LMFDB - Embedded newform 648.2.v.b.35.16

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			35.16
Character	$\chi$	$=$	648.35
Dual form			648.2.v.b.611.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.133842 - 1.40787i) q^{2} +(-1.96417 + 0.376862i) q^{4} +(2.47648 + 0.901367i) q^{5} +(-2.55949 - 0.451307i) q^{7} +(0.793459 + 2.71485i) q^{8} +(0.937547 - 3.60720i) q^{10} +(-0.556608 - 1.52927i) q^{11} +(-1.88389 - 2.24514i) q^{13} +(-0.292814 + 3.66382i) q^{14} +(3.71595 - 1.48044i) q^{16} +(3.28845 - 1.89859i) q^{17} +(4.30904 - 7.46347i) q^{19} +(-5.20394 - 0.837147i) q^{20} +(-2.07851 + 0.988309i) q^{22} +(-1.07009 - 6.06879i) q^{23} +(1.49029 + 1.25050i) q^{25} +(-2.90871 + 2.95276i) q^{26} +(5.19736 - 0.0781292i) q^{28} +(3.88174 + 3.25716i) q^{29} +(3.57300 - 0.630016i) q^{31} +(-2.58162 - 5.03341i) q^{32} +(-3.11309 - 4.37559i) q^{34} +(-5.93174 - 3.42469i) q^{35} +(6.40179 - 3.69607i) q^{37} +(-11.0843 - 5.06762i) q^{38} +(-0.482088 + 7.43849i) q^{40} +(4.43232 + 5.28224i) q^{41} +(-3.77811 + 1.37512i) q^{43} +(1.66960 + 2.79398i) q^{44} +(-8.40082 + 2.31880i) q^{46} +(0.253807 - 1.43941i) q^{47} +(-0.230541 - 0.0839100i) q^{49} +(1.56108 - 2.26550i) q^{50} +(4.54640 + 3.69987i) q^{52} +0.180986 q^{53} -4.28892i q^{55} +(-0.805618 - 7.30673i) q^{56} +(4.06611 - 5.90091i) q^{58} +(-0.253090 + 0.695359i) q^{59} +(-11.1190 - 1.96057i) q^{61} +(-1.36519 - 4.94598i) q^{62} +(-6.74085 + 4.30825i) q^{64} +(-2.64174 - 7.25812i) q^{65} +(-10.5159 + 8.82387i) q^{67} +(-5.74359 + 4.96845i) q^{68} +(-4.02760 + 8.80947i) q^{70} +(2.57253 + 4.45576i) q^{71} +(-2.62831 + 4.55236i) q^{73} +(-6.06040 - 8.51817i) q^{74} +(-5.65100 + 16.2835i) q^{76} +(0.734463 + 4.16534i) q^{77} +(6.72831 - 8.01849i) q^{79} +(10.5369 - 0.316864i) q^{80} +(6.84345 - 6.94710i) q^{82} +(-7.39656 + 8.81488i) q^{83} +(9.85513 - 1.73773i) q^{85} +(2.44165 + 5.13502i) q^{86} +(3.71009 - 2.72452i) q^{88} +(0.211259 + 0.121971i) q^{89} +(3.80856 + 6.59662i) q^{91} +(4.38894 + 11.5169i) q^{92} +(-2.06047 - 0.164673i) q^{94} +(17.3986 - 14.5992i) q^{95} +(1.95441 - 0.711348i) q^{97} +(-0.0872781 + 0.335801i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{18}\right)$

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 $

$2$	−0.133842	−	1.40787i	−0.0946403	−	0.995512i
$2$	−0.133842	−	1.40787i	−0.0946403	−	0.995512i
$3$		0			0
$3$		0			0
$4$	−1.96417	+	0.376862i	−0.982086	+	0.188431i
$5$	2.47648	+	0.901367i	1.10752	+	0.403103i	0.830082	−	0.557641i	$-0.188293\pi$
$5$	2.47648	+	0.901367i	1.10752	+	0.403103i	0.277435	+	0.960744i	$0.410516\pi$
$6$		0			0
$7$	−2.55949	−	0.451307i	−0.967396	−	0.170578i	−0.332438	−	0.943125i	$-0.607871\pi$
$7$	−2.55949	−	0.451307i	−0.967396	−	0.170578i	−0.634958	+	0.772547i	$0.718982\pi$
$8$	0.793459	+	2.71485i	0.280530	+	0.959845i
$9$		0			0
$10$	0.937547	−	3.60720i	0.296478	−	1.14070i
$11$	−0.556608	−	1.52927i	−0.167824	−	0.461091i	0.827061	−	0.562113i	$-0.190011\pi$
$11$	−0.556608	−	1.52927i	−0.167824	−	0.461091i	−0.994884	+	0.101021i	$0.967789\pi$
$12$		0			0
$13$	−1.88389	−	2.24514i	−0.522498	−	0.622689i	0.438672	−	0.898647i	$-0.355449\pi$
$13$	−1.88389	−	2.24514i	−0.522498	−	0.622689i	−0.961169	+	0.275959i	$0.911005\pi$
$14$	−0.292814	+	3.66382i	−0.0782577	+	0.979197i
$15$		0			0
$16$	3.71595	−	1.48044i	0.928988	−	0.370111i
$17$	3.28845	−	1.89859i	0.797567	−	0.460476i	−0.0450525	−	0.998985i	$-0.514346\pi$
$17$	3.28845	−	1.89859i	0.797567	−	0.460476i	0.842620	+	0.538509i	$0.181012\pi$
$18$		0			0
$19$	4.30904	−	7.46347i	0.988561	−	1.71224i	0.363666	−	0.931530i	$-0.381525\pi$
$19$	4.30904	−	7.46347i	0.988561	−	1.71224i	0.624895	−	0.780708i	$-0.285142\pi$
$20$	−5.20394	−	0.837147i	−1.16364	−	0.187192i
$21$		0			0
$22$	−2.07851	+	0.988309i	−0.443139	+	0.210708i
$23$	−1.07009	−	6.06879i	−0.223129	−	1.26543i	−0.866229	−	0.499647i	$-0.833463\pi$
$23$	−1.07009	−	6.06879i	−0.223129	−	1.26543i	0.643100	−	0.765783i	$-0.277648\pi$
$24$		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	$-0.121858\pi$
$29$	3.88174	+	3.25716i	0.720820	+	0.604840i	−0.206792	+	0.978385i	$0.566302\pi$
$30$		0			0
$31$	3.57300	−	0.630016i	0.641729	−	0.113154i	0.156692	−	0.987648i	$-0.449917\pi$
$31$	3.57300	−	0.630016i	0.641729	−	0.113154i	0.485037	+	0.874493i	$0.338806\pi$
$32$	−2.58162	−	5.03341i	−0.456369	−	0.889790i
$33$		0			0
$34$	−3.11309	−	4.37559i	−0.533891	−	0.750408i
$35$	−5.93174	−	3.42469i	−1.00265	−	0.578879i
$36$		0			0
$37$	6.40179	−	3.69607i	1.05245	−	0.607631i	0.129114	−	0.991630i	$-0.458787\pi$
$37$	6.40179	−	3.69607i	1.05245	−	0.607631i	0.923333	+	0.383999i	$0.125453\pi$
$38$	−11.0843	−	5.06762i	−1.79811	−	0.822077i
$39$		0			0
$40$	−0.482088	+	7.43849i	−0.0762248	+	1.17613i
$41$	4.43232	+	5.28224i	0.692212	+	0.824947i	0.991621	−	0.129178i	$-0.0412339\pi$
$41$	4.43232	+	5.28224i	0.692212	+	0.824947i	−0.299409	+	0.954125i	$0.596789\pi$
$42$		0			0
$43$	−3.77811	+	1.37512i	−0.576156	+	0.209704i	−0.613630	−	0.789594i	$-0.710291\pi$
$43$	−3.77811	+	1.37512i	−0.576156	+	0.209704i	0.0374734	+	0.999298i	$0.488069\pi$
$44$	1.66960	+	2.79398i	0.251701	+	0.421209i
$45$		0			0
$46$	−8.40082	+	2.31880i	−1.23863	+	0.341889i
$47$	0.253807	−	1.43941i	0.0370215	−	0.209960i	−0.960686	−	0.277639i	$-0.910448\pi$
$47$	0.253807	−	1.43941i	0.0370215	−	0.209960i	0.997707	+	0.0676790i	$0.0215594\pi$
$48$		0			0
$49$	−0.230541	−	0.0839100i	−0.0329344	−	0.0119871i
$50$	1.56108	−	2.26550i	0.220770	−	0.320390i
$51$		0			0
$52$	4.54640	+	3.69987i	0.630472	+	0.513079i
$53$	0.180986			0.0248604			0.0124302	−	0.999923i	$-0.496043\pi$
$53$	0.180986			0.0248604			0.0124302	+	0.999923i	$0.496043\pi$
$54$		0			0
$55$		−	4.28892i		−	0.578317i
$56$	−0.805618	−	7.30673i	−0.107655	−	0.976403i
$57$		0			0
$58$	4.06611	−	5.90091i	0.533906	−	0.774827i
$59$	−0.253090	+	0.695359i	−0.0329495	+	0.0905280i	−0.955077	−	0.296359i	$-0.904227\pi$
$59$	−0.253090	+	0.695359i	−0.0329495	+	0.0905280i	0.922127	+	0.386887i	$0.126450\pi$
$60$		0			0
$61$	−11.1190	−	1.96057i	−1.42364	−	0.251026i	−0.591817	−	0.806072i	$-0.701589\pi$
$61$	−11.1190	−	1.96057i	−1.42364	−	0.251026i	−0.831819	+	0.555047i	$0.812700\pi$
$62$	−1.36519	−	4.94598i	−0.173380	−	0.628140i
$63$		0			0
$64$	−6.74085	+	4.30825i	−0.842606	+	0.538531i
$65$	−2.64174	−	7.25812i	−0.327668	−	0.900259i
$66$		0			0
$67$	−10.5159	+	8.82387i	−1.28472	+	1.07801i	−0.292144	+	0.956374i	$0.594369\pi$
$67$	−10.5159	+	8.82387i	−1.28472	+	1.07801i	−0.992575	+	0.121633i	$0.961187\pi$
$68$	−5.74359	+	4.96845i	−0.696512	+	0.602513i
$69$		0			0
$70$	−4.02760	+	8.80947i	−0.481390	+	1.05293i
$71$	2.57253	+	4.45576i	0.305303	+	0.528801i	0.977329	−	0.211727i	$-0.0679088\pi$
$71$	2.57253	+	4.45576i	0.305303	+	0.528801i	−0.672025	+	0.740528i	$0.734575\pi$
$72$		0			0
$73$	−2.62831	+	4.55236i	−0.307620	+	0.532814i	−0.977841	−	0.209348i	$-0.932866\pi$
$73$	−2.62831	+	4.55236i	−0.307620	+	0.532814i	0.670221	+	0.742161i	$0.266199\pi$
$74$	−6.06040	−	8.51817i	−0.704507	−	0.990217i
$75$		0			0
$76$	−5.65100	+	16.2835i	−0.648214	+	1.86784i
$77$	0.734463	+	4.16534i	0.0836998	+	0.474685i
$78$		0			0
$79$	6.72831	−	8.01849i	0.756994	−	0.902151i	−0.240660	−	0.970610i	$-0.577364\pi$
$79$	6.72831	−	8.01849i	0.756994	−	0.902151i	0.997654	+	0.0684588i	$0.0218082\pi$
$80$	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	−0.999893	−	0.0146072i	$-0.995350\pi$
$83$	−7.39656	+	8.81488i	−0.811878	+	0.967559i	0.188015	+	0.982166i	$0.439795\pi$
$84$		0			0
$85$	9.85513	−	1.73773i	1.06894	−	0.188483i
$86$	2.44165	+	5.13502i	0.263290	+	0.553724i
$87$		0			0
$88$	3.71009	−	2.72452i	0.395497	−	0.290435i
$89$	0.211259	+	0.121971i	0.0223934	+	0.0129289i	0.511155	−	0.859489i	$-0.329218\pi$
$89$	0.211259	+	0.121971i	0.0223934	+	0.0129289i	−0.488761	+	0.872417i	$0.662551\pi$
$90$		0			0
$91$	3.80856	+	6.59662i	0.399245	+	0.691513i
$92$	4.38894	+	11.5169i	0.457579	+	1.20072i
$93$		0			0
$94$	−2.06047	−	0.164673i	−0.212521	−	0.0169847i
$95$	17.3986	−	14.5992i	1.78506	−	1.49784i
$96$		0			0
$97$	1.95441	−	0.711348i	0.198441	−	0.0722264i	−0.240888	−	0.970553i	$-0.577439\pi$
$97$	1.95441	−	0.711348i	0.198441	−	0.0722264i	0.439329	+	0.898326i	$0.355216\pi$
$98$	−0.0872781	+	0.335801i	−0.00881642	+	0.0339211i
$99$		0			0
$100$	−3.39846	−	1.89457i	−0.339846	−	0.189457i
$101$	−3.09813	+	17.5704i	−0.308276	+	1.74832i	0.299394	+	0.954130i	$0.403216\pi$
$101$	−3.09813	+	17.5704i	−0.308276	+	1.74832i	−0.607670	+	0.794190i	$0.707896\pi$
$102$		0			0
$103$	4.29301	−	11.7949i	0.423003	−	1.16219i	−0.526977	−	0.849879i	$-0.676675\pi$
$103$	4.29301	−	11.7949i	0.423003	−	1.16219i	0.949980	−	0.312311i	$-0.101103\pi$
$104$	4.60042	−	6.89591i	0.451108	−	0.676200i
$105$		0			0
$106$	−0.0242235	−	0.254804i	−0.00235279	−	0.0247488i
$107$			10.9395i			1.05757i	0.848757	+	0.528783i	$0.177351\pi$
$107$			10.9395i			1.05757i	−0.848757	+	0.528783i	$0.822649\pi$
$108$		0			0
$109$			6.35577i			0.608772i	0.952549	+	0.304386i	$0.0984513\pi$
$109$			6.35577i			0.608772i	−0.952549	+	0.304386i	$0.901549\pi$
$110$	−6.03822	+	0.574035i	−0.575721	+	0.0547321i
$111$		0			0
$112$	−10.1791	+	2.11215i	−0.961832	+	0.199579i
$113$	1.20684	−	3.31577i	0.113530	−	0.311921i	−0.869895	−	0.493237i	$-0.835813\pi$
$113$	1.20684	−	3.31577i	0.113530	−	0.311921i	0.983425	+	0.181316i	$0.0580356\pi$
$114$		0			0
$115$	2.82014	−	15.9938i	0.262979	−	1.49143i
$116$	−8.85190	−	4.93475i	−0.821878	−	0.458180i
$117$		0			0
$118$	1.01285	+	0.263249i	0.0932400	+	0.0242340i
$119$	−9.27361	+	3.37532i	−0.850110	+	0.309415i
$120$		0			0
$121$	6.39764	−	5.36826i	0.581604	−	0.488024i
$122$	−1.27204	+	15.9164i	−0.115165	+	1.44100i
$123$		0			0
$124$	−6.78056	+	2.58399i	−0.608912	+	0.232049i
$125$	−4.02503	−	6.97155i	−0.360009	−	0.623554i
$126$		0			0
$127$	15.7942	+	9.11876i	1.40150	+	0.809159i	0.994547	−	0.104288i	$-0.0332563\pi$
$127$	15.7942	+	9.11876i	1.40150	+	0.809159i	0.406958	+	0.913447i	$0.366590\pi$
$128$	6.96764	+	8.91358i	0.615858	+	0.787857i
$129$		0			0
$130$	−9.86489	+	4.69066i	−0.865208	+	0.411398i
$131$	−4.10519	+	0.723856i	−0.358672	+	0.0632436i	−0.350081	−	0.936719i	$-0.613846\pi$
$131$	−4.10519	+	0.723856i	−0.358672	+	0.0632436i	−0.00859153	+	0.999963i	$0.502735\pi$
$132$		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	−0.123347	−	0.992364i	$-0.539363\pi$
$137$	10.2458	−	12.2105i	0.875360	−	1.04321i	0.998706	−	0.0508494i	$-0.0161928\pi$
$138$		0			0
$139$	−0.411616	−	2.33439i	−0.0349128	−	0.198000i	0.962363	−	0.271769i	$-0.0876086\pi$
$139$	−0.411616	−	2.33439i	−0.0349128	−	0.198000i	−0.997275	+	0.0737683i	$0.976497\pi$
$140$	12.9416	+	4.49124i	1.09377	+	0.379579i
$141$		0			0
$142$	5.92880	−	4.21815i	0.497534	−	0.353979i
$143$	−2.38482	+	4.13064i	−0.199429	+	0.345421i
$144$		0			0
$145$	6.67716	+	11.5652i	0.554508	+	0.960436i
$146$	6.76089	+	3.09101i	0.559535	+	0.255814i
$147$		0			0
$148$	−11.1813	+	9.67232i	−0.919098	+	0.795060i
$149$	12.2426	−	10.2728i	1.00295	−	0.841578i	0.0155632	−	0.999879i	$-0.495046\pi$
$149$	12.2426	−	10.2728i	1.00295	−	0.841578i	0.987391	+	0.158300i	$0.0506014\pi$
$150$		0			0
$151$	−0.806403	−	2.21557i	−0.0656242	−	0.180301i	0.902546	−	0.430593i	$-0.141696\pi$
$151$	−0.806403	−	2.21557i	−0.0656242	−	0.180301i	−0.968170	+	0.250292i	$0.919473\pi$
$152$	23.6813	+	5.77644i	1.92080	+	0.468531i
$153$		0			0
$154$	5.76595	−	1.59152i	0.464633	−	0.128248i
$155$	9.41635	+	1.66036i	0.756339	+	0.133363i
$156$		0			0
$157$	−0.284046	+	0.780410i	−0.0226693	+	0.0622835i	−0.950511	−	0.310691i	$-0.899440\pi$
$157$	−0.284046	+	0.780410i	−0.0226693	+	0.0622835i	0.927842	+	0.372974i	$0.121662\pi$
$158$	−12.1895	−	8.39936i	−0.969744	−	0.668217i
$159$		0			0
$160$	−1.85638	−	14.7922i	−0.146760	−	1.16942i
$161$			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	$0.645447\pi$
$164$	−10.6965	−	8.70485i	−0.835258	−	0.679735i
$165$		0			0
$166$	13.4001	+	9.23357i	1.04005	+	0.716664i
$167$	−16.4192	−	5.97611i	−1.27056	−	0.462445i	−0.383260	−	0.923641i	$-0.625199\pi$
$167$	−16.4192	−	5.97611i	−1.27056	−	0.462445i	−0.887299	+	0.461195i	$0.847421\pi$
$168$		0			0
$169$	0.765842	−	4.34331i	0.0589110	−	0.334101i
$170$	−3.76551	−	13.6421i	−0.288802	−	1.04630i
$171$		0			0
$172$	6.90263	−	4.12480i	0.526321	−	0.314513i
$173$	17.4791	−	6.36186i	1.32891	−	0.483683i	0.422606	−	0.906313i	$-0.361115\pi$
$173$	17.4791	−	6.36186i	1.32891	−	0.483683i	0.906302	+	0.422630i	$0.138893\pi$
$174$		0			0
$175$	−3.25003	−	3.87323i	−0.245679	−	0.292789i
$176$	−4.33232	−	4.85865i	−0.326561	−	0.366235i
$177$		0			0
$178$	0.143443	−	0.313749i	0.0107515	−	0.0235165i
$179$	6.13650	−	3.54291i	0.458663	−	0.264809i	−0.252819	−	0.967514i	$-0.581358\pi$
$179$	6.13650	−	3.54291i	0.458663	−	0.264809i	0.711482	+	0.702704i	$0.248024\pi$
$180$		0			0
$181$	0.129860	+	0.0749748i	0.00965242	+	0.00557283i	0.504818	−	0.863226i	$-0.331559\pi$
$181$	0.129860	+	0.0749748i	0.00965242	+	0.00557283i	−0.495166	+	0.868798i	$0.664893\pi$
$182$	8.77741	−	6.24484i	0.650625	−	0.462898i
$183$		0			0
$184$	15.6268	−	7.72047i	1.15202	−	0.569161i
$185$	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	$-0.148347\pi$
$191$	8.37441	+	7.02696i	0.605951	+	0.508453i	−0.287401	+	0.957810i	$0.592791\pi$
$192$		0			0
$193$	0.508999	+	2.88668i	0.0366385	+	0.207788i	0.997631	−	0.0687854i	$-0.0219124\pi$
$193$	0.508999	+	2.88668i	0.0366385	+	0.207788i	−0.960993	+	0.276573i	$0.910801\pi$
$194$	−1.26306	−	2.65634i	−0.0906827	−	0.190714i
$195$		0			0
$196$	0.484445	+	0.0779317i	0.0346032	+	0.00556655i
$197$	−1.40635	+	2.43587i	−0.100198	+	0.173548i	−0.911766	−	0.410710i	$-0.865281\pi$
$197$	−1.40635	+	2.43587i	−0.100198	+	0.173548i	0.811568	+	0.584258i	$0.198614\pi$
$198$		0			0
$199$	0.874354	−	0.504808i	0.0619813	−	0.0357849i	−0.468689	−	0.883363i	$-0.655274\pi$
$199$	0.874354	−	0.504808i	0.0619813	−	0.0357849i	0.530670	+	0.847578i	$0.321940\pi$
$200$	−2.21245	+	5.03815i	−0.156444	+	0.356251i
$201$		0			0
$202$	25.1514	+	2.01011i	1.76965	+	0.141431i
$203$	−8.46528	−	10.0885i	−0.594146	−	0.708076i
$204$		0			0
$205$	6.21535	+	17.0765i	0.434099	+	1.19268i
$206$	−17.1803	−	4.46533i	−1.19701	−	0.311114i
$207$		0			0
$208$	−10.3243	−	5.55382i	−0.715858	−	0.385088i
$209$	−13.8121	−	2.43544i	−0.955402	−	0.168463i
$210$		0			0
$211$	−3.98399	−	1.45005i	−0.274269	−	0.0998257i	0.201224	−	0.979545i	$-0.435508\pi$
$211$	−3.98399	−	1.45005i	−0.274269	−	0.0998257i	−0.475493	+	0.879720i	$0.657730\pi$
$212$	−0.355488	+	0.0682068i	−0.0244150	+	0.00468447i
$213$		0			0
$214$	15.4014	−	1.46417i	1.05282	−	0.100088i
$215$	−10.5959			−0.722636
$216$		0			0
$217$	−9.42938			−0.640108
$218$	8.94807	−	0.850666i	0.606040	−	0.0576144i
$219$		0			0
$220$	1.61633	+	8.42417i	0.108973	+	0.567958i
$221$	−10.4577	−	3.80629i	−0.703460	−	0.256039i
$222$		0			0
$223$	−15.7442	−	2.77613i	−1.05431	−	0.185903i	−0.380480	−	0.924789i	$-0.624241\pi$
$223$	−15.7442	−	2.77613i	−1.05431	−	0.185903i	−0.673831	+	0.738886i	$0.735352\pi$
$224$	4.33600	+	14.0481i	0.289711	+	0.938626i
$225$		0			0
$226$	−4.82969	−	1.25528i	−0.321266	−	0.0835002i
$227$	−0.588042	−	1.61563i	−0.0390297	−	0.107233i	0.918647	−	0.395080i	$-0.129283\pi$
$227$	−0.588042	−	1.61563i	−0.0390297	−	0.107233i	−0.957677	+	0.287846i	$0.907061\pi$
$228$		0			0
$229$	5.91992	+	7.05508i	0.391199	+	0.466213i	0.925316	−	0.379198i	$-0.123800\pi$
$229$	5.91992	+	7.05508i	0.391199	+	0.466213i	−0.534116	+	0.845411i	$0.679356\pi$
$230$	−22.8946	−	1.82974i	−1.50962	−	0.120650i
$231$		0			0
$232$	−5.76272	+	13.1228i	−0.378341	+	0.861552i
$233$	−16.7671	+	9.68050i	−1.09845	+	0.634191i	−0.935814	−	0.352495i	$-0.885333\pi$
$233$	−16.7671	+	9.68050i	−1.09845	+	0.634191i	−0.162637	+	0.986686i	$0.552000\pi$
$234$		0			0
$235$	1.92599	−	3.33590i	0.125637	−	0.217610i
$236$	0.235058	−	1.46118i	0.0153010	−	0.0951150i
$237$		0			0
$238$	5.99319	+	12.6042i	0.388481	+	0.817012i
$239$	0.803749	+	4.55829i	0.0519902	+	0.294851i	0.999706	−	0.0242659i	$-0.00772482\pi$
$239$	0.803749	+	4.55829i	0.0519902	+	0.294851i	−0.947715	+	0.319117i	$0.896614\pi$
$240$		0			0
$241$	21.1035	+	17.7079i	1.35939	+	1.14067i	0.976169	+	0.217012i	$0.0696312\pi$
$241$	21.1035	+	17.7079i	1.35939	+	1.14067i	0.383226	+	0.923655i	$0.374813\pi$
$242$	−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
$248$	4.54543	+	9.20027i	0.288635	+	0.584218i
$249$		0			0
$250$	−9.27629	+	6.59978i	−0.586684	+	0.417407i
$251$	12.0234	+	6.94172i	0.758911	+	0.438158i	0.828905	−	0.559390i	$-0.188964\pi$
$251$	12.0234	+	6.94172i	0.758911	+	0.438158i	−0.0699933	+	0.997547i	$0.522298\pi$
$252$		0			0
$253$	−8.68518	+	5.01439i	−0.546033	+	0.315252i
$254$	10.7241	−	23.4565i	0.672888	−	1.47179i
$255$		0			0
$256$	11.6166	−	11.0025i	0.726036	−	0.687657i
$257$	1.09064	+	1.29978i	0.0680325	+	0.0810779i	0.798987	−	0.601348i	$-0.205369\pi$
$257$	1.09064	+	1.29978i	0.0680325	+	0.0810779i	−0.730955	+	0.682426i	$0.760925\pi$
$258$		0			0
$259$	−18.0534	+	6.57089i	−1.12178	+	0.408295i
$260$	7.92415	+	13.2606i	0.491435	+	0.822390i
$261$		0			0
$262$	1.56854	+	5.68268i	0.0969046	+	0.351077i
$263$	−0.720517	+	4.08625i	−0.0444290	+	0.251969i	−0.998931	−	0.0462368i	$-0.985277\pi$
$263$	−0.720517	+	4.08625i	−0.0444290	+	0.251969i	0.954502	+	0.298206i	$0.0963882\pi$
$264$		0			0
$265$	0.448210	+	0.163135i	0.0275333	+	0.0100213i
$266$	26.0831	+	17.9730i	1.59926	+	1.10199i
$267$		0			0
$268$	17.3296	−	21.2946i	1.05858	−	1.30078i
$269$	−31.4461			−1.91730			−0.958650	−	0.284588i	$-0.908143\pi$
$269$	−31.4461			−1.91730			−0.958650	+	0.284588i	$0.908143\pi$
$270$		0			0
$271$			28.1714i			1.71129i	0.517564	+	0.855644i	$0.326839\pi$
$271$			28.1714i			1.71129i	−0.517564	+	0.855644i	$0.673161\pi$
$272$	9.40898	−	11.9234i	0.570503	−	0.722965i
$273$		0			0
$274$	−18.5621	−	12.7905i	−1.12137	−	0.772701i
$275$	1.08285	−	2.97510i	0.0652981	−	0.179405i
$276$		0			0
$277$	−24.3185	−	4.28801i	−1.46116	−	0.257641i	−0.614136	−	0.789201i	$-0.710495\pi$
$277$	−24.3185	−	4.28801i	−1.46116	−	0.257641i	−0.847021	+	0.531559i	$0.821606\pi$
$278$	−3.23142	+	0.891939i	−0.193808	+	0.0534949i
$279$		0			0
$280$	4.59094	−	18.8212i	0.274361	−	1.12478i
$281$	6.58678	+	18.0970i	0.392935	+	1.07958i	0.965655	+	0.259828i	$0.0836659\pi$
$281$	6.58678	+	18.0970i	0.392935	+	1.07958i	−0.572720	+	0.819751i	$0.694112\pi$
$282$		0			0
$283$	6.85978	−	5.75604i	0.407772	−	0.342161i	−0.415717	−	0.909494i	$-0.636469\pi$
$283$	6.85978	−	5.75604i	0.407772	−	0.342161i	0.823488	+	0.567333i	$0.192025\pi$
$284$	−6.73210	−	7.78239i	−0.399477	−	0.461800i
$285$		0			0
$286$	6.13457	+	2.80466i	0.362745	+	0.165843i
$287$	−8.96057	−	15.5202i	−0.528926	−	0.916126i
$288$		0			0
$289$	−1.29071	+	2.23558i	−0.0759243	+	0.131505i
$290$	15.3885	−	10.9484i	0.903646	−	0.642915i
$291$		0			0
$292$	3.44684	−	9.93214i	0.201711	−	0.581234i
$293$	3.69497	+	20.9552i	0.215863	+	1.22422i	0.879403	+	0.476078i	$0.157942\pi$
$293$	3.69497	+	20.9552i	0.215863	+	1.22422i	−0.663540	+	0.748140i	$0.730947\pi$
$294$		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
$302$	−3.01130	+	1.43184i	−0.173281	+	0.0823933i
$303$		0			0
$304$	4.96291	−	34.1132i	0.284643	−	1.95653i
$305$	−25.7687	−	14.8776i	−1.47551	−	0.851888i
$306$		0			0
$307$	4.48896	+	7.77511i	0.256199	+	0.443749i	0.965220	−	0.261438i	$-0.0841966\pi$
$307$	4.48896	+	7.77511i	0.256199	+	0.443749i	−0.709022	+	0.705187i	$0.750863\pi$
$308$	−3.01237	−	7.90467i	−0.171646	−	0.450410i
$309$		0			0
$310$	1.07726	−	13.4792i	0.0611843	−	0.765566i
$311$	13.0417	−	10.9433i	0.739525	−	0.620535i	−0.193185	−	0.981162i	$-0.561882\pi$
$311$	13.0417	−	10.9433i	0.739525	−	0.620535i	0.932710	+	0.360627i	$0.117437\pi$
$312$		0			0
$313$	−9.04413	+	3.29179i	−0.511204	+	0.186063i	−0.584727	−	0.811230i	$-0.698798\pi$
$313$	−9.04413	+	3.29179i	−0.511204	+	0.186063i	0.0735224	+	0.997294i	$0.476576\pi$
$314$	1.13673	+	0.295447i	0.0641494	+	0.0166731i
$315$		0			0
$316$	−10.1937	+	18.2853i	−0.573441	+	1.02863i
$317$	1.05306	−	5.97220i	0.0591457	−	0.335432i	−0.940849	−	0.338827i	$-0.889970\pi$
$317$	1.05306	−	5.97220i	0.0591457	−	0.335432i	0.999994	+	0.00339548i	$0.00108082\pi$
$318$		0			0
$319$	2.82047	−	7.74917i	0.157916	−	0.433870i
$320$	−20.5769	+	4.59334i	−1.15028	+	0.256775i
$321$		0			0
$322$	22.5483	−	2.14360i	1.25657	−	0.119458i
$323$		−	32.7244i		−	1.82083i
$324$		0			0
$325$		−	5.70173i		−	0.316275i
$326$	1.50782	+	15.8607i	0.0835107	+	0.878440i
$327$		0			0
$328$	−10.8236	+	16.2243i	−0.597635	+	0.895839i
$329$	−1.29923	+	3.56961i	−0.0716290	+	0.196799i
$330$		0			0
$331$	0.638218	−	3.61951i	0.0350796	−	0.198946i	−0.962231	−	0.272233i	$-0.912238\pi$
$331$	0.638218	−	3.61951i	0.0350796	−	0.198946i	0.997311	+	0.0732869i	$0.0233489\pi$
$332$	11.2061	−	20.1014i	0.615017	−	1.10321i
$333$		0			0
$334$	−6.21599	+	23.9159i	−0.340124	+	1.30862i
$335$	−33.9960	+	12.3735i	−1.85740	+	0.676037i
$336$		0			0
$337$	14.8826	−	12.4880i	0.810707	−	0.680264i	−0.140070	−	0.990142i	$-0.544733\pi$
$337$	14.8826	−	12.4880i	0.810707	−	0.680264i	0.950776	+	0.309878i	$0.100288\pi$
$338$	−6.21730	−	0.496888i	−0.338176	−	0.0270272i
$339$		0			0
$340$	−18.7023	+	7.12722i	−1.01427	+	0.386528i
$341$	−2.95222	−	5.11340i	−0.159872	−	0.276906i
$342$		0			0
$343$	16.3076	+	9.41522i	0.880530	+	0.508374i
$344$	−6.73102	−	9.16591i	−0.362912	−	0.494193i
$345$		0			0
$346$	−11.2961	−	23.7567i	−0.607280	−	1.27717i
$347$	−14.8923	+	2.62591i	−0.799458	+	0.140966i	−0.558430	−	0.829552i	$-0.688596\pi$
$347$	−14.8923	+	2.62591i	−0.799458	+	0.140966i	−0.241029	+	0.970518i	$0.577485\pi$
$348$		0			0
$349$	14.4505	−	17.2214i	0.773518	−	0.921843i	−0.225104	−	0.974335i	$-0.572272\pi$
$349$	14.4505	−	17.2214i	0.773518	−	0.921843i	0.998621	+	0.0524923i	$0.0167165\pi$
$350$	−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	−0.280648	−	0.959811i	$-0.590549\pi$
$353$	13.4020	−	15.9719i	0.713316	−	0.850096i	0.993963	+	0.109715i	$0.0349937\pi$
$354$		0			0
$355$	2.35457	+	13.3534i	0.124967	+	0.708725i
$356$	−0.460916	−	0.159956i	−0.0244285	−	0.00847764i
$357$		0			0
$358$	−5.80926	−	8.16517i	−0.307029	−	0.431543i
$359$	−5.43854	+	9.41983i	−0.287035	+	0.497159i	−0.973101	−	0.230380i	$-0.926003\pi$
$359$	−5.43854	+	9.41983i	−0.287035	+	0.497159i	0.686066	+	0.727540i	$0.259336\pi$
$360$		0			0
$361$	−27.6356	−	47.8663i	−1.45451	−	2.51928i
$362$	0.0881737	−	0.192860i	0.00463431	−	0.0101365i
$363$		0			0
$364$	−9.96668	−	11.5216i	−0.522396	−	0.603896i
$365$	−10.6123	+	8.90479i	−0.555474	+	0.466098i
$366$		0			0
$367$	3.96735	+	10.9002i	0.207094	+	0.568985i	0.999139	−	0.0414764i	$-0.0132061\pi$
$367$	3.96735	+	10.9002i	0.207094	+	0.568985i	−0.792046	+	0.610462i	$0.790984\pi$
$368$	−12.9609	−	20.9671i	−0.675634	−	1.09299i
$369$		0			0
$370$	−7.33050	−	26.5578i	−0.381094	−	1.38067i
$371$	−0.463232	−	0.0816804i	−0.0240498	−	0.00424063i
$372$		0			0
$373$	1.65913	−	4.55843i	0.0859066	−	0.236027i	−0.889299	−	0.457326i	$-0.848807\pi$
$373$	1.65913	−	4.55843i	0.0859066	−	0.236027i	0.975206	+	0.221299i	$0.0710297\pi$
$374$	−4.95868	+	7.19624i	−0.256407	+	0.372109i
$375$		0			0
$376$	4.10917	−	0.453065i	0.211914	−	0.0233650i
$377$		−	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	$0.198794\pi$
$380$	−28.6720	+	35.2321i	−1.47084	+	1.80737i
$381$		0			0
$382$	8.77218	−	12.7305i	0.448824	−	0.651351i
$383$	5.33286	+	1.94100i	0.272496	+	0.0991805i	0.474654	−	0.880172i	$-0.342573\pi$
$383$	5.33286	+	1.94100i	0.272496	+	0.0991805i	−0.202158	+	0.979353i	$0.564795\pi$
$384$		0			0
$385$	−1.93562	+	10.9774i	−0.0986482	+	0.559462i
$386$	3.99593	−	1.10296i	0.203387	−	0.0561392i
$387$		0			0
$388$	−3.57072	+	2.13375i	−0.181276	+	0.108325i
$389$	7.70166	−	2.80317i	0.390490	−	0.142127i	−0.139311	−	0.990249i	$-0.544489\pi$
$389$	7.70166	−	2.80317i	0.390490	−	0.142127i	0.529801	+	0.848122i	$0.322267\pi$
$390$		0			0
$391$	−15.0411	−	17.9253i	−0.760660	−	0.906520i
$392$	0.0448785	−	0.692464i	0.00226671	−	0.0349747i
$393$		0			0
$394$	3.61760	+	1.65393i	0.182252	+	0.0833237i
$395$	23.8902	−	13.7930i	1.20204	−	0.694001i
$396$		0			0
$397$	−25.2112	−	14.5557i	−1.26532	−	0.730531i	−0.291218	−	0.956657i	$-0.594061\pi$
$397$	−25.2112	−	14.5557i	−1.26532	−	0.730531i	−0.974098	+	0.226126i	$0.927394\pi$
$398$	−0.827727	−	1.16341i	−0.0414902	−	0.0583164i
$399$		0			0
$400$	7.38915	+	2.44052i	0.369458	+	0.122026i
$401$	−13.6729	+	2.41090i	−0.682792	+	0.120395i	−0.504276	−	0.863542i	$-0.668241\pi$
$401$	−13.6729	+	2.41090i	−0.682792	+	0.120395i	−0.178516	+	0.983937i	$0.557130\pi$
$402$		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	−0.970229	−	0.242190i	$-0.922134\pi$
$409$	−2.85854	−	16.2116i	−0.141346	−	0.801613i	0.828883	−	0.559422i	$-0.188977\pi$
$410$	23.2096	−	11.0359i	1.14624	−	0.545025i
$411$		0			0
$412$	−3.98715	+	24.7852i	−0.196433	+	1.22108i
$413$	0.961601	−	1.66554i	0.0473173	−	0.0819559i
$414$		0			0
$415$	−26.2629	+	15.1629i	−1.28920	+	0.744318i
$416$	−6.43721	+	15.2785i	−0.315610	+	0.749090i
$417$		0			0
$418$	−1.58015	+	19.7715i	−0.0772875	+	0.967057i
$419$	−10.4296	−	12.4295i	−0.509520	−	0.607223i	0.448549	−	0.893758i	$-0.351941\pi$
$419$	−10.4296	−	12.4295i	−0.509520	−	0.607223i	−0.958070	+	0.286535i	$0.907496\pi$
$420$		0			0
$421$	0.181389	+	0.498362i	0.00884036	+	0.0242887i	0.944034	−	0.329847i	$-0.106997\pi$
$421$	0.181389	+	0.498362i	0.00884036	+	0.0242887i	−0.935194	+	0.354136i	$0.884775\pi$
$422$	−1.50826	+	5.80300i	−0.0734208	+	0.282485i
$423$		0			0
$424$	0.143605	+	0.491351i	0.00697409	+	0.0238621i
$425$	7.27495	+	1.28277i	0.352887	+	0.0622235i
$426$		0			0
$427$	27.5740	+	10.0361i	1.33440	+	0.485682i
$428$	−4.12270	−	21.4872i	−0.199278	−	1.03862i
$429$		0			0
$430$	1.41817	+	14.9176i	0.0683905	+	0.719392i
$431$	12.2920			0.592084			0.296042	−	0.955175i	$-0.404333\pi$
$431$	12.2920			0.592084			0.296042	+	0.955175i	$0.404333\pi$
$432$		0			0
$433$	14.6907			0.705991			0.352996	−	0.935625i	$-0.385163\pi$
$433$	14.6907			0.705991			0.352996	+	0.935625i	$0.385163\pi$
$434$	1.26204	+	13.2753i	0.0605800	+	0.637235i
$435$		0			0
$436$	−2.39525	−	12.4838i	−0.114712	−	0.597867i
$437$	−49.9053	−	18.1640i	−2.38729	−	0.868904i
$438$		0			0
$439$	28.8488	+	5.08682i	1.37688	+	0.242781i	0.812609	−	0.582810i	$-0.198047\pi$
$439$	28.8488	+	5.08682i	1.37688	+	0.242781i	0.564270	+	0.825591i	$0.309158\pi$
$440$	11.6438	−	3.40308i	0.555095	−	0.162235i
$441$		0			0
$442$	−3.95907	+	15.2325i	−0.188314	+	0.724534i
$443$	11.6096	+	31.8970i	0.551588	+	1.51547i	0.831543	+	0.555461i	$0.187458\pi$
$443$	11.6096	+	31.8970i	0.551588	+	1.51547i	−0.279955	+	0.960013i	$0.590320\pi$
$444$		0			0
$445$	0.413240	+	0.492480i	0.0195895	+	0.0233458i
$446$	−1.80119	+	22.5373i	−0.0852887	+	1.06717i
$447$		0			0
$448$	19.1975	−	7.98473i	0.906995	−	0.377243i
$449$	15.4011	−	8.89184i	0.726823	−	0.419632i	−0.0904355	−	0.995902i	$-0.528826\pi$
$449$	15.4011	−	8.89184i	0.726823	−	0.419632i	0.817259	+	0.576271i	$0.195493\pi$
$450$		0			0
$451$	5.61089	−	9.71834i	0.264206	−	0.457619i
$452$	−1.12086	+	6.96756i	−0.0527207	+	0.327726i
$453$		0			0
$454$	−2.19589	+	1.04412i	−0.103058	+	0.0490031i
$455$	3.48587	+	19.7693i	0.163420	+	0.926800i
$456$		0			0
$457$	9.21939	+	7.73598i	0.431265	+	0.361874i	0.832429	−	0.554132i	$-0.186950\pi$
$457$	9.21939	+	7.73598i	0.431265	+	0.361874i	−0.401164	+	0.916006i	$0.631394\pi$
$458$	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	$-0.152512\pi$
$461$	12.6139	+	10.5843i	0.587487	+	0.492960i	−0.299909	+	0.953968i	$0.596956\pi$
$462$		0			0
$463$	3.83957	−	0.677019i	0.178440	−	0.0314638i	−0.0837142	−	0.996490i	$-0.526678\pi$
$463$	3.83957	−	0.677019i	0.178440	−	0.0314638i	0.262154	+	0.965026i	$0.415567\pi$
$464$	19.2464	+	6.35676i	0.893491	+	0.295105i
$465$		0			0
$466$	15.8730	+	22.3102i	0.735302	+	1.03350i
$467$	8.38005	+	4.83822i	0.387782	+	0.223886i	0.681199	−	0.732098i	$-0.261459\pi$
$467$	8.38005	+	4.83822i	0.387782	+	0.223886i	−0.293416	+	0.955985i	$0.594792\pi$
$468$		0			0
$469$	30.8975	−	17.8387i	1.42672	−	0.823715i
$470$	−4.95428	−	2.26505i	−0.228524	−	0.104479i
$471$		0			0
$472$	−2.08861	−	0.135363i	−0.0961362	−	0.00623058i
$473$	4.20585	+	5.01234i	0.193385	+	0.230468i
$474$		0			0
$475$	15.7548	−	5.73429i	0.722881	−	0.263107i
$476$	16.9429	−	10.1246i	0.776579	−	0.464059i
$477$		0			0
$478$	6.30988	−	1.74166i	0.288607	−	0.0796616i
$479$	−0.352574	+	1.99955i	−0.0161095	+	0.0913616i	−0.991802	−	0.127780i	$-0.959215\pi$
$479$	−0.352574	+	1.99955i	−0.0161095	+	0.0913616i	0.975693	+	0.219142i	$0.0703258\pi$
$480$		0			0
$481$	−20.3585	−	7.40988i	−0.928266	−	0.337861i
$482$	22.1059	−	32.0809i	1.00689	−	1.46125i
$483$		0			0
$484$	−10.5430	+	12.9552i	−0.479226	+	0.588874i
$485$	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	$-0.0556544\pi$
$488$	−3.49977	−	31.7420i	−0.158427	−	1.43689i
$489$		0			0
$490$	−0.518823	+	0.752937i	−0.0234380	+	0.0340142i
$491$	−6.23136	+	17.1205i	−0.281217	+	0.772638i	0.716001	+	0.698100i	$0.245971\pi$
$491$	−6.23136	+	17.1205i	−0.281217	+	0.772638i	−0.997218	+	0.0745389i	$0.976251\pi$
$492$		0			0
$493$	18.9489	+	3.34121i	0.853417	+	0.150480i
$494$	9.50412	+	34.4326i	0.427611	+	1.54920i
$495$		0			0
$496$	12.3444	−	7.63073i	0.554279	−	0.342630i
$497$	−4.57346	−	12.5655i	−0.205148	−	0.563638i
$498$		0			0
$499$	−0.594620	+	0.498945i	−0.0266189	+	0.0223359i	−0.656000	−	0.754761i	$-0.727753\pi$
$499$	−0.594620	+	0.498945i	−0.0266189	+	0.0223359i	0.629381	+	0.777097i	$0.283308\pi$
$500$	10.5332	+	12.1764i	0.471057	+	0.544547i
$501$		0			0
$502$	8.16378	−	17.8565i	0.364367	−	0.796972i
$503$	16.6264	+	28.7978i	0.741335	+	1.28403i	0.951887	+	0.306448i	$0.0991406\pi$
$503$	16.6264	+	28.7978i	0.741335	+	1.28403i	−0.210552	+	0.977583i	$0.567526\pi$
$504$		0			0
$505$	−23.5098	+	40.7203i	−1.04617	+	1.81203i
$506$	8.22203	+	11.5564i	0.365514	+	0.513746i
$507$		0			0
$508$	−34.4590	−	11.9586i	−1.52887	−	0.530577i
$509$	5.59821	+	31.7490i	0.248136	+	1.40725i	0.813095	+	0.582132i	$0.197781\pi$
$509$	5.59821	+	31.7490i	0.248136	+	1.40725i	−0.564958	+	0.825119i	$0.691108\pi$
$510$		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
$518$	11.6672	+	24.5373i	0.512628	+	1.07811i
$519$		0			0
$520$	17.6086	−	12.9310i	0.772189	−	0.567060i
$521$	27.9816	+	16.1552i	1.22590	+	0.707773i	0.966169	−	0.257909i	$-0.0830335\pi$
$521$	27.9816	+	16.1552i	1.22590	+	0.707773i	0.259729	+	0.965682i	$0.416367\pi$
$522$		0			0
$523$	−1.25831	−	2.17946i	−0.0550222	−	0.0953012i	0.837202	−	0.546893i	$-0.184190\pi$
$523$	−1.25831	−	2.17946i	−0.0550222	−	0.0953012i	−0.892225	+	0.451592i	$0.850856\pi$
$524$	7.79052	−	2.96887i	0.340330	−	0.129696i
$525$		0			0
$526$	5.84933	+	0.467480i	0.255043	+	0.0203831i
$527$	10.5535	−	8.85544i	0.459718	−	0.385749i
$528$		0			0
$529$	−14.0722	+	5.12185i	−0.611833	+	0.222689i
$530$	0.169683	−	0.652853i	0.00737056	−	0.0283581i
$531$		0			0
$532$	21.8125	−	39.1270i	0.945692	−	1.69637i
$533$	3.50932	−	19.9023i	0.152005	−	0.862066i
$534$		0			0
$535$	−9.86054	+	27.0916i	−0.426308	+	1.17127i
$536$	−32.2994	−	21.5477i	−1.39512	−	0.930718i
$537$		0			0
$538$	4.20879	+	44.2718i	0.181454	+	1.90869i
$539$			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	$0.852458\pi$
$542$	39.6615	−	3.77050i	1.70361	−	0.161957i
$543$		0			0
$544$	−18.0459	−	11.6507i	−0.773712	−	0.499521i
$545$	−5.72888	+	15.7400i	−0.245398	+	0.674226i
$546$		0			0
$547$	−3.11764	+	17.6810i	−0.133301	+	0.755985i	0.842727	+	0.538341i	$0.180949\pi$
$547$	−3.11764	+	17.6810i	−0.133301	+	0.755985i	−0.976028	+	0.217645i	$0.930163\pi$
$548$	−15.5229	+	27.8448i	−0.663105	+	1.18947i
$549$		0			0
$550$	−4.33347	−	1.12631i	−0.184780	−	0.0480261i
$551$	41.0363	−	14.9360i	1.74820	−	0.636294i
$552$		0			0
$553$	−20.8398	+	17.4867i	−0.886200	+	0.743610i
$554$	−2.78211	+	34.8111i	−0.118201	+	1.47898i
$555$		0			0
$556$	1.68823	+	4.43002i	0.0715968	+	0.187875i
$557$	−15.8779	−	27.5013i	−0.672766	−	1.16527i	−0.977116	−	0.212705i	$-0.931773\pi$
$557$	−15.8779	−	27.5013i	−0.672766	−	1.16527i	0.304350	−	0.952560i	$-0.401561\pi$
$558$		0			0
$559$	10.2049	+	5.89179i	0.431621	+	0.249196i
$560$	−27.1121	−	3.94438i	−1.14570	−	0.166680i
$561$		0			0
$562$	24.5966	−	11.6954i	1.03755	−	0.493343i
$563$	−21.2510	+	3.74712i	−0.895621	+	0.157922i	−0.602468	−	0.798143i	$-0.705816\pi$
$563$	−21.2510	+	3.74712i	−0.895621	+	0.157922i	−0.293153	+	0.956065i	$0.594705\pi$
$564$		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	−0.274701	+	0.961530i	$0.588579\pi$
$569$	−28.0024	+	33.3720i	−1.17392	+	1.39903i	−0.899221	+	0.437495i	$0.855866\pi$
$570$		0			0
$571$	5.33260	+	30.2427i	0.223162	+	1.26562i	0.866167	+	0.499754i	$0.166576\pi$
$571$	5.33260	+	30.2427i	0.223162	+	1.26562i	−0.643005	+	0.765862i	$0.722313\pi$
$572$	3.12753	−	9.01203i	0.130768	−	0.376812i
$573$		0			0
$574$	−20.6510	+	14.6925i	−0.861957	+	0.613254i
$575$	5.99429	−	10.3824i	0.249979	−	0.432977i
$576$		0			0
$577$	−18.5251	−	32.0864i	−0.771210	−	1.33578i	−0.936900	−	0.349597i	$-0.886318\pi$
$577$	−18.5251	−	32.0864i	−0.771210	−	1.33578i	0.165690	−	0.986178i	$-0.447015\pi$
$578$	3.32015	+	1.51794i	0.138100	+	0.0631379i
$579$		0			0
$580$	−17.4736	−	20.1996i	−0.725551	−	0.838745i
$581$	22.9096	−	19.2235i	0.950452	−	0.797524i
$582$		0			0
$583$	−0.100738	−	0.276776i	−0.00417216	−	0.0114629i
$584$	−14.4444	−	3.52335i	−0.597715	−	0.145797i
$585$		0			0
$586$	29.0076	−	8.00671i	1.19829	−	0.330754i
$587$	−2.18563	−	0.385385i	−0.0902104	−	0.0159065i	0.128361	−	0.991728i	$-0.459028\pi$
$587$	−2.18563	−	0.385385i	−0.0902104	−	0.0159065i	−0.218571	+	0.975821i	$0.570140\pi$
$588$		0			0
$589$	10.6941	−	29.3817i	0.440642	−	1.21065i
$590$	2.27101	+	1.56488i	0.0934961	+	0.0644249i
$591$		0			0
$592$	18.3169	−	23.2119i	0.752820	−	0.954004i
$593$			7.72015i			0.317028i	0.987357	+	0.158514i	$0.0506704\pi$
$593$			7.72015i			0.317028i	−0.987357	+	0.158514i	$0.949330\pi$
$594$		0			0
$595$	−26.0084			−1.06624
$596$	−20.1752	+	24.7913i	−0.826408	+	1.01549i
$597$		0			0
$598$	21.0323	+	14.4926i	0.860073	+	0.592647i
$599$	−5.13051	−	1.86735i	−0.209627	−	0.0762980i	0.235072	−	0.971978i	$-0.424467\pi$
$599$	−5.13051	−	1.86735i	−0.209627	−	0.0762980i	−0.444699	+	0.895680i	$0.646689\pi$
$600$		0			0
$601$	2.68385	−	15.2209i	0.109477	−	0.620872i	−0.879861	−	0.475231i	$-0.842364\pi$
$601$	2.68385	−	15.2209i	0.109477	−	0.620872i	0.989337	−	0.145641i	$-0.0465245\pi$
$602$	−3.93191	−	14.2450i	−0.160253	−	0.580582i
$603$		0			0
$604$	2.41888	+	4.04787i	0.0984229	+	0.164705i
$605$	20.6824	−	7.52779i	0.840860	−	0.306048i
$606$		0			0
$607$	0.0926471	+	0.110413i	0.00376043	+	0.00448151i	0.767921	−	0.640544i	$-0.221291\pi$
$607$	0.0926471	+	0.110413i	0.00376043	+	0.00448151i	−0.764161	+	0.645026i	$0.776847\pi$
$608$	−48.6910	−	2.42136i	−1.97468	−	0.0981990i
$609$		0			0
$610$	−17.4967	+	38.2702i	−0.708421	+	1.54951i
$611$	−3.70982	+	2.14186i	−0.150083	+	0.0866505i
$612$		0			0
$613$	−30.3578	−	17.5271i	−1.22614	−	0.707913i	−0.259921	−	0.965630i	$-0.583696\pi$
$613$	−30.3578	−	17.5271i	−1.22614	−	0.707913i	−0.966220	+	0.257717i	$0.917030\pi$
$614$	10.3455	−	7.36049i	0.417510	−	0.297045i
$615$		0			0
$616$	−10.7255	+	5.29899i	−0.432144	+	0.213502i
$617$	−1.95314	+	0.344391i	−0.0786304	+	0.0138647i	−0.212825	−	0.977090i	$-0.568266\pi$
$617$	−1.95314	+	0.344391i	−0.0786304	+	0.0138647i	0.134195	+	0.990955i	$0.457155\pi$
$618$		0			0
$619$	30.9839	+	25.9986i	1.24535	+	1.04497i	0.997087	+	0.0762782i	$0.0243037\pi$
$619$	30.9839	+	25.9986i	1.24535	+	1.04497i	0.248262	+	0.968693i	$0.420141\pi$
$620$	−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
$626$	5.84488	+	12.2923i	0.233608	+	0.491301i
$627$		0			0
$628$	0.263809	−	1.63991i	0.0105271	−	0.0654394i
$629$	14.0347	−	24.3087i	0.559598	−	0.969253i
$630$		0			0
$631$	−28.0718	+	16.2073i	−1.11752	+	0.645202i	−0.940767	−	0.339053i	$-0.889893\pi$
$631$	−28.0718	+	16.2073i	−1.11752	+	0.645202i	−0.176755	+	0.984255i	$0.556560\pi$
$632$	27.1077	+	11.9040i	1.07828	+	0.473517i
$633$		0			0
$634$	−8.54900	−	0.683238i	−0.339524	−	0.0271349i
$635$	30.8946	+	36.8188i	1.22602	+	1.46111i
$636$		0			0
$637$	0.245925	+	0.675673i	0.00974390	+	0.0267711i
$638$	−11.2873	−	2.93368i	−0.446868	−	0.116146i
$639$		0			0
$640$	9.22085	+	28.3548i	0.364486	+	1.12082i
$641$	−16.3026	−	2.87458i	−0.643912	−	0.113539i	−0.157850	−	0.987463i	$-0.550456\pi$
$641$	−16.3026	−	2.87458i	−0.643912	−	0.113539i	−0.486063	+	0.873924i	$0.661567\pi$
$642$		0			0
$643$	−25.2314	−	9.18349i	−0.995030	−	0.362161i	−0.207364	−	0.978264i	$-0.566489\pi$
$643$	−25.2314	−	9.18349i	−0.995030	−	0.362161i	−0.787666	+	0.616102i	$0.788711\pi$
$644$	−6.03580	−	31.4581i	−0.237844	−	1.23962i
$645$		0			0
$646$	−46.0715	+	4.37988i	−1.81266	+	0.172324i
$647$	29.0527			1.14218			0.571090	−	0.820887i	$-0.306521\pi$
$647$	29.0527			1.14218			0.571090	+	0.820887i	$0.306521\pi$
$648$		0			0
$649$	1.20426			0.0472714
$650$	−8.02726	+	0.763128i	−0.314855	+	0.0299323i
$651$		0			0
$652$	22.1279	−	4.24563i	0.866594	−	0.166272i
$653$	32.5052	+	11.8309i	1.27203	+	0.462980i	0.887788	−	0.460253i	$-0.152241\pi$
$653$	32.5052	+	11.8309i	1.27203	+	0.462980i	0.384240	+	0.923233i	$0.374463\pi$
$654$		0			0
$655$	−10.8189	−	1.90767i	−0.422730	−	0.0745387i
$656$	24.2903	+	13.0667i	0.948379	+	0.510170i
$657$		0			0
$658$	5.19942	+	1.35138i	0.202695	+	0.0526824i
$659$	−7.44079	−	20.4434i	−0.289852	−	0.796362i	−0.996086	−	0.0883842i	$-0.971830\pi$
$659$	−7.44079	−	20.4434i	−0.289852	−	0.796362i	0.706234	−	0.707978i	$-0.250393\pi$
$660$		0			0
$661$	16.3906	+	19.5335i	0.637519	+	0.759766i	0.983976	−	0.178300i	$-0.0570597\pi$
$661$	16.3906	+	19.5335i	0.637519	+	0.759766i	−0.346457	+	0.938066i	$0.612615\pi$
$662$	−5.18121	−	0.414084i	−0.201373	−	0.0160938i
$663$		0			0
$664$	−29.8000	−	13.0863i	−1.15646	−	0.507848i
$665$	−51.1202	+	29.5143i	−1.98236	+	1.14451i
$666$		0			0
$667$	15.6132	−	27.0429i	0.604546	−	1.04710i
$668$	34.5024	+	5.55033i	1.33494	+	0.214749i
$669$		0			0
$670$	21.9703	+	46.2056i	0.848788	+	1.78508i
$671$	3.19066	+	18.0951i	0.123174	+	0.698555i
$672$		0			0
$673$	−6.18349	−	5.18857i	−0.238356	−	0.200005i	0.515783	−	0.856719i	$-0.327501\pi$
$673$	−6.18349	−	5.18857i	−0.238356	−	0.200005i	−0.754139	+	0.656715i	$0.771946\pi$
$674$	−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	$-0.373743\pi$
$677$	−11.8370	−	9.93243i	−0.454933	−	0.381734i	−0.841263	+	0.540627i	$0.818187\pi$
$678$		0			0
$679$	−5.32333	+	0.938647i	−0.204291	+	0.0360220i
$680$	12.5373	+	25.3764i	0.480784	+	0.973141i
$681$		0			0
$682$	−6.80385	+	4.84072i	−0.260533	+	0.185361i
$683$	1.82111	+	1.05142i	0.0696830	+	0.0402315i	0.534437	−	0.845209i	$-0.320524\pi$
$683$	1.82111	+	1.05142i	0.0696830	+	0.0402315i	−0.464754	+	0.885440i	$0.653857\pi$
$684$		0			0
$685$	36.3798	−	21.0039i	1.39000	−	0.802516i
$686$	11.0727	−	24.2191i	0.422759	−	0.924690i
$687$		0			0
$688$	−12.0035	+	10.7032i	−0.457628	+	0.408054i
$689$	−0.340959	−	0.406339i	−0.0129895	−	0.0154803i
$690$		0			0
$691$	−21.9905	+	8.00388i	−0.836557	+	0.304482i	−0.724547	−	0.689225i	$-0.757951\pi$
$691$	−21.9905	+	8.00388i	−0.836557	+	0.304482i	−0.112010	+	0.993707i	$0.535729\pi$
$692$	−31.9344	+	19.0830i	−1.21396	+	0.725426i
$693$		0			0
$694$	5.69013	+	20.6149i	0.215994	+	0.782529i
$695$	1.08478	−	6.15210i	0.0411481	−	0.233362i
$696$		0			0
$697$	24.6043	+	8.95523i	0.931954	+	0.339203i
$698$	−26.1796	−	18.0394i	−0.990911	−	0.682802i
$699$		0			0
$700$	7.84329	+	6.38288i	0.296448	+	0.241250i
$701$	40.5028			1.52977			0.764884	−	0.644168i	$-0.222796\pi$
$701$	40.5028			1.52977			0.764884	+	0.644168i	$0.222796\pi$
$702$		0			0
$703$		−	63.7061i		−	2.40272i
$704$	10.3405	+	7.91055i	0.389721	+	0.298140i
$705$		0			0
$706$	−24.2800	−	16.7305i	−0.913789	−	0.629660i
$707$	15.8593	−	43.5730i	0.596450	−	1.63873i
$708$		0			0
$709$	12.4782	+	2.20024i	0.468628	+	0.0826317i	0.402975	−	0.915211i	$-0.367976\pi$
$709$	12.4782	+	2.20024i	0.468628	+	0.0826317i	0.0656523	+	0.997843i	$0.479087\pi$
$710$	18.4847	−	5.10216i	0.693717	−	0.191480i
$711$		0			0
$712$	−0.163507	+	0.670316i	−0.00612767	+	0.0251212i
$713$	−7.64687	−	21.0096i	−0.286377	−	0.786815i
$714$		0			0
$715$	−9.62920	+	8.07986i	−0.360112	+	0.302170i
$716$	−10.7180	+	9.27149i	−0.400549	+	0.346492i
$717$		0			0
$718$	13.9898	+	6.39597i	0.522093	+	0.238695i
$719$	23.2178	+	40.2145i	0.865879	+	1.49975i	0.866171	+	0.499747i	$0.166574\pi$
$719$	23.2178	+	40.2145i	0.865879	+	1.49975i	−0.000291815		1.00000i	$0.500093\pi$
$720$		0			0
$721$	−16.3111	+	28.2516i	−0.607455	+	1.05214i
$722$	−63.6905	+	45.3137i	−2.37032	+	1.68640i
$723$		0			0
$724$	−0.283323	−	0.0983241i	−0.0105296	−	0.00365418i
$725$	1.71183	+	9.70825i	0.0635756	+	0.360555i
$726$		0			0
$727$	7.82850	−	9.32964i	0.290343	−	0.346017i	−0.601081	−	0.799188i	$-0.705263\pi$
$727$	7.82850	−	9.32964i	0.290343	−	0.346017i	0.891424	+	0.453171i	$0.149707\pi$
$728$	−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	$-0.614712\pi$
$733$	−9.85329	+	1.73740i	−0.363939	+	0.0641723i	−0.0113117	+	0.999936i	$0.503601\pi$
$734$	14.8150	−	7.04439i	0.546832	−	0.260013i
$735$		0			0
$736$	−27.7842	+	21.0535i	−1.02414	+	0.776042i
$737$	19.3473	+	11.1702i	0.712666	+	0.411458i
$738$		0			0
$739$	22.0318	+	38.1602i	0.810454	+	1.40375i	0.912547	+	0.408972i	$0.134113\pi$
$739$	22.0318	+	38.1602i	0.810454	+	1.40375i	−0.102093	+	0.994775i	$0.532554\pi$
$740$	−36.4086	+	13.8749i	−1.33841	+	0.510051i
$741$		0			0
$742$	−0.0529953	+	0.663101i	−0.00194552	+	0.0243432i
$743$	6.42946	−	5.39496i	0.235874	−	0.197922i	−0.517187	−	0.855872i	$-0.673021\pi$
$743$	6.42946	−	5.39496i	0.235874	−	0.197922i	0.753061	+	0.657950i	$0.228576\pi$
$744$		0			0
$745$	39.5782	−	14.4053i	1.45003	−	0.527769i
$746$	−6.63972	−	1.72573i	−0.243097	−	0.0631834i
$747$		0			0
$748$	10.7950	+	6.01800i	0.394705	+	0.220040i
$749$	4.93709	−	27.9996i	0.180397	−	1.02308i
$750$		0			0
$751$	−7.74342	+	21.2749i	−0.282561	+	0.776331i	0.714494	+	0.699642i	$0.246657\pi$
$751$	−7.74342	+	21.2749i	−0.282561	+	0.776331i	−0.997055	+	0.0766890i	$0.975565\pi$
$752$	−1.18783	−	5.72452i	−0.0433158	−	0.208752i
$753$		0			0
$754$	−20.9085	+	1.98770i	−0.761441	+	0.0723879i
$755$		−	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	$-0.115359\pi$
$758$	−4.22755	−	44.4692i	−0.153552	−	1.61519i
$759$		0			0
$760$	53.4396	+	35.6508i	1.93846	+	1.29319i
$761$	9.62500	−	26.4445i	0.348906	−	0.958612i	−0.633809	−	0.773489i	$-0.718510\pi$
$761$	9.62500	−	26.4445i	0.348906	−	0.958612i	0.982715	−	0.185122i	$-0.0592682\pi$
$762$		0			0
$763$	2.86840	−	16.2675i	0.103843	−	0.588924i
$764$	−19.0970	−	10.6462i	−0.690904	−	0.385165i
$765$		0			0
$766$	2.01891	−	7.76774i	0.0729463	−	0.280660i
$767$	2.03797	−	0.741760i	0.0735868	−	0.0267834i
$768$		0			0
$769$	12.3157	−	10.3341i	0.444117	−	0.372658i	−0.393130	−	0.919483i	$-0.628608\pi$
$769$	12.3157	−	10.3341i	0.444117	−	0.372658i	0.837247	+	0.546824i	$0.184163\pi$
$770$	15.7138	+	1.25585i	0.566287	+	0.0452578i
$771$		0			0
$772$	−2.08764	−	5.47811i	−0.0751358	−	0.197161i
$773$	6.27436	+	10.8675i	0.225673	+	0.390877i	0.956521	−	0.291663i	$-0.0942086\pi$
$773$	6.27436	+	10.8675i	0.225673	+	0.390877i	−0.730848	+	0.682540i	$0.760875\pi$
$774$		0			0
$775$	6.11265	+	3.52914i	0.219573	+	0.126770i
$776$	3.48195	+	4.74152i	0.124995	+	0.170210i
$777$		0			0
$778$	−4.97730	−	10.4677i	−0.178445	−	0.375286i
$779$	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	−0.978363	−	0.206894i	$-0.933665\pi$
$787$	−3.64035	−	20.6454i	−0.129764	−	0.735930i	0.848599	−	0.529037i	$-0.177447\pi$
$788$	1.84432	−	5.31446i	0.0657013	−	0.189320i
$789$		0			0
$790$	−22.6162	−	31.7881i	−0.804648	−	1.13097i
$791$	−4.58533	+	7.94202i	−0.163036	+	0.282386i
$792$		0			0
$793$	16.5452	+	28.6571i	0.587536	+	1.01764i
$794$	−17.1182	+	37.4422i	−0.607502	+	1.32877i
$795$		0			0
$796$	−1.52714	+	1.32104i	−0.0541280	+	0.0468231i
$797$	−21.2235	+	17.8086i	−0.751775	+	0.630814i	−0.935972	−	0.352075i	$-0.885476\pi$
$797$	−21.2235	+	17.8086i	−0.751775	+	0.630814i	0.184197	+	0.982889i	$0.441032\pi$
$798$		0			0
$799$	−1.89822	−	5.21531i	−0.0671541	−	0.184504i
$800$	2.44694	−	10.7296i	0.0865125	−	0.379348i
$801$		0			0
$802$	5.22423	+	18.9269i	0.184474	+	0.668333i
$803$	8.42472	+	1.48550i	0.297302	+	0.0524223i
$804$		0			0
$805$	−14.4362	+	39.6632i	−0.508810	+	1.39794i
$806$	−8.53252	+	12.3827i	−0.300545	+	0.436163i
$807$		0			0
$808$	−50.1593	+	5.53041i	−1.76460	+	0.194559i
$809$		−	21.9542i		−	0.771867i	−0.922527	−	0.385933i	$-0.873879\pi$
$809$		−	21.9542i		−	0.771867i	0.922527	−	0.385933i	$-0.126121\pi$
$810$		0			0
$811$	−17.4685			−0.613401			−0.306700	−	0.951806i	$-0.599225\pi$
$811$	−17.4685			−0.613401			−0.306700	+	0.951806i	$0.599225\pi$
$812$	20.4293	+	16.6254i	0.716926	+	0.583436i
$813$		0			0
$814$	−9.65329	+	14.0093i	−0.338348	+	0.491024i
$815$	−27.8994	−	10.1546i	−0.977274	−	0.355699i
$816$		0			0
$817$	−6.01685	+	34.1233i	−0.210503	+	1.19382i
$818$	−22.4412	+	6.19424i	−0.784638	+	0.216576i
$819$		0			0
$820$	−18.6435	−	31.1989i	−0.651060	−	1.08951i
$821$	−40.3394	+	14.6823i	−1.40786	+	0.512417i	−0.930500	−	0.366293i	$-0.880627\pi$
$821$	−40.3394	+	14.6823i	−1.40786	+	0.512417i	−0.477355	+	0.878710i	$0.658405\pi$
$822$		0			0
$823$	17.8062	+	21.2206i	0.620686	+	0.739705i	0.981188	−	0.193053i	$-0.0618390\pi$
$823$	17.8062	+	21.2206i	0.620686	+	0.739705i	−0.360502	+	0.932758i	$0.617395\pi$
$824$	35.4279	+	2.29608i	1.23419	+	0.0799877i
$825$		0			0
$826$	−2.47356	−	1.13089i	−0.0860662	−	0.0393486i
$827$	−23.1043	+	13.3392i	−0.803414	+	0.463851i	−0.844663	−	0.535298i	$-0.820199\pi$
$827$	−23.1043	+	13.3392i	−0.803414	+	0.463851i	0.0412497	+	0.999149i	$0.486866\pi$
$828$		0			0
$829$	2.23315	+	1.28931i	0.0775606	+	0.0447796i	0.538279	−	0.842767i	$-0.319075\pi$
$829$	2.23315	+	1.28931i	0.0775606	+	0.0447796i	−0.460718	+	0.887547i	$0.652408\pi$
$830$	24.8624	+	34.9452i	0.862987	+	1.21297i
$831$		0			0
$832$	22.3716	+	7.01784i	0.775597	+	0.243300i
$833$	−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	$-0.486439\pi$
$839$	−27.0517	−	22.6991i	−0.933928	−	0.783659i	−0.976518	+	0.215434i	$0.930883\pi$
$840$		0			0
$841$	−0.577037	−	3.27254i	−0.0198978	−	0.112846i
$842$	0.677349	−	0.322073i	0.0233430	−	0.0110994i
$843$		0			0
$844$	8.37171	+	1.34674i	0.288166	+	0.0463567i
$845$	5.81151	−	10.0658i	0.199922	−	0.346275i
$846$		0			0
$847$	−18.7974	+	10.8527i	−0.645887	+	0.372903i
$848$	0.672536	−	0.267940i	0.0230950	−	0.00920110i
$849$		0			0
$850$	0.832278	−	10.4138i	0.0285469	−	0.357192i
$851$	−29.2812	−	34.8959i	−1.00375	−	1.19622i
$852$		0			0
$853$	−11.8972	−	32.6874i	−0.407354	−	1.11919i	−0.958576	−	0.284837i	$-0.908061\pi$
$853$	−11.8972	−	32.6874i	−0.407354	−	1.11919i	0.551222	−	0.834358i	$-0.314162\pi$
$854$	10.4390	−	40.1638i	0.357214	−	1.37438i
$855$		0			0
$856$	−29.6992	+	8.68008i	−1.01510	+	0.296679i
$857$	14.7995	+	2.60955i	0.505541	+	0.0891405i	0.420601	−	0.907246i	$-0.361819\pi$
$857$	14.7995	+	2.60955i	0.505541	+	0.0891405i	0.0849397	+	0.996386i	$0.472930\pi$
$858$		0			0
$859$	−11.2421	−	4.09177i	−0.383574	−	0.139610i	0.143034	−	0.989718i	$-0.454314\pi$
$859$	−11.2421	−	4.09177i	−0.383574	−	0.139610i	−0.526608	+	0.850108i	$0.676536\pi$
$860$	20.8122	−	3.99320i	0.709691	−	0.136167i
$861$		0			0
$862$	−1.64518	−	17.3055i	−0.0560350	−	0.589427i
$863$	−4.99128			−0.169905			−0.0849526	−	0.996385i	$-0.527074\pi$
$863$	−4.99128			−0.169905			−0.0849526	+	0.996385i	$0.527074\pi$
$864$		0			0
$865$	49.0210			1.66676
$866$	−1.96623	−	20.6826i	−0.0668152	−	0.702822i
$867$		0			0
$868$	18.5209	−	3.55357i	0.628641	−	0.120616i
$869$	−16.0074	−	5.82624i	−0.543016	−	0.197641i
$870$		0			0
$871$	39.6216	+	6.98635i	1.34253	+	0.236724i
$872$	−17.2550	+	5.04304i	−0.584327	+	0.170779i
$873$		0			0
$874$	−18.8931	+	72.6911i	−0.639070	+	2.45881i
$875$	7.15570	+	19.6601i	0.241907	+	0.664634i
$876$		0			0
$877$	−13.3228	−	15.8774i	−0.449878	−	0.536143i	0.492670	−	0.870217i	$-0.336021\pi$
$877$	−13.3228	−	15.8774i	−0.449878	−	0.536143i	−0.942547	+	0.334073i	$0.891577\pi$
$878$	3.30039	−	41.2961i	0.111383	−	1.39367i
$879$		0			0
$880$	−6.34950	−	15.9374i	−0.214042	−	0.537249i
$881$	−7.33774	+	4.23645i	−0.247215	+	0.142729i	−0.618488	−	0.785794i	$-0.712255\pi$
$881$	−7.33774	+	4.23645i	−0.247215	+	0.142729i	0.371274	+	0.928524i	$0.378921\pi$
$882$		0			0
$883$	9.03674	−	15.6521i	0.304111	−	0.526735i	−0.672952	−	0.739686i	$-0.734974\pi$
$883$	9.03674	−	15.6521i	0.304111	−	0.526735i	0.977063	+	0.212951i	$0.0683074\pi$
$884$	21.9752	+	3.53510i	0.739104	+	0.118898i
$885$		0			0
$886$	43.3529	−	20.6139i	1.45647	−	0.692537i
$887$	3.87890	+	21.9983i	0.130241	+	0.738632i	0.978056	+	0.208341i	$0.0668063\pi$
$887$	3.87890	+	21.9983i	0.130241	+	0.738632i	−0.847816	+	0.530291i	$0.822083\pi$
$888$		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
$896$	−13.8108	−	25.9588i	−0.461388	−	0.867222i
$897$		0			0
$898$	−14.5798	−	20.4926i	−0.486535	−	0.683847i
$899$	15.9215	+	9.19228i	0.531012	+	0.306580i
$900$		0			0
$901$	0.595165	−	0.343619i	0.0198278	−	0.0114476i
$902$	−14.4331	−	6.59866i	−0.480569	−	0.219711i
$903$		0			0
$904$	9.95941	+	0.645469i	0.331245	+	0.0214680i
$905$	0.254017	+	0.302725i	0.00844380	+	0.0100629i
$906$		0			0
$907$	37.7812	−	13.7512i	1.25450	−	0.456602i	0.372583	−	0.927999i	$-0.378472\pi$
$907$	37.7812	−	13.7512i	1.25450	−	0.456602i	0.881921	+	0.471397i	$0.156250\pi$
$908$	1.76389	+	2.95177i	0.0585366	+	0.0979579i
$909$		0			0
$910$	27.3660	−	7.55359i	0.907174	−	0.250399i
$911$	−1.26349	+	7.16560i	−0.0418613	+	0.237407i	−0.998558	−	0.0536786i	$-0.982905\pi$
$911$	−1.26349	+	7.16560i	−0.0418613	+	0.237407i	0.956697	+	0.291086i	$0.0940165\pi$
$912$		0			0
$913$	17.5973	+	6.40489i	0.582386	+	0.211971i
$914$	9.65729	−	14.0151i	0.319435	−	0.463577i
$915$		0			0
$916$	−14.2865	−	11.6264i	−0.472040	−	0.384147i
$917$	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	$-0.134775\pi$
$920$	45.6585	−	5.03417i	1.50532	−	0.165972i
$921$		0			0
$922$	13.2130	−	19.1753i	0.435148	−	0.631504i
$923$	5.15741	−	14.1699i	0.169758	−	0.466406i
$924$		0			0
$925$	14.1625	+	2.49723i	0.465660	+	0.0821084i
$926$	−1.46705	−	5.31498i	−0.0482101	−	0.174661i
$927$		0			0
$928$	6.37350	−	27.9471i	0.209220	−	0.917409i
$929$	−12.8203	−	35.2236i	−0.420621	−	1.15565i	−0.951352	−	0.308107i	$-0.900305\pi$
$929$	−12.8203	−	35.2236i	−0.420621	−	1.15565i	0.530730	−	0.847541i	$-0.321918\pi$
$930$		0			0
$931$	−1.61967	+	1.35906i	−0.0530825	+	0.0445415i
$932$	29.2853	−	25.3331i	0.959272	−	0.829812i
$933$		0			0
$934$	5.68997	−	12.4455i	0.186181	−	0.407230i
$935$	−8.14289	−	14.1039i	−0.266301	−	0.461247i
$936$		0			0
$937$	4.91136	−	8.50673i	0.160447	−	0.277903i	−0.774582	−	0.632474i	$-0.782040\pi$
$937$	4.91136	−	8.50673i	0.160447	−	0.277903i	0.935029	+	0.354571i	$0.115373\pi$
$938$	−29.2499	−	41.1120i	−0.955043	−	1.34236i
$939$		0			0
$940$	−2.52579	+	7.27812i	−0.0823823	+	0.237386i
$941$	−1.11021	−	6.29630i	−0.0361918	−	0.205254i	0.961350	−	0.275330i	$-0.0887870\pi$
$941$	−1.11021	−	6.29630i	−0.0361918	−	0.205254i	−0.997542	+	0.0700759i	$0.977676\pi$
$942$		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	−0.806177	−	0.591674i	$-0.798467\pi$
$947$	−2.56959	+	3.06232i	−0.0835006	+	0.0995121i	0.722677	+	0.691186i	$0.242912\pi$
$948$		0			0
$949$	15.1721	−	2.67525i	0.492508	−	0.0868424i
$950$	−10.1818	−	21.4132i	−0.330340	−	0.694736i
$951$		0			0
$952$	−16.5217	−	22.4983i	−0.535472	−	0.729174i
$953$	−38.3667	−	22.1510i	−1.24282	−	0.717542i	−0.273152	−	0.961971i	$-0.588066\pi$
$953$	−38.3667	−	22.1510i	−1.24282	−	0.717542i	−0.969667	+	0.244428i	$0.921400\pi$
$954$		0			0
$955$	14.4052	+	24.9506i	0.466142	+	0.807382i
$956$	−3.29655	−	8.65036i	−0.106618	−	0.279773i
$957$		0			0
$958$	2.86228	+	0.228754i	0.0924761	+	0.00739072i
$959$	−31.7348	+	26.6286i	−1.02477	+	0.859883i
$960$		0			0
$961$	−16.7611	+	6.10053i	−0.540680	+	0.196791i
$962$	−7.70730	+	29.6537i	−0.248493	+	0.956075i
$963$		0			0
$964$	−48.1243	−	26.8283i	−1.54998	−	0.864082i
$965$	−1.34143	+	7.60761i	−0.0431820	+	0.244897i
$966$		0			0
$967$	−8.11445	+	22.2943i	−0.260943	+	0.716935i	0.738161	+	0.674624i	$0.235694\pi$
$967$	−8.11445	+	22.2943i	−0.260943	+	0.716935i	−0.999104	+	0.0423110i	$0.986528\pi$
$968$	19.6503	+	13.1092i	0.631584	+	0.421344i
$969$		0			0
$970$	−0.733620	−	7.71688i	−0.0235551	−	0.247774i
$971$			23.3729i			0.750071i	0.927010	+	0.375036i	$0.122369\pi$
$971$			23.3729i			0.750071i	−0.927010	+	0.375036i	$0.877631\pi$
$972$		0			0
$973$			6.16061i			0.197500i
$974$	−10.8091	+	1.02759i	−0.346346	+	0.0329261i
$975$		0			0
$976$	−44.2200	+	9.17561i	−1.41545	+	0.293704i
$977$	−17.9667	+	49.3632i	−0.574807	+	1.57927i	0.222007	+	0.975045i	$0.428739\pi$
$977$	−17.9667	+	49.3632i	−0.574807	+	1.57927i	−0.796814	+	0.604224i	$0.793483\pi$
$978$		0			0
$979$	0.0689371	−	0.390962i	0.00220324	−	0.0124952i
$980$	1.12947	+	0.629659i	0.0360797	+	0.0201137i
$981$		0			0
$982$	24.9374	+	6.48148i	0.795785	+	0.206832i
$983$	−10.1837	+	3.70656i	−0.324809	+	0.118221i	−0.499278	−	0.866442i	$-0.666401\pi$
$983$	−10.1837	+	3.70656i	−0.324809	+	0.118221i	0.174469	+	0.984663i	$0.444179\pi$
$984$		0			0
$985$	−5.67841	+	4.76475i	−0.180929	+	0.151817i
$986$	2.16782	−	27.1247i	0.0690374	−	0.863828i
$987$		0			0
$988$	47.2045	−	17.9890i	1.50177	−	0.572308i
$989$	12.3882	+	21.4570i	0.393923	+	0.682294i
$990$		0			0
$991$	−37.1953	−	21.4747i	−1.18155	−	0.682167i	−0.225175	−	0.974318i	$-0.572295\pi$
$991$	−37.1953	−	21.4747i	−1.18155	−	0.682167i	−0.956372	+	0.292152i	$0.905629\pi$
$992$	−12.3952	−	16.3579i	−0.393549	−	0.519364i
$993$		0			0
$994$	−17.0784	+	8.12059i	−0.541693	+	0.257570i
$995$	2.62034	−	0.462037i	0.0830704	−	0.0146475i
$996$		0			0
$997$	−27.5401	+	32.8210i	−0.872204	+	1.03945i	0.126667	+	0.991945i	$0.459572\pi$
$997$	−27.5401	+	32.8210i	−0.872204	+	1.03945i	−0.998871	+	0.0475071i	$0.984872\pi$
$998$	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.35.16		192
3.2	odd	2		216.2.v.b.11.17	yes	192
8.3	odd	2	inner	648.2.v.b.35.31		192
12.11	even	2		864.2.bh.b.335.17		192
24.5	odd	2		864.2.bh.b.335.18		192
24.11	even	2		216.2.v.b.11.2	✓	192
27.5	odd	18	inner	648.2.v.b.611.31		192
27.22	even	9		216.2.v.b.59.2	yes	192
108.103	odd	18		864.2.bh.b.815.18		192
216.59	even	18	inner	648.2.v.b.611.16		192
216.157	even	18		864.2.bh.b.815.17		192
216.211	odd	18		216.2.v.b.59.17	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.2	✓	192	24.11	even	2
216.2.v.b.11.17	yes	192	3.2	odd	2
216.2.v.b.59.2	yes	192	27.22	even	9
216.2.v.b.59.17	yes	192	216.211	odd	18
648.2.v.b.35.16		192	1.1	even	1	trivial
648.2.v.b.35.31		192	8.3	odd	2	inner
648.2.v.b.611.16		192	216.59	even	18	inner
648.2.v.b.611.31		192	27.5	odd	18	inner
864.2.bh.b.335.17		192	12.11	even	2
864.2.bh.b.335.18		192	24.5	odd	2
864.2.bh.b.815.17		192	216.157	even	18
864.2.bh.b.815.18		192	108.103	odd	18

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)

\(f(q)\)	\(=\)	\(q+(-0.133842 - 1.40787i) q^{2} +(-1.96417 + 0.376862i) q^{4} +(2.47648 + 0.901367i) q^{5} +(-2.55949 - 0.451307i) q^{7} +(0.793459 + 2.71485i) q^{8} +(0.937547 - 3.60720i) q^{10} +(-0.556608 - 1.52927i) q^{11} +(-1.88389 - 2.24514i) q^{13} +(-0.292814 + 3.66382i) q^{14} +(3.71595 - 1.48044i) q^{16} +(3.28845 - 1.89859i) q^{17} +(4.30904 - 7.46347i) q^{19} +(-5.20394 - 0.837147i) q^{20} +(-2.07851 + 0.988309i) q^{22} +(-1.07009 - 6.06879i) q^{23} +(1.49029 + 1.25050i) q^{25} +(-2.90871 + 2.95276i) q^{26} +(5.19736 - 0.0781292i) q^{28} +(3.88174 + 3.25716i) q^{29} +(3.57300 - 0.630016i) q^{31} +(-2.58162 - 5.03341i) q^{32} +(-3.11309 - 4.37559i) q^{34} +(-5.93174 - 3.42469i) q^{35} +(6.40179 - 3.69607i) q^{37} +(-11.0843 - 5.06762i) q^{38} +(-0.482088 + 7.43849i) q^{40} +(4.43232 + 5.28224i) q^{41} +(-3.77811 + 1.37512i) q^{43} +(1.66960 + 2.79398i) q^{44} +(-8.40082 + 2.31880i) q^{46} +(0.253807 - 1.43941i) q^{47} +(-0.230541 - 0.0839100i) q^{49} +(1.56108 - 2.26550i) q^{50} +(4.54640 + 3.69987i) q^{52} +0.180986 q^{53} -4.28892i q^{55} +(-0.805618 - 7.30673i) q^{56} +(4.06611 - 5.90091i) q^{58} +(-0.253090 + 0.695359i) q^{59} +(-11.1190 - 1.96057i) q^{61} +(-1.36519 - 4.94598i) q^{62} +(-6.74085 + 4.30825i) q^{64} +(-2.64174 - 7.25812i) q^{65} +(-10.5159 + 8.82387i) q^{67} +(-5.74359 + 4.96845i) q^{68} +(-4.02760 + 8.80947i) q^{70} +(2.57253 + 4.45576i) q^{71} +(-2.62831 + 4.55236i) q^{73} +(-6.06040 - 8.51817i) q^{74} +(-5.65100 + 16.2835i) q^{76} +(0.734463 + 4.16534i) q^{77} +(6.72831 - 8.01849i) q^{79} +(10.5369 - 0.316864i) q^{80} +(6.84345 - 6.94710i) q^{82} +(-7.39656 + 8.81488i) q^{83} +(9.85513 - 1.73773i) q^{85} +(2.44165 + 5.13502i) q^{86} +(3.71009 - 2.72452i) q^{88} +(0.211259 + 0.121971i) q^{89} +(3.80856 + 6.59662i) q^{91} +(4.38894 + 11.5169i) q^{92} +(-2.06047 - 0.164673i) q^{94} +(17.3986 - 14.5992i) q^{95} +(1.95441 - 0.711348i) q^{97} +(-0.0872781 + 0.335801i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8} - 3 q^{10} + 30 q^{11} - 9 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} + 27 q^{20} - 18 q^{22} - 12 q^{25} - 12 q^{28} + 36 q^{32} + 12 q^{34} + 18 q^{35} + 102 q^{38} + 9 q^{40}+ \cdots - 162 q^{98}+O(q^{100}) \) 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

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