LMFDB - Embedded newform 675.2.r.a.181.2

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			181.2
Character	$\chi$	$=$	675.181
Dual form			675.2.r.a.496.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.43022 - 0.516560i) q^{2} +(3.81206 + 1.69724i) q^{4} +(2.22233 - 0.247525i) q^{5} +(-0.644527 + 1.11635i) q^{7} +(-4.36740 - 3.17310i) q^{8} +(-5.52861 - 0.546422i) q^{10} +(-0.502326 - 0.106773i) q^{11} +(-4.87743 + 1.03673i) q^{13} +(2.14301 - 2.38005i) q^{14} +(3.39033 + 3.76535i) q^{16} +(-5.60571 - 4.07278i) q^{17} +(-4.21905 - 3.06532i) q^{19} +(8.89175 + 2.82823i) q^{20} +(1.16561 + 0.518963i) q^{22} +(-2.78826 + 3.09668i) q^{23} +(4.87746 - 1.10016i) q^{25} +12.3888 q^{26} +(-4.35169 + 3.16169i) q^{28} +(-0.724325 - 6.89149i) q^{29} +(0.160665 - 1.52862i) q^{31} +(-0.895838 - 1.55164i) q^{32} +(11.5193 + 12.7935i) q^{34} +(-1.15602 + 2.64044i) q^{35} +(2.27325 - 6.99635i) q^{37} +(8.66982 + 9.62881i) q^{38} +(-10.4912 - 5.97062i) q^{40} +(3.98547 - 0.847138i) q^{41} +(2.08364 - 3.60897i) q^{43} +(-1.73368 - 1.25959i) q^{44} +(8.37572 - 6.08531i) q^{46} +(-0.841878 - 8.00993i) q^{47} +(2.66917 + 4.62314i) q^{49} +(-12.4216 + 0.154142i) q^{50} +(-20.3526 - 4.32609i) q^{52} +(-2.21350 + 1.60820i) q^{53} +(-1.14276 - 0.112945i) q^{55} +(6.35720 - 2.83041i) q^{56} +(-1.79960 + 17.1220i) q^{58} +(-2.99263 + 0.636103i) q^{59} +(-7.17717 - 1.52555i) q^{61} +(-1.18008 + 3.63190i) q^{62} +(-1.75586 - 5.40400i) q^{64} +(-10.5826 + 3.51124i) q^{65} +(0.0475303 - 0.452221i) q^{67} +(-14.4568 - 25.0399i) q^{68} +(4.17334 - 5.81969i) q^{70} +(-1.33759 + 0.971819i) q^{71} +(-2.72548 - 8.38816i) q^{73} +(-9.13854 + 15.8284i) q^{74} +(-10.8807 - 18.8459i) q^{76} +(0.442959 - 0.491955i) q^{77} +(0.359882 + 3.42405i) q^{79} +(8.46644 + 7.52863i) q^{80} -10.1232 q^{82} +(-13.4120 + 5.97142i) q^{83} +(-13.4658 - 7.66350i) q^{85} +(-6.92795 + 7.69427i) q^{86} +(1.85506 + 2.06025i) q^{88} +(2.98202 + 9.17771i) q^{89} +(1.98628 - 6.11314i) q^{91} +(-15.8848 + 7.07238i) q^{92} +(-2.09166 + 19.9008i) q^{94} +(-10.1349 - 5.76782i) q^{95} +(-0.842924 - 8.01989i) q^{97} +(-4.09855 - 12.6140i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

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

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 $

$2$	−2.43022	−	0.516560i	−1.71843	−	0.365263i	−0.759851	−	0.650098i	$-0.774728\pi$
$2$	−2.43022	−	0.516560i	−1.71843	−	0.365263i	−0.958577	+	0.284835i	$0.908061\pi$
$3$		0			0
$3$		0			0
$4$	3.81206	+	1.69724i	1.90603	+	0.848619i
$5$	2.22233	−	0.247525i	0.993854	−	0.110697i
$5$	2.22233	−	0.247525i	0.993854	−	0.110697i
$6$		0			0
$7$	−0.644527	+	1.11635i	−0.243608	+	0.421942i	−0.961739	−	0.273966i	$-0.911664\pi$
$7$	−0.644527	+	1.11635i	−0.243608	+	0.421942i	0.718131	+	0.695908i	$0.244998\pi$
$8$	−4.36740	−	3.17310i	−1.54411	−	1.12186i
$9$		0			0
$10$	−5.52861	−	0.546422i	−1.74830	−	0.172794i
$11$	−0.502326	−	0.106773i	−0.151457	−	0.0321932i	0.131559	−	0.991308i	$-0.458002\pi$
$11$	−0.502326	−	0.106773i	−0.151457	−	0.0321932i	−0.283016	+	0.959115i	$0.591335\pi$
$12$		0			0
$13$	−4.87743	+	1.03673i	−1.35276	+	0.287537i	−0.826571	−	0.562833i	$-0.809712\pi$
$13$	−4.87743	+	1.03673i	−1.35276	+	0.287537i	−0.526185	+	0.850370i	$0.676378\pi$
$14$	2.14301	−	2.38005i	0.572743	−	0.636095i
$15$		0			0
$16$	3.39033	+	3.76535i	0.847583	+	0.941337i
$17$	−5.60571	−	4.07278i	−1.35958	−	0.987795i	−0.998471	−	0.0552732i	$-0.982397\pi$
$17$	−5.60571	−	4.07278i	−1.35958	−	0.987795i	−0.361113	−	0.932522i	$-0.617603\pi$
$18$		0			0
$19$	−4.21905	−	3.06532i	−0.967917	−	0.703233i	−0.0129412	−	0.999916i	$-0.504119\pi$
$19$	−4.21905	−	3.06532i	−0.967917	−	0.703233i	−0.954976	+	0.296683i	$0.904119\pi$
$20$	8.89175	+	2.82823i	1.98825	+	0.632412i
$21$		0			0
$22$	1.16561	+	0.518963i	0.248509	+	0.110643i
$23$	−2.78826	+	3.09668i	−0.581393	+	0.645702i	−0.960048	−	0.279836i	$-0.909720\pi$
$23$	−2.78826	+	3.09668i	−0.581393	+	0.645702i	0.378655	+	0.925538i	$0.376387\pi$
$24$		0			0
$25$	4.87746	−	1.10016i	0.975492	−	0.220033i
$26$	12.3888			2.42964
$27$		0			0
$28$	−4.35169	+	3.16169i	−0.822392	+	0.597503i
$29$	−0.724325	−	6.89149i	−0.134504	−	1.27972i	−0.828602	−	0.559838i	$-0.810863\pi$
$29$	−0.724325	−	6.89149i	−0.134504	−	1.27972i	0.694098	−	0.719880i	$-0.255803\pi$
$30$		0			0
$31$	0.160665	−	1.52862i	0.0288562	−	0.274548i	−0.970574	−	0.240802i	$-0.922590\pi$
$31$	0.160665	−	1.52862i	0.0288562	−	0.274548i	0.999430	−	0.0337463i	$-0.0107438\pi$
$32$	−0.895838	−	1.55164i	−0.158363	−	0.274293i
$33$		0			0
$34$	11.5193	+	12.7935i	1.97554	+	2.19406i
$35$	−1.15602	+	2.64044i	−0.195403	+	0.446315i
$36$		0			0
$37$	2.27325	−	6.99635i	0.373720	−	1.15019i	−0.570618	−	0.821216i	$-0.693296\pi$
$37$	2.27325	−	6.99635i	0.373720	−	1.15019i	0.944338	−	0.328977i	$-0.106704\pi$
$38$	8.66982	+	9.62881i	1.40643	+	1.56200i
$39$		0			0
$40$	−10.4912	−	5.97062i	−1.65880	−	0.944038i
$41$	3.98547	−	0.847138i	0.622426	−	0.132301i	0.114105	−	0.993469i	$-0.463600\pi$
$41$	3.98547	−	0.847138i	0.622426	−	0.132301i	0.508321	+	0.861168i	$0.330267\pi$
$42$		0			0
$43$	2.08364	−	3.60897i	0.317752	−	0.550362i	−0.662267	−	0.749268i	$-0.730405\pi$
$43$	2.08364	−	3.60897i	0.317752	−	0.550362i	0.980019	+	0.198906i	$0.0637387\pi$
$44$	−1.73368	−	1.25959i	−0.261362	−	0.189890i
$45$		0			0
$46$	8.37572	−	6.08531i	1.23493	−	0.897231i
$47$	−0.841878	−	8.00993i	−0.122801	−	1.16837i	−0.866262	−	0.499590i	$-0.833484\pi$
$47$	−0.841878	−	8.00993i	−0.122801	−	1.16837i	0.743461	−	0.668779i	$-0.233183\pi$
$48$		0			0
$49$	2.66917	+	4.62314i	0.381310	+	0.660448i
$50$	−12.4216	+	0.154142i	−1.75668	+	0.0217990i
$51$		0			0
$52$	−20.3526	−	4.32609i	−2.82240	−	0.599920i
$53$	−2.21350	+	1.60820i	−0.304047	+	0.220903i	−0.729338	−	0.684153i	$-0.760172\pi$
$53$	−2.21350	+	1.60820i	−0.304047	+	0.220903i	0.425291	+	0.905057i	$0.360172\pi$
$54$		0			0
$55$	−1.14276	−	0.112945i	−0.154090	−	0.0152295i
$56$	6.35720	−	2.83041i	0.849517	−	0.378229i
$57$		0			0
$58$	−1.79960	+	17.1220i	−0.236299	+	2.24823i
$59$	−2.99263	+	0.636103i	−0.389607	+	0.0828136i	−0.398550	−	0.917146i	$-0.630487\pi$
$59$	−2.99263	+	0.636103i	−0.389607	+	0.0828136i	0.00894310	+	0.999960i	$0.497153\pi$
$60$		0			0
$61$	−7.17717	−	1.52555i	−0.918942	−	0.195327i	−0.275925	−	0.961179i	$-0.588984\pi$
$61$	−7.17717	−	1.52555i	−0.918942	−	0.195327i	−0.643017	+	0.765852i	$0.722318\pi$
$62$	−1.18008	+	3.63190i	−0.149870	+	0.461251i
$63$		0			0
$64$	−1.75586	−	5.40400i	−0.219483	−	0.675499i
$65$	−10.5826	+	3.51124i	−1.31261	+	0.435516i
$66$		0			0
$67$	0.0475303	−	0.452221i	0.00580675	−	0.0552476i	−0.991235	−	0.132112i	$-0.957824\pi$
$67$	0.0475303	−	0.452221i	0.00580675	−	0.0552476i	0.997042	+	0.0768644i	$0.0244908\pi$
$68$	−14.4568	−	25.0399i	−1.75314	−	3.03654i
$69$		0			0
$70$	4.17334	−	5.81969i	0.498809	−	0.695587i
$71$	−1.33759	+	0.971819i	−0.158743	+	0.115334i	−0.664321	−	0.747447i	$-0.731279\pi$
$71$	−1.33759	+	0.971819i	−0.158743	+	0.115334i	0.505578	+	0.862781i	$0.331279\pi$
$72$		0			0
$73$	−2.72548	−	8.38816i	−0.318993	−	0.981760i	−0.974079	−	0.226206i	$-0.927368\pi$
$73$	−2.72548	−	8.38816i	−0.318993	−	0.981760i	0.655086	−	0.755554i	$-0.272632\pi$
$74$	−9.13854	+	15.8284i	−1.06233	+	1.84002i
$75$		0			0
$76$	−10.8807	−	18.8459i	−1.24810	−	2.16178i
$77$	0.442959	−	0.491955i	0.0504798	−	0.0560635i
$78$		0			0
$79$	0.359882	+	3.42405i	0.0404899	+	0.385236i	0.995936	+	0.0900686i	$0.0287086\pi$
$79$	0.359882	+	3.42405i	0.0404899	+	0.385236i	−0.955446	+	0.295167i	$0.904625\pi$
$80$	8.46644	+	7.52863i	0.946577	+	0.841727i
$81$		0			0
$82$	−10.1232			−1.11792
$83$	−13.4120	+	5.97142i	−1.47216	+	0.655448i	−0.976978	−	0.213341i	$-0.931566\pi$
$83$	−13.4120	+	5.97142i	−1.47216	+	0.655448i	−0.495183	+	0.868789i	$0.664899\pi$
$84$		0			0
$85$	−13.4658	−	7.66350i	−1.46057	−	0.831223i
$86$	−6.92795	+	7.69427i	−0.747061	+	0.829695i
$87$		0			0
$88$	1.85506	+	2.06025i	0.197750	+	0.219623i
$89$	2.98202	+	9.17771i	0.316093	+	0.972835i	0.975302	+	0.220875i	$0.0708913\pi$
$89$	2.98202	+	9.17771i	0.316093	+	0.972835i	−0.659209	+	0.751960i	$0.729109\pi$
$90$		0			0
$91$	1.98628	−	6.11314i	0.208219	−	0.640831i
$92$	−15.8848	+	7.07238i	−1.65611	+	0.737346i
$93$		0			0
$94$	−2.09166	+	19.9008i	−0.215738	+	2.05261i
$95$	−10.1349	−	5.76782i	−1.03981	−	0.591766i
$96$		0			0
$97$	−0.842924	−	8.01989i	−0.0855860	−	0.814296i	−0.950154	−	0.311781i	$-0.899075\pi$
$97$	−0.842924	−	8.01989i	−0.0855860	−	0.814296i	0.864568	−	0.502516i	$-0.167592\pi$
$98$	−4.09855	−	12.6140i	−0.414016	−	1.27421i
$99$		0			0
$100$	20.4604	+	4.08432i	2.04604	+	0.408432i
$101$	7.80298	−	13.5152i	0.776425	−	1.34481i	−0.157565	−	0.987509i	$-0.550364\pi$
$101$	7.80298	−	13.5152i	0.776425	−	1.34481i	0.933990	−	0.357299i	$-0.116302\pi$
$102$		0			0
$103$	13.8836	+	6.18136i	1.36799	+	0.609068i	0.953612	−	0.301038i	$-0.0973330\pi$
$103$	13.8836	+	6.18136i	1.36799	+	0.609068i	0.414376	+	0.910106i	$0.364000\pi$
$104$	24.5913	+	10.9488i	2.41138	+	1.07361i
$105$		0			0
$106$	6.21002	−	2.76488i	0.603171	−	0.268549i
$107$	10.6981			1.03422			0.517111	−	0.855919i	$-0.327008\pi$
$107$	10.6981			1.03422			0.517111	+	0.855919i	$0.327008\pi$
$108$		0			0
$109$	−4.10780	+	12.6425i	−0.393456	+	1.21093i	0.536702	+	0.843772i	$0.319670\pi$
$109$	−4.10780	+	12.6425i	−0.393456	+	1.21093i	−0.930158	+	0.367160i	$0.880330\pi$
$110$	2.71882	+	0.864787i	0.259229	+	0.0824542i
$111$		0			0
$112$	−6.38861	+	1.35794i	−0.603667	+	0.128313i
$113$	−9.31537	+	1.98004i	−0.876316	+	0.186267i	−0.624044	−	0.781390i	$-0.714511\pi$
$113$	−9.31537	+	1.98004i	−0.876316	+	0.186267i	−0.252272	+	0.967656i	$0.581178\pi$
$114$		0			0
$115$	−5.42992	+	7.57199i	−0.506343	+	0.706092i
$116$	8.93533	−	27.5001i	0.829625	−	2.55332i
$117$		0			0
$118$	7.60135			0.699761
$119$	8.15969	−	3.63293i	0.747998	−	0.333030i
$120$		0			0
$121$	−9.80807	−	4.36683i	−0.891643	−	0.396985i
$122$	16.6541	+	7.41487i	1.50779	+	0.671311i
$123$		0			0
$124$	3.20690	−	5.55451i	0.287988	−	0.498810i
$125$	10.5670	−	3.65222i	0.945140	−	0.326664i
$126$		0			0
$127$	4.08839	+	12.5828i	0.362786	+	1.11654i	0.951356	+	0.308094i	$0.0996913\pi$
$127$	4.08839	+	12.5828i	0.362786	+	1.11654i	−0.588570	+	0.808447i	$0.700309\pi$
$128$	1.85022	+	17.6036i	0.163538	+	1.55596i
$129$		0			0
$130$	27.5319	−	3.06654i	2.41471	−	0.268953i
$131$	1.04806	−	9.97167i	0.0915699	−	0.871229i	−0.848259	−	0.529582i	$-0.822349\pi$
$131$	1.04806	−	9.97167i	0.0915699	−	0.871229i	0.939828	−	0.341647i	$-0.110985\pi$
$132$		0			0
$133$	6.14127	−	2.73427i	0.532516	−	0.237091i
$134$	−0.349108	+	1.07445i	−0.0301584	+	0.0928179i
$135$		0			0
$136$	11.5590	+	35.5749i	0.991176	+	3.05053i
$137$	−7.07228	−	7.85456i	−0.604226	−	0.671060i	0.360974	−	0.932576i	$-0.382444\pi$
$137$	−7.07228	−	7.85456i	−0.604226	−	0.671060i	−0.965199	+	0.261516i	$0.915778\pi$
$138$		0			0
$139$	0.398014	−	0.442039i	0.0337591	−	0.0374933i	−0.726029	−	0.687664i	$-0.758636\pi$
$139$	0.398014	−	0.442039i	0.0337591	−	0.0374933i	0.759788	+	0.650171i	$0.225303\pi$
$140$	−8.88827	+	8.10345i	−0.751196	+	0.684867i
$141$		0			0
$142$	3.75266	−	1.67079i	0.314916	−	0.140210i
$143$	2.56076			0.214141
$144$		0			0
$145$	−3.31550	−	15.1358i	−0.275338	−	1.25696i
$146$	2.29053	+	21.7930i	0.189566	+	1.80360i
$147$		0			0
$148$	20.5402	−	22.8122i	1.68840	−	1.87515i
$149$	1.01642	+	1.76049i	0.0832683	+	0.144225i	0.904652	−	0.426151i	$-0.140131\pi$
$149$	1.01642	+	1.76049i	0.0832683	+	0.144225i	−0.821384	+	0.570376i	$0.806797\pi$
$150$		0			0
$151$	−2.10363	+	3.64359i	−0.171191	+	0.296511i	−0.938836	−	0.344363i	$-0.888095\pi$
$151$	−2.10363	+	3.64359i	−0.171191	+	0.296511i	0.767646	+	0.640874i	$0.221428\pi$
$152$	8.69971	+	26.7750i	0.705640	+	2.17174i
$153$		0			0
$154$	−1.33061	+	0.966746i	−0.107224	+	0.0779027i
$155$	−0.0213235	−	3.43686i	−0.00171275	−	0.276055i
$156$		0			0
$157$	0.279109	+	0.483431i	0.0222753	+	0.0385820i	0.876948	−	0.480585i	$-0.159576\pi$
$157$	0.279109	+	0.483431i	0.0222753	+	0.0385820i	−0.854673	+	0.519167i	$0.826242\pi$
$158$	0.894133	−	8.50710i	0.0711334	−	0.676789i
$159$		0			0
$160$	−2.37491	−	3.22650i	−0.187753	−	0.255077i
$161$	−1.65988	−	5.10858i	−0.130817	−	0.402612i
$162$		0			0
$163$	−5.35439	+	16.4791i	−0.419388	+	1.29074i	0.488879	+	0.872352i	$0.337406\pi$
$163$	−5.35439	+	16.4791i	−0.419388	+	1.29074i	−0.908267	+	0.418392i	$0.862594\pi$
$164$	16.6306	+	3.53495i	1.29864	+	0.276033i
$165$		0			0
$166$	35.6788	−	7.58376i	2.76921	−	0.588614i
$167$	−0.685292	+	6.52012i	−0.0530295	+	0.504542i	0.935480	+	0.353381i	$0.114968\pi$
$167$	−0.685292	+	6.52012i	−0.0530295	+	0.504542i	−0.988509	+	0.151161i	$0.951699\pi$
$168$		0			0
$169$	10.8384	−	4.82559i	0.833727	−	0.371199i
$170$	28.7663	+	25.5799i	2.20627	+	1.96189i
$171$		0			0
$172$	14.0682	−	10.2212i	1.07269	−	0.779357i
$173$	−1.05159	−	0.223521i	−0.0799506	−	0.0169940i	0.167763	−	0.985827i	$-0.446346\pi$
$173$	−1.05159	−	0.223521i	−0.0799506	−	0.0169940i	−0.247713	+	0.968833i	$0.579679\pi$
$174$		0			0
$175$	−1.91548	+	6.15405i	−0.144797	+	0.465203i
$176$	−1.30102	−	2.25343i	−0.0980678	−	0.169858i
$177$		0			0
$178$	−2.50613	−	23.8443i	−0.187843	−	1.78720i
$179$	−15.2398	+	11.0724i	−1.13908	+	0.827587i	−0.986990	−	0.160781i	$-0.948599\pi$
$179$	−15.2398	+	11.0724i	−1.13908	+	0.827587i	−0.152085	+	0.988367i	$0.548599\pi$
$180$		0			0
$181$	−11.6647	−	8.47488i	−0.867029	−	0.629933i	0.0627594	−	0.998029i	$-0.480010\pi$
$181$	−11.6647	−	8.47488i	−0.867029	−	0.629933i	−0.929788	+	0.368096i	$0.880010\pi$
$182$	−7.98490	+	13.8303i	−0.591880	+	1.02517i
$183$		0			0
$184$	22.0035	−	4.67699i	1.62212	−	0.344792i
$185$	3.32013	−	16.1109i	0.244101	−	1.18449i
$186$		0			0
$187$	2.38103	+	2.64440i	0.174118	+	0.193378i
$188$	10.3855	−	31.9632i	0.757439	−	2.33116i
$189$		0			0
$190$	21.6505	+	19.2523i	1.57069	+	1.39671i
$191$	12.3893	+	13.7597i	0.896455	+	0.995614i	1.00000		0.000989586i	$0.000314995\pi$
$191$	12.3893	+	13.7597i	0.896455	+	0.995614i	−0.103544	+	0.994625i	$0.533018\pi$
$192$		0			0
$193$	−2.70053	−	4.67746i	−0.194388	−	0.336691i	0.752311	−	0.658808i	$-0.228939\pi$
$193$	−2.70053	−	4.67746i	−0.194388	−	0.336691i	−0.946700	+	0.322117i	$0.895606\pi$
$194$	−2.09426	+	19.9255i	−0.150359	+	1.43057i
$195$		0			0
$196$	2.32847	+	22.1539i	0.166319	+	1.58242i
$197$	12.6037	−	9.15716i	0.897980	−	0.652421i	−0.0399665	−	0.999201i	$-0.512725\pi$
$197$	12.6037	−	9.15716i	0.897980	−	0.652421i	0.937946	+	0.346780i	$0.112725\pi$
$198$		0			0
$199$	−17.1285			−1.21421			−0.607104	−	0.794623i	$-0.707669\pi$
$199$	−17.1285			−1.21421			−0.607104	+	0.794623i	$0.707669\pi$
$200$	−24.7927	−	10.6718i	−1.75311	−	0.754612i
$201$		0			0
$202$	−25.9444	+	28.8141i	−1.82544	+	2.02736i
$203$	8.16018	+	3.63315i	0.572733	+	0.254997i
$204$		0			0
$205$	8.64733	−	2.86912i	0.603955	−	0.200388i
$206$	−30.5471	−	22.1938i	−2.12832	−	1.54631i
$207$		0			0
$208$	−20.4398	−	14.8504i	−1.41724	−	1.02969i
$209$	1.79205	+	1.99027i	0.123959	+	0.137670i
$210$		0			0
$211$	−9.68372	+	10.7549i	−0.666655	+	0.740395i	−0.977702	−	0.209999i	$-0.932654\pi$
$211$	−9.68372	+	10.7549i	−0.666655	+	0.740395i	0.311047	+	0.950395i	$0.399320\pi$
$212$	−11.1675	+	2.37372i	−0.766986	+	0.163028i
$213$		0			0
$214$	−25.9987	−	5.52619i	−1.77723	−	0.377763i
$215$	3.73721	−	8.53606i	0.254876	−	0.582154i
$216$		0			0
$217$	1.60293	+	1.16460i	0.108814	+	0.0790579i
$218$	16.5135	−	28.6022i	1.11843	−	1.93718i
$219$		0			0
$220$	−4.16458	−	2.37009i	−0.280776	−	0.159792i
$221$	31.5638	+	14.0531i	2.12321	+	0.945316i
$222$		0			0
$223$	18.2430	+	3.87767i	1.22164	+	0.259668i	0.773210	−	0.634150i	$-0.218650\pi$
$223$	18.2430	+	3.87767i	1.22164	+	0.259668i	0.448431	+	0.893818i	$0.351983\pi$
$224$	2.30957			0.154314
$225$		0			0
$226$	23.6612			1.57392
$227$	16.6360	+	3.53610i	1.10417	+	0.234699i	0.723714	−	0.690100i	$-0.242433\pi$
$227$	16.6360	+	3.53610i	1.10417	+	0.234699i	0.380457	+	0.924799i	$0.375767\pi$
$228$		0			0
$229$	−19.8898	−	8.85552i	−1.31436	−	0.585189i	−0.374649	−	0.927167i	$-0.622237\pi$
$229$	−19.8898	−	8.85552i	−1.31436	−	0.585189i	−0.939708	+	0.341977i	$0.888903\pi$
$230$	17.1073	−	15.5968i	1.12802	−	1.02842i
$231$		0			0
$232$	−18.7040	+	32.3962i	−1.22798	+	2.12692i
$233$	7.60150	+	5.52281i	0.497991	+	0.361811i	0.808249	−	0.588841i	$-0.200416\pi$
$233$	7.60150	+	5.52281i	0.497991	+	0.361811i	−0.310258	+	0.950652i	$0.600416\pi$
$234$		0			0
$235$	−3.85359	−	17.5923i	−0.251380	−	1.14759i
$236$	−12.4877	−	2.65434i	−0.812880	−	0.172783i
$237$		0			0
$238$	−21.7065	+	4.61386i	−1.40702	+	0.299072i
$239$	−3.28802	+	3.65172i	−0.212684	+	0.236210i	−0.840042	−	0.542521i	$-0.817470\pi$
$239$	−3.28802	+	3.65172i	−0.212684	+	0.236210i	0.627358	+	0.778731i	$0.284136\pi$
$240$		0			0
$241$	−5.34404	−	5.93515i	−0.344240	−	0.382317i	0.546019	−	0.837773i	$-0.316143\pi$
$241$	−5.34404	−	5.93515i	−0.344240	−	0.382317i	−0.890258	+	0.455456i	$0.849476\pi$
$242$	21.5801	+	15.6788i	1.38722	+	1.00787i
$243$		0			0
$244$	−24.7706	−	17.9969i	−1.58577	−	1.15213i
$245$	7.07611	+	9.61343i	0.452076	+	0.614180i
$246$		0			0
$247$	23.7561	+	10.5769i	1.51156	+	0.672991i
$248$	−5.55215	+	6.16629i	−0.352562	+	0.391560i
$249$		0			0
$250$	−27.5667	+	3.41722i	−1.74347	+	0.216124i
$251$	−21.5099			−1.35769			−0.678847	−	0.734279i	$-0.737520\pi$
$251$	−21.5099			−1.35769			−0.678847	+	0.734279i	$0.737520\pi$
$252$		0			0
$253$	1.73126	−	1.25783i	0.108843	−	0.0790792i
$254$	−3.43595	−	32.6909i	−0.215591	−	2.05121i
$255$		0			0
$256$	3.40901	−	32.4346i	0.213063	−	2.02716i
$257$	−4.80713	−	8.32619i	−0.299860	−	0.519373i	0.676243	−	0.736678i	$-0.263607\pi$
$257$	−4.80713	−	8.32619i	−0.299860	−	0.519373i	−0.976104	+	0.217305i	$0.930273\pi$
$258$		0			0
$259$	6.34522	+	7.04708i	0.394273	+	0.437884i
$260$	−46.3010	−	4.57618i	−2.87147	−	0.283803i
$261$		0			0
$262$	−7.69800	+	23.6920i	−0.475584	+	1.46370i
$263$	−6.46203	−	7.17681i	−0.398466	−	0.442541i	0.510206	−	0.860052i	$-0.329569\pi$
$263$	−6.46203	−	7.17681i	−0.398466	−	0.442541i	−0.908672	+	0.417511i	$0.862902\pi$
$264$		0			0
$265$	−4.52104	+	4.12184i	−0.277725	+	0.253203i
$266$	−16.3371	+	3.47255i	−1.00169	+	0.212916i
$267$		0			0
$268$	0.948715	−	1.64322i	0.0579520	−	0.100376i
$269$	−14.7015	−	10.6812i	−0.896364	−	0.651246i	0.0411659	−	0.999152i	$-0.486893\pi$
$269$	−14.7015	−	10.6812i	−0.896364	−	0.651246i	−0.937529	+	0.347906i	$0.886893\pi$
$270$		0			0
$271$	−2.02436	+	1.47078i	−0.122971	+	0.0893437i	−0.647571	−	0.762005i	$-0.724215\pi$
$271$	−2.02436	+	1.47078i	−0.122971	+	0.0893437i	0.524600	+	0.851349i	$0.324215\pi$
$272$	−3.66977	−	34.9155i	−0.222512	−	2.11706i
$273$		0			0
$274$	13.1299	+	22.7416i	0.793204	+	1.37387i
$275$	−2.56754	+	0.0318612i	−0.154829	+	0.00192130i
$276$		0			0
$277$	−13.1783	−	2.80114i	−0.791809	−	0.168304i	−0.205784	−	0.978597i	$-0.565974\pi$
$277$	−13.1783	−	2.80114i	−0.791809	−	0.168304i	−0.586025	+	0.810293i	$0.699308\pi$
$278$	−1.19560	+	0.868656i	−0.0717075	+	0.0520985i
$279$		0			0
$280$	13.4272	−	7.86366i	0.802427	−	0.469944i
$281$	0.690611	−	0.307480i	0.0411984	−	0.0183427i	−0.386034	−	0.922485i	$-0.626155\pi$
$281$	0.690611	−	0.307480i	0.0411984	−	0.0183427i	0.427232	+	0.904142i	$0.359489\pi$
$282$		0			0
$283$	0.437736	−	4.16478i	0.0260207	−	0.247571i	−0.973778	−	0.227501i	$-0.926945\pi$
$283$	0.437736	−	4.16478i	0.0260207	−	0.247571i	0.999799	−	0.0200697i	$-0.00638881\pi$
$284$	−6.74840	+	1.43442i	−0.400444	+	0.0851169i
$285$		0			0
$286$	−6.22321	−	1.32278i	−0.367986	−	0.0782178i
$287$	−1.62304	+	4.99519i	−0.0958049	+	0.294857i
$288$		0			0
$289$	9.58309	+	29.4937i	0.563711	+	1.73492i
$290$	0.238844	+	38.4961i	0.0140254	+	2.26057i
$291$		0			0
$292$	3.84702	−	36.6020i	0.225130	−	2.14197i
$293$	13.1006	+	22.6909i	0.765344	+	1.32561i	0.940065	+	0.340997i	$0.110764\pi$
$293$	13.1006	+	22.6909i	0.765344	+	1.32561i	−0.174721	+	0.984618i	$0.555902\pi$
$294$		0			0
$295$	−6.49315	+	2.15438i	−0.378046	+	0.125433i
$296$	−32.1283	+	23.3426i	−1.86742	+	1.35676i
$297$		0			0
$298$	−1.56073	−	4.80343i	−0.0904105	−	0.278255i
$299$	10.3891	−	17.9945i	0.600819	−	1.04065i
$300$		0			0
$301$	2.68592	+	4.65215i	0.154814	+	0.268146i
$302$	6.99441	−	7.76808i	0.402483	−	0.447003i
$303$		0			0
$304$	−2.76200	−	26.2787i	−0.158411	−	1.50718i
$305$	−16.3276	−	1.61375i	−0.934917	−	0.0924029i
$306$		0			0
$307$	13.6647			0.779887			0.389944	−	0.920839i	$-0.372495\pi$
$307$	13.6647			0.779887			0.389944	+	0.920839i	$0.372495\pi$
$308$	2.52355	−	1.12356i	0.143793	−	0.0640206i
$309$		0			0
$310$	−1.72352	+	8.36336i	−0.0978896	+	0.475007i
$311$	−0.639250	+	0.709959i	−0.0362486	+	0.0402581i	−0.760996	−	0.648756i	$-0.775290\pi$
$311$	−0.639250	+	0.709959i	−0.0362486	+	0.0402581i	0.724748	+	0.689014i	$0.241956\pi$
$312$		0			0
$313$	−8.02015	−	8.90728i	−0.453326	−	0.503469i	0.472547	−	0.881306i	$-0.343335\pi$
$313$	−8.02015	−	8.90728i	−0.453326	−	0.503469i	−0.925872	+	0.377836i	$0.876668\pi$
$314$	−0.428576	−	1.31902i	−0.0241859	−	0.0744367i
$315$		0			0
$316$	−4.43953	+	13.6635i	−0.249743	+	0.768631i
$317$	−2.06249	+	0.918281i	−0.115841	+	0.0515758i	−0.463839	−	0.885920i	$-0.653528\pi$
$317$	−2.06249	+	0.918281i	−0.115841	+	0.0515758i	0.347998	+	0.937495i	$0.386862\pi$
$318$		0			0
$319$	−0.371976	+	3.53911i	−0.0208266	+	0.198152i
$320$	−5.23973	−	11.5748i	−0.292910	−	0.647052i
$321$		0			0
$322$	1.39499	+	13.2724i	0.0777395	+	0.739642i
$323$	11.1664	+	34.3666i	0.621314	+	1.91221i
$324$		0			0
$325$	−22.6489	+	10.4226i	−1.25634	+	0.578141i
$326$	21.5248	−	37.2821i	1.19215	−	2.06486i
$327$		0			0
$328$	−20.0942	−	8.94651i	−1.10952	−	0.493988i
$329$	9.48453	+	4.22278i	0.522899	+	0.232810i
$330$		0			0
$331$	12.2444	−	5.45156i	0.673014	−	0.299645i	−0.0416306	−	0.999133i	$-0.513255\pi$
$331$	12.2444	−	5.45156i	0.673014	−	0.299645i	0.714644	+	0.699488i	$0.246589\pi$
$332$	−61.2623			−3.36221
$333$		0			0
$334$	5.03344	−	15.4913i	0.275418	−	0.847649i
$335$	−0.00630826	−	1.01675i	−0.000344657	−	0.0555508i
$336$		0			0
$337$	−11.7817	+	2.50428i	−0.641790	+	0.136417i	−0.517300	−	0.855804i	$-0.673063\pi$
$337$	−11.7817	+	2.50428i	−0.641790	+	0.136417i	−0.124490	+	0.992221i	$0.539730\pi$
$338$	−28.8326	+	6.12855i	−1.56828	+	0.333349i
$339$		0			0
$340$	−38.3257	−	52.0684i	−2.07850	−	2.82381i
$341$	−0.243921	+	0.750712i	−0.0132091	+	0.0406533i
$342$		0			0
$343$	−15.9048			−0.858777
$344$	−20.5517	+	9.15020i	−1.10807	+	0.493346i
$345$		0			0
$346$	2.44013	+	1.08641i	0.131182	+	0.0584060i
$347$	−0.638552	−	0.284302i	−0.0342793	−	0.0152621i	0.389525	−	0.921016i	$-0.372639\pi$
$347$	−0.638552	−	0.284302i	−0.0342793	−	0.0152621i	−0.423805	+	0.905754i	$0.639306\pi$
$348$		0			0
$349$	8.65614	−	14.9929i	0.463353	−	0.802551i	−0.535773	−	0.844362i	$-0.679980\pi$
$349$	8.65614	−	14.9929i	0.463353	−	0.802551i	0.999126	+	0.0418117i	$0.0133130\pi$
$350$	7.83399	−	13.9663i	0.418744	−	0.746528i
$351$		0			0
$352$	0.284330	+	0.875079i	0.0151549	+	0.0466419i
$353$	−0.551935	−	5.25131i	−0.0293765	−	0.279499i	−0.999342	−	0.0362582i	$-0.988456\pi$
$353$	−0.551935	−	5.25131i	−0.0293765	−	0.279499i	0.969966	−	0.243241i	$-0.0782105\pi$
$354$		0			0
$355$	−2.73202	+	2.49079i	−0.145001	+	0.132197i
$356$	−4.20912	+	40.0471i	−0.223083	+	2.12249i
$357$		0			0
$358$	42.7556	−	19.0360i	2.25970	−	1.00609i
$359$	−0.334961	+	1.03090i	−0.0176786	+	0.0544091i	−0.959507	−	0.281686i	$-0.909106\pi$
$359$	−0.334961	+	1.03090i	−0.0176786	+	0.0544091i	0.941828	+	0.336095i	$0.109106\pi$
$360$		0			0
$361$	2.53289	+	7.79543i	0.133310	+	0.410286i
$362$	23.9700	+	26.6214i	1.25983	+	1.39919i
$363$		0			0
$364$	17.9473	−	19.9324i	0.940692	−	1.04474i
$365$	−8.13319	−	17.9666i	−0.425710	−	0.940415i
$366$		0			0
$367$	28.5328	−	12.7036i	1.48940	−	0.663123i	0.509111	−	0.860701i	$-0.329974\pi$
$367$	28.5328	−	12.7036i	1.48940	−	0.663123i	0.980287	+	0.197578i	$0.0633075\pi$
$368$	−21.1132			−1.10060
$369$		0			0
$370$	−16.3909	+	37.4379i	−0.852121	+	1.94630i
$371$	−0.368661	−	3.50757i	−0.0191399	−	0.182104i
$372$		0			0
$373$	−0.165419	+	0.183716i	−0.00856507	+	0.00951248i	−0.747412	−	0.664361i	$-0.768704\pi$
$373$	−0.165419	+	0.183716i	−0.00856507	+	0.00951248i	0.738847	+	0.673873i	$0.235371\pi$
$374$	−4.42044	−	7.65643i	−0.228576	−	0.395905i
$375$		0			0
$376$	−21.7395	+	37.6539i	−1.12113	+	1.94185i
$377$	10.6775	+	32.8619i	0.549917	+	1.69247i
$378$		0			0
$379$	18.0726	−	13.1305i	0.928325	−	0.674467i	−0.0172574	−	0.999851i	$-0.505493\pi$
$379$	18.0726	−	13.1305i	0.928325	−	0.674467i	0.945582	+	0.325384i	$0.105493\pi$
$380$	−28.8453	−	39.1885i	−1.47973	−	2.01033i
$381$		0			0
$382$	−23.0010	−	39.8388i	−1.17683	−	2.03833i
$383$	2.77196	−	26.3735i	0.141641	−	1.34762i	−0.660653	−	0.750692i	$-0.729720\pi$
$383$	2.77196	−	26.3735i	0.141641	−	1.34762i	0.802293	−	0.596930i	$-0.203613\pi$
$384$		0			0
$385$	0.862627	−	1.20293i	0.0439635	−	0.0613069i
$386$	4.14671	+	12.7622i	0.211062	+	0.649581i
$387$		0			0
$388$	10.3984	−	32.0029i	0.527898	−	1.62470i
$389$	−12.7219	−	2.70413i	−0.645028	−	0.137105i	−0.126229	−	0.992001i	$-0.540287\pi$
$389$	−12.7219	−	2.70413i	−0.645028	−	0.137105i	−0.518799	+	0.854896i	$0.673621\pi$
$390$		0			0
$391$	28.2423	−	6.00308i	1.42827	−	0.303589i
$392$	3.01235	−	28.6606i	0.152147	−	1.44758i
$393$		0			0
$394$	−35.3601	+	15.7433i	−1.78142	+	0.793138i
$395$	1.64731	+	7.52027i	0.0828854	+	0.378386i
$396$		0			0
$397$	24.8748	−	18.0726i	1.24843	−	0.907040i	0.250303	−	0.968168i	$-0.419470\pi$
$397$	24.8748	−	18.0726i	1.24843	−	0.907040i	0.998130	+	0.0611280i	$0.0194698\pi$
$398$	41.6261	+	8.84790i	2.08653	+	0.443505i
$399$		0			0
$400$	20.6787	+	14.6354i	1.03394	+	0.731771i
$401$	−5.05931	−	8.76298i	−0.252650	−	0.437602i	0.711605	−	0.702580i	$-0.247969\pi$
$401$	−5.05931	−	8.76298i	−0.252650	−	0.437602i	−0.964255	+	0.264978i	$0.914635\pi$
$402$		0			0
$403$	0.801137	+	7.62231i	0.0399075	+	0.379694i
$404$	52.6838	−	38.2771i	2.62112	−	1.90435i
$405$		0			0
$406$	−17.9543	−	13.0446i	−0.891058	−	0.647392i
$407$	−1.88893	+	3.27173i	−0.0936309	+	0.162173i
$408$		0			0
$409$	17.3238	−	3.68229i	0.856607	−	0.182077i	0.241383	−	0.970430i	$-0.422399\pi$
$409$	17.3238	−	3.68229i	0.856607	−	0.182077i	0.615224	+	0.788353i	$0.289066\pi$
$410$	−22.4970	+	2.50574i	−1.11105	+	0.123750i
$411$		0			0
$412$	42.4337	+	47.1274i	2.09056	+	2.32180i
$413$	1.21871	−	3.75082i	0.0599690	−	0.184566i
$414$		0			0
$415$	−28.3278	+	16.5902i	−1.39056	+	0.814383i
$416$	5.97802	+	6.63927i	0.293097	+	0.325517i
$417$		0			0
$418$	−3.32698	−	5.76250i	−0.162728	−	0.281853i
$419$	−1.40339	+	13.3523i	−0.0685600	+	0.652305i	0.905240	+	0.424900i	$0.139691\pi$
$419$	−1.40339	+	13.3523i	−0.0685600	+	0.652305i	−0.973800	+	0.227405i	$0.926976\pi$
$420$		0			0
$421$	3.40776	+	32.4227i	0.166084	+	1.58019i	0.687051	+	0.726609i	$0.258905\pi$
$421$	3.40776	+	32.4227i	0.166084	+	1.58019i	−0.520967	+	0.853577i	$0.674428\pi$
$422$	29.0891	−	21.1345i	1.41604	−	1.02881i
$423$		0			0
$424$	14.7702			0.717304
$425$	−31.8224	−	13.6977i	−1.54361	−	0.664434i
$426$		0			0
$427$	6.32893	−	7.02899i	0.306279	−	0.340157i
$428$	40.7817	+	18.1572i	1.97126	+	0.877660i
$429$		0			0
$430$	−13.4916	+	18.8140i	−0.650625	+	0.907293i
$431$	−7.24479	−	5.26365i	−0.348969	−	0.253541i	0.399467	−	0.916747i	$-0.369195\pi$
$431$	−7.24479	−	5.26365i	−0.348969	−	0.253541i	−0.748436	+	0.663206i	$0.769195\pi$
$432$		0			0
$433$	22.5500	+	16.3836i	1.08369	+	0.787344i	0.978322	−	0.207090i	$-0.0663992\pi$
$433$	22.5500	+	16.3836i	1.08369	+	0.787344i	0.105364	+	0.994434i	$0.466399\pi$
$434$	−3.29389	−	3.65823i	−0.158112	−	0.175601i
$435$		0			0
$436$	−37.1165	+	41.2220i	−1.77756	+	1.97418i
$437$	21.2561	−	4.51813i	1.01682	−	0.216132i
$438$		0			0
$439$	3.07587	+	0.653797i	0.146803	+	0.0312040i	0.280727	−	0.959788i	$-0.409424\pi$
$439$	3.07587	+	0.653797i	0.146803	+	0.0312040i	−0.133924	+	0.990992i	$0.542758\pi$
$440$	4.63250	+	4.11937i	0.220846	+	0.196383i
$441$		0			0
$442$	−69.4479	−	50.4568i	−3.30330	−	2.39999i
$443$	−9.86697	+	17.0901i	−0.468794	+	0.811975i	−0.999364	−	0.0356665i	$-0.988645\pi$
$443$	−9.86697	+	17.0901i	−0.468794	+	0.811975i	0.530570	+	0.847641i	$0.321978\pi$
$444$		0			0
$445$	8.89873	+	19.6577i	0.421840	+	0.931866i
$446$	−42.3315	−	18.8472i	−2.00445	−	0.892440i
$447$		0			0
$448$	7.16447	+	1.52285i	0.338489	+	0.0719481i
$449$	13.7726			0.649970			0.324985	−	0.945719i	$-0.394641\pi$
$449$	13.7726			0.649970			0.324985	+	0.945719i	$0.394641\pi$
$450$		0			0
$451$	−2.09246			−0.0985300
$452$	−38.8713	−	8.26235i	−1.82835	−	0.388628i
$453$		0			0
$454$	−38.6026	−	17.1870i	−1.81171	−	0.806626i
$455$	2.90100	−	14.0770i	0.136001	−	0.659942i
$456$		0			0
$457$	8.03370	−	13.9148i	0.375801	−	0.650906i	−0.614646	−	0.788803i	$-0.710701\pi$
$457$	8.03370	−	13.9148i	0.375801	−	0.650906i	0.990447	+	0.137897i	$0.0440344\pi$
$458$	43.7623	+	31.7952i	2.04488	+	1.48569i
$459$		0			0
$460$	−33.5506	+	19.6490i	−1.56431	+	0.916140i
$461$	10.0438	+	2.13487i	0.467785	+	0.0994309i	0.435773	−	0.900057i	$-0.356475\pi$
$461$	10.0438	+	2.13487i	0.467785	+	0.0994309i	0.0320125	+	0.999487i	$0.489808\pi$
$462$		0			0
$463$	−17.6285	+	3.74706i	−0.819268	+	0.174141i	−0.598435	−	0.801171i	$-0.704211\pi$
$463$	−17.6285	+	3.74706i	−0.819268	+	0.174141i	−0.220832	+	0.975312i	$0.570877\pi$
$464$	23.4931	−	26.0918i	1.09064	−	1.21128i
$465$		0			0
$466$	−15.6205	−	17.3483i	−0.723604	−	0.803644i
$467$	−28.5731	−	20.7596i	−1.32221	−	0.960639i	−0.999902	−	0.0140027i	$-0.995543\pi$
$467$	−28.5731	−	20.7596i	−1.32221	−	0.960639i	−0.322304	−	0.946636i	$-0.604457\pi$
$468$		0			0
$469$	0.474203	+	0.344529i	0.0218967	+	0.0159089i
$470$	0.277607	+	44.7438i	0.0128050	+	2.06388i
$471$		0			0
$472$	15.0884	+	6.71780i	0.694501	+	0.309212i
$473$	−1.43201	+	1.59040i	−0.0658437	+	0.0731268i
$474$		0			0
$475$	−23.9506	−	10.3093i	−1.09893	−	0.473025i
$476$	37.2712			1.70832
$477$		0			0
$478$	9.87695	−	7.17603i	0.451761	−	0.328224i
$479$	−0.178641	−	1.69966i	−0.00816233	−	0.0776594i	0.989682	−	0.143278i	$-0.0457645\pi$
$479$	−0.178641	−	1.69966i	−0.00816233	−	0.0776594i	−0.997845	+	0.0656191i	$0.979098\pi$
$480$		0			0
$481$	−3.83430	+	36.4810i	−0.174829	+	1.66339i
$482$	9.92134	+	17.1843i	0.451905	+	0.782722i
$483$		0			0
$484$	−29.9774	−	33.2933i	−1.36261	−	1.51333i
$485$	−3.85838	−	17.6142i	−0.175200	−	0.799818i
$486$		0			0
$487$	10.1084	−	31.1106i	0.458057	−	1.40975i	−0.409452	−	0.912332i	$-0.634280\pi$
$487$	10.1084	−	31.1106i	0.458057	−	1.40975i	0.867509	−	0.497422i	$-0.165720\pi$
$488$	26.5048	+	29.4366i	1.19982	+	1.33253i
$489$		0			0
$490$	−12.2306	−	27.0180i	−0.552523	−	1.22055i
$491$	40.3627	−	8.57936i	1.82154	−	0.387181i	0.834943	−	0.550336i	$-0.185500\pi$
$491$	40.3627	−	8.57936i	1.82154	−	0.387181i	0.986600	+	0.163155i	$0.0521671\pi$
$492$		0			0
$493$	−24.0072	+	41.5817i	−1.08123	+	1.87275i
$494$	−52.2689	−	37.9756i	−2.35169	−	1.70860i
$495$		0			0
$496$	6.30049	−	4.57758i	0.282901	−	0.205539i
$497$	−0.222778	−	2.11959i	−0.00999296	−	0.0950766i
$498$		0			0
$499$	1.73929	+	3.01255i	0.0778615	+	0.134860i	0.902327	−	0.431052i	$-0.141857\pi$
$499$	1.73929	+	3.01255i	0.0778615	+	0.134860i	−0.824466	+	0.565912i	$0.808524\pi$
$500$	46.4807	+	4.01223i	2.07868	+	0.179432i
$501$		0			0
$502$	52.2739	+	11.1112i	2.33310	+	0.495916i
$503$	−13.8073	+	10.0316i	−0.615638	+	0.447287i	−0.851395	−	0.524525i	$-0.824243\pi$
$503$	−13.8073	+	10.0316i	−0.615638	+	0.447287i	0.235757	+	0.971812i	$0.424243\pi$
$504$		0			0
$505$	13.9954	−	31.9665i	0.622788	−	1.42249i
$506$	−4.85709	+	2.16251i	−0.215924	+	0.0961355i
$507$		0			0
$508$	−5.77078	+	54.9053i	−0.256037	+	2.43603i
$509$	7.62861	−	1.62151i	0.338132	−	0.0718723i	−0.0357163	−	0.999362i	$-0.511371\pi$
$509$	7.62861	−	1.62151i	0.338132	−	0.0718723i	0.373849	+	0.927490i	$0.378038\pi$
$510$		0			0
$511$	11.1208	+	2.36380i	0.491955	+	0.104568i
$512$	−14.0995	+	43.3938i	−0.623115	+	1.91775i
$513$		0			0
$514$	7.38142	+	22.7177i	0.325580	+	1.00203i
$515$	32.3839	+	10.3005i	1.42700	+	0.453893i
$516$		0			0
$517$	−0.432345	+	4.11349i	−0.0190145	+	0.180911i
$518$	−11.7801	−	20.4037i	−0.517586	−	0.896486i
$519$		0			0
$520$	57.3601	+	18.2447i	2.51540	+	0.800085i
$521$	9.24944	−	6.72011i	0.405225	−	0.294413i	−0.366441	−	0.930441i	$-0.619424\pi$
$521$	9.24944	−	6.72011i	0.405225	−	0.294413i	0.771666	+	0.636028i	$0.219424\pi$
$522$		0			0
$523$	6.03668	+	18.5790i	0.263966	+	0.812403i	0.991930	+	0.126788i	$0.0404667\pi$
$523$	6.03668	+	18.5790i	0.263966	+	0.812403i	−0.727964	+	0.685615i	$0.759533\pi$
$524$	20.9196	−	36.2338i	0.913876	−	1.58288i
$525$		0			0
$526$	11.9969	+	20.7793i	0.523090	+	0.906019i
$527$	−7.12638	+	7.91465i	−0.310430	+	0.344768i
$528$		0			0
$529$	0.589142	+	5.60531i	0.0256149	+	0.243709i
$530$	13.1163	−	7.68160i	0.569736	−	0.333668i
$531$		0			0
$532$	28.0516			1.21619
$533$	−18.5606	+	8.26372i	−0.803949	+	0.357941i
$534$		0			0
$535$	23.7746	−	2.64804i	1.02786	−	0.114485i
$536$	−1.64253	+	1.82421i	−0.0709463	+	0.0787938i
$537$		0			0
$538$	30.2103	+	33.5520i	1.30246	+	1.44653i
$539$	−0.847169	−	2.60732i	−0.0364902	−	0.112305i
$540$		0			0
$541$	2.36879	−	7.29039i	0.101842	−	0.313439i	−0.887134	−	0.461512i	$-0.847307\pi$
$541$	2.36879	−	7.29039i	0.101842	−	0.313439i	0.988976	+	0.148073i	$0.0473072\pi$
$542$	5.67939	−	2.52863i	0.243951	−	0.108614i
$543$		0			0
$544$	−1.29768	+	12.3466i	−0.0556375	+	0.529355i
$545$	−5.99952	+	29.1125i	−0.256991	+	1.24704i
$546$		0			0
$547$	1.50602	+	14.3288i	0.0643929	+	0.612657i	0.978366	+	0.206882i	$0.0663317\pi$
$547$	1.50602	+	14.3288i	0.0643929	+	0.612657i	−0.913973	+	0.405775i	$0.867002\pi$
$548$	−13.6289	−	41.9454i	−0.582197	−	1.79182i
$549$		0			0
$550$	6.25616	+	1.24886i	0.266764	+	0.0532516i
$551$	−18.0687	+	31.2959i	−0.769751	+	1.33325i
$552$		0			0
$553$	−4.05440	−	1.80514i	−0.172411	−	0.0767622i
$554$	30.5793	+	13.6148i	1.29919	+	0.578437i
$555$		0			0
$556$	2.26750	−	1.00956i	0.0961633	−	0.0428147i
$557$	−11.9602			−0.506771			−0.253386	−	0.967365i	$-0.581544\pi$
$557$	−11.9602			−0.506771			−0.253386	+	0.967365i	$0.581544\pi$
$558$		0			0
$559$	−6.42128	+	19.7627i	−0.271591	+	0.835872i
$560$	−13.8615	+	4.59913i	−0.585753	+	0.194349i
$561$		0			0
$562$	−1.83717	+	0.390502i	−0.0774963	+	0.0164724i
$563$	−40.3973	+	8.58670i	−1.70254	+	0.361886i	−0.953676	−	0.300836i	$-0.902734\pi$
$563$	−40.3973	+	8.58670i	−1.70254	+	0.361886i	−0.748865	+	0.662722i	$0.769401\pi$
$564$		0			0
$565$	−20.2117	+	6.70609i	−0.850311	+	0.282127i
$566$	−3.21516	+	9.89523i	−0.135143	+	0.415928i
$567$		0			0
$568$	8.92549			0.374505
$569$	13.3805	−	5.95739i	0.560941	−	0.249747i	−0.106623	−	0.994300i	$-0.534004\pi$
$569$	13.3805	−	5.95739i	0.560941	−	0.249747i	0.667564	+	0.744553i	$0.267337\pi$
$570$		0			0
$571$	−21.3865	−	9.52187i	−0.894996	−	0.398478i	−0.0929016	−	0.995675i	$-0.529614\pi$
$571$	−21.3865	−	9.52187i	−0.894996	−	0.398478i	−0.802094	+	0.597197i	$0.796281\pi$
$572$	9.76175	+	4.34621i	0.408159	+	0.181724i
$573$		0			0
$574$	6.52466	−	11.3010i	0.272334	−	0.471696i
$575$	−10.1928	+	18.1715i	−0.425069	+	0.757803i
$576$		0			0
$577$	0.219132	+	0.674419i	0.00912259	+	0.0280764i	0.955514	−	0.294945i	$-0.0953014\pi$
$577$	0.219132	+	0.674419i	0.00912259	+	0.0280764i	−0.946392	+	0.323022i	$0.895301\pi$
$578$	−8.05378	−	76.6266i	−0.334993	−	3.18724i
$579$		0			0
$580$	13.0502	−	63.3259i	0.541882	−	2.62947i
$581$	1.97820	−	18.8213i	0.0820694	−	0.780839i
$582$		0			0
$583$	1.28361	−	0.571500i	0.0531617	−	0.0236691i
$584$	−14.7132	+	45.2827i	−0.608838	+	1.87381i
$585$		0			0
$586$	−20.1161	−	61.9111i	−0.830990	−	2.55752i
$587$	7.12521	+	7.91335i	0.294089	+	0.326619i	0.872023	−	0.489464i	$-0.162808\pi$
$587$	7.12521	+	7.91335i	0.294089	+	0.326619i	−0.577934	+	0.816083i	$0.696141\pi$
$588$		0			0
$589$	−5.36357	+	5.95685i	−0.221002	+	0.245448i
$590$	16.8927	−	1.88153i	0.695460	−	0.0774612i
$591$		0			0
$592$	34.0507	−	15.1604i	1.39948	−	0.623087i
$593$	47.7160			1.95946			0.979730	−	0.200323i	$-0.0641990\pi$
$593$	47.7160			1.95946			0.979730	+	0.200323i	$0.0641990\pi$
$594$		0			0
$595$	17.2343	−	10.0933i	0.706535	−	0.413784i
$596$	0.886680	+	8.43620i	0.0363198	+	0.345560i
$597$		0			0
$598$	−34.5432	+	38.3641i	−1.41257	+	1.56882i
$599$	−1.95259	−	3.38199i	−0.0797808	−	0.138184i	0.823374	−	0.567498i	$-0.192089\pi$
$599$	−1.95259	−	3.38199i	−0.0797808	−	0.138184i	−0.903155	+	0.429314i	$0.858755\pi$
$600$		0			0
$601$	−3.54162	+	6.13427i	−0.144466	+	0.250222i	−0.929174	−	0.369644i	$-0.879480\pi$
$601$	−3.54162	+	6.13427i	−0.144466	+	0.250222i	0.784708	+	0.619866i	$0.212813\pi$
$602$	−4.12427	−	12.6932i	−0.168093	−	0.517336i
$603$		0			0
$604$	−14.2032	+	10.3192i	−0.577920	+	0.419883i
$605$	−22.8776	−	7.27678i	−0.930108	−	0.295843i
$606$		0			0
$607$	2.38982	+	4.13929i	0.0969997	+	0.168008i	0.910441	−	0.413638i	$-0.135742\pi$
$607$	2.38982	+	4.13929i	0.0969997	+	0.168008i	−0.813442	+	0.581646i	$0.802409\pi$
$608$	−0.976678	+	9.29247i	−0.0396095	+	0.376860i
$609$		0			0
$610$	38.8462	+	12.3560i	1.57284	+	0.500278i
$611$	12.4103	+	38.1951i	0.502069	+	1.54521i
$612$		0			0
$613$	14.0778	−	43.3269i	0.568596	−	1.74996i	−0.0884219	−	0.996083i	$-0.528182\pi$
$613$	14.0778	−	43.3269i	0.568596	−	1.74996i	0.657018	−	0.753875i	$-0.271818\pi$
$614$	−33.2083	−	7.05865i	−1.34018	−	0.284864i
$615$		0			0
$616$	−3.49560	+	0.743013i	−0.140842	+	0.0299368i
$617$	−2.02983	+	19.3126i	−0.0817179	+	0.777494i	0.874537	+	0.484959i	$0.161166\pi$
$617$	−2.02983	+	19.3126i	−0.0817179	+	0.777494i	−0.956255	+	0.292535i	$0.905501\pi$
$618$		0			0
$619$	24.9267	−	11.0981i	1.00189	−	0.446070i	0.160812	−	0.986985i	$-0.448589\pi$
$619$	24.9267	−	11.0981i	1.00189	−	0.446070i	0.841077	+	0.540915i	$0.181922\pi$
$620$	5.75189	−	13.1377i	0.231001	−	0.527623i
$621$		0			0
$622$	1.92026	−	1.39515i	0.0769953	−	0.0559404i
$623$	−12.1675	−	2.58629i	−0.487482	−	0.103618i
$624$		0			0
$625$	22.5793	−	10.7320i	0.903171	−	0.429281i
$626$	14.8896	+	25.7896i	0.595109	+	1.03076i
$627$		0			0
$628$	0.243482	+	2.31658i	0.00971601	+	0.0924416i
$629$	−41.2378	+	29.9610i	−1.64426	+	1.19462i
$630$		0			0
$631$	12.6772	+	9.21053i	0.504672	+	0.366665i	0.810799	−	0.585325i	$-0.199033\pi$
$631$	12.6772	+	9.21053i	0.504672	+	0.366665i	−0.306127	+	0.951991i	$0.599033\pi$
$632$	9.29310	−	16.0961i	0.369660	−	0.640269i
$633$		0			0
$634$	5.48667	−	1.16623i	0.217903	−	0.0463168i
$635$	12.2003	+	26.9511i	0.484154	+	1.06952i
$636$		0			0
$637$	−17.8116	−	19.7818i	−0.705723	−	0.783785i
$638$	2.73215	−	8.40869i	0.108167	−	0.332903i
$639$		0			0
$640$	8.46913	+	38.6631i	0.334772	+	1.52829i
$641$	−23.6349	−	26.2493i	−0.933524	−	1.03678i	−0.999241	−	0.0389455i	$-0.987600\pi$
$641$	−23.6349	−	26.2493i	−0.933524	−	1.03678i	0.0657170	−	0.997838i	$-0.479067\pi$
$642$		0			0
$643$	5.45444	+	9.44736i	0.215102	+	0.372567i	0.953304	−	0.302012i	$-0.0976583\pi$
$643$	5.45444	+	9.44736i	0.215102	+	0.372567i	−0.738202	+	0.674580i	$0.764325\pi$
$644$	2.34292	−	22.2914i	0.0923240	−	0.878404i
$645$		0			0
$646$	−9.38440	−	89.2866i	−0.369224	−	3.51293i
$647$	28.4306	−	20.6560i	1.11772	−	0.812072i	0.133860	−	0.991000i	$-0.457263\pi$
$647$	28.4306	−	20.6560i	1.11772	−	0.812072i	0.983862	+	0.178928i	$0.0572629\pi$
$648$		0			0
$649$	1.57119			0.0616748
$650$	60.4258	−	13.6297i	2.37010	−	0.534600i
$651$		0			0
$652$	−48.3802	+	53.7317i	−1.89472	+	2.10429i
$653$	11.5270	+	5.13214i	0.451086	+	0.200836i	0.619689	−	0.784848i	$-0.287259\pi$
$653$	11.5270	+	5.13214i	0.451086	+	0.200836i	−0.168603	+	0.985684i	$0.553926\pi$
$654$		0			0
$655$	−0.139100	−	22.4197i	−0.00543509	−	0.876011i
$656$	16.7018	+	12.1346i	0.652097	+	0.473776i
$657$		0			0
$658$	−20.8682	−	15.1616i	−0.813527	−	0.591062i
$659$	11.9432	+	13.2643i	0.465242	+	0.516703i	0.929413	−	0.369043i	$-0.120314\pi$
$659$	11.9432	+	13.2643i	0.465242	+	0.516703i	−0.464171	+	0.885746i	$0.653648\pi$
$660$		0			0
$661$	24.5369	−	27.2510i	0.954375	−	1.05994i	−0.0437689	−	0.999042i	$-0.513937\pi$
$661$	24.5369	−	27.2510i	0.954375	−	1.05994i	0.998144	−	0.0608991i	$-0.0193968\pi$
$662$	−32.5727	+	6.92354i	−1.26597	+	0.269091i
$663$		0			0
$664$	77.5235	+	16.4781i	3.00850	+	0.639476i
$665$	12.9711	−	7.59656i	0.502998	−	0.294582i
$666$		0			0
$667$	23.3603	+	16.9723i	0.904516	+	0.657169i
$668$	−13.6786	+	23.6920i	−0.529240	+	0.916670i
$669$		0			0
$670$	−0.509880	+	2.47418i	−0.0196984	+	0.0955859i
$671$	3.44239	+	1.53265i	0.132892	+	0.0591674i
$672$		0			0
$673$	−20.3716	−	4.33013i	−0.785269	−	0.166914i	−0.202208	−	0.979343i	$-0.564812\pi$
$673$	−20.3716	−	4.33013i	−0.785269	−	0.166914i	−0.583061	+	0.812428i	$0.698145\pi$
$674$	29.9258			1.15270
$675$		0			0
$676$	49.5070			1.90411
$677$	6.76634	+	1.43823i	0.260052	+	0.0552757i	0.336092	−	0.941829i	$-0.390895\pi$
$677$	6.76634	+	1.43823i	0.260052	+	0.0552757i	−0.0760407	+	0.997105i	$0.524228\pi$
$678$		0			0
$679$	9.49631	+	4.22803i	0.364435	+	0.162257i
$680$	34.4936	+	76.1980i	1.32277	+	2.92206i
$681$		0			0
$682$	0.980570	−	1.69840i	0.0375480	−	0.0650350i
$683$	−25.6445	−	18.6318i	−0.981258	−	0.712926i	−0.0232689	−	0.999729i	$-0.507407\pi$
$683$	−25.6445	−	18.6318i	−0.981258	−	0.712926i	−0.957989	+	0.286803i	$0.907407\pi$
$684$		0			0
$685$	−17.6611	−	15.7048i	−0.674796	−	0.600050i
$686$	38.6522	+	8.21577i	1.47575	+	0.313680i
$687$		0			0
$688$	20.6532	−	4.38998i	0.787398	−	0.167367i
$689$	9.12892	−	10.1387i	0.347784	−	0.386253i
$690$		0			0
$691$	−2.74243	−	3.04578i	−0.104327	−	0.115867i	0.688720	−	0.725028i	$-0.258173\pi$
$691$	−2.74243	−	3.04578i	−0.104327	−	0.115867i	−0.793047	+	0.609161i	$0.791506\pi$
$692$	−3.62934	−	2.63687i	−0.137967	−	0.100239i
$693$		0			0
$694$	1.40496	+	1.02077i	0.0533317	+	0.0387478i
$695$	0.775101	−	1.08087i	0.0294012	−	0.0409999i
$696$		0			0
$697$	−25.7916	−	11.4832i	−0.976926	−	0.434956i
$698$	−28.7811	+	31.9646i	−1.08938	+	1.20988i
$699$		0			0
$700$	−17.7468	+	20.2086i	−0.670767	+	0.763813i
$701$	−1.75231			−0.0661838			−0.0330919	−	0.999452i	$-0.510535\pi$
$701$	−1.75231			−0.0661838			−0.0330919	+	0.999452i	$0.510535\pi$
$702$		0			0
$703$	−31.0370	+	22.5497i	−1.17058	+	0.850479i
$704$	0.305017	+	2.90205i	0.0114958	+	0.109375i
$705$		0			0
$706$	−1.37129	+	13.0470i	−0.0516092	+	0.491029i
$707$	10.0585	+	17.4218i	0.378287	+	0.655213i
$708$		0			0
$709$	−17.0356	−	18.9200i	−0.639787	−	0.710556i	0.332825	−	0.942989i	$-0.391998\pi$
$709$	−17.0356	−	18.9200i	−0.639787	−	0.710556i	−0.972612	+	0.232433i	$0.925331\pi$
$710$	7.92606	−	4.64192i	0.297460	−	0.174208i
$711$		0			0
$712$	16.0981	−	49.5449i	0.603303	−	1.85677i
$713$	4.28567	+	4.75972i	0.160500	+	0.178253i
$714$		0			0
$715$	5.69083	−	0.633852i	0.212825	−	0.0237047i
$716$	−76.8874	+	16.3429i	−2.87342	+	0.610763i
$717$		0			0
$718$	1.34655	−	2.33230i	0.0502530	−	0.0870407i
$719$	−9.49736	−	6.90024i	−0.354192	−	0.257335i	0.396434	−	0.918063i	$-0.370248\pi$
$719$	−9.49736	−	6.90024i	−0.354192	−	0.257335i	−0.750625	+	0.660728i	$0.770248\pi$
$720$		0			0
$721$	−15.8489	+	11.5149i	−0.590244	+	0.428838i
$722$	−2.12868	−	20.2530i	−0.0792213	−	0.753740i
$723$		0			0
$724$	−30.0825	−	52.1045i	−1.11801	−	1.93645i
$725$	−11.1146	−	32.8161i	−0.412787	−	1.21876i
$726$		0			0
$727$	−19.9336	−	4.23701i	−0.739295	−	0.157142i	−0.177154	−	0.984183i	$-0.556689\pi$
$727$	−19.9336	−	4.23701i	−0.739295	−	0.157142i	−0.562141	+	0.827041i	$0.690022\pi$
$728$	−28.0725	+	20.3958i	−1.04043	+	0.755920i
$729$		0			0
$730$	10.4846	+	47.8641i	0.388054	+	1.77153i
$731$	−26.3788	+	11.7446i	−0.975656	+	0.434390i
$732$		0			0
$733$	4.53737	−	43.1702i	0.167592	−	1.59453i	−0.510716	−	0.859749i	$-0.670620\pi$
$733$	4.53737	−	43.1702i	0.167592	−	1.59453i	0.678308	−	0.734778i	$-0.262714\pi$
$734$	−75.9032	+	16.1337i	−2.80164	+	0.595506i
$735$		0			0
$736$	7.30275	+	1.55225i	0.269183	+	0.0572166i
$737$	−0.0721606	+	0.222087i	−0.00265807	+	0.00818069i
$738$		0			0
$739$	−2.42742	−	7.47084i	−0.0892942	−	0.274819i	0.896431	−	0.443184i	$-0.146151\pi$
$739$	−2.42742	−	7.47084i	−0.0892942	−	0.274819i	−0.985725	+	0.168365i	$0.946151\pi$
$740$	40.0005	−	55.7805i	1.47045	−	2.05053i
$741$		0			0
$742$	−0.915943	+	8.71462i	−0.0336253	+	0.319924i
$743$	16.6131	+	28.7747i	0.609475	+	1.05564i	0.991327	+	0.131418i	$0.0419529\pi$
$743$	16.6131	+	28.7747i	0.609475	+	1.05564i	−0.381852	+	0.924223i	$0.624714\pi$
$744$		0			0
$745$	2.69458	+	3.66079i	0.0987218	+	0.134121i
$746$	0.496906	−	0.361023i	0.0181930	−	0.0132180i
$747$		0			0
$748$	4.58845	+	14.1218i	0.167770	+	0.516344i
$749$	−6.89519	+	11.9428i	−0.251945	+	0.436381i
$750$		0			0
$751$	−16.9328	−	29.3284i	−0.617886	−	1.07021i	−0.989871	−	0.141971i	$-0.954656\pi$
$751$	−16.9328	−	29.3284i	−0.617886	−	1.07021i	0.371985	−	0.928239i	$-0.378677\pi$
$752$	27.3059	−	30.3263i	0.995745	−	1.10589i
$753$		0			0
$754$	−8.97350	−	85.3772i	−0.326796	−	3.10925i
$755$	−3.77306	+	8.61794i	−0.137316	+	0.313639i
$756$		0			0
$757$	−9.25569			−0.336404			−0.168202	−	0.985753i	$-0.553796\pi$
$757$	−9.25569			−0.336404			−0.168202	+	0.985753i	$0.553796\pi$
$758$	−50.7030	+	22.5744i	−1.84162	+	0.819940i
$759$		0			0
$760$	25.9611	+	57.3493i	0.941707	+	2.08028i
$761$	−10.3134	+	11.4542i	−0.373861	+	0.415214i	−0.900487	−	0.434882i	$-0.856790\pi$
$761$	−10.3134	+	11.4542i	−0.373861	+	0.415214i	0.526627	+	0.850097i	$0.323457\pi$
$762$		0			0
$763$	−11.4659	−	12.7342i	−0.415094	−	0.461008i
$764$	23.8752	+	73.4802i	0.863773	+	2.65842i
$765$		0			0
$766$	−20.3600	+	62.6615i	−0.735636	+	2.26405i
$767$	13.9369	−	6.20510i	0.503232	−	0.224053i
$768$		0			0
$769$	−1.77895	+	16.9256i	−0.0641505	+	0.610351i	0.914467	+	0.404661i	$0.132611\pi$
$769$	−1.77895	+	16.9256i	−0.0641505	+	0.610351i	−0.978617	+	0.205690i	$0.934056\pi$
$770$	−2.71776	+	2.47779i	−0.0979413	+	0.0892932i
$771$		0			0
$772$	−2.35583	−	22.4142i	−0.0847880	−	0.806704i
$773$	−8.95270	−	27.5536i	−0.322006	−	0.991033i	−0.972774	−	0.231756i	$-0.925553\pi$
$773$	−8.95270	−	27.5536i	−0.322006	−	0.991033i	0.650768	−	0.759277i	$-0.274447\pi$
$774$		0			0
$775$	−0.898098	−	7.63255i	−0.0322606	−	0.274169i
$776$	−21.7665	+	37.7007i	−0.781372	+	1.35338i
$777$		0			0
$778$	29.5203	+	13.1433i	1.05835	+	0.471210i
$779$	−19.4117	−	8.64263i	−0.695495	−	0.309654i
$780$		0			0
$781$	0.775672	−	0.345352i	0.0277557	−	0.0123576i
$782$	−71.7360			−2.56527
$783$		0			0
$784$	−8.35834	+	25.7243i	−0.298512	+	0.918726i
$785$	0.739932	+	1.00525i	0.0264093	+	0.0358791i
$786$		0			0
$787$	−7.31133	+	1.55407i	−0.260621	+	0.0553967i	−0.336369	−	0.941730i	$-0.609199\pi$
$787$	−7.31133	+	1.55407i	−0.260621	+	0.0553967i	0.0757480	+	0.997127i	$0.475866\pi$
$788$	63.5881	−	13.5161i	2.26523	−	0.481490i
$789$		0			0
$790$	−0.118670	−	19.1269i	−0.00422209	−	0.680504i
$791$	3.79358	−	11.6754i	0.134884	−	0.415130i
$792$		0			0
$793$	36.5877			1.29927
$794$	−69.7870	+	31.0712i	−2.47665	+	1.10268i
$795$		0			0
$796$	−65.2949	−	29.0711i	−2.31431	−	1.03040i
$797$	−14.5045	−	6.45782i	−0.513776	−	0.228748i	0.133437	−	0.991057i	$-0.457399\pi$
$797$	−14.5045	−	6.45782i	−0.513776	−	0.228748i	−0.647212	+	0.762310i	$0.724065\pi$
$798$		0			0
$799$	−27.9034	+	48.3301i	−0.987152	+	1.70980i
$800$	−6.07647	−	6.58249i	−0.214836	−	0.232726i
$801$		0			0
$802$	7.76865	+	23.9094i	0.274320	+	0.844271i
$803$	0.473453	+	4.50460i	0.0167078	+	0.158964i
$804$		0			0
$805$	−4.95329	−	10.9421i	−0.174580	−	0.385657i
$806$	1.99044	−	18.9378i	0.0701102	−	0.667054i
$807$		0			0
$808$	−76.9636	+	34.2664i	−2.70757	+	1.20549i
$809$	0.927281	−	2.85388i	0.0326015	−	0.100337i	−0.933432	−	0.358755i	$-0.883201\pi$
$809$	0.927281	−	2.85388i	0.0326015	−	0.100337i	0.966033	+	0.258418i	$0.0832013\pi$
$810$		0			0
$811$	−11.0539	−	34.0205i	−0.388156	−	1.19462i	−0.934165	−	0.356841i	$-0.883854\pi$
$811$	−11.0539	−	34.0205i	−0.388156	−	1.19462i	0.546009	−	0.837779i	$-0.316146\pi$
$812$	24.9408	+	27.6995i	0.875250	+	0.972063i
$813$		0			0
$814$	6.28057	−	6.97528i	0.220134	−	0.244483i
$815$	−7.82020	+	37.9473i	−0.273930	+	1.32924i
$816$		0			0
$817$	−19.8536	+	8.83941i	−0.694591	+	0.309252i
$818$	−44.0028			−1.53852
$819$		0			0
$820$	37.8337	+	3.73931i	1.32121	+	0.130582i
$821$	−4.85653	−	46.2068i	−0.169494	−	1.61263i	−0.666924	−	0.745126i	$-0.732389\pi$
$821$	−4.85653	−	46.2068i	−0.169494	−	1.61263i	0.497430	−	0.867504i	$-0.334277\pi$
$822$		0			0
$823$	27.4590	−	30.4963i	0.957159	−	1.06303i	−0.0407992	−	0.999167i	$-0.512990\pi$
$823$	27.4590	−	30.4963i	0.957159	−	1.06303i	0.997959	−	0.0638657i	$-0.0203429\pi$
$824$	−41.0210	−	71.0504i	−1.42903	−	2.47516i
$825$		0			0
$826$	−4.89927	+	8.48578i	−0.170467	+	0.295258i
$827$	−12.0368	−	37.0454i	−0.418560	−	1.28820i	−0.909028	−	0.416736i	$-0.863174\pi$
$827$	−12.0368	−	37.0454i	−0.418560	−	1.28820i	0.490468	−	0.871459i	$-0.336826\pi$
$828$		0			0
$829$	−4.44553	+	3.22987i	−0.154400	+	0.112178i	−0.662303	−	0.749236i	$-0.730421\pi$
$829$	−4.44553	+	3.22987i	−0.154400	+	0.112178i	0.507903	+	0.861414i	$0.330421\pi$
$830$	77.4127	−	25.6850i	2.68704	−	0.891539i
$831$		0			0
$832$	14.1666	+	24.5373i	0.491138	+	0.850677i
$833$	3.86646	−	36.7869i	0.133965	−	1.27459i
$834$		0			0
$835$	0.0909525	+	14.6595i	0.00314754	+	0.507311i
$836$	3.45343	+	10.6286i	0.119439	+	0.367596i
$837$		0			0
$838$	10.3078	−	31.7242i	0.356078	−	1.09590i
$839$	15.3782	+	3.26874i	0.530916	+	0.112850i	0.465567	−	0.885013i	$-0.345851\pi$
$839$	15.3782	+	3.26874i	0.530916	+	0.112850i	0.0653491	+	0.997862i	$0.479184\pi$
$840$		0			0
$841$	−18.6017	+	3.95392i	−0.641439	+	0.136342i
$842$	8.46664	−	80.5547i	0.291780	−	2.77610i
$843$		0			0
$844$	−55.1685	+	24.5626i	−1.89898	+	0.845479i
$845$	22.8921	−	13.4068i	0.787512	−	0.461209i
$846$		0			0
$847$	11.1965	−	8.13473i	0.384716	−	0.279512i
$848$	−13.5599	−	2.88225i	−0.465650	−	0.0989769i
$849$		0			0
$850$	70.2598	+	49.7265i	2.40989	+	1.70561i
$851$	15.3270	+	26.5472i	0.525403	+	0.910025i
$852$		0			0
$853$	−0.145516	−	1.38449i	−0.00498237	−	0.0474041i	0.991748	−	0.128201i	$-0.0409202\pi$
$853$	−0.145516	−	1.38449i	−0.00498237	−	0.0474041i	−0.996731	+	0.0807967i	$0.974254\pi$
$854$	−19.0116	+	13.8127i	−0.650564	+	0.472662i
$855$		0			0
$856$	−46.7227	−	33.9460i	−1.59695	−	1.16025i
$857$	12.7340	−	22.0559i	0.434985	−	0.753415i	−0.562310	−	0.826927i	$-0.690087\pi$
$857$	12.7340	−	22.0559i	0.434985	−	0.753415i	0.997294	+	0.0735113i	$0.0234205\pi$
$858$		0			0
$859$	6.26793	−	1.33229i	0.213859	−	0.0454572i	−0.0997361	−	0.995014i	$-0.531800\pi$
$859$	6.26793	−	1.33229i	0.213859	−	0.0454572i	0.313595	+	0.949557i	$0.398467\pi$
$860$	28.7342	−	26.1970i	0.979828	−	0.893311i
$861$		0			0
$862$	14.8875	+	16.5342i	0.507069	+	0.563157i
$863$	3.68829	−	11.3514i	0.125551	−	0.386406i	−0.868450	−	0.495777i	$-0.834883\pi$
$863$	3.68829	−	11.3514i	0.125551	−	0.386406i	0.994001	+	0.109370i	$0.0348835\pi$
$864$		0			0
$865$	−2.39229	−	0.236443i	−0.0813404	−	0.00803931i
$866$	−46.3386	−	51.4642i	−1.57465	−	1.74882i
$867$		0			0
$868$	4.13386	+	7.16006i	0.140312	+	0.243028i
$869$	0.184817	−	1.75841i	0.00626948	−	0.0596501i
$870$		0			0
$871$	0.237005	+	2.25495i	0.00803061	+	0.0764062i
$872$	58.0563	−	42.1804i	1.96603	−	1.42841i
$873$		0			0
$874$	−53.9910			−1.82627
$875$	−2.73354	+	14.1504i	−0.0924106	+	0.478372i
$876$		0			0
$877$	−0.560532	+	0.622534i	−0.0189278	+	0.0210215i	−0.752534	−	0.658553i	$-0.771169\pi$
$877$	−0.560532	+	0.622534i	−0.0189278	+	0.0210215i	0.733607	+	0.679574i	$0.237836\pi$
$878$	−7.13733	−	3.17775i	−0.240873	−	0.107244i
$879$		0			0
$880$	−3.44906	−	4.68581i	−0.116268	−	0.157959i
$881$	8.77572	+	6.37593i	0.295661	+	0.214811i	0.725720	−	0.687991i	$-0.241507\pi$
$881$	8.77572	+	6.37593i	0.295661	+	0.214811i	−0.430058	+	0.902801i	$0.641507\pi$
$882$		0			0
$883$	−29.2715	−	21.2670i	−0.985064	−	0.715691i	−0.0262292	−	0.999656i	$-0.508350\pi$
$883$	−29.2715	−	21.2670i	−0.985064	−	0.715691i	−0.958835	+	0.283965i	$0.908350\pi$
$884$	96.4717	+	107.143i	3.24469	+	3.60360i
$885$		0			0
$886$	32.8070	−	36.4358i	1.10217	−	1.22409i
$887$	−44.3753	+	9.43226i	−1.48998	+	0.316704i	−0.879717	−	0.475497i	$-0.842268\pi$
$887$	−44.3753	+	9.43226i	−1.48998	+	0.316704i	−0.610259	+	0.792202i	$0.708935\pi$
$888$		0			0
$889$	−16.6819	−	3.54585i	−0.559493	−	0.118924i
$890$	−11.4715	−	52.3694i	−0.384526	−	1.75543i
$891$		0			0
$892$	62.9620	+	45.7446i	2.10812	+	1.53164i
$893$	−21.0011	+	36.3750i	−0.702775	+	1.21724i
$894$		0			0
$895$	−31.1271	+	28.3786i	−1.04046	+	0.948592i
$896$	−20.8444	−	9.28052i	−0.696362	−	0.310041i
$897$		0			0
$898$	−33.4705	−	7.11438i	−1.11693	−	0.237410i
$899$	−10.6509			−0.355226
$900$		0			0
$901$	18.9581			0.631585
$902$	5.08514	+	1.08088i	0.169317	+	0.0359893i
$903$		0			0
$904$	46.9668	+	20.9110i	1.56209	+	0.695488i
$905$	−28.0205	−	15.9466i	−0.931432	−	0.530084i
$906$		0			0
$907$	−8.10153	+	14.0323i	−0.269007	+	0.465933i	−0.968606	−	0.248602i	$-0.920029\pi$
$907$	−8.10153	+	14.0323i	−0.269007	+	0.465933i	0.699599	+	0.714536i	$0.253362\pi$
$908$	57.4159	+	41.7151i	1.90541	+	1.38436i
$909$		0			0
$910$	−14.3217	+	32.7118i	−0.474760	+	1.08439i
$911$	−13.5590	−	2.88206i	−0.449231	−	0.0954869i	−0.0222596	−	0.999752i	$-0.507086\pi$
$911$	−13.5590	−	2.88206i	−0.449231	−	0.0954869i	−0.426971	+	0.904265i	$0.640419\pi$
$912$		0			0
$913$	7.37479	−	1.56756i	0.244070	−	0.0518787i
$914$	−26.7115	+	29.6661i	−0.883538	+	0.981268i
$915$		0			0
$916$	−60.7913	−	67.5156i	−2.00860	−	2.23078i
$917$	10.4564	+	7.59702i	0.345301	+	0.250876i
$918$		0			0
$919$	33.8071	+	24.5623i	1.11519	+	0.810236i	0.983474	−	0.181051i	$-0.0579500\pi$
$919$	33.8071	+	24.5623i	1.11519	+	0.810236i	0.131720	+	0.991287i	$0.457950\pi$
$920$	47.7413	−	15.8402i	1.57398	−	0.522237i
$921$		0			0
$922$	−23.3058	−	10.3764i	−0.767537	−	0.341729i
$923$	5.51651	−	6.12671i	0.181578	−	0.201663i
$924$		0			0
$925$	3.39057	−	36.6254i	0.111481	−	1.20423i
$926$	44.7769			1.47146
$927$		0			0
$928$	−10.0442	+	7.29755i	−0.329718	+	0.239554i
$929$	−3.25692	−	30.9875i	−0.106856	−	1.01667i	−0.908221	−	0.418491i	$-0.862559\pi$
$929$	−3.25692	−	30.9875i	−0.106856	−	1.01667i	0.801365	−	0.598176i	$-0.204108\pi$
$930$		0			0
$931$	2.91004	−	27.6871i	0.0953726	−	0.907409i
$932$	19.6038	+	33.9548i	0.642145	+	1.11223i
$933$		0			0
$934$	58.7155	+	65.2101i	1.92123	+	2.13374i
$935$	5.94598	+	5.28736i	0.194454	+	0.172915i
$936$		0			0
$937$	−11.2706	+	34.6872i	−0.368193	+	1.13318i	0.579764	+	0.814784i	$0.303145\pi$
$937$	−11.2706	+	34.6872i	−0.368193	+	1.13318i	−0.947957	+	0.318398i	$0.896855\pi$
$938$	−0.974450	−	1.08224i	−0.0318169	−	0.0353363i
$939$		0			0
$940$	15.1682	−	73.6033i	0.494732	−	2.40068i
$941$	15.2034	−	3.23158i	0.495617	−	0.105347i	0.0466795	−	0.998910i	$-0.485136\pi$
$941$	15.2034	−	3.23158i	0.495617	−	0.105347i	0.448937	+	0.893563i	$0.351803\pi$
$942$		0			0
$943$	−8.48922	+	14.7038i	−0.276447	+	0.478820i
$944$	−12.5412	−	9.11169i	−0.408180	−	0.296560i
$945$		0			0
$946$	4.30163	−	3.12532i	0.139858	−	0.101613i
$947$	−1.69965	−	16.1711i	−0.0552313	−	0.525490i	−0.986802	−	0.161931i	$-0.948228\pi$
$947$	−1.69965	−	16.1711i	−0.0552313	−	0.525490i	0.931571	−	0.363560i	$-0.118439\pi$
$948$		0			0
$949$	21.9896	+	38.0871i	0.713813	+	1.23636i
$950$	52.8800	+	37.4259i	1.71565	+	1.21426i
$951$		0			0
$952$	−47.1643	−	10.0251i	−1.52860	−	0.324915i
$953$	−29.6469	+	21.5397i	−0.960357	+	0.697741i	−0.953234	−	0.302234i	$-0.902268\pi$
$953$	−29.6469	+	21.5397i	−0.960357	+	0.697741i	−0.00712369	+	0.999975i	$0.502268\pi$
$954$		0			0
$955$	30.9388	+	27.5118i	1.00116	+	0.890261i
$956$	−18.7320	+	8.34000i	−0.605835	+	0.269735i
$957$		0			0
$958$	−0.443837	+	4.22283i	−0.0143397	+	0.136433i
$959$	13.3267	−	2.83268i	0.430343	−	0.0914722i
$960$		0			0
$961$	28.0117	+	5.95407i	0.903603	+	0.192067i
$962$	28.1628	−	86.6762i	0.908006	−	2.79455i
$963$		0			0
$964$	−10.2984	−	31.6953i	−0.331690	−	1.02084i
$965$	−7.15925	−	9.72638i	−0.230464	−	0.313103i
$966$		0			0
$967$	4.26366	−	40.5660i	0.137110	−	1.30452i	−0.682200	−	0.731165i	$-0.738977\pi$
$967$	4.26366	−	40.5660i	0.137110	−	1.30452i	0.819310	−	0.573350i	$-0.194357\pi$
$968$	28.9793	+	50.1937i	0.931431	+	1.61329i
$969$		0			0
$970$	0.277952	+	44.7994i	0.00892449	+	1.43842i
$971$	−36.3301	+	26.3954i	−1.16589	+	0.847068i	−0.990511	−	0.137433i	$-0.956115\pi$
$971$	−36.3301	+	26.3954i	−1.16589	+	0.847068i	−0.175378	+	0.984501i	$0.556115\pi$
$972$		0			0
$973$	0.236941	+	0.729230i	0.00759599	+	0.0233780i
$974$	−40.6362	+	70.3840i	−1.30207	+	2.25525i
$975$		0			0
$976$	−18.5888	−	32.1967i	−0.595011	−	1.03059i
$977$	4.45973	−	4.95303i	0.142679	−	0.158462i	−0.667569	−	0.744548i	$-0.732665\pi$
$977$	4.45973	−	4.95303i	0.142679	−	0.158462i	0.810249	+	0.586086i	$0.199332\pi$
$978$		0			0
$979$	−0.518017	−	4.92860i	−0.0165559	−	0.157519i
$980$	10.6583	+	48.6568i	0.340466	+	1.55429i
$981$		0			0
$982$	−102.522			−3.27161
$983$	28.5768	−	12.7232i	0.911458	−	0.405807i	0.103217	−	0.994659i	$-0.467086\pi$
$983$	28.5768	−	12.7232i	0.911458	−	0.405807i	0.808241	+	0.588851i	$0.200420\pi$
$984$		0			0
$985$	25.7430	−	23.4699i	0.820240	−	0.747814i
$986$	79.8223	−	88.6517i	2.54206	−	2.82324i
$987$		0			0
$988$	72.6080	+	80.6394i	2.30997	+	2.56548i
$989$	5.36608	+	16.5151i	0.170632	+	0.525150i
$990$		0			0
$991$	−1.60963	+	4.95394i	−0.0511317	+	0.157367i	−0.973362	−	0.229274i	$-0.926365\pi$
$991$	−1.60963	+	4.95394i	−0.0511317	+	0.157367i	0.922230	+	0.386641i	$0.126365\pi$
$992$	−2.51580	+	1.12010i	−0.0798766	+	0.0355634i
$993$		0			0
$994$	−0.553495	+	5.26616i	−0.0175558	+	0.167032i
$995$	−38.0651	+	4.23974i	−1.20675	+	0.134409i
$996$		0			0
$997$	2.39822	+	22.8176i	0.0759524	+	0.722639i	0.964541	+	0.263934i	$0.0850200\pi$
$997$	2.39822	+	22.8176i	0.0759524	+	0.722639i	−0.888588	+	0.458705i	$0.848313\pi$
$998$	−2.67071	−	8.21961i	−0.0845399	−	0.260187i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.r.a.181.2		224
3.2	odd	2		225.2.q.a.106.27	yes	224
9.4	even	3	inner	675.2.r.a.631.27		224
9.5	odd	6		225.2.q.a.31.2	✓	224
25.21	even	5	inner	675.2.r.a.46.27		224
75.71	odd	10		225.2.q.a.196.2	yes	224
225.121	even	15	inner	675.2.r.a.496.2		224
225.221	odd	30		225.2.q.a.121.27	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.2	✓	224	9.5	odd	6
225.2.q.a.106.27	yes	224	3.2	odd	2
225.2.q.a.121.27	yes	224	225.221	odd	30
225.2.q.a.196.2	yes	224	75.71	odd	10
675.2.r.a.46.27		224	25.21	even	5	inner
675.2.r.a.181.2		224	1.1	even	1	trivial
675.2.r.a.496.2		224	225.121	even	15	inner
675.2.r.a.631.27		224	9.4	even	3	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)

\(f(q)\)	\(=\)	\(q+(-2.43022 - 0.516560i) q^{2} +(3.81206 + 1.69724i) q^{4} +(2.22233 - 0.247525i) q^{5} +(-0.644527 + 1.11635i) q^{7} +(-4.36740 - 3.17310i) q^{8} +(-5.52861 - 0.546422i) q^{10} +(-0.502326 - 0.106773i) q^{11} +(-4.87743 + 1.03673i) q^{13} +(2.14301 - 2.38005i) q^{14} +(3.39033 + 3.76535i) q^{16} +(-5.60571 - 4.07278i) q^{17} +(-4.21905 - 3.06532i) q^{19} +(8.89175 + 2.82823i) q^{20} +(1.16561 + 0.518963i) q^{22} +(-2.78826 + 3.09668i) q^{23} +(4.87746 - 1.10016i) q^{25} +12.3888 q^{26} +(-4.35169 + 3.16169i) q^{28} +(-0.724325 - 6.89149i) q^{29} +(0.160665 - 1.52862i) q^{31} +(-0.895838 - 1.55164i) q^{32} +(11.5193 + 12.7935i) q^{34} +(-1.15602 + 2.64044i) q^{35} +(2.27325 - 6.99635i) q^{37} +(8.66982 + 9.62881i) q^{38} +(-10.4912 - 5.97062i) q^{40} +(3.98547 - 0.847138i) q^{41} +(2.08364 - 3.60897i) q^{43} +(-1.73368 - 1.25959i) q^{44} +(8.37572 - 6.08531i) q^{46} +(-0.841878 - 8.00993i) q^{47} +(2.66917 + 4.62314i) q^{49} +(-12.4216 + 0.154142i) q^{50} +(-20.3526 - 4.32609i) q^{52} +(-2.21350 + 1.60820i) q^{53} +(-1.14276 - 0.112945i) q^{55} +(6.35720 - 2.83041i) q^{56} +(-1.79960 + 17.1220i) q^{58} +(-2.99263 + 0.636103i) q^{59} +(-7.17717 - 1.52555i) q^{61} +(-1.18008 + 3.63190i) q^{62} +(-1.75586 - 5.40400i) q^{64} +(-10.5826 + 3.51124i) q^{65} +(0.0475303 - 0.452221i) q^{67} +(-14.4568 - 25.0399i) q^{68} +(4.17334 - 5.81969i) q^{70} +(-1.33759 + 0.971819i) q^{71} +(-2.72548 - 8.38816i) q^{73} +(-9.13854 + 15.8284i) q^{74} +(-10.8807 - 18.8459i) q^{76} +(0.442959 - 0.491955i) q^{77} +(0.359882 + 3.42405i) q^{79} +(8.46644 + 7.52863i) q^{80} -10.1232 q^{82} +(-13.4120 + 5.97142i) q^{83} +(-13.4658 - 7.66350i) q^{85} +(-6.92795 + 7.69427i) q^{86} +(1.85506 + 2.06025i) q^{88} +(2.98202 + 9.17771i) q^{89} +(1.98628 - 6.11314i) q^{91} +(-15.8848 + 7.07238i) q^{92} +(-2.09166 + 19.9008i) q^{94} +(-10.1349 - 5.76782i) q^{95} +(-0.842924 - 8.01989i) q^{97} +(-4.09855 - 12.6140i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28}+ \cdots - 146 q^{98}+O(q^{100}) \) 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

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