LMFDB - Embedded newform 324.2.l.a.143.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(35,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("324.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.l (of order $18$, degree $6$, 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:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			143.9
Character	$\chi$	$=$	324.143
Dual form			324.2.l.a.179.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0680456 - 1.41258i) q^{2} +(-1.99074 - 0.192239i) q^{4} +(-2.23728 + 0.394492i) q^{5} +(-0.842213 + 1.00371i) q^{7} +(-0.407013 + 2.79899i) q^{8} +O(q^{10})$	\(q+(0.0680456 - 1.41258i) q^{2} +(-1.99074 - 0.192239i) q^{4} +(-2.23728 + 0.394492i) q^{5} +(-0.842213 + 1.00371i) q^{7} +(-0.407013 + 2.79899i) q^{8} +(0.405013 + 3.18717i) q^{10} +(-0.469629 + 2.66340i) q^{11} +(-4.27030 - 1.55426i) q^{13} +(1.36051 + 1.25799i) q^{14} +(3.92609 + 0.765396i) q^{16} +(-4.20783 + 2.42939i) q^{17} +(5.44971 + 3.14639i) q^{19} +(4.52967 - 0.355239i) q^{20} +(3.73029 + 0.844619i) q^{22} +(-1.94350 + 1.63079i) q^{23} +(0.151321 - 0.0550764i) q^{25} +(-2.48609 + 5.92636i) q^{26} +(1.86958 - 1.83622i) q^{28} +(-1.68452 - 4.62818i) q^{29} +(-1.87889 - 2.23918i) q^{31} +(1.34833 - 5.49381i) q^{32} +(3.14537 + 6.10919i) q^{34} +(1.48831 - 2.57783i) q^{35} +(-3.86074 - 6.68701i) q^{37} +(4.81534 - 7.48403i) q^{38} +(-0.193578 - 6.42268i) q^{40} +(-1.35861 + 3.73275i) q^{41} +(-8.37644 - 1.47699i) q^{43} +(1.44692 - 5.21185i) q^{44} +(2.17137 + 2.85631i) q^{46} +(9.17264 + 7.69676i) q^{47} +(0.917425 + 5.20298i) q^{49} +(-0.0675028 - 0.217500i) q^{50} +(8.20227 + 3.91505i) q^{52} -3.84281i q^{53} -6.14402i q^{55} +(-2.46658 - 2.76587i) q^{56} +(-6.65228 + 2.06458i) q^{58} +(-1.99002 - 11.2860i) q^{59} +(0.0301227 + 0.0252759i) q^{61} +(-3.29086 + 2.50171i) q^{62} +(-7.66868 - 2.27845i) q^{64} +(10.1670 + 1.79271i) q^{65} +(-4.08179 + 11.2146i) q^{67} +(8.84372 - 4.02738i) q^{68} +(-3.54010 - 2.27776i) q^{70} +(1.22570 + 2.12297i) q^{71} +(3.09175 - 5.35507i) q^{73} +(-9.70861 + 4.99857i) q^{74} +(-10.2441 - 7.31129i) q^{76} +(-2.27775 - 2.71452i) q^{77} +(-2.06018 - 5.66029i) q^{79} +(-9.08569 - 0.163591i) q^{80} +(5.18035 + 2.17314i) q^{82} +(-8.97051 + 3.26500i) q^{83} +(8.45570 - 7.09518i) q^{85} +(-2.65634 + 11.7318i) q^{86} +(-7.26367 - 2.39852i) q^{88} +(5.99050 + 3.45862i) q^{89} +(5.15653 - 2.97713i) q^{91} +(4.18250 - 2.87286i) q^{92} +(11.4964 - 12.4333i) q^{94} +(-13.4337 - 4.88948i) q^{95} +(-1.52040 + 8.62260i) q^{97} +(7.41203 - 0.941893i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) $ 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8	$ 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38} - 21 q^{40} + 42 q^{41} - 63 q^{44} - 3 q^{46} - 12 q^{49} - 87 q^{50} - 33 q^{52} - 99 q^{56} - 33 q^{58} - 12 q^{61} - 90 q^{62} - 3 q^{64} - 12 q^{65} - 51 q^{68} - 21 q^{70} - 6 q^{73} - 21 q^{74} - 18 q^{76} - 12 q^{77} - 12 q^{82} - 42 q^{85} + 30 q^{86} + 18 q^{88} + 123 q^{92} + 21 q^{94} - 30 q^{97} + 180 q^{98}+O(q^{100}) $ 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{7}{18}\right)$

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 $

$2$	0.0680456	−	1.41258i	0.0481155	−	0.998842i
$2$	0.0680456	−	1.41258i	0.0481155	−	0.998842i
$3$		0			0
$3$		0			0
$4$	−1.99074	−	0.192239i	−0.995370	−	0.0961195i
$5$	−2.23728	+	0.394492i	−1.00054	+	0.176422i	−0.649845	−	0.760067i	$-0.725166\pi$
$5$	−2.23728	+	0.394492i	−1.00054	+	0.176422i	−0.350696	+	0.936489i	$0.614055\pi$
$6$		0			0
$7$	−0.842213	+	1.00371i	−0.318327	+	0.379367i	−0.901352	−	0.433087i	$-0.857424\pi$
$7$	−0.842213	+	1.00371i	−0.318327	+	0.379367i	0.583025	+	0.812454i	$0.301869\pi$
$8$	−0.407013	+	2.79899i	−0.143901	+	0.989592i
$9$		0			0
$10$	0.405013	+	3.18717i	0.128076	+	1.00787i
$11$	−0.469629	+	2.66340i	−0.141598	+	0.803044i	0.828437	+	0.560082i	$0.189230\pi$
$11$	−0.469629	+	2.66340i	−0.141598	+	0.803044i	−0.970036	+	0.242963i	$0.921881\pi$
$12$		0			0
$13$	−4.27030	−	1.55426i	−1.18437	−	0.431075i	−0.326625	−	0.945154i	$-0.605912\pi$
$13$	−4.27030	−	1.55426i	−1.18437	−	0.431075i	−0.857743	+	0.514079i	$0.828134\pi$
$14$	1.36051	+	1.25799i	0.363611	+	0.336211i
$15$		0			0
$16$	3.92609	+	0.765396i	0.981522	+	0.191349i
$17$	−4.20783	+	2.42939i	−1.02055	+	0.589214i	−0.914263	−	0.405122i	$-0.867229\pi$
$17$	−4.20783	+	2.42939i	−1.02055	+	0.589214i	−0.106286	+	0.994336i	$0.533896\pi$
$18$		0			0
$19$	5.44971	+	3.14639i	1.25025	+	0.721832i	0.971159	−	0.238433i	$-0.0766339\pi$
$19$	5.44971	+	3.14639i	1.25025	+	0.721832i	0.279090	+	0.960265i	$0.409967\pi$
$20$	4.52967	−	0.355239i	1.01287	−	0.0794339i
$21$		0			0
$22$	3.73029	+	0.844619i	0.795301	+	0.180073i
$23$	−1.94350	+	1.63079i	−0.405248	+	0.340043i	−0.822518	−	0.568739i	$-0.807431\pi$
$23$	−1.94350	+	1.63079i	−0.405248	+	0.340043i	0.417270	+	0.908782i	$0.362987\pi$
$24$		0			0
$25$	0.151321	−	0.0550764i	0.0302642	−	0.0110153i
$26$	−2.48609	+	5.92636i	−0.487562	+	1.16226i
$27$		0			0
$28$	1.86958	−	1.83622i	0.353317	−	0.347013i
$29$	−1.68452	−	4.62818i	−0.312807	−	0.859431i	−0.992087	−	0.125552i	$-0.959930\pi$
$29$	−1.68452	−	4.62818i	−0.312807	−	0.859431i	0.679280	−	0.733879i	$-0.262292\pi$
$30$		0			0
$31$	−1.87889	−	2.23918i	−0.337459	−	0.402168i	0.570452	−	0.821331i	$-0.306768\pi$
$31$	−1.87889	−	2.23918i	−0.337459	−	0.402168i	−0.907911	+	0.419163i	$0.862324\pi$
$32$	1.34833	−	5.49381i	0.238354	−	0.971178i
$33$		0			0
$34$	3.14537	+	6.10919i	0.539427	+	1.04772i
$35$	1.48831	−	2.57783i	0.251570	−	0.435732i
$36$		0			0
$37$	−3.86074	−	6.68701i	−0.634703	−	1.09934i	−0.986578	−	0.163290i	$-0.947789\pi$
$37$	−3.86074	−	6.68701i	−0.634703	−	1.09934i	0.351876	−	0.936047i	$-0.385544\pi$
$38$	4.81534	−	7.48403i	0.781152	−	1.21407i
$39$		0			0
$40$	−0.193578	−	6.42268i	−0.0306074	−	1.01551i
$41$	−1.35861	+	3.73275i	−0.212179	+	0.582958i	−0.999433	−	0.0336714i	$-0.989280\pi$
$41$	−1.35861	+	3.73275i	−0.212179	+	0.582958i	0.787254	+	0.616629i	$0.211502\pi$
$42$		0			0
$43$	−8.37644	−	1.47699i	−1.27739	−	0.225239i	−0.506521	−	0.862228i	$-0.669069\pi$
$43$	−8.37644	−	1.47699i	−1.27739	−	0.225239i	−0.770873	+	0.636988i	$0.780180\pi$
$44$	1.44692	−	5.21185i	0.218131	−	0.785716i
$45$		0			0
$46$	2.17137	+	2.85631i	0.320151	+	0.421140i
$47$	9.17264	+	7.69676i	1.33797	+	1.12269i	0.982143	+	0.188135i	$0.0602443\pi$
$47$	9.17264	+	7.69676i	1.33797	+	1.12269i	0.355824	+	0.934553i	$0.384200\pi$
$48$		0			0
$49$	0.917425	+	5.20298i	0.131061	+	0.743282i
$50$	−0.0675028	−	0.217500i	−0.00954634	−	0.0307592i
$51$		0			0
$52$	8.20227	+	3.91505i	1.13745	+	0.542920i
$53$		−	3.84281i		−	0.527851i	−0.964543	−	0.263925i	$-0.914983\pi$
$53$		−	3.84281i		−	0.527851i	0.964543	−	0.263925i	$-0.0850173\pi$
$54$		0			0
$55$		−	6.14402i		−	0.828460i
$56$	−2.46658	−	2.76587i	−0.329611	−	0.369605i
$57$		0			0
$58$	−6.65228	+	2.06458i	−0.873487	+	0.271093i
$59$	−1.99002	−	11.2860i	−0.259079	−	1.46931i	−0.785382	−	0.619011i	$-0.787534\pi$
$59$	−1.99002	−	11.2860i	−0.259079	−	1.46931i	0.526303	−	0.850297i	$-0.323578\pi$
$60$		0			0
$61$	0.0301227	+	0.0252759i	0.00385681	+	0.00323625i	0.644714	−	0.764424i	$-0.276976\pi$
$61$	0.0301227	+	0.0252759i	0.00385681	+	0.00323625i	−0.640857	+	0.767660i	$0.721421\pi$
$62$	−3.29086	+	2.50171i	−0.417939	+	0.317718i
$63$		0			0
$64$	−7.66868	−	2.27845i	−0.958585	−	0.284806i
$65$	10.1670	+	1.79271i	1.26106	+	0.222359i
$66$		0			0
$67$	−4.08179	+	11.2146i	−0.498670	+	1.37008i	0.393891	+	0.919157i	$0.371129\pi$
$67$	−4.08179	+	11.2146i	−0.498670	+	1.37008i	−0.892561	+	0.450927i	$0.851093\pi$
$68$	8.84372	−	4.02738i	1.07246	−	0.488391i
$69$		0			0
$70$	−3.54010	−	2.27776i	−0.423123	−	0.272244i
$71$	1.22570	+	2.12297i	0.145463	+	0.251950i	0.929546	−	0.368707i	$-0.120199\pi$
$71$	1.22570	+	2.12297i	0.145463	+	0.251950i	−0.784082	+	0.620657i	$0.786866\pi$
$72$		0			0
$73$	3.09175	−	5.35507i	0.361862	−	0.626764i	−0.626405	−	0.779498i	$-0.715474\pi$
$73$	3.09175	−	5.35507i	0.361862	−	0.626764i	0.988267	+	0.152734i	$0.0488077\pi$
$74$	−9.70861	+	4.99857i	−1.12860	+	0.581072i
$75$		0			0
$76$	−10.2441	−	7.31129i	−1.17508	−	0.838663i
$77$	−2.27775	−	2.71452i	−0.259574	−	0.309348i
$78$		0			0
$79$	−2.06018	−	5.66029i	−0.231788	−	0.636833i	0.768206	−	0.640203i	$-0.221150\pi$
$79$	−2.06018	−	5.66029i	−0.231788	−	0.636833i	−0.999994	+	0.00336970i	$0.998927\pi$
$80$	−9.08569	−	0.163591i	−1.01581	−	0.0182900i
$81$		0			0
$82$	5.18035	+	2.17314i	0.572074	+	0.239983i
$83$	−8.97051	+	3.26500i	−0.984641	+	0.358380i	−0.783643	−	0.621211i	$-0.786641\pi$
$83$	−8.97051	+	3.26500i	−0.984641	+	0.358380i	−0.200998	+	0.979592i	$0.564419\pi$
$84$		0			0
$85$	8.45570	−	7.09518i	0.917150	−	0.769580i
$86$	−2.65634	+	11.7318i	−0.286441	+	1.26508i
$87$		0			0
$88$	−7.26367	−	2.39852i	−0.774310	−	0.255683i
$89$	5.99050	+	3.45862i	0.634991	+	0.366613i	0.782683	−	0.622421i	$-0.213851\pi$
$89$	5.99050	+	3.45862i	0.634991	+	0.366613i	−0.147691	+	0.989034i	$0.547184\pi$
$90$		0			0
$91$	5.15653	−	2.97713i	0.540552	−	0.312088i
$92$	4.18250	−	2.87286i	0.436056	−	0.299516i
$93$		0			0
$94$	11.4964	−	12.4333i	1.18576	−	1.28240i
$95$	−13.4337	−	4.88948i	−1.37827	−	0.501650i
$96$		0			0
$97$	−1.52040	+	8.62260i	−0.154373	+	0.875493i	0.804984	+	0.593297i	$0.202174\pi$
$97$	−1.52040	+	8.62260i	−0.154373	+	0.875493i	−0.959357	+	0.282196i	$0.908937\pi$
$98$	7.41203	−	0.941893i	0.748728	−	0.0951455i
$99$		0			0
$100$	−0.311829	+	0.0805529i	−0.0311829	+	0.00805529i
$101$	−1.41538	+	1.68678i	−0.140835	+	0.167841i	−0.831851	−	0.554998i	$-0.812719\pi$
$101$	−1.41538	+	1.68678i	−0.140835	+	0.167841i	0.691016	+	0.722839i	$0.257163\pi$
$102$		0			0
$103$	−1.93720	+	0.341580i	−0.190878	+	0.0336569i	−0.268270	−	0.963344i	$-0.586452\pi$
$103$	−1.93720	+	0.341580i	−0.190878	+	0.0336569i	0.0773920	+	0.997001i	$0.475341\pi$
$104$	6.08843	−	11.3199i	0.597020	−	1.11001i
$105$		0			0
$106$	−5.42826	−	0.261486i	−0.527239	−	0.0253978i
$107$	4.06709			0.393180			0.196590	−	0.980486i	$-0.437013\pi$
$107$	4.06709			0.393180			0.196590	+	0.980486i	$0.437013\pi$
$108$		0			0
$109$	−1.81021			−0.173387			−0.0866934	−	0.996235i	$-0.527630\pi$
$109$	−1.81021			−0.173387			−0.0866934	+	0.996235i	$0.527630\pi$
$110$	−8.67889	−	0.418074i	−0.827500	−	0.0398618i
$111$		0			0
$112$	−4.07484	+	3.29603i	−0.385036	+	0.311446i
$113$	−3.45706	+	0.609573i	−0.325213	+	0.0573438i	−0.333871	−	0.942619i	$-0.608355\pi$
$113$	−3.45706	+	0.609573i	−0.325213	+	0.0573438i	0.00865836	+	0.999963i	$0.497244\pi$
$114$		0			0
$115$	3.70481	−	4.41522i	0.345475	−	0.411722i
$116$	2.46372	+	9.53733i	0.228751	+	0.885519i
$117$		0			0
$118$	−16.0777	+	2.04309i	−1.48007	+	0.188082i
$119$	1.10548	−	6.26951i	0.101340	−	0.574725i
$120$		0			0
$121$	3.46349	+	1.26061i	0.314862	+	0.114601i
$122$	0.0377539	−	0.0408306i	0.00341807	−	0.00369663i
$123$		0			0
$124$	3.30993	+	4.81882i	0.297240	+	0.432742i
$125$	9.52032	−	5.49656i	0.851523	−	0.491627i
$126$		0			0
$127$	9.71588	+	5.60947i	0.862145	+	0.497760i	0.864730	−	0.502237i	$-0.167489\pi$
$127$	9.71588	+	5.60947i	0.862145	+	0.497760i	−0.00258477	+	0.999997i	$0.500823\pi$
$128$	−3.74030	+	10.6776i	−0.330599	+	0.943771i
$129$		0			0
$130$	3.22416	−	14.2397i	0.282778	−	1.24890i
$131$	3.93034	−	3.29795i	0.343396	−	0.288143i	−0.454736	−	0.890626i	$-0.650266\pi$
$131$	3.93034	−	3.29795i	0.343396	−	0.288143i	0.798132	+	0.602483i	$0.205822\pi$
$132$		0			0
$133$	−7.74788	+	2.82000i	−0.671827	+	0.244525i
$134$	15.5638	+	6.52894i	1.34450	+	0.564015i
$135$		0			0
$136$	−5.08720	−	12.7665i	−0.436224	−	1.09472i
$137$	0.618497	+	1.69931i	0.0528418	+	0.145182i	0.963306	−	0.268407i	$-0.0864973\pi$
$137$	0.618497	+	1.69931i	0.0528418	+	0.145182i	−0.910464	+	0.413589i	$0.864275\pi$
$138$		0			0
$139$	8.35679	+	9.95924i	0.708814	+	0.844732i	0.993493	−	0.113891i	$-0.0363316\pi$
$139$	8.35679	+	9.95924i	0.708814	+	0.844732i	−0.284679	+	0.958623i	$0.591887\pi$
$140$	−3.45839	+	4.84567i	−0.292288	+	0.409534i
$141$		0			0
$142$	3.08226	−	1.58693i	0.258657	−	0.133172i
$143$	6.14507	−	10.6436i	0.513877	−	0.890061i
$144$		0			0
$145$	5.59452	+	9.68999i	0.464599	+	0.804710i
$146$	−7.35407	−	4.73173i	−0.608627	−	0.391600i
$147$		0			0
$148$	6.40023	+	14.0543i	0.526096	+	1.15525i
$149$	0.880225	−	2.41840i	0.0721108	−	0.198123i	−0.898401	−	0.439176i	$-0.855271\pi$
$149$	0.880225	−	2.41840i	0.0721108	−	0.198123i	0.970512	+	0.241053i	$0.0774928\pi$
$150$		0			0
$151$	5.17039	+	0.911679i	0.420760	+	0.0741914i	0.380020	−	0.924978i	$-0.375917\pi$
$151$	5.17039	+	0.911679i	0.420760	+	0.0741914i	0.0407405	+	0.999170i	$0.487028\pi$
$152$	−11.0248	+	13.9731i	−0.894231	+	1.13336i
$153$		0			0
$154$	−3.98946	+	3.03279i	−0.321479	+	0.244389i
$155$	5.08694	+	4.26845i	0.408593	+	0.342850i
$156$		0			0
$157$	3.62805	+	20.5757i	0.289550	+	1.64212i	0.688565	+	0.725175i	$0.258241\pi$
$157$	3.62805	+	20.5757i	0.289550	+	1.64212i	−0.399015	+	0.916945i	$0.630648\pi$
$158$	−8.13578	+	2.52500i	−0.647248	+	0.200878i
$159$		0			0
$160$	−0.849326	+	12.8231i	−0.0671451	+	1.01375i
$161$		−	3.32418i		−	0.261982i
$162$		0			0
$163$		−	3.28308i		−	0.257151i	−0.991700	−	0.128575i	$-0.958960\pi$
$163$		−	3.28308i		−	0.257151i	0.991700	−	0.128575i	$-0.0410404\pi$
$164$	3.42222	−	7.16976i	0.267231	−	0.559864i
$165$		0			0
$166$	4.00165	+	12.8937i	0.310589	+	1.00074i
$167$	3.32534	+	18.8590i	0.257323	+	1.45935i	0.790039	+	0.613056i	$0.210060\pi$
$167$	3.32534	+	18.8590i	0.257323	+	1.45935i	−0.532717	+	0.846294i	$0.678829\pi$
$168$		0			0
$169$	5.86116	+	4.91809i	0.450858	+	0.378315i
$170$	−9.44710	−	12.4271i	−0.724560	−	0.953116i
$171$		0			0
$172$	16.3914	+	4.55058i	1.24983	+	0.346979i
$173$	8.60928	+	1.51805i	0.654551	+	0.115415i	0.491055	−	0.871129i	$-0.336612\pi$
$173$	8.60928	+	1.51805i	0.654551	+	0.115415i	0.163497	+	0.986544i	$0.447723\pi$
$174$		0			0
$175$	−0.0721639	+	0.198269i	−0.00545508	+	0.0149877i
$176$	−3.88236	+	10.0973i	−0.292644	+	0.761111i
$177$		0			0
$178$	5.29318	−	8.22669i	0.396741	−	0.616616i
$179$	−3.03371	−	5.25454i	−0.226750	−	0.392743i	0.730093	−	0.683348i	$-0.239477\pi$
$179$	−3.03371	−	5.25454i	−0.226750	−	0.392743i	−0.956843	+	0.290605i	$0.906143\pi$
$180$		0			0
$181$	−8.01419	+	13.8810i	−0.595690	+	1.03177i	0.397759	+	0.917490i	$0.369788\pi$
$181$	−8.01419	+	13.8810i	−0.595690	+	1.03177i	−0.993449	+	0.114276i	$0.963545\pi$
$182$	−3.85454	−	7.48657i	−0.285717	−	0.554942i
$183$		0			0
$184$	−3.77353	−	6.10359i	−0.278188	−	0.449962i
$185$	11.2755	+	13.4377i	0.828993	+	0.987956i
$186$		0			0
$187$	−4.49432	−	12.3480i	−0.328657	−	0.902977i
$188$	−16.7807	−	17.0856i	−1.22386	−	1.24609i
$189$		0			0
$190$	−7.82087	+	18.6435i	−0.567385	+	1.35254i
$191$	−10.9918	+	4.00067i	−0.795335	+	0.289478i	−0.707552	−	0.706661i	$-0.750201\pi$
$191$	−10.9918	+	4.00067i	−0.795335	+	0.289478i	−0.0877833	+	0.996140i	$0.527978\pi$
$192$		0			0
$193$	13.4605	−	11.2947i	0.968907	−	0.813010i	−0.0134718	−	0.999909i	$-0.504288\pi$
$193$	13.4605	−	11.2947i	0.968907	−	0.813010i	0.982379	+	0.186900i	$0.0598439\pi$
$194$	12.0766	+	2.73441i	0.867051	+	0.196319i
$195$		0			0
$196$	−0.826139	−	10.5341i	−0.0590099	−	0.752438i
$197$	−19.9607	−	11.5243i	−1.42214	−	0.821074i	−0.425660	−	0.904883i	$-0.639958\pi$
$197$	−19.9607	−	11.5243i	−1.42214	−	0.821074i	−0.996482	+	0.0838089i	$0.973291\pi$
$198$		0			0
$199$	2.70763	−	1.56325i	0.191939	−	0.110816i	−0.400951	−	0.916099i	$-0.631320\pi$
$199$	2.70763	−	1.56325i	0.191939	−	0.110816i	0.592890	+	0.805284i	$0.297987\pi$
$200$	0.0925685	+	0.445963i	0.00654558	+	0.0315343i
$201$		0			0
$202$	2.28640	+	2.11411i	0.160870	+	0.148748i
$203$	6.06408	+	2.20714i	0.425615	+	0.154911i
$204$		0			0
$205$	1.56705	−	8.88716i	0.109447	−	0.620706i
$206$	0.350690	+	2.75968i	0.0244337	+	0.192276i
$207$		0			0
$208$	−15.5760	−	9.37064i	−1.08000	−	0.649737i
$209$	−10.9394	+	13.0371i	−0.756696	+	0.901795i
$210$		0			0
$211$	12.6580	−	2.23195i	0.871414	−	0.153654i	0.279978	−	0.960006i	$-0.409673\pi$
$211$	12.6580	−	2.23195i	0.871414	−	0.153654i	0.591435	+	0.806353i	$0.298562\pi$
$212$	−0.738739	+	7.65004i	−0.0507368	+	0.525407i
$213$		0			0
$214$	0.276748	−	5.74507i	0.0189181	−	0.392725i
$215$	19.3231			1.31782
$216$		0			0
$217$	3.82992			0.259992
$218$	−0.123177	+	2.55706i	−0.00834259	+	0.173186i
$219$		0			0
$220$	−1.18112	+	12.2311i	−0.0796312	+	0.824624i
$221$	21.7446	−	3.83416i	1.46270	−	0.257914i
$222$		0			0
$223$	−6.64592	+	7.92030i	−0.445044	+	0.530382i	−0.941200	−	0.337851i	$-0.890300\pi$
$223$	−6.64592	+	7.92030i	−0.445044	+	0.530382i	0.496156	+	0.868233i	$0.334744\pi$
$224$	4.37862	+	5.98030i	0.292559	+	0.399576i
$225$		0			0
$226$	0.625830	+	4.92484i	0.0416296	+	0.327595i
$227$	−0.0166779	+	0.0945849i	−0.00110695	+	0.00627782i	−0.985356	−	0.170508i	$-0.945459\pi$
$227$	−0.0166779	+	0.0945849i	−0.00110695	+	0.00627782i	0.984249	+	0.176786i	$0.0565701\pi$
$228$		0			0
$229$	−25.2522	−	9.19106i	−1.66871	−	0.607363i	−0.677019	−	0.735966i	$-0.736728\pi$
$229$	−25.2522	−	9.19106i	−1.66871	−	0.607363i	−0.991696	+	0.128603i	$0.958951\pi$
$230$	−5.98474	−	5.53376i	−0.394622	−	0.364886i
$231$		0			0
$232$	13.6398	−	2.83122i	0.895500	−	0.185879i
$233$	−6.26494	+	3.61706i	−0.410430	+	0.236962i	−0.690974	−	0.722879i	$-0.742818\pi$
$233$	−6.26494	+	3.61706i	−0.410430	+	0.236962i	0.280545	+	0.959841i	$0.409485\pi$
$234$		0			0
$235$	−23.5581	−	13.6013i	−1.53676	−	0.887248i
$236$	1.79201	+	22.8500i	0.116650	+	1.48741i
$237$		0			0
$238$	−8.78093	−	1.98819i	−0.569183	−	0.128875i
$239$	−9.77252	+	8.20012i	−0.632132	+	0.530421i	−0.901591	−	0.432590i	$-0.857600\pi$
$239$	−9.77252	+	8.20012i	−0.632132	+	0.530421i	0.269459	+	0.963012i	$0.413155\pi$
$240$		0			0
$241$	7.11615	−	2.59007i	0.458391	−	0.166841i	−0.102495	−	0.994733i	$-0.532683\pi$
$241$	7.11615	−	2.59007i	0.458391	−	0.166841i	0.560886	+	0.827893i	$0.310460\pi$
$242$	2.01638	−	4.80666i	0.129618	−	0.308984i
$243$		0			0
$244$	−0.0551074	−	0.0561085i	−0.00352789	−	0.00359198i
$245$	−4.10507	−	11.2786i	−0.262263	−	0.720562i
$246$		0			0
$247$	−18.3816	−	21.9063i	−1.16959	−	1.39387i
$248$	7.03217	−	4.34763i	0.446543	−	0.276075i
$249$		0			0
$250$	−7.11649	−	13.8222i	−0.450086	−	0.874192i
$251$	−5.95007	+	10.3058i	−0.375565	+	0.650498i	−0.990411	−	0.138149i	$-0.955885\pi$
$251$	−5.95007	+	10.3058i	−0.375565	+	0.650498i	0.614846	+	0.788647i	$0.289218\pi$
$252$		0			0
$253$	−3.43072	−	5.94217i	−0.215687	−	0.373581i
$254$	8.58492	−	13.3427i	0.538666	−	0.837197i
$255$		0			0
$256$	14.8283	+	6.01002i	0.926771	+	0.375626i
$257$	1.86711	−	5.12985i	0.116467	−	0.319991i	−0.867738	−	0.497022i	$-0.834427\pi$
$257$	1.86711	−	5.12985i	0.116467	−	0.319991i	0.984205	+	0.177031i	$0.0566492\pi$
$258$		0			0
$259$	9.96339	+	1.75681i	0.619095	+	0.109163i
$260$	−19.8952	−	5.52332i	−1.23385	−	0.342542i
$261$		0			0
$262$	−4.39116	−	5.77632i	−0.271287	−	0.356862i
$263$	−15.6031	−	13.0925i	−0.962128	−	0.807321i	0.0191703	−	0.999816i	$-0.493898\pi$
$263$	−15.6031	−	13.0925i	−0.962128	−	0.807321i	−0.981298	+	0.192495i	$0.938342\pi$
$264$		0			0
$265$	1.51596	+	8.59743i	0.0931247	+	0.528136i
$266$	3.45625	+	11.1364i	0.211916	+	0.682814i
$267$		0			0
$268$	10.2817	−	21.5407i	0.628053	−	1.31581i
$269$			9.12305i			0.556242i	0.960546	+	0.278121i	$0.0897116\pi$
$269$			9.12305i			0.556242i	−0.960546	+	0.278121i	$0.910288\pi$
$270$		0			0
$271$			21.2629i			1.29163i	0.763495	+	0.645813i	$0.223482\pi$
$271$			21.2629i			1.29163i	−0.763495	+	0.645813i	$0.776518\pi$
$272$	−18.3798	+	6.31735i	−1.11444	+	0.383046i
$273$		0			0
$274$	2.44248	−	0.758043i	0.147556	−	0.0457951i
$275$	0.0756255	+	0.428894i	0.00456039	+	0.0258633i
$276$		0			0
$277$	−19.5527	−	16.4067i	−1.17481	−	0.985783i	−0.999999	−	0.00118043i	$-0.999624\pi$
$277$	−19.5527	−	16.4067i	−1.17481	−	0.985783i	−0.174811	−	0.984602i	$-0.555931\pi$
$278$	14.6368	−	11.1269i	0.877858	−	0.667348i
$279$		0			0
$280$	6.60954	+	5.21497i	0.394996	+	0.311654i
$281$	−12.1392	−	2.14046i	−0.724162	−	0.127689i	−0.200595	−	0.979674i	$-0.564288\pi$
$281$	−12.1392	−	2.14046i	−0.724162	−	0.127689i	−0.523566	+	0.851985i	$0.675399\pi$
$282$		0			0
$283$	−5.71416	+	15.6995i	−0.339672	+	0.933240i	0.645816	+	0.763493i	$0.276517\pi$
$283$	−5.71416	+	15.6995i	−0.339672	+	0.933240i	−0.985488	+	0.169747i	$0.945705\pi$
$284$	−2.03192	−	4.46190i	−0.120573	−	0.264765i
$285$		0			0
$286$	−14.6167	−	9.40463i	−0.864304	−	0.556107i
$287$	−2.60236	−	4.50743i	−0.153613	−	0.266065i
$288$		0			0
$289$	3.30388	−	5.72249i	0.194346	−	0.336617i
$290$	14.0685	−	7.24332i	0.826132	−	0.425342i
$291$		0			0
$292$	−7.18433	+	10.0662i	−0.420431	+	0.589080i
$293$	−8.56800	−	10.2109i	−0.500548	−	0.596530i	0.455319	−	0.890328i	$-0.349525\pi$
$293$	−8.56800	−	10.2109i	−0.500548	−	0.596530i	−0.955867	+	0.293798i	$0.905081\pi$
$294$		0			0
$295$	8.90446	+	24.4648i	0.518437	+	1.42440i
$296$	20.2882	−	8.08448i	1.17923	−	0.469901i
$297$		0			0
$298$	−3.35627	−	1.40794i	−0.194424	−	0.0815601i
$299$	10.8340	−	3.94325i	0.626546	−	0.228044i
$300$		0			0
$301$	8.53722	−	7.16358i	0.492077	−	0.412902i
$302$	1.63964	−	7.24153i	0.0943505	−	0.416703i
$303$		0			0
$304$	18.9878	+	16.5242i	1.08903	+	0.947727i
$305$	−0.0773639	−	0.0446661i	−0.00442984	−	0.00255757i
$306$		0			0
$307$	−18.8505	+	10.8833i	−1.07585	+	0.621144i	−0.929775	−	0.368129i	$-0.879998\pi$
$307$	−18.8505	+	10.8833i	−1.07585	+	0.621144i	−0.146078	+	0.989273i	$0.546665\pi$
$308$	4.01258	+	5.84178i	0.228638	+	0.332866i
$309$		0			0
$310$	6.37565	−	6.89524i	0.362113	−	0.391623i
$311$	13.4052	+	4.87909i	0.760139	+	0.276668i	0.692866	−	0.721067i	$-0.256348\pi$
$311$	13.4052	+	4.87909i	0.760139	+	0.276668i	0.0672731	+	0.997735i	$0.478570\pi$
$312$		0			0
$313$	3.69449	−	20.9525i	0.208825	−	1.18430i	−0.682482	−	0.730902i	$-0.739099\pi$
$313$	3.69449	−	20.9525i	0.208825	−	1.18430i	0.891307	−	0.453401i	$-0.149789\pi$
$314$	29.3116	−	3.72481i	1.65415	−	0.210203i
$315$		0			0
$316$	3.01315	+	11.6642i	0.169503	+	0.656164i
$317$	4.33285	−	5.16369i	0.243357	−	0.290022i	−0.630516	−	0.776177i	$-0.717156\pi$
$317$	4.33285	−	5.16369i	0.243357	−	0.290022i	0.873873	+	0.486155i	$0.161601\pi$
$318$		0			0
$319$	13.1178	−	2.31302i	0.734454	−	0.129504i
$320$	18.0558	+	2.07229i	1.00935	+	0.115845i
$321$		0			0
$322$	−4.69566	−	0.226196i	−0.261679	−	0.0126054i
$323$	−30.5753			−1.70125
$324$		0			0
$325$	−0.731790			−0.0405924
$326$	−4.63760	−	0.223399i	−0.256853	−	0.0123729i
$327$		0			0
$328$	−9.89496	−	5.32202i	−0.546358	−	0.293859i
$329$	−15.4506	+	2.72437i	−0.851822	+	0.150199i
$330$		0			0
$331$	15.5537	−	18.5362i	0.854910	−	1.01884i	−0.144658	−	0.989482i	$-0.546208\pi$
$331$	15.5537	−	18.5362i	0.854910	−	1.01884i	0.999569	−	0.0293609i	$-0.00934722\pi$
$332$	18.4856	−	4.77528i	1.01453	−	0.262077i
$333$		0			0
$334$	26.8660	−	3.41403i	1.47004	−	0.186807i
$335$	4.70801	−	26.7004i	0.257226	−	1.45880i
$336$		0			0
$337$	−20.5343	−	7.47387i	−1.11857	−	0.407127i	−0.284442	−	0.958693i	$-0.591808\pi$
$337$	−20.5343	−	7.47387i	−1.11857	−	0.407127i	−0.834131	+	0.551566i	$0.814031\pi$
$338$	7.34601	−	7.94467i	0.399570	−	0.432133i
$339$		0			0
$340$	−18.1971	+	12.4991i	−0.986875	+	0.677861i
$341$	6.84620	−	3.95266i	0.370743	−	0.214048i
$342$		0			0
$343$	−13.9379	−	8.04707i	−0.752577	−	0.434501i
$344$	7.54340	−	22.8444i	0.406713	−	1.23169i
$345$		0			0
$346$	2.73018	−	12.0580i	0.146775	−	0.648240i
$347$	9.92193	−	8.32549i	0.532637	−	0.446936i	−0.336374	−	0.941729i	$-0.609201\pi$
$347$	9.92193	−	8.32549i	0.532637	−	0.446936i	0.869011	+	0.494793i	$0.164756\pi$
$348$		0			0
$349$	3.63433	−	1.32279i	0.194541	−	0.0708071i	−0.242912	−	0.970048i	$-0.578103\pi$
$349$	3.63433	−	1.32279i	0.194541	−	0.0708071i	0.437453	+	0.899241i	$0.355881\pi$
$350$	0.275159	+	0.115428i	0.0147079	+	0.00616990i
$351$		0			0
$352$	13.9990	+	6.17120i	0.746149	+	0.328926i
$353$	1.04065	+	2.85915i	0.0553880	+	0.152177i	0.964301	−	0.264808i	$-0.0853087\pi$
$353$	1.04065	+	2.85915i	0.0553880	+	0.152177i	−0.908913	+	0.416986i	$0.863086\pi$
$354$		0			0
$355$	−3.57972	−	4.26614i	−0.189992	−	0.226423i
$356$	−11.2606	−	8.03681i	−0.596813	−	0.425950i
$357$		0			0
$358$	−7.62887	+	3.92780i	−0.403198	+	0.207591i
$359$	−8.27544	+	14.3335i	−0.436761	+	0.756492i	−0.997438	−	0.0715425i	$-0.977208\pi$
$359$	−8.27544	+	14.3335i	−0.436761	+	0.756492i	0.560676	+	0.828035i	$0.310541\pi$
$360$		0			0
$361$	10.2995	+	17.8393i	0.542082	+	0.938913i
$362$	19.0626	+	12.2652i	1.00191	+	0.644644i
$363$		0			0
$364$	−10.8376	+	4.93540i	−0.568046	+	0.258685i
$365$	−4.80457	+	13.2005i	−0.251483	+	0.690944i
$366$		0			0
$367$	−2.17336	−	0.383223i	−0.113449	−	0.0200041i	0.116636	−	0.993175i	$-0.462789\pi$
$367$	−2.17336	−	0.383223i	−0.113449	−	0.0200041i	−0.230084	+	0.973171i	$0.573900\pi$
$368$	−8.87855	+	4.91508i	−0.462826	+	0.256216i
$369$		0			0
$370$	19.7489	−	15.0132i	1.02670	−	0.780497i
$371$	3.85707	+	3.23647i	0.200249	+	0.168029i
$372$		0			0
$373$	−1.82112	−	10.3281i	−0.0942938	−	0.534767i	−0.994961	−	0.100258i	$-0.968033\pi$
$373$	−1.82112	−	10.3281i	−0.0942938	−	0.534767i	0.900668	−	0.434509i	$-0.143078\pi$
$374$	−17.7483	+	5.50833i	−0.917745	+	0.284829i
$375$		0			0
$376$	−25.2765	+	22.5414i	−1.30354	+	1.16249i
$377$			22.3819i			1.15273i
$378$		0			0
$379$			3.08694i			0.158565i	0.996852	+	0.0792826i	$0.0252630\pi$
$379$			3.08694i			0.158565i	−0.996852	+	0.0792826i	$0.974737\pi$
$380$	25.8031	+	12.3162i	1.32367	+	0.631806i
$381$		0			0
$382$	4.90331	+	15.7989i	0.250875	+	0.808343i
$383$	−2.78976	−	15.8215i	−0.142550	−	0.808442i	−0.969302	−	0.245875i	$-0.920925\pi$
$383$	−2.78976	−	15.8215i	−0.142550	−	0.808442i	0.826752	−	0.562567i	$-0.190186\pi$
$384$		0			0
$385$	6.16682	+	5.17458i	0.314290	+	0.263721i
$386$	−15.0387	−	19.7825i	−0.765449	−	1.00690i
$387$		0			0
$388$	4.68432	−	16.8731i	0.237810	−	0.856601i
$389$	−17.3835	−	3.06519i	−0.881381	−	0.155411i	−0.285399	−	0.958409i	$-0.592126\pi$
$389$	−17.3835	−	3.06519i	−0.881381	−	0.155411i	−0.595982	+	0.802998i	$0.703237\pi$
$390$		0			0
$391$	4.21609	−	11.5836i	0.213217	−	0.585808i
$392$	−14.9365	+	0.450183i	−0.754406	+	0.0227377i
$393$		0			0
$394$	−17.6372	+	27.4118i	−0.888550	+	1.38099i
$395$	6.84213	+	11.8509i	0.344265	+	0.596285i
$396$		0			0
$397$	6.73828	−	11.6710i	0.338185	−	0.585753i	−0.645907	−	0.763416i	$-0.723520\pi$
$397$	6.73828	−	11.6710i	0.338185	−	0.585753i	0.984091	+	0.177663i	$0.0568538\pi$
$398$	−2.02397	−	3.93110i	−0.101452	−	0.197048i
$399$		0			0
$400$	0.636255	−	0.100414i	0.0318128	−	0.00502071i
$401$	−4.34436	−	5.17741i	−0.216947	−	0.258547i	0.646584	−	0.762842i	$-0.276197\pi$
$401$	−4.34436	−	5.17741i	−0.216947	−	0.258547i	−0.863531	+	0.504295i	$0.831752\pi$
$402$		0			0
$403$	4.54317	+	12.4823i	0.226311	+	0.621785i
$404$	3.14191	−	3.08585i	0.156316	−	0.153527i
$405$		0			0
$406$	3.53039	−	8.41578i	0.175210	−	0.417668i
$407$	19.6233	−	7.14229i	0.972689	−	0.354030i
$408$		0			0
$409$	14.4348	−	12.1122i	0.713756	−	0.598912i	−0.211895	−	0.977293i	$-0.567963\pi$
$409$	14.4348	−	12.1122i	0.713756	−	0.598912i	0.925650	+	0.378381i	$0.123519\pi$
$410$	−12.4472	−	2.81830i	−0.614721	−	0.139186i
$411$		0			0
$412$	3.92212	−	0.307592i	0.193229	−	0.0151540i
$413$	13.0039	+	7.50779i	0.639879	+	0.369434i
$414$		0			0
$415$	18.7815	−	10.8435i	0.921947	−	0.532287i
$416$	−14.2966	+	21.3646i	−0.700949	+	1.04748i
$417$		0			0
$418$	17.6715	+	16.3399i	0.864342	+	0.799210i
$419$	17.9428	+	6.53066i	0.876565	+	0.319043i	0.740823	−	0.671701i	$-0.234436\pi$
$419$	17.9428	+	6.53066i	0.876565	+	0.319043i	0.135742	+	0.990744i	$0.456658\pi$
$420$		0			0
$421$	−3.91452	+	22.2004i	−0.190782	+	1.08198i	0.727516	+	0.686091i	$0.240675\pi$
$421$	−3.91452	+	22.2004i	−0.190782	+	1.08198i	−0.918298	+	0.395889i	$0.870436\pi$
$422$	−2.29148	−	18.0323i	−0.111547	−	0.877797i
$423$		0			0
$424$	10.7560	+	1.56408i	0.522357	+	0.0759582i
$425$	−0.502931	+	0.599370i	−0.0243957	+	0.0290737i
$426$		0			0
$427$	−0.0507394	+	0.00894673i	−0.00245545	+	0.000432962i
$428$	−8.09652	−	0.781854i	−0.391360	−	0.0377923i
$429$		0			0
$430$	1.31485	−	27.2953i	0.0634077	−	1.31630i
$431$	−10.8059			−0.520500			−0.260250	−	0.965541i	$-0.583805\pi$
$431$	−10.8059			−0.520500			−0.260250	+	0.965541i	$0.583805\pi$
$432$		0			0
$433$	−37.5914			−1.80653			−0.903264	−	0.429084i	$-0.858836\pi$
$433$	−37.5914			−1.80653			−0.903264	+	0.429084i	$0.858836\pi$
$434$	0.260609	−	5.41004i	0.0125096	−	0.259690i
$435$		0			0
$436$	3.60366	+	0.347993i	0.172584	+	0.0166659i
$437$	−15.7226	+	2.77232i	−0.752114	+	0.132618i
$438$		0			0
$439$	−20.5267	+	24.4627i	−0.979685	+	1.16754i	0.00617703	+	0.999981i	$0.498034\pi$
$439$	−20.5267	+	24.4627i	−0.979685	+	1.16754i	−0.985862	+	0.167562i	$0.946411\pi$
$440$	17.1970	+	2.50070i	0.819837	+	0.119216i
$441$		0			0
$442$	−3.93642	−	30.9768i	−0.187236	−	1.47342i
$443$	−6.52594	+	37.0104i	−0.310057	+	1.75842i	0.288634	+	0.957439i	$0.406799\pi$
$443$	−6.52594	+	37.0104i	−0.310057	+	1.75842i	−0.598691	+	0.800980i	$0.704312\pi$
$444$		0			0
$445$	−14.7668	−	5.37468i	−0.700013	−	0.254784i
$446$	10.7358	+	9.92680i	0.508354	+	0.470048i
$447$		0			0
$448$	8.74557	−	5.77819i	0.413189	−	0.272994i
$449$	6.99926	−	4.04102i	0.330315	−	0.190708i	−0.325666	−	0.945485i	$-0.605588\pi$
$449$	6.99926	−	4.04102i	0.330315	−	0.190708i	0.655981	+	0.754777i	$0.272255\pi$
$450$		0			0
$451$	−9.30376	−	5.37153i	−0.438097	−	0.252935i
$452$	6.99929	−	0.548919i	0.329219	−	0.0258190i
$453$		0			0
$454$	0.132474	+	0.0299949i	0.00621729	+	0.00140773i
$455$	−10.3621	+	8.69487i	−0.485785	+	0.407622i
$456$		0			0
$457$	2.32495	−	0.846211i	0.108756	−	0.0395841i	−0.287069	−	0.957910i	$-0.592681\pi$
$457$	2.32495	−	0.846211i	0.108756	−	0.0395841i	0.395825	+	0.918326i	$0.370459\pi$
$458$	−14.7014	+	35.0453i	−0.686950	+	1.63756i
$459$		0			0
$460$	−8.22409	+	8.07735i	−0.383450	+	0.376608i
$461$	3.09034	+	8.49063i	0.143931	+	0.395448i	0.990621	−	0.136639i	$-0.0436301\pi$
$461$	3.09034	+	8.49063i	0.143931	+	0.395448i	−0.846690	+	0.532087i	$0.821408\pi$
$462$		0			0
$463$	−0.896443	−	1.06834i	−0.0416612	−	0.0496499i	0.744811	−	0.667275i	$-0.232539\pi$
$463$	−0.896443	−	1.06834i	−0.0416612	−	0.0496499i	−0.786473	+	0.617625i	$0.788095\pi$
$464$	−3.07118	−	19.4600i	−0.142576	−	0.903406i
$465$		0			0
$466$	4.68308	+	9.09583i	0.216939	+	0.421356i
$467$	−10.5492	+	18.2717i	−0.488158	+	0.845515i	−0.999907	−	0.0136203i	$-0.995664\pi$
$467$	−10.5492	+	18.2717i	−0.488158	+	0.845515i	0.511749	+	0.859135i	$0.328998\pi$
$468$		0			0
$469$	−7.81850	−	13.5420i	−0.361025	−	0.625313i
$470$	−20.8158	+	32.3520i	−0.960162	+	1.49229i
$471$		0			0
$472$	32.3993	−	0.976508i	1.49130	−	0.0449474i
$473$	7.86763	−	21.6161i	0.361754	−	0.993911i
$474$		0			0
$475$	0.997948	+	0.175965i	0.0457890	+	0.00807383i
$476$	−3.40597	+	12.2684i	−0.156113	+	0.562323i
$477$		0			0
$478$	10.9183	+	14.3624i	0.499392	+	0.656921i
$479$	−11.1877	−	9.38756i	−0.511177	−	0.428928i	0.350366	−	0.936613i	$-0.386057\pi$
$479$	−11.1877	−	9.38756i	−0.511177	−	0.428928i	−0.861543	+	0.507684i	$0.830502\pi$
$480$		0			0
$481$	6.09318	+	34.5561i	0.277825	+	1.57562i
$482$	−3.17444	−	10.2283i	−0.144592	−	0.465888i
$483$		0			0
$484$	−6.65256	−	3.17536i	−0.302389	−	0.144334i
$485$		−	19.8909i		−	0.903201i
$486$		0			0
$487$			0.282541i			0.0128032i	0.999980	+	0.00640158i	$0.00203770\pi$
$487$			0.282541i			0.0128032i	−0.999980	+	0.00640158i	$0.997962\pi$
$488$	−0.0830073	+	0.0740254i	−0.00375757	+	0.00335097i
$489$		0			0
$490$	−16.2112	+	5.03126i	−0.732347	+	0.227289i
$491$	2.69135	+	15.2634i	0.121459	+	0.688829i	0.983348	+	0.181732i	$0.0581703\pi$
$491$	2.69135	+	15.2634i	0.121459	+	0.688829i	−0.861889	+	0.507097i	$0.830719\pi$
$492$		0			0
$493$	18.3318	+	15.3822i	0.825624	+	0.692781i
$494$	−32.1951	+	24.4747i	−1.44853	+	1.10117i
$495$		0			0
$496$	−5.66284	−	10.2293i	−0.254269	−	0.459309i
$497$	−3.16314	−	0.557747i	−0.141886	−	0.0250184i
$498$		0			0
$499$	13.9873	−	38.4299i	0.626159	−	1.72036i	−0.0652259	−	0.997871i	$-0.520777\pi$
$499$	13.9873	−	38.4299i	0.626159	−	1.72036i	0.691385	−	0.722487i	$-0.257001\pi$
$500$	−20.0091	+	9.11204i	−0.894836	+	0.407503i
$501$		0			0
$502$	14.1529	+	9.10619i	0.631674	+	0.406429i
$503$	9.96192	+	17.2546i	0.444180	+	0.769343i	0.997995	−	0.0632975i	$-0.0201617\pi$
$503$	9.96192	+	17.2546i	0.444180	+	0.769343i	−0.553815	+	0.832640i	$0.686828\pi$
$504$		0			0
$505$	2.50117	−	4.33215i	0.111301	−	0.192778i
$506$	−8.62722	+	4.44181i	−0.383527	+	0.197462i
$507$		0			0
$508$	−18.2634	−	13.0348i	−0.810309	−	0.578324i
$509$	−18.1997	−	21.6895i	−0.806686	−	0.961371i	0.193118	−	0.981176i	$-0.438140\pi$
$509$	−18.1997	−	21.6895i	−0.806686	−	0.961371i	−0.999804	+	0.0198048i	$0.993696\pi$
$510$		0			0
$511$	2.77103	+	7.61334i	0.122583	+	0.336794i
$512$	9.49862	−	20.5372i	0.419783	−	0.907624i
$513$		0			0
$514$	−7.11925	−	2.98650i	−0.314017	−	0.131729i
$515$	4.19929	−	1.52842i	0.185043	−	0.0673502i
$516$		0			0
$517$	−24.8073	+	20.8158i	−1.09102	+	0.915476i
$518$	3.15960	−	13.9545i	0.138825	−	0.613125i
$519$		0			0
$520$	−9.15589	+	27.7276i	−0.401512	+	1.21594i
$521$	18.4642	+	10.6603i	0.808931	+	0.467036i	0.846584	−	0.532255i	$-0.178655\pi$
$521$	18.4642	+	10.6603i	0.808931	+	0.467036i	−0.0376537	+	0.999291i	$0.511988\pi$
$522$		0			0
$523$	−17.0213	+	9.82725i	−0.744289	+	0.429716i	−0.823627	−	0.567132i	$-0.808053\pi$
$523$	−17.0213	+	9.82725i	−0.744289	+	0.429716i	0.0793376	+	0.996848i	$0.474719\pi$
$524$	−8.45828	+	5.80979i	−0.369502	+	0.253802i
$525$		0			0
$526$	−19.5559	+	21.1497i	−0.852679	+	0.922169i
$527$	13.3459	+	4.85751i	0.581356	+	0.211596i
$528$		0			0
$529$	−2.87619	+	16.3117i	−0.125052	+	0.709205i
$530$	12.2477	−	1.55639i	0.532005	−	0.0676053i
$531$		0			0
$532$	15.9661	−	4.12444i	0.692220	−	0.178817i
$533$	11.6034	−	13.8283i	0.502597	−	0.598972i
$534$		0			0
$535$	−9.09921	+	1.60444i	−0.393393	+	0.0693658i
$536$	−29.7283	−	15.9894i	−1.28407	−	0.690636i
$537$		0			0
$538$	12.8870	+	0.620783i	0.555598	+	0.0267639i
$539$	−14.2884			−0.615447
$540$		0			0
$541$	41.1619			1.76969			0.884844	−	0.465888i	$-0.154265\pi$
$541$	41.1619			1.76969			0.884844	+	0.465888i	$0.154265\pi$
$542$	30.0354	+	1.44684i	1.29013	+	0.0621473i
$543$		0			0
$544$	7.67307	+	26.3927i	0.328980	+	1.13158i
$545$	4.04994	−	0.714115i	0.173481	−	0.0305893i
$546$		0			0
$547$	4.66923	−	5.56458i	0.199642	−	0.237924i	−0.656930	−	0.753952i	$-0.728145\pi$
$547$	4.66923	−	5.56458i	0.199642	−	0.237924i	0.856572	+	0.516027i	$0.172590\pi$
$548$	−0.904593	−	3.50178i	−0.0386423	−	0.149588i
$549$		0			0
$550$	0.610991	−	0.0776424i	0.0260527	−	0.00331068i
$551$	5.38192	−	30.5224i	0.229277	−	1.30030i
$552$		0			0
$553$	7.41641	+	2.69935i	0.315378	+	0.114788i
$554$	−24.5062	+	26.5033i	−1.04117	+	1.12602i
$555$		0			0
$556$	−14.7216	−	21.4328i	−0.624337	−	0.908951i
$557$	−32.2123	+	18.5978i	−1.36488	+	0.788012i	−0.990268	−	0.139170i	$-0.955556\pi$
$557$	−32.2123	+	18.5978i	−1.36488	+	0.788012i	−0.374609	+	0.927183i	$0.622223\pi$
$558$		0			0
$559$	33.4743	+	19.3264i	1.41581	+	0.817419i
$560$	7.81629	−	8.98163i	0.330298	−	0.379543i
$561$		0			0
$562$	−3.84958	+	17.0018i	−0.162385	+	0.717179i
$563$	34.0010	−	28.5303i	1.43297	−	1.20241i	0.489044	−	0.872259i	$-0.337346\pi$
$563$	34.0010	−	28.5303i	1.43297	−	1.20241i	0.943929	−	0.330148i	$-0.107099\pi$
$564$		0			0
$565$	7.49393	−	2.72757i	0.315272	−	0.114750i
$566$	21.7879	+	9.13997i	0.915816	+	0.384181i
$567$		0			0
$568$	−6.44104	+	2.56663i	−0.270260	+	0.107694i
$569$	10.0872	+	27.7143i	0.422877	+	1.16184i	0.950053	+	0.312089i	$0.101029\pi$
$569$	10.0872	+	27.7143i	0.422877	+	1.16184i	−0.527176	+	0.849756i	$0.676749\pi$
$570$		0			0
$571$	−8.42058	−	10.0353i	−0.352390	−	0.419962i	0.560508	−	0.828149i	$-0.310606\pi$
$571$	−8.42058	−	10.0353i	−0.352390	−	0.419962i	−0.912899	+	0.408187i	$0.866161\pi$
$572$	−14.2794	+	20.0073i	−0.597050	+	0.836546i
$573$		0			0
$574$	−6.54416	+	3.36932i	−0.273148	+	0.140633i
$575$	−0.204274	+	0.353814i	−0.00851883	+	0.0147550i
$576$		0			0
$577$	2.02124	+	3.50090i	0.0841455	+	0.145744i	0.905027	−	0.425355i	$-0.139851\pi$
$577$	2.02124	+	3.50090i	0.0841455	+	0.145744i	−0.820881	+	0.571099i	$0.806517\pi$
$578$	−7.85864	−	5.05638i	−0.326876	−	0.210317i
$579$		0			0
$580$	−9.27443	−	20.3657i	−0.385100	−	0.845641i
$581$	4.27797	−	11.7536i	0.177480	−	0.487622i
$582$		0			0
$583$	10.2349	+	1.80469i	0.423888	+	0.0747428i
$584$	13.7304	+	10.8334i	0.568168	+	0.448288i
$585$		0			0
$586$	−15.0068	+	11.4081i	−0.619923	+	0.471266i
$587$	−5.57370	−	4.67689i	−0.230051	−	0.193036i	0.520474	−	0.853877i	$-0.325755\pi$
$587$	−5.57370	−	4.67689i	−0.230051	−	0.193036i	−0.750525	+	0.660842i	$0.770200\pi$
$588$		0			0
$589$	−3.19409	−	18.1146i	−0.131610	−	0.746399i
$590$	35.1643	−	10.9135i	1.44769	−	0.449302i
$591$		0			0
$592$	−10.0394	−	29.2088i	−0.412618	−	1.20047i
$593$		−	2.93118i		−	0.120369i	−0.998187	−	0.0601846i	$-0.980831\pi$
$593$		−	2.93118i		−	0.120369i	0.998187	−	0.0601846i	$-0.0191689\pi$
$594$		0			0
$595$			14.4627i			0.592914i
$596$	−2.21721	+	4.64519i	−0.0908204	+	0.190274i
$597$		0			0
$598$	−4.83294	−	15.5722i	−0.197633	−	0.636793i
$599$	0.235737	+	1.33693i	0.00963195	+	0.0546255i	0.989245	−	0.146269i	$-0.0467264\pi$
$599$	0.235737	+	1.33693i	0.00963195	+	0.0546255i	−0.979613	+	0.200894i	$0.935615\pi$
$600$		0			0
$601$	5.92810	+	4.97426i	0.241812	+	0.202904i	0.755637	−	0.654991i	$-0.227327\pi$
$601$	5.92810	+	4.97426i	0.241812	+	0.202904i	−0.513825	+	0.857895i	$0.671772\pi$
$602$	−9.53817	−	12.5469i	−0.388747	−	0.511374i
$603$		0			0
$604$	−10.1176	−	2.80887i	−0.411681	−	0.114291i
$605$	−8.24608	−	1.45401i	−0.335251	−	0.0591138i
$606$		0			0
$607$	3.90767	−	10.7362i	0.158607	−	0.435770i	−0.834780	−	0.550584i	$-0.814405\pi$
$607$	3.90767	−	10.7362i	0.158607	−	0.435770i	0.993387	+	0.114814i	$0.0366272\pi$
$608$	24.6337	−	25.6973i	0.999029	−	1.04216i
$609$		0			0
$610$	−0.0683585	+	0.106243i	−0.00276775	+	0.00430165i
$611$	−27.2072	−	47.1242i	−1.10068	−	1.90644i
$612$		0			0
$613$	−12.0261	+	20.8298i	−0.485729	+	0.841307i	−0.999865	−	0.0164015i	$-0.994779\pi$
$613$	−12.0261	+	20.8298i	−0.485729	+	0.841307i	0.514137	+	0.857708i	$0.328112\pi$
$614$	14.0908	+	27.3683i	0.568659	+	1.10449i
$615$		0			0
$616$	8.52499	−	5.27056i	0.343482	−	0.212357i
$617$	31.0148	+	36.9620i	1.24861	+	1.48803i	0.806685	+	0.590981i	$0.201259\pi$
$617$	31.0148	+	36.9620i	1.24861	+	1.48803i	0.441923	+	0.897053i	$0.354296\pi$
$618$		0			0
$619$	−1.54241	−	4.23775i	−0.0619949	−	0.170329i	0.904828	−	0.425777i	$-0.139999\pi$
$619$	−1.54241	−	4.23775i	−0.0619949	−	0.170329i	−0.966823	+	0.255448i	$0.917777\pi$
$620$	−9.30621	−	9.47528i	−0.373747	−	0.380537i
$621$		0			0
$622$	7.80425	−	18.6038i	0.312922	−	0.745946i
$623$	−8.51673	+	3.09983i	−0.341215	+	0.124192i
$624$		0			0
$625$	−19.7480	+	16.5706i	−0.789921	+	0.662823i
$626$	−29.3455	−	6.64446i	−1.17288	−	0.265566i
$627$		0			0
$628$	−3.26705	−	41.6583i	−0.130370	−	1.66235i
$629$	32.4907	+	18.7585i	1.29549	+	0.747951i
$630$		0			0
$631$	9.73065	−	5.61799i	0.387371	−	0.223649i	−0.293649	−	0.955913i	$-0.594870\pi$
$631$	9.73065	−	5.61799i	0.387371	−	0.223649i	0.681020	+	0.732264i	$0.261536\pi$
$632$	16.6816	−	3.46260i	0.663559	−	0.137735i
$633$		0			0
$634$	−6.99927	−	6.47185i	−0.277977	−	0.257030i
$635$	−23.9500	−	8.71709i	−0.950427	−	0.345927i
$636$		0			0
$637$	4.16911	−	23.6442i	0.165186	−	0.936817i
$638$	−2.37471	−	18.6872i	−0.0940155	−	0.739835i
$639$		0			0
$640$	4.15589	−	25.3642i	0.164276	−	1.00261i
$641$	26.0352	−	31.0276i	1.02833	−	1.22551i	0.0544338	−	0.998517i	$-0.482665\pi$
$641$	26.0352	−	31.0276i	1.02833	−	1.22551i	0.973895	−	0.226998i	$-0.0728910\pi$
$642$		0			0
$643$	31.7725	−	5.60234i	1.25298	−	0.220935i	0.492512	−	0.870306i	$-0.336079\pi$
$643$	31.7725	−	5.60234i	1.25298	−	0.220935i	0.760472	+	0.649371i	$0.224968\pi$
$644$	−0.639038	+	6.61758i	−0.0251816	+	0.260769i
$645$		0			0
$646$	−2.08051	+	43.1899i	−0.0818566	+	1.69928i
$647$	7.00490			0.275391			0.137696	−	0.990475i	$-0.456030\pi$
$647$	7.00490			0.275391			0.137696	+	0.990475i	$0.456030\pi$
$648$		0			0
$649$	30.9936			1.21660
$650$	−0.0497951	+	1.03371i	−0.00195312	+	0.0405454i
$651$		0			0
$652$	−0.631137	+	6.53576i	−0.0247172	+	0.255960i
$653$	34.5742	−	6.09636i	1.35299	−	0.238569i	0.550302	−	0.834966i	$-0.314513\pi$
$653$	34.5742	−	6.09636i	1.35299	−	0.238569i	0.802689	+	0.596397i	$0.203402\pi$
$654$		0			0
$655$	−7.49225	+	8.92892i	−0.292746	+	0.348882i
$656$	−8.19106	+	13.6152i	−0.319807	+	0.531586i
$657$		0			0
$658$	2.79702	+	22.0106i	0.109039	+	0.858062i
$659$	−1.55544	+	8.82132i	−0.0605912	+	0.343630i	0.939408	+	0.342800i	$0.111375\pi$
$659$	−1.55544	+	8.82132i	−0.0605912	+	0.343630i	−1.00000		0.000830029i	$0.999736\pi$
$660$		0			0
$661$	33.4732	+	12.1833i	1.30196	+	0.473874i	0.897634	−	0.440742i	$-0.145285\pi$
$661$	33.4732	+	12.1833i	1.30196	+	0.473874i	0.404324	+	0.914616i	$0.367507\pi$
$662$	−25.1254	−	23.2321i	−0.976528	−	0.902942i
$663$		0			0
$664$	−5.48758	−	26.4373i	−0.212959	−	1.02596i
$665$	16.2217	−	9.36560i	0.629050	−	0.363182i
$666$		0			0
$667$	10.8214	+	6.24776i	0.419008	+	0.241914i
$668$	−2.99446	−	38.1825i	−0.115859	−	1.47733i
$669$		0			0
$670$	−37.3960	−	8.46727i	−1.44474	−	0.327119i
$671$	−0.0814663	+	0.0683583i	−0.00314497	+	0.00263894i
$672$		0			0
$673$	3.17294	−	1.15485i	0.122308	−	0.0445164i	−0.280141	−	0.959959i	$-0.590381\pi$
$673$	3.17294	−	1.15485i	0.122308	−	0.0445164i	0.402449	+	0.915442i	$0.368159\pi$
$674$	−11.9547	+	28.4977i	−0.460477	+	1.09769i
$675$		0			0
$676$	−10.7226	−	10.9174i	−0.412407	−	0.419900i
$677$	−0.395252	−	1.08595i	−0.0151908	−	0.0417363i	0.931865	−	0.362804i	$-0.118181\pi$
$677$	−0.395252	−	1.08595i	−0.0151908	−	0.0417363i	−0.947056	+	0.321068i	$0.895958\pi$
$678$		0			0
$679$	−7.37410	−	8.78811i	−0.282992	−	0.337257i
$680$	16.4177	+	26.5553i	0.629592	+	1.01835i
$681$		0			0
$682$	−5.11757	−	9.93974i	−0.195962	−	0.380612i
$683$	21.5897	−	37.3945i	0.826107	−	1.43086i	−0.0749630	−	0.997186i	$-0.523884\pi$
$683$	21.5897	−	37.3945i	0.826107	−	1.43086i	0.901070	−	0.433673i	$-0.142783\pi$
$684$		0			0
$685$	−2.05411	−	3.55783i	−0.0784836	−	0.135938i
$686$	−12.3155	+	19.1408i	−0.470208	+	0.730800i
$687$		0			0
$688$	−31.7561	−	12.2101i	−1.21069	−	0.465505i
$689$	−5.97274	+	16.4100i	−0.227543	+	0.625170i
$690$		0			0
$691$	12.6458	+	2.22980i	0.481070	+	0.0848255i	0.408924	−	0.912569i	$-0.365904\pi$
$691$	12.6458	+	2.22980i	0.481070	+	0.0848255i	0.0721458	+	0.997394i	$0.477015\pi$
$692$	−16.8470	−	4.67708i	−0.640427	−	0.177796i
$693$		0			0
$694$	−11.0852	−	14.5820i	−0.420790	−	0.553525i
$695$	−22.6253	−	18.9849i	−0.858227	−	0.720138i
$696$		0			0
$697$	−3.35151	−	19.0074i	−0.126948	−	0.719956i
$698$	−1.62124	−	5.22377i	−0.0613647	−	0.197723i
$699$		0			0
$700$	0.181774	−	0.380829i	0.00687043	−	0.0143940i
$701$			3.10248i			0.117179i	0.998282	+	0.0585896i	$0.0186603\pi$
$701$			3.10248i			0.117179i	−0.998282	+	0.0585896i	$0.981340\pi$
$702$		0			0
$703$		−	48.5896i		−	1.83259i
$704$	9.66985	−	19.3547i	0.364446	−	0.729458i
$705$		0			0
$706$	4.10958	−	1.27544i	0.154666	−	0.0480018i
$707$	−0.500991	−	2.84126i	−0.0188417	−	0.106857i
$708$		0			0
$709$	7.39499	+	6.20513i	0.277725	+	0.233039i	0.771001	−	0.636834i	$-0.219756\pi$
$709$	7.39499	+	6.20513i	0.277725	+	0.233039i	−0.493276	+	0.869873i	$0.664201\pi$
$710$	−6.26983	+	4.76633i	−0.235302	+	0.178877i
$711$		0			0
$712$	−12.1188	+	15.3596i	−0.454173	+	0.575627i
$713$	7.30325	+	1.28776i	0.273509	+	0.0482270i
$714$		0			0
$715$	−9.54942	+	26.2368i	−0.357128	+	0.981201i
$716$	5.02920	+	11.0436i	0.187950	+	0.412720i
$717$		0			0
$718$	19.6840	+	12.6650i	0.734601	+	0.472654i
$719$	20.9190	+	36.2327i	0.780146	+	1.35125i	0.931856	+	0.362827i	$0.118188\pi$
$719$	20.9190	+	36.2327i	0.780146	+	1.35125i	−0.151711	+	0.988425i	$0.548478\pi$
$720$		0			0
$721$	1.28869	−	2.23207i	0.0479931	−	0.0831266i
$722$	25.9003	−	13.3350i	0.963908	−	0.496277i
$723$		0			0
$724$	18.6226	−	26.0928i	0.692105	−	0.969731i
$725$	−0.509807	−	0.607564i	−0.0189337	−	0.0225644i
$726$		0			0
$727$	0.167774	+	0.460954i	0.00622238	+	0.0170958i	0.942765	−	0.333458i	$-0.108216\pi$
$727$	0.167774	+	0.460954i	0.00622238	+	0.0170958i	−0.936543	+	0.350554i	$0.885993\pi$
$728$	6.23417	+	15.6448i	0.231054	+	0.579835i
$729$		0			0
$730$	18.3197	+	7.68506i	0.678043	+	0.284437i
$731$	38.8348	−	14.1347i	1.43636	−	0.522791i
$732$		0			0
$733$	22.4492	−	18.8371i	0.829179	−	0.695764i	−0.125923	−	0.992040i	$-0.540189\pi$
$733$	22.4492	−	18.8371i	0.829179	−	0.695764i	0.955102	+	0.296276i	$0.0957448\pi$
$734$	−0.689219	+	3.04397i	−0.0254395	+	0.112355i
$735$		0			0
$736$	6.33877	+	12.8761i	0.233650	+	0.474618i
$737$	−27.9521	−	16.1381i	−1.02963	−	0.594456i
$738$		0			0
$739$	−34.8536	+	20.1228i	−1.28211	+	0.740227i	−0.977234	−	0.212164i	$-0.931949\pi$
$739$	−34.8536	+	20.1228i	−1.28211	+	0.740227i	−0.304877	+	0.952392i	$0.598616\pi$
$740$	−19.8634	−	28.9185i	−0.730193	−	1.06306i
$741$		0			0
$742$	4.83421	−	5.22818i	0.177469	−	0.191932i
$743$	−36.9693	−	13.4557i	−1.35627	−	0.493643i	−0.441373	−	0.897324i	$-0.645509\pi$
$743$	−36.9693	−	13.4557i	−1.35627	−	0.493643i	−0.914900	+	0.403680i	$0.867731\pi$
$744$		0			0
$745$	−1.01527	+	5.75787i	−0.0371965	+	0.210952i
$746$	−14.7131	+	1.86969i	−0.538685	+	0.0684541i
$747$		0			0
$748$	6.57324	+	25.4457i	0.240341	+	0.930387i
$749$	−3.42536	+	4.08218i	−0.125160	+	0.149160i
$750$		0			0
$751$	−27.0058	+	4.76186i	−0.985457	+	0.173763i	−0.643079	−	0.765800i	$-0.722343\pi$
$751$	−27.0058	+	4.76186i	−0.985457	+	0.173763i	−0.342378	+	0.939562i	$0.611232\pi$
$752$	30.1215	+	37.2389i	1.09842	+	1.35796i
$753$		0			0
$754$	31.6161	+	1.52299i	1.15139	+	0.0554640i
$755$	−11.9272			−0.434077
$756$		0			0
$757$	−13.2822			−0.482750			−0.241375	−	0.970432i	$-0.577598\pi$
$757$	−13.2822			−0.482750			−0.241375	+	0.970432i	$0.577598\pi$
$758$	4.36053	+	0.210052i	0.158382	+	0.00762945i
$759$		0			0
$760$	19.1533	−	35.6108i	0.694764	−	1.29174i
$761$	−12.6761	+	2.23515i	−0.459510	+	0.0810240i	−0.398611	−	0.917120i	$-0.630508\pi$
$761$	−12.6761	+	2.23515i	−0.459510	+	0.0810240i	−0.0608985	+	0.998144i	$0.519397\pi$
$762$		0			0
$763$	1.52458	−	1.81693i	0.0551937	−	0.0657772i
$764$	22.6508	−	5.85125i	0.819477	−	0.211691i
$765$		0			0
$766$	−22.5389	+	2.86416i	−0.814364	+	0.103486i
$767$	−9.04337	+	51.2875i	−0.326537	+	1.85188i
$768$		0			0
$769$	−27.3171	−	9.94262i	−0.985080	−	0.358540i	−0.201267	−	0.979536i	$-0.564506\pi$
$769$	−27.3171	−	9.94262i	−0.985080	−	0.358540i	−0.783813	+	0.620996i	$0.786728\pi$
$770$	7.72911	−	8.35899i	0.278538	−	0.301237i
$771$		0			0
$772$	−28.9676	+	19.8972i	−1.04257	+	0.716114i
$773$	−4.16046	+	2.40204i	−0.149641	+	0.0863954i	−0.572951	−	0.819590i	$-0.694202\pi$
$773$	−4.16046	+	2.40204i	−0.149641	+	0.0863954i	0.423310	+	0.905985i	$0.360868\pi$
$774$		0			0
$775$	−0.407642	−	0.235352i	−0.0146429	−	0.00845410i
$776$	−23.5158	−	7.76509i	−0.844166	−	0.278751i
$777$		0			0
$778$	−5.51268	+	24.3470i	−0.197639	+	0.872882i
$779$	−19.1487	+	16.0677i	−0.686074	+	0.575685i
$780$		0			0
$781$	−6.22993	+	2.26751i	−0.222924	+	0.0811378i
$782$	−16.0758	−	6.74375i	−0.574870	−	0.241156i
$783$		0			0
$784$	−0.380445	+	21.1295i	−0.0135873	+	0.754626i
$785$	−16.2339	−	44.6023i	−0.579413	−	1.59192i
$786$		0			0
$787$	25.7907	+	30.7362i	0.919339	+	1.09563i	0.995137	+	0.0985027i	$0.0314053\pi$
$787$	25.7907	+	30.7362i	0.919339	+	1.09563i	−0.0757975	+	0.997123i	$0.524150\pi$
$788$	37.5212	+	26.7792i	1.33664	+	0.953968i
$789$		0			0
$790$	17.2059	−	8.85863i	0.612158	−	0.315176i
$791$	2.29975	−	3.98328i	0.0817696	−	0.141629i
$792$		0			0
$793$	−0.0893474	−	0.154754i	−0.00317282	−	0.00549548i
$794$	−16.0277	−	10.3125i	−0.568803	−	0.365977i
$795$		0			0
$796$	−5.69070	+	2.59151i	−0.201702	+	0.0918537i
$797$	−10.6320	+	29.2112i	−0.376605	+	1.03471i	0.596150	+	0.802873i	$0.296697\pi$
$797$	−10.6320	+	29.2112i	−0.376605	+	1.03471i	−0.972754	+	0.231839i	$0.925526\pi$
$798$		0			0
$799$	−57.2954	−	10.1027i	−2.02696	−	0.357408i
$800$	−0.0985482	−	0.905591i	−0.00348421	−	0.0320175i
$801$		0			0
$802$	−7.60909	+	5.78444i	−0.268686	+	0.204256i
$803$	12.8107	+	10.7495i	0.452080	+	0.379340i
$804$		0			0
$805$	1.31136	+	7.43712i	0.0462195	+	0.262124i
$806$	17.9413	−	5.56821i	0.631954	−	0.196132i
$807$		0			0
$808$	−4.14521	−	4.64817i	−0.145828	−	0.163522i
$809$		−	26.7938i		−	0.942021i	−0.882128	−	0.471010i	$-0.843889\pi$
$809$		−	26.7938i		−	0.942021i	0.882128	−	0.471010i	$-0.156111\pi$
$810$		0			0
$811$		−	22.6335i		−	0.794769i	−0.917652	−	0.397384i	$-0.869918\pi$
$811$		−	22.6335i		−	0.794769i	0.917652	−	0.397384i	$-0.130082\pi$
$812$	−11.6477	−	5.55960i	−0.408754	−	0.195104i
$813$		0			0
$814$	−8.75374	−	28.2054i	−0.306818	−	0.988597i
$815$	1.29515	+	7.34517i	0.0453672	+	0.257290i
$816$		0			0
$817$	−41.0019	−	34.4047i	−1.43448	−	1.20367i
$818$	−16.1272	−	21.2144i	−0.563876	−	0.741746i
$819$		0			0
$820$	−4.82804	+	17.3908i	−0.168603	+	0.607312i
$821$	12.6018	+	2.22203i	0.439805	+	0.0775495i	0.389166	−	0.921168i	$-0.372763\pi$
$821$	12.6018	+	2.22203i	0.439805	+	0.0775495i	0.0506388	+	0.998717i	$0.483874\pi$
$822$		0			0
$823$	−8.87992	+	24.3974i	−0.309534	+	0.850439i	0.683213	+	0.730219i	$0.260582\pi$
$823$	−8.87992	+	24.3974i	−0.309534	+	0.850439i	−0.992747	+	0.120220i	$0.961640\pi$
$824$	−0.167614	−	5.56122i	−0.00583911	−	0.193734i
$825$		0			0
$826$	11.4902	−	17.8581i	0.399794	−	0.621362i
$827$	−9.69134	−	16.7859i	−0.337001	−	0.583703i	0.646866	−	0.762603i	$-0.276079\pi$
$827$	−9.69134	−	16.7859i	−0.337001	−	0.583703i	−0.983867	+	0.178901i	$0.942746\pi$
$828$		0			0
$829$	−15.3678	+	26.6178i	−0.533745	+	0.924474i	0.465478	+	0.885060i	$0.345883\pi$
$829$	−15.3678	+	26.6178i	−0.533745	+	0.924474i	−0.999223	+	0.0394143i	$0.987451\pi$
$830$	−14.0393	−	27.2681i	−0.487310	−	0.946491i
$831$		0			0
$832$	29.2063	+	21.6488i	1.01254	+	0.750538i
$833$	−16.5004	−	19.6645i	−0.571706	−	0.681333i
$834$		0			0
$835$	−14.8794	−	40.8809i	−0.514924	−	1.41474i
$836$	24.2838	−	23.8505i	0.839872	−	0.824886i
$837$		0			0
$838$	10.4460	−	24.9012i	0.360850	−	0.860199i
$839$	10.2752	−	3.73987i	0.354740	−	0.129115i	−0.158502	−	0.987359i	$-0.550667\pi$
$839$	10.2752	−	3.73987i	0.354740	−	0.129115i	0.513242	+	0.858244i	$0.328444\pi$
$840$		0			0
$841$	3.63286	−	3.04833i	0.125271	−	0.105115i
$842$	31.0933	+	7.04020i	1.07155	+	0.242621i
$843$		0			0
$844$	−25.6279	+	2.00987i	−0.882148	+	0.0691824i
$845$	−15.0532	−	8.69096i	−0.517845	−	0.298978i
$846$		0			0
$847$	−4.18228	+	2.41464i	−0.143705	+	0.0829680i
$848$	2.94127	−	15.0872i	0.101004	−	0.518097i
$849$		0			0
$850$	0.812433	+	0.751213i	0.0278662	+	0.0257664i
$851$	18.4085	+	6.70013i	0.631034	+	0.229677i
$852$		0			0
$853$	1.11668	−	6.33302i	0.0382345	−	0.216838i	−0.959704	−	0.281012i	$-0.909330\pi$
$853$	1.11668	−	6.33302i	0.0382345	−	0.216838i	0.997939	+	0.0641734i	$0.0204411\pi$
$854$	0.00918534	+	0.0722820i	0.000314316	+	0.00247344i
$855$		0			0
$856$	−1.65536	+	11.3837i	−0.0565790	+	0.389088i
$857$	2.04068	−	2.43199i	0.0697083	−	0.0830751i	−0.730063	−	0.683380i	$-0.760509\pi$
$857$	2.04068	−	2.43199i	0.0697083	−	0.0830751i	0.799772	+	0.600304i	$0.204954\pi$
$858$		0			0
$859$	−27.9109	+	4.92145i	−0.952309	+	0.167918i	−0.628156	−	0.778087i	$-0.716190\pi$
$859$	−27.9109	+	4.92145i	−0.952309	+	0.167918i	−0.324152	+	0.946005i	$0.605079\pi$
$860$	−38.4672	−	3.71465i	−1.31172	−	0.126668i
$861$		0			0
$862$	−0.735291	+	15.2641i	−0.0250441	+	0.519897i
$863$	53.5310			1.82222			0.911108	−	0.412168i	$-0.135228\pi$
$863$	53.5310			1.82222			0.911108	+	0.412168i	$0.135228\pi$
$864$		0			0
$865$	−19.8602			−0.675267
$866$	−2.55793	+	53.1007i	−0.0869220	+	1.80444i
$867$		0			0
$868$	−7.62436	−	0.736259i	−0.258788	−	0.0249903i
$869$	16.0431	−	2.82884i	0.544226	−	0.0959617i
$870$		0			0
$871$	34.8609	−	41.5456i	1.18122	−	1.40772i
$872$	0.736780	−	5.06676i	0.0249505	−	0.171582i
$873$		0			0
$874$	2.84626	+	22.3980i	0.0962761	+	0.757624i
$875$	−2.50119	+	14.1849i	−0.0845555	+	0.479538i
$876$		0			0
$877$	28.0872	+	10.2229i	0.948439	+	0.345204i	0.769493	−	0.638655i	$-0.220509\pi$
$877$	28.0872	+	10.2229i	0.948439	+	0.345204i	0.178946	+	0.983859i	$0.442731\pi$
$878$	33.1587	+	30.6601i	1.11905	+	1.03473i
$879$		0			0
$880$	4.70261	−	24.1220i	0.158525	−	0.813151i
$881$	−14.9002	+	8.60262i	−0.502000	+	0.289830i	−0.729539	−	0.683939i	$-0.760265\pi$
$881$	−14.9002	+	8.60262i	−0.502000	+	0.289830i	0.227539	+	0.973769i	$0.426932\pi$
$882$		0			0
$883$	−19.9228	−	11.5024i	−0.670455	−	0.387088i	0.125794	−	0.992056i	$-0.459852\pi$
$883$	−19.9228	−	11.5024i	−0.670455	−	0.387088i	−0.796249	+	0.604969i	$0.793186\pi$
$884$	−44.0249	+	3.45265i	−1.48072	+	0.116125i
$885$		0			0
$886$	51.8360	+	11.7368i	1.74146	+	0.394305i
$887$	−21.8640	+	18.3460i	−0.734120	+	0.616000i	−0.931251	−	0.364377i	$-0.881282\pi$
$887$	−21.8640	+	18.3460i	−0.734120	+	0.616000i	0.197132	+	0.980377i	$0.436837\pi$
$888$		0			0
$889$	−13.8131	+	5.02757i	−0.463278	+	0.168619i
$890$	−8.59695	+	20.4935i	−0.288170	+	0.686944i
$891$		0			0
$892$	14.7529	−	14.4896i	0.493963	−	0.485149i
$893$	25.7712	+	70.8058i	0.862401	+	2.36943i
$894$		0			0
$895$	8.86013	+	10.5591i	0.296162	+	0.352952i
$896$	−7.56704	−	12.7470i	−0.252797	−	0.425846i
$897$		0			0
$898$	−5.23198	−	10.1620i	−0.174593	−	0.339109i
$899$	−7.19828	+	12.4678i	−0.240076	+	0.415824i
$900$		0			0
$901$	9.33569	+	16.1699i	0.311017	+	0.538697i
$902$	−8.22077	+	12.7768i	−0.273722	+	0.425419i
$903$		0			0
$904$	−0.299119	−	9.92437i	−0.00994854	−	0.330080i
$905$	12.4540	−	34.2172i	0.413986	−	1.13742i
$906$		0			0
$907$	57.4172	+	10.1242i	1.90651	+	0.336169i	0.996858	−	0.0792103i	$-0.0252399\pi$
$907$	57.4172	+	10.1242i	1.90651	+	0.336169i	0.909649	+	0.415379i	$0.136351\pi$
$908$	0.0513842	−	0.185088i	0.00170525	−	0.00614236i
$909$		0			0
$910$	11.5771	+	15.2290i	0.383776	+	0.504835i
$911$	−3.02058	−	2.53457i	−0.100076	−	0.0839741i	0.591377	−	0.806395i	$-0.298585\pi$
$911$	−3.02058	−	2.53457i	−0.100076	−	0.0839741i	−0.691453	+	0.722421i	$0.743029\pi$
$912$		0			0
$913$	−4.48318	−	25.4254i	−0.148372	−	0.841457i
$914$	−1.03713	−	3.34174i	−0.0343054	−	0.110535i
$915$		0			0
$916$	48.5037	+	23.1515i	1.60261	+	0.764946i
$917$			6.72250i			0.221997i
$918$		0			0
$919$			6.45794i			0.213028i	0.994311	+	0.106514i	$0.0339689\pi$
$919$			6.45794i			0.213028i	−0.994311	+	0.106514i	$0.966031\pi$
$920$	10.8503	+	12.1668i	0.357722	+	0.401127i
$921$		0			0
$922$	12.2039	−	3.78758i	0.401915	−	0.124737i
$923$	−1.93444	−	10.9708i	−0.0636729	−	0.361107i
$924$		0			0
$925$	−0.952508	−	0.799249i	−0.0313183	−	0.0262792i
$926$	−1.57011	+	1.19360i	−0.0515970	+	0.0392240i
$927$		0			0
$928$	−27.6976	+	3.01411i	−0.909220	+	0.0989431i
$929$	−56.1170	−	9.89493i	−1.84114	−	0.324642i	−0.858880	−	0.512177i	$-0.828839\pi$
$929$	−56.1170	−	9.89493i	−1.84114	−	0.324642i	−0.982258	+	0.187535i	$0.939950\pi$
$930$		0			0
$931$	−11.3709	+	31.2413i	−0.372666	+	1.02389i
$932$	13.1672	−	5.99627i	0.431306	−	0.196414i
$933$		0			0
$934$	25.0924	+	16.1448i	0.821047	+	0.528275i
$935$	14.9262	+	25.8530i	0.488140	+	0.845483i
$936$		0			0
$937$	9.57464	−	16.5838i	0.312790	−	0.541768i	−0.666175	−	0.745795i	$-0.732070\pi$
$937$	9.57464	−	16.5838i	0.312790	−	0.541768i	0.978965	+	0.204027i	$0.0654031\pi$
$938$	−19.6612	+	10.1227i	−0.641960	+	0.330519i
$939$		0			0
$940$	44.2833	+	31.6053i	1.44436	+	1.03085i
$941$	12.0148	+	14.3187i	0.391671	+	0.466775i	0.925462	−	0.378841i	$-0.123677\pi$
$941$	12.0148	+	14.3187i	0.391671	+	0.466775i	−0.533791	+	0.845617i	$0.679233\pi$
$942$		0			0
$943$	−3.44687	−	9.47021i	−0.112246	−	0.308392i
$944$	0.825237	−	45.8329i	0.0268592	−	1.49173i
$945$		0			0
$946$	−29.9991	−	12.5845i	−0.975354	−	0.409158i
$947$	−26.7426	+	9.73349i	−0.869016	+	0.316296i	−0.737769	−	0.675054i	$-0.764120\pi$
$947$	−26.7426	+	9.73349i	−0.869016	+	0.316296i	−0.131247	+	0.991350i	$0.541898\pi$
$948$		0			0
$949$	−21.5259	+	18.0624i	−0.698761	+	0.586330i
$950$	0.316470	−	1.39770i	0.0102676	−	0.0453475i
$951$		0			0
$952$	17.0983	+	5.64601i	0.554160	+	0.182988i
$953$	−39.0891	−	22.5681i	−1.26622	−	0.731052i	−0.291949	−	0.956434i	$-0.594304\pi$
$953$	−39.0891	−	22.5681i	−1.26622	−	0.731052i	−0.974270	+	0.225382i	$0.927637\pi$
$954$		0			0
$955$	23.0134	−	13.2868i	0.744695	−	0.429950i
$956$	21.0309	−	14.4456i	0.680189	−	0.467205i
$957$		0			0
$958$	−14.0219	+	15.1646i	−0.453027	+	0.489947i
$959$	−2.22652	−	0.810386i	−0.0718980	−	0.0261687i
$960$		0			0
$961$	3.89942	−	22.1147i	0.125788	−	0.713377i
$962$	49.2278	−	6.25568i	1.58717	−	0.201691i
$963$		0			0
$964$	−14.6643	+	3.78814i	−0.472305	+	0.122008i
$965$	−25.6592	+	30.5794i	−0.825998	+	0.984386i
$966$		0			0
$967$	−9.02769	+	1.59182i	−0.290311	+	0.0511896i	−0.316907	−	0.948457i	$-0.602644\pi$
$967$	−9.02769	+	1.59182i	−0.290311	+	0.0511896i	0.0265962	+	0.999646i	$0.491533\pi$
$968$	−4.93811	+	9.18118i	−0.158717	+	0.295094i
$969$		0			0
$970$	−28.0975	−	1.35349i	−0.902155	−	0.0434580i
$971$	10.7197			0.344010			0.172005	−	0.985096i	$-0.444975\pi$
$971$	10.7197			0.344010			0.172005	+	0.985096i	$0.444975\pi$
$972$		0			0
$973$	−17.0344			−0.546098
$974$	0.399111	+	0.0192257i	0.0127883	+	0.000616031i
$975$		0			0
$976$	0.0989181	+	0.122291i	0.00316629	+	0.00391445i
$977$	−49.0395	+	8.64698i	−1.56891	+	0.276641i	−0.889437	−	0.457057i	$-0.848903\pi$
$977$	−49.0395	+	8.64698i	−1.56891	+	0.276641i	−0.679475	+	0.733699i	$0.737792\pi$
$978$		0			0
$979$	−12.0250	+	14.3308i	−0.384320	+	0.458015i
$980$	6.00394	+	23.2419i	0.191789	+	0.742435i
$981$		0			0
$982$	21.7439	−	2.76313i	0.693875	−	0.0881751i
$983$	0.315908	−	1.79160i	0.0100759	−	0.0571433i	−0.979355	−	0.202147i	$-0.935208\pi$
$983$	0.315908	−	1.79160i	0.0100759	−	0.0571433i	0.989431	+	0.145003i	$0.0463193\pi$
$984$		0			0
$985$	49.2039	+	17.9088i	1.56777	+	0.570620i
$986$	22.9760	−	24.8484i	0.731704	−	0.791334i
$987$		0			0
$988$	32.3817	+	47.1434i	1.03020	+	1.49983i
$989$	18.6883	−	10.7897i	0.594252	−	0.343092i
$990$		0			0
$991$	48.8792	+	28.2204i	1.55270	+	0.896451i	0.997921	+	0.0644516i	$0.0205298\pi$
$991$	48.8792	+	28.2204i	1.55270	+	0.896451i	0.554777	+	0.831999i	$0.312804\pi$
$992$	−14.8350	+	7.30313i	−0.471012	+	0.231875i
$993$		0			0
$994$	−1.00310	+	4.43023i	−0.0318163	+	0.140518i
$995$	−5.44102	+	4.56556i	−0.172492	+	0.144738i
$996$		0			0
$997$	−11.0934	+	4.03767i	−0.351331	+	0.127874i	−0.511657	−	0.859190i	$-0.670968\pi$
$997$	−11.0934	+	4.03767i	−0.351331	+	0.127874i	0.160325	+	0.987064i	$0.448746\pi$
$998$	−53.3333	−	22.3731i	−1.68824	−	0.708209i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.l.a.143.9		96
3.2	odd	2		108.2.l.a.47.8	yes	96
4.3	odd	2	inner	324.2.l.a.143.4		96
9.2	odd	6		972.2.l.d.107.15		96
9.4	even	3		972.2.l.b.755.13		96
9.5	odd	6		972.2.l.c.755.4		96
9.7	even	3		972.2.l.a.107.2		96
12.11	even	2		108.2.l.a.47.13	yes	96
27.4	even	9		108.2.l.a.23.13	yes	96
27.5	odd	18		972.2.l.b.215.15		96
27.13	even	9		972.2.l.d.863.10		96
27.14	odd	18		972.2.l.a.863.7		96
27.22	even	9		972.2.l.c.215.2		96
27.23	odd	18	inner	324.2.l.a.179.4		96
36.7	odd	6		972.2.l.a.107.7		96
36.11	even	6		972.2.l.d.107.10		96
36.23	even	6		972.2.l.c.755.2		96
36.31	odd	6		972.2.l.b.755.15		96
108.23	even	18	inner	324.2.l.a.179.9		96
108.31	odd	18		108.2.l.a.23.8	✓	96
108.59	even	18		972.2.l.b.215.13		96
108.67	odd	18		972.2.l.d.863.15		96
108.95	even	18		972.2.l.a.863.2		96
108.103	odd	18		972.2.l.c.215.4		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.23.8	✓	96	108.31	odd	18
108.2.l.a.23.13	yes	96	27.4	even	9
108.2.l.a.47.8	yes	96	3.2	odd	2
108.2.l.a.47.13	yes	96	12.11	even	2
324.2.l.a.143.4		96	4.3	odd	2	inner
324.2.l.a.143.9		96	1.1	even	1	trivial
324.2.l.a.179.4		96	27.23	odd	18	inner
324.2.l.a.179.9		96	108.23	even	18	inner
972.2.l.a.107.2		96	9.7	even	3
972.2.l.a.107.7		96	36.7	odd	6
972.2.l.a.863.2		96	108.95	even	18
972.2.l.a.863.7		96	27.14	odd	18
972.2.l.b.215.13		96	108.59	even	18
972.2.l.b.215.15		96	27.5	odd	18
972.2.l.b.755.13		96	9.4	even	3
972.2.l.b.755.15		96	36.31	odd	6
972.2.l.c.215.2		96	27.22	even	9
972.2.l.c.215.4		96	108.103	odd	18
972.2.l.c.755.2		96	36.23	even	6
972.2.l.c.755.4		96	9.5	odd	6
972.2.l.d.107.10		96	36.11	even	6
972.2.l.d.107.15		96	9.2	odd	6
972.2.l.d.863.10		96	27.13	even	9
972.2.l.d.863.15		96	108.67	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.l (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0680456 - 1.41258i) q^{2} +(-1.99074 - 0.192239i) q^{4} +(-2.23728 + 0.394492i) q^{5} +(-0.842213 + 1.00371i) q^{7} +(-0.407013 + 2.79899i) q^{8} +O(q^{10})\)	\(q+(0.0680456 - 1.41258i) q^{2} +(-1.99074 - 0.192239i) q^{4} +(-2.23728 + 0.394492i) q^{5} +(-0.842213 + 1.00371i) q^{7} +(-0.407013 + 2.79899i) q^{8} +(0.405013 + 3.18717i) q^{10} +(-0.469629 + 2.66340i) q^{11} +(-4.27030 - 1.55426i) q^{13} +(1.36051 + 1.25799i) q^{14} +(3.92609 + 0.765396i) q^{16} +(-4.20783 + 2.42939i) q^{17} +(5.44971 + 3.14639i) q^{19} +(4.52967 - 0.355239i) q^{20} +(3.73029 + 0.844619i) q^{22} +(-1.94350 + 1.63079i) q^{23} +(0.151321 - 0.0550764i) q^{25} +(-2.48609 + 5.92636i) q^{26} +(1.86958 - 1.83622i) q^{28} +(-1.68452 - 4.62818i) q^{29} +(-1.87889 - 2.23918i) q^{31} +(1.34833 - 5.49381i) q^{32} +(3.14537 + 6.10919i) q^{34} +(1.48831 - 2.57783i) q^{35} +(-3.86074 - 6.68701i) q^{37} +(4.81534 - 7.48403i) q^{38} +(-0.193578 - 6.42268i) q^{40} +(-1.35861 + 3.73275i) q^{41} +(-8.37644 - 1.47699i) q^{43} +(1.44692 - 5.21185i) q^{44} +(2.17137 + 2.85631i) q^{46} +(9.17264 + 7.69676i) q^{47} +(0.917425 + 5.20298i) q^{49} +(-0.0675028 - 0.217500i) q^{50} +(8.20227 + 3.91505i) q^{52} -3.84281i q^{53} -6.14402i q^{55} +(-2.46658 - 2.76587i) q^{56} +(-6.65228 + 2.06458i) q^{58} +(-1.99002 - 11.2860i) q^{59} +(0.0301227 + 0.0252759i) q^{61} +(-3.29086 + 2.50171i) q^{62} +(-7.66868 - 2.27845i) q^{64} +(10.1670 + 1.79271i) q^{65} +(-4.08179 + 11.2146i) q^{67} +(8.84372 - 4.02738i) q^{68} +(-3.54010 - 2.27776i) q^{70} +(1.22570 + 2.12297i) q^{71} +(3.09175 - 5.35507i) q^{73} +(-9.70861 + 4.99857i) q^{74} +(-10.2441 - 7.31129i) q^{76} +(-2.27775 - 2.71452i) q^{77} +(-2.06018 - 5.66029i) q^{79} +(-9.08569 - 0.163591i) q^{80} +(5.18035 + 2.17314i) q^{82} +(-8.97051 + 3.26500i) q^{83} +(8.45570 - 7.09518i) q^{85} +(-2.65634 + 11.7318i) q^{86} +(-7.26367 - 2.39852i) q^{88} +(5.99050 + 3.45862i) q^{89} +(5.15653 - 2.97713i) q^{91} +(4.18250 - 2.87286i) q^{92} +(11.4964 - 12.4333i) q^{94} +(-13.4337 - 4.88948i) q^{95} +(-1.52040 + 8.62260i) q^{97} +(7.41203 - 0.941893i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) \) 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38} - 21 q^{40} + 42 q^{41} - 63 q^{44} - 3 q^{46} - 12 q^{49} - 87 q^{50} - 33 q^{52} - 99 q^{56} - 33 q^{58} - 12 q^{61} - 90 q^{62} - 3 q^{64} - 12 q^{65} - 51 q^{68} - 21 q^{70} - 6 q^{73} - 21 q^{74} - 18 q^{76} - 12 q^{77} - 12 q^{82} - 42 q^{85} + 30 q^{86} + 18 q^{88} + 123 q^{92} + 21 q^{94} - 30 q^{97} + 180 q^{98}+O(q^{100}) \) 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Introduction

L-functions

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