LMFDB - Embedded newform 380.2.bj.a.23.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(23,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 27, 4]))

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

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

chi := DirichletCharacter("380.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bj (of order $36$, degree $12$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$56$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			23.27
Character	$\chi$	$=$	380.23
Dual form			380.2.bj.a.347.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.261615 - 1.38980i) q^{2} +(-1.49450 - 1.04646i) q^{3} +(-1.86311 + 0.727188i) q^{4} +(2.23475 + 0.0767528i) q^{5} +(-1.06339 + 2.35083i) q^{6} +(3.56968 - 0.956492i) q^{7} +(1.49807 + 2.39912i) q^{8} +(0.112392 + 0.308794i) q^{9} +O(q^{10})$	\(q+(-0.261615 - 1.38980i) q^{2} +(-1.49450 - 1.04646i) q^{3} +(-1.86311 + 0.727188i) q^{4} +(2.23475 + 0.0767528i) q^{5} +(-1.06339 + 2.35083i) q^{6} +(3.56968 - 0.956492i) q^{7} +(1.49807 + 2.39912i) q^{8} +(0.112392 + 0.308794i) q^{9} +(-0.477973 - 3.12595i) q^{10} +(1.25503 - 0.724594i) q^{11} +(3.54540 + 0.862893i) q^{12} +(1.43625 - 1.00567i) q^{13} +(-2.26322 - 4.71092i) q^{14} +(-3.25952 - 2.45329i) q^{15} +(2.94239 - 2.70967i) q^{16} +(2.70456 - 1.26116i) q^{17} +(0.399761 - 0.236988i) q^{18} +(-4.14223 + 1.35717i) q^{19} +(-4.21941 + 1.48209i) q^{20} +(-6.33582 - 2.30605i) q^{21} +(-1.33538 - 1.55469i) q^{22} +(-2.89729 + 0.253480i) q^{23} +(0.271722 - 5.15316i) q^{24} +(4.98822 + 0.343047i) q^{25} +(-1.77344 - 1.73301i) q^{26} +(-1.26143 + 4.70774i) q^{27} +(-5.95517 + 4.37788i) q^{28} +(-0.843569 - 2.31769i) q^{29} +(-2.55685 + 5.17191i) q^{30} +(-3.46816 - 2.00234i) q^{31} +(-4.53569 - 3.38046i) q^{32} +(-2.63391 - 0.230437i) q^{33} +(-2.46032 - 3.42888i) q^{34} +(8.05075 - 1.86354i) q^{35} +(-0.433951 - 0.493589i) q^{36} +(-2.69446 + 2.69446i) q^{37} +(2.96987 + 5.40184i) q^{38} -3.19888 q^{39} +(3.16367 + 5.47642i) q^{40} +(-1.47047 - 8.33946i) q^{41} +(-1.54741 + 9.40885i) q^{42} +(0.813252 - 9.29551i) q^{43} +(-1.81136 + 2.26265i) q^{44} +(0.227467 + 0.698705i) q^{45} +(1.11026 + 3.96035i) q^{46} +(7.48285 + 3.48931i) q^{47} +(-7.23297 + 0.970506i) q^{48} +(5.76555 - 3.32874i) q^{49} +(-0.828226 - 7.02240i) q^{50} +(-5.36173 - 0.945417i) q^{51} +(-1.94459 + 2.91811i) q^{52} +(1.17104 + 13.3850i) q^{53} +(6.87285 + 0.521532i) q^{54} +(2.86030 - 1.52296i) q^{55} +(7.64237 + 7.13120i) q^{56} +(7.61079 + 2.30639i) q^{57} +(-3.00044 + 1.77874i) q^{58} +(8.54159 + 3.10888i) q^{59} +(7.85686 + 2.20047i) q^{60} +(-7.83784 - 6.57673i) q^{61} +(-1.87554 + 5.34390i) q^{62} +(0.696563 + 0.994795i) q^{63} +(-3.51158 + 7.18810i) q^{64} +(3.28685 - 2.13719i) q^{65} +(0.368808 + 3.72090i) q^{66} +(2.66437 + 1.24242i) q^{67} +(-4.12181 + 4.31641i) q^{68} +(4.59526 + 2.65307i) q^{69} +(-4.69616 - 10.7014i) q^{70} +(-1.72712 - 2.05830i) q^{71} +(-0.572465 + 0.732238i) q^{72} +(4.43946 - 6.34020i) q^{73} +(4.44969 + 3.03987i) q^{74} +(-7.09591 - 5.73266i) q^{75} +(6.73054 - 5.54075i) q^{76} +(3.78700 - 3.78700i) q^{77} +(0.836875 + 4.44581i) q^{78} +(1.28046 + 7.26184i) q^{79} +(6.78349 - 5.82960i) q^{80} +(7.56687 - 6.34936i) q^{81} +(-11.2055 + 4.22540i) q^{82} +(1.51489 + 5.65367i) q^{83} +(13.4813 - 0.310899i) q^{84} +(6.14082 - 2.61079i) q^{85} +(-13.1317 + 1.30159i) q^{86} +(-1.16465 + 4.34655i) q^{87} +(3.61852 + 1.92549i) q^{88} +(2.65698 + 0.468497i) q^{89} +(0.911554 - 0.498927i) q^{90} +(4.16504 - 4.96370i) q^{91} +(5.21366 - 2.57914i) q^{92} +(3.08779 + 6.62179i) q^{93} +(2.89183 - 11.3126i) q^{94} +(-9.36102 + 2.71501i) q^{95} +(3.24107 + 9.79852i) q^{96} +(-7.86923 + 3.66948i) q^{97} +(-6.13466 - 7.14214i) q^{98} +(0.364806 + 0.306109i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−0.261615	−	1.38980i	−0.184990	−	0.982740i
$2$	−0.261615	−	1.38980i	−0.184990	−	0.982740i
$3$	−1.49450	−	1.04646i	−0.862850	−	0.604174i	0.0561538	−	0.998422i	$-0.482116\pi$
$3$	−1.49450	−	1.04646i	−0.862850	−	0.604174i	−0.919004	+	0.394248i	$0.871005\pi$
$4$	−1.86311	+	0.727188i	−0.931557	+	0.363594i
$5$	2.23475	+	0.0767528i	0.999411	+	0.0343249i
$5$	2.23475	+	0.0767528i	0.999411	+	0.0343249i
$6$	−1.06339	+	2.35083i	−0.434128	+	0.959724i
$7$	3.56968	−	0.956492i	1.34921	−	0.361520i	0.489368	−	0.872077i	$-0.337228\pi$
$7$	3.56968	−	0.956492i	1.34921	−	0.361520i	0.859844	+	0.510557i	$0.170561\pi$
$8$	1.49807	+	2.39912i	0.529647	+	0.848218i
$9$	0.112392	+	0.308794i	0.0374640	+	0.102931i
$10$	−0.477973	−	3.12595i	−0.151148	−	0.988511i
$11$	1.25503	−	0.724594i	0.378407	−	0.218473i	−0.298718	−	0.954341i	$-0.596559\pi$
$11$	1.25503	−	0.724594i	0.378407	−	0.218473i	0.677125	+	0.735868i	$0.263226\pi$
$12$	3.54540	+	0.862893i	1.02347	+	0.249096i
$13$	1.43625	−	1.00567i	0.398344	−	0.278924i	−0.357191	−	0.934031i	$-0.616266\pi$
$13$	1.43625	−	1.00567i	0.398344	−	0.278924i	0.755536	+	0.655107i	$0.227377\pi$
$14$	−2.26322	−	4.71092i	−0.604871	−	1.25905i
$15$	−3.25952	−	2.45329i	−0.841604	−	0.633436i
$16$	2.94239	−	2.70967i	0.735599	−	0.677418i
$17$	2.70456	−	1.26116i	0.655953	−	0.305876i	−0.0659982	−	0.997820i	$-0.521023\pi$
$17$	2.70456	−	1.26116i	0.655953	−	0.305876i	0.721951	+	0.691944i	$0.243245\pi$
$18$	0.399761	−	0.236988i	0.0942245	−	0.0558587i
$19$	−4.14223	+	1.35717i	−0.950293	+	0.311356i
$19$	−4.14223	+	1.35717i	−0.950293	+	0.311356i
$20$	−4.21941	+	1.48209i	−0.943489	+	0.331404i
$21$	−6.33582	−	2.30605i	−1.38259	−	0.503221i
$22$	−1.33538	−	1.55469i	−0.284704	−	0.331460i
$23$	−2.89729	+	0.253480i	−0.604127	+	0.0528542i	−0.385116	−	0.922868i	$-0.625839\pi$
$23$	−2.89729	+	0.253480i	−0.604127	+	0.0528542i	−0.219011	+	0.975722i	$0.570283\pi$
$24$	0.271722	−	5.15316i	0.0554650	−	1.05188i
$25$	4.98822	+	0.343047i	0.997644	+	0.0686093i
$26$	−1.77344	−	1.73301i	−0.347799	−	0.339871i
$27$	−1.26143	+	4.70774i	−0.242763	+	0.906005i
$28$	−5.95517	+	4.37788i	−1.12542	+	0.827342i
$29$	−0.843569	−	2.31769i	−0.156647	−	0.430384i	0.836398	−	0.548123i	$-0.184657\pi$
$29$	−0.843569	−	2.31769i	−0.156647	−	0.430384i	−0.993045	+	0.117739i	$0.962435\pi$
$30$	−2.55685	+	5.17191i	−0.466814	+	0.944257i
$31$	−3.46816	−	2.00234i	−0.622899	−	0.359631i	0.155098	−	0.987899i	$-0.450431\pi$
$31$	−3.46816	−	2.00234i	−0.622899	−	0.359631i	−0.777997	+	0.628268i	$0.783764\pi$
$32$	−4.53569	−	3.38046i	−0.801804	−	0.597587i
$33$	−2.63391	−	0.230437i	−0.458505	−	0.0401139i
$34$	−2.46032	−	3.42888i	−0.421941	−	0.588048i
$35$	8.05075	−	1.86354i	1.36083	−	0.314996i
$36$	−0.433951	−	0.493589i	−0.0723251	−	0.0822649i
$37$	−2.69446	+	2.69446i	−0.442967	+	0.442967i	−0.893008	−	0.450041i	$-0.851409\pi$
$37$	−2.69446	+	2.69446i	−0.442967	+	0.442967i	0.450041	+	0.893008i	$0.351409\pi$
$38$	2.96987	+	5.40184i	0.481777	+	0.876294i
$39$	−3.19888			−0.512230
$40$	3.16367	+	5.47642i	0.500220	+	0.865898i
$41$	−1.47047	−	8.33946i	−0.229649	−	1.30240i	−0.853595	−	0.520937i	$-0.825583\pi$
$41$	−1.47047	−	8.33946i	−0.229649	−	1.30240i	0.623946	−	0.781467i	$-0.285529\pi$
$42$	−1.54741	+	9.40885i	−0.238771	+	1.45182i
$43$	0.813252	−	9.29551i	0.124020	−	1.41755i	−0.638019	−	0.770021i	$-0.720246\pi$
$43$	0.813252	−	9.29551i	0.124020	−	1.41755i	0.762039	−	0.647531i	$-0.224199\pi$
$44$	−1.81136	+	2.26265i	−0.273072	+	0.341107i
$45$	0.227467	+	0.698705i	0.0339088	+	0.104157i
$46$	1.11026	+	3.96035i	0.163699	+	0.583922i
$47$	7.48285	+	3.48931i	1.09149	+	0.508968i	0.883151	−	0.469089i	$-0.155418\pi$
$47$	7.48285	+	3.48931i	1.09149	+	0.508968i	0.208335	+	0.978058i	$0.433196\pi$
$48$	−7.23297	+	0.970506i	−1.04399	+	0.140080i
$49$	5.76555	−	3.32874i	0.823650	−	0.475534i
$50$	−0.828226	−	7.02240i	−0.117129	−	0.993117i
$51$	−5.36173	−	0.945417i	−0.750792	−	0.132385i
$52$	−1.94459	+	2.91811i	−0.269666	+	0.404669i
$53$	1.17104	+	13.3850i	0.160854	+	1.83857i	0.464243	+	0.885708i	$0.346326\pi$
$53$	1.17104	+	13.3850i	0.160854	+	1.83857i	−0.303388	+	0.952867i	$0.598118\pi$
$54$	6.87285	+	0.521532i	0.935276	+	0.0709715i
$55$	2.86030	−	1.52296i	0.385683	−	0.205356i
$56$	7.64237	+	7.13120i	1.02125	+	0.952947i
$57$	7.61079	+	2.30639i	1.00807	+	0.305489i
$58$	−3.00044	+	1.77874i	−0.393977	+	0.233560i
$59$	8.54159	+	3.10888i	1.11202	+	0.404742i	0.831734	−	0.555174i	$-0.187348\pi$
$59$	8.54159	+	3.10888i	1.11202	+	0.404742i	0.280286	+	0.959917i	$0.409571\pi$
$60$	7.85686	+	2.20047i	1.01432	+	0.284079i
$61$	−7.83784	−	6.57673i	−1.00353	−	0.842064i	−0.0160624	−	0.999871i	$-0.505113\pi$
$61$	−7.83784	−	6.57673i	−1.00353	−	0.842064i	−0.987470	+	0.157807i	$0.949557\pi$
$62$	−1.87554	+	5.34390i	−0.238194	+	0.678676i
$63$	0.696563	+	0.994795i	0.0877587	+	0.125332i
$64$	−3.51158	+	7.18810i	−0.438947	+	0.898513i
$65$	3.28685	−	2.13719i	0.407684	−	0.265086i
$66$	0.368808	+	3.72090i	0.0453971	+	0.458012i
$67$	2.66437	+	1.24242i	0.325504	+	0.151785i	0.578500	−	0.815682i	$-0.303638\pi$
$67$	2.66437	+	1.24242i	0.325504	+	0.151785i	−0.252996	+	0.967467i	$0.581416\pi$
$68$	−4.12181	+	4.31641i	−0.499843	+	0.523442i
$69$	4.59526	+	2.65307i	0.553204	+	0.319393i
$70$	−4.69616	−	10.7014i	−0.561298	−	1.27907i
$71$	−1.72712	−	2.05830i	−0.204971	−	0.244275i	0.653760	−	0.756702i	$-0.273191\pi$
$71$	−1.72712	−	2.05830i	−0.204971	−	0.244275i	−0.858731	+	0.512427i	$0.828746\pi$
$72$	−0.572465	+	0.732238i	−0.0674656	+	0.0862950i
$73$	4.43946	−	6.34020i	0.519599	−	0.742064i	−0.470505	−	0.882397i	$-0.655928\pi$
$73$	4.43946	−	6.34020i	0.519599	−	0.742064i	0.990104	+	0.140333i	$0.0448173\pi$
$74$	4.44969	+	3.03987i	0.517266	+	0.353377i
$75$	−7.09591	−	5.73266i	−0.819365	−	0.661950i
$76$	6.73054	−	5.54075i	0.772046	−	0.635567i
$77$	3.78700	−	3.78700i	0.431568	−	0.431568i
$78$	0.836875	+	4.44581i	0.0947575	+	0.503389i
$79$	1.28046	+	7.26184i	0.144063	+	0.817021i	0.968115	+	0.250507i	$0.0805973\pi$
$79$	1.28046	+	7.26184i	0.144063	+	0.817021i	−0.824052	+	0.566514i	$0.808292\pi$
$80$	6.78349	−	5.82960i	0.758417	−	0.651769i
$81$	7.56687	−	6.34936i	0.840764	−	0.705484i
$82$	−11.2055	+	4.22540i	−1.23744	+	0.466617i
$83$	1.51489	+	5.65367i	0.166281	+	0.620570i	0.997873	+	0.0651833i	$0.0207632\pi$
$83$	1.51489	+	5.65367i	0.166281	+	0.620570i	−0.831592	+	0.555387i	$0.812570\pi$
$84$	13.4813	−	0.310899i	1.47093	−	0.0339218i
$85$	6.14082	−	2.61079i	0.666066	−	0.283180i
$86$	−13.1317	+	1.30159i	−1.41603	+	0.140354i
$87$	−1.16465	+	4.34655i	−0.124864	+	0.465999i
$88$	3.61852	+	1.92549i	0.385735	+	0.205258i
$89$	2.65698	+	0.468497i	0.281639	+	0.0496606i	0.312683	−	0.949857i	$-0.398772\pi$
$89$	2.65698	+	0.468497i	0.281639	+	0.0496606i	−0.0310442	+	0.999518i	$0.509883\pi$
$90$	0.911554	−	0.498927i	0.0960863	−	0.0525915i
$91$	4.16504	−	4.96370i	0.436614	−	0.520337i
$92$	5.21366	−	2.57914i	0.543561	−	0.268894i
$93$	3.08779	+	6.62179i	0.320189	+	0.686647i
$94$	2.89183	−	11.3126i	0.298270	−	1.16680i
$95$	−9.36102	+	2.71501i	−0.960421	+	0.278554i
$96$	3.24107	+	9.79852i	0.330790	+	1.00006i
$97$	−7.86923	+	3.66948i	−0.798999	+	0.372579i	−0.778844	−	0.627217i	$-0.784194\pi$
$97$	−7.86923	+	3.66948i	−0.798999	+	0.372579i	−0.0201549	+	0.999797i	$0.506416\pi$
$98$	−6.13466	−	7.14214i	−0.619694	−	0.721465i
$99$	0.364806	+	0.306109i	0.0366644	+	0.0307651i
$100$	−9.54308	+	2.98824i	−0.954308	+	0.298824i
$101$	−2.97125	+	16.8508i	−0.295650	+	1.67671i	0.368899	+	0.929470i	$0.379735\pi$
$101$	−2.97125	+	16.8508i	−0.295650	+	1.67671i	−0.664549	+	0.747245i	$0.731376\pi$
$102$	0.0887645	+	7.69909i	0.00878899	+	0.762323i
$103$	−2.12583	−	0.569613i	−0.209464	−	0.0561257i	0.152561	−	0.988294i	$-0.451248\pi$
$103$	−2.12583	−	0.569613i	−0.209464	−	0.0561257i	−0.362025	+	0.932168i	$0.617915\pi$
$104$	4.56434	+	1.93917i	0.447570	+	0.190152i
$105$	−13.9820	−	5.63974i	−1.36450	−	0.550382i
$106$	18.2962	−	5.12924i	1.77709	−	0.498196i
$107$	−6.65817	+	1.78405i	−0.643669	+	0.172471i	−0.565865	−	0.824498i	$-0.691458\pi$
$107$	−6.65817	+	1.78405i	−0.643669	+	0.172471i	−0.0778043	+	0.996969i	$0.524791\pi$
$108$	−1.07321	−	9.68836i	−0.103270	−	0.932263i
$109$	−8.14891	−	9.71150i	−0.780524	−	0.930193i	0.218433	−	0.975852i	$-0.429906\pi$
$109$	−8.14891	−	9.71150i	−0.780524	−	0.930193i	−0.998957	+	0.0456593i	$0.985461\pi$
$110$	−2.86492	−	3.57683i	−0.273159	−	0.341037i
$111$	6.84653	−	1.20723i	0.649844	−	0.114585i
$112$	7.91162	−	12.4870i	0.747578	−	1.17991i
$113$	4.01747	+	4.01747i	0.377932	+	0.377932i	0.870356	−	0.492424i	$-0.163889\pi$
$113$	4.01747	+	4.01747i	0.377932	+	0.377932i	−0.492424	+	0.870356i	$0.663889\pi$
$114$	1.21433	−	11.1809i	0.113733	−	1.04719i
$115$	−6.49417	+	0.344090i	−0.605585	+	0.0320865i
$116$	3.25706	+	3.70468i	0.302411	+	0.343971i
$117$	0.471970	+	0.330477i	0.0436336	+	0.0305526i
$118$	2.08613	−	12.6845i	0.192044	−	1.16770i
$119$	8.44814	−	7.08883i	0.774439	−	0.649832i
$120$	1.00275	−	11.4952i	0.0915381	−	1.04936i
$121$	−4.44993	+	7.70750i	−0.404539	+	0.700682i
$122$	−7.08987	+	12.6136i	−0.641887	+	1.14199i
$123$	−6.52929	+	14.0021i	−0.588727	+	1.26253i
$124$	7.91765	+	1.20859i	0.711026	+	0.108534i
$125$	11.1211	+	1.14948i	0.994701	+	0.102813i
$126$	1.20034	−	1.22834i	0.106935	−	0.109429i
$127$	16.4025	−	11.4851i	1.45548	−	1.01914i	0.464438	−	0.885605i	$-0.346256\pi$
$127$	16.4025	−	11.4851i	1.45548	−	1.01914i	0.991044	−	0.133534i	$-0.0426326\pi$
$128$	10.9087	+	2.99989i	0.964206	+	0.265155i
$129$	−10.9428	+	13.0411i	−0.963459	+	1.14821i
$130$	−3.83017	−	4.00896i	−0.335928	−	0.351609i
$131$	−5.21063	+	14.3161i	−0.455255	+	1.25080i	0.473725	+	0.880673i	$0.342909\pi$
$131$	−5.21063	+	14.3161i	−0.455255	+	1.25080i	−0.928980	+	0.370130i	$0.879313\pi$
$132$	5.07484	−	1.48602i	0.441708	−	0.129341i
$133$	−13.4883	+	8.80667i	−1.16959	+	0.763636i
$134$	1.02968	−	4.02799i	0.0889504	−	0.347965i
$135$	−3.18032	+	10.4238i	−0.273719	+	0.897138i
$136$	7.07730	+	4.59928i	0.606873	+	0.394385i
$137$	19.0460	−	1.66631i	1.62721	−	0.142362i	0.763310	−	0.646032i	$-0.223573\pi$
$137$	19.0460	−	1.66631i	1.62721	−	0.142362i	0.863896	+	0.503670i	$0.168017\pi$
$138$	2.48506	−	7.08060i	0.211543	−	0.602740i
$139$	−2.64152	+	14.9808i	−0.224051	+	1.27066i	0.640440	+	0.768008i	$0.278752\pi$
$139$	−2.64152	+	14.9808i	−0.224051	+	1.27066i	−0.864491	+	0.502649i	$0.832359\pi$
$140$	−13.6443	+	9.32640i	−1.15316	+	0.788225i
$141$	−7.53170	−	13.0453i	−0.634283	−	1.09861i
$142$	−2.40879	+	2.93884i	−0.202141	+	0.246622i
$143$	1.07384	−	2.30285i	0.0897989	−	0.192574i
$144$	1.16743	+	0.604050i	0.0972861	+	0.0503375i
$145$	−1.70728	−	5.24420i	−0.141782	−	0.435507i
$146$	−9.97307	−	4.51128i	−0.825377	−	0.373357i
$147$	−12.1000	−	1.05861i	−0.997992	−	0.0873130i
$148$	3.06071	−	6.97948i	0.251589	−	0.573710i
$149$	−21.0607	+	3.71356i	−1.72536	+	0.304227i	−0.946435	−	0.322895i	$-0.895344\pi$
$149$	−21.0607	+	3.71356i	−1.72536	+	0.304227i	−0.778921	+	0.627122i	$0.784233\pi$
$150$	−6.11088	+	11.3617i	−0.498951	+	0.927677i
$151$			13.1509i			1.07020i	0.844787	+	0.535102i	$0.179727\pi$
$151$			13.1509i			1.07020i	−0.844787	+	0.535102i	$0.820273\pi$
$152$	−9.46137	−	7.90459i	−0.767418	−	0.641147i
$153$	0.693410	+	0.693410i	0.0560589	+	0.0560589i
$154$	−6.25392	−	4.27245i	−0.503956	−	0.344284i
$155$	−7.59678	−	4.74092i	−0.610188	−	0.380800i
$156$	5.95988	−	2.32619i	0.477172	−	0.186244i
$157$	1.13449	−	12.9673i	0.0905422	−	1.03490i	−0.805992	−	0.591927i	$-0.798367\pi$
$157$	1.13449	−	12.9673i	0.0905422	−	1.03490i	0.896534	−	0.442975i	$-0.146077\pi$
$158$	9.75756	−	3.67940i	0.776269	−	0.292717i
$159$	12.2568	−	21.2294i	0.972026	−	1.68360i
$160$	−9.87667	−	7.90262i	−0.780820	−	0.624757i
$161$	−10.0999	+	3.67608i	−0.795987	+	0.289716i
$162$	−10.8040	−	8.85539i	−0.848841	−	0.695745i
$163$	2.20191	+	0.590000i	0.172467	+	0.0462124i	0.344019	−	0.938963i	$-0.388212\pi$
$163$	2.20191	+	0.590000i	0.172467	+	0.0462124i	−0.171552	+	0.985175i	$0.554878\pi$
$164$	8.80401	+	14.4681i	0.687478	+	1.12977i
$165$	−5.86844	−	0.717129i	−0.456857	−	0.0558284i
$166$	7.46117	−	3.58449i	0.579099	−	0.278211i
$167$	0.432407	+	4.94244i	0.0334607	+	0.382457i	0.994399	+	0.105694i	$0.0337063\pi$
$167$	0.432407	+	4.94244i	0.0334607	+	0.382457i	−0.960938	+	0.276764i	$0.910738\pi$
$168$	−3.95900	−	18.6550i	−0.305444	−	1.43927i
$169$	−3.39482	+	9.32720i	−0.261140	+	0.717477i
$170$	−5.23503	−	7.85152i	−0.401508	−	0.602184i
$171$	−0.884640	−	1.12656i	−0.0676501	−	0.0861504i
$172$	5.24441	+	17.9100i	0.399882	+	1.36562i
$173$	9.04772	+	19.4029i	0.687886	+	1.47518i	0.870591	+	0.492008i	$0.163737\pi$
$173$	9.04772	+	19.4029i	0.687886	+	1.47518i	−0.182705	+	0.983168i	$0.558485\pi$
$174$	6.34554	+	0.481518i	0.481054	+	0.0365038i
$175$	18.1345	−	3.54663i	1.37084	−	0.268100i
$176$	1.72939	−	5.53277i	0.130358	−	0.417048i
$177$	−9.51209	−	13.5847i	−0.714972	−	1.02109i
$178$	−0.0439868	−	3.81525i	−0.00329695	−	0.285965i
$179$	−2.33527	−	4.04480i	−0.174546	−	0.302322i	0.765458	−	0.643486i	$-0.222512\pi$
$179$	−2.33527	−	4.04480i	−0.174546	−	0.302322i	−0.940004	+	0.341163i	$0.889179\pi$
$180$	−0.931888	−	1.13636i	−0.0694588	−	0.0846990i
$181$	−3.10753	+	1.13105i	−0.230981	+	0.0840702i	−0.454918	−	0.890533i	$-0.650331\pi$
$181$	−3.10753	+	1.13105i	−0.230981	+	0.0840702i	0.223937	+	0.974604i	$0.428109\pi$
$182$	−7.98821	−	4.49001i	−0.592125	−	0.332822i
$183$	4.83137	+	18.0309i	0.357145	+	1.33288i
$184$	−4.94847	−	6.57122i	−0.364806	−	0.484437i
$185$	−6.22826	+	5.81465i	−0.457911	+	0.427501i
$186$	8.39518	−	6.02379i	0.615564	−	0.441685i
$187$	2.48049	−	3.54251i	0.181391	−	0.259054i
$188$	−16.4788	−	1.05954i	−1.20184	−	0.0772752i
$189$			18.0117i			1.31016i
$190$	6.22232	+	12.2997i	0.451414	+	0.892314i
$191$		−	9.23832i		−	0.668461i	−0.942491	−	0.334231i	$-0.891524\pi$
$191$		−	9.23832i		−	0.668461i	0.942491	−	0.334231i	$-0.108476\pi$
$192$	12.7701	−	7.06790i	0.921604	−	0.510082i
$193$	−0.281879	+	0.402565i	−0.0202901	+	0.0289773i	−0.829169	−	0.558998i	$-0.811186\pi$
$193$	−0.281879	+	0.402565i	−0.0202901	+	0.0289773i	0.808879	+	0.587975i	$0.200075\pi$
$194$	7.15857	+	9.97670i	0.513956	+	0.716285i
$195$	−7.14869	−	0.245523i	−0.511928	−	0.0175822i
$196$	−8.32126	+	10.3945i	−0.594376	+	0.742462i
$197$	4.93990	+	18.4360i	0.351953	+	1.31351i	0.884275	+	0.466966i	$0.154653\pi$
$197$	4.93990	+	18.4360i	0.351953	+	1.31351i	−0.532322	+	0.846542i	$0.678681\pi$
$198$	0.329993	−	0.587092i	0.0234516	−	0.0417228i
$199$	11.2947	−	4.11094i	0.800660	−	0.291417i	0.0909003	−	0.995860i	$-0.471026\pi$
$199$	11.2947	−	4.11094i	0.800660	−	0.291417i	0.709760	+	0.704443i	$0.248803\pi$
$200$	6.64969	+	12.4813i	0.470204	+	0.882558i
$201$	−2.68176	−	4.64495i	−0.189157	−	0.327629i
$202$	24.1966	−	0.278968i	1.70247	−	0.0196281i
$203$	−5.22812	−	7.46653i	−0.366942	−	0.524048i
$204$	10.6770	−	2.13756i	0.747540	−	0.149659i
$205$	−2.64606	−	18.7495i	−0.184809	−	1.30952i
$206$	−0.235503	+	3.10350i	−0.0164083	+	0.216231i
$207$	−0.403905	−	0.866178i	−0.0280734	−	0.0602035i
$208$	1.50097	−	6.85086i	0.104074	−	0.475022i
$209$	−4.21524	+	4.70473i	−0.291575	+	0.325433i
$210$	−4.18023	+	20.9077i	−0.288464	+	1.44277i
$211$	7.65682	−	21.0370i	0.527118	−	1.44824i	−0.335332	−	0.942100i	$-0.608848\pi$
$211$	7.65682	−	21.0370i	0.527118	−	1.44824i	0.862449	−	0.506143i	$-0.168929\pi$
$212$	−11.9152	−	24.0863i	−0.818340	−	1.65425i
$213$	0.427250	+	4.88349i	0.0292747	+	0.334611i
$214$	4.22136	+	8.78682i	0.288566	+	0.600654i
$215$	2.53087	−	20.7107i	0.172604	−	1.41246i
$216$	−13.1842	+	4.02618i	−0.897068	+	0.273947i
$217$	−14.2954	−	3.83045i	−0.970437	−	0.260028i
$218$	−11.3652	+	13.8661i	−0.769749	+	0.939129i
$219$	−13.2695	+	4.82972i	−0.896672	+	0.326362i
$220$	−4.22159	+	4.91743i	−0.284620	+	0.331533i
$221$	2.61612	−	4.53125i	0.175979	−	0.304805i
$222$	−3.46897	−	9.19951i	−0.232822	−	0.617431i
$223$	1.09821	−	12.5526i	0.0735418	−	0.840587i	−0.866422	−	0.499313i	$-0.833586\pi$
$223$	1.09821	−	12.5526i	0.0735418	−	0.840587i	0.939964	−	0.341274i	$-0.110859\pi$
$224$	−19.4243	−	7.72881i	−1.29784	−	0.516403i
$225$	0.454705	+	1.57889i	0.0303137	+	0.105259i
$226$	4.53247	−	6.63453i	0.301495	−	0.441322i
$227$	−15.6148	−	15.6148i	−1.03639	−	1.03639i	−0.999312	−	0.0370778i	$-0.988195\pi$
$227$	−15.6148	−	15.6148i	−1.03639	−	1.03639i	−0.0370778	−	0.999312i	$-0.511805\pi$
$228$	−15.8570	+	1.23741i	−1.05015	+	0.0819494i
$229$		−	5.68132i		−	0.375432i	−0.982223	−	0.187716i	$-0.939891\pi$
$229$		−	5.68132i		−	0.375432i	0.982223	−	0.187716i	$-0.0601085\pi$
$230$	2.17719	+	8.93562i	0.143560	+	0.589197i
$231$	−9.62262	+	1.69673i	−0.633122	+	0.111636i
$232$	4.29669	−	5.49588i	0.282092	−	0.360822i
$233$	−16.7861	−	1.46860i	−1.09970	−	0.0962109i	−0.477171	−	0.878811i	$-0.658338\pi$
$233$	−16.7861	−	1.46860i	−1.09970	−	0.0962109i	−0.622525	+	0.782600i	$0.713893\pi$
$234$	0.335824	−	0.742404i	0.0219535	−	0.0485324i
$235$	16.4545	+	8.37207i	1.07337	+	0.546133i
$236$	−18.1747	+	0.419136i	−1.18307	+	0.0272834i
$237$	5.68559	−	12.1928i	0.369318	−	0.792006i
$238$	−12.0622	−	9.88671i	−0.781879	−	0.640860i
$239$	5.47203	+	9.47783i	0.353956	+	0.613070i	0.986939	−	0.161096i	$-0.0515029\pi$
$239$	5.47203	+	9.47783i	0.353956	+	0.613070i	−0.632983	+	0.774166i	$0.718170\pi$
$240$	−16.2384	+	1.61369i	−1.04818	+	0.104163i
$241$	2.43737	−	13.8230i	0.157005	−	0.890419i	−0.799925	−	0.600100i	$-0.795128\pi$
$241$	2.43737	−	13.8230i	0.157005	−	0.890419i	0.956930	−	0.290319i	$-0.0937613\pi$
$242$	11.8761	+	4.16813i	0.763424	+	0.267938i
$243$	−3.38726	+	0.296347i	−0.217293	+	0.0190107i
$244$	19.3853	+	6.55361i	1.24102	+	0.419552i
$245$	13.1401	−	6.99638i	0.839487	−	0.446983i
$246$	21.1684	+	5.41128i	1.34965	+	0.345010i
$247$	−4.58442	+	6.11497i	−0.291699	+	0.389086i
$248$	−0.391677	−	11.3202i	−0.0248715	−	0.718832i
$249$	3.65233	−	10.0347i	0.231457	−	0.635922i
$250$	−1.31189	−	15.7569i	−0.0829712	−	0.996552i
$251$	−0.850481	+	1.01356i	−0.0536819	+	0.0639756i	−0.792217	−	0.610239i	$-0.791073\pi$
$251$	−0.850481	+	1.01356i	−0.0536819	+	0.0639756i	0.738535	+	0.674215i	$0.235518\pi$
$252$	−2.02118	−	1.34688i	−0.127322	−	0.0848457i
$253$	−3.45253	+	2.41749i	−0.217058	+	0.151986i
$254$	−20.2532	−	19.7915i	−1.27080	−	1.24183i
$255$	−11.9096	−	2.52430i	−0.745805	−	0.158078i
$256$	1.31537	−	15.9458i	0.0822104	−	0.996615i
$257$	0.740058	−	1.58706i	0.0461635	−	0.0989980i	−0.881873	−	0.471486i	$-0.843718\pi$
$257$	0.740058	−	1.58706i	0.0461635	−	0.0989980i	0.928037	+	0.372488i	$0.121495\pi$
$258$	20.9874	+	11.7966i	1.30662	+	0.734424i
$259$	−7.04114	+	12.1956i	−0.437515	+	0.757798i
$260$	−4.56964	+	6.37200i	−0.283397	+	0.395175i
$261$	0.620878	−	0.520979i	0.0384314	−	0.0322478i
$262$	21.2598	+	3.49645i	1.31343	+	0.216012i
$263$	4.64747	+	3.25419i	0.286575	+	0.200662i	0.708021	−	0.706191i	$-0.249588\pi$
$263$	4.64747	+	3.25419i	0.286575	+	0.200662i	−0.421446	+	0.906854i	$0.638477\pi$
$264$	−3.39293	−	6.66428i	−0.208820	−	0.410158i
$265$	1.58964	+	30.0021i	0.0976508	+	1.84301i
$266$	15.7683	+	16.4422i	0.966817	+	1.00813i
$267$	−3.48059	−	3.48059i	−0.213009	−	0.213009i
$268$	−5.86749	−	0.377265i	−0.358414	−	0.0230451i
$269$	0.699204	−	0.123288i	0.0426312	−	0.00751703i	−0.152292	−	0.988336i	$-0.548665\pi$
$269$	0.699204	−	0.123288i	0.0426312	−	0.00751703i	0.194923	+	0.980819i	$0.437554\pi$
$270$	15.3191	+	1.69300i	0.932289	+	0.103033i
$271$	0.239492	+	0.285416i	0.0145481	+	0.0173378i	0.773269	−	0.634078i	$-0.218620\pi$
$271$	0.239492	+	0.285416i	0.0145481	+	0.0173378i	−0.758721	+	0.651415i	$0.774176\pi$
$272$	4.54057	−	11.0393i	0.275312	−	0.669356i
$273$	−11.4190	+	3.05970i	−0.691107	+	0.185182i
$274$	−7.29855	−	26.0342i	−0.440922	−	1.57279i
$275$	6.50895	−	3.18390i	0.392505	−	0.191996i
$276$	−10.4908	−	1.60136i	−0.631471	−	0.0963907i
$277$	20.4764	+	5.48663i	1.23031	+	0.329660i	0.814699	−	0.579884i	$-0.196902\pi$
$277$	20.4764	+	5.48663i	1.23031	+	0.329660i	0.415608	+	0.909544i	$0.363569\pi$
$278$	21.5115	−	0.248011i	1.29017	−	0.0148747i
$279$	0.228519	−	1.29599i	0.0136811	−	0.0775891i
$280$	16.5314	+	16.5230i	0.987943	+	0.987440i
$281$	14.3109	+	12.0083i	0.853720	+	0.716356i	0.960606	−	0.277916i	$-0.0896435\pi$
$281$	14.3109	+	12.0083i	0.853720	+	0.716356i	−0.106886	+	0.994271i	$0.534088\pi$
$282$	−16.1600	+	13.8804i	−0.962313	+	0.826568i
$283$	−2.37506	+	1.10751i	−0.141182	+	0.0658345i	−0.491926	−	0.870637i	$-0.663707\pi$
$283$	−2.37506	+	1.10751i	−0.141182	+	0.0658345i	0.350743	+	0.936472i	$0.385929\pi$
$284$	4.71459	+	2.57890i	0.279759	+	0.153030i
$285$	16.8312	+	5.73836i	0.996994	+	0.339911i
$286$	−3.48145	−	0.889964i	−0.205862	−	0.0526247i
$287$	−13.2257	−	28.3627i	−0.780691	−	1.67420i
$288$	0.534093	−	1.78053i	0.0314717	−	0.104919i
$289$	−5.20324	+	6.20098i	−0.306073	+	0.364764i
$290$	−6.84176	+	3.74475i	−0.401762	+	0.219899i
$291$	15.6005	+	2.75080i	0.914520	+	0.161254i
$292$	−3.66070	+	15.0408i	−0.214226	+	0.880199i
$293$	7.04774	−	26.3025i	0.411733	−	1.53661i	−0.379557	−	0.925168i	$-0.623924\pi$
$293$	7.04774	−	26.3025i	0.411733	−	1.53661i	0.791290	−	0.611441i	$-0.209410\pi$
$294$	1.69428	+	17.0936i	0.0988125	+	0.996919i
$295$	18.8497	+	7.60317i	1.09747	+	0.442674i
$296$	−10.5008	−	2.42786i	−0.610349	−	0.141116i
$297$	1.82806	+	6.82240i	0.106075	+	0.395876i
$298$	10.6709	+	28.2987i	0.618150	+	1.63930i
$299$	−3.90632	+	3.27779i	−0.225908	+	0.189560i
$300$	17.3892	+	5.52054i	1.00397	+	0.318728i
$301$	−5.98804	−	33.9598i	−0.345145	−	1.95741i
$302$	18.2772	−	3.44047i	1.05173	−	0.197977i
$303$	22.0742	−	22.0742i	1.26813	−	1.26813i
$304$	−8.51060	+	15.2174i	−0.488116	+	0.872779i
$305$	−17.0108	−	15.2989i	−0.974037	−	0.876014i
$306$	0.782298	−	1.14511i	0.0447210	−	0.0654617i
$307$	−11.6735	+	16.6715i	−0.666241	+	0.951491i	0.333720	+	0.942672i	$0.391696\pi$
$307$	−11.6735	+	16.6715i	−0.666241	+	0.951491i	−0.999961	+	0.00881875i	$0.997193\pi$
$308$	−4.30175	+	9.80947i	−0.245115	+	0.558947i
$309$	2.58097	+	3.07588i	0.146826	+	0.174981i
$310$	−4.60152	+	11.7983i	−0.261349	+	0.670100i
$311$	14.6115	+	8.43597i	0.828543	+	0.478360i	0.853354	−	0.521332i	$-0.174565\pi$
$311$	14.6115	+	8.43597i	0.828543	+	0.478360i	−0.0248102	+	0.999692i	$0.507898\pi$
$312$	−4.79214	−	7.67450i	−0.271301	−	0.434483i
$313$	−11.6912	−	5.45170i	−0.660826	−	0.308148i	0.0631191	−	0.998006i	$-0.479895\pi$
$313$	−11.6912	−	5.45170i	−0.660826	−	0.308148i	−0.723945	+	0.689858i	$0.757673\pi$
$314$	−18.3188	+	1.81572i	−1.03379	+	0.102467i
$315$	1.48029	+	2.27658i	0.0834049	+	0.128271i
$316$	−7.66637	−	12.5985i	−0.431267	−	0.708722i
$317$	19.8855	+	28.3995i	1.11688	+	1.59507i	0.745377	+	0.666643i	$0.232270\pi$
$317$	19.8855	+	28.3995i	1.11688	+	1.59507i	0.371506	+	0.928431i	$0.378842\pi$
$318$	−32.7113	−	11.4806i	−1.83436	−	0.643801i
$319$	−2.73809	−	2.29753i	−0.153304	−	0.128637i
$320$	−8.39920	+	15.7941i	−0.469530	+	0.882917i
$321$	11.8176	+	4.30124i	0.659593	+	0.240072i
$322$	7.75133	+	13.0752i	0.431965	+	0.728654i
$323$	−9.49133	+	8.89457i	−0.528112	+	0.494907i
$324$	−9.48077	+	17.3321i	−0.526710	+	0.962896i
$325$	7.50933	−	4.52382i	0.416543	−	0.250936i
$326$	0.243932	−	3.21458i	0.0135101	−	0.178039i
$327$	2.01586	+	23.0414i	0.111477	+	1.27419i
$328$	17.8045	−	16.0209i	0.983090	−	0.884608i
$329$	30.0489	+	5.29843i	1.65665	+	0.292112i
$330$	0.538604	+	8.34360i	0.0296492	+	0.459300i
$331$	−19.7925	+	11.4272i	−1.08790	+	0.628097i	−0.933016	−	0.359836i	$-0.882833\pi$
$331$	−19.7925	+	11.4272i	−1.08790	+	0.628097i	−0.154881	+	0.987933i	$0.549499\pi$
$332$	−6.93370	−	9.43181i	−0.380536	−	0.517638i
$333$	−1.13487	−	0.529199i	−0.0621906	−	0.0290000i
$334$	6.75590	−	1.89398i	0.369666	−	0.103634i
$335$	5.85884	+	2.98099i	0.320103	+	0.162869i
$336$	−24.8911	+	10.3827i	−1.35792	+	0.566422i
$337$	−0.249363	+	2.85024i	−0.0135837	+	0.155262i	−0.999957	−	0.00925956i	$-0.997053\pi$
$337$	−0.249363	+	2.85024i	−0.0135837	+	0.155262i	0.986373	+	0.164522i	$0.0526081\pi$
$338$	13.8511	+	2.27800i	0.753402	+	0.123907i
$339$	−1.79999	−	10.2082i	−0.0977619	−	0.554435i
$340$	−9.54252	+	9.32974i	−0.517516	+	0.505976i
$341$	−5.80354			−0.314279
$342$	−1.33427	+	1.52420i	−0.0721489	+	0.0824195i
$343$	−0.895062	+	0.895062i	−0.0483288	+	0.0483288i
$344$	23.5194	−	11.9742i	1.26808	−	0.645607i
$345$	10.0656	+	6.28166i	0.541915	+	0.338193i
$346$	24.5992	−	17.6507i	1.32246	−	0.948906i
$347$	−5.82423	−	0.509554i	−0.312661	−	0.0273543i	−0.0702545	−	0.997529i	$-0.522381\pi$
$347$	−5.82423	−	0.509554i	−0.312661	−	0.0273543i	−0.242406	+	0.970175i	$0.577937\pi$
$348$	−0.990875	−	8.94504i	−0.0531165	−	0.479504i
$349$	−5.42727	−	3.13344i	−0.290515	−	0.167729i	0.347659	−	0.937621i	$-0.386977\pi$
$349$	−5.42727	−	3.13344i	−0.290515	−	0.167729i	−0.638174	+	0.769892i	$0.720310\pi$
$350$	−9.67337	−	24.2755i	−0.517063	−	1.29758i
$351$	2.92271	+	8.03009i	0.156003	+	0.428614i
$352$	−8.14191	−	0.956061i	−0.433965	−	0.0509582i
$353$	−2.17797	+	8.12830i	−0.115922	+	0.432626i	−0.999354	−	0.0359327i	$-0.988560\pi$
$353$	−2.17797	+	8.12830i	−0.115922	+	0.432626i	0.883432	+	0.468558i	$0.155226\pi$
$354$	−16.3915	+	16.7739i	−0.871200	+	0.891523i
$355$	−3.70169	−	4.73234i	−0.196465	−	0.251167i
$356$	−5.29094	+	1.05926i	−0.280419	+	0.0561407i
$357$	−20.0439	+	1.75362i	−1.06084	+	0.0928112i
$358$	−5.01054	+	4.30374i	−0.264815	+	0.227460i
$359$	16.7290	+	6.08887i	0.882925	+	0.321358i	0.743390	−	0.668859i	$-0.233217\pi$
$359$	16.7290	+	6.08887i	0.882925	+	0.321358i	0.139535	+	0.990217i	$0.455439\pi$
$360$	−1.33552	+	1.59243i	−0.0703879	+	0.0839284i
$361$	15.3162	−	11.2434i	0.806115	−	0.591759i
$362$	2.38492	+	4.02296i	0.125348	+	0.211442i
$363$	14.7160	−	6.86219i	0.772390	−	0.360172i
$364$	−4.15040	+	12.2767i	−0.217540	+	0.643474i
$365$	10.4077	−	13.8280i	0.544764	−	0.723792i
$366$	23.7955	−	11.4318i	1.24381	−	0.597551i
$367$	5.42878	−	3.80127i	0.283380	−	0.198425i	−0.423241	−	0.906017i	$-0.639108\pi$
$367$	5.42878	−	3.80127i	0.283380	−	0.198425i	0.706621	+	0.707592i	$0.250219\pi$
$368$	−7.83812	+	8.59654i	−0.408590	+	0.448126i
$369$	2.40991	−	1.39136i	0.125455	−	0.0724314i
$370$	9.71064	+	7.13487i	0.504832	+	0.370924i
$371$	16.9829	+	46.6602i	0.881709	+	2.42247i
$372$	−10.5682	−	10.0917i	−0.547935	−	0.523233i
$373$	4.55305	−	1.21999i	0.235748	−	0.0631686i	−0.139011	−	0.990291i	$-0.544392\pi$
$373$	4.55305	−	1.21999i	0.235748	−	0.0631686i	0.374759	+	0.927122i	$0.377726\pi$
$374$	−5.57233	−	2.52062i	−0.288138	−	0.130338i
$375$	−15.4176	−	13.3557i	−0.796161	−	0.689685i
$376$	2.83854	+	23.1795i	0.146387	+	1.19539i
$377$	−3.54242	−	2.48043i	−0.182444	−	0.127748i
$378$	25.0327	−	4.71213i	1.28754	−	0.242366i
$379$	−10.0688			−0.517201			−0.258601	−	0.965984i	$-0.583261\pi$
$379$	−10.0688			−0.517201			−0.258601	+	0.965984i	$0.583261\pi$
$380$	15.4663	−	11.8656i	0.793406	−	0.608692i
$381$	−36.5322			−1.87160
$382$	−12.8395	+	2.41689i	−0.656924	+	0.123659i
$383$	−6.81602	−	4.77263i	−0.348283	−	0.243870i	0.386324	−	0.922363i	$-0.373745\pi$
$383$	−6.81602	−	4.77263i	−0.348283	−	0.243870i	−0.734607	+	0.678493i	$0.762633\pi$
$384$	−13.1639	−	15.8989i	−0.671765	−	0.811338i
$385$	8.75366	−	8.17233i	0.446128	−	0.416501i
$386$	0.633231	+	0.286440i	0.0322306	+	0.0145794i
$387$	2.96180	−	0.793613i	0.150557	−	0.0403416i
$388$	11.9929	−	12.5591i	0.608846	−	0.637591i
$389$	0.855706	+	2.35103i	0.0433860	+	0.119202i	0.959494	−	0.281730i	$-0.0909084\pi$
$389$	0.855706	+	2.35103i	0.0433860	+	0.119202i	−0.916108	+	0.400933i	$0.868686\pi$
$390$	1.52898	+	9.99952i	0.0774228	+	0.506345i
$391$	−7.51623	+	4.33950i	−0.380112	+	0.219458i
$392$	16.6232	+	8.84557i	0.839601	+	0.446769i
$393$	22.7685	−	15.9427i	1.14852	−	0.804202i
$394$	24.3300	−	11.6886i	1.22573	−	0.588864i
$395$	2.30414	+	16.3267i	0.115934	+	0.821485i
$396$	−0.902275	−	0.305033i	−0.0453410	−	0.0153285i
$397$	−33.7554	+	15.7404i	−1.69413	+	0.789987i	−0.696780	+	0.717285i	$0.745385\pi$
$397$	−33.7554	+	15.7404i	−1.69413	+	0.789987i	−0.997354	+	0.0727025i	$0.976838\pi$
$398$	−8.66827	−	14.6220i	−0.434501	−	0.732932i
$399$	29.3741	+	0.953410i	1.47055	+	0.0477302i
$400$	15.6068	−	12.5071i	0.780342	−	0.625353i
$401$	15.3592	+	5.59029i	0.767001	+	0.279166i	0.695742	−	0.718292i	$-0.255076\pi$
$401$	15.3592	+	5.59029i	0.767001	+	0.279166i	0.0712597	+	0.997458i	$0.477298\pi$
$402$	−5.75398	+	4.94231i	−0.286982	+	0.246500i
$403$	−6.99485	+	0.611970i	−0.348438	+	0.0304844i
$404$	−6.71791	−	33.5556i	−0.334229	−	1.66945i
$405$	17.3974	−	13.6085i	0.864484	−	0.676210i
$406$	−9.00926	+	9.21943i	−0.447122	+	0.457552i
$407$	−1.42925	+	5.33404i	−0.0708453	+	0.264398i
$408$	−5.76407	−	14.2797i	−0.285364	−	0.706952i
$409$	−6.19941	−	17.0327i	−0.306541	−	0.842215i	−0.993325	−	0.115353i	$-0.963200\pi$
$409$	−6.19941	−	17.0327i	−0.306541	−	0.842215i	0.686783	−	0.726862i	$-0.259022\pi$
$410$	−25.3659	+	8.58265i	−1.25273	+	0.423867i
$411$	−30.2079	−	17.4406i	−1.49005	−	0.860279i
$412$	4.37487	−	0.484621i	0.215535	−	0.0238756i
$413$	33.4643	+	2.92775i	1.64667	+	0.144065i
$414$	−1.09815	+	0.787955i	−0.0539711	+	0.0387259i
$415$	2.95148	+	12.7508i	0.144882	+	0.625912i
$416$	−9.91403	−	0.293769i	−0.486075	−	0.0144032i
$417$	19.6246	−	19.6246i	0.961021	−	0.961021i
$418$	7.64143	+	4.62754i	0.373755	+	0.226340i
$419$	−26.1306			−1.27656			−0.638281	−	0.769803i	$-0.720354\pi$
$419$	−26.1306			−1.27656			−0.638281	+	0.769803i	$0.720354\pi$
$420$	30.1512	+	0.339945i	1.47123	+	0.0165876i
$421$	0.937711	+	5.31803i	0.0457013	+	0.259185i	0.999095	−	0.0425458i	$-0.0135468\pi$
$421$	0.937711	+	5.31803i	0.0457013	+	0.259185i	−0.953393	+	0.301731i	$0.902436\pi$
$422$	−31.2404	−	5.13790i	−1.52076	−	0.250109i
$423$	−0.236467	+	2.70283i	−0.0114974	+	0.131416i
$424$	−30.3580	+	22.8612i	−1.47432	+	1.11024i
$425$	13.9236	−	5.36314i	0.675393	−	0.260151i
$426$	6.67532	−	1.87139i	0.323420	−	0.0906690i
$427$	−34.2692	−	15.9800i	−1.65840	−	0.773325i
$428$	11.1076	−	8.16563i	0.536905	−	0.394701i
$429$	−4.01470	+	2.31789i	−0.193831	+	0.111909i
$430$	−29.4460	+	1.90083i	−1.42001	+	0.0916660i
$431$	−17.9158	−	3.15904i	−0.862975	−	0.152166i	−0.275394	−	0.961331i	$-0.588808\pi$
$431$	−17.9158	−	3.15904i	−0.862975	−	0.152166i	−0.587581	+	0.809166i	$0.699920\pi$
$432$	9.04478	+	17.2701i	0.435167	+	0.830908i
$433$	0.334373	+	3.82190i	0.0160689	+	0.183669i	0.999987	+	0.00504975i	$0.00160739\pi$
$433$	0.334373	+	3.82190i	0.0160689	+	0.183669i	−0.983918	+	0.178619i	$0.942837\pi$
$434$	−1.58367	+	20.8700i	−0.0760187	+	1.00179i
$435$	−2.93632	+	9.62406i	−0.140786	+	0.461438i
$436$	22.2444	+	12.1678i	1.06532	+	0.582734i
$437$	11.6572	−	4.98209i	0.557641	−	0.238326i
$438$	10.1839	+	17.1785i	0.486605	+	0.820822i
$439$	−30.6188	−	11.1443i	−1.46135	−	0.531890i	−0.515616	−	0.856820i	$-0.672437\pi$
$439$	−30.6188	−	11.1443i	−1.46135	−	0.531890i	−0.945738	+	0.324930i	$0.894659\pi$
$440$	7.93870	+	4.58071i	0.378462	+	0.218377i
$441$	1.67590	+	1.40625i	0.0798047	+	0.0669641i
$442$	−6.98197	−	2.45045i	−0.332099	−	0.116556i
$443$	12.0663	+	17.2324i	0.573285	+	0.818736i	0.996169	−	0.0874479i	$-0.0278711\pi$
$443$	12.0663	+	17.2324i	0.573285	+	0.818736i	−0.422884	+	0.906184i	$0.638982\pi$
$444$	−11.8780	+	7.22792i	−0.563705	+	0.343022i
$445$	5.90172	+	1.25090i	0.279768	+	0.0592985i
$446$	−17.7330	+	1.75766i	−0.839683	+	0.0832276i
$447$	35.3613	+	16.4892i	1.67253	+	0.779914i
$448$	−5.65983	+	29.0180i	−0.267402	+	1.37097i
$449$	−3.23960	−	1.87038i	−0.152886	−	0.0882689i	0.421605	−	0.906779i	$-0.361467\pi$
$449$	−3.23960	−	1.87038i	−0.152886	−	0.0882689i	−0.574491	+	0.818511i	$0.694800\pi$
$450$	2.07539	−	1.04501i	0.0978349	−	0.0492624i
$451$	−7.88821	−	9.40081i	−0.371441	−	0.442667i
$452$	−10.4065	−	4.56355i	−0.489479	−	0.214651i
$453$	13.7619	−	19.6540i	0.646590	−	0.923426i
$454$	−17.6164	+	25.7866i	−0.826781	+	1.21022i
$455$	9.68879	−	10.7729i	0.454218	−	0.505043i
$456$	5.86818	+	21.7144i	0.274803	+	1.01687i
$457$	−19.7227	+	19.7227i	−0.922590	+	0.922590i	−0.997212	−	0.0746215i	$-0.976225\pi$
$457$	−19.7227	+	19.7227i	−0.922590	+	0.922590i	0.0746215	+	0.997212i	$0.476225\pi$
$458$	−7.89593	+	1.48632i	−0.368952	+	0.0694512i
$459$	2.52558	+	14.3233i	0.117884	+	0.668552i
$460$	11.8492	−	5.36357i	0.552471	−	0.250078i
$461$	8.89150	−	7.46086i	0.414119	−	0.347487i	−0.411802	−	0.911273i	$-0.635100\pi$
$461$	8.89150	−	7.46086i	0.414119	−	0.347487i	0.825920	+	0.563787i	$0.190656\pi$
$462$	4.87554	+	12.9297i	0.226831	+	0.601543i
$463$	8.02731	+	29.9583i	0.373061	+	1.39228i	0.856158	+	0.516715i	$0.172845\pi$
$463$	8.02731	+	29.9583i	0.373061	+	1.39228i	−0.483097	+	0.875567i	$0.660488\pi$
$464$	−8.76228	−	4.53375i	−0.406779	−	0.210474i
$465$	6.39220	+	15.0350i	0.296431	+	0.697233i
$466$	2.35045	+	23.7137i	0.108882	+	1.09851i
$467$	7.03778	−	26.2653i	0.325669	−	1.21541i	−0.587968	−	0.808884i	$-0.700072\pi$
$467$	7.03778	−	26.2653i	0.325669	−	1.21541i	0.913637	−	0.406531i	$-0.133262\pi$
$468$	−1.11965	−	0.272505i	−0.0517560	−	0.0125966i
$469$	10.6993	+	1.88657i	0.494048	+	0.0871139i
$470$	7.33079	−	25.0588i	0.338144	−	1.15588i
$471$	−15.2653	+	18.1924i	−0.703386	+	0.838263i
$472$	5.33730	+	25.1496i	0.245669	+	1.15761i
$473$	−5.71481	−	12.2555i	−0.262767	−	0.563506i
$474$	−18.4330	−	4.71204i	−0.846657	−	0.216431i
$475$	−21.1279	+	5.34888i	−0.969416	+	0.245423i
$476$	−10.5849	+	19.3507i	−0.485160	+	0.886937i
$477$	−4.00161	+	1.86598i	−0.183221	+	0.0854373i
$478$	11.7408	−	10.0846i	0.537010	−	0.461259i
$479$	−26.3116	−	22.0781i	−1.20221	−	1.00877i	−0.999564	−	0.0295199i	$-0.990602\pi$
$479$	−26.3116	−	22.0781i	−1.20221	−	1.00877i	−0.202644	−	0.979252i	$-0.564953\pi$
$480$	6.49092	+	22.1460i	0.296269	+	1.01082i
$481$	−1.16018	+	6.57968i	−0.0528995	+	0.300008i
$482$	−19.8489	+	0.228843i	−0.904095	+	0.0104235i
$483$	18.9412	+	5.07529i	0.861856	+	0.230934i
$484$	2.68592	−	17.5959i	0.122087	−	0.799813i
$485$	−17.8674	+	7.59639i	−0.811317	+	0.344934i
$486$	1.29802	+	4.63010i	0.0588796	+	0.210026i
$487$	26.0902	−	6.99084i	1.18226	−	0.316785i	0.386436	−	0.922316i	$-0.373706\pi$
$487$	26.0902	−	6.99084i	1.18226	−	0.316785i	0.795822	+	0.605531i	$0.207039\pi$
$488$	4.03675	−	28.6563i	0.182735	−	1.29721i
$489$	−2.67334	−	3.18597i	−0.120893	−	0.144074i
$490$	−13.1612	−	16.4317i	−0.594564	−	0.742311i
$491$	24.6257	−	4.34217i	1.11134	−	0.195959i	0.412305	−	0.911046i	$-0.364724\pi$
$491$	24.6257	−	4.34217i	1.11134	−	0.195959i	0.699036	+	0.715086i	$0.253613\pi$
$492$	1.98265	−	30.8356i	0.0893847	−	1.39018i
$493$	−5.20446	−	5.20446i	−0.234397	−	0.234397i
$494$	9.69797	+	4.77167i	0.436332	+	0.214688i
$495$	0.791756	+	0.712077i	0.0355868	+	0.0320055i
$496$	−15.6304	+	3.50589i	−0.701824	+	0.157419i
$497$	−8.13400	−	5.69548i	−0.364860	−	0.255477i
$498$	−14.9018	−	2.45079i	−0.667764	−	0.109823i
$499$	−4.27496	+	3.58711i	−0.191373	+	0.160581i	−0.733440	−	0.679754i	$-0.762086\pi$
$499$	−4.27496	+	3.58711i	−0.191373	+	0.160581i	0.542067	+	0.840335i	$0.317642\pi$
$500$	−21.5558	+	5.94551i	−0.964003	+	0.265891i
$501$	4.52583	−	7.83897i	0.202199	−	0.350219i
$502$	1.63116	+	0.916839i	0.0728020	+	0.0409205i
$503$	0.732366	−	1.57056i	0.0326546	−	0.0700280i	−0.889304	−	0.457317i	$-0.848811\pi$
$503$	0.732366	−	1.57056i	0.0326546	−	0.0700280i	0.921958	+	0.387289i	$0.126588\pi$
$504$	−1.34314	+	3.16141i	−0.0598280	+	0.140820i
$505$	−7.93334	+	37.4292i	−0.353029	+	1.66558i
$506$	4.26307	+	4.16589i	0.189516	+	0.185196i
$507$	14.8341	−	10.3870i	0.658806	−	0.461301i
$508$	−22.2078	+	33.3258i	−0.985312	+	1.47859i
$509$	17.0633	−	20.3352i	0.756317	−	0.901343i	−0.241292	−	0.970452i	$-0.577571\pi$
$509$	17.0633	−	20.3352i	0.756317	−	0.901343i	0.997609	+	0.0691092i	$0.0220157\pi$
$510$	−0.392560	+	17.2124i	−0.0173829	+	0.762176i
$511$	9.78308	−	26.8788i	0.432778	−	1.18905i
$512$	−22.5057	+	2.34357i	−0.994622	+	0.103572i
$513$	−1.16405	−	21.2125i	−0.0513939	−	0.936556i
$514$	−2.39931	−	0.613337i	−0.105829	−	0.0270531i
$515$	−4.70697	−	1.43611i	−0.207414	−	0.0632824i
$516$	10.9043	−	32.2546i	0.480036	−	1.41993i
$517$	11.9196	−	1.04283i	0.524222	−	0.0458635i
$518$	18.7916	+	6.59525i	0.825655	+	0.289779i
$519$	6.78255	−	38.4657i	0.297721	−	1.68846i
$520$	10.0513	+	4.68389i	0.440780	+	0.205402i
$521$	17.9741	+	31.1320i	0.787458	+	1.36392i	0.927519	+	0.373775i	$0.121937\pi$
$521$	17.9741	+	31.1320i	0.787458	+	1.36392i	−0.140061	+	0.990143i	$0.544730\pi$
$522$	−0.886490	−	0.726604i	−0.0388006	−	0.0318026i
$523$	14.8332	−	31.8098i	0.648609	−	1.39095i	−0.256825	−	0.966458i	$-0.582676\pi$
$523$	14.8332	−	31.8098i	0.648609	−	1.39095i	0.905434	−	0.424488i	$-0.139546\pi$
$524$	−0.702491	−	30.4616i	−0.0306885	−	1.33072i
$525$	−30.8134	−	13.6766i	−1.34481	−	0.596894i
$526$	3.30685	−	7.31043i	0.144185	−	0.318750i
$527$	−11.9051	−	1.04156i	−0.518595	−	0.0453712i
$528$	−8.37440	+	6.45899i	−0.364449	+	0.281091i
$529$	−14.3205	+	2.52510i	−0.622632	+	0.109787i
$530$	41.2812	−	10.0583i	1.79314	−	0.436904i
$531$			2.98701i			0.129625i
$532$	18.7262	−	26.2164i	0.811882	−	1.13662i
$533$	−10.4987	−	10.4987i	−0.454751	−	0.454751i
$534$	−3.92677	+	5.74792i	−0.169928	+	0.248737i
$535$	−15.0163	+	3.47587i	−0.649210	+	0.150275i
$536$	1.01070	+	8.25337i	0.0436557	+	0.356491i
$537$	−0.742667	+	8.48872i	−0.0320484	+	0.366315i
$538$	−0.354269	−	0.939503i	−0.0152736	−	0.0405048i
$539$	4.82397	−	8.35536i	0.207783	−	0.359891i
$540$	−1.65476	−	21.7334i	−0.0712095	−	0.935258i
$541$	−27.7414	+	10.0970i	−1.19270	+	0.434106i	−0.860669	−	0.509164i	$-0.829955\pi$
$541$	−27.7414	+	10.0970i	−1.19270	+	0.434106i	−0.332026	+	0.943270i	$0.607732\pi$
$542$	0.334017	−	0.407516i	0.0143473	−	0.0175043i
$543$	5.82781	+	1.56156i	0.250095	+	0.0670128i
$544$	−16.5304	−	3.42245i	−0.708733	−	0.146736i
$545$	−17.4654	−	22.3282i	−0.748136	−	0.956436i
$546$	7.23976	+	15.0697i	0.309833	+	0.644922i
$547$	2.51303	+	28.7241i	0.107449	+	1.22815i	0.838144	+	0.545448i	$0.183641\pi$
$547$	2.51303	+	28.7241i	0.107449	+	1.22815i	−0.730695	+	0.682704i	$0.760804\pi$
$548$	−34.2731	+	16.9545i	−1.46407	+	0.724261i
$549$	1.14995	−	3.15945i	0.0490785	−	0.134842i
$550$	−6.12784	−	8.21322i	−0.261292	−	0.350213i
$551$	6.63976	+	8.45553i	0.282863	+	0.360218i
$552$	0.518967	+	14.9991i	0.0220887	+	0.638403i
$553$	11.5167	+	24.6977i	0.489741	+	1.05025i
$554$	2.26841	−	29.8936i	0.0963755	−	1.27006i
$555$	15.3929	−	2.17236i	0.653394	−	0.0922117i
$556$	−5.97242	−	29.8319i	−0.253287	−	1.26515i
$557$	−21.8595	−	31.2186i	−0.926216	−	1.32277i	−0.946407	−	0.322977i	$-0.895316\pi$
$557$	−21.8595	−	31.2186i	−0.926216	−	1.32277i	0.0201906	−	0.999796i	$-0.493573\pi$
$558$	−1.86096	+	0.0214554i	−0.0787808	+	0.000908281i
$559$	−8.18022	−	14.1686i	−0.345986	−	0.599266i
$560$	18.6389	−	27.2982i	0.787638	−	1.15356i
$561$	−7.41419	+	2.69854i	−0.313027	+	0.113933i
$562$	12.9452	−	23.0310i	0.546062	−	0.971503i
$563$	−10.9515	−	40.8715i	−0.461551	−	1.72253i	−0.668080	−	0.744090i	$-0.732884\pi$
$563$	−10.9515	−	40.8715i	−0.461551	−	1.72253i	0.206529	−	0.978440i	$-0.433783\pi$
$564$	23.5188	+	18.8279i	0.990320	+	0.792798i
$565$	8.66969	+	9.28639i	0.364737	+	0.390682i
$566$	2.16057	+	3.01112i	0.0908155	+	0.126567i
$567$	20.9382	−	29.9028i	0.879321	−	1.25580i
$568$	2.35077	−	7.22703i	0.0986360	−	0.303240i
$569$		−	28.7547i		−	1.20546i	−0.797945	−	0.602730i	$-0.794079\pi$
$569$		−	28.7547i		−	1.20546i	0.797945	−	0.602730i	$-0.205921\pi$
$570$	3.57190	−	24.8933i	0.149610	−	1.04267i
$571$		−	43.1979i		−	1.80777i	−0.427770	−	0.903887i	$-0.640701\pi$
$571$		−	43.1979i		−	1.80777i	0.427770	−	0.903887i	$-0.359299\pi$
$572$	−0.326076	+	5.07136i	−0.0136339	+	0.212044i
$573$	−9.66754	+	13.8067i	−0.403867	+	0.576782i
$574$	−35.9585	+	25.8013i	−1.50088	+	1.07693i
$575$	−14.5393	+	0.270508i	−0.606329	+	0.0112810i
$576$	−2.61432	−	0.276470i	−0.108930	−	0.0115196i
$577$	−1.70954	−	6.38007i	−0.0711689	−	0.265606i	0.921168	−	0.389164i	$-0.127236\pi$
$577$	−1.70954	−	6.38007i	−0.0711689	−	0.265606i	−0.992337	+	0.123558i	$0.960569\pi$
$578$	9.97941	+	5.60922i	0.415089	+	0.233313i
$579$	0.842537	−	0.306658i	0.0350146	−	0.0127443i
$580$	6.99437	+	8.52903i	0.290426	+	0.354149i
$581$	10.8154	+	18.7328i	0.448697	+	0.777167i
$582$	−0.258270	−	22.4013i	−0.0107056	−	0.928566i
$583$	11.1684	+	15.9501i	0.462548	+	0.660587i
$584$	21.8615	+	1.15274i	0.904636	+	0.0477007i
$585$	1.02937	+	0.774758i	0.0425592	+	0.0320323i
$586$	−38.3992	−	2.91384i	−1.58625	−	0.120370i
$587$	4.69696	+	10.0727i	0.193864	+	0.415744i	0.979079	−	0.203480i	$-0.0652252\pi$
$587$	4.69696	+	10.0727i	0.193864	+	0.415744i	−0.785215	+	0.619224i	$0.787447\pi$
$588$	23.3135	−	6.82667i	0.961434	−	0.281527i
$589$	17.0834	+	3.58728i	0.703910	+	0.147811i
$590$	5.63555	−	28.1865i	0.232012	−	1.16042i
$591$	11.9098	−	32.7220i	0.489904	−	1.34600i
$592$	−0.627064	+	15.2293i	−0.0257722	+	0.625920i
$593$	−0.706451	−	8.07477i	−0.0290105	−	0.331591i	−0.996806	−	0.0798553i	$-0.974554\pi$
$593$	−0.706451	−	8.07477i	−0.0290105	−	0.331591i	0.967796	−	0.251736i	$-0.0810014\pi$
$594$	9.00355	−	4.32549i	0.369420	−	0.177477i
$595$	19.4236	−	15.1933i	0.796288	−	0.622866i
$596$	36.5380	−	22.2339i	1.49665	−	0.910734i
$597$	−21.1819	−	5.67567i	−0.866917	−	0.232290i
$598$	5.57744	+	4.57150i	0.228079	+	0.186943i
$599$	−1.29816	+	0.472492i	−0.0530414	+	0.0193055i	−0.368405	−	0.929666i	$-0.620096\pi$
$599$	−1.29816	+	0.472492i	−0.0530414	+	0.0193055i	0.315363	+	0.948971i	$0.397874\pi$
$600$	3.12318	−	25.6119i	0.127503	−	1.04560i
$601$	0.00476483	−	0.00825292i	0.000194361	−	0.000336644i	−0.865928	−	0.500168i	$-0.833271\pi$
$601$	0.00476483	−	0.00825292i	0.000194361	−	0.000336644i	0.866123	+	0.499832i	$0.166605\pi$
$602$	−45.6310	+	17.2066i	−1.85978	+	0.701289i
$603$	−0.0841973	+	0.962379i	−0.00342878	+	0.0391911i
$604$	−9.56317	−	24.5016i	−0.389120	−	0.996957i
$605$	−10.5360	+	16.8828i	−0.428351	+	0.686383i
$606$	−36.4538	−	24.9039i	−1.48083	−	1.01165i
$607$	4.47283	+	4.47283i	0.181547	+	0.181547i	0.792030	−	0.610483i	$-0.209025\pi$
$607$	4.47283	+	4.47283i	0.181547	+	0.181547i	−0.610483	+	0.792030i	$0.709025\pi$
$608$	23.3757	+	7.84696i	0.948011	+	0.318236i
$609$			16.6298i			0.673872i
$610$	−16.8122	+	27.6442i	−0.680707	+	1.11928i
$611$	14.2564	−	2.51378i	0.576751	−	0.101697i
$612$	−1.79614	−	0.787663i	−0.0726048	−	0.0318394i
$613$	−5.69989	−	0.498676i	−0.230217	−	0.0201413i	−0.0285363	−	0.999593i	$-0.509085\pi$
$613$	−5.69989	−	0.498676i	−0.230217	−	0.0201413i	−0.201680	+	0.979451i	$0.564640\pi$
$614$	26.2241	+	11.8624i	1.05832	+	0.478726i
$615$	−15.6660	+	30.7901i	−0.631716	+	1.24158i
$616$	14.7587	+	3.41229i	0.594643	+	0.137485i
$617$	−14.6041	+	31.3186i	−0.587940	+	1.26084i	0.357155	+	0.934045i	$0.383747\pi$
$617$	−14.6041	+	31.3186i	−0.587940	+	1.26084i	−0.945095	+	0.326796i	$0.894031\pi$
$618$	3.59965	−	4.39174i	0.144799	−	0.176662i
$619$	−9.48809	−	16.4339i	−0.381358	−	0.660532i	0.609898	−	0.792480i	$-0.291210\pi$
$619$	−9.48809	−	16.4339i	−0.381358	−	0.660532i	−0.991257	+	0.131947i	$0.957877\pi$
$620$	17.6012	+	3.30859i	0.706882	+	0.132876i
$621$	2.46142	−	13.9594i	0.0987736	−	0.560173i
$622$	7.90175	−	22.5141i	0.316831	−	0.902735i
$623$	9.93267	−	0.868996i	0.397944	−	0.0348156i
$624$	−9.41236	+	8.66790i	−0.376796	+	0.346994i
$625$	24.7646	+	3.42238i	0.990586	+	0.136895i
$626$	−4.51820	+	17.6747i	−0.180583	+	0.706424i
$627$	11.2230	−	2.62014i	0.448203	−	0.104638i
$628$	7.31597	+	24.9845i	0.291939	+	0.996992i
$629$	−3.88920	+	10.6855i	−0.155073	+	0.426059i
$630$	2.77674	−	2.65290i	0.110628	−	0.105694i
$631$	−26.6447	+	31.7539i	−1.06071	+	1.26410i	−0.0975310	+	0.995232i	$0.531095\pi$
$631$	−26.6447	+	31.7539i	−1.06071	+	1.26410i	−0.963177	+	0.268870i	$0.913350\pi$
$632$	−15.5038	+	13.9507i	−0.616709	+	0.554930i
$633$	−33.4575	+	23.4272i	−1.32982	+	0.931147i
$634$	34.2674	−	35.0667i	1.36093	−	1.39268i
$635$	37.5369	−	24.4074i	1.48961	−	0.968580i
$636$	−7.39805	+	48.4658i	−0.293352	+	1.92179i
$637$	4.93315	−	10.5792i	0.195458	−	0.419162i
$638$	−2.47679	+	4.40648i	−0.0980572	+	0.174454i
$639$	0.441477	−	0.764660i	0.0174645	−	0.0302495i
$640$	24.1481	+	7.54128i	0.954536	+	0.298095i
$641$	−14.1764	+	11.8954i	−0.559935	+	0.469841i	−0.878289	−	0.478131i	$-0.841314\pi$
$641$	−14.1764	+	11.8954i	−0.559935	+	0.469841i	0.318354	+	0.947972i	$0.396870\pi$
$642$	2.88623	−	17.5494i	0.113911	−	0.692619i
$643$	−31.6019	−	22.1279i	−1.24626	−	0.872640i	−0.250819	−	0.968034i	$-0.580700\pi$
$643$	−31.6019	−	22.1279i	−1.24626	−	0.872640i	−0.995440	+	0.0953942i	$0.969589\pi$
$644$	16.1442	−	14.1935i	0.636169	−	0.559303i
$645$	−25.4553	+	28.3037i	−1.00230	+	1.11446i
$646$	14.8448	+	10.8641i	0.584060	+	0.427444i
$647$	−34.4411	−	34.4411i	−1.35402	−	1.35402i	−0.881110	−	0.472911i	$-0.843203\pi$
$647$	−34.4411	−	34.4411i	−1.35402	−	1.35402i	−0.472911	−	0.881110i	$-0.656797\pi$
$648$	26.5686	+	8.64207i	1.04371	+	0.339493i
$649$	12.9727	−	2.28743i	0.509221	−	0.0897895i
$650$	−8.25178	−	9.25300i	−0.323662	−	0.362933i
$651$	17.3561	+	20.6842i	0.680240	+	0.810678i
$652$	−4.53145	+	0.501966i	−0.177465	+	0.0196585i
$653$	−6.16014	+	1.65061i	−0.241065	+	0.0645932i	−0.377329	−	0.926079i	$-0.623157\pi$
$653$	−6.16014	+	1.65061i	−0.241065	+	0.0645932i	0.136264	+	0.990673i	$0.456491\pi$
$654$	31.4956	−	8.82962i	1.23158	−	0.345265i
$655$	−12.7433	+	31.5930i	−0.497920	+	1.23444i
$656$	−26.9239	−	20.5535i	−1.05120	−	0.802479i
$657$	2.45678	+	0.658292i	0.0958480	+	0.0256824i
$658$	−0.497465	−	43.1482i	−0.0193932	−	1.68209i
$659$	−6.58560	+	37.3488i	−0.256538	+	1.45490i	0.535554	+	0.844501i	$0.320103\pi$
$659$	−6.58560	+	37.3488i	−0.256538	+	1.45490i	−0.792092	+	0.610401i	$0.791008\pi$
$660$	11.4551	−	2.93137i	0.445888	−	0.114103i
$661$	15.6747	+	13.1526i	0.609674	+	0.511577i	0.894539	−	0.446991i	$-0.147504\pi$
$661$	15.6747	+	13.1526i	0.609674	+	0.511577i	−0.284865	+	0.958568i	$0.591949\pi$
$662$	21.0596	+	24.5182i	0.818506	+	0.952928i
$663$	−8.65157	+	4.03429i	−0.335999	+	0.156679i
$664$	−11.2944	+	12.1040i	−0.438308	+	0.469726i
$665$	−30.8190	+	18.6455i	−1.19511	+	0.723040i
$666$	−0.438584	+	1.71570i	−0.0169948	+	0.0664819i
$667$	3.03155	+	6.50118i	0.117382	+	0.251727i
$668$	−4.39971	−	8.89389i	−0.170230	−	0.344115i
$669$	−14.7771	+	17.6107i	−0.571317	+	0.680869i
$670$	2.61023	−	8.92251i	0.100842	−	0.344707i
$671$	−14.6022	−	2.57476i	−0.563712	−	0.0993976i
$672$	20.9418	+	31.8775i	0.807847	+	1.22970i
$673$	7.37274	−	27.5155i	0.284198	−	1.06064i	−0.665225	−	0.746643i	$-0.731664\pi$
$673$	7.37274	−	27.5155i	0.284198	−	1.06064i	0.949423	−	0.314000i	$-0.101669\pi$
$674$	4.02651	−	0.399099i	0.155095	−	0.0153727i
$675$	−7.90728	+	23.0505i	−0.304352	+	0.887214i
$676$	−0.457686	−	19.8463i	−0.0176033	−	0.763320i
$677$	−1.49118	−	5.56517i	−0.0573108	−	0.213887i	0.931332	−	0.364171i	$-0.118648\pi$
$677$	−1.49118	−	5.56517i	−0.0573108	−	0.213887i	−0.988643	+	0.150284i	$0.951981\pi$
$678$	−13.7166	+	5.17226i	−0.526781	+	0.198640i
$679$	−24.5808	+	20.6257i	−0.943324	+	0.791543i
$680$	15.4630	+	10.8214i	0.592979	+	0.414983i
$681$	6.99605	+	39.6766i	0.268089	+	1.52041i
$682$	1.51829	+	8.06578i	0.0581385	+	0.308855i
$683$	3.79394	−	3.79394i	0.145171	−	0.145171i	−0.630786	−	0.775957i	$-0.717267\pi$
$683$	3.79394	−	3.79394i	0.145171	−	0.145171i	0.775957	+	0.630786i	$0.217267\pi$
$684$	2.46741	+	1.45562i	0.0943438	+	0.0556569i
$685$	42.6909	−	2.26195i	1.63113	−	0.0864245i
$686$	1.47812	+	1.00980i	0.0564350	+	0.0385543i
$687$	−5.94528	+	8.49074i	−0.226827	+	0.323942i
$688$	−22.7949	−	29.5547i	−0.869046	−	1.12676i
$689$	15.1429	+	18.0466i	0.576898	+	0.687520i
$690$	6.09696	−	15.6326i	0.232107	−	0.595124i
$691$	0.184618	+	0.106589i	0.00702318	+	0.00405484i	0.503507	−	0.863991i	$-0.332043\pi$
$691$	0.184618	+	0.106589i	0.00702318	+	0.00405484i	−0.496484	+	0.868046i	$0.665376\pi$
$692$	−30.9665	−	29.5704i	−1.17717	−	1.12410i
$693$	1.59503	+	0.743776i	0.0605903	+	0.0282537i
$694$	0.815526	+	8.22784i	0.0309570	+	0.312325i
$695$	−7.05297	+	33.2757i	−0.267534	+	1.26222i
$696$	−12.1726	+	3.71728i	−0.461402	+	0.140903i
$697$	−14.4944	−	20.7001i	−0.549013	−	0.784072i
$698$	−2.93501	+	8.36261i	−0.111092	+	0.316529i
$699$	23.5501	+	19.7608i	0.890745	+	0.747424i
$700$	−31.2075	+	19.7949i	−1.17953	+	0.748178i
$701$	14.6848	+	5.34482i	0.554636	+	0.201871i	0.604105	−	0.796905i	$-0.293531\pi$
$701$	14.6848	+	5.34482i	0.554636	+	0.201871i	−0.0494691	+	0.998776i	$0.515753\pi$
$702$	10.3956	−	6.16279i	0.392358	−	0.232600i
$703$	7.50425	−	14.8179i	0.283028	−	0.558869i
$704$	0.801309	+	11.5658i	0.0302005	+	0.435902i
$705$	−15.8302	−	29.7310i	−0.596200	−	1.11974i
$706$	11.8665	+	0.900468i	0.446603	+	0.0338895i
$707$	5.51125	+	62.9938i	0.207272	+	2.36913i
$708$	27.6007	+	18.3927i	1.03730	+	0.691241i
$709$	17.6590	+	3.11375i	0.663196	+	0.116939i	0.495106	−	0.868832i	$-0.335129\pi$
$709$	17.6590	+	3.11375i	0.663196	+	0.116939i	0.168090	+	0.985772i	$0.446240\pi$
$710$	−5.60861	+	6.38268i	−0.210487	+	0.239538i
$711$	−2.09850	+	1.21157i	−0.0787000	+	0.0454375i
$712$	2.85636	+	7.07625i	0.107046	+	0.265194i
$713$	10.5558	+	4.92225i	0.395318	+	0.184340i
$714$	7.68098	+	27.3984i	0.287453	+	1.02536i
$715$	2.57651	−	5.06388i	0.0963561	−	0.189379i
$716$	7.29220	+	5.83775i	0.272522	+	0.218167i
$717$	1.74023	−	19.8909i	0.0649900	−	0.742839i
$718$	4.08577	−	24.8430i	0.152480	−	0.927134i
$719$	0.476092	+	2.70005i	0.0177552	+	0.100695i	0.992398	−	0.123074i	$-0.0392751\pi$
$719$	0.476092	+	2.70005i	0.0177552	+	0.100695i	−0.974642	+	0.223769i	$0.928164\pi$
$720$	2.56256	+	1.43950i	0.0955009	+	0.0536471i
$721$	−8.13335			−0.302902
$722$	−19.6331	−	18.3450i	−0.730669	−	0.682732i
$723$	−18.1079	+	18.1079i	−0.673440	+	0.673440i
$724$	4.96720	−	4.36704i	0.184605	−	0.162300i
$725$	−3.41283	−	11.8505i	−0.126749	−	0.440117i
$726$	−13.3870	−	18.6571i	−0.496840	−	0.692431i
$727$	24.8385	+	2.17309i	0.921208	+	0.0805953i	0.537884	−	0.843019i	$-0.319224\pi$
$727$	24.8385	+	2.17309i	0.921208	+	0.0805953i	0.383324	+	0.923614i	$0.374779\pi$
$728$	18.1480	+	2.55647i	0.672611	+	0.0947491i
$729$	−20.2910	−	11.7150i	−0.751520	−	0.433890i
$730$	−21.9411	−	10.8471i	−0.812075	−	0.401467i
$731$	−9.52362	−	26.1659i	−0.352244	−	0.967782i
$732$	−22.1133	−	30.0803i	−0.817330	−	1.11180i
$733$	−0.975433	+	3.64037i	−0.0360285	+	0.134460i	−0.981598	−	0.190961i	$-0.938839\pi$
$733$	−0.975433	+	3.64037i	−0.0360285	+	0.134460i	0.945569	+	0.325421i	$0.105506\pi$
$734$	−6.70328	−	6.55047i	−0.247422	−	0.241782i
$735$	−26.9593	−	3.29445i	−0.994407	−	0.121518i
$736$	13.9981	+	8.64447i	0.515976	+	0.318639i
$737$	4.24412	−	0.371312i	0.156334	−	0.0136775i
$738$	−2.56419	−	2.98530i	−0.0943891	−	0.109890i
$739$	10.3871	+	3.78061i	0.382097	+	0.139072i	0.525925	−	0.850531i	$-0.323719\pi$
$739$	10.3871	+	3.78061i	0.382097	+	0.139072i	−0.143828	+	0.989603i	$0.545941\pi$
$740$	7.37563	−	15.3625i	0.271133	−	0.564736i
$741$	13.2505	−	4.34142i	0.486769	−	0.159486i
$742$	60.4055	−	35.8099i	2.21756	−	1.31462i
$743$	−13.5908	+	6.33748i	−0.498597	+	0.232500i	−0.655614	−	0.755096i	$-0.727590\pi$
$743$	−13.5908	+	6.33748i	−0.498597	+	0.232500i	0.157017	+	0.987596i	$0.449812\pi$
$744$	−11.2608	+	17.3279i	−0.412839	+	0.635271i
$745$	−47.3503	+	6.68242i	−1.73478	+	0.244825i
$746$	−2.88669	−	6.00869i	−0.105689	−	0.219994i
$747$	−1.57556	+	1.10322i	−0.0576467	+	0.0403646i
$748$	−2.04537	+	8.40388i	−0.0747861	+	0.307276i
$749$	−22.0611	+	12.7370i	−0.806094	+	0.465399i
$750$	−14.5283	+	24.9215i	−0.530499	+	0.910004i
$751$	8.28994	+	22.7764i	0.302504	+	0.831124i	0.994063	+	0.108804i	$0.0347020\pi$
$751$	8.28994	+	22.7764i	0.302504	+	0.831124i	−0.691559	+	0.722320i	$0.743076\pi$
$752$	31.4724	−	10.0091i	1.14768	−	0.364996i
$753$	2.33170	−	0.624777i	0.0849719	−	0.0227681i
$754$	−2.52056	+	5.57218i	−0.0917933	+	0.202927i
$755$	−1.00937	+	29.3890i	−0.0367346	+	1.06957i
$756$	−13.0979	−	33.5578i	−0.476365	−	1.22049i
$757$	4.47980	+	3.13679i	0.162821	+	0.114009i	0.652147	−	0.758092i	$-0.273868\pi$
$757$	4.47980	+	3.13679i	0.162821	+	0.114009i	−0.489326	+	0.872101i	$0.662757\pi$
$758$	2.63416	+	13.9937i	0.0956770	+	0.508275i
$759$	7.68961			0.279115
$760$	−20.5371	−	18.3910i	−0.744959	−	0.667110i
$761$	−18.2163			−0.660340			−0.330170	−	0.943922i	$-0.607106\pi$
$761$	−18.2163			−0.660340			−0.330170	+	0.943922i	$0.607106\pi$
$762$	9.55738	+	50.7726i	0.346228	+	1.83930i
$763$	−38.3780	−	26.8725i	−1.38938	−	0.972851i
$764$	6.71800	+	17.2121i	0.243049	+	0.622710i
$765$	1.49638	+	1.60282i	0.0541016	+	0.0579501i
$766$	−4.84985	+	10.7215i	−0.175232	+	0.387385i
$767$	15.3944	−	4.12492i	0.555859	−	0.148942i
$768$	−18.6525	+	22.4546i	−0.673064	+	0.810260i
$769$	−16.8252	−	46.2269i	−0.606733	−	1.66699i	−0.737316	−	0.675548i	$-0.763907\pi$
$769$	−16.8252	−	46.2269i	−0.606733	−	1.66699i	0.130583	−	0.991437i	$-0.458315\pi$
$770$	−13.6480	−	10.0279i	−0.491841	−	0.361379i
$771$	−2.76681	+	1.59742i	−0.0996443	+	0.0575297i
$772$	0.232432	−	0.955004i	0.00836543	−	0.0343713i
$773$	−14.0033	+	9.80524i	−0.503665	+	0.352670i	−0.797631	−	0.603146i	$-0.793914\pi$
$773$	−14.0033	+	9.80524i	−0.503665	+	0.352670i	0.293966	+	0.955816i	$0.405025\pi$
$774$	−1.87782	−	3.90871i	−0.0674969	−	0.140496i
$775$	−16.6130	−	11.1778i	−0.596757	−	0.401520i
$776$	−20.5922	−	13.3821i	−0.739216	−	0.480390i
$777$	23.2852	−	10.8581i	0.835352	−	0.389531i
$778$	3.04361	−	1.80433i	0.109119	−	0.0646884i
$779$	17.4091	+	32.5483i	0.623746	+	1.16616i
$780$	13.4974	−	4.74101i	0.483284	−	0.169755i
$781$	−3.65902	−	1.33177i	−0.130930	−	0.0476546i
$782$	7.99741	+	9.31081i	0.285987	+	0.332954i
$783$	11.9752	−	1.04769i	0.427958	−	0.0374415i
$784$	7.94472	−	25.4172i	0.283740	−	0.907757i
$785$	3.53058	−	28.8916i	0.126012	−	1.03118i
$786$	−28.1138	−	27.4730i	−1.00279	−	0.979928i
$787$	−11.5885	+	43.2488i	−0.413084	+	1.54165i	0.375558	+	0.926799i	$0.377451\pi$
$787$	−11.5885	+	43.2488i	−0.413084	+	1.54165i	−0.788642	+	0.614853i	$0.789215\pi$
$788$	−22.6100	−	30.7561i	−0.805448	−	1.09564i
$789$	−3.54026	−	9.72679i	−0.126037	−	0.346283i
$790$	22.0881	−	7.47361i	0.785860	−	0.265899i
$791$	18.1838	+	10.4984i	0.646540	+	0.373280i
$792$	−0.187887	+	1.33379i	−0.00667629	+	0.0473941i
$793$	−17.8712	−	1.56352i	−0.634623	−	0.0555223i
$794$	30.7070	+	42.7955i	1.08975	+	1.51875i
$795$	29.0203	−	46.5016i	1.02924	−	1.64924i
$796$	−18.0539	+	15.8725i	−0.639904	+	0.562587i
$797$	34.7672	−	34.7672i	1.23152	−	1.23152i	0.268137	−	0.963381i	$-0.413592\pi$
$797$	34.7672	−	34.7672i	1.23152	−	1.23152i	0.963381	−	0.268137i	$-0.0864079\pi$
$798$	−6.35967	−	41.0737i	−0.225130	−	1.45399i
$799$	24.6384			0.871645
$800$	−21.4654	−	18.4184i	−0.758915	−	0.651190i
$801$	0.153954	+	0.873115i	0.00543969	+	0.0308500i
$802$	3.75121	−	22.8088i	0.132460	−	0.805406i
$803$	0.977596	−	11.1740i	0.0344986	−	0.394321i
$804$	8.37418	+	6.70392i	0.295335	+	0.236429i
$805$	−22.8530	+	7.43992i	−0.805462	+	0.262223i
$806$	2.68048	+	9.56137i	0.0944158	+	0.336785i
$807$	−1.17398	−	0.547434i	−0.0413259	−	0.0192706i
$808$	−44.8782	+	18.1152i	−1.57881	+	0.637292i
$809$	−21.9850	+	12.6931i	−0.772953	+	0.446265i	−0.833927	−	0.551875i	$-0.813913\pi$
$809$	−21.9850	+	12.6931i	−0.772953	+	0.446265i	0.0609740	+	0.998139i	$0.480579\pi$
$810$	−23.4645	−	20.6188i	−0.824459	−	0.724471i
$811$	39.6787	+	6.99643i	1.39331	+	0.245678i	0.819391	−	0.573235i	$-0.194312\pi$
$811$	39.6787	+	6.99643i	1.39331	+	0.245678i	0.573918	+	0.818913i	$0.305423\pi$
$812$	15.1702	+	10.1092i	0.532368	+	0.354763i
$813$	−0.0592450	−	0.677173i	−0.00207781	−	0.0237495i
$814$	7.78718	+	0.590914i	0.272941	+	0.0207115i
$815$	4.87543	+	1.48751i	0.170779	+	0.0521050i
$816$	−18.3381	+	11.7467i	−0.641961	+	0.411218i
$817$	9.24691	+	39.6079i	0.323508	+	1.38570i
$818$	−22.0503	+	13.0720i	−0.770972	+	0.457052i
$819$	2.00088	+	0.728260i	0.0699164	+	0.0254475i
$820$	18.5643	+	33.0082i	0.648294	+	1.15270i
$821$	22.8216	+	19.1496i	0.796479	+	0.668325i	0.947340	−	0.320230i	$-0.103760\pi$
$821$	22.8216	+	19.1496i	0.796479	+	0.668325i	−0.150861	+	0.988555i	$0.548204\pi$
$822$	−16.3361	+	46.5458i	−0.569787	+	1.62347i
$823$	15.2466	+	21.7744i	0.531463	+	0.759008i	0.991670	−	0.128804i	$-0.0411137\pi$
$823$	15.2466	+	21.7744i	0.531463	+	0.759008i	−0.460207	+	0.887812i	$0.652225\pi$
$824$	−1.81806	−	5.95344i	−0.0633352	−	0.207398i
$825$	−13.0595	−	2.05302i	−0.454672	−	0.0714771i
$826$	−4.68578	−	47.2749i	−0.163039	−	1.64490i
$827$	−6.73479	−	3.14049i	−0.234192	−	0.109205i	0.301980	−	0.953314i	$-0.402352\pi$
$827$	−6.73479	−	3.14049i	−0.234192	−	0.109205i	−0.536172	+	0.844109i	$0.680130\pi$
$828$	1.38240	+	1.32007i	0.0480416	+	0.0458757i
$829$	20.7120	+	11.9581i	0.719358	+	0.415321i	0.814516	−	0.580141i	$-0.197002\pi$
$829$	20.7120	+	11.9581i	0.719358	+	0.415321i	−0.0951585	+	0.995462i	$0.530336\pi$
$830$	16.9490	−	7.43778i	0.588308	−	0.258169i
$831$	−24.8604	−	29.6275i	−0.862398	−	1.02777i
$832$	2.18538	+	13.8554i	0.0757645	+	0.480350i
$833$	11.3952	−	16.2741i	0.394821	−	0.563863i
$834$	−32.4085	−	22.1403i	−1.12221	−	0.766655i
$835$	0.586976	+	11.0783i	0.0203132	+	0.383380i
$836$	4.43226	−	11.8307i	0.153293	−	0.409174i
$837$	13.8013	−	13.8013i	0.477044	−	0.477044i
$838$	6.83616	+	36.3164i	0.236151	+	1.25453i
$839$	1.03851	+	5.88969i	0.0358534	+	0.203335i	0.997473	−	0.0710531i	$-0.0226360\pi$
$839$	1.03851	+	5.88969i	0.0358534	+	0.203335i	−0.961619	+	0.274388i	$0.911525\pi$
$840$	−7.41555	−	41.9932i	−0.255861	−	1.44890i
$841$	17.5552	−	14.7306i	0.605353	−	0.507951i
$842$	7.14570	−	2.69451i	0.246257	−	0.0928590i
$843$	−8.82150	−	32.9223i	−0.303828	−	1.13390i
$844$	1.03228	+	44.7622i	0.0355327	+	1.54078i
$845$	−8.30247	+	20.5834i	−0.285614	+	0.708091i
$846$	3.81827	−	0.378459i	0.131275	−	0.0130117i
$847$	−8.51264	+	31.7696i	−0.292498	+	1.09162i
$848$	39.7147	+	36.2109i	1.36381	+	1.24349i
$849$	4.70849	+	0.830233i	0.161595	+	0.0284935i
$850$	−11.0963	−	17.9480i	−0.380602	−	0.615611i
$851$	7.12365	−	8.48964i	0.244196	−	0.291021i
$852$	−4.34723	−	8.78780i	−0.148934	−	0.301065i
$853$	−14.0027	−	30.0288i	−0.479442	−	1.02817i	−0.986120	−	0.166032i	$-0.946904\pi$
$853$	−14.0027	−	30.0288i	−0.479442	−	1.02817i	0.506678	−	0.862135i	$-0.330873\pi$
$854$	−13.2437	+	51.8080i	−0.453190	+	1.77283i
$855$	−1.89048	−	2.58549i	−0.0646532	−	0.0884218i
$856$	−14.2545	−	13.3011i	−0.487210	−	0.454623i
$857$	−48.6348	+	22.6788i	−1.66133	+	0.774693i	−0.661644	+	0.749818i	$0.730141\pi$
$857$	−48.6348	+	22.6788i	−1.66133	+	0.774693i	−0.999691	+	0.0248748i	$0.992081\pi$
$858$	4.27172	+	4.97325i	0.145834	+	0.169784i
$859$	−11.8249	−	9.92228i	−0.403461	−	0.338544i	0.418369	−	0.908277i	$-0.362602\pi$
$859$	−11.8249	−	9.92228i	−0.403461	−	0.338544i	−0.821829	+	0.569734i	$0.807046\pi$
$860$	10.3453	+	40.4269i	0.352772	+	1.37855i
$861$	−9.91456	+	56.2283i	−0.337887	+	1.91625i
$862$	0.296600	+	25.7260i	0.0101022	+	0.876230i
$863$	−5.78423	−	1.54988i	−0.196898	−	0.0527586i	0.159022	−	0.987275i	$-0.449166\pi$
$863$	−5.78423	−	1.54988i	−0.196898	−	0.0527586i	−0.355920	+	0.934516i	$0.615832\pi$
$864$	21.6358	−	17.0886i	0.736065	−	0.581366i
$865$	18.7302	+	44.0551i	0.636845	+	1.49792i
$866$	5.22422	−	1.46458i	0.177526	−	0.0497685i
$867$	14.2653	−	3.82239i	0.484476	−	0.129815i
$868$	29.4195	−	3.25890i	0.998562	−	0.110614i
$869$	6.86891	+	8.18604i	0.233012	+	0.277693i
$870$	14.1437	+	1.56311i	0.479518	+	0.0529944i
$871$	5.07617	−	0.895065i	0.171999	−	0.0303281i
$872$	11.0914	−	34.0987i	0.375603	−	1.15473i
$873$	−2.01755	−	2.01755i	−0.0682838	−	0.0682838i
$874$	−9.97384	−	14.8979i	−0.337370	−	0.503929i
$875$	40.7982	−	6.53396i	1.37923	−	0.220888i
$876$	21.2106	−	18.6478i	0.716638	−	0.630050i
$877$	21.5291	+	15.0749i	0.726987	+	0.509042i	0.877506	−	0.479565i	$-0.159206\pi$
$877$	21.5291	+	15.0749i	0.726987	+	0.509042i	−0.150519	+	0.988607i	$0.548095\pi$
$878$	−7.47809	+	45.4696i	−0.252373	+	1.53453i
$879$	−38.0574	+	31.9339i	−1.28364	+	1.07711i
$880$	4.28942	−	12.2316i	0.144596	−	0.412328i
$881$	12.2079	−	21.1447i	0.411294	−	0.712382i	−0.583737	−	0.811942i	$-0.698410\pi$
$881$	12.2079	−	21.1447i	0.411294	−	0.712382i	0.995032	+	0.0995603i	$0.0317436\pi$
$882$	1.51597	−	2.69707i	0.0510452	−	0.0908150i
$883$	−4.72937	+	10.1422i	−0.159156	+	0.341311i	−0.969674	−	0.244403i	$-0.921408\pi$
$883$	−4.72937	+	10.1422i	−0.159156	+	0.341311i	0.810518	+	0.585714i	$0.199186\pi$
$884$	−1.57906	+	10.3447i	−0.0531094	+	0.347928i
$885$	−20.2145	−	31.0884i	−0.679502	−	1.04503i
$886$	20.7930	−	21.2780i	0.698553	−	0.714848i
$887$	−0.599872	+	0.420035i	−0.0201417	+	0.0141034i	−0.583604	−	0.812038i	$-0.698358\pi$
$887$	−0.599872	+	0.420035i	−0.0201417	+	0.0141034i	0.563462	+	0.826142i	$0.309469\pi$
$888$	13.1529	+	14.6172i	0.441381	+	0.490520i
$889$	47.5661	−	56.6870i	1.59531	−	1.90122i
$890$	0.194531	−	8.52950i	0.00652070	−	0.285909i
$891$	4.89597	−	13.4516i	0.164021	−	0.450645i
$892$	7.08204	+	24.1856i	0.237124	+	0.809795i
$893$	−35.7313	−	4.29803i	−1.19570	−	0.143828i
$894$	13.6658	−	53.4591i	0.457051	−	1.78794i
$895$	−4.90829	−	9.21835i	−0.164066	−	0.308136i
$896$	41.8101	+	0.274509i	1.39678	+	0.00917069i
$897$	9.26807	−	0.810851i	0.309452	−	0.0270735i
$898$	−1.75194	+	4.99173i	−0.0584630	+	0.166576i
$899$	−1.71517	+	9.72721i	−0.0572041	+	0.324421i
$900$	−1.99532	−	2.61100i	−0.0665106	−	0.0870332i
$901$	20.0478	+	34.7238i	0.667889	+	1.15682i
$902$	−11.0016	+	13.4225i	−0.366313	+	0.446919i
$903$	−26.5885	+	57.0193i	−0.884811	+	1.89748i
$904$	−3.61995	+	15.6569i	−0.120398	+	0.520739i
$905$	−7.03137	+	2.28910i	−0.233731	+	0.0760923i
$906$	−30.9156	−	13.9845i	−1.02710	−	0.464605i
$907$	−35.7252	−	3.12555i	−1.18624	−	0.103782i	−0.523093	−	0.852275i	$-0.675222\pi$
$907$	−35.7252	−	3.12555i	−1.18624	−	0.103782i	−0.663143	+	0.748493i	$0.730778\pi$
$908$	40.4470	+	17.7373i	1.34228	+	0.588632i
$909$	−5.53737	+	0.976388i	−0.183663	+	0.0323847i
$910$	−17.5070	−	10.6472i	−0.580352	−	0.352950i
$911$		−	36.9833i		−	1.22531i	−0.790350	−	0.612656i	$-0.790101\pi$
$911$		−	36.9833i		−	1.22531i	0.790350	−	0.612656i	$-0.209899\pi$
$912$	28.6435	−	13.8364i	0.948482	−	0.458170i
$913$	5.99786	+	5.99786i	0.198500	+	0.198500i
$914$	32.5705	+	22.2510i	1.07734	+	0.735997i
$915$	9.41298	+	40.6654i	0.311183	+	1.34436i
$916$	4.13139	+	10.5850i	0.136505	+	0.349737i
$917$	−4.90705	+	56.0878i	−0.162045	+	1.85218i
$918$	19.2458	−	7.25724i	0.635206	−	0.239525i
$919$	2.68819	−	4.65609i	0.0886753	−	0.153590i	−0.818276	−	0.574825i	$-0.805070\pi$
$919$	2.68819	−	4.65609i	0.0886753	−	0.153590i	0.906951	+	0.421235i	$0.138403\pi$
$920$	−10.5542	−	15.0649i	−0.347963	−	0.496673i
$921$	34.8921	−	12.6997i	1.14973	−	0.418469i
$922$	−12.6953	−	10.4056i	−0.418097	−	0.342690i
$923$	−4.55055	−	1.21932i	−0.149783	−	0.0401343i
$924$	16.6942	−	10.1587i	0.549199	−	0.334195i
$925$	−14.3649	+	12.5163i	−0.472315	+	0.411532i
$926$	39.5362	−	18.9940i	1.29924	−	0.624180i
$927$	−0.0630324	−	0.720463i	−0.00207025	−	0.0236631i
$928$	−4.00869	+	13.3640i	−0.131592	+	0.438694i
$929$	−5.34036	+	14.6725i	−0.175212	+	0.481390i	−0.995949	−	0.0899151i	$-0.971340\pi$
$929$	−5.34036	+	14.6725i	−0.175212	+	0.481390i	0.820738	+	0.571305i	$0.193563\pi$
$930$	19.2235	−	12.8173i	0.630362	−	0.420296i
$931$	−19.3646	+	21.6132i	−0.634648	+	0.708346i
$932$	32.3424	−	9.47052i	1.05941	−	0.310217i
$933$	−13.0090	−	27.8979i	−0.425896	−	0.913338i
$934$	−38.3449	−	2.90972i	−1.25468	−	0.0952090i
$935$	5.81518	−	7.72624i	0.190177	−	0.252675i
$936$	−0.0858109	+	1.62739i	−0.00280482	+	0.0531929i
$937$	−31.7236	−	45.3060i	−1.03636	−	1.48008i	−0.869394	−	0.494119i	$-0.835491\pi$
$937$	−31.7236	−	45.3060i	−1.03636	−	1.48008i	−0.166970	−	0.985962i	$-0.553398\pi$
$938$	−0.177129	−	15.3635i	−0.00578347	−	0.501636i
$939$	11.7675	+	20.3819i	0.384019	+	0.665140i
$940$	−36.7447	−	3.63261i	−1.19848	−	0.118483i
$941$	46.7746	−	17.0246i	1.52481	−	0.554985i	0.562466	−	0.826821i	$-0.309853\pi$
$941$	46.7746	−	17.0246i	1.52481	−	0.554985i	0.962344	+	0.271835i	$0.0876306\pi$
$942$	29.2775	+	16.4563i	0.953914	+	0.536175i
$943$	6.37427	+	23.7891i	0.207575	+	0.774679i
$944$	33.5568	−	13.9973i	1.09218	−	0.455574i
$945$	−1.38245	+	40.2516i	−0.0449710	+	1.30938i
$946$	−15.5376	+	11.1487i	−0.505171	+	0.362475i
$947$	20.6761	−	29.5285i	0.671883	−	0.959548i	−0.328006	−	0.944675i	$-0.606377\pi$
$947$	20.6761	−	29.5285i	0.671883	−	0.959548i	0.999889	−	0.0148728i	$-0.00473434\pi$
$948$	−1.72645	+	26.8510i	−0.0560726	+	0.872081i
$949$		−	13.5708i		−	0.440526i
$950$	12.9613	+	27.9644i	0.420520	+	0.907283i
$951$		−	63.2525i		−	2.05110i
$952$	29.6629	+	9.64856i	0.961379	+	0.312712i
$953$	6.74982	−	9.63975i	0.218648	−	0.312262i	−0.694811	−	0.719192i	$-0.744512\pi$
$953$	6.74982	−	9.63975i	0.218648	−	0.312262i	0.913459	+	0.406930i	$0.133401\pi$
$954$	3.64023	+	5.07328i	0.117857	+	0.164254i
$955$	0.709067	−	20.6453i	0.0229449	−	0.668068i
$956$	−17.0872	−	13.6791i	−0.552639	−	0.442413i
$957$	1.68780	+	6.29896i	0.0545589	+	0.203617i
$958$	−23.8007	+	42.3440i	−0.768965	+	1.36807i
$959$	66.3942	−	24.1655i	2.14398	−	0.780345i
$960$	29.0805	−	14.8148i	0.938570	−	0.478147i
$961$	−7.48127	−	12.9579i	−0.241331	−	0.417998i
$962$	9.44799	−	0.108928i	0.304616	−	0.00351198i
$963$	−1.29923	−	1.85549i	−0.0418671	−	0.0597924i
$964$	5.51083	+	27.5263i	0.177492	+	0.886562i
$965$	−0.660827	+	0.877997i	−0.0212728	+	0.0282637i
$966$	2.09834	−	27.6524i	0.0675131	−	0.889701i
$967$	5.15104	+	11.0464i	0.165646	+	0.355229i	0.971556	−	0.236808i	$-0.0761014\pi$
$967$	5.15104	+	11.0464i	0.165646	+	0.355229i	−0.805910	+	0.592038i	$0.798324\pi$
$968$	−25.1575	+	0.870449i	−0.808594	+	0.0279773i
$969$	23.4926	−	3.36064i	0.754691	−	0.107959i
$970$	15.2319	+	22.8449i	0.489066	+	0.733505i
$971$	2.96300	−	8.14078i	0.0950872	−	0.261250i	−0.883026	−	0.469325i	$-0.844497\pi$
$971$	2.96300	−	8.14078i	0.0950872	−	0.261250i	0.978113	+	0.208075i	$0.0667197\pi$
$972$	6.09536	−	3.01531i	0.195509	−	0.0967160i
$973$	4.89966	+	56.0033i	0.157076	+	1.79538i
$974$	−16.5415	−	34.4313i	−0.530023	−	1.10325i
$975$	−15.9567	−	1.09736i	−0.511023	−	0.0351438i
$976$	−40.8828	+	1.88664i	−1.30863	+	0.0603899i
$977$	−1.33905	−	0.358797i	−0.0428399	−	0.0114789i	0.237335	−	0.971428i	$-0.423726\pi$
$977$	−1.33905	−	0.358797i	−0.0428399	−	0.0114789i	−0.280175	+	0.959949i	$0.590393\pi$
$978$	−3.72849	+	4.54892i	−0.119224	+	0.145459i
$979$	3.67407	−	1.33725i	0.117424	−	0.0427387i
$980$	−19.3937	+	22.5904i	−0.619510	+	0.721623i
$981$	2.08298	−	3.60783i	0.0665045	−	0.115189i
$982$	−12.4772	−	33.0889i	−0.398164	−	1.05591i
$983$	0.667009	−	7.62395i	0.0212743	−	0.243166i	−0.978110	−	0.208087i	$-0.933276\pi$
$983$	0.667009	−	7.62395i	0.0212743	−	0.243166i	0.999385	−	0.0350789i	$-0.0111683\pi$
$984$	−43.3741	+	5.31156i	−1.38272	+	0.169326i
$985$	9.62443	+	41.5789i	0.306660	+	1.32481i
$986$	−5.87162	+	8.59475i	−0.186990	+	0.273713i
$987$	−39.3635	−	39.3635i	−1.25295	−	1.25295i
$988$	4.09456	−	14.7266i	0.130265	−	0.468517i
$989$			27.1379i			0.862936i
$990$	0.782512	−	1.28668i	0.0248699	−	0.0408933i
$991$	−2.84862	+	0.502288i	−0.0904893	+	0.0159557i	−0.218709	−	0.975790i	$-0.570185\pi$
$991$	−2.84862	+	0.502288i	−0.0904893	+	0.0159557i	0.128220	+	0.991746i	$0.459074\pi$
$992$	8.96164	+	20.8060i	0.284532	+	0.660590i
$993$	41.5381	+	3.63411i	1.31817	+	0.115325i
$994$	−5.78763	+	12.7947i	−0.183573	+	0.405823i
$995$	25.5564	−	8.32002i	0.810191	−	0.263762i
$996$	0.492402	+	21.3517i	0.0156024	+	0.676554i
$997$	12.6561	−	27.1411i	0.400823	−	0.859568i	−0.597510	−	0.801861i	$-0.703843\pi$
$997$	12.6561	−	27.1411i	0.400823	−	0.859568i	0.998334	−	0.0577069i	$-0.0183789\pi$
$998$	6.10378	+	5.00291i	0.193212	+	0.158364i
$999$	−9.28594	−	16.0837i	−0.293794	−	0.508867i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bj.a.23.27	✓	672
4.3	odd	2	inner	380.2.bj.a.23.41	yes	672
5.2	odd	4	inner	380.2.bj.a.327.54	yes	672
19.5	even	9	inner	380.2.bj.a.43.13	yes	672
20.7	even	4	inner	380.2.bj.a.327.13	yes	672
76.43	odd	18	inner	380.2.bj.a.43.54	yes	672
95.62	odd	36	inner	380.2.bj.a.347.41	yes	672
380.347	even	36	inner	380.2.bj.a.347.27	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bj.a.23.27	✓	672	1.1	even	1	trivial
380.2.bj.a.23.41	yes	672	4.3	odd	2	inner
380.2.bj.a.43.13	yes	672	19.5	even	9	inner
380.2.bj.a.43.54	yes	672	76.43	odd	18	inner
380.2.bj.a.327.13	yes	672	20.7	even	4	inner
380.2.bj.a.327.54	yes	672	5.2	odd	4	inner
380.2.bj.a.347.27	yes	672	380.347	even	36	inner
380.2.bj.a.347.41	yes	672	95.62	odd	36	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bj (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.261615 - 1.38980i) q^{2} +(-1.49450 - 1.04646i) q^{3} +(-1.86311 + 0.727188i) q^{4} +(2.23475 + 0.0767528i) q^{5} +(-1.06339 + 2.35083i) q^{6} +(3.56968 - 0.956492i) q^{7} +(1.49807 + 2.39912i) q^{8} +(0.112392 + 0.308794i) q^{9} +O(q^{10})\)	\(q+(-0.261615 - 1.38980i) q^{2} +(-1.49450 - 1.04646i) q^{3} +(-1.86311 + 0.727188i) q^{4} +(2.23475 + 0.0767528i) q^{5} +(-1.06339 + 2.35083i) q^{6} +(3.56968 - 0.956492i) q^{7} +(1.49807 + 2.39912i) q^{8} +(0.112392 + 0.308794i) q^{9} +(-0.477973 - 3.12595i) q^{10} +(1.25503 - 0.724594i) q^{11} +(3.54540 + 0.862893i) q^{12} +(1.43625 - 1.00567i) q^{13} +(-2.26322 - 4.71092i) q^{14} +(-3.25952 - 2.45329i) q^{15} +(2.94239 - 2.70967i) q^{16} +(2.70456 - 1.26116i) q^{17} +(0.399761 - 0.236988i) q^{18} +(-4.14223 + 1.35717i) q^{19} +(-4.21941 + 1.48209i) q^{20} +(-6.33582 - 2.30605i) q^{21} +(-1.33538 - 1.55469i) q^{22} +(-2.89729 + 0.253480i) q^{23} +(0.271722 - 5.15316i) q^{24} +(4.98822 + 0.343047i) q^{25} +(-1.77344 - 1.73301i) q^{26} +(-1.26143 + 4.70774i) q^{27} +(-5.95517 + 4.37788i) q^{28} +(-0.843569 - 2.31769i) q^{29} +(-2.55685 + 5.17191i) q^{30} +(-3.46816 - 2.00234i) q^{31} +(-4.53569 - 3.38046i) q^{32} +(-2.63391 - 0.230437i) q^{33} +(-2.46032 - 3.42888i) q^{34} +(8.05075 - 1.86354i) q^{35} +(-0.433951 - 0.493589i) q^{36} +(-2.69446 + 2.69446i) q^{37} +(2.96987 + 5.40184i) q^{38} -3.19888 q^{39} +(3.16367 + 5.47642i) q^{40} +(-1.47047 - 8.33946i) q^{41} +(-1.54741 + 9.40885i) q^{42} +(0.813252 - 9.29551i) q^{43} +(-1.81136 + 2.26265i) q^{44} +(0.227467 + 0.698705i) q^{45} +(1.11026 + 3.96035i) q^{46} +(7.48285 + 3.48931i) q^{47} +(-7.23297 + 0.970506i) q^{48} +(5.76555 - 3.32874i) q^{49} +(-0.828226 - 7.02240i) q^{50} +(-5.36173 - 0.945417i) q^{51} +(-1.94459 + 2.91811i) q^{52} +(1.17104 + 13.3850i) q^{53} +(6.87285 + 0.521532i) q^{54} +(2.86030 - 1.52296i) q^{55} +(7.64237 + 7.13120i) q^{56} +(7.61079 + 2.30639i) q^{57} +(-3.00044 + 1.77874i) q^{58} +(8.54159 + 3.10888i) q^{59} +(7.85686 + 2.20047i) q^{60} +(-7.83784 - 6.57673i) q^{61} +(-1.87554 + 5.34390i) q^{62} +(0.696563 + 0.994795i) q^{63} +(-3.51158 + 7.18810i) q^{64} +(3.28685 - 2.13719i) q^{65} +(0.368808 + 3.72090i) q^{66} +(2.66437 + 1.24242i) q^{67} +(-4.12181 + 4.31641i) q^{68} +(4.59526 + 2.65307i) q^{69} +(-4.69616 - 10.7014i) q^{70} +(-1.72712 - 2.05830i) q^{71} +(-0.572465 + 0.732238i) q^{72} +(4.43946 - 6.34020i) q^{73} +(4.44969 + 3.03987i) q^{74} +(-7.09591 - 5.73266i) q^{75} +(6.73054 - 5.54075i) q^{76} +(3.78700 - 3.78700i) q^{77} +(0.836875 + 4.44581i) q^{78} +(1.28046 + 7.26184i) q^{79} +(6.78349 - 5.82960i) q^{80} +(7.56687 - 6.34936i) q^{81} +(-11.2055 + 4.22540i) q^{82} +(1.51489 + 5.65367i) q^{83} +(13.4813 - 0.310899i) q^{84} +(6.14082 - 2.61079i) q^{85} +(-13.1317 + 1.30159i) q^{86} +(-1.16465 + 4.34655i) q^{87} +(3.61852 + 1.92549i) q^{88} +(2.65698 + 0.468497i) q^{89} +(0.911554 - 0.498927i) q^{90} +(4.16504 - 4.96370i) q^{91} +(5.21366 - 2.57914i) q^{92} +(3.08779 + 6.62179i) q^{93} +(2.89183 - 11.3126i) q^{94} +(-9.36102 + 2.71501i) q^{95} +(3.24107 + 9.79852i) q^{96} +(-7.86923 + 3.66948i) q^{97} +(-6.13466 - 7.14214i) q^{98} +(0.364806 + 0.306109i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more