414i
$269$	−3.66042	−	2.65945i	−0.223180	−	0.162149i	0.470577	−	0.882359i	$-0.344046\pi$
$269$	−3.66042	−	2.65945i	−0.223180	−	0.162149i	−0.693757	+	0.720209i	$0.744046\pi$
$270$		0			0
$271$	−6.72447	+	20.6958i	−0.408482	+	1.25718i	0.509470	+	0.860488i	$0.329841\pi$
$271$	−6.72447	+	20.6958i	−0.408482	+	1.25718i	−0.917952	+	0.396691i	$0.870159\pi$
$272$	5.89608	+	18.1463i	0.357502	+	1.10028i
$273$		0			0
$274$	−45.3688			−2.74083
$275$	−2.22899	+	2.45593i	−0.134413	+	0.148098i
$276$		0			0
$277$	10.5452	−	7.66154i	0.633600	−	0.460337i	−0.224046	−	0.974579i	$-0.571926\pi$
$277$	10.5452	−	7.66154i	0.633600	−	0.460337i	0.857645	+	0.514241i	$0.171926\pi$
$278$	−13.1552	−	40.4877i	−0.788999	−	2.42829i
$279$		0			0
$280$	−10.1473	−	7.37245i	−0.606417	−	0.440588i
$281$	7.59310	+	5.51671i	0.452966	+	0.329099i	0.790766	−	0.612119i	$-0.209683\pi$
$281$	7.59310	+	5.51671i	0.452966	+	0.329099i	−0.337799	+	0.941218i	$0.609683\pi$
$282$		0			0
$283$	4.30760	+	13.2574i	0.256060	+	0.788072i	0.993619	+	0.112789i	$0.0359785\pi$
$283$	4.30760	+	13.2574i	0.256060	+	0.788072i	−0.737559	+	0.675283i	$0.764021\pi$
$284$	−39.9943	+	29.0575i	−2.37322	+	1.72425i
$285$		0			0
$286$	−10.5612	+	2.20119i	−0.624495	+	0.130159i
$287$	10.6912			0.631083
$288$		0			0
$289$	−2.48832	−	7.65828i	−0.146372	−	0.450487i
$290$	0.477925	−	1.47090i	0.0280647	−	0.0863744i
$291$		0			0
$292$	39.3326	+	28.5768i	2.30176	+	1.67233i
$293$	−9.41576	+	28.9787i	−0.550075	+	1.69296i	0.158534	+	0.987354i	$0.449323\pi$
$293$	−9.41576	+	28.9787i	−0.550075	+	1.69296i	−0.708608	+	0.705602i	$0.750677\pi$
$294$		0			0
$295$	5.25393	−	3.81720i	0.305895	−	0.222246i
$296$	11.2083			0.651468
$297$		0			0
$298$	5.89138			0.341278
$299$	9.15089	−	6.64851i	0.529210	−	0.384493i
$300$		0			0
$301$	3.34649	−	10.2994i	0.192888	−	0.593649i
$302$	−8.04468	−	5.84480i	−0.462919	−	0.336330i
$303$		0			0
$304$	4.24044	−	13.0507i	0.243206	−	0.748511i
$305$	0.155265	+	0.477858i	0.00889047	+	0.0273621i
$306$		0			0
$307$	5.08609			0.290278			0.145139	−	0.989411i	$-0.453637\pi$
$307$	5.08609			0.290278			0.145139	+	0.989411i	$0.453637\pi$
$308$	3.29351	−	30.1858i	0.187665	−	1.72000i
$309$		0			0
$310$	7.44450	−	5.40875i	0.422819	−	0.307196i
$311$	−4.25249	−	13.0878i	−0.241136	−	0.742141i	−0.996248	−	0.0865451i	$-0.972417\pi$
$311$	−4.25249	−	13.0878i	−0.241136	−	0.742141i	0.755112	−	0.655596i	$-0.227583\pi$
$312$		0			0
$313$	−12.9060	−	9.37676i	−0.729491	−	0.530006i	0.159912	−	0.987131i	$-0.448879\pi$
$313$	−12.9060	−	9.37676i	−0.729491	−	0.530006i	−0.889402	+	0.457125i	$0.848879\pi$
$314$	−9.96903	−	7.24292i	−0.562585	−	0.408742i
$315$		0			0
$316$	7.24225	+	22.2894i	0.407408	+	1.25387i
$317$	8.66246	−	6.29364i	0.486532	−	0.353486i	−0.317317	−	0.948320i	$-0.602782\pi$
$317$	8.66246	−	6.29364i	0.486532	−	0.353486i	0.803849	+	0.594833i	$0.202782\pi$
$318$		0			0
$319$	1.98912	−	0.414578i	0.111369	−	0.0232119i
$320$	2.35499			0.131648
$321$		0			0
$322$	14.3375	+	44.1263i	0.798997	+	2.45906i
$323$	1.98855	−	6.12014i	0.110646	−	0.340534i
$324$		0			0
$325$	−1.04238	−	0.757336i	−0.0578210	−	0.0420094i
$326$	5.48871	−	16.8925i	0.303992	−	0.935590i
$327$		0			0
$328$	24.7530	−	17.9841i	1.36676	−	0.993006i
$329$	15.2966			0.843330
$330$		0			0
$331$	−8.84618			−0.486230			−0.243115	−	0.969997i	$-0.578169\pi$
$331$	−8.84618			−0.486230			−0.243115	+	0.969997i	$0.578169\pi$
$332$	38.3710	−	27.8782i	2.10588	−	1.53001i
$333$		0			0
$334$	8.36248	−	25.7371i	0.457575	−	1.40827i
$335$	−6.31813	−	4.59039i	−0.345196	−	0.250800i
$336$		0			0
$337$	−3.58143	+	11.0225i	−0.195093	+	0.600434i	0.804883	+	0.593434i	$0.202228\pi$
$337$	−3.58143	+	11.0225i	−0.195093	+	0.600434i	−0.999976	+	0.00699978i	$0.997772\pi$
$338$	8.84648	+	27.2267i	0.481185	+	1.48093i
$339$		0			0
$340$	−13.0814			−0.709440
$341$	11.0244	+	4.96077i	0.597005	+	0.268641i
$342$		0			0
$343$	16.2885	−	11.8343i	0.879498	−	0.638993i
$344$	−9.57705	−	29.4751i	−0.516360	−	1.58919i
$345$		0			0
$346$	−17.1802	−	12.4821i	−0.923611	−	0.671043i
$347$	−3.95529	−	2.87368i	−0.212331	−	0.154267i	0.476537	−	0.879155i	$-0.341892\pi$
$347$	−3.95529	−	2.87368i	−0.212331	−	0.154267i	−0.688868	+	0.724887i	$0.741892\pi$
$348$		0			0
$349$	0.294654	+	0.906853i	0.0157725	+	0.0485427i	0.958633	−	0.284645i	$-0.0918757\pi$
$349$	0.294654	+	0.906853i	0.0157725	+	0.0485427i	−0.942861	+	0.333188i	$0.891876\pi$
$350$	4.27575	−	3.10651i	0.228548	−	0.166050i
$351$		0			0
$352$	−6.78615	−	11.8621i	−0.361703	−	0.632254i
$353$	15.5166			0.825865			0.412933	−	0.910762i	$-0.364505\pi$
$353$	15.5166			0.825865			0.412933	+	0.910762i	$0.364505\pi$
$354$		0			0
$355$	−3.49318	−	10.7509i	−0.185399	−	0.570598i
$356$	5.84258	−	17.9816i	0.309656	−	0.953024i
$357$		0			0
$358$	−42.9645	−	31.2155i	−2.27074	−	1.64979i
$359$	−6.25915	+	19.2637i	−0.330345	+	1.01670i	0.638624	+	0.769519i	$0.279504\pi$
$359$	−6.25915	+	19.2637i	−0.330345	+	1.01670i	−0.968970	+	0.247180i	$0.920496\pi$
$360$		0			0
$361$	11.6271	−	8.44759i	0.611953	−	0.444610i
$362$	4.40051			0.231286
$363$		0			0
$364$	11.7963			0.618295
$365$	−8.99396	+	6.53449i	−0.470765	+	0.342031i
$366$		0			0
$367$	11.0180	−	33.9099i	0.575135	−	1.77008i	−0.0605844	−	0.998163i	$-0.519296\pi$
$367$	11.0180	−	33.9099i	0.575135	−	1.77008i	0.635719	−	0.771920i	$-0.280704\pi$
$368$	45.3024	+	32.9141i	2.36155	+	1.71577i
$369$		0			0
$370$	−1.45943	+	4.49166i	−0.0758721	+	0.233510i
$371$	1.90340	+	5.85807i	0.0988198	+	0.304136i
$372$		0			0
$373$	12.1358			0.628370			0.314185	−	0.949362i	$-0.398269\pi$
$373$	12.1358			0.628370			0.314185	+	0.949362i	$0.398269\pi$
$374$	−12.4368	−	21.7394i	−0.643091	−	1.12412i
$375$		0			0
$376$	35.4157	−	25.7310i	1.82643	−	1.32698i
$377$	0.243922	+	0.750713i	0.0125626	+	0.0386637i
$378$		0			0
$379$	−5.77971	−	4.19921i	−0.296884	−	0.215699i	0.429364	−	0.903131i	$-0.358738\pi$
$379$	−5.77971	−	4.19921i	−0.296884	−	0.215699i	−0.726248	+	0.687433i	$0.758738\pi$
$380$	7.61133	+	5.52996i	0.390453	+	0.283681i
$381$		0			0
$382$	0.0194691	+	0.0599198i	0.000996127	+	0.00306576i
$383$	12.9143	−	9.38279i	0.659890	−	0.479438i	−0.206736	−	0.978397i	$-0.566284\pi$
$383$	12.9143	−	9.38279i	0.659890	−	0.479438i	0.866626	+	0.498959i	$0.166284\pi$
$384$		0			0
$385$	6.33187	+	2.84922i	0.322702	+	0.145209i
$386$	−3.67885			−0.187249
$387$		0			0
$388$	−0.475223	−	1.46259i	−0.0241258	−	0.0742516i
$389$	7.75336	−	23.8624i	0.393111	−	1.20987i	−0.537312	−	0.843384i	$-0.680560\pi$
$389$	7.75336	−	23.8624i	0.393111	−	1.20987i	0.930423	−	0.366488i	$-0.119440\pi$
$390$		0			0
$391$	21.2445	+	15.4351i	1.07438	+	0.780585i
$392$	4.84551	−	14.9130i	0.244735	−	0.753218i
$393$		0			0
$394$	−46.3677	+	33.6881i	−2.33597	+	1.69718i
$395$	−5.35907			−0.269644
$396$		0			0
$397$	3.57490			0.179419			0.0897094	−	0.995968i	$-0.471406\pi$
$397$	3.57490			0.179419			0.0897094	+	0.995968i	$0.471406\pi$
$398$	−13.5376	+	9.83564i	−0.678579	+	0.493016i
$399$		0			0
$400$	1.97110	−	6.06643i	0.0985552	−	0.303322i
$401$	23.3675	+	16.9775i	1.16692	+	0.847815i	0.990637	−	0.136524i	$-0.0435932\pi$
$401$	23.3675	+	16.9775i	1.16692	+	0.847815i	0.176281	+	0.984340i	$0.443593\pi$
$402$		0			0
$403$	−1.45128	+	4.46657i	−0.0722933	+	0.222496i
$404$	21.2162	+	65.2969i	1.05555	+	3.24864i
$405$		0			0
$406$	−3.23782			−0.160690
$407$	−6.07412	+	1.26599i	−0.301083	+	0.0627526i
$408$		0			0
$409$	−7.78197	+	5.65393i	−0.384794	+	0.279569i	−0.763319	−	0.646022i	$-0.776431\pi$
$409$	−7.78197	+	5.65393i	−0.384794	+	0.279569i	0.378525	+	0.925591i	$0.376431\pi$
$410$	3.98395	+	12.2613i	0.196753	+	0.605545i
$411$		0			0
$412$	−23.6336	−	17.1708i	−1.16434	−	0.845945i
$413$	−10.9991	−	7.99135i	−0.541233	−	0.393229i
$414$		0			0
$415$	3.35140	+	10.3145i	0.164514	+	0.506321i
$416$	4.29512	−	3.12059i	0.210586	−	0.152999i
$417$		0			0
$418$	−1.95373	+	17.9064i	−0.0955599	+	0.875829i
$419$	30.6537			1.49753			0.748765	−	0.662836i	$-0.230647\pi$
$419$	30.6537			1.49753			0.748765	+	0.662836i	$0.230647\pi$
$420$		0			0
$421$	−2.14755	−	6.60949i	−0.104665	−	0.322127i	0.884986	−	0.465617i	$-0.154168\pi$
$421$	−2.14755	−	6.60949i	−0.104665	−	0.322127i	−0.989652	+	0.143490i	$0.954168\pi$
$422$	−4.41361	+	13.5837i	−0.214851	+	0.661244i
$423$		0			0
$424$	14.2610	+	10.3612i	0.692574	+	0.503184i
$425$	0.924349	−	2.84485i	0.0448375	−	0.137996i
$426$		0			0
$427$	0.850991	−	0.618281i	0.0411823	−	0.0299207i
$428$	−68.2571			−3.29933
$429$		0			0
$430$	13.0590			0.629763
$431$	−2.61636	+	1.90090i	−0.126026	+	0.0915631i	−0.649013	−	0.760778i	$-0.724818\pi$
$431$	−2.61636	+	1.90090i	−0.126026	+	0.0915631i	0.522987	+	0.852341i	$0.324818\pi$
$432$		0			0
$433$	−9.39161	+	28.9044i	−0.451332	+	1.38906i	0.424056	+	0.905636i	$0.360606\pi$
$433$	−9.39161	+	28.9044i	−0.451332	+	1.38906i	−0.875388	+	0.483421i	$0.839394\pi$
$434$	−15.5851	−	11.3233i	−0.748110	−	0.543534i
$435$		0			0
$436$	15.5506	−	47.8598i	0.744739	−	2.29207i
$437$	−5.83606	−	17.9616i	−0.279177	−	0.859218i
$438$		0			0
$439$	36.5311			1.74353			0.871767	−	0.489921i	$-0.162974\pi$
$439$	36.5311			1.74353			0.871767	+	0.489921i	$0.162974\pi$
$440$	19.4527	−	4.05439i	0.927372	−	0.193286i
$441$		0			0
$442$	7.87155	−	5.71902i	0.374412	−	0.272026i
$443$	0.667949	+	2.05574i	0.0317352	+	0.0976710i	0.965669	−	0.259774i	$-0.0836480\pi$
$443$	0.667949	+	2.05574i	0.0317352	+	0.0976710i	−0.933934	+	0.357445i	$0.883648\pi$
$444$		0			0
$445$	3.49767	+	2.54120i	0.165805	+	0.120465i
$446$	16.1030	+	11.6995i	0.762499	+	0.553988i
$447$		0			0
$448$	−1.52352	−	4.68890i	−0.0719793	−	0.221530i
$449$	−9.32124	+	6.77228i	−0.439897	+	0.319604i	−0.785594	−	0.618742i	$-0.787642\pi$
$449$	−9.32124	+	6.77228i	−0.439897	+	0.319604i	0.345697	+	0.938346i	$0.387642\pi$
$450$		0			0
$451$	−11.3831	+	12.5420i	−0.536010	+	0.590581i
$452$	−39.5699			−1.86121
$453$		0			0
$454$	−8.74624	−	26.9182i	−0.410482	−	1.26333i
$455$	−0.833541	+	2.56538i	−0.0390770	+	0.120267i
$456$		0			0
$457$	12.8888	+	9.36427i	0.602913	+	0.438042i	0.846912	−	0.531734i	$-0.178459\pi$
$457$	12.8888	+	9.36427i	0.602913	+	0.438042i	−0.243999	+	0.969776i	$0.578459\pi$
$458$	−21.0560	+	64.8038i	−0.983883	+	3.02808i
$459$		0			0
$460$	−31.0596	+	22.5661i	−1.44816	+	1.05215i
$461$	−1.52527			−0.0710387			−0.0355193	−	0.999369i	$-0.511309\pi$
$461$	−1.52527			−0.0710387			−0.0355193	+	0.999369i	$0.511309\pi$
$462$		0			0
$463$	14.2073			0.660268			0.330134	−	0.943934i	$-0.392906\pi$
$463$	14.2073			0.660268			0.330134	+	0.943934i	$0.392906\pi$
$464$	−3.16143	+	2.29691i	−0.146765	+	0.106631i
$465$		0			0
$466$	−8.46491	+	26.0523i	−0.392129	+	1.20685i
$467$	−4.90020	−	3.56020i	−0.226754	−	0.164746i	0.468608	−	0.883406i	$-0.344756\pi$
$467$	−4.90020	−	3.56020i	−0.226754	−	0.164746i	−0.695362	+	0.718660i	$0.744756\pi$
$468$		0			0
$469$	−5.05229	+	15.5494i	−0.233293	+	0.718002i
$470$	5.70010	+	17.5431i	0.262926	+	0.809203i
$471$		0			0
$472$	−38.9085			−1.79091
$473$	8.51936	+	14.8918i	0.391720	+	0.684725i
$474$		0			0
$475$	−1.74044	+	1.26450i	−0.0798569	+	0.0580194i
$476$	8.46277	+	26.0457i	0.387890	+	1.19380i
$477$		0			0
$478$	23.4185	+	17.0146i	1.07114	+	0.778227i
$479$	−14.2455	−	10.3500i	−0.650894	−	0.472902i	0.212681	−	0.977122i	$-0.431780\pi$
$479$	−14.2455	−	10.3500i	−0.650894	−	0.472902i	−0.863576	+	0.504219i	$0.831780\pi$
$480$		0			0
$481$	−0.744857	−	2.29243i	−0.0339626	−	0.104526i
$482$	26.0490	−	18.9257i	1.18650	−	0.862043i
$483$		0			0
$484$	31.9048	+	36.0030i	1.45022	+	1.63650i
$485$	0.351653			0.0159677
$486$		0			0
$487$	2.09619	+	6.45140i	0.0949874	+	0.292341i	0.987250	−	0.159175i	$-0.0508834\pi$
$487$	2.09619	+	6.45140i	0.0949874	+	0.292341i	−0.892263	+	0.451516i	$0.850883\pi$
$488$	0.930235	−	2.86297i	0.0421097	−	0.129600i
$489$		0			0
$490$	5.34536	+	3.88363i	0.241479	+	0.175445i
$491$	−0.160261	+	0.493232i	−0.00723247	+	0.0222592i	−0.954608	−	0.297866i	$-0.903725\pi$
$491$	−0.160261	+	0.493232i	−0.00723247	+	0.0222592i	0.947375	+	0.320125i	$0.103725\pi$
$492$		0			0
$493$	−1.48255	+	1.07714i	−0.0667707	+	0.0485117i
$494$	−6.99762			−0.314838
$495$		0			0
$496$	−23.2501			−1.04396
$497$	−19.1457	+	13.9102i	−0.858802	+	0.623956i
$498$		0			0
$499$	6.75534	−	20.7908i	0.302411	−	0.930725i	−0.678220	−	0.734859i	$-0.737248\pi$
$499$	6.75534	−	20.7908i	0.302411	−	0.930725i	0.980631	−	0.195866i	$-0.0627516\pi$
$500$	3.53801	+	2.57052i	0.158225	+	0.114957i
$501$		0			0
$502$	−9.51872	+	29.2956i	−0.424841	+	1.30753i
$503$	−0.932202	−	2.86902i	−0.0415649	−	0.127923i	0.928121	−	0.372279i	$-0.121424\pi$
$503$	−0.932202	−	2.86902i	−0.0415649	−	0.127923i	−0.969686	+	0.244356i	$0.921424\pi$
$504$		0			0
$505$	−15.6995			−0.698617
$506$	−67.0306	−	30.1624i	−2.97987	−	1.34088i
$507$		0			0
$508$	−66.6352	+	48.4133i	−2.95646	+	2.14799i
$509$	7.94418	+	24.4497i	0.352119	+	1.08371i	0.957661	+	0.287898i	$0.0929565\pi$
$509$	7.94418	+	24.4497i	0.352119	+	1.08371i	−0.605542	+	0.795814i	$0.707043\pi$
$510$		0			0
$511$	18.8289	+	13.6800i	0.832943	+	0.605169i
$512$	−40.5713	−	29.4768i	−1.79302	−	1.30270i
$513$		0			0
$514$	−4.59962	−	14.1562i	−0.202881	−	0.624403i
$515$	5.40416	−	3.92635i	0.238136	−	0.173016i
$516$		0			0
$517$	−16.2866	+	17.9447i	−0.716282	+	0.789207i
$518$	9.88725			0.434421
$519$		0			0
$520$	2.38545	+	7.34165i	0.104609	+	0.321953i
$521$	−3.44017	+	10.5877i	−0.150716	+	0.463858i	−0.997702	−	0.0677588i	$-0.978415\pi$
$521$	−3.44017	+	10.5877i	−0.150716	+	0.463858i	0.846985	+	0.531616i	$0.178415\pi$
$522$		0			0
$523$	5.28968	+	3.84318i	0.231302	+	0.168050i	0.697399	−	0.716683i	$-0.254340\pi$
$523$	5.28968	+	3.84318i	0.231302	+	0.168050i	−0.466098	+	0.884733i	$0.654340\pi$
$524$	27.1627	−	83.5981i	1.18661	−	3.65200i
$525$		0			0
$526$	44.3820	−	32.2454i	1.93515	−	1.40597i
$527$	−10.9032			−0.474949
$528$		0			0
$529$	54.0677			2.35077
$530$	−6.00911	+	4.36588i	−0.261019	+	0.189642i
$531$		0			0
$532$	6.08640	−	18.7320i	0.263879	−	0.812135i
$533$	−5.32328	−	3.86759i	−0.230577	−	0.167524i
$534$		0			0
$535$	4.82313	−	14.8441i	0.208522	−	0.641765i
$536$	14.4588	+	44.4995i	0.624524	+	1.92209i
$537$		0			0
$538$	−11.4223			−0.492449
$539$	−0.941505	+	8.62911i	−0.0405535	+	0.371682i
$540$		0			0
$541$	−33.7684	+	24.5342i	−1.45182	+	1.05481i	−0.466413	+	0.884567i	$0.654454\pi$
$541$	−33.7684	+	24.5342i	−1.45182	+	1.05481i	−0.985403	+	0.170239i	$0.945546\pi$
$542$	16.9761	+	52.2470i	0.729185	+	2.24420i
$543$		0			0
$544$	9.97147	+	7.24470i	0.427523	+	0.310614i
$545$	9.30939	+	6.76367i	0.398770	+	0.289724i
$546$		0			0
$547$	−1.37703	−	4.23806i	−0.0588775	−	0.181206i	0.917292	−	0.398215i	$-0.130370\pi$
$547$	−1.37703	−	4.23806i	−0.0588775	−	0.181206i	−0.976170	+	0.217008i	$0.930370\pi$
$548$	−63.5825	+	46.1954i	−2.71611	+	1.97337i
$549$		0			0
$550$	−0.908160	+	8.32350i	−0.0387241	+	0.354915i
$551$	1.31795			0.0561466
$552$		0			0
$553$	3.46695	+	10.6702i	0.147430	+	0.453742i
$554$	10.1686	−	31.2956i	0.432020	−	1.32962i
$555$		0			0
$556$	−59.6618	−	43.3468i	−2.53022	−	1.83831i
$557$	−5.98608	+	18.4233i	−0.253638	+	0.780619i	0.740456	+	0.672104i	$0.234609\pi$
$557$	−5.98608	+	18.4233i	−0.253638	+	0.780619i	−0.994095	+	0.108514i	$0.965391\pi$
$558$		0			0
$559$	−5.39211	+	3.91760i	−0.228062	+	0.165697i
$560$	−13.3537			−0.564298
$561$		0			0
$562$	23.6941			0.999477
$563$	16.7816	−	12.1925i	0.707259	−	0.513853i	−0.175030	−	0.984563i	$-0.556002\pi$
$563$	16.7816	−	12.1925i	0.707259	−	0.513853i	0.882288	+	0.470710i	$0.156002\pi$
$564$		0			0
$565$	2.79606	−	8.60538i	0.117631	−	0.362031i
$566$	28.4702	+	20.6848i	1.19669	+	0.869447i
$567$		0			0
$568$	−20.9285	+	64.4114i	−0.878141	+	2.70264i
$569$	13.0945	+	40.3007i	0.548950	+	1.68949i	0.711408	+	0.702779i	$0.248058\pi$
$569$	13.0945	+	40.3007i	0.548950	+	1.68949i	−0.162458	+	0.986716i	$0.551942\pi$
$570$		0			0
$571$	−5.03980			−0.210909			−0.105455	−	0.994424i	$-0.533630\pi$
$571$	−5.03980			−0.210909			−0.105455	+	0.994424i	$0.533630\pi$
$572$	−12.5597	+	13.8384i	−0.525148	+	0.578614i
$573$		0			0
$574$	21.8356	−	15.8645i	0.911399	−	0.662170i
$575$	−2.71281	−	8.34916i	−0.113132	−	0.348184i
$576$		0			0
$577$	−28.1877	−	20.4796i	−1.17347	−	0.852576i	−0.182050	−	0.983289i	$-0.558273\pi$
$577$	−28.1877	−	20.4796i	−1.17347	−	0.852576i	−0.991420	+	0.130713i	$0.958273\pi$
$578$	−16.4461	−	11.9488i	−0.684066	−	0.497003i
$579$		0			0
$580$	−0.827908	−	2.54804i	−0.0343770	−	0.105802i
$581$	18.3686	−	13.3456i	0.762059	−	0.553668i
$582$		0			0
$583$	−8.89878	−	4.00427i	−0.368550	−	0.165840i
$584$	66.6057			2.75616
$585$		0			0
$586$	23.7703	+	73.1575i	0.981943	+	3.02211i
$587$	4.25772	−	13.1039i	0.175735	−	0.540857i	−0.823931	−	0.566690i	$-0.808224\pi$
$587$	4.25772	−	13.1039i	0.175735	−	0.540857i	0.999666	+	0.0258331i	$0.00822386\pi$
$588$		0			0
$589$	6.34392	+	4.60913i	0.261397	+	0.189916i
$590$	5.06627	−	15.5924i	0.208575	−	0.641928i
$591$		0			0
$592$	9.65397	−	7.01402i	0.396776	−	0.288274i
$593$	25.1595			1.03318			0.516588	−	0.856234i	$-0.327202\pi$
$593$	25.1595			1.03318			0.516588	+	0.856234i	$0.327202\pi$
$594$		0			0
$595$	−6.26222			−0.256726
$596$	8.25651	−	5.99871i	0.338200	−	0.245717i
$597$		0			0
$598$	8.82405	−	27.1576i	0.360842	−	1.11056i
$599$	−13.3539	−	9.70216i	−0.545624	−	0.396419i	0.280545	−	0.959841i	$-0.409485\pi$
$599$	−13.3539	−	9.70216i	−0.545624	−	0.396419i	−0.826170	+	0.563421i	$0.809485\pi$
$600$		0			0
$601$	12.2509	−	37.7045i	0.499726	−	1.53800i	−0.309734	−	0.950823i	$-0.600240\pi$
$601$	12.2509	−	37.7045i	0.499726	−	1.53800i	0.809460	−	0.587175i	$-0.199760\pi$
$602$	−8.44829	−	26.0011i	−0.344326	−	1.05973i
$603$		0			0
$604$	−17.2255			−0.700897
$605$	−10.0841	+	4.39441i	−0.409977	+	0.178658i
$606$		0			0
$607$	−11.4795	+	8.34036i	−0.465939	+	0.338525i	−0.795857	−	0.605485i	$-0.792979\pi$
$607$	−11.4795	+	8.34036i	−0.465939	+	0.338525i	0.329917	+	0.944010i	$0.392979\pi$
$608$	−2.73925	−	8.43055i	−0.111091	−	0.341904i
$609$		0			0
$610$	1.02619	+	0.745574i	0.0415494	+	0.0301874i
$611$	−7.61636	−	5.53361i	−0.308125	−	0.223866i
$612$		0			0
$613$	9.31820	+	28.6785i	0.376359	+	1.15831i	0.942557	+	0.334044i	$0.108414\pi$
$613$	9.31820	+	28.6785i	0.376359	+	1.15831i	−0.566199	+	0.824269i	$0.691586\pi$
$614$	10.3877	−	7.54714i	0.419215	−	0.304578i
$615$		0			0
$616$	−20.6570	−	36.1084i	−0.832296	−	1.45485i
$617$	31.3844			1.26349			0.631744	−	0.775177i	$-0.282339\pi$
$617$	31.3844			1.26349			0.631744	+	0.775177i	$0.282339\pi$
$618$		0			0
$619$	10.8876	+	33.5087i	0.437611	+	1.34683i	0.890387	+	0.455205i	$0.150434\pi$
$619$	10.8876	+	33.5087i	0.437611	+	1.34683i	−0.452775	+	0.891625i	$0.649566\pi$
$620$	4.92586	−	15.1602i	0.197827	−	0.608850i
$621$		0			0
$622$	−28.1059	−	20.4201i	−1.12694	−	0.818773i
$623$	2.79691	−	8.60800i	0.112056	−	0.344872i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	−40.2730			−1.60963
$627$		0			0
$628$	−21.3460			−0.851799
$629$	4.52723	−	3.28922i	0.180512	−	0.131150i
$630$		0			0
$631$	1.77213	−	5.45404i	0.0705472	−	0.217122i	−0.909567	−	0.415558i	$-0.863586\pi$
$631$	1.77213	−	5.45404i	0.0705472	−	0.217122i	0.980114	+	0.198436i	$0.0635863\pi$
$632$	25.9756	+	18.8724i	1.03325	+	0.750702i
$633$		0			0
$634$	8.35306	−	25.7081i	0.331742	−	1.02100i
$635$	−5.82005	−	17.9123i	−0.230962	−	0.710827i
$636$		0			0
$637$	−3.37217			−0.133610
$638$	3.44736	−	3.79834i	0.136482	−	0.150378i
$639$		0			0
$640$	11.4769	−	8.33844i	0.453663	−	0.329606i
$641$	2.20167	+	6.77605i	0.0869608	+	0.267638i	0.985075	−	0.172124i	$-0.0550629\pi$
$641$	2.20167	+	6.77605i	0.0869608	+	0.267638i	−0.898115	+	0.439762i	$0.855063\pi$
$642$		0			0
$643$	17.1427	+	12.4549i	0.676042	+	0.491173i	0.872042	−	0.489431i	$-0.162795\pi$
$643$	17.1427	+	12.4549i	0.676042	+	0.491173i	−0.196000	+	0.980604i	$0.562795\pi$
$644$	65.0235	+	47.2423i	2.56229	+	1.86161i
$645$		0			0
$646$	−5.02015	−	15.4504i	−0.197515	−	0.607889i
$647$	−4.57074	+	3.32083i	−0.179694	+	0.130555i	−0.673996	−	0.738735i	$-0.735424\pi$
$647$	−4.57074	+	3.32083i	−0.179694	+	0.130555i	0.494302	+	0.869290i	$0.335424\pi$
$648$		0			0
$649$	21.0857	−	4.39475i	0.827688	−	0.172509i
$650$	−3.25274			−0.127583
$651$		0			0
$652$	−9.50807	−	29.2628i	−0.372365	−	1.14602i
$653$	4.85563	−	14.9441i	0.190016	−	0.584808i	−0.809983	−	0.586453i	$-0.800524\pi$
$653$	4.85563	−	14.9441i	0.190016	−	0.584808i	0.999999	+	0.00164558i	$0.000523804\pi$
$654$		0			0
$655$	16.2610	+	11.8143i	0.635368	+	0.461622i
$656$	10.0661	−	30.9803i	0.393016	−	1.20958i
$657$		0			0
$658$	31.2416	−	22.6983i	1.21792	−	0.884872i
$659$	41.7884			1.62784			0.813922	−	0.580975i	$-0.197329\pi$
$659$	41.7884			1.62784			0.813922	+	0.580975i	$0.197329\pi$
$660$		0			0
$661$	15.8742			0.617435			0.308717	−	0.951154i	$-0.400100\pi$
$661$	15.8742			0.617435			0.308717	+	0.951154i	$0.400100\pi$
$662$	−18.0673	+	13.1266i	−0.702205	+	0.510182i
$663$		0			0
$664$	20.0791	−	61.7971i	0.779220	−	2.39819i
$665$	3.64363	+	2.64725i	0.141294	+	0.102656i
$666$		0			0
$667$	−1.66195	+	5.11494i	−0.0643508	+	0.198051i
$668$	−14.4863	−	44.5842i	−0.560491	−	1.72502i
$669$		0			0
$670$	−19.7156			−0.761681
$671$	−0.180749	+	1.65660i	−0.00697773	+	0.0639525i
$672$		0			0
$673$	−26.0864	+	18.9529i	−1.00556	+	0.730580i	−0.963273	−	0.268525i	$-0.913464\pi$
$673$	−26.0864	+	18.9529i	−1.00556	+	0.730580i	−0.0422850	+	0.999106i	$0.513464\pi$
$674$	9.04140	+	27.8266i	0.348262	+	1.07184i
$675$		0			0
$676$	40.1206	+	29.1493i	1.54310	+	1.12113i
$677$	14.2084	+	10.3230i	0.546073	+	0.396745i	0.826336	−	0.563178i	$-0.190422\pi$
$677$	14.2084	+	10.3230i	0.546073	+	0.396745i	−0.280263	+	0.959923i	$0.590422\pi$
$678$		0			0
$679$	−0.227495	−	0.700157i	−0.00873044	−	0.0268695i
$680$	−14.4987	+	10.5339i	−0.556000	+	0.403957i
$681$		0			0
$682$	29.8772	−	6.22710i	1.14406	−	0.238448i
$683$	5.93856			0.227233			0.113616	−	0.993525i	$-0.463757\pi$
$683$	5.93856			0.227233			0.113616	+	0.993525i	$0.463757\pi$
$684$		0			0
$685$	−5.55342	−	17.0917i	−0.212185	−	0.653039i
$686$	15.7067	−	48.3404i	0.599686	−	1.84565i
$687$		0			0
$688$	−26.6942	−	19.3945i	−1.01771	−	0.739407i
$689$	1.17145	−	3.60537i	0.0446289	−	0.137353i
$690$		0			0
$691$	−17.7463	+	12.8934i	−0.675100	+	0.490489i	−0.871728	−	0.489989i	$-0.837001\pi$
$691$	−17.7463	+	12.8934i	−0.675100	+	0.490489i	0.196629	+	0.980478i	$0.437001\pi$
$692$	−36.7868			−1.39842
$693$		0			0
$694$	−12.3424			−0.468511
$695$	13.6425	−	9.91187i	0.517490	−	0.375979i
$696$		0			0
$697$	4.72050	−	14.5282i	0.178802	−	0.550295i
$698$	1.94746	+	1.41491i	0.0737123	+	0.0535551i
$699$		0			0
$700$	2.82917	−	8.70729i	0.106933	−	0.329105i
$701$	−10.0186	−	30.8341i	−0.378397	−	1.16459i	−0.941158	−	0.337967i	$-0.890261\pi$
$701$	−10.0186	−	30.8341i	−0.378397	−	1.16459i	0.562761	−	0.826620i	$-0.309739\pi$
$702$		0			0
$703$	−4.02460			−0.151791
$704$	7.12273	+	3.20509i	0.268448	+	0.120796i
$705$		0			0
$706$	31.6908	−	23.0247i	1.19270	−	0.866547i
$707$	10.1565	+	31.2584i	0.381973	+	1.17559i
$708$		0			0
$709$	13.0256	+	9.46362i	0.489185	+	0.355414i	0.804871	−	0.593450i	$-0.202235\pi$
$709$	13.0256	+	9.46362i	0.489185	+	0.355414i	−0.315686	+	0.948864i	$0.602235\pi$
$710$	−23.0874	−	16.7740i	−0.866456	−	0.629517i
$711$		0			0
$712$	−8.00426	−	24.6346i	−0.299972	−	0.923220i
$713$	−25.8876	+	18.8085i	−0.969499	+	0.704383i
$714$		0			0
$715$	−2.12200	−	3.70924i	−0.0793582	−	0.138718i
$716$	−91.9971			−3.43809
$717$		0			0
$718$	15.8014	+	48.6316i	0.589702	+	1.81492i
$719$	2.41409	−	7.42981i	0.0900304	−	0.277085i	−0.895896	−	0.444263i	$-0.853466\pi$
$719$	2.41409	−	7.42981i	0.0900304	−	0.277085i	0.985927	+	0.167178i	$0.0534655\pi$
$720$		0			0
$721$	−11.3137	−	8.21985i	−0.421343	−	0.306123i
$722$	11.2118	−	34.5064i	0.417261	−	1.28420i
$723$		0			0
$724$	6.16712	−	4.48068i	0.229199	−	0.166523i
$725$	0.612630			0.0227525
$726$		0			0
$727$	−49.1218			−1.82183			−0.910914	−	0.412597i	$-0.864622\pi$
$727$	−49.1218			−1.82183			−0.910914	+	0.412597i	$0.864622\pi$
$728$	13.0744	−	9.49907i	0.484568	−	0.352059i
$729$		0			0
$730$	−8.67272	+	26.6919i	−0.320992	+	0.987911i
$731$	−12.5182	−	9.09503i	−0.463003	−	0.336392i
$732$		0			0
$733$	−0.206407	+	0.635255i	−0.00762382	+	0.0234637i	−0.954796	−	0.297262i	$-0.903927\pi$
$733$	−0.206407	+	0.635255i	−0.00762382	+	0.0234637i	0.947172	+	0.320725i	$0.103927\pi$
$734$	−27.8152	−	85.6064i	−1.02668	−	3.15979i
$735$		0			0
$736$	36.1730			1.33335
$737$	−12.8619	−	22.4826i	−0.473775	−	0.828156i
$738$		0			0
$739$	−30.8186	+	22.3911i	−1.13368	+	0.823668i	−0.986227	−	0.165400i	$-0.947108\pi$
$739$	−30.8186	+	22.3911i	−1.13368	+	0.823668i	−0.147456	+	0.989069i	$0.547108\pi$
$740$	2.52816	+	7.78088i	0.0929371	+	0.286031i
$741$		0			0
$742$	12.5801	+	9.14001i	0.461832	+	0.335540i
$743$	−25.3511	−	18.4186i	−0.930041	−	0.675714i	0.0159622	−	0.999873i	$-0.494919\pi$
$743$	−25.3511	−	18.4186i	−0.930041	−	0.675714i	−0.946003	+	0.324159i	$0.894919\pi$
$744$		0			0
$745$	0.721140	+	2.21944i	0.0264205	+	0.0813140i
$746$	24.7860	−	18.0081i	0.907480	−	0.659323i
$747$		0			0
$748$	−39.5651	−	17.8035i	−1.44664	−	0.650960i
$749$	−32.6754			−1.19393
$750$		0			0
$751$	−11.4915	−	35.3673i	−0.419332	−	1.29057i	−0.908318	−	0.418280i	$-0.862633\pi$
$751$	−11.4915	−	35.3673i	−0.419332	−	1.29057i	0.488986	−	0.872292i	$-0.337367\pi$
$752$	14.4022	−	44.3255i	0.525196	−	1.61639i
$753$		0			0
$754$	1.61215	+	1.17129i	0.0587110	+	0.0426560i
$755$	1.21718	−	3.74609i	0.0442976	−	0.136334i
$756$		0			0
$757$	−5.40478	+	3.92680i	−0.196440	+	0.142722i	−0.681657	−	0.731672i	$-0.738741\pi$
$757$	−5.40478	+	3.92680i	−0.196440	+	0.142722i	0.485217	+	0.874394i	$0.338741\pi$
$758$	−18.0355			−0.655079
$759$		0			0
$760$	12.8890			0.467533
$761$	−18.5213	+	13.4565i	−0.671398	+	0.487799i	−0.870493	−	0.492181i	$-0.836200\pi$
$761$	−18.5213	+	13.4565i	−0.671398	+	0.487799i	0.199095	+	0.979980i	$0.436200\pi$
$762$		0			0
$763$	7.44425	−	22.9110i	0.269500	−	0.829435i
$764$	0.0882966	+	0.0641512i	0.00319446	+	0.00232091i
$765$		0			0
$766$	12.4530	−	38.3265i	0.449947	−	1.38479i
$767$	2.58570	+	7.95797i	0.0933643	+	0.287346i
$768$		0			0
$769$	−13.1946			−0.475808			−0.237904	−	0.971289i	$-0.576460\pi$
$769$	−13.1946			−0.475808			−0.237904	+	0.971289i	$0.576460\pi$
$770$	17.1600	−	3.57654i	0.618403	−	0.128889i
$771$		0			0
$772$	−5.15575	+	3.74587i	−0.185560	+	0.134817i
$773$	3.83827	+	11.8130i	0.138053	+	0.424883i	0.996052	−	0.0887673i	$-0.0282928\pi$
$773$	3.83827	+	11.8130i	0.138053	+	0.424883i	−0.857999	+	0.513651i	$0.828293\pi$
$774$		0			0
$775$	2.94887	+	2.14248i	0.105927	+	0.0769602i
$776$	−1.70447	−	1.23837i	−0.0611869	−	0.0444549i
$777$		0			0
$778$	−19.5735	−	60.2412i	−0.701746	−	2.15975i
$779$	−8.88815	+	6.45762i	−0.318451	+	0.231368i
$780$		0			0
$781$	4.06650	−	37.2705i	0.145511	−	1.33364i
$782$	66.2932			2.37064
$783$		0			0
$784$	−5.15881	−	15.8772i	−0.184243	−	0.567042i
$785$	1.50834	−	4.64218i	0.0538348	−	0.165686i
$786$		0			0
$787$	−17.3818	−	12.6286i	−0.619595	−	0.450162i	0.233185	−	0.972432i	$-0.425085\pi$
$787$	−17.3818	−	12.6286i	−0.619595	−	0.450162i	−0.852780	+	0.522270i	$0.825085\pi$
$788$	−30.6805	+	94.4247i	−1.09295	+	3.36374i
$789$		0			0
$790$	−10.9453	+	7.95221i	−0.389416	+	0.282927i
$791$	−18.9426			−0.673520
$792$		0			0
$793$	−0.647384			−0.0229893
$794$	7.30130	−	5.30471i	0.259114	−	0.188257i
$795$		0			0
$796$	−8.95753	+	27.5685i	−0.317491	+	0.977138i
$797$	1.72264	+	1.25157i	0.0610191	+	0.0443330i	0.617877	−	0.786275i	$-0.287993\pi$
$797$	1.72264	+	1.25157i	0.0610191	+	0.0443330i	−0.556858	+	0.830608i	$0.687993\pi$
$798$		0			0
$799$	6.75393	−	20.7864i	0.238937	−	0.735372i
$800$	−1.27330	−	3.91881i	−0.0450179	−	0.138551i
$801$		0			0
$802$	72.9179			2.57482
$803$	−36.0957	+	7.52318i	−1.27379	+	0.265487i
$804$		0			0
$805$	−14.8686	+	10.8026i	−0.524048	+	0.380743i
$806$	3.66378	+	11.2760i	0.129051	+	0.397179i
$807$		0			0
$808$	76.0957	+	55.2868i	2.67704	+	1.94498i
$809$	−4.33820	−	3.15189i	−0.152523	−	0.110815i	0.508906	−	0.860822i	$-0.330050\pi$
$809$	−4.33820	−	3.15189i	−0.152523	−	0.110815i	−0.661430	+	0.750007i	$0.730050\pi$
$810$		0			0
$811$	6.05047	+	18.6214i	0.212461	+	0.653887i	0.999324	+	0.0367600i	$0.0117037\pi$
$811$	6.05047	+	18.6214i	0.212461	+	0.653887i	−0.786863	+	0.617127i	$0.788296\pi$
$812$	−4.53766	+	3.29681i	−0.159241	+	0.115695i
$813$		0			0
$814$	−10.5271	+	11.5989i	−0.368975	+	0.406541i
$815$	7.03572			0.246450
$816$		0			0
$817$	3.43887	+	10.5837i	0.120311	+	0.370278i
$818$	−7.50402	+	23.0950i	−0.262372	+	0.807497i
$819$		0			0
$820$	18.0681	+	13.1272i	0.630964	+	0.458422i
$821$	5.14095	−	15.8222i	0.179420	−	0.552199i	−0.820387	−	0.571808i	$-0.806242\pi$
$821$	5.14095	−	15.8222i	0.179420	−	0.552199i	0.999808	+	0.0196092i	$0.00624219\pi$
$822$		0			0
$823$	14.7993	−	10.7523i	0.515870	−	0.374801i	−0.299176	−	0.954198i	$-0.596712\pi$
$823$	14.7993	−	10.7523i	0.515870	−	0.374801i	0.815046	+	0.579397i	$0.196712\pi$
$824$	−40.0210			−1.39420
$825$		0			0
$826$	−34.3227			−1.19424
$827$	−30.7575	+	22.3466i	−1.06954	+	0.777069i	−0.975830	−	0.218530i	$-0.929874\pi$
$827$	−30.7575	+	22.3466i	−1.06954	+	0.777069i	−0.0937136	+	0.995599i	$0.529874\pi$
$828$		0			0
$829$	15.9762	−	49.1698i	0.554877	−	1.70774i	−0.141389	−	0.989954i	$-0.545157\pi$
$829$	15.9762	−	49.1698i	0.554877	−	1.70774i	0.696267	−	0.717783i	$-0.254843\pi$
$830$	22.1504	+	16.0932i	0.768851	+	0.558603i
$831$		0			0
$832$	−0.937652	+	2.88580i	−0.0325072	+	0.100047i
$833$	−2.41922	−	7.44560i	−0.0838210	−	0.257975i
$834$		0			0
$835$	10.7195			0.370963
$836$	15.4945	+	27.0843i	0.535889	+	0.936731i
$837$		0			0
$838$	62.6065	−	45.4863i	2.16271	−	1.57130i
$839$	−11.9288	−	36.7132i	−0.411829	−	1.26748i	−0.915056	−	0.403326i	$-0.867854\pi$
$839$	−11.9288	−	36.7132i	−0.411829	−	1.26748i	0.503227	−	0.864154i	$-0.332146\pi$
$840$		0			0
$841$	23.1579	+	16.8252i	0.798547	+	0.580178i
$842$	−14.1938	−	10.3124i	−0.489151	−	0.355389i
$843$		0			0
$844$	7.64568	+	23.5310i	0.263175	+	0.809969i
$845$	−9.17416	+	6.66541i	−0.315601	+	0.229297i
$846$		0			0
$847$	15.2732	+	17.2350i	0.524793	+	0.592203i
$848$	18.7672			0.644470
$849$		0			0
$850$	−2.33354	−	7.18190i	−0.0800398	−	0.246337i
$851$	5.07504	−	15.6194i	0.173970	−	0.535425i
$852$		0			0
$853$	−27.4303	−	19.9293i	−0.939197	−	0.682366i	0.00903033	−	0.999959i	$-0.497126\pi$
$853$	−27.4303	−	19.9293i	−0.939197	−	0.682366i	−0.948227	+	0.317593i	$0.897126\pi$
$854$	0.820596	−	2.52553i	0.0280802	−	0.0864220i
$855$		0			0
$856$	−75.6523	+	54.9646i	−2.58574	+	1.87865i
$857$	56.7117			1.93723			0.968617	−	0.248558i	$-0.0799568\pi$
$857$	56.7117			1.93723			0.968617	+	0.248558i	$0.0799568\pi$
$858$		0			0
$859$	−25.7505			−0.878597			−0.439298	−	0.898341i	$-0.644773\pi$
$859$	−25.7505			−0.878597			−0.439298	+	0.898341i	$0.644773\pi$
$860$	18.3017	−	13.2969i	0.624082	−	0.453422i
$861$		0			0
$862$	−2.52291	+	7.76473i	−0.0859308	+	0.264468i
$863$	28.9345	+	21.0222i	0.984942	+	0.715603i	0.958808	−	0.284056i	$-0.0916801\pi$
$863$	28.9345	+	21.0222i	0.984942	+	0.715603i	0.0261347	+	0.999658i	$0.491680\pi$
$864$		0			0
$865$	2.59940	−	8.00012i	0.0883821	−	0.272012i
$866$	23.7093	+	72.9698i	0.805676	+	2.47962i
$867$		0			0
$868$	−33.3714			−1.13270
$869$	−16.2086	−	7.29357i	−0.549841	−	0.247417i
$870$		0			0
$871$	8.14064	−	5.91452i	0.275835	−	0.200406i
$872$	−21.3041	−	65.5674i	−0.721449	−	2.22039i
$873$		0			0
$874$	−38.5722	−	28.0244i	−1.30473	−	0.947938i
$875$	1.69369	+	1.23053i	0.0572570	+	0.0415996i
$876$		0			0
$877$	5.34913	+	16.4629i	0.180627	+	0.555913i	0.999846	−	0.0175682i	$-0.00559241\pi$
$877$	5.34913	+	16.4629i	0.180627	+	0.555913i	−0.819218	+	0.573482i	$0.805592\pi$
$878$	74.6105	−	54.2077i	2.51798	−	1.82942i
$879$		0			0
$880$	14.2179	−	15.6655i	0.479286	−	0.528082i
$881$	4.15822			0.140094			0.0700470	−	0.997544i	$-0.477685\pi$
$881$	4.15822			0.140094			0.0700470	+	0.997544i	$0.477685\pi$
$882$		0			0
$883$	−12.7533	−	39.2505i	−0.429182	−	1.32088i	−0.898933	−	0.438086i	$-0.855656\pi$
$883$	−12.7533	−	39.2505i	−0.429182	−	1.32088i	0.469751	−	0.882799i	$-0.344344\pi$
$884$	5.20843	−	16.0299i	0.175179	−	0.539144i
$885$		0			0
$886$	4.41467	+	3.20744i	0.148314	+	0.107756i
$887$	−9.41854	+	28.9873i	−0.316243	+	0.973297i	0.658996	+	0.752146i	$0.270981\pi$
$887$	−9.41854	+	28.9873i	−0.316243	+	0.973297i	−0.975240	+	0.221151i	$0.929019\pi$
$888$		0			0
$889$	−31.8990	+	23.1760i	−1.06986	+	0.777298i
$890$	10.9144			0.365852
$891$		0			0
$892$	34.4803			1.15449
$893$	−12.7168	+	9.23933i	−0.425553	+	0.309182i
$894$		0			0
$895$	6.50062	−	20.0069i	0.217292	−	0.668756i
$896$	−24.0270	−	17.4566i	−0.802684	−	0.583184i
$897$		0			0
$898$	−8.98831	+	27.6632i	−0.299944	+	0.923132i
$899$	−0.690047	−	2.12375i	−0.0230144	−	0.0708309i
$900$		0			0
$901$	8.80090			0.293200
$902$	−4.63783	+	42.5068i	−0.154423	+	1.41532i
$903$		0			0
$904$	−43.8570	+	31.8640i	−1.45866	+	1.05978i
$905$	0.538649	+	1.65779i	0.0179053	+	0.0551068i
$906$		0			0
$907$	−9.13337	−	6.63578i	−0.303269	−	0.220338i	0.425734	−	0.904848i	$-0.360016\pi$
$907$	−9.13337	−	6.63578i	−0.303269	−	0.220338i	−0.729003	+	0.684511i	$0.760016\pi$
$908$	−39.6660	−	28.8191i	−1.31636	−	0.956394i
$909$		0			0
$910$	2.10429	+	6.47635i	0.0697567	+	0.214689i
$911$	40.9417	−	29.7459i	1.35646	−	0.985525i	0.357797	−	0.933799i	$-0.383528\pi$
$911$	40.9417	−	29.7459i	1.35646	−	0.985525i	0.998661	−	0.0517251i	$-0.0164719\pi$
$912$		0			0
$913$	−3.90146	+	35.7578i	−0.129119	+	1.18341i
$914$	40.2193			1.33034
$915$		0			0
$916$	36.4753	+	112.259i	1.20518	+	3.70915i
$917$	13.0031	−	40.0193i	0.429399	−	1.32156i
$918$		0			0
$919$	22.0198	+	15.9983i	0.726366	+	0.527736i	0.888412	−	0.459048i	$-0.151809\pi$
$919$	22.0198	+	15.9983i	0.726366	+	0.527736i	−0.162046	+	0.986783i	$0.551809\pi$
$920$	−16.2531	+	50.0219i	−0.535849	+	1.64917i
$921$		0			0
$922$	−3.11518	+	2.26331i	−0.102593	+	0.0745381i
$923$	14.5649			0.479410
$924$		0			0
$925$	−1.87077			−0.0615106
$926$	29.0167	−	21.0819i	0.953547	−	0.692793i
$927$		0			0
$928$	−0.780061	+	2.40078i	−0.0256068	+	0.0788095i
$929$	−18.7776	−	13.6427i	−0.616073	−	0.447603i	0.235475	−	0.971880i	$-0.424336\pi$
$929$	−18.7776	−	13.6427i	−0.616073	−	0.447603i	−0.851548	+	0.524277i	$0.824336\pi$
$930$		0			0
$931$	−1.73990	+	5.35485i	−0.0570228	+	0.175498i
$932$	14.6637	+	45.1303i	0.480326	+	1.47829i
$933$		0			0
$934$	−15.2910			−0.500336
$935$	6.66749	−	7.34631i	0.218050	−	0.240250i
$936$		0			0
$937$	34.1500	−	24.8114i	1.11563	−	0.810554i	0.132090	−	0.991238i	$-0.457831\pi$
$937$	34.1500	−	24.8114i	1.11563	−	0.810554i	0.983541	+	0.180684i	$0.0578311\pi$
$938$	12.7546	+	39.2547i	0.416453	+	1.28171i
$939$		0			0
$940$	25.8511	+	18.7819i	0.843171	+	0.612600i
$941$	−23.6336	−	17.1708i	−0.770435	−	0.559754i	0.131658	−	0.991295i	$-0.457970\pi$
$941$	−23.6336	−	17.1708i	−0.770435	−	0.559754i	−0.902093	+	0.431542i	$0.857970\pi$
$942$		0			0
$943$	−13.8539	−	42.6378i	−0.451144	−	1.38848i
$944$	−33.5128	+	24.3485i	−1.09075	+	0.792476i
$945$		0			0
$946$	39.4974	+	17.7730i	1.28417	+	0.577851i
$947$	−9.63809			−0.313196			−0.156598	−	0.987662i	$-0.550053\pi$
$947$	−9.63809			−0.313196			−0.156598	+	0.987662i	$0.550053\pi$
$948$		0			0
$949$	−4.42634	−	13.6229i	−0.143685	−	0.442218i
$950$	−1.67828	+	5.16520i	−0.0544505	+	0.167581i
$951$		0			0
$952$	30.3532	+	22.0529i	0.983752	+	0.714738i
$953$	−1.61353	+	4.96593i	−0.0522673	+	0.160862i	−0.973783	−	0.227479i	$-0.926952\pi$
$953$	−1.61353	+	4.96593i	−0.0522673	+	0.160862i	0.921516	+	0.388341i	$0.126952\pi$
$954$		0			0
$955$	−0.0201903	+	0.0146691i	−0.000653342	+	0.000474681i
$956$	50.1446			1.62179
$957$		0			0
$958$	−44.4529			−1.43621
$959$	−30.4376	+	22.1142i	−0.982882	+	0.714106i
$960$		0			0
$961$	−5.47390	+	16.8469i	−0.176577	+	0.543450i
$962$	−4.92298	−	3.57675i	−0.158723	−	0.115319i
$963$		0			0
$964$	17.2361	−	53.0471i	0.555136	−	1.70853i
$965$	−0.450314	−	1.38592i	−0.0144961	−	0.0446145i
$966$		0			0
$967$	38.4583			1.23674			0.618368	−	0.785889i	$-0.287794\pi$
$967$	38.4583			1.23674			0.618368	+	0.785889i	$0.287794\pi$
$968$	64.3532	+	14.2121i	2.06839	+	0.456793i
$969$		0			0
$970$	0.718209	−	0.521810i	0.0230603	−	0.0167543i
$971$	−13.4928	−	41.5267i	−0.433006	−	1.33265i	−0.895116	−	0.445832i	$-0.852908\pi$
$971$	−13.4928	−	41.5267i	−0.433006	−	1.33265i	0.462111	−	0.886822i	$-0.347092\pi$
$972$		0			0
$973$	−28.5608	−	20.7506i	−0.915616	−	0.665234i
$974$	13.8543	+	10.0658i	0.443921	+	0.322527i
$975$		0			0
$976$	−0.990380	−	3.04808i	−0.0317013	−	0.0975665i
$977$	−9.50330	+	6.90455i	−0.304038	+	0.220896i	−0.729334	−	0.684158i	$-0.760170\pi$
$977$	−9.50330	+	6.90455i	−0.304038	+	0.220896i	0.425296	+	0.905054i	$0.360170\pi$
$978$		0			0
$979$	7.12027	+	12.4462i	0.227565	+	0.397782i
$980$	11.4457			0.365618
$981$		0			0
$982$	0.404582	+	1.24518i	0.0129107	+	0.0397351i
$983$	−2.88989	+	8.89417i	−0.0921733	+	0.283680i	−0.986507	−	0.163721i	$-0.947650\pi$
$983$	−2.88989	+	8.89417i	−0.0921733	+	0.283680i	0.894333	+	0.447401i	$0.147650\pi$
$984$		0			0
$985$	−18.3669	−	13.3443i	−0.585218	−	0.425186i
$986$	−1.42960	+	4.39985i	−0.0455276	+	0.140120i
$987$		0			0
$988$	−9.80687	+	7.12510i	−0.311998	+	0.226680i
$989$	−45.4117			−1.44401
$990$		0			0
$991$	−32.3450			−1.02747			−0.513737	−	0.857948i	$-0.671739\pi$
$991$	−32.3450			−1.02747			−0.513737	+	0.857948i	$0.671739\pi$
$992$	−12.1508	+	8.82806i	−0.385788	+	0.280291i
$993$		0			0
$994$	−18.4619	+	56.8197i	−0.585574	+	1.80221i
$995$	−5.36244	−	3.89604i	−0.170001	−	0.123513i
$996$		0			0
$997$	−8.99777	+	27.6923i	−0.284962	+	0.877023i	0.701448	+	0.712721i	$0.252537\pi$
$997$	−8.99777	+	27.6923i	−0.284962	+	0.877023i	−0.986410	+	0.164302i	$0.947463\pi$
$998$	−17.0540	−	52.4869i	−0.539836	−	1.66144i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.n.f.91.2		8
3.2	odd	2		55.2.g.a.36.1	yes	8
11.2	odd	10		5445.2.a.bu.1.4		4
11.4	even	5	inner	495.2.n.f.136.2		8
11.9	even	5		5445.2.a.bg.1.1		4
12.11	even	2		880.2.bo.e.641.2		8
15.2	even	4		275.2.z.b.124.1		16
15.8	even	4		275.2.z.b.124.4		16
15.14	odd	2		275.2.h.b.201.2		8
33.2	even	10		605.2.a.i.1.1		4
33.5	odd	10		605.2.g.j.251.2		8
33.8	even	10		605.2.g.g.511.1		8
33.14	odd	10		605.2.g.j.511.2		8
33.17	even	10		605.2.g.g.251.1		8
33.20	odd	10		605.2.a.l.1.4		4
33.26	odd	10		55.2.g.a.26.1	✓	8
33.29	even	10		605.2.g.n.81.2		8
33.32	even	2		605.2.g.n.366.2		8
132.35	odd	10		9680.2.a.cv.1.4		4
132.59	even	10		880.2.bo.e.81.2		8
132.119	even	10		9680.2.a.cs.1.4		4
165.59	odd	10		275.2.h.b.26.2		8
165.92	even	20		275.2.z.b.224.4		16
165.119	odd	10		3025.2.a.v.1.1		4
165.134	even	10		3025.2.a.be.1.4		4
165.158	even	20		275.2.z.b.224.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.a.26.1	✓	8	33.26	odd	10
55.2.g.a.36.1	yes	8	3.2	odd	2
275.2.h.b.26.2		8	165.59	odd	10
275.2.h.b.201.2		8	15.14	odd	2
275.2.z.b.124.1		16	15.2	even	4
275.2.z.b.124.4		16	15.8	even	4
275.2.z.b.224.1		16	165.158	even	20
275.2.z.b.224.4		16	165.92	even	20
495.2.n.f.91.2		8	1.1	even	1	trivial
495.2.n.f.136.2		8	11.4	even	5	inner
605.2.a.i.1.1		4	33.2	even	10
605.2.a.l.1.4		4	33.20	odd	10
605.2.g.g.251.1		8	33.17	even	10
605.2.g.g.511.1		8	33.8	even	10
605.2.g.j.251.2		8	33.5	odd	10
605.2.g.j.511.2		8	33.14	odd	10
605.2.g.n.81.2		8	33.29	even	10
605.2.g.n.366.2		8	33.32	even	2
880.2.bo.e.81.2		8	132.59	even	10
880.2.bo.e.641.2		8	12.11	even	2
3025.2.a.v.1.1		4	165.119	odd	10
3025.2.a.be.1.4		4	165.134	even	10
5445.2.a.bg.1.1		4	11.9	even	5
5445.2.a.bu.1.4		4	11.2	odd	10
9680.2.a.cs.1.4		4	132.119	even	10
9680.2.a.cv.1.4		4	132.35	odd	10

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:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.04238 - 1.48388i) q^{2} +(1.35140 - 4.15918i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.646930 - 1.99105i) q^{7} +(-1.85140 - 5.69802i) q^{8} +O(q^{10})\)	\(q+(2.04238 - 1.48388i) q^{2} +(1.35140 - 4.15918i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.646930 - 1.99105i) q^{7} +(-1.85140 - 5.69802i) q^{8} +2.52452 q^{10} +(1.64693 + 2.87882i) q^{11} +(-1.04238 + 0.757336i) q^{13} +(-1.63319 - 5.02644i) q^{14} +(-5.16042 - 3.74926i) q^{16} +(-2.41998 - 1.75822i) q^{17} +(0.664789 + 2.04601i) q^{19} +(3.53801 - 2.57052i) q^{20} +(7.63548 + 3.43582i) q^{22} -8.77882 q^{23} +(0.309017 + 0.951057i) q^{25} +(-1.00515 + 3.09354i) q^{26} +(-7.40686 - 5.38140i) q^{28} +(0.189313 - 0.582646i) q^{29} +(2.94887 - 2.14248i) q^{31} -4.12048 q^{32} -7.55150 q^{34} +(1.69369 - 1.23053i) q^{35} +(-0.578100 + 1.77921i) q^{37} +(4.39378 + 3.19227i) q^{38} +(1.85140 - 5.69802i) q^{40} +(1.57810 + 4.85689i) q^{41} +5.17287 q^{43} +(14.1992 - 2.95944i) q^{44} +(-17.9297 + 13.0267i) q^{46} +(2.25789 + 6.94907i) q^{47} +(2.11737 + 1.53836i) q^{49} +(2.04238 + 1.48388i) q^{50} +(1.74122 + 5.35892i) q^{52} +(-2.38030 + 1.72939i) q^{53} +(-0.359735 + 3.29706i) q^{55} -12.5428 q^{56} +(-0.477925 - 1.47090i) q^{58} +(2.00682 - 6.17636i) q^{59} +(0.406490 + 0.295332i) q^{61} +(2.84355 - 8.75154i) q^{62} +(1.90523 - 1.38423i) q^{64} -1.28846 q^{65} -7.80964 q^{67} +(-10.5831 + 7.68907i) q^{68} +(1.63319 - 5.02644i) q^{70} +(-9.14526 - 6.64442i) q^{71} +(-3.43539 + 10.5730i) q^{73} +(1.45943 + 4.49166i) q^{74} +9.40812 q^{76} +(6.79732 - 1.41672i) q^{77} +(-4.33558 + 3.14998i) q^{79} +(-1.97110 - 6.06643i) q^{80} +(10.4301 + 7.57793i) q^{82} +(8.77408 + 6.37474i) q^{83} +(-0.924349 - 2.84485i) q^{85} +(10.5650 - 7.67591i) q^{86} +(13.3545 - 14.7141i) q^{88} +4.32336 q^{89} +(0.833541 + 2.56538i) q^{91} +(-11.8637 + 36.5127i) q^{92} +(14.9230 + 10.8422i) q^{94} +(-0.664789 + 2.04601i) q^{95} +(0.284493 - 0.206696i) q^{97} +6.60723 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 6 q^{4} + 2 q^{5} - 3 q^{7} + 2 q^{8}+O(q^{10}) \) 8 * q + 4 * q^2 - 6 * q^4 + 2 * q^5 - 3 * q^7 + 2 * q^8	\( 8 q + 4 q^{2} - 6 q^{4} + 2 q^{5} - 3 q^{7} + 2 q^{8} + 6 q^{10} + 5 q^{11} + 4 q^{13} - 16 q^{14} - 20 q^{16} - q^{17} - q^{19} + q^{20} + 33 q^{22} + 18 q^{23} - 2 q^{25} + 14 q^{26} + 4 q^{28} - 19 q^{29} + 6 q^{31} - 12 q^{32} - 20 q^{34} + 8 q^{35} + 4 q^{37} + 6 q^{38} - 2 q^{40} + 4 q^{41} + 42 q^{43} + 28 q^{44} - 41 q^{46} - 4 q^{47} - 15 q^{49} + 4 q^{50} - 26 q^{52} - 3 q^{53} + 5 q^{55} - 30 q^{56} - 6 q^{58} + 19 q^{59} - 2 q^{61} + 38 q^{62} + 6 q^{64} - 14 q^{65} - 2 q^{67} - 35 q^{68} + 16 q^{70} - 40 q^{71} - 23 q^{73} - 48 q^{74} + 16 q^{76} + 28 q^{77} + 17 q^{79} - 15 q^{80} + 2 q^{82} + 25 q^{83} - 4 q^{85} + 31 q^{86} + 22 q^{88} - 12 q^{91} - 81 q^{92} + 33 q^{94} + q^{95} + 12 q^{97} + 84 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 - 6 * q^4 + 2 * q^5 - 3 * q^7 + 2 * q^8 + 6 * q^10 + 5 * q^11 + 4 * q^13 - 16 * q^14 - 20 * q^16 - q^17 - q^19 + q^20 + 33 * q^22 + 18 * q^23 - 2 * q^25 + 14 * q^26 + 4 * q^28 - 19 * q^29 + 6 * q^31 - 12 * q^32 - 20 * q^34 + 8 * q^35 + 4 * q^37 + 6 * q^38 - 2 * q^40 + 4 * q^41 + 42 * q^43 + 28 * q^44 - 41 * q^46 - 4 * q^47 - 15 * q^49 + 4 * q^50 - 26 * q^52 - 3 * q^53 + 5 * q^55 - 30 * q^56 - 6 * q^58 + 19 * q^59 - 2 * q^61 + 38 * q^62 + 6 * q^64 - 14 * q^65 - 2 * q^67 - 35 * q^68 + 16 * q^70 - 40 * q^71 - 23 * q^73 - 48 * q^74 + 16 * q^76 + 28 * q^77 + 17 * q^79 - 15 * q^80 + 2 * q^82 + 25 * q^83 - 4 * q^85 + 31 * q^86 + 22 * q^88 - 12 * q^91 - 81 * q^92 + 33 * q^94 + q^95 + 12 * q^97 + 84 * q^98

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