LMFDB - Embedded newform 80.2.q.c.69.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,2,Mod(29,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("80.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	80.q (of order $4$, degree $2$, 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:	$0.638803216170$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.534694406811304329216.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} - 2x^{12} + 4x^{10} + 4x^{8} + 16x^{6} - 32x^{4} - 128x^{2} + 256 $ x^16 - 2x^14 - 2x^12 + 4x^10 + 4x^8 + 16x^6 - 32x^4 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			69.3
Root			$-1.32661 + 0.490008i$ of defining polynomial
Character	$\chi$	$=$	80.69
Dual form			80.2.q.c.29.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.490008 + 1.32661i) q^{2} +(-1.99154 - 1.99154i) q^{3} +(-1.51978 - 1.30010i) q^{4} +(-0.569800 - 2.16225i) q^{5} +(3.61786 - 1.66612i) q^{6} -1.09033 q^{7} +(2.46943 - 1.37910i) q^{8} +4.93244i q^{9} +O(q^{10})$	\(q+(-0.490008 + 1.32661i) q^{2} +(-1.99154 - 1.99154i) q^{3} +(-1.51978 - 1.30010i) q^{4} +(-0.569800 - 2.16225i) q^{5} +(3.61786 - 1.66612i) q^{6} -1.09033 q^{7} +(2.46943 - 1.37910i) q^{8} +4.93244i q^{9} +(3.14767 + 0.303617i) q^{10} +(-2.33225 - 2.33225i) q^{11} +(0.437515 + 5.61590i) q^{12} +(1.80775 + 1.80775i) q^{13} +(0.534268 - 1.44644i) q^{14} +(-3.17142 + 5.44098i) q^{15} +(0.619491 + 3.95174i) q^{16} -4.93886i q^{17} +(-6.54342 - 2.41694i) q^{18} +(2.03957 - 2.03957i) q^{19} +(-1.94516 + 4.02695i) q^{20} +(2.17142 + 2.17142i) q^{21} +(4.23680 - 1.95116i) q^{22} +1.45791 q^{23} +(-7.66449 - 2.17142i) q^{24} +(-4.35066 + 2.46410i) q^{25} +(-3.28398 + 1.51236i) q^{26} +(3.84853 - 3.84853i) q^{27} +(1.65706 + 1.41753i) q^{28} +(-0.707323 + 0.707323i) q^{29} +(-5.66403 - 6.87336i) q^{30} +10.1286 q^{31} +(-5.54597 - 1.11456i) q^{32} +9.28951i q^{33} +(6.55193 + 2.42008i) q^{34} +(0.621268 + 2.35756i) q^{35} +(6.41266 - 7.49625i) q^{36} +(4.35066 - 4.35066i) q^{37} +(1.70631 + 3.70512i) q^{38} -7.20039i q^{39} +(-4.38905 - 4.55371i) q^{40} -10.2753i q^{41} +(-3.94465 + 1.81662i) q^{42} +(-2.22457 + 2.22457i) q^{43} +(0.512364 + 6.57666i) q^{44} +(10.6652 - 2.81051i) q^{45} +(-0.714386 + 1.93407i) q^{46} +2.09458i q^{47} +(6.63629 - 9.10377i) q^{48} -5.81119 q^{49} +(-1.13705 - 6.97905i) q^{50} +(-9.83592 + 9.83592i) q^{51} +(-0.397138 - 5.09763i) q^{52} +(0.215297 - 0.215297i) q^{53} +(3.21969 + 6.99131i) q^{54} +(-3.71399 + 6.37182i) q^{55} +(-2.69248 + 1.50367i) q^{56} -8.12376 q^{57} +(-0.591747 - 1.28493i) q^{58} +(-1.16082 - 1.16082i) q^{59} +(11.8937 - 4.14596i) q^{60} +(-3.46410 + 3.46410i) q^{61} +(-4.96309 + 13.4367i) q^{62} -5.37797i q^{63} +(4.19615 - 6.81119i) q^{64} +(2.87875 - 4.93886i) q^{65} +(-12.3236 - 4.55193i) q^{66} +(-5.04189 - 5.04189i) q^{67} +(-6.42100 + 7.50600i) q^{68} +(-2.90348 - 2.90348i) q^{69} +(-3.43198 - 0.331042i) q^{70} +6.40078i q^{71} +(6.80234 + 12.1803i) q^{72} +5.24343 q^{73} +(3.63977 + 7.90348i) q^{74} +(13.5718 + 3.75714i) q^{75} +(-5.75135 + 0.448067i) q^{76} +(2.54291 + 2.54291i) q^{77} +(9.55211 + 3.52825i) q^{78} +2.61504 q^{79} +(8.19166 - 3.59120i) q^{80} -0.531659 q^{81} +(13.6313 + 5.03497i) q^{82} +(5.67856 + 5.67856i) q^{83} +(-0.477033 - 6.12316i) q^{84} +(-10.6790 + 2.81416i) q^{85} +(-1.86108 - 4.04120i) q^{86} +2.81732 q^{87} +(-8.97572 - 2.54291i) q^{88} +6.87875i q^{89} +(-1.49758 + 15.5257i) q^{90} +(-1.97103 - 1.97103i) q^{91} +(-2.21570 - 1.89542i) q^{92} +(-20.1715 - 20.1715i) q^{93} +(-2.77868 - 1.02636i) q^{94} +(-5.57221 - 3.24791i) q^{95} +(8.82531 + 13.2647i) q^{96} +3.77310i q^{97} +(2.84753 - 7.70918i) q^{98} +(11.5037 - 11.5037i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} - 8 q^{5} - 4 q^{6}+O(q^{10}) $ 16 * q - 4 * q^4 - 8 * q^5 - 4 * q^6	$ 16 q - 4 q^{4} - 8 q^{5} - 4 q^{6} - 12 q^{10} + 8 q^{11} - 4 q^{14} + 16 q^{16} - 8 q^{19} - 4 q^{20} - 16 q^{21} - 32 q^{24} + 32 q^{26} - 16 q^{29} - 36 q^{30} + 16 q^{31} + 48 q^{34} - 24 q^{35} + 60 q^{36} + 24 q^{40} - 8 q^{44} + 8 q^{45} - 28 q^{46} + 16 q^{49} + 24 q^{50} - 16 q^{51} + 40 q^{54} - 56 q^{56} - 24 q^{59} + 48 q^{60} - 16 q^{64} - 72 q^{66} + 32 q^{69} + 20 q^{70} + 48 q^{75} - 88 q^{76} + 16 q^{79} + 16 q^{80} - 16 q^{81} - 80 q^{84} - 28 q^{86} - 84 q^{90} - 16 q^{91} + 12 q^{94} + 32 q^{95} + 56 q^{96} + 88 q^{99}+O(q^{100}) $ 16 * q - 4 * q^4 - 8 * q^5 - 4 * q^6 - 12 * q^10 + 8 * q^11 - 4 * q^14 + 16 * q^16 - 8 * q^19 - 4 * q^20 - 16 * q^21 - 32 * q^24 + 32 * q^26 - 16 * q^29 - 36 * q^30 + 16 * q^31 + 48 * q^34 - 24 * q^35 + 60 * q^36 + 24 * q^40 - 8 * q^44 + 8 * q^45 - 28 * q^46 + 16 * q^49 + 24 * q^50 - 16 * q^51 + 40 * q^54 - 56 * q^56 - 24 * q^59 + 48 * q^60 - 16 * q^64 - 72 * q^66 + 32 * q^69 + 20 * q^70 + 48 * q^75 - 88 * q^76 + 16 * q^79 + 16 * q^80 - 16 * q^81 - 80 * q^84 - 28 * q^86 - 84 * q^90 - 16 * q^91 + 12 * q^94 + 32 * q^95 + 56 * q^96 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.490008	+	1.32661i	−0.346488	+	0.938054i
$2$	−0.490008	+	1.32661i	−0.346488	+	0.938054i
$3$	−1.99154	−	1.99154i	−1.14981	−	1.14981i	−0.986589	−	0.163226i	$-0.947810\pi$
$3$	−1.99154	−	1.99154i	−1.14981	−	1.14981i	−0.163226	−	0.986589i	$-0.552190\pi$
$4$	−1.51978	−	1.30010i	−0.759892	−	0.650049i
$5$	−0.569800	−	2.16225i	−0.254822	−	0.966988i
$5$	−0.569800	−	2.16225i	−0.254822	−	0.966988i
$6$	3.61786	−	1.66612i	1.47699	−	0.680192i
$7$	−1.09033			−0.412104			−0.206052	−	0.978541i	$-0.566062\pi$
$7$	−1.09033			−0.412104			−0.206052	+	0.978541i	$0.566062\pi$
$8$	2.46943	−	1.37910i	0.873075	−	0.487586i
$9$			4.93244i			1.64415i
$10$	3.14767	+	0.303617i	0.995380	+	0.0960123i
$11$	−2.33225	−	2.33225i	−0.703199	−	0.703199i	0.261897	−	0.965096i	$-0.415652\pi$
$11$	−2.33225	−	2.33225i	−0.703199	−	0.703199i	−0.965096	+	0.261897i	$0.915652\pi$
$12$	0.437515	+	5.61590i	0.126300	+	1.62117i
$13$	1.80775	+	1.80775i	0.501379	+	0.501379i	0.911866	−	0.410487i	$-0.134641\pi$
$13$	1.80775	+	1.80775i	0.501379	+	0.501379i	−0.410487	+	0.911866i	$0.634641\pi$
$14$	0.534268	−	1.44644i	0.142789	−	0.386576i
$15$	−3.17142	+	5.44098i	−0.818858	+	1.40486i
$16$	0.619491	+	3.95174i	0.154873	+	0.987934i
$17$		−	4.93886i		−	1.19785i	−0.800806	−	0.598924i	$-0.795595\pi$
$17$		−	4.93886i		−	1.19785i	0.800806	−	0.598924i	$-0.204405\pi$
$18$	−6.54342	−	2.41694i	−1.54230	−	0.569677i
$19$	2.03957	−	2.03957i	0.467909	−	0.467909i	−0.433327	−	0.901237i	$-0.642661\pi$
$19$	2.03957	−	2.03957i	0.467909	−	0.467909i	0.901237	+	0.433327i	$0.142661\pi$
$20$	−1.94516	+	4.02695i	−0.434952	+	0.900454i
$21$	2.17142	+	2.17142i	0.473844	+	0.473844i
$22$	4.23680	−	1.95116i	0.903289	−	0.415989i
$23$	1.45791			0.303995			0.151997	−	0.988381i	$-0.451430\pi$
$23$	1.45791			0.303995			0.151997	+	0.988381i	$0.451430\pi$
$24$	−7.66449	−	2.17142i	−1.56451	−	0.443240i
$25$	−4.35066	+	2.46410i	−0.870131	+	0.492820i
$26$	−3.28398	+	1.51236i	−0.644042	+	0.296599i
$27$	3.84853	−	3.84853i	0.740650	−	0.740650i
$28$	1.65706	+	1.41753i	0.313155	+	0.267888i
$29$	−0.707323	+	0.707323i	−0.131347	+	0.131347i	−0.769724	−	0.638377i	$-0.779606\pi$
$29$	−0.707323	+	0.707323i	−0.131347	+	0.131347i	0.638377	+	0.769724i	$0.279606\pi$
$30$	−5.66403	−	6.87336i	−1.03411	−	1.25490i
$31$	10.1286			1.81915			0.909575	−	0.415541i	$-0.136408\pi$
$31$	10.1286			1.81915			0.909575	+	0.415541i	$0.136408\pi$
$32$	−5.54597	−	1.11456i	−0.980398	−	0.197028i
$33$			9.28951i			1.61710i
$34$	6.55193	+	2.42008i	1.12365	+	0.415040i
$35$	0.621268	+	2.35756i	0.105013	+	0.398500i
$36$	6.41266	−	7.49625i	1.06878	−	1.24938i
$37$	4.35066	−	4.35066i	0.715243	−	0.715243i	−0.252384	−	0.967627i	$-0.581215\pi$
$37$	4.35066	−	4.35066i	0.715243	−	0.715243i	0.967627	+	0.252384i	$0.0812146\pi$
$38$	1.70631	+	3.70512i	0.276800	+	0.601049i
$39$		−	7.20039i		−	1.15299i
$40$	−4.38905	−	4.55371i	−0.693969	−	0.720005i
$41$		−	10.2753i		−	1.60473i	−0.596833	−	0.802365i	$-0.703575\pi$
$41$		−	10.2753i		−	1.60473i	0.596833	−	0.802365i	$-0.296425\pi$
$42$	−3.94465	+	1.81662i	−0.608672	+	0.280310i
$43$	−2.22457	+	2.22457i	−0.339244	+	0.339244i	−0.856083	−	0.516839i	$-0.827109\pi$
$43$	−2.22457	+	2.22457i	−0.339244	+	0.339244i	0.516839	+	0.856083i	$0.327109\pi$
$44$	0.512364	+	6.57666i	0.0772418	+	0.991469i
$45$	10.6652	−	2.81051i	1.58987	−	0.418966i
$46$	−0.714386	+	1.93407i	−0.105330	+	0.285163i
$47$			2.09458i			0.305525i	0.988263	+	0.152763i	$0.0488170\pi$
$47$			2.09458i			0.305525i	−0.988263	+	0.152763i	$0.951183\pi$
$48$	6.63629	−	9.10377i	0.957866	−	1.31402i
$49$	−5.81119			−0.830170
$50$	−1.13705	−	6.97905i	−0.160802	−	0.986987i
$51$	−9.83592	+	9.83592i	−1.37730	+	1.37730i
$52$	−0.397138	−	5.09763i	−0.0550732	−	0.706915i
$53$	0.215297	−	0.215297i	0.0295733	−	0.0295733i	−0.692166	−	0.721739i	$-0.743343\pi$
$53$	0.215297	−	0.215297i	0.0295733	−	0.0295733i	0.721739	+	0.692166i	$0.243343\pi$
$54$	3.21969	+	6.99131i	0.438144	+	0.951396i
$55$	−3.71399	+	6.37182i	−0.500794	+	0.859175i
$56$	−2.69248	+	1.50367i	−0.359798	+	0.200936i
$57$	−8.12376			−1.07602
$58$	−0.591747	−	1.28493i	−0.0777002	−	0.168720i
$59$	−1.16082	−	1.16082i	−0.151126	−	0.151126i	0.627495	−	0.778621i	$-0.284080\pi$
$59$	−1.16082	−	1.16082i	−0.151126	−	0.151126i	−0.778621	+	0.627495i	$0.784080\pi$
$60$	11.8937	−	4.14596i	1.53547	−	0.535241i
$61$	−3.46410	+	3.46410i	−0.443533	+	0.443533i	−0.893197	−	0.449665i	$-0.851543\pi$
$61$	−3.46410	+	3.46410i	−0.443533	+	0.443533i	0.449665	+	0.893197i	$0.351543\pi$
$62$	−4.96309	+	13.4367i	−0.630313	+	1.70646i
$63$		−	5.37797i		−	0.677560i
$64$	4.19615	−	6.81119i	0.524519	−	0.851399i
$65$	2.87875	−	4.93886i	0.357065	−	0.612590i
$66$	−12.3236	−	4.55193i	−1.51692	−	0.560304i
$67$	−5.04189	−	5.04189i	−0.615965	−	0.615965i	0.328529	−	0.944494i	$-0.393447\pi$
$67$	−5.04189	−	5.04189i	−0.615965	−	0.615965i	−0.944494	+	0.328529i	$0.893447\pi$
$68$	−6.42100	+	7.50600i	−0.778660	+	0.910236i
$69$	−2.90348	−	2.90348i	−0.349537	−	0.349537i
$70$	−3.43198	−	0.331042i	−0.410201	−	0.0395671i
$71$			6.40078i			0.759633i	0.925062	+	0.379817i	$0.124013\pi$
$71$			6.40078i			0.759633i	−0.925062	+	0.379817i	$0.875987\pi$
$72$	6.80234	+	12.1803i	0.801664	+	1.43546i
$73$	5.24343			0.613696			0.306848	−	0.951758i	$-0.400726\pi$
$73$	5.24343			0.613696			0.306848	+	0.951758i	$0.400726\pi$
$74$	3.63977	+	7.90348i	0.423114	+	0.918760i
$75$	13.5718	+	3.75714i	1.56714	+	0.433837i
$76$	−5.75135	+	0.448067i	−0.659725	+	0.0513968i
$77$	2.54291	+	2.54291i	0.289791	+	0.289791i
$78$	9.55211	+	3.52825i	1.08156	+	0.399495i
$79$	2.61504			0.294215			0.147107	−	0.989121i	$-0.453004\pi$
$79$	2.61504			0.294215			0.147107	+	0.989121i	$0.453004\pi$
$80$	8.19166	−	3.59120i	0.915856	−	0.401508i
$81$	−0.531659			−0.0590733
$82$	13.6313	+	5.03497i	1.50532	+	0.556020i
$83$	5.67856	+	5.67856i	0.623303	+	0.623303i	0.946375	−	0.323071i	$-0.104715\pi$
$83$	5.67856	+	5.67856i	0.623303	+	0.623303i	−0.323071	+	0.946375i	$0.604715\pi$
$84$	−0.477033	−	6.12316i	−0.0520486	−	0.668092i
$85$	−10.6790	+	2.81416i	−1.15831	+	0.305239i
$86$	−1.86108	−	4.04120i	−0.200686	−	0.435774i
$87$	2.81732			0.302048
$88$	−8.97572	−	2.54291i	−0.956815	−	0.271075i
$89$			6.87875i			0.729146i	0.931175	+	0.364573i	$0.118785\pi$
$89$			6.87875i			0.729146i	−0.931175	+	0.364573i	$0.881215\pi$
$90$	−1.49758	+	15.5257i	−0.157858	+	1.63655i
$91$	−1.97103	−	1.97103i	−0.206620	−	0.206620i
$92$	−2.21570	−	1.89542i	−0.231003	−	0.197611i
$93$	−20.1715	−	20.1715i	−2.09168	−	2.09168i
$94$	−2.77868	−	1.02636i	−0.286599	−	0.105861i
$95$	−5.57221	−	3.24791i	−0.571696	−	0.333229i
$96$	8.82531	+	13.2647i	0.900730	+	1.35382i
$97$			3.77310i			0.383100i	0.981483	+	0.191550i	$0.0613515\pi$
$97$			3.77310i			0.383100i	−0.981483	+	0.191550i	$0.938649\pi$
$98$	2.84753	−	7.70918i	0.287644	−	0.778745i
$99$	11.5037	−	11.5037i	1.15616	−	1.15616i
$100$	9.81563	+	1.91137i	0.981563	+	0.191137i
$101$	−0.707323	−	0.707323i	−0.0703813	−	0.0703813i	0.671040	−	0.741421i	$-0.265848\pi$
$101$	−0.707323	−	0.707323i	−0.0703813	−	0.0703813i	−0.741421	+	0.671040i	$0.765848\pi$
$102$	−8.22874	−	17.8681i	−0.814767	−	1.76921i
$103$	12.9320			1.27422			0.637112	−	0.770771i	$-0.280129\pi$
$103$	12.9320			1.27422			0.637112	+	0.770771i	$0.280129\pi$
$104$	6.95717	+	1.97103i	0.682207	+	0.193276i
$105$	3.45789	−	5.93244i	0.337455	−	0.578947i
$106$	0.180117	+	0.391111i	0.0174946	+	0.0379881i
$107$	1.56094	−	1.56094i	0.150902	−	0.150902i	−0.627619	−	0.778521i	$-0.715970\pi$
$107$	1.56094	−	1.56094i	0.150902	−	0.150902i	0.778521	+	0.627619i	$0.215970\pi$
$108$	−10.8524	+	0.845472i	−1.04427	+	0.0813556i
$109$	−7.13283	+	7.13283i	−0.683202	+	0.683202i	−0.960720	−	0.277519i	$-0.910488\pi$
$109$	−7.13283	+	7.13283i	−0.683202	+	0.683202i	0.277519	+	0.960720i	$0.410488\pi$
$110$	−6.63303	−	8.04925i	−0.632434	−	0.767466i
$111$	−17.3290			−1.64479
$112$	−0.675447	−	4.30868i	−0.0638238	−	0.407132i
$113$		−	9.23949i		−	0.869178i	−0.900629	−	0.434589i	$-0.856894\pi$
$113$		−	9.23949i		−	0.869178i	0.900629	−	0.434589i	$-0.143106\pi$
$114$	3.98070	−	10.7771i	0.372827	−	1.00936i
$115$	−0.830715	−	3.15236i	−0.0774646	−	0.293959i
$116$	1.99457	−	0.155390i	0.185191	−	0.0144276i
$117$	−8.91661	+	8.91661i	−0.824341	+	0.824341i
$118$	2.10877	−	0.971145i	0.194128	−	0.0894012i
$119$			5.38496i			0.493639i
$120$	−0.327935	+	17.8098i	−0.0299362	+	1.62581i
$121$		−	0.121253i		−	0.0110230i
$122$	−2.89807	−	6.29295i	−0.262379	−	0.569737i
$123$	−20.4636	+	20.4636i	−1.84514	+	1.84514i
$124$	−15.3933	−	13.1682i	−1.38236	−	1.18254i
$125$	7.80701	+	8.00316i	0.698280	+	0.715825i
$126$	7.13446	+	2.63525i	0.635589	+	0.234766i
$127$		−	1.99608i		−	0.177124i	−0.996071	−	0.0885618i	$-0.971773\pi$
$127$		−	1.99608i		−	0.177124i	0.996071	−	0.0885618i	$-0.0282271\pi$
$128$	6.97964	+	8.90419i	0.616919	+	0.787027i
$129$	8.86065			0.780136
$130$	5.14132	+	6.23905i	0.450924	+	0.547201i
$131$	11.2894	−	11.2894i	0.986361	−	0.986361i	−0.0135473	−	0.999908i	$-0.504312\pi$
$131$	11.2894	−	11.2894i	0.986361	−	0.986361i	0.999908	+	0.0135473i	$0.00431238\pi$
$132$	12.0773	−	14.1181i	1.05119	−	1.22882i
$133$	−2.22380	+	2.22380i	−0.192827	+	0.192827i
$134$	9.15919	−	4.21806i	0.791234	−	0.364385i
$135$	−10.5144	−	6.12859i	−0.904934	−	0.527465i
$136$	−6.81119	−	12.1962i	−0.584055	−	1.04581i
$137$	15.9429			1.36210			0.681049	−	0.732238i	$-0.261524\pi$
$137$	15.9429			1.36210			0.681049	+	0.732238i	$0.261524\pi$
$138$	5.27450	−	2.42905i	0.448996	−	0.206775i
$139$	3.79635	+	3.79635i	0.322002	+	0.322002i	0.849535	−	0.527533i	$-0.176883\pi$
$139$	3.79635	+	3.79635i	0.322002	+	0.322002i	−0.527533	+	0.849535i	$0.676883\pi$
$140$	2.12086	−	4.39069i	0.179246	−	0.371081i
$141$	4.17142	−	4.17142i	0.351297	−	0.351297i
$142$	−8.49134	−	3.13643i	−0.712577	−	0.263204i
$143$		−	8.43222i		−	0.705138i
$144$	−19.4917	+	3.05560i	−1.62431	+	0.254634i
$145$	1.93244	+	1.12638i	0.160481	+	0.0935405i
$146$	−2.56932	+	6.95598i	−0.212638	+	0.575681i
$147$	11.5732	+	11.5732i	0.954542	+	0.954542i
$148$	−12.2683	+	0.955782i	−1.00845	+	0.0785648i
$149$	13.3290	+	13.3290i	1.09195	+	1.09195i	0.995320	+	0.0966330i	$0.0308073\pi$
$149$	13.3290	+	13.3290i	1.09195	+	1.09195i	0.0966330	+	0.995320i	$0.469193\pi$
$150$	−11.6346	+	16.1635i	−0.949959	+	1.31974i
$151$		−	5.60117i		−	0.455817i	−0.973683	−	0.227909i	$-0.926811\pi$
$151$		−	5.60117i		−	0.455817i	0.973683	−	0.227909i	$-0.0731887\pi$
$152$	2.22380	−	7.84935i	0.180374	−	0.636666i
$153$	24.3606			1.96944
$154$	−4.61949	+	2.12740i	−0.372249	+	0.171431i
$155$	−5.77128	−	21.9006i	−0.463560	−	1.75910i
$156$	−9.36121	+	10.9430i	−0.749497	+	0.876145i
$157$	7.11951	+	7.11951i	0.568199	+	0.568199i	0.931624	−	0.363425i	$-0.118393\pi$
$157$	7.11951	+	7.11951i	0.568199	+	0.568199i	−0.363425	+	0.931624i	$0.618393\pi$
$158$	−1.28139	+	3.46913i	−0.101942	+	0.275989i
$159$	−0.857542			−0.0680075
$160$	0.750136	+	12.6268i	0.0593035	+	0.998240i
$161$	−1.58959			−0.125277
$162$	0.260517	−	0.705304i	0.0204682	−	0.0554139i
$163$	0.546047	+	0.546047i	0.0427697	+	0.0427697i	0.728168	−	0.685398i	$-0.240372\pi$
$163$	0.546047	+	0.546047i	0.0427697	+	0.0427697i	−0.685398	+	0.728168i	$0.740372\pi$
$164$	−13.3589	+	15.6162i	−1.04315	+	1.21942i
$165$	20.0863	−	5.29317i	1.56371	−	0.412072i
$166$	−10.3158	+	4.75069i	−0.800659	+	0.368725i
$167$	−21.3103			−1.64904			−0.824519	−	0.565834i	$-0.808554\pi$
$167$	−21.3103			−1.64904			−0.824519	+	0.565834i	$0.808554\pi$
$168$	8.35679	+	2.36756i	0.644741	+	0.182661i
$169$		−	6.46410i		−	0.497239i
$170$	1.49952	−	15.5459i	0.115008	−	1.19231i
$171$	10.0601	+	10.0601i	0.769312	+	0.769312i
$172$	6.27304	−	0.488710i	0.478315	−	0.0372638i
$173$	−2.64673	−	2.64673i	−0.201227	−	0.201227i	0.599299	−	0.800525i	$-0.295446\pi$
$173$	−2.64673	−	2.64673i	−0.201227	−	0.201227i	−0.800525	+	0.599299i	$0.795446\pi$
$174$	−1.38051	+	3.73748i	−0.104656	+	0.283338i
$175$	4.74363	−	2.68667i	0.358585	−	0.203093i
$176$	7.77162	−	10.6612i	0.585808	−	0.803621i
$177$			4.62364i			0.347534i
$178$	−9.12541	−	3.37064i	−0.683978	−	0.252640i
$179$	−13.4747	+	13.4747i	−1.00715	+	1.00715i	−0.00717240	+	0.999974i	$0.502283\pi$
$179$	−13.4747	+	13.4747i	−1.00715	+	1.00715i	−0.999974	+	0.00717240i	$0.997717\pi$
$180$	−19.8627	−	9.59441i	−1.48048	−	0.715125i
$181$	−1.63553	−	1.63553i	−0.121568	−	0.121568i	0.643706	−	0.765273i	$-0.277396\pi$
$181$	−1.63553	−	1.63553i	−0.121568	−	0.121568i	−0.765273	+	0.643706i	$0.777396\pi$
$182$	3.58061	−	1.64897i	0.265413	−	0.122230i
$183$	13.7978			1.01996
$184$	3.60020	−	2.01060i	0.265410	−	0.148224i
$185$	−11.8862	−	6.92820i	−0.873892	−	0.509372i
$186$	36.6438	−	16.8755i	2.68686	−	1.23737i
$187$	−11.5186	+	11.5186i	−0.842326	+	0.842326i
$188$	2.72315	−	3.18330i	0.198606	−	0.232166i
$189$	−4.19615	+	4.19615i	−0.305225	+	0.305225i
$190$	7.03914	−	5.80064i	0.510673	−	0.420823i
$191$	5.07180			0.366982			0.183491	−	0.983021i	$-0.441260\pi$
$191$	5.07180			0.366982			0.183491	+	0.983021i	$0.441260\pi$
$192$	−21.9215	+	5.20794i	−1.58205	+	0.375851i
$193$			22.0369i			1.58625i	0.609058	+	0.793126i	$0.291548\pi$
$193$			22.0369i			1.58625i	−0.609058	+	0.793126i	$0.708452\pi$
$194$	−5.00543	−	1.84885i	−0.359369	−	0.132740i
$195$	−15.5691	+	4.10278i	−1.11492	+	0.293806i
$196$	8.83176	+	7.55512i	0.630840	+	0.539651i
$197$	−8.06997	+	8.06997i	−0.574961	+	0.574961i	−0.933511	−	0.358549i	$-0.883271\pi$
$197$	−8.06997	+	8.06997i	−0.574961	+	0.574961i	0.358549	+	0.933511i	$0.383271\pi$
$198$	9.62399	+	20.8978i	0.683947	+	1.48514i
$199$		−	21.8564i		−	1.54936i	−0.632354	−	0.774680i	$-0.717911\pi$
$199$		−	21.8564i		−	1.54936i	0.632354	−	0.774680i	$-0.282089\pi$
$200$	−7.34538	+	12.0849i	−0.519397	+	0.854533i
$201$			20.0822i			1.41649i
$202$	1.28493	−	0.591747i	0.0904077	−	0.0416352i
$203$	0.771212	−	0.771212i	0.0541285	−	0.0541285i
$204$	27.7361	−	2.16082i	1.94192	−	0.151288i
$205$	−22.2178	+	5.85486i	−1.55176	+	0.408921i
$206$	−6.33676	+	17.1557i	−0.441503	+	1.19529i
$207$			7.19104i			0.499812i
$208$	−6.02386	+	8.26363i	−0.417679	+	0.572979i
$209$	−9.51356			−0.658067
$210$	6.17564	+	7.49421i	0.426160	+	0.517149i
$211$	5.18203	−	5.18203i	0.356745	−	0.356745i	−0.505866	−	0.862612i	$-0.668827\pi$
$211$	5.18203	−	5.18203i	0.356745	−	0.356745i	0.862612	+	0.505866i	$0.168827\pi$
$212$	−0.607111	+	0.0472978i	−0.0416966	+	0.00324843i
$213$	12.7474	−	12.7474i	0.873437	−	0.873437i
$214$	1.30589	+	2.83564i	0.0892687	+	0.193840i
$215$	6.07765	+	3.54252i	0.414492	+	0.241598i
$216$	4.19615	−	14.8112i	0.285512	−	1.00777i
$217$	−11.0435			−0.749679
$218$	−5.96734	−	12.9576i	−0.404159	−	0.877601i
$219$	−10.4425	−	10.4425i	−0.705637	−	0.705637i
$220$	13.9284	−	4.85524i	0.939056	−	0.327340i
$221$	8.92820	−	8.92820i	0.600576	−	0.600576i
$222$	8.49134	−	22.9888i	0.569901	−	1.54291i
$223$		−	18.7097i		−	1.25289i	−0.779465	−	0.626446i	$-0.784509\pi$
$223$		−	18.7097i		−	1.25289i	0.779465	−	0.626446i	$-0.215491\pi$
$224$	6.04691	+	1.21523i	0.404026	+	0.0811962i
$225$	−12.1540	−	21.4594i	−0.810269	−	1.43062i
$226$	12.2572	+	4.52742i	0.815336	+	0.301160i
$227$	8.68435	+	8.68435i	0.576401	+	0.576401i	0.933910	−	0.357509i	$-0.116374\pi$
$227$	8.68435	+	8.68435i	0.576401	+	0.576401i	−0.357509	+	0.933910i	$0.616374\pi$
$228$	12.3464	+	10.5617i	0.817658	+	0.699464i
$229$	−4.22936	−	4.22936i	−0.279484	−	0.279484i	0.553419	−	0.832903i	$-0.313323\pi$
$229$	−4.22936	−	4.22936i	−0.279484	−	0.279484i	−0.832903	+	0.553419i	$0.813323\pi$
$230$	4.58901	+	0.442646i	0.302590	+	0.0291872i
$231$		−	10.1286i		−	0.666413i
$232$	−0.771212	+	2.72215i	−0.0506326	+	0.178718i
$233$	−19.7054			−1.29094			−0.645472	−	0.763784i	$-0.723339\pi$
$233$	−19.7054			−1.29094			−0.645472	+	0.763784i	$0.723339\pi$
$234$	−7.45965	−	16.1981i	−0.487652	−	1.05890i
$235$	4.52900	−	1.19349i	0.295439	−	0.0778547i
$236$	0.255017	+	3.27338i	0.0166002	+	0.213079i
$237$	−5.20794	−	5.20794i	−0.338292	−	0.338292i
$238$	−7.14374	−	2.63867i	−0.463060	−	0.171040i
$239$	−0.957886			−0.0619605			−0.0309803	−	0.999520i	$-0.509863\pi$
$239$	−0.957886			−0.0619605			−0.0309803	+	0.999520i	$0.509863\pi$
$240$	−23.4660	−	9.16200i	−1.51472	−	0.591404i
$241$	10.4599			0.673779			0.336889	−	0.941544i	$-0.390625\pi$
$241$	10.4599			0.673779			0.336889	+	0.941544i	$0.390625\pi$
$242$	0.160855	+	0.0594147i	0.0103401	+	0.00381932i
$243$	−10.4868	−	10.4868i	−0.672727	−	0.672727i
$244$	9.76836	−	0.761018i	0.625355	−	0.0487192i
$245$	3.31122	+	12.5652i	0.211546	+	0.802764i
$246$	−17.1199	−	37.1746i	−1.09153	−	2.37016i
$247$	7.37405			0.469200
$248$	25.0118	−	13.9684i	1.58825	−	0.886992i
$249$		−	22.6181i		−	1.43337i
$250$	−14.4426	+	6.43524i	−0.913428	+	0.407000i
$251$	7.29013	+	7.29013i	0.460149	+	0.460149i	0.898704	−	0.438555i	$-0.144510\pi$
$251$	7.29013	+	7.29013i	0.460149	+	0.460149i	−0.438555	+	0.898704i	$0.644510\pi$
$252$	−6.99189	+	8.17335i	−0.440447	+	0.514873i
$253$	−3.40020	−	3.40020i	−0.213769	−	0.213769i
$254$	2.64802	+	0.978096i	0.166152	+	0.0613712i
$255$	26.8722	+	15.6632i	1.68280	+	0.980868i
$256$	−15.2325	+	4.89613i	−0.952029	+	0.306008i
$257$		−	20.2830i		−	1.26522i	−0.774472	−	0.632608i	$-0.781984\pi$
$257$		−	20.2830i		−	1.26522i	0.774472	−	0.632608i	$-0.218016\pi$
$258$	−4.34179	+	11.7546i	−0.270308	+	0.731810i
$259$	−4.74363	+	4.74363i	−0.294755	+	0.294755i
$260$	−10.7961	+	3.76335i	−0.669544	+	0.233393i
$261$	−3.48883	−	3.48883i	−0.215953	−	0.215953i
$262$	9.44474	+	20.5085i	0.583498	+	1.26702i
$263$	−20.2075			−1.24605			−0.623025	−	0.782202i	$-0.714096\pi$
$263$	−20.2075			−1.24605			−0.623025	+	0.782202i	$0.714096\pi$
$264$	12.8112	+	22.9398i	0.788474	+	1.41185i
$265$	−0.588201	−	0.342849i	−0.0361329	−	0.0210611i
$266$	−1.86043	−	4.03978i	−0.114070	−	0.247695i
$267$	13.6993	−	13.6993i	0.838382	−	0.838382i
$268$	1.10764	+	14.2175i	0.0676598	+	0.868475i
$269$	16.2657	−	16.2657i	0.991735	−	0.991735i	−0.00823090	−	0.999966i	$-0.502620\pi$
$269$	16.2657	−	16.2657i	0.991735	−	0.991735i	0.999966	+	0.00823090i	$0.00262000\pi$
$270$	13.2824	−	10.9454i	0.808340	−	0.666117i
$271$	−24.4714			−1.48653			−0.743267	−	0.668995i	$-0.766725\pi$
$271$	−24.4714			−1.48653			−0.743267	+	0.668995i	$0.766725\pi$
$272$	19.5171	−	3.05958i	1.18340	−	0.185514i
$273$			7.85077i			0.475150i
$274$	−7.81217	+	21.1501i	−0.471950	+	1.27772i
$275$	15.8937	+	4.39991i	0.958426	+	0.265324i
$276$	0.637855	+	8.18746i	0.0383944	+	0.492827i
$277$	13.7978	−	13.7978i	0.829028	−	0.829028i	−0.158354	−	0.987382i	$-0.550619\pi$
$277$	13.7978	−	13.7978i	0.829028	−	0.829028i	0.987382	+	0.158354i	$0.0506188\pi$
$278$	−6.89651	+	3.17603i	−0.413625	+	0.190486i
$279$			49.9587i			2.99095i
$280$	4.78549	+	4.96503i	0.285988	+	0.296717i
$281$			16.5673i			0.988319i	0.869371	+	0.494160i	$0.164524\pi$
$281$			16.5673i			0.988319i	−0.869371	+	0.494160i	$0.835476\pi$
$282$	3.48982	+	7.57788i	0.207816	+	0.451256i
$283$	13.6823	−	13.6823i	0.813330	−	0.813330i	−0.171802	−	0.985132i	$-0.554959\pi$
$283$	13.6823	−	13.6823i	0.813330	−	0.813330i	0.985132	+	0.171802i	$0.0549589\pi$
$284$	8.32164	−	9.72781i	0.493799	−	0.577239i
$285$	4.62892	+	17.5656i	0.274193	+	1.04050i
$286$	11.1863	+	4.13186i	0.661458	+	0.244322i
$287$			11.2034i			0.661317i
$288$	5.49750	−	27.3552i	0.323943	−	1.61192i
$289$	−7.39230			−0.434841
$290$	−2.44117	+	2.01166i	−0.143351	+	0.118129i
$291$	7.51427	−	7.51427i	0.440495	−	0.440495i
$292$	−7.96888	−	6.81697i	−0.466343	−	0.398933i
$293$	−23.0518	+	23.0518i	−1.34670	+	1.34670i	−0.457482	+	0.889219i	$0.651249\pi$
$293$	−23.0518	+	23.0518i	−1.34670	+	1.34670i	−0.889219	+	0.457482i	$0.848751\pi$
$294$	−21.0241	+	9.68216i	−1.22615	+	0.564675i
$295$	−1.84855	+	3.17142i	−0.107627	+	0.184647i
$296$	4.74363	−	16.7436i	0.275718	−	0.973204i
$297$	−17.9514			−1.04165
$298$	−24.2137	+	11.1511i	−1.40266	+	0.645963i
$299$	2.63553	+	2.63553i	0.152416	+	0.152416i
$300$	−15.7416	−	23.3548i	−0.908843	−	1.34839i
$301$	2.42551	−	2.42551i	0.139804	−	0.139804i
$302$	7.43057	+	2.74462i	0.427581	+	0.157935i
$303$			2.81732i			0.161851i
$304$	9.32334	+	6.79635i	0.534730	+	0.389797i
$305$	9.46410	+	5.51641i	0.541913	+	0.315869i
$306$	−11.9369	+	32.3170i	−0.682387	+	1.84744i
$307$	−23.3518	−	23.3518i	−1.33276	−	1.33276i	−0.902892	−	0.429867i	$-0.858560\pi$
$307$	−23.3518	−	23.3518i	−1.33276	−	1.33276i	−0.429867	−	0.902892i	$-0.641440\pi$
$308$	−0.558644	−	7.17070i	−0.0318317	−	0.408589i
$309$	−25.7545	−	25.7545i	−1.46512	−	1.46512i
$310$	31.8815	+	3.07522i	1.81075	+	0.174661i
$311$			17.8004i			1.00937i	0.863304	+	0.504685i	$0.168391\pi$
$311$			17.8004i			1.00937i	−0.863304	+	0.504685i	$0.831609\pi$
$312$	−9.93008	−	17.7809i	−0.562180	−	1.00664i
$313$	23.7909			1.34474			0.672370	−	0.740216i	$-0.265277\pi$
$313$	23.7909			1.34474			0.672370	+	0.740216i	$0.265277\pi$
$314$	−12.9334	+	5.95619i	−0.729875	+	0.336127i
$315$	−11.6285	+	3.06437i	−0.655193	+	0.172658i
$316$	−3.97429	−	3.39980i	−0.223571	−	0.191254i
$317$	13.6940	+	13.6940i	0.769129	+	0.769129i	0.977953	−	0.208824i	$-0.0669635\pi$
$317$	13.6940	+	13.6940i	0.769129	+	0.769129i	−0.208824	+	0.977953i	$0.566964\pi$
$318$	0.420202	−	1.13762i	0.0235638	−	0.0637948i
$319$	3.29930			0.184725
$320$	−17.1185	−	5.19212i	−0.956951	−	0.290248i
$321$	−6.21736			−0.347019
$322$	0.778913	−	2.10877i	0.0434071	−	0.117517i
$323$	−10.0731	−	10.0731i	−0.560485	−	0.560485i
$324$	0.808008	+	0.691209i	0.0448893	+	0.0384005i
$325$	−12.3194	−	3.41041i	−0.683355	−	0.189176i
$326$	−0.991959	+	0.456824i	−0.0549395	+	0.0253011i
$327$	28.4106			1.57111
$328$	−14.1707	−	25.3741i	−0.782445	−	1.40105i
$329$		−	2.28377i		−	0.125908i
$330$	−2.82046	+	29.2403i	−0.155261	+	1.60963i
$331$	1.96043	+	1.96043i	0.107755	+	0.107755i	0.758929	−	0.651174i	$-0.225723\pi$
$331$	1.96043	+	1.96043i	0.107755	+	0.107755i	−0.651174	+	0.758929i	$0.725723\pi$
$332$	−1.24751	−	16.0129i	−0.0684658	−	0.878821i
$333$	21.4594	+	21.4594i	1.17597	+	1.17597i
$334$	10.4422	−	28.2704i	0.571372	−	1.54689i
$335$	−8.02897	+	13.7747i	−0.438669	+	0.752593i
$336$	−7.23572	+	9.92608i	−0.394741	+	0.541512i
$337$			18.5606i			1.01106i	0.862809	+	0.505530i	$0.168703\pi$
$337$			18.5606i			1.01106i	−0.862809	+	0.505530i	$0.831297\pi$
$338$	8.57534	+	3.16746i	0.466437	+	0.172287i
$339$	−18.4008	+	18.4008i	−0.999393	+	0.999393i
$340$	19.8885	+	9.60688i	1.07861	+	0.521006i
$341$	−23.6224	−	23.6224i	−1.27922	−	1.27922i
$342$	−18.2753	+	8.41626i	−0.988214	+	0.455099i
$343$	13.9684			0.754221
$344$	−2.42551	+	8.56134i	−0.130775	+	0.461597i
$345$	−4.62364	+	7.93244i	−0.248928	+	0.427068i
$346$	4.80809	−	2.21425i	0.258484	−	0.119039i
$347$	8.01007	−	8.01007i	0.430003	−	0.430003i	−0.458626	−	0.888629i	$-0.651658\pi$
$347$	8.01007	−	8.01007i	0.430003	−	0.430003i	0.888629	+	0.458626i	$0.151658\pi$
$348$	−4.28172	−	3.66279i	−0.229524	−	0.196346i
$349$	19.2579	−	19.2579i	1.03085	−	1.03085i	0.0313434	−	0.999509i	$-0.490021\pi$
$349$	19.2579	−	19.2579i	1.03085	−	1.03085i	0.999509	−	0.0313434i	$-0.00997854\pi$
$350$	1.23975	+	7.60944i	0.0662674	+	0.406742i
$351$	13.9143			0.742693
$352$	10.3351	+	15.5340i	0.550865	+	0.827965i
$353$			6.05459i			0.322253i	0.986934	+	0.161127i	$0.0515127\pi$
$353$			6.05459i			0.322253i	−0.986934	+	0.161127i	$0.948487\pi$
$354$	−6.13376	−	2.26562i	−0.326006	−	0.120416i
$355$	13.8401	−	3.64717i	0.734556	−	0.193572i
$356$	8.94304	−	10.4542i	0.473980	−	0.554072i
$357$	10.7244	−	10.7244i	0.567593	−	0.567593i
$358$	−11.2730	−	24.4784i	−0.595794	−	1.29372i
$359$		−	8.74167i		−	0.461368i	−0.973029	−	0.230684i	$-0.925904\pi$
$359$		−	8.74167i		−	0.461368i	0.973029	−	0.230684i	$-0.0740964\pi$
$360$	22.4609	−	21.6487i	1.18379	−	1.14099i
$361$			10.6803i			0.562122i
$362$	2.97112	−	1.36828i	0.156159	−	0.0719154i
$363$	−0.241479	+	0.241479i	−0.0126744	+	0.0126744i
$364$	0.433010	+	5.55808i	0.0226959	+	0.291323i
$365$	−2.98770	−	11.3376i	−0.156384	−	0.593437i
$366$	−6.76102	+	18.3043i	−0.353404	+	0.956779i
$367$			22.7558i			1.18784i	0.804524	+	0.593920i	$0.202421\pi$
$367$			22.7558i			1.18784i	−0.804524	+	0.593920i	$0.797579\pi$
$368$	0.903160	+	5.76126i	0.0470805	+	0.300327i
$369$	50.6823			2.63841
$370$	15.0154	−	12.3735i	0.780611	−	0.643267i
$371$	−0.234743	+	0.234743i	−0.0121873	+	0.0121873i
$372$	4.43141	+	56.8812i	0.229758	+	2.94915i
$373$	19.1172	−	19.1172i	0.989851	−	0.989851i	−0.0100979	−	0.999949i	$-0.503214\pi$
$373$	19.1172	−	19.1172i	0.989851	−	0.989851i	0.999949	+	0.0100979i	$0.00321433\pi$
$374$	−9.63650	−	20.9249i	−0.498292	−	1.08200i
$375$	0.390645	−	31.4865i	0.0201728	−	1.62596i
$376$	2.88863	+	5.17240i	0.148970	+	0.266746i
$377$	−2.55732			−0.131709
$378$	−3.51051	−	7.62280i	−0.180561	−	0.392075i
$379$	19.2110	+	19.2110i	0.986802	+	0.986802i	0.999914	−	0.0131116i	$-0.00417366\pi$
$379$	19.2110	+	19.2110i	0.986802	+	0.986802i	−0.0131116	+	0.999914i	$0.504174\pi$
$380$	4.24595	+	12.1805i	0.217813	+	0.624849i
$381$	−3.97527	+	3.97527i	−0.203659	+	0.203659i
$382$	−2.48522	+	6.72829i	−0.127155	+	0.344249i
$383$			20.7721i			1.06140i	0.847558	+	0.530702i	$0.178072\pi$
$383$			20.7721i			1.06140i	−0.847558	+	0.530702i	$0.821928\pi$
$384$	3.83281	−	31.6332i	0.195592	−	1.61428i
$385$	4.04946	−	6.94736i	0.206379	−	0.354070i
$386$	−29.2344	−	10.7983i	−1.48799	−	0.549617i
$387$	−10.9726	−	10.9726i	−0.557768	−	0.557768i
$388$	4.90540	−	5.73430i	0.249034	−	0.291115i
$389$	22.9514	+	22.9514i	1.16368	+	1.16368i	0.983664	+	0.180017i	$0.0576152\pi$
$389$	22.9514	+	22.9514i	1.16368	+	1.16368i	0.180017	+	0.983664i	$0.442385\pi$
$390$	2.18616	−	22.6644i	0.110701	−	1.14766i
$391$		−	7.20039i		−	0.364139i
$392$	−14.3503	+	8.01423i	−0.724800	+	0.404780i
$393$	−44.9666			−2.26826
$394$	−6.75135	−	14.6600i	−0.340128	−	0.738562i
$395$	−1.49005	−	5.65437i	−0.0749725	−	0.284502i
$396$	−32.4390	+	2.52721i	−1.63012	+	0.126997i
$397$	−19.9562	−	19.9562i	−1.00157	−	1.00157i	−0.999999	−	0.00157311i	$-0.999499\pi$
$397$	−19.9562	−	19.9562i	−1.00157	−	1.00157i	−0.00157311	−	0.999999i	$-0.500501\pi$
$398$	28.9949	+	10.7098i	1.45338	+	0.536834i
$399$	8.85754			0.443432
$400$	−12.4327	−	15.6662i	−0.621634	−	0.783308i
$401$	−35.5367			−1.77462			−0.887310	−	0.461174i	$-0.847428\pi$
$401$	−35.5367			−1.77462			−0.887310	+	0.461174i	$0.847428\pi$
$402$	−26.6413	−	9.84046i	−1.32875	−	0.490797i
$403$	18.3099	+	18.3099i	0.912083	+	0.912083i
$404$	0.155390	+	1.99457i	0.00773092	+	0.0992334i
$405$	0.302940	+	1.14958i	0.0150532	+	0.0571231i
$406$	0.645198	+	1.40100i	0.0320206	+	0.0695303i
$407$	−20.2936			−1.00592
$408$	−10.7244	+	37.8538i	−0.530935	+	1.87404i
$409$			6.50932i			0.321865i	0.986965	+	0.160933i	$0.0514502\pi$
$409$			6.50932i			0.321865i	−0.986965	+	0.160933i	$0.948550\pi$
$410$	3.11976	−	32.3432i	0.154074	−	1.59732i
$411$	−31.7510	−	31.7510i	−1.56616	−	1.56616i
$412$	−19.6538	−	16.8128i	−0.968274	−	0.828308i
$413$	1.26567	+	1.26567i	0.0622798	+	0.0622798i
$414$	−9.53970	−	3.52367i	−0.468851	−	0.173179i
$415$	9.04283	−	15.5141i	0.443895	−	0.761558i
$416$	−8.01086	−	12.0405i	−0.392765	−	0.590336i
$417$		−	15.1211i		−	0.740485i
$418$	4.66172	−	12.6208i	0.228012	−	0.617302i
$419$	10.8597	−	10.8597i	0.530529	−	0.530529i	−0.390200	−	0.920730i	$-0.627594\pi$
$419$	10.8597	−	10.8597i	0.530529	−	0.530529i	0.920730	+	0.390200i	$0.127594\pi$
$420$	−12.9680	+	4.52044i	−0.632773	+	0.220575i
$421$	17.0865	+	17.0865i	0.832744	+	0.832744i	0.987891	−	0.155147i	$-0.0495852\pi$
$421$	17.0865	+	17.0865i	0.832744	+	0.832744i	−0.155147	+	0.987891i	$0.549585\pi$
$422$	4.33529	+	9.41376i	0.211039	+	0.458255i
$423$	−10.3314			−0.502328
$424$	0.234743	−	0.828575i	0.0114001	−	0.0402392i
$425$	12.1698	+	21.4873i	0.590324	+	1.04229i
$426$	10.6645	+	23.1571i	0.516696	+	1.12197i
$427$	3.77700	−	3.77700i	0.182782	−	0.182782i
$428$	−4.40168	+	0.342919i	−0.212763	+	0.0165756i
$429$	−16.7931	+	16.7931i	−0.810778	+	0.810778i
$430$	−7.67764	+	6.32680i	−0.370249	+	0.305106i
$431$	24.6877			1.18916			0.594581	−	0.804036i	$-0.297318\pi$
$431$	24.6877			1.18916			0.594581	+	0.804036i	$0.297318\pi$
$432$	17.5925	+	12.8243i	0.846420	+	0.617007i
$433$		−	34.7872i		−	1.67176i	−0.548909	−	0.835882i	$-0.684957\pi$
$433$		−	34.7872i		−	1.67176i	0.548909	−	0.835882i	$-0.315043\pi$
$434$	5.41139	−	14.6504i	0.259755	−	0.703240i
$435$	−1.60531	−	6.09175i	−0.0769687	−	0.292077i
$436$	20.1138	−	1.56699i	0.963274	−	0.0750452i
$437$	2.97350	−	2.97350i	0.142242	−	0.142242i
$438$	18.9700	−	8.73619i	0.906421	−	0.417431i
$439$			1.12777i			0.0538257i	0.999638	+	0.0269128i	$0.00856766\pi$
$439$			1.12777i			0.0538257i	−0.999638	+	0.0269128i	$0.991432\pi$
$440$	−0.384037	+	20.8567i	−0.0183082	+	0.994305i
$441$		−	28.6634i		−	1.36492i
$442$	7.46935	+	16.2191i	0.355281	+	0.771465i
$443$	−1.20401	+	1.20401i	−0.0572043	+	0.0572043i	−0.735130	−	0.677926i	$-0.762879\pi$
$443$	−1.20401	+	1.20401i	−0.0572043	+	0.0572043i	0.677926	+	0.735130i	$0.262879\pi$
$444$	26.3363	+	22.5294i	1.24987	+	1.06920i
$445$	14.8736	−	3.91951i	0.705075	−	0.185803i
$446$	24.8204	+	9.16788i	1.17528	+	0.434112i
$447$		−	53.0903i		−	2.51109i
$448$	−4.57517	+	7.42642i	−0.216157	+	0.350865i
$449$	−18.1896			−0.858422			−0.429211	−	0.903204i	$-0.641208\pi$
$449$	−18.1896			−0.858422			−0.429211	+	0.903204i	$0.641208\pi$
$450$	34.4238	−	5.60841i	1.62275	−	0.264383i
$451$	−23.9645	+	23.9645i	−1.12844	+	1.12844i
$452$	−12.0122	+	14.0420i	−0.565008	+	0.660482i
$453$	−11.1549	+	11.1549i	−0.524105	+	0.524105i
$454$	−15.7761	+	7.26534i	−0.740411	+	0.340979i
$455$	−3.13877	+	5.38496i	−0.147148	+	0.252451i
$456$	−20.0610	+	11.2035i	−0.939444	+	0.524652i
$457$	4.25060			0.198835			0.0994174	−	0.995046i	$-0.468302\pi$
$457$	4.25060			0.198835			0.0994174	+	0.995046i	$0.468302\pi$
$458$	7.68312	−	3.53829i	0.359009	−	0.165333i
$459$	−19.0073	−	19.0073i	−0.887187	−	0.887187i
$460$	−2.83587	+	5.87092i	−0.132223	+	0.273733i
$461$	−25.7081	+	25.7081i	−1.19735	+	1.19735i	−0.222390	+	0.974958i	$0.571386\pi$
$461$	−25.7081	+	25.7081i	−1.19735	+	1.19735i	−0.974958	+	0.222390i	$0.928614\pi$
$462$	13.4367	+	4.96309i	0.625131	+	0.230904i
$463$			32.8289i			1.52569i	0.646582	+	0.762844i	$0.276198\pi$
$463$			32.8289i			1.52569i	−0.646582	+	0.762844i	$0.723802\pi$
$464$	−3.23334	−	2.35697i	−0.150104	−	0.109420i
$465$	−32.1221	+	55.1095i	−1.48963	+	2.55564i
$466$	9.65580	−	26.1414i	0.447296	−	1.21098i
$467$	17.1611	+	17.1611i	0.794123	+	0.794123i	0.982162	−	0.188039i	$-0.0602130\pi$
$467$	17.1611	+	17.1611i	0.794123	+	0.794123i	−0.188039	+	0.982162i	$0.560213\pi$
$468$	25.1438	−	1.95886i	1.16227	−	0.0905484i
$469$	5.49731	+	5.49731i	0.253842	+	0.253842i
$470$	−0.635949	+	6.59303i	−0.0293342	+	0.304114i
$471$		−	28.3575i		−	1.30665i
$472$	−4.46746	−	1.26567i	−0.205631	−	0.0582574i
$473$	10.3765			0.477112
$474$	9.46084	−	4.35697i	0.434551	−	0.200122i
$475$	−3.84776	+	13.8992i	−0.176547	+	0.637738i
$476$	7.00098	−	8.18398i	0.320889	−	0.375112i
$477$	1.06194	+	1.06194i	0.0486228	+	0.0486228i
$478$	0.469372	−	1.27074i	0.0214686	−	0.0581223i
$479$	−25.2711			−1.15466			−0.577332	−	0.816510i	$-0.695906\pi$
$479$	−25.2711			−1.15466			−0.577332	+	0.816510i	$0.695906\pi$
$480$	23.6529	−	26.6408i	1.07960	−	1.21598i
$481$	15.7298			0.717216
$482$	−5.12541	+	13.8762i	−0.233456	+	0.632041i
$483$	3.16573	+	3.16573i	0.144046	+	0.144046i
$484$	−0.157640	+	0.184278i	−0.00716546	+	0.00837626i
$485$	8.15839	−	2.14991i	0.370454	−	0.0976226i
$486$	19.0505	−	8.77325i	0.864146	−	0.397963i
$487$	−12.9056			−0.584807			−0.292404	−	0.956295i	$-0.594455\pi$
$487$	−12.9056			−0.584807			−0.292404	+	0.956295i	$0.594455\pi$
$488$	−3.77700	+	13.3317i	−0.170977	+	0.603498i
$489$		−	2.17495i		−	0.0983545i
$490$	−18.2917	−	1.76438i	−0.826335	−	0.0797065i
$491$	10.3909	+	10.3909i	0.468935	+	0.468935i	0.901569	−	0.432635i	$-0.142416\pi$
$491$	10.3909	+	10.3909i	0.468935	+	0.468935i	−0.432635	+	0.901569i	$0.642416\pi$
$492$	57.7050	−	4.49559i	2.60154	−	0.202677i
$493$	3.49337	+	3.49337i	0.157333	+	0.157333i
$494$	−3.61334	+	9.78249i	−0.162572	+	0.440135i
$495$	−31.4286	−	18.3190i	−1.41261	−	0.823379i
$496$	6.27458	+	40.0255i	0.281737	+	1.79720i
$497$		−	6.97894i		−	0.313048i
$498$	30.0054	+	11.0831i	1.34458	+	0.496644i
$499$	−19.8755	+	19.8755i	−0.889749	+	0.889749i	−0.994499	−	0.104750i	$-0.966596\pi$
$499$	−19.8755	+	19.8755i	−0.889749	+	0.889749i	0.104750	+	0.994499i	$0.466596\pi$
$500$	−1.46008	−	22.3130i	−0.0652968	−	0.997866i
$501$	42.4402	+	42.4402i	1.89609	+	1.89609i
$502$	−13.2434	+	6.09894i	−0.591081	+	0.272209i
$503$	−12.8059			−0.570989			−0.285494	−	0.958380i	$-0.592158\pi$
$503$	−12.8059			−0.570989			−0.285494	+	0.958380i	$0.592158\pi$
$504$	−7.41677	−	13.2805i	−0.330369	−	0.591561i
$505$	−1.12638	+	1.93244i	−0.0501231	+	0.0859925i
$506$	6.17686	−	2.84461i	0.274595	−	0.126458i
$507$	−12.8735	+	12.8735i	−0.571732	+	0.571732i
$508$	−2.59510	+	3.03362i	−0.115139	+	0.134595i
$509$	5.77064	−	5.77064i	0.255779	−	0.255779i	−0.567556	−	0.823335i	$-0.692111\pi$
$509$	5.77064	−	5.77064i	0.255779	−	0.255779i	0.823335	+	0.567556i	$0.192111\pi$
$510$	−33.9466	+	27.9739i	−1.50318	+	1.23870i
$511$	−5.71704			−0.252907
$512$	0.968769	−	22.6067i	0.0428139	−	0.999083i
$513$		−	15.6987i		−	0.693114i
$514$	26.9076	+	9.93881i	1.18684	+	0.438382i
$515$	−7.36864	−	27.9622i	−0.324701	−	1.23216i
$516$	−13.4663	−	11.5197i	−0.592820	−	0.507127i
$517$	4.88507	−	4.88507i	0.214845	−	0.214845i
$518$	−3.96853	−	8.61736i	−0.174367	−	0.378625i
$519$			10.5421i			0.462747i
$520$	0.297671	−	16.1662i	0.0130537	−	0.708937i
$521$		−	18.9514i		−	0.830274i	−0.909759	−	0.415137i	$-0.863734\pi$
$521$		−	18.9514i		−	0.830274i	0.909759	−	0.415137i	$-0.136266\pi$
$522$	6.33787	−	2.91876i	0.277401	−	0.127751i
$523$	−7.32161	+	7.32161i	−0.320152	+	0.320152i	−0.848825	−	0.528674i	$-0.822690\pi$
$523$	−7.32161	+	7.32161i	−0.320152	+	0.320152i	0.528674	+	0.848825i	$0.322690\pi$
$524$	−31.8348	+	2.48014i	−1.39071	+	0.108345i
$525$	−14.7977	−	4.09651i	−0.645826	−	0.178786i
$526$	9.90185	−	26.8075i	0.431741	−	1.16886i
$527$		−	50.0237i		−	2.17907i
$528$	−36.7097	+	5.75477i	−1.59759	+	0.250444i
$529$	−20.8745			−0.907587
$530$	0.743050	−	0.612314i	0.0322760	−	0.0265972i
$531$	5.72569	−	5.72569i	0.248474	−	0.248474i
$532$	6.27084	−	0.488539i	0.271875	−	0.0211808i
$533$	18.5751	−	18.5751i	0.804578	−	0.804578i
$534$	11.4608	+	24.8864i	0.495959	+	1.07694i
$535$	−4.26458	−	2.48573i	−0.184374	−	0.107467i
$536$	−19.4039	−	5.49731i	−0.838120	−	0.237448i
$537$	53.6708			2.31606
$538$	13.6079	+	29.5485i	0.586677	+	1.27393i
$539$	13.5531	+	13.5531i	0.583774	+	0.583774i
$540$	8.01182	+	22.9839i	0.344774	+	0.989068i
$541$	−6.08576	+	6.08576i	−0.261647	+	0.261647i	−0.825723	−	0.564076i	$-0.809233\pi$
$541$	−6.08576	+	6.08576i	−0.261647	+	0.261647i	0.564076	+	0.825723i	$0.309233\pi$
$542$	11.9912	−	32.4640i	0.515066	−	1.39445i
$543$			6.51442i			0.279561i
$544$	−5.50465	+	27.3907i	−0.236010	+	1.17437i
$545$	19.4873	+	11.3587i	0.834743	+	0.486553i
$546$	−10.4149	−	3.84694i	−0.445717	−	0.164634i
$547$	−3.68638	−	3.68638i	−0.157618	−	0.157618i	0.623892	−	0.781510i	$-0.285550\pi$
$547$	−3.68638	−	3.68638i	−0.157618	−	0.157618i	−0.781510	+	0.623892i	$0.785550\pi$
$548$	−24.2298	−	20.7274i	−1.03505	−	0.885430i
$549$	−17.0865	−	17.0865i	−0.729233	−	0.729233i
$550$	−13.6250	+	18.9287i	−0.580972	+	0.807124i
$551$			2.88527i			0.122917i
$552$	−11.1741	−	3.16573i	−0.475602	−	0.134743i
$553$	−2.85124			−0.121247
$554$	11.5432	+	25.0653i	0.490425	+	1.06492i
$555$	9.87406	+	37.4696i	0.419130	+	1.59050i
$556$	−0.834008	−	10.7053i	−0.0353698	−	0.454004i
$557$	−3.92396	−	3.92396i	−0.166264	−	0.166264i	0.619071	−	0.785335i	$-0.287509\pi$
$557$	−3.92396	−	3.92396i	−0.166264	−	0.166264i	−0.785335	+	0.619071i	$0.787509\pi$
$558$	−66.2757	−	24.4802i	−2.80567	−	1.03633i
$559$	−8.04293			−0.340180
$560$	−8.93158	+	3.91557i	−0.377428	+	0.165463i
$561$	45.8796			1.93704
$562$	−21.9783	−	8.11808i	−0.927097	−	0.342441i
$563$	2.42213	+	2.42213i	0.102081	+	0.102081i	0.756303	−	0.654222i	$-0.227004\pi$
$563$	2.42213	+	2.42213i	0.102081	+	0.102081i	−0.654222	+	0.756303i	$0.727004\pi$
$564$	−11.7629	+	0.916407i	−0.495309	+	0.0385877i
$565$	−19.9781	+	5.26466i	−0.840484	+	0.221486i
$566$	11.4467	+	24.8555i	0.481139	+	1.04476i
$567$	0.579682			0.0243444
$568$	8.82734	+	15.8063i	0.370387	+	0.663217i
$569$			0.577163i			0.0241959i	0.999927	+	0.0120980i	$0.00385099\pi$
$569$			0.577163i			0.0241959i	−0.999927	+	0.0120980i	$0.996149\pi$
$570$	−25.5709	−	2.46651i	−1.07105	−	0.103311i
$571$	−18.5485	−	18.5485i	−0.776229	−	0.776229i	0.202959	−	0.979187i	$-0.434944\pi$
$571$	−18.5485	−	18.5485i	−0.776229	−	0.776229i	−0.979187	+	0.202959i	$0.934944\pi$
$572$	−10.9627	+	12.8152i	−0.458374	+	0.535829i
$573$	−10.1007	−	10.1007i	−0.421962	−	0.421962i
$574$	−14.8626	−	5.48976i	−0.620351	−	0.229138i
$575$	−6.34285	+	3.59243i	−0.264515	+	0.149815i
$576$	33.5958	+	20.6973i	1.39982	+	0.862387i
$577$			9.63346i			0.401046i	0.979689	+	0.200523i	$0.0642642\pi$
$577$			9.63346i			0.401046i	−0.979689	+	0.200523i	$0.935736\pi$
$578$	3.62229	−	9.80670i	0.150667	−	0.407905i
$579$	43.8873	−	43.8873i	1.82390	−	1.82390i
$580$	−1.47250	−	4.22421i	−0.0611421	−	0.175401i
$581$	−6.19148	−	6.19148i	−0.256866	−	0.256866i
$582$	6.28645	+	13.6506i	0.260582	+	0.565834i
$583$	−1.00425			−0.0415918
$584$	12.9483	−	7.23122i	0.535803	−	0.299230i
$585$	24.3606	+	14.1993i	1.00719	+	0.587067i
$586$	−19.2852	−	41.8763i	−0.796663	−	1.72989i
$587$	−17.5202	+	17.5202i	−0.723136	+	0.723136i	−0.969243	−	0.246107i	$-0.920849\pi$
$587$	−17.5202	+	17.5202i	−0.723136	+	0.723136i	0.246107	+	0.969243i	$0.420849\pi$
$588$	−2.54248	−	32.6351i	−0.104850	−	1.34585i
$589$	20.6580	−	20.6580i	0.851197	−	0.851197i
$590$	−3.30144	−	4.00633i	−0.135918	−	0.164938i
$591$	32.1433			1.32220
$592$	19.8878	+	14.4975i	0.817385	+	0.595842i
$593$		−	15.7065i		−	0.644988i	−0.946571	−	0.322494i	$-0.895479\pi$
$593$		−	15.7065i		−	0.644988i	0.946571	−	0.322494i	$-0.104521\pi$
$594$	8.79635	−	23.8146i	0.360919	−	0.977123i
$595$	11.6436	−	3.06835i	0.477343	−	0.125790i
$596$	−2.92820	−	37.5862i	−0.119944	−	1.53959i
$597$	−43.5279	+	43.5279i	−1.78148	+	1.78148i
$598$	−4.78774	+	2.20489i	−0.195785	+	0.0901645i
$599$		−	29.6865i		−	1.21296i	−0.795099	−	0.606479i	$-0.792581\pi$
$599$		−	29.6865i		−	1.21296i	0.795099	−	0.606479i	$-0.207419\pi$
$600$	38.6962	−	9.43897i	1.57976	−	0.385344i
$601$		−	13.3688i		−	0.545325i	−0.962110	−	0.272663i	$-0.912096\pi$
$601$		−	13.3688i		−	0.545325i	0.962110	−	0.272663i	$-0.0879043\pi$
$602$	2.02919	+	4.40622i	0.0827034	+	0.179584i
$603$	24.8689	−	24.8689i	1.01274	−	1.01274i
$604$	−7.28207	+	8.51258i	−0.296303	+	0.346372i
$605$	−0.262178	+	0.0690897i	−0.0106591	+	0.00280890i
$606$	−3.73748	−	1.38051i	−0.151825	−	0.0560793i
$607$			39.5508i			1.60532i	0.596439	+	0.802659i	$0.296582\pi$
$607$			39.5508i			1.60532i	−0.596439	+	0.802659i	$0.703418\pi$
$608$	−13.5846	+	9.03816i	−0.550929	+	0.366546i
$609$	−3.07180			−0.124475
$610$	−11.9556	+	9.85208i	−0.484068	+	0.398899i
$611$	−3.78646	+	3.78646i	−0.153184	+	0.153184i
$612$	−37.0229	−	31.6712i	−1.49656	−	1.28023i
$613$	−15.1788	+	15.1788i	−0.613067	+	0.613067i	−0.943744	−	0.330677i	$-0.892723\pi$
$613$	−15.1788	+	15.1788i	−0.613067	+	0.613067i	0.330677	+	0.943744i	$0.392723\pi$
$614$	42.4213	−	19.5362i	1.71199	−	0.788416i
$615$	55.9077	+	32.5873i	2.25441	+	1.31405i
$616$	9.78646	+	2.77260i	0.394308	+	0.111711i
$617$	18.6184			0.749549			0.374774	−	0.927116i	$-0.377720\pi$
$617$	18.6184			0.749549			0.374774	+	0.927116i	$0.377720\pi$
$618$	46.7861	−	21.5463i	1.88201	−	0.866717i
$619$	−15.6388	−	15.6388i	−0.628576	−	0.628576i	0.319134	−	0.947710i	$-0.396608\pi$
$619$	−15.6388	−	15.6388i	−0.628576	−	0.628576i	−0.947710	+	0.319134i	$0.896608\pi$
$620$	−19.7018	+	40.7874i	−0.791242	+	1.63806i
$621$	5.61080	−	5.61080i	0.225154	−	0.225154i
$622$	−23.6142	−	8.72235i	−0.946844	−	0.349734i
$623$		−	7.50008i		−	0.300484i
$624$	28.4541	−	4.46058i	1.13907	−	0.178566i
$625$	12.8564	−	21.4409i	0.514256	−	0.857637i
$626$	−11.6577	+	31.5612i	−0.465936	+	1.26144i
$627$	18.9466	+	18.9466i	0.756655	+	0.756655i
$628$	−1.56406	−	20.0762i	−0.0624129	−	0.801127i
$629$	−21.4873	−	21.4873i	−0.856753	−	0.856753i
$630$	1.63284	−	16.9281i	0.0650541	−	0.674430i
$631$			32.2591i			1.28422i	0.766614	+	0.642108i	$0.221940\pi$
$631$			32.2591i			1.28422i	−0.766614	+	0.642108i	$0.778060\pi$
$632$	6.45765	−	3.60640i	0.256871	−	0.143455i
$633$	−20.6404			−0.820382
$634$	−24.8767	+	11.4564i	−0.987979	+	0.454991i
$635$	−4.31603	+	1.13737i	−0.171276	+	0.0451351i
$636$	1.30328	+	1.11489i	0.0516784	+	0.0442082i
$637$	−10.5052	−	10.5052i	−0.416230	−	0.416230i
$638$	−1.61668	+	4.37689i	−0.0640051	+	0.173283i
$639$	−31.5715			−1.24895
$640$	15.2761	−	20.1653i	0.603841	−	0.797105i
$641$	−8.87760			−0.350644			−0.175322	−	0.984511i	$-0.556097\pi$
$641$	−8.87760			−0.350644			−0.175322	+	0.984511i	$0.556097\pi$
$642$	3.04655	−	8.24800i	0.120238	−	0.325523i
$643$	19.5500	+	19.5500i	0.770977	+	0.770977i	0.978277	−	0.207301i	$-0.0664678\pi$
$643$	19.5500	+	19.5500i	0.770977	+	0.770977i	−0.207301	+	0.978277i	$0.566468\pi$
$644$	2.41584	+	2.06663i	0.0951974	+	0.0814365i
$645$	−5.04880	−	19.1589i	−0.198796	−	0.754382i
$646$	18.2990	−	8.42721i	0.719966	−	0.331564i
$647$	33.1992			1.30519			0.652597	−	0.757705i	$-0.273679\pi$
$647$	33.1992			1.30519			0.652597	+	0.757705i	$0.273679\pi$
$648$	−1.31289	+	0.733213i	−0.0515754	+	0.0288033i
$649$			5.41465i			0.212543i
$650$	10.5609	−	14.6718i	0.414231	−	0.575477i
$651$	21.9935	+	21.9935i	0.861992	+	0.861992i
$652$	−0.119959	−	1.53979i	−0.00469797	−	0.0603028i
$653$	10.3869	+	10.3869i	0.406472	+	0.406472i	0.880506	−	0.474034i	$-0.157203\pi$
$653$	10.3869	+	10.3869i	0.406472	+	0.406472i	−0.474034	+	0.880506i	$0.657203\pi$
$654$	−13.9214	+	37.6898i	−0.544371	+	1.47379i
$655$	−30.8433	−	17.9778i	−1.20515	−	0.702452i
$656$	40.6053	−	6.36545i	1.58537	−	0.248529i
$657$			25.8629i			1.00901i
$658$	3.02967	+	1.11906i	0.118109	+	0.0436257i
$659$	3.29013	−	3.29013i	0.128165	−	0.128165i	−0.640114	−	0.768280i	$-0.721113\pi$
$659$	3.29013	−	3.29013i	0.128165	−	0.128165i	0.768280	+	0.640114i	$0.221113\pi$
$660$	−37.4084	−	18.0696i	−1.45612	−	0.703359i
$661$	−8.43866	−	8.43866i	−0.328226	−	0.328226i	0.523686	−	0.851912i	$-0.324557\pi$
$661$	−8.43866	−	8.43866i	−0.328226	−	0.328226i	−0.851912	+	0.523686i	$0.824557\pi$
$662$	−3.56135	+	1.64010i	−0.138416	+	0.0637443i
$663$	−35.5617			−1.38110
$664$	21.8541	+	6.19148i	0.848105	+	0.240276i
$665$	6.07552	+	3.54128i	0.235599	+	0.137325i
$666$	−38.9834	+	17.9529i	−1.51058	+	0.695662i
$667$	−1.03121	+	1.03121i	−0.0399286	+	0.0399286i
$668$	32.3870	+	27.7054i	1.25309	+	1.07196i
$669$	−37.2610	+	37.2610i	−1.44059	+	1.44059i
$670$	−14.3394	−	17.4010i	−0.553980	−	0.672260i
$671$	16.1583			0.623783
$672$	−9.62247	−	14.4628i	−0.371195	−	0.557916i
$673$			7.49618i			0.288956i	0.989508	+	0.144478i	$0.0461504\pi$
$673$			7.49618i			0.288956i	−0.989508	+	0.144478i	$0.953850\pi$
$674$	−24.6226	−	9.09483i	−0.948429	−	0.350320i
$675$	−7.26046	+	26.2268i	−0.279455	+	1.00947i
$676$	−8.40396	+	9.82404i	−0.323229	+	0.377848i
$677$	−11.2336	+	11.2336i	−0.431741	+	0.431741i	−0.889220	−	0.457479i	$-0.848752\pi$
$677$	−11.2336	+	11.2336i	−0.431741	+	0.431741i	0.457479	+	0.889220i	$0.348752\pi$
$678$	−15.3941	−	33.4272i	−0.591208	−	1.28376i
$679$		−	4.11391i		−	0.157877i
$680$	−22.4901	+	21.6769i	−0.862457	+	0.831270i
$681$		−	34.5904i		−	1.32551i
$682$	42.9128	−	19.7625i	1.64322	−	0.756746i
$683$	24.1607	−	24.1607i	0.924482	−	0.924482i	−0.0728605	−	0.997342i	$-0.523213\pi$
$683$	24.1607	−	24.1607i	0.924482	−	0.924482i	0.997342	+	0.0728605i	$0.0232128\pi$
$684$	−2.21006	−	28.3682i	−0.0845039	−	1.08468i
$685$	−9.08429	−	34.4726i	−0.347093	−	1.31713i
$686$	−6.84461	+	18.5306i	−0.261328	+	0.707500i
$687$			16.8458i			0.642709i
$688$	−10.1690	−	7.41283i	−0.387691	−	0.282611i
$689$	0.778403			0.0296548
$690$	−8.25763	−	10.0207i	−0.314363	−	0.381482i
$691$	20.6744	−	20.6744i	0.786490	−	0.786490i	−0.194427	−	0.980917i	$-0.562285\pi$
$691$	20.6744	−	20.6744i	0.786490	−	0.786490i	0.980917	+	0.194427i	$0.0622846\pi$
$692$	0.581451	+	7.46345i	0.0221034	+	0.283718i
$693$	−12.5427	+	12.5427i	−0.476460	+	0.476460i
$694$	6.70124	+	14.5512i	0.254376	+	0.552357i
$695$	6.04550	−	10.3718i	0.229319	−	0.393425i
$696$	6.95717	−	3.88537i	0.263711	−	0.147275i
$697$	−50.7482			−1.92222
$698$	16.1112	+	34.9842i	0.609818	+	1.32417i
$699$	39.2440	+	39.2440i	1.48435	+	1.48435i
$700$	−10.7022	−	2.08402i	−0.404507	−	0.0787686i
$701$	−5.10967	+	5.10967i	−0.192990	+	0.192990i	−0.796987	−	0.603997i	$-0.793574\pi$
$701$	−5.10967	+	5.10967i	−0.192990	+	0.192990i	0.603997	+	0.796987i	$0.293574\pi$
$702$	−6.81814	+	18.4589i	−0.257334	+	0.696686i
$703$		−	17.7469i		−	0.669338i
$704$	−25.6718	+	6.09891i	−0.967544	+	0.229861i
$705$	−11.3965	−	6.64279i	−0.429219	−	0.250182i
$706$	−8.03207	−	2.96679i	−0.302291	−	0.111657i
$707$	0.771212	+	0.771212i	0.0290044	+	0.0290044i
$708$	6.01119	−	7.02694i	0.225914	−	0.264089i
$709$	13.7429	+	13.7429i	0.516126	+	0.516126i	0.916397	−	0.400271i	$-0.131084\pi$
$709$	13.7429	+	13.7429i	0.516126	+	0.516126i	−0.400271	+	0.916397i	$0.631084\pi$
$710$	−1.94339	+	20.1475i	−0.0729341	+	0.756124i
$711$			12.8985i			0.483732i
$712$	9.48650	+	16.9866i	0.355522	+	0.636599i
$713$	14.7665			0.553011
$714$	8.97201	+	19.4820i	0.335769	+	0.729097i
$715$	−18.2326	+	4.80468i	−0.681860	+	0.179685i
$716$	37.9971	−	2.96022i	1.42002	−	0.110628i
$717$	1.90767	+	1.90767i	0.0712431	+	0.0712431i
$718$	11.5968	+	4.28349i	0.432788	+	0.159858i
$719$	23.0266			0.858747			0.429373	−	0.903127i	$-0.358734\pi$
$719$	23.0266			0.858747			0.429373	+	0.903127i	$0.358734\pi$
$720$	17.7134	+	40.4049i	0.660138	+	1.50580i
$721$	−14.1001			−0.525114
$722$	−14.1686	−	5.23344i	−0.527301	−	0.194768i
$723$	−20.8312	−	20.8312i	−0.774721	−	0.774721i
$724$	0.359304	+	4.61199i	0.0133534	+	0.171403i
$725$	1.33440	−	4.82023i	0.0495585	−	0.179019i
$726$	−0.202022	−	0.438675i	−0.00749773	−	0.0162807i
$727$	43.6601			1.61926			0.809631	−	0.586939i	$-0.199667\pi$
$727$	43.6601			1.61926			0.809631	+	0.586939i	$0.199667\pi$
$728$	−7.58558	−	2.14907i	−0.281140	−	0.0796498i
$729$			43.3646i			1.60610i
$730$	16.5046	+	1.59200i	0.610861	+	0.0589224i
$731$	10.9869	+	10.9869i	0.406363	+	0.406363i
$732$	−20.9696	−	17.9385i	−0.775061	−	0.663025i
$733$	20.4799	+	20.4799i	0.756444	+	0.756444i	0.975673	−	0.219229i	$-0.0703543\pi$
$733$	20.4799	+	20.4799i	0.756444	+	0.756444i	−0.219229	+	0.975673i	$0.570354\pi$
$734$	−30.1880	−	11.1505i	−1.11426	−	0.411572i
$735$	18.4297	−	31.6186i	0.679792	−	1.16627i
$736$	−8.08550	−	1.62492i	−0.298036	−	0.0598955i
$737$			23.5179i			0.866292i
$738$	−24.8347	+	67.2356i	−0.914178	+	2.47498i
$739$	−5.57362	+	5.57362i	−0.205029	+	0.205029i	−0.802151	−	0.597122i	$-0.796311\pi$
$739$	−5.57362	+	5.57362i	−0.205029	+	0.205029i	0.597122	+	0.802151i	$0.296311\pi$
$740$	9.05714	+	25.9826i	0.332947	+	0.955140i
$741$	−14.6857	−	14.6857i	−0.539493	−	0.539493i
$742$	−0.196387	−	0.426439i	−0.00720958	−	0.0156551i
$743$	13.1917			0.483957			0.241978	−	0.970282i	$-0.422204\pi$
$743$	13.1917			0.483957			0.241978	+	0.970282i	$0.422204\pi$
$744$	−77.6305	−	21.9935i	−2.84607	−	0.806320i
$745$	21.2257	−	36.4155i	0.777651	−	1.33416i
$746$	15.9935	+	34.7286i	0.585563	+	1.27151i
$747$	−28.0092	+	28.0092i	−1.02480	+	1.02480i
$748$	32.4812	−	2.53049i	1.18763	−	0.0925240i
$749$	−1.70194	+	1.70194i	−0.0621875	+	0.0621875i
$750$	41.5789	+	15.9469i	1.51825	+	0.582298i
$751$	−16.1003			−0.587510			−0.293755	−	0.955881i	$-0.594905\pi$
$751$	−16.1003			−0.587510			−0.293755	+	0.955881i	$0.594905\pi$
$752$	−8.27721	+	1.29757i	−0.301839	+	0.0473175i
$753$		−	29.0371i		−	1.05817i
$754$	1.25311	−	3.39257i	0.0456355	−	0.123550i
$755$	−12.1111	+	3.19155i	−0.440770	+	0.116152i
$756$	11.8327	−	0.921840i	0.430350	−	0.0335270i
$757$	23.2342	−	23.2342i	0.844463	−	0.844463i	−0.144973	−	0.989436i	$-0.546309\pi$
$757$	23.2342	−	23.2342i	0.844463	−	0.844463i	0.989436	+	0.144973i	$0.0463094\pi$
$758$	−34.8990	+	16.0719i	−1.26759	+	0.583759i
$759$			13.5432i			0.491588i
$760$	−18.2394	−	0.335844i	−0.661612	−	0.0121823i
$761$		−	15.4641i		−	0.560573i	−0.959916	−	0.280287i	$-0.909570\pi$
$761$		−	15.4641i		−	0.560573i	0.959916	−	0.280287i	$-0.0904295\pi$
$762$	−3.32572	−	7.22155i	−0.120478	−	0.261609i
$763$	7.77711	−	7.77711i	0.281550	−	0.281550i
$764$	−7.70804	−	6.59383i	−0.278867	−	0.238556i
$765$	−13.8807	−	52.6738i	−0.501857	−	1.90442i
$766$	−27.5565	−	10.1785i	−0.995655	−	0.367764i
$767$		−	4.19694i		−	0.151543i
$768$	40.0868	+	20.5852i	1.44651	+	0.742804i

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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	80.q (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.490008 + 1.32661i) q^{2} +(-1.99154 - 1.99154i) q^{3} +(-1.51978 - 1.30010i) q^{4} +(-0.569800 - 2.16225i) q^{5} +(3.61786 - 1.66612i) q^{6} -1.09033 q^{7} +(2.46943 - 1.37910i) q^{8} +4.93244i q^{9} +O(q^{10})\)	\(q+(-0.490008 + 1.32661i) q^{2} +(-1.99154 - 1.99154i) q^{3} +(-1.51978 - 1.30010i) q^{4} +(-0.569800 - 2.16225i) q^{5} +(3.61786 - 1.66612i) q^{6} -1.09033 q^{7} +(2.46943 - 1.37910i) q^{8} +4.93244i q^{9} +(3.14767 + 0.303617i) q^{10} +(-2.33225 - 2.33225i) q^{11} +(0.437515 + 5.61590i) q^{12} +(1.80775 + 1.80775i) q^{13} +(0.534268 - 1.44644i) q^{14} +(-3.17142 + 5.44098i) q^{15} +(0.619491 + 3.95174i) q^{16} -4.93886i q^{17} +(-6.54342 - 2.41694i) q^{18} +(2.03957 - 2.03957i) q^{19} +(-1.94516 + 4.02695i) q^{20} +(2.17142 + 2.17142i) q^{21} +(4.23680 - 1.95116i) q^{22} +1.45791 q^{23} +(-7.66449 - 2.17142i) q^{24} +(-4.35066 + 2.46410i) q^{25} +(-3.28398 + 1.51236i) q^{26} +(3.84853 - 3.84853i) q^{27} +(1.65706 + 1.41753i) q^{28} +(-0.707323 + 0.707323i) q^{29} +(-5.66403 - 6.87336i) q^{30} +10.1286 q^{31} +(-5.54597 - 1.11456i) q^{32} +9.28951i q^{33} +(6.55193 + 2.42008i) q^{34} +(0.621268 + 2.35756i) q^{35} +(6.41266 - 7.49625i) q^{36} +(4.35066 - 4.35066i) q^{37} +(1.70631 + 3.70512i) q^{38} -7.20039i q^{39} +(-4.38905 - 4.55371i) q^{40} -10.2753i q^{41} +(-3.94465 + 1.81662i) q^{42} +(-2.22457 + 2.22457i) q^{43} +(0.512364 + 6.57666i) q^{44} +(10.6652 - 2.81051i) q^{45} +(-0.714386 + 1.93407i) q^{46} +2.09458i q^{47} +(6.63629 - 9.10377i) q^{48} -5.81119 q^{49} +(-1.13705 - 6.97905i) q^{50} +(-9.83592 + 9.83592i) q^{51} +(-0.397138 - 5.09763i) q^{52} +(0.215297 - 0.215297i) q^{53} +(3.21969 + 6.99131i) q^{54} +(-3.71399 + 6.37182i) q^{55} +(-2.69248 + 1.50367i) q^{56} -8.12376 q^{57} +(-0.591747 - 1.28493i) q^{58} +(-1.16082 - 1.16082i) q^{59} +(11.8937 - 4.14596i) q^{60} +(-3.46410 + 3.46410i) q^{61} +(-4.96309 + 13.4367i) q^{62} -5.37797i q^{63} +(4.19615 - 6.81119i) q^{64} +(2.87875 - 4.93886i) q^{65} +(-12.3236 - 4.55193i) q^{66} +(-5.04189 - 5.04189i) q^{67} +(-6.42100 + 7.50600i) q^{68} +(-2.90348 - 2.90348i) q^{69} +(-3.43198 - 0.331042i) q^{70} +6.40078i q^{71} +(6.80234 + 12.1803i) q^{72} +5.24343 q^{73} +(3.63977 + 7.90348i) q^{74} +(13.5718 + 3.75714i) q^{75} +(-5.75135 + 0.448067i) q^{76} +(2.54291 + 2.54291i) q^{77} +(9.55211 + 3.52825i) q^{78} +2.61504 q^{79} +(8.19166 - 3.59120i) q^{80} -0.531659 q^{81} +(13.6313 + 5.03497i) q^{82} +(5.67856 + 5.67856i) q^{83} +(-0.477033 - 6.12316i) q^{84} +(-10.6790 + 2.81416i) q^{85} +(-1.86108 - 4.04120i) q^{86} +2.81732 q^{87} +(-8.97572 - 2.54291i) q^{88} +6.87875i q^{89} +(-1.49758 + 15.5257i) q^{90} +(-1.97103 - 1.97103i) q^{91} +(-2.21570 - 1.89542i) q^{92} +(-20.1715 - 20.1715i) q^{93} +(-2.77868 - 1.02636i) q^{94} +(-5.57221 - 3.24791i) q^{95} +(8.82531 + 13.2647i) q^{96} +3.77310i q^{97} +(2.84753 - 7.70918i) q^{98} +(11.5037 - 11.5037i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} - 8 q^{5} - 4 q^{6}+O(q^{10}) \) 16 * q - 4 * q^4 - 8 * q^5 - 4 * q^6	\( 16 q - 4 q^{4} - 8 q^{5} - 4 q^{6} - 12 q^{10} + 8 q^{11} - 4 q^{14} + 16 q^{16} - 8 q^{19} - 4 q^{20} - 16 q^{21} - 32 q^{24} + 32 q^{26} - 16 q^{29} - 36 q^{30} + 16 q^{31} + 48 q^{34} - 24 q^{35} + 60 q^{36} + 24 q^{40} - 8 q^{44} + 8 q^{45} - 28 q^{46} + 16 q^{49} + 24 q^{50} - 16 q^{51} + 40 q^{54} - 56 q^{56} - 24 q^{59} + 48 q^{60} - 16 q^{64} - 72 q^{66} + 32 q^{69} + 20 q^{70} + 48 q^{75} - 88 q^{76} + 16 q^{79} + 16 q^{80} - 16 q^{81} - 80 q^{84} - 28 q^{86} - 84 q^{90} - 16 q^{91} + 12 q^{94} + 32 q^{95} + 56 q^{96} + 88 q^{99}+O(q^{100}) \) 16 * q - 4 * q^4 - 8 * q^5 - 4 * q^6 - 12 * q^10 + 8 * q^11 - 4 * q^14 + 16 * q^16 - 8 * q^19 - 4 * q^20 - 16 * q^21 - 32 * q^24 + 32 * q^26 - 16 * q^29 - 36 * q^30 + 16 * q^31 + 48 * q^34 - 24 * q^35 + 60 * q^36 + 24 * q^40 - 8 * q^44 + 8 * q^45 - 28 * q^46 + 16 * q^49 + 24 * q^50 - 16 * q^51 + 40 * q^54 - 56 * q^56 - 24 * q^59 + 48 * q^60 - 16 * q^64 - 72 * q^66 + 32 * q^69 + 20 * q^70 + 48 * q^75 - 88 * q^76 + 16 * q^79 + 16 * q^80 - 16 * q^81 - 80 * q^84 - 28 * q^86 - 84 * q^90 - 16 * q^91 + 12 * q^94 + 32 * q^95 + 56 * q^96 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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