LMFDB - Embedded newform 648.2.v.b.611.31

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [648,2,Mod(35,648)] 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("648.35"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(648, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 9, 13])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.v (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [192] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			611.31
Character	$\chi$	$=$	648.611
Dual form			648.2.v.b.35.31

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.40972 + 0.112665i) q^{2} +(1.97461 + 0.317652i) q^{4} +(-2.47648 + 0.901367i) q^{5} +(2.55949 - 0.451307i) q^{7} +(2.74786 + 0.670270i) q^{8} +(-3.59270 + 0.991660i) q^{10} +(-0.556608 + 1.52927i) q^{11} +(1.88389 - 2.24514i) q^{13} +(3.65901 - 0.347851i) q^{14} +(3.79819 + 1.25448i) q^{16} +(3.28845 + 1.89859i) q^{17} +(4.30904 + 7.46347i) q^{19} +(-5.17642 + 0.993190i) q^{20} +(-0.956956 + 2.09313i) q^{22} +(1.07009 - 6.06879i) q^{23} +(1.49029 - 1.25050i) q^{25} +(2.90871 - 2.95276i) q^{26} +(5.19736 - 0.0781292i) q^{28} +(-3.88174 + 3.25716i) q^{29} +(-3.57300 - 0.630016i) q^{31} +(5.21305 + 2.19639i) q^{32} +(4.42189 + 3.04697i) q^{34} +(-5.93174 + 3.42469i) q^{35} +(-6.40179 - 3.69607i) q^{37} +(5.23366 + 11.0069i) q^{38} +(-7.40919 + 0.816916i) q^{40} +(4.43232 - 5.28224i) q^{41} +(-3.77811 - 1.37512i) q^{43} +(-1.58486 + 2.84290i) q^{44} +(2.19227 - 8.43472i) q^{46} +(-0.253807 - 1.43941i) q^{47} +(-0.230541 + 0.0839100i) q^{49} +(2.24178 - 1.59495i) q^{50} +(4.43313 - 3.83485i) q^{52} -0.180986 q^{53} -4.28892i q^{55} +(7.33562 + 0.475421i) q^{56} +(-5.83912 + 4.15435i) q^{58} +(-0.253090 - 0.695359i) q^{59} +(11.1190 - 1.96057i) q^{61} +(-4.96594 - 1.29070i) q^{62} +(7.10148 + 3.68362i) q^{64} +(-2.64174 + 7.25812i) q^{65} +(-10.5159 - 8.82387i) q^{67} +(5.89033 + 4.79357i) q^{68} +(-8.74793 + 4.15955i) q^{70} +(-2.57253 + 4.45576i) q^{71} +(-2.62831 - 4.55236i) q^{73} +(-8.60830 - 5.93168i) q^{74} +(6.13789 + 16.1062i) q^{76} +(-0.734463 + 4.16534i) q^{77} +(-6.72831 - 8.01849i) q^{79} +(-10.5369 + 0.316864i) q^{80} +(6.84345 - 6.94710i) q^{82} +(-7.39656 - 8.81488i) q^{83} +(-9.85513 - 1.73773i) q^{85} +(-5.17114 - 2.36419i) q^{86} +(-2.55450 + 3.82914i) q^{88} +(0.211259 - 0.121971i) q^{89} +(3.80856 - 6.59662i) q^{91} +(4.04078 - 11.6436i) q^{92} +(-0.195625 - 2.05776i) q^{94} +(-17.3986 - 14.5992i) q^{95} +(1.95441 + 0.711348i) q^{97} +(-0.334451 + 0.0923156i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8} - 3 q^{10} + 30 q^{11} - 9 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} + 27 q^{20} - 18 q^{22} - 12 q^{25} - 12 q^{28} + 36 q^{32} + 12 q^{34} + 18 q^{35} + 102 q^{38} + 9 q^{40}+ \cdots - 162 q^{98}+O(q^{100}) $ 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8 - 3 * q^10 + 30 * q^11 - 9 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 + 27 * q^20 - 18 * q^22 - 12 * q^25 - 12 * q^28 + 36 * q^32 + 12 * q^34 + 18 * q^35 + 102 * q^38 + 9 * q^40 - 18 * q^41 - 42 * q^43 + 81 * q^44 - 3 * q^46 - 12 * q^49 - 57 * q^50 + 21 * q^52 + 69 * q^56 - 33 * q^58 + 84 * q^59 - 90 * q^62 - 51 * q^64 + 12 * q^65 + 30 * q^67 - 63 * q^68 - 33 * q^70 - 6 * q^73 - 51 * q^74 + 30 * q^76 - 12 * q^82 + 72 * q^83 - 42 * q^86 - 78 * q^88 - 144 * q^89 - 6 * q^91 + 3 * q^92 - 33 * q^94 - 42 * q^97 - 162 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{18}\right)$

Coefficient data

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

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

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

$2$	1.40972	+	0.112665i	0.996822	+	0.0796663i
$2$	1.40972	+	0.112665i	0.996822	+	0.0796663i
$3$		0			0
$3$		0			0
$4$	1.97461	+	0.317652i	0.987307	+	0.158826i
$5$	−2.47648	+	0.901367i	−1.10752	+	0.403103i	−0.830082	−	0.557641i	$-0.811707\pi$
$5$	−2.47648	+	0.901367i	−1.10752	+	0.403103i	−0.277435	+	0.960744i	$0.589484\pi$
$6$		0			0
$7$	2.55949	−	0.451307i	0.967396	−	0.170578i	0.332438	−	0.943125i	$-0.392129\pi$
$7$	2.55949	−	0.451307i	0.967396	−	0.170578i	0.634958	+	0.772547i	$0.281018\pi$
$8$	2.74786	+	0.670270i	0.971515	+	0.236976i
$9$		0			0
$10$	−3.59270	+	0.991660i	−1.13611	+	0.313590i
$11$	−0.556608	+	1.52927i	−0.167824	+	0.461091i	−0.994884	−	0.101021i	$-0.967789\pi$
$11$	−0.556608	+	1.52927i	−0.167824	+	0.461091i	0.827061	+	0.562113i	$0.190011\pi$
$12$		0			0
$13$	1.88389	−	2.24514i	0.522498	−	0.622689i	−0.438672	−	0.898647i	$-0.644551\pi$
$13$	1.88389	−	2.24514i	0.522498	−	0.622689i	0.961169	+	0.275959i	$0.0889953\pi$
$14$	3.65901	−	0.347851i	0.977911	−	0.0929670i
$15$		0			0
$16$	3.79819	+	1.25448i	0.949549	+	0.313620i
$17$	3.28845	+	1.89859i	0.797567	+	0.460476i	0.842620	−	0.538509i	$-0.181012\pi$
$17$	3.28845	+	1.89859i	0.797567	+	0.460476i	−0.0450525	+	0.998985i	$0.514346\pi$
$18$		0			0
$19$	4.30904	+	7.46347i	0.988561	+	1.71224i	0.624895	+	0.780708i	$0.285142\pi$
$19$	4.30904	+	7.46347i	0.988561	+	1.71224i	0.363666	+	0.931530i	$0.381525\pi$
$20$	−5.17642	+	0.993190i	−1.15748	+	0.222084i
$21$		0			0
$22$	−0.956956	+	2.09313i	−0.204024	+	0.446256i
$23$	1.07009	−	6.06879i	0.223129	−	1.26543i	−0.643100	−	0.765783i	$-0.722352\pi$
$23$	1.07009	−	6.06879i	0.223129	−	1.26543i	0.866229	−	0.499647i	$-0.166537\pi$
$24$		0			0
$25$	1.49029	−	1.25050i	0.298059	−	0.250101i
$26$	2.90871	−	2.95276i	0.570444	−	0.579084i
$27$		0			0
$28$	5.19736	−	0.0781292i	0.982209	−	0.0147650i
$29$	−3.88174	+	3.25716i	−0.720820	+	0.604840i	−0.927612	−	0.373545i	$-0.878142\pi$
$29$	−3.88174	+	3.25716i	−0.720820	+	0.604840i	0.206792	+	0.978385i	$0.433698\pi$
$30$		0			0
$31$	−3.57300	−	0.630016i	−0.641729	−	0.113154i	−0.156692	−	0.987648i	$-0.550083\pi$
$31$	−3.57300	−	0.630016i	−0.641729	−	0.113154i	−0.485037	+	0.874493i	$0.661194\pi$
$32$	5.21305	+	2.19639i	0.921546	+	0.388270i
$33$		0			0
$34$	4.42189	+	3.04697i	0.758348	+	0.522551i
$35$	−5.93174	+	3.42469i	−1.00265	+	0.578879i
$36$		0			0
$37$	−6.40179	−	3.69607i	−1.05245	−	0.607631i	−0.129114	−	0.991630i	$-0.541213\pi$
$37$	−6.40179	−	3.69607i	−1.05245	−	0.607631i	−0.923333	+	0.383999i	$0.874547\pi$
$38$	5.23366	+	11.0069i	0.849011	+	1.78555i
$39$		0			0
$40$	−7.40919	+	0.816916i	−1.17150	+	0.129166i
$41$	4.43232	−	5.28224i	0.692212	−	0.824947i	−0.299409	−	0.954125i	$-0.596789\pi$
$41$	4.43232	−	5.28224i	0.692212	−	0.824947i	0.991621	+	0.129178i	$0.0412339\pi$
$42$		0			0
$43$	−3.77811	−	1.37512i	−0.576156	−	0.209704i	0.0374734	−	0.999298i	$-0.488069\pi$
$43$	−3.77811	−	1.37512i	−0.576156	−	0.209704i	−0.613630	+	0.789594i	$0.710291\pi$
$44$	−1.58486	+	2.84290i	−0.238927	+	0.428584i
$45$		0			0
$46$	2.19227	−	8.43472i	0.323232	−	1.24363i
$47$	−0.253807	−	1.43941i	−0.0370215	−	0.209960i	0.960686	−	0.277639i	$-0.0895517\pi$
$47$	−0.253807	−	1.43941i	−0.0370215	−	0.209960i	−0.997707	+	0.0676790i	$0.978441\pi$
$48$		0			0
$49$	−0.230541	+	0.0839100i	−0.0329344	+	0.0119871i
$50$	2.24178	−	1.59495i	0.317036	−	0.225561i
$51$		0			0
$52$	4.43313	−	3.83485i	0.614765	−	0.531798i
$53$	−0.180986			−0.0248604			−0.0124302	−	0.999923i	$-0.503957\pi$
$53$	−0.180986			−0.0248604			−0.0124302	+	0.999923i	$0.503957\pi$
$54$		0			0
$55$		−	4.28892i		−	0.578317i
$56$	7.33562	+	0.475421i	0.980263	+	0.0635308i
$57$		0			0
$58$	−5.83912	+	4.15435i	−0.766714	+	0.545492i
$59$	−0.253090	−	0.695359i	−0.0329495	−	0.0905280i	0.922127	−	0.386887i	$-0.126450\pi$
$59$	−0.253090	−	0.695359i	−0.0329495	−	0.0905280i	−0.955077	+	0.296359i	$0.904227\pi$
$60$		0			0
$61$	11.1190	−	1.96057i	1.42364	−	0.251026i	0.591817	−	0.806072i	$-0.298411\pi$
$61$	11.1190	−	1.96057i	1.42364	−	0.251026i	0.831819	+	0.555047i	$0.187300\pi$
$62$	−4.96594	−	1.29070i	−0.630675	−	0.163919i
$63$		0			0
$64$	7.10148	+	3.68362i	0.887684	+	0.460452i
$65$	−2.64174	+	7.25812i	−0.327668	+	0.900259i
$66$		0			0
$67$	−10.5159	−	8.82387i	−1.28472	−	1.07801i	−0.992575	−	0.121633i	$-0.961187\pi$
$67$	−10.5159	−	8.82387i	−1.28472	−	1.07801i	−0.292144	−	0.956374i	$-0.594369\pi$
$68$	5.89033	+	4.79357i	0.714308	+	0.581305i
$69$		0			0
$70$	−8.74793	+	4.15955i	−1.04558	+	0.497162i
$71$	−2.57253	+	4.45576i	−0.305303	+	0.528801i	−0.977329	−	0.211727i	$-0.932091\pi$
$71$	−2.57253	+	4.45576i	−0.305303	+	0.528801i	0.672025	+	0.740528i	$0.265425\pi$
$72$		0			0
$73$	−2.62831	−	4.55236i	−0.307620	−	0.532814i	0.670221	−	0.742161i	$-0.266199\pi$
$73$	−2.62831	−	4.55236i	−0.307620	−	0.532814i	−0.977841	+	0.209348i	$0.932866\pi$
$74$	−8.60830	−	5.93168i	−1.00069	−	0.689544i
$75$		0			0
$76$	6.13789	+	16.1062i	0.704065	+	1.84751i
$77$	−0.734463	+	4.16534i	−0.0836998	+	0.474685i
$78$		0			0
$79$	−6.72831	−	8.01849i	−0.756994	−	0.902151i	0.240660	−	0.970610i	$-0.422636\pi$
$79$	−6.72831	−	8.01849i	−0.756994	−	0.902151i	−0.997654	+	0.0684588i	$0.978192\pi$
$80$	−10.5369	+	0.316864i	−1.17806	+	0.0354264i
$81$		0			0
$82$	6.84345	−	6.94710i	0.755733	−	0.767179i
$83$	−7.39656	−	8.81488i	−0.811878	−	0.967559i	0.188015	−	0.982166i	$-0.439795\pi$
$83$	−7.39656	−	8.81488i	−0.811878	−	0.967559i	−0.999893	+	0.0146072i	$0.995350\pi$
$84$		0			0
$85$	−9.85513	−	1.73773i	−1.06894	−	0.188483i
$86$	−5.17114	−	2.36419i	−0.557619	−	0.254938i
$87$		0			0
$88$	−2.55450	+	3.82914i	−0.272311	+	0.408187i
$89$	0.211259	−	0.121971i	0.0223934	−	0.0129289i	−0.488761	−	0.872417i	$-0.662551\pi$
$89$	0.211259	−	0.121971i	0.0223934	−	0.0129289i	0.511155	+	0.859489i	$0.329218\pi$
$90$		0			0
$91$	3.80856	−	6.59662i	0.399245	−	0.691513i
$92$	4.04078	−	11.6436i	0.421280	−	1.21393i
$93$		0			0
$94$	−0.195625	−	2.05776i	−0.0201772	−	0.212242i
$95$	−17.3986	−	14.5992i	−1.78506	−	1.49784i
$96$		0			0
$97$	1.95441	+	0.711348i	0.198441	+	0.0722264i	0.439329	−	0.898326i	$-0.355216\pi$
$97$	1.95441	+	0.711348i	0.198441	+	0.0722264i	−0.240888	+	0.970553i	$0.577439\pi$
$98$	−0.334451	+	0.0923156i	−0.0337847	+	0.00932528i
$99$		0			0
$100$	3.33998	−	1.99587i	0.333998	−	0.199587i
$101$	3.09813	+	17.5704i	0.308276	+	1.74832i	0.607670	+	0.794190i	$0.292104\pi$
$101$	3.09813	+	17.5704i	0.308276	+	1.74832i	−0.299394	+	0.954130i	$0.596784\pi$
$102$		0			0
$103$	−4.29301	−	11.7949i	−0.423003	−	1.16219i	−0.949980	−	0.312311i	$-0.898897\pi$
$103$	−4.29301	−	11.7949i	−0.423003	−	1.16219i	0.526977	−	0.849879i	$-0.323325\pi$
$104$	6.68152	−	4.90660i	0.655177	−	0.481132i
$105$		0			0
$106$	−0.255140	−	0.0203908i	−0.0247814	−	0.00198053i
$107$		−	10.9395i		−	1.05757i	−0.848757	−	0.528783i	$-0.822649\pi$
$107$		−	10.9395i		−	1.05757i	0.848757	−	0.528783i	$-0.177351\pi$
$108$		0			0
$109$			6.35577i			0.608772i	0.952549	+	0.304386i	$0.0984513\pi$
$109$			6.35577i			0.608772i	−0.952549	+	0.304386i	$0.901549\pi$
$110$	0.483211	−	6.04616i	0.0460724	−	0.576479i
$111$		0			0
$112$	10.2876	+	1.49668i	0.972086	+	0.141423i
$113$	1.20684	+	3.31577i	0.113530	+	0.311921i	0.983425	−	0.181316i	$-0.0580356\pi$
$113$	1.20684	+	3.31577i	0.113530	+	0.311921i	−0.869895	+	0.493237i	$0.835813\pi$
$114$		0			0
$115$	2.82014	+	15.9938i	0.262979	+	1.49143i
$116$	−8.69957	+	5.19859i	−0.807735	+	0.482677i
$117$		0			0
$118$	−0.278443	−	1.00877i	−0.0256327	−	0.0928652i
$119$	9.27361	+	3.37532i	0.850110	+	0.309415i
$120$		0			0
$121$	6.39764	+	5.36826i	0.581604	+	0.488024i
$122$	15.8955	−	1.51114i	1.43911	−	0.136812i
$123$		0			0
$124$	−6.85516	−	2.37901i	−0.615612	−	0.213641i
$125$	4.02503	−	6.97155i	0.360009	−	0.623554i
$126$		0			0
$127$	−15.7942	+	9.11876i	−1.40150	+	0.809159i	−0.994547	−	0.104288i	$-0.966744\pi$
$127$	−15.7942	+	9.11876i	−1.40150	+	0.809159i	−0.406958	+	0.913447i	$0.633410\pi$
$128$	9.59607	+	5.99295i	0.848180	+	0.529707i
$129$		0			0
$130$	−4.54185	+	9.93428i	−0.398347	+	0.871294i
$131$	−4.10519	−	0.723856i	−0.358672	−	0.0632436i	−0.00859153	−	0.999963i	$-0.502735\pi$
$131$	−4.10519	−	0.723856i	−0.358672	−	0.0632436i	−0.350081	+	0.936719i	$0.613846\pi$
$132$		0			0
$133$	14.3973	+	17.1580i	1.24840	+	1.48779i
$134$	−13.8303	−	13.6239i	−1.19475	−	1.17693i
$135$		0			0
$136$	7.76365	+	7.42121i	0.665727	+	0.636364i
$137$	10.2458	+	12.2105i	0.875360	+	1.04321i	0.998706	+	0.0508494i	$0.0161928\pi$
$137$	10.2458	+	12.2105i	0.875360	+	1.04321i	−0.123347	+	0.992364i	$0.539363\pi$
$138$		0			0
$139$	−0.411616	+	2.33439i	−0.0349128	+	0.198000i	−0.997275	−	0.0737683i	$-0.976497\pi$
$139$	−0.411616	+	2.33439i	−0.0349128	+	0.198000i	0.962363	+	0.271769i	$0.0876086\pi$
$140$	−12.8008	+	4.87821i	−1.08186	+	0.412284i
$141$		0			0
$142$	−4.12856	+	5.99153i	−0.346461	+	0.502798i
$143$	2.38482	+	4.13064i	0.199429	+	0.345421i
$144$		0			0
$145$	6.67716	−	11.5652i	0.554508	−	0.960436i
$146$	−3.19228	−	6.71367i	−0.264195	−	0.555627i
$147$		0			0
$148$	−11.4670	−	9.33186i	−0.942580	−	0.767074i
$149$	−12.2426	−	10.2728i	−1.00295	−	0.841578i	−0.0155632	−	0.999879i	$-0.504954\pi$
$149$	−12.2426	−	10.2728i	−1.00295	−	0.841578i	−0.987391	+	0.158300i	$0.949399\pi$
$150$		0			0
$151$	0.806403	−	2.21557i	0.0656242	−	0.180301i	−0.902546	−	0.430593i	$-0.858304\pi$
$151$	0.806403	−	2.21557i	0.0656242	−	0.180301i	0.968170	+	0.250292i	$0.0805267\pi$
$152$	6.83809	+	23.3968i	0.554642	+	1.89773i
$153$		0			0
$154$	−1.50467	+	5.78922i	−0.121250	+	0.466508i
$155$	9.41635	−	1.66036i	0.756339	−	0.133363i
$156$		0			0
$157$	0.284046	+	0.780410i	0.0226693	+	0.0622835i	0.950511	−	0.310691i	$-0.100560\pi$
$157$	0.284046	+	0.780410i	0.0226693	+	0.0622835i	−0.927842	+	0.372974i	$0.878338\pi$
$158$	−8.58162	−	12.0619i	−0.682717	−	0.959590i
$159$		0			0
$160$	−14.8898	−	0.740454i	−1.17714	−	0.0585381i
$161$		−	16.0159i		−	1.26223i
$162$		0			0
$163$	−11.2657			−0.882401			−0.441200	−	0.897409i	$-0.645447\pi$
$163$	−11.2657			−0.882401			−0.441200	+	0.897409i	$0.645447\pi$
$164$	10.4300	−	9.02244i	0.814449	−	0.704534i
$165$		0			0
$166$	−9.43394	−	13.2598i	−0.732216	−	1.02916i
$167$	16.4192	−	5.97611i	1.27056	−	0.462445i	0.383260	−	0.923641i	$-0.374801\pi$
$167$	16.4192	−	5.97611i	1.27056	−	0.462445i	0.887299	+	0.461195i	$0.152579\pi$
$168$		0			0
$169$	0.765842	+	4.34331i	0.0589110	+	0.334101i
$170$	−13.6972	−	3.56003i	−1.05053	−	0.273042i
$171$		0			0
$172$	−7.02350	−	3.91545i	−0.535537	−	0.298551i
$173$	−17.4791	−	6.36186i	−1.32891	−	0.483683i	−0.422606	−	0.906313i	$-0.638885\pi$
$173$	−17.4791	−	6.36186i	−1.32891	−	0.483683i	−0.906302	+	0.422630i	$0.861107\pi$
$174$		0			0
$175$	3.25003	−	3.87323i	0.245679	−	0.292789i
$176$	−4.03254	+	5.11020i	−0.303964	+	0.385196i
$177$		0			0
$178$	0.311558	−	0.148143i	0.0233523	−	0.0111038i
$179$	6.13650	+	3.54291i	0.458663	+	0.264809i	0.711482	−	0.702704i	$-0.248024\pi$
$179$	6.13650	+	3.54291i	0.458663	+	0.264809i	−0.252819	+	0.967514i	$0.581358\pi$
$180$		0			0
$181$	−0.129860	+	0.0749748i	−0.00965242	+	0.00557283i	−0.504818	−	0.863226i	$-0.668441\pi$
$181$	−0.129860	+	0.0749748i	−0.00965242	+	0.00557283i	0.495166	+	0.868798i	$0.335107\pi$
$182$	6.11220	−	8.87028i	0.453067	−	0.657509i
$183$		0			0
$184$	7.00819	−	15.9589i	0.516651	−	1.17651i
$185$	19.1854	+	3.38291i	1.41054	+	0.248717i
$186$		0			0
$187$	−4.73383	+	3.97216i	−0.346172	+	0.290473i
$188$	−0.0439385	−	2.92290i	−0.00320454	−	0.213174i
$189$		0			0
$190$	−22.8823	−	22.5409i	−1.66006	−	1.63529i
$191$	−8.37441	+	7.02696i	−0.605951	+	0.508453i	−0.893352	−	0.449357i	$-0.851653\pi$
$191$	−8.37441	+	7.02696i	−0.605951	+	0.508453i	0.287401	+	0.957810i	$0.407209\pi$
$192$		0			0
$193$	0.508999	−	2.88668i	0.0366385	−	0.207788i	−0.960993	−	0.276573i	$-0.910801\pi$
$193$	0.508999	−	2.88668i	0.0366385	−	0.207788i	0.997631	+	0.0687854i	$0.0219124\pi$
$194$	2.67503	+	1.22299i	0.192056	+	0.0878059i
$195$		0			0
$196$	−0.481883	+	0.0924580i	−0.0344202	+	0.00660414i
$197$	1.40635	+	2.43587i	0.100198	+	0.173548i	0.911766	−	0.410710i	$-0.134719\pi$
$197$	1.40635	+	2.43587i	0.100198	+	0.173548i	−0.811568	+	0.584258i	$0.801386\pi$
$198$		0			0
$199$	−0.874354	−	0.504808i	−0.0619813	−	0.0357849i	0.468689	−	0.883363i	$-0.344726\pi$
$199$	−0.874354	−	0.504808i	−0.0619813	−	0.0357849i	−0.530670	+	0.847578i	$0.678060\pi$
$200$	4.93329	−	2.43731i	0.348836	−	0.172344i
$201$		0			0
$202$	2.38793	+	25.1184i	0.168014	+	1.76732i
$203$	−8.46528	+	10.0885i	−0.594146	+	0.708076i
$204$		0			0
$205$	−6.21535	+	17.0765i	−0.434099	+	1.19268i
$206$	−4.72306	−	17.1112i	−0.329071	−	1.19220i
$207$		0			0
$208$	9.97187	−	6.16416i	0.691425	−	0.427407i
$209$	−13.8121	+	2.43544i	−0.955402	+	0.168463i
$210$		0			0
$211$	−3.98399	+	1.45005i	−0.274269	+	0.0998257i	−0.475493	−	0.879720i	$-0.657730\pi$
$211$	−3.98399	+	1.45005i	−0.274269	+	0.0998257i	0.201224	+	0.979545i	$0.435508\pi$
$212$	−0.357378	−	0.0574907i	−0.0245448	−	0.00394848i
$213$		0			0
$214$	1.23250	−	15.4217i	0.0842523	−	1.05420i
$215$	10.5959			0.722636
$216$		0			0
$217$	−9.42938			−0.640108
$218$	−0.716074	+	8.95985i	−0.0484986	+	0.606837i
$219$		0			0
$220$	1.36238	−	8.46895i	0.0918519	−	0.570976i
$221$	10.4577	−	3.80629i	0.703460	−	0.256039i
$222$		0			0
$223$	15.7442	−	2.77613i	1.05431	−	0.185903i	0.380480	−	0.924789i	$-0.375759\pi$
$223$	15.7442	−	2.77613i	1.05431	−	0.185903i	0.673831	+	0.738886i	$0.264648\pi$
$224$	14.3340	+	3.26895i	0.957730	+	0.218416i
$225$		0			0
$226$	1.32774	+	4.81027i	0.0883197	+	0.319975i
$227$	−0.588042	+	1.61563i	−0.0390297	+	0.107233i	−0.957677	−	0.287846i	$-0.907061\pi$
$227$	−0.588042	+	1.61563i	−0.0390297	+	0.107233i	0.918647	+	0.395080i	$0.129283\pi$
$228$		0			0
$229$	−5.91992	+	7.05508i	−0.391199	+	0.466213i	−0.925316	−	0.379198i	$-0.876200\pi$
$229$	−5.91992	+	7.05508i	−0.391199	+	0.466213i	0.534116	+	0.845411i	$0.320644\pi$
$230$	2.17366	+	22.8645i	0.143327	+	1.50764i
$231$		0			0
$232$	−12.8496	+	6.34842i	−0.843621	+	0.416794i
$233$	−16.7671	−	9.68050i	−1.09845	−	0.634191i	−0.162637	−	0.986686i	$-0.552000\pi$
$233$	−16.7671	−	9.68050i	−1.09845	−	0.634191i	−0.935814	+	0.352495i	$0.885333\pi$
$234$		0			0
$235$	1.92599	+	3.33590i	0.125637	+	0.217610i
$236$	−0.278872	−	1.45346i	−0.0181530	−	0.0946121i
$237$		0			0
$238$	12.6929	+	5.80306i	0.822759	+	0.376157i
$239$	−0.803749	+	4.55829i	−0.0519902	+	0.294851i	−0.999706	−	0.0242659i	$-0.992275\pi$
$239$	−0.803749	+	4.55829i	−0.0519902	+	0.294851i	0.947715	+	0.319117i	$0.103386\pi$
$240$		0			0
$241$	21.1035	−	17.7079i	1.35939	−	1.14067i	0.383226	−	0.923655i	$-0.374813\pi$
$241$	21.1035	−	17.7079i	1.35939	−	1.14067i	0.976169	−	0.217012i	$-0.0696312\pi$
$242$	8.41406	+	8.28853i	0.540876	+	0.532807i
$243$		0			0
$244$	22.5784	−	0.339410i	1.44544	−	0.0217285i
$245$	0.495297	−	0.415604i	0.0316434	−	0.0265519i
$246$		0			0
$247$	24.8743	+	4.38601i	1.58271	+	0.279075i
$248$	−9.39582	−	4.12607i	−0.596635	−	0.262006i
$249$		0			0
$250$	6.45960	−	9.37444i	0.408541	−	0.592892i
$251$	12.0234	−	6.94172i	0.758911	−	0.438158i	−0.0699933	−	0.997547i	$-0.522298\pi$
$251$	12.0234	−	6.94172i	0.758911	−	0.438158i	0.828905	+	0.559390i	$0.188964\pi$
$252$		0			0
$253$	8.68518	+	5.01439i	0.546033	+	0.315252i
$254$	−23.2927	+	11.0754i	−1.46151	+	0.694935i
$255$		0			0
$256$	12.8526	+	9.52952i	0.803285	+	0.595595i
$257$	1.09064	−	1.29978i	0.0680325	−	0.0810779i	−0.730955	−	0.682426i	$-0.760925\pi$
$257$	1.09064	−	1.29978i	0.0680325	−	0.0810779i	0.798987	+	0.601348i	$0.205369\pi$
$258$		0			0
$259$	−18.0534	−	6.57089i	−1.12178	−	0.408295i
$260$	−7.52198	+	13.4928i	−0.466493	+	0.836790i
$261$		0			0
$262$	−5.70561	−	1.48295i	−0.352494	−	0.0916167i
$263$	0.720517	+	4.08625i	0.0444290	+	0.251969i	0.998931	−	0.0462368i	$-0.0147229\pi$
$263$	0.720517	+	4.08625i	0.0444290	+	0.251969i	−0.954502	+	0.298206i	$0.903612\pi$
$264$		0			0
$265$	0.448210	−	0.163135i	0.0275333	−	0.0100213i
$266$	18.3630	+	25.8100i	1.12591	+	1.58251i
$267$		0			0
$268$	−17.9619	−	20.7641i	−1.09720	−	1.26837i
$269$	31.4461			1.91730			0.958650	−	0.284588i	$-0.0918567\pi$
$269$	31.4461			1.91730			0.958650	+	0.284588i	$0.0918567\pi$
$270$		0			0
$271$			28.1714i			1.71129i	0.517564	+	0.855644i	$0.326839\pi$
$271$			28.1714i			1.71129i	−0.517564	+	0.855644i	$0.673161\pi$
$272$	10.1084	+	11.3365i	0.612914	+	0.687377i
$273$		0			0
$274$	13.0680	+	18.3677i	0.789469	+	1.10963i
$275$	1.08285	+	2.97510i	0.0652981	+	0.179405i
$276$		0			0
$277$	24.3185	−	4.28801i	1.46116	−	0.257641i	0.614136	−	0.789201i	$-0.289505\pi$
$277$	24.3185	−	4.28801i	1.46116	−	0.257641i	0.847021	+	0.531559i	$0.178394\pi$
$278$	−0.843267	+	3.24446i	−0.0505758	+	0.194590i
$279$		0			0
$280$	−18.5951	+	5.43471i	−1.11127	+	0.324786i
$281$	6.58678	−	18.0970i	0.392935	−	1.07958i	−0.572720	−	0.819751i	$-0.694112\pi$
$281$	6.58678	−	18.0970i	0.392935	−	1.07958i	0.965655	−	0.259828i	$-0.0836659\pi$
$282$		0			0
$283$	6.85978	+	5.75604i	0.407772	+	0.342161i	0.823488	−	0.567333i	$-0.192025\pi$
$283$	6.85978	+	5.75604i	0.407772	+	0.342161i	−0.415717	+	0.909494i	$0.636469\pi$
$284$	−6.49514	+	7.98123i	−0.385416	+	0.473599i
$285$		0			0
$286$	2.89655	+	6.09172i	0.171277	+	0.360211i
$287$	8.96057	−	15.5202i	0.528926	−	0.916126i
$288$		0			0
$289$	−1.29071	−	2.23558i	−0.0759243	−	0.131505i
$290$	10.7159	−	15.5514i	0.629260	−	0.913208i
$291$		0			0
$292$	−3.74382	−	9.82404i	−0.219091	−	0.574909i
$293$	−3.69497	+	20.9552i	−0.215863	+	1.22422i	0.663540	+	0.748140i	$0.269053\pi$
$293$	−3.69497	+	20.9552i	−0.215863	+	1.22422i	−0.879403	+	0.476078i	$0.842058\pi$
$294$		0			0
$295$	1.25355	+	1.49392i	0.0729843	+	0.0869793i
$296$	−15.1138	−	14.4472i	−0.878475	−	0.839728i
$297$		0			0
$298$	−16.1013	−	15.8610i	−0.932721	−	0.918805i
$299$	−11.6093	−	13.8354i	−0.671384	−	0.800125i
$300$		0			0
$301$	−10.2906	−	1.81452i	−0.593142	−	0.104587i
$302$	1.38642	−	3.03248i	0.0797795	−	0.174500i
$303$		0			0
$304$	7.00378	+	33.7533i	0.401694	+	1.93589i
$305$	−25.7687	+	14.8776i	−1.47551	+	0.851888i
$306$		0			0
$307$	4.48896	−	7.77511i	0.256199	−	0.443749i	−0.709022	−	0.705187i	$-0.750863\pi$
$307$	4.48896	−	7.77511i	0.256199	−	0.443749i	0.965220	+	0.261438i	$0.0841966\pi$
$308$	−2.77341	+	7.99164i	−0.158030	+	0.455366i
$309$		0			0
$310$	13.4615	−	1.27974i	0.764560	−	0.0726844i
$311$	−13.0417	−	10.9433i	−0.739525	−	0.620535i	0.193185	−	0.981162i	$-0.438118\pi$
$311$	−13.0417	−	10.9433i	−0.739525	−	0.620535i	−0.932710	+	0.360627i	$0.882563\pi$
$312$		0			0
$313$	−9.04413	−	3.29179i	−0.511204	−	0.186063i	0.0735224	−	0.997294i	$-0.476576\pi$
$313$	−9.04413	−	3.29179i	−0.511204	−	0.186063i	−0.584727	+	0.811230i	$0.698798\pi$
$314$	0.312500	+	1.13216i	0.0176354	+	0.0638915i
$315$		0			0
$316$	−10.7387	−	17.9707i	−0.604100	−	1.01093i
$317$	−1.05306	−	5.97220i	−0.0591457	−	0.335432i	0.940849	−	0.338827i	$-0.110030\pi$
$317$	−1.05306	−	5.97220i	−0.0591457	−	0.335432i	−0.999994	+	0.00339548i	$0.998919\pi$
$318$		0			0
$319$	−2.82047	−	7.74917i	−0.157916	−	0.433870i
$320$	−20.9070	−	2.72139i	−1.16874	−	0.152130i
$321$		0			0
$322$	1.80444	−	22.5780i	0.100557	−	1.25822i
$323$			32.7244i			1.82083i
$324$		0			0
$325$		−	5.70173i		−	0.316275i
$326$	−15.8815	−	1.26926i	−0.879596	−	0.0702976i
$327$		0			0
$328$	15.7199	−	11.5440i	0.867988	−	0.637410i
$329$	−1.29923	−	3.56961i	−0.0716290	−	0.196799i
$330$		0			0
$331$	0.638218	+	3.61951i	0.0350796	+	0.198946i	0.997311	−	0.0732869i	$-0.0233489\pi$
$331$	0.638218	+	3.61951i	0.0350796	+	0.198946i	−0.962231	+	0.272233i	$0.912238\pi$
$332$	−11.8053	−	19.7555i	−0.647899	−	1.08422i
$333$		0			0
$334$	23.8198	−	6.57476i	1.30336	−	0.359755i
$335$	33.9960	+	12.3735i	1.85740	+	0.676037i
$336$		0			0
$337$	14.8826	+	12.4880i	0.810707	+	0.680264i	0.950776	−	0.309878i	$-0.100288\pi$
$337$	14.8826	+	12.4880i	0.810707	+	0.680264i	−0.140070	+	0.990142i	$0.544733\pi$
$338$	0.590283	+	6.20913i	0.0321072	+	0.337732i
$339$		0			0
$340$	−18.9081	−	6.56184i	−1.02543	−	0.355866i
$341$	2.95222	−	5.11340i	0.159872	−	0.276906i
$342$		0			0
$343$	−16.3076	+	9.41522i	−0.880530	+	0.508374i
$344$	−9.46002	−	6.31099i	−0.510050	−	0.340266i
$345$		0			0
$346$	−23.9238	−	10.9377i	−1.28615	−	0.588015i
$347$	−14.8923	−	2.62591i	−0.799458	−	0.140966i	−0.241029	−	0.970518i	$-0.577485\pi$
$347$	−14.8923	−	2.62591i	−0.799458	−	0.140966i	−0.558430	+	0.829552i	$0.688596\pi$
$348$		0			0
$349$	−14.4505	−	17.2214i	−0.773518	−	0.921843i	0.225104	−	0.974335i	$-0.427728\pi$
$349$	−14.4505	−	17.2214i	−0.773518	−	0.921843i	−0.998621	+	0.0524923i	$0.983284\pi$
$350$	5.01800	−	5.09400i	0.268223	−	0.272286i
$351$		0			0
$352$	−6.26049	+	6.74962i	−0.333685	+	0.359756i
$353$	13.4020	+	15.9719i	0.713316	+	0.850096i	0.993963	−	0.109715i	$-0.0349937\pi$
$353$	13.4020	+	15.9719i	0.713316	+	0.850096i	−0.280648	+	0.959811i	$0.590549\pi$
$354$		0			0
$355$	2.35457	−	13.3534i	0.124967	−	0.708725i
$356$	0.455900	−	0.173738i	0.0241626	−	0.00920808i
$357$		0			0
$358$	8.25157	+	5.68587i	0.436109	+	0.300508i
$359$	5.43854	+	9.41983i	0.287035	+	0.497159i	0.973101	−	0.230380i	$-0.0739970\pi$
$359$	5.43854	+	9.41983i	0.287035	+	0.497159i	−0.686066	+	0.727540i	$0.740664\pi$
$360$		0			0
$361$	−27.6356	+	47.8663i	−1.45451	+	2.51928i
$362$	−0.191513	+	0.0910626i	−0.0100657	+	0.00478614i
$363$		0			0
$364$	9.61586	−	11.8160i	0.504008	−	0.619325i
$365$	10.6123	+	8.90479i	0.555474	+	0.466098i
$366$		0			0
$367$	−3.96735	+	10.9002i	−0.207094	+	0.568985i	−0.999139	−	0.0414764i	$-0.986794\pi$
$367$	−3.96735	+	10.9002i	−0.207094	+	0.568985i	0.792046	+	0.610462i	$0.209016\pi$
$368$	11.6776	−	21.7080i	0.608736	−	1.13161i
$369$		0			0
$370$	26.6649	+	6.93048i	1.38624	+	0.360299i
$371$	−0.463232	+	0.0816804i	−0.0240498	+	0.00424063i
$372$		0			0
$373$	−1.65913	−	4.55843i	−0.0859066	−	0.236027i	0.889299	−	0.457326i	$-0.151193\pi$
$373$	−1.65913	−	4.55843i	−0.0859066	−	0.236027i	−0.975206	+	0.221299i	$0.928970\pi$
$374$	−7.12089	+	5.06628i	−0.368213	+	0.261971i
$375$		0			0
$376$	0.267368	−	4.12542i	0.0137885	−	0.212752i
$377$			14.8512i			0.764874i
$378$		0			0
$379$	31.5863			1.62248			0.811238	−	0.584715i	$-0.198794\pi$
$379$	31.5863			1.62248			0.811238	+	0.584715i	$0.198794\pi$
$380$	−29.7180	−	34.3544i	−1.52450	−	1.76234i
$381$		0			0
$382$	−12.5973	+	8.96253i	−0.644531	+	0.458563i
$383$	−5.33286	+	1.94100i	−0.272496	+	0.0991805i	−0.474654	−	0.880172i	$-0.657427\pi$
$383$	−5.33286	+	1.94100i	−0.272496	+	0.0991805i	0.202158	+	0.979353i	$0.435205\pi$
$384$		0			0
$385$	−1.93562	−	10.9774i	−0.0986482	−	0.559462i
$386$	1.04277	−	4.01206i	0.0530758	−	0.204208i
$387$		0			0
$388$	3.63325	+	2.02546i	0.184450	+	0.102827i
$389$	−7.70166	−	2.80317i	−0.390490	−	0.142127i	0.139311	−	0.990249i	$-0.455511\pi$
$389$	−7.70166	−	2.80317i	−0.390490	−	0.142127i	−0.529801	+	0.848122i	$0.677733\pi$
$390$		0			0
$391$	15.0411	−	17.9253i	0.760660	−	0.906520i
$392$	−0.689737	+	0.0760483i	−0.0348370	+	0.00384102i
$393$		0			0
$394$	1.70812	+	3.59233i	0.0860537	+	0.180979i
$395$	23.8902	+	13.7930i	1.20204	+	0.694001i
$396$		0			0
$397$	25.2112	−	14.5557i	1.26532	−	0.730531i	0.291218	−	0.956657i	$-0.405939\pi$
$397$	25.2112	−	14.5557i	1.26532	−	0.730531i	0.974098	+	0.226126i	$0.0726061\pi$
$398$	−1.17572	−	0.810147i	−0.0589334	−	0.0406090i
$399$		0			0
$400$	7.22915	−	2.88011i	0.361458	−	0.144006i
$401$	−13.6729	−	2.41090i	−0.682792	−	0.120395i	−0.178516	−	0.983937i	$-0.557130\pi$
$401$	−13.6729	−	2.41090i	−0.682792	−	0.120395i	−0.504276	+	0.863542i	$0.668241\pi$
$402$		0			0
$403$	−8.14562	+	6.83498i	−0.405762	+	0.340475i
$404$	0.536342	+	35.6789i	0.0266840	+	1.77509i
$405$		0			0
$406$	−13.0703	+	13.2682i	−0.648667	+	0.658492i
$407$	9.21557	−	7.73278i	0.456799	−	0.383300i
$408$		0			0
$409$	−2.85854	+	16.2116i	−0.141346	+	0.801613i	0.828883	+	0.559422i	$0.188977\pi$
$409$	−2.85854	+	16.2116i	−0.141346	+	0.801613i	−0.970229	+	0.242190i	$0.922134\pi$
$410$	−10.6858	+	23.3728i	−0.527735	+	1.15430i
$411$		0			0
$412$	−4.73034	−	24.6541i	−0.233047	−	1.21462i
$413$	−0.961601	−	1.66554i	−0.0473173	−	0.0819559i
$414$		0			0
$415$	26.2629	+	15.1629i	1.28920	+	0.744318i
$416$	14.7520	−	7.56624i	0.723277	−	0.370966i
$417$		0			0
$418$	−19.7455	+	1.87715i	−0.965786	+	0.0918144i
$419$	−10.4296	+	12.4295i	−0.509520	+	0.607223i	−0.958070	−	0.286535i	$-0.907496\pi$
$419$	−10.4296	+	12.4295i	−0.509520	+	0.607223i	0.448549	+	0.893758i	$0.351941\pi$
$420$		0			0
$421$	−0.181389	+	0.498362i	−0.00884036	+	0.0242887i	−0.944034	−	0.329847i	$-0.893003\pi$
$421$	−0.181389	+	0.498362i	−0.00884036	+	0.0242887i	0.935194	+	0.354136i	$0.115225\pi$
$422$	−5.77967	+	1.59531i	−0.281350	+	0.0776585i
$423$		0			0
$424$	−0.497325	−	0.121310i	−0.0241522	−	0.00589132i
$425$	7.27495	−	1.28277i	0.352887	−	0.0622235i
$426$		0			0
$427$	27.5740	−	10.0361i	1.33440	−	0.485682i
$428$	3.47497	−	21.6014i	0.167969	−	1.04414i
$429$		0			0
$430$	14.9373	+	1.19379i	0.720339	+	0.0575697i
$431$	−12.2920			−0.592084			−0.296042	−	0.955175i	$-0.595667\pi$
$431$	−12.2920			−0.592084			−0.296042	+	0.955175i	$0.595667\pi$
$432$		0			0
$433$	14.6907			0.705991			0.352996	−	0.935625i	$-0.385163\pi$
$433$	14.6907			0.705991			0.352996	+	0.935625i	$0.385163\pi$
$434$	−13.2928	−	1.06236i	−0.638073	−	0.0509950i
$435$		0			0
$436$	−2.01892	+	12.5502i	−0.0966889	+	0.601045i
$437$	49.9053	−	18.1640i	2.38729	−	0.868904i
$438$		0			0
$439$	−28.8488	+	5.08682i	−1.37688	+	0.242781i	−0.812609	−	0.582810i	$-0.801953\pi$
$439$	−28.8488	+	5.08682i	−1.37688	+	0.242781i	−0.564270	+	0.825591i	$0.690842\pi$
$440$	2.87473	−	11.7853i	0.137048	−	0.561844i
$441$		0			0
$442$	15.1712	−	4.18758i	0.721622	−	0.199183i
$443$	11.6096	−	31.8970i	0.551588	−	1.51547i	−0.279955	−	0.960013i	$-0.590320\pi$
$443$	11.6096	−	31.8970i	0.551588	−	1.51547i	0.831543	−	0.555461i	$-0.187458\pi$
$444$		0			0
$445$	−0.413240	+	0.492480i	−0.0195895	+	0.0233458i
$446$	22.5077	−	2.13974i	1.06577	−	0.101319i
$447$		0			0
$448$	19.8386	+	6.22324i	0.937285	+	0.294020i
$449$	15.4011	+	8.89184i	0.726823	+	0.419632i	0.817259	−	0.576271i	$-0.195493\pi$
$449$	15.4011	+	8.89184i	0.726823	+	0.419632i	−0.0904355	+	0.995902i	$0.528826\pi$
$450$		0			0
$451$	5.61089	+	9.71834i	0.264206	+	0.457619i
$452$	1.32978	+	6.93072i	0.0625478	+	0.325994i
$453$		0			0
$454$	−1.01100	+	2.21133i	−0.0474485	+	0.103783i
$455$	−3.48587	+	19.7693i	−0.163420	+	0.926800i
$456$		0			0
$457$	9.21939	−	7.73598i	0.431265	−	0.361874i	−0.401164	−	0.916006i	$-0.631394\pi$
$457$	9.21939	−	7.73598i	0.431265	−	0.361874i	0.832429	+	0.554132i	$0.186950\pi$
$458$	−9.14028	+	9.27871i	−0.427097	+	0.433566i
$459$		0			0
$460$	0.488216	+	32.4774i	0.0227632	+	1.51427i
$461$	−12.6139	+	10.5843i	−0.587487	+	0.492960i	−0.887396	−	0.461008i	$-0.847488\pi$
$461$	−12.6139	+	10.5843i	−0.587487	+	0.492960i	0.299909	+	0.953968i	$0.403044\pi$
$462$		0			0
$463$	−3.83957	−	0.677019i	−0.178440	−	0.0314638i	0.0837142	−	0.996490i	$-0.473322\pi$
$463$	−3.83957	−	0.677019i	−0.178440	−	0.0314638i	−0.262154	+	0.965026i	$0.584433\pi$
$464$	−18.8296	+	7.50177i	−0.874144	+	0.348261i
$465$		0			0
$466$	−22.5463	−	15.5359i	−1.04444	−	0.719685i
$467$	8.38005	−	4.83822i	0.387782	−	0.223886i	−0.293416	−	0.955985i	$-0.594792\pi$
$467$	8.38005	−	4.83822i	0.387782	−	0.223886i	0.681199	+	0.732098i	$0.261459\pi$
$468$		0			0
$469$	−30.8975	−	17.8387i	−1.42672	−	0.823715i
$470$	2.33926	+	4.91968i	0.107902	+	0.226928i
$471$		0			0
$472$	−0.229377	−	2.08039i	−0.0105579	−	0.0957576i
$473$	4.20585	−	5.01234i	0.193385	−	0.230468i
$474$		0			0
$475$	15.7548	+	5.73429i	0.722881	+	0.263107i
$476$	17.2396	+	9.61073i	0.790176	+	0.440507i
$477$		0			0
$478$	−1.64662	+	6.33535i	−0.0753146	+	0.289772i
$479$	0.352574	+	1.99955i	0.0161095	+	0.0913616i	0.991802	−	0.127780i	$-0.0407853\pi$
$479$	0.352574	+	1.99955i	0.0161095	+	0.0913616i	−0.975693	+	0.219142i	$0.929674\pi$
$480$		0			0
$481$	−20.3585	+	7.40988i	−0.928266	+	0.337861i
$482$	31.7450	−	22.5856i	1.44595	−	1.02874i
$483$		0			0
$484$	10.9276	+	12.6325i	0.496710	+	0.574203i
$485$	−5.48126			−0.248891
$486$		0			0
$487$		−	7.67766i		−	0.347908i	−0.984754	−	0.173954i	$-0.944346\pi$
$487$		−	7.67766i		−	0.347908i	0.984754	−	0.173954i	$-0.0556544\pi$
$488$	31.8675	+	2.06533i	1.44257	+	0.0934930i
$489$		0			0
$490$	0.745054	−	0.530082i	0.0336581	−	0.0239466i
$491$	−6.23136	−	17.1205i	−0.281217	−	0.772638i	−0.997218	−	0.0745389i	$-0.976251\pi$
$491$	−6.23136	−	17.1205i	−0.281217	−	0.772638i	0.716001	−	0.698100i	$-0.245971\pi$
$492$		0			0
$493$	−18.9489	+	3.34121i	−0.853417	+	0.150480i
$494$	34.5716	+	8.98550i	1.55545	+	0.404277i
$495$		0			0
$496$	−12.7806	−	6.87518i	−0.573866	−	0.308705i
$497$	−4.57346	+	12.5655i	−0.205148	+	0.563638i
$498$		0			0
$499$	−0.594620	−	0.498945i	−0.0266189	−	0.0223359i	0.629381	−	0.777097i	$-0.283308\pi$
$499$	−0.594620	−	0.498945i	−0.0266189	−	0.0223359i	−0.656000	+	0.754761i	$0.727753\pi$
$500$	10.1624	−	12.4876i	0.454476	−	0.558460i
$501$		0			0
$502$	17.7317	−	8.43126i	0.791406	−	0.376305i
$503$	−16.6264	+	28.7978i	−0.741335	+	1.28403i	0.210552	+	0.977583i	$0.432474\pi$
$503$	−16.6264	+	28.7978i	−0.741335	+	1.28403i	−0.951887	+	0.306448i	$0.900859\pi$
$504$		0			0
$505$	−23.5098	−	40.7203i	−1.04617	−	1.81203i
$506$	11.6787	+	8.04740i	0.519182	+	0.357750i
$507$		0			0
$508$	−34.0839	+	12.9890i	−1.51223	+	0.576293i
$509$	−5.59821	+	31.7490i	−0.248136	+	1.40725i	0.564958	+	0.825119i	$0.308892\pi$
$509$	−5.59821	+	31.7490i	−0.248136	+	1.40725i	−0.813095	+	0.582132i	$0.802219\pi$
$510$		0			0
$511$	−8.78164	−	10.4655i	−0.388477	−	0.462969i
$512$	17.0448	+	14.8820i	0.753283	+	0.657697i
$513$		0			0
$514$	1.68394	−	1.70944i	0.0742754	−	0.0754003i
$515$	21.2631	+	25.3404i	0.936966	+	1.11663i
$516$		0			0
$517$	2.34251	+	0.413048i	0.103024	+	0.0181658i
$518$	−24.7099	−	11.2971i	−1.08569	−	0.496366i
$519$		0			0
$520$	−12.1240	+	18.1736i	−0.531674	+	0.796966i
$521$	27.9816	−	16.1552i	1.22590	−	0.707773i	0.259729	−	0.965682i	$-0.416367\pi$
$521$	27.9816	−	16.1552i	1.22590	−	0.707773i	0.966169	+	0.257909i	$0.0830335\pi$
$522$		0			0
$523$	−1.25831	+	2.17946i	−0.0550222	+	0.0953012i	−0.892225	−	0.451592i	$-0.850856\pi$
$523$	−1.25831	+	2.17946i	−0.0550222	+	0.0953012i	0.837202	+	0.546893i	$0.184190\pi$
$524$	−7.87623	−	2.73336i	−0.344075	−	0.119407i
$525$		0			0
$526$	0.555348	+	5.84165i	0.0242143	+	0.254708i
$527$	−10.5535	−	8.85544i	−0.459718	−	0.385749i
$528$		0			0
$529$	−14.0722	−	5.12185i	−0.611833	−	0.222689i
$530$	0.650229	−	0.179477i	0.0282442	−	0.00779598i
$531$		0			0
$532$	22.9787	+	38.4537i	0.996255	+	1.66718i
$533$	−3.50932	−	19.9023i	−0.152005	−	0.862066i
$534$		0			0
$535$	9.86054	+	27.0916i	0.426308	+	1.17127i
$536$	−22.9818	−	31.2952i	−0.992662	−	1.35175i
$537$		0			0
$538$	44.3301	+	3.54287i	1.91121	+	0.152744i
$539$		−	0.399264i		−	0.0171975i
$540$		0			0
$541$			20.7984i			0.894192i	0.894486	+	0.447096i	$0.147542\pi$
$541$			20.7984i			0.894192i	−0.894486	+	0.447096i	$0.852458\pi$
$542$	−3.17393	+	39.7137i	−0.136332	+	1.70585i
$543$		0			0
$544$	12.9728	+	17.1202i	0.556206	+	0.734021i
$545$	−5.72888	−	15.7400i	−0.245398	−	0.674226i
$546$		0			0
$547$	−3.11764	−	17.6810i	−0.133301	−	0.755985i	−0.976028	−	0.217645i	$-0.930163\pi$
$547$	−3.11764	−	17.6810i	−0.133301	−	0.755985i	0.842727	−	0.538341i	$-0.180949\pi$
$548$	16.3528	+	27.3656i	0.698559	+	1.16900i
$549$		0			0
$550$	1.19132	+	4.31605i	0.0507980	+	0.184037i
$551$	−41.0363	−	14.9360i	−1.74820	−	0.636294i
$552$		0			0
$553$	−20.8398	−	17.4867i	−0.886200	−	0.743610i
$554$	34.7653	−	3.30504i	1.47704	−	0.140418i
$555$		0			0
$556$	−1.55431	+	4.47877i	−0.0659173	+	0.189942i
$557$	15.8779	−	27.5013i	0.672766	−	1.16527i	−0.304350	−	0.952560i	$-0.598439\pi$
$557$	15.8779	−	27.5013i	0.672766	−	1.16527i	0.977116	−	0.212705i	$-0.0682274\pi$
$558$		0			0
$559$	−10.2049	+	5.89179i	−0.431621	+	0.249196i
$560$	−26.8261	+	5.56639i	−1.13361	+	0.235223i
$561$		0			0
$562$	11.3244	−	24.7696i	0.477692	−	1.04484i
$563$	−21.2510	−	3.74712i	−0.895621	−	0.157922i	−0.293153	−	0.956065i	$-0.594705\pi$
$563$	−21.2510	−	3.74712i	−0.895621	−	0.157922i	−0.602468	+	0.798143i	$0.705816\pi$
$564$		0			0
$565$	−5.97745	−	7.12365i	−0.251473	−	0.299694i
$566$	9.02186	+	8.88726i	0.379217	+	0.373559i
$567$		0			0
$568$	−10.0555	+	10.5195i	−0.421920	+	0.441389i
$569$	−28.0024	−	33.3720i	−1.17392	−	1.39903i	−0.899221	−	0.437495i	$-0.855866\pi$
$569$	−28.0024	−	33.3720i	−1.17392	−	1.39903i	−0.274701	−	0.961530i	$-0.588579\pi$
$570$		0			0
$571$	5.33260	−	30.2427i	0.223162	−	1.26562i	−0.643005	−	0.765862i	$-0.722313\pi$
$571$	5.33260	−	30.2427i	0.223162	−	1.26562i	0.866167	−	0.499754i	$-0.166576\pi$
$572$	3.39700	+	8.91395i	0.142036	+	0.372711i
$573$		0			0
$574$	14.3805	−	20.8695i	0.600229	−	0.871077i
$575$	−5.99429	−	10.3824i	−0.249979	−	0.432977i
$576$		0			0
$577$	−18.5251	+	32.0864i	−0.771210	+	1.33578i	0.165690	+	0.986178i	$0.447015\pi$
$577$	−18.5251	+	32.0864i	−0.771210	+	1.33578i	−0.936900	+	0.349597i	$0.886318\pi$
$578$	−1.56767	−	3.29696i	−0.0652065	−	0.137135i
$579$		0			0
$580$	16.8585	−	20.7157i	0.700012	−	0.860174i
$581$	−22.9096	−	19.2235i	−0.950452	−	0.797524i
$582$		0			0
$583$	0.100738	−	0.276776i	0.00417216	−	0.0114629i
$584$	−4.17091	−	14.2709i	−0.172593	−	0.590535i
$585$		0			0
$586$	−7.56980	+	29.1247i	−0.312706	+	1.20313i
$587$	−2.18563	+	0.385385i	−0.0902104	+	0.0159065i	−0.218571	−	0.975821i	$-0.570140\pi$
$587$	−2.18563	+	0.385385i	−0.0902104	+	0.0159065i	0.128361	+	0.991728i	$0.459028\pi$
$588$		0			0
$589$	−10.6941	−	29.3817i	−0.440642	−	1.21065i
$590$	1.59883	+	2.24724i	0.0658230	+	0.0925172i
$591$		0			0
$592$	−19.6786	−	22.0693i	−0.808784	−	0.907043i
$593$		−	7.72015i		−	0.317028i	−0.987357	−	0.158514i	$-0.949330\pi$
$593$		−	7.72015i		−	0.317028i	0.987357	−	0.158514i	$-0.0506704\pi$
$594$		0			0
$595$	−26.0084			−1.06624
$596$	−20.9113	−	24.1736i	−0.856559	−	0.990191i
$597$		0			0
$598$	−14.8071	−	20.8121i	−0.605507	−	0.851068i
$599$	5.13051	−	1.86735i	0.209627	−	0.0762980i	−0.235072	−	0.971978i	$-0.575533\pi$
$599$	5.13051	−	1.86735i	0.209627	−	0.0762980i	0.444699	+	0.895680i	$0.353311\pi$
$600$		0			0
$601$	2.68385	+	15.2209i	0.109477	+	0.620872i	0.989337	+	0.145641i	$0.0465245\pi$
$601$	2.68385	+	15.2209i	0.109477	+	0.620872i	−0.879861	+	0.475231i	$0.842364\pi$
$602$	−14.3025	−	3.71735i	−0.582925	−	0.151508i
$603$		0			0
$604$	2.29612	−	4.11875i	0.0934277	−	0.167589i
$605$	−20.6824	−	7.52779i	−0.840860	−	0.306048i
$606$		0			0
$607$	−0.0926471	+	0.110413i	−0.00376043	+	0.00448151i	−0.767921	−	0.640544i	$-0.778709\pi$
$607$	−0.0926471	+	0.110413i	−0.00376043	+	0.00448151i	0.764161	+	0.645026i	$0.223153\pi$
$608$	6.07054	+	48.3718i	0.246193	+	1.96173i
$609$		0			0
$610$	−38.0028	+	18.0700i	−1.53869	+	0.731632i
$611$	−3.70982	−	2.14186i	−0.150083	−	0.0866505i
$612$		0			0
$613$	30.3578	−	17.5271i	1.22614	−	0.707913i	0.259921	−	0.965630i	$-0.416304\pi$
$613$	30.3578	−	17.5271i	1.22614	−	0.707913i	0.966220	+	0.257717i	$0.0829702\pi$
$614$	7.20416	−	10.4550i	0.290736	−	0.421928i
$615$		0			0
$616$	−4.81011	+	10.9535i	−0.193805	+	0.441329i
$617$	−1.95314	−	0.344391i	−0.0786304	−	0.0138647i	0.134195	−	0.990955i	$-0.457155\pi$
$617$	−1.95314	−	0.344391i	−0.0786304	−	0.0138647i	−0.212825	+	0.977090i	$0.568266\pi$
$618$		0			0
$619$	30.9839	−	25.9986i	1.24535	−	1.04497i	0.248262	−	0.968693i	$-0.420141\pi$
$619$	30.9839	−	25.9986i	1.24535	−	1.04497i	0.997087	−	0.0762782i	$-0.0243037\pi$
$620$	19.1211	−	0.287437i	0.767920	−	0.0115438i
$621$		0			0
$622$	−17.1522	−	16.8962i	−0.687739	−	0.677478i
$623$	0.485670	−	0.407525i	0.0194579	−	0.0163272i
$624$		0			0
$625$	−5.37310	+	30.4724i	−0.214924	+	1.21890i
$626$	−12.3788	−	5.65946i	−0.494756	−	0.226197i
$627$		0			0
$628$	0.312982	+	1.63124i	0.0124893	+	0.0650934i
$629$	−14.0347	−	24.3087i	−0.559598	−	0.969253i
$630$		0			0
$631$	28.0718	+	16.2073i	1.11752	+	0.645202i	0.940767	−	0.339053i	$-0.110107\pi$
$631$	28.0718	+	16.2073i	1.11752	+	0.645202i	0.176755	+	0.984255i	$0.443440\pi$
$632$	−13.1139	−	26.5435i	−0.521643	−	1.05584i
$633$		0			0
$634$	−0.811659	−	8.53776i	−0.0322351	−	0.339078i
$635$	30.8946	−	36.8188i	1.22602	−	1.46111i
$636$		0			0
$637$	−0.245925	+	0.675673i	−0.00974390	+	0.0267711i
$638$	−3.10301	−	11.2419i	−0.122849	−	0.445072i
$639$		0			0
$640$	−29.1664	−	6.19189i	−1.15290	−	0.244756i
$641$	−16.3026	+	2.87458i	−0.643912	+	0.113539i	−0.486063	−	0.873924i	$-0.661567\pi$
$641$	−16.3026	+	2.87458i	−0.643912	+	0.113539i	−0.157850	+	0.987463i	$0.550456\pi$
$642$		0			0
$643$	−25.2314	+	9.18349i	−0.995030	+	0.362161i	−0.787666	−	0.616102i	$-0.788711\pi$
$643$	−25.2314	+	9.18349i	−0.995030	+	0.362161i	−0.207364	+	0.978264i	$0.566489\pi$
$644$	5.08750	−	31.6253i	0.200476	−	1.24621i
$645$		0			0
$646$	−3.68690	+	46.1322i	−0.145059	+	1.81505i
$647$	−29.0527			−1.14218			−0.571090	−	0.820887i	$-0.693479\pi$
$647$	−29.0527			−1.14218			−0.571090	+	0.820887i	$0.693479\pi$
$648$		0			0
$649$	1.20426			0.0472714
$650$	0.642386	−	8.03783i	0.0251964	−	0.315270i
$651$		0			0
$652$	−22.2455	−	3.57859i	−0.871200	−	0.140148i
$653$	−32.5052	+	11.8309i	−1.27203	+	0.462980i	−0.887788	−	0.460253i	$-0.847759\pi$
$653$	−32.5052	+	11.8309i	−1.27203	+	0.462980i	−0.384240	+	0.923233i	$0.625537\pi$
$654$		0			0
$655$	10.8189	−	1.90767i	0.422730	−	0.0745387i
$656$	23.4613	−	14.5027i	0.916009	−	0.566235i
$657$		0			0
$658$	−1.42938	−	5.17852i	−0.0557231	−	0.201880i
$659$	−7.44079	+	20.4434i	−0.289852	+	0.796362i	0.706234	+	0.707978i	$0.250393\pi$
$659$	−7.44079	+	20.4434i	−0.289852	+	0.796362i	−0.996086	+	0.0883842i	$0.971830\pi$
$660$		0			0
$661$	−16.3906	+	19.5335i	−0.637519	+	0.759766i	−0.983976	−	0.178300i	$-0.942940\pi$
$661$	−16.3906	+	19.5335i	−0.637519	+	0.759766i	0.346457	+	0.938066i	$0.387385\pi$
$662$	0.491915	+	5.17440i	0.0191188	+	0.201109i
$663$		0			0
$664$	−14.4164	−	29.1798i	−0.559464	−	1.13239i
$665$	−51.1202	−	29.5143i	−1.98236	−	1.14451i
$666$		0			0
$667$	15.6132	+	27.0429i	0.604546	+	1.04710i
$668$	34.3200	−	6.58490i	1.32788	−	0.254778i
$669$		0			0
$670$	46.5307	+	21.2733i	1.79764	+	0.821860i
$671$	−3.19066	+	18.0951i	−0.123174	+	0.698555i
$672$		0			0
$673$	−6.18349	+	5.18857i	−0.238356	+	0.200005i	−0.754139	−	0.656715i	$-0.771946\pi$
$673$	−6.18349	+	5.18857i	−0.238356	+	0.200005i	0.515783	+	0.856719i	$0.327501\pi$
$674$	19.5733	+	19.2813i	0.753936	+	0.742687i
$675$		0			0
$676$	0.132581	+	8.81963i	0.00509927	+	0.339216i
$677$	11.8370	−	9.93243i	0.454933	−	0.381734i	−0.386330	−	0.922361i	$-0.626257\pi$
$677$	11.8370	−	9.93243i	0.454933	−	0.381734i	0.841263	+	0.540627i	$0.181813\pi$
$678$		0			0
$679$	5.32333	+	0.938647i	0.204291	+	0.0360220i
$680$	−25.9158	−	11.3806i	−0.993825	−	0.436427i
$681$		0			0
$682$	4.73790	−	6.87584i	0.181424	−	0.263289i
$683$	1.82111	−	1.05142i	0.0696830	−	0.0402315i	−0.464754	−	0.885440i	$-0.653857\pi$
$683$	1.82111	−	1.05142i	0.0696830	−	0.0402315i	0.534437	+	0.845209i	$0.320524\pi$
$684$		0			0
$685$	−36.3798	−	21.0039i	−1.39000	−	0.802516i
$686$	−24.0499	+	11.4355i	−0.918231	+	0.436610i
$687$		0			0
$688$	−12.6249	−	9.96254i	−0.481321	−	0.379818i
$689$	−0.340959	+	0.406339i	−0.0129895	+	0.0154803i
$690$		0			0
$691$	−21.9905	−	8.00388i	−0.836557	−	0.304482i	−0.112010	−	0.993707i	$-0.535729\pi$
$691$	−21.9905	−	8.00388i	−0.836557	−	0.304482i	−0.724547	+	0.689225i	$0.757951\pi$
$692$	−32.4935	−	18.1145i	−1.23522	−	0.688609i
$693$		0			0
$694$	−20.6981	−	5.37963i	−0.785687	−	0.204208i
$695$	−1.08478	−	6.15210i	−0.0411481	−	0.233362i
$696$		0			0
$697$	24.6043	−	8.95523i	0.931954	−	0.339203i
$698$	−18.4309	−	25.9055i	−0.697619	−	0.980536i
$699$		0			0
$700$	7.64789	−	6.61575i	0.289063	−	0.250052i
$701$	−40.5028			−1.52977			−0.764884	−	0.644168i	$-0.777204\pi$
$701$	−40.5028			−1.52977			−0.764884	+	0.644168i	$0.777204\pi$
$702$		0			0
$703$		−	63.7061i		−	2.40272i
$704$	−9.58598	+	8.80972i	−0.361285	+	0.332029i
$705$		0			0
$706$	17.0936	+	24.0258i	0.643324	+	0.904222i
$707$	15.8593	+	43.5730i	0.596450	+	1.63873i
$708$		0			0
$709$	−12.4782	+	2.20024i	−0.468628	+	0.0826317i	−0.402975	−	0.915211i	$-0.632024\pi$
$709$	−12.4782	+	2.20024i	−0.468628	+	0.0826317i	−0.0656523	+	0.997843i	$0.520913\pi$
$710$	4.82374	−	18.5593i	0.181032	−	0.696517i
$711$		0			0
$712$	0.662264	−	0.193557i	0.0248194	−	0.00725387i
$713$	−7.64687	+	21.0096i	−0.286377	+	0.786815i
$714$		0			0
$715$	−9.62920	−	8.07986i	−0.360112	−	0.302170i
$716$	10.9918	+	8.94514i	0.410783	+	0.334296i
$717$		0			0
$718$	6.60552	+	13.8920i	0.246516	+	0.518446i
$719$	−23.2178	+	40.2145i	−0.865879	+	1.49975i	0.000291815		1.00000i	$0.499907\pi$
$719$	−23.2178	+	40.2145i	−0.865879	+	1.49975i	−0.866171	+	0.499747i	$0.833426\pi$
$720$		0			0
$721$	−16.3111	−	28.2516i	−0.607455	−	1.05214i
$722$	−44.3513	+	64.3644i	−1.65058	+	2.39540i
$723$		0			0
$724$	−0.280239	+	0.106796i	−0.0104150	+	0.00396903i
$725$	−1.71183	+	9.70825i	−0.0635756	+	0.360555i
$726$		0			0
$727$	−7.82850	−	9.32964i	−0.290343	−	0.346017i	0.601081	−	0.799188i	$-0.294737\pi$
$727$	−7.82850	−	9.32964i	−0.290343	−	0.346017i	−0.891424	+	0.453171i	$0.850293\pi$
$728$	14.8869	−	15.5738i	0.551745	−	0.577204i
$729$		0			0
$730$	13.9571	+	13.7489i	0.516576	+	0.508869i
$731$	−9.81335	−	11.6951i	−0.362960	−	0.432559i
$732$		0			0
$733$	9.85329	+	1.73740i	0.363939	+	0.0641723i	0.352628	−	0.935764i	$-0.385288\pi$
$733$	9.85329	+	1.73740i	0.363939	+	0.0641723i	0.0113117	+	0.999936i	$0.496399\pi$
$734$	−6.82091	+	14.9192i	−0.251764	+	0.550679i
$735$		0			0
$736$	18.9079	−	29.2866i	0.696953	−	1.07952i
$737$	19.3473	−	11.1702i	0.712666	−	0.411458i
$738$		0			0
$739$	22.0318	−	38.1602i	0.810454	−	1.40375i	−0.102093	−	0.994775i	$-0.532554\pi$
$739$	22.0318	−	38.1602i	0.810454	−	1.40375i	0.912547	−	0.408972i	$-0.134113\pi$
$740$	36.8092	+	12.7742i	1.35313	+	0.469590i
$741$		0			0
$742$	−0.662230	+	0.0629562i	−0.0243112	+	0.00231119i
$743$	−6.42946	−	5.39496i	−0.235874	−	0.197922i	0.517187	−	0.855872i	$-0.326979\pi$
$743$	−6.42946	−	5.39496i	−0.235874	−	0.197922i	−0.753061	+	0.657950i	$0.771424\pi$
$744$		0			0
$745$	39.5782	+	14.4053i	1.45003	+	0.527769i
$746$	−1.82533	−	6.61303i	−0.0668302	−	0.242120i
$747$		0			0
$748$	−10.6092	+	6.33976i	−0.387913	+	0.231805i
$749$	−4.93709	−	27.9996i	−0.180397	−	1.02308i
$750$		0			0
$751$	7.74342	+	21.2749i	0.282561	+	0.776331i	0.997055	+	0.0766890i	$0.0244348\pi$
$751$	7.74342	+	21.2749i	0.282561	+	0.776331i	−0.714494	+	0.699642i	$0.753343\pi$
$752$	0.841704	−	5.78556i	0.0306938	−	0.210977i
$753$		0			0
$754$	−1.67321	+	20.9360i	−0.0609347	+	0.762443i
$755$			6.21370i			0.226140i
$756$		0			0
$757$		−	19.5088i		−	0.709058i	−0.935045	−	0.354529i	$-0.884641\pi$
$757$		−	19.5088i		−	0.709058i	0.935045	−	0.354529i	$-0.115359\pi$
$758$	44.5277	+	3.55867i	1.61732	+	0.129257i
$759$		0			0
$760$	−38.0235	−	51.7782i	−1.37926	−	1.87819i
$761$	9.62500	+	26.4445i	0.348906	+	0.958612i	0.982715	+	0.185122i	$0.0592682\pi$
$761$	9.62500	+	26.4445i	0.348906	+	0.958612i	−0.633809	+	0.773489i	$0.718510\pi$
$762$		0			0
$763$	2.86840	+	16.2675i	0.103843	+	0.588924i
$764$	−18.7683	+	11.2154i	−0.679015	+	0.405758i
$765$		0			0
$766$	−7.73651	+	2.13544i	−0.279532	+	0.0771565i
$767$	−2.03797	−	0.741760i	−0.0735868	−	0.0267834i
$768$		0			0
$769$	12.3157	+	10.3341i	0.444117	+	0.372658i	0.837247	−	0.546824i	$-0.184163\pi$
$769$	12.3157	+	10.3341i	0.444117	+	0.372658i	−0.393130	+	0.919483i	$0.628608\pi$
$770$	−1.49190	−	15.6932i	−0.0537644	−	0.565543i
$771$		0			0
$772$	1.92204	−	5.53839i	0.0691756	−	0.199331i
$773$	−6.27436	+	10.8675i	−0.225673	+	0.390877i	−0.956521	−	0.291663i	$-0.905791\pi$
$773$	−6.27436	+	10.8675i	−0.225673	+	0.390877i	0.730848	+	0.682540i	$0.239125\pi$
$774$		0			0
$775$	−6.11265	+	3.52914i	−0.219573	+	0.126770i
$776$	4.89366	+	3.26467i	0.175672	+	0.117195i
$777$		0			0
$778$	−10.5413	−	4.81939i	−0.377926	−	0.172784i
$779$	58.5229	+	10.3192i	2.09680	+	0.369722i
$780$		0			0
$781$	−5.38215	−	6.41420i	−0.192589	−	0.229518i
$782$	23.2232	−	23.5750i	0.830462	−	0.843039i
$783$		0			0
$784$	−0.980902	+	0.0294975i	−0.0350322	+	0.00105348i
$785$	−1.40687	−	1.67664i	−0.0502134	−	0.0598420i
$786$		0			0
$787$	−3.64035	+	20.6454i	−0.129764	+	0.735930i	0.848599	+	0.529037i	$0.177447\pi$
$787$	−3.64035	+	20.6454i	−0.129764	+	0.735930i	−0.978363	+	0.206894i	$0.933665\pi$
$788$	2.00323	+	5.25662i	0.0713623	+	0.187259i
$789$		0			0
$790$	32.1244	+	22.1358i	1.14294	+	0.787557i
$791$	4.58533	+	7.94202i	0.163036	+	0.282386i
$792$		0			0
$793$	16.5452	−	28.6571i	0.587536	−	1.01764i
$794$	37.1807	−	17.6790i	1.31949	−	0.627406i
$795$		0			0
$796$	−1.56616	−	1.27454i	−0.0555109	−	0.0451749i
$797$	21.2235	+	17.8086i	0.751775	+	0.630814i	0.935972	−	0.352075i	$-0.114524\pi$
$797$	21.2235	+	17.8086i	0.751775	+	0.630814i	−0.184197	+	0.982889i	$0.558968\pi$
$798$		0			0
$799$	1.89822	−	5.21531i	0.0671541	−	0.184504i
$800$	10.5156	−	3.24568i	0.371781	−	0.114752i
$801$		0			0
$802$	−19.0033	−	4.93915i	−0.671030	−	0.174407i
$803$	8.42472	−	1.48550i	0.297302	−	0.0524223i
$804$		0			0
$805$	14.4362	+	39.6632i	0.508810	+	1.39794i
$806$	−12.2531	+	8.71768i	−0.431597	+	0.307067i
$807$		0			0
$808$	−3.26367	+	50.3576i	−0.114816	+	1.77157i
$809$			21.9542i			0.771867i	0.922527	+	0.385933i	$0.126121\pi$
$809$			21.9542i			0.771867i	−0.922527	+	0.385933i	$0.873879\pi$
$810$		0			0
$811$	−17.4685			−0.613401			−0.306700	−	0.951806i	$-0.599225\pi$
$811$	−17.4685			−0.613401			−0.306700	+	0.951806i	$0.599225\pi$
$812$	−19.9203	+	17.2319i	−0.699065	+	0.604722i
$813$		0			0
$814$	13.8626	−	9.86277i	0.485883	−	0.345690i
$815$	27.8994	−	10.1546i	0.977274	−	0.355699i
$816$		0			0
$817$	−6.01685	−	34.1233i	−0.210503	−	1.19382i
$818$	−5.85623	+	22.5318i	−0.204758	+	0.787804i
$819$		0			0
$820$	−17.6973	+	31.7452i	−0.618017	+	1.10859i
$821$	40.3394	+	14.6823i	1.40786	+	0.512417i	0.930500	−	0.366293i	$-0.119373\pi$
$821$	40.3394	+	14.6823i	1.40786	+	0.512417i	0.477355	+	0.878710i	$0.341595\pi$
$822$		0			0
$823$	−17.8062	+	21.2206i	−0.620686	+	0.739705i	−0.981188	−	0.193053i	$-0.938161\pi$
$823$	−17.8062	+	21.2206i	−0.620686	+	0.739705i	0.360502	+	0.932758i	$0.382605\pi$
$824$	−3.89079	−	35.2883i	−0.135542	−	1.22933i
$825$		0			0
$826$	−1.16794	−	2.45628i	−0.0406378	−	0.0854650i
$827$	−23.1043	−	13.3392i	−0.803414	−	0.463851i	0.0412497	−	0.999149i	$-0.486866\pi$
$827$	−23.1043	−	13.3392i	−0.803414	−	0.463851i	−0.844663	+	0.535298i	$0.820199\pi$
$828$		0			0
$829$	−2.23315	+	1.28931i	−0.0775606	+	0.0447796i	−0.538279	−	0.842767i	$-0.680925\pi$
$829$	−2.23315	+	1.28931i	−0.0775606	+	0.0447796i	0.460718	+	0.887547i	$0.347592\pi$
$830$	35.3150	+	24.3343i	1.22580	+	0.844657i
$831$		0			0
$832$	21.6486	−	9.00424i	0.750532	−	0.312166i
$833$	−0.917434	−	0.161768i	−0.0317872	−	0.00560494i
$834$		0			0
$835$	−35.2753	+	29.5995i	−1.22075	+	1.02433i
$836$	−28.0472	+	0.421619i	−0.970031	+	0.0145820i
$837$		0			0
$838$	−16.1032	+	16.3471i	−0.556276	+	0.564701i
$839$	27.0517	−	22.6991i	0.933928	−	0.783659i	−0.0425905	−	0.999093i	$-0.513561\pi$
$839$	27.0517	−	22.6991i	0.933928	−	0.783659i	0.976518	+	0.215434i	$0.0691166\pi$
$840$		0			0
$841$	−0.577037	+	3.27254i	−0.0198978	+	0.112846i
$842$	−0.311855	+	0.682114i	−0.0107472	+	0.0235072i
$843$		0			0
$844$	−8.32744	+	1.59777i	−0.286642	+	0.0549975i
$845$	−5.81151	−	10.0658i	−0.199922	−	0.346275i
$846$		0			0
$847$	18.7974	+	10.8527i	0.645887	+	0.372903i
$848$	−0.687421	−	0.227044i	−0.0236061	−	0.00779671i
$849$		0			0
$850$	10.4002	−	0.988712i	0.356723	−	0.0339125i
$851$	−29.2812	+	34.8959i	−1.00375	+	1.19622i
$852$		0			0
$853$	11.8972	−	32.6874i	0.407354	−	1.11919i	−0.551222	−	0.834358i	$-0.685838\pi$
$853$	11.8972	−	32.6874i	0.407354	−	1.11919i	0.958576	−	0.284837i	$-0.0919393\pi$
$854$	40.0023	−	11.0415i	1.36885	−	0.377832i
$855$		0			0
$856$	7.33245	−	30.0603i	0.250618	−	1.02744i
$857$	14.7995	−	2.60955i	0.505541	−	0.0891405i	0.0849397	−	0.996386i	$-0.472930\pi$
$857$	14.7995	−	2.60955i	0.505541	−	0.0891405i	0.420601	+	0.907246i	$0.361819\pi$
$858$		0			0
$859$	−11.2421	+	4.09177i	−0.383574	+	0.139610i	−0.526608	−	0.850108i	$-0.676536\pi$
$859$	−11.2421	+	4.09177i	−0.383574	+	0.139610i	0.143034	+	0.989718i	$0.454314\pi$
$860$	20.9228	+	3.36582i	0.713463	+	0.114773i
$861$		0			0
$862$	−17.3282	−	1.38488i	−0.590203	−	0.0471692i
$863$	4.99128			0.169905			0.0849526	−	0.996385i	$-0.472926\pi$
$863$	4.99128			0.169905			0.0849526	+	0.996385i	$0.472926\pi$
$864$		0			0
$865$	49.0210			1.66676
$866$	20.7098	+	1.65513i	0.703747	+	0.0562437i
$867$		0			0
$868$	−18.6194	−	2.99526i	−0.631983	−	0.101666i
$869$	16.0074	−	5.82624i	0.543016	−	0.197641i
$870$		0			0
$871$	−39.6216	+	6.98635i	−1.34253	+	0.236724i
$872$	−4.26008	+	17.4648i	−0.144265	+	0.591432i
$873$		0			0
$874$	72.3989	−	19.9836i	2.44893	−	0.675955i
$875$	7.15570	−	19.6601i	0.241907	−	0.664634i
$876$		0			0
$877$	13.3228	−	15.8774i	0.449878	−	0.536143i	−0.492670	−	0.870217i	$-0.663979\pi$
$877$	13.3228	−	15.8774i	0.449878	−	0.536143i	0.942547	+	0.334073i	$0.108423\pi$
$878$	−41.2418	+	3.92073i	−1.39184	+	0.132318i
$879$		0			0
$880$	5.38036	−	16.2901i	0.181372	−	0.549140i
$881$	−7.33774	−	4.23645i	−0.247215	−	0.142729i	0.371274	−	0.928524i	$-0.378921\pi$
$881$	−7.33774	−	4.23645i	−0.247215	−	0.142729i	−0.618488	+	0.785794i	$0.712255\pi$
$882$		0			0
$883$	9.03674	+	15.6521i	0.304111	+	0.526735i	0.977063	−	0.212951i	$-0.0683074\pi$
$883$	9.03674	+	15.6521i	0.304111	+	0.526735i	−0.672952	+	0.739686i	$0.734974\pi$
$884$	21.8590	−	4.19404i	0.735197	−	0.141061i
$885$		0			0
$886$	19.9599	−	43.6579i	0.670567	−	1.46671i
$887$	−3.87890	+	21.9983i	−0.130241	+	0.738632i	0.847816	+	0.530291i	$0.177917\pi$
$887$	−3.87890	+	21.9983i	−0.130241	+	0.738632i	−0.978056	+	0.208341i	$0.933194\pi$
$888$		0			0
$889$	−36.3096	+	30.4674i	−1.21779	+	1.02184i
$890$	−0.638038	+	0.647701i	−0.0213871	+	0.0217110i
$891$		0			0
$892$	31.9706	−	0.480597i	1.07045	−	0.0160916i
$893$	9.64933	−	8.09675i	0.322903	−	0.270948i
$894$		0			0
$895$	−18.3904	−	3.24272i	−0.614723	−	0.108392i
$896$	27.2657	+	11.0081i	0.910883	+	0.367756i
$897$		0			0
$898$	20.7094	+	14.2702i	0.691083	+	0.476201i
$899$	15.9215	−	9.19228i	0.531012	−	0.306580i
$900$		0			0
$901$	−0.595165	−	0.343619i	−0.0198278	−	0.0114476i
$902$	6.81485	+	14.3323i	0.226910	+	0.477213i
$903$		0			0
$904$	1.09377	+	9.92019i	0.0363783	+	0.329940i
$905$	0.254017	−	0.302725i	0.00844380	−	0.0100629i
$906$		0			0
$907$	37.7812	+	13.7512i	1.25450	+	0.456602i	0.881921	−	0.471397i	$-0.156250\pi$
$907$	37.7812	+	13.7512i	1.25450	+	0.456602i	0.372583	+	0.927999i	$0.378472\pi$
$908$	−1.67436	+	3.00345i	−0.0555657	+	0.0996731i
$909$		0			0
$910$	−7.14140	+	27.4765i	−0.236735	+	0.910836i
$911$	1.26349	+	7.16560i	0.0418613	+	0.237407i	0.998558	−	0.0536786i	$-0.0170946\pi$
$911$	1.26349	+	7.16560i	0.0418613	+	0.237407i	−0.956697	+	0.291086i	$0.905984\pi$
$912$		0			0
$913$	17.5973	−	6.40489i	0.582386	−	0.211971i
$914$	13.8683	−	9.86686i	0.458723	−	0.326367i
$915$		0			0
$916$	−13.9306	+	12.0506i	−0.460280	+	0.398162i
$917$	−10.8339			−0.357766
$918$		0			0
$919$		−	24.9111i		−	0.821741i	−0.911694	−	0.410870i	$-0.865225\pi$
$919$		−	24.9111i		−	0.821741i	0.911694	−	0.410870i	$-0.134775\pi$
$920$	−2.97082	+	45.8390i	−0.0979451	+	1.51127i
$921$		0			0
$922$	−18.9745	+	13.4997i	−0.624892	+	0.444591i
$923$	5.15741	+	14.1699i	0.169758	+	0.466406i
$924$		0			0
$925$	−14.1625	+	2.49723i	−0.465660	+	0.0821084i
$926$	−5.33643	−	1.38699i	−0.175366	−	0.0455794i
$927$		0			0
$928$	−27.3897	+	8.45395i	−0.899110	+	0.277514i
$929$	−12.8203	+	35.2236i	−0.420621	+	1.15565i	0.530730	+	0.847541i	$0.321918\pi$
$929$	−12.8203	+	35.2236i	−0.420621	+	1.15565i	−0.951352	+	0.308107i	$0.900305\pi$
$930$		0			0
$931$	−1.61967	−	1.35906i	−0.0530825	−	0.0445415i
$932$	−30.0336	−	24.4414i	−0.983782	−	0.800604i
$933$		0			0
$934$	12.3586	−	5.87639i	0.404386	−	0.192281i
$935$	8.14289	−	14.1039i	0.266301	−	0.461247i
$936$		0			0
$937$	4.91136	+	8.50673i	0.160447	+	0.277903i	0.935029	−	0.354571i	$-0.115373\pi$
$937$	4.91136	+	8.50673i	0.160447	+	0.277903i	−0.774582	+	0.632474i	$0.782040\pi$
$938$	−41.5470	−	28.6286i	−1.35656	−	0.934758i
$939$		0			0
$940$	2.74342	+	7.19891i	0.0894804	+	0.234803i
$941$	1.11021	−	6.29630i	0.0361918	−	0.205254i	−0.961350	−	0.275330i	$-0.911213\pi$
$941$	1.11021	−	6.29630i	0.0361918	−	0.205254i	0.997542	+	0.0700759i	$0.0223242\pi$
$942$		0			0
$943$	−27.3138	−	32.5513i	−0.889459	−	1.06002i
$944$	−0.0889704	−	2.95860i	−0.00289574	−	0.0962943i
$945$		0			0
$946$	6.49378	−	6.59213i	0.211131	−	0.214329i
$947$	−2.56959	−	3.06232i	−0.0835006	−	0.0995121i	0.722677	−	0.691186i	$-0.242912\pi$
$947$	−2.56959	−	3.06232i	−0.0835006	−	0.0995121i	−0.806177	+	0.591674i	$0.798467\pi$
$948$		0			0
$949$	−15.1721	−	2.67525i	−0.492508	−	0.0868424i
$950$	21.5638	+	9.85875i	0.699623	+	0.319860i
$951$		0			0
$952$	23.2202	+	15.4907i	0.752571	+	0.502057i
$953$	−38.3667	+	22.1510i	−1.24282	+	0.717542i	−0.969667	−	0.244428i	$-0.921400\pi$
$953$	−38.3667	+	22.1510i	−1.24282	+	0.717542i	−0.273152	+	0.961971i	$0.588066\pi$
$954$		0			0
$955$	14.4052	−	24.9506i	0.466142	−	0.807382i
$956$	−3.03504	+	8.74554i	−0.0981603	+	0.282851i
$957$		0			0
$958$	0.271751	+	2.85852i	0.00877987	+	0.0923546i
$959$	31.7348	+	26.6286i	1.02477	+	0.859883i
$960$		0			0
$961$	−16.7611	−	6.10053i	−0.540680	−	0.196791i
$962$	−29.5345	+	8.15215i	−0.952232	+	0.262836i
$963$		0			0
$964$	47.2962	−	28.2627i	1.52331	−	0.910281i
$965$	1.34143	+	7.60761i	0.0431820	+	0.244897i
$966$		0			0
$967$	8.11445	+	22.2943i	0.260943	+	0.716935i	0.999104	+	0.0423110i	$0.0134720\pi$
$967$	8.11445	+	22.2943i	0.260943	+	0.716935i	−0.738161	+	0.674624i	$0.764306\pi$
$968$	13.9816	+	19.0394i	0.449387	+	0.611949i
$969$		0			0
$970$	−7.72703	−	0.617547i	−0.248100	−	0.0198282i
$971$		−	23.3729i		−	0.750071i	−0.927010	−	0.375036i	$-0.877631\pi$
$971$		−	23.3729i		−	0.750071i	0.927010	−	0.375036i	$-0.122369\pi$
$972$		0			0
$973$			6.16061i			0.197500i
$974$	0.865004	−	10.8233i	0.0277165	−	0.346802i
$975$		0			0
$976$	44.6915	+	6.50188i	1.43054	+	0.208120i
$977$	−17.9667	−	49.3632i	−0.574807	−	1.57927i	−0.796814	−	0.604224i	$-0.793483\pi$
$977$	−17.9667	−	49.3632i	−0.574807	−	1.57927i	0.222007	−	0.975045i	$-0.428739\pi$
$978$		0			0
$979$	0.0689371	+	0.390962i	0.00220324	+	0.0124952i
$980$	1.11004	−	0.663324i	0.0354589	−	0.0211891i
$981$		0			0
$982$	−6.85558	−	24.8372i	−0.218770	−	0.792586i
$983$	10.1837	+	3.70656i	0.324809	+	0.118221i	0.499278	−	0.866442i	$-0.333599\pi$
$983$	10.1837	+	3.70656i	0.324809	+	0.118221i	−0.174469	+	0.984663i	$0.555821\pi$
$984$		0			0
$985$	−5.67841	−	4.76475i	−0.180929	−	0.151817i
$986$	−27.0891	+	2.57528i	−0.862692	+	0.0820136i
$987$		0			0
$988$	47.7239	+	16.5620i	1.51830	+	0.526909i
$989$	−12.3882	+	21.4570i	−0.393923	+	0.682294i
$990$		0			0
$991$	37.1953	−	21.4747i	1.18155	−	0.682167i	0.225175	−	0.974318i	$-0.427705\pi$
$991$	37.1953	−	21.4747i	1.18155	−	0.682167i	0.956372	+	0.292152i	$0.0943712\pi$
$992$	−17.2425	−	11.1320i	−0.547448	−	0.353441i
$993$		0			0
$994$	−7.86297	+	17.1985i	−0.249398	+	0.545503i
$995$	2.62034	+	0.462037i	0.0830704	+	0.0146475i
$996$		0			0
$997$	27.5401	+	32.8210i	0.872204	+	1.03945i	0.998871	+	0.0475071i	$0.0151277\pi$
$997$	27.5401	+	32.8210i	0.872204	+	1.03945i	−0.126667	+	0.991945i	$0.540428\pi$
$998$	−0.782033	−	0.770366i	−0.0247548	−	0.0243855i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.v.b.611.31		192
3.2	odd	2		216.2.v.b.59.2	yes	192
8.3	odd	2	inner	648.2.v.b.611.16		192
12.11	even	2		864.2.bh.b.815.18		192
24.5	odd	2		864.2.bh.b.815.17		192
24.11	even	2		216.2.v.b.59.17	yes	192
27.11	odd	18	inner	648.2.v.b.35.16		192
27.16	even	9		216.2.v.b.11.17	yes	192
108.43	odd	18		864.2.bh.b.335.17		192
216.11	even	18	inner	648.2.v.b.35.31		192
216.43	odd	18		216.2.v.b.11.2	✓	192
216.205	even	18		864.2.bh.b.335.18		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.2	✓	192	216.43	odd	18
216.2.v.b.11.17	yes	192	27.16	even	9
216.2.v.b.59.2	yes	192	3.2	odd	2
216.2.v.b.59.17	yes	192	24.11	even	2
648.2.v.b.35.16		192	27.11	odd	18	inner
648.2.v.b.35.31		192	216.11	even	18	inner
648.2.v.b.611.16		192	8.3	odd	2	inner
648.2.v.b.611.31		192	1.1	even	1	trivial
864.2.bh.b.335.17		192	108.43	odd	18
864.2.bh.b.335.18		192	216.205	even	18
864.2.bh.b.815.17		192	24.5	odd	2
864.2.bh.b.815.18		192	12.11	even	2

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:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.v (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.40972 + 0.112665i) q^{2} +(1.97461 + 0.317652i) q^{4} +(-2.47648 + 0.901367i) q^{5} +(2.55949 - 0.451307i) q^{7} +(2.74786 + 0.670270i) q^{8} +(-3.59270 + 0.991660i) q^{10} +(-0.556608 + 1.52927i) q^{11} +(1.88389 - 2.24514i) q^{13} +(3.65901 - 0.347851i) q^{14} +(3.79819 + 1.25448i) q^{16} +(3.28845 + 1.89859i) q^{17} +(4.30904 + 7.46347i) q^{19} +(-5.17642 + 0.993190i) q^{20} +(-0.956956 + 2.09313i) q^{22} +(1.07009 - 6.06879i) q^{23} +(1.49029 - 1.25050i) q^{25} +(2.90871 - 2.95276i) q^{26} +(5.19736 - 0.0781292i) q^{28} +(-3.88174 + 3.25716i) q^{29} +(-3.57300 - 0.630016i) q^{31} +(5.21305 + 2.19639i) q^{32} +(4.42189 + 3.04697i) q^{34} +(-5.93174 + 3.42469i) q^{35} +(-6.40179 - 3.69607i) q^{37} +(5.23366 + 11.0069i) q^{38} +(-7.40919 + 0.816916i) q^{40} +(4.43232 - 5.28224i) q^{41} +(-3.77811 - 1.37512i) q^{43} +(-1.58486 + 2.84290i) q^{44} +(2.19227 - 8.43472i) q^{46} +(-0.253807 - 1.43941i) q^{47} +(-0.230541 + 0.0839100i) q^{49} +(2.24178 - 1.59495i) q^{50} +(4.43313 - 3.83485i) q^{52} -0.180986 q^{53} -4.28892i q^{55} +(7.33562 + 0.475421i) q^{56} +(-5.83912 + 4.15435i) q^{58} +(-0.253090 - 0.695359i) q^{59} +(11.1190 - 1.96057i) q^{61} +(-4.96594 - 1.29070i) q^{62} +(7.10148 + 3.68362i) q^{64} +(-2.64174 + 7.25812i) q^{65} +(-10.5159 - 8.82387i) q^{67} +(5.89033 + 4.79357i) q^{68} +(-8.74793 + 4.15955i) q^{70} +(-2.57253 + 4.45576i) q^{71} +(-2.62831 - 4.55236i) q^{73} +(-8.60830 - 5.93168i) q^{74} +(6.13789 + 16.1062i) q^{76} +(-0.734463 + 4.16534i) q^{77} +(-6.72831 - 8.01849i) q^{79} +(-10.5369 + 0.316864i) q^{80} +(6.84345 - 6.94710i) q^{82} +(-7.39656 - 8.81488i) q^{83} +(-9.85513 - 1.73773i) q^{85} +(-5.17114 - 2.36419i) q^{86} +(-2.55450 + 3.82914i) q^{88} +(0.211259 - 0.121971i) q^{89} +(3.80856 - 6.59662i) q^{91} +(4.04078 - 11.6436i) q^{92} +(-0.195625 - 2.05776i) q^{94} +(-17.3986 - 14.5992i) q^{95} +(1.95441 + 0.711348i) q^{97} +(-0.334451 + 0.0923156i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8} - 3 q^{10} + 30 q^{11} - 9 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} + 27 q^{20} - 18 q^{22} - 12 q^{25} - 12 q^{28} + 36 q^{32} + 12 q^{34} + 18 q^{35} + 102 q^{38} + 9 q^{40}+ \cdots - 162 q^{98}+O(q^{100}) \) 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8 - 3 * q^10 + 30 * q^11 - 9 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 + 27 * q^20 - 18 * q^22 - 12 * q^25 - 12 * q^28 + 36 * q^32 + 12 * q^34 + 18 * q^35 + 102 * q^38 + 9 * q^40 - 18 * q^41 - 42 * q^43 + 81 * q^44 - 3 * q^46 - 12 * q^49 - 57 * q^50 + 21 * q^52 + 69 * q^56 - 33 * q^58 + 84 * q^59 - 90 * q^62 - 51 * q^64 + 12 * q^65 + 30 * q^67 - 63 * q^68 - 33 * q^70 - 6 * q^73 - 51 * q^74 + 30 * q^76 - 12 * q^82 + 72 * q^83 - 42 * q^86 - 78 * q^88 - 144 * q^89 - 6 * q^91 + 3 * q^92 - 33 * q^94 - 42 * q^97 - 162 * q^98

Introduction

L-functions

Modular forms

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