LMFDB - Embedded newform 300.3.l.g.107.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [300,3,Mod(107,300)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("300.107"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(300, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	300.l (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,0,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$8.17440793081$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.6
Character	$\chi$	$=$	300.107
Dual form			300.3.l.g.143.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.07935 - 1.68375i) q^{2} +(2.99716 - 0.130491i) q^{3} +(-1.67002 + 3.63470i) q^{4} +(-3.45469 - 4.90562i) q^{6} +(1.91561 - 1.91561i) q^{7} +(7.92245 - 1.11122i) q^{8} +(8.96594 - 0.782204i) q^{9} +6.87236 q^{11} +(-4.53101 + 11.1117i) q^{12} +(-12.2746 + 12.2746i) q^{13} +(-5.29303 - 1.15780i) q^{14} +(-10.4221 - 12.1400i) q^{16} +(9.47120 - 9.47120i) q^{17} +(-10.9944 - 14.2521i) q^{18} +33.2524 q^{19} +(5.49143 - 5.99137i) q^{21} +(-7.41767 - 11.5713i) q^{22} +(7.20994 - 7.20994i) q^{23} +(23.5998 - 4.36430i) q^{24} +(33.9159 + 7.41877i) q^{26} +(26.7703 - 3.51436i) q^{27} +(3.76357 + 10.1618i) q^{28} -2.29155 q^{29} -12.1558i q^{31} +(-9.19168 + 30.6515i) q^{32} +(20.5976 - 0.896780i) q^{33} +(-26.1698 - 5.72440i) q^{34} +(-12.1302 + 33.8948i) q^{36} +(20.7290 + 20.7290i) q^{37} +(-35.8909 - 55.9886i) q^{38} +(-35.1872 + 38.3906i) q^{39} -50.9173i q^{41} +(-16.0151 - 2.77942i) q^{42} +(-15.1975 - 15.1975i) q^{43} +(-11.4770 + 24.9790i) q^{44} +(-19.9218 - 4.35769i) q^{46} +(-26.7793 - 26.7793i) q^{47} +(-32.8208 - 35.0256i) q^{48} +41.6608i q^{49} +(27.1508 - 29.6226i) q^{51} +(-24.1157 - 65.1132i) q^{52} +(15.5183 + 15.5183i) q^{53} +(-34.8118 - 41.2812i) q^{54} +(13.0477 - 17.3050i) q^{56} +(99.6627 - 4.33913i) q^{57} +(2.47338 + 3.85839i) q^{58} -63.0946i q^{59} +28.4752 q^{61} +(-20.4672 + 13.1203i) q^{62} +(15.6769 - 18.6737i) q^{63} +(61.5304 - 17.6071i) q^{64} +(-23.7419 - 33.7132i) q^{66} +(-32.4542 + 32.4542i) q^{67} +(18.6079 + 50.2420i) q^{68} +(20.6685 - 22.5502i) q^{69} -88.8377 q^{71} +(70.1630 - 16.1601i) q^{72} +(-71.1740 + 71.1740i) q^{73} +(12.5286 - 57.2763i) q^{74} +(-55.5320 + 120.862i) q^{76} +(13.1648 - 13.1648i) q^{77} +(102.619 + 17.8095i) q^{78} -75.1410 q^{79} +(79.7763 - 14.0264i) q^{81} +(-85.7318 + 54.9574i) q^{82} +(-58.6543 + 58.6543i) q^{83} +(12.6061 + 29.9654i) q^{84} +(-9.18537 + 41.9921i) q^{86} +(-6.86815 + 0.299026i) q^{87} +(54.4459 - 7.63668i) q^{88} +41.1063 q^{89} +47.0267i q^{91} +(14.1653 + 38.2467i) q^{92} +(-1.58621 - 36.4327i) q^{93} +(-16.1854 + 73.9937i) q^{94} +(-23.5492 + 93.0668i) q^{96} +(-30.3484 - 30.3484i) q^{97} +(70.1464 - 44.9665i) q^{98} +(61.6172 - 5.37559i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{6} + 20 q^{12} + 8 q^{13} - 36 q^{16} + 24 q^{18} - 24 q^{21} + 76 q^{22} + 84 q^{28} + 40 q^{33} + 172 q^{36} + 40 q^{37} - 236 q^{42} + 240 q^{46} - 196 q^{48} - 304 q^{52} + 72 q^{57} - 180 q^{58}+ \cdots - 72 q^{97}+O(q^{100}) $ 40 * q - 4 * q^6 + 20 * q^12 + 8 * q^13 - 36 * q^16 + 24 * q^18 - 24 * q^21 + 76 * q^22 + 84 * q^28 + 40 * q^33 + 172 * q^36 + 40 * q^37 - 236 * q^42 + 240 * q^46 - 196 * q^48 - 304 * q^52 + 72 * q^57 - 180 * q^58 + 48 * q^61 - 552 * q^66 + 600 * q^72 - 104 * q^73 - 736 * q^76 + 408 * q^78 + 72 * q^81 + 720 * q^82 + 580 * q^88 - 368 * q^93 + 884 * q^96 - 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.07935	−	1.68375i	−0.539674	−	0.841874i
$2$	−1.07935	−	1.68375i	−0.539674	−	0.841874i
$3$	2.99716	−	0.130491i	0.999054	−	0.0434969i
$3$	2.99716	−	0.130491i	0.999054	−	0.0434969i
$4$	−1.67002	+	3.63470i	−0.417504	+	0.908675i
$5$		0			0
$5$		0			0
$6$	−3.45469	−	4.90562i	−0.575782	−	0.817603i
$7$	1.91561	−	1.91561i	0.273659	−	0.273659i	−0.556912	−	0.830571i	$-0.688014\pi$
$7$	1.91561	−	1.91561i	0.273659	−	0.273659i	0.830571	+	0.556912i	$0.188014\pi$
$8$	7.92245	−	1.11122i	0.990306	−	0.138902i
$9$	8.96594	−	0.782204i	0.996216	−	0.0869115i
$10$		0			0
$11$	6.87236			0.624760			0.312380	−	0.949957i	$-0.398874\pi$
$11$	6.87236			0.624760			0.312380	+	0.949957i	$0.398874\pi$
$12$	−4.53101	+	11.1117i	−0.377585	+	0.925975i
$13$	−12.2746	+	12.2746i	−0.944199	+	0.944199i	−0.998523	−	0.0543246i	$-0.982699\pi$
$13$	−12.2746	+	12.2746i	−0.944199	+	0.944199i	0.0543246	+	0.998523i	$0.482699\pi$
$14$	−5.29303	−	1.15780i	−0.378073	−	0.0826999i
$15$		0			0
$16$	−10.4221	−	12.1400i	−0.651380	−	0.758751i
$17$	9.47120	−	9.47120i	0.557129	−	0.557129i	−0.371360	−	0.928489i	$-0.621108\pi$
$17$	9.47120	−	9.47120i	0.557129	−	0.557129i	0.928489	+	0.371360i	$0.121108\pi$
$18$	−10.9944	−	14.2521i	−0.610800	−	0.791785i
$19$	33.2524			1.75013			0.875063	−	0.484010i	$-0.160820\pi$
$19$	33.2524			1.75013			0.875063	+	0.484010i	$0.160820\pi$
$20$		0			0
$21$	5.49143	−	5.99137i	0.261497	−	0.285303i
$22$	−7.41767	−	11.5713i	−0.337167	−	0.525969i
$23$	7.20994	−	7.20994i	0.313476	−	0.313476i	−0.532779	−	0.846255i	$-0.678852\pi$
$23$	7.20994	−	7.20994i	0.313476	−	0.313476i	0.846255	+	0.532779i	$0.178852\pi$
$24$	23.5998	−	4.36430i	0.983327	−	0.181846i
$25$		0			0
$26$	33.9159	+	7.41877i	1.30446	+	0.285337i
$27$	26.7703	−	3.51436i	0.991493	−	0.130162i
$28$	3.76357	+	10.1618i	0.134413	+	0.362921i
$29$	−2.29155			−0.0790190			−0.0395095	−	0.999219i	$-0.512580\pi$
$29$	−2.29155			−0.0790190			−0.0395095	+	0.999219i	$0.512580\pi$
$30$		0			0
$31$		−	12.1558i		−	0.392121i	−0.980592	−	0.196061i	$-0.937185\pi$
$31$		−	12.1558i		−	0.392121i	0.980592	−	0.196061i	$-0.0628149\pi$
$32$	−9.19168	+	30.6515i	−0.287240	+	0.957859i
$33$	20.5976	−	0.896780i	0.624169	−	0.0271752i
$34$	−26.1698	−	5.72440i	−0.769701	−	0.168365i
$35$		0			0
$36$	−12.1302	+	33.8948i	−0.336950	+	0.941523i
$37$	20.7290	+	20.7290i	0.560244	+	0.560244i	0.929377	−	0.369133i	$-0.120345\pi$
$37$	20.7290	+	20.7290i	0.560244	+	0.560244i	−0.369133	+	0.929377i	$0.620345\pi$
$38$	−35.8909	−	55.9886i	−0.944497	−	1.47339i
$39$	−35.1872	+	38.3906i	−0.902235	+	0.984375i
$40$		0			0
$41$		−	50.9173i		−	1.24188i	−0.783856	−	0.620942i	$-0.786750\pi$
$41$		−	50.9173i		−	1.24188i	0.783856	−	0.620942i	$-0.213250\pi$
$42$	−16.0151	−	2.77942i	−0.381313	−	0.0661766i
$43$	−15.1975	−	15.1975i	−0.353430	−	0.353430i	0.507954	−	0.861384i	$-0.330402\pi$
$43$	−15.1975	−	15.1975i	−0.353430	−	0.353430i	−0.861384	+	0.507954i	$0.830402\pi$
$44$	−11.4770	+	24.9790i	−0.260840	+	0.567704i
$45$		0			0
$46$	−19.9218	−	4.35769i	−0.433082	−	0.0947325i
$47$	−26.7793	−	26.7793i	−0.569772	−	0.569772i	0.362293	−	0.932064i	$-0.381994\pi$
$47$	−26.7793	−	26.7793i	−0.569772	−	0.569772i	−0.932064	+	0.362293i	$0.881994\pi$
$48$	−32.8208	−	35.0256i	−0.683767	−	0.729700i
$49$			41.6608i			0.850221i
$50$		0			0
$51$	27.1508	−	29.6226i	0.532368	−	0.580835i
$52$	−24.1157	−	65.1132i	−0.463763	−	1.25218i
$53$	15.5183	+	15.5183i	0.292799	+	0.292799i	0.838185	−	0.545386i	$-0.183617\pi$
$53$	15.5183	+	15.5183i	0.292799	+	0.292799i	−0.545386	+	0.838185i	$0.683617\pi$
$54$	−34.8118	−	41.2812i	−0.644662	−	0.764467i
$55$		0			0
$56$	13.0477	−	17.3050i	0.232994	−	0.309018i
$57$	99.6627	−	4.33913i	1.74847	−	0.0761251i
$58$	2.47338	+	3.85839i	0.0426445	+	0.0665240i
$59$		−	63.0946i		−	1.06940i	−0.845042	−	0.534700i	$-0.820425\pi$
$59$		−	63.0946i		−	1.06940i	0.845042	−	0.534700i	$-0.179575\pi$
$60$		0			0
$61$	28.4752			0.466806			0.233403	−	0.972380i	$-0.425014\pi$
$61$	28.4752			0.466806			0.233403	+	0.972380i	$0.425014\pi$
$62$	−20.4672	+	13.1203i	−0.330117	+	0.211617i
$63$	15.6769	−	18.6737i	0.248839	−	0.296408i
$64$	61.5304	−	17.6071i	0.961412	−	0.275111i
$65$		0			0
$66$	−23.7419	−	33.7132i	−0.359726	−	0.510806i
$67$	−32.4542	+	32.4542i	−0.484392	+	0.484392i	−0.906531	−	0.422139i	$-0.861279\pi$
$67$	−32.4542	+	32.4542i	−0.484392	+	0.484392i	0.422139	+	0.906531i	$0.361279\pi$
$68$	18.6079	+	50.2420i	0.273646	+	0.738853i
$69$	20.6685	−	22.5502i	0.299544	−	0.326814i
$70$		0			0
$71$	−88.8377			−1.25124			−0.625618	−	0.780130i	$-0.715153\pi$
$71$	−88.8377			−1.25124			−0.625618	+	0.780130i	$0.715153\pi$
$72$	70.1630	−	16.1601i	0.974487	−	0.224446i
$73$	−71.1740	+	71.1740i	−0.974987	+	0.974987i	−0.999695	−	0.0247079i	$-0.992134\pi$
$73$	−71.1740	+	71.1740i	−0.974987	+	0.974987i	0.0247079	+	0.999695i	$0.492134\pi$
$74$	12.5286	−	57.2763i	0.169306	−	0.774004i
$75$		0			0
$76$	−55.5320	+	120.862i	−0.730685	+	1.59029i
$77$	13.1648	−	13.1648i	0.170971	−	0.170971i
$78$	102.619	+	17.8095i	1.31563	+	0.228327i
$79$	−75.1410			−0.951153			−0.475576	−	0.879675i	$-0.657760\pi$
$79$	−75.1410			−0.951153			−0.475576	+	0.879675i	$0.657760\pi$
$80$		0			0
$81$	79.7763	−	14.0264i	0.984893	−	0.173165i
$82$	−85.7318	+	54.9574i	−1.04551	+	0.670213i
$83$	−58.6543	+	58.6543i	−0.706678	+	0.706678i	−0.965835	−	0.259157i	$-0.916555\pi$
$83$	−58.6543	+	58.6543i	−0.706678	+	0.706678i	0.259157	+	0.965835i	$0.416555\pi$
$84$	12.6061	+	29.9654i	0.150072	+	0.356731i
$85$		0			0
$86$	−9.18537	+	41.9921i	−0.106807	+	0.488281i
$87$	−6.86815	+	0.299026i	−0.0789442	+	0.00343708i
$88$	54.4459	−	7.63668i	0.618704	−	0.0867805i
$89$	41.1063			0.461868			0.230934	−	0.972969i	$-0.425822\pi$
$89$	41.1063			0.461868			0.230934	+	0.972969i	$0.425822\pi$
$90$		0			0
$91$			47.0267i			0.516777i
$92$	14.1653	+	38.2467i	0.153970	+	0.415725i
$93$	−1.58621	−	36.4327i	−0.0170561	−	0.391750i
$94$	−16.1854	+	73.9937i	−0.172185	+	0.787167i
$95$		0			0
$96$	−23.5492	+	93.0668i	−0.245304	+	0.969446i
$97$	−30.3484	−	30.3484i	−0.312870	−	0.312870i	0.533150	−	0.846020i	$-0.321008\pi$
$97$	−30.3484	−	30.3484i	−0.312870	−	0.312870i	−0.846020	+	0.533150i	$0.821008\pi$
$98$	70.1464	−	44.9665i	0.715779	−	0.458842i
$99$	61.6172	−	5.37559i	0.622396	−	0.0542989i
$100$		0			0
$101$			124.297i			1.23067i	0.788267	+	0.615333i	$0.210978\pi$
$101$			124.297i			1.23067i	−0.788267	+	0.615333i	$0.789022\pi$
$102$	−79.1822	−	13.7420i	−0.776296	−	0.134726i
$103$	131.168	+	131.168i	1.27348	+	1.27348i	0.944252	+	0.329223i	$0.106787\pi$
$103$	131.168	+	131.168i	1.27348	+	1.27348i	0.329223	+	0.944252i	$0.393213\pi$
$104$	−83.6050	+	110.884i	−0.803895	+	1.06620i
$105$		0			0
$106$	9.37929	−	42.8786i	0.0884839	−	0.404516i
$107$	−11.4672	−	11.4672i	−0.107170	−	0.107170i	0.651488	−	0.758659i	$-0.274145\pi$
$107$	−11.4672	−	11.4672i	−0.107170	−	0.107170i	−0.758659	+	0.651488i	$0.774145\pi$
$108$	−31.9332	+	103.171i	−0.295678	+	0.955288i
$109$			80.0130i			0.734065i	0.930208	+	0.367032i	$0.119626\pi$
$109$			80.0130i			0.734065i	−0.930208	+	0.367032i	$0.880374\pi$
$110$		0			0
$111$	64.8331	+	59.4232i	0.584082	+	0.535345i
$112$	−43.2203	−	3.29090i	−0.385895	−	0.0293830i
$113$	64.8556	+	64.8556i	0.573943	+	0.573943i	0.933228	−	0.359285i	$-0.116979\pi$
$113$	64.8556	+	64.8556i	0.573943	+	0.573943i	−0.359285	+	0.933228i	$0.616979\pi$
$114$	−114.877	−	163.124i	−1.00769	−	1.43091i
$115$		0			0
$116$	3.82693	−	8.32910i	0.0329908	−	0.0718026i
$117$	−100.452	+	119.654i	−0.858564	+	1.02269i
$118$	−106.235	+	68.1010i	−0.900301	+	0.577127i
$119$		−	36.2863i		−	0.304927i
$120$		0			0
$121$	−73.7706			−0.609675
$122$	−30.7346	−	47.9450i	−0.251923	−	0.392992i
$123$	−6.64423	−	152.607i	−0.0540182	−	1.24071i
$124$	44.1825	+	20.3003i	0.356311	+	0.163712i
$125$		0			0
$126$	−48.3626	−	6.24053i	−0.383830	−	0.0495280i
$127$	63.5895	−	63.5895i	0.500705	−	0.500705i	−0.410952	−	0.911657i	$-0.634804\pi$
$127$	63.5895	−	63.5895i	0.500705	−	0.500705i	0.911657	+	0.410952i	$0.134804\pi$
$128$	−96.0586	−	84.5975i	−0.750458	−	0.660918i
$129$	−47.5325	−	43.5662i	−0.368469	−	0.337722i
$130$		0			0
$131$	−144.030			−1.09947			−0.549734	−	0.835340i	$-0.685271\pi$
$131$	−144.030			−1.09947			−0.549734	+	0.835340i	$0.685271\pi$
$132$	−31.1388	+	76.3636i	−0.235900	+	0.578512i
$133$	63.6987	−	63.6987i	0.478938	−	0.478938i
$134$	89.6742	+	19.6154i	0.669210	+	0.146383i
$135$		0			0
$136$	64.5105	−	85.5596i	0.474342	−	0.629115i
$137$	−13.6200	+	13.6200i	−0.0994161	+	0.0994161i	−0.755065	−	0.655649i	$-0.772395\pi$
$137$	−13.6200	+	13.6200i	−0.0994161	+	0.0994161i	0.655649	+	0.755065i	$0.272395\pi$
$138$	−60.2774	−	10.4611i	−0.436793	−	0.0758051i
$139$	62.7261			0.451267			0.225634	−	0.974212i	$-0.427555\pi$
$139$	62.7261			0.451267			0.225634	+	0.974212i	$0.427555\pi$
$140$		0			0
$141$	−83.7563	−	76.7674i	−0.594016	−	0.544449i
$142$	95.8868	+	149.580i	0.675259	+	1.05338i
$143$	−84.3554	+	84.3554i	−0.589898	+	0.589898i
$144$	−102.940	−	100.695i	−0.714860	−	0.699268i
$145$		0			0
$146$	196.661	+	43.0176i	1.34699	+	0.294641i
$147$	5.43636	+	124.864i	0.0369820	+	0.849417i
$148$	−109.962	+	40.7259i	−0.742983	+	0.275175i
$149$	−167.292			−1.12277			−0.561383	−	0.827556i	$-0.689730\pi$
$149$	−167.292			−1.12277			−0.561383	+	0.827556i	$0.689730\pi$
$150$		0			0
$151$			75.2596i			0.498408i	0.968451	+	0.249204i	$0.0801690\pi$
$151$			75.2596i			0.498408i	−0.968451	+	0.249204i	$0.919831\pi$
$152$	263.440	−	36.9506i	1.73316	−	0.243096i
$153$	77.5098	−	92.3266i	0.506600	−	0.603442i
$154$	−36.3756	−	7.95681i	−0.236205	−	0.0516676i
$155$		0			0
$156$	−80.7752	−	192.008i	−0.517790	−	1.23082i
$157$	−71.6852	−	71.6852i	−0.456593	−	0.456593i	0.440942	−	0.897536i	$-0.354644\pi$
$157$	−71.6852	−	71.6852i	−0.456593	−	0.456593i	−0.897536	+	0.440942i	$0.854644\pi$
$158$	81.1033	+	126.519i	0.513312	+	0.800751i
$159$	48.5359	+	44.4859i	0.305258	+	0.279786i
$160$		0			0
$161$		−	27.6229i		−	0.171571i
$162$	−109.723	−	119.184i	−0.677304	−	0.735703i
$163$	−61.4502	−	61.4502i	−0.376995	−	0.376995i	0.493022	−	0.870017i	$-0.335892\pi$
$163$	−61.4502	−	61.4502i	−0.376995	−	0.376995i	−0.870017	+	0.493022i	$0.835892\pi$
$164$	185.069	+	85.0327i	1.12847	+	0.518492i
$165$		0			0
$166$	162.067	+	35.4507i	0.976309	+	0.213558i
$167$	−36.7847	−	36.7847i	−0.220268	−	0.220268i	0.588344	−	0.808611i	$-0.299780\pi$
$167$	−36.7847	−	36.7847i	−0.220268	−	0.220268i	−0.808611	+	0.588344i	$0.799780\pi$
$168$	36.8479	−	53.5685i	0.219333	−	0.318860i
$169$		−	132.331i		−	0.783022i
$170$		0			0
$171$	298.139	−	26.0101i	1.74350	−	0.152106i
$172$	80.6184	−	29.8583i	0.468712	−	0.173595i
$173$	−137.897	−	137.897i	−0.797091	−	0.797091i	0.185545	−	0.982636i	$-0.440595\pi$
$173$	−137.897	−	137.897i	−0.797091	−	0.797091i	−0.982636	+	0.185545i	$0.940595\pi$
$174$	7.91660	+	11.2415i	0.0454977	+	0.0646062i
$175$		0			0
$176$	−71.6244	−	83.4306i	−0.406957	−	0.474038i
$177$	−8.23327	−	189.105i	−0.0465156	−	1.06839i
$178$	−44.3680	−	69.2126i	−0.249258	−	0.388835i
$179$			106.971i			0.597602i	0.954315	+	0.298801i	$0.0965867\pi$
$179$			106.971i			0.597602i	−0.954315	+	0.298801i	$0.903413\pi$
$180$		0			0
$181$	−11.6057			−0.0641199			−0.0320600	−	0.999486i	$-0.510207\pi$
$181$	−11.6057			−0.0641199			−0.0320600	+	0.999486i	$0.510207\pi$
$182$	79.1812	−	50.7582i	0.435061	−	0.278891i
$183$	85.3446	−	3.71575i	0.466364	−	0.0203046i
$184$	49.1086	−	65.1322i	0.266895	−	0.353979i
$185$		0			0
$186$	−59.6315	+	41.9944i	−0.320599	+	0.225776i
$187$	65.0895	−	65.0895i	0.348072	−	0.348072i
$188$	142.057	−	52.6128i	0.755620	−	0.279855i
$189$	44.5494	−	58.0137i	0.235711	−	0.306951i
$190$		0			0
$191$	−135.925			−0.711648			−0.355824	−	0.934553i	$-0.615800\pi$
$191$	−135.925			−0.711648			−0.355824	+	0.934553i	$0.615800\pi$
$192$	182.119	−	60.8005i	0.948536	−	0.316669i
$193$	62.7362	−	62.7362i	0.325058	−	0.325058i	−0.525646	−	0.850704i	$-0.676176\pi$
$193$	62.7362	−	62.7362i	0.325058	−	0.325058i	0.850704	+	0.525646i	$0.176176\pi$
$194$	−18.3426	+	83.8556i	−0.0945494	+	0.432245i
$195$		0			0
$196$	−151.425	−	69.5743i	−0.772575	−	0.354971i
$197$	−96.9852	+	96.9852i	−0.492311	+	0.492311i	−0.909034	−	0.416723i	$-0.863179\pi$
$197$	−96.9852	+	96.9852i	−0.492311	+	0.492311i	0.416723	+	0.909034i	$0.363179\pi$
$198$	−75.5575	−	97.9457i	−0.381604	−	0.494675i
$199$	−29.0286			−0.145872			−0.0729361	−	0.997337i	$-0.523237\pi$
$199$	−29.0286			−0.145872			−0.0729361	+	0.997337i	$0.523237\pi$
$200$		0			0
$201$	−93.0356	+	101.506i	−0.462864	+	0.505003i
$202$	209.285	−	134.160i	1.03607	−	0.664158i
$203$	−4.38973	+	4.38973i	−0.0216243	+	0.0216243i
$204$	62.3270	+	148.155i	0.305524	+	0.726251i
$205$		0			0
$206$	79.2780	−	362.430i	0.384845	−	1.75937i
$207$	59.0043	−	70.2836i	0.285045	−	0.339534i
$208$	276.940	+	21.0869i	1.33144	+	0.101379i
$209$	228.522			1.09341
$210$		0			0
$211$		−	376.951i		−	1.78650i	−0.449561	−	0.893250i	$-0.648420\pi$
$211$		−	376.951i		−	1.78650i	0.449561	−	0.893250i	$-0.351580\pi$
$212$	−82.3204	+	30.4886i	−0.388304	+	0.143814i
$213$	−266.261	+	11.5925i	−1.25005	+	0.0544249i
$214$	−6.93079	+	31.6850i	−0.0323869	+	0.148061i
$215$		0			0
$216$	208.181	−	57.5900i	0.963802	−	0.266620i
$217$	−23.2857	−	23.2857i	−0.107307	−	0.107307i
$218$	134.722	−	86.3619i	0.617990	−	0.396155i
$219$	−204.032	+	222.608i	−0.931655	+	1.01647i
$220$		0			0
$221$			232.510i			1.05208i
$222$	30.0763	−	173.301i	0.135479	−	0.780635i
$223$	−255.505	−	255.505i	−1.14576	−	1.14576i	−0.987377	−	0.158385i	$-0.949371\pi$
$223$	−255.505	−	255.505i	−1.14576	−	1.14576i	−0.158385	−	0.987377i	$-0.550629\pi$
$224$	41.1087	+	76.3241i	0.183521	+	0.340733i
$225$		0			0
$226$	39.1988	−	179.202i	0.173446	−	0.792930i
$227$	109.045	+	109.045i	0.480375	+	0.480375i	0.905251	−	0.424876i	$-0.139682\pi$
$227$	109.045	+	109.045i	0.480375	+	0.480375i	−0.424876	+	0.905251i	$0.639682\pi$
$228$	−150.667	+	369.490i	−0.660820	+	1.62057i
$229$		−	223.738i		−	0.977023i	−0.872557	−	0.488512i	$-0.837540\pi$
$229$		−	223.738i		−	0.977023i	0.872557	−	0.488512i	$-0.162460\pi$
$230$		0			0
$231$	37.7391	−	41.1749i	0.163373	−	0.178246i
$232$	−18.1547	+	2.54641i	−0.0782530	+	0.0109759i
$233$	−62.4244	−	62.4244i	−0.267916	−	0.267916i	0.560344	−	0.828260i	$-0.310669\pi$
$233$	−62.4244	−	62.4244i	−0.267916	−	0.267916i	−0.828260	+	0.560344i	$0.810669\pi$
$234$	309.891	+	39.9871i	1.32432	+	0.170885i
$235$		0			0
$236$	229.330	+	105.369i	0.971737	+	0.446479i
$237$	−225.210	+	9.80522i	−0.950252	+	0.0413722i
$238$	−61.0970	+	39.1655i	−0.256710	+	0.164561i
$239$		−	310.217i		−	1.29798i	−0.760798	−	0.648989i	$-0.775192\pi$
$239$		−	310.217i		−	1.29798i	0.760798	−	0.648989i	$-0.224808\pi$
$240$		0			0
$241$	−119.905			−0.497529			−0.248765	−	0.968564i	$-0.580025\pi$
$241$	−119.905			−0.497529			−0.248765	+	0.968564i	$0.580025\pi$
$242$	79.6242	+	124.211i	0.329026	+	0.513269i
$243$	237.272	−	52.4494i	0.976428	−	0.215841i
$244$	−47.5540	+	103.499i	−0.194893	+	0.424175i
$245$		0			0
$246$	−249.781	+	175.903i	−1.01537	+	0.715055i
$247$	−408.159	+	408.159i	−1.65247	+	1.65247i
$248$	−13.5077	−	96.3033i	−0.0544664	−	0.388320i
$249$	−168.142	+	183.450i	−0.675271	+	0.736747i
$250$		0			0
$251$	336.252			1.33965			0.669825	−	0.742519i	$-0.266369\pi$
$251$	336.252			1.33965			0.669825	+	0.742519i	$0.266369\pi$
$252$	41.6926	+	88.1662i	0.165447	+	0.349866i
$253$	49.5493	−	49.5493i	0.195847	−	0.195847i
$254$	−175.704	−	38.4336i	−0.691748	−	0.151313i
$255$		0			0
$256$	−38.7602	+	253.049i	−0.151407	+	0.988472i
$257$	−199.642	+	199.642i	−0.776816	+	0.776816i	−0.979288	−	0.202472i	$-0.935102\pi$
$257$	−199.642	+	199.642i	−0.776816	+	0.776816i	0.202472	+	0.979288i	$0.435102\pi$
$258$	−22.0505	+	127.056i	−0.0854669	+	0.492464i
$259$	79.4176			0.306632
$260$		0			0
$261$	−20.5459	+	1.79246i	−0.0787200	+	0.00686766i
$262$	155.459	+	242.511i	0.593354	+	0.925613i
$263$	−107.927	+	107.927i	−0.410368	+	0.410368i	−0.881867	−	0.471499i	$-0.843713\pi$
$263$	−107.927	+	107.927i	−0.410368	+	0.410368i	0.471499	+	0.881867i	$0.343713\pi$
$264$	162.187	−	29.9931i	0.614344	−	0.113610i
$265$		0			0
$266$	−176.006	−	38.4995i	−0.661675	−	0.144735i
$267$	123.202	−	5.36399i	0.461431	−	0.0200899i
$268$	−63.7623	−	172.161i	−0.237919	−	0.642390i
$269$	−279.355			−1.03850			−0.519248	−	0.854624i	$-0.673788\pi$
$269$	−279.355			−1.03850			−0.519248	+	0.854624i	$0.673788\pi$
$270$		0			0
$271$			353.019i			1.30265i	0.758797	+	0.651327i	$0.225787\pi$
$271$			353.019i			1.30265i	−0.758797	+	0.651327i	$0.774213\pi$
$272$	−213.690	−	16.2709i	−0.785626	−	0.0598194i
$273$	6.13656	+	140.947i	0.0224782	+	0.516288i
$274$	37.6334	+	8.23194i	0.137348	+	0.0300436i
$275$		0			0
$276$	47.4464	+	112.783i	0.171907	+	0.408634i
$277$	−9.06443	−	9.06443i	−0.0327236	−	0.0327236i	0.690556	−	0.723279i	$-0.257366\pi$
$277$	−9.06443	−	9.06443i	−0.0327236	−	0.0327236i	−0.723279	+	0.690556i	$0.757366\pi$
$278$	−67.7033	−	105.615i	−0.243537	−	0.379910i
$279$	−9.50828	−	108.988i	−0.0340798	−	0.390637i
$280$		0			0
$281$		−	204.501i		−	0.727762i	−0.931445	−	0.363881i	$-0.881451\pi$
$281$		−	204.501i		−	0.727762i	0.931445	−	0.363881i	$-0.118549\pi$
$282$	−38.8548	+	223.883i	−0.137783	+	0.793912i
$283$	−4.95961	−	4.95961i	−0.0175251	−	0.0175251i	0.698290	−	0.715815i	$-0.253945\pi$
$283$	−4.95961	−	4.95961i	−0.0175251	−	0.0175251i	−0.715815	+	0.698290i	$0.753945\pi$
$284$	148.360	−	322.898i	0.522396	−	1.13697i
$285$		0			0
$286$	233.082	+	50.9844i	0.814972	+	0.178267i
$287$	−97.5378	−	97.5378i	−0.339853	−	0.339853i
$288$	−58.4364	+	282.009i	−0.202904	+	0.979199i
$289$			109.593i			0.379214i
$290$		0			0
$291$	−94.9192	−	86.9988i	−0.326183	−	0.298965i
$292$	−139.834	−	377.558i	−0.478885	−	1.29301i
$293$	195.635	+	195.635i	0.667697	+	0.667697i	0.957182	−	0.289485i	$-0.0934842\pi$
$293$	195.635	+	195.635i	0.667697	+	0.667697i	−0.289485	+	0.957182i	$0.593484\pi$
$294$	204.372	−	143.925i	0.695144	−	0.489542i
$295$		0			0
$296$	187.259	+	141.190i	0.632632	+	0.476994i
$297$	183.975	−	24.1520i	0.619445	−	0.0813198i
$298$	180.566	+	281.678i	0.605927	+	0.945227i
$299$			176.998i			0.591967i
$300$		0			0
$301$	−58.2251			−0.193439
$302$	126.718	−	81.2313i	0.419597	−	0.268978i
$303$	16.2196	+	372.539i	0.0535302	+	1.22950i
$304$	−346.559	−	403.685i	−1.14000	−	1.32791i
$305$		0			0
$306$	−239.115	−	30.8545i	−0.781421	−	0.100832i
$307$	323.877	−	323.877i	1.05497	−	1.05497i	0.0565751	−	0.998398i	$-0.481982\pi$
$307$	323.877	−	323.877i	1.05497	−	1.05497i	0.998398	−	0.0565751i	$-0.0180180\pi$
$308$	25.8646	+	69.8355i	0.0839761	+	0.226739i
$309$	410.248	+	376.015i	1.32766	+	1.21688i
$310$		0			0
$311$	−428.968			−1.37932			−0.689660	−	0.724133i	$-0.742240\pi$
$311$	−428.968			−1.37932			−0.689660	+	0.724133i	$0.742240\pi$
$312$	−236.108	+	343.248i	−0.756757	+	1.10015i
$313$	144.149	−	144.149i	0.460541	−	0.460541i	−0.438292	−	0.898833i	$-0.644416\pi$
$313$	144.149	−	144.149i	0.460541	−	0.460541i	0.898833	+	0.438292i	$0.144416\pi$
$314$	−43.3266	+	198.073i	−0.137983	+	0.630806i
$315$		0			0
$316$	125.487	−	273.115i	0.397110	−	0.864288i
$317$	299.797	−	299.797i	0.945733	−	0.945733i	−0.0528685	−	0.998601i	$-0.516836\pi$
$317$	299.797	−	299.797i	0.945733	−	0.945733i	0.998601	+	0.0528685i	$0.0168364\pi$
$318$	22.5160	−	129.738i	0.0708049	−	0.407981i
$319$	−15.7484			−0.0493679
$320$		0			0
$321$	−35.8655	−	32.8727i	−0.111730	−	0.102407i
$322$	−46.5101	+	29.8148i	−0.144441	+	0.0925924i
$323$	314.940	−	314.940i	0.975046	−	0.975046i
$324$	−82.2461	+	313.387i	−0.253846	+	0.967245i
$325$		0			0
$326$	−37.1405	+	169.793i	−0.113928	+	0.520837i
$327$	10.4410	+	239.812i	0.0319296	+	0.733370i
$328$	−56.5801	−	403.389i	−0.172500	−	1.22985i
$329$	−102.598			−0.311847
$330$		0			0
$331$			89.1276i			0.269268i	0.990895	+	0.134634i	$0.0429858\pi$
$331$			89.1276i			0.269268i	−0.990895	+	0.134634i	$0.957014\pi$
$332$	−115.237	−	311.144i	−0.347100	−	0.937181i
$333$	202.070	+	169.641i	0.606815	+	0.509432i
$334$	−22.2327	+	101.640i	−0.0665649	+	0.304310i
$335$		0			0
$336$	−129.968	−	4.22350i	−0.386808	−	0.0125699i
$337$	176.973	+	176.973i	0.525141	+	0.525141i	0.919120	−	0.393978i	$-0.128902\pi$
$337$	176.973	+	176.973i	0.525141	+	0.525141i	−0.393978	+	0.919120i	$0.628902\pi$
$338$	−222.812	+	142.831i	−0.659206	+	0.422577i
$339$	202.846	+	185.920i	0.598365	+	0.548435i
$340$		0			0
$341$		−	83.5387i		−	0.244982i
$342$	−365.590	−	473.917i	−1.06898	−	1.38572i
$343$	173.671	+	173.671i	0.506330	+	0.506330i
$344$	−137.289	−	103.514i	−0.399096	−	0.300912i
$345$		0			0
$346$	−83.3448	+	381.022i	−0.240881	+	1.10122i
$347$	−341.548	−	341.548i	−0.984288	−	0.984288i	0.0155906	−	0.999878i	$-0.495037\pi$
$347$	−341.548	−	341.548i	−0.984288	−	0.984288i	−0.999878	+	0.0155906i	$0.995037\pi$
$348$	10.3830	−	25.4630i	0.0298363	−	0.0731696i
$349$		−	190.129i		−	0.544782i	−0.962187	−	0.272391i	$-0.912186\pi$
$349$		−	190.129i		−	0.544782i	0.962187	−	0.272391i	$-0.0878144\pi$
$350$		0			0
$351$	−285.457	+	371.732i	−0.813268	+	1.05906i
$352$	−63.1686	+	210.648i	−0.179456	+	0.598432i
$353$	66.4041	+	66.4041i	0.188114	+	0.188114i	0.794880	−	0.606767i	$-0.207534\pi$
$353$	66.4041	+	66.4041i	0.188114	+	0.188114i	−0.606767	+	0.794880i	$0.707534\pi$
$354$	−309.518	+	217.972i	−0.874345	+	0.615742i
$355$		0			0
$356$	−68.6482	+	149.409i	−0.192832	+	0.419688i
$357$	−4.73503	−	108.756i	−0.0132634	−	0.304638i
$358$	180.112	−	115.459i	0.503106	−	0.322510i
$359$		−	402.003i		−	1.11979i	−0.828565	−	0.559893i	$-0.810842\pi$
$359$		−	402.003i		−	1.11979i	0.828565	−	0.559893i	$-0.189158\pi$
$360$		0			0
$361$	744.721			2.06294
$362$	12.5266	+	19.5411i	0.0346038	+	0.0539809i
$363$	−221.102	+	9.62639i	−0.609098	+	0.0265190i
$364$	−170.928	−	78.5354i	−0.469582	−	0.215757i
$365$		0			0
$366$	−98.3729	−	139.688i	−0.268779	−	0.381662i
$367$	183.244	−	183.244i	0.499301	−	0.499301i	−0.411919	−	0.911220i	$-0.635141\pi$
$367$	183.244	−	183.244i	0.499301	−	0.499301i	0.911220	+	0.411919i	$0.135141\pi$
$368$	−162.672	−	12.3862i	−0.442042	−	0.0336582i
$369$	−39.8277	−	456.521i	−0.107934	−	1.23719i
$370$		0			0
$371$	59.4543			0.160254
$372$	135.071	+	55.0779i	0.363094	+	0.148059i
$373$	78.2141	−	78.2141i	0.209689	−	0.209689i	−0.594446	−	0.804135i	$-0.702629\pi$
$373$	78.2141	−	78.2141i	0.209689	−	0.209689i	0.804135	+	0.594446i	$0.202629\pi$
$374$	−179.848	−	39.3401i	−0.480878	−	0.105187i
$375$		0			0
$376$	−241.915	−	182.400i	−0.643391	−	0.485106i
$377$	28.1278	−	28.1278i	0.0746096	−	0.0746096i
$378$	−145.765	−	12.3930i	−0.385621	−	0.0327857i
$379$	−116.155			−0.306478			−0.153239	−	0.988189i	$-0.548970\pi$
$379$	−116.155			−0.306478			−0.153239	+	0.988189i	$0.548970\pi$
$380$		0			0
$381$	182.290	−	198.886i	0.478452	−	0.522010i
$382$	146.710	+	228.863i	0.384058	+	0.599118i
$383$	−439.765	+	439.765i	−1.14821	+	1.14821i	−0.161308	+	0.986904i	$0.551571\pi$
$383$	−439.765	+	439.765i	−1.14821	+	1.14821i	−0.986904	+	0.161308i	$0.948429\pi$
$384$	−298.942	−	241.018i	−0.778496	−	0.627650i
$385$		0			0
$386$	−173.346	−	37.9178i	−0.449083	−	0.0982326i
$387$	−148.147	−	124.372i	−0.382810	−	0.321376i
$388$	160.990	−	59.6250i	0.414922	−	0.153673i
$389$	120.985			0.311017			0.155508	−	0.987835i	$-0.450298\pi$
$389$	120.985			0.311017			0.155508	+	0.987835i	$0.450298\pi$
$390$		0			0
$391$		−	136.574i		−	0.349293i
$392$	46.2942	+	330.056i	0.118098	+	0.841979i
$393$	−431.682	+	18.7946i	−1.09843	+	0.0478235i
$394$	267.980	+	58.6179i	0.680151	+	0.148776i
$395$		0			0
$396$	−83.3631	+	232.937i	−0.210513	+	0.588226i
$397$	549.267	+	549.267i	1.38355	+	1.38355i	0.838233	+	0.545313i	$0.183589\pi$
$397$	549.267	+	549.267i	1.38355	+	1.38355i	0.545313	+	0.838233i	$0.316411\pi$
$398$	31.3319	+	48.8768i	0.0787234	+	0.122806i
$399$	182.603	−	199.227i	0.457652	−	0.499317i
$400$		0			0
$401$			177.597i			0.442885i	0.975173	+	0.221442i	$0.0710765\pi$
$401$			177.597i			0.442885i	−0.975173	+	0.221442i	$0.928924\pi$
$402$	271.328	+	47.0887i	0.674944	+	0.117136i
$403$	149.207	+	149.207i	0.370240	+	0.370240i
$404$	−451.783	−	207.578i	−1.11827	−	0.513808i
$405$		0			0
$406$	12.1292	+	2.65315i	0.0298750	+	0.00653486i
$407$	142.457	+	142.457i	0.350018	+	0.350018i
$408$	182.184	−	264.854i	0.446529	−	0.649152i
$409$			348.822i			0.852865i	0.904519	+	0.426433i	$0.140230\pi$
$409$			348.822i			0.852865i	−0.904519	+	0.426433i	$0.859770\pi$
$410$		0			0
$411$	−39.0441	+	42.5986i	−0.0949977	+	0.103646i
$412$	−695.809	+	257.703i	−1.68886	+	0.625494i
$413$	−120.865	−	120.865i	−0.292651	−	0.292651i
$414$	−182.026	−	23.4880i	−0.439676	−	0.0567342i
$415$		0			0
$416$	−263.410	−	489.058i	−0.633197	−	1.17562i
$417$	188.000	−	8.18518i	0.450840	−	0.0196287i
$418$	−246.655	−	384.774i	−0.590084	−	0.920512i
$419$			104.631i			0.249716i	0.992175	+	0.124858i	$0.0398476\pi$
$419$			104.631i			0.249716i	−0.992175	+	0.124858i	$0.960152\pi$
$420$		0			0
$421$	207.644			0.493217			0.246609	−	0.969115i	$-0.420684\pi$
$421$	207.644			0.493217			0.246609	+	0.969115i	$0.420684\pi$
$422$	−634.691	+	406.862i	−1.50401	+	0.964127i
$423$	−261.048	−	219.155i	−0.617136	−	0.518096i
$424$	140.187	+	105.699i	0.330631	+	0.249290i
$425$		0			0
$426$	306.907	+	435.804i	0.720439	+	1.02301i
$427$	54.5474	−	54.5474i	0.127746	−	0.127746i
$428$	60.8303	−	22.5294i	0.142127	−	0.0526389i
$429$	−241.819	+	263.834i	−0.563681	+	0.614998i
$430$		0			0
$431$	135.966			0.315467			0.157734	−	0.987482i	$-0.449581\pi$
$431$	135.966			0.315467			0.157734	+	0.987482i	$0.449581\pi$
$432$	−321.667	−	288.365i	−0.744599	−	0.667512i
$433$	−426.207	+	426.207i	−0.984312	+	0.984312i	−0.999879	−	0.0155664i	$-0.995045\pi$
$433$	−426.207	+	426.207i	−0.984312	+	0.984312i	0.0155664	+	0.999879i	$0.495045\pi$
$434$	−14.0739	+	64.3407i	−0.0324284	+	0.148250i
$435$		0			0
$436$	−290.823	−	133.623i	−0.667026	−	0.306475i
$437$	239.748	−	239.748i	0.548622	−	0.548622i
$438$	595.037	+	103.268i	1.35853	+	0.235772i
$439$	−408.305			−0.930080			−0.465040	−	0.885290i	$-0.653960\pi$
$439$	−408.305			−0.930080			−0.465040	+	0.885290i	$0.653960\pi$
$440$		0			0
$441$	32.5873	+	373.529i	0.0738940	+	0.847004i
$442$	391.488	−	250.959i	0.885720	−	0.567781i
$443$	354.483	−	354.483i	0.800188	−	0.800188i	−0.182937	−	0.983125i	$-0.558560\pi$
$443$	354.483	−	354.483i	0.800188	−	0.800188i	0.983125	+	0.182937i	$0.0585604\pi$
$444$	−324.258	+	136.411i	−0.730311	+	0.307232i
$445$		0			0
$446$	−154.427	+	705.985i	−0.346250	+	1.58293i
$447$	−501.401	+	21.8301i	−1.12170	+	0.0488368i
$448$	84.1400	−	151.597i	0.187813	−	0.338386i
$449$	452.663			1.00816			0.504079	−	0.863657i	$-0.331832\pi$
$449$	452.663			1.00816			0.504079	+	0.863657i	$0.331832\pi$
$450$		0			0
$451$		−	349.922i		−	0.775880i
$452$	−344.041	+	127.421i	−0.761152	+	0.281904i
$453$	9.82069	+	225.565i	0.0216792	+	0.497936i
$454$	65.9070	−	301.302i	0.145170	−	0.663661i
$455$		0			0
$456$	784.751	−	145.123i	1.72095	−	0.318253i
$457$	−270.489	−	270.489i	−0.591879	−	0.591879i	0.346260	−	0.938139i	$-0.387452\pi$
$457$	−270.489	−	270.489i	−0.591879	−	0.591879i	−0.938139	+	0.346260i	$0.887452\pi$
$458$	−376.719	+	241.491i	−0.822531	+	0.527274i
$459$	220.262	−	286.832i	0.479873	−	0.624906i
$460$		0			0
$461$		−	582.469i		−	1.26349i	−0.775176	−	0.631745i	$-0.782339\pi$
$461$		−	582.469i		−	1.26349i	0.775176	−	0.631745i	$-0.217661\pi$
$462$	−110.062	−	19.1012i	−0.238229	−	0.0413445i
$463$	318.146	+	318.146i	0.687140	+	0.687140i	0.961599	−	0.274459i	$-0.0884986\pi$
$463$	318.146	+	318.146i	0.687140	+	0.687140i	−0.274459	+	0.961599i	$0.588499\pi$
$464$	23.8827	+	27.8195i	0.0514714	+	0.0599558i
$465$		0			0
$466$	−37.7293	+	172.485i	−0.0809642	+	0.370139i
$467$	554.211	+	554.211i	1.18675	+	1.18675i	0.977961	+	0.208786i	$0.0669514\pi$
$467$	554.211	+	554.211i	1.18675	+	1.18675i	0.208786	+	0.977961i	$0.433049\pi$
$468$	−267.151	−	564.938i	−0.570837	−	1.20713i
$469$			124.340i			0.265116i
$470$		0			0
$471$	−224.206	−	205.498i	−0.476022	−	0.436301i
$472$	−70.1118	−	499.864i	−0.148542	−	1.05903i
$473$	−104.443	−	104.443i	−0.220809	−	0.220809i
$474$	259.589	+	368.613i	0.547657	+	0.777665i
$475$		0			0
$476$	131.890	+	60.5987i	0.277080	+	0.127308i
$477$	151.275	+	126.998i	0.317138	+	0.266243i
$478$	−522.327	+	334.832i	−1.09273	+	0.700485i
$479$			857.141i			1.78944i	0.446629	+	0.894719i	$0.352625\pi$
$479$			857.141i			1.78944i	−0.446629	+	0.894719i	$0.647375\pi$
$480$		0			0
$481$	−508.880			−1.05796
$482$	129.419	+	201.889i	0.268504	+	0.418857i
$483$	−3.60454	−	82.7904i	−0.00746281	−	0.171409i
$484$	123.198	−	268.134i	0.254542	−	0.553996i
$485$		0			0
$486$	−344.411	−	342.895i	−0.708664	−	0.705546i
$487$	97.7824	−	97.7824i	0.200785	−	0.200785i	−0.599551	−	0.800336i	$-0.704654\pi$
$487$	97.7824	−	97.7824i	0.200785	−	0.200785i	0.800336	+	0.599551i	$0.204654\pi$
$488$	225.593	−	31.6421i	0.462281	−	0.0648403i
$489$	−192.195	−	176.157i	−0.393036	−	0.360240i
$490$		0			0
$491$	770.213			1.56866			0.784331	−	0.620342i	$-0.213006\pi$
$491$	770.213			1.56866			0.784331	+	0.620342i	$0.213006\pi$
$492$	565.777	+	230.707i	1.14995	+	0.468916i
$493$	−21.7037	+	21.7037i	−0.0440238	+	0.0440238i
$494$	1127.78	+	246.692i	2.28296	+	0.499376i
$495$		0			0
$496$	−147.571	+	126.688i	−0.297522	+	0.255420i
$497$	−170.179	+	170.179i	−0.342412	+	0.342412i
$498$	490.368	+	85.1031i	0.984675	+	0.170890i
$499$	66.3836			0.133033			0.0665166	−	0.997785i	$-0.478811\pi$
$499$	66.3836			0.133033			0.0665166	+	0.997785i	$0.478811\pi$
$500$		0			0
$501$	−115.050	−	105.450i	−0.229640	−	0.210478i
$502$	−362.933	−	566.164i	−0.722974	−	1.12782i
$503$	349.224	−	349.224i	0.694282	−	0.694282i	−0.268889	−	0.963171i	$-0.586656\pi$
$503$	349.224	−	349.224i	0.694282	−	0.694282i	0.963171	+	0.268889i	$0.0866564\pi$
$504$	103.449	−	165.362i	0.205256	−	0.328099i
$505$		0			0
$506$	−136.910	−	29.9477i	−0.270572	−	0.0591851i
$507$	−17.2680	−	396.617i	−0.0340591	−	0.782281i
$508$	124.933	+	337.325i	0.245932	+	0.664025i
$509$	447.822			0.879807			0.439904	−	0.898045i	$-0.355013\pi$
$509$	447.822			0.879807			0.439904	+	0.898045i	$0.355013\pi$
$510$		0			0
$511$			272.684i			0.533628i
$512$	467.906	−	207.865i	0.913879	−	0.405987i
$513$	890.176	−	116.861i	1.73524	−	0.227799i
$514$	551.629	+	120.664i	1.07321	+	0.234754i
$515$		0			0
$516$	237.730	−	100.010i	0.460717	−	0.193818i
$517$	−184.037	−	184.037i	−0.355971	−	0.355971i
$518$	−85.7192	−	133.719i	−0.165481	−	0.258145i
$519$	−431.293	−	395.304i	−0.831007	−	0.761665i
$520$		0			0
$521$		−	373.093i		−	0.716109i	−0.933701	−	0.358054i	$-0.883440\pi$
$521$		−	373.093i		−	0.716109i	0.933701	−	0.358054i	$-0.116560\pi$
$522$	25.1942	+	32.6595i	0.0482648	+	0.0625660i
$523$	−593.137	−	593.137i	−1.13411	−	1.13411i	−0.989488	−	0.144618i	$-0.953805\pi$
$523$	−593.137	−	593.137i	−1.13411	−	1.13411i	−0.144618	−	0.989488i	$-0.546195\pi$
$524$	240.533	−	523.507i	0.459032	−	0.999058i
$525$		0			0
$526$	298.212	+	65.2311i	0.566943	+	0.124013i
$527$	−115.130	−	115.130i	−0.218462	−	0.218462i
$528$	−225.557	−	240.709i	−0.427191	−	0.455888i
$529$			425.033i			0.803466i
$530$		0			0
$531$	−49.3529	−	565.703i	−0.0929432	−	1.06535i
$532$	125.148	+	337.904i	0.235240	+	0.635157i
$533$	624.988	+	624.988i	1.17259	+	1.17259i
$534$	−142.010	−	201.652i	−0.265935	−	0.377625i
$535$		0			0
$536$	−221.053	+	293.181i	−0.412413	+	0.546979i
$537$	13.9587	+	320.609i	0.0259939	+	0.597036i
$538$	301.522	+	470.364i	0.560449	+	0.874283i
$539$			286.308i			0.531184i
$540$		0			0
$541$	−46.0398			−0.0851012			−0.0425506	−	0.999094i	$-0.513548\pi$
$541$	−46.0398			−0.0851012			−0.0425506	+	0.999094i	$0.513548\pi$
$542$	594.395	−	381.030i	1.09667	−	0.703008i
$543$	−34.7842	+	1.51444i	−0.0640592	+	0.00278902i
$544$	203.250	+	377.362i	0.373621	+	0.693681i
$545$		0			0
$546$	230.695	−	162.463i	0.422519	−	0.297551i
$547$	−586.492	+	586.492i	−1.07220	+	1.07220i	−0.0750146	+	0.997182i	$0.523900\pi$
$547$	−586.492	+	586.492i	−1.07220	+	1.07220i	−0.997182	+	0.0750146i	$0.976100\pi$
$548$	−26.7590	−	72.2503i	−0.0488303	−	0.131844i
$549$	255.307	−	22.2734i	0.465040	−	0.0405708i
$550$		0			0
$551$	−76.1995			−0.138293
$552$	138.687	−	201.620i	0.251245	−	0.365254i
$553$	−143.941	+	143.941i	−0.260292	+	0.260292i
$554$	−5.47855	+	25.0459i	−0.00988908	+	0.0452092i
$555$		0			0
$556$	−104.754	+	227.991i	−0.188406	+	0.410055i
$557$	413.911	−	413.911i	0.743108	−	0.743108i	−0.230067	−	0.973175i	$-0.573894\pi$
$557$	413.911	−	413.911i	0.743108	−	0.743108i	0.973175	+	0.230067i	$0.0738945\pi$
$558$	−173.245	+	133.645i	−0.310475	+	0.239508i
$559$	373.086			0.667416
$560$		0			0
$561$	186.590	−	203.577i	0.332603	−	0.362883i
$562$	−344.328	+	220.728i	−0.612684	+	0.392754i
$563$	185.957	−	185.957i	0.330296	−	0.330296i	−0.522403	−	0.852699i	$-0.674964\pi$
$563$	185.957	−	185.957i	0.330296	−	0.330296i	0.852699	+	0.522403i	$0.174964\pi$
$564$	418.901	−	176.226i	0.742732	−	0.312458i
$565$		0			0
$566$	−2.99759	+	13.7039i	−0.00529610	+	0.0242118i
$567$	125.951	−	179.690i	0.222137	−	0.316913i
$568$	−703.812	+	98.7180i	−1.23911	+	0.173799i
$569$	−745.467			−1.31014			−0.655068	−	0.755570i	$-0.727360\pi$
$569$	−745.467			−1.31014			−0.655068	+	0.755570i	$0.727360\pi$
$570$		0			0
$571$		−	406.663i		−	0.712195i	−0.934449	−	0.356097i	$-0.884107\pi$
$571$		−	406.663i		−	0.712195i	0.934449	−	0.356097i	$-0.115893\pi$
$572$	−165.732	−	447.481i	−0.289741	−	0.782310i
$573$	−407.388	+	17.7369i	−0.710975	+	0.0309545i
$574$	−58.9519	+	269.506i	−0.102704	+	0.469523i
$575$		0			0
$576$	537.906	−	205.994i	0.933864	−	0.357628i
$577$	−73.9694	−	73.9694i	−0.128197	−	0.128197i	0.640097	−	0.768294i	$-0.278894\pi$
$577$	−73.9694	−	73.9694i	−0.128197	−	0.128197i	−0.768294	+	0.640097i	$0.778894\pi$
$578$	184.527	−	118.289i	0.319251	−	0.204652i
$579$	179.844	−	196.217i	0.310611	−	0.338889i
$580$		0			0
$581$			224.718i			0.386778i
$582$	−44.0333	+	253.722i	−0.0756586	+	0.435949i
$583$	106.648	+	106.648i	0.182929	+	0.182929i
$584$	−484.783	+	642.962i	−0.830108	+	1.10096i
$585$		0			0
$586$	118.242	−	540.559i	0.201778	−	0.922456i
$587$	422.201	+	422.201i	0.719251	+	0.719251i	0.968452	−	0.249200i	$-0.0801678\pi$
$587$	422.201	+	422.201i	0.719251	+	0.719251i	−0.249200	+	0.968452i	$0.580168\pi$
$588$	−462.923	−	188.766i	−0.787284	−	0.321030i
$589$		−	404.208i		−	0.686261i
$590$		0			0
$591$	−278.025	+	303.336i	−0.470431	+	0.513259i
$592$	35.6111	−	467.690i	0.0601538	−	0.790017i
$593$	−406.869	−	406.869i	−0.686119	−	0.686119i	0.275253	−	0.961372i	$-0.411238\pi$
$593$	−406.869	−	406.869i	−0.686119	−	0.686119i	−0.961372	+	0.275253i	$0.911238\pi$
$594$	−239.239	−	283.700i	−0.402759	−	0.477609i
$595$		0			0
$596$	279.381	−	608.056i	0.468759	−	1.02023i
$597$	−87.0033	+	3.78796i	−0.145734	+	0.00634500i
$598$	298.020	−	191.043i	0.498362	−	0.319469i
$599$		−	293.225i		−	0.489525i	−0.969583	−	0.244762i	$-0.921290\pi$
$599$		−	293.225i		−	0.489525i	0.969583	−	0.244762i	$-0.0787100\pi$
$600$		0			0
$601$	−1087.24			−1.80905			−0.904523	−	0.426424i	$-0.859773\pi$
$601$	−1087.24			−1.80905			−0.904523	+	0.426424i	$0.859773\pi$
$602$	62.8451	+	98.0363i	0.104394	+	0.162851i
$603$	−265.597	+	316.369i	−0.440459	+	0.524658i
$604$	−273.546	−	125.685i	−0.452891	−	0.208087i
$605$		0			0
$606$	609.755	−	429.409i	1.00620	−	0.708595i
$607$	74.9651	−	74.9651i	0.123501	−	0.123501i	−0.642655	−	0.766156i	$-0.722167\pi$
$607$	74.9651	−	74.9651i	0.123501	−	0.123501i	0.766156	+	0.642655i	$0.222167\pi$
$608$	−305.645	+	1019.23i	−0.502706	+	1.67637i
$609$	−12.5839	+	13.7295i	−0.0206632	+	0.0225444i
$610$		0			0
$611$	657.409			1.07596
$612$	206.137	+	435.912i	0.336825	+	0.712274i
$613$	−22.9005	+	22.9005i	−0.0373581	+	0.0373581i	−0.725539	−	0.688181i	$-0.758410\pi$
$613$	−22.9005	+	22.9005i	−0.0373581	+	0.0373581i	0.688181	+	0.725539i	$0.258410\pi$
$614$	−894.903	−	195.751i	−1.45750	−	0.318813i
$615$		0			0
$616$	89.6684	−	118.926i	0.145566	−	0.193062i
$617$	−115.002	+	115.002i	−0.186389	+	0.186389i	−0.794133	−	0.607744i	$-0.792075\pi$
$617$	−115.002	+	115.002i	−0.186389	+	0.186389i	0.607744	+	0.794133i	$0.292075\pi$
$618$	190.315	−	1096.60i	0.307953	−	1.77444i
$619$	710.704			1.14815			0.574074	−	0.818803i	$-0.305362\pi$
$619$	710.704			1.14815			0.574074	+	0.818803i	$0.305362\pi$
$620$		0			0
$621$	167.674	−	218.351i	0.270006	−	0.351612i
$622$	463.006	+	722.275i	0.744383	+	1.16121i
$623$	78.7438	−	78.7438i	0.126394	−	0.126394i
$624$	832.787	+	27.0627i	1.33459	+	0.0433697i
$625$		0			0
$626$	−398.299	−	87.1240i	−0.636260	−	0.139176i
$627$	684.918	−	29.8201i	1.09237	−	0.0475599i
$628$	380.270	−	140.839i	0.605525	−	0.224265i
$629$	392.657			0.624256
$630$		0			0
$631$			209.771i			0.332443i	0.986088	+	0.166221i	$0.0531566\pi$
$631$			209.771i			0.332443i	−0.986088	+	0.166221i	$0.946843\pi$
$632$	−595.301	+	83.4980i	−0.941932	+	0.132117i
$633$	−49.1887	−	1129.78i	−0.0777072	−	1.78481i
$634$	−828.369	−	181.198i	−1.30658	−	0.285801i
$635$		0			0
$636$	−242.749	+	102.121i	−0.381681	+	0.160568i
$637$	−511.370	−	511.370i	−0.802778	−	0.802778i
$638$	16.9980	+	26.5163i	0.0266426	+	0.0415616i
$639$	−796.514	+	69.4892i	−1.24650	+	0.108747i
$640$		0			0
$641$			1193.44i			1.86184i	0.365221	+	0.930921i	$0.380993\pi$
$641$			1193.44i			1.86184i	−0.365221	+	0.930921i	$0.619007\pi$
$642$	−16.6381	+	95.8695i	−0.0259160	+	0.149329i
$643$	−424.387	−	424.387i	−0.660012	−	0.660012i	0.295371	−	0.955383i	$-0.404557\pi$
$643$	−424.387	−	424.387i	−0.660012	−	0.660012i	−0.955383	+	0.295371i	$0.904557\pi$
$644$	100.401	+	46.1308i	0.155902	+	0.0716316i
$645$		0			0
$646$	−870.209	−	190.350i	−1.34707	−	0.294659i
$647$	−556.306	−	556.306i	−0.859824	−	0.859824i	0.131493	−	0.991317i	$-0.458023\pi$
$647$	−556.306	−	556.306i	−0.859824	−	0.859824i	−0.991317	+	0.131493i	$0.958023\pi$
$648$	616.437	−	199.772i	0.951292	−	0.308290i
$649$		−	433.609i		−	0.668119i
$650$		0			0
$651$	−72.8296	−	66.7525i	−0.111873	−	0.102538i
$652$	325.976	−	120.730i	0.499963	−	0.185169i
$653$	−730.267	−	730.267i	−1.11833	−	1.11833i	−0.991987	−	0.126340i	$-0.959677\pi$
$653$	−730.267	−	730.267i	−1.11833	−	1.11833i	−0.126340	−	0.991987i	$-0.540323\pi$
$654$	392.513	−	276.420i	0.600174	−	0.422661i
$655$		0			0
$656$	−618.137	+	530.664i	−0.942281	+	0.808939i
$657$	−582.470	+	693.815i	−0.886560	+	1.05604i
$658$	110.738	+	172.748i	0.168295	+	0.262536i
$659$			929.519i			1.41050i	0.708959	+	0.705250i	$0.249165\pi$
$659$			929.519i			1.41050i	−0.708959	+	0.705250i	$0.750835\pi$
$660$		0			0
$661$	564.895			0.854607			0.427303	−	0.904108i	$-0.359464\pi$
$661$	564.895			0.854607			0.427303	+	0.904108i	$0.359464\pi$
$662$	150.068	−	96.1997i	0.226690	−	0.145317i
$663$	30.3404	+	696.870i	0.0457623	+	1.05109i
$664$	−399.508	+	529.863i	−0.601668	+	0.797986i
$665$		0			0
$666$	67.5293	−	523.336i	0.101395	−	0.785789i
$667$	−16.5220	+	16.5220i	−0.0247705	+	0.0247705i
$668$	195.132	−	72.2703i	0.292114	−	0.108189i
$669$	−799.131	−	732.449i	−1.19452	−	1.09484i
$670$		0			0
$671$	195.692			0.291642
$672$	133.169	+	223.391i	0.198168	+	0.332428i
$673$	−301.487	+	301.487i	−0.447975	+	0.447975i	−0.894681	−	0.446706i	$-0.852597\pi$
$673$	−301.487	+	301.487i	−0.447975	+	0.447975i	0.446706	+	0.894681i	$0.352597\pi$
$674$	106.962	−	488.992i	0.158698	−	0.725508i
$675$		0			0
$676$	480.983	+	220.995i	0.711513	+	0.326915i
$677$	−530.496	+	530.496i	−0.783598	+	0.783598i	−0.980436	−	0.196838i	$-0.936933\pi$
$677$	−530.496	+	530.496i	−0.783598	+	0.783598i	0.196838	+	0.980436i	$0.436933\pi$
$678$	94.1007	−	542.213i	0.138792	−	0.799724i
$679$	−116.272			−0.171240
$680$		0			0
$681$	341.055	+	312.596i	0.500815	+	0.459026i
$682$	−140.658	+	90.1673i	−0.206244	+	0.132210i
$683$	−378.401	+	378.401i	−0.554028	+	0.554028i	−0.927601	−	0.373573i	$-0.878133\pi$
$683$	−378.401	+	378.401i	−0.554028	+	0.554028i	0.373573	+	0.927601i	$0.378133\pi$
$684$	−403.358	+	1127.08i	−0.589705	+	1.64778i
$685$		0			0
$686$	104.967	−	479.870i	0.153013	−	0.699519i
$687$	−29.1958	−	670.580i	−0.0424975	−	0.976099i
$688$	−26.1083	+	342.887i	−0.0379481	+	0.498383i
$689$	−380.962			−0.552920
$690$		0			0
$691$			690.583i			0.999396i	0.866200	+	0.499698i	$0.166556\pi$
$691$			690.583i			0.999396i	−0.866200	+	0.499698i	$0.833444\pi$
$692$	731.503	−	270.923i	1.05708	−	0.391508i
$693$	107.737	−	128.332i	0.155465	−	0.185184i
$694$	−206.432	+	943.730i	−0.297452	+	1.35984i
$695$		0			0
$696$	−54.0802	+	10.0010i	−0.0777015	+	0.0143693i
$697$	−482.247	−	482.247i	−0.691890	−	0.691890i
$698$	−320.129	+	205.215i	−0.458638	+	0.294004i
$699$	−195.242	−	178.950i	−0.279316	−	0.256009i
$700$		0			0
$701$			129.593i			0.184869i	0.995719	+	0.0924343i	$0.0294648\pi$
$701$			129.593i			0.184869i	−0.995719	+	0.0924343i	$0.970535\pi$
$702$	934.010	+	79.4100i	1.33050	+	0.113120i
$703$	689.289	+	689.289i	0.980496	+	0.980496i
$704$	422.859	−	121.002i	0.600652	−	0.171879i
$705$		0			0
$706$	40.1347	−	183.481i	0.0568480	−	0.259888i
$707$	238.105	+	238.105i	0.336783	+	0.336783i
$708$	701.089	+	285.883i	0.990238	+	0.403789i
$709$			86.8545i			0.122503i	0.998122	+	0.0612514i	$0.0195091\pi$
$709$			86.8545i			0.122503i	−0.998122	+	0.0612514i	$0.980491\pi$
$710$		0			0
$711$	−673.710	+	58.7756i	−0.947553	+	0.0826661i
$712$	325.662	−	45.6780i	0.457391	−	0.0641545i
$713$	−87.6423	−	87.6423i	−0.122920	−	0.122920i
$714$	−178.007	+	125.358i	−0.249309	+	0.175571i
$715$		0			0
$716$	−388.807	−	178.643i	−0.543026	−	0.249501i
$717$	−40.4804	−	929.769i	−0.0564581	−	1.29675i
$718$	−676.872	+	433.901i	−0.942719	+	0.604319i
$719$			104.099i			0.144782i	0.997376	+	0.0723912i	$0.0230630\pi$
$719$			104.099i			0.144782i	−0.997376	+	0.0723912i	$0.976937\pi$
$720$		0			0
$721$	502.534			0.696996
$722$	−803.812	−	1253.92i	−1.11331	−	1.73673i
$723$	−359.373	+	15.6464i	−0.497059	+	0.0216410i
$724$	19.3817	−	42.1833i	0.0267703	−	0.0582642i
$725$		0			0
$726$	254.855	+	361.891i	0.351040	+	0.498472i
$727$	−252.054	+	252.054i	−0.346704	+	0.346704i	−0.858880	−	0.512176i	$-0.828839\pi$
$727$	−252.054	+	252.054i	−0.346704	+	0.346704i	0.512176	+	0.858880i	$0.328839\pi$
$728$	52.2569	+	372.567i	0.0717814	+	0.511768i
$729$	704.298	−	188.161i	0.966116	−	0.258109i
$730$		0			0
$731$	−287.877			−0.393812
$732$	−129.021	+	316.408i	−0.176259	+	0.432251i
$733$	795.114	−	795.114i	1.08474	−	1.08474i	0.0886791	−	0.996060i	$-0.471735\pi$
$733$	795.114	−	795.114i	1.08474	−	1.08474i	0.996060	−	0.0886791i	$-0.0282646\pi$
$734$	−506.320	−	110.753i	−0.689809	−	0.150889i
$735$		0			0
$736$	154.724	+	287.267i	0.210223	+	0.390308i
$737$	−223.037	+	223.037i	−0.302629	+	0.302629i
$738$	−725.679	+	559.805i	−0.983305	+	0.758543i
$739$	622.137			0.841863			0.420931	−	0.907092i	$-0.361703\pi$
$739$	622.137			0.841863			0.420931	+	0.907092i	$0.361703\pi$
$740$		0			0
$741$	−1170.06	+	1276.58i	−1.57902	+	1.72278i
$742$	−64.1718	−	100.106i	−0.0864850	−	0.134914i
$743$	487.618	−	487.618i	0.656283	−	0.656283i	−0.298216	−	0.954499i	$-0.596391\pi$
$743$	487.618	−	487.618i	0.656283	−	0.656283i	0.954499	+	0.298216i	$0.0963914\pi$
$744$	−53.0514	−	286.874i	−0.0713056	−	0.385583i
$745$		0			0
$746$	−216.113	−	47.2726i	−0.289696	−	0.0633681i
$747$	−480.011	+	571.770i	−0.642585	+	0.765422i
$748$	127.880	+	345.281i	0.170963	+	0.461606i
$749$	−43.9335			−0.0586562
$750$		0			0
$751$			1089.00i			1.45007i	0.688711	+	0.725036i	$0.258177\pi$
$751$			1089.00i			1.45007i	−0.688711	+	0.725036i	$0.741823\pi$
$752$	−46.0050	+	604.197i	−0.0611769	+	0.803454i
$753$	1007.80	−	43.8778i	1.33838	−	0.0582706i
$754$	−77.7199	−	17.0005i	−0.103077	−	0.0225470i
$755$		0			0
$756$	136.464	+	258.808i	0.180508	+	0.342338i
$757$	628.144	+	628.144i	0.829781	+	0.829781i	0.987486	−	0.157705i	$-0.0504097\pi$
$757$	628.144	+	628.144i	0.829781	+	0.829781i	−0.157705	+	0.987486i	$0.550410\pi$
$758$	125.372	+	195.576i	0.165398	+	0.258016i
$759$	142.042	−	154.973i	0.187143	−	0.204181i
$760$		0			0
$761$		−	723.259i		−	0.950407i	−0.879876	−	0.475203i	$-0.842375\pi$
$761$		−	723.259i		−	0.950407i	0.879876	−	0.475203i	$-0.157625\pi$
$762$	−531.628	−	92.2638i	−0.697675	−	0.121081i
$763$	153.274	+	153.274i	0.200883	+	0.200883i
$764$	226.997	−	494.046i	0.297116	−	0.646657i
$765$		0			0
$766$	1215.11	+	265.794i	1.58631	+	0.346990i
$767$	774.460	+	774.460i	1.00973	+	1.00973i
$768$	−83.1500	+	763.485i	−0.108268	+	0.994122i
$769$			180.270i			0.234421i	0.993107	+	0.117210i	$0.0373952\pi$
$769$			180.270i			0.234421i	−0.993107	+	0.117210i	$0.962605\pi$
$770$		0			0
$771$	−572.307	+	624.410i	−0.742292	+	0.809870i
$772$	123.257	+	332.798i	0.159659	+	0.431085i
$773$	482.107	+	482.107i	0.623683	+	0.623683i	0.946471	−	0.322788i	$-0.104620\pi$
$773$	482.107	+	482.107i	0.623683	+	0.623683i	−0.322788	+	0.946471i	$0.604620\pi$
$774$	−49.5091	+	383.684i	−0.0639653	+	0.495716i
$775$		0			0
$776$	−274.157	−	206.710i	−0.353296	−	0.266379i
$777$	238.027	−	10.3633i	0.306341	−	0.0133375i
$778$	−130.585	−	203.709i	−0.167848	−	0.261837i
$779$		−	1693.12i		−	2.17345i
$780$		0			0
$781$	−610.525			−0.781722
$782$	−229.956	+	147.410i	−0.294061	+	0.188504i
$783$	−61.3455	+	8.05334i	−0.0783468	+	0.0102852i
$784$	505.764	−	434.193i	0.645107	−	0.553818i
$785$		0			0
$786$	497.580	+	706.557i	0.633053	+	0.898928i
$787$	279.225	−	279.225i	0.354797	−	0.354797i	−0.507094	−	0.861891i	$-0.669280\pi$
$787$	279.225	−	279.225i	0.354797	−	0.354797i	0.861891	+	0.507094i	$0.169280\pi$
$788$	−190.545	−	514.479i	−0.241809	−	0.652892i
$789$	−309.391	+	337.558i	−0.392130	+	0.427830i
$790$		0			0
$791$	248.477			0.314130
$792$	482.186	−	111.058i	0.608820	−	0.140225i
$793$	−349.521	+	349.521i	−0.440758	+	0.440758i
$794$	331.978	−	1517.68i	0.418108	−	1.91143i
$795$		0			0
$796$	48.4782	−	105.510i	0.0609023	−	0.132550i
$797$	−861.626	+	861.626i	−1.08109	+	1.08109i	−0.0846783	+	0.996408i	$0.526986\pi$
$797$	−861.626	+	861.626i	−1.08109	+	1.08109i	−0.996408	+	0.0846783i	$0.973014\pi$
$798$	−532.541	−	92.4222i	−0.667345	−	0.115817i
$799$	−507.264			−0.634873
$800$		0			0
$801$	368.557	−	32.1535i	0.460121	−	0.0401417i
$802$	299.028	−	191.689i	0.372853	−	0.239013i
$803$	−489.134	+	489.134i	−0.609133	+	0.609133i
$804$	−213.571	−	507.672i	−0.265636	−	0.631433i
$805$		0			0
$806$	90.1807	−	412.273i	0.111887	−	0.511505i
$807$	−837.273	+	36.4533i	−1.03751	+	0.0451714i
$808$	138.121	+	984.738i	0.170942	+	1.21874i
$809$	−430.022			−0.531548			−0.265774	−	0.964035i	$-0.585627\pi$
$809$	−430.022			−0.531548			−0.265774	+	0.964035i	$0.585627\pi$
$810$		0			0
$811$		−	1351.37i		−	1.66630i	−0.553047	−	0.833150i	$-0.686535\pi$
$811$		−	1351.37i		−	1.66630i	0.553047	−	0.833150i	$-0.313465\pi$
$812$	−8.62442	−	23.2863i	−0.0106212	−	0.0286777i
$813$	46.0658	+	1058.06i	0.0566614	+	1.30142i
$814$	86.1013	−	393.623i	0.105776	−	0.483567i
$815$		0			0
$816$	−642.587	−	20.8819i	−0.787484	−	0.0255905i
$817$	−505.353	−	505.353i	−0.618547	−	0.618547i
$818$	587.328	−	376.500i	0.718005	−	0.460269i
$819$	36.7845	+	421.639i	0.0449139	+	0.514822i
$820$		0			0
$821$		−	901.925i		−	1.09857i	−0.835636	−	0.549284i	$-0.814900\pi$
$821$		−	901.925i		−	1.09857i	0.835636	−	0.549284i	$-0.185100\pi$
$822$	113.867	+	19.7616i	0.138525	+	0.0240409i
$823$	−512.252	−	512.252i	−0.622421	−	0.622421i	0.323729	−	0.946150i	$-0.395063\pi$
$823$	−512.252	−	512.252i	−0.622421	−	0.622421i	−0.946150	+	0.323729i	$0.895063\pi$
$824$	1184.93	+	893.415i	1.43802	+	1.08424i
$825$		0			0
$826$	−73.0508	+	333.961i	−0.0884393	+	0.404312i
$827$	−683.717	−	683.717i	−0.826744	−	0.826744i	0.160321	−	0.987065i	$-0.448747\pi$
$827$	−683.717	−	683.717i	−0.826744	−	0.826744i	−0.987065	+	0.160321i	$0.948747\pi$
$828$	156.922	+	331.838i	0.189519	+	0.400770i
$829$			1001.78i			1.20842i	0.796827	+	0.604208i	$0.206510\pi$
$829$			1001.78i			1.20842i	−0.796827	+	0.604208i	$0.793490\pi$
$830$		0			0
$831$	−28.3504	−	25.9847i	−0.0341160	−	0.0312692i
$832$	−539.140	+	971.380i	−0.648005	+	1.16752i
$833$	394.578	+	394.578i	0.473683	+	0.473683i
$834$	−216.699	−	307.711i	−0.259832	−	0.368957i
$835$		0			0
$836$	−381.636	+	830.610i	−0.456503	+	0.993553i
$837$	−42.7197	−	325.413i	−0.0510391	−	0.388785i
$838$	176.173	−	112.933i	0.210230	−	0.134765i
$839$			189.192i			0.225497i	0.993624	+	0.112749i	$0.0359654\pi$
$839$			189.192i			0.225497i	−0.993624	+	0.112749i	$0.964035\pi$
$840$		0			0
$841$	−835.749			−0.993756
$842$	−224.120	−	349.621i	−0.266176	−	0.415227i
$843$	−26.6855	−	612.923i	−0.0316554	−	0.727073i
$844$	1370.10	+	629.515i	1.62335	+	0.745871i
$845$		0			0
$846$	−87.2393	+	676.084i	−0.103120	+	0.799154i
$847$	−141.316	+	141.316i	−0.166843	+	0.166843i
$848$	26.6595	−	350.126i	0.0314381	−	0.412885i
$849$	−15.5119	−	14.2176i	−0.0182708	−	0.0167462i
$850$		0			0
$851$	298.910			0.351246
$852$	402.525	−	987.138i	0.472447	−	1.15861i
$853$	430.775	−	430.775i	0.505011	−	0.505011i	−0.407980	−	0.912991i	$-0.633767\pi$
$853$	430.775	−	430.775i	0.505011	−	0.505011i	0.912991	+	0.407980i	$0.133767\pi$
$854$	−150.720	−	32.9685i	−0.176487	−	0.0386048i
$855$		0			0
$856$	−103.591	−	78.1059i	−0.121018	−	0.0912452i
$857$	684.012	−	684.012i	0.798147	−	0.798147i	−0.184656	−	0.982803i	$-0.559117\pi$
$857$	684.012	−	684.012i	0.798147	−	0.798147i	0.982803	+	0.184656i	$0.0591172\pi$
$858$	705.237	+	122.393i	0.821955	+	0.142650i
$859$	−1397.70			−1.62712			−0.813560	−	0.581481i	$-0.802473\pi$
$859$	−1397.70			−1.62712			−0.813560	+	0.581481i	$0.802473\pi$
$860$		0			0
$861$	−305.064	−	279.609i	−0.354314	−	0.324749i
$862$	−146.755	−	228.933i	−0.170249	−	0.265584i
$863$	90.1987	−	90.1987i	0.104518	−	0.104518i	−0.652914	−	0.757432i	$-0.726454\pi$
$863$	90.1987	−	90.1987i	0.104518	−	0.104518i	0.757432	+	0.652914i	$0.226454\pi$
$864$	−138.344	+	852.852i	−0.160120	+	0.987098i
$865$		0			0
$866$	1177.65	+	257.600i	1.35987	+	0.297459i
$867$	14.3009	+	328.468i	0.0164947	+	0.378855i
$868$	123.524	−	45.7491i	0.142309	−	0.0527063i
$869$	−516.396			−0.594242
$870$		0			0
$871$		−	796.724i		−	0.914724i
$872$	88.9118	+	633.899i	0.101963	+	0.726949i
$873$	−295.841	−	248.363i	−0.338878	−	0.284494i
$874$	−662.446	−	144.904i	−0.757948	−	0.165794i
$875$		0			0
$876$	−468.374	−	1113.36i	−0.534674	−	1.27095i
$877$	−19.3296	−	19.3296i	−0.0220406	−	0.0220406i	0.696001	−	0.718041i	$-0.254961\pi$
$877$	−19.3296	−	19.3296i	−0.0220406	−	0.0220406i	−0.718041	+	0.696001i	$0.754961\pi$
$878$	440.703	+	687.483i	0.501940	+	0.783010i
$879$	611.879	+	560.822i	0.696108	+	0.638022i
$880$		0			0
$881$			721.297i			0.818725i	0.912372	+	0.409363i	$0.134249\pi$
$881$			721.297i			0.818725i	−0.912372	+	0.409363i	$0.865751\pi$
$882$	593.756	−	458.036i	0.673192	−	0.519315i
$883$	941.983	+	941.983i	1.06680	+	1.06680i	0.997603	+	0.0691949i	$0.0220430\pi$
$883$	941.983	+	941.983i	1.06680	+	1.06680i	0.0691949	+	0.997603i	$0.477957\pi$
$884$	−845.104	−	388.296i	−0.956000	−	0.439248i
$885$		0			0
$886$	−979.471	−	214.250i	−1.10550	−	0.241817i
$887$	−489.902	−	489.902i	−0.552313	−	0.552313i	0.374795	−	0.927108i	$-0.377713\pi$
$887$	−489.902	−	489.902i	−0.552313	−	0.552313i	−0.927108	+	0.374795i	$0.877713\pi$
$888$	579.669	+	398.734i	0.652781	+	0.449025i
$889$		−	243.626i		−	0.274045i
$890$		0			0
$891$	548.252	−	96.3944i	0.615322	−	0.108187i
$892$	1355.38	−	501.986i	1.51949	−	0.562765i
$893$	−890.475	−	890.475i	−0.997172	−	0.997172i
$894$	577.942	+	820.671i	0.646468	+	0.917976i
$895$		0			0
$896$	−346.067	+	21.9551i	−0.386236	+	0.0245035i
$897$	23.0966	+	530.492i	0.0257487	+	0.591407i
$898$	−488.581	−	762.171i	−0.544077	−	0.848743i
$899$			27.8555i			0.0309850i
$900$		0			0
$901$	293.954			0.326253
$902$	−589.180	+	377.687i	−0.653193	+	0.418722i
$903$	−174.510	+	7.59784i	−0.193256	+	0.00841399i
$904$	585.884	+	441.746i	0.648101	+	0.488658i
$905$		0			0
$906$	369.195	−	259.999i	0.407500	−	0.286974i
$907$	−193.827	+	193.827i	−0.213701	+	0.213701i	−0.805838	−	0.592137i	$-0.798285\pi$
$907$	−193.827	+	193.827i	−0.213701	+	0.213701i	0.592137	+	0.805838i	$0.298285\pi$
$908$	−578.454	+	214.239i	−0.637064	+	0.235946i
$909$	97.2258	+	1114.44i	0.106959	+	1.22601i
$910$		0			0
$911$	−830.304			−0.911421			−0.455710	−	0.890128i	$-0.650615\pi$
$911$	−830.304			−0.911421			−0.455710	+	0.890128i	$0.650615\pi$
$912$	−1091.37	−	1164.68i	−1.19668	−	1.27707i
$913$	−403.093	+	403.093i	−0.441504	+	0.441504i
$914$	−163.484	+	747.386i	−0.178866	+	0.817709i
$915$		0			0
$916$	813.222	+	373.647i	0.887797	+	0.407911i
$917$	−275.906	+	275.906i	−0.300879	+	0.300879i
$918$	−720.692	−	61.2736i	−0.785067	−	0.0667468i
$919$	−1072.00			−1.16649			−0.583245	−	0.812296i	$-0.698217\pi$
$919$	−1072.00			−1.16649			−0.583245	+	0.812296i	$0.698217\pi$
$920$		0			0
$921$	928.448	−	1012.97i	1.00809	−	1.09986i
$922$	−980.731	+	628.687i	−1.06370	+	0.681873i
$923$	1090.45	−	1090.45i	1.18141	−	1.18141i
$924$	86.6334	+	205.933i	0.0937591	+	0.222871i
$925$		0			0
$926$	192.288	−	879.068i	0.207654	−	0.949317i
$927$	1278.64	+	1073.44i	1.37934	+	1.15798i
$928$	21.0632	−	70.2394i	0.0226974	−	0.0756890i
$929$	1289.64			1.38821			0.694103	−	0.719876i	$-0.255801\pi$
$929$	1289.64			1.38821			0.694103	+	0.719876i	$0.255801\pi$
$930$		0			0
$931$			1385.32i			1.48799i
$932$	331.144	−	122.644i	0.355304	−	0.131592i
$933$	−1285.69	+	55.9764i	−1.37801	+	0.0599962i
$934$	334.966	−	1531.34i	0.358636	−	1.63955i
$935$		0			0
$936$	−662.864	+	1059.58i	−0.708188	+	1.13203i
$937$	507.002	+	507.002i	0.541091	+	0.541091i	0.923849	−	0.382758i	$-0.125026\pi$
$937$	507.002	+	507.002i	0.541091	+	0.541091i	−0.382758	+	0.923849i	$0.625026\pi$
$938$	209.357	−	134.206i	0.223195	−	0.143076i
$939$	413.229	−	450.849i	0.440073	−	0.480138i
$940$		0			0
$941$			707.695i			0.752067i	0.926606	+	0.376033i	$0.122712\pi$
$941$			707.695i			0.752067i	−0.926606	+	0.376033i	$0.877288\pi$
$942$	−104.010	+	599.310i	−0.110414	+	0.636211i
$943$	−367.111	−	367.111i	−0.389301	−	0.389301i
$944$	−765.970	+	657.578i	−0.811409	+	0.696586i
$945$		0			0
$946$	−63.1252	+	288.585i	−0.0667286	+	0.305058i
$947$	−233.033	−	233.033i	−0.246075	−	0.246075i	0.573283	−	0.819358i	$-0.305670\pi$
$947$	−233.033	−	233.033i	−0.246075	−	0.246075i	−0.819358	+	0.573283i	$0.805670\pi$
$948$	340.465	−	834.945i	0.359140	−	0.880744i
$949$		−	1747.26i		−	1.84116i
$950$		0			0
$951$	859.420	−	937.662i	0.903701	−	0.985974i
$952$	−40.3220	−	287.476i	−0.0423550	−	0.301971i
$953$	414.033	+	414.033i	0.434452	+	0.434452i	0.890140	−	0.455688i	$-0.150607\pi$
$953$	414.033	+	414.033i	0.434452	+	0.434452i	−0.455688	+	0.890140i	$0.650607\pi$
$954$	50.5544	−	391.784i	0.0529920	−	0.410675i
$955$		0			0
$956$	1127.54	+	518.067i	1.17944	+	0.541911i
$957$	−47.2004	+	2.05502i	−0.0493212	+	0.00214735i
$958$	1443.21	−	925.153i	1.50648	−	0.965713i
$959$			52.1813i			0.0544122i
$960$		0			0
$961$	813.238			0.846241
$962$	549.259	+	856.826i	0.570955	+	0.890671i
$963$	−111.784	−	93.8447i	−0.116079	−	0.0974504i
$964$	200.243	−	435.817i	0.207721	−	0.452093i
$965$		0			0
$966$	−135.508	+	95.4288i	−0.140277	+	0.0987875i
$967$	534.588	−	534.588i	0.552831	−	0.552831i	−0.374426	−	0.927257i	$-0.622160\pi$
$967$	534.588	−	534.588i	0.552831	−	0.552831i	0.927257	+	0.374426i	$0.122160\pi$
$968$	−584.444	+	81.9752i	−0.603765	+	0.0846851i
$969$	902.828	−	985.022i	0.931711	−	1.01653i
$970$		0			0
$971$	−438.396			−0.451490			−0.225745	−	0.974186i	$-0.572482\pi$
$971$	−438.396			−0.451490			−0.225745	+	0.974186i	$0.572482\pi$
$972$	−205.611	+	950.004i	−0.211533	+	0.977371i
$973$	120.159	−	120.159i	0.123493	−	0.123493i
$974$	−270.182	−	59.0997i	−0.277394	−	0.0606773i
$975$		0			0
$976$	−296.771	−	345.689i	−0.304068	−	0.354190i
$977$	1230.19	−	1230.19i	1.25915	−	1.25915i	0.307644	−	0.951501i	$-0.400459\pi$
$977$	1230.19	−	1230.19i	1.25915	−	1.25915i	0.951501	−	0.307644i	$-0.0995406\pi$
$978$	−89.1597	+	513.743i	−0.0911654	+	0.525299i
$979$	282.497			0.288557
$980$		0			0
$981$	62.5865	+	717.392i	0.0637987	+	0.731287i
$982$	−831.328	−	1296.85i	−0.846566	−	1.32062i
$983$	−1245.00	+	1245.00i	−1.26653	+	1.26653i	−0.318665	+	0.947867i	$0.603235\pi$
$983$	−1245.00	+	1245.00i	−1.26653	+	1.26653i	−0.947867	+	0.318665i	$0.896765\pi$
$984$	−222.218	−	1201.64i	−0.225832	−	1.22118i
$985$		0			0
$986$	59.9695	+	13.1177i	0.0608210	+	0.0133040i
$987$	−307.501	+	13.3880i	−0.311551	+	0.0135644i
$988$	−801.903	−	2165.17i	−0.811643	−	2.19147i
$989$	−219.146			−0.221584
$990$		0			0
$991$		−	1328.35i		−	1.34041i	−0.742176	−	0.670205i	$-0.766206\pi$
$991$		−	1328.35i		−	1.34041i	0.742176	−	0.670205i	$-0.233794\pi$
$992$	372.592	+	111.732i	0.375597	+	0.112633i
$993$	11.6303	+	267.130i	0.0117123	+	0.269013i
$994$	470.220	+	102.856i	0.473059	+	0.103477i
$995$		0			0
$996$	−385.985	−	917.512i	−0.387536	−	0.921197i
$997$	553.349	+	553.349i	0.555014	+	0.555014i	0.927884	−	0.372870i	$-0.121626\pi$
$997$	553.349	+	553.349i	0.555014	+	0.555014i	−0.372870	+	0.927884i	$0.621626\pi$
$998$	−71.6510	−	111.773i	−0.0717945	−	0.111997i
$999$	627.771	+	482.073i	0.628400	+	0.482555i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.3.l.g.107.6		40
3.2	odd	2	inner	300.3.l.g.107.15		40
4.3	odd	2	inner	300.3.l.g.107.16		40
5.2	odd	4		60.3.l.a.23.16	yes	40
5.3	odd	4	inner	300.3.l.g.143.5		40
5.4	even	2		60.3.l.a.47.15	yes	40
12.11	even	2	inner	300.3.l.g.107.5		40
15.2	even	4		60.3.l.a.23.5	✓	40
15.8	even	4	inner	300.3.l.g.143.16		40
15.14	odd	2		60.3.l.a.47.6	yes	40
20.3	even	4	inner	300.3.l.g.143.15		40
20.7	even	4		60.3.l.a.23.6	yes	40
20.19	odd	2		60.3.l.a.47.5	yes	40
60.23	odd	4	inner	300.3.l.g.143.6		40
60.47	odd	4		60.3.l.a.23.15	yes	40
60.59	even	2		60.3.l.a.47.16	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.l.a.23.5	✓	40	15.2	even	4
60.3.l.a.23.6	yes	40	20.7	even	4
60.3.l.a.23.15	yes	40	60.47	odd	4
60.3.l.a.23.16	yes	40	5.2	odd	4
60.3.l.a.47.5	yes	40	20.19	odd	2
60.3.l.a.47.6	yes	40	15.14	odd	2
60.3.l.a.47.15	yes	40	5.4	even	2
60.3.l.a.47.16	yes	40	60.59	even	2
300.3.l.g.107.5		40	12.11	even	2	inner
300.3.l.g.107.6		40	1.1	even	1	trivial
300.3.l.g.107.15		40	3.2	odd	2	inner
300.3.l.g.107.16		40	4.3	odd	2	inner
300.3.l.g.143.5		40	5.3	odd	4	inner
300.3.l.g.143.6		40	60.23	odd	4	inner
300.3.l.g.143.15		40	20.3	even	4	inner
300.3.l.g.143.16		40	15.8	even	4	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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	300.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07935 - 1.68375i) q^{2} +(2.99716 - 0.130491i) q^{3} +(-1.67002 + 3.63470i) q^{4} +(-3.45469 - 4.90562i) q^{6} +(1.91561 - 1.91561i) q^{7} +(7.92245 - 1.11122i) q^{8} +(8.96594 - 0.782204i) q^{9} +6.87236 q^{11} +(-4.53101 + 11.1117i) q^{12} +(-12.2746 + 12.2746i) q^{13} +(-5.29303 - 1.15780i) q^{14} +(-10.4221 - 12.1400i) q^{16} +(9.47120 - 9.47120i) q^{17} +(-10.9944 - 14.2521i) q^{18} +33.2524 q^{19} +(5.49143 - 5.99137i) q^{21} +(-7.41767 - 11.5713i) q^{22} +(7.20994 - 7.20994i) q^{23} +(23.5998 - 4.36430i) q^{24} +(33.9159 + 7.41877i) q^{26} +(26.7703 - 3.51436i) q^{27} +(3.76357 + 10.1618i) q^{28} -2.29155 q^{29} -12.1558i q^{31} +(-9.19168 + 30.6515i) q^{32} +(20.5976 - 0.896780i) q^{33} +(-26.1698 - 5.72440i) q^{34} +(-12.1302 + 33.8948i) q^{36} +(20.7290 + 20.7290i) q^{37} +(-35.8909 - 55.9886i) q^{38} +(-35.1872 + 38.3906i) q^{39} -50.9173i q^{41} +(-16.0151 - 2.77942i) q^{42} +(-15.1975 - 15.1975i) q^{43} +(-11.4770 + 24.9790i) q^{44} +(-19.9218 - 4.35769i) q^{46} +(-26.7793 - 26.7793i) q^{47} +(-32.8208 - 35.0256i) q^{48} +41.6608i q^{49} +(27.1508 - 29.6226i) q^{51} +(-24.1157 - 65.1132i) q^{52} +(15.5183 + 15.5183i) q^{53} +(-34.8118 - 41.2812i) q^{54} +(13.0477 - 17.3050i) q^{56} +(99.6627 - 4.33913i) q^{57} +(2.47338 + 3.85839i) q^{58} -63.0946i q^{59} +28.4752 q^{61} +(-20.4672 + 13.1203i) q^{62} +(15.6769 - 18.6737i) q^{63} +(61.5304 - 17.6071i) q^{64} +(-23.7419 - 33.7132i) q^{66} +(-32.4542 + 32.4542i) q^{67} +(18.6079 + 50.2420i) q^{68} +(20.6685 - 22.5502i) q^{69} -88.8377 q^{71} +(70.1630 - 16.1601i) q^{72} +(-71.1740 + 71.1740i) q^{73} +(12.5286 - 57.2763i) q^{74} +(-55.5320 + 120.862i) q^{76} +(13.1648 - 13.1648i) q^{77} +(102.619 + 17.8095i) q^{78} -75.1410 q^{79} +(79.7763 - 14.0264i) q^{81} +(-85.7318 + 54.9574i) q^{82} +(-58.6543 + 58.6543i) q^{83} +(12.6061 + 29.9654i) q^{84} +(-9.18537 + 41.9921i) q^{86} +(-6.86815 + 0.299026i) q^{87} +(54.4459 - 7.63668i) q^{88} +41.1063 q^{89} +47.0267i q^{91} +(14.1653 + 38.2467i) q^{92} +(-1.58621 - 36.4327i) q^{93} +(-16.1854 + 73.9937i) q^{94} +(-23.5492 + 93.0668i) q^{96} +(-30.3484 - 30.3484i) q^{97} +(70.1464 - 44.9665i) q^{98} +(61.6172 - 5.37559i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{6} + 20 q^{12} + 8 q^{13} - 36 q^{16} + 24 q^{18} - 24 q^{21} + 76 q^{22} + 84 q^{28} + 40 q^{33} + 172 q^{36} + 40 q^{37} - 236 q^{42} + 240 q^{46} - 196 q^{48} - 304 q^{52} + 72 q^{57} - 180 q^{58}+ \cdots - 72 q^{97}+O(q^{100}) \) 40 * q - 4 * q^6 + 20 * q^12 + 8 * q^13 - 36 * q^16 + 24 * q^18 - 24 * q^21 + 76 * q^22 + 84 * q^28 + 40 * q^33 + 172 * q^36 + 40 * q^37 - 236 * q^42 + 240 * q^46 - 196 * q^48 - 304 * q^52 + 72 * q^57 - 180 * q^58 + 48 * q^61 - 552 * q^66 + 600 * q^72 - 104 * q^73 - 736 * q^76 + 408 * q^78 + 72 * q^81 + 720 * q^82 + 580 * q^88 - 368 * q^93 + 884 * q^96 - 72 * q^97

Introduction

L-functions

Modular forms

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Database

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