LMFDB - Embedded newform 864.2.bn.a.35.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [864,2,Mod(35,864)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(864, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([12, 9, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("864.35"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bn (of order $24$, degree $8$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			35.16
Character	$\chi$	$=$	864.35
Dual form			864.2.bn.a.395.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.728560 - 1.21211i) q^{2} +(-0.938401 + 1.76618i) q^{4} +(-2.86669 - 2.19969i) q^{5} +(-0.326320 + 0.0874372i) q^{7} +(2.82448 - 0.149329i) q^{8} +(-0.577700 + 5.07734i) q^{10} +(0.285551 - 2.16897i) q^{11} +(3.11610 - 0.410243i) q^{13} +(0.343727 + 0.331831i) q^{14} +(-2.23881 - 3.31478i) q^{16} -5.19359 q^{17} +(-6.00299 - 2.48652i) q^{19} +(6.57516 - 2.99891i) q^{20} +(-2.83706 + 1.23411i) q^{22} +(-1.35356 + 5.05154i) q^{23} +(2.08519 + 7.78203i) q^{25} +(-2.76752 - 3.47816i) q^{26} +(0.151789 - 0.658392i) q^{28} +(0.686119 + 0.894167i) q^{29} +(-2.41169 + 1.39239i) q^{31} +(-2.38675 + 5.12868i) q^{32} +(3.78384 + 6.29518i) q^{34} +(1.12779 + 0.467147i) q^{35} +(0.498481 + 1.20344i) q^{37} +(1.35961 + 9.08784i) q^{38} +(-8.42539 - 5.78490i) q^{40} +(8.63084 + 2.31263i) q^{41} +(7.07855 + 0.931909i) q^{43} +(3.56284 + 2.53970i) q^{44} +(7.10915 - 2.03970i) q^{46} +(4.11008 + 2.37296i) q^{47} +(-5.96334 + 3.44293i) q^{49} +(7.91346 - 8.19714i) q^{50} +(-2.19959 + 5.88858i) q^{52} +(4.79184 + 11.5685i) q^{53} +(-5.58965 + 5.58965i) q^{55} +(-0.908628 + 0.295694i) q^{56} +(0.583947 - 1.48310i) q^{58} +(-7.50078 + 9.77521i) q^{59} +(2.08513 - 1.59998i) q^{61} +(3.44479 + 1.90879i) q^{62} +(7.95540 - 0.843554i) q^{64} +(-9.83531 - 5.67842i) q^{65} +(-3.45892 + 0.455376i) q^{67} +(4.87367 - 9.17283i) q^{68} +(-0.255433 - 1.70735i) q^{70} +(-4.59606 + 4.59606i) q^{71} +(-9.75895 - 9.75895i) q^{73} +(1.09552 - 1.48099i) q^{74} +(10.0249 - 8.26903i) q^{76} +(0.0964679 + 0.732747i) q^{77} +(-4.76659 + 8.25597i) q^{79} +(-0.873510 + 14.4271i) q^{80} +(-3.48493 - 12.1464i) q^{82} +(-6.13939 - 8.00100i) q^{83} +(14.8884 + 11.4243i) q^{85} +(-4.02758 - 9.25890i) q^{86} +(0.482642 - 6.16886i) q^{88} +(-6.07191 - 6.07191i) q^{89} +(-0.980976 + 0.406334i) q^{91} +(-7.65177 - 7.13100i) q^{92} +(-0.118166 - 6.71070i) q^{94} +(11.7391 + 20.3328i) q^{95} +(-4.89585 + 8.47985i) q^{97} +(8.51785 + 4.71981i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) $ 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.728560	−	1.21211i	−0.515170	−	0.857088i
$2$	−0.728560	−	1.21211i	−0.515170	−	0.857088i
$3$		0			0
$3$		0			0
$4$	−0.938401	+	1.76618i	−0.469201	+	0.883092i
$5$	−2.86669	−	2.19969i	−1.28202	−	0.983731i	−0.999702	−	0.0244109i	$-0.992229\pi$
$5$	−2.86669	−	2.19969i	−1.28202	−	0.983731i	−0.282321	−	0.959320i	$-0.591104\pi$
$6$		0			0
$7$	−0.326320	+	0.0874372i	−0.123337	+	0.0330481i	−0.319960	−	0.947431i	$-0.603669\pi$
$7$	−0.326320	+	0.0874372i	−0.123337	+	0.0330481i	0.196622	+	0.980479i	$0.437003\pi$
$8$	2.82448	−	0.149329i	0.998605	−	0.0527958i
$9$		0			0
$10$	−0.577700	+	5.07734i	−0.182685	+	1.60560i
$11$	0.285551	−	2.16897i	0.0860967	−	0.653970i	−0.892924	−	0.450208i	$-0.851350\pi$
$11$	0.285551	−	2.16897i	0.0860967	−	0.653970i	0.979021	−	0.203762i	$-0.0653168\pi$
$12$		0			0
$13$	3.11610	−	0.410243i	0.864251	−	0.113781i	0.314650	−	0.949208i	$-0.398113\pi$
$13$	3.11610	−	0.410243i	0.864251	−	0.113781i	0.549601	+	0.835427i	$0.314780\pi$
$14$	0.343727	+	0.331831i	0.0918648	+	0.0886856i
$15$		0			0
$16$	−2.23881	−	3.31478i	−0.559702	−	0.828694i
$17$	−5.19359			−1.25963			−0.629815	−	0.776745i	$-0.716869\pi$
$17$	−5.19359			−1.25963			−0.629815	+	0.776745i	$0.716869\pi$
$18$		0			0
$19$	−6.00299	−	2.48652i	−1.37718	−	0.570447i	−0.433455	−	0.901175i	$-0.642706\pi$
$19$	−6.00299	−	2.48652i	−1.37718	−	0.570447i	−0.943726	+	0.330728i	$0.892706\pi$
$20$	6.57516	−	2.99891i	1.47025	−	0.670577i
$21$		0			0
$22$	−2.83706	+	1.23411i	−0.604864	+	0.263113i
$23$	−1.35356	+	5.05154i	−0.282236	+	1.05332i	0.668599	+	0.743623i	$0.266894\pi$
$23$	−1.35356	+	5.05154i	−0.282236	+	1.05332i	−0.950835	+	0.309697i	$0.899772\pi$
$24$		0			0
$25$	2.08519	+	7.78203i	0.417038	+	1.55641i
$26$	−2.76752	−	3.47816i	−0.542756	−	0.682123i
$27$		0			0
$28$	0.151789	−	0.658392i	0.0286854	−	0.124424i
$29$	0.686119	+	0.894167i	0.127409	+	0.166043i	0.852702	−	0.522398i	$-0.174962\pi$
$29$	0.686119	+	0.894167i	0.127409	+	0.166043i	−0.725293	+	0.688440i	$0.758296\pi$
$30$		0			0
$31$	−2.41169	+	1.39239i	−0.433153	+	0.250081i	−0.700689	−	0.713467i	$-0.747124\pi$
$31$	−2.41169	+	1.39239i	−0.433153	+	0.250081i	0.267536	+	0.963548i	$0.413791\pi$
$32$	−2.38675	+	5.12868i	−0.421923	+	0.906632i
$33$		0			0
$34$	3.78384	+	6.29518i	0.648923	+	1.07961i
$35$	1.12779	+	0.467147i	0.190632	+	0.0789623i
$36$		0			0
$37$	0.498481	+	1.20344i	0.0819498	+	0.197844i	0.959543	−	0.281561i	$-0.0908523\pi$
$37$	0.498481	+	1.20344i	0.0819498	+	0.197844i	−0.877593	+	0.479406i	$0.840852\pi$
$38$	1.35961	+	9.08784i	0.220558	+	1.47424i
$39$		0			0
$40$	−8.42539	−	5.78490i	−1.33217	−	0.914674i
$41$	8.63084	+	2.31263i	1.34791	+	0.361171i	0.859363	−	0.511366i	$-0.170860\pi$
$41$	8.63084	+	2.31263i	1.34791	+	0.361171i	0.488547	+	0.872537i	$0.337527\pi$
$42$		0			0
$43$	7.07855	+	0.931909i	1.07947	+	0.142115i	0.649224	−	0.760597i	$-0.275094\pi$
$43$	7.07855	+	0.931909i	1.07947	+	0.142115i	0.430245	+	0.902712i	$0.358427\pi$
$44$	3.56284	+	2.53970i	0.537118	+	0.382874i
$45$		0			0
$46$	7.10915	−	2.03970i	1.04819	−	0.300737i
$47$	4.11008	+	2.37296i	0.599517	+	0.346131i	0.768852	−	0.639427i	$-0.220828\pi$
$47$	4.11008	+	2.37296i	0.599517	+	0.346131i	−0.169334	+	0.985559i	$0.554162\pi$
$48$		0			0
$49$	−5.96334	+	3.44293i	−0.851905	+	0.491848i
$50$	7.91346	−	8.19714i	1.11913	−	1.15925i
$51$		0			0
$52$	−2.19959	+	5.88858i	−0.305028	+	0.816599i
$53$	4.79184	+	11.5685i	0.658210	+	1.58906i	0.800566	+	0.599244i	$0.204532\pi$
$53$	4.79184	+	11.5685i	0.658210	+	1.58906i	−0.142356	+	0.989815i	$0.545468\pi$
$54$		0			0
$55$	−5.58965	+	5.58965i	−0.753708	+	0.753708i
$56$	−0.908628	+	0.295694i	−0.121421	+	0.0395137i
$57$		0			0
$58$	0.583947	−	1.48310i	0.0766760	−	0.194741i
$59$	−7.50078	+	9.77521i	−0.976519	+	1.27262i	−0.0144276	+	0.999896i	$0.504593\pi$
$59$	−7.50078	+	9.77521i	−0.976519	+	1.27262i	−0.962091	+	0.272728i	$0.912074\pi$
$60$		0			0
$61$	2.08513	−	1.59998i	0.266974	−	0.204856i	−0.466595	−	0.884471i	$-0.654520\pi$
$61$	2.08513	−	1.59998i	0.266974	−	0.204856i	0.733570	+	0.679614i	$0.237853\pi$
$62$	3.44479	+	1.90879i	0.437488	+	0.242416i
$63$		0			0
$64$	7.95540	−	0.843554i	0.994425	−	0.105444i
$65$	−9.83531	−	5.67842i	−1.21992	−	0.704321i
$66$		0			0
$67$	−3.45892	+	0.455376i	−0.422575	+	0.0556330i	−0.338815	−	0.940853i	$-0.610026\pi$
$67$	−3.45892	+	0.455376i	−0.422575	+	0.0556330i	−0.0837596	+	0.996486i	$0.526693\pi$
$68$	4.87367	−	9.17283i	0.591019	−	1.11237i
$69$		0			0
$70$	−0.255433	−	1.70735i	−0.0305301	−	0.204067i
$71$	−4.59606	+	4.59606i	−0.545452	+	0.545452i	−0.925122	−	0.379670i	$-0.876038\pi$
$71$	−4.59606	+	4.59606i	−0.545452	+	0.545452i	0.379670	+	0.925122i	$0.376038\pi$
$72$		0			0
$73$	−9.75895	−	9.75895i	−1.14220	−	1.14220i	−0.988047	−	0.154151i	$-0.950736\pi$
$73$	−9.75895	−	9.75895i	−1.14220	−	1.14220i	−0.154151	−	0.988047i	$-0.549264\pi$
$74$	1.09552	−	1.48099i	0.127352	−	0.172162i
$75$		0			0
$76$	10.0249	−	8.26903i	1.14993	−	0.948523i
$77$	0.0964679	+	0.732747i	0.0109935	+	0.0835042i
$78$		0			0
$79$	−4.76659	+	8.25597i	−0.536283	+	0.928869i	0.462817	+	0.886454i	$0.346839\pi$
$79$	−4.76659	+	8.25597i	−0.536283	+	0.928869i	−0.999100	+	0.0424156i	$0.986495\pi$
$80$	−0.873510	+	14.4271i	−0.0976614	+	1.61300i
$81$		0			0
$82$	−3.48493	−	12.1464i	−0.384847	−	1.34134i
$83$	−6.13939	−	8.00100i	−0.673885	−	0.878224i	0.323807	−	0.946123i	$-0.395037\pi$
$83$	−6.13939	−	8.00100i	−0.673885	−	0.878224i	−0.997692	+	0.0678990i	$0.978370\pi$
$84$		0			0
$85$	14.8884	+	11.4243i	1.61487	+	1.23914i
$86$	−4.02758	−	9.25890i	−0.434305	−	0.998413i
$87$		0			0
$88$	0.482642	−	6.16886i	0.0514498	−	0.657603i
$89$	−6.07191	−	6.07191i	−0.643621	−	0.643621i	0.307822	−	0.951444i	$-0.400400\pi$
$89$	−6.07191	−	6.07191i	−0.643621	−	0.643621i	−0.951444	+	0.307822i	$0.900400\pi$
$90$		0			0
$91$	−0.980976	+	0.406334i	−0.102834	+	0.0425953i
$92$	−7.65177	−	7.13100i	−0.797753	−	0.743459i
$93$		0			0
$94$	−0.118166	−	6.71070i	−0.0121879	−	0.692156i
$95$	11.7391	+	20.3328i	1.20441	+	2.08610i
$96$		0			0
$97$	−4.89585	+	8.47985i	−0.497098	+	0.860999i	−0.999994	−	0.00334789i	$-0.998934\pi$
$97$	−4.89585	+	8.47985i	−0.497098	+	0.860999i	0.502897	+	0.864347i	$0.332268\pi$
$98$	8.51785	+	4.71981i	0.860433	+	0.476773i
$99$		0			0
$100$	−15.7012	−	3.61984i	−1.57012	−	0.361984i
$101$	0.707950	−	5.37742i	0.0704437	−	0.535073i	−0.919444	−	0.393221i	$-0.871361\pi$
$101$	0.707950	−	5.37742i	0.0704437	−	0.535073i	0.989888	−	0.141852i	$-0.0453058\pi$
$102$		0			0
$103$	−3.39471	+	12.6692i	−0.334490	+	1.24834i	0.569930	+	0.821693i	$0.306970\pi$
$103$	−3.39471	+	12.6692i	−0.334490	+	1.24834i	−0.904421	+	0.426642i	$0.859696\pi$
$104$	8.74012	−	1.62405i	0.857039	−	0.159251i
$105$		0			0
$106$	10.5311	−	14.2366i	1.02287	−	1.38278i
$107$	2.81325	−	1.16529i	0.271967	−	0.112652i	−0.242532	−	0.970143i	$-0.577978\pi$
$107$	2.81325	−	1.16529i	0.271967	−	0.112652i	0.514499	+	0.857491i	$0.327978\pi$
$108$		0			0
$109$	1.73974	−	4.20010i	0.166637	−	0.402297i	−0.818398	−	0.574652i	$-0.805138\pi$
$109$	1.73974	−	4.20010i	0.166637	−	0.402297i	0.985035	+	0.172355i	$0.0551376\pi$
$110$	10.8476	+	2.70285i	1.03428	+	0.257707i
$111$		0			0
$112$	1.02040	+	0.885923i	0.0964189	+	0.0837118i
$113$	−5.84502	−	10.1239i	−0.549853	−	0.952373i	−0.998284	−	0.0585559i	$-0.981350\pi$
$113$	−5.84502	−	10.1239i	−0.549853	−	0.952373i	0.448431	−	0.893817i	$-0.351983\pi$
$114$		0			0
$115$	14.9921	−	11.5038i	1.39802	−	1.07274i
$116$	−2.22312	+	0.372724i	−0.206411	+	0.0346065i
$117$		0			0
$118$	17.3134	+	1.96992i	1.59382	+	0.181346i
$119$	1.69477	−	0.454113i	0.155359	−	0.0416284i
$120$		0			0
$121$	6.00228	+	1.60831i	0.545662	+	0.146210i
$122$	−3.45849	−	1.36172i	−0.313117	−	0.123285i
$123$		0			0
$124$	−0.196084	−	5.56611i	−0.0176088	−	0.499851i
$125$	4.22654	−	10.2038i	0.378033	−	0.912653i
$126$		0			0
$127$			2.63721i			0.234015i	0.993131	+	0.117007i	$0.0373301\pi$
$127$			2.63721i			0.234015i	−0.993131	+	0.117007i	$0.962670\pi$
$128$	−6.81846	−	9.02821i	−0.602673	−	0.797988i
$129$		0			0
$130$	0.282768	+	16.0585i	0.0248004	+	1.40842i
$131$	0.188336	+	1.43056i	0.0164550	+	0.124988i	0.997701	−	0.0677725i	$-0.0215892\pi$
$131$	0.188336	+	1.43056i	0.0164550	+	0.124988i	−0.981246	+	0.192761i	$0.938256\pi$
$132$		0			0
$133$	2.17631	+	0.286517i	0.188710	+	0.0248441i
$134$	3.07200	+	3.86081i	0.265380	+	0.333523i
$135$		0			0
$136$	−14.6692	+	0.775553i	−1.25787	+	0.0665031i
$137$	−5.15642	−	19.2440i	−0.440543	−	1.64413i	−0.727444	−	0.686167i	$-0.759292\pi$
$137$	−5.15642	−	19.2440i	−0.440543	−	1.64413i	0.286901	−	0.957960i	$-0.407375\pi$
$138$		0			0
$139$	−6.32406	+	8.24167i	−0.536400	+	0.699050i	−0.980409	−	0.196973i	$-0.936889\pi$
$139$	−6.32406	+	8.24167i	−0.536400	+	0.699050i	0.444009	+	0.896022i	$0.353556\pi$
$140$	−1.88339	+	1.55352i	−0.159175	+	0.131296i
$141$		0			0
$142$	8.91942	+	2.22241i	0.748501	+	0.186500i
$143$		−	6.87588i		−	0.574990i
$144$		0			0
$145$		−	4.07255i		−	0.338207i
$146$	−4.71890	+	18.9389i	−0.390539	+	1.56739i
$147$		0			0
$148$	−2.59327	−	0.248900i	−0.213166	−	0.0204595i
$149$	3.65105	−	4.75815i	0.299106	−	0.389803i	−0.619487	−	0.785007i	$-0.712659\pi$
$149$	3.65105	−	4.75815i	0.299106	−	0.389803i	0.918593	+	0.395204i	$0.129326\pi$
$150$		0			0
$151$	0.208106	+	0.776662i	0.0169354	+	0.0632038i	0.973876	−	0.227079i	$-0.0729174\pi$
$151$	0.208106	+	0.776662i	0.0169354	+	0.0632038i	−0.956941	+	0.290282i	$0.906251\pi$
$152$	−17.3267	−	6.12671i	−1.40538	−	0.496942i
$153$		0			0
$154$	0.817884	−	0.650779i	0.0659070	−	0.0524413i
$155$	9.97640	+	1.31342i	0.801324	+	0.105496i
$156$		0			0
$157$	−2.39047	−	18.1574i	−0.190780	−	1.44912i	−0.772130	−	0.635464i	$-0.780809\pi$
$157$	−2.39047	−	18.1574i	−0.190780	−	1.44912i	0.581350	−	0.813654i	$-0.302525\pi$
$158$	13.4799	−	0.237361i	1.07240	−	0.0188835i
$159$		0			0
$160$	18.1236	−	9.45223i	1.43280	−	0.747265i
$161$		−	1.76677i		−	0.139241i
$162$		0			0
$163$	2.99169	−	7.22259i	0.234327	−	0.565717i	−0.762350	−	0.647165i	$-0.775955\pi$
$163$	2.99169	−	7.22259i	0.234327	−	0.565717i	0.996678	+	0.0814482i	$0.0259545\pi$
$164$	−12.1837	+	13.0735i	−0.951388	+	1.02087i
$165$		0			0
$166$	−5.22515	+	13.2708i	−0.405550	+	1.03001i
$167$	−8.44045	−	2.26161i	−0.653142	−	0.175009i	−0.0829929	−	0.996550i	$-0.526448\pi$
$167$	−8.44045	−	2.26161i	−0.653142	−	0.175009i	−0.570149	+	0.821541i	$0.693115\pi$
$168$		0			0
$169$	−3.01524	+	0.807931i	−0.231942	+	0.0621485i
$170$	3.00034	−	26.3696i	0.230115	−	2.02246i
$171$		0			0
$172$	−8.28844	+	11.6275i	−0.631988	+	0.886590i
$173$	2.37032	−	1.81881i	0.180212	−	0.138282i	−0.514716	−	0.857361i	$-0.672103\pi$
$173$	2.37032	−	1.81881i	0.180212	−	0.138282i	0.694929	+	0.719079i	$0.255436\pi$
$174$		0			0
$175$	−1.36088	−	2.35711i	−0.102873	−	0.178181i
$176$	−7.82895	+	3.90937i	−0.590129	+	0.294680i
$177$		0			0
$178$	−2.93605	+	11.7836i	−0.220066	+	0.883215i
$179$	−2.62554	+	6.33861i	−0.196242	+	0.473770i	−0.991115	−	0.133006i	$-0.957537\pi$
$179$	−2.62554	+	6.33861i	−0.196242	+	0.473770i	0.794873	+	0.606775i	$0.207537\pi$
$180$		0			0
$181$	14.4026	−	5.96576i	1.07054	−	0.443431i	0.223357	−	0.974737i	$-0.428298\pi$
$181$	14.4026	−	5.96576i	1.07054	−	0.443431i	0.847180	+	0.531306i	$0.178298\pi$
$182$	1.20722	+	0.893008i	0.0894850	+	0.0661942i
$183$		0			0
$184$	−3.06876	+	14.4701i	−0.226232	+	1.06675i
$185$	1.21820	−	4.54639i	0.0895640	−	0.334258i
$186$		0			0
$187$	−1.48303	+	11.2647i	−0.108450	+	0.823760i
$188$	−8.04798	+	5.03237i	−0.586960	+	0.367024i
$189$		0			0
$190$	16.0928	−	29.0428i	1.16750	−	2.10698i
$191$	−10.4588	+	18.1152i	−0.756771	+	1.31077i	0.187717	+	0.982223i	$0.439891\pi$
$191$	−10.4588	+	18.1152i	−0.756771	+	1.31077i	−0.944489	+	0.328544i	$0.893442\pi$
$192$		0			0
$193$	−4.85291	−	8.40549i	−0.349320	−	0.605041i	0.636809	−	0.771022i	$-0.280254\pi$
$193$	−4.85291	−	8.40549i	−0.349320	−	0.605041i	−0.986129	+	0.165981i	$0.946921\pi$
$194$	13.8454	−	0.243798i	0.994042	−	0.0175037i
$195$		0			0
$196$	−0.484852	−	13.7632i	−0.0346323	−	0.983086i
$197$	−23.0259	+	9.53766i	−1.64053	+	0.679530i	−0.996351	−	0.0853449i	$-0.972801\pi$
$197$	−23.0259	+	9.53766i	−1.64053	+	0.679530i	−0.644179	+	0.764875i	$0.722801\pi$
$198$		0			0
$199$	15.9180	+	15.9180i	1.12840	+	1.12840i	0.990438	+	0.137959i	$0.0440542\pi$
$199$	15.9180	+	15.9180i	1.12840	+	1.12840i	0.137959	+	0.990438i	$0.455946\pi$
$200$	7.05166	+	21.6688i	0.498628	+	1.53222i
$201$		0			0
$202$	−7.03378	+	3.05966i	−0.494895	+	0.215277i
$203$	−0.302078	−	0.231792i	−0.0212017	−	0.0162686i
$204$		0			0
$205$	−19.6549	−	25.6147i	−1.37276	−	1.78901i
$206$	17.8297	−	5.11554i	1.24225	−	0.356417i
$207$		0			0
$208$	−8.33621	−	9.41073i	−0.578013	−	0.652517i
$209$	−7.10735	+	12.3103i	−0.491626	+	0.851521i
$210$		0			0
$211$	2.65660	+	20.1789i	0.182888	+	1.38917i	0.798913	+	0.601446i	$0.205409\pi$
$211$	2.65660	+	20.1789i	0.182888	+	1.38917i	−0.616025	+	0.787726i	$0.711258\pi$
$212$	−24.9288	−	2.39265i	−1.71212	−	0.164328i
$213$		0			0
$214$	−3.46207	−	2.56098i	−0.236662	−	0.175065i
$215$	−18.2421	−	18.2421i	−1.24410	−	1.24410i
$216$		0			0
$217$	0.665236	−	0.665236i	0.0451592	−	0.0451592i
$218$	−6.35847	+	0.951278i	−0.430650	+	0.0644286i
$219$		0			0
$220$	−4.62701	−	15.1177i	−0.311953	−	1.01923i
$221$	−16.1837	+	2.13063i	−1.08864	+	0.143322i
$222$		0			0
$223$	−10.4284	−	6.02086i	−0.698339	−	0.403186i	0.108389	−	0.994109i	$-0.465431\pi$
$223$	−10.4284	−	6.02086i	−0.698339	−	0.403186i	−0.806729	+	0.590922i	$0.798764\pi$
$224$	0.330408	−	1.88228i	0.0220763	−	0.125765i
$225$		0			0
$226$	−8.01275	+	14.4606i	−0.533000	+	0.961906i
$227$	6.40250	−	4.91281i	0.424949	−	0.326075i	−0.374049	−	0.927409i	$-0.622031\pi$
$227$	6.40250	−	4.91281i	0.424949	−	0.326075i	0.798998	+	0.601334i	$0.205364\pi$
$228$		0			0
$229$	1.54865	−	2.01824i	0.102338	−	0.133369i	−0.739377	−	0.673292i	$-0.764880\pi$
$229$	1.54865	−	2.01824i	0.102338	−	0.133369i	0.841715	+	0.539923i	$0.181546\pi$
$230$	−24.8664	−	9.79075i	−1.63964	−	0.645583i
$231$		0			0
$232$	2.07145	+	2.42310i	0.135998	+	0.159084i
$233$	4.35606	−	4.35606i	0.285375	−	0.285375i	−0.549873	−	0.835248i	$-0.685324\pi$
$233$	4.35606	−	4.35606i	0.285375	−	0.285375i	0.835248	+	0.549873i	$0.185324\pi$
$234$		0			0
$235$	−6.56257	−	15.8434i	−0.428095	−	1.03351i
$236$	−10.2261	−	22.4208i	−0.665661	−	1.45947i
$237$		0			0
$238$	−1.78517	−	1.72339i	−0.115716	−	0.111711i
$239$	15.0367	−	8.68147i	0.972646	−	0.561558i	0.0726043	−	0.997361i	$-0.476869\pi$
$239$	15.0367	−	8.68147i	0.972646	−	0.561558i	0.900042	+	0.435803i	$0.143536\pi$
$240$		0			0
$241$	−6.10357	−	3.52390i	−0.393166	−	0.226994i	0.290365	−	0.956916i	$-0.406223\pi$
$241$	−6.10357	−	3.52390i	−0.393166	−	0.226994i	−0.683531	+	0.729922i	$0.739557\pi$
$242$	−2.42359	−	8.44715i	−0.155794	−	0.543004i
$243$		0			0
$244$	0.869166	+	5.18415i	0.0556426	+	0.331881i
$245$	24.6684	+	3.24766i	1.57601	+	0.207485i
$246$		0			0
$247$	−19.7260	−	5.28557i	−1.25514	−	0.336313i
$248$	−6.60386	+	4.29292i	−0.419345	+	0.272601i
$249$		0			0
$250$	−15.4473	+	2.31104i	−0.976976	+	0.146163i
$251$	−4.83125	−	11.6637i	−0.304946	−	0.736204i	−0.999854	−	0.0171056i	$-0.994555\pi$
$251$	−4.83125	−	11.6637i	−0.304946	−	0.736204i	0.694908	−	0.719099i	$-0.255445\pi$
$252$		0			0
$253$	10.5701	+	4.37830i	0.664540	+	0.275261i
$254$	3.19658	−	1.92137i	0.200571	−	0.120557i
$255$		0			0
$256$	−5.97549	+	14.8423i	−0.373468	+	0.927643i
$257$	1.76322	−	1.01799i	0.109987	−	0.0635008i	−0.443998	−	0.896028i	$-0.646440\pi$
$257$	1.76322	−	1.01799i	0.109987	−	0.0635008i	0.553984	+	0.832527i	$0.313107\pi$
$258$		0			0
$259$	−0.267890	−	0.349121i	−0.0166459	−	0.0216933i
$260$	19.2586	−	12.0423i	1.19437	−	0.746833i
$261$		0			0
$262$	1.59677	−	1.27053i	0.0986488	−	0.0784936i
$263$	−6.23478	−	23.2685i	−0.384453	−	1.43480i	−0.839028	−	0.544089i	$-0.816875\pi$
$263$	−6.23478	−	23.2685i	−0.384453	−	1.43480i	0.454575	−	0.890709i	$-0.349791\pi$
$264$		0			0
$265$	11.7104	−	43.7040i	0.719367	−	2.68471i
$266$	−1.23828	−	2.84666i	−0.0759241	−	0.174540i
$267$		0			0
$268$	2.44158	−	6.53642i	0.149143	−	0.399275i
$269$	−11.8731	−	4.91801i	−0.723918	−	0.299857i	−0.00986781	−	0.999951i	$-0.503141\pi$
$269$	−11.8731	−	4.91801i	−0.723918	−	0.299857i	−0.714050	+	0.700095i	$0.753141\pi$
$270$		0			0
$271$	−17.3296			−1.05270			−0.526348	−	0.850269i	$-0.676439\pi$
$271$	−17.3296			−1.05270			−0.526348	+	0.850269i	$0.676439\pi$
$272$	11.6274	+	17.2156i	0.705017	+	1.04385i
$273$		0			0
$274$	−19.5690	+	20.2705i	−1.18221	+	1.22459i
$275$	17.4744	−	2.30055i	1.05375	−	0.138728i
$276$		0			0
$277$	−1.13328	+	8.60814i	−0.0680924	+	0.517213i	0.923077	+	0.384614i	$0.125665\pi$
$277$	−1.13328	+	8.60814i	−0.0680924	+	0.517213i	−0.991170	+	0.132599i	$0.957668\pi$
$278$	14.5972	+	1.66088i	0.875484	+	0.0996127i
$279$		0			0
$280$	3.25519	+	1.15104i	0.194535	+	0.0687876i
$281$	19.9277	−	5.33960i	1.18878	−	0.318534i	0.390379	−	0.920654i	$-0.372344\pi$
$281$	19.9277	−	5.33960i	1.18878	−	0.318534i	0.798405	+	0.602120i	$0.205677\pi$
$282$		0			0
$283$	−6.29803	−	4.83265i	−0.374379	−	0.287271i	0.404384	−	0.914589i	$-0.367486\pi$
$283$	−6.29803	−	4.83265i	−0.374379	−	0.287271i	−0.778763	+	0.627318i	$0.784153\pi$
$284$	−3.80454	−	12.4304i	−0.225758	−	0.737611i
$285$		0			0
$286$	−8.33430	+	5.00949i	−0.492817	+	0.296218i
$287$	−3.01862			−0.178184
$288$		0			0
$289$	9.97334			0.586667
$290$	−4.93636	+	2.96710i	−0.289873	+	0.174234i
$291$		0			0
$292$	26.3939	−	8.07828i	1.54459	−	0.472746i
$293$	−4.90011	−	3.75999i	−0.286268	−	0.219661i	0.455638	−	0.890165i	$-0.349411\pi$
$293$	−4.90011	−	3.75999i	−0.286268	−	0.219661i	−0.741906	+	0.670504i	$0.766078\pi$
$294$		0			0
$295$	43.0049	−	11.5231i	2.50384	−	0.670902i
$296$	1.58766	+	3.32466i	0.0922808	+	0.193242i
$297$		0			0
$298$	−8.42739	−	0.958870i	−0.488186	−	0.0555458i
$299$	−2.14546	+	16.2964i	−0.124075	+	0.942446i
$300$		0			0
$301$	−2.39136	+	0.314828i	−0.137835	+	0.0181464i
$302$	0.789778	−	0.818091i	0.0454466	−	0.0470758i
$303$		0			0
$304$	5.19728	+	25.4654i	0.298084	+	1.46054i
$305$	−9.49689			−0.543791
$306$		0			0
$307$	−15.5108	−	6.42477i	−0.885246	−	0.366681i	−0.106717	−	0.994289i	$-0.534034\pi$
$307$	−15.5108	−	6.42477i	−0.885246	−	0.366681i	−0.778529	+	0.627609i	$0.784034\pi$
$308$	−1.38469	−	0.517230i	−0.0789001	−	0.0294719i
$309$		0			0
$310$	−5.67640	−	13.0494i	−0.322398	−	0.741154i
$311$	−8.09305	+	30.2037i	−0.458914	+	1.71269i	0.217403	+	0.976082i	$0.430241\pi$
$311$	−8.09305	+	30.2037i	−0.458914	+	1.71269i	−0.676317	+	0.736610i	$0.736425\pi$
$312$		0			0
$313$	5.43381	+	20.2793i	0.307137	+	1.14625i	0.931090	+	0.364790i	$0.118859\pi$
$313$	5.43381	+	20.2793i	0.307137	+	1.14625i	−0.623952	+	0.781462i	$0.714474\pi$
$314$	−20.2671	+	16.1262i	−1.14374	+	0.910057i
$315$		0			0
$316$	−10.1086	−	16.1661i	−0.568653	−	0.909413i
$317$	19.8745	+	25.9009i	1.11626	+	1.45474i	0.874900	+	0.484303i	$0.160927\pi$
$317$	19.8745	+	25.9009i	1.11626	+	1.45474i	0.241360	+	0.970436i	$0.422406\pi$
$318$		0			0
$319$	2.13534	−	1.23284i	0.119556	−	0.0690259i
$320$	−24.6612	−	15.0812i	−1.37860	−	0.843065i
$321$		0			0
$322$	−2.14151	+	1.28720i	−0.119342	+	0.0717328i
$323$	31.1771	+	12.9140i	1.73474	+	0.718552i
$324$		0			0
$325$	9.69018	+	23.3942i	0.537514	+	1.29767i
$326$	−10.9342	+	1.63584i	−0.605587	+	0.0906007i
$327$		0			0
$328$	24.7230	+	5.24314i	1.36510	+	0.289504i
$329$	−1.54869	−	0.414969i	−0.0853819	−	0.0228780i
$330$		0			0
$331$	−25.9032	−	3.41022i	−1.42377	−	0.187442i	−0.621035	−	0.783783i	$-0.713288\pi$
$331$	−25.9032	−	3.41022i	−1.42377	−	0.187442i	−0.802732	+	0.596340i	$0.796621\pi$
$332$	19.8924	−	3.33513i	1.09174	−	0.183039i
$333$		0			0
$334$	3.40806	+	11.8784i	0.186481	+	0.649959i
$335$	10.9173	+	6.30313i	0.596478	+	0.344377i
$336$		0			0
$337$	−11.6478	+	6.72488i	−0.634498	+	0.366327i	−0.782492	−	0.622661i	$-0.786052\pi$
$337$	−11.6478	+	6.72488i	−0.634498	+	0.366327i	0.147994	+	0.988988i	$0.452718\pi$
$338$	3.17608	+	3.06616i	0.172756	+	0.166777i
$339$		0			0
$340$	−34.1487	+	15.5751i	−1.85197	+	0.844679i
$341$	2.33140	+	5.62849i	0.126252	+	0.304800i
$342$		0			0
$343$	3.31710	−	3.31710i	0.179106	−	0.179106i
$344$	20.1324	+	1.57513i	1.08547	+	0.0849252i
$345$		0			0
$346$	−3.93152	−	1.54797i	−0.211360	−	0.0832194i
$347$	8.91361	−	11.6164i	0.478508	−	0.623603i	−0.490259	−	0.871577i	$-0.663098\pi$
$347$	8.91361	−	11.6164i	0.478508	−	0.623603i	0.968767	+	0.247973i	$0.0797645\pi$
$348$		0			0
$349$	20.6796	−	15.8680i	1.10695	−	0.849394i	0.117331	−	0.993093i	$-0.462566\pi$
$349$	20.6796	−	15.8680i	1.10695	−	0.849394i	0.989621	+	0.143699i	$0.0458996\pi$
$350$	−1.86558	+	3.36682i	−0.0997197	+	0.179964i
$351$		0			0
$352$	10.4424	+	6.64130i	0.556583	+	0.353983i
$353$	14.8602	+	8.57952i	0.790927	+	0.456642i	0.840289	−	0.542139i	$-0.182385\pi$
$353$	14.8602	+	8.57952i	0.790927	+	0.456642i	−0.0493620	+	0.998781i	$0.515719\pi$
$354$		0			0
$355$	23.2854	−	3.06558i	1.23586	−	0.162704i
$356$	16.4220	−	5.02622i	0.870364	−	0.266389i
$357$		0			0
$358$	9.59592	−	1.43563i	0.507160	−	0.0758752i
$359$	−8.04157	+	8.04157i	−0.424418	+	0.424418i	−0.886722	−	0.462304i	$-0.847023\pi$
$359$	−8.04157	+	8.04157i	−0.424418	+	0.424418i	0.462304	+	0.886722i	$0.347023\pi$
$360$		0			0
$361$	16.4181	+	16.4181i	0.864110	+	0.864110i
$362$	−17.7243	−	13.1111i	−0.931568	−	0.689103i
$363$		0			0
$364$	0.202889	−	2.11389i	0.0106343	−	0.110798i
$365$	6.50923	+	49.4425i	0.340709	+	2.58794i
$366$		0			0
$367$	0.666895	−	1.15510i	0.0348116	−	0.0602955i	−0.848095	−	0.529845i	$-0.822250\pi$
$367$	0.666895	−	1.15510i	0.0348116	−	0.0602955i	0.882906	+	0.469549i	$0.155584\pi$
$368$	19.7751	−	6.82269i	1.03085	−	0.355657i
$369$		0			0
$370$	−6.39824	+	1.83573i	−0.332629	+	0.0954350i
$371$	−2.57519	−	3.35606i	−0.133697	−	0.174238i
$372$		0			0
$373$	−12.9829	−	9.96215i	−0.672231	−	0.515821i	0.215313	−	0.976545i	$-0.430923\pi$
$373$	−12.9829	−	9.96215i	−0.672231	−	0.515821i	−0.887543	+	0.460725i	$0.847590\pi$
$374$	14.7345	−	6.40945i	0.761905	−	0.331425i
$375$		0			0
$376$	11.9632	+	6.08862i	0.616955	+	0.313997i
$377$	2.50484	+	2.50484i	0.129006	+	0.129006i
$378$		0			0
$379$	−2.28676	+	0.947206i	−0.117463	+	0.0486547i	−0.440641	−	0.897683i	$-0.645249\pi$
$379$	−2.28676	+	0.947206i	−0.117463	+	0.0486547i	0.323178	+	0.946338i	$0.395249\pi$
$380$	−46.9275	+	1.65317i	−2.40733	+	0.0848056i
$381$		0			0
$382$	29.5773	−	0.520815i	1.51331	−	0.0266472i
$383$	−11.9607	−	20.7165i	−0.611162	−	1.05856i	−0.991045	−	0.133529i	$-0.957369\pi$
$383$	−11.9607	−	20.7165i	−0.611162	−	1.05856i	0.379883	−	0.925035i	$-0.375964\pi$
$384$		0			0
$385$	1.33527	−	2.31276i	0.0680517	−	0.117869i
$386$	−6.65271	+	12.0061i	−0.338614	+	0.611097i
$387$		0			0
$388$	−10.3827	−	16.6045i	−0.527102	−	0.842964i
$389$	−0.855262	+	6.49636i	−0.0433635	+	0.329379i	0.955989	+	0.293402i	$0.0947875\pi$
$389$	−0.855262	+	6.49636i	−0.0433635	+	0.329379i	−0.999353	+	0.0359765i	$0.988546\pi$
$390$		0			0
$391$	7.02982	−	26.2356i	0.355513	−	1.32679i
$392$	−16.3292	+	10.6150i	−0.824750	+	0.536139i
$393$		0			0
$394$	28.3364	+	20.9611i	1.42757	+	1.05601i
$395$	31.8249	−	13.1823i	1.60128	−	0.663274i
$396$		0			0
$397$	5.36519	−	12.9527i	0.269271	−	0.650078i	−0.730178	−	0.683257i	$-0.760563\pi$
$397$	5.36519	−	12.9527i	0.269271	−	0.650078i	0.999449	+	0.0331786i	$0.0105630\pi$
$398$	7.69708	−	30.8915i	0.385820	−	1.54845i
$399$		0			0
$400$	21.1273	−	24.3344i	1.05637	−	1.21672i
$401$	11.7994	+	20.4372i	0.589236	+	1.02059i	0.994333	+	0.106312i	$0.0339044\pi$
$401$	11.7994	+	20.4372i	0.589236	+	1.02059i	−0.405097	+	0.914274i	$0.632762\pi$
$402$		0			0
$403$	−6.94386	+	5.32821i	−0.345898	+	0.265417i
$404$	8.83316	+	6.29654i	0.439466	+	0.313265i
$405$		0			0
$406$	−0.0608752	+	0.535025i	−0.00302118	+	0.0265528i
$407$	2.75257	−	0.737549i	0.136440	−	0.0365589i
$408$		0			0
$409$	−4.14858	−	1.11161i	−0.205134	−	0.0549655i	0.154789	−	0.987948i	$-0.450530\pi$
$409$	−4.14858	−	1.11161i	−0.205134	−	0.0549655i	−0.359923	+	0.932982i	$0.617197\pi$
$410$	−16.7280	+	42.4857i	−0.826138	+	2.09822i
$411$		0			0
$412$	−19.1906	−	17.8845i	−0.945451	−	0.881105i
$413$	1.59294	−	3.84569i	0.0783834	−	0.189234i
$414$		0			0
$415$			36.4411i			1.78883i
$416$	−5.33337	+	16.9607i	−0.261490	+	0.831564i
$417$		0			0
$418$	20.0995	−	0.353924i	0.983099	−	0.0173110i
$419$	−2.16132	−	16.4168i	−0.105587	−	0.802015i	−0.959522	−	0.281634i	$-0.909124\pi$
$419$	−2.16132	−	16.4168i	−0.105587	−	0.802015i	0.853935	−	0.520380i	$-0.174210\pi$
$420$		0			0
$421$	−9.49857	−	1.25051i	−0.462932	−	0.0609462i	−0.104547	−	0.994520i	$-0.533339\pi$
$421$	−9.49857	−	1.25051i	−0.462932	−	0.0609462i	−0.358385	+	0.933574i	$0.616673\pi$
$422$	22.5235	−	17.9216i	1.09643	−	0.872411i
$423$		0			0
$424$	15.2620	+	31.9595i	0.741188	+	1.55209i
$425$	−10.8296	−	40.4166i	−0.525313	−	1.96049i
$426$		0			0
$427$	−0.540523	+	0.704424i	−0.0261578	+	0.0340895i
$428$	−0.581847	+	6.06222i	−0.0281247	+	0.293028i
$429$		0			0
$430$	−8.82090	+	35.4018i	−0.425381	+	1.70723i
$431$			28.6503i			1.38004i	0.723791	+	0.690019i	$0.242398\pi$
$431$			28.6503i			1.38004i	−0.723791	+	0.690019i	$0.757602\pi$
$432$		0			0
$433$		−	2.24451i		−	0.107864i	−0.998545	−	0.0539321i	$-0.982825\pi$
$433$		−	2.24451i		−	0.107864i	0.998545	−	0.0539321i	$-0.0171755\pi$
$434$	−1.29100	−	0.321672i	−0.0619701	−	0.0154408i
$435$		0			0
$436$	5.78558	+	7.01408i	0.277079	+	0.335913i
$437$	20.6862	−	26.9587i	0.989553	−	1.28961i
$438$		0			0
$439$	3.78576	+	14.1287i	0.180685	+	0.674324i	0.995513	+	0.0946223i	$0.0301643\pi$
$439$	3.78576	+	14.1287i	0.180685	+	0.674324i	−0.814829	+	0.579702i	$0.803169\pi$
$440$	−14.9532	+	16.6226i	−0.712864	+	0.792449i
$441$		0			0
$442$	14.3734	+	18.0641i	0.683672	+	0.859223i
$443$	−18.8870	−	2.48652i	−0.897349	−	0.118138i	−0.332279	−	0.943181i	$-0.607817\pi$
$443$	−18.8870	−	2.48652i	−0.897349	−	0.118138i	−0.565070	+	0.825043i	$0.691151\pi$
$444$		0			0
$445$	4.04998	+	30.7626i	0.191987	+	1.45829i
$446$	0.299820	+	17.0269i	0.0141969	+	0.806248i
$447$		0			0
$448$	−2.52225	+	0.970866i	−0.119165	+	0.0458691i
$449$		−	6.68952i		−	0.315698i	−0.987463	−	0.157849i	$-0.949544\pi$
$449$		−	6.68952i		−	0.315698i	0.987463	−	0.157849i	$-0.0504559\pi$
$450$		0			0
$451$	7.48056	−	18.0597i	0.352246	−	0.850397i
$452$	23.3656	−	0.823125i	1.09902	−	0.0387165i
$453$		0			0
$454$	−10.6195	−	4.18123i	−0.498396	−	0.196235i
$455$	3.70596	+	0.993010i	0.173738	+	0.0465530i
$456$		0			0
$457$	−15.5301	+	4.16127i	−0.726466	+	0.194656i	−0.603055	−	0.797700i	$-0.706050\pi$
$457$	−15.5301	+	4.16127i	−0.726466	+	0.194656i	−0.123411	+	0.992356i	$0.539383\pi$
$458$	−3.57461	−	0.406719i	−0.167030	−	0.0190047i
$459$		0			0
$460$	6.24928	+	37.2739i	0.291374	+	1.73790i
$461$	−0.276368	+	0.212065i	−0.0128718	+	0.00987684i	−0.615177	−	0.788389i	$-0.710916\pi$
$461$	−0.276368	+	0.212065i	−0.0128718	+	0.00987684i	0.602306	+	0.798266i	$0.294249\pi$
$462$		0			0
$463$	18.9935	+	32.8977i	0.882702	+	1.52888i	0.848325	+	0.529475i	$0.177611\pi$
$463$	18.9935	+	32.8977i	0.882702	+	1.52888i	0.0343766	+	0.999409i	$0.489055\pi$
$464$	1.42788	−	4.27620i	0.0662875	−	0.198517i
$465$		0			0
$466$	−8.45366	−	2.10636i	−0.391608	−	0.0975751i
$467$	−3.91506	+	9.45180i	−0.181168	+	0.437377i	−0.988208	−	0.153119i	$-0.951068\pi$
$467$	−3.91506	+	9.45180i	−0.181168	+	0.437377i	0.807040	+	0.590497i	$0.201068\pi$
$468$		0			0
$469$	1.08890	−	0.451037i	0.0502807	−	0.0208269i
$470$	−14.4227	+	19.4974i	−0.665270	+	0.899349i
$471$		0			0
$472$	−19.7261	+	28.7300i	−0.907968	+	1.32241i
$473$	4.04257	−	15.0871i	0.185877	−	0.693704i
$474$		0			0
$475$	6.83281	−	51.9003i	0.313511	−	2.38135i
$476$	−0.788329	+	3.41942i	−0.0361330	+	0.156729i
$477$		0			0
$478$	−21.4780	−	11.9012i	−0.982382	−	0.544346i
$479$	3.42795	−	5.93739i	0.156627	−	0.271286i	−0.777023	−	0.629472i	$-0.783271\pi$
$479$	3.42795	−	5.93739i	0.156627	−	0.271286i	0.933650	+	0.358186i	$0.116605\pi$
$480$		0			0
$481$	2.04702	+	3.54554i	0.0933361	+	0.161663i
$482$	0.175479	+	9.96554i	0.00799286	+	0.453918i
$483$		0			0
$484$	−8.47312	+	9.09190i	−0.385142	+	0.413268i
$485$	32.6879	−	13.5398i	1.48428	−	0.614810i
$486$		0			0
$487$	−24.9342	−	24.9342i	−1.12988	−	1.12988i	−0.990197	−	0.139678i	$-0.955393\pi$
$487$	−24.9342	−	24.9342i	−1.12988	−	1.12988i	−0.139678	−	0.990197i	$-0.544607\pi$
$488$	5.65050	−	4.83049i	0.255786	−	0.218666i
$489$		0			0
$490$	−14.0359	−	32.2669i	−0.634078	−	1.45767i
$491$	0.263984	+	0.202562i	0.0119134	+	0.00914148i	0.614701	−	0.788760i	$-0.289277\pi$
$491$	0.263984	+	0.202562i	0.0119134	+	0.00914148i	−0.602788	+	0.797902i	$0.705943\pi$
$492$		0			0
$493$	−3.56342	−	4.64393i	−0.160488	−	0.209152i
$494$	7.96491	+	27.7609i	0.358358	+	1.24902i
$495$		0			0
$496$	10.0148	+	4.87692i	0.449677	+	0.218980i
$497$	1.09792	−	1.90165i	0.0492485	−	0.0853008i
$498$		0			0
$499$	1.29015	+	9.79966i	0.0577551	+	0.438693i	0.995754	+	0.0920549i	$0.0293435\pi$
$499$	1.29015	+	9.79966i	0.0577551	+	0.438693i	−0.937999	+	0.346638i	$0.887323\pi$
$500$	14.0555	+	17.0401i	0.628583	+	0.762055i
$501$		0			0
$502$	−10.6177	+	14.3537i	−0.473893	+	0.640636i
$503$	−16.8400	−	16.8400i	−0.750858	−	0.750858i	0.223782	−	0.974639i	$-0.428160\pi$
$503$	−16.8400	−	16.8400i	−0.750858	−	0.750858i	−0.974639	+	0.223782i	$0.928160\pi$
$504$		0			0
$505$	−13.8581	+	13.8581i	−0.616678	+	0.616678i
$506$	−2.39402	−	16.0020i	−0.106427	−	0.711375i
$507$		0			0
$508$	−4.65780	−	2.47476i	−0.206657	−	0.109800i
$509$	−19.1181	+	2.51695i	−0.847395	+	0.111562i	−0.541704	−	0.840569i	$-0.682221\pi$
$509$	−19.1181	+	2.51695i	−0.847395	+	0.111562i	−0.305691	+	0.952131i	$0.598887\pi$
$510$		0			0
$511$	4.03783	+	2.33124i	0.178623	+	0.103128i
$512$	22.3439	−	3.57058i	0.987471	−	0.157799i
$513$		0			0
$514$	−2.51853	−	1.39554i	−0.111087	−	0.0615545i
$515$	37.5999	−	28.8514i	1.65685	−	1.27135i
$516$		0			0
$517$	6.32051	−	8.23705i	0.277976	−	0.362265i
$518$	−0.227998	+	0.579066i	−0.0100176	+	0.0254427i
$519$		0			0
$520$	−28.6276	−	14.5699i	−1.25540	−	0.638932i
$521$	−24.6409	+	24.6409i	−1.07954	+	1.07954i	−0.0829879	+	0.996551i	$0.526446\pi$
$521$	−24.6409	+	24.6409i	−1.07954	+	1.07954i	−0.996551	+	0.0829879i	$0.973554\pi$
$522$		0			0
$523$	−1.23077	−	2.97134i	−0.0538178	−	0.129928i	0.894684	−	0.446700i	$-0.147401\pi$
$523$	−1.23077	−	2.97134i	−0.0538178	−	0.129928i	−0.948502	+	0.316772i	$0.897401\pi$
$524$	−2.70336	−	1.00980i	−0.118097	−	0.0441133i
$525$		0			0
$526$	−23.6615	+	24.5097i	−1.03169	+	1.06867i
$527$	12.5253	−	7.23150i	0.545612	−	0.315009i
$528$		0			0
$529$	−3.76740	−	2.17511i	−0.163800	−	0.0945700i
$530$	−61.5056	+	17.6467i	−2.67163	+	0.766522i
$531$		0			0
$532$	−2.54829	+	3.57490i	−0.110483	+	0.154991i
$533$	27.8433	+	3.66564i	1.20603	+	0.158777i
$534$		0			0
$535$	−10.6280	−	2.84776i	−0.459488	−	0.123119i
$536$	−9.70166	+	1.80272i	−0.419048	+	0.0778656i
$537$		0			0
$538$	2.68914	+	17.9746i	0.115937	+	0.774938i
$539$	5.76479	+	13.9174i	0.248307	+	0.599467i
$540$		0			0
$541$	−4.07207	−	1.68670i	−0.175072	−	0.0725171i	0.293426	−	0.955982i	$-0.405205\pi$
$541$	−4.07207	−	1.68670i	−0.175072	−	0.0725171i	−0.468498	+	0.883465i	$0.655205\pi$
$542$	12.6256	+	21.0053i	0.542317	+	0.902254i
$543$		0			0
$544$	12.3958	−	26.6363i	0.531466	−	1.14202i
$545$	−14.2262	+	8.21351i	−0.609384	+	0.351828i
$546$		0			0
$547$	6.80220	+	8.86480i	0.290841	+	0.379032i	0.915806	−	0.401622i	$-0.131553\pi$
$547$	6.80220	+	8.86480i	0.290841	+	0.379032i	−0.624965	+	0.780653i	$0.714887\pi$
$548$	38.8273	+	8.95143i	1.65862	+	0.382386i
$549$		0			0
$550$	−15.5197	−	19.5048i	−0.661761	−	0.831686i
$551$	−1.89540	−	7.07373i	−0.0807467	−	0.301351i
$552$		0			0
$553$	0.833554	−	3.11087i	0.0354463	−	0.132287i
$554$	11.2596	−	4.89788i	0.478376	−	0.208091i
$555$		0			0
$556$	−8.62180	−	18.9034i	−0.365646	−	0.801684i
$557$	−13.5251	−	5.60228i	−0.573076	−	0.237376i	0.0772746	−	0.997010i	$-0.475378\pi$
$557$	−13.5251	−	5.60228i	−0.573076	−	0.237376i	−0.650351	+	0.759634i	$0.725378\pi$
$558$		0			0
$559$	22.4398			0.949102
$560$	−0.976423	−	4.78423i	−0.0412614	−	0.202171i
$561$		0			0
$562$	−20.9907	−	20.2642i	−0.885437	−	0.854794i
$563$	−2.86087	+	0.376641i	−0.120571	+	0.0158735i	−0.190570	−	0.981674i	$-0.561034\pi$
$563$	−2.86087	+	0.376641i	−0.120571	+	0.0158735i	0.0699990	+	0.997547i	$0.477700\pi$
$564$		0			0
$565$	−5.51350	+	41.8792i	−0.231955	+	1.76187i
$566$	−1.26919	+	11.1547i	−0.0533480	+	0.468869i
$567$		0			0
$568$	−12.2952	+	13.6678i	−0.515894	+	0.573489i
$569$	−29.0618	+	7.78708i	−1.21833	+	0.326451i	−0.810026	−	0.586393i	$-0.800547\pi$
$569$	−29.0618	+	7.78708i	−1.21833	+	0.326451i	−0.408307	+	0.912845i	$0.633881\pi$
$570$		0			0
$571$	−15.8500	−	12.1621i	−0.663301	−	0.508969i	0.221367	−	0.975191i	$-0.428948\pi$
$571$	−15.8500	−	12.1621i	−0.663301	−	0.508969i	−0.884668	+	0.466222i	$0.845615\pi$
$572$	12.1441	+	6.45234i	0.507769	+	0.269786i
$573$		0			0
$574$	2.19925	+	3.65889i	0.0917949	+	0.152719i
$575$	−42.1337			−1.75710
$576$		0			0
$577$	−37.0391			−1.54196			−0.770978	−	0.636862i	$-0.780232\pi$
$577$	−37.0391			−1.54196			−0.770978	+	0.636862i	$0.780232\pi$
$578$	−7.26618	−	12.0887i	−0.302233	−	0.502826i
$579$		0			0
$580$	7.19287	+	3.82168i	0.298668	+	0.158687i
$581$	2.70299	+	2.07408i	0.112139	+	0.0860472i
$582$		0			0
$583$	26.4601	−	7.08997i	1.09587	−	0.293636i
$584$	−29.0213	−	26.1067i	−1.20091	−	1.08030i
$585$		0			0
$586$	−0.987478	+	8.67883i	−0.0407924	+	0.358519i
$587$	−3.30190	+	25.0804i	−0.136284	+	1.03518i	0.777472	+	0.628917i	$0.216502\pi$
$587$	−3.30190	+	25.0804i	−0.136284	+	1.03518i	−0.913756	+	0.406263i	$0.866832\pi$
$588$		0			0
$589$	17.9396	−	2.36179i	0.739187	−	0.0973158i
$590$	−45.2988	−	43.7312i	−1.86492	−	1.80038i
$591$		0			0
$592$	2.87313	−	4.34662i	0.118085	−	0.178645i
$593$	29.5317			1.21272			0.606360	−	0.795190i	$-0.292629\pi$
$593$	29.5317			1.21272			0.606360	+	0.795190i	$0.292629\pi$
$594$		0			0
$595$	−5.85729	−	2.42617i	−0.240126	−	0.0994633i
$596$	4.97761	+	10.9135i	0.203891	+	0.447034i
$597$		0			0
$598$	21.3161	−	9.27239i	0.871679	−	0.379176i
$599$	0.867041	−	3.23584i	0.0354263	−	0.132213i	−0.945948	−	0.324319i	$-0.894865\pi$
$599$	0.867041	−	3.23584i	0.0354263	−	0.132213i	0.981374	+	0.192106i	$0.0615317\pi$
$600$		0			0
$601$	−6.88998	−	25.7137i	−0.281048	−	1.04889i	−0.951679	−	0.307094i	$-0.900643\pi$
$601$	−6.88998	−	25.7137i	−0.281048	−	1.04889i	0.670631	−	0.741791i	$-0.266023\pi$
$602$	2.12385	+	2.66921i	0.0865617	+	0.108789i
$603$		0			0
$604$	−1.56701	−	0.361267i	−0.0637609	−	0.0146997i
$605$	−13.6689	−	17.8137i	−0.555721	−	0.724229i
$606$		0			0
$607$	−23.0060	+	13.2825i	−0.933785	+	0.539121i	−0.888007	−	0.459830i	$-0.847910\pi$
$607$	−23.0060	+	13.2825i	−0.933785	+	0.539121i	−0.0457787	+	0.998952i	$0.514577\pi$
$608$	27.0802	−	24.8527i	1.09825	−	1.00791i
$609$		0			0
$610$	6.91906	+	11.5112i	0.280144	+	0.466077i
$611$	13.7809	+	5.70825i	0.557517	+	0.230931i
$612$		0			0
$613$	1.77061	+	4.27462i	0.0715141	+	0.172650i	0.955595	−	0.294684i	$-0.0952144\pi$
$613$	1.77061	+	4.27462i	0.0715141	+	0.172650i	−0.884081	+	0.467334i	$0.845214\pi$
$614$	3.51302	+	23.4815i	0.141774	+	0.947636i
$615$		0			0
$616$	0.381892	+	2.05522i	0.0153869	+	0.0828074i
$617$	32.5448	+	8.72036i	1.31021	+	0.351069i	0.845300	−	0.534292i	$-0.179422\pi$
$617$	32.5448	+	8.72036i	1.31021	+	0.351069i	0.464905	+	0.885360i	$0.346088\pi$
$618$		0			0
$619$	−12.2571	−	1.61368i	−0.492654	−	0.0648592i	−0.119894	−	0.992787i	$-0.538255\pi$
$619$	−12.2571	−	1.61368i	−0.492654	−	0.0648592i	−0.372761	+	0.927928i	$0.621589\pi$
$620$	−11.6816	+	16.3876i	−0.469144	+	0.658143i
$621$		0			0
$622$	42.5063	−	12.1955i	1.70435	−	0.488997i
$623$	2.51230	+	1.45048i	0.100653	+	0.0581121i
$624$		0			0
$625$	0.324562	−	0.187386i	0.0129825	−	0.00749545i
$626$	20.6218	−	21.3610i	0.824211	−	0.853758i
$627$		0			0
$628$	34.3125	+	12.8169i	1.36922	+	0.511451i
$629$	−2.58890	−	6.25017i	−0.103226	−	0.249211i
$630$		0			0
$631$	13.3996	−	13.3996i	0.533428	−	0.533428i	−0.388163	−	0.921591i	$-0.626890\pi$
$631$	13.3996	−	13.3996i	0.533428	−	0.533428i	0.921591	+	0.388163i	$0.126890\pi$
$632$	−12.2303	+	24.0306i	−0.486495	+	0.955887i
$633$		0			0
$634$	16.9149	−	42.9603i	0.671776	−	1.70617i
$635$	5.80105	−	7.56008i	0.230208	−	0.300012i
$636$		0			0
$637$	−17.1699	+	13.1750i	−0.680298	+	0.522011i
$638$	−3.05006	−	1.69006i	−0.120753	−	0.0669103i
$639$		0			0
$640$	−0.312828	+	40.8796i	−0.0123656	+	1.61591i
$641$	−31.5373	−	18.2081i	−1.24565	−	0.719175i	−0.275410	−	0.961327i	$-0.588813\pi$
$641$	−31.5373	−	18.2081i	−1.24565	−	0.719175i	−0.970238	+	0.242152i	$0.922147\pi$
$642$		0			0
$643$	37.0620	−	4.87931i	1.46158	−	0.192421i	0.642584	−	0.766215i	$-0.277862\pi$
$643$	37.0620	−	4.87931i	1.46158	−	0.192421i	0.819000	+	0.573794i	$0.194529\pi$
$644$	3.12044	+	1.65794i	0.122963	+	0.0653320i
$645$		0			0
$646$	−7.06127	−	47.1985i	−0.277822	−	1.85700i
$647$	4.70488	−	4.70488i	0.184968	−	0.184968i	−0.608549	−	0.793517i	$-0.708248\pi$
$647$	4.70488	−	4.70488i	0.184968	−	0.184968i	0.793517	+	0.608549i	$0.208248\pi$
$648$		0			0
$649$	19.0603	+	19.0603i	0.748182	+	0.748182i
$650$	21.2963	−	28.7896i	0.835311	−	1.12922i
$651$		0			0
$652$	9.94900	+	12.0616i	0.389633	+	0.472367i
$653$	−6.00604	−	45.6204i	−0.235034	−	1.78526i	−0.548993	−	0.835827i	$-0.684989\pi$
$653$	−6.00604	−	45.6204i	−0.235034	−	1.78526i	0.313959	−	0.949437i	$-0.398345\pi$
$654$		0			0
$655$	2.60688	−	4.51524i	0.101859	−	0.176425i
$656$	−11.6569	−	33.7868i	−0.455127	−	1.31915i
$657$		0			0
$658$	0.625324	+	2.17950i	0.0243777	+	0.0849659i
$659$	−7.21245	−	9.39944i	−0.280957	−	0.366150i	0.631463	−	0.775406i	$-0.282455\pi$
$659$	−7.21245	−	9.39944i	−0.280957	−	0.366150i	−0.912420	+	0.409256i	$0.865788\pi$
$660$		0			0
$661$	11.5386	+	8.85387i	0.448799	+	0.344376i	0.808302	−	0.588768i	$-0.200387\pi$
$661$	11.5386	+	8.85387i	0.448799	+	0.344376i	−0.359503	+	0.933144i	$0.617054\pi$
$662$	14.7385	+	33.8819i	0.572827	+	1.31686i
$663$		0			0
$664$	−18.5354	−	21.6819i	−0.719312	−	0.841421i
$665$	−5.60856	−	5.60856i	−0.217491	−	0.217491i
$666$		0			0
$667$	−5.44563	+	2.25565i	−0.210855	+	0.0873392i
$668$	11.9150	−	12.7851i	0.461003	−	0.494670i
$669$		0			0
$670$	−0.313876	−	17.8252i	−0.0121261	−	0.688647i
$671$	−2.87490	−	4.97947i	−0.110984	−	0.192230i
$672$		0			0
$673$	5.34192	−	9.25247i	0.205916	−	0.356657i	−0.744508	−	0.667613i	$-0.767316\pi$
$673$	5.34192	−	9.25247i	0.205916	−	0.356657i	0.950424	+	0.310957i	$0.100649\pi$
$674$	16.6374	+	9.21893i	0.640849	+	0.355100i
$675$		0			0
$676$	1.40255	−	6.08363i	0.0539442	−	0.233986i
$677$	−3.15179	+	23.9402i	−0.121133	+	0.920099i	0.817680	+	0.575673i	$0.195260\pi$
$677$	−3.15179	+	23.9402i	−0.121133	+	0.920099i	−0.938814	+	0.344426i	$0.888074\pi$
$678$		0			0
$679$	0.856158	−	3.19522i	0.0328563	−	0.122621i
$680$	43.7580	+	30.0444i	1.67804	+	1.15215i
$681$		0			0
$682$	5.12376	−	6.92659i	0.196199	−	0.265233i
$683$	−20.4615	+	8.47545i	−0.782939	+	0.324304i	−0.738101	−	0.674690i	$-0.764277\pi$
$683$	−20.4615	+	8.47545i	−0.782939	+	0.324304i	−0.0448383	+	0.998994i	$0.514277\pi$
$684$		0			0
$685$	−27.5490	+	66.5092i	−1.05259	+	2.54118i
$686$	−6.43737	−	1.60397i	−0.245780	−	0.0612398i
$687$		0			0
$688$	−12.7584	−	25.5502i	−0.486411	−	0.974091i
$689$	19.6778	+	34.0829i	0.749663	+	1.29846i
$690$		0			0
$691$	11.5915	−	8.89447i	0.440961	−	0.338361i	−0.364300	−	0.931282i	$-0.618692\pi$
$691$	11.5915	−	8.89447i	0.440961	−	0.338361i	0.805261	+	0.592920i	$0.202025\pi$
$692$	0.988044	+	5.89321i	0.0375598	+	0.224026i
$693$		0			0
$694$	−20.5745	−	2.34096i	−0.780996	−	0.0888618i
$695$	36.2582	−	9.71537i	1.37535	−	0.368525i
$696$		0			0
$697$	−44.8250	−	12.0108i	−1.69787	−	0.454942i
$698$	−34.3000	−	13.5050i	−1.29827	−	0.511174i
$699$		0			0
$700$	5.44013	−	0.191646i	0.205618	−	0.00724352i
$701$	10.6579	−	25.7305i	0.402544	−	0.971828i	−0.584502	−	0.811392i	$-0.698710\pi$
$701$	10.6579	−	25.7305i	0.402544	−	0.971828i	0.987046	−	0.160435i	$-0.0512898\pi$
$702$		0			0
$703$		−	8.46372i		−	0.319215i
$704$	0.442024	−	17.4959i	0.0166594	−	0.659402i
$705$		0			0
$706$	−0.427233	−	24.2628i	−0.0160791	−	0.913142i
$707$	0.239168	+	1.81666i	0.00899483	+	0.0683225i
$708$		0			0
$709$	2.94957	+	0.388319i	0.110774	+	0.0145836i	0.185709	−	0.982605i	$-0.440542\pi$
$709$	2.94957	+	0.388319i	0.110774	+	0.0145836i	−0.0749356	+	0.997188i	$0.523875\pi$
$710$	−20.6806	−	25.9909i	−0.776130	−	0.975421i
$711$		0			0
$712$	−18.0567	−	16.2433i	−0.676704	−	0.608743i
$713$	−3.76936	−	14.0674i	−0.141164	−	0.526830i
$714$		0			0
$715$	−15.1248	+	19.7110i	−0.565636	+	0.737151i
$716$	−8.73133	−	10.5853i	−0.326305	−	0.395592i
$717$		0			0
$718$	15.6060	+	3.88847i	0.582411	+	0.145116i
$719$			39.9035i			1.48815i	0.668096	+	0.744075i	$0.267110\pi$
$719$			39.9035i			1.48815i	−0.668096	+	0.744075i	$0.732890\pi$
$720$		0			0
$721$		−	4.43104i		−	0.165021i
$722$	7.93890	−	31.8620i	0.295455	−	1.18578i
$723$		0			0
$724$	−2.97880	+	31.0359i	−0.110706	+	1.15344i
$725$	−5.52775	+	7.20390i	−0.205295	+	0.267546i
$726$		0			0
$727$	−2.39756	−	8.94781i	−0.0889205	−	0.331856i	0.907107	−	0.420900i	$-0.138286\pi$
$727$	−2.39756	−	8.94781i	−0.0889205	−	0.331856i	−0.996028	+	0.0890438i	$0.971619\pi$
$728$	−2.71007	+	1.29417i	−0.100442	+	0.0479651i
$729$		0			0
$730$	55.1872	−	43.9117i	2.04257	−	1.62525i
$731$	−36.7631	−	4.83995i	−1.35973	−	0.179012i
$732$		0			0
$733$	−4.41392	−	33.5271i	−0.163032	−	1.23835i	−0.855844	−	0.517233i	$-0.826962\pi$
$733$	−4.41392	−	33.5271i	−0.163032	−	1.23835i	0.692812	−	0.721118i	$-0.256371\pi$
$734$	−1.88597	+	0.0332093i	−0.0696125	+	0.00122578i
$735$		0			0
$736$	−22.6772	−	18.9988i	−0.835891	−	0.700304i
$737$			7.63234i			0.281141i
$738$		0			0
$739$	1.57623	−	3.80535i	0.0579824	−	0.139982i	−0.892233	−	0.451575i	$-0.850862\pi$
$739$	1.57623	−	3.80535i	0.0579824	−	0.139982i	0.950216	+	0.311593i	$0.100862\pi$
$740$	6.88660	+	6.41791i	0.253157	+	0.235927i
$741$		0			0
$742$	−2.19171	+	5.56649i	−0.0804603	+	0.204352i
$743$	8.43884	+	2.26118i	0.309591	+	0.0829547i	0.410269	−	0.911964i	$-0.365435\pi$
$743$	8.43884	+	2.26118i	0.309591	+	0.0829547i	−0.100678	+	0.994919i	$0.532101\pi$
$744$		0			0
$745$	−20.9329	+	5.60895i	−0.766922	+	0.205496i
$746$	−2.61634	+	22.9947i	−0.0957911	+	0.841896i
$747$		0			0
$748$	−18.5039	−	13.1902i	−0.676570	−	0.482280i
$749$	−0.816130	+	0.626239i	−0.0298208	+	0.0228823i
$750$		0			0
$751$	21.8306	+	37.8117i	0.796610	+	1.37977i	0.921812	+	0.387637i	$0.126709\pi$
$751$	21.8306	+	37.8117i	0.796610	+	1.37977i	−0.125202	+	0.992131i	$0.539958\pi$
$752$	−1.33586	−	18.9366i	−0.0487138	−	0.690547i
$753$		0			0
$754$	1.21121	−	4.86106i	0.0441095	−	0.177029i
$755$	1.11184	−	2.68422i	0.0404640	−	0.0976886i
$756$		0			0
$757$	16.7337	−	6.93133i	0.608197	−	0.251923i	−0.0572605	−	0.998359i	$-0.518237\pi$
$757$	16.7337	−	6.93133i	0.608197	−	0.251923i	0.665457	+	0.746436i	$0.268237\pi$
$758$	2.81416	+	2.08170i	0.102215	+	0.0756106i
$759$		0			0
$760$	36.1933	+	55.6766i	1.31287	+	2.01960i
$761$	−11.2400	+	41.9483i	−0.407451	+	1.52063i	0.392040	+	0.919948i	$0.371769\pi$
$761$	−11.2400	+	41.9483i	−0.407451	+	1.52063i	−0.799491	+	0.600678i	$0.794897\pi$
$762$		0			0
$763$	−0.200467	+	1.52269i	−0.00725738	+	0.0551253i
$764$	−22.1801	−	35.4714i	−0.802450	−	1.28331i
$765$		0			0
$766$	−16.3965	+	29.5908i	−0.592430	+	1.06916i
$767$	−19.3630	+	33.5377i	−0.699157	+	1.21098i
$768$		0			0
$769$	16.2165	+	28.0879i	0.584783	+	1.01287i	0.994902	+	0.100842i	$0.0321537\pi$
$769$	16.2165	+	28.0879i	0.584783	+	1.01287i	−0.410119	+	0.912032i	$0.634513\pi$
$770$	−3.77613	+	0.0664924i	−0.136082	+	0.00239622i
$771$		0			0
$772$	19.3996	−	0.683412i	0.698208	−	0.0245965i
$773$	25.6739	−	10.6345i	0.923428	−	0.382496i	0.130246	−	0.991482i	$-0.458423\pi$
$773$	25.6739	−	10.6345i	0.923428	−	0.382496i	0.793181	+	0.608985i	$0.208423\pi$
$774$		0			0
$775$	−15.8645	−	15.8645i	−0.569868	−	0.569868i
$776$	−12.5619	+	24.6823i	−0.450947	+	0.886043i
$777$		0			0
$778$	8.49739	−	3.69632i	0.304646	−	0.132519i
$779$	−46.0604	−	35.3434i	−1.65029	−	1.26631i
$780$		0			0
$781$	8.65632	+	11.2811i	0.309748	+	0.403671i
$782$	−36.9220	+	10.5933i	−1.32033	+	0.378817i
$783$		0			0
$784$	24.7633	+	12.0591i	0.884404	+	0.430681i
$785$	−33.0879	+	57.3099i	−1.18096	+	2.04548i
$786$		0			0
$787$	−3.68563	−	27.9951i	−0.131378	−	0.997918i	−0.922429	−	0.386167i	$-0.873799\pi$
$787$	−3.68563	−	27.9951i	−0.131378	−	0.997918i	0.791050	−	0.611751i	$-0.209535\pi$
$788$	4.76232	−	49.6182i	0.169650	−	1.76757i
$789$		0			0
$790$	−39.1647	−	28.9711i	−1.39342	−	1.03074i
$791$	2.79255	+	2.79255i	0.0992916	+	0.0992916i
$792$		0			0
$793$	5.84111	−	5.84111i	0.207424	−	0.207424i
$794$	−19.6089	+	2.93365i	−0.695895	+	0.104111i
$795$		0			0
$796$	−43.0516	+	13.1766i	−1.52592	+	0.467034i
$797$	−28.7850	+	3.78962i	−1.01962	+	0.134235i	−0.621757	−	0.783210i	$-0.713581\pi$
$797$	−28.7850	+	3.78962i	−1.01962	+	0.134235i	−0.397861	+	0.917446i	$0.630247\pi$
$798$		0			0
$799$	−21.3461	−	12.3242i	−0.755170	−	0.435997i
$800$	−44.8884	−	7.87952i	−1.58704	−	0.278583i
$801$		0			0
$802$	16.1755	−	29.1919i	0.571176	−	1.03080i
$803$	−23.9536	+	18.3802i	−0.845303	+	0.648623i
$804$		0			0
$805$	−3.88635	+	5.06479i	−0.136976	+	0.178510i
$806$	11.5174	+	4.53477i	0.405682	+	0.159731i
$807$		0			0
$808$	1.19659	−	15.2941i	0.0420959	−	0.538046i
$809$	10.8261	−	10.8261i	0.380624	−	0.380624i	−0.490703	−	0.871327i	$-0.663260\pi$
$809$	10.8261	−	10.8261i	0.380624	−	0.380624i	0.871327	+	0.490703i	$0.163260\pi$
$810$		0			0
$811$	4.06716	+	9.81899i	0.142817	+	0.344791i	0.979061	−	0.203566i	$-0.0652532\pi$
$811$	4.06716	+	9.81899i	0.142817	+	0.344791i	−0.836244	+	0.548358i	$0.815253\pi$
$812$	0.692858	−	0.316010i	0.0243145	−	0.0110898i
$813$		0			0
$814$	−2.89940	−	2.79906i	−0.101624	−	0.0981069i
$815$	−24.4637	+	14.1241i	−0.856926	+	0.494747i
$816$		0			0
$817$	−40.1753	−	23.1952i	−1.40555	−	0.811497i
$818$	1.67510	+	5.83839i	0.0585686	+	0.204135i
$819$		0			0
$820$	63.6845	−	10.6772i	2.22396	−	0.372865i
$821$	−1.37179	−	0.180600i	−0.0478758	−	0.00630297i	0.106550	−	0.994307i	$-0.466020\pi$
$821$	−1.37179	−	0.180600i	−0.0478758	−	0.00630297i	−0.154426	+	0.988004i	$0.549353\pi$
$822$		0			0
$823$	33.2419	+	8.90714i	1.15874	+	0.310483i	0.786462	−	0.617638i	$-0.211910\pi$
$823$	33.2419	+	8.90714i	1.15874	+	0.310483i	0.372277	+	0.928122i	$0.378577\pi$
$824$	−7.69641	+	36.2909i	−0.268117	+	1.26425i
$825$		0			0
$826$	−5.82194	+	0.871008i	−0.202571	+	0.0303063i
$827$	−12.7639	−	30.8147i	−0.443843	−	1.07153i	−0.974589	−	0.224000i	$-0.928088\pi$
$827$	−12.7639	−	30.8147i	−0.443843	−	1.07153i	0.530746	−	0.847531i	$-0.321912\pi$
$828$		0			0
$829$	36.2935	+	15.0332i	1.26052	+	0.522126i	0.910070	−	0.414454i	$-0.136027\pi$
$829$	36.2935	+	15.0332i	1.26052	+	0.522126i	0.350454	+	0.936580i	$0.386027\pi$
$830$	44.1705	−	26.5496i	1.53318	−	0.921548i
$831$		0			0
$832$	24.4438	−	5.89225i	0.847436	−	0.204277i
$833$	30.9711	−	17.8812i	1.07309	−	0.619546i
$834$		0			0
$835$	19.2213	+	25.0497i	0.665181	+	0.866881i
$836$	−15.0727	−	24.1049i	−0.521300	−	0.833684i
$837$		0			0
$838$	−18.3243	+	14.5804i	−0.633002	+	0.503671i
$839$	−2.51155	−	9.37322i	−0.0867082	−	0.323599i	0.908924	−	0.416962i	$-0.136905\pi$
$839$	−2.51155	−	9.37322i	−0.0867082	−	0.323599i	−0.995632	+	0.0933624i	$0.970238\pi$
$840$		0			0
$841$	7.17698	−	26.7848i	0.247482	−	0.923615i
$842$	5.40453	+	12.4243i	0.186252	+	0.428171i
$843$		0			0
$844$	−38.1326	−	14.2438i	−1.31258	−	0.490294i
$845$	10.4210	+	4.31650i	0.358492	+	0.148492i
$846$		0			0
$847$	−2.09929			−0.0721325
$848$	27.6191	−	41.7836i	0.948443	−	1.43485i
$849$		0			0
$850$	−41.0992	+	42.5726i	−1.40969	+	1.46023i
$851$	−6.75395	+	0.889175i	−0.231523	+	0.0304805i
$852$		0			0
$853$	−3.57465	+	27.1522i	−0.122394	+	0.929673i	0.814526	+	0.580128i	$0.196997\pi$
$853$	−3.57465	+	27.1522i	−0.122394	+	0.929673i	−0.936919	+	0.349545i	$0.886336\pi$
$854$	1.24764	+	0.141957i	0.0426934	+	0.00485766i
$855$		0			0
$856$	7.77196	−	3.71143i	0.265640	−	0.126854i
$857$	12.4894	−	3.34654i	0.426631	−	0.114316i	−0.0391130	−	0.999235i	$-0.512453\pi$
$857$	12.4894	−	3.34654i	0.426631	−	0.114316i	0.465745	+	0.884919i	$0.345787\pi$
$858$		0			0
$859$	−26.6945	−	20.4834i	−0.910805	−	0.698885i	0.0430753	−	0.999072i	$-0.486284\pi$
$859$	−26.6945	−	20.4834i	−0.910805	−	0.698885i	−0.953881	+	0.300186i	$0.902951\pi$
$860$	49.3373	−	15.1005i	1.68239	−	0.514923i
$861$		0			0
$862$	34.7272	−	20.8735i	1.18281	−	0.710954i
$863$	−17.8151			−0.606432			−0.303216	−	0.952922i	$-0.598060\pi$
$863$	−17.8151			−0.606432			−0.303216	+	0.952922i	$0.598060\pi$
$864$		0			0
$865$	−10.7958			−0.367069
$866$	−2.72058	+	1.63526i	−0.0924492	+	0.0555684i
$867$		0			0
$868$	0.550671	+	1.79919i	0.0186910	+	0.0610684i
$869$	16.5459	+	12.6961i	0.561280	+	0.430685i
$870$		0			0
$871$	−10.5915	+	2.83800i	−0.358881	+	0.0961618i
$872$	4.28667	−	12.1229i	0.145165	−	0.410533i
$873$		0			0
$874$	−47.7479	−	5.43277i	−1.61510	−	0.183766i
$875$	−0.487016	+	3.69925i	−0.0164641	+	0.125058i
$876$		0			0
$877$	−24.2406	+	3.19133i	−0.818547	+	0.107764i	−0.528159	−	0.849145i	$-0.677118\pi$
$877$	−24.2406	+	3.19133i	−0.818547	+	0.107764i	−0.290387	+	0.956909i	$0.593784\pi$
$878$	14.3673	−	14.8823i	0.484872	−	0.502254i
$879$		0			0
$880$	31.0426	+	6.01429i	1.04645	+	0.202742i
$881$	−17.0010			−0.572778			−0.286389	−	0.958113i	$-0.592455\pi$
$881$	−17.0010			−0.572778			−0.286389	+	0.958113i	$0.592455\pi$
$882$		0			0
$883$	−5.46596	−	2.26408i	−0.183944	−	0.0761922i	0.288810	−	0.957386i	$-0.406740\pi$
$883$	−5.46596	−	2.26408i	−0.183944	−	0.0761922i	−0.472755	+	0.881194i	$0.656740\pi$
$884$	11.4238	−	30.5829i	0.384223	−	1.02861i
$885$		0			0
$886$	10.7464	+	24.7046i	0.361032	+	0.829968i
$887$	3.02494	−	11.2892i	0.101568	−	0.379055i	−0.896366	−	0.443316i	$-0.853802\pi$
$887$	3.02494	−	11.2892i	0.101568	−	0.379055i	0.997933	+	0.0642603i	$0.0204688\pi$
$888$		0			0
$889$	−0.230591	−	0.860576i	−0.00773376	−	0.0288628i
$890$	34.3369	−	27.3214i	1.15098	−	0.915816i
$891$		0			0
$892$	20.4200	−	12.7685i	0.683712	−	0.427522i
$893$	−18.7724	−	24.4646i	−0.628194	−	0.818678i
$894$		0			0
$895$	21.4696	−	12.3955i	0.717648	−	0.414334i
$896$	3.01440	+	2.34990i	0.100704	+	0.0785046i
$897$		0			0
$898$	−8.10840	+	4.87371i	−0.270581	+	0.162638i
$899$	−2.89974	−	1.20111i	−0.0967116	−	0.0400593i
$900$		0			0
$901$	−24.8868	−	60.0822i	−0.829101	−	2.00163i
$902$	−27.3403	+	4.09032i	−0.910331	+	0.136193i
$903$		0			0
$904$	−18.0209	−	27.7219i	−0.599367	−	0.922015i
$905$	−54.4106	−	14.5793i	−1.80867	−	0.484632i
$906$		0			0
$907$	11.8555	+	1.56081i	0.393656	+	0.0518258i	0.324756	−	0.945798i	$-0.394718\pi$
$907$	11.8555	+	1.56081i	0.393656	+	0.0518258i	0.0689000	+	0.997624i	$0.478051\pi$
$908$	2.66881	+	15.9182i	0.0885677	+	0.528263i
$909$		0			0
$910$	−1.49638	−	5.21549i	−0.0496046	−	0.172892i
$911$	28.7369	+	16.5912i	0.952095	+	0.549692i	0.893731	−	0.448603i	$-0.148078\pi$
$911$	28.7369	+	16.5912i	0.952095	+	0.549692i	0.0583639	+	0.998295i	$0.481412\pi$
$912$		0			0
$913$	−19.1071	+	11.0315i	−0.632351	+	0.365088i
$914$	16.3585	+	15.7924i	0.541091	+	0.522365i
$915$		0			0
$916$	2.11133	+	4.62912i	0.0697603	+	0.152951i
$917$	−0.186542	−	0.450351i	−0.00616015	−	0.0148719i
$918$		0			0
$919$	−13.1527	+	13.1527i	−0.433868	+	0.433868i	−0.889942	−	0.456074i	$-0.849255\pi$
$919$	−13.1527	+	13.1527i	−0.433868	+	0.433868i	0.456074	+	0.889942i	$0.349255\pi$
$920$	40.6270	−	34.7311i	1.33943	−	1.14505i
$921$		0			0
$922$	0.458396	+	0.180486i	0.0150965	+	0.00594398i
$923$	−12.4363	+	16.2073i	−0.409346	+	0.533470i
$924$		0			0
$925$	−8.32578	+	6.38859i	−0.273750	+	0.210056i
$926$	26.0376	−	46.9900i	0.855648	−	1.54419i
$927$		0			0
$928$	−6.22350	+	1.38473i	−0.204296	+	0.0454559i
$929$	5.07912	+	2.93243i	0.166641	+	0.0962099i	0.581001	−	0.813903i	$-0.302661\pi$
$929$	5.07912	+	2.93243i	0.166641	+	0.0962099i	−0.414360	+	0.910113i	$0.635995\pi$
$930$		0			0
$931$	44.3588	−	5.83995i	1.45380	−	0.191397i
$932$	3.60587	+	11.7813i	0.118114	+	0.385911i
$933$		0			0
$934$	14.3089	−	2.14073i	0.468203	−	0.0700469i
$935$	29.0303	−	29.0303i	0.949393	−	0.949393i
$936$		0			0
$937$	36.0996	+	36.0996i	1.17932	+	1.17932i	0.979917	+	0.199407i	$0.0639014\pi$
$937$	36.0996	+	36.0996i	1.17932	+	1.17932i	0.199407	+	0.979917i	$0.436099\pi$
$938$	−1.34003	−	0.991253i	−0.0437536	−	0.0323656i
$939$		0			0
$940$	34.1407	+	3.27680i	1.11355	+	0.106878i
$941$	4.88844	+	37.1314i	0.159359	+	1.21045i	0.864961	+	0.501840i	$0.167343\pi$
$941$	4.88844	+	37.1314i	0.159359	+	1.21045i	−0.705602	+	0.708608i	$0.749323\pi$
$942$		0			0
$943$	−23.3647	+	40.4688i	−0.760858	+	1.31784i
$944$	49.1954	+	2.97861i	1.60118	+	0.0969454i
$945$		0			0
$946$	−21.2324	+	6.09181i	−0.690324	+	0.198062i
$947$	−5.97671	−	7.78900i	−0.194217	−	0.253109i	0.686086	−	0.727520i	$-0.259327\pi$
$947$	−5.97671	−	7.78900i	−0.194217	−	0.253109i	−0.880303	+	0.474412i	$0.842661\pi$
$948$		0			0
$949$	−34.4134	−	26.4063i	−1.11711	−	0.857186i
$950$	−67.8868	+	29.5304i	−2.20254	+	0.958093i
$951$		0			0
$952$	4.71904	−	1.53571i	0.152945	−	0.0497727i
$953$	10.0260	+	10.0260i	0.324773	+	0.324773i	0.850595	−	0.525822i	$-0.176242\pi$
$953$	10.0260	+	10.0260i	0.324773	+	0.324773i	−0.525822	+	0.850595i	$0.676242\pi$
$954$		0			0
$955$	69.8298	−	28.9245i	2.25964	−	0.935974i
$956$	1.22257	+	34.7044i	0.0395407	+	1.12242i
$957$		0			0
$958$	−9.69421	+	0.170701i	−0.313206	+	0.00551511i
$959$	3.36529	+	5.82885i	0.108671	+	0.188223i
$960$		0			0
$961$	−11.6225	+	20.1308i	−0.374919	+	0.649379i
$962$	2.80620	−	5.06435i	0.0904754	−	0.163281i
$963$		0			0
$964$	11.9514	−	7.47319i	0.384930	−	0.240695i
$965$	−4.57767	+	34.7708i	−0.147360	+	1.11931i
$966$		0			0
$967$	−0.575958	+	2.14950i	−0.0185216	+	0.0691234i	−0.974568	−	0.224092i	$-0.928059\pi$
$967$	−0.575958	+	2.14950i	−0.0185216	+	0.0691234i	0.956047	+	0.293215i	$0.0947252\pi$
$968$	17.1935	+	3.64632i	0.552621	+	0.117197i
$969$		0			0
$970$	−40.2268	−	29.7567i	−1.29160	−	0.955429i
$971$	11.0650	−	4.58326i	0.355092	−	0.147084i	−0.198005	−	0.980201i	$-0.563446\pi$
$971$	11.0650	−	4.58326i	0.355092	−	0.147084i	0.553096	+	0.833117i	$0.313446\pi$
$972$		0			0
$973$	1.34304	−	3.24238i	0.0430558	−	0.103946i
$974$	−12.0568	+	48.3889i	−0.386325	+	1.55048i
$975$		0			0
$976$	−9.97179	−	3.32971i	−0.319189	−	0.106581i
$977$	−8.10950	−	14.0461i	−0.259446	−	0.449374i	0.706648	−	0.707566i	$-0.250207\pi$
$977$	−8.10950	−	14.0461i	−0.259446	−	0.449374i	−0.966094	+	0.258192i	$0.916873\pi$
$978$		0			0
$979$	−14.9036	+	11.4360i	−0.476323	+	0.365495i
$980$	−28.8848	+	40.5214i	−0.922693	+	1.29441i
$981$		0			0
$982$	0.0531984	−	0.467554i	0.00169763	−	0.0149203i
$983$	−14.5337	+	3.89430i	−0.463554	+	0.124209i	−0.483035	−	0.875601i	$-0.660465\pi$
$983$	−14.5337	+	3.89430i	−0.463554	+	0.124209i	0.0194805	+	0.999810i	$0.493799\pi$
$984$		0			0
$985$	86.9881	+	23.3084i	2.77167	+	0.742667i
$986$	−3.03278	+	7.70262i	−0.0965833	+	0.245301i
$987$		0			0
$988$	27.8462	−	29.8798i	0.885905	−	0.950602i
$989$	−14.2888	+	34.4962i	−0.454358	+	1.09692i
$990$		0			0
$991$		−	39.6344i		−	1.25903i	−0.776990	−	0.629513i	$-0.783254\pi$
$991$		−	39.6344i		−	1.25903i	0.776990	−	0.629513i	$-0.216746\pi$
$992$	−1.38502	−	15.6921i	−0.0439743	−	0.498225i
$993$		0			0
$994$	−3.10491	+	0.0546730i	−0.0984817	+	0.00173412i
$995$	−10.6173	−	80.6466i	−0.336592	−	2.55667i
$996$		0			0
$997$	0.703567	+	0.0926264i	0.0222822	+	0.00293351i	0.141659	−	0.989916i	$-0.454756\pi$
$997$	0.703567	+	0.0926264i	0.0222822	+	0.00293351i	−0.119377	+	0.992849i	$0.538090\pi$
$998$	10.9383	−	8.70344i	0.346245	−	0.275503i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bn.a.35.16		368
3.2	odd	2		288.2.bf.a.227.31	yes	368
9.4	even	3		288.2.bf.a.131.46	yes	368
9.5	odd	6	inner	864.2.bn.a.611.1		368
32.11	odd	8	inner	864.2.bn.a.683.1		368
96.11	even	8		288.2.bf.a.11.46	✓	368
288.139	odd	24		288.2.bf.a.203.31	yes	368
288.203	even	24	inner	864.2.bn.a.395.16		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.46	✓	368	96.11	even	8
288.2.bf.a.131.46	yes	368	9.4	even	3
288.2.bf.a.203.31	yes	368	288.139	odd	24
288.2.bf.a.227.31	yes	368	3.2	odd	2
864.2.bn.a.35.16		368	1.1	even	1	trivial
864.2.bn.a.395.16		368	288.203	even	24	inner
864.2.bn.a.611.1		368	9.5	odd	6	inner
864.2.bn.a.683.1		368	32.11	odd	8	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bn (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.728560 - 1.21211i) q^{2} +(-0.938401 + 1.76618i) q^{4} +(-2.86669 - 2.19969i) q^{5} +(-0.326320 + 0.0874372i) q^{7} +(2.82448 - 0.149329i) q^{8} +(-0.577700 + 5.07734i) q^{10} +(0.285551 - 2.16897i) q^{11} +(3.11610 - 0.410243i) q^{13} +(0.343727 + 0.331831i) q^{14} +(-2.23881 - 3.31478i) q^{16} -5.19359 q^{17} +(-6.00299 - 2.48652i) q^{19} +(6.57516 - 2.99891i) q^{20} +(-2.83706 + 1.23411i) q^{22} +(-1.35356 + 5.05154i) q^{23} +(2.08519 + 7.78203i) q^{25} +(-2.76752 - 3.47816i) q^{26} +(0.151789 - 0.658392i) q^{28} +(0.686119 + 0.894167i) q^{29} +(-2.41169 + 1.39239i) q^{31} +(-2.38675 + 5.12868i) q^{32} +(3.78384 + 6.29518i) q^{34} +(1.12779 + 0.467147i) q^{35} +(0.498481 + 1.20344i) q^{37} +(1.35961 + 9.08784i) q^{38} +(-8.42539 - 5.78490i) q^{40} +(8.63084 + 2.31263i) q^{41} +(7.07855 + 0.931909i) q^{43} +(3.56284 + 2.53970i) q^{44} +(7.10915 - 2.03970i) q^{46} +(4.11008 + 2.37296i) q^{47} +(-5.96334 + 3.44293i) q^{49} +(7.91346 - 8.19714i) q^{50} +(-2.19959 + 5.88858i) q^{52} +(4.79184 + 11.5685i) q^{53} +(-5.58965 + 5.58965i) q^{55} +(-0.908628 + 0.295694i) q^{56} +(0.583947 - 1.48310i) q^{58} +(-7.50078 + 9.77521i) q^{59} +(2.08513 - 1.59998i) q^{61} +(3.44479 + 1.90879i) q^{62} +(7.95540 - 0.843554i) q^{64} +(-9.83531 - 5.67842i) q^{65} +(-3.45892 + 0.455376i) q^{67} +(4.87367 - 9.17283i) q^{68} +(-0.255433 - 1.70735i) q^{70} +(-4.59606 + 4.59606i) q^{71} +(-9.75895 - 9.75895i) q^{73} +(1.09552 - 1.48099i) q^{74} +(10.0249 - 8.26903i) q^{76} +(0.0964679 + 0.732747i) q^{77} +(-4.76659 + 8.25597i) q^{79} +(-0.873510 + 14.4271i) q^{80} +(-3.48493 - 12.1464i) q^{82} +(-6.13939 - 8.00100i) q^{83} +(14.8884 + 11.4243i) q^{85} +(-4.02758 - 9.25890i) q^{86} +(0.482642 - 6.16886i) q^{88} +(-6.07191 - 6.07191i) q^{89} +(-0.980976 + 0.406334i) q^{91} +(-7.65177 - 7.13100i) q^{92} +(-0.118166 - 6.71070i) q^{94} +(11.7391 + 20.3328i) q^{95} +(-4.89585 + 8.47985i) q^{97} +(8.51785 + 4.71981i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) \) 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Introduction

L-functions

Modular forms

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