LMFDB - Embedded newform 882.2.bl.a.395.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(17,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 25]))

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

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

chi := DirichletCharacter("882.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.bl (of order $42$, degree $12$, 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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$20$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			395.7
Character	$\chi$	$=$	882.395
Dual form			882.2.bl.a.719.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.930874 - 0.365341i) q^{2} +(0.733052 + 0.680173i) q^{4} +(1.34171 + 0.914763i) q^{5} +(2.55989 + 0.668535i) q^{7} +(-0.433884 - 0.900969i) q^{8} +O(q^{10})$	\(q+(-0.930874 - 0.365341i) q^{2} +(0.733052 + 0.680173i) q^{4} +(1.34171 + 0.914763i) q^{5} +(2.55989 + 0.668535i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(-0.914763 - 1.34171i) q^{10} +(-0.648044 - 4.29949i) q^{11} +(1.49142 - 1.18937i) q^{13} +(-2.13870 - 1.55756i) q^{14} +(0.0747301 + 0.997204i) q^{16} +(0.908745 + 0.280311i) q^{17} +(2.29692 - 1.32613i) q^{19} +(0.361347 + 1.58316i) q^{20} +(-0.967534 + 4.23904i) q^{22} +(-1.27855 - 4.14496i) q^{23} +(-0.863309 - 2.19967i) q^{25} +(-1.82285 + 0.562276i) q^{26} +(1.42182 + 2.23124i) q^{28} +(-1.57164 + 0.358717i) q^{29} +(7.66784 + 4.42703i) q^{31} +(0.294755 - 0.955573i) q^{32} +(-0.743518 - 0.592936i) q^{34} +(2.82309 + 3.23868i) q^{35} +(-3.30398 + 3.06565i) q^{37} +(-2.62263 + 0.395298i) q^{38} +(0.242026 - 1.60574i) q^{40} +(-2.95143 + 1.42134i) q^{41} +(6.58296 + 3.17019i) q^{43} +(2.44935 - 3.59253i) q^{44} +(-0.324154 + 4.32554i) q^{46} +(-1.85342 + 4.72244i) q^{47} +(6.10612 + 3.42276i) q^{49} +2.36302i q^{50} +(1.90227 + 0.142555i) q^{52} +(2.33205 - 2.51335i) q^{53} +(3.06353 - 6.36148i) q^{55} +(-0.508368 - 2.59645i) q^{56} +(1.59405 + 0.240265i) q^{58} +(3.96539 - 2.70356i) q^{59} +(-6.01356 - 6.48108i) q^{61} +(-5.52042 - 6.92239i) q^{62} +(-0.623490 + 0.781831i) q^{64} +(3.08905 - 0.231492i) q^{65} +(-2.38545 + 4.13172i) q^{67} +(0.475497 + 0.823586i) q^{68} +(-1.44472 - 4.04619i) q^{70} +(8.72361 + 1.99111i) q^{71} +(7.10809 - 2.78972i) q^{73} +(4.19560 - 1.64665i) q^{74} +(2.58575 + 0.590181i) q^{76} +(1.21544 - 11.4395i) q^{77} +(-6.01655 - 10.4210i) q^{79} +(-0.811939 + 1.40632i) q^{80} +(3.26668 - 0.244804i) q^{82} +(5.11368 - 6.41235i) q^{83} +(0.962855 + 1.20738i) q^{85} +(-4.96970 - 5.35607i) q^{86} +(-3.59253 + 2.44935i) q^{88} +(5.36628 + 0.808837i) q^{89} +(4.61302 - 2.04759i) q^{91} +(1.88204 - 3.90810i) q^{92} +(3.45060 - 3.71887i) q^{94} +(4.29489 + 0.321857i) q^{95} -10.8504i q^{97} +(-4.43356 - 5.41697i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 20 q^{4} - 4 q^{7}+O(q^{10}) $ 240 * q - 20 * q^4 - 4 * q^7	$ 240 q - 20 q^{4} - 4 q^{7} - 12 q^{10} + 20 q^{16} + 24 q^{19} - 20 q^{22} + 24 q^{25} + 4 q^{28} + 12 q^{31} - 32 q^{37} + 44 q^{40} - 48 q^{43} + 204 q^{49} + 140 q^{55} + 136 q^{58} + 88 q^{61} + 40 q^{64} - 32 q^{67} - 16 q^{70} - 24 q^{73} - 28 q^{79} - 48 q^{82} - 112 q^{85} + 4 q^{88} + 80 q^{91} + 80 q^{94}+O(q^{100}) $ 240 * q - 20 * q^4 - 4 * q^7 - 12 * q^10 + 20 * q^16 + 24 * q^19 - 20 * q^22 + 24 * q^25 + 4 * q^28 + 12 * q^31 - 32 * q^37 + 44 * q^40 - 48 * q^43 + 204 * q^49 + 140 * q^55 + 136 * q^58 + 88 * q^61 + 40 * q^64 - 32 * q^67 - 16 * q^70 - 24 * q^73 - 28 * q^79 - 48 * q^82 - 112 * q^85 + 4 * q^88 + 80 * q^91 + 80 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{42}\right)$	$-1$

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 $

$2$	−0.930874	−	0.365341i	−0.658227	−	0.258335i
$2$	−0.930874	−	0.365341i	−0.658227	−	0.258335i
$3$		0			0
$3$		0			0
$4$	0.733052	+	0.680173i	0.366526	+	0.340086i
$5$	1.34171	+	0.914763i	0.600031	+	0.409094i	0.824887	−	0.565298i	$-0.191239\pi$
$5$	1.34171	+	0.914763i	0.600031	+	0.409094i	−0.224856	+	0.974392i	$0.572191\pi$
$6$		0			0
$7$	2.55989	+	0.668535i	0.967549	+	0.252682i
$7$	2.55989	+	0.668535i	0.967549	+	0.252682i
$8$	−0.433884	−	0.900969i	−0.153401	−	0.318541i
$9$		0			0
$10$	−0.914763	−	1.34171i	−0.289273	−	0.424286i
$11$	−0.648044	−	4.29949i	−0.195393	−	1.29635i	−0.844461	−	0.535616i	$-0.820079\pi$
$11$	−0.648044	−	4.29949i	−0.195393	−	1.29635i	0.649069	−	0.760730i	$-0.275159\pi$
$12$		0			0
$13$	1.49142	−	1.18937i	0.413646	−	0.329872i	−0.394455	−	0.918915i	$-0.629067\pi$
$13$	1.49142	−	1.18937i	0.413646	−	0.329872i	0.808102	+	0.589043i	$0.200495\pi$
$14$	−2.13870	−	1.55756i	−0.571590	−	0.416274i
$15$		0			0
$16$	0.0747301	+	0.997204i	0.0186825	+	0.249301i
$17$	0.908745	+	0.280311i	0.220403	+	0.0679853i	0.402990	−	0.915204i	$-0.367971\pi$
$17$	0.908745	+	0.280311i	0.220403	+	0.0679853i	−0.182587	+	0.983190i	$0.558447\pi$
$18$		0			0
$19$	2.29692	−	1.32613i	0.526949	−	0.304234i	−0.212824	−	0.977091i	$-0.568266\pi$
$19$	2.29692	−	1.32613i	0.526949	−	0.304234i	0.739773	+	0.672856i	$0.234933\pi$
$20$	0.361347	+	1.58316i	0.0807996	+	0.354006i
$21$		0			0
$22$	−0.967534	+	4.23904i	−0.206279	+	0.903767i
$23$	−1.27855	−	4.14496i	−0.266596	−	0.864283i	−0.985573	−	0.169250i	$-0.945866\pi$
$23$	−1.27855	−	4.14496i	−0.266596	−	0.864283i	0.718977	−	0.695034i	$-0.244611\pi$
$24$		0			0
$25$	−0.863309	−	2.19967i	−0.172662	−	0.439935i
$26$	−1.82285	+	0.562276i	−0.357491	+	0.110271i
$27$		0			0
$28$	1.42182	+	2.23124i	0.268698	+	0.421665i
$29$	−1.57164	+	0.358717i	−0.291846	+	0.0666120i	−0.365937	−	0.930639i	$-0.619252\pi$
$29$	−1.57164	+	0.358717i	−0.291846	+	0.0666120i	0.0740911	+	0.997251i	$0.476394\pi$
$30$		0			0
$31$	7.66784	+	4.42703i	1.37719	+	0.795118i	0.991820	−	0.127646i	$-0.0407420\pi$
$31$	7.66784	+	4.42703i	1.37719	+	0.795118i	0.385366	+	0.922764i	$0.374075\pi$
$32$	0.294755	−	0.955573i	0.0521058	−	0.168923i
$33$		0			0
$34$	−0.743518	−	0.592936i	−0.127512	−	0.101688i
$35$	2.82309	+	3.23868i	0.477189	+	0.547436i
$36$		0			0
$37$	−3.30398	+	3.06565i	−0.543171	+	0.503989i	−0.903356	−	0.428892i	$-0.858904\pi$
$37$	−3.30398	+	3.06565i	−0.543171	+	0.503989i	0.360185	+	0.932881i	$0.382714\pi$
$38$	−2.62263	+	0.395298i	−0.425446	+	0.0641257i
$39$		0			0
$40$	0.242026	−	1.60574i	0.0382677	−	0.253890i
$41$	−2.95143	+	1.42134i	−0.460936	+	0.221975i	−0.649916	−	0.760006i	$-0.725196\pi$
$41$	−2.95143	+	1.42134i	−0.460936	+	0.221975i	0.188980	+	0.981981i	$0.439482\pi$
$42$		0			0
$43$	6.58296	+	3.17019i	1.00389	+	0.483449i	0.862257	−	0.506470i	$-0.169050\pi$
$43$	6.58296	+	3.17019i	1.00389	+	0.483449i	0.141634	+	0.989919i	$0.454764\pi$
$44$	2.44935	−	3.59253i	0.369253	−	0.541595i
$45$		0			0
$46$	−0.324154	+	4.32554i	−0.0477939	+	0.637766i
$47$	−1.85342	+	4.72244i	−0.270349	+	0.688839i	0.729638	+	0.683833i	$0.239689\pi$
$47$	−1.85342	+	4.72244i	−0.270349	+	0.688839i	−0.999987	+	0.00500539i	$0.998407\pi$
$48$		0			0
$49$	6.10612	+	3.42276i	0.872303	+	0.488965i
$50$			2.36302i			0.334182i
$51$		0			0
$52$	1.90227	+	0.142555i	0.263797	+	0.0197689i
$53$	2.33205	−	2.51335i	0.320331	−	0.345235i	−0.552273	−	0.833664i	$-0.686239\pi$
$53$	2.33205	−	2.51335i	0.320331	−	0.345235i	0.872604	+	0.488429i	$0.162430\pi$
$54$		0			0
$55$	3.06353	−	6.36148i	0.413086	−	0.857782i
$56$	−0.508368	−	2.59645i	−0.0679335	−	0.346965i
$57$		0			0
$58$	1.59405	+	0.240265i	0.209309	+	0.0315483i
$59$	3.96539	−	2.70356i	0.516250	−	0.351973i	−0.276999	−	0.960870i	$-0.589340\pi$
$59$	3.96539	−	2.70356i	0.516250	−	0.351973i	0.793250	+	0.608897i	$0.208388\pi$
$60$		0			0
$61$	−6.01356	−	6.48108i	−0.769957	−	0.829817i	0.219352	−	0.975646i	$-0.429606\pi$
$61$	−6.01356	−	6.48108i	−0.769957	−	0.829817i	−0.989310	+	0.145829i	$0.953415\pi$
$62$	−5.52042	−	6.92239i	−0.701094	−	0.879144i
$63$		0			0
$64$	−0.623490	+	0.781831i	−0.0779362	+	0.0977289i
$65$	3.08905	−	0.231492i	0.383150	−	0.0287131i
$66$		0			0
$67$	−2.38545	+	4.13172i	−0.291429	+	0.504770i	−0.974148	−	0.225911i	$-0.927464\pi$
$67$	−2.38545	+	4.13172i	−0.291429	+	0.504770i	0.682719	+	0.730681i	$0.260797\pi$
$68$	0.475497	+	0.823586i	0.0576625	+	0.0998744i
$69$		0			0
$70$	−1.44472	−	4.04619i	−0.172677	−	0.483612i
$71$	8.72361	+	1.99111i	1.03530	+	0.236301i	0.706214	−	0.707998i	$-0.250402\pi$
$71$	8.72361	+	1.99111i	1.03530	+	0.236301i	0.329088	+	0.944299i	$0.393259\pi$
$72$		0			0
$73$	7.10809	−	2.78972i	0.831939	−	0.326512i	0.0891336	−	0.996020i	$-0.471590\pi$
$73$	7.10809	−	2.78972i	0.831939	−	0.326512i	0.742805	+	0.669508i	$0.233495\pi$
$74$	4.19560	−	1.64665i	0.487728	−	0.191419i
$75$		0			0
$76$	2.58575	+	0.590181i	0.296606	+	0.0676985i
$77$	1.21544	−	11.4395i	0.138512	−	1.30365i
$78$		0			0
$79$	−6.01655	−	10.4210i	−0.676914	−	1.17245i	−0.975905	−	0.218194i	$-0.929983\pi$
$79$	−6.01655	−	10.4210i	−0.676914	−	1.17245i	0.298991	−	0.954256i	$-0.403350\pi$
$80$	−0.811939	+	1.40632i	−0.0907775	+	0.157231i
$81$		0			0
$82$	3.26668	−	0.244804i	0.360745	−	0.0270341i
$83$	5.11368	−	6.41235i	0.561299	−	0.703847i	−0.417498	−	0.908678i	$-0.637093\pi$
$83$	5.11368	−	6.41235i	0.561299	−	0.703847i	0.978797	+	0.204831i	$0.0656645\pi$
$84$		0			0
$85$	0.962855	+	1.20738i	0.104436	+	0.130959i
$86$	−4.96970	−	5.35607i	−0.535897	−	0.577560i
$87$		0			0
$88$	−3.59253	+	2.44935i	−0.382965	+	0.261101i
$89$	5.36628	+	0.808837i	0.568825	+	0.0857366i	0.427157	−	0.904178i	$-0.359515\pi$
$89$	5.36628	+	0.808837i	0.568825	+	0.0857366i	0.141668	+	0.989914i	$0.454753\pi$
$90$		0			0
$91$	4.61302	−	2.04759i	0.483576	−	0.214646i
$92$	1.88204	−	3.90810i	0.196217	−	0.407448i
$93$		0			0
$94$	3.45060	−	3.71887i	0.355903	−	0.383572i
$95$	4.29489	+	0.321857i	0.440646	+	0.0330219i
$96$		0			0
$97$		−	10.8504i		−	1.10169i	−0.834607	−	0.550845i	$-0.814305\pi$
$97$		−	10.8504i		−	1.10169i	0.834607	−	0.550845i	$-0.185695\pi$
$98$	−4.43356	−	5.41697i	−0.447857	−	0.547197i
$99$		0			0
$100$	0.863309	−	2.19967i	0.0863309	−	0.219967i
$101$	−0.759129	+	10.1299i	−0.0755361	+	1.00796i	0.822708	+	0.568464i	$0.192462\pi$
$101$	−0.759129	+	10.1299i	−0.0755361	+	1.00796i	−0.898245	+	0.439496i	$0.855157\pi$
$102$		0			0
$103$	−8.23006	+	12.0713i	−0.810932	+	1.18942i	0.168111	+	0.985768i	$0.446233\pi$
$103$	−8.23006	+	12.0713i	−0.810932	+	1.18942i	−0.979044	+	0.203651i	$0.934719\pi$
$104$	−1.71869	−	0.827678i	−0.168531	−	0.0811605i
$105$		0			0
$106$	−3.08907	+	1.48762i	−0.300037	+	0.144490i
$107$	−2.21826	+	14.7172i	−0.214447	+	1.42276i	0.579596	+	0.814904i	$0.303210\pi$
$107$	−2.21826	+	14.7172i	−0.214447	+	1.42276i	−0.794044	+	0.607861i	$0.792028\pi$
$108$		0			0
$109$	−6.83146	+	1.02968i	−0.654335	+	0.0986252i	−0.467816	−	0.883826i	$-0.654959\pi$
$109$	−6.83146	+	1.02968i	−0.654335	+	0.0986252i	−0.186520	+	0.982451i	$0.559721\pi$
$110$	−5.17587	+	4.80250i	−0.493500	+	0.457901i
$111$		0			0
$112$	−0.475364	+	2.60270i	−0.0449177	+	0.245932i
$113$	10.5416	+	8.40667i	0.991673	+	0.790833i	0.977900	−	0.209072i	$-0.0670444\pi$
$113$	10.5416	+	8.40667i	0.991673	+	0.790833i	0.0137728	+	0.999905i	$0.495616\pi$
$114$		0			0
$115$	2.07621	−	6.73090i	0.193607	−	0.627660i
$116$	−1.39608	−	0.806029i	−0.129623	−	0.0748379i
$117$		0			0
$118$	−4.67900	+	1.06795i	−0.430737	+	0.0983129i
$119$	2.13889	+	1.32509i	0.196072	+	0.121471i
$120$		0			0
$121$	−7.55438	+	2.33022i	−0.686762	+	0.211838i
$122$	3.23006	+	8.23006i	0.292436	+	0.745115i
$123$		0			0
$124$	2.60978	+	8.46070i	0.234365	+	0.759794i
$125$	2.66060	−	11.6569i	0.237972	−	1.04262i
$126$		0			0
$127$	−3.53956	−	15.5078i	−0.314085	−	1.37610i	−0.847747	−	0.530400i	$-0.822042\pi$
$127$	−3.53956	−	15.5078i	−0.314085	−	1.37610i	0.533662	−	0.845698i	$-0.320815\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−2.96009	−	0.913067i	−0.259617	−	0.0800813i
$131$	0.825650	+	11.0175i	0.0721374	+	0.962606i	0.909432	+	0.415854i	$0.136517\pi$
$131$	0.825650	+	11.0175i	0.0721374	+	0.962606i	−0.837294	+	0.546753i	$0.815864\pi$
$132$		0			0
$133$	6.76643	−	1.85917i	0.586724	−	0.161211i
$134$	3.73004	−	2.97461i	0.322226	−	0.256967i
$135$		0			0
$136$	−0.141738	−	0.940373i	−0.0121540	−	0.0806363i
$137$	−1.65642	−	2.42952i	−0.141518	−	0.207568i	0.748936	−	0.662642i	$-0.230565\pi$
$137$	−1.65642	−	2.42952i	−0.141518	−	0.207568i	−0.890453	+	0.455074i	$0.849613\pi$
$138$		0			0
$139$	−1.71324	−	3.55757i	−0.145315	−	0.301749i	0.815589	−	0.578631i	$-0.196413\pi$
$139$	−1.71324	−	3.55757i	−0.145315	−	0.301749i	−0.960904	+	0.276882i	$0.910699\pi$
$140$	−0.133390	+	4.29431i	−0.0112735	+	0.362935i
$141$		0			0
$142$	−7.39315	−	5.04056i	−0.620419	−	0.422995i
$143$	−6.08020	−	5.64160i	−0.508452	−	0.471774i
$144$		0			0
$145$	−2.43683	−	0.956385i	−0.202368	−	0.0794234i
$146$	−7.63593			−0.631954
$147$		0			0
$148$	−4.50716			−0.370486
$149$	−7.19151	−	2.82246i	−0.589152	−	0.231225i	0.0519900	−	0.998648i	$-0.483444\pi$
$149$	−7.19151	−	2.82246i	−0.589152	−	0.231225i	−0.641142	+	0.767423i	$0.721539\pi$
$150$		0			0
$151$	6.70446	+	6.22083i	0.545601	+	0.506244i	0.904120	−	0.427279i	$-0.140528\pi$
$151$	6.70446	+	6.22083i	0.545601	+	0.506244i	−0.358519	+	0.933522i	$0.616718\pi$
$152$	−2.19139	−	1.49407i	−0.177745	−	0.121185i
$153$		0			0
$154$	−5.31073	+	10.2047i	−0.427951	+	0.822316i
$155$	6.23834	+	12.9541i	0.501076	+	1.04049i
$156$		0			0
$157$	−1.11591	−	1.63674i	−0.0890596	−	0.130626i	0.779123	−	0.626870i	$-0.215664\pi$
$157$	−1.11591	−	1.63674i	−0.0890596	−	0.130626i	−0.868183	+	0.496244i	$0.834712\pi$
$158$	1.79344	+	11.8987i	0.142678	+	0.946609i
$159$		0			0
$160$	1.26960	−	1.01247i	0.100371	−	0.0800429i
$161$	−0.501905	−	11.4654i	−0.0395557	−	0.903601i
$162$		0			0
$163$	0.421350	+	5.62253i	0.0330027	+	0.440390i	0.989090	+	0.147310i	$0.0470614\pi$
$163$	0.421350	+	5.62253i	0.0330027	+	0.440390i	−0.956088	+	0.293081i	$0.905320\pi$
$164$	−3.13031	−	0.965572i	−0.244436	−	0.0753985i
$165$		0			0
$166$	−7.10288	+	4.10085i	−0.551291	+	0.318288i
$167$	3.81465	+	16.7131i	0.295186	+	1.29330i	0.877203	+	0.480119i	$0.159406\pi$
$167$	3.81465	+	16.7131i	0.295186	+	1.29330i	−0.582017	+	0.813176i	$0.697736\pi$
$168$		0			0
$169$	−2.08303	+	9.12635i	−0.160233	+	0.702027i
$170$	−0.455190	−	1.47569i	−0.0349115	−	0.113180i
$171$		0			0
$172$	2.66938	+	6.80146i	0.203538	+	0.518606i
$173$	−16.6347	+	5.13111i	−1.26471	+	0.390111i	−0.853339	−	0.521357i	$-0.825426\pi$
$173$	−16.6347	+	5.13111i	−1.26471	+	0.390111i	−0.411371	+	0.911468i	$0.634950\pi$
$174$		0			0
$175$	−0.739420	−	6.20809i	−0.0558949	−	0.469287i
$176$	4.23904	−	0.967534i	0.319530	−	0.0729306i
$177$		0			0
$178$	−4.69983	−	2.71345i	−0.352267	−	0.203382i
$179$	6.08774	−	19.7360i	0.455019	−	1.47514i	−0.380037	−	0.924971i	$-0.624089\pi$
$179$	6.08774	−	19.7360i	0.455019	−	1.47514i	0.835056	−	0.550164i	$-0.185435\pi$
$180$		0			0
$181$	−18.7741	−	14.9718i	−1.39547	−	1.11285i	−0.979038	−	0.203679i	$-0.934710\pi$
$181$	−18.7741	−	14.9718i	−1.39547	−	1.11285i	−0.416429	−	0.909168i	$-0.636718\pi$
$182$	−5.04221	+	0.220726i	−0.373754	+	0.0163613i
$183$		0			0
$184$	−3.17974	+	2.95036i	−0.234413	+	0.217504i
$185$	−7.23733	+	1.09085i	−0.532099	+	0.0802010i
$186$		0			0
$187$	0.616287	−	4.08880i	0.0450674	−	0.299002i
$188$	−4.57073	+	2.20115i	−0.333355	+	0.160535i
$189$		0			0
$190$	−3.88041	−	1.86871i	−0.281515	−	0.135570i
$191$	−14.6498	+	21.4874i	−1.06002	+	1.55477i	−0.250115	+	0.968216i	$0.580468\pi$
$191$	−14.6498	+	21.4874i	−1.06002	+	1.55477i	−0.809910	+	0.586554i	$0.800484\pi$
$192$		0			0
$193$	−1.02211	+	13.6391i	−0.0735730	+	0.981763i	0.831229	+	0.555930i	$0.187638\pi$
$193$	−1.02211	+	13.6391i	−0.0735730	+	0.981763i	−0.904802	+	0.425833i	$0.859981\pi$
$194$	−3.96409	+	10.1003i	−0.284605	+	0.725162i
$195$		0			0
$196$	2.14804	+	6.66228i	0.153431	+	0.475877i
$197$			1.72423i			0.122846i	0.998112	+	0.0614231i	$0.0195639\pi$
$197$			1.72423i			0.122846i	−0.998112	+	0.0614231i	$0.980436\pi$
$198$		0			0
$199$	15.2005	+	1.13912i	1.07754	+	0.0807502i	0.601653	−	0.798758i	$-0.294509\pi$
$199$	15.2005	+	1.13912i	1.07754	+	0.0807502i	0.475884	+	0.879508i	$0.342128\pi$
$200$	−1.60726	+	1.73222i	−0.113651	+	0.122486i
$201$		0			0
$202$	4.40751	−	9.15229i	0.310111	−	0.643953i
$203$	−4.26305	−	0.132420i	−0.299207	−	0.00929403i
$204$		0			0
$205$	−5.26015	−	0.792841i	−0.367385	−	0.0553744i
$206$	12.0713	−	8.23006i	0.841046	−	0.573416i
$207$		0			0
$208$	1.29750	+	1.39837i	0.0899654	+	0.0969596i
$209$	−7.19017	−	9.01619i	−0.497355	−	0.623663i
$210$		0			0
$211$	−10.4970	+	13.1628i	−0.722643	+	0.906166i	−0.998484	−	0.0550374i	$-0.982472\pi$
$211$	−10.4970	+	13.1628i	−0.722643	+	0.906166i	0.275841	+	0.961203i	$0.411044\pi$
$212$	3.41902	−	0.256220i	0.234819	−	0.0175973i
$213$		0			0
$214$	7.44171	−	12.8894i	0.508705	−	0.881103i
$215$	5.93246	+	10.2753i	0.404590	+	0.700771i
$216$		0			0
$217$	16.6692	+	16.4590i	1.13158	+	1.11731i
$218$	6.73541	+	1.53731i	0.456180	+	0.104120i
$219$		0			0
$220$	6.57263	−	2.57957i	0.443127	−	0.173914i
$221$	1.68872	−	0.662772i	0.113595	−	0.0445829i
$222$		0			0
$223$	2.87058	+	0.655191i	0.192228	+	0.0438748i	0.317551	−	0.948241i	$-0.397140\pi$
$223$	2.87058	+	0.655191i	0.192228	+	0.0438748i	−0.125323	+	0.992116i	$0.539997\pi$
$224$	1.39338	−	2.24911i	0.0930988	−	0.150275i
$225$		0			0
$226$	−6.74162	−	11.6768i	−0.448446	−	0.776732i
$227$	−2.78755	+	4.82818i	−0.185016	+	0.320457i	−0.943582	−	0.331139i	$-0.892567\pi$
$227$	−2.78755	+	4.82818i	−0.185016	+	0.320457i	0.758566	+	0.651596i	$0.225900\pi$
$228$		0			0
$229$	−27.6962	+	2.07555i	−1.83022	+	0.137156i	−0.944802	−	0.327641i	$-0.893746\pi$
$229$	−27.6962	+	2.07555i	−1.83022	+	0.137156i	−0.885417	+	0.464797i	$0.846127\pi$
$230$	−4.39176	+	5.50710i	−0.289584	+	0.363127i
$231$		0			0
$232$	1.00510	+	1.26036i	0.0659882	+	0.0827466i
$233$	−16.3610	−	17.6330i	−1.07184	−	1.15517i	−0.987318	−	0.158752i	$-0.949253\pi$
$233$	−16.3610	−	17.6330i	−1.07184	−	1.15517i	−0.0845261	−	0.996421i	$-0.526938\pi$
$234$		0			0
$235$	−6.80667	+	4.64071i	−0.444018	+	0.302726i
$236$	4.74573	+	0.715303i	0.308920	+	0.0465623i
$237$		0			0
$238$	−1.50693	−	2.01492i	−0.0976797	−	0.130608i
$239$	−6.87773	+	14.2818i	−0.444884	+	0.923810i	0.551114	+	0.834430i	$0.314203\pi$
$239$	−6.87773	+	14.2818i	−0.444884	+	0.923810i	−0.995998	+	0.0893802i	$0.971511\pi$
$240$		0			0
$241$	−12.8852	+	13.8869i	−0.830006	+	0.894534i	−0.995793	−	0.0916277i	$-0.970793\pi$
$241$	−12.8852	+	13.8869i	−0.830006	+	0.894534i	0.165787	+	0.986162i	$0.446984\pi$
$242$	7.88350	+	0.590787i	0.506770	+	0.0379772i
$243$		0			0
$244$		−	8.84122i		−	0.566001i
$245$	5.06164	+	10.1780i	0.323376	+	0.650249i
$246$		0			0
$247$	1.84842	−	4.70970i	0.117612	−	0.299671i
$248$	0.661665	−	8.82931i	0.0420158	−	0.560661i
$249$		0			0
$250$	−6.73542	+	9.87904i	−0.425985	+	0.624806i
$251$	13.3145	+	6.41192i	0.840402	+	0.404716i	0.804006	−	0.594621i	$-0.202698\pi$
$251$	13.3145	+	6.41192i	0.840402	+	0.404716i	0.0363963	+	0.999337i	$0.488412\pi$
$252$		0			0
$253$	−16.9927	+	8.18323i	−1.06832	+	0.514475i
$254$	−2.37076	+	15.7290i	−0.148755	+	0.986924i
$255$		0			0
$256$	−0.988831	+	0.149042i	−0.0618019	+	0.00931514i
$257$	−3.43748	+	3.18952i	−0.214424	+	0.198957i	−0.780071	−	0.625691i	$-0.784817\pi$
$257$	−3.43748	+	3.18952i	−0.214424	+	0.198957i	0.565647	+	0.824648i	$0.308627\pi$
$258$		0			0
$259$	−10.5073	+	5.63891i	−0.652894	+	0.350385i
$260$	2.42189	+	1.93139i	0.150199	+	0.119780i
$261$		0			0
$262$	3.25658	−	10.5576i	0.201192	−	0.652249i
$263$	24.2357	+	13.9925i	1.49444	+	0.862815i	0.999980	−	0.00638598i	$-0.00203274\pi$
$263$	24.2357	+	13.9925i	1.49444	+	0.862815i	0.494459	+	0.869201i	$0.335366\pi$
$264$		0			0
$265$	5.42805	−	1.23892i	0.333442	−	0.0761060i
$266$	−6.97792	−	0.741398i	−0.427844	−	0.0454580i
$267$		0			0
$268$	−4.55894	+	1.40625i	−0.278482	+	0.0859002i
$269$	−9.27112	−	23.6224i	−0.565270	−	1.44028i	−0.872483	−	0.488644i	$-0.837492\pi$
$269$	−9.27112	−	23.6224i	−0.565270	−	1.44028i	0.307214	−	0.951641i	$-0.400603\pi$
$270$		0			0
$271$	−6.48974	−	21.0392i	−0.394224	−	1.27804i	−0.907585	−	0.419869i	$-0.862076\pi$
$271$	−6.48974	−	21.0392i	−0.394224	−	1.27804i	0.513361	−	0.858173i	$-0.328400\pi$
$272$	−0.211616	+	0.927151i	−0.0128311	+	0.0562168i
$273$		0			0
$274$	0.654314	+	2.86674i	0.0395286	+	0.173186i
$275$	−8.89802	+	5.13728i	−0.536571	+	0.309789i
$276$		0			0
$277$	4.07244	+	1.25618i	0.244689	+	0.0754767i	0.414674	−	0.909970i	$-0.363896\pi$
$277$	4.07244	+	1.25618i	0.244689	+	0.0754767i	−0.169985	+	0.985447i	$0.554372\pi$
$278$	0.295080	+	3.93756i	0.0176977	+	0.236159i
$279$		0			0
$280$	1.69306	−	3.94872i	0.101179	−	0.235981i
$281$	−2.83257	+	2.25890i	−0.168977	+	0.134755i	−0.704327	−	0.709876i	$-0.748751\pi$
$281$	−2.83257	+	2.25890i	−0.168977	+	0.134755i	0.535350	+	0.844630i	$0.320180\pi$
$282$		0			0
$283$	−1.45338	−	9.64252i	−0.0863943	−	0.573188i	−0.989585	−	0.143949i	$-0.954020\pi$
$283$	−1.45338	−	9.64252i	−0.0863943	−	0.573188i	0.903191	−	0.429239i	$-0.141218\pi$
$284$	5.04056	+	7.39315i	0.299102	+	0.438703i
$285$		0			0
$286$	3.59879	+	7.47296i	0.212801	+	0.441886i
$287$	−8.50557	+	1.66533i	−0.502068	+	0.0983015i
$288$		0			0
$289$	−13.2988	−	9.06698i	−0.782283	−	0.533352i
$290$	1.91897	+	1.78055i	0.112686	+	0.104557i
$291$		0			0
$292$	7.10809	+	2.78972i	0.415969	+	0.163256i
$293$	10.8206			0.632146			0.316073	−	0.948735i	$-0.397636\pi$
$293$	10.8206			0.632146			0.316073	+	0.948735i	$0.397636\pi$
$294$		0			0
$295$	7.79353			0.453757
$296$	4.19560	+	1.64665i	0.243864	+	0.0957096i
$297$		0			0
$298$	5.66323	+	5.25471i	0.328062	+	0.304397i
$299$	−6.83675	−	4.66122i	−0.395379	−	0.269565i
$300$		0			0
$301$	14.7323	+	12.5163i	0.849156	+	0.721426i
$302$	−3.96828	−	8.24022i	−0.228349	−	0.474171i
$303$		0			0
$304$	1.49407	+	2.19139i	0.0856906	+	0.125685i
$305$	−2.13981	−	14.1967i	−0.122525	−	0.812901i
$306$		0			0
$307$	1.86039	−	1.48361i	0.106178	−	0.0846744i	−0.568962	−	0.822364i	$-0.692655\pi$
$307$	1.86039	−	1.48361i	0.106178	−	0.0846744i	0.675140	+	0.737690i	$0.264083\pi$
$308$	8.67181	−	7.55903i	0.494122	−	0.430716i
$309$		0			0
$310$	−1.07446	−	14.3377i	−0.0610254	−	0.814327i
$311$	−31.0901	−	9.59002i	−1.76296	−	0.543800i	−0.767676	−	0.640838i	$-0.778587\pi$
$311$	−31.0901	−	9.59002i	−1.76296	−	0.543800i	−0.995281	+	0.0970380i	$0.969063\pi$
$312$		0			0
$313$	−5.52052	+	3.18727i	−0.312038	+	0.180155i	−0.647838	−	0.761778i	$-0.724327\pi$
$313$	−5.52052	+	3.18727i	−0.312038	+	0.180155i	0.335800	+	0.941933i	$0.390993\pi$
$314$	0.440804	+	1.93129i	0.0248760	+	0.108989i
$315$		0			0
$316$	2.67762	−	11.7314i	0.150628	−	0.659943i
$317$	−1.55148	−	5.02977i	−0.0871398	−	0.282500i	0.901506	−	0.432767i	$-0.142463\pi$
$317$	−1.55148	−	5.02977i	−0.0871398	−	0.282500i	−0.988645	+	0.150267i	$0.951987\pi$
$318$		0			0
$319$	2.56079	+	6.52480i	0.143377	+	0.365318i
$320$	−1.55173	+	0.478646i	−0.0867445	+	0.0267571i
$321$		0			0
$322$	−3.72157	+	10.8562i	−0.207395	+	0.604993i
$323$	2.45904	−	0.561259i	0.136825	−	0.0312293i
$324$		0			0
$325$	−3.90379	−	2.25385i	−0.216543	−	0.125021i
$326$	1.66192	−	5.38780i	0.0920450	−	0.298403i
$327$		0			0
$328$	2.56116	+	2.04246i	0.141416	+	0.112776i
$329$	−7.90168	+	10.8499i	−0.435634	+	0.598173i
$330$		0			0
$331$	2.82757	−	2.62360i	0.155417	−	0.144206i	−0.598632	−	0.801025i	$-0.704289\pi$
$331$	2.82757	−	2.62360i	0.155417	−	0.144206i	0.754049	+	0.656818i	$0.228098\pi$
$332$	8.11009	−	1.22240i	0.445099	−	0.0670879i
$333$		0			0
$334$	2.55501	−	16.9514i	0.139804	−	0.927539i
$335$	−6.98013	+	3.36145i	−0.381365	+	0.183656i
$336$		0			0
$337$	−2.27361	−	1.09491i	−0.123851	−	0.0596436i	0.370932	−	0.928660i	$-0.379038\pi$
$337$	−2.27361	−	1.09491i	−0.123851	−	0.0596436i	−0.494783	+	0.869016i	$0.664753\pi$
$338$	5.27327	−	7.73447i	0.286828	−	0.420699i
$339$		0			0
$340$	−0.115406	+	1.53998i	−0.00625875	+	0.0835172i
$341$	14.0649	−	35.8368i	0.761657	−	1.94067i
$342$		0			0
$343$	13.3428	+	12.8441i	0.720443	+	0.693514i
$344$		−	7.30653i		−	0.393942i
$345$		0			0
$346$	17.3594	+	1.30091i	0.933246	+	0.0699371i
$347$	11.9977	−	12.9304i	0.644069	−	0.694142i	−0.323649	−	0.946177i	$-0.604910\pi$
$347$	11.9977	−	12.9304i	0.644069	−	0.694142i	0.967718	+	0.252036i	$0.0811000\pi$
$348$		0			0
$349$	9.77114	−	20.2900i	0.523037	−	1.08610i	−0.457399	−	0.889262i	$-0.651219\pi$
$349$	9.77114	−	20.2900i	0.523037	−	1.08610i	0.980436	−	0.196837i	$-0.0630668\pi$
$350$	−1.57976	+	6.04909i	−0.0844418	+	0.323337i
$351$		0			0
$352$	−4.29949	−	0.648044i	−0.229164	−	0.0345409i
$353$	16.9246	−	11.5390i	0.900806	−	0.614159i	−0.0218595	−	0.999761i	$-0.506959\pi$
$353$	16.9246	−	11.5390i	0.900806	−	0.614159i	0.922665	+	0.385602i	$0.126006\pi$
$354$		0			0
$355$	9.88317	+	10.6515i	0.524544	+	0.565324i
$356$	3.38361	+	4.24292i	0.179331	+	0.224874i
$357$		0			0
$358$	−12.8773	+	16.1476i	−0.680585	+	0.853427i
$359$	−30.6677	+	2.29823i	−1.61858	+	0.121296i	−0.852953	−	0.521988i	$-0.825191\pi$
$359$	−30.6677	+	2.29823i	−1.61858	+	0.121296i	−0.765628	+	0.643283i	$0.777572\pi$
$360$		0			0
$361$	−5.98278	+	10.3625i	−0.314883	+	0.545394i
$362$	12.0065	+	20.7958i	0.631046	+	1.09300i
$363$		0			0
$364$	4.77430	+	1.63666i	0.250241	+	0.0857842i
$365$	12.0889	+	2.75922i	0.632763	+	0.144424i
$366$		0			0
$367$	29.7416	−	11.6727i	1.55250	−	0.609311i	0.574609	−	0.818428i	$-0.305154\pi$
$367$	29.7416	−	11.6727i	1.55250	−	0.609311i	0.977891	+	0.209117i	$0.0670588\pi$
$368$	4.03782	−	1.58473i	0.210486	−	0.0826097i
$369$		0			0
$370$	7.13557	+	1.62865i	0.370961	+	0.0846694i
$371$	7.65005	−	4.87485i	0.397171	−	0.253090i
$372$		0			0
$373$	9.19831	+	15.9319i	0.476271	+	0.824925i	0.999630	−	0.0271870i	$-0.00865495\pi$
$373$	9.19831	+	15.9319i	0.476271	+	0.824925i	−0.523360	+	0.852112i	$0.675322\pi$
$374$	−2.06749	+	3.58100i	−0.106907	+	0.185169i
$375$		0			0
$376$	5.05894	−	0.379115i	0.260895	−	0.0195514i
$377$	−1.91733	+	2.40426i	−0.0987478	+	0.123826i
$378$		0			0
$379$	−0.104337	−	0.130835i	−0.00535945	−	0.00672053i	0.779145	−	0.626844i	$-0.215654\pi$
$379$	−0.104337	−	0.130835i	−0.00535945	−	0.00672053i	−0.784504	+	0.620124i	$0.787082\pi$
$380$	2.92946	+	3.15720i	0.150278	+	0.161961i
$381$		0			0
$382$	21.4874	−	14.6498i	1.09939	−	0.749551i
$383$	6.74017	+	1.01592i	0.344407	+	0.0519109i	0.318968	−	0.947765i	$-0.396664\pi$
$383$	6.74017	+	1.01592i	0.344407	+	0.0519109i	0.0254385	+	0.999676i	$0.491902\pi$
$384$		0			0
$385$	12.0952	−	14.2367i	0.616428	−	0.725567i
$386$	5.93437	−	12.3229i	0.302052	−	0.627217i
$387$		0			0
$388$	7.38014	−	7.95390i	0.374670	−	0.403798i
$389$	−34.0283	−	2.55007i	−1.72531	−	0.129294i	−0.825164	−	0.564893i	$-0.808918\pi$
$389$	−34.0283	−	2.55007i	−1.72531	−	0.129294i	−0.900141	+	0.435599i	$0.856537\pi$
$390$		0			0
$391$		−	4.12510i		−	0.208615i
$392$	0.434451	−	6.98651i	0.0219431	−	0.352872i
$393$		0			0
$394$	0.629931	−	1.60504i	0.0317355	−	0.0808607i
$395$	1.46025	−	19.4856i	0.0734730	−	0.980429i
$396$		0			0
$397$	−11.0894	+	16.2651i	−0.556559	+	0.816322i	−0.996663	−	0.0816249i	$-0.973989\pi$
$397$	−11.0894	+	16.2651i	−0.556559	+	0.816322i	0.440104	+	0.897947i	$0.354941\pi$
$398$	−13.7336	−	6.61376i	−0.688403	−	0.331518i
$399$		0			0
$400$	2.12901	−	1.02528i	0.106450	−	0.0512638i
$401$	−3.12229	+	20.7150i	−0.155919	+	1.03446i	0.764810	+	0.644256i	$0.222833\pi$
$401$	−3.12229	+	20.7150i	−0.155919	+	1.03446i	−0.920729	+	0.390202i	$0.872405\pi$
$402$		0			0
$403$	16.7014	−	2.51733i	0.831955	−	0.125397i
$404$	−7.44654	+	6.90938i	−0.370479	+	0.343754i
$405$		0			0
$406$	3.91998	+	1.68073i	0.194545	+	0.0834134i
$407$	15.3219	+	12.2188i	0.759476	+	0.605662i
$408$		0			0
$409$	3.95904	−	12.8349i	0.195762	−	0.634644i	−0.803466	−	0.595351i	$-0.797013\pi$
$409$	3.95904	−	12.8349i	0.195762	−	0.634644i	0.999228	−	0.0392935i	$-0.0125107\pi$
$410$	4.60688	+	2.65978i	0.227518	+	0.131357i
$411$		0			0
$412$	−14.2436	+	3.25101i	−0.701733	+	0.160166i
$413$	11.9584	−	4.26982i	0.588435	−	0.210104i
$414$		0			0
$415$	12.7269	−	3.92571i	0.624737	−	0.192706i
$416$	−0.696925	−	1.77574i	−0.0341696	−	0.0870627i
$417$		0			0
$418$	3.39916	+	11.0198i	0.166258	+	0.538996i
$419$	0.595876	−	2.61070i	0.0291105	−	0.127541i	−0.958285	−	0.285815i	$-0.907736\pi$
$419$	0.595876	−	2.61070i	0.0291105	−	0.127541i	0.987395	+	0.158274i	$0.0505929\pi$
$420$		0			0
$421$	2.97734	+	13.0446i	0.145107	+	0.635754i	0.994203	+	0.107517i	$0.0342899\pi$
$421$	2.97734	+	13.0446i	0.145107	+	0.635754i	−0.849097	+	0.528238i	$0.822853\pi$
$422$	14.5803	−	8.41794i	0.709758	−	0.409779i
$423$		0			0
$424$	−3.27629	−	1.01060i	−0.159110	−	0.0490791i
$425$	−0.167935	−	2.24094i	−0.00814604	−	0.108701i
$426$		0			0
$427$	−11.0613	−	20.6111i	−0.535292	−	0.997443i
$428$	−11.6363	+	9.27966i	−0.562463	+	0.448550i
$429$		0			0
$430$	−1.76837	−	11.7324i	−0.0852785	−	0.565786i
$431$	1.75324	+	2.57153i	0.0844506	+	0.123866i	0.866140	−	0.499802i	$-0.166594\pi$
$431$	1.75324	+	2.57153i	0.0844506	+	0.123866i	−0.781689	+	0.623668i	$0.785642\pi$
$432$		0			0
$433$	−6.54701	−	13.5950i	−0.314629	−	0.653335i	0.682348	−	0.731027i	$-0.260959\pi$
$433$	−6.54701	−	13.5950i	−0.314629	−	0.653335i	−0.996977	+	0.0776930i	$0.975245\pi$
$434$	−9.50383	−	21.4112i	−0.456199	−	1.02777i
$435$		0			0
$436$	−5.70817	−	3.89177i	−0.273372	−	0.186382i
$437$	−8.43346	−	7.82510i	−0.403427	−	0.374326i
$438$		0			0
$439$	−18.2432	−	7.15992i	−0.870700	−	0.341725i	−0.112426	−	0.993660i	$-0.535862\pi$
$439$	−18.2432	−	7.15992i	−0.870700	−	0.341725i	−0.758274	+	0.651936i	$0.773957\pi$
$440$	−7.06071			−0.336606
$441$		0			0
$442$	−1.81412			−0.0862889
$443$	21.9633	+	8.61997i	1.04351	+	0.409547i	0.824313	−	0.566134i	$-0.191562\pi$
$443$	21.9633	+	8.61997i	1.04351	+	0.409547i	0.219195	+	0.975681i	$0.429657\pi$
$444$		0			0
$445$	6.46011	+	5.99410i	0.306238	+	0.284148i
$446$	−2.43278	−	1.65864i	−0.115195	−	0.0785389i
$447$		0			0
$448$	−2.11875	+	1.58458i	−0.100102	+	0.0748644i
$449$	−3.75137	−	7.78981i	−0.177038	−	0.367624i	0.793500	−	0.608570i	$-0.208257\pi$
$449$	−3.75137	−	7.78981i	−0.177038	−	0.367624i	−0.970538	+	0.240946i	$0.922542\pi$
$450$		0			0
$451$	8.02368	+	11.7686i	0.377820	+	0.554161i
$452$	2.00957	+	13.3327i	0.0945224	+	0.627115i
$453$		0			0
$454$	4.35879	−	3.47602i	0.204568	−	0.163138i
$455$	8.06241	+	1.47254i	0.377971	+	0.0690338i
$456$		0			0
$457$	0.0941673	+	1.25658i	0.00440496	+	0.0587801i	0.998973	−	0.0453076i	$-0.0144268\pi$
$457$	0.0941673	+	1.25658i	0.00440496	+	0.0587801i	−0.994568	+	0.104088i	$0.966808\pi$
$458$	26.5400	+	8.18650i	1.24013	+	0.382530i
$459$		0			0
$460$	6.10015	−	3.52192i	0.284421	−	0.164210i
$461$	−1.71118	−	7.49715i	−0.0796974	−	0.349177i	0.919319	−	0.393512i	$-0.128740\pi$
$461$	−1.71118	−	7.49715i	−0.0796974	−	0.349177i	−0.999017	+	0.0443352i	$0.985883\pi$
$462$		0			0
$463$	−5.74310	+	25.1622i	−0.266904	+	1.16938i	0.646689	+	0.762754i	$0.276153\pi$
$463$	−5.74310	+	25.1622i	−0.266904	+	1.16938i	−0.913593	+	0.406630i	$0.866704\pi$
$464$	−0.475163	−	1.54044i	−0.0220589	−	0.0715131i
$465$		0			0
$466$	8.78798	+	22.3914i	0.407095	+	1.03726i
$467$	27.1797	−	8.38382i	1.25773	−	0.387957i	0.406933	−	0.913458i	$-0.366598\pi$
$467$	27.1797	−	8.38382i	1.25773	−	0.387957i	0.850793	+	0.525501i	$0.176122\pi$
$468$		0			0
$469$	−8.86870	+	8.98201i	−0.409518	+	0.414751i
$470$	8.03159	−	1.83316i	0.370470	−	0.0845573i
$471$		0			0
$472$	−4.15634	−	2.39967i	−0.191311	−	0.110454i
$473$	9.36414	−	30.3578i	0.430564	−	1.39585i
$474$		0			0
$475$	−4.89999	−	3.90761i	−0.224827	−	0.179294i
$476$	0.666628	+	2.42618i	0.0305548	+	0.111204i
$477$		0			0
$478$	11.6200	−	10.7818i	0.531487	−	0.493148i
$479$	−23.2533	+	3.50487i	−1.06247	+	0.160142i	−0.656942	−	0.753941i	$-0.728150\pi$
$479$	−23.2533	+	3.50487i	−1.06247	+	0.160142i	−0.405528	+	0.914083i	$0.632912\pi$
$480$		0			0
$481$	−1.28145	+	8.50184i	−0.0584289	+	0.387650i
$482$	17.0679	−	8.21947i	0.777422	−	0.374387i
$483$		0			0
$484$	−7.12270	−	3.43011i	−0.323759	−	0.155914i
$485$	9.92554	−	14.5581i	0.450695	−	0.661049i
$486$		0			0
$487$	−2.19340	+	29.2689i	−0.0993925	+	1.32630i	0.695050	+	0.718961i	$0.255382\pi$
$487$	−2.19340	+	29.2689i	−0.0993925	+	1.32630i	−0.794442	+	0.607339i	$0.792237\pi$
$488$	−3.23006	+	8.23006i	−0.146218	+	0.372557i
$489$		0			0
$490$	−0.993303	−	11.3237i	−0.0448729	−	0.511551i
$491$		−	12.3451i		−	0.557127i	−0.960418	−	0.278564i	$-0.910142\pi$
$491$		−	12.3451i		−	0.557127i	0.960418	−	0.278564i	$-0.0898583\pi$
$492$		0			0
$493$	−1.52877	−	0.114566i	−0.0688525	−	0.00515978i
$494$	−3.44129	+	3.70883i	−0.154831	+	0.166868i
$495$		0			0
$496$	−3.84163	+	7.97724i	−0.172494	+	0.358188i
$497$	21.0004	+	10.9291i	0.941997	+	0.490236i
$498$		0			0
$499$	−0.739393	−	0.111446i	−0.0330998	−	0.00498899i	0.132472	−	0.991187i	$-0.457709\pi$
$499$	−0.739393	−	0.111446i	−0.0330998	−	0.00498899i	−0.165571	+	0.986198i	$0.552947\pi$
$500$	9.87904	−	6.73542i	0.441804	−	0.301217i
$501$		0			0
$502$	−10.0516	−	10.8330i	−0.448623	−	0.483501i
$503$	−21.4587	−	26.9083i	−0.956796	−	1.19978i	−0.979786	−	0.200048i	$-0.935890\pi$
$503$	−21.4587	−	26.9083i	−0.956796	−	1.19978i	0.0229906	−	0.999736i	$-0.492681\pi$
$504$		0			0
$505$	−10.2850	+	12.8969i	−0.457675	+	0.573906i
$506$	18.8077	−	1.40944i	0.836104	−	0.0626573i
$507$		0			0
$508$	7.95332	−	13.7756i	0.352872	−	0.611192i
$509$	−5.51608	−	9.55414i	−0.244496	−	0.423480i	0.717494	−	0.696565i	$-0.245289\pi$
$509$	−5.51608	−	9.55414i	−0.244496	−	0.423480i	−0.961990	+	0.273085i	$0.911956\pi$
$510$		0			0
$511$	20.0610	−	2.38938i	0.887445	−	0.105700i
$512$	0.974928	+	0.222521i	0.0430861	+	0.00983413i
$513$		0			0
$514$	4.36512	−	1.71318i	0.192537	−	0.0755653i
$515$	−22.0847	+	8.66762i	−0.973169	+	0.381941i
$516$		0			0
$517$	21.5052	+	4.90842i	0.945798	+	0.215872i
$518$	11.8411	−	1.41035i	0.520269	−	0.0619672i
$519$		0			0
$520$	−1.54886	−	2.68270i	−0.0679218	−	0.117644i
$521$	−11.5969	+	20.0864i	−0.508070	+	0.880003i	0.491887	+	0.870659i	$0.336307\pi$
$521$	−11.5969	+	20.0864i	−0.508070	+	0.880003i	−0.999956	+	0.00934346i	$0.997026\pi$
$522$		0			0
$523$	2.58564	−	0.193767i	0.113062	−	0.00847285i	−0.0180788	−	0.999837i	$-0.505755\pi$
$523$	2.58564	−	0.193767i	0.113062	−	0.00847285i	0.131141	+	0.991364i	$0.458136\pi$
$524$	−6.88858	+	8.63801i	−0.300929	+	0.377353i
$525$		0			0
$526$	−17.4484	−	21.8796i	−0.760785	−	0.953994i
$527$	5.72717	+	6.17242i	0.249479	+	0.268875i
$528$		0			0
$529$	3.45751	−	2.35729i	0.150327	−	0.102491i
$530$	−5.50546	−	0.829814i	−0.239142	−	0.0360448i
$531$		0			0
$532$	6.22470	+	3.23947i	0.269875	+	0.140449i
$533$	−2.71134	+	5.63016i	−0.117441	+	0.243869i
$534$		0			0
$535$	−16.4390	+	17.7170i	−0.710720	+	0.765974i
$536$	4.75756	+	0.356530i	0.205495	+	0.0153997i
$537$		0			0
$538$			25.3766i			1.09406i
$539$	10.7591	−	28.4713i	0.463427	−	1.22635i
$540$		0			0
$541$	13.8981	−	35.4117i	0.597525	−	1.52247i	−0.237006	−	0.971508i	$-0.576166\pi$
$541$	13.8981	−	35.4117i	0.597525	−	1.52247i	0.834531	−	0.550961i	$-0.185739\pi$
$542$	−1.64536	+	21.9558i	−0.0706743	+	0.943083i
$543$		0			0
$544$	0.535714	−	0.785749i	0.0229686	−	0.0336887i
$545$	−10.1078	−	4.86764i	−0.432969	−	0.208507i
$546$		0			0
$547$	26.1700	−	12.6028i	1.11895	−	0.538857i	0.219381	−	0.975639i	$-0.429596\pi$
$547$	26.1700	−	12.6028i	1.11895	−	0.538857i	0.899567	+	0.436782i	$0.143882\pi$
$548$	0.438253	−	2.90762i	0.0187212	−	0.124207i
$549$		0			0
$550$	10.1598	−	1.53134i	0.433215	−	0.0652967i
$551$	−3.13423	+	2.90814i	−0.133522	+	0.123891i
$552$		0			0
$553$	−8.43495	−	30.6988i	−0.358690	−	1.30545i
$554$	−3.33200	−	2.65718i	−0.141563	−	0.112893i
$555$		0			0
$556$	1.16387	−	3.77318i	0.0493591	−	0.160018i
$557$	12.8654	+	7.42782i	0.545123	+	0.314727i	0.747153	−	0.664653i	$-0.231420\pi$
$557$	12.8654	+	7.42782i	0.545123	+	0.314727i	−0.202030	+	0.979379i	$0.564754\pi$
$558$		0			0
$559$	13.5885	−	3.10149i	0.574732	−	0.131179i
$560$	−3.01865	+	3.05722i	−0.127561	+	0.129191i
$561$		0			0
$562$	3.46203	−	1.06789i	0.146037	−	0.0450464i
$563$	−3.34839	−	8.53157i	−0.141118	−	0.359563i	0.842789	−	0.538244i	$-0.180912\pi$
$563$	−3.34839	−	8.53157i	−0.141118	−	0.359563i	−0.983907	+	0.178681i	$0.942817\pi$
$564$		0			0
$565$	6.45371	+	20.9224i	0.271510	+	0.880212i
$566$	−2.16990	+	9.50695i	−0.0912077	+	0.399607i
$567$		0			0
$568$	−1.99111	−	8.72361i	−0.0835450	−	0.366035i
$569$	−11.7066	+	6.75881i	−0.490766	+	0.283344i	−0.724892	−	0.688862i	$-0.758110\pi$
$569$	−11.7066	+	6.75881i	−0.490766	+	0.283344i	0.234126	+	0.972206i	$0.424777\pi$
$570$		0			0
$571$	−36.0564	−	11.1219i	−1.50891	−	0.465439i	−0.573564	−	0.819161i	$-0.694440\pi$
$571$	−36.0564	−	11.1219i	−1.50891	−	0.465439i	−0.935351	+	0.353722i	$0.884916\pi$
$572$	−0.619839	−	8.27117i	−0.0259168	−	0.345835i
$573$		0			0
$574$	8.52603	+	1.55722i	0.355869	+	0.0649971i
$575$	−8.01377	+	6.39077i	−0.334197	+	0.266514i
$576$		0			0
$577$	4.37965	+	29.0570i	0.182327	+	1.20966i	0.873446	+	0.486920i	$0.161880\pi$
$577$	4.37965	+	29.0570i	0.182327	+	1.20966i	−0.691119	+	0.722741i	$0.742882\pi$
$578$	9.06698	+	13.2988i	0.377137	+	0.553158i
$579$		0			0
$580$	−1.13581	−	2.35854i	−0.0471621	−	0.0979332i
$581$	17.3774	−	12.9963i	0.720934	−	0.539176i
$582$		0			0
$583$	−12.3174	−	8.39786i	−0.510134	−	0.347804i
$584$	−5.59753	−	5.19375i	−0.231628	−	0.214919i
$585$		0			0
$586$	−10.0726	−	3.95321i	−0.416096	−	0.163306i
$587$	−12.9063			−0.532700			−0.266350	−	0.963876i	$-0.585818\pi$
$587$	−12.9063			−0.532700			−0.266350	+	0.963876i	$0.585818\pi$
$588$		0			0
$589$	23.4832			0.967608
$590$	−7.25479	−	2.84729i	−0.298675	−	0.117221i
$591$		0			0
$592$	−3.30398	−	3.06565i	−0.135793	−	0.125997i
$593$	1.19492	+	0.814685i	0.0490696	+	0.0334551i	0.587606	−	0.809147i	$-0.300070\pi$
$593$	1.19492	+	0.814685i	0.0490696	+	0.0334551i	−0.538537	+	0.842602i	$0.681023\pi$
$594$		0			0
$595$	1.65763	+	3.73447i	0.0679562	+	0.153098i
$596$	−3.35199	−	6.96048i	−0.137303	−	0.285112i
$597$		0			0
$598$	4.66122	+	6.83675i	0.190611	+	0.279575i
$599$	−0.250504	−	1.66199i	−0.0102353	−	0.0679070i	0.983130	−	0.182908i	$-0.0585510\pi$
$599$	−0.250504	−	1.66199i	−0.0102353	−	0.0679070i	−0.993365	+	0.115001i	$0.963313\pi$
$600$		0			0
$601$	14.9484	−	11.9210i	0.609759	−	0.486266i	−0.269251	−	0.963070i	$-0.586776\pi$
$601$	14.9484	−	11.9210i	0.609759	−	0.486266i	0.879010	+	0.476804i	$0.158205\pi$
$602$	−9.14120	−	17.0334i	−0.372568	−	0.694229i
$603$		0			0
$604$	0.683478	+	9.12038i	0.0278103	+	0.371103i
$605$	−12.2674	−	3.78399i	−0.498740	−	0.153841i
$606$		0			0
$607$	12.6602	−	7.30934i	0.513860	−	0.296677i	−0.220559	−	0.975374i	$-0.570788\pi$
$607$	12.6602	−	7.30934i	0.513860	−	0.296677i	0.734419	+	0.678697i	$0.237455\pi$
$608$	−0.590181	−	2.58575i	−0.0239350	−	0.104866i
$609$		0			0
$610$	−3.19475	+	13.9971i	−0.129352	+	0.566726i
$611$	2.85250	+	9.24756i	0.115400	+	0.374116i
$612$		0			0
$613$	9.00331	+	22.9401i	0.363640	+	0.926540i	0.989228	+	0.146386i	$0.0467642\pi$
$613$	9.00331	+	22.9401i	0.363640	+	0.926540i	−0.625587	+	0.780154i	$0.715141\pi$
$614$	−2.27382	+	0.701380i	−0.0917638	+	0.0283054i
$615$		0			0
$616$	−10.8340	+	3.86834i	−0.436514	+	0.155860i
$617$	−44.5663	+	10.1720i	−1.79417	+	0.409508i	−0.984215	−	0.176978i	$-0.943368\pi$
$617$	−44.5663	+	10.1720i	−1.79417	+	0.409508i	−0.809959	+	0.586487i	$0.800511\pi$
$618$		0			0
$619$	−18.2253	−	10.5224i	−0.732538	−	0.422931i	0.0868122	−	0.996225i	$-0.472332\pi$
$619$	−18.2253	−	10.5224i	−0.732538	−	0.422931i	−0.819350	+	0.573294i	$0.805665\pi$
$620$	−4.23797	+	13.7391i	−0.170201	+	0.551777i
$621$		0			0
$622$	25.4373	+	20.2856i	1.01994	+	0.813378i
$623$	13.1964	+	5.65808i	0.528702	+	0.226686i
$624$		0			0
$625$	5.57195	−	5.17001i	0.222878	−	0.206800i
$626$	6.30335	−	0.950077i	0.251933	−	0.0379727i
$627$		0			0
$628$	0.295246	−	1.95883i	0.0117816	−	0.0781659i
$629$	−3.86181	+	1.85975i	−0.153980	+	0.0741531i
$630$		0			0
$631$	26.0923	+	12.5654i	1.03872	+	0.500220i	0.873901	−	0.486105i	$-0.161583\pi$
$631$	26.0923	+	12.5654i	1.03872	+	0.500220i	0.164816	+	0.986324i	$0.447297\pi$
$632$	−6.77848	+	9.94221i	−0.269634	+	0.395480i
$633$		0			0
$634$	−0.393351	+	5.24890i	−0.0156220	+	0.208461i
$635$	9.43692	−	24.0449i	0.374493	−	0.954192i
$636$		0			0
$637$	13.1777	−	2.15766i	0.522121	−	0.0854896i
$638$		−	7.00932i		−	0.277502i
$639$		0			0
$640$	1.61934	+	0.121353i	0.0640099	+	0.00479688i
$641$	−20.5700	+	22.1692i	−0.812465	+	0.875630i	−0.994181	−	0.107722i	$-0.965644\pi$
$641$	−20.5700	+	22.1692i	−0.812465	+	0.875630i	0.181716	+	0.983351i	$0.441835\pi$
$642$		0			0
$643$	−19.6635	+	40.8316i	−0.775452	+	1.61024i	0.0166569	+	0.999861i	$0.494698\pi$
$643$	−19.6635	+	40.8316i	−0.775452	+	1.61024i	−0.792108	+	0.610380i	$0.791017\pi$
$644$	7.43054	−	8.74612i	0.292804	−	0.344645i
$645$		0			0
$646$	−2.49411	−	0.375926i	−0.0981293	−	0.0147906i
$647$	13.2272	−	9.01816i	0.520015	−	0.354540i	−0.274693	−	0.961532i	$-0.588576\pi$
$647$	13.2272	−	9.01816i	0.520015	−	0.354540i	0.794708	+	0.606992i	$0.207624\pi$
$648$		0			0
$649$	−14.1937	−	15.2972i	−0.557151	−	0.600466i
$650$	2.81051	+	3.52427i	0.110237	+	0.138233i
$651$		0			0
$652$	−3.51542	+	4.40820i	−0.137674	+	0.172638i
$653$	−15.2548	+	1.14319i	−0.596965	+	0.0447363i	−0.369786	−	0.929117i	$-0.620569\pi$
$653$	−15.2548	+	1.14319i	−0.596965	+	0.0447363i	−0.227179	+	0.973853i	$0.572950\pi$
$654$		0			0
$655$	−8.97064	+	15.5376i	−0.350512	+	0.607105i
$656$	−1.63792	−	2.83696i	−0.0639501	−	0.110765i
$657$		0			0
$658$	11.3194	−	7.21306i	0.441275	−	0.281194i
$659$	3.31217	+	0.755980i	0.129024	+	0.0294488i	0.286545	−	0.958067i	$-0.407493\pi$
$659$	3.31217	+	0.755980i	0.129024	+	0.0294488i	−0.157521	+	0.987516i	$0.550350\pi$
$660$		0			0
$661$	24.2723	−	9.52616i	0.944082	−	0.370525i	0.157157	−	0.987574i	$-0.449767\pi$
$661$	24.2723	−	9.52616i	0.944082	−	0.370525i	0.786925	+	0.617049i	$0.211672\pi$
$662$	−3.59062	+	1.40922i	−0.139553	+	0.0547707i
$663$		0			0
$664$	−7.99607	−	1.82505i	−0.310308	−	0.0708257i
$665$	10.7793	+	3.69520i	0.418003	+	0.143294i
$666$		0			0
$667$	3.49629	+	6.05575i	0.135377	+	0.234479i
$668$	−8.57143	+	14.8462i	−0.331639	+	0.574415i
$669$		0			0
$670$	7.72569	−	0.578961i	0.298470	−	0.0223672i
$671$	−23.9683	+	30.0553i	−0.925286	+	1.16027i
$672$		0			0
$673$	−5.24624	−	6.57858i	−0.202228	−	0.253586i	0.670368	−	0.742029i	$-0.266136\pi$
$673$	−5.24624	−	6.57858i	−0.202228	−	0.253586i	−0.872596	+	0.488443i	$0.837565\pi$
$674$	1.71642	+	1.84986i	0.0661142	+	0.0712541i
$675$		0			0
$676$	−7.73447	+	5.27327i	−0.297479	+	0.202818i
$677$	9.20202	+	1.38698i	0.353662	+	0.0533060i	0.323471	−	0.946238i	$-0.395150\pi$
$677$	9.20202	+	1.38698i	0.353662	+	0.0533060i	0.0301914	+	0.999544i	$0.490388\pi$
$678$		0			0
$679$	7.25386	−	27.7759i	0.278378	−	1.06594i
$680$	0.670046	−	1.39137i	0.0256951	−	0.0533564i
$681$		0			0
$682$	−26.1853	+	28.2210i	−1.00269	+	1.08064i
$683$	−7.75184	−	0.580920i	−0.296616	−	0.0222283i	−0.0744089	−	0.997228i	$-0.523707\pi$
$683$	−7.75184	−	0.580920i	−0.296616	−	0.0222283i	−0.222207	+	0.975000i	$0.571326\pi$
$684$		0			0
$685$		−	4.77495i		−	0.182442i
$686$	−7.72800	−	16.8309i	−0.295056	−	0.642605i
$687$		0			0
$688$	−2.66938	+	6.80146i	−0.101769	+	0.259303i
$689$	0.488766	−	6.52213i	0.0186205	−	0.248473i
$690$		0			0
$691$	11.0559	−	16.2161i	0.420587	−	0.616888i	−0.556214	−	0.831039i	$-0.687746\pi$
$691$	11.0559	−	16.2161i	0.420587	−	0.616888i	0.976800	+	0.214152i	$0.0686987\pi$
$692$	−15.6841	−	7.55307i	−0.596220	−	0.287125i
$693$		0			0
$694$	−15.8923	+	7.65335i	−0.603265	+	0.290517i
$695$	0.955666	−	6.34043i	0.0362505	−	0.240506i
$696$		0			0
$697$	−3.08051	+	0.464313i	−0.116683	+	0.0175871i
$698$	−16.5085	+	15.3176i	−0.624855	+	0.579780i
$699$		0			0
$700$	3.68054	−	5.05378i	0.139111	−	0.191015i
$701$	−12.0423	−	9.60341i	−0.454831	−	0.362716i	0.369115	−	0.929384i	$-0.379661\pi$
$701$	−12.0423	−	9.60341i	−0.454831	−	0.362716i	−0.823946	+	0.566668i	$0.808232\pi$
$702$		0			0
$703$	−3.52354	+	11.4230i	−0.132893	+	0.430828i
$704$	3.76553	+	2.17403i	0.141919	+	0.0819368i
$705$		0			0
$706$	−19.9703	+	4.55810i	−0.751594	+	0.171546i
$707$	−8.71546	+	25.4239i	−0.327779	+	0.956164i
$708$		0			0
$709$	−6.07678	+	1.87444i	−0.228218	+	0.0703960i	−0.406755	−	0.913537i	$-0.633340\pi$
$709$	−6.07678	+	1.87444i	−0.228218	+	0.0703960i	0.178537	+	0.983933i	$0.442864\pi$
$710$	−5.30855	−	13.5260i	−0.199226	−	0.507620i
$711$		0			0
$712$	−1.59961	−	5.18580i	−0.0599478	−	0.194346i
$713$	8.54614	−	37.4431i	0.320055	−	1.40225i
$714$		0			0
$715$	−2.99714	−	13.1313i	−0.112087	−	0.491084i
$716$	17.8865	−	10.3268i	0.668450	−	0.385930i
$717$		0			0
$718$	29.3874	+	9.06482i	1.09673	+	0.338296i
$719$	3.31405	+	44.2229i	0.123593	+	1.64923i	0.622529	+	0.782596i	$0.286105\pi$
$719$	3.31405	+	44.2229i	0.123593	+	1.64923i	−0.498936	+	0.866639i	$0.666276\pi$
$720$		0			0
$721$	−29.1382	+	25.3991i	−1.08516	+	0.945913i
$722$	9.35505	−	7.46041i	0.348159	−	0.277648i
$723$		0			0
$724$	−3.57894	−	23.7447i	−0.133010	−	0.882467i
$725$	2.14587	+	3.14741i	0.0796957	+	0.116892i
$726$		0			0
$727$	0.503576	+	1.04569i	0.0186766	+	0.0387823i	0.910098	−	0.414392i	$-0.136006\pi$
$727$	0.503576	+	1.04569i	0.0186766	+	0.0387823i	−0.891422	+	0.453174i	$0.850291\pi$
$728$	−3.84633	−	3.26777i	−0.142555	−	0.121112i
$729$		0			0
$730$	−10.2452	−	6.98507i	−0.379192	−	0.258529i
$731$	5.09359	+	4.72616i	0.188393	+	0.174803i
$732$		0			0
$733$	−37.2505	−	14.6197i	−1.37588	−	0.539993i	−0.441818	−	0.897105i	$-0.645666\pi$
$733$	−37.2505	−	14.6197i	−1.37588	−	0.539993i	−0.934062	+	0.357112i	$0.883761\pi$
$734$	−31.9502			−1.17930
$735$		0			0
$736$	−4.33767			−0.159889
$737$	19.3102	+	7.57869i	0.711299	+	0.279164i
$738$		0			0
$739$	−18.1209	−	16.8137i	−0.666587	−	0.618503i	0.272510	−	0.962153i	$-0.412146\pi$
$739$	−18.1209	−	16.8137i	−0.666587	−	0.618503i	−0.939098	+	0.343650i	$0.888337\pi$
$740$	−6.04730	−	4.12298i	−0.222303	−	0.151564i
$741$		0			0
$742$	−8.90222	+	1.74299i	−0.326811	+	0.0639873i
$743$	14.4587	+	30.0237i	0.530437	+	1.10146i	0.978268	+	0.207346i	$0.0664825\pi$
$743$	14.4587	+	30.0237i	0.530437	+	1.10146i	−0.447831	+	0.894118i	$0.647803\pi$
$744$		0			0
$745$	−7.06705	−	10.3655i	−0.258917	−	0.379761i
$746$	−2.74187	−	18.1911i	−0.100387	−	0.666025i
$747$		0			0
$748$	3.23286	−	2.57812i	0.118205	−	0.0942653i
$749$	−15.5175	+	36.1915i	−0.566996	+	1.32241i
$750$		0			0
$751$	3.61879	+	48.2894i	0.132052	+	1.76211i	0.533103	+	0.846050i	$0.321026\pi$
$751$	3.61879	+	48.2894i	0.132052	+	1.76211i	−0.401052	+	0.916055i	$0.631355\pi$
$752$	−4.84774	−	1.49533i	−0.176779	−	0.0545291i
$753$		0			0
$754$	2.66317	−	1.53758i	0.0969870	−	0.0559955i
$755$	3.30486	+	14.4795i	0.120276	+	0.526965i
$756$		0			0
$757$	−3.68140	+	16.1292i	−0.133803	+	0.586227i	0.862921	+	0.505339i	$0.168633\pi$
$757$	−3.68140	+	16.1292i	−0.133803	+	0.586227i	−0.996723	+	0.0808879i	$0.974224\pi$
$758$	0.0493255	+	0.159909i	0.00179158	+	0.00580817i
$759$		0			0
$760$	−1.57350	−	4.00921i	−0.0570768	−	0.145429i
$761$	34.3827	−	10.6057i	1.24637	−	0.384455i	0.399738	−	0.916629i	$-0.369101\pi$
$761$	34.3827	−	10.6057i	1.24637	−	0.384455i	0.846635	+	0.532174i	$0.178625\pi$
$762$		0			0
$763$	−18.1762	−	1.93121i	−0.658023	−	0.0699143i
$764$	−25.3542	+	5.78693i	−0.917283	+	0.209364i
$765$		0			0
$766$	−5.90309	−	3.40815i	−0.213287	−	0.123142i
$767$	2.69855	−	8.74847i	0.0974389	−	0.315889i
$768$		0			0
$769$	−37.5445	−	29.9408i	−1.35389	−	1.07969i	−0.988884	−	0.148687i	$-0.952495\pi$
$769$	−37.5445	−	29.9408i	−1.35389	−	1.07969i	−0.365006	−	0.931005i	$-0.618933\pi$
$770$	−16.4603	+	8.83366i	−0.593189	+	0.318343i
$771$		0			0
$772$	−10.0262	+	9.30295i	−0.360851	+	0.334820i
$773$	6.36699	−	0.959670i	0.229005	−	0.0345169i	−0.0335373	−	0.999437i	$-0.510677\pi$
$773$	6.36699	−	0.959670i	0.229005	−	0.0345169i	0.262542	+	0.964921i	$0.415439\pi$
$774$		0			0
$775$	3.11831	−	20.6887i	0.112013	−	0.743158i
$776$	−9.77586	+	4.70781i	−0.350933	+	0.169000i
$777$		0			0
$778$	30.7444	+	14.8057i	1.10224	+	0.530812i
$779$	−4.89433	+	7.17866i	−0.175357	+	0.257202i
$780$		0			0
$781$	2.90747	−	38.7974i	0.104037	−	1.38828i
$782$	−1.50707	+	3.83995i	−0.0538926	+	0.137316i
$783$		0			0
$784$	−2.95688	+	6.34483i	−0.105603	+	0.226601i
$785$		−	3.21683i		−	0.114814i
$786$		0			0
$787$	−33.8379	−	2.53580i	−1.20619	−	0.0903916i	−0.543582	−	0.839356i	$-0.682932\pi$
$787$	−33.8379	−	2.53580i	−1.20619	−	0.0903916i	−0.662610	+	0.748964i	$0.730551\pi$
$788$	−1.17277	+	1.26395i	−0.0417783	+	0.0450263i
$789$		0			0
$790$	−8.47821	+	17.6052i	−0.301641	+	0.626364i
$791$	21.3653	+	28.5676i	0.759663	+	1.01575i
$792$		0			0
$793$	−16.6772	−	2.51368i	−0.592224	−	0.0892633i
$794$	16.2651	−	11.0894i	0.577227	−	0.393546i
$795$		0			0
$796$	10.3680	+	11.1740i	0.367483	+	0.396053i
$797$	31.9868	+	40.1101i	1.13303	+	1.42077i	0.893028	+	0.450001i	$0.148576\pi$
$797$	31.9868	+	40.1101i	1.13303	+	1.42077i	0.240001	+	0.970773i	$0.422852\pi$
$798$		0			0
$799$	−3.00804	+	3.77196i	−0.106417	+	0.133442i
$800$	−2.35641	+	0.176589i	−0.0833118	+	0.00624336i
$801$		0			0
$802$	10.4745	−	18.1424i	0.369867	−	0.640629i
$803$	−16.6007	−	28.7533i	−0.585827	−	1.01468i
$804$		0			0
$805$	9.81472	−	15.8424i	0.345923	−	0.558371i
$806$	−16.4666	−	3.75839i	−0.580010	−	0.132383i
$807$		0			0
$808$	9.45607	−	3.71123i	0.332663	−	0.130561i
$809$	−7.61156	+	2.98732i	−0.267608	+	0.105028i	−0.495351	−	0.868693i	$-0.664961\pi$
$809$	−7.61156	+	2.98732i	−0.267608	+	0.105028i	0.227743	+	0.973721i	$0.426865\pi$
$810$		0			0
$811$	35.3228	+	8.06219i	1.24035	+	0.283102i	0.791869	−	0.610690i	$-0.209108\pi$
$811$	35.3228	+	8.06219i	1.24035	+	0.283102i	0.448481	+	0.893792i	$0.351965\pi$
$812$	−3.03497	−	2.99668i	−0.106507	−	0.105163i
$813$		0			0
$814$	−9.79869	−	16.9718i	−0.343444	−	0.594863i
$815$	−4.57795	+	7.92924i	−0.160359	+	0.277749i
$816$		0			0
$817$	19.3246	−	1.44818i	0.676081	−	0.0506653i
$818$	−8.37448	+	10.5013i	−0.292807	+	0.367168i
$819$		0			0
$820$	−3.31670	−	4.15901i	−0.115824	−	0.145239i
$821$	25.6977	+	27.6955i	0.896856	+	0.966581i	0.999604	−	0.0281263i	$-0.00895407\pi$
$821$	25.6977	+	27.6955i	0.896856	+	0.966581i	−0.102748	+	0.994707i	$0.532764\pi$
$822$		0			0
$823$	6.09735	−	4.15710i	0.212540	−	0.144908i	−0.452371	−	0.891830i	$-0.649422\pi$
$823$	6.09735	−	4.15710i	0.212540	−	0.144908i	0.664911	+	0.746922i	$0.268469\pi$
$824$	14.4467	+	2.17750i	0.503276	+	0.0758567i
$825$		0			0
$826$	−12.6917	−	0.394232i	−0.441601	−	0.0137171i
$827$	14.4161	−	29.9353i	0.501297	−	1.04095i	−0.484776	−	0.874638i	$-0.661099\pi$
$827$	14.4161	−	29.9353i	0.501297	−	1.04095i	0.986073	−	0.166315i	$-0.0531868\pi$
$828$		0			0
$829$	−32.1937	+	34.6966i	−1.11813	+	1.20506i	−0.141549	+	0.989931i	$0.545208\pi$
$829$	−32.1937	+	34.6966i	−1.11813	+	1.20506i	−0.976585	+	0.215131i	$0.930982\pi$
$830$	−13.2813	−	0.995297i	−0.461001	−	0.0345473i
$831$		0			0
$832$			1.90760i			0.0661342i
$833$	4.58947	+	4.82202i	0.159016	+	0.167073i
$834$		0			0
$835$	−10.1703	+	25.9136i	−0.351959	+	0.896777i
$836$	0.861798	−	11.4999i	0.0298059	−	0.397732i
$837$		0			0
$838$	−1.50848	+	2.21254i	−0.0521097	+	0.0764308i
$839$	15.7328	+	7.57653i	0.543157	+	0.261571i	0.685282	−	0.728278i	$-0.259679\pi$
$839$	15.7328	+	7.57653i	0.543157	+	0.261571i	−0.142125	+	0.989849i	$0.545393\pi$
$840$		0			0
$841$	−23.7867	+	11.4551i	−0.820232	+	0.395003i
$842$	1.99419	−	13.2306i	0.0687244	−	0.455957i
$843$		0			0
$844$	−16.6478	+	2.50926i	−0.573042	+	0.0863722i
$845$	−11.1433	+	10.3394i	−0.383340	+	0.355688i
$846$		0			0
$847$	−20.8962	+	0.914746i	−0.718004	+	0.0314310i
$848$	2.68059	+	2.13770i	0.0920520	+	0.0734090i
$849$		0			0
$850$	−0.662380	+	2.14738i	−0.0227194	+	0.0736546i
$851$	16.9313	+	9.77528i	0.580397	+	0.335092i
$852$		0			0
$853$	−45.7346	+	10.4386i	−1.56592	+	0.357412i	−0.915551	−	0.402203i	$-0.868245\pi$
$853$	−45.7346	+	10.4386i	−1.56592	+	0.357412i	−0.650373	+	0.759615i	$0.725387\pi$
$854$	2.76653	+	23.2275i	0.0946689	+	0.794829i
$855$		0			0
$856$	14.2222	−	4.38697i	0.486105	−	0.149943i
$857$	15.3478	+	39.1056i	0.524272	+	1.33582i	0.910534	+	0.413434i	$0.135671\pi$
$857$	15.3478	+	39.1056i	0.524272	+	1.33582i	−0.386262	+	0.922389i	$0.626234\pi$
$858$		0			0
$859$	−10.2255	−	33.1502i	−0.348889	−	1.13107i	−0.944697	−	0.327944i	$-0.893644\pi$
$859$	−10.2255	−	33.1502i	−0.348889	−	1.13107i	0.595808	−	0.803127i	$-0.296832\pi$
$860$	−2.64019	+	11.5674i	−0.0900298	+	0.394446i
$861$		0			0
$862$	−0.692560	−	3.03430i	−0.0235887	−	0.103349i
$863$	−33.9801	+	19.6184i	−1.15670	+	0.667819i	−0.950510	−	0.310693i	$-0.899439\pi$
$863$	−33.9801	+	19.6184i	−1.15670	+	0.667819i	−0.206187	+	0.978513i	$0.566105\pi$
$864$		0			0
$865$	−27.0127	−	8.33230i	−0.918458	−	0.283307i
$866$	1.12763	+	15.0471i	0.0383183	+	0.511322i
$867$		0			0
$868$	1.02449	+	23.4032i	0.0347735	+	0.794358i
$869$	−40.9059	+	32.6213i	−1.38764	+	1.10660i
$870$		0			0
$871$	1.35643	+	8.99933i	0.0459609	+	0.304931i
$872$	3.89177	+	5.70817i	0.131792	+	0.193303i
$873$		0			0
$874$	4.99165	+	10.3653i	0.168845	+	0.350611i
$875$	14.6039	−	28.0616i	0.493702	−	0.948657i
$876$		0			0
$877$	25.0087	+	17.0506i	0.844483	+	0.575759i	0.906447	−	0.422319i	$-0.138784\pi$
$877$	25.0087	+	17.0506i	0.844483	+	0.575759i	−0.0619636	+	0.998078i	$0.519736\pi$
$878$	14.3663	+	13.3300i	0.484839	+	0.449865i
$879$		0			0
$880$	6.57263	+	2.57957i	0.221563	+	0.0869572i
$881$	31.8194			1.07202			0.536011	−	0.844211i	$-0.319931\pi$
$881$	31.8194			1.07202			0.536011	+	0.844211i	$0.319931\pi$
$882$		0			0
$883$	41.9292			1.41103			0.705516	−	0.708694i	$-0.250715\pi$
$883$	41.9292			1.41103			0.705516	+	0.708694i	$0.250715\pi$
$884$	1.68872	+	0.662772i	0.0567977	+	0.0222914i
$885$		0			0
$886$	−17.2958	−	16.0482i	−0.581065	−	0.539150i
$887$	3.79381	+	2.58658i	0.127384	+	0.0868487i	0.625336	−	0.780356i	$-0.284962\pi$
$887$	3.79381	+	2.58658i	0.127384	+	0.0868487i	−0.497952	+	0.867205i	$0.665914\pi$
$888$		0			0
$889$	1.30662	−	42.0648i	0.0438227	−	1.41081i
$890$	−3.82365	−	7.93989i	−0.128169	−	0.266146i
$891$		0			0
$892$	1.65864	+	2.43278i	0.0555354	+	0.0814554i
$893$	2.00539	+	13.3049i	0.0671080	+	0.445232i
$894$		0			0
$895$	26.2217	−	20.9111i	0.876495	−	0.698982i
$896$	2.55120	−	0.700979i	0.0852297	−	0.0234181i
$897$		0			0
$898$	0.646119	+	8.62186i	0.0215613	+	0.287715i
$899$	−13.6391	−	4.20712i	−0.454891	−	0.140315i
$900$		0			0
$901$	2.82375	−	1.63029i	0.0940728	−	0.0543130i
$902$	−3.16949	−	13.8864i	−0.105532	−	0.462368i
$903$		0			0
$904$	3.00031	−	13.1452i	0.0997887	−	0.437203i
$905$	−11.4937	−	37.2617i	−0.382064	−	1.23862i
$906$		0			0
$907$	−15.6548	−	39.8878i	−0.519810	−	1.32445i	−0.914108	−	0.405471i	$-0.867108\pi$
$907$	−15.6548	−	39.8878i	−0.519810	−	1.32445i	0.394298	−	0.918983i	$-0.370988\pi$
$908$	−5.32741	+	1.64329i	−0.176796	+	0.0545345i
$909$		0			0
$910$	−6.96710	−	4.31628i	−0.230957	−	0.143083i
$911$	18.5861	−	4.24216i	0.615785	−	0.140549i	0.0967596	−	0.995308i	$-0.469152\pi$
$911$	18.5861	−	4.24216i	0.615785	−	0.140549i	0.519025	+	0.854759i	$0.326295\pi$
$912$		0			0
$913$	−30.8837	−	17.8307i	−1.02210	−	0.590111i
$914$	0.371421	−	1.20412i	0.0122855	−	0.0398286i
$915$		0			0
$916$	−21.7145	−	17.3167i	−0.717468	−	0.572162i
$917$	−5.25203	+	28.7557i	−0.173437	+	0.949597i
$918$		0			0
$919$	28.2970	−	26.2558i	0.933432	−	0.866099i	−0.0577867	−	0.998329i	$-0.518404\pi$
$919$	28.2970	−	26.2558i	0.933432	−	0.866099i	0.991219	+	0.132230i	$0.0422139\pi$
$920$	−6.96517	+	1.04983i	−0.229635	+	0.0346119i
$921$		0			0
$922$	−1.14613	+	7.60407i	−0.0377457	+	0.250427i
$923$	15.3788	−	7.40602i	0.506198	−	0.243772i
$924$		0			0
$925$	9.59578	+	4.62108i	0.315507	+	0.151940i
$926$	14.5389	−	21.3246i	0.477777	−	0.700770i
$927$		0			0
$928$	−0.120469	+	1.60755i	−0.00395460	+	0.0527704i
$929$	18.6826	−	47.6025i	0.612956	−	1.56179i	−0.200209	−	0.979753i	$-0.564162\pi$
$929$	18.6826	−	47.6025i	0.612956	−	1.56179i	0.813165	−	0.582034i	$-0.197743\pi$
$930$		0			0
$931$	18.5643	−	0.235695i	0.608419	−	0.00772459i
$932$		−	24.0542i		−	0.787921i
$933$		0			0
$934$	−28.3638	−	2.12557i	−0.928092	−	0.0695509i
$935$	4.56716	−	4.92222i	0.149362	−	0.160974i
$936$		0			0
$937$	−9.80260	+	20.3553i	−0.320237	+	0.664979i	−0.997493	−	0.0707686i	$-0.977455\pi$
$937$	−9.80260	+	20.3553i	−0.320237	+	0.664979i	0.677256	+	0.735748i	$0.263169\pi$
$938$	11.5371	−	5.12102i	0.376701	−	0.167207i
$939$		0			0
$940$	−8.14613	−	1.22783i	−0.265697	−	0.0400474i
$941$	32.1758	−	21.9371i	1.04890	−	0.715129i	0.0891610	−	0.996017i	$-0.471581\pi$
$941$	32.1758	−	21.9371i	1.04890	−	0.715129i	0.959740	+	0.280888i	$0.0906291\pi$
$942$		0			0
$943$	9.66493	+	10.4163i	0.314733	+	0.339202i
$944$	2.99233	+	3.75227i	0.0973922	+	0.122126i
$945$		0			0
$946$	−19.8078	+	24.8382i	−0.644007	+	0.807559i
$947$	26.3334	−	1.97342i	0.855721	−	0.0641274i	0.360358	−	0.932814i	$-0.382654\pi$
$947$	26.3334	−	1.97342i	0.855721	−	0.0641274i	0.495362	+	0.868687i	$0.335035\pi$
$948$		0			0
$949$	7.28316	−	12.6148i	0.236421	−	0.409494i
$950$	3.13366	+	5.42766i	0.101669	+	0.176097i
$951$		0			0
$952$	0.265837	−	2.50201i	0.00861582	−	0.0810907i
$953$	−21.2664	−	4.85392i	−0.688887	−	0.157234i	−0.136273	−	0.990671i	$-0.543512\pi$
$953$	−21.2664	−	4.85392i	−0.688887	−	0.157234i	−0.552614	+	0.833437i	$0.686370\pi$
$954$		0			0
$955$	−39.3117	+	15.4287i	−1.27210	+	0.499261i
$956$	−14.7558	+	5.79122i	−0.477237	+	0.187302i
$957$		0			0
$958$	22.9264	+	5.23279i	0.740717	+	0.169064i
$959$	−2.61604	−	7.32670i	−0.0844764	−	0.236592i
$960$		0			0
$961$	23.6972	+	41.0448i	0.764426	+	1.32403i
$962$	4.29893	−	7.44597i	0.138603	−	0.240068i
$963$		0			0
$964$	−18.8910	+	1.41568i	−0.608438	+	0.0455961i
$965$	−13.8479	+	17.3647i	−0.445780	+	0.558990i
$966$		0			0
$967$	−18.9564	−	23.7706i	−0.609598	−	0.764411i	0.377242	−	0.926115i	$-0.376873\pi$
$967$	−18.9564	−	23.7706i	−0.609598	−	0.764411i	−0.986839	+	0.161704i	$0.948301\pi$
$968$	5.37718	+	5.79522i	0.172829	+	0.186265i
$969$		0			0
$970$	−14.5581	+	9.92554i	−0.467432	+	0.318690i
$971$	27.5238	+	4.14855i	0.883281	+	0.133133i	0.574992	−	0.818159i	$-0.305005\pi$
$971$	27.5238	+	4.14855i	0.883281	+	0.133133i	0.308290	+	0.951293i	$0.400243\pi$
$972$		0			0
$973$	−2.00734	−	10.2524i	−0.0643524	−	0.328676i
$974$	12.7349	−	26.4443i	0.408053	−	0.847331i
$975$		0			0
$976$	6.01356	−	6.48108i	0.192489	−	0.207454i
$977$	6.01387	+	0.450678i	0.192401	+	0.0144185i	0.170582	−	0.985343i	$-0.445435\pi$
$977$	6.01387	+	0.450678i	0.192401	+	0.0144185i	0.0218189	+	0.999762i	$0.493054\pi$
$978$		0			0
$979$		−	23.5965i		−	0.754146i
$980$	−3.21236	+	10.9038i	−0.102615	+	0.348309i
$981$		0			0
$982$	−4.51018	+	11.4917i	−0.143925	+	0.366716i
$983$	1.18800	−	15.8528i	0.0378914	−	0.505626i	−0.945679	−	0.325101i	$-0.894602\pi$
$983$	1.18800	−	15.8528i	0.0378914	−	0.505626i	0.983571	−	0.180524i	$-0.0577794\pi$
$984$		0			0
$985$	−1.57726	+	2.31342i	−0.0502557	+	0.0737115i
$986$	1.38124	+	0.665169i	0.0439876	+	0.0211833i
$987$		0			0
$988$	4.55840	−	2.19521i	0.145022	−	0.0698389i
$989$	4.72364	−	31.3393i	0.150203	−	0.996532i
$990$		0			0
$991$	−8.42557	+	1.26995i	−0.267647	+	0.0403413i	−0.281495	−	0.959563i	$-0.590830\pi$
$991$	−8.42557	+	1.26995i	−0.267647	+	0.0403413i	0.0138476	+	0.999904i	$0.495592\pi$
$992$	6.49049	−	6.02229i	0.206073	−	0.191208i
$993$		0			0
$994$	−15.5559	−	17.8459i	−0.493403	−	0.566037i
$995$	19.3527	+	15.4333i	0.613521	+	0.489267i
$996$		0			0
$997$	12.2236	−	39.6278i	0.387124	−	1.25503i	−0.527095	−	0.849806i	$-0.676719\pi$
$997$	12.2236	−	39.6278i	0.387124	−	1.25503i	0.914219	−	0.405219i	$-0.132805\pi$
$998$	0.647566	+	0.373872i	0.0204983	+	0.0118347i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.bl.a.395.7	✓	240
3.2	odd	2	inner	882.2.bl.a.395.14	yes	240
49.33	odd	42	inner	882.2.bl.a.719.14	yes	240
147.131	even	42	inner	882.2.bl.a.719.7	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.bl.a.395.7	✓	240	1.1	even	1	trivial
882.2.bl.a.395.14	yes	240	3.2	odd	2	inner
882.2.bl.a.719.7	yes	240	147.131	even	42	inner
882.2.bl.a.719.14	yes	240	49.33	odd	42	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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.bl (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.930874 - 0.365341i) q^{2} +(0.733052 + 0.680173i) q^{4} +(1.34171 + 0.914763i) q^{5} +(2.55989 + 0.668535i) q^{7} +(-0.433884 - 0.900969i) q^{8} +O(q^{10})\)	\(q+(-0.930874 - 0.365341i) q^{2} +(0.733052 + 0.680173i) q^{4} +(1.34171 + 0.914763i) q^{5} +(2.55989 + 0.668535i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(-0.914763 - 1.34171i) q^{10} +(-0.648044 - 4.29949i) q^{11} +(1.49142 - 1.18937i) q^{13} +(-2.13870 - 1.55756i) q^{14} +(0.0747301 + 0.997204i) q^{16} +(0.908745 + 0.280311i) q^{17} +(2.29692 - 1.32613i) q^{19} +(0.361347 + 1.58316i) q^{20} +(-0.967534 + 4.23904i) q^{22} +(-1.27855 - 4.14496i) q^{23} +(-0.863309 - 2.19967i) q^{25} +(-1.82285 + 0.562276i) q^{26} +(1.42182 + 2.23124i) q^{28} +(-1.57164 + 0.358717i) q^{29} +(7.66784 + 4.42703i) q^{31} +(0.294755 - 0.955573i) q^{32} +(-0.743518 - 0.592936i) q^{34} +(2.82309 + 3.23868i) q^{35} +(-3.30398 + 3.06565i) q^{37} +(-2.62263 + 0.395298i) q^{38} +(0.242026 - 1.60574i) q^{40} +(-2.95143 + 1.42134i) q^{41} +(6.58296 + 3.17019i) q^{43} +(2.44935 - 3.59253i) q^{44} +(-0.324154 + 4.32554i) q^{46} +(-1.85342 + 4.72244i) q^{47} +(6.10612 + 3.42276i) q^{49} +2.36302i q^{50} +(1.90227 + 0.142555i) q^{52} +(2.33205 - 2.51335i) q^{53} +(3.06353 - 6.36148i) q^{55} +(-0.508368 - 2.59645i) q^{56} +(1.59405 + 0.240265i) q^{58} +(3.96539 - 2.70356i) q^{59} +(-6.01356 - 6.48108i) q^{61} +(-5.52042 - 6.92239i) q^{62} +(-0.623490 + 0.781831i) q^{64} +(3.08905 - 0.231492i) q^{65} +(-2.38545 + 4.13172i) q^{67} +(0.475497 + 0.823586i) q^{68} +(-1.44472 - 4.04619i) q^{70} +(8.72361 + 1.99111i) q^{71} +(7.10809 - 2.78972i) q^{73} +(4.19560 - 1.64665i) q^{74} +(2.58575 + 0.590181i) q^{76} +(1.21544 - 11.4395i) q^{77} +(-6.01655 - 10.4210i) q^{79} +(-0.811939 + 1.40632i) q^{80} +(3.26668 - 0.244804i) q^{82} +(5.11368 - 6.41235i) q^{83} +(0.962855 + 1.20738i) q^{85} +(-4.96970 - 5.35607i) q^{86} +(-3.59253 + 2.44935i) q^{88} +(5.36628 + 0.808837i) q^{89} +(4.61302 - 2.04759i) q^{91} +(1.88204 - 3.90810i) q^{92} +(3.45060 - 3.71887i) q^{94} +(4.29489 + 0.321857i) q^{95} -10.8504i q^{97} +(-4.43356 - 5.41697i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 20 q^{4} - 4 q^{7}+O(q^{10}) \) 240 * q - 20 * q^4 - 4 * q^7	\( 240 q - 20 q^{4} - 4 q^{7} - 12 q^{10} + 20 q^{16} + 24 q^{19} - 20 q^{22} + 24 q^{25} + 4 q^{28} + 12 q^{31} - 32 q^{37} + 44 q^{40} - 48 q^{43} + 204 q^{49} + 140 q^{55} + 136 q^{58} + 88 q^{61} + 40 q^{64} - 32 q^{67} - 16 q^{70} - 24 q^{73} - 28 q^{79} - 48 q^{82} - 112 q^{85} + 4 q^{88} + 80 q^{91} + 80 q^{94}+O(q^{100}) \) 240 * q - 20 * q^4 - 4 * q^7 - 12 * q^10 + 20 * q^16 + 24 * q^19 - 20 * q^22 + 24 * q^25 + 4 * q^28 + 12 * q^31 - 32 * q^37 + 44 * q^40 - 48 * q^43 + 204 * q^49 + 140 * q^55 + 136 * q^58 + 88 * q^61 + 40 * q^64 - 32 * q^67 - 16 * q^70 - 24 * q^73 - 28 * q^79 - 48 * q^82 - 112 * q^85 + 4 * q^88 + 80 * q^91 + 80 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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