LMFDB - Embedded newform 927.2.u.d.64.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [927,2,Mod(64,927)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(927, base_ring=CyclotomicField(34))

chi = DirichletCharacter(H, H._module([0, 20]))

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

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

chi := DirichletCharacter("927.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 927 = 3^{2} \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	927.u (of order $17$, degree $16$, 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:	$7.40213226737$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{17})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{17}]$

Embedding invariants

Embedding label			64.8
Character	$\chi$	$=$	927.64
Dual form			927.2.u.d.478.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.638851 + 0.247492i) q^{2} +(-1.13114 + 1.03117i) q^{4} +(-0.611516 + 2.14926i) q^{5} +(-0.0403670 - 0.0810678i) q^{7} +(1.07819 - 2.16529i) q^{8} +O(q^{10})$	\(q+(-0.638851 + 0.247492i) q^{2} +(-1.13114 + 1.03117i) q^{4} +(-0.611516 + 2.14926i) q^{5} +(-0.0403670 - 0.0810678i) q^{7} +(1.07819 - 2.16529i) q^{8} +(-0.141256 - 1.52440i) q^{10} +(-3.31353 + 1.28367i) q^{11} +(-2.01891 - 4.05451i) q^{13} +(0.0458521 + 0.0417997i) q^{14} +(0.129547 - 1.39803i) q^{16} +(-2.93360 - 1.81641i) q^{17} +(-0.409898 - 0.0766232i) q^{19} +(-1.52454 - 3.06168i) q^{20} +(1.79915 - 1.64014i) q^{22} +(3.69198 + 1.43028i) q^{23} +(0.00573925 + 0.00355359i) q^{25} +(2.29324 + 2.09057i) q^{26} +(0.129255 + 0.0500738i) q^{28} +(-1.43979 + 5.06035i) q^{29} +(0.650460 - 7.01958i) q^{31} +(1.58716 + 5.57828i) q^{32} +(2.32368 + 0.434371i) q^{34} +(0.198920 - 0.0371847i) q^{35} +(5.77431 - 7.64642i) q^{37} +(0.280827 - 0.0524957i) q^{38} +(3.99444 + 3.64141i) q^{40} +(-0.716868 - 2.51953i) q^{41} +(2.58537 + 3.42358i) q^{43} +(2.42438 - 4.86881i) q^{44} -2.71261 q^{46} -8.03506 q^{47} +(4.21350 - 5.57958i) q^{49} +(-0.00454601 - 0.000849797i) q^{50} +(6.46456 + 2.50438i) q^{52} +(6.21215 + 1.16125i) q^{53} +(-0.732654 - 7.90660i) q^{55} -0.219059 q^{56} +(-0.332584 - 3.58915i) q^{58} +(2.51556 - 5.05192i) q^{59} +(-9.40237 - 5.82170i) q^{61} +(1.32174 + 4.64545i) q^{62} +(-0.702313 - 0.930013i) q^{64} +(9.94877 - 1.85975i) q^{65} +(1.31292 - 2.63670i) q^{67} +(5.19133 - 0.970428i) q^{68} +(-0.117878 + 0.0729867i) q^{70} +(-1.78049 - 6.25777i) q^{71} +(0.411735 + 1.44710i) q^{73} +(-1.79649 + 6.31402i) q^{74} +(0.542663 - 0.336003i) q^{76} +(0.237821 + 0.216803i) q^{77} +(1.04331 - 3.66686i) q^{79} +(2.92551 + 1.13335i) q^{80} +(1.08154 + 1.43219i) q^{82} +(-0.619075 - 1.24327i) q^{83} +(5.69786 - 5.19429i) q^{85} +(-2.49897 - 1.54730i) q^{86} +(-0.793088 + 8.55879i) q^{88} +(-11.1393 - 10.1548i) q^{89} +(-0.247193 + 0.327337i) q^{91} +(-5.65100 + 2.18921i) q^{92} +(5.13321 - 1.98862i) q^{94} +(0.415342 - 0.834119i) q^{95} +(-15.2069 + 9.41572i) q^{97} +(-1.31090 + 4.60733i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 20 q^{4} - 8 q^{7}+O(q^{10}) $ 288 * q - 20 * q^4 - 8 * q^7	$ 288 q - 20 q^{4} - 8 q^{7} + 72 q^{10} - 8 q^{13} - 32 q^{16} - 34 q^{19} - 28 q^{22} + 22 q^{25} + 88 q^{28} + 16 q^{31} + 110 q^{34} - 16 q^{37} + 28 q^{40} - 32 q^{43} - 176 q^{46} - 82 q^{49} - 32 q^{55} + 68 q^{58} - 24 q^{61} + 54 q^{64} + 28 q^{67} + 44 q^{70} + 48 q^{73} - 242 q^{82} + 18 q^{85} + 214 q^{88} + 114 q^{91} + 108 q^{94} + 196 q^{97}+O(q^{100}) $ 288 * q - 20 * q^4 - 8 * q^7 + 72 * q^10 - 8 * q^13 - 32 * q^16 - 34 * q^19 - 28 * q^22 + 22 * q^25 + 88 * q^28 + 16 * q^31 + 110 * q^34 - 16 * q^37 + 28 * q^40 - 32 * q^43 - 176 * q^46 - 82 * q^49 - 32 * q^55 + 68 * q^58 - 24 * q^61 + 54 * q^64 + 28 * q^67 + 44 * q^70 + 48 * q^73 - 242 * q^82 + 18 * q^85 + 214 * q^88 + 114 * q^91 + 108 * q^94 + 196 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/927\mathbb{Z}\right)^\times$.

$n$	$722$	$829$
$\chi(n)$	$1$	$e\left(\frac{10}{17}\right)$

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 $

$2$	−0.638851	+	0.247492i	−0.451736	+	0.175003i	−0.576352	−	0.817202i	$-0.695524\pi$
$2$	−0.638851	+	0.247492i	−0.451736	+	0.175003i	0.124616	+	0.992205i	$0.460230\pi$
$3$		0			0
$3$		0			0
$4$	−1.13114	+	1.03117i	−0.565570	+	0.515585i
$5$	−0.611516	+	2.14926i	−0.273478	+	0.961176i	0.696414	+	0.717641i	$0.254778\pi$
$5$	−0.611516	+	2.14926i	−0.273478	+	0.961176i	−0.969892	+	0.243536i	$0.921693\pi$
$6$		0			0
$7$	−0.0403670	−	0.0810678i	−0.0152573	−	0.0306408i	0.887404	−	0.460993i	$-0.152507\pi$
$7$	−0.0403670	−	0.0810678i	−0.0152573	−	0.0306408i	−0.902661	+	0.430353i	$0.858389\pi$
$8$	1.07819	−	2.16529i	0.381197	−	0.765547i
$9$		0			0
$10$	−0.141256	−	1.52440i	−0.0446692	−	0.482057i
$11$	−3.31353	+	1.28367i	−0.999066	+	0.387040i	−0.804566	−	0.593863i	$-0.797602\pi$
$11$	−3.31353	+	1.28367i	−0.999066	+	0.387040i	−0.194499	+	0.980903i	$0.562308\pi$
$12$		0			0
$13$	−2.01891	−	4.05451i	−0.559944	−	1.12452i	−0.976522	−	0.215419i	$-0.930888\pi$
$13$	−2.01891	−	4.05451i	−0.559944	−	1.12452i	0.416578	−	0.909100i	$-0.363229\pi$
$14$	0.0458521	+	0.0417997i	0.0122545	+	0.0111715i
$15$		0			0
$16$	0.129547	−	1.39803i	0.0323867	−	0.349508i
$17$	−2.93360	−	1.81641i	−0.711502	−	0.440543i	0.122382	−	0.992483i	$-0.460947\pi$
$17$	−2.93360	−	1.81641i	−0.711502	−	0.440543i	−0.833884	+	0.551940i	$0.813888\pi$
$18$		0			0
$19$	−0.409898	−	0.0766232i	−0.0940371	−	0.0175786i	0.136521	−	0.990637i	$-0.456408\pi$
$19$	−0.409898	−	0.0766232i	−0.0940371	−	0.0175786i	−0.230558	+	0.973059i	$0.574055\pi$
$20$	−1.52454	−	3.06168i	−0.340897	−	0.684613i
$21$		0			0
$22$	1.79915	−	1.64014i	0.383581	−	0.349680i
$23$	3.69198	+	1.43028i	0.769830	+	0.298234i	0.713944	−	0.700203i	$-0.246907\pi$
$23$	3.69198	+	1.43028i	0.769830	+	0.298234i	0.0558867	+	0.998437i	$0.482201\pi$
$24$		0			0
$25$	0.00573925	+	0.00355359i	0.00114785	+	0.000710719i
$26$	2.29324	+	2.09057i	0.449742	+	0.409994i
$27$		0			0
$28$	0.129255	+	0.0500738i	0.0244270	+	0.00946306i
$29$	−1.43979	+	5.06035i	−0.267363	+	0.939684i	0.705578	+	0.708632i	$0.250687\pi$
$29$	−1.43979	+	5.06035i	−0.267363	+	0.939684i	−0.972941	+	0.231052i	$0.925783\pi$
$30$		0			0
$31$	0.650460	−	7.01958i	0.116826	−	1.26075i	−0.712374	−	0.701801i	$-0.752380\pi$
$31$	0.650460	−	7.01958i	0.116826	−	1.26075i	0.829199	−	0.558953i	$-0.188797\pi$
$32$	1.58716	+	5.57828i	0.280572	+	0.986110i
$33$		0			0
$34$	2.32368	+	0.434371i	0.398508	+	0.0744940i
$35$	0.198920	−	0.0371847i	0.0336237	−	0.00628536i
$36$		0			0
$37$	5.77431	−	7.64642i	0.949291	−	1.25706i	−0.0170650	−	0.999854i	$-0.505432\pi$
$37$	5.77431	−	7.64642i	0.949291	−	1.25706i	0.966356	−	0.257210i	$-0.0828031\pi$
$38$	0.280827	−	0.0524957i	0.0455562	−	0.00851593i
$39$		0			0
$40$	3.99444	+	3.64141i	0.631576	+	0.575758i
$41$	−0.716868	−	2.51953i	−0.111956	−	0.393484i	0.885511	−	0.464619i	$-0.153809\pi$
$41$	−0.716868	−	2.51953i	−0.111956	−	0.393484i	−0.997467	+	0.0711344i	$0.977338\pi$
$42$		0			0
$43$	2.58537	+	3.42358i	0.394265	+	0.522091i	0.951246	−	0.308434i	$-0.0998050\pi$
$43$	2.58537	+	3.42358i	0.394265	+	0.522091i	−0.556981	+	0.830525i	$0.688040\pi$
$44$	2.42438	−	4.86881i	0.365489	−	0.734001i
$45$		0			0
$46$	−2.71261			−0.399952
$47$	−8.03506			−1.17203			−0.586017	−	0.810299i	$-0.699305\pi$
$47$	−8.03506			−1.17203			−0.586017	+	0.810299i	$0.699305\pi$
$48$		0			0
$49$	4.21350	−	5.57958i	0.601929	−	0.797082i
$50$	−0.00454601		0.000849797i	−0.000642903		0.000120179i
$51$		0			0
$52$	6.46456	+	2.50438i	0.896473	+	0.347295i
$53$	6.21215	+	1.16125i	0.853304	+	0.159510i	0.592191	−	0.805798i	$-0.298263\pi$
$53$	6.21215	+	1.16125i	0.853304	+	0.159510i	0.261114	+	0.965308i	$0.415910\pi$
$54$		0			0
$55$	−0.732654	−	7.90660i	−0.0987910	−	1.06613i
$56$	−0.219059			−0.0292729
$57$		0			0
$58$	−0.332584	−	3.58915i	−0.0436704	−	0.471279i
$59$	2.51556	−	5.05192i	0.327498	−	0.657704i	−0.668822	−	0.743423i	$-0.733201\pi$
$59$	2.51556	−	5.05192i	0.327498	−	0.657704i	0.996319	+	0.0857190i	$0.0273187\pi$
$60$		0			0
$61$	−9.40237	−	5.82170i	−1.20385	−	0.745392i	−0.230134	−	0.973159i	$-0.573917\pi$
$61$	−9.40237	−	5.82170i	−1.20385	−	0.745392i	−0.973716	+	0.227766i	$0.926858\pi$
$62$	1.32174	+	4.64545i	0.167862	+	0.589973i
$63$		0			0
$64$	−0.702313	−	0.930013i	−0.0877892	−	0.116252i
$65$	9.94877	−	1.85975i	1.23399	−	0.230673i
$66$		0			0
$67$	1.31292	−	2.63670i	0.160399	−	0.322124i	−0.800355	−	0.599526i	$-0.795356\pi$
$67$	1.31292	−	2.63670i	0.160399	−	0.322124i	0.960754	+	0.277402i	$0.0894734\pi$
$68$	5.19133	−	0.970428i	0.629542	−	0.117682i
$69$		0			0
$70$	−0.117878	+	0.0729867i	−0.0140891	+	0.00872358i
$71$	−1.78049	−	6.25777i	−0.211305	−	0.742660i	−0.992908	−	0.118884i	$-0.962068\pi$
$71$	−1.78049	−	6.25777i	−0.211305	−	0.742660i	0.781603	−	0.623776i	$-0.214402\pi$
$72$		0			0
$73$	0.411735	+	1.44710i	0.0481899	+	0.169370i	0.982185	−	0.187915i	$-0.0601730\pi$
$73$	0.411735	+	1.44710i	0.0481899	+	0.169370i	−0.933995	+	0.357285i	$0.883702\pi$
$74$	−1.79649	+	6.31402i	−0.208838	+	0.733990i
$75$		0			0
$76$	0.542663	−	0.336003i	0.0622478	−	0.0385422i
$77$	0.237821	+	0.216803i	0.0271022	+	0.0247069i
$78$		0			0
$79$	1.04331	−	3.66686i	0.117382	−	0.412554i	−0.880755	−	0.473572i	$-0.842964\pi$
$79$	1.04331	−	3.66686i	0.117382	−	0.412554i	0.998137	+	0.0610186i	$0.0194349\pi$
$80$	2.92551	+	1.13335i	0.327082	+	0.126712i
$81$		0			0
$82$	1.08154	+	1.43219i	0.119436	+	0.158158i
$83$	−0.619075	−	1.24327i	−0.0679523	−	0.136467i	0.858583	−	0.512675i	$-0.171345\pi$
$83$	−0.619075	−	1.24327i	−0.0679523	−	0.136467i	−0.926535	+	0.376208i	$0.877228\pi$
$84$		0			0
$85$	5.69786	−	5.19429i	0.618020	−	0.563400i
$86$	−2.49897	−	1.54730i	−0.269471	−	0.166850i
$87$		0			0
$88$	−0.793088	+	8.55879i	−0.0845435	+	0.912370i
$89$	−11.1393	−	10.1548i	−1.18077	−	1.07641i	−0.995600	−	0.0937023i	$-0.970130\pi$
$89$	−11.1393	−	10.1548i	−1.18077	−	1.07641i	−0.185165	−	0.982707i	$-0.559282\pi$
$90$		0			0
$91$	−0.247193	+	0.327337i	−0.0259129	+	0.0343142i
$92$	−5.65100	+	2.18921i	−0.589158	+	0.228241i
$93$		0			0
$94$	5.13321	−	1.98862i	0.529450	−	0.205110i
$95$	0.415342	−	0.834119i	0.0426132	−	0.0855788i
$96$		0			0
$97$	−15.2069	+	9.41572i	−1.54403	+	0.956022i	−0.551477	+	0.834190i	$0.685936\pi$
$97$	−15.2069	+	9.41572i	−1.54403	+	0.956022i	−0.992551	+	0.121832i	$0.961123\pi$
$98$	−1.31090	+	4.60733i	−0.132421	+	0.465410i
$99$		0			0
$100$	−0.0101563	+	0.00189853i	−0.00101563	+	0.000189853i
$101$	−6.80655	+	2.63687i	−0.677277	+	0.262379i	−0.675217	−	0.737619i	$-0.735950\pi$
$101$	−6.80655	+	2.63687i	−0.677277	+	0.262379i	−0.00206031	+	0.999998i	$0.500656\pi$
$102$		0			0
$103$	−7.29903	+	7.05153i	−0.719195	+	0.694808i
$103$	−7.29903	+	7.05153i	−0.719195	+	0.694808i
$104$	−10.9560			−1.07432
$105$		0			0
$106$	−4.25604	+	0.795592i	−0.413383	+	0.0772747i
$107$	12.4877	−	11.3840i	1.20723	−	1.10054i	0.214936	−	0.976628i	$-0.431046\pi$
$107$	12.4877	−	11.3840i	1.20723	−	1.10054i	0.992294	−	0.123907i	$-0.0395425\pi$
$108$		0			0
$109$	6.57707	−	4.07235i	0.629969	−	0.390060i	−0.173988	−	0.984748i	$-0.555665\pi$
$109$	6.57707	−	4.07235i	0.629969	−	0.390060i	0.803957	+	0.594687i	$0.202724\pi$
$110$	2.42488	+	4.86981i	0.231203	+	0.464318i
$111$		0			0
$112$	−0.118565	+	0.0459323i	−0.0112033	+	0.00434019i
$113$	−0.435144	−	4.69596i	−0.0409349	−	0.441758i	−0.991394	−	0.130910i	$-0.958210\pi$
$113$	−0.435144	−	4.69596i	−0.0409349	−	0.441758i	0.950459	−	0.310849i	$-0.100613\pi$
$114$		0			0
$115$	−5.33174	+	7.06036i	−0.497187	+	0.658382i
$116$	−3.58948	−	7.20864i	−0.333274	−	0.669305i
$117$		0			0
$118$	−0.356755	+	3.85000i	−0.0328420	+	0.354422i
$119$	−0.0288317	+	0.311143i	−0.00264299	+	0.0285225i
$120$		0			0
$121$	1.20256	−	1.09627i	0.109323	−	0.0996613i
$122$	7.44754	+	1.39219i	0.674269	+	0.126043i
$123$		0			0
$124$	6.50262	+	8.61086i	0.583952	+	0.773278i
$125$	−8.26794	+	7.53722i	−0.739507	+	0.674150i
$126$		0			0
$127$	2.04572	−	7.18997i	0.181529	−	0.638007i	−0.816619	−	0.577176i	$-0.804154\pi$
$127$	2.04572	−	7.18997i	0.181529	−	0.638007i	0.998148	−	0.0608305i	$-0.0193749\pi$
$128$	−9.18312	−	5.68595i	−0.811681	−	0.502572i
$129$		0			0
$130$	−5.89551	+	3.65035i	−0.517071	+	0.320157i
$131$	8.11508	+	3.14380i	0.709018	+	0.274675i	0.688626	−	0.725117i	$-0.258214\pi$
$131$	8.11508	+	3.14380i	0.709018	+	0.274675i	0.0203922	+	0.999792i	$0.493509\pi$
$132$		0			0
$133$	0.0103347	+	0.0363226i	0.000896129	+	0.00314957i
$134$	−0.186198	+	2.00940i	−0.0160851	+	0.173585i
$135$		0			0
$136$	−7.09602	+	4.39367i	−0.608479	+	0.376754i
$137$	−5.29868	−	0.990494i	−0.452696	−	0.0846236i	−0.0475366	−	0.998869i	$-0.515137\pi$
$137$	−5.29868	−	0.990494i	−0.452696	−	0.0846236i	−0.405160	+	0.914246i	$0.632784\pi$
$138$		0			0
$139$	3.03085	−	6.08676i	0.257073	−	0.516272i	−0.728600	−	0.684940i	$-0.759829\pi$
$139$	3.03085	−	6.08676i	0.257073	−	0.516272i	0.985673	+	0.168667i	$0.0539463\pi$
$140$	−0.186663	+	0.247182i	−0.0157759	+	0.0208907i
$141$		0			0
$142$	2.68622	+	3.55712i	0.225422	+	0.298507i
$143$	11.8943	+	10.8431i	0.994655	+	0.906748i
$144$		0			0
$145$	−9.99554	−	6.18897i	−0.830084	−	0.513966i
$146$	−0.621183	−	0.822579i	−0.0514095	−	0.0680771i
$147$		0			0
$148$	1.35321	+	14.6035i	0.111233	+	1.20040i
$149$	4.42709			0.362681			0.181341	−	0.983420i	$-0.441956\pi$
$149$	4.42709			0.362681			0.181341	+	0.983420i	$0.441956\pi$
$150$		0			0
$151$	0.852651	+	9.20156i	0.0693877	+	0.748813i	0.957357	+	0.288909i	$0.0932925\pi$
$151$	0.852651	+	9.20156i	0.0693877	+	0.748813i	−0.887969	+	0.459904i	$0.847884\pi$
$152$	−0.607859	+	0.804935i	−0.0493038	+	0.0652888i
$153$		0			0
$154$	−0.205589	−	0.0796457i	−0.0165668	−	0.00641803i
$155$	14.6891	+	5.69059i	1.17986	+	0.457079i
$156$		0			0
$157$	−4.12524	+	5.46269i	−0.329230	+	0.435970i	−0.932283	−	0.361731i	$-0.882186\pi$
$157$	−4.12524	+	5.46269i	−0.329230	+	0.435970i	0.603053	+	0.797701i	$0.293951\pi$
$158$	0.240998	+	2.60079i	0.0191728	+	0.206907i
$159$		0			0
$160$	−12.9597			−1.02456
$161$	−0.0330843	−	0.357036i	−0.00260741	−	0.0281384i
$162$		0			0
$163$	2.43955	+	3.23048i	0.191080	+	0.253031i	0.883465	−	0.468498i	$-0.155205\pi$
$163$	2.43955	+	3.23048i	0.191080	+	0.253031i	−0.692385	+	0.721529i	$0.743440\pi$
$164$	3.40894	+	2.11073i	0.266194	+	0.164820i
$165$		0			0
$166$	0.703197	+	0.641049i	0.0545787	+	0.0497550i
$167$	−8.88521	−	11.7659i	−0.687558	−	0.910474i	0.311653	−	0.950196i	$-0.399117\pi$
$167$	−8.88521	−	11.7659i	−0.687558	−	0.910474i	−0.999211	+	0.0397220i	$0.987353\pi$
$168$		0			0
$169$	−4.52883	+	5.99714i	−0.348371	+	0.461318i
$170$	−2.35454	+	4.72856i	−0.180585	+	0.362664i
$171$		0			0
$172$	−6.45470	−	1.20659i	−0.492167	−	0.0920019i
$173$	19.8637	−	12.2991i	1.51021	−	0.935083i	0.513164	−	0.858291i	$-0.328473\pi$
$173$	19.8637	−	12.2991i	1.51021	−	0.935083i	0.997047	−	0.0767922i	$-0.0244678\pi$
$174$		0			0
$175$	5.64059e−5	0	0.000608716i	4.26388e−6	0	4.60146e-5i
$176$	1.36535	+	4.79871i	0.102917	+	0.361716i
$177$		0			0
$178$	9.62961	+	3.73053i	0.721770	+	0.279615i
$179$	1.21327	−	0.751227i	0.0906842	−	0.0561493i	−0.480341	−	0.877082i	$-0.659487\pi$
$179$	1.21327	−	0.751227i	0.0906842	−	0.0561493i	0.571025	+	0.820933i	$0.306546\pi$
$180$		0			0
$181$	−12.0774	−	7.47803i	−0.897708	−	0.555837i	−0.00176135	−	0.999998i	$-0.500561\pi$
$181$	−12.0774	−	7.47803i	−0.897708	−	0.555837i	−0.895947	+	0.444161i	$0.853502\pi$
$182$	0.0769064	−	0.270298i	0.00570068	−	0.0200358i
$183$		0			0
$184$	7.07762	−	6.45210i	0.521769	−	0.475655i
$185$	12.9030	+	17.0864i	0.948650	+	1.25622i
$186$		0			0
$187$	12.0522	+	2.25295i	0.881345	+	0.164752i
$188$	9.08878	−	8.28551i	0.662867	−	0.604283i
$189$		0			0
$190$	−0.0589037	+	0.635672i	−0.00427332	+	0.0461165i
$191$	1.76602	−	19.0584i	0.127785	−	1.37901i	−0.654485	−	0.756075i	$-0.727115\pi$
$191$	1.76602	−	19.0584i	0.127785	−	1.37901i	0.782270	−	0.622940i	$-0.214062\pi$
$192$		0			0
$193$	−0.318431	−	0.639496i	−0.0229212	−	0.0460319i	0.883407	−	0.468607i	$-0.155244\pi$
$193$	−0.318431	−	0.639496i	−0.0229212	−	0.0460319i	−0.906328	+	0.422575i	$0.861126\pi$
$194$	7.38463	−	9.77884i	0.530186	−	0.702080i
$195$		0			0
$196$	0.987434	+	10.6561i	0.0705310	+	0.761151i
$197$	−21.9262	+	8.49427i	−1.56218	+	0.605192i	−0.978400	−	0.206720i	$-0.933721\pi$
$197$	−21.9262	+	8.49427i	−1.56218	+	0.605192i	−0.583780	+	0.811912i	$0.698427\pi$
$198$		0			0
$199$	5.37497	+	10.7944i	0.381021	+	0.765194i	0.999792	−	0.0203774i	$-0.00648679\pi$
$199$	5.37497	+	10.7944i	0.381021	+	0.765194i	−0.618771	+	0.785571i	$0.712369\pi$
$200$	0.0138826	−	0.00859572i	0.000981645	−	0.000607809i
$201$		0			0
$202$	3.69577	−	3.36914i	0.260033	−	0.237052i
$203$	0.468352	−	0.0875502i	0.0328719	−	0.00614482i
$204$		0			0
$205$	5.85349			0.408825
$206$	2.91779	−	6.31133i	0.203292	−	0.439732i
$207$		0			0
$208$	−5.92988	+	2.29725i	−0.411163	+	0.159285i
$209$	1.45657	−	0.272279i	0.100753	−	0.0188340i
$210$		0			0
$211$	−4.18887	+	14.7223i	−0.288374	+	1.01353i	0.673309	+	0.739362i	$0.264873\pi$
$211$	−4.18887	+	14.7223i	−0.288374	+	1.01353i	−0.961682	+	0.274167i	$0.911598\pi$
$212$	−8.22426	+	5.09224i	−0.564844	+	0.349737i
$213$		0			0
$214$	−5.16031	+	10.3633i	−0.352752	+	0.708421i
$215$	−8.93914	+	3.46304i	−0.609644	+	0.236177i
$216$		0			0
$217$	−0.595319	+	0.230628i	−0.0404129	+	0.0156560i
$218$	−3.19389	+	4.22940i	−0.216318	+	0.286451i
$219$		0			0
$220$	8.98178	+	8.18797i	0.605551	+	0.552033i
$221$	−1.44198	+	15.5615i	−0.0969982	+	1.04678i
$222$		0			0
$223$	5.61901	+	3.47915i	0.376277	+	0.232981i	0.701520	−	0.712650i	$-0.252505\pi$
$223$	5.61901	+	3.47915i	0.376277	+	0.232981i	−0.325243	+	0.945630i	$0.605446\pi$
$224$	0.388150	−	0.353846i	0.0259344	−	0.0236423i
$225$		0			0
$226$	1.44021	+	2.89232i	0.0958010	+	0.192394i
$227$	−1.99133	−	2.63695i	−0.132169	−	0.175020i	0.727120	−	0.686510i	$-0.240858\pi$
$227$	−1.99133	−	2.63695i	−0.132169	−	0.175020i	−0.859289	+	0.511490i	$0.829094\pi$
$228$		0			0
$229$	−17.5686	−	6.80611i	−1.16097	−	0.449760i	−0.297774	−	0.954636i	$-0.596244\pi$
$229$	−17.5686	−	6.80611i	−1.16097	−	0.449760i	−0.863192	+	0.504876i	$0.831538\pi$
$230$	1.65880	−	5.83008i	0.109378	−	0.384424i
$231$		0			0
$232$	9.40478	+	8.57359i	0.617454	+	0.562884i
$233$	−6.55616	+	4.05940i	−0.429508	+	0.265940i	−0.724116	−	0.689678i	$-0.757752\pi$
$233$	−6.55616	+	4.05940i	−0.429508	+	0.265940i	0.294608	+	0.955618i	$0.404811\pi$
$234$		0			0
$235$	4.91357	−	17.2694i	0.320526	−	1.12653i
$236$	2.36394	+	8.30839i	0.153879	+	0.540830i
$237$		0			0
$238$	−0.0585864	−	0.205910i	−0.00379759	−	0.0133472i
$239$	−21.0566	+	13.0377i	−1.36204	+	0.843339i	−0.996179	−	0.0873308i	$-0.972166\pi$
$239$	−21.0566	+	13.0377i	−1.36204	+	0.843339i	−0.365860	+	0.930670i	$0.619225\pi$
$240$		0			0
$241$	−20.2347	+	3.78251i	−1.30343	+	0.243653i	−0.789273	−	0.614043i	$-0.789542\pi$
$241$	−20.2347	+	3.78251i	−1.30343	+	0.243653i	−0.514157	+	0.857696i	$0.671895\pi$
$242$	−0.496934	+	0.997979i	−0.0319442	+	0.0641525i
$243$		0			0
$244$	16.6386	−	3.11028i	1.06517	−	0.199116i
$245$	9.41531	+	12.4679i	0.601522	+	0.796544i
$246$		0			0
$247$	0.516876	+	1.81663i	0.0328880	+	0.115589i
$248$	−14.4981	−	8.97686i	−0.920632	−	0.570031i
$249$		0			0
$250$	3.41658	−	6.86141i	0.216083	−	0.433954i
$251$	−0.597562	−	6.44872i	−0.0377178	−	0.407039i	−0.993572	−	0.113199i	$-0.963890\pi$
$251$	−0.597562	−	6.44872i	−0.0377178	−	0.407039i	0.955855	−	0.293840i	$-0.0949333\pi$
$252$		0			0
$253$	−14.0695			−0.884539
$254$	0.472550	+	5.09962i	0.0296504	+	0.319979i
$255$		0			0
$256$	9.56500	+	1.78801i	0.597813	+	0.111751i
$257$	−14.6500	−	5.67545i	−0.913844	−	0.354025i	−0.142022	−	0.989864i	$-0.545360\pi$
$257$	−14.6500	−	5.67545i	−0.913844	−	0.354025i	−0.771822	+	0.635839i	$0.780654\pi$
$258$		0			0
$259$	−0.852970	−	0.159448i	−0.0530010	−	0.00990760i
$260$	−9.33573	+	12.3625i	−0.578978	+	0.766690i
$261$		0			0
$262$	−5.96239			−0.368358
$263$	−18.3971			−1.13441			−0.567207	−	0.823576i	$-0.691976\pi$
$263$	−18.3971			−1.13441			−0.567207	+	0.823576i	$0.691976\pi$
$264$		0			0
$265$	−6.29465	+	12.6414i	−0.386678	+	0.776553i
$266$	−0.0155919	−	0.0206470i	−0.000955999	−	0.00126595i
$267$		0			0
$268$	1.23379	+	4.33632i	0.0753657	+	0.264883i
$269$	0.0789573	+	0.0719791i	0.00481411	+	0.00438864i	0.676099	−	0.736811i	$-0.263669\pi$
$269$	0.0789573	+	0.0719791i	0.00481411	+	0.00438864i	−0.671285	+	0.741199i	$0.734257\pi$
$270$		0			0
$271$	6.58416	−	1.23079i	0.399960	−	0.0747654i	0.0200731	−	0.999799i	$-0.493610\pi$
$271$	6.58416	−	1.23079i	0.399960	−	0.0747654i	0.379886	+	0.925033i	$0.375963\pi$
$272$	−2.91943	+	3.86596i	−0.177017	+	0.234408i
$273$		0			0
$274$	3.63020	−	0.678603i	0.219309	−	0.0409959i
$275$	−0.0235788	−	0.00440764i	−0.00142185	−	0.000265791i
$276$		0			0
$277$	3.61007	+	12.6881i	0.216908	+	0.762352i	0.991524	+	0.129921i	$0.0414723\pi$
$277$	3.61007	+	12.6881i	0.216908	+	0.762352i	−0.774616	+	0.632431i	$0.782057\pi$
$278$	−0.429834	+	4.63865i	−0.0257797	+	0.278208i
$279$		0			0
$280$	0.133958	−	0.470813i	0.00800551	−	0.0281365i
$281$	−5.94712	−	2.30393i	−0.354775	−	0.137441i	0.177257	−	0.984165i	$-0.443278\pi$
$281$	−5.94712	−	2.30393i	−0.354775	−	0.137441i	−0.532033	+	0.846724i	$0.678572\pi$
$282$		0			0
$283$	−13.3762	−	12.1940i	−0.795133	−	0.724859i	0.170334	−	0.985386i	$-0.445515\pi$
$283$	−13.3762	−	12.1940i	−0.795133	−	0.724859i	−0.965467	+	0.260527i	$0.916104\pi$
$284$	8.46680	+	5.24242i	0.502412	+	0.311080i
$285$		0			0
$286$	−10.2823	−	3.98339i	−0.608005	−	0.235543i
$287$	−0.175315	+	0.159821i	−0.0103485	+	0.00943392i
$288$		0			0
$289$	−2.27089	−	4.56056i	−0.133582	−	0.268268i
$290$	7.91738	+	1.48002i	0.464925	+	0.0869095i
$291$		0			0
$292$	−1.95793	−	1.21230i	−0.114579	−	0.0709446i
$293$	−2.49698	+	26.9467i	−0.145875	+	1.57424i	0.536919	+	0.843634i	$0.319588\pi$
$293$	−2.49698	+	26.9467i	−0.145875	+	1.57424i	−0.682795	+	0.730610i	$0.739236\pi$
$294$		0			0
$295$	9.31956	+	8.49590i	0.542606	+	0.494651i
$296$	−10.3310	−	20.7473i	−0.600474	−	1.20592i
$297$		0			0
$298$	−2.82825	+	1.09567i	−0.163836	+	0.0634705i
$299$	−1.65467	−	17.8568i	−0.0956922	−	1.03268i
$300$		0			0
$301$	0.173179	−	0.347790i	0.00998185	−	0.0200463i
$302$	−2.82203	−	5.66741i	−0.162390	−	0.326123i
$303$		0			0
$304$	−0.160223	+	0.563124i	−0.00918940	+	0.0322974i
$305$	18.2620	−	16.6480i	1.04568	−	0.953263i
$306$		0			0
$307$	6.83321	−	2.64720i	0.389992	−	0.151084i	−0.158259	−	0.987398i	$-0.550588\pi$
$307$	6.83321	−	2.64720i	0.389992	−	0.151084i	0.548251	+	0.836314i	$0.315294\pi$
$308$	−0.492569			−0.0280667
$309$		0			0
$310$	−10.7925			−0.612974
$311$	−7.61089	+	2.94847i	−0.431574	+	0.167193i	−0.567223	−	0.823564i	$-0.691982\pi$
$311$	−7.61089	+	2.94847i	−0.431574	+	0.167193i	0.135649	+	0.990757i	$0.456688\pi$
$312$		0			0
$313$	−2.62943	+	2.39704i	−0.148624	+	0.135489i	−0.744593	−	0.667519i	$-0.767356\pi$
$313$	−2.62943	+	2.39704i	−0.148624	+	0.135489i	0.595969	+	0.803008i	$0.296768\pi$
$314$	1.28344	−	4.51081i	0.0724285	−	0.254560i
$315$		0			0
$316$	2.60102	+	5.22356i	0.146319	+	0.293848i
$317$	12.7233	−	25.5519i	0.714613	−	1.43514i	−0.177869	−	0.984054i	$-0.556920\pi$
$317$	12.7233	−	25.5519i	0.714613	−	1.43514i	0.892482	−	0.451083i	$-0.148962\pi$
$318$		0			0
$319$	−1.72501	−	18.6158i	−0.0965821	−	1.04229i
$320$	2.42831	−	0.940733i	0.135747	−	0.0525886i
$321$		0			0
$322$	0.109500	+	0.219905i	0.00610218	+	0.0122548i
$323$	1.06330	+	0.969323i	0.0591634	+	0.0539346i
$324$		0			0
$325$	0.00282107	−	0.0304442i	0.000156485	−	0.00168874i
$326$	−2.35803	−	1.46003i	−0.130599	−	0.0808634i
$327$		0			0
$328$	−6.22844	−	1.16430i	−0.343908	−	0.0642875i
$329$	0.324351	+	0.651385i	0.0178821	+	0.0359120i
$330$		0			0
$331$	8.97289	−	8.17987i	0.493195	−	0.449606i	−0.388485	−	0.921455i	$-0.627001\pi$
$331$	8.97289	−	8.17987i	0.493195	−	0.449606i	0.881679	+	0.471849i	$0.156413\pi$
$332$	1.98228	+	0.767941i	0.108792	+	0.0421462i
$333$		0			0
$334$	8.58830	+	5.31765i	0.469931	+	0.290969i
$335$	4.86407	+	4.43418i	0.265752	+	0.242265i
$336$		0			0
$337$	9.64413	+	3.73616i	0.525349	+	0.203521i	0.609287	−	0.792950i	$-0.291456\pi$
$337$	9.64413	+	3.73616i	0.525349	+	0.203521i	−0.0839379	+	0.996471i	$0.526750\pi$
$338$	1.40900	−	4.95213i	0.0766396	−	0.269360i
$339$		0			0
$340$	−1.08888	+	11.7509i	−0.0590530	+	0.637284i
$341$	6.85548	+	24.0945i	0.371245	+	1.30479i
$342$		0			0
$343$	−1.24555	−	0.232834i	−0.0672534	−	0.0125718i
$344$	10.2006	−	1.90682i	0.549977	−	0.102809i
$345$		0			0
$346$	−9.64603	+	12.7734i	−0.518574	+	0.686703i
$347$	−14.1838	+	2.65140i	−0.761424	+	0.142335i	−0.550120	−	0.835086i	$-0.685418\pi$
$347$	−14.1838	+	2.65140i	−0.761424	+	0.142335i	−0.211304	+	0.977420i	$0.567771\pi$
$348$		0			0
$349$	1.72722	+	1.57457i	0.0924559	+	0.0842847i	0.718604	−	0.695419i	$-0.244781\pi$
$349$	1.72722	+	1.57457i	0.0924559	+	0.0842847i	−0.626148	+	0.779704i	$0.715370\pi$
$350$	0.000114618	0	0.000402839i	6.12657e−6	0	2.15327e-5i
$351$		0			0
$352$	−12.4197	−	16.4464i	−0.661974	−	0.876595i
$353$	−4.93174	+	9.90428i	−0.262490	+	0.527151i	−0.986725	−	0.162402i	$-0.948076\pi$
$353$	−4.93174	+	9.90428i	−0.262490	+	0.527151i	0.724234	+	0.689554i	$0.242193\pi$
$354$		0			0
$355$	14.5383			0.771615
$356$	23.0715			1.22279
$357$		0			0
$358$	−0.589178	+	0.780197i	−0.0311390	+	0.0412347i
$359$	22.5359	+	4.21269i	1.18940	+	0.222337i	0.741005	−	0.671499i	$-0.234349\pi$
$359$	22.5359	+	4.21269i	1.18940	+	0.222337i	0.448394	+	0.893836i	$0.351996\pi$
$360$		0			0
$361$	−17.5548	−	6.80078i	−0.923938	−	0.357936i
$362$	9.56643	+	1.78828i	0.502801	+	0.0939897i
$363$		0			0
$364$	−0.0579298	−	0.625162i	−0.00303634	−	0.0327674i
$365$	−3.36197			−0.175973
$366$		0			0
$367$	3.25792	+	35.1585i	0.170062	+	1.83526i	0.471608	+	0.881809i	$0.343674\pi$
$367$	3.25792	+	35.1585i	0.170062	+	1.83526i	−0.301546	+	0.953452i	$0.597503\pi$
$368$	2.47786	−	4.97621i	0.129167	−	0.259403i
$369$		0			0
$370$	−12.4719	−	7.72225i	−0.648381	−	0.401461i
$371$	−0.156626	−	0.550482i	−0.00813159	−	0.0285796i
$372$		0			0
$373$	−19.9450	−	26.4115i	−1.03271	−	1.36753i	−0.927811	−	0.373051i	$-0.878312\pi$
$373$	−19.9450	−	26.4115i	−1.03271	−	1.36753i	−0.104903	−	0.994482i	$-0.533453\pi$
$374$	−8.25716	+	1.54353i	−0.426968	+	0.0798141i
$375$		0			0
$376$	−8.66331	+	17.3983i	−0.446776	+	0.897247i
$377$	23.4241	−	4.37872i	1.20640	−	0.225515i
$378$		0			0
$379$	32.2785	−	19.9860i	1.65803	−	1.02661i	0.712193	−	0.701984i	$-0.247702\pi$
$379$	32.2785	−	19.9860i	1.65803	−	1.02661i	0.945842	−	0.324628i	$-0.105239\pi$
$380$	0.390309	+	1.37179i	0.0200224	+	0.0703715i
$381$		0			0
$382$	3.58857	+	12.6125i	0.183607	+	0.645313i
$383$	10.4630	−	36.7738i	0.534636	−	1.87905i	0.0614061	−	0.998113i	$-0.480442\pi$
$383$	10.4630	−	36.7738i	0.534636	−	1.87905i	0.473230	−	0.880939i	$-0.343088\pi$
$384$		0			0
$385$	−0.611395	+	0.378560i	−0.0311596	+	0.0192932i
$386$	0.361701	+	0.329734i	0.0184101	+	0.0167830i
$387$		0			0
$388$	7.49193	−	26.3314i	0.380345	−	1.33677i
$389$	12.9969	+	5.03504i	0.658970	+	0.255286i	0.667424	−	0.744678i	$-0.267397\pi$
$389$	12.9969	+	5.03504i	0.658970	+	0.255286i	−0.00845380	+	0.999964i	$0.502691\pi$
$390$		0			0
$391$	−8.23281	−	10.9020i	−0.416351	−	0.551338i
$392$	−7.53847	−	15.1393i	−0.380750	−	0.764650i
$393$		0			0
$394$	11.9053	−	10.8532i	0.599782	−	0.546774i
$395$	7.24301	+	4.48468i	0.364435	+	0.225649i
$396$		0			0
$397$	0.974781	−	10.5196i	0.0489229	−	0.527962i	−0.935643	−	0.352948i	$-0.885179\pi$
$397$	0.974781	−	10.5196i	0.0489229	−	0.527962i	0.984566	−	0.175014i	$-0.0559971\pi$
$398$	−6.10533	−	5.56574i	−0.306033	−	0.278986i
$399$		0			0
$400$	0.00571154	−	0.00756330i	0.000285577	−	0.000378165i
$401$	−31.0037	+	12.0109i	−1.54825	+	0.599795i	−0.975512	−	0.219944i	$-0.929412\pi$
$401$	−31.0037	+	12.0109i	−1.54825	+	0.599795i	−0.572737	+	0.819739i	$0.694118\pi$
$402$		0			0
$403$	−29.7742	+	11.5346i	−1.48316	+	0.574578i
$404$	4.98010	−	10.0014i	0.247769	−	0.497587i
$405$		0			0
$406$	−0.277539	+	0.171845i	−0.0137740	+	0.00852852i
$407$	−9.31787	+	32.7489i	−0.461870	+	1.62330i
$408$		0			0
$409$	−3.77320	+	0.705334i	−0.186573	+	0.0348765i	−0.276207	−	0.961098i	$-0.589077\pi$
$409$	−3.77320	+	0.705334i	−0.186573	+	0.0348765i	0.0896338	+	0.995975i	$0.471430\pi$
$410$	−3.73951	+	1.44869i	−0.184681	+	0.0715459i
$411$		0			0
$412$	0.984892	−	15.5028i	0.0485221	−	0.763769i
$413$	−0.511093			−0.0251493
$414$		0			0
$415$	3.05068	−	0.570271i	0.149752	−	0.0279935i
$416$	19.4129	−	17.6972i	0.951794	−	0.867675i
$417$		0			0
$418$	−0.863142	+	0.534435i	−0.0422177	+	0.0261401i
$419$	11.0977	+	22.2872i	0.542159	+	1.08880i	0.981674	+	0.190567i	$0.0610326\pi$
$419$	11.0977	+	22.2872i	0.542159	+	1.08880i	−0.439515	+	0.898235i	$0.644850\pi$
$420$		0			0
$421$	25.3114	−	9.80568i	1.23360	−	0.477900i	0.345879	−	0.938279i	$-0.387581\pi$
$421$	25.3114	−	9.80568i	1.23360	−	0.477900i	0.887722	+	0.460379i	$0.152287\pi$
$422$	−0.967603	−	10.4421i	−0.0471022	−	0.508314i
$423$		0			0
$424$	9.21231	−	12.1991i	0.447389	−	0.592439i
$425$	−0.0103819	−	0.0208496i	−0.000503595	−	0.00101136i
$426$		0			0
$427$	−0.0924073	+	0.997234i	−0.00447190	+	0.0482595i
$428$	−2.38645	+	25.7538i	−0.115353	+	1.24486i
$429$		0			0
$430$	4.85370	−	4.42474i	0.234066	−	0.213380i
$431$	−24.5952	−	4.59764i	−1.18471	−	0.221461i	−0.445717	−	0.895174i	$-0.647051\pi$
$431$	−24.5952	−	4.59764i	−1.18471	−	0.221461i	−0.738993	+	0.673713i	$0.764698\pi$
$432$		0			0
$433$	2.87869	+	3.81200i	0.138341	+	0.183193i	0.861914	−	0.507055i	$-0.169266\pi$
$433$	2.87869	+	3.81200i	0.138341	+	0.183193i	−0.723573	+	0.690248i	$0.757501\pi$
$434$	0.323242	−	0.294674i	0.0155161	−	0.0141448i
$435$		0			0
$436$	−3.24030	+	11.3885i	−0.155182	+	0.545409i
$437$	−1.40374	−	0.869160i	−0.0671500	−	0.0415775i
$438$		0			0
$439$	28.1099	−	17.4049i	1.34161	−	0.830692i	0.347359	−	0.937732i	$-0.387079\pi$
$439$	28.1099	−	17.4049i	1.34161	−	0.830692i	0.994255	+	0.107041i	$0.0341375\pi$
$440$	−17.9100	−	6.93838i	−0.853827	−	0.330774i
$441$		0			0
$442$	−2.93013	−	10.2983i	−0.139372	−	0.489842i
$443$	−0.496270	+	5.35560i	−0.0235785	+	0.254452i	0.975784	+	0.218738i	$0.0701941\pi$
$443$	−0.496270	+	5.35560i	−0.0235785	+	0.254452i	−0.999362	+	0.0357141i	$0.988629\pi$
$444$		0			0
$445$	28.6372	−	17.7314i	1.35753	−	0.840549i
$446$	−4.45077	−	0.831994i	−0.210750	−	0.0393961i
$447$		0			0
$448$	−0.0470439	+	0.0944768i	−0.00222261	+	0.00446361i
$449$	14.7278	−	19.5028i	0.695050	−	0.920395i	−0.304433	−	0.952534i	$-0.598467\pi$
$449$	14.7278	−	19.5028i	0.695050	−	0.920395i	0.999483	+	0.0321386i	$0.0102318\pi$
$450$		0			0
$451$	5.60960	+	7.42831i	0.264146	+	0.349785i
$452$	5.33454	+	4.86307i	0.250916	+	0.228740i
$453$		0			0
$454$	1.92479	+	1.19178i	0.0903348	+	0.0559329i
$455$	−0.552368	−	0.731453i	−0.0258954	−	0.0342910i
$456$		0			0
$457$	−0.989793	−	10.6816i	−0.0463005	−	0.499662i	−0.987034	−	0.160514i	$-0.948685\pi$
$457$	−0.989793	−	10.6816i	−0.0463005	−	0.499662i	0.940733	−	0.339148i	$-0.110139\pi$
$458$	12.9082			0.603160
$459$		0			0
$460$	−1.24949	−	13.4842i	−0.0582579	−	0.628703i
$461$	9.34010	−	12.3683i	0.435012	−	0.576049i	−0.526721	−	0.850038i	$-0.676579\pi$
$461$	9.34010	−	12.3683i	0.435012	−	0.576049i	0.961733	+	0.273990i	$0.0883434\pi$
$462$		0			0
$463$	−5.96827	−	2.31212i	−0.277369	−	0.107453i	0.218539	−	0.975828i	$-0.429871\pi$
$463$	−5.96827	−	2.31212i	−0.277369	−	0.107453i	−0.495909	+	0.868375i	$0.665165\pi$
$464$	6.88802	+	2.66843i	0.319768	+	0.123879i
$465$		0			0
$466$	3.18374	−	4.21595i	0.147484	−	0.195300i
$467$	1.04836	+	11.3136i	0.0485124	+	0.523533i	0.984967	+	0.172743i	$0.0552631\pi$
$467$	1.04836	+	11.3136i	0.0485124	+	0.523533i	−0.936454	+	0.350789i	$0.885913\pi$
$468$		0			0
$469$	−0.266750			−0.0123174
$470$	1.13500	+	12.2486i	0.0523538	+	0.564988i
$471$		0			0
$472$	−8.22664	−	10.8938i	−0.378662	−	0.501429i
$473$	−12.9614	−	8.02537i	−0.595967	−	0.369007i
$474$		0			0
$475$	−0.00208022	−	0.00189637i	−9.54470e−5	−	8.70114e-5i
$476$	−0.288229	−	0.381677i	−0.0132110	−	0.0174941i
$477$		0			0
$478$	10.2253	−	13.5405i	0.467695	−	0.619328i
$479$	5.74451	−	11.5365i	0.262473	−	0.527118i	−0.724248	−	0.689540i	$-0.757813\pi$
$479$	5.74451	−	11.5365i	0.262473	−	0.527118i	0.986721	+	0.162422i	$0.0519306\pi$
$480$		0			0
$481$	−42.6603	−	7.97459i	−1.94514	−	0.363610i
$482$	11.9908	−	7.42439i	0.546166	−	0.338172i
$483$		0			0
$484$	−0.229813	+	2.48008i	−0.0104460	+	0.112731i
$485$	−10.9375	−	38.4414i	−0.496647	−	1.74553i
$486$		0			0
$487$	31.8857	+	12.3526i	1.44488	+	0.559748i	0.950837	−	0.309691i	$-0.100226\pi$
$487$	31.8857	+	12.3526i	1.44488	+	0.559748i	0.494040	+	0.869439i	$0.335520\pi$
$488$	−22.7432	+	14.0820i	−1.02954	+	0.637462i
$489$		0			0
$490$	−9.10069	−	5.63491i	−0.411127	−	0.254559i
$491$	−9.05587	+	31.8281i	−0.408686	+	1.43638i	0.435432	+	0.900222i	$0.356596\pi$
$491$	−9.05587	+	31.8281i	−0.408686	+	1.43638i	−0.844117	+	0.536159i	$0.819875\pi$
$492$		0			0
$493$	13.4154	−	12.2298i	0.604201	−	0.550802i
$494$	−0.779809	−	1.03263i	−0.0350853	−	0.0464604i
$495$		0			0
$496$	−9.72933	−	1.81873i	−0.436860	−	0.0816633i
$497$	−0.435430	+	0.396947i	−0.0195317	+	0.0178055i
$498$		0			0
$499$	0.0912586	−	0.984838i	0.00408530	−	0.0440874i	−0.993447	−	0.114289i	$-0.963541\pi$
$499$	0.0912586	−	0.984838i	0.00408530	−	0.0440874i	0.997533	+	0.0702021i	$0.0223644\pi$
$500$	1.58004	−	17.0513i	0.0706613	−	0.762557i
$501$		0			0
$502$	1.97776	+	3.97188i	0.0882717	+	0.177274i
$503$	−0.586592	+	0.776773i	−0.0261548	+	0.0346346i	−0.810907	−	0.585175i	$-0.801026\pi$
$503$	−0.586592	+	0.776773i	−0.0261548	+	0.0346346i	0.784752	+	0.619810i	$0.212790\pi$
$504$		0			0
$505$	−1.50500	−	16.2415i	−0.0669715	−	0.722737i
$506$	8.98829	−	3.48208i	0.399578	−	0.154797i
$507$		0			0
$508$	5.10009	+	10.2424i	0.226280	+	0.454431i
$509$	30.1953	−	18.6961i	1.33838	−	0.828692i	0.344464	−	0.938800i	$-0.388061\pi$
$509$	30.1953	−	18.6961i	1.33838	−	0.828692i	0.993920	+	0.110108i	$0.0351196\pi$
$510$		0			0
$511$	0.100693	−	0.0917934i	0.00445438	−	0.00406070i
$512$	14.6809	−	2.74433i	0.648810	−	0.121284i
$513$		0			0
$514$	10.7638			0.474772
$515$	−10.6921	−	19.9996i	−0.471149	−	0.881288i
$516$		0			0
$517$	26.6244	−	10.3143i	1.17094	−	0.453624i
$518$	0.584383	−	0.109240i	0.0256763	−	0.00479973i
$519$		0			0
$520$	6.69975	−	23.5472i	0.293803	−	1.03261i
$521$	4.83031	−	2.99080i	0.211620	−	0.131029i	−0.416530	−	0.909122i	$-0.636754\pi$
$521$	4.83031	−	2.99080i	0.211620	−	0.131029i	0.628150	+	0.778093i	$0.283813\pi$
$522$		0			0
$523$	−7.17682	+	14.4130i	−0.313821	+	0.630237i	−0.994775	−	0.102089i	$-0.967447\pi$
$523$	−7.17682	+	14.4130i	−0.313821	+	0.630237i	0.680955	+	0.732326i	$0.261565\pi$
$524$	−12.4211	+	4.81195i	−0.542617	+	0.210211i
$525$		0			0
$526$	11.7530	−	4.55314i	0.512455	−	0.198526i
$527$	−14.6586	+	19.4111i	−0.638539	+	0.845562i
$528$		0			0
$529$	−5.41222	−	4.93389i	−0.235314	−	0.214517i
$530$	0.892706	−	9.63383i	0.0387767	−	0.418467i
$531$		0			0
$532$	−0.0491447	−	0.0304291i	−0.00213069	−	0.00131927i
$533$	−8.76817	+	7.99325i	−0.379792	+	0.346226i
$534$		0			0
$535$	16.8308	+	33.8007i	0.727657	+	1.46133i
$536$	−4.29365	−	5.68571i	−0.185457	−	0.245585i
$537$		0			0
$538$	−0.0682563	−	0.0264426i	−0.00294274	−	0.00114002i
$539$	−6.79923	+	23.8968i	−0.292863	+	1.02931i
$540$		0			0
$541$	−0.619011	−	0.564303i	−0.0266134	−	0.0242613i	0.660280	−	0.751020i	$-0.270438\pi$
$541$	−0.619011	−	0.564303i	−0.0266134	−	0.0242613i	−0.686893	+	0.726758i	$0.741026\pi$
$542$	−3.90169	+	2.41582i	−0.167592	+	0.103769i
$543$		0			0
$544$	5.47634	−	19.2474i	0.234796	−	0.825223i
$545$	4.73054	+	16.6261i	0.202634	+	0.712184i
$546$		0			0
$547$	2.67184	+	9.39056i	0.114240	+	0.401511i	0.997761	−	0.0668799i	$-0.0213044\pi$
$547$	2.67184	+	9.39056i	0.114240	+	0.401511i	−0.883521	+	0.468391i	$0.844834\pi$
$548$	7.01491	−	4.34345i	0.299662	−	0.185543i
$549$		0			0
$550$	0.0161542	−	0.00301974i	0.000688817	−	0.000128762i
$551$	0.977910	−	1.96391i	0.0416604	−	0.0836653i
$552$		0			0
$553$	−0.339379	+	0.0634410i	−0.0144319	+	0.00269778i
$554$	−5.44649	−	7.21232i	−0.231399	−	0.306422i
$555$		0			0
$556$	2.84817	+	10.0103i	0.120790	+	0.424531i
$557$	−7.75742	−	4.80319i	−0.328692	−	0.203518i	0.352157	−	0.935941i	$-0.385448\pi$
$557$	−7.75742	−	4.80319i	−0.328692	−	0.203518i	−0.680850	+	0.732423i	$0.738389\pi$
$558$		0			0
$559$	8.66133	−	17.3943i	0.366335	−	0.735700i
$560$	−0.0262159	−	0.282914i	−0.00110782	−	0.0119553i
$561$		0			0
$562$	4.36953			0.184317
$563$	−3.37662	−	36.4396i	−0.142308	−	1.53574i	−0.705077	−	0.709130i	$-0.749088\pi$
$563$	−3.37662	−	36.4396i	−0.142308	−	1.53574i	0.562770	−	0.826614i	$-0.309736\pi$
$564$		0			0
$565$	10.3589	+	1.93642i	0.435802	+	0.0814656i
$566$	11.5633	+	4.47966i	0.486043	+	0.188294i
$567$		0			0
$568$	−15.4696	−	2.89177i	−0.649090	−	0.121336i
$569$	0.376849	−	0.499028i	0.0157983	−	0.0209203i	−0.790050	−	0.613043i	$-0.789945\pi$
$569$	0.376849	−	0.499028i	0.0157983	−	0.0209203i	0.805848	+	0.592123i	$0.201710\pi$
$570$		0			0
$571$	10.7728			0.450826			0.225413	−	0.974263i	$-0.427627\pi$
$571$	10.7728			0.450826			0.225413	+	0.974263i	$0.427627\pi$
$572$	−24.6353			−1.03005
$573$		0			0
$574$	0.0724458	−	0.145491i	0.00302383	−	0.00607267i
$575$	0.0161065	+	0.0213285i	0.000671689	+	0.000889460i
$576$		0			0
$577$	−6.99067	−	24.5697i	−0.291025	−	1.02285i	−0.960101	−	0.279654i	$-0.909780\pi$
$577$	−6.99067	−	24.5697i	−0.291025	−	1.02285i	0.669075	−	0.743195i	$-0.266690\pi$
$578$	2.57946	+	2.35149i	0.107291	+	0.0978091i
$579$		0			0
$580$	17.6882	−	3.30650i	0.734464	−	0.137295i
$581$	−0.0757990	+	0.100374i	−0.00314467	+	0.00416422i
$582$		0			0
$583$	−22.0748	+	4.12649i	−0.914244	+	0.170902i
$584$	3.57732	+	0.668717i	0.148030	+	0.0276717i
$585$		0			0
$586$	−5.07390	−	17.8329i	−0.209601	−	0.736671i
$587$	−2.65712	+	28.6749i	−0.109671	+	1.18354i	0.745973	+	0.665976i	$0.231985\pi$
$587$	−2.65712	+	28.6749i	−0.109671	+	1.18354i	−0.855644	+	0.517564i	$0.826839\pi$
$588$		0			0
$589$	−0.804485	+	2.82747i	−0.0331482	+	0.116504i
$590$	−8.05648	−	3.12110i	−0.331680	−	0.128494i
$591$		0			0
$592$	−9.94190	−	9.06324i	−0.408610	−	0.372497i
$593$	−12.6386	−	7.82549i	−0.519005	−	0.321354i	0.241809	−	0.970324i	$-0.422259\pi$
$593$	−12.6386	−	7.82549i	−0.519005	−	0.321354i	−0.760815	+	0.648969i	$0.775200\pi$
$594$		0			0
$595$	−0.651095	−	0.252236i	−0.0266923	−	0.0103407i
$596$	−5.00766	+	4.56508i	−0.205122	+	0.186993i
$597$		0			0
$598$	5.47650	+	10.9983i	0.223951	+	0.449754i
$599$	42.0543	+	7.86130i	1.71829	+	0.321204i	0.948425	−	0.317002i	$-0.102676\pi$
$599$	42.0543	+	7.86130i	1.71829	+	0.321204i	0.769865	+	0.638206i	$0.220323\pi$
$600$		0			0
$601$	−27.5719	−	17.0718i	−1.12468	−	0.696374i	−0.167504	−	0.985871i	$-0.553571\pi$
$601$	−27.5719	−	17.0718i	−1.12468	−	0.696374i	−0.957179	+	0.289497i	$0.906512\pi$
$602$	−0.0245601	+	0.265046i	−0.00100100	+	0.0108025i
$603$		0			0
$604$	−10.4528	−	9.52903i	−0.425320	−	0.387731i
$605$	1.62079	+	3.25499i	0.0658945	+	0.132334i
$606$		0			0
$607$	−10.7976	+	4.18300i	−0.438260	+	0.169783i	−0.570255	−	0.821467i	$-0.693156\pi$
$607$	−10.7976	+	4.18300i	−0.438260	+	0.169783i	0.131995	+	0.991250i	$0.457862\pi$
$608$	−0.223147	−	2.40814i	−0.00904980	−	0.0976629i
$609$		0			0
$610$	−7.54645	+	15.1553i	−0.305547	+	0.613621i
$611$	16.2220	+	32.5783i	0.656274	+	1.31798i
$612$		0			0
$613$	−5.54339	+	19.4830i	−0.223896	+	0.786911i	0.765720	+	0.643174i	$0.222383\pi$
$613$	−5.54339	+	19.4830i	−0.223896	+	0.786911i	−0.989616	+	0.143737i	$0.954088\pi$
$614$	−3.71024	+	3.38233i	−0.149733	+	0.136500i
$615$		0			0
$616$	0.725857	−	0.281198i	0.0292456	−	0.0113298i
$617$	7.58897			0.305520			0.152760	−	0.988263i	$-0.451184\pi$
$617$	7.58897			0.305520			0.152760	+	0.988263i	$0.451184\pi$
$618$		0			0
$619$	21.6254			0.869197			0.434598	−	0.900624i	$-0.356890\pi$
$619$	21.6254			0.869197			0.434598	+	0.900624i	$0.356890\pi$
$620$	−22.4834	+	8.71011i	−0.902954	+	0.349806i
$621$		0			0
$622$	4.13250	−	3.76727i	0.165698	−	0.151054i
$623$	−0.373569	+	1.31296i	−0.0149667	+	0.0526026i
$624$		0			0
$625$	−11.1284	−	22.3488i	−0.445136	−	0.893953i
$626$	1.08656	−	2.18212i	0.0434279	−	0.0872149i
$627$		0			0
$628$	−0.966749	−	10.4329i	−0.0385775	−	0.416318i
$629$	−30.8285	+	11.9430i	−1.22921	+	0.476200i
$630$		0			0
$631$	−4.99720	−	10.0357i	−0.198935	−	0.399516i	0.773123	−	0.634257i	$-0.218694\pi$
$631$	−4.99720	−	10.0357i	−0.198935	−	0.399516i	−0.972058	+	0.234740i	$0.924576\pi$
$632$	−6.81493	−	6.21263i	−0.271083	−	0.247125i
$633$		0			0
$634$	−1.80442	+	19.4728i	−0.0716626	+	0.773363i
$635$	14.2021	+	8.79357i	0.563593	+	0.348962i
$636$		0			0
$637$	−31.1291	−	5.81904i	−1.23338	−	0.230559i
$638$	5.70930	+	11.4658i	0.226033	+	0.453936i
$639$		0			0
$640$	17.8362	−	16.2598i	0.705037	−	0.642726i
$641$	−32.2930	−	12.5104i	−1.27550	−	0.494129i	−0.374205	−	0.927346i	$-0.622084\pi$
$641$	−32.2930	−	12.5104i	−1.27550	−	0.494129i	−0.901290	+	0.433216i	$0.857379\pi$
$642$		0			0
$643$	9.99765	+	6.19028i	0.394269	+	0.244121i	0.709220	−	0.704987i	$-0.249047\pi$
$643$	9.99765	+	6.19028i	0.394269	+	0.244121i	−0.314952	+	0.949108i	$0.601988\pi$
$644$	0.405588	+	0.369742i	0.0159824	+	0.0145699i
$645$		0			0
$646$	−0.919189	−	0.356096i	−0.0361650	−	0.0140104i
$647$	−4.18102	+	14.6948i	−0.164373	+	0.577711i	0.835240	+	0.549886i	$0.185329\pi$
$647$	−4.18102	+	14.6948i	−0.164373	+	0.577711i	−0.999613	+	0.0278252i	$0.991142\pi$
$648$		0			0
$649$	−1.85038	+	19.9688i	−0.0726338	+	0.783844i
$650$	0.00573246	+	0.0201475i	0.000224846	+	0.000790251i
$651$		0			0
$652$	−6.09064	−	1.13854i	−0.238528	−	0.0445886i
$653$	6.33139	−	1.18354i	0.247766	−	0.0463156i	−0.0584012	−	0.998293i	$-0.518600\pi$
$653$	6.33139	−	1.18354i	0.247766	−	0.0463156i	0.306168	+	0.951978i	$0.400953\pi$
$654$		0			0
$655$	−11.7193	+	15.5189i	−0.457912	+	0.606373i
$656$	−3.61525	+	0.675808i	−0.141152	+	0.0263859i
$657$		0			0
$658$	−0.368425	−	0.335864i	−0.0143627	−	0.0130933i
$659$	−10.8794	−	38.2371i	−0.423801	−	1.48951i	−0.820547	−	0.571578i	$-0.806331\pi$
$659$	−10.8794	−	38.2371i	−0.423801	−	1.48951i	0.396746	−	0.917928i	$-0.370139\pi$
$660$		0			0
$661$	18.3781	+	24.3366i	0.714827	+	0.946584i	0.999929	−	0.0119135i	$-0.00379227\pi$
$661$	18.3781	+	24.3366i	0.714827	+	0.946584i	−0.285102	+	0.958497i	$0.592028\pi$
$662$	−3.70789	+	7.44644i	−0.144111	+	0.289414i
$663$		0			0
$664$	−3.35952			−0.130375
$665$	−0.0843863			−0.00327236
$666$		0			0
$667$	−12.5534	+	16.6234i	−0.486070	+	0.643661i
$668$	22.1831	+	4.14673i	0.858289	+	0.160442i
$669$		0			0
$670$	−4.20484	−	1.62896i	−0.162447	−	0.0629324i
$671$	38.6281	+	7.22085i	1.49122	+	0.278758i
$672$		0			0
$673$	3.42447	+	36.9559i	0.132003	+	1.42454i	0.761814	+	0.647796i	$0.224309\pi$
$673$	3.42447	+	36.9559i	0.132003	+	1.42454i	−0.629811	+	0.776749i	$0.716867\pi$
$674$	−7.08583			−0.272936
$675$		0			0
$676$	−1.06133	−	11.4536i	−0.0408204	−	0.440523i
$677$	2.50662	−	5.03397i	0.0963372	−	0.193471i	−0.841753	−	0.539864i	$-0.818476\pi$
$677$	2.50662	−	5.03397i	0.0963372	−	0.193471i	0.938090	+	0.346393i	$0.112593\pi$
$678$		0			0
$679$	1.37717	+	0.852707i	0.0528509	+	0.0327239i
$680$	−5.10379	−	17.9380i	−0.195721	−	0.687889i
$681$		0			0
$682$	−10.3428	−	13.6961i	−0.396048	−	0.524452i
$683$	−37.6360	+	7.03538i	−1.44010	+	0.269201i	−0.845136	−	0.534551i	$-0.820481\pi$
$683$	−37.6360	+	7.03538i	−1.44010	+	0.269201i	−0.594964	+	0.803752i	$0.702834\pi$
$684$		0			0
$685$	5.36905	−	10.7825i	0.205141	−	0.411978i
$686$	0.853346	−	0.159518i	0.0325809	−	0.00609042i
$687$		0			0
$688$	5.12120	−	3.17091i	0.195244	−	0.120890i
$689$	−7.83344	−	27.5317i	−0.298430	−	1.04887i
$690$		0			0
$691$	11.8135	+	41.5201i	0.449406	+	1.57950i	0.773706	+	0.633544i	$0.218401\pi$
$691$	11.8135	+	41.5201i	0.449406	+	1.57950i	−0.324300	+	0.945954i	$0.605129\pi$
$692$	−9.78618	+	34.3949i	−0.372015	+	1.30750i
$693$		0			0
$694$	8.40511	−	5.20422i	0.319053	−	0.197550i
$695$	11.2286	+	10.2362i	0.425925	+	0.388282i
$696$		0			0
$697$	−2.47349	+	8.69341i	−0.0936901	+	0.329287i
$698$	−1.49313	−	0.578441i	−0.0565158	−	0.0218943i
$699$		0			0
$700$	0.000563887	0	0.000746707i	2.13129e−5	0	2.82229e-5i
$701$	15.4274	+	30.9824i	0.582685	+	1.17019i	0.968824	+	0.247749i	$0.0796909\pi$
$701$	15.4274	+	30.9824i	0.582685	+	1.17019i	−0.386139	+	0.922441i	$0.626191\pi$
$702$		0			0
$703$	−2.95277	+	2.69181i	−0.111366	+	0.101523i
$704$	3.52096	+	2.18009i	0.132701	+	0.0821651i
$705$		0			0
$706$	0.699418	−	7.54793i	0.0263230	−	0.284070i
$707$	0.488525	+	0.445350i	0.0183729	+	0.0167491i
$708$		0			0
$709$	4.80706	−	6.36558i	0.180533	−	0.239064i	−0.698748	−	0.715368i	$-0.746259\pi$
$709$	4.80706	−	6.36558i	0.180533	−	0.239064i	0.879281	+	0.476304i	$0.158024\pi$
$710$	−9.28783	+	3.59812i	−0.348566	+	0.135035i
$711$		0			0
$712$	−33.9985	+	13.1711i	−1.27415	+	0.493607i
$713$	12.4414	−	24.9858i	0.465935	−	0.935725i
$714$		0			0
$715$	−30.5782	+	18.9332i	−1.14356	+	0.708063i
$716$	−0.597738	+	2.10083i	−0.0223385	+	0.0785118i
$717$		0			0
$718$	−15.4397	+	2.88618i	−0.576204	+	0.107711i
$719$	26.8436	−	10.3993i	1.00110	−	0.387827i	0.195764	−	0.980651i	$-0.437281\pi$
$719$	26.8436	−	10.3993i	1.00110	−	0.387827i	0.805332	+	0.592824i	$0.201987\pi$
$720$		0			0
$721$	0.866292	+	0.307067i	0.0322624	+	0.0114358i
$722$	12.8981			0.480016
$723$		0			0
$724$	21.3724	−	3.99519i	0.794298	−	0.148480i
$725$	−0.0262458	+	0.0239262i	−0.000974744	+	0.000888596i
$726$		0			0
$727$	23.9598	−	14.8353i	0.888620	−	0.550210i	−0.00451969	−	0.999990i	$-0.501439\pi$
$727$	23.9598	−	14.8353i	0.888620	−	0.550210i	0.893140	+	0.449780i	$0.148497\pi$
$728$	0.442259	+	0.888176i	0.0163912	+	0.0329180i
$729$		0			0
$730$	2.14780	−	0.832060i	0.0794935	−	0.0307959i
$731$	−1.36581	−	14.7395i	−0.0505165	−	0.545160i
$732$		0			0
$733$	−10.5054	+	13.9114i	−0.388027	+	0.513830i	−0.949544	−	0.313635i	$-0.898453\pi$
$733$	−10.5054	+	13.9114i	−0.388027	+	0.513830i	0.561517	+	0.827465i	$0.310218\pi$
$734$	−10.7828	−	21.6548i	−0.398000	−	0.799292i
$735$		0			0
$736$	−2.11875	+	22.8649i	−0.0780981	+	0.842813i
$737$	−0.965752	+	10.4221i	−0.0355739	+	0.383904i
$738$		0			0
$739$	24.0734	−	21.9458i	0.885555	−	0.807290i	−0.0966078	−	0.995323i	$-0.530799\pi$
$739$	24.0734	−	21.9458i	0.885555	−	0.807290i	0.982163	+	0.188032i	$0.0602110\pi$
$740$	−32.2141	−	6.02186i	−1.18421	−	0.221368i
$741$		0			0
$742$	0.236300	+	0.312912i	0.00867486	+	0.0114874i
$743$	27.6622	−	25.2175i	1.01483	−	0.925139i	0.0176233	−	0.999845i	$-0.494390\pi$
$743$	27.6622	−	25.2175i	1.01483	−	0.925139i	0.997206	+	0.0747059i	$0.0238018\pi$
$744$		0			0
$745$	−2.70724	+	9.51495i	−0.0991855	+	0.348601i
$746$	19.2785	+	11.9368i	0.705837	+	0.437036i
$747$		0			0
$748$	−15.9559	+	9.87948i	−0.583406	+	0.361230i
$749$	−1.42697	−	0.552810i	−0.0521403	−	0.0201992i
$750$		0			0
$751$	5.26496	+	18.5044i	0.192121	+	0.675236i	0.996684	+	0.0813686i	$0.0259291\pi$
$751$	5.26496	+	18.5044i	0.192121	+	0.675236i	−0.804563	+	0.593868i	$0.797600\pi$
$752$	−1.04092	+	11.2333i	−0.0379583	+	0.409635i
$753$		0			0
$754$	−13.8808	+	8.59463i	−0.505509	+	0.312998i
$755$	−20.2979	−	3.79434i	−0.738717	−	0.138090i
$756$		0			0
$757$	−12.0239	+	24.1473i	−0.437017	+	0.877648i	0.561716	+	0.827330i	$0.310141\pi$
$757$	−12.0239	+	24.1473i	−0.437017	+	0.877648i	−0.998733	+	0.0503182i	$0.983976\pi$
$758$	−15.6748	+	20.7568i	−0.569333	+	0.753919i
$759$		0			0
$760$	−1.35830	−	1.79867i	−0.0492706	−	0.0652448i
$761$	13.7605	+	12.5443i	0.498817	+	0.454732i	0.883578	−	0.468285i	$-0.155128\pi$
$761$	13.7605	+	12.5443i	0.498817	+	0.454732i	−0.384761	+	0.923016i	$0.625716\pi$
$762$		0			0
$763$	−0.595633	−	0.368800i	−0.0215634	−	0.0133515i
$764$	17.6548	+	23.3787i	0.638728	+	0.845813i
$765$		0			0
$766$	2.41690	+	26.0825i	0.0873261	+	0.942398i
$767$	−25.5617			−0.922981
$768$		0			0
$769$	−3.70847	−	40.0208i	−0.133731	−	1.44319i	−0.753007	−	0.658012i	$-0.771397\pi$
$769$	−3.70847	−	40.0208i	−0.133731	−	1.44319i	0.619276	−	0.785173i	$-0.287426\pi$
$770$	0.296900	−	0.393159i	0.0106995	−	0.0141685i
$771$		0			0
$772$	1.01962	+	0.395003i	0.0366969	+	0.0142165i
$773$	−4.75032	−	1.84029i	−0.170857	−	0.0661905i	0.274294	−	0.961646i	$-0.411556\pi$
$773$	−4.75032	−	1.84029i	−0.170857	−	0.0661905i	−0.445151	+	0.895455i	$0.646850\pi$
$774$		0			0
$775$	0.0286779	−	0.0379756i	0.00103014	−	0.00136413i
$776$	3.99189	+	43.0793i	0.143300	+	1.54646i
$777$		0			0
$778$	−9.54923			−0.342357
$779$	0.100788	+	1.08768i	0.00361112	+	0.0389701i
$780$		0			0
$781$	13.9326	+	18.4497i	0.498547	+	0.660183i
$782$	7.95770	+	4.92720i	0.284567	+	0.176196i
$783$		0			0
$784$	−7.25458	−	6.61343i	−0.259092	−	0.236194i
$785$	−9.21808	−	12.2067i	−0.329007	−	0.435676i
$786$		0			0
$787$	−4.02897	+	5.33521i	−0.143617	+	0.190180i	−0.864140	−	0.503251i	$-0.832137\pi$
$787$	−4.02897	+	5.33521i	−0.143617	+	0.190180i	0.720523	+	0.693431i	$0.243902\pi$
$788$	16.0426	−	32.2179i	0.571494	−	1.14771i
$789$		0			0
$790$	−5.73713	−	1.07246i	−0.204118	−	0.0381562i
$791$	−0.363125	+	0.224838i	−0.0129113	+	0.00799431i
$792$		0			0
$793$	−4.62164	+	49.8755i	−0.164119	+	1.77113i
$794$	1.98077	+	6.96168i	0.0702949	+	0.247061i
$795$		0			0
$796$	−17.2107	−	6.66746i	−0.610017	−	0.236322i
$797$	13.0702	−	8.09273i	0.462970	−	0.286659i	−0.275060	−	0.961427i	$-0.588698\pi$
$797$	13.0702	−	8.09273i	0.462970	−	0.286659i	0.738030	+	0.674768i	$0.235756\pi$
$798$		0			0
$799$	23.5716	+	14.5949i	0.833905	+	0.516332i
$800$	−0.0107138	+	0.0376552i	−0.000378791	+	0.00133131i
$801$		0			0
$802$	16.8341	−	15.3463i	0.594434	−	0.541898i
$803$	−3.22189	−	4.26647i	−0.113698	−	0.150560i
$804$		0			0
$805$	0.787594	+	0.147227i	0.0277590	+	0.00518906i
$806$	16.1665	−	14.7378i	0.569442	−	0.519115i
$807$		0			0
$808$	−1.62914	+	17.5812i	−0.0573129	+	0.618505i
$809$	3.98032	−	42.9545i	0.139941	−	1.51020i	−0.579114	−	0.815246i	$-0.696602\pi$
$809$	3.98032	−	42.9545i	0.139941	−	1.51020i	0.719055	−	0.694953i	$-0.244575\pi$
$810$		0			0
$811$	0.670405	+	1.34635i	0.0235411	+	0.0472769i	0.906622	−	0.421944i	$-0.138652\pi$
$811$	0.670405	+	1.34635i	0.0235411	+	0.0472769i	−0.883081	+	0.469221i	$0.844535\pi$
$812$	−0.439492	+	0.581982i	−0.0154232	+	0.0204236i
$813$		0			0
$814$	−2.15237	−	23.2278i	−0.0754405	−	0.814133i
$815$	−8.43495	+	3.26772i	−0.295463	+	0.114463i
$816$		0			0
$817$	−0.797411	−	1.60142i	−0.0278979	−	0.0560265i
$818$	2.23595	−	1.38444i	0.0781781	−	0.0484059i
$819$		0			0
$820$	−6.62111	+	6.03594i	−0.231219	+	0.210784i
$821$	37.7320	−	7.05334i	1.31686	−	0.246163i	0.521993	−	0.852950i	$-0.325189\pi$
$821$	37.7320	−	7.05334i	1.31686	−	0.246163i	0.794865	+	0.606787i	$0.207542\pi$
$822$		0			0
$823$	8.12109			0.283083			0.141542	−	0.989932i	$-0.454794\pi$
$823$	8.12109			0.283083			0.141542	+	0.989932i	$0.454794\pi$
$824$	7.39891	+	23.4074i	0.257753	+	0.815436i
$825$		0			0
$826$	0.326513	−	0.126492i	0.0113608	−	0.00440121i
$827$	4.99330	−	0.933409i	0.173634	−	0.0324578i	−0.0962144	−	0.995361i	$-0.530673\pi$
$827$	4.99330	−	0.933409i	0.173634	−	0.0324578i	0.269848	+	0.962903i	$0.413026\pi$
$828$		0			0
$829$	−10.8735	+	38.2164i	−0.377653	+	1.32731i	0.507356	+	0.861736i	$0.330623\pi$
$829$	−10.8735	+	38.2164i	−0.377653	+	1.32731i	−0.885009	+	0.465574i	$0.845848\pi$
$830$	−1.80779	+	1.11934i	−0.0627494	+	0.0388528i
$831$		0			0
$832$	−2.35284	+	4.72515i	−0.0815702	+	0.163815i
$833$	−22.4955	+	8.71480i	−0.779423	+	0.301950i
$834$		0			0
$835$	30.7214	−	11.9015i	1.06316	−	0.411870i
$836$	−1.36681	+	1.80995i	−0.0472722	+	0.0625985i
$837$		0			0
$838$	−12.6057	−	11.4916i	−0.435457	−	0.396971i
$839$	−3.88024	+	41.8744i	−0.133961	+	1.44567i	0.617855	+	0.786292i	$0.288002\pi$
$839$	−3.88024	+	41.8744i	−0.133961	+	1.44567i	−0.751816	+	0.659373i	$0.770822\pi$
$840$		0			0
$841$	1.12212	+	0.694788i	0.0386938	+	0.0239582i
$842$	−13.7434	+	12.5287i	−0.473628	+	0.431769i
$843$		0			0
$844$	−10.4430	−	20.9725i	−0.359465	−	0.721902i
$845$	−10.1199	−	13.4010i	−0.348136	−	0.461007i
$846$		0			0
$847$	−0.137416	−	0.0532352i	−0.00472167	−	0.00182918i
$848$	2.42823	−	8.53435i	0.0833858	−	0.293071i
$849$		0			0
$850$	0.0117926	+	0.0107504i	0.000404483	+	0.000368735i
$851$	32.2551	−	19.9715i	1.10569	−	0.684615i
$852$		0			0
$853$	−0.0455209	+	0.159989i	−0.00155861	+	0.00547793i	−0.962601	−	0.270923i	$-0.912671\pi$
$853$	−0.0455209	+	0.159989i	−0.00155861	+	0.00547793i	0.961042	+	0.276401i	$0.0891417\pi$
$854$	−0.187773	−	0.659954i	−0.00642546	−	0.0225832i
$855$		0			0
$856$	−11.1857	−	39.3136i	−0.382319	−	1.34371i
$857$	−35.4467	+	21.9476i	−1.21084	+	0.749717i	−0.975028	−	0.222082i	$-0.928715\pi$
$857$	−35.4467	+	21.9476i	−1.21084	+	0.749717i	−0.235807	+	0.971800i	$0.575773\pi$
$858$		0			0
$859$	−5.30190	+	0.991097i	−0.180899	+	0.0338158i	−0.273419	−	0.961895i	$-0.588155\pi$
$859$	−5.30190	+	0.991097i	−0.180899	+	0.0338158i	0.0925207	+	0.995711i	$0.470508\pi$
$860$	6.54043	−	13.1350i	0.223027	−	0.447898i
$861$		0			0
$862$	16.8506	−	3.14992i	0.573933	−	0.107287i
$863$	13.5482	+	17.9407i	0.461185	+	0.610708i	0.967879	−	0.251418i	$-0.0808970\pi$
$863$	13.5482	+	17.9407i	0.461185	+	0.610708i	−0.506693	+	0.862126i	$0.669132\pi$
$864$		0			0
$865$	14.2869	+	50.2133i	0.485770	+	1.70730i
$866$	−2.78249	−	1.72285i	−0.0945530	−	0.0585447i
$867$		0			0
$868$	0.435572	−	0.874747i	0.0147843	−	0.0296908i
$869$	1.24998	+	13.4895i	0.0424028	+	0.457599i
$870$		0			0
$871$	−13.3412			−0.452049
$872$	−1.72651	−	18.6320i	−0.0584671	−	0.630960i
$873$		0			0
$874$	1.11189	+	0.207849i	0.0376103	+	0.00703058i
$875$	0.944778	+	0.366009i	0.0319393	+	0.0123734i
$876$		0			0
$877$	−35.6901	−	6.67163i	−1.20517	−	0.225285i	−0.457410	−	0.889256i	$-0.651223\pi$
$877$	−35.6901	−	6.67163i	−1.20517	−	0.225285i	−0.747758	+	0.663971i	$0.768870\pi$
$878$	−13.6505	+	18.0761i	−0.460681	+	0.610040i
$879$		0			0
$880$	−11.1486			−0.375819
$881$	−47.6107			−1.60405			−0.802023	−	0.597293i	$-0.796243\pi$
$881$	−47.6107			−1.60405			−0.802023	+	0.597293i	$0.796243\pi$
$882$		0			0
$883$	−16.5061	+	33.1488i	−0.555475	+	1.11554i	0.422410	+	0.906405i	$0.361184\pi$
$883$	−16.5061	+	33.1488i	−0.555475	+	1.11554i	−0.977886	+	0.209140i	$0.932933\pi$
$884$	−14.4154	−	19.0891i	−0.484843	−	0.642036i
$885$		0			0
$886$	−1.00843	−	3.54426i	−0.0338788	−	0.119072i
$887$	−25.4043	−	23.1591i	−0.852995	−	0.777607i	0.123682	−	0.992322i	$-0.460530\pi$
$887$	−25.4043	−	23.1591i	−0.852995	−	0.777607i	−0.976677	+	0.214715i	$0.931118\pi$
$888$		0			0
$889$	−0.665455	+	0.124395i	−0.0223186	+	0.00417208i
$890$	−13.9065	+	18.4152i	−0.466147	+	0.617279i
$891$		0			0
$892$	−9.94348	+	1.85876i	−0.332932	+	0.0622358i
$893$	3.29356	+	0.615672i	0.110215	+	0.0206027i
$894$		0			0
$895$	0.872642	+	3.06702i	0.0291692	+	0.102519i
$896$	−0.0902526	+	0.973980i	−0.00301513	+	0.0325384i
$897$		0			0
$898$	−4.58210	+	16.1044i	−0.152907	+	0.537412i
$899$	34.5850	+	13.3983i	1.15347	+	0.446859i
$900$		0			0
$901$	−16.1146	−	14.6904i	−0.536857	−	0.489410i
$902$	−5.42215	−	3.35725i	−0.180538	−	0.111784i
$903$		0			0
$904$	−10.6373	−	4.12091i	−0.353791	−	0.137059i
$905$	23.4577	−	21.3845i	0.779761	−	0.710846i
$906$		0			0
$907$	19.7148	+	39.5926i	0.654618	+	1.31465i	0.934961	+	0.354750i	$0.115434\pi$
$907$	19.7148	+	39.5926i	0.654618	+	1.31465i	−0.280344	+	0.959900i	$0.590448\pi$
$908$	4.97161	+	0.929356i	0.164989	+	0.0308418i
$909$		0			0
$910$	0.533910	+	0.330583i	0.0176989	+	0.0109587i
$911$	4.77030	−	51.4797i	0.158047	−	1.70560i	−0.434999	−	0.900431i	$-0.643251\pi$
$911$	4.77030	−	51.4797i	0.158047	−	1.70560i	0.593046	−	0.805168i	$-0.297925\pi$
$912$		0			0
$913$	3.64727	+	3.32492i	0.120707	+	0.110039i
$914$	3.27593	+	6.57896i	0.108358	+	0.217613i
$915$		0			0
$916$	26.8908	−	10.4175i	0.888497	−	0.344205i
$917$	−0.0727203	−	0.784777i	−0.00240144	−	0.0259156i
$918$		0			0
$919$	10.8482	−	21.7860i	0.357847	−	0.718655i	−0.640955	−	0.767578i	$-0.721462\pi$
$919$	10.8482	−	21.7860i	0.357847	−	0.718655i	0.998803	+	0.0489238i	$0.0155792\pi$
$920$	9.53913	+	19.1572i	0.314496	+	0.631593i
$921$		0			0
$922$	−2.90588	+	10.2131i	−0.0957000	+	0.336350i
$923$	−21.7775	+	19.8529i	−0.716817	+	0.653465i
$924$		0			0
$925$	0.0603125	−	0.0233652i	0.00198306	−	0.000768242i
$926$	4.38507			0.144102
$927$		0			0
$928$	−30.5132			−1.00165
$929$	1.34790	−	0.522178i	0.0442231	−	0.0171321i	−0.339029	−	0.940776i	$-0.610098\pi$
$929$	1.34790	−	0.522178i	0.0442231	−	0.0171321i	0.383252	+	0.923644i	$0.374804\pi$
$930$		0			0
$931$	−2.15463	+	1.96421i	−0.0706152	+	0.0643742i
$932$	3.23000	−	11.3523i	0.105802	−	0.371856i
$933$		0			0
$934$	−3.46978	−	6.96827i	−0.113535	−	0.228009i
$935$	−12.2123	+	24.5256i	−0.399384	+	0.802072i
$936$		0			0
$937$	−0.295728	−	3.19141i	−0.00966102	−	0.104259i	0.989538	−	0.144271i	$-0.0460838\pi$
$937$	−0.295728	−	3.19141i	−0.00966102	−	0.104259i	−0.999199	+	0.0400123i	$0.987260\pi$
$938$	0.170414	−	0.0660186i	0.00556420	−	0.00215558i
$939$		0			0
$940$	12.2498	+	24.6008i	0.399543	+	0.802390i
$941$	−33.2770	−	30.3359i	−1.08480	−	0.988924i	−0.0848255	−	0.996396i	$-0.527033\pi$
$941$	−33.2770	−	30.3359i	−1.08480	−	0.988924i	−0.999972	+	0.00747217i	$0.997622\pi$
$942$		0			0
$943$	0.956971	−	10.3274i	0.0311633	−	0.336305i
$944$	−6.73686	−	4.17129i	−0.219266	−	0.135764i
$945$		0			0
$946$	10.2666	+	1.91917i	0.333797	+	0.0623975i
$947$	−9.58635	−	19.2520i	−0.311514	−	0.625605i	0.682975	−	0.730442i	$-0.260686\pi$
$947$	−9.58635	−	19.2520i	−0.311514	−	0.625605i	−0.994489	+	0.104836i	$0.966568\pi$
$948$		0			0
$949$	5.03602	−	4.59094i	0.163476	−	0.149028i
$950$	0.00179829		0.000696660i	5.83441e−5		2.26026e-5i
$951$		0			0
$952$	0.642630	+	0.397900i	0.0208278	+	0.0128960i
$953$	−13.2210	−	12.0525i	−0.428269	−	0.390419i	0.430659	−	0.902515i	$-0.358281\pi$
$953$	−13.2210	−	12.0525i	−0.428269	−	0.390419i	−0.858928	+	0.512096i	$0.828869\pi$
$954$		0			0
$955$	39.8813	+	15.4501i	1.29053	+	0.499954i
$956$	10.3739	−	36.4604i	0.335515	−	1.17921i
$957$		0			0
$958$	−0.814685	+	8.79185i	−0.0263213	+	0.284052i
$959$	0.133594	+	0.469535i	0.00431399	+	0.0151621i
$960$		0			0
$961$	−18.3792	−	3.43567i	−0.592877	−	0.110828i
$962$	29.2272	−	5.46352i	0.942324	−	0.176151i
$963$		0			0
$964$	18.9878	−	25.1439i	0.611556	−	0.809831i
$965$	1.56917	−	0.293328i	0.0505133	−	0.00944256i
$966$		0			0
$967$	44.4102	+	40.4853i	1.42814	+	1.30192i	0.887614	+	0.460588i	$0.152362\pi$
$967$	44.4102	+	40.4853i	1.42814	+	1.30192i	0.540522	+	0.841330i	$0.318227\pi$
$968$	−1.07717	−	3.78587i	−0.0346217	−	0.121683i
$969$		0			0
$970$	16.5014	+	21.8514i	0.529828	+	0.701605i
$971$	−7.47407	+	15.0100i	−0.239854	+	0.481692i	−0.982082	−	0.188456i	$-0.939652\pi$
$971$	−7.47407	+	15.0100i	−0.239854	+	0.481692i	0.742227	+	0.670148i	$0.233769\pi$
$972$		0			0
$973$	−0.615787			−0.0197412
$974$	−23.4274			−0.750661
$975$		0			0
$976$	−9.35697	+	12.3906i	−0.299509	+	0.396615i
$977$	34.8720	+	6.51871i	1.11565	+	0.208552i	0.709123	−	0.705085i	$-0.249091\pi$
$977$	34.8720	+	6.51871i	1.11565	+	0.208552i	0.406531	+	0.913637i	$0.366738\pi$
$978$		0			0
$979$	49.9458	+	19.3491i	1.59628	+	0.618400i
$980$	−23.5065	−	4.39413i	−0.750889	−	0.140365i
$981$		0			0
$982$	−2.09185	−	22.5747i	−0.0667536	−	0.720386i
$983$	39.4661			1.25877			0.629386	−	0.777093i	$-0.283307\pi$
$983$	39.4661			1.25877			0.629386	+	0.777093i	$0.283307\pi$
$984$		0			0
$985$	−4.84811	−	52.3195i	−0.154474	−	1.66704i
$986$	−5.54369	+	11.1332i	−0.176547	+	0.354554i
$987$		0			0
$988$	−2.45791	−	1.52188i	−0.0781967	−	0.0484173i
$989$	4.64844	+	16.3376i	0.147812	+	0.519505i
$990$		0			0
$991$	20.0974	+	26.6132i	0.638414	+	0.845396i	0.996080	−	0.0884531i	$-0.0281923\pi$
$991$	20.0974	+	26.6132i	0.638414	+	0.845396i	−0.357667	+	0.933849i	$0.616428\pi$
$992$	40.1895	−	7.51273i	1.27602	−	0.238529i
$993$		0			0
$994$	0.179934	−	0.361356i	0.00570715	−	0.0114615i
$995$	−26.4868	+	4.95124i	−0.839687	+	0.156965i
$996$		0			0
$997$	−28.7308	+	17.7894i	−0.909914	+	0.563395i	−0.899679	−	0.436552i	$-0.856199\pi$
$997$	−28.7308	+	17.7894i	−0.909914	+	0.563395i	−0.0102356	+	0.999948i	$0.503258\pi$
$998$	0.185439	+	0.651750i	0.00586997	+	0.0206308i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	927.2.u.d.64.8	✓	288
3.2	odd	2	inner	927.2.u.d.64.11	yes	288
103.66	even	17	inner	927.2.u.d.478.8	yes	288
309.272	odd	34	inner	927.2.u.d.478.11	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
927.2.u.d.64.8	✓	288	1.1	even	1	trivial
927.2.u.d.64.11	yes	288	3.2	odd	2	inner
927.2.u.d.478.8	yes	288	103.66	even	17	inner
927.2.u.d.478.11	yes	288	309.272	odd	34	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 927 = 3^{2} \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	927.u (of order \(17\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.638851 + 0.247492i) q^{2} +(-1.13114 + 1.03117i) q^{4} +(-0.611516 + 2.14926i) q^{5} +(-0.0403670 - 0.0810678i) q^{7} +(1.07819 - 2.16529i) q^{8} +O(q^{10})\)	\(q+(-0.638851 + 0.247492i) q^{2} +(-1.13114 + 1.03117i) q^{4} +(-0.611516 + 2.14926i) q^{5} +(-0.0403670 - 0.0810678i) q^{7} +(1.07819 - 2.16529i) q^{8} +(-0.141256 - 1.52440i) q^{10} +(-3.31353 + 1.28367i) q^{11} +(-2.01891 - 4.05451i) q^{13} +(0.0458521 + 0.0417997i) q^{14} +(0.129547 - 1.39803i) q^{16} +(-2.93360 - 1.81641i) q^{17} +(-0.409898 - 0.0766232i) q^{19} +(-1.52454 - 3.06168i) q^{20} +(1.79915 - 1.64014i) q^{22} +(3.69198 + 1.43028i) q^{23} +(0.00573925 + 0.00355359i) q^{25} +(2.29324 + 2.09057i) q^{26} +(0.129255 + 0.0500738i) q^{28} +(-1.43979 + 5.06035i) q^{29} +(0.650460 - 7.01958i) q^{31} +(1.58716 + 5.57828i) q^{32} +(2.32368 + 0.434371i) q^{34} +(0.198920 - 0.0371847i) q^{35} +(5.77431 - 7.64642i) q^{37} +(0.280827 - 0.0524957i) q^{38} +(3.99444 + 3.64141i) q^{40} +(-0.716868 - 2.51953i) q^{41} +(2.58537 + 3.42358i) q^{43} +(2.42438 - 4.86881i) q^{44} -2.71261 q^{46} -8.03506 q^{47} +(4.21350 - 5.57958i) q^{49} +(-0.00454601 - 0.000849797i) q^{50} +(6.46456 + 2.50438i) q^{52} +(6.21215 + 1.16125i) q^{53} +(-0.732654 - 7.90660i) q^{55} -0.219059 q^{56} +(-0.332584 - 3.58915i) q^{58} +(2.51556 - 5.05192i) q^{59} +(-9.40237 - 5.82170i) q^{61} +(1.32174 + 4.64545i) q^{62} +(-0.702313 - 0.930013i) q^{64} +(9.94877 - 1.85975i) q^{65} +(1.31292 - 2.63670i) q^{67} +(5.19133 - 0.970428i) q^{68} +(-0.117878 + 0.0729867i) q^{70} +(-1.78049 - 6.25777i) q^{71} +(0.411735 + 1.44710i) q^{73} +(-1.79649 + 6.31402i) q^{74} +(0.542663 - 0.336003i) q^{76} +(0.237821 + 0.216803i) q^{77} +(1.04331 - 3.66686i) q^{79} +(2.92551 + 1.13335i) q^{80} +(1.08154 + 1.43219i) q^{82} +(-0.619075 - 1.24327i) q^{83} +(5.69786 - 5.19429i) q^{85} +(-2.49897 - 1.54730i) q^{86} +(-0.793088 + 8.55879i) q^{88} +(-11.1393 - 10.1548i) q^{89} +(-0.247193 + 0.327337i) q^{91} +(-5.65100 + 2.18921i) q^{92} +(5.13321 - 1.98862i) q^{94} +(0.415342 - 0.834119i) q^{95} +(-15.2069 + 9.41572i) q^{97} +(-1.31090 + 4.60733i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 20 q^{4} - 8 q^{7}+O(q^{10}) \) 288 * q - 20 * q^4 - 8 * q^7	\( 288 q - 20 q^{4} - 8 q^{7} + 72 q^{10} - 8 q^{13} - 32 q^{16} - 34 q^{19} - 28 q^{22} + 22 q^{25} + 88 q^{28} + 16 q^{31} + 110 q^{34} - 16 q^{37} + 28 q^{40} - 32 q^{43} - 176 q^{46} - 82 q^{49} - 32 q^{55} + 68 q^{58} - 24 q^{61} + 54 q^{64} + 28 q^{67} + 44 q^{70} + 48 q^{73} - 242 q^{82} + 18 q^{85} + 214 q^{88} + 114 q^{91} + 108 q^{94} + 196 q^{97}+O(q^{100}) \) 288 * q - 20 * q^4 - 8 * q^7 + 72 * q^10 - 8 * q^13 - 32 * q^16 - 34 * q^19 - 28 * q^22 + 22 * q^25 + 88 * q^28 + 16 * q^31 + 110 * q^34 - 16 * q^37 + 28 * q^40 - 32 * q^43 - 176 * q^46 - 82 * q^49 - 32 * q^55 + 68 * q^58 - 24 * q^61 + 54 * q^64 + 28 * q^67 + 44 * q^70 + 48 * q^73 - 242 * q^82 + 18 * q^85 + 214 * q^88 + 114 * q^91 + 108 * q^94 + 196 * q^97

Introduction

L-functions

Modular forms

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Representations

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Database

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