LMFDB - Embedded newform 483.2.bc.a.11.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(11,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([33, 44, 27]))

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

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

chi := DirichletCharacter("483.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.bc (of order $66$, degree $20$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$1200$
Relative dimension:	$60$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			11.13
Character	$\chi$	$=$	483.11
Dual form			483.2.bc.a.44.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.839508 + 1.62842i) q^{2} +(1.58694 + 0.693981i) q^{3} +(-0.786858 - 1.10499i) q^{4} +(-1.28009 - 1.22056i) q^{5} +(-2.46234 + 2.00161i) q^{6} +(-1.82028 + 1.92005i) q^{7} +(-1.16691 + 0.167776i) q^{8} +(2.03678 + 2.20262i) q^{9} +O(q^{10})$	\(q+(-0.839508 + 1.62842i) q^{2} +(1.58694 + 0.693981i) q^{3} +(-0.786858 - 1.10499i) q^{4} +(-1.28009 - 1.22056i) q^{5} +(-2.46234 + 2.00161i) q^{6} +(-1.82028 + 1.92005i) q^{7} +(-1.16691 + 0.167776i) q^{8} +(2.03678 + 2.20262i) q^{9} +(3.06224 - 1.05985i) q^{10} +(-1.43861 + 0.741654i) q^{11} +(-0.481859 - 2.29962i) q^{12} +(-2.50372 + 2.88945i) q^{13} +(-1.59851 - 4.57607i) q^{14} +(-1.18438 - 2.82533i) q^{15} +(1.59377 - 4.60489i) q^{16} +(2.10363 + 0.200872i) q^{17} +(-5.29667 + 1.46762i) q^{18} +(-0.0495015 - 0.518403i) q^{19} +(-0.341458 + 2.37490i) q^{20} +(-4.22116 + 1.78377i) q^{21} -2.96528i q^{22} +(-3.70659 + 3.04322i) q^{23} +(-1.96826 - 0.543562i) q^{24} +(-0.0890537 - 1.86947i) q^{25} +(-2.60333 - 6.50281i) q^{26} +(1.70368 + 4.90892i) q^{27} +(3.55393 + 0.500576i) q^{28} +(-6.63808 + 3.03151i) q^{29} +(5.59511 + 0.443211i) q^{30} +(-4.45840 - 1.78487i) q^{31} +(4.53362 + 4.75472i) q^{32} +(-2.79769 + 0.178597i) q^{33} +(-2.09312 + 3.25695i) q^{34} +(4.67367 - 0.236074i) q^{35} +(0.831207 - 3.98376i) q^{36} +(2.84100 - 0.689218i) q^{37} +(0.885734 + 0.354594i) q^{38} +(-5.97848 + 2.84785i) q^{39} +(1.69854 + 1.20952i) q^{40} +(2.41842 + 8.23639i) q^{41} +(0.638963 - 8.37130i) q^{42} +(8.55608 + 1.23018i) q^{43} +(1.95150 + 1.00607i) q^{44} +(0.0811716 - 5.30558i) q^{45} +(-1.84392 - 8.59068i) q^{46} +(-4.47113 + 2.58141i) q^{47} +(5.72493 - 6.20166i) q^{48} +(-0.373184 - 6.99005i) q^{49} +(3.11903 + 1.42442i) q^{50} +(3.19894 + 1.77865i) q^{51} +(5.16287 + 0.492994i) q^{52} +(8.56794 - 1.65134i) q^{53} +(-9.42402 - 1.34677i) q^{54} +(2.74679 + 0.806530i) q^{55} +(1.80196 - 2.54593i) q^{56} +(0.281206 - 0.857030i) q^{57} +(0.636155 - 13.3545i) q^{58} +(2.36455 - 0.818378i) q^{59} +(-2.19001 + 3.53186i) q^{60} +(3.66243 + 4.65716i) q^{61} +(6.64938 - 5.76172i) q^{62} +(-7.93664 - 0.0986526i) q^{63} +(-2.19767 + 0.645295i) q^{64} +(6.73175 - 0.642804i) q^{65} +(2.05785 - 4.70573i) q^{66} +(-12.2539 + 0.583726i) q^{67} +(-1.43330 - 2.48254i) q^{68} +(-7.99409 + 2.25711i) q^{69} +(-3.53915 + 7.80887i) q^{70} +(0.585578 + 0.911177i) q^{71} +(-2.74629 - 2.22854i) q^{72} +(3.82466 + 5.37099i) q^{73} +(-1.26270 + 5.20493i) q^{74} +(1.15605 - 3.02854i) q^{75} +(-0.533878 + 0.462608i) q^{76} +(1.19465 - 4.11222i) q^{77} +(0.381485 - 12.1263i) q^{78} +(1.56110 - 8.09974i) q^{79} +(-7.66074 + 3.94938i) q^{80} +(-0.703048 + 8.97250i) q^{81} +(-15.4426 - 2.97631i) q^{82} +(6.80410 + 1.99787i) q^{83} +(5.29249 + 3.26075i) q^{84} +(-2.44766 - 2.82475i) q^{85} +(-9.18614 + 12.9001i) q^{86} +(-12.6381 + 0.204134i) q^{87} +(1.55430 - 1.10681i) q^{88} +(4.72860 - 1.89305i) q^{89} +(8.57155 + 4.58625i) q^{90} +(-0.990419 - 10.0669i) q^{91} +(6.27928 + 1.70115i) q^{92} +(-5.83656 - 5.92654i) q^{93} +(-0.450063 - 9.44798i) q^{94} +(-0.569378 + 0.724023i) q^{95} +(3.89491 + 10.6917i) q^{96} +(3.90524 + 13.3000i) q^{97} +(11.6960 + 5.26050i) q^{98} +(-4.56371 - 1.65812i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1200 q - 9 q^{3} - 74 q^{4} - 20 q^{6} - 44 q^{7} - 13 q^{9}+O(q^{10}) $ 1200 * q - 9 * q^3 - 74 * q^4 - 20 * q^6 - 44 * q^7 - 13 * q^9	$ 1200 q - 9 q^{3} - 74 q^{4} - 20 q^{6} - 44 q^{7} - 13 q^{9} - 22 q^{10} - 25 q^{12} - 72 q^{13} - 44 q^{15} + 38 q^{16} - 45 q^{18} - 22 q^{19} + 44 q^{21} + 2 q^{24} + 18 q^{25} - 90 q^{27} - 44 q^{28} - 55 q^{30} - 18 q^{31} - 11 q^{33} - 88 q^{34} - 108 q^{36} - 66 q^{37} + q^{39} - 22 q^{40} - 22 q^{42} - 2 q^{46} - 228 q^{48} - 128 q^{49} - 11 q^{51} - 166 q^{52} + 35 q^{54} - 160 q^{55} - 44 q^{57} - 126 q^{58} - 11 q^{60} + 66 q^{61} + 33 q^{63} + 40 q^{64} + 22 q^{66} - 22 q^{67} - 24 q^{69} + 68 q^{70} - 149 q^{72} - 42 q^{73} + 123 q^{75} - 88 q^{76} - 108 q^{78} - 66 q^{79} - 81 q^{81} - 14 q^{82} + 44 q^{84} - 200 q^{85} + 75 q^{87} + 66 q^{88} + 16 q^{93} - 146 q^{94} + 5 q^{96} - 88 q^{97} - 308 q^{99}+O(q^{100}) $ 1200 * q - 9 * q^3 - 74 * q^4 - 20 * q^6 - 44 * q^7 - 13 * q^9 - 22 * q^10 - 25 * q^12 - 72 * q^13 - 44 * q^15 + 38 * q^16 - 45 * q^18 - 22 * q^19 + 44 * q^21 + 2 * q^24 + 18 * q^25 - 90 * q^27 - 44 * q^28 - 55 * q^30 - 18 * q^31 - 11 * q^33 - 88 * q^34 - 108 * q^36 - 66 * q^37 + q^39 - 22 * q^40 - 22 * q^42 - 2 * q^46 - 228 * q^48 - 128 * q^49 - 11 * q^51 - 166 * q^52 + 35 * q^54 - 160 * q^55 - 44 * q^57 - 126 * q^58 - 11 * q^60 + 66 * q^61 + 33 * q^63 + 40 * q^64 + 22 * q^66 - 22 * q^67 - 24 * q^69 + 68 * q^70 - 149 * q^72 - 42 * q^73 + 123 * q^75 - 88 * q^76 - 108 * q^78 - 66 * q^79 - 81 * q^81 - 14 * q^82 + 44 * q^84 - 200 * q^85 + 75 * q^87 + 66 * q^88 + 16 * q^93 - 146 * q^94 + 5 * q^96 - 88 * q^97 - 308 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{22}\right)$

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 $

$2$	−0.839508	+	1.62842i	−0.593622	+	1.15147i	0.380360	+	0.924838i	$0.375800\pi$
$2$	−0.839508	+	1.62842i	−0.593622	+	1.15147i	−0.973982	+	0.226627i	$0.927230\pi$
$3$	1.58694	+	0.693981i	0.916222	+	0.400670i
$3$	1.58694	+	0.693981i	0.916222	+	0.400670i
$4$	−0.786858	−	1.10499i	−0.393429	−	0.552493i
$5$	−1.28009	−	1.22056i	−0.572474	−	0.545853i	0.347577	−	0.937652i	$-0.387005\pi$
$5$	−1.28009	−	1.22056i	−0.572474	−	0.545853i	−0.920051	+	0.391798i	$0.871853\pi$
$6$	−2.46234	+	2.00161i	−1.00525	+	0.817152i
$7$	−1.82028	+	1.92005i	−0.688000	+	0.725711i
$7$	−1.82028	+	1.92005i	−0.688000	+	0.725711i
$8$	−1.16691	+	0.167776i	−0.412565	+	0.0593179i
$9$	2.03678	+	2.20262i	0.678927	+	0.734206i
$10$	3.06224	−	1.05985i	0.968364	−	0.335154i
$11$	−1.43861	+	0.741654i	−0.433757	+	0.223617i	−0.661255	−	0.750161i	$-0.729976\pi$
$11$	−1.43861	+	0.741654i	−0.433757	+	0.223617i	0.227498	+	0.973779i	$0.426945\pi$
$12$	−0.481859	−	2.29962i	−0.139101	−	0.663842i
$13$	−2.50372	+	2.88945i	−0.694407	+	0.801388i	−0.987985	−	0.154547i	$-0.950608\pi$
$13$	−2.50372	+	2.88945i	−0.694407	+	0.801388i	0.293579	+	0.955935i	$0.405154\pi$
$14$	−1.59851	−	4.57607i	−0.427219	−	1.22301i
$15$	−1.18438	−	2.82533i	−0.305807	−	0.729496i
$16$	1.59377	−	4.60489i	0.398442	−	1.15122i
$17$	2.10363	+	0.200872i	0.510205	+	0.0487187i	0.346984	−	0.937871i	$-0.387206\pi$
$17$	2.10363	+	0.200872i	0.510205	+	0.0487187i	0.163221	+	0.986590i	$0.447812\pi$
$18$	−5.29667	+	1.46762i	−1.24844	+	0.345920i
$19$	−0.0495015	−	0.518403i	−0.0113564	−	0.118930i	0.988016	−	0.154351i	$-0.0493287\pi$
$19$	−0.0495015	−	0.518403i	−0.0113564	−	0.118930i	−0.999372	+	0.0354214i	$0.988723\pi$
$20$	−0.341458	+	2.37490i	−0.0763524	+	0.531043i
$21$	−4.22116	+	1.78377i	−0.921132	+	0.389251i
$22$		−	2.96528i		−	0.632200i
$23$	−3.70659	+	3.04322i	−0.772878	+	0.634555i
$23$	−3.70659	+	3.04322i	−0.772878	+	0.634555i
$24$	−1.96826	−	0.543562i	−0.401769	−	0.110954i
$25$	−0.0890537	−	1.86947i	−0.0178107	−	0.373893i
$26$	−2.60333	−	6.50281i	−0.510556	−	1.27531i
$27$	1.70368	+	4.90892i	0.327874	+	0.944722i
$28$	3.55393	+	0.500576i	0.671629	+	0.0946000i
$29$	−6.63808	+	3.03151i	−1.23266	+	0.562937i	−0.921854	−	0.387536i	$-0.873326\pi$
$29$	−6.63808	+	3.03151i	−1.23266	+	0.562937i	−0.310806	+	0.950473i	$0.600599\pi$
$30$	5.59511	+	0.443211i	1.02152	+	0.0809189i
$31$	−4.45840	−	1.78487i	−0.800752	−	0.320573i	−0.0650535	−	0.997882i	$-0.520722\pi$
$31$	−4.45840	−	1.78487i	−0.800752	−	0.320573i	−0.735699	+	0.677309i	$0.763146\pi$
$32$	4.53362	+	4.75472i	0.801439	+	0.840525i
$33$	−2.79769	+	0.178597i	−0.487014	+	0.0310897i
$34$	−2.09312	+	3.25695i	−0.358967	+	0.558563i
$35$	4.67367	−	0.236074i	0.789994	−	0.0399038i
$36$	0.831207	−	3.98376i	0.138535	−	0.663960i
$37$	2.84100	−	0.689218i	0.467057	−	0.113307i	0.00467765	−	0.999989i	$-0.498511\pi$
$37$	2.84100	−	0.689218i	0.467057	−	0.113307i	0.462379	+	0.886682i	$0.346996\pi$
$38$	0.885734	+	0.354594i	0.143685	+	0.0575228i
$39$	−5.97848	+	2.84785i	−0.957323	+	0.456022i
$40$	1.69854	+	1.20952i	0.268562	+	0.191242i
$41$	2.41842	+	8.23639i	0.377694	+	1.28631i	0.900872	+	0.434084i	$0.142928\pi$
$41$	2.41842	+	8.23639i	0.377694	+	1.28631i	−0.523178	+	0.852223i	$0.675254\pi$
$42$	0.638963	−	8.37130i	0.0985942	−	1.29172i
$43$	8.55608	+	1.23018i	1.30479	+	0.187600i	0.759423	−	0.650597i	$-0.225481\pi$
$43$	8.55608	+	1.23018i	1.30479	+	0.187600i	0.545367	+	0.838198i	$0.316390\pi$
$44$	1.95150	+	1.00607i	0.294199	+	0.151670i
$45$	0.0811716	−	5.30558i	0.0121003	−	0.790909i
$46$	−1.84392	−	8.59068i	−0.271871	−	1.26663i
$47$	−4.47113	+	2.58141i	−0.652182	+	0.376537i	−0.789292	−	0.614019i	$-0.789552\pi$
$47$	−4.47113	+	2.58141i	−0.652182	+	0.376537i	0.137110	+	0.990556i	$0.456219\pi$
$48$	5.72493	−	6.20166i	0.826322	−	0.895132i
$49$	−0.373184	−	6.99005i	−0.0533121	−	0.998578i
$50$	3.11903	+	1.42442i	0.441098	+	0.201443i
$51$	3.19894	+	1.77865i	0.447941	+	0.249061i
$52$	5.16287	+	0.492994i	0.715961	+	0.0683660i
$53$	8.56794	−	1.65134i	1.17690	−	0.226828i	0.436945	−	0.899488i	$-0.356060\pi$
$53$	8.56794	−	1.65134i	1.17690	−	0.226828i	0.739952	+	0.672660i	$0.234848\pi$
$54$	−9.42402	−	1.34677i	−1.28245	−	0.183272i
$55$	2.74679	+	0.806530i	0.370377	+	0.108752i
$56$	1.80196	−	2.54593i	0.240797	−	0.340214i
$57$	0.281206	−	0.857030i	0.0372466	−	0.113516i
$58$	0.636155	−	13.3545i	0.0835313	−	1.75354i
$59$	2.36455	−	0.818378i	0.307838	−	0.106544i	−0.168781	−	0.985653i	$-0.553983\pi$
$59$	2.36455	−	0.818378i	0.307838	−	0.106544i	0.476619	+	0.879110i	$0.341862\pi$
$60$	−2.19001	+	3.53186i	−0.282729	+	0.455961i
$61$	3.66243	+	4.65716i	0.468926	+	0.596288i	0.961780	−	0.273824i	$-0.0882886\pi$
$61$	3.66243	+	4.65716i	0.468926	+	0.596288i	−0.492854	+	0.870112i	$0.664046\pi$
$62$	6.64938	−	5.76172i	0.844472	−	0.731739i
$63$	−7.93664	−	0.0986526i	−0.999923	−	0.0124291i
$64$	−2.19767	+	0.645295i	−0.274709	+	0.0806618i
$65$	6.73175	−	0.642804i	0.834970	−	0.0797300i
$66$	2.05785	−	4.70573i	0.253304	−	0.579236i
$67$	−12.2539	+	0.583726i	−1.49705	+	0.0713134i	−0.780033	−	0.625739i	$-0.784798\pi$
$67$	−12.2539	+	0.583726i	−1.49705	+	0.0713134i	−0.717021	+	0.697052i	$0.754495\pi$
$68$	−1.43330	−	2.48254i	−0.173813	−	0.301052i
$69$	−7.99409	+	2.25711i	−0.962375	+	0.271725i
$70$	−3.53915	+	7.80887i	−0.423010	+	0.933338i
$71$	0.585578	+	0.911177i	0.0694953	+	0.108137i	0.874262	−	0.485455i	$-0.161346\pi$
$71$	0.585578	+	0.911177i	0.0694953	+	0.108137i	−0.804767	+	0.593591i	$0.797710\pi$
$72$	−2.74629	−	2.22854i	−0.323653	−	0.262635i
$73$	3.82466	+	5.37099i	0.447643	+	0.628627i	0.975314	−	0.220822i	$-0.0708740\pi$
$73$	3.82466	+	5.37099i	0.447643	+	0.628627i	−0.527671	+	0.849449i	$0.676935\pi$
$74$	−1.26270	+	5.20493i	−0.146786	+	0.605061i
$75$	1.15605	−	3.02854i	0.133489	−	0.349706i
$76$	−0.533878	+	0.462608i	−0.0612400	+	0.0530648i
$77$	1.19465	−	4.11222i	0.136143	−	0.468631i
$78$	0.381485	−	12.1263i	0.0431946	−	1.37303i
$79$	1.56110	−	8.09974i	0.175637	−	0.911292i	−0.781992	−	0.623288i	$-0.785796\pi$
$79$	1.56110	−	8.09974i	0.175637	−	0.911292i	0.957629	−	0.288004i	$-0.0929915\pi$
$80$	−7.66074	+	3.94938i	−0.856496	+	0.441555i
$81$	−0.703048	+	8.97250i	−0.0781164	+	0.996944i
$82$	−15.4426	−	2.97631i	−1.70535	−	0.328678i
$83$	6.80410	+	1.99787i	0.746847	+	0.219294i	0.632944	−	0.774198i	$-0.281846\pi$
$83$	6.80410	+	1.99787i	0.746847	+	0.219294i	0.113904	+	0.993492i	$0.463665\pi$
$84$	5.29249	+	3.26075i	0.577459	+	0.355776i
$85$	−2.44766	−	2.82475i	−0.265486	−	0.306387i
$86$	−9.18614	+	12.9001i	−0.990567	+	1.39106i
$87$	−12.6381	+	0.204134i	−1.35494	+	0.0218854i
$88$	1.55430	−	1.10681i	0.165689	−	0.117986i
$89$	4.72860	−	1.89305i	0.501231	−	0.200663i	−0.107248	−	0.994232i	$-0.534204\pi$
$89$	4.72860	−	1.89305i	0.501231	−	0.200663i	0.608479	+	0.793570i	$0.291780\pi$
$90$	8.57155	+	4.58625i	0.903521	+	0.483434i
$91$	−0.990419	−	10.0669i	−0.103824	−	1.05529i
$92$	6.27928	+	1.70115i	0.654660	+	0.177358i
$93$	−5.83656	−	5.92654i	−0.605223	−	0.614554i
$94$	−0.450063	−	9.44798i	−0.0464205	−	0.974485i
$95$	−0.569378	+	0.724023i	−0.0584170	+	0.0742832i
$96$	3.89491	+	10.6917i	0.397523	+	1.09122i
$97$	3.90524	+	13.3000i	0.396517	+	1.35041i	0.879964	+	0.475041i	$0.157567\pi$
$97$	3.90524	+	13.3000i	0.396517	+	1.35041i	−0.483446	+	0.875374i	$0.660615\pi$
$98$	11.6960	+	5.26050i	1.18147	+	0.531390i
$99$	−4.56371	−	1.65812i	−0.458670	−	0.166647i
$100$	−1.99566	+	1.56941i	−0.199566	+	0.156941i
$101$	6.71587	+	7.04340i	0.668254	+	0.700845i	0.967369	−	0.253372i	$-0.0815398\pi$
$101$	6.71587	+	7.04340i	0.668254	+	0.700845i	−0.299115	+	0.954217i	$0.596691\pi$
$102$	−5.58192	+	3.71602i	−0.552693	+	0.367941i
$103$	9.71897	+	0.462971i	0.957638	+	0.0456179i	0.520578	−	0.853814i	$-0.325717\pi$
$103$	9.71897	+	0.462971i	0.957638	+	0.0456179i	0.437060	+	0.899432i	$0.356020\pi$
$104$	2.43684	−	3.79179i	0.238951	−	0.371816i
$105$	7.58068	+	2.86880i	0.739798	+	0.279966i
$106$	−4.50379	+	15.3385i	−0.437447	+	1.48981i
$107$	2.32331	−	1.82707i	0.224603	−	0.176629i	−0.499517	−	0.866304i	$-0.666489\pi$
$107$	2.32331	−	1.82707i	0.224603	−	0.176629i	0.724119	+	0.689675i	$0.242247\pi$
$108$	4.08373	−	5.74516i	0.392957	−	0.552829i
$109$	−1.00553	+	10.5304i	−0.0963123	+	1.00863i	0.810116	+	0.586269i	$0.199404\pi$
$109$	−1.00553	+	10.5304i	−0.0963123	+	1.00863i	−0.906429	+	0.422359i	$0.861202\pi$
$110$	−3.61932	+	3.79583i	−0.345088	+	0.361918i
$111$	4.98680	+	0.877847i	0.473327	+	0.0833215i
$112$	5.94052	+	11.4423i	0.561326	+	1.08119i
$113$	10.5245	−	6.76366i	0.990057	−	0.636271i	0.0578991	−	0.998322i	$-0.481560\pi$
$113$	10.5245	−	6.76366i	0.990057	−	0.636271i	0.932158	+	0.362051i	$0.117923\pi$
$114$	1.15953	+	1.17740i	0.108600	+	0.110274i
$115$	8.45922	+	0.628535i	0.788827	+	0.0586112i
$116$	8.57300	+	4.94962i	0.795983	+	0.459561i
$117$	−11.4639	+	0.370432i	−1.05984	+	0.0342465i
$118$	−0.652395	+	4.53751i	−0.0600578	+	0.417711i
$119$	−4.21487	+	3.67343i	−0.386377	+	0.336743i
$120$	1.85610	+	3.09819i	0.169438	+	0.282825i
$121$	−4.86108	+	6.82643i	−0.441917	+	0.620585i
$122$	−10.6584	+	2.05425i	−0.964970	+	0.185983i
$123$	−1.87800	+	14.7490i	−0.169333	+	1.32987i
$124$	1.53586	+	6.33092i	0.137925	+	0.568533i
$125$	−7.95917	+	9.18538i	−0.711890	+	0.821565i
$126$	6.82352	−	12.8413i	0.607887	−	1.14400i
$127$	16.0784	+	10.3329i	1.42673	+	0.916901i	0.999921	+	0.0125565i	$0.00399697\pi$
$127$	16.0784	+	10.3329i	1.42673	+	0.916901i	0.426804	+	0.904344i	$0.359639\pi$
$128$	−1.69250	+	8.78152i	−0.149597	+	0.776184i
$129$	12.7243	+	7.88998i	1.12031	+	0.694674i
$130$	−4.60460	+	11.5017i	−0.403850	+	1.00877i
$131$	−6.88425	−	2.38266i	−0.601480	−	0.208174i	0.00932359	−	0.999957i	$-0.497032\pi$
$131$	−6.88425	−	2.38266i	−0.601480	−	0.208174i	−0.610803	+	0.791782i	$0.709153\pi$
$132$	2.39873	+	2.95088i	0.208782	+	0.256841i
$133$	1.08547	+	0.848592i	0.0941219	+	0.0735823i
$134$	9.33670	−	20.4445i	0.806568	−	1.76614i
$135$	3.81078	−	8.36332i	0.327980	−	0.719800i
$136$	−2.48845	+	0.118540i	−0.213383	+	0.0101647i
$137$	2.25261	−	3.90163i	0.192453	−	0.333339i	−0.753609	−	0.657323i	$-0.771689\pi$
$137$	2.25261	−	3.90163i	0.192453	−	0.333339i	0.946063	+	0.323984i	$0.105022\pi$
$138$	3.03557	−	14.9126i	0.258405	−	1.26944i
$139$	−12.5871			−1.06763			−0.533813	−	0.845602i	$-0.679242\pi$
$139$	−12.5871			−1.06763			−0.533813	+	0.845602i	$0.679242\pi$
$140$	−3.93837	−	4.97858i	−0.332853	−	0.420767i
$141$	−8.88688	+	0.993671i	−0.748411	+	0.0836822i
$142$	−1.97537	+	0.188625i	−0.165770	+	0.0158291i
$143$	1.45890	−	6.01368i	0.122000	−	0.502889i
$144$	13.3890	−	5.86869i	1.11575	−	0.489058i
$145$	12.1975	+	4.22160i	1.01295	+	0.350584i
$146$	−11.9570	+	1.71916i	−0.989572	+	0.142279i
$147$	4.25874	−	11.3518i	0.351255	−	0.936280i
$148$	−2.99704	−	2.59695i	−0.246355	−	0.213468i
$149$	0.907659	−	19.0541i	0.0743584	−	1.56097i	−0.586179	−	0.810181i	$-0.699369\pi$
$149$	0.907659	−	19.0541i	0.0743584	−	1.56097i	0.660538	−	0.750793i	$-0.270328\pi$
$150$	3.96121	+	4.42502i	0.323432	+	0.361301i
$151$	−3.95492	−	11.4270i	−0.321847	−	0.929915i	−0.983627	−	0.180217i	$-0.942320\pi$
$151$	−3.95492	−	11.4270i	−0.321847	−	0.929915i	0.661780	−	0.749698i	$-0.269801\pi$
$152$	0.144740	+	0.596625i	0.0117399	+	0.0483927i
$153$	3.84219	+	5.04262i	0.310622	+	0.407672i
$154$	5.69349	+	5.39763i	0.458794	+	0.434954i
$155$	3.52861	+	7.72657i	0.283424	+	0.620613i
$156$	7.85106	+	4.36529i	0.628588	+	0.349503i
$157$	−18.6149	+	13.2556i	−1.48563	+	1.05791i	−0.504759	+	0.863260i	$0.668419\pi$
$157$	−18.6149	+	13.2556i	−1.48563	+	1.05791i	−0.980872	+	0.194653i	$0.937642\pi$
$158$	11.8792	+	9.34191i	0.945059	+	0.743202i
$159$	14.7428	+	3.32541i	1.16918	+	0.263722i
$160$		−	11.6201i		−	0.918647i
$161$	0.903887	−	12.6563i	0.0712363	−	0.997459i
$162$	−14.0208	−	8.67734i	−1.10158	−	0.681756i
$163$	−7.88542	−	4.06522i	−0.617634	−	0.318412i	0.120863	−	0.992669i	$-0.461434\pi$
$163$	−7.88542	−	4.06522i	−0.617634	−	0.318412i	−0.738497	+	0.674257i	$0.764464\pi$
$164$	7.19815	−	9.15319i	0.562081	−	0.714744i
$165$	3.79928	+	3.18614i	0.295774	+	0.248040i
$166$	−8.96546	+	9.40270i	−0.695854	+	0.729791i
$167$	−20.4808	+	9.35328i	−1.58485	+	0.723779i	−0.996402	−	0.0847527i	$-0.972990\pi$
$167$	−20.4808	+	9.35328i	−1.58485	+	0.723779i	−0.588453	+	0.808532i	$0.700263\pi$
$168$	4.62644	−	2.78972i	0.356937	−	0.215231i
$169$	−0.230195	−	1.60104i	−0.0177073	−	0.123157i
$170$	6.65471	−	1.61441i	0.510393	−	0.123820i
$171$	1.04102	−	1.16491i	0.0796088	−	0.0890826i
$172$	−5.37308	−	10.4223i	−0.409694	−	0.794695i
$173$	3.70763	+	0.176616i	0.281886	+	0.0134279i	0.188049	−	0.982160i	$-0.439784\pi$
$173$	3.70763	+	0.176616i	0.281886	+	0.0134279i	0.0938371	+	0.995588i	$0.470087\pi$
$174$	10.2773	−	20.7514i	0.779123	−	1.57316i
$175$	3.75157	+	3.23196i	0.283592	+	0.244313i
$176$	1.12243	+	7.80666i	0.0846062	+	0.588449i
$177$	4.32034	+	0.342231i	0.324737	+	0.0257237i
$178$	−0.887027	+	9.28937i	−0.0664855	+	0.696268i
$179$	−8.73106	−	2.11813i	−0.652590	−	0.158317i	−0.104222	−	0.994554i	$-0.533235\pi$
$179$	−8.73106	−	2.11813i	−0.652590	−	0.158317i	−0.548368	+	0.836237i	$0.684751\pi$
$180$	−5.92646	+	4.08504i	−0.441732	+	0.304481i
$181$	−8.79357	−	1.26432i	−0.653621	−	0.0939765i	−0.192476	−	0.981302i	$-0.561652\pi$
$181$	−8.79357	−	1.26432i	−0.653621	−	0.0939765i	−0.461144	+	0.887325i	$0.652561\pi$
$182$	17.2245	+	6.83839i	1.27677	+	0.506895i
$183$	2.58009	+	9.93231i	0.190726	+	0.734217i
$184$	3.81468	−	4.17305i	0.281222	−	0.307641i
$185$	−4.47797	−	2.58536i	−0.329227	−	0.190079i
$186$	14.5507	−	4.52898i	1.06691	−	0.332081i
$187$	−3.17528	+	1.27119i	−0.232199	+	0.0929586i
$188$	6.37057	+	2.90934i	0.464621	+	0.212185i
$189$	−12.5265	−	5.66443i	−0.911172	−	0.412027i
$190$	−0.701015	−	1.53501i	−0.0508570	−	0.111361i
$191$	1.65490	−	4.78151i	0.119744	−	0.345978i	−0.869160	−	0.494530i	$-0.835340\pi$
$191$	1.65490	−	4.78151i	0.119744	−	0.345978i	0.988905	+	0.148552i	$0.0474613\pi$
$192$	−3.93540	−	0.501096i	−0.284013	−	0.0361635i
$193$	9.58774	−	9.14189i	0.690140	−	0.658048i	−0.261521	−	0.965198i	$-0.584224\pi$
$193$	9.58774	−	9.14189i	0.690140	−	0.658048i	0.951661	+	0.307150i	$0.0993754\pi$
$194$	−24.9365	−	4.80612i	−1.79034	−	0.345059i
$195$	11.1290	+	3.65161i	0.796964	+	0.261497i
$196$	−7.43027	+	5.91253i	−0.530733	+	0.422324i
$197$	20.5237	+	17.7839i	1.46225	+	1.26705i	0.896923	+	0.442186i	$0.145797\pi$
$197$	20.5237	+	17.7839i	1.46225	+	1.26705i	0.565331	+	0.824864i	$0.308748\pi$
$198$	6.53138	−	6.03963i	0.464165	−	0.429218i
$199$	3.46120	−	8.64567i	0.245358	−	0.612875i	−0.753656	−	0.657269i	$-0.771711\pi$
$199$	3.46120	−	8.64567i	0.245358	−	0.612875i	0.999014	+	0.0443939i	$0.0141357\pi$
$200$	0.417570	+	2.16656i	0.0295267	+	0.153199i
$201$	−19.8514	−	7.57764i	−1.40021	−	0.534486i
$202$	−17.1076	+	5.02325i	−1.20369	+	0.353435i
$203$	6.26249	−	18.2636i	0.439541	−	1.28186i
$204$	−0.551723	−	4.93433i	−0.0386284	−	0.345472i
$205$	6.95724	−	13.4952i	0.485915	−	0.942544i
$206$	−8.91306	+	15.4379i	−0.621002	+	1.07561i
$207$	−14.2526	−	1.96583i	−0.990622	−	0.136635i
$208$	9.31523	+	16.1345i	0.645895	+	1.11872i
$209$	0.455689	+	0.709066i	0.0315207	+	0.0490471i
$210$	−11.0356	+	9.93613i	−0.761532	+	0.685658i
$211$	3.59135	−	7.86395i	0.247238	−	0.541377i	−0.744804	−	0.667284i	$-0.767457\pi$
$211$	3.59135	−	7.86395i	0.247238	−	0.541377i	0.992042	+	0.125907i	$0.0401841\pi$
$212$	−8.56645	−	8.16810i	−0.588346	−	0.560987i
$213$	0.296940	+	1.85237i	0.0203460	+	0.126922i
$214$	1.02480	+	5.31715i	0.0700537	+	0.363473i
$215$	−9.45105	−	12.0180i	−0.644556	−	0.819620i
$216$	−2.81165	−	5.44243i	−0.191308	−	0.370311i
$217$	11.5426	−	5.31139i	0.783561	−	0.360560i
$218$	−16.3037	−	10.4778i	−1.10423	−	0.709644i
$219$	2.34216	+	11.1777i	0.158269	+	0.755319i
$220$	−1.27013	−	3.66979i	−0.0856319	−	0.247417i
$221$	−5.84731	+	5.57540i	−0.393332	+	0.375042i
$222$	−5.61596	+	7.38364i	−0.376919	+	0.495558i
$223$	−7.42588	−	8.56993i	−0.497274	−	0.573885i	0.450521	−	0.892766i	$-0.351238\pi$
$223$	−7.42588	−	8.56993i	−0.497274	−	0.573885i	−0.947795	+	0.318881i	$0.896693\pi$
$224$	−17.3818	+	0.0498637i	−1.16137	+	0.00333166i
$225$	3.93634	−	4.00384i	0.262422	−	0.266923i
$226$	2.17870	+	22.8163i	0.144925	+	1.51772i
$227$	−7.59527	−	5.97298i	−0.504116	−	0.396441i	0.333458	−	0.942765i	$-0.391784\pi$
$227$	−7.59527	−	5.97298i	−0.504116	−	0.396441i	−0.837574	+	0.546324i	$0.816027\pi$
$228$	−1.16828	+	0.363632i	−0.0773709	+	0.0240821i
$229$	13.2487	−	7.64914i	0.875499	−	0.505470i	0.00632742	−	0.999980i	$-0.497986\pi$
$229$	13.2487	−	7.64914i	0.875499	−	0.505470i	0.869172	+	0.494510i	$0.164653\pi$
$230$	−8.12510	+	13.2475i	−0.535753	+	0.873514i
$231$	4.74965	−	5.69679i	0.312504	−	0.374821i
$232$	7.23743	−	4.65121i	0.475161	−	0.305367i
$233$	−6.04664	−	15.1038i	−0.396128	−	0.989481i	−0.983621	−	0.180251i	$-0.942309\pi$
$233$	−6.04664	−	15.1038i	−0.396128	−	0.989481i	0.587492	−	0.809230i	$-0.300115\pi$
$234$	9.02079	−	18.9790i	0.589707	−	1.24069i
$235$	8.87424	+	2.15287i	0.578891	+	0.140438i
$236$	−2.76486	−	1.96885i	−0.179977	−	0.128161i
$237$	8.09844	−	11.7705i	0.526050	−	0.764573i
$238$	−2.44346	−	9.94745i	−0.158386	−	0.644797i
$239$	−0.630209	+	2.14630i	−0.0407649	+	0.138832i	−0.977361	−	0.211578i	$-0.932140\pi$
$239$	−0.630209	+	2.14630i	−0.0407649	+	0.138832i	0.936596	+	0.350410i	$0.113958\pi$
$240$	−14.8980	+	0.951045i	−0.961659	+	0.0613897i
$241$	−11.7384	−	22.7693i	−0.756136	−	1.46670i	−0.880290	−	0.474436i	$-0.842652\pi$
$241$	−11.7384	−	22.7693i	−0.756136	−	1.46670i	0.124154	−	0.992263i	$-0.460378\pi$
$242$	−7.03537	−	13.6467i	−0.452251	−	0.877244i
$243$	−7.34244	+	13.7509i	−0.471018	+	0.882124i
$244$	2.26429	−	7.71146i	0.144956	−	0.493676i
$245$	−8.05409	+	9.40339i	−0.514557	+	0.600761i
$246$	−22.4410	−	15.4401i	−1.43078	−	0.984424i
$247$	1.62184	+	1.15490i	0.103195	+	0.0734848i
$248$	5.50202	+	1.33477i	0.349378	+	0.0847583i
$249$	9.41125	+	7.89242i	0.596414	+	0.500162i
$250$	−8.27584	−	20.6721i	−0.523410	−	1.30742i
$251$	−4.05187	+	2.60398i	−0.255752	+	0.164362i	−0.662234	−	0.749297i	$-0.730392\pi$
$251$	−4.05187	+	2.60398i	−0.255752	+	0.164362i	0.406482	+	0.913659i	$0.366755\pi$
$252$	6.13600	+	8.84751i	0.386531	+	0.557341i
$253$	3.07532	−	7.12701i	0.193344	−	0.448071i
$254$	−30.3243	+	17.5077i	−1.90271	+	1.09853i
$255$	−1.92398	−	6.18135i	−0.120484	−	0.387091i
$256$	−16.4800	−	12.9600i	−1.03000	−	0.809999i
$257$	2.02425	+	21.1989i	0.126269	+	1.32235i	0.807320	+	0.590114i	$0.200917\pi$
$257$	2.02425	+	21.1989i	0.126269	+	1.32235i	−0.681051	+	0.732236i	$0.738477\pi$
$258$	−23.5303	+	14.0968i	−1.46493	+	0.877627i
$259$	−3.84807	+	6.70942i	−0.239107	+	0.416903i
$260$	−6.00722	−	6.93270i	−0.372552	−	0.429948i
$261$	−20.1976	−	8.44663i	−1.25020	−	0.522833i
$262$	9.65935	−	9.21017i	0.596757	−	0.569006i
$263$	9.18544	+	26.5396i	0.566398	+	1.63650i	0.755949	+	0.654630i	$0.227176\pi$
$263$	9.18544	+	26.5396i	0.566398	+	1.63650i	−0.189551	+	0.981871i	$0.560703\pi$
$264$	3.23469	−	0.677792i	0.199081	−	0.0417152i
$265$	−12.9833	−	8.34387i	−0.797559	−	0.512560i
$266$	−2.29312	+	1.05519i	−0.140600	+	0.0646981i
$267$	8.81777	+	0.277401i	0.539638	+	0.0169767i
$268$	10.2871	+	13.0811i	0.628384	+	0.799055i
$269$	−0.357114	−	1.85288i	−0.0217736	−	0.112972i	0.969416	−	0.245424i	$-0.0789272\pi$
$269$	−0.357114	−	1.85288i	−0.0217736	−	0.112972i	−0.991189	+	0.132452i	$0.957715\pi$
$270$	10.4198	+	13.2266i	0.634129	+	0.804946i
$271$	10.8057	+	10.3032i	0.656402	+	0.625878i	0.943244	−	0.332100i	$-0.107757\pi$
$271$	10.8057	+	10.3032i	0.656402	+	0.625878i	−0.286842	+	0.957978i	$0.592606\pi$
$272$	4.27769	−	9.36684i	0.259373	−	0.567948i
$273$	5.41447	−	16.6629i	0.327699	−	1.00848i
$274$	4.46241	+	6.94364i	0.269584	+	0.419481i
$275$	1.51461	+	2.62338i	0.0913345	+	0.158196i
$276$	8.78429	+	7.05733i	0.528752	+	0.424802i
$277$	4.78232	−	8.28322i	0.287342	−	0.497690i	−0.685833	−	0.727759i	$-0.740562\pi$
$277$	4.78232	−	8.28322i	0.287342	−	0.497690i	0.973174	+	0.230069i	$0.0738952\pi$
$278$	10.5670	−	20.4971i	0.633766	−	1.22934i
$279$	−5.14939	−	13.4555i	−0.308286	−	0.805563i
$280$	−5.41415	+	1.05961i	−0.323557	+	0.0633237i
$281$	10.7531	−	3.15741i	0.641479	−	0.188355i	0.0552138	−	0.998475i	$-0.482416\pi$
$281$	10.7531	−	3.15741i	0.641479	−	0.188355i	0.586265	+	0.810119i	$0.300598\pi$
$282$	5.84250	−	15.3058i	0.347916	−	0.911444i
$283$	−0.203985	−	1.05837i	−0.0121256	−	0.0629138i	0.975362	−	0.220611i	$-0.0708051\pi$
$283$	−0.203985	−	1.05837i	−0.0121256	−	0.0629138i	−0.987488	+	0.157697i	$0.949593\pi$
$284$	0.546072	−	1.36402i	0.0324034	−	0.0809398i
$285$	−1.40603	+	0.753847i	−0.0832860	+	0.0446540i
$286$	8.56802	+	7.42423i	0.506638	+	0.439004i
$287$	−20.2165	−	10.3490i	−1.19334	−	0.610883i
$288$	−1.23885	+	19.6702i	−0.0729998	+	1.15908i
$289$	−12.3079	−	2.37215i	−0.723993	−	0.139538i
$290$	−17.1144	+	16.3186i	−1.00499	+	0.958259i
$291$	−3.03257	+	23.8166i	−0.177773	+	1.39615i
$292$	2.92541	−	8.45241i	0.171196	−	0.494640i
$293$	−11.6353	−	25.4777i	−0.679741	−	1.48842i	−0.862918	−	0.505345i	$-0.831365\pi$
$293$	−11.6353	−	25.4777i	−0.679741	−	1.48842i	0.183177	−	0.983080i	$-0.441362\pi$
$294$	14.9102	+	16.4649i	0.869582	+	0.960254i
$295$	−4.02572	−	1.83849i	−0.234387	−	0.107041i
$296$	−3.19955	+	1.28091i	−0.185970	+	0.0744513i
$297$	−6.09165	−	5.79847i	−0.353473	−	0.336461i
$298$	30.2661	+	17.4741i	1.75327	+	1.01225i
$299$	0.487044	−	18.3294i	0.0281665	−	1.06001i
$300$	−4.25614	+	1.10561i	−0.245729	+	0.0638323i
$301$	−17.9364	+	14.1888i	−1.03384	+	0.817831i
$302$	21.9281	+	3.15279i	1.26182	+	0.181422i
$303$	5.76972	+	15.8382i	0.331462	+	0.909879i
$304$	−2.46608	−	0.598265i	−0.141440	−	0.0343129i
$305$	0.996119	−	10.4318i	0.0570376	−	0.597325i
$306$	−11.4370	+	2.02336i	−0.653812	+	0.115668i
$307$	−1.21653	−	8.46113i	−0.0694309	−	0.482902i	−0.994636	−	0.103435i	$-0.967016\pi$
$307$	−1.21653	−	8.46113i	−0.0694309	−	0.482902i	0.925205	−	0.379467i	$-0.123893\pi$
$308$	−5.48397	+	1.91565i	−0.312478	+	0.109154i
$309$	15.1022	+	7.47949i	0.859132	+	0.425493i
$310$	−15.5444	−	0.740470i	−0.882861	−	0.0420559i
$311$	−6.74535	−	13.0841i	−0.382494	−	0.741934i	0.616473	−	0.787376i	$-0.288561\pi$
$311$	−6.74535	−	13.0841i	−0.382494	−	0.741934i	−0.998967	+	0.0454417i	$0.985530\pi$
$312$	6.49855	−	4.32624i	0.367908	−	0.244925i
$313$	0.0150786	−	0.00365802i	0.000852290	−	0.000206763i	−0.235333	−	0.971915i	$-0.575618\pi$
$313$	0.0150786	−	0.00365802i	0.000852290	−	0.000206763i	0.236185	+	0.971708i	$0.424103\pi$
$314$	−5.95832	−	41.4410i	−0.336247	−	2.33865i
$315$	10.0392	+	9.81347i	0.565646	+	0.552926i
$316$	−10.1785	+	4.64835i	−0.572583	+	0.261490i
$317$	5.42987	−	5.69468i	0.304972	−	0.319845i	−0.553358	−	0.832944i	$-0.686654\pi$
$317$	5.42987	−	5.69468i	0.304972	−	0.319845i	0.858330	+	0.513098i	$0.171502\pi$
$318$	−17.7919	+	21.2158i	−0.997719	+	1.18972i
$319$	7.30127	−	9.28431i	0.408792	−	0.519822i
$320$	3.60085	+	1.85636i	0.201293	+	0.103774i
$321$	4.95491	−	1.28712i	0.276556	−	0.0718403i
$322$	19.8510	+	12.0970i	1.10625	+	0.674140i
$323$		−	1.10047i		−	0.0612319i
$324$	10.4677	−	6.28322i	0.581538	−	0.349068i
$325$	5.62469	+	4.42330i	0.312002	+	0.245361i
$326$	13.2397	−	9.42798i	0.733281	−	0.522167i
$327$	−8.90361	+	16.0133i	−0.492371	+	0.885538i
$328$	−4.20396	−	9.20538i	−0.232125	−	0.508282i
$329$	3.18226	−	13.2837i	0.175444	−	0.732353i
$330$	−8.37789	+	3.51203i	−0.461188	+	0.193331i
$331$	5.88832	+	24.2720i	0.323651	+	1.33411i	0.868548	+	0.495605i	$0.165054\pi$
$331$	5.88832	+	24.2720i	0.323651	+	1.33411i	−0.544897	+	0.838503i	$0.683431\pi$
$332$	−3.14625	−	9.09048i	−0.172673	−	0.498905i
$333$	7.30457	+	4.85384i	0.400288	+	0.265989i
$334$	1.96277	−	41.2035i	0.107398	−	2.25456i
$335$	16.3986	+	14.2095i	0.895951	+	0.776346i
$336$	1.48654	+	22.2809i	0.0810975	+	1.21552i
$337$	6.41882	−	0.922887i	0.349655	−	0.0502729i	0.0347503	−	0.999396i	$-0.488936\pi$
$337$	6.41882	−	0.922887i	0.349655	−	0.0502729i	0.314905	+	0.949123i	$0.398027\pi$
$338$	2.80042	+	0.969234i	0.152323	+	0.0527194i
$339$	21.3956	−	3.42977i	1.16205	−	0.186280i
$340$	−1.19535	+	4.92731i	−0.0648271	+	0.267221i
$341$	7.73765	−	0.738856i	0.419017	−	0.0400113i
$342$	1.02301	+	2.67316i	0.0553181	+	0.144548i
$343$	14.1005	+	12.0073i	0.761357	+	0.648332i
$344$	−10.1906			−0.549439
$345$	12.9881	+	6.86799i	0.699257	+	0.369760i
$346$	−3.40019	+	5.88930i	−0.182795	+	0.316611i
$347$	13.1966	−	0.628632i	0.708431	−	0.0337467i	0.309726	−	0.950826i	$-0.399763\pi$
$347$	13.1966	−	0.628632i	0.708431	−	0.0337467i	0.398705	+	0.917079i	$0.369460\pi$
$348$	10.1699	+	13.8043i	0.545165	+	0.739987i
$349$	−6.29619	+	13.7867i	−0.337028	+	0.737987i	−0.999943	−	0.0107071i	$-0.996592\pi$
$349$	−6.29619	+	13.7867i	−0.337028	+	0.737987i	0.662915	+	0.748695i	$0.269319\pi$
$350$	−8.41245	+	3.39587i	−0.449665	+	0.181517i
$351$	−18.4496	−	7.36785i	−0.984766	−	0.393267i
$352$	−10.0485	−	3.47781i	−0.535585	−	0.185368i
$353$	8.96444	−	22.3921i	0.477129	−	1.19181i	−0.473309	−	0.880896i	$-0.656941\pi$
$353$	8.96444	−	22.3921i	0.477129	−	1.19181i	0.950438	−	0.310914i	$-0.100635\pi$
$354$	−4.18426	+	6.74802i	−0.222391	+	0.358653i
$355$	0.362557	−	1.88113i	0.0192425	−	0.0998398i
$356$	−5.81253	−	3.73549i	−0.308063	−	0.197980i
$357$	−9.23806	+	2.90449i	−0.488930	+	0.153722i
$358$	10.7790	−	12.4396i	0.569688	−	0.657455i
$359$	7.37959	+	30.4191i	0.389480	+	1.60546i	0.742503	+	0.669843i	$0.233638\pi$
$359$	7.37959	+	30.4191i	0.389480	+	1.60546i	−0.353023	+	0.935615i	$0.614846\pi$
$360$	0.795431	+	6.20475i	0.0419229	+	0.327019i
$361$	18.3904	−	3.54445i	0.967913	−	0.186550i
$362$	9.44112	−	13.2582i	0.496214	−	0.696835i
$363$	−12.4517	+	7.45967i	−0.653544	+	0.391531i
$364$	−10.3444	+	9.01558i	−0.542195	+	0.472545i
$365$	1.65972	−	11.5436i	0.0868737	−	0.604220i
$366$	−18.3400	−	4.13678i	−0.958645	−	0.216233i
$367$	10.3246	+	5.96090i	0.538939	+	0.311156i	0.744649	−	0.667457i	$-0.232617\pi$
$367$	10.3246	+	5.96090i	0.538939	+	0.311156i	−0.205710	+	0.978613i	$0.565950\pi$
$368$	8.10625	+	21.9186i	0.422567	+	1.14259i
$369$	−13.2158	+	22.1026i	−0.687988	+	1.15061i
$370$	7.96933	−	5.12158i	0.414306	−	0.266258i
$371$	−12.4254	+	19.4568i	−0.645094	+	1.01014i
$372$	−1.95621	+	11.1127i	−0.101425	+	0.576165i
$373$	12.1975	−	12.7923i	0.631560	−	0.662361i	−0.327734	−	0.944770i	$-0.606285\pi$
$373$	12.1975	−	12.7923i	0.631560	−	0.662361i	0.959294	+	0.282409i	$0.0911335\pi$
$374$	0.595643	−	6.23785i	0.0307999	−	0.322552i
$375$	−19.0052	+	9.05316i	−0.981426	+	0.467503i
$376$	4.78431	−	3.76243i	0.246732	−	0.194032i
$377$	7.86050	−	26.7704i	0.404836	−	1.37875i
$378$	19.7402	−	15.6431i	1.01533	−	0.804594i
$379$	−4.91160	+	7.64259i	−0.252292	+	0.392574i	−0.944179	−	0.329431i	$-0.893143\pi$
$379$	−4.91160	+	7.64259i	−0.252292	+	0.392574i	0.691888	+	0.722005i	$0.256779\pi$
$380$	1.24806	+	0.0594522i	0.0640239	+	0.00304984i
$381$	18.3446	+	27.5559i	0.939823	+	1.41173i
$382$	6.39700	+	6.70898i	0.327299	+	0.343261i
$383$	−7.82139	+	6.15081i	−0.399654	+	0.314291i	−0.797678	−	0.603084i	$-0.793939\pi$
$383$	−7.82139	+	6.15081i	−0.399654	+	0.314291i	0.398024	+	0.917375i	$0.369696\pi$
$384$	−8.78011	+	12.7612i	−0.448058	+	0.651218i
$385$	−6.54849	+	3.80586i	−0.333742	+	0.193965i
$386$	6.83784	+	23.2875i	0.348037	+	1.18530i
$387$	14.7172	+	21.3514i	0.748120	+	1.08535i
$388$	11.6235	−	14.7805i	0.590094	−	0.750365i
$389$	−1.36463	−	28.6471i	−0.0691895	−	1.45247i	−0.720394	−	0.693565i	$-0.756039\pi$
$389$	−1.36463	−	28.6471i	−0.0691895	−	1.45247i	0.651205	−	0.758902i	$-0.274264\pi$
$390$	−15.2892	+	15.0571i	−0.774200	+	0.762446i
$391$	−8.40859	+	5.65726i	−0.425241	+	0.286100i
$392$	1.60824	+	8.09415i	0.0812283	+	0.408816i
$393$	−9.27139	−	8.55869i	−0.467680	−	0.431729i
$394$	−46.1894	+	18.4915i	−2.32699	+	0.931586i
$395$	−11.8846	+	8.46299i	−0.597979	+	0.425819i
$396$	1.75879	+	6.34754i	0.0883827	+	0.318976i
$397$	−14.8518	+	20.8564i	−0.745390	+	1.04675i	0.251493	+	0.967859i	$0.419078\pi$
$397$	−14.8518	+	20.8564i	−0.745390	+	1.04675i	−0.996883	+	0.0788943i	$0.974861\pi$
$398$	11.1731	+	12.8944i	0.560055	+	0.646338i
$399$	1.13367	+	2.09996i	0.0567544	+	0.105130i
$400$	−8.75062	−	2.56941i	−0.437531	−	0.128471i
$401$	17.0499	+	3.28610i	0.851432	+	0.164100i	0.596256	−	0.802794i	$-0.296654\pi$
$401$	17.0499	+	3.28610i	0.851432	+	0.164100i	0.255176	+	0.966895i	$0.417866\pi$
$402$	29.0049	−	25.9648i	1.44663	−	1.29501i
$403$	16.3199	−	8.41348i	0.812951	−	0.419105i
$404$	2.49843	−	12.9631i	0.124302	−	0.644939i
$405$	11.8515	−	10.6275i	0.588905	−	0.528085i
$406$	24.4834	+	25.5304i	1.21509	+	1.26705i
$407$	−3.57592	+	3.09855i	−0.177252	+	0.153590i
$408$	−4.03130	−	1.53882i	−0.199579	−	0.0761830i
$409$	−6.49108	+	26.7566i	−0.320963	+	1.32303i	0.551429	+	0.834222i	$0.314083\pi$
$409$	−6.49108	+	26.7566i	−0.320963	+	1.32303i	−0.872392	+	0.488806i	$0.837432\pi$
$410$	16.1351	+	22.6586i	0.796857	+	1.11903i
$411$	6.28242	−	4.62841i	0.309889	−	0.228302i
$412$	−7.13587	−	11.1036i	−0.351559	−	0.547036i
$413$	−2.73280	+	6.02972i	−0.134473	+	0.296703i
$414$	15.1663	−	21.5588i	0.745384	−	1.05956i
$415$	−6.27135	−	10.8623i	−0.307849	−	0.533209i
$416$	−25.0894	+	1.19516i	−1.23011	+	0.0585974i
$417$	−19.9751	−	8.73523i	−0.978184	−	0.427766i
$418$	−1.53721	+	0.146786i	−0.0751875	+	0.00717953i
$419$	22.5502	−	6.62134i	1.10165	−	0.323474i	0.320142	−	0.947369i	$-0.396269\pi$
$419$	22.5502	−	6.62134i	1.10165	−	0.323474i	0.781507	+	0.623896i	$0.214451\pi$
$420$	−2.79493	−	10.6339i	−0.136378	−	0.518881i
$421$	2.65740	−	2.30265i	0.129514	−	0.112224i	−0.587695	−	0.809082i	$-0.699965\pi$
$421$	2.65740	−	2.30265i	0.129514	−	0.112224i	0.717209	+	0.696858i	$0.245419\pi$
$422$	9.79083	+	12.4501i	0.476610	+	0.606059i
$423$	−14.7926	−	4.59043i	−0.719240	−	0.223194i
$424$	−9.72097	+	3.36446i	−0.472092	+	0.163393i
$425$	0.188188	−	3.95055i	0.00912846	−	0.191630i
$426$	−3.26571	−	1.07153i	−0.158224	−	0.0519160i
$427$	−15.6086	−	1.44527i	−0.755354	−	0.0699415i
$428$	−3.84700	−	1.12958i	−0.185952	−	0.0546003i
$429$	6.48857	−	8.53092i	0.313271	−	0.411876i
$430$	27.5045	−	5.30107i	1.32639	−	0.255640i
$431$	−30.2350	−	2.88709i	−1.45637	−	0.139066i	−0.663370	−	0.748292i	$-0.730874\pi$
$431$	−30.2350	−	2.88709i	−1.45637	−	0.139066i	−0.792997	+	0.609226i	$0.791480\pi$
$432$	25.3203	−	0.0215928i	1.21822	−	0.00103888i
$433$	11.2926	+	5.15715i	0.542687	+	0.247837i	0.667845	−	0.744300i	$-0.267217\pi$
$433$	11.2926	+	5.15715i	0.542687	+	0.247837i	−0.125159	+	0.992137i	$0.539944\pi$
$434$	−1.04092	+	23.2551i	−0.0499658	+	1.11628i
$435$	16.4270	+	15.1643i	0.787616	+	0.727071i
$436$	12.4271	−	7.17482i	0.595152	−	0.343611i
$437$	1.76110	+	1.77086i	0.0842447	+	0.0847119i
$438$	−20.1682	−	5.56975i	−0.963675	−	0.266133i
$439$	−11.3876	−	5.87070i	−0.543499	−	0.280193i	0.164535	−	0.986371i	$-0.447387\pi$
$439$	−11.3876	−	5.87070i	−0.543499	−	0.280193i	−0.708034	+	0.706178i	$0.750418\pi$
$440$	−3.34057	−	0.480302i	−0.159256	−	0.0228975i
$441$	14.6363	−	15.0592i	0.696967	−	0.717103i
$442$	−4.17021	−	14.2024i	−0.198357	−	0.675542i
$443$	−17.1432	−	12.2076i	−0.814498	−	0.580001i	0.0951113	−	0.995467i	$-0.469679\pi$
$443$	−17.1432	−	12.2076i	−0.814498	−	0.580001i	−0.909609	+	0.415466i	$0.863619\pi$
$444$	−2.95390	−	6.20109i	−0.140186	−	0.294291i
$445$	−8.36363	−	3.34829i	−0.396474	−	0.158724i
$446$	20.1895	−	4.89792i	0.956001	−	0.231923i
$447$	14.6636	−	29.6079i	0.693564	−	1.40041i
$448$	2.76137	−	5.39425i	0.130463	−	0.254855i
$449$	19.7797	−	30.7779i	0.933463	−	1.45250i	0.0421489	−	0.999111i	$-0.486580\pi$
$449$	19.7797	−	30.7779i	0.933463	−	1.45250i	0.891314	−	0.453386i	$-0.149784\pi$
$450$	3.21535	+	9.77126i	0.151573	+	0.460622i
$451$	−9.58771	−	10.0553i	−0.451468	−	0.473486i
$452$	−15.7550	−	6.30735i	−0.741053	−	0.296673i
$453$	1.65388	−	20.8786i	0.0777060	−	0.980964i
$454$	16.1028	−	7.35390i	0.755742	−	0.345136i
$455$	−11.0194	+	14.0954i	−0.516599	+	0.660801i
$456$	−0.184353	+	1.04726i	−0.00863311	+	0.0490423i
$457$	4.28204	+	10.6960i	0.200306	+	0.500339i	0.994179	−	0.107744i	$-0.0343628\pi$
$457$	4.28204	+	10.6960i	0.200306	+	0.500339i	−0.793873	+	0.608084i	$0.791939\pi$
$458$	1.33361	+	27.9959i	0.0623156	+	1.30816i
$459$	2.59785	+	10.6688i	0.121257	+	0.497975i
$460$	−5.96168	−	9.84190i	−0.277965	−	0.458881i
$461$			41.2226i			1.91993i	0.280122	+	0.959964i	$0.409625\pi$
$461$			41.2226i			1.91993i	−0.280122	+	0.959964i	$0.590375\pi$
$462$	5.28939	+	12.5169i	0.246085	+	0.582339i
$463$	1.62836	−	11.3255i	0.0756761	−	0.526339i	−0.916357	−	0.400362i	$-0.868884\pi$
$463$	1.62836	−	11.3255i	0.0756761	−	0.526339i	0.992033	−	0.125977i	$-0.0402066\pi$
$464$	3.38021	+	35.3991i	0.156922	+	1.64336i
$465$	0.237607	+	14.7104i	0.0110188	+	0.682179i
$466$	29.6714	+	2.83328i	1.37450	+	0.131249i
$467$	−0.964428	+	2.78653i	−0.0446284	+	0.128945i	−0.965113	−	0.261833i	$-0.915673\pi$
$467$	−0.964428	+	2.78653i	−0.0446284	+	0.128945i	0.920485	+	0.390779i	$0.127794\pi$
$468$	9.42976	+	12.3759i	0.435891	+	0.572078i
$469$	21.1847	−	24.5907i	0.978220	−	1.13549i
$470$	−10.9558	+	12.6436i	−0.505351	+	0.583207i
$471$	−38.7399	+	8.11752i	−1.78504	+	0.374036i
$472$	−2.62191	+	1.35169i	−0.120683	+	0.0622166i
$473$	−13.2212	+	4.57591i	−0.607912	+	0.210400i
$474$	12.3685	+	23.0690i	0.568105	+	1.05960i
$475$	−0.964729	+	0.138707i	−0.0442648	+	0.00636432i
$476$	7.37560	+	1.76691i	0.338060	+	0.0809863i
$477$	21.0883	+	15.5085i	0.965566	+	0.710085i
$478$	−2.96600	−	2.82808i	−0.135662	−	0.129353i
$479$	−17.4751	−	24.5403i	−0.798456	−	1.12127i	−0.990176	−	0.139825i	$-0.955346\pi$
$479$	−17.4751	−	24.5403i	−0.798456	−	1.12127i	0.191721	−	0.981450i	$-0.438593\pi$
$480$	8.06410	−	18.4404i	0.368074	−	0.841685i
$481$	−5.12160	+	9.93451i	−0.233525	+	0.452975i
$482$	46.9324			2.13771
$483$	10.2177	−	19.4576i	0.464920	−	0.885352i
$484$	11.3681			0.516732
$485$	11.2345	−	21.7919i	0.510132	−	0.989518i
$486$	−16.2283	−	23.5006i	−0.736129	−	1.06601i
$487$	−14.1553	−	19.8783i	−0.641438	−	0.900773i	0.358020	−	0.933714i	$-0.383452\pi$
$487$	−14.1553	−	19.8783i	−0.641438	−	0.900773i	−0.999457	+	0.0329408i	$0.989513\pi$
$488$	−5.05509	−	4.82002i	−0.228833	−	0.218192i
$489$	−9.69253	−	11.9236i	−0.438312	−	0.539204i
$490$	−8.55118	−	21.0097i	−0.386303	−	0.949119i
$491$	−12.8441	+	1.84670i	−0.579646	+	0.0833405i	−0.425900	−	0.904770i	$-0.640043\pi$
$491$	−12.8441	+	1.84670i	−0.579646	+	0.0833405i	−0.153745	+	0.988111i	$0.549133\pi$
$492$	17.7752	−	9.53022i	0.801368	−	0.429655i
$493$	−14.5730	+	5.04377i	−0.656335	+	0.227160i
$494$	−3.24221	+	1.67148i	−0.145874	+	0.0752032i
$495$	3.81813	+	7.69285i	0.171612	+	0.345768i
$496$	−15.3248	+	17.6858i	−0.688104	+	0.794114i
$497$	−2.81542	−	0.534255i	−0.126289	−	0.0239646i
$498$	−20.7530	+	8.69970i	−0.929963	+	0.389843i
$499$	−2.34445	+	6.77385i	−0.104952	+	0.303239i	−0.985234	−	0.171211i	$-0.945232\pi$
$499$	−2.34445	+	6.77385i	−0.104952	+	0.303239i	0.880282	+	0.474450i	$0.157353\pi$
$500$	16.4125	+	1.56720i	0.733987	+	0.0700873i
$501$	−38.9929	+	0.629825i	−1.74208	+	0.0281385i
$502$	−0.838790	−	8.78421i	−0.0374370	−	0.392058i
$503$	−2.37036	+	16.4862i	−0.105689	+	0.735083i	0.866209	+	0.499681i	$0.166550\pi$
$503$	−2.37036	+	16.4862i	−0.105689	+	0.735083i	−0.971898	+	0.235401i	$0.924360\pi$
$504$	9.27791	−	1.21646i	0.413271	−	0.0541856i
$505$		−	17.2134i		−	0.765984i
$506$	9.02400	+	10.9911i	0.401166	+	0.488613i
$507$	0.745786	−	2.70052i	0.0331215	−	0.119934i
$508$	−1.23362	−	25.8970i	−0.0547332	−	1.14899i
$509$	5.07796	+	12.6841i	0.225076	+	0.562214i	0.997324	−	0.0731079i	$-0.0232917\pi$
$509$	5.07796	+	12.6841i	0.225076	+	0.562214i	−0.772248	+	0.635322i	$0.780867\pi$
$510$	11.6810	+	2.05625i	0.517244	+	0.0910525i
$511$	−17.2745	−	2.43314i	−0.764179	−	0.107636i
$512$	18.6694	−	8.52602i	0.825078	−	0.376800i
$513$	2.46046	−	1.12619i	0.108632	−	0.0497226i
$514$	−36.2200	−	14.5003i	−1.59760	−	0.639581i
$515$	−11.8761	−	12.4553i	−0.523323	−	0.548845i
$516$	−1.29388	−	20.2685i	−0.0569601	−	0.892270i
$517$	4.51770	−	7.02967i	0.198688	−	0.309165i
$518$	−7.69526	−	11.8989i	−0.338110	−	0.522806i
$519$	5.76123	+	2.85330i	0.252890	+	0.125246i
$520$	−7.74750	+	1.87952i	−0.339750	+	0.0824226i
$521$	15.7847	+	6.31926i	0.691542	+	0.276852i	0.690693	−	0.723148i	$-0.257306\pi$
$521$	15.7847	+	6.31926i	0.691542	+	0.276852i	0.000848954		1.00000i	$0.499730\pi$
$522$	30.7107	−	25.7991i	1.34417	−	1.12919i
$523$	19.4418	+	13.8444i	0.850130	+	0.605375i	0.919884	−	0.392189i	$-0.128282\pi$
$523$	19.4418	+	13.8444i	0.850130	+	0.605375i	−0.0697545	+	0.997564i	$0.522222\pi$
$524$	2.78411	+	9.48182i	0.121625	+	0.414215i
$525$	3.71061	+	7.73246i	0.161945	+	0.337472i
$526$	−50.9288	−	7.32245i	−2.22060	−	0.319274i
$527$	−9.02029	−	4.65028i	−0.392930	−	0.202570i
$528$	−3.63644	+	13.1677i	−0.158256	+	0.573049i
$529$	4.47763	−	22.5599i	0.194680	−	0.980867i
$530$	24.4869	−	14.1375i	1.06364	−	0.614094i
$531$	6.61864	+	3.54134i	0.287224	+	0.153681i
$532$	0.0835754	−	1.86715i	0.00362345	−	0.0809511i
$533$	−29.8536	−	13.6337i	−1.29310	−	0.590541i
$534$	−7.85431	+	14.1261i	−0.339889	+	0.611297i
$535$	−5.20410	−	0.496931i	−0.224993	−	0.0214842i
$536$	14.2013	−	2.73707i	0.613402	−	0.118224i
$537$	−12.3858	−	9.42054i	−0.534485	−	0.406527i
$538$	3.31707	+	0.973979i	0.143009	+	0.0419912i
$539$	5.72106	+	9.77917i	0.246424	+	0.421219i
$540$	−12.2399	+	2.36988i	−0.526721	+	0.101983i
$541$	0.00763673	−	0.160315i	0.000328329	−	0.00689247i	−0.998697	−	0.0510279i	$-0.983750\pi$
$541$	0.00763673	−	0.160315i	0.000328329	−	0.00689247i	0.999026	+	0.0441354i	$0.0140533\pi$
$542$	−25.8495	+	8.94660i	−1.11033	+	0.384289i
$543$	−13.0775	−	8.10898i	−0.561209	−	0.347990i
$544$	8.58197	+	10.9129i	0.367949	+	0.467885i
$545$	14.1402	−	12.2525i	0.605699	−	0.524841i
$546$	22.5886	+	22.8056i	0.966704	+	0.975991i
$547$	4.88226	−	1.43356i	0.208750	−	0.0612946i	−0.175686	−	0.984446i	$-0.556214\pi$
$547$	4.88226	−	1.43356i	0.208750	−	0.0612946i	0.384436	+	0.923152i	$0.374396\pi$
$548$	−6.08374	+	0.580926i	−0.259884	+	0.0248159i
$549$	−2.79837	+	17.5525i	−0.119432	+	0.749124i
$550$	−5.54349	+	0.264069i	−0.236375	+	0.0112599i
$551$	1.90014	+	3.29114i	0.0809486	+	0.140207i
$552$	8.94970	−	3.97507i	0.380924	−	0.169190i
$553$	12.7103	+	17.7411i	0.540496	+	0.754430i
$554$	9.47375	+	14.7414i	0.402501	+	0.626304i
$555$	−5.31210	−	7.21044i	−0.225486	−	0.306066i
$556$	9.90428	+	13.9086i	0.420035	+	0.589857i
$557$	10.7768	−	44.4224i	0.456626	−	1.88224i	−0.0139951	−	0.999902i	$-0.504455\pi$
$557$	10.7768	−	44.4224i	0.456626	−	1.88224i	0.470621	−	0.882335i	$-0.344030\pi$
$558$	26.2342	+	2.91068i	1.11058	+	0.123219i
$559$	−24.9766	+	21.6423i	−1.05640	+	0.915372i
$560$	6.36165	−	21.8980i	0.268829	−	0.925358i
$561$	−5.92117	−	0.186276i	−0.249992	−	0.00786459i
$562$	−3.88577	+	20.1613i	−0.163911	+	0.850452i
$563$	−19.1650	+	9.88024i	−0.807708	+	0.416403i	−0.812050	−	0.583588i	$-0.801648\pi$
$563$	−19.1650	+	9.88024i	−0.807708	+	0.416403i	0.00434155	+	0.999991i	$0.498618\pi$
$564$	8.09071	+	9.03801i	0.340680	+	0.380569i
$565$	−21.7277	−	4.18768i	−0.914093	−	0.176177i
$566$	1.89472	+	0.556340i	0.0796411	+	0.0233847i
$567$	−15.9479	−	17.6823i	−0.669749	−	0.742588i
$568$	−0.836191	−	0.965016i	−0.0350858	−	0.0404912i
$569$	10.5947	−	14.8781i	0.444152	−	0.623724i	−0.530437	−	0.847724i	$-0.677972\pi$
$569$	10.5947	−	14.8781i	0.444152	−	0.623724i	0.974589	+	0.224000i	$0.0719117\pi$
$570$	−0.0472045	−	2.92246i	−0.00197718	−	0.122409i
$571$	−30.0931	+	21.4292i	−1.25936	+	0.896783i	−0.997660	−	0.0683676i	$-0.978221\pi$
$571$	−30.0931	+	21.4292i	−1.25936	+	0.896783i	−0.261695	+	0.965151i	$0.584282\pi$
$572$	−7.79298	+	3.11984i	−0.325841	+	0.130447i
$573$	5.94451	−	6.43953i	0.248335	−	0.269015i
$574$	33.8244	−	24.2328i	1.41180	−	1.01146i
$575$	6.01928	+	6.65834i	0.251021	+	0.277672i
$576$	−5.89751	−	3.52631i	−0.245730	−	0.146929i
$577$	1.15232	+	24.1902i	0.0479718	+	1.00705i	0.886655	+	0.462432i	$0.153023\pi$
$577$	1.15232	+	24.1902i	0.0479718	+	1.00705i	−0.838683	+	0.544620i	$0.816674\pi$
$578$	14.1954	−	18.0509i	0.590451	−	0.750820i
$579$	21.5595	−	7.85396i	0.895982	−	0.326399i
$580$	−4.93289	−	16.7999i	−0.204827	−	0.697577i
$581$	−16.2214	+	9.42755i	−0.672975	+	0.391121i
$582$	−36.2375	−	24.9325i	−1.50209	−	1.03349i
$583$	−11.1012	+	8.73008i	−0.459765	+	0.361563i
$584$	−5.36417	−	5.62578i	−0.221971	−	0.232796i
$585$	15.1269	+	13.5182i	0.625422	+	0.558909i
$586$	51.2563	+	2.44164i	2.11738	+	0.100863i
$587$	−17.7483	+	27.6169i	−0.732550	+	1.13987i	0.252499	+	0.967597i	$0.418748\pi$
$587$	−17.7483	+	27.6169i	−0.732550	+	1.13987i	−0.985049	+	0.172273i	$0.944889\pi$
$588$	−15.8946	+	4.22640i	−0.655482	+	0.174294i
$589$	−0.704587	+	2.39960i	−0.0290320	+	0.0988739i
$590$	6.37345	−	5.01213i	0.262391	−	0.206346i
$591$	20.2283	+	42.4651i	0.832081	+	1.74678i
$592$	1.35411	−	14.1809i	0.0556538	−	0.582832i
$593$	26.7467	−	28.0512i	1.09836	−	1.15192i	0.110933	−	0.993828i	$-0.464616\pi$
$593$	26.7467	−	28.0512i	1.09836	−	1.15192i	0.987424	−	0.158095i	$-0.0505353\pi$
$594$	14.5563	−	5.05189i	0.597253	−	0.207282i
$595$	9.87909	+	0.442198i	0.405003	+	0.0181283i
$596$	−21.7687	+	13.9899i	−0.891683	+	0.573050i
$597$	11.4927	−	11.3182i	0.470364	−	0.463222i
$598$	29.4390	+	16.1808i	1.20385	+	0.661680i
$599$	25.1055	+	14.4947i	1.02578	+	0.592237i	0.915774	−	0.401694i	$-0.131578\pi$
$599$	25.1055	+	14.4947i	1.02578	+	0.592237i	0.110010	+	0.993930i	$0.464912\pi$
$600$	−0.840891	+	3.72800i	−0.0343292	+	0.152195i
$601$	3.90813	−	27.1816i	0.159416	−	1.10876i	−0.740297	−	0.672280i	$-0.765315\pi$
$601$	3.90813	−	27.1816i	0.159416	−	1.10876i	0.899713	−	0.436482i	$-0.143776\pi$
$602$	−8.04757	−	41.1196i	−0.327995	−	1.67591i
$603$	−26.2443	−	25.8018i	−1.06875	−	1.05073i
$604$	−9.51472	+	13.3616i	−0.387148	+	0.543674i
$605$	14.5547	−	2.80520i	0.591734	−	0.114047i
$606$	−30.6349	−	3.90075i	−1.24446	−	0.158457i
$607$	3.37049	+	13.8934i	0.136804	+	0.563914i	0.998412	+	0.0563391i	$0.0179428\pi$
$607$	3.37049	+	13.8934i	0.136804	+	0.563914i	−0.861608	+	0.507575i	$0.830542\pi$
$608$	2.24044	−	2.58561i	0.0908620	−	0.104860i
$609$	22.6128	−	24.6373i	0.916318	−	0.998354i
$610$	16.1511	+	10.3797i	0.653940	+	0.420262i
$611$	3.73562	−	19.3822i	0.151127	−	0.784121i
$612$	2.54878	−	8.21339i	0.103028	−	0.332007i
$613$	−10.3488	+	25.8501i	−0.417985	+	1.04408i	0.558694	+	0.829374i	$0.311303\pi$
$613$	−10.3488	+	25.8501i	−0.417985	+	1.04408i	−0.976679	+	0.214703i	$0.931122\pi$
$614$	14.7995	+	5.12217i	0.597261	+	0.206714i
$615$	20.4061	−	16.5879i	0.822855	−	0.668888i
$616$	−0.704120	+	4.99903i	−0.0283698	+	0.201417i
$617$	−9.48873	+	20.7774i	−0.382002	+	0.836468i	0.616780	+	0.787135i	$0.288437\pi$
$617$	−9.48873	+	20.7774i	−0.382002	+	0.836468i	−0.998782	+	0.0493325i	$0.984291\pi$
$618$	−24.8581	+	18.3135i	−0.999940	+	0.736679i
$619$	−16.6862	+	0.794860i	−0.670673	+	0.0319481i	−0.380157	−	0.924922i	$-0.624130\pi$
$619$	−16.6862	+	0.794860i	−0.670673	+	0.0319481i	−0.290516	+	0.956870i	$0.593827\pi$
$620$	5.76125	−	9.97877i	0.231377	−	0.400757i
$621$	−21.2538	−	13.0107i	−0.852884	−	0.522100i
$622$	26.9692			1.08137
$623$	−4.97262	+	12.5250i	−0.199224	+	0.501805i
$624$	3.58574	+	32.0691i	0.143545	+	1.28379i
$625$	12.0843	−	1.15391i	0.483371	−	0.0461563i
$626$	−0.00670178	+	0.0276251i	−0.000267857	+	0.00110412i
$627$	0.231075	+	1.44149i	0.00922823	+	0.0575675i
$628$	29.2946	+	10.1389i	1.16898	+	0.404588i
$629$	6.11485	−	0.879182i	0.243815	−	0.0350553i
$630$	−24.4084	+	8.10955i	−0.972455	+	0.323092i
$631$	−22.7791	−	19.7382i	−0.906821	−	0.785765i	0.0705033	−	0.997512i	$-0.477539\pi$
$631$	−22.7791	−	19.7382i	−0.906821	−	0.785765i	−0.977325	+	0.211746i	$0.932085\pi$
$632$	−0.462715	+	9.71359i	−0.0184058	+	0.386386i
$633$	11.1567	−	9.98732i	0.443439	−	0.396960i
$634$	4.71491	+	13.6228i	0.187253	+	0.541032i
$635$	−7.96977	−	32.8518i	−0.316271	−	1.30368i
$636$	−7.92598	−	18.9073i	−0.314285	−	0.749722i
$637$	21.1317	+	16.4228i	0.837269	+	0.650696i
$638$	8.98927	+	19.6838i	0.355889	+	0.779288i
$639$	−0.814281	+	3.14567i	−0.0322124	+	0.124441i
$640$	12.8850	−	9.17535i	0.509323	−	0.362687i
$641$	−11.5145	−	9.05513i	−0.454797	−	0.357656i	0.364329	−	0.931270i	$-0.381298\pi$
$641$	−11.5145	−	9.05513i	−0.454797	−	0.357656i	−0.819125	+	0.573614i	$0.805541\pi$
$642$	−2.06371	+	9.14921i	−0.0814480	+	0.361091i
$643$			36.2663i			1.43020i	0.699021	+	0.715101i	$0.253619\pi$
$643$			36.2663i			1.43020i	−0.699021	+	0.715101i	$0.746381\pi$
$644$	−14.6963	+	8.95995i	−0.579116	+	0.353072i
$645$	−6.65803	−	25.6307i	−0.262160	−	1.00921i
$646$	1.79203	+	0.923855i	0.0705064	+	0.0363486i
$647$	0.0324503	−	0.0412640i	0.00127575	−	0.00162225i	−0.785415	−	0.618970i	$-0.787550\pi$
$647$	0.0324503	−	0.0412640i	0.00127575	−	0.00162225i	0.786691	+	0.617348i	$0.211793\pi$
$648$	−0.684980	−	10.5881i	−0.0269085	−	0.415938i
$649$	−2.79471	+	2.93100i	−0.109702	+	0.115052i
$650$	−11.9250	+	5.44594i	−0.467735	+	0.213608i
$651$	22.0034	−	0.418547i	0.862382	−	0.0164041i
$652$	1.71269	+	11.9120i	0.0670742	+	0.466511i
$653$	−7.00564	+	1.69955i	−0.274152	+	0.0665085i	−0.370478	−	0.928841i	$-0.620806\pi$
$653$	−7.00564	+	1.69955i	−0.274152	+	0.0665085i	0.0963259	+	0.995350i	$0.469291\pi$
$654$	−18.6017	−	27.9421i	−0.727385	−	1.09262i
$655$	5.90428	+	11.4527i	0.230699	+	0.447494i
$656$	41.7821	+	1.99032i	1.63132	+	0.0777091i
$657$	−4.04023	+	19.3638i	−0.157624	+	0.755454i
$658$	18.9598	+	16.3338i	0.739132	+	0.636758i
$659$	4.95294	+	34.4484i	0.192939	+	1.34192i	0.824177	+	0.566332i	$0.191638\pi$
$659$	4.95294	+	34.4484i	0.192939	+	1.34192i	−0.631238	+	0.775589i	$0.717453\pi$
$660$	0.531145	−	6.70519i	0.0206748	−	0.260999i
$661$	2.69548	−	28.2284i	0.104842	−	1.09796i	−0.777993	−	0.628273i	$-0.783762\pi$
$661$	2.69548	−	28.2284i	0.104842	−	1.09796i	0.882835	−	0.469683i	$-0.155632\pi$
$662$	−44.4682	−	10.7879i	−1.72831	−	0.419283i
$663$	−13.1486	+	4.78992i	−0.510648	+	0.186025i
$664$	−8.27498	−	1.18976i	−0.321132	−	0.0461717i
$665$	−0.353735	−	2.41116i	−0.0137173	−	0.0935007i
$666$	−14.0363	+	7.82005i	−0.543896	+	0.303021i
$667$	15.3791	−	31.4377i	0.595481	−	1.21727i
$668$	26.4508	+	15.2714i	1.02341	+	0.590866i
$669$	−5.83709	−	18.7534i	−0.225675	−	0.725049i
$670$	−36.9057	+	14.7748i	−1.42579	+	0.570801i
$671$	−8.72281	−	3.98357i	−0.336740	−	0.153784i
$672$	−27.6185	−	11.9835i	−1.06541	−	0.462273i
$673$	13.6099	+	29.8015i	0.524623	+	1.14876i	0.967660	+	0.252260i	$0.0811738\pi$
$673$	13.6099	+	29.8015i	0.524623	+	1.14876i	−0.443037	+	0.896503i	$0.646099\pi$
$674$	−3.88580	+	11.2273i	−0.149676	+	0.432459i
$675$	9.02534	−	3.62213i	0.347385	−	0.139416i
$676$	−1.58800	+	1.51416i	−0.0610769	+	0.0582367i
$677$	−26.9024	−	5.18501i	−1.03394	−	0.199276i	−0.356073	−	0.934458i	$-0.615884\pi$
$677$	−26.9024	−	5.18501i	−1.03394	−	0.199276i	−0.677870	+	0.735182i	$0.737097\pi$
$678$	−12.3766	+	37.7202i	−0.475322	+	1.44864i
$679$	−32.6454	−	16.7115i	−1.25281	−	0.641328i
$680$	3.33013	+	2.88557i	0.127705	+	0.110657i
$681$	−7.90812	−	14.7498i	−0.303040	−	0.565212i
$682$	−5.29265	+	13.2204i	−0.202666	+	0.506236i
$683$	−5.45084	−	28.2816i	−0.208571	−	1.08217i	−0.923683	−	0.383157i	$-0.874837\pi$
$683$	−5.45084	−	28.2816i	−0.208571	−	1.08217i	0.715113	−	0.699009i	$-0.246375\pi$
$684$	−2.10634	−	0.233698i	−0.0805380	−	0.00893567i
$685$	−7.64574	+	2.24499i	−0.292129	+	0.0857768i
$686$	−31.3904	+	12.8814i	−1.19849	+	0.491812i
$687$	26.3333	−	2.94441i	1.00468	−	0.112336i
$688$	19.3012	−	37.4392i	0.735853	−	1.42736i
$689$	−16.6803	+	28.8911i	−0.635468	+	1.10066i
$690$	−22.0876	+	15.3844i	−0.840860	+	0.585672i
$691$	−12.7853	−	22.1448i	−0.486375	−	0.842426i	0.513502	−	0.858088i	$-0.328348\pi$
$691$	−12.7853	−	22.1448i	−0.486375	−	0.842426i	−0.999877	+	0.0156619i	$0.995014\pi$
$692$	−2.72222	−	4.23585i	−0.103483	−	0.161023i
$693$	11.4909	−	5.74432i	0.436503	−	0.218209i
$694$	−10.0550	+	22.0173i	−0.381682	+	0.835766i
$695$	16.1127	+	15.3634i	0.611189	+	0.582768i
$696$	14.7133	−	2.35858i	0.557704	−	0.0894016i
$697$	3.43300	+	17.8121i	0.130034	+	0.674681i
$698$	−17.1649	−	21.8269i	−0.649700	−	0.826161i
$699$	0.886056	−	28.1651i	0.0335137	−	1.06530i
$700$	0.619320	−	6.68853i	0.0234081	−	0.252803i
$701$	−18.8808	−	12.1340i	−0.713119	−	0.458294i	0.133118	−	0.991100i	$-0.457501\pi$
$701$	−18.8808	−	12.1340i	−0.713119	−	0.458294i	−0.846237	+	0.532807i	$0.821137\pi$
$702$	27.4865	−	23.8583i	1.03741	−	0.900473i
$703$	−0.497926	−	1.43866i	−0.0187797	−	0.0542602i
$704$	2.68300	−	2.55824i	0.101120	−	0.0964173i
$705$	12.5889	+	9.57503i	0.474124	+	0.360617i
$706$	28.9380	+	33.3962i	1.08909	+	1.25688i
$707$	−25.7484	+	0.0738655i	−0.968369	+	0.00277800i
$708$	−3.02133	−	5.04321i	−0.113549	−	0.189535i
$709$	−2.49406	−	26.1190i	−0.0936665	−	0.980920i	−0.913097	−	0.407742i	$-0.866316\pi$
$709$	−2.49406	−	26.1190i	−0.0936665	−	0.980920i	0.819431	−	0.573178i	$-0.194290\pi$
$710$	2.75889	+	2.16961i	0.103539	+	0.0814242i
$711$	21.0202	−	13.0589i	0.788320	−	0.489747i
$712$	−5.20025	+	3.00237i	−0.194888	+	0.112518i
$713$	21.9572	−	6.95209i	0.822305	−	0.260358i
$714$	3.02570	−	17.4818i	0.113234	−	0.654238i
$715$	−9.20761	+	5.91737i	−0.344345	+	0.221297i
$716$	4.52959	+	11.3144i	0.169279	+	0.422838i
$717$	−2.48960	+	2.96870i	−0.0929756	+	0.110868i
$718$	−55.7302	−	13.5200i	−2.07983	−	0.504562i
$719$	37.3208	+	26.5761i	1.39183	+	0.991119i	0.997390	+	0.0721988i	$0.0230016\pi$
$719$	37.3208	+	26.5761i	1.39183	+	0.991119i	0.394442	+	0.918921i	$0.370938\pi$
$720$	−24.3022	−	8.82964i	−0.905690	−	0.329061i
$721$	−18.5801	+	17.8182i	−0.691961	+	0.663583i
$722$	−9.66700	+	32.9228i	−0.359768	+	1.22526i
$723$	−2.82670	−	44.2798i	−0.105126	−	1.64678i
$724$	5.52223	+	10.7116i	0.205232	+	0.398094i
$725$	6.25845	+	12.1397i	0.232433	+	0.450857i
$726$	−1.69418	−	26.5390i	−0.0628768	−	0.984954i
$727$	7.18307	−	24.4633i	0.266405	−	0.907294i	−0.712274	−	0.701901i	$-0.752335\pi$
$727$	7.18307	−	24.4633i	0.266405	−	0.907294i	0.978680	−	0.205392i	$-0.0658471\pi$
$728$	2.84471	+	11.5810i	0.105432	+	0.429219i
$729$	−21.1949	+	16.7265i	−0.784998	+	0.619499i
$730$	17.4045	+	12.3937i	0.644168	+	0.458710i
$731$	17.7517	+	4.30652i	0.656571	+	0.159282i
$732$	8.94491	−	10.6663i	0.330613	−	0.394237i
$733$	−7.23339	−	18.0681i	−0.267171	−	0.667362i	0.732742	−	0.680506i	$-0.238240\pi$
$733$	−7.23339	−	18.0681i	−0.267171	−	0.667362i	−0.999914	+	0.0131446i	$0.995816\pi$
$734$	−18.3744	+	11.8085i	−0.678211	+	0.435860i
$735$	−19.3072	+	9.33327i	−0.712156	+	0.344263i
$736$	−31.2739	−	3.82702i	−1.15277	−	0.141066i
$737$	17.1957	−	9.92792i	0.633410	−	0.365700i
$738$	−24.8974	−	40.0762i	−0.916488	−	1.47522i
$739$	32.4422	+	25.5128i	1.19341	+	0.938504i	0.999099	−	0.0424367i	$-0.0135121\pi$
$739$	32.4422	+	25.5128i	1.19341	+	0.938504i	0.194306	+	0.980941i	$0.437755\pi$
$740$	0.666739	+	6.98241i	0.0245098	+	0.256678i
$741$	1.77228	+	2.95829i	0.0651064	+	0.108676i
$742$	−21.2525	−	36.5678i	−0.780205	−	1.34245i
$743$	13.2974	+	15.3460i	0.487835	+	0.562991i	0.945286	−	0.326244i	$-0.105783\pi$
$743$	13.2974	+	15.3460i	0.487835	+	0.562991i	−0.457451	+	0.889235i	$0.651237\pi$
$744$	7.80508	+	5.93651i	0.286148	+	0.217643i
$745$	−24.4187	+	23.2832i	−0.894631	+	0.853029i
$746$	10.5914	+	30.6018i	0.387778	+	1.12041i
$747$	9.45794	+	19.0561i	0.346048	+	0.697225i
$748$	3.90314	+	2.50840i	0.142713	+	0.0917160i
$749$	−0.720998	+	7.78664i	−0.0263447	+	0.284517i
$750$	1.21272	−	38.5487i	0.0442822	−	1.40760i
$751$	11.2169	+	14.2635i	0.409312	+	0.520482i	0.946380	−	0.323057i	$-0.104710\pi$
$751$	11.2169	+	14.2635i	0.409312	+	0.520482i	−0.537068	+	0.843539i	$0.680468\pi$
$752$	4.76116	+	24.7032i	0.173622	+	0.900834i
$753$	−8.23721	+	1.32045i	−0.300181	+	0.0481198i
$754$	36.9945	+	35.2742i	1.34726	+	1.28461i
$755$	−8.88473	+	19.4548i	−0.323348	+	0.708034i
$756$	3.59748	+	18.2988i	0.130839	+	0.665520i
$757$	11.9844	+	18.6481i	0.435580	+	0.677776i	0.987766	−	0.155945i	$-0.0498423\pi$
$757$	11.9844	+	18.6481i	0.435580	+	0.677776i	−0.552185	+	0.833721i	$0.686206\pi$
$758$	−8.32201	−	14.4141i	−0.302269	−	0.523545i
$759$	9.82636	−	9.17595i	0.356674	−	0.333066i
$760$	0.542940	−	0.940399i	0.0196945	−	0.0341119i
$761$	−14.0458	+	27.2450i	−0.509158	+	0.987629i	0.484458	+	0.874815i	$0.339017\pi$
$761$	−14.0458	+	27.2450i	−0.509158	+	0.987629i	−0.993616	+	0.112814i	$0.964013\pi$
$762$	−60.2729	+	6.73931i	−2.18346	+	0.244139i
$763$	−18.3885	−	21.0989i	−0.665709	−	0.763831i
$764$	−6.58568	+	1.93373i	−0.238262	+	0.0699599i
$765$	1.23650	−	11.1447i	0.0447057	−	0.402936i
$766$	−3.44997	−	17.9001i	−0.124652	−	0.646758i
$767$	−3.55550	+	8.88122i	−0.128382	+	0.320682i
$768$	−17.1588	−	32.0035i	−0.619164	−	1.15483i
$769$	30.3400	+	26.2898i	1.09409	+	0.948034i	0.998875	−	0.0474223i	$-0.0151006\pi$
$769$	30.3400	+	26.2898i	1.09409	+	0.948034i	0.0952151	+	0.995457i	$0.469646\pi$
$770$	−0.700026	−	13.8587i	−0.0252272	−	0.499434i
$771$	−11.4993	+	35.0462i	−0.414136	+	1.26216i
$772$	−17.6459	−	3.40096i	−0.635088	−	0.122403i
$773$	13.1116	−	12.5019i	0.471591	−	0.449661i	−0.416631	−	0.909076i	$-0.636789\pi$
$773$	13.1116	−	12.5019i	0.471591	−	0.449661i	0.888222	+	0.459415i	$0.151941\pi$
$774$	−47.1242	+	6.04118i	−1.69384	+	0.217146i
$775$	−2.93973	+	8.49378i	−0.105598	+	0.305106i
$776$	−6.78851	−	14.8648i	−0.243693	−	0.533614i
$777$	−10.7629	+	7.97699i	−0.386116	+	0.286173i
$778$	47.7951	+	21.8273i	1.71354	+	0.782547i
$779$	4.15005	−	1.66143i	0.148691	−	0.0595269i
$780$	−4.72195	−	15.1707i	−0.169073	−	0.543198i
$781$	−1.51820	−	0.876531i	−0.0543253	−	0.0313647i
$782$	−2.15330	−	18.4420i	−0.0770017	−	0.659485i
$783$	−26.1906	−	27.4210i	−0.935976	−	0.979948i
$784$	−32.7832	−	9.42204i	−1.17083	−	0.336501i
$785$	40.0081	+	5.75230i	1.42795	+	0.205308i
$786$	21.7205	−	7.91262i	0.774746	−	0.282234i
$787$	3.08132	+	0.747521i	0.109837	+	0.0266462i	0.290301	−	0.956935i	$-0.406245\pi$
$787$	3.08132	+	0.747521i	0.109837	+	0.0266462i	−0.180464	+	0.983582i	$0.557760\pi$
$788$	3.50174	−	36.6718i	0.124744	−	1.30638i
$789$	−3.84119	+	48.4913i	−0.136750	+	1.72634i
$790$	−3.80406	−	26.4578i	−0.135343	−	0.941328i
$791$	−6.17086	+	32.5192i	−0.219411	+	1.15625i
$792$	5.60364	+	1.16919i	0.199117	+	0.0415454i
$793$	−22.6263	−	1.07782i	−0.803484	−	0.0382747i
$794$	−21.4948	−	41.6940i	−0.762821	−	1.47967i
$795$	−14.8133	−	22.2514i	−0.525374	−	0.789177i
$796$	−12.2768	+	2.97833i	−0.435141	+	0.105564i
$797$	−1.38532	−	9.63509i	−0.0490704	−	0.341292i	−0.999536	−	0.0304622i	$-0.990302\pi$
$797$	−1.38532	−	9.63509i	−0.0490704	−	0.341292i	0.950465	−	0.310830i	$-0.100607\pi$
$798$	−4.37134	+	0.0831512i	−0.154744	+	0.00294352i
$799$	−9.92414	+	4.53220i	−0.351091	+	0.160338i
$800$	8.48506	−	8.89888i	0.299992	−	0.314623i
$801$	13.8008	+	6.55958i	0.487627	+	0.231771i
$802$	−19.6647	+	25.0057i	−0.694384	+	0.882982i
$803$	−9.48561	−	4.89017i	−0.334740	−	0.172570i
$804$	7.24700	+	27.8980i	0.255582	+	0.983887i
$805$	−16.6049	+	15.0980i	−0.585247	+	0.532135i
$806$			33.6388i			1.18487i
$807$	0.719146	−	3.18825i	0.0253151	−	0.112232i
$808$	−9.01854	−	7.09226i	−0.317271	−	0.249505i
$809$	−17.7861	+	12.6655i	−0.625327	+	0.445294i	−0.848289	−	0.529534i	$-0.822367\pi$
$809$	−17.7861	+	12.6655i	−0.625327	+	0.445294i	0.222962	+	0.974827i	$0.428428\pi$
$810$	7.35661	+	28.2210i	0.258485	+	0.991586i
$811$	13.8416	+	30.3088i	0.486044	+	1.06429i	0.980757	+	0.195231i	$0.0625457\pi$
$811$	13.8416	+	30.3088i	0.486044	+	1.06429i	−0.494714	+	0.869056i	$0.664727\pi$
$812$	−25.1088	+	7.45090i	−0.881145	+	0.261475i
$813$	9.99784	+	23.8497i	0.350639	+	0.836444i
$814$	−2.04373	−	8.42435i	−0.0716325	−	0.295273i
$815$	5.13220	+	14.8285i	0.179773	+	0.519420i
$816$	13.2889	−	11.8960i	0.465203	−	0.416444i
$817$	0.214190	−	4.49639i	0.00749355	−	0.157309i
$818$	−38.1216	−	33.0325i	−1.33289	−	1.15496i
$819$	20.1562	−	22.6855i	0.704314	−	0.792695i
$820$	−20.3863	+	2.93111i	−0.711922	+	0.102359i
$821$	−38.5407	−	13.3391i	−1.34508	−	0.465537i	−0.442774	−	0.896633i	$-0.646006\pi$
$821$	−38.5407	−	13.3391i	−1.34508	−	0.465537i	−0.902306	+	0.431097i	$0.858127\pi$
$822$	2.26283	+	14.1160i	0.0789254	+	0.492352i
$823$	−1.17473	+	4.84231i	−0.0409486	+	0.168792i	−0.988614	−	0.150472i	$-0.951921\pi$
$823$	−1.17473	+	4.84231i	−0.0409486	+	0.168792i	0.947666	+	0.319264i	$0.103436\pi$
$824$	−11.4188	+	1.09037i	−0.397794	+	0.0379848i
$825$	0.583025	+	5.21427i	0.0202983	+	0.181538i
$826$	−7.52470	−	9.51215i	−0.261818	−	0.330970i
$827$	−19.3407			−0.672542			−0.336271	−	0.941765i	$-0.609166\pi$
$827$	−19.3407			−0.672542			−0.336271	+	0.941765i	$0.609166\pi$
$828$	9.04252	+	17.2957i	0.314249	+	0.601068i
$829$	19.9909	−	34.6252i	0.694312	−	1.20258i	−0.276100	−	0.961129i	$-0.589042\pi$
$829$	19.9909	−	34.6252i	0.694312	−	1.20258i	0.970412	−	0.241455i	$-0.0776246\pi$
$830$	22.9532	−	1.09340i	0.796718	−	0.0379523i
$831$	13.3377	−	9.82616i	0.462678	−	0.340866i
$832$	3.63781	−	7.96569i	0.126118	−	0.276161i
$833$	0.619064	−	14.7794i	0.0214493	−	0.512077i
$834$	30.9938	−	25.1945i	1.07323	−	0.872413i
$835$	37.6336	+	13.0251i	1.30237	+	0.450753i
$836$	0.424946	−	1.06146i	0.0146971	−	0.0367115i
$837$	1.16610	−	24.9268i	0.0403065	−	0.861595i
$838$	−8.14877	+	42.2798i	−0.281495	+	1.46053i
$839$	14.0449	+	9.02613i	0.484885	+	0.311617i	0.760145	−	0.649753i	$-0.225128\pi$
$839$	14.0449	+	9.02613i	0.484885	+	0.311617i	−0.275260	+	0.961370i	$0.588764\pi$
$840$	−9.32729	−	2.07578i	−0.321822	−	0.0716210i
$841$	15.8831	−	18.3300i	0.547692	−	0.632070i
$842$	1.51877	+	6.26045i	0.0523402	+	0.215749i
$843$	19.2558	+	2.45185i	0.663205	+	0.0844461i
$844$	−11.5154	+	2.21942i	−0.396378	+	0.0763955i
$845$	−1.65951	+	2.33045i	−0.0570887	+	0.0801699i
$846$	19.8936	−	20.2348i	0.683957	−	0.695686i
$847$	−4.25858	−	21.7595i	−0.146327	−	0.747666i
$848$	6.05109	−	42.0863i	0.207795	−	1.44525i
$849$	0.410779	−	1.82114i	0.0140979	−	0.0625014i
$850$	6.27517	+	3.62297i	0.215236	+	0.124267i
$851$	−8.43297	+	11.2004i	−0.289078	+	0.383946i
$852$	1.81319	−	1.78566i	0.0621189	−	0.0611758i
$853$	1.95327	−	1.25529i	0.0668788	−	0.0429804i	−0.506774	−	0.862079i	$-0.669162\pi$
$853$	1.95327	−	1.25529i	0.0668788	−	0.0429804i	0.573653	+	0.819098i	$0.305526\pi$
$854$	15.4571	−	24.2040i	0.528930	−	0.828245i
$855$	−2.75445	+	0.220554i	−0.0942001	+	0.00754280i
$856$	−2.40455	+	2.52182i	−0.0821859	+	0.0861941i
$857$	−3.32171	+	34.7865i	−0.113467	+	1.18828i	0.741990	+	0.670411i	$0.233882\pi$
$857$	−3.32171	+	34.7865i	−0.113467	+	1.18828i	−0.855457	+	0.517873i	$0.826724\pi$
$858$	8.44469	+	17.7279i	0.288297	+	0.605220i
$859$	−8.09076	+	6.36264i	−0.276053	+	0.217091i	−0.746581	−	0.665295i	$-0.768306\pi$
$859$	−8.09076	+	6.36264i	−0.276053	+	0.217091i	0.470528	+	0.882385i	$0.344064\pi$
$860$	−5.84309	+	19.8997i	−0.199248	+	0.678575i
$861$	−24.9004	−	30.4531i	−0.848603	−	1.03784i
$862$	30.0839	−	46.8114i	1.02466	−	1.59440i
$863$	16.8835	+	0.804259i	0.574720	+	0.0273773i	0.332930	−	0.942951i	$-0.391963\pi$
$863$	16.8835	+	0.804259i	0.574720	+	0.0273773i	0.241790	+	0.970329i	$0.422266\pi$
$864$	−15.6167	+	30.3557i	−0.531291	+	1.03272i
$865$	−4.53053	−	4.75149i	−0.154043	−	0.161555i
$866$	−17.8782	+	14.0596i	−0.607526	+	0.477764i
$867$	−17.8857	−	12.3059i	−0.607430	−	0.417930i
$868$	−14.9514	−	8.57508i	−0.507483	−	0.291057i
$869$	3.76140	+	12.8101i	0.127597	+	0.434554i
$870$	−38.4844	+	14.0196i	−1.30474	+	0.475308i
$871$	28.9937	−	36.8685i	0.982414	−	1.24924i
$872$	−0.593387	−	12.4567i	−0.0200946	−	0.421838i
$873$	−21.3408	+	35.6910i	−0.722276	+	1.20796i
$874$	−4.36216	+	1.38115i	−0.147552	+	0.0467180i
$875$	−3.14848	−	32.0019i	−0.106438	−	1.08186i
$876$	10.5083	−	11.3833i	0.355041	−	0.384607i
$877$	36.6767	−	14.6831i	1.23848	−	0.495814i	0.342339	−	0.939577i	$-0.388781\pi$
$877$	36.6767	−	14.6831i	1.23848	−	0.495814i	0.896144	+	0.443763i	$0.146357\pi$
$878$	19.1199	−	13.6152i	0.645265	−	0.459491i
$879$	−0.783489	−	48.5064i	−0.0264264	−	1.63608i
$880$	8.09172	−	11.3632i	0.272772	−	0.383055i
$881$	27.2498	+	31.4480i	0.918070	+	1.05951i	0.998032	+	0.0627110i	$0.0199746\pi$
$881$	27.2498	+	31.4480i	0.918070	+	1.05951i	−0.0799620	+	0.996798i	$0.525480\pi$
$882$	12.2353	+	36.4763i	0.411985	+	1.22822i
$883$	−35.0265	−	10.2847i	−1.17873	−	0.346108i	−0.367048	−	0.930202i	$-0.619632\pi$
$883$	−35.0265	−	10.2847i	−1.17873	−	0.346108i	−0.811686	+	0.584094i	$0.801450\pi$
$884$	10.7617	+	2.07415i	0.361956	+	0.0697614i
$885$	−5.11272	−	5.71135i	−0.171862	−	0.191985i
$886$	34.2709	−	17.6679i	1.15135	−	0.593565i
$887$	8.12364	−	42.1494i	0.272765	−	1.41524i	−0.544395	−	0.838829i	$-0.683241\pi$
$887$	8.12364	−	42.1494i	0.272765	−	1.41524i	0.817160	−	0.576411i	$-0.195547\pi$
$888$	−5.96644	−	0.187700i	−0.200221	−	0.00629881i
$889$	−49.1069	+	12.0625i	−1.64699	+	0.404562i
$890$	12.4738	−	10.8086i	0.418121	−	0.362304i
$891$	−5.64308	−	13.4293i	−0.189050	−	0.449900i
$892$	−3.62654	+	14.9488i	−0.121426	+	0.500523i
$893$	1.55954	+	2.19007i	0.0521880	+	0.0732878i
$894$	35.9038	+	48.7345i	1.20080	+	1.62993i
$895$	8.59124	+	13.3682i	0.287173	+	0.446851i
$896$	−13.7801	−	19.2345i	−0.460362	−	0.642579i
$897$	13.4931	−	28.7497i	0.450523	−	0.959923i
$898$	33.5140	+	58.0479i	1.11838	+	1.93708i
$899$	35.0061	−	1.66754i	1.16752	−	0.0556157i
$900$	−7.52153	−	1.19915i	−0.250718	−	0.0399715i
$901$	18.3555	−	1.75274i	0.611510	−	0.0583921i
$902$	24.4232	−	7.17130i	0.813204	−	0.238778i
$903$	−38.3109	+	10.0693i	−1.27491	+	0.335087i
$904$	−11.1463	+	9.65834i	−0.370721	+	0.321232i
$905$	9.71339	+	12.3516i	0.322884	+	0.410580i
$906$	32.6107	+	20.2210i	1.08342	+	0.671797i
$907$	1.22584	−	0.424266i	0.0407032	−	0.0140875i	−0.306640	−	0.951825i	$-0.599205\pi$
$907$	1.22584	−	0.424266i	0.0407032	−	0.0140875i	0.347344	+	0.937738i	$0.387084\pi$
$908$	−0.623675	+	13.0926i	−0.0206974	+	0.434492i
$909$	−1.83517	+	29.1384i	−0.0608686	+	0.966459i
$910$	−13.7023	−	29.7774i	−0.454225	−	0.987111i
$911$	16.4142	+	4.81964i	0.543827	+	0.159682i	0.542096	−	0.840317i	$-0.317631\pi$
$911$	16.4142	+	4.81964i	0.543827	+	0.159682i	0.00173076	+	0.999999i	$0.499449\pi$
$912$	−3.49835	−	2.66083i	−0.115842	−	0.0881088i
$913$	−11.2702	+	2.17215i	−0.372988	+	0.0718876i
$914$	−21.0124	−	2.00644i	−0.695029	−	0.0663672i
$915$	8.82027	−	15.8634i	0.291589	−	0.524429i
$916$	−18.8771	−	8.62086i	−0.623715	−	0.284841i
$917$	17.1061	−	8.88100i	0.564892	−	0.293276i
$918$	−19.5541	−	4.72613i	−0.645382	−	0.155985i
$919$	31.3669	−	18.1097i	1.03470	−	0.597384i	0.116372	−	0.993206i	$-0.462874\pi$
$919$	31.3669	−	18.1097i	1.03470	−	0.597384i	0.918327	+	0.395822i	$0.129540\pi$
$920$	−9.97662	+	0.685815i	−0.328919	+	0.0226106i
$921$	3.94131	−	14.2716i	0.129870	−	0.470265i
$922$	−67.1276	−	34.6067i	−2.21073	−	1.13971i
$923$	−4.09892	−	0.589336i	−0.134918	−	0.0193982i
$924$	−10.0322	−	0.765735i	−0.330034	−	0.0251908i
$925$	−1.54147	−	5.24977i	−0.0506833	−	0.172611i
$926$	17.0756	+	12.1595i	0.561138	+	0.399585i
$927$	18.7757	+	22.3501i	0.616673	+	0.734075i
$928$	−44.5085	−	17.8185i	−1.46106	−	0.584922i
$929$	53.6440	−	13.0139i	1.76000	−	0.426972i	0.779972	−	0.625814i	$-0.215233\pi$
$929$	53.6440	−	13.0139i	1.76000	−	0.426972i	0.980032	+	0.198842i	$0.0637181\pi$
$930$	−24.1542	−	11.9626i	−0.792047	−	0.392269i
$931$	−3.60519	+	0.539478i	−0.118155	+	0.0176807i
$932$	−11.9316	+	18.5660i	−0.390833	+	0.608148i
$933$	−1.62434	−	25.4449i	−0.0531784	−	0.833030i
$934$	−3.72799	−	3.90980i	−0.121984	−	0.127933i
$935$	5.61622	+	2.24839i	0.183670	+	0.0735303i
$936$	13.3152	−	2.35563i	0.435220	−	0.0769962i
$937$	13.5067	−	6.16828i	0.441243	−	0.201509i	−0.182390	−	0.983226i	$-0.558383\pi$
$937$	13.5067	−	6.16828i	0.441243	−	0.201509i	0.623633	+	0.781717i	$0.285656\pi$
$938$	22.2591	+	55.1416i	0.726786	+	1.80044i
$939$	0.0264674	+	0.00465916i	0.000863731	+	0.000152046i
$940$	−4.60387	−	11.4999i	−0.150162	−	0.375086i
$941$	2.08838	+	43.8405i	0.0680793	+	1.42916i	0.731974	+	0.681333i	$0.238599\pi$
$941$	2.08838	+	43.8405i	0.0680793	+	1.42916i	−0.663894	+	0.747826i	$0.731098\pi$
$942$	19.3038	−	69.8995i	0.628951	−	2.27745i
$943$	−34.0292	−	23.1691i	−1.10814	−	0.754491i
$944$		−	12.1928i		−	0.396841i
$945$	9.12131	+	22.5404i	0.296716	+	0.733241i
$946$	3.64782	−	25.3712i	0.118601	−	0.824888i
$947$	−1.78614	−	18.7053i	−0.0580418	−	0.607841i	−0.976964	−	0.213403i	$-0.931545\pi$
$947$	−1.78614	−	18.7053i	−0.0580418	−	0.607841i	0.918923	−	0.394438i	$-0.129061\pi$
$948$	−19.3785	+	0.313008i	−0.629385	+	0.0101660i
$949$	−25.0951	−	2.39629i	−0.814620	−	0.0777868i
$950$	0.584024	−	1.68743i	0.0189483	−	0.0547474i
$951$	12.5689	−	5.26892i	0.407575	−	0.170856i
$952$	4.30207	−	4.99372i	0.139431	−	0.161848i
$953$	17.5660	−	20.2723i	0.569019	−	0.656683i	−0.396188	−	0.918169i	$-0.629667\pi$
$953$	17.5660	−	20.2723i	0.569019	−	0.656683i	0.965207	+	0.261486i	$0.0842127\pi$
$954$	−42.9581	+	21.3210i	−1.39082	+	0.690294i
$955$	−7.95457	+	4.10087i	−0.257404	+	0.132701i
$956$	2.86751	−	0.992456i	0.0927420	−	0.0320983i
$957$	18.0298	−	9.66674i	0.582822	−	0.312481i
$958$	54.6323	−	7.85494i	1.76509	−	0.253781i
$959$	3.39096	+	11.4272i	0.109500	+	0.369003i
$960$	4.42606	+	5.44486i	0.142850	+	0.175732i
$961$	−5.74420	−	5.47709i	−0.185297	−	0.176680i
$962$	−11.8779	−	16.6802i	−0.382959	−	0.537791i
$963$	8.75640	+	1.39602i	0.282171	+	0.0449860i
$964$	−15.9233	+	30.8870i	−0.512856	+	0.994802i
$965$	−23.4315			−0.754285
$966$	23.1073	+	32.9735i	0.743466	+	1.06090i
$967$	37.5426			1.20729			0.603644	−	0.797254i	$-0.293715\pi$
$967$	37.5426			1.20729			0.603644	+	0.797254i	$0.293715\pi$
$968$	4.52714	−	8.78142i	0.145508	−	0.282245i
$969$	0.763707	−	1.74639i	0.0245338	−	0.0561020i
$970$	26.0548	+	36.5889i	0.836570	+	1.17480i
$971$	38.7571	+	36.9549i	1.24378	+	1.18594i	0.974871	+	0.222771i	$0.0715102\pi$
$971$	38.7571	+	36.9549i	1.24378	+	1.18594i	0.268905	+	0.963167i	$0.413338\pi$
$972$	20.9721	−	2.70674i	0.672680	−	0.0868186i
$973$	22.9121	−	24.1679i	0.734527	−	0.774788i
$974$	44.2537	−	6.36272i	1.41798	−	0.203875i
$975$	5.85637	+	10.9230i	0.187554	+	0.349815i
$976$	27.2828	−	9.44266i	0.873300	−	0.302252i
$977$	−24.2698	+	12.5119i	−0.776460	+	0.400293i	−0.800435	−	0.599420i	$-0.795398\pi$
$977$	−24.2698	+	12.5119i	−0.776460	+	0.400293i	0.0239752	+	0.999713i	$0.492368\pi$
$978$	27.5536	−	5.77354i	0.881066	−	0.184617i
$979$	−5.39862	+	6.23034i	−0.172541	+	0.199123i
$980$	16.7281	+	1.50054i	0.534358	+	0.0479329i
$981$	−25.2425	+	19.2333i	−0.805930	+	0.614072i
$982$	7.77551	−	22.4659i	0.248127	−	0.716914i
$983$	6.22889	+	0.594787i	0.198671	+	0.0189708i	0.193917	−	0.981018i	$-0.437881\pi$
$983$	6.22889	+	0.594787i	0.198671	+	0.0189708i	0.00475381	+	0.999989i	$0.498487\pi$
$984$	−0.283083	−	17.5259i	−0.00902436	−	0.558705i
$985$	−4.56583	−	47.8156i	−0.145479	−	1.52353i
$986$	4.02079	−	27.9652i	0.128048	−	0.890594i
$987$	14.2687	−	18.8720i	0.454177	−	0.600703i
$988$		−	2.70085i		−	0.0859256i
$989$	−35.4576	+	21.4783i	−1.12749	+	0.682969i
$990$	−15.7325	−	0.240697i	−0.500012	−	0.00764984i
$991$	0.778032	+	16.3329i	0.0247150	+	0.518831i	0.976950	+	0.213466i	$0.0684754\pi$
$991$	0.778032	+	16.3329i	0.0247150	+	0.518831i	−0.952235	+	0.305365i	$0.901222\pi$
$992$	−11.7261	−	29.2904i	−0.372304	−	0.929971i
$993$	−7.49986	+	42.6046i	−0.238001	+	1.35202i
$994$	3.23356	−	4.13617i	0.102562	−	0.131191i
$995$	−14.9833	+	6.84263i	−0.475001	+	0.216926i
$996$	1.31571	−	16.6095i	0.0416897	−	0.526293i
$997$	−3.92920	−	1.57301i	−0.124439	−	0.0498179i	0.308607	−	0.951190i	$-0.400137\pi$
$997$	−3.92920	−	1.57301i	−0.124439	−	0.0498179i	−0.433046	+	0.901372i	$0.642561\pi$
$998$	−9.06247	−	9.50444i	−0.286867	−	0.300858i
$999$	8.22347	+	12.7720i	0.260179	+	0.404088i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.bc.a.11.13	✓	1200
3.2	odd	2	inner	483.2.bc.a.11.48	yes	1200
7.2	even	3	inner	483.2.bc.a.149.48	yes	1200
21.2	odd	6	inner	483.2.bc.a.149.13	yes	1200
23.21	odd	22	inner	483.2.bc.a.389.13	yes	1200
69.44	even	22	inner	483.2.bc.a.389.48	yes	1200
161.44	odd	66	inner	483.2.bc.a.44.48	yes	1200
483.44	even	66	inner	483.2.bc.a.44.13	yes	1200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.bc.a.11.13	✓	1200	1.1	even	1	trivial
483.2.bc.a.11.48	yes	1200	3.2	odd	2	inner
483.2.bc.a.44.13	yes	1200	483.44	even	66	inner
483.2.bc.a.44.48	yes	1200	161.44	odd	66	inner
483.2.bc.a.149.13	yes	1200	21.2	odd	6	inner
483.2.bc.a.149.48	yes	1200	7.2	even	3	inner
483.2.bc.a.389.13	yes	1200	23.21	odd	22	inner
483.2.bc.a.389.48	yes	1200	69.44	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.bc (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.839508 + 1.62842i) q^{2} +(1.58694 + 0.693981i) q^{3} +(-0.786858 - 1.10499i) q^{4} +(-1.28009 - 1.22056i) q^{5} +(-2.46234 + 2.00161i) q^{6} +(-1.82028 + 1.92005i) q^{7} +(-1.16691 + 0.167776i) q^{8} +(2.03678 + 2.20262i) q^{9} +O(q^{10})\)	\(q+(-0.839508 + 1.62842i) q^{2} +(1.58694 + 0.693981i) q^{3} +(-0.786858 - 1.10499i) q^{4} +(-1.28009 - 1.22056i) q^{5} +(-2.46234 + 2.00161i) q^{6} +(-1.82028 + 1.92005i) q^{7} +(-1.16691 + 0.167776i) q^{8} +(2.03678 + 2.20262i) q^{9} +(3.06224 - 1.05985i) q^{10} +(-1.43861 + 0.741654i) q^{11} +(-0.481859 - 2.29962i) q^{12} +(-2.50372 + 2.88945i) q^{13} +(-1.59851 - 4.57607i) q^{14} +(-1.18438 - 2.82533i) q^{15} +(1.59377 - 4.60489i) q^{16} +(2.10363 + 0.200872i) q^{17} +(-5.29667 + 1.46762i) q^{18} +(-0.0495015 - 0.518403i) q^{19} +(-0.341458 + 2.37490i) q^{20} +(-4.22116 + 1.78377i) q^{21} -2.96528i q^{22} +(-3.70659 + 3.04322i) q^{23} +(-1.96826 - 0.543562i) q^{24} +(-0.0890537 - 1.86947i) q^{25} +(-2.60333 - 6.50281i) q^{26} +(1.70368 + 4.90892i) q^{27} +(3.55393 + 0.500576i) q^{28} +(-6.63808 + 3.03151i) q^{29} +(5.59511 + 0.443211i) q^{30} +(-4.45840 - 1.78487i) q^{31} +(4.53362 + 4.75472i) q^{32} +(-2.79769 + 0.178597i) q^{33} +(-2.09312 + 3.25695i) q^{34} +(4.67367 - 0.236074i) q^{35} +(0.831207 - 3.98376i) q^{36} +(2.84100 - 0.689218i) q^{37} +(0.885734 + 0.354594i) q^{38} +(-5.97848 + 2.84785i) q^{39} +(1.69854 + 1.20952i) q^{40} +(2.41842 + 8.23639i) q^{41} +(0.638963 - 8.37130i) q^{42} +(8.55608 + 1.23018i) q^{43} +(1.95150 + 1.00607i) q^{44} +(0.0811716 - 5.30558i) q^{45} +(-1.84392 - 8.59068i) q^{46} +(-4.47113 + 2.58141i) q^{47} +(5.72493 - 6.20166i) q^{48} +(-0.373184 - 6.99005i) q^{49} +(3.11903 + 1.42442i) q^{50} +(3.19894 + 1.77865i) q^{51} +(5.16287 + 0.492994i) q^{52} +(8.56794 - 1.65134i) q^{53} +(-9.42402 - 1.34677i) q^{54} +(2.74679 + 0.806530i) q^{55} +(1.80196 - 2.54593i) q^{56} +(0.281206 - 0.857030i) q^{57} +(0.636155 - 13.3545i) q^{58} +(2.36455 - 0.818378i) q^{59} +(-2.19001 + 3.53186i) q^{60} +(3.66243 + 4.65716i) q^{61} +(6.64938 - 5.76172i) q^{62} +(-7.93664 - 0.0986526i) q^{63} +(-2.19767 + 0.645295i) q^{64} +(6.73175 - 0.642804i) q^{65} +(2.05785 - 4.70573i) q^{66} +(-12.2539 + 0.583726i) q^{67} +(-1.43330 - 2.48254i) q^{68} +(-7.99409 + 2.25711i) q^{69} +(-3.53915 + 7.80887i) q^{70} +(0.585578 + 0.911177i) q^{71} +(-2.74629 - 2.22854i) q^{72} +(3.82466 + 5.37099i) q^{73} +(-1.26270 + 5.20493i) q^{74} +(1.15605 - 3.02854i) q^{75} +(-0.533878 + 0.462608i) q^{76} +(1.19465 - 4.11222i) q^{77} +(0.381485 - 12.1263i) q^{78} +(1.56110 - 8.09974i) q^{79} +(-7.66074 + 3.94938i) q^{80} +(-0.703048 + 8.97250i) q^{81} +(-15.4426 - 2.97631i) q^{82} +(6.80410 + 1.99787i) q^{83} +(5.29249 + 3.26075i) q^{84} +(-2.44766 - 2.82475i) q^{85} +(-9.18614 + 12.9001i) q^{86} +(-12.6381 + 0.204134i) q^{87} +(1.55430 - 1.10681i) q^{88} +(4.72860 - 1.89305i) q^{89} +(8.57155 + 4.58625i) q^{90} +(-0.990419 - 10.0669i) q^{91} +(6.27928 + 1.70115i) q^{92} +(-5.83656 - 5.92654i) q^{93} +(-0.450063 - 9.44798i) q^{94} +(-0.569378 + 0.724023i) q^{95} +(3.89491 + 10.6917i) q^{96} +(3.90524 + 13.3000i) q^{97} +(11.6960 + 5.26050i) q^{98} +(-4.56371 - 1.65812i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1200 q - 9 q^{3} - 74 q^{4} - 20 q^{6} - 44 q^{7} - 13 q^{9}+O(q^{10}) \) 1200 * q - 9 * q^3 - 74 * q^4 - 20 * q^6 - 44 * q^7 - 13 * q^9	\( 1200 q - 9 q^{3} - 74 q^{4} - 20 q^{6} - 44 q^{7} - 13 q^{9} - 22 q^{10} - 25 q^{12} - 72 q^{13} - 44 q^{15} + 38 q^{16} - 45 q^{18} - 22 q^{19} + 44 q^{21} + 2 q^{24} + 18 q^{25} - 90 q^{27} - 44 q^{28} - 55 q^{30} - 18 q^{31} - 11 q^{33} - 88 q^{34} - 108 q^{36} - 66 q^{37} + q^{39} - 22 q^{40} - 22 q^{42} - 2 q^{46} - 228 q^{48} - 128 q^{49} - 11 q^{51} - 166 q^{52} + 35 q^{54} - 160 q^{55} - 44 q^{57} - 126 q^{58} - 11 q^{60} + 66 q^{61} + 33 q^{63} + 40 q^{64} + 22 q^{66} - 22 q^{67} - 24 q^{69} + 68 q^{70} - 149 q^{72} - 42 q^{73} + 123 q^{75} - 88 q^{76} - 108 q^{78} - 66 q^{79} - 81 q^{81} - 14 q^{82} + 44 q^{84} - 200 q^{85} + 75 q^{87} + 66 q^{88} + 16 q^{93} - 146 q^{94} + 5 q^{96} - 88 q^{97} - 308 q^{99}+O(q^{100}) \) 1200 * q - 9 * q^3 - 74 * q^4 - 20 * q^6 - 44 * q^7 - 13 * q^9 - 22 * q^10 - 25 * q^12 - 72 * q^13 - 44 * q^15 + 38 * q^16 - 45 * q^18 - 22 * q^19 + 44 * q^21 + 2 * q^24 + 18 * q^25 - 90 * q^27 - 44 * q^28 - 55 * q^30 - 18 * q^31 - 11 * q^33 - 88 * q^34 - 108 * q^36 - 66 * q^37 + q^39 - 22 * q^40 - 22 * q^42 - 2 * q^46 - 228 * q^48 - 128 * q^49 - 11 * q^51 - 166 * q^52 + 35 * q^54 - 160 * q^55 - 44 * q^57 - 126 * q^58 - 11 * q^60 + 66 * q^61 + 33 * q^63 + 40 * q^64 + 22 * q^66 - 22 * q^67 - 24 * q^69 + 68 * q^70 - 149 * q^72 - 42 * q^73 + 123 * q^75 - 88 * q^76 - 108 * q^78 - 66 * q^79 - 81 * q^81 - 14 * q^82 + 44 * q^84 - 200 * q^85 + 75 * q^87 + 66 * q^88 + 16 * q^93 - 146 * q^94 + 5 * q^96 - 88 * q^97 - 308 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more