LMFDB - Embedded newform 648.2.t.a.397.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [648,2,Mod(37,648)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("648.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(648, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.t (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			397.24
Character	$\chi$	$=$	648.397
Dual form			648.2.t.a.253.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.691259 + 1.23376i) q^{2} +(-1.04432 + 1.70569i) q^{4} +(-1.90914 - 2.27523i) q^{5} +(1.28267 - 0.466852i) q^{7} +(-2.82631 - 0.109365i) q^{8} +(1.48737 - 3.92819i) q^{10} +(2.78354 - 3.31729i) q^{11} +(4.65386 - 0.820601i) q^{13} +(1.46264 + 1.25978i) q^{14} +(-1.81878 - 3.56259i) q^{16} +(-0.356888 - 0.618149i) q^{17} +(-6.43384 - 3.71458i) q^{19} +(5.87460 - 0.880343i) q^{20} +(6.01689 + 1.14111i) q^{22} +(4.17513 + 1.51962i) q^{23} +(-0.663593 + 3.76342i) q^{25} +(4.22945 + 5.17449i) q^{26} +(-0.543209 + 2.67538i) q^{28} +(6.69820 + 1.18107i) q^{29} +(5.02097 + 1.82748i) q^{31} +(3.13812 - 4.70661i) q^{32} +(0.515944 - 0.867615i) q^{34} +(-3.51099 - 2.02707i) q^{35} +(0.547039 - 0.315833i) q^{37} +(0.135445 - 10.5055i) q^{38} +(5.14700 + 6.63929i) q^{40} +(-0.356345 - 2.02093i) q^{41} +(2.43534 - 2.90233i) q^{43} +(2.75138 + 8.21219i) q^{44} +(1.01125 + 6.20155i) q^{46} +(-5.10473 + 1.85797i) q^{47} +(-3.93503 + 3.30188i) q^{49} +(-5.10187 + 1.78279i) q^{50} +(-3.46043 + 8.79504i) q^{52} -11.4745i q^{53} -12.8618 q^{55} +(-3.67627 + 1.17919i) q^{56} +(3.17303 + 9.08039i) q^{58} +(0.803086 + 0.957081i) q^{59} +(0.216792 + 0.595632i) q^{61} +(1.21612 + 7.45793i) q^{62} +(7.97608 + 0.618197i) q^{64} +(-10.7519 - 9.02195i) q^{65} +(-14.0227 + 2.47258i) q^{67} +(1.42708 + 0.0368039i) q^{68} +(0.0739130 - 5.73294i) q^{70} +(0.414463 + 0.717870i) q^{71} +(7.29258 - 12.6311i) q^{73} +(0.767808 + 0.456592i) q^{74} +(13.0549 - 7.09494i) q^{76} +(2.02167 - 5.55448i) q^{77} +(-1.22756 + 6.96183i) q^{79} +(-4.63338 + 10.9396i) q^{80} +(2.24702 - 1.83663i) q^{82} +(-1.29008 - 0.227475i) q^{83} +(-0.725078 + 1.99214i) q^{85} +(5.26422 + 0.998364i) q^{86} +(-8.22995 + 9.07129i) q^{88} +(-2.66374 + 4.61373i) q^{89} +(5.58625 - 3.22522i) q^{91} +(-6.95219 + 5.53452i) q^{92} +(-5.82098 - 5.01367i) q^{94} +(3.83160 + 21.7301i) q^{95} +(-1.52072 - 1.27604i) q^{97} +(-6.79385 - 2.57242i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{9}\right)$

Coefficient data

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

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

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

$2$	0.691259	+	1.23376i	0.488794	+	0.872399i
$2$	0.691259	+	1.23376i	0.488794	+	0.872399i
$3$		0			0
$3$		0			0
$4$	−1.04432	+	1.70569i	−0.522161	+	0.852847i
$5$	−1.90914	−	2.27523i	−0.853794	−	1.01751i	−0.999602	−	0.0281995i	$-0.991023\pi$
$5$	−1.90914	−	2.27523i	−0.853794	−	1.01751i	0.145808	−	0.989313i	$-0.453422\pi$
$6$		0			0
$7$	1.28267	−	0.466852i	0.484802	−	0.176454i	−0.0880438	−	0.996117i	$-0.528062\pi$
$7$	1.28267	−	0.466852i	0.484802	−	0.176454i	0.572846	+	0.819663i	$0.305839\pi$
$8$	−2.82631	−	0.109365i	−0.999252	−	0.0386662i
$9$		0			0
$10$	1.48737	−	3.92819i	0.470348	−	1.24220i
$11$	2.78354	−	3.31729i	0.839269	−	1.00020i	−0.160644	−	0.987012i	$-0.551357\pi$
$11$	2.78354	−	3.31729i	0.839269	−	1.00020i	0.999913	−	0.0131894i	$-0.00419844\pi$
$12$		0			0
$13$	4.65386	−	0.820601i	1.29075	−	0.227594i	0.514211	−	0.857664i	$-0.328085\pi$
$13$	4.65386	−	0.820601i	1.29075	−	0.227594i	0.776538	+	0.630070i	$0.216974\pi$
$14$	1.46264	+	1.25978i	0.390906	+	0.336692i
$15$		0			0
$16$	−1.81878	−	3.56259i	−0.454696	−	0.890647i
$17$	−0.356888	−	0.618149i	−0.0865581	−	0.149923i	0.819496	−	0.573085i	$-0.194254\pi$
$17$	−0.356888	−	0.618149i	−0.0865581	−	0.149923i	−0.906054	+	0.423162i	$0.860920\pi$
$18$		0			0
$19$	−6.43384	−	3.71458i	−1.47602	−	0.852183i	−0.476389	−	0.879234i	$-0.658055\pi$
$19$	−6.43384	−	3.71458i	−1.47602	−	0.852183i	−0.999634	+	0.0270519i	$0.991388\pi$
$20$	5.87460	−	0.880343i	1.31360	−	0.196851i
$21$		0			0
$22$	6.01689	+	1.14111i	1.28280	+	0.243285i
$23$	4.17513	+	1.51962i	0.870574	+	0.316863i	0.738400	−	0.674363i	$-0.235582\pi$
$23$	4.17513	+	1.51962i	0.870574	+	0.316863i	0.132175	+	0.991226i	$0.457804\pi$
$24$		0			0
$25$	−0.663593	+	3.76342i	−0.132719	+	0.752685i
$26$	4.22945	+	5.17449i	0.829463	+	1.01480i
$27$		0			0
$28$	−0.543209	+	2.67538i	−0.102657	+	0.505599i
$29$	6.69820	+	1.18107i	1.24382	+	0.219320i	0.756554	−	0.653931i	$-0.226882\pi$
$29$	6.69820	+	1.18107i	1.24382	+	0.219320i	0.487270	+	0.873251i	$0.337993\pi$
$30$		0			0
$31$	5.02097	+	1.82748i	0.901793	+	0.328226i	0.750971	−	0.660335i	$-0.229586\pi$
$31$	5.02097	+	1.82748i	0.901793	+	0.328226i	0.150822	+	0.988561i	$0.451808\pi$
$32$	3.13812	−	4.70661i	0.554747	−	0.832019i
$33$		0			0
$34$	0.515944	−	0.867615i	0.0884837	−	0.148795i
$35$	−3.51099	−	2.02707i	−0.593465	−	0.342637i
$36$		0			0
$37$	0.547039	−	0.315833i	0.0899327	−	0.0519226i	−0.454359	−	0.890819i	$-0.650132\pi$
$37$	0.547039	−	0.315833i	0.0899327	−	0.0519226i	0.544292	+	0.838896i	$0.316798\pi$
$38$	0.135445	−	10.5055i	0.0219720	−	1.70422i
$39$		0			0
$40$	5.14700	+	6.63929i	0.813812	+	1.04976i
$41$	−0.356345	−	2.02093i	−0.0556517	−	0.315617i	0.944256	−	0.329213i	$-0.106783\pi$
$41$	−0.356345	−	2.02093i	−0.0556517	−	0.315617i	−0.999908	+	0.0135959i	$0.995672\pi$
$42$		0			0
$43$	2.43534	−	2.90233i	0.371386	−	0.442601i	−0.547690	−	0.836682i	$-0.684493\pi$
$43$	2.43534	−	2.90233i	0.371386	−	0.442601i	0.919076	+	0.394081i	$0.128937\pi$
$44$	2.75138	+	8.21219i	0.414786	+	1.23803i
$45$		0			0
$46$	1.01125	+	6.20155i	0.149100	+	0.914369i
$47$	−5.10473	+	1.85797i	−0.744601	+	0.271013i	−0.686332	−	0.727288i	$-0.740780\pi$
$47$	−5.10473	+	1.85797i	−0.744601	+	0.271013i	−0.0582692	+	0.998301i	$0.518558\pi$
$48$		0			0
$49$	−3.93503	+	3.30188i	−0.562147	+	0.471697i
$50$	−5.10187	+	1.78279i	−0.721514	+	0.252124i
$51$		0			0
$52$	−3.46043	+	8.79504i	−0.479876	+	1.21965i
$53$		−	11.4745i		−	1.57614i	−0.615583	−	0.788072i	$-0.711079\pi$
$53$		−	11.4745i		−	1.57614i	0.615583	−	0.788072i	$-0.288921\pi$
$54$		0			0
$55$	−12.8618			−1.73428
$56$	−3.67627	+	1.17919i	−0.491262	+	0.157576i
$57$		0			0
$58$	3.17303	+	9.08039i	0.416639	+	1.19231i
$59$	0.803086	+	0.957081i	0.104553	+	0.124601i	0.815783	−	0.578358i	$-0.196306\pi$
$59$	0.803086	+	0.957081i	0.104553	+	0.124601i	−0.711230	+	0.702959i	$0.751862\pi$
$60$		0			0
$61$	0.216792	+	0.595632i	0.0277574	+	0.0762629i	0.952797	−	0.303607i	$-0.0981910\pi$
$61$	0.216792	+	0.595632i	0.0277574	+	0.0762629i	−0.925040	+	0.379870i	$0.875969\pi$
$62$	1.21612	+	7.45793i	0.154447	+	0.947158i
$63$		0			0
$64$	7.97608	+	0.618197i	0.997010	+	0.0772747i
$65$	−10.7519	−	9.02195i	−1.33361	−	1.11903i
$66$		0			0
$67$	−14.0227	+	2.47258i	−1.71314	+	0.302074i	−0.942255	−	0.334896i	$-0.891299\pi$
$67$	−14.0227	+	2.47258i	−1.71314	+	0.302074i	−0.770889	+	0.636969i	$0.780188\pi$
$68$	1.42708	+	0.0368039i	0.173059	+	0.00446312i
$69$		0			0
$70$	0.0739130	−	5.73294i	0.00883429	−	0.685217i
$71$	0.414463	+	0.717870i	0.0491877	+	0.0851955i	0.889571	−	0.456797i	$-0.151003\pi$
$71$	0.414463	+	0.717870i	0.0491877	+	0.0851955i	−0.840383	+	0.541993i	$0.817670\pi$
$72$		0			0
$73$	7.29258	−	12.6311i	0.853532	−	1.47836i	−0.0244686	−	0.999701i	$-0.507789\pi$
$73$	7.29258	−	12.6311i	0.853532	−	1.47836i	0.878000	−	0.478660i	$-0.158877\pi$
$74$	0.767808	+	0.456592i	0.0892558	+	0.0530777i
$75$		0			0
$76$	13.0549	−	7.09494i	1.49750	−	0.813846i
$77$	2.02167	−	5.55448i	0.230390	−	0.632992i
$78$		0			0
$79$	−1.22756	+	6.96183i	−0.138111	+	0.783267i	0.834532	+	0.550960i	$0.185738\pi$
$79$	−1.22756	+	6.96183i	−0.138111	+	0.783267i	−0.972643	+	0.232306i	$0.925373\pi$
$80$	−4.63338	+	10.9396i	−0.518027	+	1.22309i
$81$		0			0
$82$	2.24702	−	1.83663i	0.248141	−	0.202822i
$83$	−1.29008	−	0.227475i	−0.141604	−	0.0249686i	0.102397	−	0.994744i	$-0.467349\pi$
$83$	−1.29008	−	0.227475i	−0.141604	−	0.0249686i	−0.244001	+	0.969775i	$0.578460\pi$
$84$		0			0
$85$	−0.725078	+	1.99214i	−0.0786458	+	0.216077i
$86$	5.26422	+	0.998364i	0.567656	+	0.107656i
$87$		0			0
$88$	−8.22995	+	9.07129i	−0.877315	+	0.967002i
$89$	−2.66374	+	4.61373i	−0.282356	+	0.489054i	−0.971964	−	0.235128i	$-0.924449\pi$
$89$	−2.66374	+	4.61373i	−0.282356	+	0.489054i	0.689609	+	0.724182i	$0.257782\pi$
$90$		0			0
$91$	5.58625	−	3.22522i	0.585598	−	0.338095i
$92$	−6.95219	+	5.53452i	−0.724816	+	0.577013i
$93$		0			0
$94$	−5.82098	−	5.01367i	−0.600388	−	0.517120i
$95$	3.83160	+	21.7301i	0.393114	+	2.22946i
$96$		0			0
$97$	−1.52072	−	1.27604i	−0.154406	−	0.129562i	0.562312	−	0.826925i	$-0.309912\pi$
$97$	−1.52072	−	1.27604i	−0.154406	−	0.129562i	−0.716718	+	0.697363i	$0.754356\pi$
$98$	−6.79385	−	2.57242i	−0.686283	−	0.259854i
$99$		0			0
$100$	−5.72624	−	5.06211i	−0.572624	−	0.506211i
$101$	−1.46496	−	4.02494i	−0.145769	−	0.400497i	0.845224	−	0.534412i	$-0.179467\pi$
$101$	−1.46496	−	4.02494i	−0.145769	−	0.400497i	−0.990993	+	0.133916i	$0.957245\pi$
$102$		0			0
$103$	−8.54275	+	7.16822i	−0.841743	+	0.706306i	−0.957955	−	0.286919i	$-0.907369\pi$
$103$	−8.54275	+	7.16822i	−0.841743	+	0.706306i	0.116212	+	0.993224i	$0.462925\pi$
$104$	−13.2430	+	1.81031i	−1.29858	+	0.177515i
$105$		0			0
$106$	14.1568	−	7.93185i	1.37503	−	0.770410i
$107$			11.6290i			1.12422i	0.827064	+	0.562108i	$0.190009\pi$
$107$			11.6290i			1.12422i	−0.827064	+	0.562108i	$0.809991\pi$
$108$		0			0
$109$		−	2.12823i		−	0.203848i	−0.994792	−	0.101924i	$-0.967500\pi$
$109$		−	2.12823i		−	0.203848i	0.994792	−	0.101924i	$-0.0324998\pi$
$110$	−8.89082	−	15.8683i	−0.847706	−	1.51299i
$111$		0			0
$112$	−3.99609	−	3.72051i	−0.377595	−	0.351555i
$113$	13.3788	−	11.2261i	1.25857	−	1.05607i	0.262739	−	0.964867i	$-0.415374\pi$
$113$	13.3788	−	11.2261i	1.25857	−	1.05607i	0.995833	−	0.0912002i	$-0.0290703\pi$
$114$		0			0
$115$	−4.51343	−	12.4005i	−0.420879	−	1.15636i
$116$	−9.00962	+	10.1917i	−0.836522	+	0.946271i
$117$		0			0
$118$	−0.625666	+	1.65241i	−0.0575973	+	0.152116i
$119$	−0.746353	−	0.626264i	−0.0684180	−	0.0574096i
$120$		0			0
$121$	−1.34621	−	7.63476i	−0.122383	−	0.694069i
$122$	−0.585007	+	0.679206i	−0.0529641	+	0.0614924i
$123$		0			0
$124$	−8.36063	+	6.65576i	−0.750807	+	0.597705i
$125$	−3.03136	+	1.75016i	−0.271133	+	0.156539i
$126$		0			0
$127$	2.78247	−	4.81937i	0.246904	−	0.427650i	−0.715761	−	0.698345i	$-0.753920\pi$
$127$	2.78247	−	4.81937i	0.246904	−	0.427650i	0.962665	+	0.270695i	$0.0872534\pi$
$128$	4.75083	+	10.2679i	0.419918	+	0.907562i
$129$		0			0
$130$	3.69853	−	19.5018i	0.324383	−	1.71042i
$131$	−3.27187	+	8.98940i	−0.285865	+	0.785407i	0.710769	+	0.703426i	$0.248347\pi$
$131$	−3.27187	+	8.98940i	−0.285865	+	0.785407i	−0.996634	+	0.0819818i	$0.973875\pi$
$132$		0			0
$133$	−9.98662	−	1.76091i	−0.865950	−	0.152690i
$134$	−12.7439	−	15.5914i	−1.10090	−	1.34689i
$135$		0			0
$136$	0.941074	+	1.78611i	0.0806964	+	0.153158i
$137$	−0.661480	+	3.75144i	−0.0565140	+	0.320507i	−0.999939	−	0.0110802i	$-0.996473\pi$
$137$	−0.661480	+	3.75144i	−0.0565140	+	0.320507i	0.943425	+	0.331587i	$0.107584\pi$
$138$		0			0
$139$	−0.433062	+	1.18983i	−0.0367318	+	0.100920i	−0.956703	−	0.291067i	$-0.905990\pi$
$139$	−0.433062	+	1.18983i	−0.0367318	+	0.100920i	0.919971	+	0.391987i	$0.128212\pi$
$140$	7.12416	−	3.87176i	0.602101	−	0.327223i
$141$		0			0
$142$	−0.599178	+	1.00758i	−0.0502819	+	0.0845544i
$143$	10.2320	−	17.7224i	0.855646	−	1.48202i
$144$		0			0
$145$	−10.1006	−	17.4948i	−0.838809	−	1.45286i
$146$	20.6248	+	0.265909i	1.70692	+	0.0220068i
$147$		0			0
$148$	−0.0325701	+	1.26291i	−0.00267724	+	0.103811i
$149$	9.84675	−	1.73625i	0.806677	−	0.142239i	0.244922	−	0.969543i	$-0.421238\pi$
$149$	9.84675	−	1.73625i	0.806677	−	0.142239i	0.561755	+	0.827304i	$0.310126\pi$
$150$		0			0
$151$	16.1625	+	13.5620i	1.31529	+	1.10366i	0.987281	+	0.158983i	$0.0508216\pi$
$151$	16.1625	+	13.5620i	1.31529	+	1.10366i	0.328008	+	0.944675i	$0.393623\pi$
$152$	17.7778	+	11.2022i	1.44197	+	0.908618i
$153$		0			0
$154$	8.25039	−	1.34534i	0.664835	−	0.108410i
$155$	−5.42780	−	14.9128i	−0.435972	−	1.19782i
$156$		0			0
$157$	5.71532	+	6.81126i	0.456133	+	0.543598i	0.944271	−	0.329168i	$-0.106768\pi$
$157$	5.71532	+	6.81126i	0.456133	+	0.543598i	−0.488139	+	0.872766i	$0.662324\pi$
$158$	−9.43777	+	3.29792i	−0.750829	+	0.262368i
$159$		0			0
$160$	−16.6997	+	1.84565i	−1.32023	+	0.145912i
$161$	6.06473			0.477968
$162$		0			0
$163$			17.7771i			1.39241i	0.717845	+	0.696203i	$0.245129\pi$
$163$			17.7771i			1.39241i	−0.717845	+	0.696203i	$0.754871\pi$
$164$	3.81923	+	1.50269i	0.298232	+	0.117340i
$165$		0			0
$166$	−0.611127	−	1.74889i	−0.0474327	−	0.135740i
$167$	5.29501	−	4.44304i	0.409740	−	0.343813i	−0.414504	−	0.910048i	$-0.636045\pi$
$167$	5.29501	−	4.44304i	0.409740	−	0.343813i	0.824244	+	0.566235i	$0.191600\pi$
$168$		0			0
$169$	8.76904	−	3.19167i	0.674541	−	0.245513i
$170$	−2.95903	+	0.482510i	−0.226947	+	0.0370069i
$171$		0			0
$172$	2.40720	+	7.18491i	0.183547	+	0.547844i
$173$	−14.6599	+	17.4709i	−1.11457	+	1.32829i	−0.175531	+	0.984474i	$0.556164\pi$
$173$	−14.6599	+	17.4709i	−1.11457	+	1.32829i	−0.939037	+	0.343817i	$0.888280\pi$
$174$		0			0
$175$	0.905794	+	5.13702i	0.0684716	+	0.388322i
$176$	−16.8808	−	3.88316i	−1.27244	−	0.292704i
$177$		0			0
$178$	−7.53356	−	0.0971278i	−0.564664	−	0.00728004i
$179$	−10.8469	+	6.26245i	−0.810734	+	0.468077i	−0.847211	−	0.531257i	$-0.821720\pi$
$179$	−10.8469	+	6.26245i	−0.810734	+	0.468077i	0.0364770	+	0.999334i	$0.488386\pi$
$180$		0			0
$181$	−10.6636	−	6.15662i	−0.792618	−	0.457618i	0.0482656	−	0.998835i	$-0.484631\pi$
$181$	−10.6636	−	6.15662i	−0.792618	−	0.457618i	−0.840883	+	0.541217i	$0.817964\pi$
$182$	7.84069	+	4.66262i	0.581191	+	0.345616i
$183$		0			0
$184$	−11.6340	−	4.75154i	−0.857671	−	0.350288i
$185$	−1.76297	−	0.641668i	−0.129616	−	0.0471763i
$186$		0			0
$187$	−3.04399	−	0.536738i	−0.222599	−	0.0392502i
$188$	2.16185	−	10.6474i	0.157669	−	0.776543i
$189$		0			0
$190$	−24.1611	+	19.7484i	−1.75283	+	1.43270i
$191$	−0.0708406	+	0.401757i	−0.00512584	+	0.0290701i	−0.987263	−	0.159094i	$-0.949143\pi$
$191$	−0.0708406	+	0.401757i	−0.00512584	+	0.0290701i	0.982138	+	0.188164i	$0.0602538\pi$
$192$		0			0
$193$	20.6767	+	7.52571i	1.48834	+	0.541712i	0.953013	−	0.302930i	$-0.0979650\pi$
$193$	20.6767	+	7.52571i	1.48834	+	0.541712i	0.535330	+	0.844643i	$0.320187\pi$
$194$	0.523109	−	2.75828i	0.0375571	−	0.198033i
$195$		0			0
$196$	−1.52256	−	10.1602i	−0.108755	−	0.725727i
$197$	18.0410	+	10.4160i	1.28537	+	0.742108i	0.977824	−	0.209426i	$-0.0671596\pi$
$197$	18.0410	+	10.4160i	1.28537	+	0.742108i	0.307544	+	0.951534i	$0.400493\pi$
$198$		0			0
$199$	−1.53489	−	2.65851i	−0.108805	−	0.188457i	0.806481	−	0.591260i	$-0.201369\pi$
$199$	−1.53489	−	2.65851i	−0.108805	−	0.188457i	−0.915287	+	0.402803i	$0.868036\pi$
$200$	2.28711	−	10.5640i	0.161723	−	0.746990i
$201$		0			0
$202$	3.95314	−	4.58968i	0.278142	−	0.322929i
$203$	9.14294	−	1.61215i	0.641708	−	0.113150i
$204$		0			0
$205$	−3.91777	+	4.66901i	−0.273629	+	0.326098i
$206$	−14.7491	−	5.58460i	−1.02762	−	0.389097i
$207$		0			0
$208$	−11.3878	−	15.0873i	−0.789604	−	1.04612i
$209$	−30.2312	+	11.0033i	−2.09114	+	0.761111i
$210$		0			0
$211$	1.48569	+	1.77058i	0.102279	+	0.121892i	0.814756	−	0.579804i	$-0.196871\pi$
$211$	1.48569	+	1.77058i	0.102279	+	0.121892i	−0.712477	+	0.701696i	$0.752427\pi$
$212$	19.5720	+	11.9831i	1.34421	+	0.823001i
$213$		0			0
$214$	−14.3473	+	8.03863i	−0.980764	+	0.549510i
$215$	−11.2529			−0.767439
$216$		0			0
$217$	7.29339			0.495108
$218$	2.62573	−	1.47116i	0.177837	−	0.0996395i
$219$		0			0
$220$	13.4318	−	21.9382i	0.905574	−	1.47908i
$221$	−2.16816	−	2.58392i	−0.145846	−	0.173813i
$222$		0			0
$223$	3.40012	−	1.23754i	0.227689	−	0.0828721i	−0.225656	−	0.974207i	$-0.572453\pi$
$223$	3.40012	−	1.23754i	0.227689	−	0.0828721i	0.453345	+	0.891335i	$0.350230\pi$
$224$	1.82787	−	7.50205i	0.122130	−	0.501252i
$225$		0			0
$226$	23.0986	+	8.74604i	1.53649	+	0.581778i
$227$	−12.6692	+	15.0985i	−0.840883	+	1.00212i	0.159007	+	0.987277i	$0.449171\pi$
$227$	−12.6692	+	15.0985i	−0.840883	+	1.00212i	−0.999890	+	0.0148475i	$0.995274\pi$
$228$		0			0
$229$	17.3012	−	3.05066i	1.14329	−	0.201593i	0.430247	−	0.902711i	$-0.358426\pi$
$229$	17.3012	−	3.05066i	1.14329	−	0.201593i	0.713045	+	0.701118i	$0.247315\pi$
$230$	12.1793	−	14.1405i	0.803081	−	0.932394i
$231$		0			0
$232$	−18.8020	−	4.07063i	−1.23441	−	0.267250i
$233$	−9.53675	−	16.5181i	−0.624774	−	1.08214i	−0.988585	−	0.150667i	$-0.951858\pi$
$233$	−9.53675	−	16.5181i	−0.624774	−	1.08214i	0.363811	−	0.931473i	$-0.381475\pi$
$234$		0			0
$235$	13.9730	+	8.06729i	0.911495	+	0.526252i
$236$	−2.47117	+	0.370319i	−0.160859	+	0.0241057i
$237$		0			0
$238$	0.256736	−	1.35373i	0.0166417	−	0.0877493i
$239$	1.39969	+	0.509446i	0.0905384	+	0.0329533i	0.386892	−	0.922125i	$-0.373549\pi$
$239$	1.39969	+	0.509446i	0.0905384	+	0.0329533i	−0.296354	+	0.955078i	$0.595771\pi$
$240$		0			0
$241$	0.766076	−	4.34463i	0.0493473	−	0.279862i	−0.950142	−	0.311817i	$-0.899062\pi$
$241$	0.766076	−	4.34463i	0.0493473	−	0.279862i	0.999489	+	0.0319552i	$0.0101734\pi$
$242$	8.48887	−	6.93850i	0.545685	−	0.446024i
$243$		0			0
$244$	−1.24237	−	0.252250i	−0.0795345	−	0.0161487i
$245$	15.0251	+	2.64932i	0.959916	+	0.169259i
$246$		0			0
$247$	−32.9904	−	12.0075i	−2.09913	−	0.764020i
$248$	−13.9910	−	5.71415i	−0.888427	−	0.362849i
$249$		0			0
$250$	−4.25473	−	2.53016i	−0.269093	−	0.160021i
$251$	−23.4897	−	13.5618i	−1.48265	−	0.856011i	−0.482848	−	0.875704i	$-0.660398\pi$
$251$	−23.4897	−	13.5618i	−1.48265	−	0.856011i	−0.999806	+	0.0196931i	$0.993731\pi$
$252$		0			0
$253$	16.6627	−	9.62020i	1.04757	−	0.604817i
$254$	7.86935	+	0.101457i	0.493767	+	0.00636598i
$255$		0			0
$256$	−9.38405	+	12.9592i	−0.586503	+	0.809947i
$257$	2.75518	+	15.6254i	0.171864	+	0.974687i	0.941702	+	0.336448i	$0.109226\pi$
$257$	2.75518	+	15.6254i	0.171864	+	0.974687i	−0.769839	+	0.638239i	$0.779663\pi$
$258$		0			0
$259$	0.554221	−	0.660495i	0.0344376	−	0.0410412i
$260$	26.6172	−	8.91770i	1.65073	−	0.553052i
$261$		0			0
$262$	−13.3525	+	2.17730i	−0.824918	+	0.134514i
$263$	−1.51313	+	0.550733i	−0.0933034	+	0.0339597i	−0.388250	−	0.921554i	$-0.626920\pi$
$263$	−1.51313	+	0.550733i	−0.0933034	+	0.0339597i	0.294947	+	0.955514i	$0.404698\pi$
$264$		0			0
$265$	−26.1071	+	21.9065i	−1.60375	+	1.34570i
$266$	−4.73080	−	13.5383i	−0.290064	−	0.830088i
$267$		0			0
$268$	10.4267	−	26.5006i	0.636914	−	1.61878i
$269$		−	2.95858i		−	0.180388i	−0.995924	−	0.0901940i	$-0.971251\pi$
$269$		−	2.95858i		−	0.180388i	0.995924	−	0.0901940i	$-0.0287487\pi$
$270$		0			0
$271$	6.23755			0.378904			0.189452	−	0.981890i	$-0.439329\pi$
$271$	6.23755			0.378904			0.189452	+	0.981890i	$0.439329\pi$
$272$	−1.55311	+	2.39572i	−0.0941709	+	0.145262i
$273$		0			0
$274$	−5.08562	+	1.77711i	−0.307234	+	0.107359i
$275$	10.6372	+	12.6770i	0.641450	+	0.764450i
$276$		0			0
$277$	7.97956	+	21.9237i	0.479445	+	1.31727i	0.909965	+	0.414684i	$0.136108\pi$
$277$	7.97956	+	21.9237i	0.479445	+	1.31727i	−0.430520	+	0.902581i	$0.641670\pi$
$278$	−1.76732	+	0.288185i	−0.105997	+	0.0172842i
$279$		0			0
$280$	9.70145	+	6.11311i	0.579773	+	0.365328i
$281$	5.53822	+	4.64712i	0.330383	+	0.277224i	0.792856	−	0.609409i	$-0.208593\pi$
$281$	5.53822	+	4.64712i	0.330383	+	0.277224i	−0.462473	+	0.886633i	$0.653038\pi$
$282$		0			0
$283$	1.34312	−	0.236829i	0.0798404	−	0.0140780i	−0.133585	−	0.991037i	$-0.542649\pi$
$283$	1.34312	−	0.236829i	0.0798404	−	0.0140780i	0.213426	+	0.976959i	$0.431538\pi$
$284$	−1.65730	−	0.0427412i	−0.0983426	−	0.00253622i
$285$		0			0
$286$	28.9382	+	0.373090i	1.71115	+	0.0220613i
$287$	−1.40055	−	2.42582i	−0.0826718	−	0.143192i
$288$		0			0
$289$	8.24526	−	14.2812i	0.485015	−	0.840071i
$290$	14.6022	−	24.5551i	0.857469	−	1.44193i
$291$		0			0
$292$	13.9290	+	25.6299i	0.815134	+	1.49987i
$293$	−5.01243	+	13.7715i	−0.292829	+	0.804541i	0.702821	+	0.711367i	$0.251924\pi$
$293$	−5.01243	+	13.7715i	−0.292829	+	0.804541i	−0.995650	+	0.0931743i	$0.970299\pi$
$294$		0			0
$295$	0.644371	−	3.65441i	0.0375167	−	0.212768i
$296$	−1.58064	+	0.832816i	−0.0918731	+	0.0484065i
$297$		0			0
$298$	8.94876	+	10.9483i	0.518388	+	0.634219i
$299$	20.6775	+	3.64600i	1.19581	+	0.210853i
$300$		0			0
$301$	1.76877	−	4.85966i	0.101950	−	0.280106i
$302$	−5.55971	+	29.3155i	−0.319925	+	1.68692i
$303$		0			0
$304$	−1.53174	+	29.6771i	−0.0878515	+	1.70210i
$305$	0.941311	−	1.63040i	0.0538993	−	0.0933564i
$306$		0			0
$307$	9.62473	−	5.55684i	0.549313	−	0.317146i	−0.199532	−	0.979891i	$-0.563942\pi$
$307$	9.62473	−	5.55684i	0.549313	−	0.317146i	0.748845	+	0.662746i	$0.230609\pi$
$308$	7.36298	+	9.24901i	0.419545	+	0.527011i
$309$		0			0
$310$	14.6467	−	17.0052i	0.831879	−	0.965830i
$311$	−1.91302	−	10.8493i	−0.108477	−	0.615206i	−0.989774	−	0.142643i	$-0.954440\pi$
$311$	−1.91302	−	10.8493i	−0.108477	−	0.615206i	0.881297	−	0.472563i	$-0.156671\pi$
$312$		0			0
$313$	−1.97229	−	1.65494i	−0.111480	−	0.0935430i	0.585344	−	0.810785i	$-0.300960\pi$
$313$	−1.97229	−	1.65494i	−0.111480	−	0.0935430i	−0.696824	+	0.717242i	$0.745404\pi$
$314$	−4.45268	+	11.7597i	−0.251279	+	0.663637i
$315$		0			0
$316$	−10.5928	−	9.36422i	−0.595890	−	0.526779i
$317$	1.43808	+	3.95110i	0.0807708	+	0.221916i	0.973504	−	0.228669i	$-0.0734375\pi$
$317$	1.43808	+	3.95110i	0.0807708	+	0.221916i	−0.892733	+	0.450585i	$0.851215\pi$
$318$		0			0
$319$	22.5627	−	18.9323i	1.26327	−	1.06001i
$320$	−13.8209	−	19.3276i	−0.772613	−	1.08045i
$321$		0			0
$322$	4.19230	+	7.48242i	0.233628	+	0.416979i
$323$			5.30276i			0.295053i
$324$		0			0
$325$			18.0590i			1.00173i
$326$	−21.9326	+	12.2886i	−1.21473	+	0.680600i
$327$		0			0
$328$	0.786123	+	5.75076i	0.0434064	+	0.317532i
$329$	−5.68027	+	4.76631i	−0.313163	+	0.262775i
$330$		0			0
$331$	0.147225	+	0.404498i	0.00809223	+	0.0222332i	0.943673	−	0.330880i	$-0.107345\pi$
$331$	0.147225	+	0.404498i	0.00809223	+	0.0222332i	−0.935581	+	0.353113i	$0.885123\pi$
$332$	1.73526	−	1.96292i	0.0952346	−	0.107729i
$333$		0			0
$334$	9.14187	+	3.46148i	0.500221	+	0.189403i
$335$	32.3970	+	27.1843i	1.77004	+	1.48524i
$336$		0			0
$337$	2.69206	+	15.2674i	0.146646	+	0.831671i	0.966031	+	0.258427i	$0.0832041\pi$
$337$	2.69206	+	15.2674i	0.146646	+	0.831671i	−0.819385	+	0.573244i	$0.805685\pi$
$338$	9.99943	+	8.61261i	0.543897	+	0.468464i
$339$		0			0
$340$	−2.64076	−	3.31719i	−0.143215	−	0.179900i
$341$	20.0384	−	11.5692i	1.08514	−	0.626505i
$342$		0			0
$343$	−8.28328	+	14.3471i	−0.447255	+	0.774669i
$344$	−7.20045	+	7.93654i	−0.388222	+	0.427910i
$345$		0			0
$346$	−31.6887	−	6.00978i	−1.70359	−	0.323088i
$347$	2.18648	−	6.00732i	0.117377	−	0.322490i	−0.867067	−	0.498192i	$-0.833997\pi$
$347$	2.18648	−	6.00732i	0.117377	−	0.322490i	0.984443	+	0.175702i	$0.0562197\pi$
$348$		0			0
$349$	35.8064	+	6.31363i	1.91667	+	0.337961i	0.998327	−	0.0578197i	$-0.0184148\pi$
$349$	35.8064	+	6.31363i	1.91667	+	0.337961i	0.918345	+	0.395781i	$0.129526\pi$
$350$	−5.71170	+	4.66854i	−0.305303	+	0.249544i
$351$		0			0
$352$	−6.87813	−	23.5111i	−0.366605	−	1.25315i
$353$	2.81872	−	15.9857i	0.150025	−	0.850835i	−0.813169	−	0.582028i	$-0.802259\pi$
$353$	2.81872	−	15.9857i	0.150025	−	0.850835i	0.963194	−	0.268807i	$-0.0866295\pi$
$354$		0			0
$355$	0.842050	−	2.31351i	0.0446914	−	0.122789i
$356$	−5.08781	−	9.36174i	−0.269653	−	0.496171i
$357$		0			0
$358$	−15.2244	−	9.05346i	−0.804632	−	0.478490i
$359$	2.92393	−	5.06440i	0.154319	−	0.267289i	−0.778492	−	0.627655i	$-0.784015\pi$
$359$	2.92393	−	5.06440i	0.154319	−	0.267289i	0.932811	+	0.360366i	$0.117348\pi$
$360$		0			0
$361$	18.0962	+	31.3435i	0.952430	+	1.64966i
$362$	0.224489	−	17.4121i	0.0117989	−	0.915160i
$363$		0			0
$364$	−0.332599	+	12.8966i	−0.0174329	+	0.675966i
$365$	−42.6612	+	7.52233i	−2.23299	+	0.393737i
$366$		0			0
$367$	14.7699	+	12.3934i	0.770981	+	0.646930i	0.940960	−	0.338518i	$-0.109925\pi$
$367$	14.7699	+	12.3934i	0.770981	+	0.646930i	−0.169979	+	0.985448i	$0.554370\pi$
$368$	−2.17987	−	17.6381i	−0.113634	−	0.919450i
$369$		0			0
$370$	−0.427004	−	2.61864i	−0.0221989	−	0.136136i
$371$	−5.35690	−	14.7180i	−0.278116	−	0.764118i
$372$		0			0
$373$	−4.04624	−	4.82212i	−0.209506	−	0.249680i	0.651050	−	0.759034i	$-0.274329\pi$
$373$	−4.04624	−	4.82212i	−0.209506	−	0.249680i	−0.860557	+	0.509355i	$0.829884\pi$
$374$	−1.44198	−	4.12658i	−0.0745632	−	0.213380i
$375$		0			0
$376$	14.6308	−	4.69293i	0.754524	−	0.242019i
$377$	32.1417			1.65538
$378$		0			0
$379$			17.2449i			0.885812i	0.896568	+	0.442906i	$0.146052\pi$
$379$			17.2449i			0.885812i	−0.896568	+	0.442906i	$0.853948\pi$
$380$	−41.0663	−	16.1577i	−2.10666	−	0.828871i
$381$		0			0
$382$	−0.544640	+	0.190318i	−0.0278662	+	0.00973751i
$383$	−20.5611	+	17.2528i	−1.05062	+	0.881578i	−0.993159	−	0.116770i	$-0.962746\pi$
$383$	−20.5611	+	17.2528i	−1.05062	+	0.881578i	−0.0574646	+	0.998348i	$0.518302\pi$
$384$		0			0
$385$	−16.4974	+	6.00455i	−0.840783	+	0.306020i
$386$	5.00806	+	30.7123i	0.254903	+	1.56321i
$387$		0			0
$388$	3.76465	−	1.26129i	0.191121	−	0.0640324i
$389$	−10.1688	+	12.1187i	−0.515578	+	0.614442i	−0.959529	−	0.281609i	$-0.909132\pi$
$389$	−10.1688	+	12.1187i	−0.515578	+	0.614442i	0.443951	+	0.896051i	$0.353576\pi$
$390$		0			0
$391$	−0.550702	−	3.12319i	−0.0278502	−	0.157946i
$392$	11.4827	−	8.90180i	0.579966	−	0.449609i
$393$		0			0
$394$	−0.379797	+	29.4584i	−0.0191339	+	1.48409i
$395$	18.1833	−	10.4981i	0.914902	−	0.528219i
$396$		0			0
$397$	−31.3595	−	18.1054i	−1.57389	−	0.908686i	−0.995685	−	0.0927941i	$-0.970420\pi$
$397$	−31.3595	−	18.1054i	−1.57389	−	0.908686i	−0.578205	−	0.815892i	$-0.696246\pi$
$398$	2.21895	−	3.73140i	0.111226	−	0.187038i
$399$		0			0
$400$	14.6145	−	4.48075i	0.730723	−	0.224037i
$401$	29.9275	+	10.8927i	1.49451	+	0.543957i	0.954632	−	0.297788i	$-0.0962488\pi$
$401$	29.9275	+	10.8927i	1.49451	+	0.543957i	0.539876	+	0.841744i	$0.318471\pi$
$402$		0			0
$403$	24.8665	+	4.38464i	1.23869	+	0.218414i
$404$	8.39521	+	1.70456i	0.417677	+	0.0848051i
$405$		0			0
$406$	8.30914	+	10.1658i	0.412376	+	0.504519i
$407$	0.474994	−	2.69382i	0.0235446	−	0.133528i
$408$		0			0
$409$	−15.5146	−	5.64685i	−0.767147	−	0.279219i	−0.0713442	−	0.997452i	$-0.522729\pi$
$409$	−15.5146	−	5.64685i	−0.767147	−	0.279219i	−0.695802	+	0.718233i	$0.744951\pi$
$410$	−8.46863	−	1.60608i	−0.418236	−	0.0793187i
$411$		0			0
$412$	−3.30541	−	22.0573i	−0.162846	−	1.08668i
$413$	1.47691	+	0.852693i	0.0726738	+	0.0419583i
$414$		0			0
$415$	1.94538	+	3.36950i	0.0954950	+	0.165402i
$416$	10.7421	−	24.4791i	0.526676	−	1.20018i
$417$		0			0
$418$	−34.4729	−	29.6919i	−1.68613	−	1.45228i
$419$	18.1570	−	3.20156i	0.887026	−	0.156407i	0.288471	−	0.957489i	$-0.406853\pi$
$419$	18.1570	−	3.20156i	0.887026	−	0.156407i	0.598555	+	0.801082i	$0.295742\pi$
$420$		0			0
$421$	−6.32940	+	7.54309i	−0.308476	+	0.367627i	−0.897902	−	0.440195i	$-0.854909\pi$
$421$	−6.32940	+	7.54309i	−0.308476	+	0.367627i	0.589426	+	0.807822i	$0.299354\pi$
$422$	−1.15747	+	3.05692i	−0.0563448	+	0.148808i
$423$		0			0
$424$	−1.25491	+	32.4305i	−0.0609436	+	1.57497i
$425$	2.56318	−	0.932923i	0.124333	−	0.0452534i
$426$		0			0
$427$	0.556145	+	0.662787i	0.0269137	+	0.0320745i
$428$	−19.8355	−	12.1444i	−0.958783	−	0.587021i
$429$		0			0
$430$	−7.77865	−	13.8833i	−0.375120	−	0.669513i
$431$	−5.60936			−0.270193			−0.135097	−	0.990832i	$-0.543134\pi$
$431$	−5.60936			−0.270193			−0.135097	+	0.990832i	$0.543134\pi$
$432$		0			0
$433$	−21.7801			−1.04669			−0.523343	−	0.852122i	$-0.675315\pi$
$433$	−21.7801			−1.04669			−0.523343	+	0.852122i	$0.675315\pi$
$434$	5.04162	+	8.99829i	0.242006	+	0.431932i
$435$		0			0
$436$	3.63011	+	2.22256i	0.173851	+	0.106441i
$437$	−21.2173	−	25.2858i	−1.01496	−	1.20959i
$438$		0			0
$439$	14.2403	−	5.18304i	0.679652	−	0.247373i	0.0209536	−	0.999780i	$-0.493330\pi$
$439$	14.2403	−	5.18304i	0.679652	−	0.247373i	0.658698	+	0.752408i	$0.271108\pi$
$440$	36.3514	+	1.40662i	1.73298	+	0.0670581i
$441$		0			0
$442$	1.68917	−	4.46115i	0.0803455	−	0.212195i
$443$	−6.71247	+	7.99962i	−0.318919	+	0.380073i	−0.901558	−	0.432658i	$-0.857576\pi$
$443$	−6.71247	+	7.99962i	−0.318919	+	0.380073i	0.582639	+	0.812731i	$0.302020\pi$
$444$		0			0
$445$	15.5827	−	2.74766i	0.738692	−	0.130251i
$446$	3.87720	+	3.33947i	0.183591	+	0.158128i
$447$		0			0
$448$	10.5193	−	2.93071i	0.496988	−	0.138463i
$449$	13.4948	+	23.3737i	0.636860	+	1.10307i	0.986118	+	0.166047i	$0.0531004\pi$
$449$	13.4948	+	23.3737i	0.636860	+	1.10307i	−0.349258	+	0.937027i	$0.613566\pi$
$450$		0			0
$451$	−7.69593	−	4.44325i	−0.362387	−	0.209224i
$452$	5.17660	+	34.5439i	0.243487	+	1.62481i
$453$		0			0
$454$	−27.3856	−	5.19371i	−1.28527	−	0.243753i
$455$	−18.0031	−	6.55258i	−0.843996	−	0.307190i
$456$		0			0
$457$	5.06627	−	28.7322i	0.236990	−	1.34404i	−0.601392	−	0.798954i	$-0.705387\pi$
$457$	5.06627	−	28.7322i	0.236990	−	1.34404i	0.838382	−	0.545083i	$-0.183502\pi$
$458$	15.7234	+	19.2367i	0.734704	+	0.898870i
$459$		0			0
$460$	25.8650	+	5.25163i	1.20596	+	0.244858i
$461$	4.19983	+	0.740544i	0.195606	+	0.0344906i	0.270593	−	0.962694i	$-0.412780\pi$
$461$	4.19983	+	0.740544i	0.195606	+	0.0344906i	−0.0749868	+	0.997185i	$0.523891\pi$
$462$		0			0
$463$	−26.4209	−	9.61641i	−1.22788	−	0.446912i	−0.355010	−	0.934862i	$-0.615523\pi$
$463$	−26.4209	−	9.61641i	−1.22788	−	0.446912i	−0.872872	+	0.487950i	$0.837745\pi$
$464$	−7.97490	−	26.0110i	−0.370225	−	1.20753i
$465$		0			0
$466$	13.7870	−	23.1844i	0.638672	−	1.07400i
$467$	5.86716	+	3.38741i	0.271500	+	0.156750i	0.629569	−	0.776945i	$-0.283231\pi$
$467$	5.86716	+	3.38741i	0.271500	+	0.156750i	−0.358069	+	0.933695i	$0.616565\pi$
$468$		0			0
$469$	−16.8321	+	9.71802i	−0.777234	+	0.448736i
$470$	−0.294157	+	22.8158i	−0.0135685	+	1.05242i
$471$		0			0
$472$	−2.16510	−	2.79284i	−0.0996569	−	0.128551i
$473$	−2.84900	−	16.1575i	−0.130997	−	0.742922i
$474$		0			0
$475$	18.2490	−	21.7483i	0.837321	−	0.997880i
$476$	1.84765	−	0.619028i	0.0846868	−	0.0283731i
$477$		0			0
$478$	0.339016	+	2.07904i	0.0155062	+	0.0950930i
$479$	33.0606	−	12.0331i	1.51058	−	0.549806i	0.551804	−	0.833974i	$-0.313940\pi$
$479$	33.0606	−	12.0331i	1.51058	−	0.549806i	0.958775	+	0.284168i	$0.0917173\pi$
$480$		0			0
$481$	2.28667	−	1.91874i	0.104263	−	0.0874872i
$482$	5.88978	−	2.05811i	0.268272	−	0.0937445i
$483$		0			0
$484$	14.4284	+	5.67691i	0.655838	+	0.258042i
$485$			5.89612i			0.267729i
$486$		0			0
$487$	−6.71410			−0.304245			−0.152122	−	0.988362i	$-0.548611\pi$
$487$	−6.71410			−0.304245			−0.152122	+	0.988362i	$0.548611\pi$
$488$	−0.547582	−	1.70715i	−0.0247879	−	0.0772792i
$489$		0			0
$490$	7.11758	+	20.3687i	0.321540	+	0.920163i
$491$	2.85750	+	3.40543i	0.128957	+	0.153685i	0.826659	−	0.562703i	$-0.190239\pi$
$491$	2.85750	+	3.40543i	0.128957	+	0.153685i	−0.697702	+	0.716388i	$0.745794\pi$
$492$		0			0
$493$	−1.66043	−	4.56199i	−0.0747820	−	0.205462i
$494$	−7.99052	−	49.0025i	−0.359510	−	2.20473i
$495$		0			0
$496$	−2.62149	−	21.2114i	−0.117708	−	0.952422i
$497$	0.866757	+	0.727295i	0.0388793	+	0.0326236i
$498$		0			0
$499$	−19.6511	+	3.46501i	−0.879702	+	0.155115i	−0.595217	−	0.803565i	$-0.702934\pi$
$499$	−19.6511	+	3.46501i	−0.879702	+	0.155115i	−0.284485	+	0.958680i	$0.591823\pi$
$500$	0.180484	−	6.99831i	0.00807148	−	0.312974i
$501$		0			0
$502$	0.494502	−	38.3553i	0.0220707	−	1.71188i
$503$	−17.6903	−	30.6405i	−0.788771	−	1.36619i	−0.926720	−	0.375753i	$-0.877384\pi$
$503$	−17.6903	−	30.6405i	−0.788771	−	1.36619i	0.137949	−	0.990439i	$-0.455949\pi$
$504$		0			0
$505$	−6.36084	+	11.0173i	−0.283054	+	0.490263i
$506$	23.3872	+	13.9077i	1.03969	+	0.618271i
$507$		0			0
$508$	5.31459	+	9.77901i	0.235797	+	0.433874i
$509$	10.5192	−	28.9013i	0.466256	−	1.28103i	−0.454451	−	0.890772i	$-0.650164\pi$
$509$	10.5192	−	28.9013i	0.466256	−	1.28103i	0.920707	−	0.390255i	$-0.127613\pi$
$510$		0			0
$511$	3.45708	−	19.6061i	0.152932	−	0.867321i
$512$	−22.4753	−	2.61952i	−0.993276	−	0.115768i
$513$		0			0
$514$	−17.3734	+	14.2004i	−0.766310	+	0.626355i
$515$	32.6187	+	5.75155i	1.43735	+	0.253444i
$516$		0			0
$517$	−8.04579	+	22.1056i	−0.353853	+	0.972204i
$518$	1.19800	+	0.227202i	0.0526372	+	0.00998268i
$519$		0			0
$520$	29.4016	+	26.6747i	1.28935	+	1.16976i
$521$	7.26319	−	12.5802i	0.318206	−	0.551149i	−0.661908	−	0.749585i	$-0.730253\pi$
$521$	7.26319	−	12.5802i	0.318206	−	0.551149i	0.980114	+	0.198436i	$0.0635863\pi$
$522$		0			0
$523$	−27.5376	+	15.8989i	−1.20414	+	0.695209i	−0.961472	−	0.274901i	$-0.911355\pi$
$523$	−27.5376	+	15.8989i	−1.20414	+	0.695209i	−0.242665	+	0.970110i	$0.578021\pi$
$524$	−11.9163	−	14.9686i	−0.520565	−	0.653908i
$525$		0			0
$526$	−1.72544	−	1.48614i	−0.0752326	−	0.0647986i
$527$	−0.662269	−	3.75591i	−0.0288489	−	0.163610i
$528$		0			0
$529$	−2.49659	−	2.09488i	−0.108547	−	0.0910819i
$530$	−45.0741	−	17.0668i	−1.95789	−	0.741336i
$531$		0			0
$532$	13.4328	−	15.1952i	0.582387	−	0.658794i
$533$	−3.31676	−	9.11272i	−0.143665	−	0.394716i
$534$		0			0
$535$	26.4585	−	22.2014i	1.14390	−	0.959848i
$536$	39.9029	−	5.45469i	1.72354	−	0.235607i
$537$		0			0
$538$	3.65018	−	2.04515i	0.157370	−	0.0881726i
$539$			22.2446i			0.958142i
$540$		0			0
$541$		−	35.1941i		−	1.51311i	−0.653929	−	0.756556i	$-0.726880\pi$
$541$		−	35.1941i		−	1.51311i	0.653929	−	0.756556i	$-0.273120\pi$
$542$	4.31176	+	7.69563i	0.185206	+	0.330556i
$543$		0			0
$544$	−4.02935	−	0.260091i	−0.172757	−	0.0111513i
$545$	−4.84221	+	4.06310i	−0.207418	+	0.174044i
$546$		0			0
$547$	1.10913	+	3.04730i	0.0474228	+	0.130293i	0.961143	−	0.276051i	$-0.0890258\pi$
$547$	1.10913	+	3.04730i	0.0474228	+	0.130293i	−0.913720	+	0.406344i	$0.866804\pi$
$548$	−5.70801	−	5.04599i	−0.243834	−	0.215554i
$549$		0			0
$550$	−8.28724	+	21.8869i	−0.353369	+	0.933259i
$551$	−38.7079	−	32.4798i	−1.64901	−	1.38369i
$552$		0			0
$553$	1.67560	+	9.50278i	0.0712536	+	0.404100i
$554$	−21.5326	+	24.9998i	−0.914831	+	1.06214i
$555$		0			0
$556$	−1.57723	−	1.98123i	−0.0668893	−	0.0840231i
$557$	−20.4301	+	11.7954i	−0.865653	+	0.499785i	−0.865901	−	0.500215i	$-0.833254\pi$
$557$	−20.4301	+	11.7954i	−0.865653	+	0.499785i	0.000248175		1.00000i	$0.499921\pi$
$558$		0			0
$559$	8.95209	−	15.5055i	0.378633	−	0.655812i
$560$	−0.835882	+	16.1950i	−0.0353225	+	0.684363i
$561$		0			0
$562$	−1.90508	+	10.0452i	−0.0803609	+	0.423731i
$563$	7.83509	−	21.5267i	0.330210	−	0.907244i	−0.657847	−	0.753152i	$-0.728533\pi$
$563$	7.83509	−	21.5267i	0.330210	−	0.907244i	0.988057	−	0.154092i	$-0.0492452\pi$
$564$		0			0
$565$	−51.0841	−	9.00750i	−2.14912	−	0.378948i
$566$	1.22064	+	1.49338i	0.0513072	+	0.0627715i
$567$		0			0
$568$	−1.09289	−	2.07425i	−0.0458567	−	0.0870337i
$569$	−5.27628	+	29.9233i	−0.221193	+	1.25445i	0.648637	+	0.761098i	$0.275339\pi$
$569$	−5.27628	+	29.9233i	−0.221193	+	1.25445i	−0.869830	+	0.493351i	$0.835772\pi$
$570$		0			0
$571$	11.6641	−	32.0469i	0.488129	−	1.34112i	−0.414244	−	0.910166i	$-0.635954\pi$
$571$	11.6641	−	32.0469i	0.488129	−	1.34112i	0.902373	−	0.430957i	$-0.141824\pi$
$572$	19.5435	+	35.9606i	0.817153	+	1.50359i
$573$		0			0
$574$	2.02474	−	3.40481i	0.0845109	−	0.142114i
$575$	−8.48957	+	14.7044i	−0.354039	+	0.613214i
$576$		0			0
$577$	5.70949	+	9.88913i	0.237689	+	0.411690i	0.960051	−	0.279826i	$-0.0902767\pi$
$577$	5.70949	+	9.88913i	0.237689	+	0.411690i	−0.722362	+	0.691516i	$0.756943\pi$
$578$	23.3192	+	0.300647i	0.969950	+	0.0125053i
$579$		0			0
$580$	40.3890	+	1.04162i	1.67706	+	0.0432508i
$581$	−1.76093	+	0.310500i	−0.0730558	+	0.0128817i
$582$		0			0
$583$	−38.0643	−	31.9397i	−1.57646	−	1.32281i
$584$	−21.9925	+	34.9019i	−0.910056	+	1.44425i
$585$		0			0
$586$	−20.4556	+	3.33557i	−0.845014	+	0.137791i
$587$	−10.9697	−	30.1389i	−0.452766	−	1.24396i	−0.930770	−	0.365606i	$-0.880862\pi$
$587$	−10.9697	−	30.1389i	−0.452766	−	1.24396i	0.478004	−	0.878358i	$-0.341361\pi$
$588$		0			0
$589$	−25.5158	−	30.4085i	−1.05136	−	1.25296i
$590$	4.95408	−	1.73114i	0.203956	−	0.0712701i
$591$		0			0
$592$	−2.12013	−	1.37444i	−0.0871368	−	0.0564892i
$593$	−19.2802			−0.791741			−0.395871	−	0.918306i	$-0.629557\pi$
$593$	−19.2802			−0.791741			−0.395871	+	0.918306i	$0.629557\pi$
$594$		0			0
$595$			2.89375i			0.118632i
$596$	−7.32166	+	18.6087i	−0.299907	+	0.762244i
$597$		0			0
$598$	9.79521	+	28.0313i	0.400556	+	1.14629i
$599$	−31.8430	+	26.7195i	−1.30107	+	1.09173i	−0.311111	+	0.950374i	$0.600701\pi$
$599$	−31.8430	+	26.7195i	−1.30107	+	1.09173i	−0.989959	+	0.141354i	$0.954855\pi$
$600$		0			0
$601$	−5.75768	+	2.09562i	−0.234861	+	0.0854822i	−0.456769	−	0.889585i	$-0.650994\pi$
$601$	−5.75768	+	2.09562i	−0.234861	+	0.0854822i	0.221909	+	0.975067i	$0.428771\pi$
$602$	7.21833	−	1.17705i	0.294197	−	0.0479728i
$603$		0			0
$604$	−40.0115	+	13.4053i	−1.62804	+	0.545453i
$605$	−14.8007	+	17.6388i	−0.601734	+	0.717118i
$606$		0			0
$607$	3.21106	+	18.2108i	0.130333	+	0.739155i	0.977997	+	0.208621i	$0.0668975\pi$
$607$	3.21106	+	18.2108i	0.130333	+	0.739155i	−0.847664	+	0.530534i	$0.821991\pi$
$608$	−37.6732	+	18.6248i	−1.52785	+	0.755334i
$609$		0			0
$610$	2.66221	+	0.0343230i	0.107790	+	0.00138970i
$611$	−22.2321	+	12.8357i	−0.899413	+	0.519276i
$612$		0			0
$613$	−16.0146	−	9.24602i	−0.646823	−	0.373443i	0.140415	−	0.990093i	$-0.455156\pi$
$613$	−16.0146	−	9.24602i	−0.646823	−	0.373443i	−0.787238	+	0.616650i	$0.788490\pi$
$614$	13.5090	+	8.03338i	0.545178	+	0.324201i
$615$		0			0
$616$	−6.32132	+	15.4776i	−0.254693	+	0.623610i
$617$	−29.7070	−	10.8125i	−1.19596	−	0.435294i	−0.334148	−	0.942521i	$-0.608448\pi$
$617$	−29.7070	−	10.8125i	−1.19596	−	0.435294i	−0.861813	+	0.507227i	$0.830671\pi$
$618$		0			0
$619$	−15.2623	−	2.69116i	−0.613445	−	0.108167i	−0.141712	−	0.989908i	$-0.545261\pi$
$619$	−15.2623	−	2.69116i	−0.613445	−	0.108167i	−0.471734	+	0.881741i	$0.656372\pi$
$620$	31.1050	+	6.31556i	1.24921	+	0.253639i
$621$		0			0
$622$	12.0630	−	9.85987i	0.483682	−	0.395345i
$623$	−1.26276	+	7.16145i	−0.0505913	+	0.286917i
$624$		0			0
$625$	27.7244	+	10.0909i	1.10898	+	0.403634i
$626$	0.678441	−	3.57732i	0.0271160	−	0.142978i
$627$		0			0
$628$	−17.5866	+	2.63545i	−0.701780	+	0.105166i
$629$	−0.390464	−	0.225434i	−0.0155688	−	0.00898866i
$630$		0			0
$631$	11.8337	+	20.4966i	0.471093	+	0.815957i	0.999453	−	0.0330630i	$-0.0105262\pi$
$631$	11.8337	+	20.4966i	0.471093	+	0.815957i	−0.528360	+	0.849020i	$0.677193\pi$
$632$	4.23084	−	19.5420i	0.168294	−	0.777341i
$633$		0			0
$634$	−3.88062	+	4.50548i	−0.154119	+	0.178936i
$635$	−16.2773	+	2.87013i	−0.645945	+	0.113897i
$636$		0			0
$637$	−15.6036	+	18.5956i	−0.618235	+	0.736784i
$638$	38.9546	+	14.7497i	1.54223	+	0.583948i
$639$		0			0
$640$	14.2918	−	30.4121i	0.564932	−	1.20214i
$641$	11.7394	−	4.27278i	0.463677	−	0.168765i	−0.0996090	−	0.995027i	$-0.531759\pi$
$641$	11.7394	−	4.27278i	0.463677	−	0.168765i	0.563286	+	0.826262i	$0.309537\pi$
$642$		0			0
$643$	9.44368	+	11.2545i	0.372422	+	0.443836i	0.919407	−	0.393307i	$-0.128669\pi$
$643$	9.44368	+	11.2545i	0.372422	+	0.443836i	−0.546985	+	0.837142i	$0.684225\pi$
$644$	−6.33353	+	10.3446i	−0.249576	+	0.407633i
$645$		0			0
$646$	−6.54232	+	3.66558i	−0.257404	+	0.144220i
$647$	−9.10943			−0.358129			−0.179064	−	0.983837i	$-0.557307\pi$
$647$	−9.10943			−0.358129			−0.179064	+	0.983837i	$0.557307\pi$
$648$		0			0
$649$	5.41034			0.212375
$650$	−22.2805	+	12.4834i	−0.873911	+	0.489641i
$651$		0			0
$652$	−30.3222	−	18.5650i	−1.18751	−	0.727060i
$653$	11.0736	+	13.1970i	0.433345	+	0.516440i	0.937884	−	0.346949i	$-0.112782\pi$
$653$	11.0736	+	13.1970i	0.433345	+	0.516440i	−0.504540	+	0.863389i	$0.668338\pi$
$654$		0			0
$655$	26.6994	−	9.71778i	1.04323	−	0.379705i
$656$	−6.55163	+	4.94515i	−0.255798	+	0.193076i
$657$		0			0
$658$	−9.80701	−	3.71332i	−0.382317	−	0.144760i
$659$	13.0287	−	15.5270i	0.507525	−	0.604844i	−0.450059	−	0.892999i	$-0.648597\pi$
$659$	13.0287	−	15.5270i	0.507525	−	0.604844i	0.957584	+	0.288154i	$0.0930416\pi$
$660$		0			0
$661$	28.8852	−	5.09323i	1.12350	−	0.198104i	0.419125	−	0.907929i	$-0.362337\pi$
$661$	28.8852	−	5.09323i	1.12350	−	0.198104i	0.704378	+	0.709825i	$0.251226\pi$
$662$	−0.397282	+	0.461253i	−0.0154408	+	0.0179271i
$663$		0			0
$664$	3.62128	+	0.784005i	0.140533	+	0.0304253i
$665$	15.0594	+	26.0837i	0.583979	+	1.01148i
$666$		0			0
$667$	26.1710	+	15.1099i	1.01335	+	0.585056i
$668$	2.04878	+	13.6716i	0.0792695	+	0.528972i
$669$		0			0
$670$	−11.1442	+	58.7615i	−0.430536	+	2.27015i
$671$	2.57934	+	0.938803i	0.0995743	+	0.0362421i
$672$		0			0
$673$	−8.11942	+	46.0475i	−0.312980	+	1.77500i	0.270346	+	0.962763i	$0.412862\pi$
$673$	−8.11942	+	46.0475i	−0.312980	+	1.77500i	−0.583327	+	0.812237i	$0.698249\pi$
$674$	−16.9754	+	13.8751i	−0.653869	+	0.534450i
$675$		0			0
$676$	−3.71369	+	18.2904i	−0.142834	+	0.703478i
$677$	−10.5443	−	1.85925i	−0.405251	−	0.0714567i	−0.0326928	−	0.999465i	$-0.510408\pi$
$677$	−10.5443	−	1.85925i	−0.405251	−	0.0714567i	−0.372558	+	0.928009i	$0.621519\pi$
$678$		0			0
$679$	−2.54630	−	0.926777i	−0.0977180	−	0.0355664i
$680$	2.26717	−	5.55110i	0.0869419	−	0.212875i
$681$		0			0
$682$	28.1253	+	16.7252i	1.07697	+	0.640442i
$683$	17.0645	+	9.85219i	0.652955	+	0.376984i	0.789587	−	0.613638i	$-0.210295\pi$
$683$	17.0645	+	9.85219i	0.652955	+	0.376984i	−0.136632	+	0.990622i	$0.543628\pi$
$684$		0			0
$685$	9.79823	−	5.65701i	0.374371	−	0.216143i
$686$	−23.4267	−	0.302033i	−0.894436	−	0.0115317i
$687$		0			0
$688$	−14.7692	−	3.39741i	−0.563069	−	0.129525i
$689$	−9.41599	−	53.4008i	−0.358721	−	2.03441i
$690$		0			0
$691$	4.57312	−	5.45003i	0.173970	−	0.207329i	−0.672013	−	0.740539i	$-0.734570\pi$
$691$	4.57312	−	5.45003i	0.173970	−	0.207329i	0.845983	+	0.533210i	$0.179015\pi$
$692$	−14.4905	−	43.2505i	−0.550845	−	1.64414i
$693$		0			0
$694$	8.92301	−	1.45502i	0.338713	−	0.0552317i
$695$	3.53391	−	1.28624i	0.134049	−	0.0487897i
$696$		0			0
$697$	−1.12206	+	0.941521i	−0.0425011	+	0.0356627i
$698$	16.9620	+	48.5408i	0.642021	+	1.83730i
$699$		0			0
$700$	−9.70812	−	3.81969i	−0.366932	−	0.144371i
$701$		−	10.6994i		−	0.404109i	−0.979374	−	0.202055i	$-0.935238\pi$
$701$		−	10.6994i		−	0.404109i	0.979374	−	0.202055i	$-0.0647618\pi$
$702$		0			0
$703$	−4.69275			−0.176990
$704$	24.2525	−	24.7382i	0.914050	−	0.932357i
$705$		0			0
$706$	21.6710	−	7.57267i	0.815600	−	0.285001i
$707$	−3.75811	−	4.47874i	−0.141338	−	0.168440i
$708$		0			0
$709$	−9.95367	−	27.3475i	−0.373818	−	1.02706i	−0.973872	−	0.227097i	$-0.927077\pi$
$709$	−9.95367	−	27.3475i	−0.373818	−	1.02706i	0.600054	−	0.799959i	$-0.295146\pi$
$710$	3.43639	−	0.560350i	0.128965	−	0.0210296i
$711$		0			0
$712$	8.03313	−	12.7485i	0.301054	−	0.477771i
$713$	18.1861	+	15.2600i	0.681075	+	0.571490i
$714$		0			0
$715$	−59.8569	+	10.5544i	−2.23852	+	0.394712i
$716$	0.645810	−	25.0415i	0.0241351	−	0.935843i
$717$		0			0
$718$	8.26944	+	0.106615i	0.308613	+	0.00397885i
$719$	4.95129	+	8.57588i	0.184652	+	0.319826i	0.943459	−	0.331489i	$-0.107551\pi$
$719$	4.95129	+	8.57588i	0.184652	+	0.319826i	−0.758807	+	0.651315i	$0.774218\pi$
$720$		0			0
$721$	−7.61100	+	13.1826i	−0.283448	+	0.490947i
$722$	−26.1612	+	43.9928i	−0.973618	+	1.63724i
$723$		0			0
$724$	21.6375	−	11.7593i	0.804152	−	0.437031i
$725$	−8.88976	+	24.4244i	−0.330157	+	0.907100i
$726$		0			0
$727$	−4.91637	+	27.8821i	−0.182338	+	1.03409i	0.746990	+	0.664835i	$0.231498\pi$
$727$	−4.91637	+	27.8821i	−0.182338	+	1.03409i	−0.929328	+	0.369255i	$0.879613\pi$
$728$	−16.1412	+	8.50455i	−0.598233	+	0.315200i
$729$		0			0
$730$	−38.7707	−	47.4338i	−1.43497	−	1.75560i
$731$	−2.66321	−	0.469597i	−0.0985026	−	0.0173687i
$732$		0			0
$733$	−13.4575	+	36.9742i	−0.497065	+	1.36567i	0.397033	+	0.917804i	$0.370040\pi$
$733$	−13.4575	+	36.9742i	−0.497065	+	1.36567i	−0.894098	+	0.447871i	$0.852182\pi$
$734$	−5.08065	+	26.7895i	−0.187530	+	0.988819i
$735$		0			0
$736$	20.2543	−	14.8819i	0.746584	−	0.548556i
$737$	−30.8304	+	53.3999i	−1.13565	+	1.96701i
$738$		0			0
$739$	40.7334	−	23.5175i	1.49840	−	0.865104i	0.498405	−	0.866944i	$-0.333919\pi$
$739$	40.7334	−	23.5175i	1.49840	−	0.865104i	0.999998	+	0.00184073i	$0.000585924\pi$
$740$	2.93559	−	2.33698i	0.107915	−	0.0859089i
$741$		0			0
$742$	14.4554	−	16.7830i	0.530675	−	0.616125i
$743$	−4.48040	−	25.4096i	−0.164370	−	0.932189i	−0.949712	−	0.313126i	$-0.898624\pi$
$743$	−4.48040	−	25.4096i	−0.164370	−	0.932189i	0.785342	−	0.619063i	$-0.212487\pi$
$744$		0			0
$745$	−22.7492	−	19.0888i	−0.833466	−	0.699361i
$746$	3.15233	−	8.32542i	0.115415	−	0.304815i
$747$		0			0
$748$	4.09442	−	4.63160i	0.149707	−	0.169348i
$749$	5.42901	+	14.9161i	0.198372	+	0.545022i
$750$		0			0
$751$	27.2407	−	22.8576i	0.994026	−	0.834087i	0.00788021	−	0.999969i	$-0.497492\pi$
$751$	27.2407	−	22.8576i	0.994026	−	0.834087i	0.986146	+	0.165882i	$0.0530472\pi$
$752$	15.9036	+	14.8068i	0.579944	+	0.539948i
$753$		0			0
$754$	22.2182	+	39.6551i	0.809140	+	1.44415i
$755$		−	62.6652i		−	2.28062i
$756$		0			0
$757$			4.81926i			0.175159i	0.996158	+	0.0875795i	$0.0279132\pi$
$757$			4.81926i			0.175159i	−0.996158	+	0.0875795i	$0.972087\pi$
$758$	−21.2761	+	11.9207i	−0.772782	+	0.432979i
$759$		0			0
$760$	−8.45280	−	61.8351i	−0.306615	−	2.24299i
$761$	−5.92907	+	4.97508i	−0.214929	+	0.180347i	−0.743896	−	0.668296i	$-0.767024\pi$
$761$	−5.92907	+	4.97508i	−0.214929	+	0.180347i	0.528967	+	0.848642i	$0.322580\pi$
$762$		0			0
$763$	−0.993570	−	2.72981i	−0.0359697	−	0.0988258i
$764$	−0.611294	−	0.540396i	−0.0221158	−	0.0195508i
$765$		0			0
$766$	−35.4989	−	13.4413i	−1.28263	−	0.485653i
$767$	4.52284	+	3.79511i	0.163310	+	0.137033i
$768$		0			0
$769$	−5.50477	−	31.2191i	−0.198507	−	1.12579i	−0.907335	−	0.420409i	$-0.861887\pi$
$769$	−5.50477	−	31.2191i	−0.198507	−	1.12579i	0.708828	−	0.705382i	$-0.249224\pi$
$770$	−18.8121	−	16.2031i	−0.677941	−	0.583918i
$771$		0			0
$772$	−34.4297	+	27.4089i	−1.23915	+	0.986468i
$773$	27.4650	−	15.8569i	0.987847	−	0.570334i	0.0832173	−	0.996531i	$-0.473480\pi$
$773$	27.4650	−	15.8569i	0.987847	−	0.570334i	0.904630	+	0.426197i	$0.140147\pi$
$774$		0			0
$775$	−10.2095	+	17.6833i	−0.366735	+	0.635204i
$776$	4.15848	+	3.77279i	0.149281	+	0.135435i
$777$		0			0
$778$	−21.9808	−	4.16868i	−0.788050	−	0.149454i
$779$	−5.21424	+	14.3260i	−0.186820	+	0.513283i
$780$		0			0
$781$	3.53506	+	0.623327i	0.126494	+	0.0223044i
$782$	3.47258	−	2.83836i	0.124179	−	0.101500i
$783$		0			0
$784$	18.9202	+	8.01347i	0.675722	+	0.286196i
$785$	4.58579	−	26.0073i	0.163674	−	0.928241i
$786$		0			0
$787$	−2.68876	+	7.38730i	−0.0958438	+	0.263329i	−0.978345	−	0.206982i	$-0.933636\pi$
$787$	−2.68876	+	7.38730i	−0.0958438	+	0.263329i	0.882501	+	0.470311i	$0.155858\pi$
$788$	−36.6071	+	19.8948i	−1.30407	+	0.708723i
$789$		0			0
$790$	25.5216	+	15.1769i	0.908016	+	0.539969i
$791$	11.9196	−	20.6453i	0.423812	−	0.734063i
$792$		0			0
$793$	1.49770	+	2.59409i	0.0531849	+	0.0921189i
$794$	0.660178	−	51.2057i	0.0234288	−	1.81722i
$795$		0			0
$796$	6.13752	+	0.158284i	0.217539	+	0.00561024i
$797$	34.5495	−	6.09202i	1.22381	−	0.215790i	0.475844	−	0.879530i	$-0.342143\pi$
$797$	34.5495	−	6.09202i	1.22381	−	0.215790i	0.747964	+	0.663740i	$0.231032\pi$
$798$		0			0
$799$	2.97032	+	2.49239i	0.105082	+	0.0881746i
$800$	15.6305	+	14.9334i	0.552623	+	0.527974i
$801$		0			0
$802$	7.24867	+	44.4530i	0.255959	+	1.56969i
$803$	−21.6019	−	59.3509i	−0.762316	−	2.09445i
$804$		0			0
$805$	−11.5784	−	13.7986i	−0.408086	−	0.486338i
$806$	11.7796	+	33.7102i	0.414920	+	1.18739i
$807$		0			0
$808$	3.70024	+	11.5360i	0.130174	+	0.405834i
$809$	−42.6190			−1.49840			−0.749202	−	0.662341i	$-0.769563\pi$
$809$	−42.6190			−1.49840			−0.749202	+	0.662341i	$0.769563\pi$
$810$		0			0
$811$		−	40.0596i		−	1.40668i	−0.710852	−	0.703341i	$-0.751691\pi$
$811$		−	40.0596i		−	1.40668i	0.710852	−	0.703341i	$-0.248309\pi$
$812$	−6.79834	+	17.2787i	−0.238575	+	0.606362i
$813$		0			0
$814$	3.65187	−	1.27610i	0.127998	−	0.0447274i
$815$	40.4468	−	33.9389i	1.41679	−	1.18883i
$816$		0			0
$817$	−26.4495	+	9.62683i	−0.925351	+	0.336800i
$818$	−3.75775	−	23.0447i	−0.131387	−	0.805739i
$819$		0			0
$820$	−3.87250	−	11.5585i	−0.135233	−	0.403639i
$821$	−1.07655	+	1.28299i	−0.0375720	+	0.0447766i	−0.784503	−	0.620125i	$-0.787082\pi$
$821$	−1.07655	+	1.28299i	−0.0375720	+	0.0447766i	0.746931	+	0.664901i	$0.231526\pi$
$822$		0			0
$823$	0.234450	+	1.32963i	0.00817242	+	0.0463481i	0.988621	−	0.150426i	$-0.0480645\pi$
$823$	0.234450	+	1.32963i	0.00817242	+	0.0463481i	−0.980449	+	0.196774i	$0.936953\pi$
$824$	24.9284	−	19.3254i	0.868423	−	0.673231i
$825$		0			0
$826$	−0.0310917	+	2.41158i	−0.00108182	+	0.0839096i
$827$	−10.0199	+	5.78501i	−0.348427	+	0.201165i	−0.663992	−	0.747739i	$-0.731139\pi$
$827$	−10.0199	+	5.78501i	−0.348427	+	0.201165i	0.315565	+	0.948904i	$0.397806\pi$
$828$		0			0
$829$	34.1730	+	19.7298i	1.18688	+	0.685243i	0.957595	−	0.288117i	$-0.0930292\pi$
$829$	34.1730	+	19.7298i	1.18688	+	0.685243i	0.229281	+	0.973360i	$0.426363\pi$
$830$	−2.81239	+	4.72933i	−0.0976193	+	0.164157i
$831$		0			0
$832$	37.6269	−	3.66818i	1.30448	−	0.127171i
$833$	3.44542	+	1.25403i	0.119377	+	0.0434496i
$834$		0			0
$835$	−20.2179	−	3.56496i	−0.699668	−	0.123370i
$836$	12.8029	−	63.0561i	0.442798	−	2.18084i
$837$		0			0
$838$	16.5011	+	20.1882i	0.570022	+	0.697390i
$839$	6.51330	−	36.9388i	0.224864	−	1.27527i	−0.638080	−	0.769970i	$-0.720271\pi$
$839$	6.51330	−	36.9388i	0.224864	−	1.27527i	0.862945	−	0.505299i	$-0.168618\pi$
$840$		0			0
$841$	16.2198	+	5.90354i	0.559305	+	0.203570i
$842$	−13.6816	−	2.59473i	−0.471499	−	0.0894202i
$843$		0			0
$844$	−4.57161	+	0.685083i	−0.157361	+	0.0235815i
$845$	−24.0031	−	13.8582i	−0.825732	−	0.476737i
$846$		0			0
$847$	−5.29105	−	9.16436i	−0.181803	−	0.314891i
$848$	−40.8789	+	20.8696i	−1.40379	+	0.716667i
$849$		0			0
$850$	2.92283	+	2.51746i	0.100252	+	0.0863482i
$851$	2.76390	−	0.487351i	0.0947454	−	0.0167062i
$852$		0			0
$853$	16.8181	−	20.0430i	0.575840	−	0.686260i	−0.396978	−	0.917828i	$-0.629941\pi$
$853$	16.8181	−	20.0430i	0.575840	−	0.686260i	0.972819	+	0.231568i	$0.0743856\pi$
$854$	−0.433280	+	1.14431i	−0.0148265	+	0.0391574i
$855$		0			0
$856$	1.27180	−	32.8671i	0.0434692	−	1.12337i
$857$	19.6602	−	7.15571i	0.671578	−	0.244434i	0.0163509	−	0.999866i	$-0.494795\pi$
$857$	19.6602	−	7.15571i	0.671578	−	0.244434i	0.655227	+	0.755432i	$0.272573\pi$
$858$		0			0
$859$	18.2371	+	21.7341i	0.622241	+	0.741558i	0.981454	−	0.191698i	$-0.0613993\pi$
$859$	18.2371	+	21.7341i	0.622241	+	0.741558i	−0.359213	+	0.933256i	$0.616955\pi$
$860$	11.7516	−	19.1939i	0.400727	−	0.654508i
$861$		0			0
$862$	−3.87752	−	6.92060i	−0.132069	−	0.235716i
$863$	37.5798			1.27923			0.639616	−	0.768694i	$-0.279093\pi$
$863$	37.5798			1.27923			0.639616	+	0.768694i	$0.279093\pi$
$864$		0			0
$865$	67.7381			2.30316
$866$	−15.0557	−	26.8714i	−0.511614	−	0.913129i
$867$		0			0
$868$	−7.61665	+	12.4403i	−0.258526	+	0.422251i
$869$	19.6775	+	23.4507i	0.667512	+	0.795510i
$870$		0			0
$871$	−63.2307	+	23.0141i	−2.14249	+	0.779802i
$872$	−0.232753	+	6.01505i	−0.00788203	+	0.203695i
$873$		0			0
$874$	16.5299	−	43.6561i	0.559134	−	1.47669i
$875$	−3.07116	+	3.66007i	−0.103824	+	0.123733i
$876$		0			0
$877$	−23.8777	+	4.21027i	−0.806291	+	0.142171i	−0.561577	−	0.827424i	$-0.689805\pi$
$877$	−23.8777	+	4.21027i	−0.806291	+	0.142171i	−0.244714	+	0.969595i	$0.578694\pi$
$878$	16.2383	+	13.9862i	0.548018	+	0.472013i
$879$		0			0
$880$	23.3928	+	45.8212i	0.788571	+	1.54463i
$881$	15.8494	+	27.4519i	0.533980	+	0.924880i	0.999212	+	0.0396911i	$0.0126374\pi$
$881$	15.8494	+	27.4519i	0.533980	+	0.924880i	−0.465232	+	0.885189i	$0.654029\pi$
$882$		0			0
$883$	−19.1513	−	11.0570i	−0.644492	−	0.372098i	0.141851	−	0.989888i	$-0.454695\pi$
$883$	−19.1513	−	11.0570i	−0.644492	−	0.372098i	−0.786343	+	0.617790i	$0.788028\pi$
$884$	6.67163	−	0.999783i	0.224391	−	0.0336263i
$885$		0			0
$886$	−14.5097	−	2.75177i	−0.487461	−	0.0924474i
$887$	−0.923934	−	0.336285i	−0.0310227	−	0.0112913i	0.326462	−	0.945210i	$-0.394143\pi$
$887$	−0.923934	−	0.336285i	−0.0310227	−	0.0112913i	−0.357485	+	0.933919i	$0.616366\pi$
$888$		0			0
$889$	1.31904	−	7.48065i	0.0442392	−	0.250893i
$890$	14.1617	+	17.3260i	0.474700	+	0.580769i
$891$		0			0
$892$	−1.43995	+	7.09197i	−0.0482132	+	0.237457i
$893$	39.7446	+	7.00804i	1.33000	+	0.234515i
$894$		0			0
$895$	34.9567	+	12.7232i	1.16847	+	0.425290i
$896$	10.8873	+	10.9523i	0.363720	+	0.365892i
$897$		0			0
$898$	−19.5091	+	32.8067i	−0.651028	+	1.09477i
$899$	31.4731	+	18.1710i	1.04969	+	0.606036i
$900$		0			0
$901$	−7.09295	+	4.09512i	−0.236300	+	0.136428i
$902$	0.162014	−	12.5664i	0.00539447	−	0.418414i
$903$		0			0
$904$	−39.0404	+	30.2654i	−1.29846	+	1.00661i
$905$	6.35058	+	36.0159i	0.211100	+	1.19721i
$906$		0			0
$907$	−26.0101	+	30.9976i	−0.863651	+	1.02926i	0.135607	+	0.990763i	$0.456701\pi$
$907$	−26.0101	+	30.9976i	−0.863651	+	1.02926i	−0.999259	+	0.0384971i	$0.987743\pi$
$908$	−12.5228	−	37.3775i	−0.415583	−	1.24041i
$909$		0			0
$910$	−4.36048	−	26.7410i	−0.144548	−	0.886454i
$911$	−28.6333	+	10.4217i	−0.948664	+	0.345286i	−0.769582	−	0.638548i	$-0.779535\pi$
$911$	−28.6333	+	10.4217i	−0.948664	+	0.345286i	−0.179083	+	0.983834i	$0.557313\pi$
$912$		0			0
$913$	−4.34558	+	3.64637i	−0.143818	+	0.120677i
$914$	38.9507	−	13.6109i	1.28838	−	0.450207i
$915$		0			0
$916$	−12.8645	+	32.6963i	−0.425054	+	1.08032i
$917$			13.0579i			0.431209i
$918$		0			0
$919$	−28.9703			−0.955641			−0.477820	−	0.878458i	$-0.658573\pi$
$919$	−28.9703			−0.955641			−0.477820	+	0.878458i	$0.658573\pi$
$920$	11.4002	+	35.5414i	0.375852	+	1.17177i
$921$		0			0
$922$	1.98952	+	5.69349i	0.0655214	+	0.187505i
$923$	2.51794	+	3.00076i	0.0828789	+	0.0987713i
$924$		0			0
$925$	0.825603	+	2.26832i	0.0271456	+	0.0745821i
$926$	−6.39933	−	39.2444i	−0.210295	−	1.28965i
$927$		0			0
$928$	26.5786	−	27.8195i	0.872486	−	0.913219i
$929$	21.4798	+	18.0237i	0.704730	+	0.591338i	0.923115	−	0.384524i	$-0.125634\pi$
$929$	21.4798	+	18.0237i	0.704730	+	0.591338i	−0.218385	+	0.975863i	$0.570079\pi$
$930$		0			0
$931$	37.5824	−	6.62680i	1.23171	−	0.217185i
$932$	38.1343	+	0.983471i	1.24913	+	0.0322147i
$933$		0			0
$934$	−0.123515	+	9.58023i	−0.00404153	+	0.313475i
$935$	4.59022	+	7.95049i	0.150116	+	0.260009i
$936$		0			0
$937$	−10.0264	+	17.3662i	−0.327548	+	0.567329i	−0.982025	−	0.188753i	$-0.939556\pi$
$937$	−10.0264	+	17.3662i	−0.327548	+	0.567329i	0.654477	+	0.756082i	$0.272889\pi$
$938$	−23.6250	−	14.0491i	−0.771385	−	0.458719i
$939$		0			0
$940$	−28.3526	+	15.4087i	−0.924760	+	0.502578i
$941$	7.11484	−	19.5479i	0.231937	−	0.637242i	−0.768058	−	0.640380i	$-0.778777\pi$
$941$	7.11484	−	19.5479i	0.231937	−	0.637242i	0.999995	+	0.00313816i	$0.000998909\pi$
$942$		0			0
$943$	1.58327	−	8.97916i	0.0515583	−	0.292402i
$944$	1.94904	−	4.60179i	0.0634360	−	0.149775i
$945$		0			0
$946$	17.9650	−	14.6840i	0.584094	−	0.477418i
$947$	−31.3017	−	5.51933i	−1.01717	−	0.179354i	−0.359884	−	0.932997i	$-0.617184\pi$
$947$	−31.3017	−	5.51933i	−1.01717	−	0.179354i	−0.657284	+	0.753643i	$0.728295\pi$
$948$		0			0
$949$	23.5735	−	64.7678i	0.765230	−	2.10245i
$950$	39.4469	+	7.48114i	1.27983	+	0.242720i
$951$		0			0
$952$	2.04093	+	1.85164i	0.0661471	+	0.0600121i
$953$	6.86849	−	11.8966i	0.222492	−	0.385368i	−0.733072	−	0.680151i	$-0.761914\pi$
$953$	6.86849	−	11.8966i	0.222492	−	0.385368i	0.955564	+	0.294783i	$0.0952475\pi$
$954$		0			0
$955$	1.04933	−	0.605833i	0.0339556	−	0.0196043i
$956$	−2.33069	+	1.85542i	−0.0753798	+	0.0600085i
$957$		0			0
$958$	37.6994	+	32.4709i	1.21801	+	1.04909i
$959$	0.902910	+	5.12065i	0.0291565	+	0.165355i
$960$		0			0
$961$	−1.87694	−	1.57494i	−0.0605465	−	0.0508046i
$962$	3.94795	+	1.49485i	0.127287	+	0.0481959i
$963$		0			0
$964$	6.61058	+	5.84388i	0.212913	+	0.188219i
$965$	−22.3521	−	61.4119i	−0.719539	−	1.97692i
$966$		0			0
$967$	10.5560	−	8.85755i	0.339458	−	0.284839i	−0.457082	−	0.889424i	$-0.651105\pi$
$967$	10.5560	−	8.85755i	0.339458	−	0.284839i	0.796541	+	0.604585i	$0.206661\pi$
$968$	2.96985	+	21.7254i	0.0954545	+	0.698282i
$969$		0			0
$970$	−7.27439	+	4.07575i	−0.233567	+	0.130864i
$971$			1.88573i			0.0605161i	0.999542	+	0.0302580i	$0.00963290\pi$
$971$			1.88573i			0.0605161i	−0.999542	+	0.0302580i	$0.990367\pi$
$972$		0			0
$973$			1.72833i			0.0554077i
$974$	−4.64118	−	8.28358i	−0.148713	−	0.265423i
$975$		0			0
$976$	1.72769	−	1.85567i	0.0553021	−	0.0593985i
$977$	19.2464	−	16.1496i	0.615746	−	0.516672i	−0.280717	−	0.959790i	$-0.590572\pi$
$977$	19.2464	−	16.1496i	0.615746	−	0.516672i	0.896463	+	0.443119i	$0.146128\pi$
$978$		0			0
$979$	7.89048	+	21.6789i	0.252181	+	0.692861i
$980$	−20.2099	+	22.8614i	−0.645583	+	0.730281i
$981$		0			0
$982$	−2.22621	+	5.87949i	−0.0710412	+	0.187622i
$983$	38.8553	+	32.6035i	1.23929	+	1.03989i	0.997579	+	0.0695429i	$0.0221541\pi$
$983$	38.8553	+	32.6035i	1.23929	+	1.03989i	0.241714	+	0.970348i	$0.422290\pi$
$984$		0			0
$985$	−10.7441	−	60.9330i	−0.342336	−	1.94149i
$986$	4.48061	−	5.20209i	0.142692	−	0.165668i
$987$		0			0
$988$	54.9337	−	43.7318i	1.74767	−	1.39129i
$989$	14.5783	−	8.41679i	0.463563	−	0.267638i
$990$		0			0
$991$	−16.9675	+	29.3886i	−0.538991	+	0.933559i	0.459968	+	0.887936i	$0.347861\pi$
$991$	−16.9675	+	29.3886i	−0.538991	+	0.933559i	−0.998959	+	0.0456239i	$0.985472\pi$
$992$	24.3577	−	17.8969i	0.773357	−	0.568227i
$993$		0			0
$994$	−0.298153	+	1.57212i	−0.00945685	+	0.0498646i
$995$	−3.11838	+	8.56769i	−0.0988594	+	0.271614i
$996$		0			0
$997$	−14.9293	−	2.63244i	−0.472817	−	0.0833703i	−0.0678377	−	0.997696i	$-0.521610\pi$
$997$	−14.9293	−	2.63244i	−0.472817	−	0.0833703i	−0.404979	+	0.914326i	$0.632721\pi$
$998$	−17.8590	−	21.8494i	−0.565316	−	0.691632i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.t.a.397.24		204
3.2	odd	2		216.2.t.a.133.11	yes	204
8.5	even	2	inner	648.2.t.a.397.8		204
12.11	even	2		864.2.bf.a.241.7		204
24.5	odd	2		216.2.t.a.133.27	yes	204
24.11	even	2		864.2.bf.a.241.28		204
27.13	even	9	inner	648.2.t.a.253.8		204
27.14	odd	18		216.2.t.a.13.27	yes	204
108.95	even	18		864.2.bf.a.337.28		204
216.13	even	18	inner	648.2.t.a.253.24		204
216.149	odd	18		216.2.t.a.13.11	✓	204
216.203	even	18		864.2.bf.a.337.7		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.11	✓	204	216.149	odd	18
216.2.t.a.13.27	yes	204	27.14	odd	18
216.2.t.a.133.11	yes	204	3.2	odd	2
216.2.t.a.133.27	yes	204	24.5	odd	2
648.2.t.a.253.8		204	27.13	even	9	inner
648.2.t.a.253.24		204	216.13	even	18	inner
648.2.t.a.397.8		204	8.5	even	2	inner
648.2.t.a.397.24		204	1.1	even	1	trivial
864.2.bf.a.241.7		204	12.11	even	2
864.2.bf.a.241.28		204	24.11	even	2
864.2.bf.a.337.7		204	216.203	even	18
864.2.bf.a.337.28		204	108.95	even	18

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.t (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.691259 + 1.23376i) q^{2} +(-1.04432 + 1.70569i) q^{4} +(-1.90914 - 2.27523i) q^{5} +(1.28267 - 0.466852i) q^{7} +(-2.82631 - 0.109365i) q^{8} +(1.48737 - 3.92819i) q^{10} +(2.78354 - 3.31729i) q^{11} +(4.65386 - 0.820601i) q^{13} +(1.46264 + 1.25978i) q^{14} +(-1.81878 - 3.56259i) q^{16} +(-0.356888 - 0.618149i) q^{17} +(-6.43384 - 3.71458i) q^{19} +(5.87460 - 0.880343i) q^{20} +(6.01689 + 1.14111i) q^{22} +(4.17513 + 1.51962i) q^{23} +(-0.663593 + 3.76342i) q^{25} +(4.22945 + 5.17449i) q^{26} +(-0.543209 + 2.67538i) q^{28} +(6.69820 + 1.18107i) q^{29} +(5.02097 + 1.82748i) q^{31} +(3.13812 - 4.70661i) q^{32} +(0.515944 - 0.867615i) q^{34} +(-3.51099 - 2.02707i) q^{35} +(0.547039 - 0.315833i) q^{37} +(0.135445 - 10.5055i) q^{38} +(5.14700 + 6.63929i) q^{40} +(-0.356345 - 2.02093i) q^{41} +(2.43534 - 2.90233i) q^{43} +(2.75138 + 8.21219i) q^{44} +(1.01125 + 6.20155i) q^{46} +(-5.10473 + 1.85797i) q^{47} +(-3.93503 + 3.30188i) q^{49} +(-5.10187 + 1.78279i) q^{50} +(-3.46043 + 8.79504i) q^{52} -11.4745i q^{53} -12.8618 q^{55} +(-3.67627 + 1.17919i) q^{56} +(3.17303 + 9.08039i) q^{58} +(0.803086 + 0.957081i) q^{59} +(0.216792 + 0.595632i) q^{61} +(1.21612 + 7.45793i) q^{62} +(7.97608 + 0.618197i) q^{64} +(-10.7519 - 9.02195i) q^{65} +(-14.0227 + 2.47258i) q^{67} +(1.42708 + 0.0368039i) q^{68} +(0.0739130 - 5.73294i) q^{70} +(0.414463 + 0.717870i) q^{71} +(7.29258 - 12.6311i) q^{73} +(0.767808 + 0.456592i) q^{74} +(13.0549 - 7.09494i) q^{76} +(2.02167 - 5.55448i) q^{77} +(-1.22756 + 6.96183i) q^{79} +(-4.63338 + 10.9396i) q^{80} +(2.24702 - 1.83663i) q^{82} +(-1.29008 - 0.227475i) q^{83} +(-0.725078 + 1.99214i) q^{85} +(5.26422 + 0.998364i) q^{86} +(-8.22995 + 9.07129i) q^{88} +(-2.66374 + 4.61373i) q^{89} +(5.58625 - 3.22522i) q^{91} +(-6.95219 + 5.53452i) q^{92} +(-5.82098 - 5.01367i) q^{94} +(3.83160 + 21.7301i) q^{95} +(-1.52072 - 1.27604i) q^{97} +(-6.79385 - 2.57242i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Introduction

L-functions

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