LMFDB - Embedded newform 675.2.r.a.46.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(46,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 18]))

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

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

chi := DirichletCharacter("675.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.r (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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			46.22
Character	$\chi$	$=$	675.46
Dual form			675.2.r.a.631.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.11303 + 1.23614i) q^{2} +(-0.0801613 + 0.762684i) q^{4} +(-2.09847 - 0.772289i) q^{5} +(0.694163 - 1.20233i) q^{7} +(1.65942 - 1.20564i) q^{8} +(-1.38100 - 3.45359i) q^{10} +(-3.04269 - 3.37925i) q^{11} +(0.454318 - 0.504572i) q^{13} +(2.25887 - 0.480138i) q^{14} +(4.83758 + 1.02826i) q^{16} +(1.73545 - 1.26088i) q^{17} +(5.56870 - 4.04590i) q^{19} +(0.757229 - 1.53856i) q^{20} +(0.790638 - 7.52241i) q^{22} +(-0.104805 + 0.0222770i) q^{23} +(3.80714 + 3.24125i) q^{25} +1.12939 q^{26} +(0.861350 + 0.625807i) q^{28} +(-1.87597 + 0.835237i) q^{29} +(-5.90734 - 2.63012i) q^{31} +(2.06213 + 3.57172i) q^{32} +(3.49024 + 0.741873i) q^{34} +(-2.38522 + 1.98695i) q^{35} +(-0.886060 - 2.72701i) q^{37} +(11.1994 + 2.38051i) q^{38} +(-4.41335 + 1.24845i) q^{40} +(-3.63522 + 4.03732i) q^{41} +(-0.613014 + 1.06177i) q^{43} +(2.82121 - 2.04973i) q^{44} +(-0.144189 - 0.104759i) q^{46} +(10.8080 - 4.81201i) q^{47} +(2.53627 + 4.39296i) q^{49} +(0.230806 + 8.31377i) q^{50} +(0.348410 + 0.386948i) q^{52} +(1.07586 + 0.781661i) q^{53} +(3.77524 + 9.44110i) q^{55} +(-0.297663 - 2.83208i) q^{56} +(-3.12049 - 1.38933i) q^{58} +(1.15888 - 1.28707i) q^{59} +(-2.52602 - 2.80543i) q^{61} +(-3.32384 - 10.2297i) q^{62} +(0.936638 - 2.88268i) q^{64} +(-1.34305 + 0.707962i) q^{65} +(-12.9879 - 5.78257i) q^{67} +(0.822536 + 1.42467i) q^{68} +(-5.11098 - 0.736948i) q^{70} +(10.9600 + 7.96294i) q^{71} +(-1.83085 + 5.63478i) q^{73} +(2.38477 - 4.13054i) q^{74} +(2.63935 + 4.57148i) q^{76} +(-6.17509 + 1.31256i) q^{77} +(-8.20200 + 3.65176i) q^{79} +(-9.35740 - 5.89378i) q^{80} -9.03682 q^{82} +(1.89564 + 18.0358i) q^{83} +(-4.61555 + 1.30565i) q^{85} +(-1.99480 + 0.424009i) q^{86} +(-9.12328 - 1.93921i) q^{88} +(-2.33361 + 7.18212i) q^{89} +(-0.291288 - 0.896494i) q^{91} +(-0.00858900 - 0.0817189i) q^{92} +(17.9779 + 8.00428i) q^{94} +(-14.8103 + 4.18954i) q^{95} +(9.93178 - 4.42191i) q^{97} +(-2.60738 + 8.02469i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28}+ \cdots - 146 q^{98}+O(q^{100}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	1.11303	+	1.23614i	0.787030	+	0.874086i	0.994562	−	0.104143i	$-0.0332098\pi$
$2$	1.11303	+	1.23614i	0.787030	+	0.874086i	−0.207532	+	0.978228i	$0.566543\pi$
$3$		0			0
$3$		0			0
$4$	−0.0801613	+	0.762684i	−0.0400807	+	0.381342i
$5$	−2.09847	−	0.772289i	−0.938464	−	0.345378i
$5$	−2.09847	−	0.772289i	−0.938464	−	0.345378i
$6$		0			0
$7$	0.694163	−	1.20233i	0.262369	−	0.454436i	−0.704502	−	0.709702i	$-0.748830\pi$
$7$	0.694163	−	1.20233i	0.262369	−	0.454436i	0.966871	+	0.255266i	$0.0821629\pi$
$8$	1.65942	−	1.20564i	0.586694	−	0.426258i
$9$		0			0
$10$	−1.38100	−	3.45359i	−0.436709	−	1.09212i
$11$	−3.04269	−	3.37925i	−0.917407	−	1.01888i	−0.999752	−	0.0222795i	$-0.992908\pi$
$11$	−3.04269	−	3.37925i	−0.917407	−	1.01888i	0.0823451	−	0.996604i	$-0.473759\pi$
$12$		0			0
$13$	0.454318	−	0.504572i	0.126005	−	0.139943i	−0.676841	−	0.736129i	$-0.736651\pi$
$13$	0.454318	−	0.504572i	0.126005	−	0.139943i	0.802846	+	0.596186i	$0.203318\pi$
$14$	2.25887	−	0.480138i	0.603709	−	0.128322i
$15$		0			0
$16$	4.83758	+	1.02826i	1.20940	+	0.257065i
$17$	1.73545	−	1.26088i	0.420909	−	0.305808i	−0.357095	−	0.934068i	$-0.616233\pi$
$17$	1.73545	−	1.26088i	0.420909	−	0.305808i	0.778003	+	0.628260i	$0.216233\pi$
$18$		0			0
$19$	5.56870	−	4.04590i	1.27755	−	0.928192i	0.278071	−	0.960560i	$-0.410305\pi$
$19$	5.56870	−	4.04590i	1.27755	−	0.928192i	0.999476	+	0.0323680i	$0.0103049\pi$
$20$	0.757229	−	1.53856i	0.169321	−	0.344033i
$21$		0			0
$22$	0.790638	−	7.52241i	0.168565	−	1.60378i
$23$	−0.104805	+	0.0222770i	−0.0218534	+	0.00464508i	−0.218825	−	0.975764i	$-0.570223\pi$
$23$	−0.104805	+	0.0222770i	−0.0218534	+	0.00464508i	0.196972	+	0.980409i	$0.436889\pi$
$24$		0			0
$25$	3.80714	+	3.24125i	0.761428	+	0.648250i
$26$	1.12939			0.221492
$27$		0			0
$28$	0.861350	+	0.625807i	0.162780	+	0.118266i
$29$	−1.87597	+	0.835237i	−0.348360	+	0.155100i	−0.573455	−	0.819237i	$-0.694397\pi$
$29$	−1.87597	+	0.835237i	−0.348360	+	0.155100i	0.225095	+	0.974337i	$0.427731\pi$
$30$		0			0
$31$	−5.90734	−	2.63012i	−1.06099	−	0.472383i	−0.199363	−	0.979926i	$-0.563887\pi$
$31$	−5.90734	−	2.63012i	−1.06099	−	0.472383i	−0.861627	+	0.507543i	$0.830554\pi$
$32$	2.06213	+	3.57172i	0.364537	+	0.631397i
$33$		0			0
$34$	3.49024	+	0.741873i	0.598571	+	0.127230i
$35$	−2.38522	+	1.98695i	−0.403176	+	0.335856i
$36$		0			0
$37$	−0.886060	−	2.72701i	−0.145667	−	0.448318i	0.851429	−	0.524470i	$-0.175737\pi$
$37$	−0.886060	−	2.72701i	−0.145667	−	0.448318i	−0.997096	+	0.0761520i	$0.975737\pi$
$38$	11.1994	+	2.38051i	1.81679	+	0.386170i
$39$		0			0
$40$	−4.41335	+	1.24845i	−0.697811	+	0.197396i
$41$	−3.63522	+	4.03732i	−0.567726	+	0.630524i	−0.956822	−	0.290673i	$-0.906121\pi$
$41$	−3.63522	+	4.03732i	−0.567726	+	0.630524i	0.389096	+	0.921197i	$0.372787\pi$
$42$		0			0
$43$	−0.613014	+	1.06177i	−0.0934837	+	0.161919i	−0.908975	−	0.416851i	$-0.863134\pi$
$43$	−0.613014	+	1.06177i	−0.0934837	+	0.161919i	0.815491	+	0.578770i	$0.196467\pi$
$44$	2.82121	−	2.04973i	0.425313	−	0.309008i
$45$		0			0
$46$	−0.144189	−	0.104759i	−0.0212595	−	0.0154459i
$47$	10.8080	−	4.81201i	1.57650	−	0.701904i	0.582662	−	0.812715i	$-0.302011\pi$
$47$	10.8080	−	4.81201i	1.57650	−	0.701904i	0.993842	+	0.110810i	$0.0353446\pi$
$48$		0			0
$49$	2.53627	+	4.39296i	0.362325	+	0.627565i
$50$	0.230806	+	8.31377i	0.0326409	+	1.17575i
$51$		0			0
$52$	0.348410	+	0.386948i	0.0483158	+	0.0536601i
$53$	1.07586	+	0.781661i	0.147781	+	0.107369i	0.659219	−	0.751951i	$-0.270887\pi$
$53$	1.07586	+	0.781661i	0.147781	+	0.107369i	−0.511438	+	0.859320i	$0.670887\pi$
$54$		0			0
$55$	3.77524	+	9.44110i	0.509053	+	1.27304i
$56$	−0.297663	−	2.83208i	−0.0397769	−	0.378452i
$57$		0			0
$58$	−3.12049	−	1.38933i	−0.409740	−	0.182428i
$59$	1.15888	−	1.28707i	0.150873	−	0.167562i	−0.662970	−	0.748646i	$-0.730705\pi$
$59$	1.15888	−	1.28707i	0.150873	−	0.167562i	0.813844	+	0.581084i	$0.197371\pi$
$60$		0			0
$61$	−2.52602	−	2.80543i	−0.323424	−	0.359199i	0.559404	−	0.828895i	$-0.311030\pi$
$61$	−2.52602	−	2.80543i	−0.323424	−	0.359199i	−0.882828	+	0.469696i	$0.844363\pi$
$62$	−3.32384	−	10.2297i	−0.422128	−	1.29918i
$63$		0			0
$64$	0.936638	−	2.88268i	0.117080	−	0.360334i
$65$	−1.34305	+	0.707962i	−0.166585	+	0.0878119i
$66$		0			0
$67$	−12.9879	−	5.78257i	−1.58672	−	0.706453i	−0.591702	−	0.806157i	$-0.701544\pi$
$67$	−12.9879	−	5.78257i	−1.58672	−	0.706453i	−0.995017	+	0.0997035i	$0.968211\pi$
$68$	0.822536	+	1.42467i	0.0997472	+	0.172767i
$69$		0			0
$70$	−5.11098	−	0.736948i	−0.610878	−	0.0880821i
$71$	10.9600	+	7.96294i	1.30072	+	0.945027i	0.999962	−	0.00867479i	$-0.00276131\pi$
$71$	10.9600	+	7.96294i	1.30072	+	0.945027i	0.300755	+	0.953701i	$0.402761\pi$
$72$		0			0
$73$	−1.83085	+	5.63478i	−0.214285	+	0.659501i	0.784919	+	0.619599i	$0.212705\pi$
$73$	−1.83085	+	5.63478i	−0.214285	+	0.659501i	−0.999204	+	0.0399023i	$0.987295\pi$
$74$	2.38477	−	4.13054i	0.277224	−	0.480166i
$75$		0			0
$76$	2.63935	+	4.57148i	0.302754	+	0.524385i
$77$	−6.17509	+	1.31256i	−0.703717	+	0.149580i
$78$		0			0
$79$	−8.20200	+	3.65176i	−0.922797	+	0.410856i	−0.812446	−	0.583037i	$-0.801864\pi$
$79$	−8.20200	+	3.65176i	−0.922797	+	0.410856i	−0.110351	+	0.993893i	$0.535198\pi$
$80$	−9.35740	−	5.89378i	−1.04619	−	0.658945i
$81$		0			0
$82$	−9.03682			−0.997950
$83$	1.89564	+	18.0358i	0.208074	+	1.97969i	0.200386	+	0.979717i	$0.435781\pi$
$83$	1.89564	+	18.0358i	0.208074	+	1.97969i	0.00768794	+	0.999970i	$0.497553\pi$
$84$		0			0
$85$	−4.61555	+	1.30565i	−0.500627	+	0.141617i
$86$	−1.99480	+	0.424009i	−0.215105	+	0.0457220i
$87$		0			0
$88$	−9.12328	−	1.93921i	−0.972545	−	0.206721i
$89$	−2.33361	+	7.18212i	−0.247363	+	0.761304i	0.747876	+	0.663838i	$0.231074\pi$
$89$	−2.33361	+	7.18212i	−0.247363	+	0.761304i	−0.995239	+	0.0974656i	$0.968926\pi$
$90$		0			0
$91$	−0.291288	−	0.896494i	−0.0305353	−	0.0939781i
$92$	−0.00858900	−	0.0817189i	−0.000895466	−	0.00851979i
$93$		0			0
$94$	17.9779	+	8.00428i	1.85428	+	0.825579i
$95$	−14.8103	+	4.18954i	−1.51951	+	0.429838i
$96$		0			0
$97$	9.93178	−	4.42191i	1.00842	−	0.448977i	0.165035	−	0.986288i	$-0.447226\pi$
$97$	9.93178	−	4.42191i	1.00842	−	0.448977i	0.843384	+	0.537311i	$0.180560\pi$
$98$	−2.60738	+	8.02469i	−0.263385	+	0.810616i
$99$		0			0
$100$	−2.77723	+	2.64382i	−0.277723	+	0.264382i
$101$	6.10657	−	10.5769i	0.607626	−	1.05244i	−0.384004	−	0.923331i	$-0.625455\pi$
$101$	6.10657	−	10.5769i	0.607626	−	1.05244i	0.991630	−	0.129108i	$-0.0412115\pi$
$102$		0			0
$103$	0.0887548	−	0.844445i	0.00874527	−	0.0832057i	−0.989279	−	0.146040i	$-0.953347\pi$
$103$	0.0887548	−	0.844445i	0.00874527	−	0.0832057i	0.998024	+	0.0628341i	$0.0200139\pi$
$104$	0.145574	−	1.38504i	0.0142747	−	0.135814i
$105$		0			0
$106$	0.231222	+	2.19993i	0.0224583	+	0.213677i
$107$	−19.0764			−1.84419			−0.922095	−	0.386964i	$-0.873524\pi$
$107$	−19.0764			−1.84419			−0.922095	+	0.386964i	$0.873524\pi$
$108$		0			0
$109$	4.05014	+	12.4651i	0.387933	+	1.19394i	0.934330	+	0.356409i	$0.115999\pi$
$109$	4.05014	+	12.4651i	0.387933	+	1.19394i	−0.546397	+	0.837526i	$0.684001\pi$
$110$	−7.46861	+	15.1749i	−0.712104	+	1.44687i
$111$		0			0
$112$	4.59438	−	5.10257i	0.434128	−	0.482148i
$113$	4.65919	−	5.17455i	0.438299	−	0.486781i	−0.483008	−	0.875616i	$-0.660456\pi$
$113$	4.65919	−	5.17455i	0.438299	−	0.486781i	0.921307	+	0.388835i	$0.127122\pi$
$114$		0			0
$115$	0.237134	+	0.0341922i	0.0221129	+	0.00318844i
$116$	−0.486642	−	1.49773i	−0.0451835	−	0.139061i
$117$		0			0
$118$	2.88087			0.265205
$119$	−0.311301	−	2.96183i	−0.0285369	−	0.271511i
$120$		0			0
$121$	−1.01156	+	9.62433i	−0.0919598	+	0.874939i
$122$	0.656382	−	6.24506i	0.0594260	−	0.565401i
$123$		0			0
$124$	2.47949	−	4.29460i	0.222665	−	0.385666i
$125$	−5.48598	−	9.74187i	−0.490681	−	0.871339i
$126$		0			0
$127$	6.85641	−	21.1019i	0.608408	−	1.87249i	0.137000	−	0.990571i	$-0.456254\pi$
$127$	6.85641	−	21.1019i	0.608408	−	1.87249i	0.471407	−	0.881916i	$-0.343746\pi$
$128$	12.1413	−	5.40566i	1.07315	−	0.477798i
$129$		0			0
$130$	−2.36999	−	0.872217i	−0.207862	−	0.0764985i
$131$	10.6170	+	4.72699i	0.927610	+	0.412999i	0.814223	−	0.580552i	$-0.197163\pi$
$131$	10.6170	+	4.72699i	0.927610	+	0.412999i	0.113387	+	0.993551i	$0.463830\pi$
$132$		0			0
$133$	−0.998901	−	9.50390i	−0.0866157	−	0.824093i
$134$	−7.30778	−	22.4910i	−0.631296	−	1.94293i
$135$		0			0
$136$	1.35968	−	4.18466i	0.116591	−	0.358832i
$137$	−16.2011	−	3.44364i	−1.38415	−	0.294210i	−0.545149	−	0.838339i	$-0.683527\pi$
$137$	−16.2011	−	3.44364i	−1.38415	−	0.294210i	−0.839002	+	0.544129i	$0.816860\pi$
$138$		0			0
$139$	16.4624	−	3.49920i	1.39633	−	0.296798i	0.552544	−	0.833484i	$-0.313657\pi$
$139$	16.4624	−	3.49920i	1.39633	−	0.296798i	0.843782	+	0.536686i	$0.180324\pi$
$140$	−1.32421	−	1.97845i	−0.111916	−	0.167209i
$141$		0			0
$142$	2.35551	+	22.4112i	0.197670	+	1.88070i
$143$	−3.08743			−0.258184
$144$		0			0
$145$	4.58172	−	0.303925i	0.380491	−	0.0252396i
$146$	−9.00319	+	4.00848i	−0.745109	+	0.331744i
$147$		0			0
$148$	2.15088	−	0.457183i	0.176801	−	0.0375802i
$149$	7.97992	+	13.8216i	0.653740	+	1.13231i	0.982208	+	0.187796i	$0.0601345\pi$
$149$	7.97992	+	13.8216i	0.653740	+	1.13231i	−0.328468	+	0.944515i	$0.606532\pi$
$150$		0			0
$151$	−4.20769	+	7.28793i	−0.342417	+	0.593084i	−0.984881	−	0.173232i	$-0.944579\pi$
$151$	−4.20769	+	7.28793i	−0.342417	+	0.593084i	0.642464	+	0.766316i	$0.277912\pi$
$152$	4.36292	−	13.4277i	0.353880	−	1.08913i
$153$		0			0
$154$	−8.49556	−	6.17239i	−0.684592	−	0.497385i
$155$	10.3652	+	10.0814i	0.832549	+	0.809757i
$156$		0			0
$157$	0.0425739	+	0.0737402i	0.00339777	+	0.00588511i	0.867719	−	0.497055i	$-0.165585\pi$
$157$	0.0425739	+	0.0737402i	0.00339777	+	0.00588511i	−0.864322	+	0.502940i	$0.832252\pi$
$158$	−13.6432	−	6.07433i	−1.08539	−	0.483248i
$159$		0			0
$160$	−1.56892	−	9.08771i	−0.124034	−	0.718446i
$161$	−0.0459676	+	0.141474i	−0.00362275	+	0.0111497i
$162$		0			0
$163$	3.81218	+	11.7327i	0.298593	+	0.918974i	0.981991	+	0.188928i	$0.0605013\pi$
$163$	3.81218	+	11.7327i	0.298593	+	0.918974i	−0.683398	+	0.730046i	$0.739499\pi$
$164$	−2.78780	−	3.09616i	−0.217690	−	0.241770i
$165$		0			0
$166$	−20.1850	+	22.4177i	−1.56666	+	1.73995i
$167$	6.11816	+	2.72398i	0.473437	+	0.210788i	0.629563	−	0.776949i	$-0.283234\pi$
$167$	6.11816	+	2.72398i	0.473437	+	0.210788i	−0.156126	+	0.987737i	$0.549901\pi$
$168$		0			0
$169$	1.31068	+	12.4703i	0.100822	+	0.959255i
$170$	−6.75121	−	4.25227i	−0.517794	−	0.326134i
$171$		0			0
$172$	−0.760656	−	0.552649i	−0.0579995	−	0.0421391i
$173$	−7.69463	−	8.54575i	−0.585012	−	0.649721i	0.375873	−	0.926671i	$-0.377343\pi$
$173$	−7.69463	−	8.54575i	−0.585012	−	0.649721i	−0.960884	+	0.276950i	$0.910676\pi$
$174$		0			0
$175$	6.53981	−	2.32747i	0.494363	−	0.175940i
$176$	−11.2445	−	19.4761i	−0.847588	−	1.46807i
$177$		0			0
$178$	−11.4755	+	5.10923i	−0.860127	+	0.382953i
$179$	3.97320	+	2.88670i	0.296971	+	0.215762i	0.726286	−	0.687393i	$-0.241245\pi$
$179$	3.97320	+	2.88670i	0.296971	+	0.215762i	−0.429315	+	0.903155i	$0.641245\pi$
$180$		0			0
$181$	−1.69167	+	1.22907i	−0.125741	+	0.0913562i	−0.648878	−	0.760892i	$-0.724762\pi$
$181$	−1.69167	+	1.22907i	−0.125741	+	0.0913562i	0.523137	+	0.852248i	$0.324762\pi$
$182$	0.783983	−	1.35790i	0.0581127	−	0.100654i
$183$		0			0
$184$	−0.147058	+	0.163324i	−0.0108412	+	0.0120404i
$185$	−0.246673	+	6.40685i	−0.0181358	+	0.471041i
$186$		0			0
$187$	−9.54128	−	2.02806i	−0.697727	−	0.148307i
$188$	2.80367	+	8.62880i	0.204478	+	0.629320i
$189$		0			0
$190$	−21.6632	−	13.6446i	−1.57161	−	0.989886i
$191$	10.0452	+	2.13518i	0.726846	+	0.154496i	0.556452	−	0.830880i	$-0.312162\pi$
$191$	10.0452	+	2.13518i	0.726846	+	0.154496i	0.170394	+	0.985376i	$0.445496\pi$
$192$		0			0
$193$	0.879316	+	1.52302i	0.0632945	+	0.109629i	0.895936	−	0.444183i	$-0.146506\pi$
$193$	0.879316	+	1.52302i	0.0632945	+	0.109629i	−0.832642	+	0.553812i	$0.813173\pi$
$194$	16.5205	+	7.35539i	1.18610	+	0.528086i
$195$		0			0
$196$	−3.55375	+	1.58223i	−0.253839	+	0.113017i
$197$	−1.28192	−	0.931373i	−0.0913333	−	0.0663576i	0.541181	−	0.840906i	$-0.317977\pi$
$197$	−1.28192	−	0.931373i	−0.0913333	−	0.0663576i	−0.632515	+	0.774548i	$0.717977\pi$
$198$		0			0
$199$	−4.83781			−0.342943			−0.171471	−	0.985189i	$-0.554852\pi$
$199$	−4.83781			−0.342943			−0.171471	+	0.985189i	$0.554852\pi$
$200$	10.2254	+	0.788557i	0.723047	+	0.0557594i
$201$		0			0
$202$	19.8713	−	4.22379i	1.39814	−	0.297184i
$203$	−0.298004	+	2.83532i	−0.0209158	+	0.199001i
$204$		0			0
$205$	10.7464	−	5.66475i	0.750560	−	0.395643i
$206$	1.14264	−	0.830178i	0.0796117	−	0.0578413i
$207$		0			0
$208$	2.71663	−	1.97375i	0.188365	−	0.136855i
$209$	−30.6160	−	6.50762i	−2.11775	−	0.450142i
$210$		0			0
$211$	4.19980	−	0.892696i	0.289126	−	0.0614557i	−0.0610653	−	0.998134i	$-0.519450\pi$
$211$	4.19980	−	0.892696i	0.289126	−	0.0614557i	0.350192	+	0.936678i	$0.386116\pi$
$212$	−0.682403	+	0.757885i	−0.0468676	+	0.0520518i
$213$		0			0
$214$	−21.2326	−	23.5812i	−1.45143	−	1.61198i
$215$	2.10638	−	1.75467i	0.143654	−	0.119667i
$216$		0			0
$217$	−7.26291	+	5.27682i	−0.493039	+	0.358214i
$218$	−10.9007	+	18.8805i	−0.738287	+	1.27875i
$219$		0			0
$220$	−7.50320	+	2.12250i	−0.505866	+	0.143099i
$221$	0.152243	−	1.44850i	0.0102410	−	0.0974367i
$222$		0			0
$223$	10.8453	+	12.0449i	0.726254	+	0.806587i	0.987321	−	0.158734i	$-0.0507411\pi$
$223$	10.8453	+	12.0449i	0.726254	+	0.806587i	−0.261067	+	0.965321i	$0.584074\pi$
$224$	5.72583			0.382573
$225$		0			0
$226$	11.5823			0.770443
$227$	−6.16408	−	6.84590i	−0.409124	−	0.454379i	0.503004	−	0.864284i	$-0.332228\pi$
$227$	−6.16408	−	6.84590i	−0.409124	−	0.454379i	−0.912128	+	0.409906i	$0.865562\pi$
$228$		0			0
$229$	0.857635	−	8.15985i	0.0566741	−	0.539218i	−0.928943	−	0.370223i	$-0.879281\pi$
$229$	0.857635	−	8.15985i	0.0566741	−	0.539218i	0.985617	−	0.168995i	$-0.0540521\pi$
$230$	0.221671	+	0.331189i	0.0146166	+	0.0218380i
$231$		0			0
$232$	−2.10604	+	3.64776i	−0.138268	+	0.239487i
$233$	6.70215	−	4.86940i	0.439073	−	0.319005i	−0.346194	−	0.938163i	$-0.612526\pi$
$233$	6.70215	−	4.86940i	0.439073	−	0.319005i	0.785266	+	0.619158i	$0.212526\pi$
$234$		0			0
$235$	−26.3964	+	1.75099i	−1.72191	+	0.114222i
$236$	0.888727	+	0.987032i	0.0578512	+	0.0642503i
$237$		0			0
$238$	3.31477	−	3.68142i	0.214864	−	0.238631i
$239$	1.05559	−	0.224373i	0.0682807	−	0.0145135i	−0.173645	−	0.984808i	$-0.555554\pi$
$239$	1.05559	−	0.224373i	0.0682807	−	0.0145135i	0.241925	+	0.970295i	$0.422221\pi$
$240$		0			0
$241$	24.5479	+	5.21783i	1.58127	+	0.336110i	0.913049	−	0.407851i	$-0.133722\pi$
$241$	24.5479	+	5.21783i	1.58127	+	0.336110i	0.668223	+	0.743961i	$0.267055\pi$
$242$	−13.0229	+	9.46173i	−0.837147	+	0.608223i
$243$		0			0
$244$	2.34215	−	1.70167i	0.149941	−	0.108938i
$245$	−1.92966	−	11.1772i	−0.123281	−	0.714086i
$246$		0			0
$247$	0.488517	−	4.64793i	0.0310836	−	0.295741i
$248$	−12.9737	+	2.75765i	−0.823833	+	0.175111i
$249$		0			0
$250$	5.93630	−	17.6244i	0.375444	−	1.11467i
$251$	23.1900			1.46374			0.731869	−	0.681445i	$-0.238648\pi$
$251$	23.1900			1.46374			0.731869	+	0.681445i	$0.238648\pi$
$252$		0			0
$253$	0.394169	+	0.286381i	0.0247812	+	0.0180046i
$254$	33.7163	−	15.0115i	2.11555	−	0.941903i
$255$		0			0
$256$	14.6579	+	6.52610i	0.916116	+	0.407881i
$257$	10.4244	+	18.0555i	0.650253	+	1.12627i	0.983061	+	0.183277i	$0.0586705\pi$
$257$	10.4244	+	18.0555i	0.650253	+	1.12627i	−0.332808	+	0.942995i	$0.607996\pi$
$258$		0			0
$259$	−3.89383	−	0.827659i	−0.241951	−	0.0514282i
$260$	−0.432291	−	1.08107i	−0.0268096	−	0.0670452i
$261$		0			0
$262$	5.97377	+	18.3854i	0.369061	+	1.13585i
$263$	−8.87330	−	1.88608i	−0.547151	−	0.116301i	−0.0739614	−	0.997261i	$-0.523564\pi$
$263$	−8.87330	−	1.88608i	−0.547151	−	0.116301i	−0.473190	+	0.880961i	$0.656897\pi$
$264$		0			0
$265$	−1.65400	−	2.47117i	−0.101604	−	0.151803i
$266$	10.6364	−	11.8129i	0.652159	−	0.724296i
$267$		0			0
$268$	5.45140	−	9.44209i	0.332997	−	0.576768i
$269$	−12.0005	+	8.71886i	−0.731683	+	0.531599i	−0.890095	−	0.455774i	$-0.849362\pi$
$269$	−12.0005	+	8.71886i	−0.731683	+	0.531599i	0.158413	+	0.987373i	$0.449362\pi$
$270$		0			0
$271$	6.34725	+	4.61155i	0.385568	+	0.280132i	0.763637	−	0.645646i	$-0.223412\pi$
$271$	6.34725	+	4.61155i	0.385568	+	0.280132i	−0.378069	+	0.925777i	$0.623412\pi$
$272$	9.69190	−	4.31511i	0.587658	−	0.261642i
$273$		0			0
$274$	−13.7754	−	23.8597i	−0.832203	−	1.44142i
$275$	−0.630957	−	22.7274i	−0.0380481	−	1.37051i
$276$		0			0
$277$	−14.8863	−	16.5329i	−0.894429	−	0.993364i	0.105571	−	0.994412i	$-0.466333\pi$
$277$	−14.8863	−	16.5329i	−0.894429	−	0.993364i	−0.999999	+	0.00104812i	$0.999666\pi$
$278$	22.6487	+	16.4552i	1.35838	+	0.986919i
$279$		0			0
$280$	−1.56255	+	6.17291i	−0.0933799	+	0.368902i
$281$	1.06166	+	10.1010i	0.0633334	+	0.602577i	0.979453	+	0.201672i	$0.0646376\pi$
$281$	1.06166	+	10.1010i	0.0633334	+	0.602577i	−0.916120	+	0.400905i	$0.868696\pi$
$282$		0			0
$283$	0.696855	+	0.310260i	0.0414237	+	0.0184430i	0.427344	−	0.904089i	$-0.359449\pi$
$283$	0.696855	+	0.310260i	0.0414237	+	0.0184430i	−0.385920	+	0.922532i	$0.626116\pi$
$284$	−6.95177	+	7.72073i	−0.412512	+	0.458141i
$285$		0			0
$286$	−3.43640	−	3.81650i	−0.203198	−	0.225675i
$287$	2.33074	+	7.17328i	0.137579	+	0.423425i
$288$		0			0
$289$	−3.83131	+	11.7916i	−0.225371	+	0.693622i
$290$	5.47528	+	5.32538i	0.321519	+	0.312717i
$291$		0			0
$292$	−4.15079	−	1.84805i	−0.242907	−	0.108149i
$293$	−3.29507	−	5.70722i	−0.192500	−	0.333419i	0.753578	−	0.657358i	$-0.228326\pi$
$293$	−3.29507	−	5.70722i	−0.192500	−	0.333419i	−0.946078	+	0.323939i	$0.894993\pi$
$294$		0			0
$295$	−3.42586	+	1.80588i	−0.199461	+	0.105142i
$296$	−4.75815	−	3.45699i	−0.276562	−	0.200934i
$297$		0			0
$298$	−8.20364	+	25.2482i	−0.475224	+	1.46259i
$299$	−0.0363745	+	0.0630025i	−0.00210359	+	0.00364353i
$300$		0			0
$301$	0.851063	+	1.47408i	0.0490545	+	0.0849648i
$302$	−13.6922	+	2.91037i	−0.787899	+	0.167473i
$303$		0			0
$304$	31.0993	−	13.8463i	1.78367	−	0.794139i
$305$	3.13418	+	7.83794i	0.179462	+	0.448799i
$306$		0			0
$307$	20.2069			1.15327			0.576634	−	0.817002i	$-0.304366\pi$
$307$	20.2069			1.15327			0.576634	+	0.817002i	$0.304366\pi$
$308$	−0.506062	−	4.81486i	−0.0288356	−	0.274352i
$309$		0			0
$310$	−0.925333	+	24.0337i	−0.0525554	+	1.36502i
$311$	17.4845	−	3.71644i	0.991455	−	0.210740i	0.316494	−	0.948594i	$-0.397494\pi$
$311$	17.4845	−	3.71644i	0.991455	−	0.210740i	0.674960	+	0.737854i	$0.264161\pi$
$312$		0			0
$313$	−17.9489	−	3.81515i	−1.01453	−	0.215645i	−0.329496	−	0.944157i	$-0.606879\pi$
$313$	−17.9489	−	3.81515i	−1.01453	−	0.215645i	−0.685033	+	0.728512i	$0.740212\pi$
$314$	−0.0437675	+	0.134702i	−0.00246994	+	0.00760170i
$315$		0			0
$316$	−2.12766	−	6.54826i	−0.119690	−	0.368369i
$317$	0.331660	+	3.15554i	0.0186279	+	0.177233i	0.999880	−	0.0154964i	$-0.00493285\pi$
$317$	0.331660	+	3.15554i	0.0186279	+	0.177233i	−0.981252	+	0.192729i	$0.938266\pi$
$318$		0			0
$319$	8.53049	+	3.79802i	0.477616	+	0.212648i
$320$	−4.19176	+	5.32585i	−0.234327	+	0.297724i
$321$		0			0
$322$	−0.226045	+	0.100642i	−0.0125970	+	0.00560855i
$323$	4.56282	−	14.0429i	0.253882	−	0.781369i
$324$		0			0
$325$	3.36509	−	0.448416i	0.186662	−	0.0248736i
$326$	−10.2602	+	17.7712i	−0.568261	+	0.984256i
$327$		0			0
$328$	−1.16481	+	11.0824i	−0.0643157	+	0.611923i
$329$	1.71688	−	16.3350i	0.0946546	−	0.900579i
$330$		0			0
$331$	1.54265	+	14.6773i	0.0847916	+	0.806738i	0.951443	+	0.307824i	$0.0996009\pi$
$331$	1.54265	+	14.6773i	0.0847916	+	0.806738i	−0.866652	+	0.498914i	$0.833732\pi$
$332$	−13.9076			−0.763278
$333$		0			0
$334$	3.44246	+	10.5948i	0.188363	+	0.579721i
$335$	22.7888	+	22.1649i	1.24509	+	1.21100i
$336$		0			0
$337$	−8.16234	+	9.06519i	−0.444631	+	0.493813i	−0.923244	−	0.384213i	$-0.874473\pi$
$337$	−8.16234	+	9.06519i	−0.444631	+	0.493813i	0.478614	+	0.878026i	$0.341139\pi$
$338$	−13.9563	+	15.5000i	−0.759121	+	0.843089i
$339$		0			0
$340$	−0.625806	−	3.62487i	−0.0339391	−	0.196586i
$341$	9.08639	+	27.9650i	0.492056	+	1.51439i
$342$		0			0
$343$	16.7606			0.904989
$344$	0.262866	+	2.50100i	0.0141728	+	0.134845i
$345$		0			0
$346$	1.99943	−	19.0233i	0.107490	−	1.02270i
$347$	2.27230	−	21.6195i	0.121983	−	1.16059i	−0.746677	−	0.665187i	$-0.768352\pi$
$347$	2.27230	−	21.6195i	0.121983	−	1.16059i	0.868661	−	0.495408i	$-0.164981\pi$
$348$		0			0
$349$	5.54554	−	9.60516i	0.296846	−	0.514152i	−0.678567	−	0.734539i	$-0.737399\pi$
$349$	5.54554	−	9.60516i	0.296846	−	0.514152i	0.975413	+	0.220387i	$0.0707319\pi$
$350$	10.1561	+	5.49361i	0.542866	+	0.293646i
$351$		0			0
$352$	5.79531	−	17.8361i	0.308891	−	0.950669i
$353$	−4.63276	+	2.06264i	−0.246577	+	0.109783i	−0.526304	−	0.850296i	$-0.676423\pi$
$353$	−4.63276	+	2.06264i	−0.246577	+	0.109783i	0.279727	+	0.960080i	$0.409756\pi$
$354$		0			0
$355$	−16.8496	−	25.1743i	−0.894284	−	1.33611i
$356$	−5.29063	−	2.35554i	−0.280403	−	0.124843i
$357$		0			0
$358$	0.853912	+	8.12443i	0.0451306	+	0.429389i
$359$	9.46581	+	29.1328i	0.499586	+	1.53757i	0.809685	+	0.586864i	$0.199638\pi$
$359$	9.46581	+	29.1328i	0.499586	+	1.53757i	−0.310099	+	0.950704i	$0.600362\pi$
$360$		0			0
$361$	8.76981	−	26.9907i	0.461569	−	1.42056i
$362$	−3.40219	−	0.723158i	−0.178815	−	0.0380083i
$363$		0			0
$364$	0.707091	−	0.150297i	0.0370617	−	0.00787770i
$365$	8.19366	−	10.4105i	0.428876	−	0.544908i
$366$		0			0
$367$	1.67022	+	15.8911i	0.0871849	+	0.829509i	0.947502	+	0.319750i	$0.103599\pi$
$367$	1.67022	+	15.8911i	0.0871849	+	0.829509i	−0.860317	+	0.509759i	$0.829735\pi$
$368$	−0.529910			−0.0276235
$369$		0			0
$370$	−8.19434	+	6.82608i	−0.426003	+	0.354871i
$371$	1.68664	−	0.750939i	0.0875658	−	0.0389868i
$372$		0			0
$373$	−11.0182	+	2.34198i	−0.570499	+	0.121263i	−0.484124	−	0.874999i	$-0.660862\pi$
$373$	−11.0182	+	2.34198i	−0.570499	+	0.121263i	−0.0863750	+	0.996263i	$0.527528\pi$
$374$	−8.11274	−	14.0517i	−0.419500	−	0.726595i
$375$		0			0
$376$	12.1334	−	21.0157i	0.625733	−	1.08380i
$377$	−0.430852	+	1.32603i	−0.0221900	+	0.0682938i
$378$		0			0
$379$	−17.8996	−	13.0048i	−0.919440	−	0.668012i	0.0239446	−	0.999713i	$-0.492377\pi$
$379$	−17.8996	−	13.0048i	−0.919440	−	0.668012i	−0.943385	+	0.331701i	$0.892377\pi$
$380$	−2.00808	−	11.6314i	−0.103012	−	0.596681i
$381$		0			0
$382$	8.54123	+	14.7938i	0.437007	+	0.756919i
$383$	−5.77940	−	2.57315i	−0.295313	−	0.131482i	0.253732	−	0.967275i	$-0.418342\pi$
$383$	−5.77940	−	2.57315i	−0.295313	−	0.131482i	−0.549045	+	0.835793i	$0.685009\pi$
$384$		0			0
$385$	13.9719	+	2.01460i	0.712074	+	0.102673i
$386$	−0.903967	+	2.78213i	−0.0460107	+	0.141606i
$387$		0			0
$388$	2.57638	+	7.92927i	0.130796	+	0.402548i
$389$	−22.1352	−	24.5837i	−1.12230	−	1.24644i	−0.965947	−	0.258740i	$-0.916693\pi$
$389$	−22.1352	−	24.5837i	−1.12230	−	1.24644i	−0.156354	−	0.987701i	$-0.549974\pi$
$390$		0			0
$391$	−0.153796	+	0.170807i	−0.00777777	+	0.00863809i
$392$	9.50508	+	4.23193i	0.480079	+	0.213745i
$393$		0			0
$394$	−0.275508	−	2.62129i	−0.0138799	−	0.132059i
$395$	20.0319	−	1.32880i	1.00791	−	0.0668591i
$396$		0			0
$397$	22.9141	+	16.6480i	1.15002	+	0.835541i	0.988484	−	0.151325i	$-0.0483539\pi$
$397$	22.9141	+	16.6480i	1.15002	+	0.835541i	0.161540	+	0.986866i	$0.448354\pi$
$398$	−5.38462	−	5.98022i	−0.269907	−	0.299762i
$399$		0			0
$400$	15.0845	+	19.5945i	0.754225	+	0.979727i
$401$	4.98614	+	8.63625i	0.248996	+	0.431274i	0.963248	−	0.268615i	$-0.0865660\pi$
$401$	4.98614	+	8.63625i	0.248996	+	0.431274i	−0.714251	+	0.699889i	$0.753233\pi$
$402$		0			0
$403$	−4.01089	+	1.78577i	−0.199797	+	0.0889553i
$404$	7.57731	+	5.50524i	0.376985	+	0.273896i
$405$		0			0
$406$	−3.83655	+	2.78742i	−0.190405	+	0.138337i
$407$	−6.51926	+	11.2917i	−0.323148	+	0.559708i
$408$		0			0
$409$	−6.46434	+	7.17938i	−0.319641	+	0.354997i	−0.881456	−	0.472265i	$-0.843436\pi$
$409$	−6.46434	+	7.17938i	−0.319641	+	0.354997i	0.561815	+	0.827263i	$0.310103\pi$
$410$	18.9635	+	6.97904i	0.936539	+	0.344670i
$411$		0			0
$412$	0.636930	+	0.135384i	0.0313793	+	0.00666988i
$413$	−0.743021	−	2.28678i	−0.0365617	−	0.112525i
$414$		0			0
$415$	9.95092	−	39.3116i	0.488471	−	1.92973i
$416$	2.73905	+	0.582204i	0.134293	+	0.0285449i
$417$		0			0
$418$	−26.0321	−	45.0889i	−1.27327	−	2.20537i
$419$	11.5515	+	5.14308i	0.564330	+	0.251256i	0.669014	−	0.743250i	$-0.266717\pi$
$419$	11.5515	+	5.14308i	0.564330	+	0.251256i	−0.104684	+	0.994506i	$0.533383\pi$
$420$		0			0
$421$	−20.9466	+	9.32602i	−1.02087	+	0.454522i	−0.847760	−	0.530380i	$-0.822049\pi$
$421$	−20.9466	+	9.32602i	−1.02087	+	0.454522i	−0.173114	+	0.984902i	$0.555383\pi$
$422$	5.77800	+	4.19797i	0.281269	+	0.204354i
$423$		0			0
$424$	2.72771			0.132470
$425$	10.6939	+	0.824687i	0.518732	+	0.0400032i
$426$		0			0
$427$	−5.12652	+	1.08968i	−0.248090	+	0.0527331i
$428$	1.52919	−	14.5493i	0.0739163	−	0.703267i
$429$		0			0
$430$	4.51349	+	0.650797i	0.217660	+	0.0313842i
$431$	−10.6124	+	7.71039i	−0.511183	+	0.371397i	−0.813272	−	0.581883i	$-0.802316\pi$
$431$	−10.6124	+	7.71039i	−0.511183	+	0.371397i	0.302089	+	0.953280i	$0.402316\pi$
$432$		0			0
$433$	−19.0904	+	13.8700i	−0.917425	+	0.666548i	−0.942882	−	0.333128i	$-0.891896\pi$
$433$	−19.0904	+	13.8700i	−0.917425	+	0.666548i	0.0254569	+	0.999676i	$0.491896\pi$
$434$	−14.6067	−	3.10476i	−0.701146	−	0.149033i
$435$		0			0
$436$	−9.83156	+	2.08976i	−0.470846	+	0.100081i
$437$	−0.493498	+	0.548085i	−0.0236072	+	0.0262184i
$438$		0			0
$439$	−5.42383	−	6.02378i	−0.258865	−	0.287499i	0.599677	−	0.800242i	$-0.295296\pi$
$439$	−5.42383	−	6.02378i	−0.258865	−	0.287499i	−0.858542	+	0.512743i	$0.828629\pi$
$440$	17.6473	+	11.1152i	0.841301	+	0.529896i
$441$		0			0
$442$	1.96001	−	1.42403i	0.0932280	−	0.0677341i
$443$	0.254259	−	0.440389i	0.0120802	−	0.0209235i	−0.859922	−	0.510425i	$-0.829488\pi$
$443$	0.254259	−	0.440389i	0.0120802	−	0.0209235i	0.872002	+	0.489502i	$0.162821\pi$
$444$		0			0
$445$	10.4437	−	13.2692i	0.495078	−	0.629022i
$446$	−2.81813	+	26.8127i	−0.133442	+	1.26962i
$447$		0			0
$448$	−2.81574	−	3.12719i	−0.133031	−	0.147746i
$449$	−7.22605			−0.341018			−0.170509	−	0.985356i	$-0.554541\pi$
$449$	−7.22605			−0.341018			−0.170509	+	0.985356i	$0.554541\pi$
$450$		0			0
$451$	24.7040			1.16327
$452$	3.57306	+	3.96829i	0.168063	+	0.186652i
$453$		0			0
$454$	1.60172	−	15.2394i	0.0751726	−	0.715219i
$455$	−0.0810927	+	2.10622i	−0.00380168	+	0.0987412i
$456$		0			0
$457$	−7.94049	+	13.7533i	−0.371441	+	0.643354i	−0.989787	−	0.142551i	$-0.954469\pi$
$457$	−7.94049	+	13.7533i	−0.371441	+	0.643354i	0.618347	+	0.785905i	$0.287803\pi$
$458$	11.0413	−	8.02199i	0.515927	−	0.374843i
$459$		0			0
$460$	−0.0450869	+	0.178118i	−0.00210219	+	0.00830478i
$461$	−22.0858	−	24.5288i	−1.02864	−	1.14242i	−0.989697	−	0.143179i	$-0.954267\pi$
$461$	−22.0858	−	24.5288i	−1.02864	−	1.14242i	−0.0389435	−	0.999241i	$-0.512399\pi$
$462$		0			0
$463$	12.3216	−	13.6845i	0.572632	−	0.635972i	−0.385360	−	0.922766i	$-0.625923\pi$
$463$	12.3216	−	13.6845i	0.572632	−	0.635972i	0.957992	+	0.286794i	$0.0925895\pi$
$464$	−9.93402	+	2.11154i	−0.461175	+	0.0980258i
$465$		0			0
$466$	13.4790	+	2.86504i	0.624401	+	0.132721i
$467$	14.9196	−	10.8397i	0.690398	−	0.501603i	−0.186393	−	0.982475i	$-0.559680\pi$
$467$	14.9196	−	10.8397i	0.690398	−	0.501603i	0.876791	+	0.480872i	$0.159680\pi$
$468$		0			0
$469$	−15.9682	+	11.6016i	−0.737344	+	0.535712i
$470$	−31.5445	−	30.6809i	−1.45504	−	1.41520i
$471$		0			0
$472$	0.371331	−	3.53298i	0.0170919	−	0.162618i
$473$	5.45321	−	1.15911i	0.250739	−	0.0532962i
$474$		0			0
$475$	34.3146	+	2.64625i	1.57446	+	0.121418i
$476$	2.28390			0.104682
$477$		0			0
$478$	1.45226	+	1.05513i	0.0664250	+	0.0482606i
$479$	21.0863	−	9.38822i	0.963457	−	0.428959i	0.136137	−	0.990690i	$-0.456531\pi$
$479$	21.0863	−	9.38822i	0.963457	−	0.428959i	0.827320	+	0.561731i	$0.189865\pi$
$480$		0			0
$481$	−1.77853	−	0.791851i	−0.0810938	−	0.0361053i
$482$	20.8726	+	36.1524i	0.950720	+	1.64670i
$483$		0			0
$484$	−7.25923	−	1.54300i	−0.329965	−	0.0701363i
$485$	−24.2565	+	1.60904i	−1.10143	+	0.0730627i
$486$		0			0
$487$	−3.52725	−	10.8558i	−0.159835	−	0.491921i	0.838784	−	0.544465i	$-0.183267\pi$
$487$	−3.52725	−	10.8558i	−0.159835	−	0.491921i	−0.998619	+	0.0525435i	$0.983267\pi$
$488$	−7.57408	−	1.60992i	−0.342863	−	0.0728777i
$489$		0			0
$490$	11.6689	−	14.8259i	0.527146	−	0.669766i
$491$	26.6271	−	29.5724i	1.20167	−	1.33459i	0.273748	−	0.961801i	$-0.411737\pi$
$491$	26.6271	−	29.5724i	1.20167	−	1.33459i	0.927918	−	0.372784i	$-0.121597\pi$
$492$		0			0
$493$	−2.20253	+	3.81489i	−0.0991969	+	0.171814i
$494$	6.28925	−	4.56941i	0.282967	−	0.205587i
$495$		0			0
$496$	−25.8728	−	18.7977i	−1.16172	−	0.844041i
$497$	17.1821	−	7.64996i	0.770723	−	0.343148i
$498$		0			0
$499$	18.1188	+	31.3826i	0.811107	+	1.40488i	0.912090	+	0.409990i	$0.134468\pi$
$499$	18.1188	+	31.3826i	0.811107	+	1.40488i	−0.100983	+	0.994888i	$0.532199\pi$
$500$	7.86973	−	3.40315i	0.351945	−	0.152193i
$501$		0			0
$502$	25.8111	+	28.6662i	1.15201	+	1.27943i
$503$	−26.1554	−	19.0030i	−1.16621	−	0.847302i	−0.175661	−	0.984451i	$-0.556206\pi$
$503$	−26.1554	−	19.0030i	−1.16621	−	0.847302i	−0.990550	+	0.137149i	$0.956206\pi$
$504$		0			0
$505$	−20.9829	+	17.4792i	−0.933725	+	0.777816i
$506$	0.0847140	+	0.806000i	0.00376600	+	0.0358311i
$507$		0			0
$508$	15.5444	+	6.92082i	0.689672	+	0.307062i
$509$	0.180712	−	0.200701i	0.00800991	−	0.00889590i	−0.739127	−	0.673567i	$-0.764761\pi$
$509$	0.180712	−	0.200701i	0.00800991	−	0.00889590i	0.747136	+	0.664671i	$0.231428\pi$
$510$		0			0
$511$	5.50393	+	6.11274i	0.243480	+	0.270411i
$512$	0.0335504	+	0.103257i	0.00148273	+	0.00456337i
$513$		0			0
$514$	−10.7166	+	32.9823i	−0.472689	+	1.45479i
$515$	−0.838405	+	1.70350i	−0.0369445	+	0.0750651i
$516$		0			0
$517$	−49.1463	−	21.8814i	−2.16145	−	0.962341i
$518$	−3.31084	−	5.73454i	−0.145470	−	0.251961i
$519$		0			0
$520$	−1.37513	+	2.79404i	−0.0603036	+	0.122527i
$521$	−22.4017	−	16.2758i	−0.981435	−	0.713054i	−0.0234061	−	0.999726i	$-0.507451\pi$
$521$	−22.4017	−	16.2758i	−0.981435	−	0.713054i	−0.958029	+	0.286672i	$0.907451\pi$
$522$		0			0
$523$	11.9194	−	36.6841i	0.521198	−	1.60408i	−0.250515	−	0.968113i	$-0.580600\pi$
$523$	11.9194	−	36.6841i	0.521198	−	1.60408i	0.771713	−	0.635971i	$-0.219400\pi$
$524$	−4.45627	+	7.71848i	−0.194673	+	0.337183i
$525$		0			0
$526$	−7.54477	−	13.0679i	−0.328968	−	0.569789i
$527$	−13.5682	+	2.88400i	−0.591038	+	0.125629i
$528$		0			0
$529$	−21.0011	+	9.35027i	−0.913089	+	0.406534i
$530$	1.21377	−	4.79506i	0.0527229	−	0.208284i
$531$		0			0
$532$	7.32855			0.317733
$533$	0.385571	+	3.66846i	0.0167009	+	0.158899i
$534$		0			0
$535$	40.0313	+	14.7325i	1.73070	+	0.636943i
$536$	−28.5240	+	6.06297i	−1.23205	+	0.261880i
$537$		0			0
$538$	−24.1347	−	5.12998i	−1.04052	−	0.221169i
$539$	7.12781	−	21.9371i	0.307016	−	0.944900i
$540$		0			0
$541$	−9.26487	−	28.5143i	−0.398328	−	1.22593i	−0.926339	−	0.376690i	$-0.877062\pi$
$541$	−9.26487	−	28.5143i	−0.398328	−	1.22593i	0.528011	−	0.849237i	$-0.322938\pi$
$542$	1.36414	+	12.9789i	0.0585948	+	0.557492i
$543$		0			0
$544$	8.08224	+	3.59845i	0.346523	+	0.154282i
$545$	1.12753	−	29.2854i	0.0482981	−	1.25445i
$546$		0			0
$547$	5.24843	−	2.33675i	0.224407	−	0.0999123i	−0.291454	−	0.956585i	$-0.594139\pi$
$547$	5.24843	−	2.33675i	0.224407	−	0.0999123i	0.515860	+	0.856673i	$0.327472\pi$
$548$	3.92511	−	12.0802i	0.167672	−	0.516042i
$549$		0			0
$550$	27.3921	−	26.0762i	1.16800	−	1.11189i
$551$	−7.06745	+	12.2412i	−0.301083	+	0.521492i
$552$		0			0
$553$	−1.30291	+	12.3964i	−0.0554055	+	0.527148i
$554$	3.86816	−	36.8031i	0.164343	−	1.56361i
$555$		0			0
$556$	1.34913	+	12.8361i	0.0572160	+	0.544373i
$557$	13.8510			0.586887			0.293444	−	0.955976i	$-0.405199\pi$
$557$	13.8510			0.586887			0.293444	+	0.955976i	$0.405199\pi$
$558$		0			0
$559$	0.257236	+	0.791691i	0.0108799	+	0.0334850i
$560$	−13.5818	+	7.15940i	−0.573936	+	0.302540i
$561$		0			0
$562$	−11.3047	+	12.5551i	−0.476859	+	0.529606i
$563$	19.9405	−	22.1462i	0.840393	−	0.933351i	−0.158144	−	0.987416i	$-0.550551\pi$
$563$	19.9405	−	22.1462i	0.840393	−	0.933351i	0.998537	+	0.0540647i	$0.0172177\pi$
$564$		0			0
$565$	−13.7734	+	7.26039i	−0.579452	+	0.305447i
$566$	0.392094	+	1.20674i	0.0164809	+	0.0507231i
$567$		0			0
$568$	27.7878			1.16595
$569$	1.71235	+	16.2919i	0.0717853	+	0.682991i	0.969945	+	0.243323i	$0.0782374\pi$
$569$	1.71235	+	16.2919i	0.0717853	+	0.682991i	−0.898160	+	0.439669i	$0.855096\pi$
$570$		0			0
$571$	0.540001	−	5.13777i	0.0225983	−	0.215009i	−0.977395	−	0.211420i	$-0.932191\pi$
$571$	0.540001	−	5.13777i	0.0225983	−	0.215009i	0.999994	−	0.00358843i	$-0.00114223\pi$
$572$	0.247492	−	2.35473i	0.0103482	−	0.0984562i
$573$		0			0
$574$	−6.27303	+	10.8652i	−0.261831	+	0.453505i
$575$	−0.471213	−	0.254888i	−0.0196509	−	0.0106295i
$576$		0			0
$577$	4.99821	−	15.3829i	0.208078	−	0.640399i	−0.791495	−	0.611176i	$-0.790697\pi$
$577$	4.99821	−	15.3829i	0.208078	−	0.640399i	0.999573	−	0.0292230i	$-0.00930328\pi$
$578$	−18.8404	+	8.38830i	−0.783659	+	0.348907i
$579$		0			0
$580$	−0.135478	+	3.51876i	−0.00562540	+	0.146109i
$581$	23.0008	+	10.2406i	0.954234	+	0.424852i
$582$		0			0
$583$	−0.632094	−	6.01397i	−0.0261787	−	0.249073i
$584$	3.75536	+	11.5578i	0.155398	+	0.478266i
$585$		0			0
$586$	3.38744	−	10.4255i	0.139934	−	0.430672i
$587$	−27.4905	−	5.84328i	−1.13465	−	0.241178i	−0.397959	−	0.917403i	$-0.630281\pi$
$587$	−27.4905	−	5.84328i	−1.13465	−	0.241178i	−0.736695	+	0.676225i	$0.763615\pi$
$588$		0			0
$589$	−43.5374	+	9.25416i	−1.79393	+	0.381311i
$590$	−6.04541	−	2.22486i	−0.248885	−	0.0915961i
$591$		0			0
$592$	−1.48231	−	14.1033i	−0.0609226	−	0.579640i
$593$	−3.80524			−0.156262			−0.0781312	−	0.996943i	$-0.524895\pi$
$593$	−3.80524			−0.156262			−0.0781312	+	0.996943i	$0.524895\pi$
$594$		0			0
$595$	−1.63414	+	6.45573i	−0.0669931	+	0.264659i
$596$	−11.1812	+	4.97820i	−0.458000	+	0.203915i
$597$		0			0
$598$	−0.118366	+	0.0251595i	−0.00484035	+	0.00102885i
$599$	−17.5681	−	30.4289i	−0.717813	−	1.24329i	−0.961864	−	0.273527i	$-0.911810\pi$
$599$	−17.5681	−	30.4289i	−0.717813	−	1.24329i	0.244051	−	0.969762i	$-0.421524\pi$
$600$		0			0
$601$	−10.6092	+	18.3758i	−0.432760	+	0.749563i	−0.997110	−	0.0759732i	$-0.975794\pi$
$601$	−10.6092	+	18.3758i	−0.432760	+	0.749563i	0.564350	+	0.825536i	$0.309127\pi$
$602$	−0.874923	+	2.69274i	−0.0356592	+	0.109748i
$603$		0			0
$604$	−5.22110	−	3.79335i	−0.212443	−	0.154349i
$605$	9.55549	−	19.4151i	0.388486	−	0.789337i
$606$		0			0
$607$	−7.55362	−	13.0833i	−0.306592	−	0.531033i	0.671023	−	0.741437i	$-0.265855\pi$
$607$	−7.55362	−	13.0833i	−0.306592	−	0.531033i	−0.977615	+	0.210404i	$0.932522\pi$
$608$	25.9342	+	11.5467i	1.05177	+	0.468279i
$609$		0			0
$610$	−6.20039	+	12.5981i	−0.251046	+	0.510084i
$611$	2.48225	−	7.63958i	0.100421	−	0.309064i
$612$		0			0
$613$	−0.267857	−	0.824379i	−0.0108186	−	0.0332963i	0.945501	−	0.325618i	$-0.105572\pi$
$613$	−0.267857	−	0.824379i	−0.0108186	−	0.0332963i	−0.956320	+	0.292321i	$0.905572\pi$
$614$	22.4909	+	24.9786i	0.907657	+	1.00806i
$615$		0			0
$616$	−8.66461	+	9.62302i	−0.349107	+	0.387723i
$617$	−18.1546	−	8.08293i	−0.730875	−	0.325407i	0.00733880	−	0.999973i	$-0.497664\pi$
$617$	−18.1546	−	8.08293i	−0.730875	−	0.325407i	−0.738214	+	0.674566i	$0.764331\pi$
$618$		0			0
$619$	−1.87214	−	17.8122i	−0.0752477	−	0.715934i	−0.965489	−	0.260445i	$-0.916131\pi$
$619$	−1.87214	−	17.8122i	−0.0752477	−	0.715934i	0.890241	−	0.455490i	$-0.150536\pi$
$620$	−8.51980	+	7.09720i	−0.342163	+	0.285030i
$621$		0			0
$622$	24.0548	+	17.4768i	0.964510	+	0.700757i
$623$	7.01535	+	7.79133i	0.281064	+	0.312153i
$624$		0			0
$625$	3.98862	+	24.6798i	0.159545	+	0.987191i
$626$	−15.2615	−	26.4337i	−0.609973	−	1.05650i
$627$		0			0
$628$	−0.0596532	+	0.0265593i	−0.00238042	+	0.00105983i
$629$	−4.97615	−	3.61538i	−0.198412	−	0.144155i
$630$		0			0
$631$	−27.5034	+	19.9824i	−1.09489	+	0.795487i	−0.980219	−	0.197916i	$-0.936583\pi$
$631$	−27.5034	+	19.9824i	−1.09489	+	0.795487i	−0.114675	+	0.993403i	$0.536583\pi$
$632$	−9.20786	+	15.9485i	−0.366269	+	0.634396i
$633$		0			0
$634$	−3.53155	+	3.92218i	−0.140256	+	0.155770i
$635$	−30.6847	+	38.9864i	−1.21768	+	1.54713i
$636$		0			0
$637$	3.36884	+	0.716068i	0.133478	+	0.0283717i
$638$	4.79979	+	14.7722i	0.190025	+	0.584838i
$639$		0			0
$640$	−29.6529	+	1.96701i	−1.17213	+	0.0777527i
$641$	−12.4589	−	2.64822i	−0.492097	−	0.104599i	−0.0448223	−	0.998995i	$-0.514272\pi$
$641$	−12.4589	−	2.64822i	−0.492097	−	0.104599i	−0.447275	+	0.894396i	$0.647606\pi$
$642$		0			0
$643$	9.31365	+	16.1317i	0.367295	+	0.636173i	0.989142	−	0.146966i	$-0.0469507\pi$
$643$	9.31365	+	16.1317i	0.367295	+	0.636173i	−0.621847	+	0.783139i	$0.713617\pi$
$644$	−0.104215	−	0.0463995i	−0.00410664	−	0.00182840i
$645$		0			0
$646$	22.4376	−	9.98987i	0.882796	−	0.393046i
$647$	2.58476	+	1.87794i	0.101617	+	0.0738294i	0.637434	−	0.770505i	$-0.279996\pi$
$647$	2.58476	+	1.87794i	0.101617	+	0.0738294i	−0.535816	+	0.844335i	$0.679996\pi$
$648$		0			0
$649$	−7.87544			−0.309138
$650$	4.29975	+	3.66064i	0.168650	+	0.143582i
$651$		0			0
$652$	−9.25391	+	1.96698i	−0.362411	+	0.0770329i
$653$	−0.528615	+	5.02943i	−0.0206863	+	0.196817i	−0.999984	−	0.00560700i	$-0.998215\pi$
$653$	−0.528615	+	5.02943i	−0.0206863	+	0.196817i	0.979298	+	0.202424i	$0.0648819\pi$
$654$		0			0
$655$	−18.6288	−	18.1188i	−0.727888	−	0.707960i
$656$	−21.7371	+	15.7929i	−0.848691	+	0.616610i
$657$		0			0
$658$	22.1034	−	16.0590i	0.861679	−	0.626046i
$659$	1.39674	+	0.296887i	0.0544094	+	0.0115651i	0.235036	−	0.971987i	$-0.424479\pi$
$659$	1.39674	+	0.296887i	0.0544094	+	0.0115651i	−0.180627	+	0.983552i	$0.557813\pi$
$660$		0			0
$661$	4.54628	−	0.966342i	0.176830	−	0.0375863i	−0.118646	−	0.992937i	$-0.537855\pi$
$661$	4.54628	−	0.966342i	0.176830	−	0.0375863i	0.295475	+	0.955350i	$0.404522\pi$
$662$	−16.4263	+	18.2432i	−0.638425	+	0.709042i
$663$		0			0
$664$	24.8904	+	27.6436i	0.965934	+	1.07278i
$665$	−5.24360	+	20.7151i	−0.203338	+	0.803296i
$666$		0			0
$667$	0.178005	−	0.129328i	0.00689238	−	0.00500761i
$668$	−2.56797	+	4.44786i	−0.0993579	+	0.172093i
$669$		0			0
$670$	−2.03444	+	52.8404i	−0.0785971	+	2.04140i
$671$	−1.79436	+	17.0722i	−0.0692703	+	0.659063i
$672$		0			0
$673$	12.5961	+	13.9894i	0.485546	+	0.539253i	0.935280	−	0.353909i	$-0.115148\pi$
$673$	12.5961	+	13.9894i	0.485546	+	0.539253i	−0.449734	+	0.893163i	$0.648481\pi$
$674$	−20.2908			−0.781572
$675$		0			0
$676$	−9.61597			−0.369845
$677$	6.63373	+	7.36751i	0.254955	+	0.283156i	0.857012	−	0.515297i	$-0.172318\pi$
$677$	6.63373	+	7.36751i	0.254955	+	0.283156i	−0.602056	+	0.798453i	$0.705652\pi$
$678$		0			0
$679$	1.57769	−	15.0108i	0.0605464	−	0.576060i
$680$	−6.08501	+	7.73131i	−0.233350	+	0.296482i
$681$		0			0
$682$	−24.4554	+	42.3580i	−0.936445	+	1.62197i
$683$	−21.4995	+	15.6203i	−0.822655	+	0.597694i	−0.917472	−	0.397801i	$-0.869774\pi$
$683$	−21.4995	+	15.6203i	−0.822655	+	0.597694i	0.0948166	+	0.995495i	$0.469774\pi$
$684$		0			0
$685$	31.3379	+	19.7383i	1.19736	+	0.754161i
$686$	18.6551	+	20.7186i	0.712254	+	0.791038i
$687$		0			0
$688$	−4.05728	+	4.50607i	−0.154682	+	0.171792i
$689$	0.883189	−	0.187728i	0.0336468	−	0.00715185i
$690$		0			0
$691$	32.4537	+	6.89825i	1.23460	+	0.262422i	0.778578	−	0.627548i	$-0.215941\pi$
$691$	32.4537	+	6.89825i	1.23460	+	0.262422i	0.456020	+	0.889970i	$0.349275\pi$
$692$	7.13452	−	5.18353i	0.271214	−	0.197048i
$693$		0			0
$694$	29.2539	−	21.2542i	1.11046	−	0.806799i
$695$	−37.2483	−	5.37080i	−1.41291	−	0.203726i
$696$		0			0
$697$	−1.21817	+	11.5902i	−0.0461416	+	0.439008i
$698$	18.0457	−	3.83573i	0.683040	−	0.145185i
$699$		0			0
$700$	1.25088	+	5.17438i	0.0472789	+	0.195573i
$701$	−26.1441			−0.987451			−0.493725	−	0.869618i	$-0.664365\pi$
$701$	−26.1441			−0.987451			−0.493725	+	0.869618i	$0.664365\pi$
$702$		0			0
$703$	−15.9674	−	11.6010i	−0.602223	−	0.437540i
$704$	−12.5912	+	5.60596i	−0.474548	+	0.211283i
$705$		0			0
$706$	−7.70611	−	3.43098i	−0.290023	−	0.129127i
$707$	−8.47791	−	14.6842i	−0.318845	−	0.552255i
$708$		0			0
$709$	−39.0480	−	8.29991i	−1.46648	−	0.311710i	−0.595629	−	0.803259i	$-0.703097\pi$
$709$	−39.0480	−	8.29991i	−1.46648	−	0.311710i	−0.870850	+	0.491550i	$0.836431\pi$
$710$	12.3649	−	48.8483i	0.464048	−	1.83324i
$711$		0			0
$712$	4.78661	+	14.7317i	0.179386	+	0.552093i
$713$	0.677710	+	0.144052i	0.0253804	+	0.00539478i
$714$		0			0
$715$	6.47887	+	2.38439i	0.242296	+	0.0891710i
$716$	−2.52014	+	2.79890i	−0.0941819	+	0.104600i
$717$		0			0
$718$	−25.4766	+	44.1267i	−0.950777	+	1.64679i
$719$	−32.4317	+	23.5630i	−1.20950	+	0.878751i	−0.995185	−	0.0980142i	$-0.968751\pi$
$719$	−32.4317	+	23.5630i	−1.20950	+	0.878751i	−0.214312	+	0.976765i	$0.568751\pi$
$720$		0			0
$721$	−0.953688	−	0.692895i	−0.0355172	−	0.0258048i
$722$	43.1254	−	19.2007i	1.60496	−	0.714575i
$723$		0			0
$724$	−0.801787	−	1.38874i	−0.0297982	−	0.0516120i
$725$	−9.84930	−	2.90063i	−0.365794	−	0.107727i
$726$		0			0
$727$	−23.6216	−	26.2344i	−0.876075	−	0.972980i	0.123738	−	0.992315i	$-0.460512\pi$
$727$	−23.6216	−	26.2344i	−0.876075	−	0.972980i	−0.999813	+	0.0193348i	$0.993845\pi$
$728$	−1.56422	−	1.13647i	−0.0579738	−	0.0421204i
$729$		0			0
$730$	21.9886	−	1.45860i	0.813835	−	0.0539852i
$731$	0.274909	+	2.61559i	0.0101679	+	0.0967410i
$732$		0			0
$733$	6.14109	+	2.73419i	0.226826	+	0.100990i	0.517003	−	0.855983i	$-0.327047\pi$
$733$	6.14109	+	2.73419i	0.226826	+	0.100990i	−0.290177	+	0.956973i	$0.593714\pi$
$734$	−17.7847	+	19.7519i	−0.656445	+	0.729055i
$735$		0			0
$736$	−0.295689	−	0.328396i	−0.0108993	−	0.0121049i
$737$	19.9773	+	61.4839i	0.735874	+	2.26479i
$738$		0			0
$739$	−3.30815	+	10.1814i	−0.121692	+	0.374530i	−0.993284	−	0.115702i	$-0.963088\pi$
$739$	−3.30815	+	10.1814i	−0.121692	+	0.374530i	0.871592	+	0.490233i	$0.163088\pi$
$740$	−4.86663	−	0.701715i	−0.178901	−	0.0257956i
$741$		0			0
$742$	2.80554	+	1.24911i	0.102995	+	0.0458562i
$743$	10.6028	+	18.3647i	0.388981	+	0.673735i	0.992313	−	0.123756i	$-0.0394939\pi$
$743$	10.6028	+	18.3647i	0.388981	+	0.673735i	−0.603332	+	0.797490i	$0.706161\pi$
$744$		0			0
$745$	−6.07132	−	35.1670i	−0.222436	−	1.28842i
$746$	−15.1586	−	11.0133i	−0.554995	−	0.403227i
$747$		0			0
$748$	2.31161	−	7.11441i	0.0845209	−	0.260129i
$749$	−13.2422	+	22.9361i	−0.483858	+	0.838067i
$750$		0			0
$751$	−24.6961	−	42.7750i	−0.901175	−	1.56088i	−0.825971	−	0.563713i	$-0.809372\pi$
$751$	−24.6961	−	42.7750i	−0.901175	−	1.56088i	−0.0752042	−	0.997168i	$-0.523961\pi$
$752$	57.2324	−	12.1651i	2.08705	−	0.443616i
$753$		0			0
$754$	−2.11871	+	0.943311i	−0.0771589	+	0.0343533i
$755$	14.4581	−	12.0439i	0.526184	−	0.438324i
$756$		0			0
$757$	−31.2549			−1.13598			−0.567989	−	0.823036i	$-0.692279\pi$
$757$	−31.2549			−1.13598			−0.567989	+	0.823036i	$0.692279\pi$
$758$	−3.84694	−	36.6012i	−0.139727	−	1.32942i
$759$		0			0
$760$	−19.5255	+	24.8082i	−0.708265	+	0.899887i
$761$	−28.3560	+	6.02725i	−1.02790	+	0.218488i	−0.690850	−	0.722998i	$-0.742764\pi$
$761$	−28.3560	+	6.02725i	−1.02790	+	0.218488i	−0.337053	+	0.941486i	$0.609430\pi$
$762$		0			0
$763$	17.7985	+	3.78319i	0.644349	+	0.136961i
$764$	−2.43370	+	7.49016i	−0.0880482	+	0.270985i
$765$		0			0
$766$	−3.25185	−	10.0082i	−0.117494	−	0.361610i
$767$	−0.122917	−	1.16948i	−0.00443827	−	0.0422273i
$768$		0			0
$769$	31.1371	+	13.8631i	1.12283	+	0.499917i	0.882282	−	0.470720i	$-0.156006\pi$
$769$	31.1371	+	13.8631i	1.12283	+	0.499917i	0.240549	+	0.970637i	$0.422673\pi$
$770$	13.0608	+	19.5136i	0.470679	+	0.703221i
$771$		0			0
$772$	−1.23207	+	0.548553i	−0.0443432	+	0.0197428i
$773$	9.44334	−	29.0636i	0.339653	−	1.04535i	−0.624731	−	0.780840i	$-0.714791\pi$
$773$	9.44334	−	29.0636i	0.339653	−	1.04535i	0.964384	−	0.264506i	$-0.0852088\pi$
$774$		0			0
$775$	−13.9652	−	29.1604i	−0.501645	−	1.04747i
$776$	11.1498	−	19.3120i	0.400253	−	0.693259i
$777$		0			0
$778$	5.75179	−	54.7247i	0.206212	−	1.96197i
$779$	−3.90887	+	37.1904i	−0.140050	+	1.33248i
$780$		0			0
$781$	−6.43927	−	61.2655i	−0.230415	−	2.19225i
$782$	−0.382321			−0.0136718
$783$		0			0
$784$	7.75234	+	23.8592i	0.276869	+	0.852116i
$785$	−0.0323913	−	0.187621i	−0.00115609	−	0.00669648i
$786$		0			0
$787$	−15.3574	+	17.0562i	−0.547434	+	0.607987i	−0.951841	−	0.306592i	$-0.900811\pi$
$787$	−15.3574	+	17.0562i	−0.547434	+	0.607987i	0.404407	+	0.914579i	$0.367478\pi$
$788$	0.813104	−	0.903043i	0.0289656	−	0.0321696i
$789$		0			0
$790$	23.9386	+	23.2833i	0.851698	+	0.828381i
$791$	−2.98726	−	9.19384i	−0.106215	−	0.326895i
$792$		0			0
$793$	−2.56316			−0.0910205
$794$	4.92464	+	46.8548i	0.174769	+	1.66282i
$795$		0			0
$796$	0.387805	−	3.68972i	0.0137454	−	0.130779i
$797$	4.54511	−	43.2438i	0.160996	−	1.53177i	−0.553923	−	0.832568i	$-0.686870\pi$
$797$	4.54511	−	43.2438i	0.160996	−	1.53177i	0.714919	−	0.699207i	$-0.246463\pi$
$798$		0			0
$799$	12.6893	−	21.9786i	0.448916	−	0.777545i
$800$	−3.72601	+	20.2819i	−0.131734	+	0.717075i
$801$		0			0
$802$	−5.12593	+	15.7760i	−0.181003	+	0.557070i
$803$	24.6121	−	10.9580i	0.868541	−	0.386699i
$804$		0			0
$805$	0.205720	−	0.261378i	0.00725068	−	0.00921236i
$806$	−6.67170	−	2.97043i	−0.235001	−	0.104629i
$807$		0			0
$808$	−2.61855	−	24.9138i	−0.0921203	−	0.876466i
$809$	8.36599	+	25.7479i	0.294133	+	0.905247i	0.983511	+	0.180846i	$0.0578836\pi$
$809$	8.36599	+	25.7479i	0.294133	+	0.905247i	−0.689379	+	0.724401i	$0.742116\pi$
$810$		0			0
$811$	−11.3390	+	34.8979i	−0.398167	+	1.22543i	0.528300	+	0.849058i	$0.322829\pi$
$811$	−11.3390	+	34.8979i	−0.398167	+	1.22543i	−0.926468	+	0.376375i	$0.877171\pi$
$812$	−2.13857	−	0.454566i	−0.0750490	−	0.0159522i
$813$		0			0
$814$	−21.2143	+	4.50923i	−0.743560	+	0.158049i
$815$	1.06128	−	27.5648i	0.0371752	−	0.965551i
$816$		0			0
$817$	0.882127	+	8.39287i	0.0308617	+	0.293630i
$818$	−16.0697			−0.561865
$819$		0			0
$820$	3.45897	+	8.65018i	0.120793	+	0.302078i
$821$	−1.38376	+	0.616087i	−0.0482934	+	0.0215016i	−0.430741	−	0.902475i	$-0.641748\pi$
$821$	−1.38376	+	0.616087i	−0.0482934	+	0.0215016i	0.382448	+	0.923977i	$0.375081\pi$
$822$		0			0
$823$	35.6064	−	7.56838i	1.24116	−	0.263817i	0.459872	−	0.887985i	$-0.347895\pi$
$823$	35.6064	−	7.56838i	1.24116	−	0.263817i	0.781290	+	0.624168i	$0.214562\pi$
$824$	−0.870816	−	1.50830i	−0.0303363	−	0.0525440i
$825$		0			0
$826$	1.99979	−	3.46374i	0.0695816	−	0.120519i
$827$	0.131104	−	0.403496i	0.00455892	−	0.0140309i	−0.948751	−	0.316024i	$-0.897652\pi$
$827$	0.131104	−	0.403496i	0.00455892	−	0.0140309i	0.953310	+	0.301993i	$0.0976520\pi$
$828$		0			0
$829$	−15.0808	−	10.9568i	−0.523778	−	0.380547i	0.294247	−	0.955729i	$-0.404931\pi$
$829$	−15.0808	−	10.9568i	−0.523778	−	0.380547i	−0.818025	+	0.575182i	$0.804931\pi$
$830$	59.6704	−	31.4541i	2.07119	−	1.09179i
$831$		0			0
$832$	−1.02898	−	1.78225i	−0.0356736	−	0.0617885i
$833$	9.94057	+	4.42583i	0.344420	+	0.153346i
$834$		0			0
$835$	−10.7351	−	10.4412i	−0.371502	−	0.361332i
$836$	7.41748	−	22.8286i	0.256539	−	0.789545i
$837$		0			0
$838$	6.49962	+	20.0038i	0.224526	+	0.691019i
$839$	19.4361	+	21.5860i	0.671008	+	0.745230i	0.978483	−	0.206326i	$-0.0661508\pi$
$839$	19.4361	+	21.5860i	0.671008	+	0.745230i	−0.307475	+	0.951556i	$0.599484\pi$
$840$		0			0
$841$	−16.5831	+	18.4174i	−0.571832	+	0.635084i
$842$	−34.8424	−	15.5129i	−1.20075	−	0.534608i
$843$		0			0
$844$	0.344183	+	3.27468i	0.0118473	+	0.112719i
$845$	6.88026	−	27.1808i	0.236688	−	0.935047i
$846$		0			0
$847$	10.8694	+	7.89708i	0.373477	+	0.271347i
$848$	4.40083	+	4.88762i	0.151125	+	0.167842i
$849$		0			0
$850$	10.8832	+	14.1371i	0.373291	+	0.484900i
$851$	0.153613	+	0.266066i	0.00526580	+	0.00912063i
$852$		0			0
$853$	16.0673	−	7.15364i	0.550135	−	0.244936i	−0.112794	−	0.993618i	$-0.535980\pi$
$853$	16.0673	−	7.15364i	0.550135	−	0.244936i	0.662929	+	0.748682i	$0.269313\pi$
$854$	−7.05296	−	5.12428i	−0.241347	−	0.175349i
$855$		0			0
$856$	−31.6559	+	22.9993i	−1.08198	+	0.786101i
$857$	4.22020	−	7.30960i	0.144159	−	0.249691i	−0.784900	−	0.619623i	$-0.787286\pi$
$857$	4.22020	−	7.30960i	0.144159	−	0.249691i	0.929059	+	0.369932i	$0.120619\pi$
$858$		0			0
$859$	−22.5902	+	25.0889i	−0.770767	+	0.856024i	−0.992895	−	0.118994i	$-0.962033\pi$
$859$	−22.5902	+	25.0889i	−0.770767	+	0.856024i	0.222128	+	0.975018i	$0.428700\pi$
$860$	1.16941	+	1.74716i	0.0398765	+	0.0595777i
$861$		0			0
$862$	−21.3431	−	4.53662i	−0.726949	−	0.154518i
$863$	−12.9265	−	39.7837i	−0.440023	−	1.35425i	−0.887851	−	0.460132i	$-0.847802\pi$
$863$	−12.9265	−	39.7837i	−0.440023	−	1.35425i	0.447828	−	0.894120i	$-0.352198\pi$
$864$		0			0
$865$	9.54714	+	23.8755i	0.324613	+	0.811790i
$866$	−38.3934	−	8.16077i	−1.30466	−	0.277314i
$867$		0			0
$868$	−3.44234	−	5.96231i	−0.116841	−	0.202374i
$869$	37.2964	+	16.6054i	1.26519	+	0.563301i
$870$		0			0
$871$	−8.81834	+	3.92618i	−0.298798	+	0.133033i
$872$	21.7493	+	15.8018i	0.736523	+	0.535115i
$873$		0			0
$874$	−1.22679			−0.0414967
$875$	−15.5211	−	0.166512i	−0.524708	−	0.00562912i
$876$		0			0
$877$	28.0496	−	5.96213i	0.947168	−	0.201327i	0.291666	−	0.956520i	$-0.405790\pi$
$877$	28.0496	−	5.96213i	0.947168	−	0.201327i	0.655502	+	0.755193i	$0.272457\pi$
$878$	1.40937	−	13.4093i	0.0475640	−	0.452541i
$879$		0			0
$880$	8.55511	+	49.5540i	0.288393	+	1.67047i
$881$	11.7352	−	8.52611i	0.395368	−	0.287252i	−0.372283	−	0.928119i	$-0.621425\pi$
$881$	11.7352	−	8.52611i	0.395368	−	0.287252i	0.767652	+	0.640867i	$0.221425\pi$
$882$		0			0
$883$	−42.8896	+	31.1611i	−1.44335	+	1.04865i	−0.456019	+	0.889970i	$0.650725\pi$
$883$	−42.8896	+	31.1611i	−1.44335	+	1.04865i	−0.987329	+	0.158684i	$0.949275\pi$
$884$	1.09254	+	0.232227i	0.0367462	+	0.00781065i
$885$		0			0
$886$	0.827382	−	0.175865i	0.0277964	−	0.00590832i
$887$	6.01958	−	6.68542i	0.202118	−	0.224474i	−0.633561	−	0.773692i	$-0.718408\pi$
$887$	6.01958	−	6.68542i	0.202118	−	0.224474i	0.835679	+	0.549218i	$0.185074\pi$
$888$		0			0
$889$	−20.6118	−	22.8918i	−0.691299	−	0.767765i
$890$	28.0268	−	1.85914i	0.939461	−	0.0623185i
$891$		0			0
$892$	−10.0558	+	7.30599i	−0.336694	+	0.244623i
$893$	40.7174	−	70.5246i	1.36256	−	2.36001i
$894$		0			0
$895$	−6.10827	−	9.12611i	−0.204177	−	0.305052i
$896$	1.92869	−	18.3502i	0.0644329	−	0.613038i
$897$		0			0
$898$	−8.04280	−	8.93243i	−0.268392	−	0.298079i
$899$	13.2788			0.442872
$900$		0			0
$901$	2.85269			0.0950369
$902$	27.4963	+	30.5377i	0.915526	+	1.01679i
$903$		0			0
$904$	1.49291	−	14.2041i	0.0496534	−	0.472420i
$905$	4.49912	−	1.27271i	0.149556	−	0.0423063i
$906$		0			0
$907$	13.0147	−	22.5421i	0.432145	−	0.748498i	−0.564912	−	0.825151i	$-0.691090\pi$
$907$	13.0147	−	22.5421i	0.432145	−	0.748498i	0.997058	+	0.0766530i	$0.0244234\pi$
$908$	5.71538	−	4.15247i	0.189672	−	0.137804i
$909$		0			0
$910$	−2.69385	+	2.24404i	−0.0893003	+	0.0743893i
$911$	−2.68314	−	2.97993i	−0.0888964	−	0.0987294i	0.697055	−	0.717017i	$-0.254493\pi$
$911$	−2.68314	−	2.97993i	−0.0888964	−	0.0987294i	−0.785952	+	0.618288i	$0.787827\pi$
$912$		0			0
$913$	55.1797	−	61.2833i	1.82618	−	2.02818i
$914$	−25.8391	+	5.49227i	−0.854682	+	0.181668i
$915$		0			0
$916$	6.15464	+	1.30821i	0.203355	+	0.0432244i
$917$	13.0533	−	9.48377i	0.431058	−	0.313182i
$918$		0			0
$919$	0.331871	−	0.241118i	0.0109474	−	0.00795375i	−0.582298	−	0.812975i	$-0.697846\pi$
$919$	0.331871	−	0.241118i	0.0109474	−	0.00795375i	0.593245	+	0.805022i	$0.297846\pi$
$920$	0.434730	−	0.229160i	0.0143326	−	0.00755517i
$921$		0			0
$922$	5.73896	−	54.6026i	0.189003	−	1.79824i
$923$	8.99722	−	1.91242i	0.296147	−	0.0629480i
$924$		0			0
$925$	5.46557	−	13.2541i	0.179707	−	0.435791i
$926$	30.6303			1.00657
$927$		0			0
$928$	−6.85175	−	4.97808i	−0.224920	−	0.163414i
$929$	6.15454	−	2.74018i	0.201924	−	0.0899023i	−0.303283	−	0.952900i	$-0.598083\pi$
$929$	6.15454	−	2.74018i	0.201924	−	0.0899023i	0.505207	+	0.862998i	$0.331416\pi$
$930$		0			0
$931$	31.8972	+	14.2016i	1.04539	+	0.465437i
$932$	3.17656	+	5.50196i	0.104052	+	0.180223i
$933$		0			0
$934$	30.0055	+	6.37786i	0.981808	+	0.208690i
$935$	18.4558	+	11.6244i	0.603570	+	0.380160i
$936$		0			0
$937$	−13.0786	−	40.2519i	−0.427260	−	1.31497i	−0.900814	−	0.434206i	$-0.857029\pi$
$937$	−13.0786	−	40.2519i	−0.427260	−	1.31497i	0.473554	−	0.880765i	$-0.342971\pi$
$938$	−32.1143	−	6.82611i	−1.04857	−	0.222880i
$939$		0			0
$940$	0.780521	−	20.2725i	0.0254578	−	0.661216i
$941$	−35.0819	+	38.9624i	−1.14364	+	1.27014i	−0.185876	+	0.982573i	$0.559512\pi$
$941$	−35.0819	+	38.9624i	−1.14364	+	1.27014i	−0.957761	+	0.287564i	$0.907154\pi$
$942$		0			0
$943$	0.291050	−	0.504114i	0.00947790	−	0.0164162i
$944$	6.92961	−	5.03466i	0.225540	−	0.163864i
$945$		0			0
$946$	7.50241	+	5.45082i	0.243924	+	0.177221i
$947$	−2.14265	+	0.953970i	−0.0696268	+	0.0309999i	−0.441255	−	0.897382i	$-0.645466\pi$
$947$	−2.14265	+	0.953970i	−0.0696268	+	0.0309999i	0.371628	+	0.928382i	$0.378800\pi$
$948$		0			0
$949$	2.01136	+	3.48378i	0.0652915	+	0.113088i
$950$	34.9220	+	45.3631i	1.13302	+	1.47177i
$951$		0			0
$952$	−4.08749	−	4.53961i	−0.132476	−	0.147130i
$953$	7.72986	+	5.61607i	0.250395	+	0.181922i	0.705902	−	0.708310i	$-0.250542\pi$
$953$	7.72986	+	5.61607i	0.250395	+	0.181922i	−0.455507	+	0.890232i	$0.650542\pi$
$954$		0			0
$955$	−19.4306	−	12.2384i	−0.628759	−	0.396026i
$956$	0.0865082	+	0.823070i	0.00279787	+	0.0266200i
$957$		0			0
$958$	35.0748	+	15.6163i	1.13322	+	0.504540i
$959$	−15.3866	+	17.0885i	−0.496858	+	0.551817i
$960$		0			0
$961$	7.23609	+	8.03649i	0.233422	+	0.259242i
$962$	−1.00071	−	3.07987i	−0.0322642	−	0.0992989i
$963$		0			0
$964$	−5.94735	+	18.3041i	−0.191551	+	0.589534i
$965$	−0.669005	−	3.87509i	−0.0215360	−	0.124744i
$966$		0			0
$967$	18.8698	+	8.40138i	0.606812	+	0.270170i	0.687055	−	0.726605i	$-0.258903\pi$
$967$	18.8698	+	8.40138i	0.606812	+	0.270170i	−0.0802433	+	0.996775i	$0.525570\pi$
$968$	9.92488	+	17.1904i	0.318998	+	0.552520i
$969$		0			0
$970$	−28.9872	−	28.1936i	−0.930723	−	0.905243i
$971$	−24.5224	−	17.8166i	−0.786962	−	0.571761i	0.120098	−	0.992762i	$-0.461679\pi$
$971$	−24.5224	−	17.8166i	−0.786962	−	0.571761i	−0.907060	+	0.421001i	$0.861679\pi$
$972$		0			0
$973$	7.22044	−	22.2222i	0.231477	−	0.712412i
$974$	9.49335	−	16.4430i	0.304186	−	0.526866i
$975$		0			0
$976$	−9.33514	−	16.1689i	−0.298810	−	0.517555i
$977$	−23.0276	+	4.89467i	−0.736718	+	0.156594i	−0.560964	−	0.827840i	$-0.689570\pi$
$977$	−23.0276	+	4.89467i	−0.736718	+	0.156594i	−0.175754	+	0.984434i	$0.556236\pi$
$978$		0			0
$979$	31.3707	−	13.9671i	1.00261	−	0.446392i
$980$	8.67937	−	0.575740i	0.277252	−	0.0183913i
$981$		0			0
$982$	66.1926			2.11229
$983$	2.02059	+	19.2246i	0.0644468	+	0.613171i	0.978310	+	0.207148i	$0.0664180\pi$
$983$	2.02059	+	19.2246i	0.0644468	+	0.613171i	−0.913863	+	0.406023i	$0.866915\pi$
$984$		0			0
$985$	1.97079	+	2.94447i	0.0627946	+	0.0938187i
$986$	−7.16723	+	1.52344i	−0.228251	+	0.0485163i
$987$		0			0
$988$	3.50574	+	0.745169i	0.111533	+	0.0237070i
$989$	0.0405939	−	0.124935i	0.00129081	−	0.00397271i
$990$		0			0
$991$	−0.458610	−	1.41146i	−0.0145682	−	0.0448364i	0.943508	−	0.331349i	$-0.107504\pi$
$991$	−0.458610	−	1.41146i	−0.0145682	−	0.0448364i	−0.958076	+	0.286513i	$0.907504\pi$
$992$	−2.78768	−	26.5230i	−0.0885090	−	0.842107i
$993$		0			0
$994$	28.5806	+	12.7249i	0.906523	+	0.403610i
$995$	10.1520	+	3.73618i	0.321839	+	0.118445i
$996$		0			0
$997$	−14.4548	+	6.43568i	−0.457787	+	0.203820i	−0.622656	−	0.782495i	$-0.713947\pi$
$997$	−14.4548	+	6.43568i	−0.457787	+	0.203820i	0.164869	+	0.986315i	$0.447280\pi$
$998$	−18.6267	+	57.3271i	−0.589619	+	1.81466i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.r.a.46.22		224
3.2	odd	2		225.2.q.a.196.7	yes	224
9.4	even	3	inner	675.2.r.a.496.7		224
9.5	odd	6		225.2.q.a.121.22	yes	224
25.6	even	5	inner	675.2.r.a.181.7		224
75.56	odd	10		225.2.q.a.106.22	yes	224
225.31	even	15	inner	675.2.r.a.631.22		224
225.131	odd	30		225.2.q.a.31.7	✓	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.7	✓	224	225.131	odd	30
225.2.q.a.106.22	yes	224	75.56	odd	10
225.2.q.a.121.22	yes	224	9.5	odd	6
225.2.q.a.196.7	yes	224	3.2	odd	2
675.2.r.a.46.22		224	1.1	even	1	trivial
675.2.r.a.181.7		224	25.6	even	5	inner
675.2.r.a.496.7		224	9.4	even	3	inner
675.2.r.a.631.22		224	225.31	even	15	inner

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.r (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.11303 + 1.23614i) q^{2} +(-0.0801613 + 0.762684i) q^{4} +(-2.09847 - 0.772289i) q^{5} +(0.694163 - 1.20233i) q^{7} +(1.65942 - 1.20564i) q^{8} +(-1.38100 - 3.45359i) q^{10} +(-3.04269 - 3.37925i) q^{11} +(0.454318 - 0.504572i) q^{13} +(2.25887 - 0.480138i) q^{14} +(4.83758 + 1.02826i) q^{16} +(1.73545 - 1.26088i) q^{17} +(5.56870 - 4.04590i) q^{19} +(0.757229 - 1.53856i) q^{20} +(0.790638 - 7.52241i) q^{22} +(-0.104805 + 0.0222770i) q^{23} +(3.80714 + 3.24125i) q^{25} +1.12939 q^{26} +(0.861350 + 0.625807i) q^{28} +(-1.87597 + 0.835237i) q^{29} +(-5.90734 - 2.63012i) q^{31} +(2.06213 + 3.57172i) q^{32} +(3.49024 + 0.741873i) q^{34} +(-2.38522 + 1.98695i) q^{35} +(-0.886060 - 2.72701i) q^{37} +(11.1994 + 2.38051i) q^{38} +(-4.41335 + 1.24845i) q^{40} +(-3.63522 + 4.03732i) q^{41} +(-0.613014 + 1.06177i) q^{43} +(2.82121 - 2.04973i) q^{44} +(-0.144189 - 0.104759i) q^{46} +(10.8080 - 4.81201i) q^{47} +(2.53627 + 4.39296i) q^{49} +(0.230806 + 8.31377i) q^{50} +(0.348410 + 0.386948i) q^{52} +(1.07586 + 0.781661i) q^{53} +(3.77524 + 9.44110i) q^{55} +(-0.297663 - 2.83208i) q^{56} +(-3.12049 - 1.38933i) q^{58} +(1.15888 - 1.28707i) q^{59} +(-2.52602 - 2.80543i) q^{61} +(-3.32384 - 10.2297i) q^{62} +(0.936638 - 2.88268i) q^{64} +(-1.34305 + 0.707962i) q^{65} +(-12.9879 - 5.78257i) q^{67} +(0.822536 + 1.42467i) q^{68} +(-5.11098 - 0.736948i) q^{70} +(10.9600 + 7.96294i) q^{71} +(-1.83085 + 5.63478i) q^{73} +(2.38477 - 4.13054i) q^{74} +(2.63935 + 4.57148i) q^{76} +(-6.17509 + 1.31256i) q^{77} +(-8.20200 + 3.65176i) q^{79} +(-9.35740 - 5.89378i) q^{80} -9.03682 q^{82} +(1.89564 + 18.0358i) q^{83} +(-4.61555 + 1.30565i) q^{85} +(-1.99480 + 0.424009i) q^{86} +(-9.12328 - 1.93921i) q^{88} +(-2.33361 + 7.18212i) q^{89} +(-0.291288 - 0.896494i) q^{91} +(-0.00858900 - 0.0817189i) q^{92} +(17.9779 + 8.00428i) q^{94} +(-14.8103 + 4.18954i) q^{95} +(9.93178 - 4.42191i) q^{97} +(-2.60738 + 8.02469i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28}+ \cdots - 146 q^{98}+O(q^{100}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Introduction

L-functions

Modular forms

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