LMFDB - Embedded newform 756.2.bt.a.103.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(103,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 14, 15]))

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

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

chi := DirichletCharacter("756.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bt (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$840$
Relative dimension:	$140$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			103.12
Character	$\chi$	$=$	756.103
Dual form			756.2.bt.a.367.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35942 - 0.389832i) q^{2} +(1.54409 + 0.784711i) q^{3} +(1.69606 + 1.05989i) q^{4} +(0.874454 + 0.154190i) q^{5} +(-1.79317 - 1.66869i) q^{6} +(2.54554 + 0.721260i) q^{7} +(-1.89249 - 2.10202i) q^{8} +(1.76846 + 2.42334i) q^{9} +O(q^{10})$	\(q+(-1.35942 - 0.389832i) q^{2} +(1.54409 + 0.784711i) q^{3} +(1.69606 + 1.05989i) q^{4} +(0.874454 + 0.154190i) q^{5} +(-1.79317 - 1.66869i) q^{6} +(2.54554 + 0.721260i) q^{7} +(-1.89249 - 2.10202i) q^{8} +(1.76846 + 2.42334i) q^{9} +(-1.12865 - 0.550499i) q^{10} +(6.30310 - 1.11141i) q^{11} +(1.78717 + 2.96749i) q^{12} +(-2.78497 + 3.31899i) q^{13} +(-3.17930 - 1.97283i) q^{14} +(1.22925 + 0.924277i) q^{15} +(1.75325 + 3.59529i) q^{16} -2.39048i q^{17} +(-1.45939 - 3.98374i) q^{18} -4.41417 q^{19} +(1.31970 + 1.18834i) q^{20} +(3.36458 + 3.11121i) q^{21} +(-9.00185 - 0.946279i) q^{22} +(1.20684 - 1.43825i) q^{23} +(-1.27270 - 4.73078i) q^{24} +(-3.95757 - 1.44044i) q^{25} +(5.07980 - 3.42625i) q^{26} +(0.829051 + 5.12959i) q^{27} +(3.55294 + 3.92130i) q^{28} +(4.07311 - 3.41775i) q^{29} +(-1.31075 - 1.73568i) q^{30} +(1.93118 - 0.702892i) q^{31} +(-0.981854 - 5.57099i) q^{32} +(10.6047 + 3.22999i) q^{33} +(-0.931887 + 3.24968i) q^{34} +(2.11475 + 1.02321i) q^{35} +(0.430939 + 5.98450i) q^{36} +(-3.35032 - 5.80293i) q^{37} +(6.00072 + 1.72078i) q^{38} +(-6.90470 + 2.93945i) q^{39} +(-1.33078 - 2.12992i) q^{40} +(-7.00385 + 8.34687i) q^{41} +(-3.36104 - 5.54107i) q^{42} +(-0.549298 + 1.50918i) q^{43} +(11.8684 + 4.79560i) q^{44} +(1.17278 + 2.39177i) q^{45} +(-2.20128 + 1.48473i) q^{46} +(-8.00134 - 2.91225i) q^{47} +(-0.114073 + 6.92726i) q^{48} +(5.95957 + 3.67200i) q^{49} +(4.81848 + 3.50095i) q^{50} +(1.87584 - 3.69114i) q^{51} +(-8.24126 + 2.67745i) q^{52} +(-5.85287 - 10.1375i) q^{53} +(0.872647 - 7.29647i) q^{54} +5.68314 q^{55} +(-3.30130 - 6.71576i) q^{56} +(-6.81589 - 3.46384i) q^{57} +(-6.86943 + 3.05833i) q^{58} +(1.45830 + 1.22366i) q^{59} +(1.10524 + 2.87050i) q^{60} +(-2.45933 + 6.75696i) q^{61} +(-2.89930 + 0.202692i) q^{62} +(2.75383 + 7.44422i) q^{63} +(-0.836997 + 7.95609i) q^{64} +(-2.94708 + 2.47289i) q^{65} +(-13.1572 - 8.52499i) q^{66} +(8.64595 + 1.52451i) q^{67} +(2.53366 - 4.05441i) q^{68} +(2.99208 - 1.27378i) q^{69} +(-2.47596 - 2.21537i) q^{70} +(10.1372 + 5.85274i) q^{71} +(1.74712 - 8.30347i) q^{72} +(9.90275 + 5.71736i) q^{73} +(2.29234 + 9.19470i) q^{74} +(-4.98053 - 5.32972i) q^{75} +(-7.48670 - 4.67855i) q^{76} +(16.8464 + 1.71704i) q^{77} +(10.5323 - 1.30428i) q^{78} +(-4.73969 + 0.835735i) q^{79} +(0.978782 + 3.41425i) q^{80} +(-2.74511 + 8.57114i) q^{81} +(12.7751 - 8.61660i) q^{82} +(-6.45572 + 5.41699i) q^{83} +(2.40899 + 8.84289i) q^{84} +(0.368589 - 2.09037i) q^{85} +(1.33506 - 1.83749i) q^{86} +(8.97121 - 2.08111i) q^{87} +(-14.2647 - 11.1459i) q^{88} -15.0043i q^{89} +(-0.661917 - 3.70862i) q^{90} +(-9.48311 + 6.43995i) q^{91} +(3.57126 - 1.16025i) q^{92} +(3.53349 + 0.430085i) q^{93} +(9.74191 + 7.07815i) q^{94} +(-3.85999 - 0.680620i) q^{95} +(2.85554 - 9.37261i) q^{96} +(4.06141 - 11.1586i) q^{97} +(-6.67011 - 7.31503i) q^{98} +(13.8401 + 13.3091i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9}+O(q^{10}) $ 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9	$ 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9} - 9 q^{12} - 21 q^{14} - 3 q^{16} - 3 q^{18} - 12 q^{21} - 12 q^{22} - 9 q^{24} - 6 q^{25} - 18 q^{26} - 12 q^{28} - 36 q^{29} - 39 q^{30} + 27 q^{32} - 18 q^{33} + 18 q^{34} + 18 q^{36} + 6 q^{37} - 99 q^{38} + 36 q^{40} + 9 q^{42} + 3 q^{44} - 18 q^{45} + 3 q^{46} - 12 q^{49} + 3 q^{50} - 9 q^{52} - 12 q^{53} - 135 q^{54} + 15 q^{56} - 42 q^{57} - 3 q^{58} - 33 q^{60} - 18 q^{61} - 99 q^{62} - 6 q^{64} + 18 q^{65} - 9 q^{66} - 54 q^{68} + 72 q^{69} - 36 q^{70} - 111 q^{72} - 18 q^{73} + 93 q^{74} - 36 q^{76} - 36 q^{77} + 6 q^{78} - 18 q^{80} - 30 q^{81} - 18 q^{82} + 84 q^{84} + 6 q^{85} + 135 q^{86} - 51 q^{88} + 81 q^{90} + 48 q^{92} - 6 q^{93} - 9 q^{94} - 9 q^{96} - 117 q^{98}+O(q^{100}) $ 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9 - 9 * q^12 - 21 * q^14 - 3 * q^16 - 3 * q^18 - 12 * q^21 - 12 * q^22 - 9 * q^24 - 6 * q^25 - 18 * q^26 - 12 * q^28 - 36 * q^29 - 39 * q^30 + 27 * q^32 - 18 * q^33 + 18 * q^34 + 18 * q^36 + 6 * q^37 - 99 * q^38 + 36 * q^40 + 9 * q^42 + 3 * q^44 - 18 * q^45 + 3 * q^46 - 12 * q^49 + 3 * q^50 - 9 * q^52 - 12 * q^53 - 135 * q^54 + 15 * q^56 - 42 * q^57 - 3 * q^58 - 33 * q^60 - 18 * q^61 - 99 * q^62 - 6 * q^64 + 18 * q^65 - 9 * q^66 - 54 * q^68 + 72 * q^69 - 36 * q^70 - 111 * q^72 - 18 * q^73 + 93 * q^74 - 36 * q^76 - 36 * q^77 + 6 * q^78 - 18 * q^80 - 30 * q^81 - 18 * q^82 + 84 * q^84 + 6 * q^85 + 135 * q^86 - 51 * q^88 + 81 * q^90 + 48 * q^92 - 6 * q^93 - 9 * q^94 - 9 * q^96 - 117 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−1.35942	−	0.389832i	−0.961257	−	0.275653i
$2$	−1.35942	−	0.389832i	−0.961257	−	0.275653i
$3$	1.54409	+	0.784711i	0.891484	+	0.453053i
$3$	1.54409	+	0.784711i	0.891484	+	0.453053i
$4$	1.69606	+	1.05989i	0.848031	+	0.529947i
$5$	0.874454	+	0.154190i	0.391068	+	0.0689558i	0.365725	−	0.930723i	$-0.380821\pi$
$5$	0.874454	+	0.154190i	0.391068	+	0.0689558i	0.0253429	+	0.999679i	$0.491932\pi$
$6$	−1.79317	−	1.66869i	−0.732060	−	0.681240i
$7$	2.54554	+	0.721260i	0.962124	+	0.272611i
$7$	2.54554	+	0.721260i	0.962124	+	0.272611i
$8$	−1.89249	−	2.10202i	−0.669095	−	0.743177i
$9$	1.76846	+	2.42334i	0.589486	+	0.807778i
$10$	−1.12865	−	0.550499i	−0.356909	−	0.174083i
$11$	6.30310	−	1.11141i	1.90046	−	0.335102i	0.904618	−	0.426224i	$-0.140157\pi$
$11$	6.30310	−	1.11141i	1.90046	−	0.335102i	0.995840	+	0.0911224i	$0.0290455\pi$
$12$	1.78717	+	2.96749i	0.515912	+	0.856642i
$13$	−2.78497	+	3.31899i	−0.772411	+	0.920523i	−0.998564	−	0.0535683i	$-0.982941\pi$
$13$	−2.78497	+	3.31899i	−0.772411	+	0.920523i	0.226153	+	0.974092i	$0.427385\pi$
$14$	−3.17930	−	1.97283i	−0.849703	−	0.527261i
$15$	1.22925	+	0.924277i	0.317390	+	0.238647i
$16$	1.75325	+	3.59529i	0.438313	+	0.898822i
$17$		−	2.39048i		−	0.579778i	−0.957060	−	0.289889i	$-0.906382\pi$
$17$		−	2.39048i		−	0.579778i	0.957060	−	0.289889i	$-0.0936183\pi$
$18$	−1.45939	−	3.98374i	−0.343981	−	0.938976i
$19$	−4.41417			−1.01268			−0.506340	−	0.862334i	$-0.669002\pi$
$19$	−4.41417			−1.01268			−0.506340	+	0.862334i	$0.669002\pi$
$20$	1.31970	+	1.18834i	0.295095	+	0.265722i
$21$	3.36458	+	3.11121i	0.734211	+	0.678921i
$22$	−9.00185	−	0.946279i	−1.91920	−	0.201747i
$23$	1.20684	−	1.43825i	0.251643	−	0.299896i	−0.625404	−	0.780301i	$-0.715066\pi$
$23$	1.20684	−	1.43825i	0.251643	−	0.299896i	0.877047	+	0.480405i	$0.159510\pi$
$24$	−1.27270	−	4.73078i	−0.259788	−	0.965666i
$25$	−3.95757	−	1.44044i	−0.791513	−	0.288087i
$26$	5.07980	−	3.42625i	0.996230	−	0.671943i
$27$	0.829051	+	5.12959i	0.159551	+	0.987190i
$28$	3.55294	+	3.92130i	0.671442	+	0.741057i
$29$	4.07311	−	3.41775i	0.756358	−	0.634659i	−0.180818	−	0.983517i	$-0.557875\pi$
$29$	4.07311	−	3.41775i	0.756358	−	0.634659i	0.937176	+	0.348857i	$0.113430\pi$
$30$	−1.31075	−	1.73568i	−0.239310	−	0.316891i
$31$	1.93118	−	0.702892i	0.346850	−	0.126243i	−0.162720	−	0.986672i	$-0.552027\pi$
$31$	1.93118	−	0.702892i	0.346850	−	0.126243i	0.509570	+	0.860429i	$0.329804\pi$
$32$	−0.981854	−	5.57099i	−0.173569	−	0.984822i
$33$	10.6047	+	3.22999i	1.84605	+	0.562270i
$34$	−0.931887	+	3.24968i	−0.159817	+	0.557315i
$35$	2.11475	+	1.02321i	0.357458	+	0.172953i
$36$	0.430939	+	5.98450i	0.0718231	+	0.997417i
$37$	−3.35032	−	5.80293i	−0.550790	−	0.953996i	−0.998218	−	0.0596760i	$-0.980993\pi$
$37$	−3.35032	−	5.80293i	−0.550790	−	0.953996i	0.447428	−	0.894320i	$-0.352340\pi$
$38$	6.00072	+	1.72078i	0.973445	+	0.279148i
$39$	−6.90470	+	2.93945i	−1.10564	+	0.470689i
$40$	−1.33078	−	2.12992i	−0.210415	−	0.336771i
$41$	−7.00385	+	8.34687i	−1.09382	+	1.30356i	−0.144410	+	0.989518i	$0.546128\pi$
$41$	−7.00385	+	8.34687i	−1.09382	+	1.30356i	−0.949408	+	0.314044i	$0.898316\pi$
$42$	−3.36104	−	5.54107i	−0.518619	−	0.855005i
$43$	−0.549298	+	1.50918i	−0.0837672	+	0.230148i	−0.974504	−	0.224372i	$-0.927967\pi$
$43$	−0.549298	+	1.50918i	−0.0837672	+	0.230148i	0.890736	+	0.454520i	$0.150189\pi$
$44$	11.8684	+	4.79560i	1.78923	+	0.722964i
$45$	1.17278	+	2.39177i	0.174828	+	0.356545i
$46$	−2.20128	+	1.48473i	−0.324561	+	0.218911i
$47$	−8.00134	−	2.91225i	−1.16711	−	0.424795i	−0.315481	−	0.948932i	$-0.602166\pi$
$47$	−8.00134	−	2.91225i	−1.16711	−	0.424795i	−0.851634	+	0.524137i	$0.824388\pi$
$48$	−0.114073	+	6.92726i	−0.0164649	+	0.999864i
$49$	5.95957	+	3.67200i	0.851367	+	0.524571i
$50$	4.81848	+	3.50095i	0.681436	+	0.495109i
$51$	1.87584	−	3.69114i	0.262670	−	0.516862i
$52$	−8.24126	+	2.67745i	−1.14286	+	0.371296i
$53$	−5.85287	−	10.1375i	−0.803954	−	1.39249i	−0.916995	−	0.398898i	$-0.869393\pi$
$53$	−5.85287	−	10.1375i	−0.803954	−	1.39249i	0.113041	−	0.993590i	$-0.463941\pi$
$54$	0.872647	−	7.29647i	0.118752	−	0.992924i
$55$	5.68314			0.766315
$56$	−3.30130	−	6.71576i	−0.441154	−	0.897431i
$57$	−6.81589	−	3.46384i	−0.902787	−	0.458797i
$58$	−6.86943	+	3.05833i	−0.902000	+	0.401579i
$59$	1.45830	+	1.22366i	0.189854	+	0.159307i	0.732760	−	0.680487i	$-0.238232\pi$
$59$	1.45830	+	1.22366i	0.189854	+	0.159307i	−0.542906	+	0.839793i	$0.682676\pi$
$60$	1.10524	+	2.87050i	0.142686	+	0.370580i
$61$	−2.45933	+	6.75696i	−0.314885	+	0.865140i	0.676767	+	0.736197i	$0.263380\pi$
$61$	−2.45933	+	6.75696i	−0.314885	+	0.865140i	−0.991652	+	0.128942i	$0.958842\pi$
$62$	−2.89930	+	0.202692i	−0.368211	+	0.0257419i
$63$	2.75383	+	7.44422i	0.346950	+	0.937884i
$64$	−0.836997	+	7.95609i	−0.104625	+	0.994512i
$65$	−2.94708	+	2.47289i	−0.365540	+	0.306725i
$66$	−13.1572	−	8.52499i	−1.61953	−	1.04935i
$67$	8.64595	+	1.52451i	1.05627	+	0.186249i	0.674701	−	0.738091i	$-0.264272\pi$
$67$	8.64595	+	1.52451i	1.05627	+	0.186249i	0.381570	+	0.924340i	$0.375384\pi$
$68$	2.53366	−	4.05441i	0.307251	−	0.491669i
$69$	2.99208	−	1.27378i	0.360204	−	0.153345i
$70$	−2.47596	−	2.21537i	−0.295934	−	0.264787i
$71$	10.1372	+	5.85274i	1.20307	+	0.694592i	0.961236	−	0.275726i	$-0.0889182\pi$
$71$	10.1372	+	5.85274i	1.20307	+	0.694592i	0.241833	+	0.970318i	$0.422252\pi$
$72$	1.74712	−	8.30347i	0.205900	−	0.978573i
$73$	9.90275	+	5.71736i	1.15903	+	0.669166i	0.951071	−	0.308972i	$-0.0999849\pi$
$73$	9.90275	+	5.71736i	1.15903	+	0.669166i	0.207958	+	0.978138i	$0.433318\pi$
$74$	2.29234	+	9.19470i	0.266479	+	1.06886i
$75$	−4.98053	−	5.32972i	−0.575103	−	0.615423i
$76$	−7.48670	−	4.67855i	−0.858784	−	0.536666i
$77$	16.8464	+	1.71704i	1.91983	+	0.195675i
$78$	10.5323	−	1.30428i	1.19255	−	0.147681i
$79$	−4.73969	+	0.835735i	−0.533257	+	0.0940275i	−0.433791	−	0.901013i	$-0.642824\pi$
$79$	−4.73969	+	0.835735i	−0.533257	+	0.0940275i	−0.0994656	+	0.995041i	$0.531713\pi$
$80$	0.978782	+	3.41425i	0.109431	+	0.381725i
$81$	−2.74511	+	8.57114i	−0.305012	+	0.952348i
$82$	12.7751	−	8.61660i	1.41077	−	0.951544i
$83$	−6.45572	+	5.41699i	−0.708607	+	0.594592i	−0.924208	−	0.381890i	$-0.875273\pi$
$83$	−6.45572	+	5.41699i	−0.708607	+	0.594592i	0.215601	+	0.976482i	$0.430829\pi$
$84$	2.40899	+	8.84289i	0.262842	+	0.964839i
$85$	0.368589	−	2.09037i	0.0399790	−	0.226732i
$86$	1.33506	−	1.83749i	0.143963	−	0.198141i
$87$	8.97121	−	2.08111i	0.961815	−	0.223118i
$88$	−14.2647	−	11.1459i	−1.52063	−	1.18816i
$89$		−	15.0043i		−	1.59045i	−0.606313	−	0.795226i	$-0.707352\pi$
$89$		−	15.0043i		−	1.59045i	0.606313	−	0.795226i	$-0.292648\pi$
$90$	−0.661917	−	3.70862i	−0.0697722	−	0.390923i
$91$	−9.48311	+	6.43995i	−0.994100	+	0.675091i
$92$	3.57126	−	1.16025i	0.372330	−	0.120964i
$93$	3.53349	+	0.430085i	0.366406	+	0.0445978i
$94$	9.74191	+	7.07815i	1.00480	+	0.730056i
$95$	−3.85999	−	0.680620i	−0.396026	−	0.0698301i
$96$	2.85554	−	9.37261i	0.291443	−	0.956588i
$97$	4.06141	−	11.1586i	0.412374	−	1.13299i	−0.543551	−	0.839376i	$-0.682920\pi$
$97$	4.06141	−	11.1586i	0.412374	−	1.13299i	0.955925	−	0.293612i	$-0.0948573\pi$
$98$	−6.67011	−	7.31503i	−0.673783	−	0.738929i
$99$	13.8401	+	13.3091i	1.39098	+	1.33761i
$100$	−5.18557	−	6.63767i	−0.518557	−	0.663767i
$101$	−6.86666	−	8.18337i	−0.683258	−	0.814276i	0.307264	−	0.951624i	$-0.400586\pi$
$101$	−6.86666	−	8.18337i	−0.683258	−	0.814276i	−0.990523	+	0.137349i	$0.956142\pi$
$102$	−3.98898	+	4.28655i	−0.394968	+	0.424432i
$103$	0.430857	−	2.44351i	0.0424536	−	0.240766i	−0.956195	−	0.292729i	$-0.905437\pi$
$103$	0.430857	−	2.44351i	0.0424536	−	0.240766i	0.998649	+	0.0519628i	$0.0165477\pi$
$104$	12.2471	−	0.427086i	1.20093	−	0.0418792i
$105$	2.46245	+	3.23939i	0.240311	+	0.316132i
$106$	4.00462	+	16.0627i	0.388963	+	1.56015i
$107$	10.2817	+	5.93615i	0.993971	+	0.573869i	0.906459	−	0.422294i	$-0.138775\pi$
$107$	10.2817	+	5.93615i	0.993971	+	0.573869i	0.0875121	+	0.996163i	$0.472108\pi$
$108$	−4.03069	+	9.57881i	−0.387854	+	0.921721i
$109$	2.95513	+	5.11844i	0.283051	+	0.490258i	0.972135	−	0.234423i	$-0.0753202\pi$
$109$	2.95513	+	5.11844i	0.283051	+	0.490258i	−0.689084	+	0.724681i	$0.741987\pi$
$110$	−7.72580	−	2.21547i	−0.736626	−	0.211237i
$111$	−0.619597	−	11.5893i	−0.0588095	−	1.10001i
$112$	1.86984	+	10.4165i	0.176683	+	0.984268i
$113$	−2.65288	+	0.965569i	−0.249562	+	0.0908331i	−0.463772	−	0.885954i	$-0.653504\pi$
$113$	−2.65288	+	0.965569i	−0.249562	+	0.0908331i	0.214210	+	0.976788i	$0.431282\pi$
$114$	7.91537	+	7.36588i	0.741342	+	0.689878i
$115$	1.27709	−	1.07160i	0.119089	−	0.0999275i
$116$	10.5307	−	1.47965i	0.977750	−	0.137382i
$117$	−12.9681	−	0.879405i	−1.19890	−	0.0813010i
$118$	−1.50542	−	2.23196i	−0.138585	−	0.205469i
$119$	1.72416	−	6.08508i	0.158054	−	0.557818i
$120$	−0.383479	−	4.33308i	−0.0350066	−	0.395555i
$121$	28.1573	−	10.2484i	2.55975	−	0.931673i
$122$	5.97735	−	8.22684i	0.541164	−	0.744823i
$123$	−17.3645	+	7.39236i	−1.56570	+	0.666547i
$124$	4.02039	+	0.854696i	0.361042	+	0.0767539i
$125$	−7.08352	−	4.08967i	−0.633569	−	0.365791i
$126$	−0.841625	−	11.1934i	−0.0749779	−	0.997185i
$127$	−4.74656	+	2.74043i	−0.421189	+	0.243173i	−0.695586	−	0.718443i	$-0.744855\pi$
$127$	−4.74656	+	2.74043i	−0.421189	+	0.243173i	0.274397	+	0.961617i	$0.411522\pi$
$128$	4.23937	−	10.4894i	0.374711	−	0.927142i
$129$	−2.03244	+	1.89928i	−0.178946	+	0.167223i
$130$	4.97034	−	2.21284i	0.435928	−	0.194079i
$131$	11.4789	+	9.63196i	1.00292	+	0.841548i	0.987386	−	0.158332i	$-0.0506115\pi$
$131$	11.4789	+	9.63196i	1.00292	+	0.841548i	0.0155317	+	0.999879i	$0.495056\pi$
$132$	14.5628	+	16.7181i	1.26753	+	1.45513i
$133$	−11.2364	−	3.18376i	−0.974324	−	0.276067i
$134$	−11.1592	−	5.44293i	−0.964008	−	0.470198i
$135$	−0.0659635	+	4.61342i	−0.00567723	+	0.397060i
$136$	−5.02485	+	4.52396i	−0.430878	+	0.387926i
$137$	−5.83943	−	2.12538i	−0.498896	−	0.181583i	0.0803013	−	0.996771i	$-0.474412\pi$
$137$	−5.83943	−	2.12538i	−0.498896	−	0.181583i	−0.579197	+	0.815187i	$0.696634\pi$
$138$	−4.56406	+	0.565196i	−0.388519	+	0.0481127i
$139$	1.11300	−	6.31212i	0.0944031	−	0.535387i	−0.900525	−	0.434803i	$-0.856818\pi$
$139$	1.11300	−	6.31212i	0.0944031	−	0.535387i	0.994929	−	0.100584i	$-0.0320710\pi$
$140$	2.50226	+	3.97683i	0.211479	+	0.336103i
$141$	−10.0696	−	10.7755i	−0.848009	−	0.907463i
$142$	−11.4992	−	11.9082i	−0.964992	−	0.999311i
$143$	−13.8652	+	24.0152i	−1.15946	+	2.00825i
$144$	−5.61204	+	10.6068i	−0.467670	+	0.883903i
$145$	4.08873	−	2.36063i	0.339551	−	0.196040i
$146$	−11.2332	−	11.6327i	−0.929668	−	0.962730i
$147$	6.32068	+	10.3464i	0.521321	+	0.853360i
$148$	0.468130	−	13.3931i	0.0384800	−	1.10091i
$149$	−5.10993	+	1.85986i	−0.418622	+	0.152366i	−0.542739	−	0.839902i	$-0.682613\pi$
$149$	−5.10993	+	1.85986i	−0.418622	+	0.152366i	0.124117	+	0.992268i	$0.460390\pi$
$150$	4.69296	+	9.18691i	0.383178	+	0.750108i
$151$	−22.6445	+	3.99284i	−1.84278	+	0.324932i	−0.982698	−	0.185218i	$-0.940701\pi$
$151$	−22.6445	+	3.99284i	−1.84278	+	0.324932i	−0.860085	+	0.510150i	$0.829590\pi$
$152$	8.35375	+	9.27868i	0.677578	+	0.752600i
$153$	5.79295	−	4.22747i	0.468332	−	0.341771i
$154$	−22.2321	−	8.90146i	−1.79151	−	0.717300i
$155$	1.79711	−	0.316878i	0.144347	−	0.0254523i
$156$	−14.8263	−	2.33276i	−1.18705	−	0.186770i
$157$	1.44185	−	1.71833i	0.115072	−	0.137138i	−0.705433	−	0.708776i	$-0.749248\pi$
$157$	1.44185	−	1.71833i	0.115072	−	0.137138i	0.820505	+	0.571639i	$0.193692\pi$
$158$	6.76904	+	0.711565i	0.538516	+	0.0566091i
$159$	−1.08241	−	20.2460i	−0.0858406	−	1.60561i
$160$	0.000404552	−	5.02297i	3.19827e−5	−	0.397101i
$161$	4.10940	−	2.79069i	0.323866	−	0.219937i
$162$	7.07307	−	10.5817i	0.555713	−	0.831374i
$163$	−2.93589	−	1.69504i	−0.229957	−	0.132766i	0.380595	−	0.924742i	$-0.375719\pi$
$163$	−2.93589	−	1.69504i	−0.229957	−	0.132766i	−0.610552	+	0.791976i	$0.709052\pi$
$164$	−20.7258	+	6.73347i	−1.61841	+	0.525796i
$165$	8.77531	+	4.45962i	0.683157	+	0.347181i
$166$	10.8878	−	4.84734i	0.845055	−	0.376226i
$167$	−9.43805	+	3.43517i	−0.730338	+	0.265821i	−0.680308	−	0.732926i	$-0.738154\pi$
$167$	−9.43805	+	3.43517i	−0.730338	+	0.265821i	−0.0500303	+	0.998748i	$0.515932\pi$
$168$	0.172413	−	12.9603i	0.0133020	−	0.999912i
$169$	−1.00226	−	5.68408i	−0.0770966	−	0.437237i
$170$	−1.31596	+	2.69801i	−0.100930	+	0.206928i
$171$	−7.80627	−	10.6970i	−0.596960	−	0.818021i
$172$	−2.53122	+	1.97747i	−0.193004	+	0.150781i
$173$	−4.74477	−	5.65460i	−0.360739	−	0.429911i	0.554898	−	0.831918i	$-0.312757\pi$
$173$	−4.74477	−	5.65460i	−0.360739	−	0.429911i	−0.915637	+	0.402007i	$0.868313\pi$
$174$	−13.0070	−	0.668155i	−0.986055	−	0.0506527i
$175$	−9.03522	−	6.52113i	−0.682999	−	0.492951i
$176$	15.0468	+	20.7129i	1.13419	+	1.56129i
$177$	1.29153	+	3.03379i	0.0970776	+	0.228033i
$178$	−5.84915	+	20.3972i	−0.438413	+	1.52883i
$179$		−	23.0263i		−	1.72107i	−0.509392	−	0.860534i	$-0.670130\pi$
$179$		−	23.0263i		−	1.72107i	0.509392	−	0.860534i	$-0.329870\pi$
$180$	−0.545914	+	5.29962i	−0.0406900	+	0.395010i
$181$	−9.24253	+	5.33618i	−0.686992	+	0.396635i	−0.802484	−	0.596674i	$-0.796489\pi$
$181$	−9.24253	+	5.33618i	−0.686992	+	0.396635i	0.115492	+	0.993308i	$0.463155\pi$
$182$	15.4021	−	5.05780i	1.14168	−	0.374909i
$183$	−9.09970	+	8.50352i	−0.672669	+	0.628598i
$184$	−5.30716	+	0.185073i	−0.391249	+	0.0136438i
$185$	−2.03495	−	5.59098i	−0.149613	−	0.411057i
$186$	−4.63585	−	1.96214i	−0.339917	−	0.143871i
$187$	−2.65680	−	15.0675i	−0.194285	−	1.10184i
$188$	−10.4841	−	13.4199i	−0.764631	−	0.978748i
$189$	−1.58938	+	13.6555i	−0.115611	+	0.993295i
$190$	4.98203	+	2.43000i	0.361434	+	0.176290i
$191$	5.85415	−	1.03225i	0.423592	−	0.0746907i	0.0422110	−	0.999109i	$-0.486560\pi$
$191$	5.85415	−	1.03225i	0.423592	−	0.0746907i	0.381381	+	0.924418i	$0.375449\pi$
$192$	−7.53563	+	11.6282i	−0.543838	+	0.839191i
$193$	−12.4646	+	4.53675i	−0.897222	+	0.326562i	−0.749139	−	0.662413i	$-0.769533\pi$
$193$	−12.4646	+	4.53675i	−0.897222	+	0.326562i	−0.148083	+	0.988975i	$0.547310\pi$
$194$	−9.87117	+	13.5860i	−0.708709	+	0.975421i
$195$	−6.49108	+	1.50578i	−0.464836	+	0.107831i
$196$	6.21587	+	12.5444i	0.443991	+	0.896031i
$197$	−9.04531	−	15.6669i	−0.644452	−	1.11622i	−0.984428	−	0.175789i	$-0.943752\pi$
$197$	−9.04531	−	15.6669i	−0.644452	−	1.11622i	0.339976	−	0.940434i	$-0.389581\pi$
$198$	−13.6262	−	23.4879i	−0.968375	−	1.66922i
$199$	−2.19670			−0.155720			−0.0778601	−	0.996964i	$-0.524809\pi$
$199$	−2.19670			−0.155720			−0.0778601	+	0.996964i	$0.524809\pi$
$200$	4.46181	+	11.0449i	0.315498	+	0.780992i
$201$	12.1539	+	9.13857i	0.857268	+	0.644585i
$202$	6.14456	+	13.8015i	0.432330	+	0.971070i
$203$	12.8334	−	5.76224i	0.900725	−	0.404430i
$204$	7.09375	−	4.27221i	0.496662	−	0.299114i
$205$	−7.41155	+	6.21903i	−0.517645	+	0.434356i
$206$	−1.53828	+	3.15380i	−0.107177	+	0.219736i
$207$	5.61960	+	0.381081i	0.390589	+	0.0264870i
$208$	−16.8155	−	4.19372i	−1.16594	−	0.290782i
$209$	−27.8230	+	4.90594i	−1.92455	+	0.339351i
$210$	−2.08470	−	5.36365i	−0.143858	−	0.370127i
$211$	1.66604	+	4.57742i	0.114695	+	0.315123i	0.983737	−	0.179617i	$-0.0574858\pi$
$211$	1.66604	+	4.57742i	0.114695	+	0.315123i	−0.869041	+	0.494739i	$0.835264\pi$
$212$	0.817803	−	23.3972i	0.0561669	−	1.60693i
$213$	11.0602	+	16.9920i	0.757829	+	1.16427i
$214$	−11.6631	−	12.0779i	−0.797273	−	0.825627i
$215$	−0.713037	+	1.23502i	−0.0486287	+	0.0842274i
$216$	9.21354	−	11.4504i	0.626902	−	0.779098i
$217$	5.42287	−	0.396358i	0.368128	−	0.0269065i
$218$	−2.02195	−	8.11014i	−0.136943	−	0.549288i
$219$	10.8043	+	16.5989i	0.730088	+	1.12165i
$220$	9.63896	+	6.02352i	0.649859	+	0.406106i
$221$	7.93400	+	6.65742i	0.533699	+	0.447827i
$222$	−3.67559	+	15.9963i	−0.246689	+	1.07360i
$223$	−0.00595348	−	0.0337639i	−0.000398675	−	0.00226100i	0.984608	−	0.174779i	$-0.0559210\pi$
$223$	−0.00595348	−	0.0337639i	−0.000398675	−	0.00226100i	−0.985006	+	0.172518i	$0.944810\pi$
$224$	1.51878	−	14.8894i	0.101478	−	0.994838i
$225$	−3.50813	−	12.1379i	−0.233876	−	0.809191i
$226$	3.98280	−	0.278440i	0.264932	−	0.0185215i
$227$	−2.18690	−	12.4025i	−0.145150	−	0.823186i	−0.967247	−	0.253838i	$-0.918307\pi$
$227$	−2.18690	−	12.4025i	−0.145150	−	0.823186i	0.822097	−	0.569348i	$-0.192804\pi$
$228$	−7.88887	−	13.0990i	−0.522453	−	0.867503i
$229$	−0.427015	−	1.17321i	−0.0282180	−	0.0775282i	0.924784	−	0.380493i	$-0.124246\pi$
$229$	−0.427015	−	1.17321i	−0.0282180	−	0.0775282i	−0.953002	+	0.302965i	$0.902024\pi$
$230$	−2.15385	+	0.958912i	−0.142020	+	0.0632288i
$231$	24.6651	+	15.8708i	1.62284	+	1.04423i
$232$	−14.8925	−	2.09374i	−0.977739	−	0.137460i
$233$	3.34678	+	5.79679i	0.219255	+	0.379760i	0.954580	−	0.297954i	$-0.0963041\pi$
$233$	3.34678	+	5.79679i	0.219255	+	0.379760i	−0.735326	+	0.677714i	$0.762971\pi$
$234$	17.2864	+	6.25088i	1.13004	+	0.408633i
$235$	−6.54776	−	3.78035i	−0.427129	−	0.246603i
$236$	1.17642	+	3.62104i	0.0765783	+	0.235710i
$237$	−7.97434	−	2.42883i	−0.517989	−	0.157769i
$238$	−4.71602	+	7.60006i	−0.305694	+	0.492639i
$239$	−16.4133	−	2.89412i	−1.06169	−	0.187205i	−0.384584	−	0.923090i	$-0.625655\pi$
$239$	−16.4133	−	2.89412i	−1.06169	−	0.187205i	−0.677106	+	0.735885i	$0.736766\pi$
$240$	−1.16787	+	6.03999i	−0.0753854	+	0.389879i
$241$	−4.86780	+	13.3742i	−0.313563	+	0.861506i	0.678368	+	0.734722i	$0.262688\pi$
$241$	−4.86780	+	13.3742i	−0.313563	+	0.861506i	−0.991930	+	0.126784i	$0.959535\pi$
$242$	−42.2728	+	2.95532i	−2.71740	+	0.189975i
$243$	−10.9646	+	11.0805i	−0.703378	+	0.710816i
$244$	−11.3328	+	8.85359i	−0.725510	+	0.566793i
$245$	4.64518	+	4.12990i	0.296770	+	0.263849i
$246$	26.4875	−	3.28011i	1.68878	−	0.209132i
$247$	12.2933	−	14.6506i	0.782205	−	0.932195i
$248$	−5.13222	−	2.72917i	−0.325897	−	0.173302i
$249$	−14.2190	+	3.29848i	−0.901093	+	0.209032i
$250$	8.03522	+	8.32098i	0.508192	+	0.526265i
$251$	−0.501668	−	0.868915i	−0.0316650	−	0.0548454i	0.849759	−	0.527172i	$-0.176748\pi$
$251$	−0.501668	−	0.868915i	−0.0316650	−	0.0548454i	−0.881424	+	0.472327i	$0.843414\pi$
$252$	−3.21941	+	15.5446i	−0.202804	+	0.979219i
$253$	6.00833	−	10.4067i	0.377740	−	0.654266i
$254$	7.52089	−	1.87504i	0.471902	−	0.117650i
$255$	2.20947	−	2.93849i	0.138362	−	0.184016i
$256$	−9.85221	+	12.6069i	−0.615763	+	0.787931i
$257$	−3.41052	−	9.37034i	−0.212743	−	0.584506i	0.786719	−	0.617311i	$-0.211778\pi$
$257$	−3.41052	−	9.37034i	−0.212743	−	0.584506i	−0.999462	+	0.0328055i	$0.989556\pi$
$258$	3.50335	−	1.78962i	0.218109	−	0.111417i
$259$	−4.34297	−	17.1881i	−0.269859	−	1.06801i
$260$	−7.61944	+	1.07059i	−0.472537	+	0.0663953i
$261$	15.4855	+	3.82637i	0.958527	+	0.236846i
$262$	−11.8499	−	17.5688i	−0.732087	−	1.08540i
$263$	−0.924742	−	1.10206i	−0.0570220	−	0.0679562i	0.736779	−	0.676133i	$-0.236346\pi$
$263$	−0.924742	−	1.10206i	−0.0570220	−	0.0679562i	−0.793802	+	0.608177i	$0.791901\pi$
$264$	−13.2798	−	28.4041i	−0.817313	−	1.74815i
$265$	−3.55497	−	9.76721i	−0.218380	−	0.599995i
$266$	14.0340	+	8.70841i	0.860477	+	0.533947i
$267$	11.7740	−	23.1681i	0.720559	−	1.41786i
$268$	13.0483	+	11.7495i	0.797049	+	0.717712i
$269$	−7.31821	+	4.22517i	−0.446199	+	0.257613i	−0.706224	−	0.707989i	$-0.749603\pi$
$269$	−7.31821	+	4.22517i	−0.446199	+	0.257613i	0.260024	+	0.965602i	$0.416269\pi$
$270$	1.88813	−	6.24588i	0.114908	−	0.380112i
$271$	9.86245	−	17.0823i	0.599101	−	1.03767i	−0.393853	−	0.919173i	$-0.628858\pi$
$271$	9.86245	−	17.0823i	0.599101	−	1.03767i	0.992954	−	0.118500i	$-0.0378085\pi$
$272$	8.59448	−	4.19112i	0.521117	−	0.254124i
$273$	−19.6963	+	2.50240i	−1.19208	+	0.151452i
$274$	7.10971	+	5.16569i	0.429514	+	0.312070i
$275$	−26.5459	−	4.68075i	−1.60078	−	0.282260i
$276$	6.42482	+	1.01088i	0.386729	+	0.0608476i
$277$	10.9860	−	9.21832i	0.660083	−	0.553875i	−0.250029	−	0.968238i	$-0.580440\pi$
$277$	10.9860	−	9.21832i	0.660083	−	0.553875i	0.910112	+	0.414363i	$0.135996\pi$
$278$	−3.97370	+	8.14696i	−0.238327	+	0.488622i
$279$	5.11855	+	3.43686i	0.306440	+	0.205759i
$280$	−1.85133	−	6.38165i	−0.110638	−	0.381377i
$281$	15.5576	+	5.66250i	0.928089	+	0.337797i	0.761452	−	0.648222i	$-0.224487\pi$
$281$	15.5576	+	5.66250i	0.928089	+	0.337797i	0.166637	+	0.986018i	$0.446709\pi$
$282$	9.48814	+	18.5739i	0.565010	+	1.10606i
$283$	5.12210	−	29.0489i	0.304477	−	1.72678i	−0.321479	−	0.946917i	$-0.604180\pi$
$283$	5.12210	−	29.0489i	0.304477	−	1.72678i	0.625956	−	0.779858i	$-0.284709\pi$
$284$	10.9901	+	20.6710i	0.652143	+	1.22660i
$285$	−5.42610	−	4.07991i	−0.321414	−	0.241673i
$286$	28.2105	−	27.2417i	1.66812	−	1.61084i
$287$	−23.8489	+	16.1957i	−1.40775	+	0.956002i
$288$	11.7640	−	12.2314i	0.693201	−	0.720744i
$289$	11.2856			0.663858
$290$	−6.47856	+	1.61518i	−0.380434	+	0.0948464i
$291$	15.0275	−	14.0430i	0.880928	−	0.823213i
$292$	10.7359	+	20.1928i	0.628271	+	1.18170i
$293$	−11.1259	−	1.96179i	−0.649979	−	0.114609i	−0.161069	−	0.986943i	$-0.551494\pi$
$293$	−11.1259	−	1.96179i	−0.649979	−	0.114609i	−0.488910	+	0.872334i	$0.662605\pi$
$294$	−4.55911	−	16.5292i	−0.265893	−	0.964003i
$295$	1.08654	+	1.29489i	0.0632608	+	0.0753913i
$296$	−5.85745	+	18.0244i	−0.340457	+	1.04765i
$297$	10.9267	+	31.4109i	0.634029	+	1.82265i
$298$	7.67160	−	0.536326i	0.444404	−	0.0310685i
$299$	1.41255	+	8.01096i	0.0816898	+	0.463286i
$300$	−2.79836	−	14.3184i	−0.161564	−	0.826671i
$301$	−2.48678	+	3.44551i	−0.143335	+	0.198596i
$302$	32.3400	+	3.39960i	1.86096	+	0.195625i
$303$	−4.18120	−	18.0242i	−0.240204	−	1.03547i
$304$	−7.73915	−	15.8702i	−0.443871	−	0.910219i
$305$	−3.19243	+	5.52945i	−0.182798	+	0.316615i
$306$	−9.52307	+	3.48865i	−0.544398	+	0.199433i
$307$	−2.56381	+	4.44065i	−0.146324	+	0.253441i	−0.929866	−	0.367898i	$-0.880078\pi$
$307$	−2.56381	+	4.44065i	−0.146324	+	0.253441i	0.783542	+	0.621339i	$0.213411\pi$
$308$	26.7527	+	20.7676i	1.52438	+	1.18335i
$309$	2.58273	−	3.43492i	0.146927	−	0.195405i
$310$	−2.56656	−	0.269798i	−0.145771	−	0.0153235i
$311$	−0.752676	+	4.26864i	−0.0426804	+	0.242052i	−0.998683	−	0.0513058i	$-0.983662\pi$
$311$	−0.752676	+	4.26864i	−0.0426804	+	0.242052i	0.956003	+	0.293358i	$0.0947728\pi$
$312$	19.2458	+	8.95098i	1.08958	+	0.506749i
$313$	19.3104	+	23.0132i	1.09149	+	1.30078i	0.950484	+	0.310773i	$0.100588\pi$
$313$	19.3104	+	23.0132i	1.09149	+	1.30078i	0.141002	+	0.990009i	$0.454968\pi$
$314$	−2.62994	+	1.77386i	−0.148416	+	0.100105i
$315$	1.26028	+	6.93424i	0.0710085	+	0.390700i
$316$	−8.92460	−	3.60611i	−0.502048	−	0.202859i
$317$	−9.04445	−	3.29191i	−0.507987	−	0.184892i	0.0752959	−	0.997161i	$-0.476010\pi$
$317$	−9.04445	−	3.29191i	−0.507987	−	0.184892i	−0.583283	+	0.812269i	$0.698232\pi$
$318$	−6.42110	+	27.9449i	−0.360077	+	1.56707i
$319$	21.8747	−	26.0693i	1.22475	−	1.45960i
$320$	−1.95866	+	6.82818i	−0.109493	+	0.381707i
$321$	11.2178	+	17.2342i	0.626116	+	0.961917i
$322$	−6.67432	+	2.19175i	−0.371945	+	0.122141i
$323$			10.5520i			0.587129i
$324$	−13.7404	+	11.6277i	−0.763354	+	0.645981i
$325$	15.8025	−	9.12358i	0.876565	−	0.506085i
$326$	3.33034	+	3.44878i	0.184450	+	0.191010i
$327$	0.546512	+	10.2223i	0.0302222	+	0.565294i
$328$	30.8000	−	1.07407i	1.70065	−	0.0593056i
$329$	−18.2672	−	13.1843i	−1.00711	−	0.726874i
$330$	−10.1909	−	9.48341i	−0.560988	−	0.522045i
$331$	−1.53211	+	4.20944i	−0.0842124	+	0.231372i	−0.974651	−	0.223733i	$-0.928176\pi$
$331$	−1.53211	+	4.20944i	−0.0842124	+	0.231372i	0.890438	+	0.455104i	$0.150398\pi$
$332$	−16.6907	+	2.34518i	−0.916023	+	0.128708i
$333$	8.13754	−	18.3812i	0.445934	−	1.00728i
$334$	14.1694	−	0.990595i	0.775317	−	0.0542029i
$335$	7.32543	+	2.66624i	0.400231	+	0.145672i
$336$	−5.28674	+	17.5514i	−0.288415	+	0.957505i
$337$	−1.62609	−	1.36445i	−0.0885787	−	0.0743264i	0.597423	−	0.801926i	$-0.296191\pi$
$337$	−1.62609	−	1.36445i	−0.0885787	−	0.0743264i	−0.686002	+	0.727600i	$0.740636\pi$
$338$	−0.853345	+	8.11778i	−0.0464158	+	0.441549i
$339$	−4.85399	−	0.590812i	−0.263633	−	0.0320885i
$340$	2.84072	−	3.15473i	0.154060	−	0.171089i
$341$	11.3912	−	6.57673i	0.616869	−	0.356150i
$342$	6.44199	+	17.5849i	0.348343	+	0.950882i
$343$	12.5219	+	13.6456i	0.676117	+	0.736794i
$344$	4.21188	−	1.70147i	0.227089	−	0.0917372i
$345$	2.81284	−	0.652513i	0.151438	−	0.0351301i
$346$	4.24581	+	9.53666i	0.228256	+	0.512694i
$347$	3.60429	+	9.90271i	0.193488	+	0.531605i	0.998061	−	0.0622497i	$-0.0198275\pi$
$347$	3.60429	+	9.90271i	0.193488	+	0.531605i	−0.804572	+	0.593855i	$0.797605\pi$
$348$	17.4215	+	5.97883i	0.933890	+	0.320499i
$349$	12.7449	+	15.1888i	0.682218	+	0.813036i	0.990391	−	0.138294i	$-0.0441619\pi$
$349$	12.7449	+	15.1888i	0.682218	+	0.813036i	−0.308173	+	0.951330i	$0.599717\pi$
$350$	9.74055	+	12.3872i	0.520654	+	0.662123i
$351$	−19.3340	−	11.5341i	−1.03197	−	0.615646i
$352$	−12.3804	−	34.0233i	−0.659876	−	1.81345i
$353$	2.10222	−	5.77581i	0.111890	−	0.307415i	−0.871091	−	0.491121i	$-0.836587\pi$
$353$	2.10222	−	5.77581i	0.111890	−	0.307415i	0.982981	+	0.183706i	$0.0588094\pi$
$354$	−0.573074	−	4.62768i	−0.0304586	−	0.245958i
$355$	7.96212	+	6.68101i	0.422585	+	0.354591i
$356$	15.9030	−	25.4482i	0.842855	−	1.34875i
$357$	7.43729	−	8.04297i	0.393623	−	0.425679i
$358$	−8.97640	+	31.3025i	−0.474417	+	1.65439i
$359$			5.54032i			0.292407i	0.989255	+	0.146203i	$0.0467054\pi$
$359$			5.54032i			0.292407i	−0.989255	+	0.146203i	$0.953295\pi$
$360$	2.80809	−	6.99161i	0.147999	−	0.368490i
$361$	0.484871			0.0255195
$362$	14.6447	−	3.65109i	0.769709	−	0.191897i
$363$	51.5195	+	6.27079i	2.70407	+	0.329131i
$364$	−22.9096	+	0.871480i	−1.20079	+	0.0456780i
$365$	7.77794	+	6.52647i	0.407116	+	0.341611i
$366$	15.6853	−	8.01253i	0.819883	−	0.418822i
$367$	3.20046	+	18.1507i	0.167062	+	0.947458i	0.946912	+	0.321492i	$0.104184\pi$
$367$	3.20046	+	18.1507i	0.167062	+	0.947458i	−0.779850	+	0.625967i	$0.784705\pi$
$368$	7.28682	+	1.81731i	0.379852	+	0.0947336i
$369$	−32.6133	−	2.21160i	−1.69778	−	0.115131i
$370$	0.586816	+	8.39380i	0.0305071	+	0.436373i
$371$	−7.58698	−	30.0268i	−0.393896	−	1.55891i
$372$	5.53718	+	4.47457i	0.287089	+	0.231996i
$373$	−0.159836	+	0.906474i	−0.00827599	+	0.0469355i	−0.988666	−	0.150131i	$-0.952030\pi$
$373$	−0.159836	+	0.906474i	−0.00827599	+	0.0469355i	0.980390	+	0.197067i	$0.0631415\pi$
$374$	−2.26206	+	21.5188i	−0.116969	+	1.11271i
$375$	−7.72842	−	11.8734i	−0.399094	−	0.613138i
$376$	9.02080	+	22.3304i	0.465212	+	1.15160i
$377$			23.0369i			1.18646i
$378$	7.48401	−	17.9441i	0.384936	−	0.922943i
$379$		−	23.3310i		−	1.19843i	−0.800587	−	0.599217i	$-0.795479\pi$
$379$		−	23.3310i		−	1.19843i	0.800587	−	0.599217i	$-0.204521\pi$
$380$	−5.82539	−	5.24555i	−0.298836	−	0.269091i
$381$	−9.47958	+	0.506804i	−0.485653	+	0.0259644i
$382$	−8.36068	−	0.878879i	−0.427769	−	0.0449673i
$383$	−1.74200	+	9.87938i	−0.0890121	+	0.504813i	0.907406	+	0.420254i	$0.138059\pi$
$383$	−1.74200	+	9.87938i	−0.0890121	+	0.504813i	−0.996419	+	0.0845584i	$0.973052\pi$
$384$	14.7771	−	12.8700i	0.754093	−	0.656768i
$385$	14.4667	+	4.09902i	0.737290	+	0.208906i
$386$	18.7132	−	1.30825i	0.952479	−	0.0665884i
$387$	−4.62867	+	1.33780i	−0.235289	+	0.0680040i
$388$	18.7154	−	14.6211i	0.950129	−	0.742273i
$389$	−2.71228	−	15.3821i	−0.137518	−	0.779905i	−0.973073	−	0.230498i	$-0.925965\pi$
$389$	−2.71228	−	15.3821i	−0.137518	−	0.779905i	0.835555	−	0.549407i	$-0.185146\pi$
$390$	9.41112	+	0.483441i	0.476551	+	0.0244800i
$391$	−3.43812	−	2.88492i	−0.173873	−	0.145897i
$392$	−3.55978	−	19.4763i	−0.179796	−	0.983704i
$393$	10.1662	+	23.8803i	0.512819	+	1.20460i
$394$	6.18893	+	24.8241i	0.311794	+	1.25062i
$395$	−4.27350			−0.215023
$396$	9.36747	+	37.2420i	0.470733	+	1.87148i
$397$		−	7.76160i		−	0.389543i	−0.980849	−	0.194772i	$-0.937603\pi$
$397$		−	7.76160i		−	0.389543i	0.980849	−	0.194772i	$-0.0623966\pi$
$398$	2.98625	+	0.856345i	0.149687	+	0.0429247i
$399$	−14.8518	−	13.7334i	−0.743520	−	0.687530i
$400$	−1.75983	−	16.7540i	−0.0879915	−	0.837702i
$401$	23.2997	+	19.5507i	1.16353	+	0.976317i	0.999948	−	0.0102125i	$-0.00325078\pi$
$401$	23.2997	+	19.5507i	1.16353	+	0.976317i	0.163582	+	0.986530i	$0.447695\pi$
$402$	−12.9597	−	17.1611i	−0.646373	−	0.855920i
$403$	−3.04538	+	8.36710i	−0.151701	+	0.416795i
$404$	−2.97279	−	21.1574i	−0.147902	−	1.05262i
$405$	−3.72205	+	7.07180i	−0.184950	+	0.351400i
$406$	−19.6923	+	2.83047i	−0.977311	+	0.140474i
$407$	−27.5669	−	32.8529i	−1.36644	−	1.62846i
$408$	−11.3088	+	3.04237i	−0.559871	+	0.150620i
$409$	−4.17125	−	11.4604i	−0.206255	−	0.566681i	0.792830	−	0.609443i	$-0.208607\pi$
$409$	−4.17125	−	11.4604i	−0.206255	−	0.566681i	−0.999085	+	0.0427613i	$0.986384\pi$
$410$	12.4998	−	5.56503i	0.617322	−	0.274837i
$411$	−7.34883	−	7.86405i	−0.362491	−	0.387905i
$412$	3.32062	−	3.68768i	0.163595	−	0.181679i
$413$	2.82958	+	4.16668i	0.139235	+	0.205029i
$414$	−7.49086	−	2.70875i	−0.368156	−	0.133128i
$415$	−6.48047	+	3.74150i	−0.318114	+	0.183663i
$416$	21.2245	+	12.2563i	1.04062	+	0.600913i
$417$	6.67176	−	8.87313i	0.326717	−	0.434519i
$418$	39.7357	+	4.17703i	1.94353	+	0.204305i
$419$	4.13649	+	3.47092i	0.202081	+	0.169566i	0.738212	−	0.674569i	$-0.235670\pi$
$419$	4.13649	+	3.47092i	0.202081	+	0.169566i	−0.536131	+	0.844135i	$0.680115\pi$
$420$	0.743063	+	8.10415i	0.0362577	+	0.395442i
$421$	−34.6184	−	12.6001i	−1.68720	−	0.614090i	−0.692931	−	0.721004i	$-0.743681\pi$
$421$	−34.6184	−	12.6001i	−1.68720	−	0.614090i	−0.994268	+	0.106913i	$0.965903\pi$
$422$	−0.480435	−	6.87213i	−0.0233872	−	0.334530i
$423$	−7.09268	−	24.5401i	−0.344858	−	1.19318i
$424$	−10.2327	+	31.4879i	−0.496945	+	1.52919i
$425$	−3.44334	+	9.46050i	−0.167027	+	0.458902i
$426$	−8.41141	−	27.4109i	−0.407534	−	1.32806i
$427$	−11.1339	+	15.4263i	−0.538805	+	0.746531i
$428$	11.1467	+	20.9656i	0.538798	+	1.01341i
$429$	−40.2541	+	26.2016i	−1.94349	+	1.26502i
$430$	1.45077	−	1.40095i	0.0699622	−	0.0675596i
$431$	6.66457	−	3.84779i	0.321021	−	0.185341i	−0.330827	−	0.943692i	$-0.607328\pi$
$431$	6.66457	−	3.84779i	0.321021	−	0.185341i	0.651848	+	0.758350i	$0.273994\pi$
$432$	−16.9888	+	11.9741i	−0.817375	+	0.576106i
$433$		−	6.67473i		−	0.320767i	−0.987055	−	0.160383i	$-0.948727\pi$
$433$		−	6.67473i		−	0.320767i	0.987055	−	0.160383i	$-0.0512731\pi$
$434$	−7.52648	−	1.57519i	−0.361283	−	0.0756115i
$435$	8.16580	−	0.436566i	0.391520	−	0.0209317i
$436$	−0.412911	+	11.8133i	−0.0197749	+	0.565756i
$437$	−5.32718	+	6.34868i	−0.254833	+	0.303699i
$438$	−8.21684	−	26.7768i	−0.392616	−	1.27945i
$439$	16.9285	+	6.16148i	0.807955	+	0.294071i	0.712779	−	0.701389i	$-0.247436\pi$
$439$	16.9285	+	6.16148i	0.807955	+	0.294071i	0.0951759	+	0.995460i	$0.469659\pi$
$440$	−10.7553	−	11.9461i	−0.512737	−	0.569508i
$441$	1.64077	+	20.9358i	0.0781320	+	0.996943i
$442$	−8.19039	−	12.1432i	−0.389577	−	0.577592i
$443$	−3.53670	−	4.21487i	−0.168034	−	0.200255i	0.675456	−	0.737400i	$-0.263947\pi$
$443$	−3.53670	−	4.21487i	−0.168034	−	0.200255i	−0.843489	+	0.537146i	$0.819502\pi$
$444$	11.2326	−	20.3129i	0.533074	−	0.964007i
$445$	2.31351	−	13.1206i	0.109671	−	0.621975i
$446$	−0.00506894	+	0.0482203i	−0.000240021	+	0.00228330i
$447$	−9.34968	−	1.13801i	−0.442225	−	0.0538262i
$448$	−7.86902	+	19.6489i	−0.371776	+	0.928322i
$449$	0.743641	−	1.28802i	0.0350946	−	0.0607856i	−0.847945	−	0.530085i	$-0.822160\pi$
$449$	0.743641	−	1.28802i	0.0350946	−	0.0607856i	0.883039	+	0.469299i	$0.155493\pi$
$450$	0.0373078	+	17.8681i	0.00175871	+	0.842309i
$451$	−34.8692	+	60.3953i	−1.64193	+	2.84390i
$452$	−5.52285	−	1.17410i	−0.259773	−	0.0552252i
$453$	−38.0985	−	11.6041i	−1.79002	−	0.545206i
$454$	−1.86198	+	17.7128i	−0.0873871	+	0.831304i
$455$	−9.28552	+	4.16925i	−0.435312	+	0.195457i
$456$	5.61790	+	20.8824i	0.263082	+	0.977910i
$457$	−4.75535	−	26.9689i	−0.222446	−	1.26155i	−0.867508	−	0.497424i	$-0.834279\pi$
$457$	−4.75535	−	26.9689i	−0.222446	−	1.26155i	0.645062	−	0.764130i	$-0.276832\pi$
$458$	0.123138	+	1.76136i	0.00575385	+	0.0823029i
$459$	12.2622	−	1.98183i	0.572351	−	0.0925041i
$460$	3.30180	−	0.463930i	0.153947	−	0.0216308i
$461$	8.66557	+	10.3272i	0.403596	+	0.480987i	0.929113	−	0.369796i	$-0.120573\pi$
$461$	8.66557	+	10.3272i	0.403596	+	0.480987i	−0.525517	+	0.850783i	$0.676128\pi$
$462$	−27.3433	−	31.1904i	−1.27213	−	1.45111i
$463$	16.4368	+	2.89824i	0.763881	+	0.134693i	0.541997	−	0.840380i	$-0.317668\pi$
$463$	16.4368	+	2.89824i	0.763881	+	0.134693i	0.221884	+	0.975073i	$0.428779\pi$
$464$	19.4290	+	8.65184i	0.901968	+	0.401651i
$465$	3.02356	+	0.920918i	0.140214	+	0.0427066i
$466$	−2.28991	−	9.18497i	−0.106078	−	0.425485i
$467$	−0.652971			−0.0302159			−0.0151080	−	0.999886i	$-0.504809\pi$
$467$	−0.652971			−0.0302159			−0.0151080	+	0.999886i	$0.504809\pi$
$468$	−21.0627	−	15.2364i	−0.973623	−	0.704301i
$469$	20.9091	+	10.1167i	0.965491	+	0.467146i
$470$	7.42748	+	7.69163i	0.342604	+	0.354788i
$471$	3.57474	−	1.52183i	0.164715	−	0.0701221i
$472$	−0.187653	−	5.38113i	−0.00863742	−	0.247687i
$473$	−1.78496	+	10.1230i	−0.0820728	+	0.465458i
$474$	9.89367	+	6.41046i	0.454431	+	0.294442i
$475$	17.4694	+	6.35833i	0.801549	+	0.291740i
$476$	9.37382	−	8.49324i	0.429648	−	0.389287i
$477$	14.2159	−	32.1112i	0.650903	−	1.47027i
$478$	21.1845	+	10.3328i	0.968955	+	0.472610i
$479$	32.8809	−	27.5904i	1.50237	−	1.26064i	0.625189	−	0.780473i	$-0.285022\pi$
$479$	32.8809	−	27.5904i	1.50237	−	1.26064i	0.877179	−	0.480163i	$-0.159423\pi$
$480$	3.94220	−	7.75563i	0.179936	−	0.353994i
$481$	28.5904	+	5.04127i	1.30361	+	0.229862i
$482$	11.8311	−	16.2835i	0.538891	−	0.741695i
$483$	8.53519	−	1.08439i	0.388365	−	0.0493415i
$484$	58.6187	+	12.4618i	2.66449	+	0.566444i
$485$	5.27207	−	9.13149i	0.239392	−	0.414640i
$486$	19.2250	−	10.7888i	0.872065	−	0.489389i
$487$	−2.45735	+	1.41875i	−0.111353	+	0.0642897i	−0.554642	−	0.832089i	$-0.687145\pi$
$487$	−2.45735	+	1.41875i	−0.111353	+	0.0642897i	0.443289	+	0.896379i	$0.353812\pi$
$488$	18.8575	−	7.61787i	0.853640	−	0.344845i
$489$	−3.20318	−	4.92112i	−0.144853	−	0.222541i
$490$	−4.70481	−	7.42512i	−0.212541	−	0.335433i
$491$	6.57978	+	18.0778i	0.296941	+	0.815839i	0.995007	+	0.0998057i	$0.0318221\pi$
$491$	6.57978	+	18.0778i	0.296941	+	0.815839i	−0.698066	+	0.716034i	$0.745956\pi$
$492$	−37.2864	−	5.86661i	−1.68100	−	0.264487i
$493$	−8.17007	−	9.73671i	−0.367961	−	0.438519i
$494$	−22.4231	+	15.1240i	−1.00886	+	0.680462i
$495$	10.0504	+	13.7722i	0.451732	+	0.619013i
$496$	5.91295	+	5.71080i	0.265499	+	0.256423i
$497$	21.5834	+	22.2100i	0.968149	+	0.996253i
$498$	20.6155	+	1.05900i	0.923803	+	0.0474549i
$499$	−4.00587	−	11.0060i	−0.179327	−	0.492698i	0.817163	−	0.576407i	$-0.195546\pi$
$499$	−4.00587	−	11.0060i	−0.179327	−	0.492698i	−0.996490	+	0.0837088i	$0.973323\pi$
$500$	−7.67948	−	14.4441i	−0.343437	−	0.645960i
$501$	−17.2689	−	2.10191i	−0.771516	−	0.0939064i
$502$	0.343249	+	1.37679i	0.0153199	+	0.0614491i
$503$	−3.33725	+	5.78029i	−0.148801	+	0.257730i	−0.930784	−	0.365568i	$-0.880875\pi$
$503$	−3.33725	+	5.78029i	−0.148801	+	0.257730i	0.781984	+	0.623299i	$0.214208\pi$
$504$	10.4363	−	19.8767i	0.464871	−	0.885378i
$505$	−4.74279	−	8.21475i	−0.211051	−	0.365552i
$506$	−12.2247	+	11.8049i	−0.543456	+	0.524792i
$507$	2.91278	−	9.56324i	0.129361	−	0.424718i
$508$	−10.9550	−	0.382911i	−0.486050	−	0.0169889i
$509$	−17.0497	+	20.3190i	−0.755714	+	0.900625i	−0.997569	−	0.0696874i	$-0.977800\pi$
$509$	−17.0497	+	20.3190i	−0.755714	+	0.900625i	0.241855	+	0.970312i	$0.422244\pi$
$510$	−4.14912	+	3.13333i	−0.183726	+	0.138746i
$511$	21.0842	+	21.6962i	0.932709	+	0.959784i
$512$	18.3079	−	13.2974i	0.809102	−	0.587668i
$513$	−3.65957	−	22.6429i	−0.161574	−	0.999707i
$514$	0.983488	+	14.0678i	0.0433798	+	0.620503i
$515$	0.753529	−	2.07030i	0.0332045	−	0.0912285i
$516$	−5.46018	+	1.06713i	−0.240371	+	0.0469779i
$517$	−53.6699	−	9.46346i	−2.36040	−	0.416202i
$518$	−0.796525	+	25.0589i	−0.0349973	+	1.10102i
$519$	−2.88916	−	12.4545i	−0.126820	−	0.546693i
$520$	10.7754	+	1.51491i	0.472532	+	0.0664333i
$521$	11.9357	+	6.89107i	0.522912	+	0.301903i	0.738125	−	0.674664i	$-0.235711\pi$
$521$	11.9357	+	6.89107i	0.522912	+	0.301903i	−0.215214	+	0.976567i	$0.569045\pi$
$522$	−19.5597	−	11.2384i	−0.856103	−	0.491891i
$523$	2.96029	+	5.12738i	0.129445	+	0.224205i	0.923462	−	0.383691i	$-0.125347\pi$
$523$	2.96029	+	5.12738i	0.129445	+	0.224205i	−0.794017	+	0.607896i	$0.792014\pi$
$524$	9.26011	+	28.5028i	0.404530	+	1.24515i
$525$	−8.83405	−	17.1593i	−0.385549	−	0.748892i
$526$	0.827496	+	1.85867i	0.0360805	+	0.0810417i
$527$	−1.68025	−	4.61645i	−0.0731929	−	0.201096i
$528$	6.98000	+	43.7900i	0.303766	+	1.90572i
$529$	3.38179	+	19.1791i	0.147035	+	0.833874i
$530$	1.02514	+	14.6636i	0.0445293	+	0.636947i
$531$	−0.386393	+	5.69793i	−0.0167680	+	0.247269i
$532$	−15.6833	−	17.3093i	−0.679956	−	0.750453i
$533$	−8.19771	−	46.4915i	−0.355082	−	2.01377i
$534$	−25.0375	+	26.9053i	−1.08348	+	1.16431i
$535$	8.07560	+	6.77623i	0.349138	+	0.292962i
$536$	−13.1578	−	21.0591i	−0.568329	−	0.909615i
$537$	18.0690	−	35.5548i	0.779735	−	1.53430i
$538$	11.5957	−	2.89092i	0.499924	−	0.124637i
$539$	41.6449	+	16.5215i	1.79377	+	0.711630i
$540$	−5.00161	+	7.75473i	−0.215235	+	0.333711i
$541$	9.26781	−	16.0523i	0.398454	−	0.690143i	−0.595081	−	0.803666i	$-0.702880\pi$
$541$	9.26781	−	16.0523i	0.398454	−	0.690143i	0.993535	+	0.113523i	$0.0362134\pi$
$542$	−20.0664	+	19.3773i	−0.861928	+	0.832327i
$543$	−18.4587	+	0.986853i	−0.792138	+	0.0423499i
$544$	−13.3174	+	2.34711i	−0.570978	+	0.100631i
$545$	1.79492	+	4.93150i	0.0768858	+	0.211242i
$546$	27.7511	+	4.27643i	1.18764	+	0.183014i
$547$	−11.3517	+	2.00162i	−0.485365	+	0.0855830i	−0.410976	−	0.911646i	$-0.634812\pi$
$547$	−11.3517	+	2.00162i	−0.485365	+	0.0855830i	−0.0743895	+	0.997229i	$0.523701\pi$
$548$	−7.65136	−	9.79395i	−0.326850	−	0.418377i
$549$	−20.7236	+	5.98961i	−0.884462	+	0.255630i
$550$	34.2624	+	16.7116i	1.46095	+	0.712583i
$551$	−17.9794	+	15.0865i	−0.765948	+	0.642707i
$552$	−8.33998	−	3.87881i	−0.354973	−	0.165093i
$553$	−12.6679	−	1.29115i	−0.538692	−	0.0549053i
$554$	−18.5282	+	8.24892i	−0.787187	+	0.350463i
$555$	1.24515	−	10.2299i	0.0528535	−	0.434233i
$556$	8.57788	−	9.52608i	0.363783	−	0.403996i
$557$	−33.3579			−1.41342			−0.706710	−	0.707503i	$-0.749821\pi$
$557$	−33.3579			−1.41342			−0.706710	+	0.707503i	$0.749821\pi$
$558$	−5.61848	−	6.66752i	−0.237849	−	0.282259i
$559$	−3.47920	−	6.02615i	−0.147154	−	0.254879i
$560$	0.0289694	+	9.39707i	0.00122418	+	0.397099i
$561$	7.72125	−	25.3504i	0.325991	−	1.07030i
$562$	−18.9419	−	13.7626i	−0.799017	−	0.580540i
$563$	−10.0995	+	3.67592i	−0.425644	+	0.154922i	−0.545955	−	0.837815i	$-0.683833\pi$
$563$	−10.0995	+	3.67592i	−0.425644	+	0.154922i	0.120311	+	0.992736i	$0.461611\pi$
$564$	−5.65768	−	28.9486i	−0.238231	−	1.21896i
$565$	−2.46870	+	0.435299i	−0.103859	+	0.0183132i
$566$	−18.2873	+	37.4929i	−0.768671	+	1.57595i
$567$	−13.1698	+	19.8382i	−0.553080	+	0.833128i
$568$	−6.88199	−	32.3849i	−0.288762	−	1.35884i
$569$	1.33504	+	7.57139i	0.0559678	+	0.317409i	0.999920	−	0.0126739i	$-0.00403433\pi$
$569$	1.33504	+	7.57139i	0.0559678	+	0.317409i	−0.943952	+	0.330083i	$0.892923\pi$
$570$	5.78588	+	7.66160i	0.242344	+	0.320909i
$571$	14.2197	+	39.0684i	0.595077	+	1.63496i	0.760947	+	0.648814i	$0.224735\pi$
$571$	14.2197	+	39.0684i	0.595077	+	1.63496i	−0.165870	+	0.986148i	$0.553043\pi$
$572$	−48.9697	+	26.0357i	−2.04753	+	1.08861i
$573$	9.84938	+	2.99993i	0.411464	+	0.125324i
$574$	38.7343	−	12.7198i	1.61674	−	0.530913i
$575$	−6.84784	+	3.95360i	−0.285575	+	0.164877i
$576$	−20.7605	+	12.0417i	−0.865020	+	0.501737i
$577$			35.9850i			1.49808i	0.662527	+	0.749038i	$0.269484\pi$
$577$			35.9850i			1.49808i	−0.662527	+	0.749038i	$0.730516\pi$
$578$	−15.3419	−	4.39948i	−0.638138	−	0.182994i
$579$	−22.8066	−	2.77594i	−0.947809	−	0.115364i
$580$	9.43676	+	0.329843i	0.391840	+	0.0136960i
$581$	−20.3404	+	9.13292i	−0.843860	+	0.378898i
$582$	−25.9031	+	13.2321i	−1.07372	+	0.548489i
$583$	−48.1581	−	57.3926i	−1.99451	−	2.37696i
$584$	−6.72280	−	31.6358i	−0.278192	−	1.30910i
$585$	−11.2044	−	2.76855i	−0.463247	−	0.114466i
$586$	14.3600	+	7.00411i	0.593205	+	0.289337i
$587$	−4.92691	−	27.9419i	−0.203355	−	1.15329i	−0.900007	−	0.435876i	$-0.856439\pi$
$587$	−4.92691	−	27.9419i	−0.203355	−	1.15329i	0.696652	−	0.717410i	$-0.254672\pi$
$588$	−0.245854	+	24.2475i	−0.0101388	+	0.999949i
$589$	−8.52455	+	3.10268i	−0.351248	+	0.127844i
$590$	−0.972278	−	2.18387i	−0.0400281	−	0.0899084i
$591$	−1.67281	−	31.2892i	−0.0688101	−	1.28707i
$592$	14.9892	−	22.2194i	0.616054	−	0.913211i
$593$	3.80259	+	2.19543i	0.156154	+	0.0901554i	0.576041	−	0.817421i	$-0.304597\pi$
$593$	3.80259	+	2.19543i	0.156154	+	0.0901554i	−0.419887	+	0.907576i	$0.637930\pi$
$594$	−2.60897	−	46.9603i	−0.107047	−	1.92680i
$595$	2.44596	−	5.05527i	0.100274	−	0.207246i
$596$	−10.6380	−	2.26154i	−0.435750	−	0.0926363i
$597$	−3.39192	−	1.72378i	−0.138822	−	0.0705495i
$598$	1.20268	−	11.4409i	0.0491812	−	0.467855i
$599$	16.7535	−	19.9660i	0.684528	−	0.815789i	−0.306154	−	0.951982i	$-0.599042\pi$
$599$	16.7535	−	19.9660i	0.684528	−	0.815789i	0.990682	+	0.136193i	$0.0434867\pi$
$600$	−1.77759	+	20.5556i	−0.0725700	+	0.839179i
$601$	−33.5889	+	5.92263i	−1.37012	+	0.241589i	−0.809809	−	0.586693i	$-0.800429\pi$
$601$	−33.5889	+	5.92263i	−1.37012	+	0.241589i	−0.560311	+	0.828282i	$0.689318\pi$
$602$	4.72375	−	3.71447i	0.192526	−	0.151391i
$603$	11.5956	+	23.6481i	0.472209	+	0.963025i
$604$	−42.6384	−	17.2286i	−1.73493	−	0.701024i
$605$	26.2024	−	4.62020i	1.06528	−	0.187838i
$606$	−1.34240	+	26.1325i	−0.0545314	+	1.06156i
$607$	−9.04113	+	3.29070i	−0.366968	+	0.133566i	−0.518921	−	0.854822i	$-0.673666\pi$
$607$	−9.04113	+	3.29070i	−0.366968	+	0.133566i	0.151953	+	0.988388i	$0.451444\pi$
$608$	4.33407	+	24.5913i	0.175770	+	0.997309i
$609$	24.3376	+	1.17302i	0.986210	+	0.0475332i
$610$	6.49541	−	6.27235i	0.262992	−	0.253960i
$611$	31.9492	−	18.4459i	1.29253	−	0.746240i
$612$	14.3059	−	1.03015i	0.578280	−	0.0416414i
$613$	22.7792	−	39.4548i	0.920044	−	1.59356i	0.120700	−	0.992689i	$-0.461486\pi$
$613$	22.7792	−	39.4548i	0.920044	−	1.59356i	0.799344	−	0.600874i	$-0.205181\pi$
$614$	5.21641	−	5.03726i	0.210517	−	0.203287i
$615$	−16.3243	+	3.78685i	−0.658259	+	0.152701i
$616$	−28.2724	−	38.6610i	−1.13913	−	1.55770i
$617$	−1.94339	+	11.0215i	−0.0782379	+	0.443709i	0.920374	+	0.391039i	$0.127884\pi$
$617$	−1.94339	+	11.0215i	−0.0782379	+	0.443709i	−0.998612	+	0.0526700i	$0.983227\pi$
$618$	−4.85007	+	3.66267i	−0.195098	+	0.147334i
$619$	−16.1500	−	5.87812i	−0.649124	−	0.236262i	−0.00359002	−	0.999994i	$-0.501143\pi$
$619$	−16.1500	−	5.87812i	−0.649124	−	0.236262i	−0.645534	+	0.763732i	$0.723365\pi$
$620$	3.38386	+	1.36730i	0.135899	+	0.0549119i
$621$	8.37816	+	4.99819i	0.336204	+	0.200570i
$622$	2.68726	−	5.50947i	0.107749	−	0.220910i
$623$	10.8220	−	38.1941i	0.433574	−	1.53021i
$624$	−22.6739	−	19.6708i	−0.907681	−	0.787462i
$625$	10.5676	+	8.86724i	0.422703	+	0.354690i
$626$	−17.2797	−	38.8125i	−0.690634	−	1.55126i
$627$	−46.8110	−	14.2577i	−1.86945	−	0.569399i
$628$	4.26671	−	1.38619i	0.170260	−	0.0553148i
$629$	−13.8718	+	8.00890i	−0.553106	+	0.319336i
$630$	0.989942	−	9.91786i	0.0394403	−	0.395137i
$631$	−9.26795	−	5.35085i	−0.368951	−	0.213014i	0.304049	−	0.952656i	$-0.401661\pi$
$631$	−9.26795	−	5.35085i	−0.368951	−	0.213014i	−0.673000	+	0.739642i	$0.734995\pi$
$632$	10.7265	+	8.38132i	0.426678	+	0.333391i
$633$	−1.01942	+	8.37533i	−0.0405183	+	0.332890i
$634$	11.0119	+	8.00092i	0.437340	+	0.317757i
$635$	−4.57319	+	1.66451i	−0.181482	+	0.0660539i
$636$	19.6228	−	35.4858i	0.778094	−	1.40710i
$637$	−28.7845	+	9.55339i	−1.14048	+	0.378519i
$638$	−39.8997	+	26.9117i	−1.57964	+	1.06545i
$639$	3.74414	+	34.9163i	0.148116	+	1.38127i
$640$	5.32450	−	8.51884i	0.210469	−	0.336737i
$641$	31.4854	−	26.4194i	1.24360	−	1.04350i	0.246363	−	0.969178i	$-0.420764\pi$
$641$	31.4854	−	26.4194i	1.24360	−	1.04350i	0.997234	−	0.0743247i	$-0.0236801\pi$
$642$	−8.53129	−	27.8016i	−0.336703	−	1.09724i
$643$	22.2519	−	8.09904i	0.877530	−	0.319395i	0.136318	−	0.990665i	$-0.456473\pi$
$643$	22.2519	−	8.09904i	0.877530	−	0.319395i	0.741213	+	0.671270i	$0.234251\pi$
$644$	9.92763	−	0.377647i	0.391204	−	0.0148814i
$645$	−2.07013	+	1.34745i	−0.0815112	+	0.0530560i
$646$	4.11351	−	14.3446i	0.161844	−	0.564382i
$647$	17.4275	+	30.1852i	0.685144	+	1.18670i	0.973392	+	0.229148i	$0.0735940\pi$
$647$	17.4275	+	30.1852i	0.685144	+	1.18670i	−0.288248	+	0.957556i	$0.593073\pi$
$648$	23.2118	−	10.4505i	0.911846	−	0.410533i
$649$	10.5518	+	6.09208i	0.414194	+	0.239135i
$650$	−25.0389	+	6.24248i	−0.982108	+	0.244850i
$651$	8.68445	+	3.64337i	0.340370	+	0.142795i
$652$	−3.18289	−	5.98662i	−0.124652	−	0.234454i
$653$	−2.08356	+	11.8165i	−0.0815362	+	0.462415i	0.916514	+	0.400002i	$0.130991\pi$
$653$	−2.08356	+	11.8165i	−0.0815362	+	0.462415i	−0.998050	+	0.0624126i	$0.980121\pi$
$654$	3.24203	−	14.1095i	0.126774	−	0.551724i
$655$	8.55264	+	10.1926i	0.334179	+	0.398259i
$656$	−42.2889	−	10.5467i	−1.65111	−	0.411780i
$657$	3.65753	+	34.1086i	0.142694	+	1.33070i
$658$	19.6933	+	25.0442i	0.767723	+	0.976324i
$659$	−13.6245	+	37.4331i	−0.530736	+	1.45819i	0.327460	+	0.944865i	$0.393807\pi$
$659$	−13.6245	+	37.4331i	−0.530736	+	1.45819i	−0.858196	+	0.513321i	$0.828415\pi$
$660$	10.1568	+	16.8647i	0.395351	+	0.656457i
$661$	38.8772	+	6.85510i	1.51215	+	0.266632i	0.867341	−	0.497714i	$-0.165827\pi$
$661$	38.8772	+	6.85510i	1.51215	+	0.266632i	0.644806	+	0.764346i	$0.276938\pi$
$662$	3.72376	−	5.12514i	0.144728	−	0.199194i
$663$	7.02671	+	16.5056i	0.272895	+	0.641024i
$664$	23.6040	+	3.31849i	0.916012	+	0.128782i
$665$	−9.33485	−	4.51660i	−0.361990	−	0.175146i
$666$	−18.2279	+	21.8156i	−0.706318	+	0.845336i
$667$		−	9.98281i		−	0.386536i
$668$	−19.6484	−	4.17707i	−0.760221	−	0.161616i
$669$	0.0173021	−	0.0568064i	0.000668939	−	0.00219626i
$670$	−8.91897	−	6.48023i	−0.344570	−	0.250353i
$671$	−7.99169	+	45.3231i	−0.308516	+	1.74968i
$672$	14.0290	−	21.7988i	0.541180	−	0.840907i
$673$	−9.08170	+	7.62046i	−0.350074	+	0.293747i	−0.800820	−	0.598905i	$-0.795603\pi$
$673$	−9.08170	+	7.62046i	−0.350074	+	0.293747i	0.450746	+	0.892652i	$0.351158\pi$
$674$	1.67864	+	2.48877i	0.0646587	+	0.0958637i
$675$	4.10782	−	21.4949i	0.158110	−	0.827339i
$676$	4.32463	−	10.7028i	0.166332	−	0.411647i
$677$	−31.2812	+	5.51572i	−1.20224	+	0.211987i	−0.738664	−	0.674073i	$-0.764543\pi$
$677$	−31.2812	+	5.51572i	−1.20224	+	0.211987i	−0.463571	+	0.886060i	$0.653432\pi$
$678$	6.36831	+	2.69540i	0.244573	+	0.103516i
$679$	18.3868	−	25.4754i	0.705620	−	0.977658i
$680$	−5.09155	+	3.18121i	−0.195252	+	0.121994i
$681$	6.35562	−	20.8668i	0.243548	−	0.799617i
$682$	−18.0493	+	4.49989i	−0.691144	+	0.172310i
$683$	−9.78171	−	5.64747i	−0.374287	−	0.216094i	0.301043	−	0.953611i	$-0.402665\pi$
$683$	−9.78171	−	5.64747i	−0.374287	−	0.216094i	−0.675330	+	0.737516i	$0.735999\pi$
$684$	−1.90224	−	26.4166i	−0.0727338	−	1.01006i
$685$	−4.77860	−	2.75893i	−0.182581	−	0.105413i
$686$	−11.7030	−	23.4316i	−0.446823	−	0.894622i
$687$	0.261282	−	2.14664i	0.00996853	−	0.0818994i
$688$	−6.38901	+	0.671096i	−0.243579	+	0.0255853i
$689$	49.9463	+	8.80687i	1.90280	+	0.335515i
$690$	−4.07821	−	0.209494i	−0.155255	−	0.00797530i
$691$	−7.70465	+	6.46497i	−0.293099	+	0.245939i	−0.777465	−	0.628926i	$-0.783495\pi$
$691$	−7.70465	+	6.46497i	−0.293099	+	0.245939i	0.484366	+	0.874865i	$0.339050\pi$
$692$	−2.05416	−	14.6195i	−0.0780874	−	0.555750i
$693$	25.6312	+	43.8611i	0.973650	+	1.66614i
$694$	−1.03936	−	14.8670i	−0.0394537	−	0.564345i
$695$	1.94653	−	5.34804i	0.0738361	−	0.202863i
$696$	−21.3524	−	14.9192i	−0.809362	−	0.565511i
$697$	19.9531	+	16.7426i	0.755776	+	0.634171i
$698$	−11.4046	−	25.6163i	−0.431672	−	0.969592i
$699$	0.618941	+	11.5770i	0.0234105	+	0.437884i
$700$	−8.41260	−	20.6366i	−0.317967	−	0.779991i
$701$	8.93380			0.337425			0.168712	−	0.985665i	$-0.446039\pi$
$701$	8.93380			0.337425			0.168712	+	0.985665i	$0.446039\pi$
$702$	21.7867	+	23.2167i	0.822284	+	0.876259i
$703$	14.7889	+	25.6151i	0.557774	+	0.966092i
$704$	3.56678	+	51.0783i	0.134428	+	1.92509i
$705$	−7.14389	−	10.9753i	−0.269054	−	0.413355i
$706$	−5.10941	+	7.03226i	−0.192295	+	0.264662i
$707$	−11.5770	−	25.7838i	−0.435399	−	0.969698i
$708$	−1.02497	+	6.51438i	−0.0385206	+	0.244825i
$709$	13.0743	+	4.75867i	0.491017	+	0.178716i	0.575649	−	0.817697i	$-0.304749\pi$
$709$	13.0743	+	4.75867i	0.491017	+	0.178716i	−0.0846323	+	0.996412i	$0.526972\pi$
$710$	−8.21941	−	12.1862i	−0.308469	−	0.457340i
$711$	−10.4072	−	10.0079i	−0.390301	−	0.375325i
$712$	−31.5394	+	28.3954i	−1.18199	+	1.06416i
$713$	1.31968	−	3.62580i	0.0494225	−	0.135787i
$714$	−13.2458	+	8.03451i	−0.495713	+	0.300684i
$715$	−15.8274	+	18.8623i	−0.591910	+	0.705411i
$716$	24.4055	−	39.0541i	0.912074	−	1.45952i
$717$	−23.0727	−	17.3485i	−0.861666	−	0.647892i
$718$	2.15979	−	7.53164i	0.0806028	−	0.281078i
$719$	24.1547	+	41.8372i	0.900819	+	1.56026i	0.826433	+	0.563035i	$0.190366\pi$
$719$	24.1547	+	41.8372i	0.900819	+	1.56026i	0.0743859	+	0.997230i	$0.476300\pi$
$720$	−6.54294	+	8.40988i	−0.243841	+	0.313418i
$721$	2.85917	−	5.90930i	0.106481	−	0.220074i
$722$	−0.659145	−	0.189018i	−0.0245308	−	0.00703453i
$723$	−18.0112	+	16.8312i	−0.669844	+	0.625958i
$724$	−21.3317	−	0.745607i	−0.792786	−	0.0277103i
$725$	−21.0427	+	7.65890i	−0.781505	+	0.284444i
$726$	−67.5923	−	28.6086i	−2.50858	−	1.06177i
$727$	−26.8269	+	22.5104i	−0.994954	+	0.834866i	−0.986277	−	0.165097i	$-0.947206\pi$
$727$	−26.8269	+	22.5104i	−0.994954	+	0.834866i	−0.00867661	+	0.999962i	$0.502762\pi$
$728$	31.4836	+	7.74619i	1.16686	+	0.287093i
$729$	−25.6253	+	8.50538i	−0.949087	+	0.315014i
$730$	−8.02929	−	11.9043i	−0.297177	−	0.440599i
$731$	3.60768	+	1.31309i	0.133435	+	0.0485663i
$732$	−24.4465	+	4.77779i	−0.903568	+	0.176592i
$733$	15.8834	−	18.9292i	0.586669	−	0.699164i	−0.388293	−	0.921536i	$-0.626935\pi$
$733$	15.8834	−	18.9292i	0.586669	−	0.699164i	0.974962	+	0.222371i	$0.0713797\pi$
$734$	2.72495	−	25.9221i	0.100580	−	0.956802i
$735$	3.93183	+	10.0221i	0.145028	+	0.369670i
$736$	−9.19742	−	5.31112i	−0.339022	−	0.195771i
$737$	56.1907			2.06981
$738$	43.4731	+	15.7202i	1.60027	+	0.578669i
$739$			36.5503i			1.34452i	0.740313	+	0.672262i	$0.234677\pi$
$739$			36.5503i			1.34452i	−0.740313	+	0.672262i	$0.765323\pi$
$740$	2.47444	−	11.6395i	0.0909623	−	0.427876i
$741$	30.4785	−	12.9752i	1.11966	−	0.476657i
$742$	−1.39150	+	43.7768i	−0.0510834	+	1.60710i
$743$	−4.52551	+	5.39330i	−0.166025	+	0.197861i	−0.842642	−	0.538474i	$-0.819001\pi$
$743$	−4.52551	+	5.39330i	−0.166025	+	0.197861i	0.676617	+	0.736335i	$0.263445\pi$
$744$	−5.78303	−	8.24141i	−0.212016	−	0.302145i
$745$	−4.75517	+	0.838466i	−0.174216	+	0.0307190i
$746$	0.570657	−	1.16997i	0.0208933	−	0.0428358i
$747$	−24.5439	−	6.06465i	−0.898013	−	0.221894i
$748$	11.4638	−	28.3713i	0.419158	−	1.03736i
$749$	21.8910	+	22.5265i	0.799881	+	0.823101i
$750$	5.87758	+	19.1537i	0.214619	+	0.699394i
$751$	32.9223	+	5.80509i	1.20135	+	0.211831i	0.738283	−	0.674491i	$-0.235637\pi$
$751$	32.9223	+	5.80509i	1.20135	+	0.211831i	0.463069	+	0.886322i	$0.346748\pi$
$752$	−3.55799	−	33.8730i	−0.129747	−	1.23522i
$753$	−0.0927767	−	1.73535i	−0.00338097	−	0.0632397i
$754$	8.98054	−	31.3169i	0.327052	−	1.14050i
$755$	−20.4172			−0.743059
$756$	−17.1691	+	21.4761i	−0.624434	+	0.781077i
$757$	−35.4889			−1.28987			−0.644933	−	0.764239i	$-0.723115\pi$
$757$	−35.4889			−1.28987			−0.644933	+	0.764239i	$0.723115\pi$
$758$	−9.09517	+	31.7167i	−0.330352	+	1.15200i
$759$	17.4437	−	11.3542i	0.633166	−	0.412131i
$760$	5.87429	+	9.40184i	0.213083	+	0.341041i
$761$	27.3094	+	4.81538i	0.989963	+	0.174557i	0.645102	−	0.764096i	$-0.276815\pi$
$761$	27.3094	+	4.81538i	0.989963	+	0.174557i	0.344861	+	0.938654i	$0.387926\pi$
$762$	13.0843	+	3.00648i	0.473995	+	0.108913i
$763$	3.83069	+	15.1606i	0.138680	+	0.548852i
$764$	11.0231	+	4.45403i	0.398801	+	0.161141i
$765$	5.71750	−	2.80352i	0.206717	−	0.101361i
$766$	6.21941	−	12.7512i	0.224716	−	0.460718i
$767$	−8.12263	+	1.43224i	−0.293291	+	0.0517151i
$768$	−25.1055	+	11.7351i	−0.905917	+	0.423455i
$769$	−21.8235	+	26.0082i	−0.786974	+	0.937879i	−0.999226	−	0.0393358i	$-0.987476\pi$
$769$	−21.8235	+	26.0082i	−0.786974	+	0.937879i	0.212252	+	0.977215i	$0.431920\pi$
$770$	−18.0684	−	11.2119i	−0.651140	−	0.404048i
$771$	2.08683	−	17.1450i	0.0751554	−	0.617461i
$772$	−25.9492	−	5.51655i	−0.933933	−	0.198545i
$773$		−	9.46459i		−	0.340418i	−0.985408	−	0.170209i	$-0.945556\pi$
$773$		−	9.46459i		−	0.340418i	0.985408	−	0.170209i	$-0.0544442\pi$
$774$	6.81384	−	0.0142270i	0.244918	−	0.000511380i
$775$	−8.65524			−0.310906
$776$	−31.1419	+	12.5804i	−1.11793	+	0.451609i
$777$	6.78170	−	29.9480i	0.243292	−	1.07438i
$778$	−2.30930	+	21.9682i	−0.0827926	+	0.787597i
$779$	30.9162	−	36.8445i	1.10769	−	1.32009i
$780$	−12.6052	−	4.32596i	−0.451340	−	0.154894i
$781$	70.4008	+	25.6238i	2.51914	+	0.916892i
$782$	3.54922	+	5.26212i	0.126920	+	0.188173i
$783$	20.9084	+	18.0599i	0.747207	+	0.645408i
$784$	−2.75326	+	27.8643i	−0.0983306	+	0.995154i
$785$	1.52578	−	1.28028i	0.0544574	−	0.0456952i
$786$	−4.51092	−	36.4265i	−0.160899	−	1.29929i
$787$	−34.5582	+	12.5781i	−1.23187	+	0.448362i	−0.874236	−	0.485501i	$-0.838637\pi$
$787$	−34.5582	+	12.5781i	−1.23187	+	0.448362i	−0.357630	+	0.933863i	$0.616415\pi$
$788$	1.26387	−	36.1592i	0.0450236	−	1.28812i
$789$	−0.563088	−	2.42735i	−0.0200465	−	0.0864159i
$790$	5.80950	+	1.66595i	0.206693	+	0.0592718i
$791$	−7.44944	+	0.544481i	−0.264872	+	0.0193595i
$792$	1.78376	−	54.2794i	0.0633833	−	1.92873i
$793$	−15.5771	−	26.9804i	−0.553161	−	0.958102i
$794$	−3.02572	+	10.5513i	−0.107379	+	0.374451i
$795$	2.17522	−	17.8711i	0.0771470	−	0.633823i
$796$	−3.72575	−	2.32827i	−0.132056	−	0.0825234i
$797$	19.8466	−	23.6523i	0.703003	−	0.837806i	−0.289860	−	0.957069i	$-0.593609\pi$
$797$	19.8466	−	23.6523i	0.703003	−	0.837806i	0.992863	+	0.119263i	$0.0380532\pi$
$798$	14.8362	+	24.4592i	0.525195	+	0.865846i
$799$	−6.96168	+	19.1271i	−0.246287	+	0.676667i
$800$	−4.13891	+	23.4619i	−0.146333	+	0.829503i
$801$	36.3604	−	26.5345i	1.28473	−	0.937550i
$802$	−24.0526	−	35.6607i	−0.849327	−	1.25922i
$803$	68.7724	+	25.0311i	2.42692	+	0.883328i
$804$	10.9278	+	28.3814i	0.385394	+	1.00093i
$805$	4.02378	−	1.80670i	0.141820	−	0.0636778i
$806$	7.40172	−	10.1872i	0.260714	−	0.358831i
$807$	−14.6156	+	0.781388i	−0.514492	+	0.0275062i
$808$	−4.20657	+	29.9208i	−0.147986	+	1.05261i
$809$	−12.4121	−	21.4984i	−0.436387	−	0.755845i	0.561020	−	0.827802i	$-0.310409\pi$
$809$	−12.4121	−	21.4984i	−0.436387	−	0.755845i	−0.997408	+	0.0719570i	$0.977076\pi$
$810$	7.81666	−	8.16259i	0.274649	−	0.286804i
$811$	31.7937			1.11643			0.558214	−	0.829697i	$-0.311487\pi$
$811$	31.7937			1.11643			0.558214	+	0.829697i	$0.311487\pi$
$812$	27.8735	+	3.82887i	0.978169	+	0.134367i
$813$	28.6332	−	18.6375i	1.00421	−	0.653644i
$814$	24.6679	+	55.4074i	0.864610	+	1.94203i
$815$	−2.30594	−	1.93492i	−0.0807737	−	0.0677772i
$816$	16.5595	+	0.272689i	0.579699	+	0.00954601i
$817$	2.42469	−	6.66179i	0.0848293	−	0.233067i
$818$	1.20286	+	17.2056i	0.0420569	+	0.601581i
$819$	−32.3767	−	11.5920i	−1.13133	−	0.405056i
$820$	−19.1620	+	2.69241i	−0.669165	+	0.0940230i
$821$	−4.07630	+	3.42042i	−0.142264	+	0.119374i	−0.711142	−	0.703048i	$-0.751822\pi$
$821$	−4.07630	+	3.42042i	−0.142264	+	0.119374i	0.568878	+	0.822422i	$0.307377\pi$
$822$	6.92451	+	13.5554i	0.241520	+	0.472798i
$823$	21.3576	+	3.76592i	0.744478	+	0.131272i	0.533005	−	0.846112i	$-0.321063\pi$
$823$	21.3576	+	3.76592i	0.744478	+	0.131272i	0.211473	+	0.977384i	$0.432174\pi$
$824$	−5.95171	+	3.71864i	−0.207337	+	0.129545i
$825$	−37.3163	−	28.0584i	−1.29919	−	0.976866i
$826$	−2.22230	−	6.76735i	−0.0773235	−	0.235466i
$827$	−21.2440	−	12.2652i	−0.738725	−	0.426503i	0.0828805	−	0.996559i	$-0.473588\pi$
$827$	−21.2440	−	12.2652i	−0.738725	−	0.426503i	−0.821606	+	0.570056i	$0.806921\pi$
$828$	9.12729	+	6.60252i	0.317195	+	0.229453i
$829$	−22.2330	−	12.8362i	−0.772185	−	0.445821i	0.0614684	−	0.998109i	$-0.480422\pi$
$829$	−22.2330	−	12.8362i	−0.772185	−	0.445821i	−0.833654	+	0.552288i	$0.813755\pi$
$830$	10.2683	−	2.55999i	0.356417	−	0.0888585i
$831$	24.1971	−	5.61316i	0.839388	−	0.194718i
$832$	−24.0752	−	24.9354i	−0.834658	−	0.864481i
$833$	8.77785	−	14.2463i	0.304134	−	0.493603i
$834$	−12.5288	+	9.46147i	−0.433836	+	0.327624i
$835$	−8.78281	+	1.54865i	−0.303942	+	0.0535931i
$836$	−52.3892	−	21.1686i	−1.81192	−	0.732131i
$837$	5.20659	+	9.32342i	0.179966	+	0.322265i
$838$	−4.27016	−	6.33099i	−0.147510	−	0.218700i
$839$	−1.85141	+	1.55352i	−0.0639177	+	0.0536333i	−0.674187	−	0.738561i	$-0.735506\pi$
$839$	−1.85141	+	1.55352i	−0.0639177	+	0.0536333i	0.610269	+	0.792194i	$0.291061\pi$
$840$	2.14912	−	11.3066i	0.0741517	−	0.390116i
$841$	−0.126552	+	0.717712i	−0.00436386	+	0.0247487i
$842$	42.1492	+	30.6242i	1.45256	+	1.05538i
$843$	19.5790	+	20.9517i	0.674336	+	0.721614i
$844$	−2.02586	+	9.52942i	−0.0697330	+	0.328016i
$845$		−	5.12500i		−	0.176305i
$846$	0.0754283	+	36.1253i	0.00259328	+	1.24202i
$847$	79.0673	−	5.77904i	2.71678	−	0.198570i
$848$	26.1856	−	38.8163i	0.899216	−	1.33296i
$849$	30.7039	−	40.8348i	1.05376	−	1.40145i
$850$	8.36897	−	11.5185i	0.287053	−	0.395081i
$851$	−12.3894	−	2.18458i	−0.424702	−	0.0748864i
$852$	0.749023	+	40.5420i	0.0256611	+	1.38895i
$853$	7.94887	−	21.8393i	0.272164	−	0.747764i	−0.726028	−	0.687665i	$-0.758636\pi$
$853$	7.94887	−	21.8393i	0.272164	−	0.747764i	0.998192	−	0.0600997i	$-0.0191419\pi$
$854$	21.1493	−	16.6305i	0.723714	−	0.569085i
$855$	−5.17686	−	10.5577i	−0.177045	−	0.361065i
$856$	−6.98008	−	32.8465i	−0.238574	−	1.12267i
$857$	−24.9011	−	29.6760i	−0.850607	−	1.01371i	−0.999690	−	0.0248889i	$-0.992077\pi$
$857$	−24.9011	−	29.6760i	−0.850607	−	1.01371i	0.149084	−	0.988825i	$-0.452368\pi$
$858$	64.9366	−	19.9267i	2.21690	−	0.680286i
$859$	5.62707	−	31.9127i	0.191993	−	1.08885i	−0.724643	−	0.689125i	$-0.757995\pi$
$859$	5.62707	−	31.9127i	0.191993	−	1.08885i	0.916636	−	0.399723i	$-0.130894\pi$
$860$	−2.51834	+	1.33892i	−0.0858747	+	0.0456568i
$861$	−49.5339	+	6.29324i	−1.68811	+	0.214473i
$862$	−10.5600	+	2.63271i	−0.359674	+	0.0896705i
$863$	−9.07263	−	5.23808i	−0.308836	−	0.178306i	0.337570	−	0.941301i	$-0.390395\pi$
$863$	−9.07263	−	5.23808i	−0.308836	−	0.178306i	−0.646405	+	0.762994i	$0.723729\pi$
$864$	27.7629	−	9.65514i	0.944513	−	0.328475i
$865$	−3.27721	−	5.67629i	−0.111428	−	0.193000i
$866$	−2.60202	+	9.07378i	−0.0884203	+	0.308339i
$867$	17.4260	+	8.85592i	0.591818	+	0.300763i
$868$	9.61761	+	5.07541i	0.326443	+	0.172271i
$869$	−28.9459	+	10.5354i	−0.981923	+	0.357391i
$870$	−11.2710	−	2.58981i	−0.382121	−	0.0878028i
$871$	−29.1386	+	24.4501i	−0.987322	+	0.828462i
$872$	5.16653	−	15.8983i	0.174961	−	0.538386i
$873$	34.2236	−	9.89142i	1.15829	−	0.334774i
$874$	9.71680	−	6.55384i	0.328676	−	0.221687i
$875$	−15.0817	−	15.5195i	−0.509854	−	0.524655i
$876$	0.731697	+	39.6042i	0.0247217	+	1.33810i
$877$	17.0415	−	6.20260i	0.575450	−	0.209447i	−0.0378677	−	0.999283i	$-0.512057\pi$
$877$	17.0415	−	6.20260i	0.575450	−	0.209447i	0.613318	+	0.789836i	$0.289834\pi$
$878$	−20.6111	−	14.9753i	−0.695591	−	0.505393i
$879$	−15.6399	−	11.7598i	−0.527522	−	0.396647i
$880$	9.96399	+	20.4325i	0.335886	+	0.688781i
$881$	27.3571	+	15.7946i	0.921682	+	0.532134i	0.884171	−	0.467163i	$-0.154724\pi$
$881$	27.3571	+	15.7946i	0.921682	+	0.532134i	0.0375110	+	0.999296i	$0.488057\pi$
$882$	5.93094	−	29.1002i	0.199705	−	0.979856i
$883$	−21.1717	+	12.2235i	−0.712485	+	0.411353i	−0.811980	−	0.583685i	$-0.801610\pi$
$883$	−21.1717	+	12.2235i	−0.712485	+	0.411353i	0.0994955	+	0.995038i	$0.468277\pi$
$884$	6.40041	+	19.7006i	0.215269	+	0.662603i
$885$	0.661608	+	2.85205i	0.0222397	+	0.0958706i
$886$	3.16478	+	7.10851i	0.106323	+	0.238815i
$887$	2.78994	+	2.34104i	0.0936770	+	0.0786043i	0.688423	−	0.725309i	$-0.258303\pi$
$887$	2.78994	+	2.34104i	0.0936770	+	0.0786043i	−0.594746	+	0.803913i	$0.702748\pi$
$888$	−23.1884	+	23.2350i	−0.778152	+	0.779716i
$889$	−14.0591	+	3.55237i	−0.471528	+	0.119143i
$890$	−8.25986	+	16.9345i	−0.276871	+	0.567647i
$891$	−7.77668	+	57.0757i	−0.260529	+	1.91211i
$892$	0.0256886	−	0.0635757i	0.000860119	−	0.00212867i
$893$	35.3192	+	12.8552i	1.18191	+	0.430181i
$894$	12.2665	+	5.19184i	0.410254	+	0.173641i
$895$	3.55043	−	20.1355i	0.118678	−	0.673055i
$896$	18.3571	−	23.6435i	0.613267	−	0.789875i
$897$	−4.10518	+	13.4781i	−0.137068	+	0.450022i
$898$	−1.51304	+	1.46107i	−0.0504907	+	0.0487567i
$899$	5.46360	−	9.46324i	0.182221	−	0.315617i
$900$	6.91483	−	24.3048i	0.230494	−	0.810161i
$901$	−24.2335	+	13.9912i	−0.807334	+	0.466114i
$902$	70.9461	−	68.5096i	2.36225	−	2.28112i
$903$	−6.54354	+	3.36879i	−0.217755	+	0.112106i
$904$	7.05018	+	3.74909i	0.234486	+	0.124693i
$905$	−8.90495	+	3.24114i	−0.296011	+	0.107739i
$906$	47.2683	+	30.6268i	1.57038	+	1.01751i
$907$	−0.433849	+	0.0764993i	−0.0144057	+	0.00254012i	−0.180846	−	0.983511i	$-0.557884\pi$
$907$	−0.433849	+	0.0764993i	−0.0144057	+	0.00254012i	0.166441	+	0.986051i	$0.446773\pi$
$908$	9.43625	−	23.3534i	0.313153	−	0.775009i
$909$	7.68764	−	31.1122i	0.254983	−	1.03193i
$910$	14.2483	−	2.04798i	0.472325	−	0.0678897i
$911$	16.8758	−	2.97565i	0.559119	−	0.0985878i	0.113055	−	0.993589i	$-0.463936\pi$
$911$	16.8758	−	2.97565i	0.559119	−	0.0985878i	0.446064	+	0.895001i	$0.352825\pi$
$912$	0.503535	−	30.5781i	0.0166737	−	1.01254i
$913$	−34.6706	+	41.3188i	−1.14743	+	1.36745i
$914$	−4.04882	+	38.5160i	−0.133923	+	1.27400i
$915$	−9.26842	+	6.03286i	−0.306405	+	0.199440i
$916$	0.519238	−	2.44244i	0.0171561	−	0.0807003i
$917$	22.2729	+	32.7978i	0.735517	+	1.08308i
$918$	−17.4421	−	2.08605i	−0.575675	−	0.0688499i
$919$	36.7839	+	21.2372i	1.21339	+	0.700550i	0.963496	−	0.267723i	$-0.0862712\pi$
$919$	36.7839	+	21.2372i	1.21339	+	0.700550i	0.249893	+	0.968273i	$0.419605\pi$
$920$	−4.66940	−	0.656472i	−0.153946	−	0.0216432i
$921$	−7.44339	+	4.84493i	−0.245268	+	0.159646i
$922$	−7.75429	−	17.4172i	−0.255374	−	0.573604i
$923$	−47.6571	+	17.3458i	−1.56865	+	0.570943i
$924$	25.0121	+	53.0603i	0.822839	+	1.74556i
$925$	4.90038	+	27.7914i	0.161123	+	0.913776i
$926$	−21.2147	−	10.3475i	−0.697158	−	0.340040i
$927$	6.68340	−	3.27714i	0.219512	−	0.107635i
$928$	−23.0394	−	19.3355i	−0.756307	−	0.634720i
$929$	21.0205	+	25.0512i	0.689659	+	0.821903i	0.991314	−	0.131514i	$-0.0419837\pi$
$929$	21.0205	+	25.0512i	0.689659	+	0.821903i	−0.301656	+	0.953417i	$0.597539\pi$
$930$	−3.75130	−	2.43060i	−0.123010	−	0.0797025i
$931$	−26.3065	−	16.2088i	−0.862162	−	0.531222i
$932$	−0.467634	+	13.3789i	−0.0153179	+	0.438242i
$933$	−4.51185	+	6.00055i	−0.147711	+	0.196449i
$934$	0.887664	+	0.254549i	0.0290453	+	0.00832910i
$935$		−	13.5855i		−	0.444292i
$936$	22.6935	+	28.9236i	0.741760	+	0.945397i
$937$	19.4399	−	11.2236i	0.635073	−	0.366659i	−0.147641	−	0.989041i	$-0.547168\pi$
$937$	19.4399	−	11.2236i	0.635073	−	0.366659i	0.782714	+	0.622382i	$0.213835\pi$
$938$	−24.4805	−	21.9039i	−0.799315	−	0.715188i
$939$	11.7583	+	50.6876i	0.383719	+	1.65413i
$940$	−7.09864	−	13.3516i	−0.231532	−	0.435483i
$941$	−19.6425	−	53.9674i	−0.640329	−	1.75929i	−0.650692	−	0.759342i	$-0.725521\pi$
$941$	−19.6425	−	53.9674i	−0.640329	−	1.75929i	0.0103631	−	0.999946i	$-0.496701\pi$
$942$	−5.45284	+	0.675260i	−0.177663	+	0.0220011i
$943$	3.55239	+	20.1466i	0.115682	+	0.656064i
$944$	−1.84264	+	7.38839i	−0.0599727	+	0.240471i
$945$	−3.49539	+	11.6961i	−0.113705	+	0.380474i
$946$	6.37281	−	13.0657i	0.207198	−	0.424801i
$947$	−42.8185	+	7.55006i	−1.39142	+	0.245344i	−0.818611	−	0.574348i	$-0.805256\pi$
$947$	−42.8185	+	7.55006i	−1.39142	+	0.245344i	−0.572804	+	0.819692i	$0.694145\pi$
$948$	−10.9507	−	12.5714i	−0.355661	−	0.408300i
$949$	−46.5547	+	16.9445i	−1.51123	+	0.550043i
$950$	−21.2696	−	15.4538i	−0.690076	−	0.501387i
$951$	−11.3823	−	12.1803i	−0.369096	−	0.394973i
$952$	−16.0539	+	7.89170i	−0.520311	+	0.255771i
$953$	12.2941	+	21.2939i	0.398244	+	0.689779i	0.993509	−	0.113751i	$-0.0362865\pi$
$953$	12.2941	+	21.2939i	0.398244	+	0.689779i	−0.595266	+	0.803529i	$0.702953\pi$
$954$	−31.8434	+	38.1108i	−1.03097	+	1.23388i
$955$	5.27835			0.170803
$956$	−24.7706	−	22.3050i	−0.801138	−	0.721395i
$957$	54.2335	−	23.0881i	1.75312	−	0.746333i
$958$	−55.4547	+	24.6890i	−1.79166	+	0.797664i
$959$	−13.3316	−	9.62199i	−0.430499	−	0.310710i
$960$	−8.38251	+	9.00638i	−0.270544	+	0.290680i
$961$	−20.5120	+	17.2116i	−0.661677	+	0.555213i
$962$	−36.9012	−	17.9987i	−1.18974	−	0.580301i
$963$	3.79750	+	35.4139i	0.122373	+	1.14120i
$964$	−22.4313	+	17.5241i	−0.722463	+	0.564412i
$965$	−11.5993	+	2.04526i	−0.373393	+	0.0658393i
$966$	−12.0257	−	1.85315i	−0.386919	−	0.0596240i
$967$	19.1882	+	52.7190i	0.617049	+	1.69533i	0.714094	+	0.700049i	$0.246839\pi$
$967$	19.1882	+	52.7190i	0.617049	+	1.69533i	−0.0970451	+	0.995280i	$0.530939\pi$
$968$	−74.8296	−	39.7922i	−2.40511	−	1.27897i
$969$	−8.28027	+	16.2933i	−0.266000	+	0.523416i
$970$	−10.7267	+	10.3583i	−0.344414	+	0.332586i
$971$	−3.60226	+	6.23930i	−0.115602	+	0.200229i	−0.918020	−	0.396533i	$-0.870213\pi$
$971$	−3.60226	+	6.23930i	−0.115602	+	0.200229i	0.802418	+	0.596762i	$0.203546\pi$
$972$	−30.3408	+	7.17200i	−0.973181	+	0.230042i
$973$	7.38586	−	15.2650i	0.236780	−	0.489373i
$974$	3.89365	−	0.970729i	0.124761	−	0.0311042i
$975$	31.5599	−	1.68728i	1.01073	−	0.0540362i
$976$	−28.6050	+	3.00465i	−0.915625	+	0.0961764i
$977$	−8.17184	−	6.85699i	−0.261440	−	0.219374i	0.502640	−	0.864496i	$-0.332362\pi$
$977$	−8.17184	−	6.85699i	−0.261440	−	0.219374i	−0.764080	+	0.645122i	$0.776807\pi$
$978$	2.43607	+	7.93859i	0.0778968	+	0.253848i
$979$	−16.6759	−	94.5736i	−0.532964	−	3.02259i
$980$	3.50127	+	11.9280i	0.111844	+	0.381025i
$981$	−7.17767	+	16.2130i	−0.229165	+	0.517642i
$982$	−1.89740	−	27.1404i	−0.0605485	−	0.866084i
$983$	5.32937	+	30.2244i	0.169981	+	0.964008i	0.943779	+	0.330576i	$0.107243\pi$
$983$	5.32937	+	30.2244i	0.169981	+	0.964008i	−0.773799	+	0.633432i	$0.781646\pi$
$984$	48.4010	+	22.5106i	1.54297	+	0.717612i
$985$	−5.49403	−	15.0947i	−0.175054	−	0.480958i
$986$	7.31090	+	16.4213i	0.232826	+	0.522959i
$987$	−17.8605	−	34.6923i	−0.568506	−	1.10427i
$988$	36.3783	−	11.8187i	1.15735	−	0.376004i
$989$	1.50767	+	2.61137i	0.0479412	+	0.0830366i
$990$	−8.29392	−	22.6402i	−0.263598	−	0.719552i
$991$	20.8248	+	12.0232i	0.661520	+	0.381929i	0.792856	−	0.609409i	$-0.208593\pi$
$991$	20.8248	+	12.0232i	0.661520	+	0.381929i	−0.131336	+	0.991338i	$0.541927\pi$
$992$	−5.81194	−	10.0685i	−0.184529	−	0.319674i
$993$	−5.66891	+	5.29751i	−0.179898	+	0.168111i
$994$	−20.6828	−	38.6067i	−0.656020	−	1.22453i
$995$	−1.92092	−	0.338709i	−0.0608972	−	0.0107378i
$996$	−27.6124	−	9.47621i	−0.874931	−	0.300265i
$997$	−4.59533	+	12.6256i	−0.145536	+	0.399856i	−0.990946	−	0.134261i	$-0.957134\pi$
$997$	−4.59533	+	12.6256i	−0.145536	+	0.399856i	0.845410	+	0.534118i	$0.179356\pi$
$998$	1.15517	+	16.5235i	0.0365662	+	0.523042i
$999$	26.9891	−	21.9967i	0.853896	−	0.695945i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bt.a.103.12	✓	840
4.3	odd	2	inner	756.2.bt.a.103.115	yes	840
7.3	odd	6		756.2.cd.a.535.106	yes	840
27.16	even	9		756.2.cd.a.691.76	yes	840
28.3	even	6		756.2.cd.a.535.76	yes	840
108.43	odd	18		756.2.cd.a.691.106	yes	840
189.178	odd	18	inner	756.2.bt.a.367.115	yes	840
756.367	even	18	inner	756.2.bt.a.367.12	yes	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bt.a.103.12	✓	840	1.1	even	1	trivial
756.2.bt.a.103.115	yes	840	4.3	odd	2	inner
756.2.bt.a.367.12	yes	840	756.367	even	18	inner
756.2.bt.a.367.115	yes	840	189.178	odd	18	inner
756.2.cd.a.535.76	yes	840	28.3	even	6
756.2.cd.a.535.106	yes	840	7.3	odd	6
756.2.cd.a.691.76	yes	840	27.16	even	9
756.2.cd.a.691.106	yes	840	108.43	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bt (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35942 - 0.389832i) q^{2} +(1.54409 + 0.784711i) q^{3} +(1.69606 + 1.05989i) q^{4} +(0.874454 + 0.154190i) q^{5} +(-1.79317 - 1.66869i) q^{6} +(2.54554 + 0.721260i) q^{7} +(-1.89249 - 2.10202i) q^{8} +(1.76846 + 2.42334i) q^{9} +O(q^{10})\)	\(q+(-1.35942 - 0.389832i) q^{2} +(1.54409 + 0.784711i) q^{3} +(1.69606 + 1.05989i) q^{4} +(0.874454 + 0.154190i) q^{5} +(-1.79317 - 1.66869i) q^{6} +(2.54554 + 0.721260i) q^{7} +(-1.89249 - 2.10202i) q^{8} +(1.76846 + 2.42334i) q^{9} +(-1.12865 - 0.550499i) q^{10} +(6.30310 - 1.11141i) q^{11} +(1.78717 + 2.96749i) q^{12} +(-2.78497 + 3.31899i) q^{13} +(-3.17930 - 1.97283i) q^{14} +(1.22925 + 0.924277i) q^{15} +(1.75325 + 3.59529i) q^{16} -2.39048i q^{17} +(-1.45939 - 3.98374i) q^{18} -4.41417 q^{19} +(1.31970 + 1.18834i) q^{20} +(3.36458 + 3.11121i) q^{21} +(-9.00185 - 0.946279i) q^{22} +(1.20684 - 1.43825i) q^{23} +(-1.27270 - 4.73078i) q^{24} +(-3.95757 - 1.44044i) q^{25} +(5.07980 - 3.42625i) q^{26} +(0.829051 + 5.12959i) q^{27} +(3.55294 + 3.92130i) q^{28} +(4.07311 - 3.41775i) q^{29} +(-1.31075 - 1.73568i) q^{30} +(1.93118 - 0.702892i) q^{31} +(-0.981854 - 5.57099i) q^{32} +(10.6047 + 3.22999i) q^{33} +(-0.931887 + 3.24968i) q^{34} +(2.11475 + 1.02321i) q^{35} +(0.430939 + 5.98450i) q^{36} +(-3.35032 - 5.80293i) q^{37} +(6.00072 + 1.72078i) q^{38} +(-6.90470 + 2.93945i) q^{39} +(-1.33078 - 2.12992i) q^{40} +(-7.00385 + 8.34687i) q^{41} +(-3.36104 - 5.54107i) q^{42} +(-0.549298 + 1.50918i) q^{43} +(11.8684 + 4.79560i) q^{44} +(1.17278 + 2.39177i) q^{45} +(-2.20128 + 1.48473i) q^{46} +(-8.00134 - 2.91225i) q^{47} +(-0.114073 + 6.92726i) q^{48} +(5.95957 + 3.67200i) q^{49} +(4.81848 + 3.50095i) q^{50} +(1.87584 - 3.69114i) q^{51} +(-8.24126 + 2.67745i) q^{52} +(-5.85287 - 10.1375i) q^{53} +(0.872647 - 7.29647i) q^{54} +5.68314 q^{55} +(-3.30130 - 6.71576i) q^{56} +(-6.81589 - 3.46384i) q^{57} +(-6.86943 + 3.05833i) q^{58} +(1.45830 + 1.22366i) q^{59} +(1.10524 + 2.87050i) q^{60} +(-2.45933 + 6.75696i) q^{61} +(-2.89930 + 0.202692i) q^{62} +(2.75383 + 7.44422i) q^{63} +(-0.836997 + 7.95609i) q^{64} +(-2.94708 + 2.47289i) q^{65} +(-13.1572 - 8.52499i) q^{66} +(8.64595 + 1.52451i) q^{67} +(2.53366 - 4.05441i) q^{68} +(2.99208 - 1.27378i) q^{69} +(-2.47596 - 2.21537i) q^{70} +(10.1372 + 5.85274i) q^{71} +(1.74712 - 8.30347i) q^{72} +(9.90275 + 5.71736i) q^{73} +(2.29234 + 9.19470i) q^{74} +(-4.98053 - 5.32972i) q^{75} +(-7.48670 - 4.67855i) q^{76} +(16.8464 + 1.71704i) q^{77} +(10.5323 - 1.30428i) q^{78} +(-4.73969 + 0.835735i) q^{79} +(0.978782 + 3.41425i) q^{80} +(-2.74511 + 8.57114i) q^{81} +(12.7751 - 8.61660i) q^{82} +(-6.45572 + 5.41699i) q^{83} +(2.40899 + 8.84289i) q^{84} +(0.368589 - 2.09037i) q^{85} +(1.33506 - 1.83749i) q^{86} +(8.97121 - 2.08111i) q^{87} +(-14.2647 - 11.1459i) q^{88} -15.0043i q^{89} +(-0.661917 - 3.70862i) q^{90} +(-9.48311 + 6.43995i) q^{91} +(3.57126 - 1.16025i) q^{92} +(3.53349 + 0.430085i) q^{93} +(9.74191 + 7.07815i) q^{94} +(-3.85999 - 0.680620i) q^{95} +(2.85554 - 9.37261i) q^{96} +(4.06141 - 11.1586i) q^{97} +(-6.67011 - 7.31503i) q^{98} +(13.8401 + 13.3091i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9	\( 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9} - 9 q^{12} - 21 q^{14} - 3 q^{16} - 3 q^{18} - 12 q^{21} - 12 q^{22} - 9 q^{24} - 6 q^{25} - 18 q^{26} - 12 q^{28} - 36 q^{29} - 39 q^{30} + 27 q^{32} - 18 q^{33} + 18 q^{34} + 18 q^{36} + 6 q^{37} - 99 q^{38} + 36 q^{40} + 9 q^{42} + 3 q^{44} - 18 q^{45} + 3 q^{46} - 12 q^{49} + 3 q^{50} - 9 q^{52} - 12 q^{53} - 135 q^{54} + 15 q^{56} - 42 q^{57} - 3 q^{58} - 33 q^{60} - 18 q^{61} - 99 q^{62} - 6 q^{64} + 18 q^{65} - 9 q^{66} - 54 q^{68} + 72 q^{69} - 36 q^{70} - 111 q^{72} - 18 q^{73} + 93 q^{74} - 36 q^{76} - 36 q^{77} + 6 q^{78} - 18 q^{80} - 30 q^{81} - 18 q^{82} + 84 q^{84} + 6 q^{85} + 135 q^{86} - 51 q^{88} + 81 q^{90} + 48 q^{92} - 6 q^{93} - 9 q^{94} - 9 q^{96} - 117 q^{98}+O(q^{100}) \) 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9 - 9 * q^12 - 21 * q^14 - 3 * q^16 - 3 * q^18 - 12 * q^21 - 12 * q^22 - 9 * q^24 - 6 * q^25 - 18 * q^26 - 12 * q^28 - 36 * q^29 - 39 * q^30 + 27 * q^32 - 18 * q^33 + 18 * q^34 + 18 * q^36 + 6 * q^37 - 99 * q^38 + 36 * q^40 + 9 * q^42 + 3 * q^44 - 18 * q^45 + 3 * q^46 - 12 * q^49 + 3 * q^50 - 9 * q^52 - 12 * q^53 - 135 * q^54 + 15 * q^56 - 42 * q^57 - 3 * q^58 - 33 * q^60 - 18 * q^61 - 99 * q^62 - 6 * q^64 + 18 * q^65 - 9 * q^66 - 54 * q^68 + 72 * q^69 - 36 * q^70 - 111 * q^72 - 18 * q^73 + 93 * q^74 - 36 * q^76 - 36 * q^77 + 6 * q^78 - 18 * q^80 - 30 * q^81 - 18 * q^82 + 84 * q^84 + 6 * q^85 + 135 * q^86 - 51 * q^88 + 81 * q^90 + 48 * q^92 - 6 * q^93 - 9 * q^94 - 9 * q^96 - 117 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more