LMFDB - Embedded newform 308.2.l.a.243.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,2,Mod(199,308)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(308, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 0]))

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

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

chi := DirichletCharacter("308.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	308.l (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.45939238226$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			243.24
Character	$\chi$	$=$	308.243
Dual form			308.2.l.a.199.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.408138 - 1.35404i) q^{2} +(0.276123 + 0.478258i) q^{3} +(-1.66685 - 1.10527i) q^{4} +(2.05090 + 1.18409i) q^{5} +(0.760277 - 0.178685i) q^{6} +(2.15909 + 1.52916i) q^{7} +(-2.17688 + 1.80587i) q^{8} +(1.34751 - 2.33396i) q^{9} +O(q^{10})$	\(q+(0.408138 - 1.35404i) q^{2} +(0.276123 + 0.478258i) q^{3} +(-1.66685 - 1.10527i) q^{4} +(2.05090 + 1.18409i) q^{5} +(0.760277 - 0.178685i) q^{6} +(2.15909 + 1.52916i) q^{7} +(-2.17688 + 1.80587i) q^{8} +(1.34751 - 2.33396i) q^{9} +(2.44035 - 2.29373i) q^{10} +(-0.866025 + 0.500000i) q^{11} +(0.0683509 - 1.10237i) q^{12} +1.59733i q^{13} +(2.95175 - 2.29939i) q^{14} +1.30781i q^{15} +(1.55675 + 3.68463i) q^{16} +(3.13348 - 1.80911i) q^{17} +(-2.61030 - 2.77716i) q^{18} +(0.876268 - 1.51774i) q^{19} +(-2.10980 - 4.24050i) q^{20} +(-0.135160 + 1.45484i) q^{21} +(0.323562 + 1.37670i) q^{22} +(-3.50081 - 2.02120i) q^{23} +(-1.46476 - 0.542470i) q^{24} +(0.304133 + 0.526774i) q^{25} +(2.16285 + 0.651933i) q^{26} +3.14505 q^{27} +(-1.90874 - 4.93525i) q^{28} -4.35122 q^{29} +(1.77083 + 0.533769i) q^{30} +(-4.05431 - 7.02227i) q^{31} +(5.62451 - 0.604068i) q^{32} +(-0.478258 - 0.276123i) q^{33} +(-1.17072 - 4.98122i) q^{34} +(2.61742 + 5.69271i) q^{35} +(-4.82575 + 2.40099i) q^{36} +(-3.37826 + 5.85133i) q^{37} +(-1.69744 - 1.80595i) q^{38} +(-0.763939 + 0.441060i) q^{39} +(-6.60289 + 1.12605i) q^{40} +4.28196i q^{41} +(1.91475 + 0.776787i) q^{42} +0.306527i q^{43} +(1.99617 + 0.123769i) q^{44} +(5.52723 - 3.19115i) q^{45} +(-4.16560 + 3.91531i) q^{46} +(-4.89788 + 8.48338i) q^{47} +(-1.33235 + 1.76194i) q^{48} +(2.32334 + 6.60319i) q^{49} +(0.837402 - 0.196812i) q^{50} +(1.73045 + 0.999074i) q^{51} +(1.76549 - 2.66251i) q^{52} +(2.64119 + 4.57468i) q^{53} +(1.28362 - 4.25852i) q^{54} -2.36818 q^{55} +(-7.46156 + 0.570242i) q^{56} +0.967830 q^{57} +(-1.77590 + 5.89172i) q^{58} +(-5.38230 - 9.32241i) q^{59} +(1.44549 - 2.17993i) q^{60} +(1.94287 + 1.12172i) q^{61} +(-11.1631 + 2.62364i) q^{62} +(6.47840 - 2.97867i) q^{63} +(1.47764 - 7.86235i) q^{64} +(-1.89139 + 3.27598i) q^{65} +(-0.569076 + 0.534885i) q^{66} +(-7.68007 + 4.43409i) q^{67} +(-7.22258 - 0.447824i) q^{68} -2.23239i q^{69} +(8.77643 - 1.22068i) q^{70} -6.85837i q^{71} +(1.28146 + 7.51420i) q^{72} +(4.67208 - 2.69743i) q^{73} +(6.54413 + 6.96245i) q^{74} +(-0.167956 + 0.290909i) q^{75} +(-3.13812 + 1.56133i) q^{76} +(-2.63441 - 0.244746i) q^{77} +(0.285420 + 1.21442i) q^{78} +(13.0380 + 7.52748i) q^{79} +(-1.17018 + 9.40016i) q^{80} +(-3.17412 - 5.49773i) q^{81} +(5.79794 + 1.74763i) q^{82} -5.27260 q^{83} +(1.83328 - 2.27560i) q^{84} +8.56860 q^{85} +(0.415049 + 0.125105i) q^{86} +(-1.20147 - 2.08101i) q^{87} +(0.982300 - 2.65237i) q^{88} +(-8.88061 - 5.12722i) q^{89} +(-2.06507 - 8.78652i) q^{90} +(-2.44258 + 3.44879i) q^{91} +(3.60135 + 7.23837i) q^{92} +(2.23897 - 3.87801i) q^{93} +(9.48782 + 10.0943i) q^{94} +(3.59428 - 2.07516i) q^{95} +(1.84195 + 2.52317i) q^{96} -4.92469i q^{97} +(9.88922 - 0.450887i) q^{98} +2.69503i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 12 q^{8} - 40 q^{9}+O(q^{10}) $ 80 * q + 12 * q^8 - 40 * q^9	$ 80 q + 12 q^{8} - 40 q^{9} - 18 q^{10} - 30 q^{12} - 4 q^{14} - 4 q^{16} - 10 q^{18} - 8 q^{21} + 40 q^{25} + 30 q^{26} + 16 q^{28} - 16 q^{29} + 36 q^{30} - 20 q^{32} - 20 q^{36} - 8 q^{37} - 12 q^{38} - 60 q^{40} + 4 q^{44} + 24 q^{45} - 10 q^{46} - 24 q^{49} - 64 q^{50} + 54 q^{52} - 30 q^{54} + 38 q^{56} + 80 q^{57} + 10 q^{58} - 12 q^{60} - 36 q^{64} - 16 q^{65} + 30 q^{66} + 60 q^{68} - 22 q^{70} - 38 q^{72} - 72 q^{73} + 28 q^{74} - 24 q^{78} + 42 q^{80} - 64 q^{81} - 90 q^{82} + 88 q^{84} - 2 q^{86} + 12 q^{88} - 120 q^{89} + 36 q^{92} + 8 q^{93} - 54 q^{94} - 42 q^{96} + 78 q^{98}+O(q^{100}) $ 80 * q + 12 * q^8 - 40 * q^9 - 18 * q^10 - 30 * q^12 - 4 * q^14 - 4 * q^16 - 10 * q^18 - 8 * q^21 + 40 * q^25 + 30 * q^26 + 16 * q^28 - 16 * q^29 + 36 * q^30 - 20 * q^32 - 20 * q^36 - 8 * q^37 - 12 * q^38 - 60 * q^40 + 4 * q^44 + 24 * q^45 - 10 * q^46 - 24 * q^49 - 64 * q^50 + 54 * q^52 - 30 * q^54 + 38 * q^56 + 80 * q^57 + 10 * q^58 - 12 * q^60 - 36 * q^64 - 16 * q^65 + 30 * q^66 + 60 * q^68 - 22 * q^70 - 38 * q^72 - 72 * q^73 + 28 * q^74 - 24 * q^78 + 42 * q^80 - 64 * q^81 - 90 * q^82 + 88 * q^84 - 2 * q^86 + 12 * q^88 - 120 * q^89 + 36 * q^92 + 8 * q^93 - 54 * q^94 - 42 * q^96 + 78 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$	0.408138	−	1.35404i	0.288597	−	0.957451i
$2$	0.408138	−	1.35404i	0.288597	−	0.957451i
$3$	0.276123	+	0.478258i	0.159419	+	0.276123i	0.934659	−	0.355544i	$-0.115704\pi$
$3$	0.276123	+	0.478258i	0.159419	+	0.276123i	−0.775240	+	0.631667i	$0.782371\pi$
$4$	−1.66685	−	1.10527i	−0.833423	−	0.552635i
$5$	2.05090	+	1.18409i	0.917191	+	0.529541i	0.882738	−	0.469866i	$-0.155698\pi$
$5$	2.05090	+	1.18409i	0.917191	+	0.529541i	0.0344534	+	0.999406i	$0.489031\pi$
$6$	0.760277	−	0.178685i	0.310382	−	0.0729480i
$7$	2.15909	+	1.52916i	0.816060	+	0.577968i
$7$	2.15909	+	1.52916i	0.816060	+	0.577968i
$8$	−2.17688	+	1.80587i	−0.769645	+	0.638473i
$9$	1.34751	−	2.33396i	0.449171	−	0.777987i
$10$	2.44035	−	2.29373i	0.771708	−	0.725341i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$12$	0.0683509	−	1.10237i	0.0197312	−	0.318228i
$13$			1.59733i			0.443021i	0.975158	+	0.221510i	$0.0710987\pi$
$13$			1.59733i			0.443021i	−0.975158	+	0.221510i	$0.928901\pi$
$14$	2.95175	−	2.29939i	0.788888	−	0.614537i
$15$			1.30781i			0.337676i
$16$	1.55675	+	3.68463i	0.389189	+	0.921158i
$17$	3.13348	−	1.80911i	0.759980	−	0.438774i	−0.0693088	−	0.997595i	$-0.522079\pi$
$17$	3.13348	−	1.80911i	0.759980	−	0.438774i	0.829288	+	0.558821i	$0.188746\pi$
$18$	−2.61030	−	2.77716i	−0.615254	−	0.654584i
$19$	0.876268	−	1.51774i	0.201030	−	0.348194i	−0.747831	−	0.663889i	$-0.768905\pi$
$19$	0.876268	−	1.51774i	0.201030	−	0.348194i	0.948860	+	0.315696i	$0.102238\pi$
$20$	−2.10980	−	4.24050i	−0.471766	−	0.948204i
$21$	−0.135160	+	1.45484i	−0.0294942	+	0.317472i
$22$	0.323562	+	1.37670i	0.0689836	+	0.293514i
$23$	−3.50081	−	2.02120i	−0.729970	−	0.421449i	0.0884410	−	0.996081i	$-0.471812\pi$
$23$	−3.50081	−	2.02120i	−0.729970	−	0.421449i	−0.818411	+	0.574633i	$0.805145\pi$
$24$	−1.46476	−	0.542470i	−0.298993	−	0.110731i
$25$	0.304133	+	0.526774i	0.0608267	+	0.105355i
$26$	2.16285	+	0.651933i	0.424171	+	0.127855i
$27$	3.14505			0.605265
$28$	−1.90874	−	4.93525i	−0.360718	−	0.932675i
$29$	−4.35122			−0.808001			−0.404000	−	0.914759i	$-0.632381\pi$
$29$	−4.35122			−0.808001			−0.404000	+	0.914759i	$0.632381\pi$
$30$	1.77083	+	0.533769i	0.323308	+	0.0974525i
$31$	−4.05431	−	7.02227i	−0.728175	−	1.26124i	−0.957654	−	0.287923i	$-0.907035\pi$
$31$	−4.05431	−	7.02227i	−0.728175	−	1.26124i	0.229479	−	0.973314i	$-0.426298\pi$
$32$	5.62451	−	0.604068i	0.994282	−	0.106785i
$33$	−0.478258	−	0.276123i	−0.0832541	−	0.0480668i
$34$	−1.17072	−	4.98122i	−0.200777	−	0.854272i
$35$	2.61742	+	5.69271i	0.442425	+	0.962244i
$36$	−4.82575	+	2.40099i	−0.804292	+	0.400165i
$37$	−3.37826	+	5.85133i	−0.555383	+	0.961952i	0.442490	+	0.896773i	$0.354095\pi$
$37$	−3.37826	+	5.85133i	−0.555383	+	0.961952i	−0.997874	+	0.0651788i	$0.979238\pi$
$38$	−1.69744	−	1.80595i	−0.275362	−	0.292964i
$39$	−0.763939	+	0.441060i	−0.122328	+	0.0706261i
$40$	−6.60289	+	1.12605i	−1.04401	+	0.178043i
$41$			4.28196i			0.668729i	0.942444	+	0.334365i	$0.108522\pi$
$41$			4.28196i			0.668729i	−0.942444	+	0.334365i	$0.891478\pi$
$42$	1.91475	+	0.776787i	0.295452	+	0.119861i
$43$			0.306527i			0.0467449i	0.999727	+	0.0233724i	$0.00744036\pi$
$43$			0.306527i			0.0467449i	−0.999727	+	0.0233724i	$0.992560\pi$
$44$	1.99617	+	0.123769i	0.300933	+	0.0186589i
$45$	5.52723	−	3.19115i	0.823951	−	0.475709i
$46$	−4.16560	+	3.91531i	−0.614184	+	0.577282i
$47$	−4.89788	+	8.48338i	−0.714430	+	1.23743i	0.248750	+	0.968568i	$0.419980\pi$
$47$	−4.89788	+	8.48338i	−0.714430	+	1.23743i	−0.963179	+	0.268860i	$0.913353\pi$
$48$	−1.33235	+	1.76194i	−0.192308	+	0.254314i
$49$	2.32334	+	6.60319i	0.331906	+	0.943312i
$50$	0.837402	−	0.196812i	0.118426	−	0.0278334i
$51$	1.73045	+	0.999074i	0.242311	+	0.139898i
$52$	1.76549	−	2.66251i	0.244829	−	0.369224i
$53$	2.64119	+	4.57468i	0.362795	+	0.628380i	0.988420	−	0.151744i	$-0.0484890\pi$
$53$	2.64119	+	4.57468i	0.362795	+	0.628380i	−0.625624	+	0.780124i	$0.715156\pi$
$54$	1.28362	−	4.25852i	0.174678	−	0.579512i
$55$	−2.36818			−0.319325
$56$	−7.46156	+	0.570242i	−0.997092	+	0.0762017i
$57$	0.967830			0.128192
$58$	−1.77590	+	5.89172i	−0.233187	+	0.773621i
$59$	−5.38230	−	9.32241i	−0.700715	−	1.21367i	−0.968216	−	0.250117i	$-0.919531\pi$
$59$	−5.38230	−	9.32241i	−0.700715	−	1.21367i	0.267500	−	0.963558i	$-0.413802\pi$
$60$	1.44549	−	2.17993i	0.186612	−	0.281427i
$61$	1.94287	+	1.12172i	0.248760	+	0.143621i	0.619196	−	0.785236i	$-0.287459\pi$
$61$	1.94287	+	1.12172i	0.248760	+	0.143621i	−0.370437	+	0.928858i	$0.620792\pi$
$62$	−11.1631	+	2.62364i	−1.41772	+	0.333202i
$63$	6.47840	−	2.97867i	0.816202	−	0.375277i
$64$	1.47764	−	7.86235i	0.184706	−	0.982794i
$65$	−1.89139	+	3.27598i	−0.234598	+	0.406335i
$66$	−0.569076	+	0.534885i	−0.0700485	+	0.0658397i
$67$	−7.68007	+	4.43409i	−0.938270	+	0.541711i	−0.889418	−	0.457095i	$-0.848890\pi$
$67$	−7.68007	+	4.43409i	−0.938270	+	0.541711i	−0.0488525	+	0.998806i	$0.515556\pi$
$68$	−7.22258	−	0.447824i	−0.875867	−	0.0543067i
$69$		−	2.23239i		−	0.268748i
$70$	8.77643	−	1.22068i	1.04898	−	0.145899i
$71$		−	6.85837i		−	0.813939i	−0.913442	−	0.406970i	$-0.866586\pi$
$71$		−	6.85837i		−	0.813939i	0.913442	−	0.406970i	$-0.133414\pi$
$72$	1.28146	+	7.51420i	0.151021	+	0.885557i
$73$	4.67208	−	2.69743i	0.546825	−	0.315710i	−0.201015	−	0.979588i	$-0.564424\pi$
$73$	4.67208	−	2.69743i	0.546825	−	0.315710i	0.747841	+	0.663878i	$0.231091\pi$
$74$	6.54413	+	6.96245i	0.760740	+	0.809369i
$75$	−0.167956	+	0.290909i	−0.0193939	+	0.0335912i
$76$	−3.13812	+	1.56133i	−0.359967	+	0.179097i
$77$	−2.63441	−	0.244746i	−0.300219	−	0.0278913i
$78$	0.285420	+	1.21442i	0.0323175	+	0.137506i
$79$	13.0380	+	7.52748i	1.46689	+	0.846907i	0.999314	−	0.0370468i	$-0.0117951\pi$
$79$	13.0380	+	7.52748i	1.46689	+	0.846907i	0.467573	+	0.883954i	$0.345128\pi$
$80$	−1.17018	+	9.40016i	−0.130830	+	1.05097i
$81$	−3.17412	−	5.49773i	−0.352680	−	0.610859i
$82$	5.79794	+	1.74763i	0.640275	+	0.192993i
$83$	−5.27260			−0.578743			−0.289371	−	0.957217i	$-0.593446\pi$
$83$	−5.27260			−0.578743			−0.289371	+	0.957217i	$0.593446\pi$
$84$	1.83328	−	2.27560i	0.200027	−	0.248289i
$85$	8.56860			0.929396
$86$	0.415049	+	0.125105i	0.0447559	+	0.0134904i
$87$	−1.20147	−	2.08101i	−0.128811	−	0.223107i
$88$	0.982300	−	2.65237i	0.104714	−	0.282744i
$89$	−8.88061	−	5.12722i	−0.941343	−	0.543485i	−0.0509620	−	0.998701i	$-0.516229\pi$
$89$	−8.88061	−	5.12722i	−0.941343	−	0.543485i	−0.890381	+	0.455216i	$0.849562\pi$
$90$	−2.06507	−	8.78652i	−0.217677	−	0.926181i
$91$	−2.44258	+	3.44879i	−0.256052	+	0.361531i
$92$	3.60135	+	7.23837i	0.375467	+	0.754652i
$93$	2.23897	−	3.87801i	0.232171	−	0.402131i
$94$	9.48782	+	10.0943i	0.978594	+	1.04115i
$95$	3.59428	−	2.07516i	0.368765	−	0.212907i
$96$	1.84195	+	2.52317i	0.187994	+	0.257520i
$97$		−	4.92469i		−	0.500027i	−0.968242	−	0.250013i	$-0.919565\pi$
$97$		−	4.92469i		−	0.500027i	0.968242	−	0.250013i	$-0.0804350\pi$
$98$	9.88922	−	0.450887i	0.998962	−	0.0455464i
$99$			2.69503i			0.270860i
$100$	0.0752846	−	1.21420i	0.00752846	−	0.121420i
$101$	−13.1353	+	7.58370i	−1.30702	+	0.754606i	−0.981597	−	0.190964i	$-0.938839\pi$
$101$	−13.1353	+	7.58370i	−1.30702	+	0.754606i	−0.325419	+	0.945570i	$0.605505\pi$
$102$	2.05905	−	1.93533i	0.203876	−	0.191627i
$103$	−1.25289	+	2.17006i	−0.123451	+	0.213823i	−0.921126	−	0.389264i	$-0.872729\pi$
$103$	−1.25289	+	2.17006i	−0.123451	+	0.213823i	0.797676	+	0.603087i	$0.206063\pi$
$104$	−2.88458	−	3.47721i	−0.282857	−	0.340969i
$105$	−1.99986	+	2.82369i	−0.195166	+	0.275564i
$106$	7.27226	−	1.70918i	0.706345	−	0.166010i
$107$	6.46586	+	3.73307i	0.625078	+	0.360889i	0.778843	−	0.627218i	$-0.215807\pi$
$107$	6.46586	+	3.73307i	0.625078	+	0.360889i	−0.153765	+	0.988107i	$0.549140\pi$
$108$	−5.24232	−	3.47613i	−0.504442	−	0.334491i
$109$	1.06377	+	1.84251i	0.101891	+	0.176480i	0.912464	−	0.409158i	$-0.134177\pi$
$109$	1.06377	+	1.84251i	0.101891	+	0.176480i	−0.810573	+	0.585638i	$0.800844\pi$
$110$	−0.966544	+	3.20661i	−0.0921563	+	0.305738i
$111$	−3.73126			−0.354156
$112$	−2.27322	+	10.3360i	−0.214799	+	0.976658i
$113$	−18.9691			−1.78446			−0.892232	−	0.451578i	$-0.850861\pi$
$113$	−18.9691			−1.78446			−0.892232	+	0.451578i	$0.850861\pi$
$114$	0.395008	−	1.31048i	0.0369959	−	0.122738i
$115$	−4.78655	−	8.29055i	−0.446348	−	0.773098i
$116$	7.25281	+	4.80927i	0.673407	+	0.446530i
$117$	3.72812	+	2.15243i	0.344664	+	0.198992i
$118$	−14.8196	+	3.48301i	−1.36426	+	0.320637i
$119$	9.53188	+	0.885545i	0.873786	+	0.0811778i
$120$	−2.36175	−	2.84696i	−0.215597	−	0.259891i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	2.31181	−	2.17291i	0.209302	−	0.196726i
$123$	−2.04788	+	1.18235i	−0.184651	+	0.106608i
$124$	−1.00360	+	16.1861i	−0.0901255	+	1.45356i
$125$		−	10.4004i		−	0.930241i
$126$	−1.38916	−	9.98772i	−0.123756	−	0.889777i
$127$		−	3.75946i		−	0.333598i	−0.985991	−	0.166799i	$-0.946657\pi$
$127$		−	3.75946i		−	0.333598i	0.985991	−	0.166799i	$-0.0533431\pi$
$128$	−10.0429	−	5.20971i	−0.887671	−	0.460478i
$129$	−0.146599	+	0.0846389i	−0.0129073	+	0.00745204i
$130$	3.66386	+	3.89806i	0.321341	+	0.341883i
$131$	8.36438	−	14.4875i	0.730799	−	1.26578i	−0.225743	−	0.974187i	$-0.572481\pi$
$131$	8.36438	−	14.4875i	0.730799	−	1.26578i	0.956542	−	0.291594i	$-0.0941857\pi$
$132$	0.491993	+	0.988859i	0.0428225	+	0.0860691i
$133$	4.21281	−	1.93699i	0.365297	−	0.167958i
$134$	2.86941	+	12.2088i	0.247879	+	1.05468i
$135$	6.45019	+	3.72402i	0.555144	+	0.320513i
$136$	−3.55418	+	9.59689i	−0.304769	+	0.822927i
$137$	−9.22675	−	15.9812i	−0.788294	−	1.36537i	−0.927011	−	0.375034i	$-0.877631\pi$
$137$	−9.22675	−	15.9812i	−0.788294	−	1.36537i	0.138717	−	0.990332i	$-0.455702\pi$
$138$	−3.02275	−	0.911124i	−0.257313	−	0.0775601i
$139$	1.94365			0.164858			0.0824292	−	0.996597i	$-0.473732\pi$
$139$	1.94365			0.164858			0.0824292	+	0.996597i	$0.473732\pi$
$140$	1.92914	−	12.3818i	0.163042	−	1.04646i
$141$	−5.40966			−0.455576
$142$	−9.28651	−	2.79916i	−0.779306	−	0.234901i
$143$	−0.798667	−	1.38333i	−0.0667879	−	0.115680i
$144$	10.6975	+	1.33169i	0.891461	+	0.110974i
$145$	−8.92392	−	5.15223i	−0.741092	−	0.427869i
$146$	−1.74557	−	7.42710i	−0.144464	−	0.614671i
$147$	−2.51650	+	2.93445i	−0.207558	+	0.242029i
$148$	12.0983	−	6.01937i	0.994478	−	0.494789i
$149$	1.11439	−	1.93018i	0.0912942	−	0.158126i	−0.816762	−	0.576975i	$-0.804233\pi$
$149$	1.11439	−	1.93018i	0.0912942	−	0.158126i	0.908056	+	0.418849i	$0.137566\pi$
$150$	0.325352	+	0.346150i	0.0265649	+	0.0282630i
$151$	−11.9971	+	6.92654i	−0.976311	+	0.563674i	−0.901154	−	0.433498i	$-0.857279\pi$
$151$	−11.9971	+	6.92654i	−0.976311	+	0.563674i	−0.0751569	+	0.997172i	$0.523946\pi$
$152$	0.833314	+	4.88637i	0.0675907	+	0.396337i
$153$		−	9.75121i		−	0.788339i
$154$	−1.40660	+	3.46720i	−0.113347	+	0.279395i
$155$		−	19.2026i		−	1.54239i
$156$	1.76086	+	0.109179i	0.140982	+	0.00874133i
$157$	15.7245	−	9.07853i	1.25495	−	0.724545i	0.282861	−	0.959161i	$-0.408716\pi$
$157$	15.7245	−	9.07853i	1.25495	−	0.724545i	0.972088	+	0.234615i	$0.0753831\pi$
$158$	15.5138	−	14.5817i	1.23421	−	1.16006i
$159$	−1.45858	+	2.52634i	−0.115673	+	0.200352i
$160$	12.2506	+	5.42103i	0.968494	+	0.428570i
$161$	−4.46784	−	9.71725i	−0.352115	−	0.765827i
$162$	−8.73963	+	2.05405i	−0.686650	+	0.161381i
$163$	17.9121	+	10.3415i	1.40298	+	0.810012i	0.994698	−	0.102843i	$-0.0327939\pi$
$163$	17.9121	+	10.3415i	1.40298	+	0.810012i	0.408284	+	0.912855i	$0.366127\pi$
$164$	4.73272	−	7.13737i	0.369563	−	0.557335i
$165$	−0.653907	−	1.13260i	−0.0509066	−	0.0881729i
$166$	−2.15195	+	7.13930i	−0.167024	+	0.554117i
$167$	22.1711			1.71565			0.857824	−	0.513943i	$-0.171816\pi$
$167$	22.1711			1.71565			0.857824	+	0.513943i	$0.171816\pi$
$168$	−2.33303	−	3.41110i	−0.179997	−	0.263172i
$169$	10.4485			0.803732
$170$	3.49717	−	11.6022i	0.268221	−	0.889850i
$171$	−2.36156	−	4.09035i	−0.180593	−	0.312797i
$172$	0.338795	−	0.510933i	0.0258329	−	0.0389583i
$173$	−10.0725	−	5.81535i	−0.765796	−	0.442133i	0.0655766	−	0.997848i	$-0.479111\pi$
$173$	−10.0725	−	5.81535i	−0.765796	−	0.442133i	−0.831373	+	0.555715i	$0.812445\pi$
$174$	−3.30813	+	0.777499i	−0.250789	+	0.0589421i
$175$	−0.148871	+	1.60242i	−0.0112536	+	0.121132i
$176$	−3.19051	−	2.41261i	−0.240493	−	0.181857i
$177$	2.97235	−	5.14826i	0.223415	−	0.386967i
$178$	−10.5670	+	9.93209i	−0.792029	+	0.744441i
$179$	−9.71506	+	5.60899i	−0.726137	+	0.419236i	−0.817007	−	0.576627i	$-0.804369\pi$
$179$	−9.71506	+	5.60899i	−0.726137	+	0.419236i	0.0908700	+	0.995863i	$0.471035\pi$
$180$	−12.7401	−	0.789931i	−0.949593	−	0.0588780i
$181$			15.5695i			1.15727i	0.815587	+	0.578634i	$0.196414\pi$
$181$			15.5695i			1.15727i	−0.815587	+	0.578634i	$0.803586\pi$
$182$	3.67289	+	4.71493i	0.272253	+	0.349494i
$183$			1.23893i			0.0915842i
$184$	11.2709	−	1.92212i	0.830901	−	0.141700i
$185$	−13.8570	+	8.00033i	−1.01879	+	0.588196i
$186$	−4.33717	−	4.61442i	−0.318017	−	0.338346i
$187$	−1.80911	+	3.13348i	−0.132295	+	0.229142i
$188$	17.5404	−	8.72701i	1.27927	−	0.636483i
$189$	6.79045	+	4.80928i	0.493932	+	0.349824i
$190$	−1.34288	−	5.71375i	−0.0974231	−	0.414519i
$191$	−16.5841	−	9.57481i	−1.19998	−	0.692809i	−0.239430	−	0.970914i	$-0.576961\pi$
$191$	−16.5841	−	9.57481i	−1.19998	−	0.692809i	−0.960551	+	0.278104i	$0.910294\pi$
$192$	4.16825	−	1.46428i	0.300817	−	0.105675i
$193$	−4.96040	−	8.59167i	−0.357058	−	0.618442i	0.630410	−	0.776262i	$-0.282887\pi$
$193$	−4.96040	−	8.59167i	−0.357058	−	0.618442i	−0.987468	+	0.157820i	$0.949553\pi$
$194$	−6.66823	−	2.00995i	−0.478751	−	0.144306i
$195$	−2.08902			−0.149598
$196$	3.42565	−	13.5744i	0.244689	−	0.969602i
$197$	22.6830			1.61610			0.808048	−	0.589117i	$-0.200524\pi$
$197$	22.6830			1.61610			0.808048	+	0.589117i	$0.200524\pi$
$198$	3.64917	+	1.09994i	0.259335	+	0.0781695i
$199$	−7.64174	−	13.2359i	−0.541708	−	0.938266i	−0.998806	−	0.0488498i	$-0.984444\pi$
$199$	−7.64174	−	13.2359i	−0.541708	−	0.938266i	0.457098	−	0.889416i	$-0.348889\pi$
$200$	−1.61335	−	0.597500i	−0.114081	−	0.0422497i
$201$	−4.24128	−	2.44871i	−0.299157	−	0.172718i
$202$	4.90759	+	20.8810i	0.345297	+	1.46918i
$203$	−9.39467	−	6.65371i	−0.659377	−	0.466999i
$204$	−1.78014	−	3.57792i	−0.124635	−	0.250504i
$205$	−5.07022	+	8.78188i	−0.354119	+	0.613353i
$206$	2.42700	+	2.58215i	0.169097	+	0.179907i
$207$	−9.43478	+	5.44718i	−0.655763	+	0.378605i
$208$	−5.88559	+	2.48666i	−0.408092	+	0.172419i
$209$			1.75254i			0.121225i
$210$	3.00717	+	3.86034i	0.207515	+	0.266389i
$211$			24.0685i			1.65694i	0.560031	+	0.828472i	$0.310789\pi$
$211$			24.0685i			1.65694i	−0.560031	+	0.828472i	$0.689211\pi$
$212$	0.653795	−	10.5445i	0.0449028	−	0.724200i
$213$	3.28007	−	1.89375i	0.224747	−	0.129758i
$214$	7.69368	−	7.23142i	0.525929	−	0.494330i
$215$	−0.362955	+	0.628656i	−0.0247533	+	0.0428740i
$216$	−6.84641	+	5.67956i	−0.465839	+	0.386445i
$217$	1.98455	−	21.3614i	0.134720	−	1.45011i
$218$	2.92900	−	0.688393i	0.198377	−	0.0466239i
$219$	2.58013	+	1.48964i	0.174349	+	0.100661i
$220$	3.94739	+	2.61748i	0.266133	+	0.176470i
$221$	2.88976	+	5.00521i	0.194386	+	0.336687i
$222$	−1.52287	+	5.05228i	−0.102208	+	0.339087i
$223$	27.5661			1.84596			0.922981	−	0.384845i	$-0.125745\pi$
$223$	27.5661			1.84596			0.922981	+	0.384845i	$0.125745\pi$
$224$	13.0675	+	7.29653i	0.873112	+	0.487520i
$225$	1.63929			0.109286
$226$	−7.74202	+	25.6849i	−0.514991	+	1.70854i
$227$	4.85621	+	8.41121i	0.322318	+	0.558271i	0.980966	−	0.194180i	$-0.0622046\pi$
$227$	4.85621	+	8.41121i	0.322318	+	0.558271i	−0.658648	+	0.752451i	$0.728871\pi$
$228$	−1.61322	−	1.06971i	−0.106838	−	0.0708435i
$229$	23.3820	+	13.4996i	1.54513	+	0.892081i	0.998503	+	0.0547039i	$0.0174215\pi$
$229$	23.3820	+	13.4996i	1.54513	+	0.892081i	0.546626	+	0.837377i	$0.315912\pi$
$230$	−13.1793	+	3.09749i	−0.869018	+	0.204243i
$231$	−0.610368	−	1.32751i	−0.0401592	−	0.0873435i
$232$	9.47210	−	7.85775i	0.621874	−	0.515886i
$233$	−5.68271	+	9.84275i	−0.372287	+	0.644820i	−0.989917	−	0.141649i	$-0.954760\pi$
$233$	−5.68271	+	9.84275i	−0.372287	+	0.644820i	0.617630	+	0.786469i	$0.288093\pi$
$234$	4.43606	−	4.16953i	0.289994	−	0.272571i
$235$	−20.0902	+	11.5991i	−1.31054	+	0.756639i
$236$	−1.33232	+	21.4879i	−0.0867269	+	1.39874i
$237$			8.31403i			0.540054i
$238$	5.08939	−	12.5451i	0.329896	−	0.813179i
$239$			7.85718i			0.508239i	0.967173	+	0.254119i	$0.0817856\pi$
$239$			7.85718i			0.508239i	−0.967173	+	0.254119i	$0.918214\pi$
$240$	−4.81882	+	2.03595i	−0.311053	+	0.131420i
$241$	6.69773	−	3.86693i	0.431438	−	0.249091i	−0.268521	−	0.963274i	$-0.586535\pi$
$241$	6.69773	−	3.86693i	0.431438	−	0.249091i	0.699959	+	0.714183i	$0.253201\pi$
$242$	−0.968564	−	1.03048i	−0.0622616	−	0.0662416i
$243$	6.47047	−	11.2072i	0.415081	−	0.718941i
$244$	−1.99867	−	4.01713i	−0.127952	−	0.257171i
$245$	−3.05381	+	16.2935i	−0.195101	+	1.04096i
$246$	0.765123	+	3.25547i	0.0487825	+	0.207561i
$247$	2.42434	+	1.39969i	0.154257	+	0.0890603i
$248$	21.5071	+	7.96509i	1.36570	+	0.505784i
$249$	−1.45588	−	2.52166i	−0.0922628	−	0.159804i
$250$	−14.0826	−	4.24480i	−0.890659	−	0.268465i
$251$	22.3099			1.40819			0.704095	−	0.710106i	$-0.251353\pi$
$251$	22.3099			1.40819			0.704095	+	0.710106i	$0.251353\pi$
$252$	−14.0907	−	2.19540i	−0.887633	−	0.138297i
$253$	4.04239			0.254143
$254$	−5.09046	−	1.53438i	−0.319404	−	0.0962755i
$255$	2.36599	+	4.09801i	0.148164	+	0.256627i
$256$	−11.1530	+	11.4721i	−0.697064	+	0.717008i
$257$	2.78766	+	1.60946i	0.173890	+	0.100395i	0.584419	−	0.811452i	$-0.301323\pi$
$257$	2.78766	+	1.60946i	0.173890	+	0.100395i	−0.410529	+	0.911848i	$0.634656\pi$
$258$	0.0547719	+	0.233045i	0.00340995	+	0.0145088i
$259$	−16.2416	+	7.46764i	−1.00920	+	0.464016i
$260$	6.77349	−	3.37006i	0.420074	−	0.209002i
$261$	−5.86332	+	10.1556i	−0.362930	+	0.628614i
$262$	−16.2029	−	17.2386i	−1.00102	−	1.06500i
$263$	2.19731	−	1.26862i	0.135492	−	0.0782265i	−0.430722	−	0.902485i	$-0.641741\pi$
$263$	2.19731	−	1.26862i	0.135492	−	0.0782265i	0.566214	+	0.824258i	$0.308408\pi$
$264$	1.53976	−	0.262587i	0.0947654	−	0.0161611i
$265$			12.5096i			0.768460i
$266$	−0.903348	−	6.49487i	−0.0553878	−	0.398226i
$267$		−	5.66297i		−	0.346568i
$268$	17.7024	+	1.09761i	1.08134	+	0.0670470i
$269$	2.49325	−	1.43948i	0.152016	−	0.0877666i	−0.422062	−	0.906567i	$-0.638694\pi$
$269$	2.49325	−	1.43948i	0.152016	−	0.0877666i	0.574079	+	0.818800i	$0.305360\pi$
$270$	7.67504	−	7.21390i	0.467088	−	0.439024i
$271$	0.472390	−	0.818204i	0.0286957	−	0.0497023i	−0.851321	−	0.524645i	$-0.824198\pi$
$271$	0.472390	−	0.818204i	0.0286957	−	0.0497023i	0.880017	+	0.474943i	$0.157531\pi$
$272$	11.5440	+	8.72936i	0.699956	+	0.529295i
$273$	−2.32386	−	0.215895i	−0.140647	−	0.0130666i
$274$	−25.4050	+	5.97085i	−1.53477	+	0.360712i
$275$	−0.526774	−	0.304133i	−0.0317657	−	0.0183399i
$276$	−2.46740	+	3.72105i	−0.148520	+	0.223981i
$277$	−2.40740	−	4.16974i	−0.144647	−	0.250536i	0.784594	−	0.620009i	$-0.212871\pi$
$277$	−2.40740	−	4.16974i	−0.144647	−	0.250536i	−0.929241	+	0.369474i	$0.879538\pi$
$278$	0.793278	−	2.63178i	0.0475777	−	0.157844i
$279$	−21.8529			−1.30830
$280$	−15.9781	−	7.66564i	−0.954876	−	0.458109i
$281$	−19.0100			−1.13404			−0.567020	−	0.823704i	$-0.691904\pi$
$281$	−19.0100			−1.13404			−0.567020	+	0.823704i	$0.691904\pi$
$282$	−2.20789	+	7.32490i	−0.131478	+	0.436191i
$283$	−10.3478	−	17.9229i	−0.615112	−	1.06541i	−0.990365	−	0.138483i	$-0.955777\pi$
$283$	−10.3478	−	17.9229i	−0.615112	−	1.06541i	0.375253	−	0.926923i	$-0.377556\pi$
$284$	−7.58036	+	11.4319i	−0.449811	+	0.678356i
$285$	1.98492	+	1.14600i	0.117577	+	0.0678830i
$286$	−2.19905	+	0.516836i	−0.130033	+	0.0305612i
$287$	−6.54779	+	9.24513i	−0.386504	+	0.545723i
$288$	6.16923	−	13.9414i	0.363525	−	0.821503i
$289$	−1.95422	+	3.38480i	−0.114954	+	0.199106i
$290$	−10.6185	+	9.98052i	−0.623541	+	0.586077i
$291$	2.35527	−	1.35982i	0.138069	−	0.0797140i
$292$	−10.7690	−	0.667716i	−0.630209	−	0.0390751i
$293$			23.0857i			1.34868i	0.738422	+	0.674339i	$0.235571\pi$
$293$			23.0857i			1.34868i	−0.738422	+	0.674339i	$0.764429\pi$
$294$	2.94628	+	4.60510i	0.171830	+	0.268575i
$295$		−	25.4925i		−	1.48423i
$296$	−3.21266	−	18.8384i	−0.186732	−	1.09496i
$297$	−2.72369	+	1.57253i	−0.158045	+	0.0912472i
$298$	−2.15871	−	2.29670i	−0.125051	−	0.133044i
$299$	3.22853	−	5.59197i	0.186711	−	0.323392i
$300$	0.601490	−	0.299263i	0.0347270	−	0.0172780i
$301$	−0.468728	+	0.661819i	−0.0270170	+	0.0381466i
$302$	4.48233	+	19.0716i	0.257929	+	1.09744i
$303$	−7.25393	−	4.18806i	−0.416728	−	0.240598i
$304$	6.95645	+	0.865976i	0.398980	+	0.0496671i
$305$	2.65643	+	4.60107i	0.152107	+	0.263457i
$306$	−13.2035	−	3.97984i	−0.754795	−	0.227512i
$307$	28.7821			1.64268			0.821340	−	0.570439i	$-0.193227\pi$
$307$	28.7821			1.64268			0.821340	+	0.570439i	$0.193227\pi$
$308$	4.12064	+	3.31969i	0.234795	+	0.189157i
$309$	−1.38380			−0.0787218
$310$	−26.0011	−	7.83733i	−1.47677	−	0.445130i
$311$	6.03307	+	10.4496i	0.342104	+	0.592542i	0.984823	−	0.173560i	$-0.0555271\pi$
$311$	6.03307	+	10.4496i	0.342104	+	0.592542i	−0.642719	+	0.766102i	$0.722194\pi$
$312$	0.866507	−	2.33971i	0.0490563	−	0.132460i
$313$	0.313439	+	0.180964i	0.0177166	+	0.0102287i	0.508832	−	0.860866i	$-0.330077\pi$
$313$	0.313439	+	0.180964i	0.0177166	+	0.0102287i	−0.491116	+	0.871094i	$0.663411\pi$
$314$	−5.87493	−	24.9969i	−0.331541	−	1.41065i
$315$	16.8136	+	1.56204i	0.947338	+	0.0880110i
$316$	−13.4124	−	26.9576i	−0.754507	−	1.51649i
$317$	10.3979	−	18.0097i	0.584003	−	1.01152i	−0.410996	−	0.911637i	$-0.634819\pi$
$317$	10.3979	−	18.0097i	0.584003	−	1.01152i	0.994999	−	0.0998856i	$-0.0318477\pi$
$318$	2.82546	+	3.00608i	0.158444	+	0.168573i
$319$	3.76827	−	2.17561i	0.210982	−	0.121811i
$320$	12.3402	−	14.3753i	0.689840	−	0.803601i
$321$			4.12313i			0.230131i
$322$	−14.9810	+	2.08366i	−0.834861	+	0.116118i
$323$		−	6.34107i		−	0.352827i
$324$	−0.785715	+	12.6721i	−0.0436508	+	0.704008i
$325$	−0.841435	+	0.485803i	−0.0466744	+	0.0269475i
$326$	21.3135	−	20.0329i	1.18044	−	1.10952i
$327$	−0.587464	+	1.01752i	−0.0324868	+	0.0562688i
$328$	−7.73267	−	9.32132i	−0.426965	−	0.514684i
$329$	−23.5474	+	10.8267i	−1.29821	+	0.596898i
$330$	−1.80047	+	0.423159i	−0.0991127	+	0.0232941i
$331$	−10.4160	−	6.01367i	−0.572514	−	0.330541i	0.185639	−	0.982618i	$-0.440565\pi$
$331$	−10.4160	−	6.01367i	−0.572514	−	0.330541i	−0.758153	+	0.652077i	$0.773898\pi$
$332$	8.78861	+	5.82764i	0.482338	+	0.319834i
$333$	9.10451	+	15.7695i	0.498924	+	0.864162i
$334$	9.04886	−	30.0205i	0.495132	−	1.64265i
$335$	−21.0014			−1.14743
$336$	−5.57096	+	1.76681i	−0.303921	+	0.0963876i
$337$	25.0435			1.36420			0.682102	−	0.731257i	$-0.261066\pi$
$337$	25.0435			1.36420			0.682102	+	0.731257i	$0.261066\pi$
$338$	4.26444	−	14.1477i	0.231955	−	0.769534i
$339$	−5.23780	−	9.07213i	−0.284478	−	0.492731i
$340$	−14.2825	−	9.47063i	−0.774580	−	0.513617i
$341$	7.02227	+	4.05431i	0.380277	+	0.219553i
$342$	−6.50234	+	1.52822i	−0.351606	+	0.0826369i
$343$	−5.08102	+	17.8096i	−0.274349	+	0.961630i
$344$	−0.553548	−	0.667273i	−0.0298453	−	0.0359769i
$345$	2.64335	−	4.57842i	0.142313	−	0.246494i
$346$	−11.9852	+	11.2651i	−0.644327	+	0.605614i
$347$	−29.9268	+	17.2783i	−1.60656	+	0.927546i	−0.616424	+	0.787415i	$0.711419\pi$
$347$	−29.9268	+	17.2783i	−1.60656	+	0.927546i	−0.990133	+	0.140131i	$0.955248\pi$
$348$	−0.297410	+	4.79667i	−0.0159428	+	0.257128i
$349$			9.33947i			0.499931i	0.968255	+	0.249965i	$0.0804192\pi$
$349$			9.33947i			0.499931i	−0.968255	+	0.249965i	$0.919581\pi$
$350$	2.10898	+	0.855586i	0.112730	+	0.0457330i
$351$			5.02370i			0.268145i
$352$	−4.56893	+	3.33539i	−0.243525	+	0.177777i
$353$	−0.791247	+	0.456826i	−0.0421138	+	0.0243144i	−0.520909	−	0.853612i	$-0.674407\pi$
$353$	−0.791247	+	0.456826i	−0.0421138	+	0.0243144i	0.478795	+	0.877927i	$0.341074\pi$
$354$	−5.75782	−	6.12588i	−0.306024	−	0.325587i
$355$	8.12092	−	14.0659i	0.431014	−	0.746538i
$356$	9.13565	+	18.3618i	0.484188	+	0.973172i
$357$	2.20845	+	4.80322i	0.116883	+	0.254213i
$358$	3.62971	+	15.4438i	0.191836	+	0.816231i
$359$	−5.41783	−	3.12799i	−0.285942	−	0.165089i	0.350168	−	0.936687i	$-0.386124\pi$
$359$	−5.41783	−	3.12799i	−0.285942	−	0.165089i	−0.636110	+	0.771598i	$0.719458\pi$
$360$	−6.26933	+	16.9282i	−0.330423	+	0.892197i
$361$	7.96431	+	13.7946i	0.419174	+	0.726031i
$362$	21.0817	+	6.35449i	1.10803	+	0.333985i
$363$	0.552245			0.0289854
$364$	7.88325	−	3.04889i	0.413195	−	0.159805i
$365$	12.7760			0.668725
$366$	1.67756	+	0.505654i	0.0876873	+	0.0264309i
$367$	−10.4231	−	18.0534i	−0.544082	−	0.942377i	−0.998664	−	0.0516727i	$-0.983545\pi$
$367$	−10.4231	−	18.0534i	−0.544082	−	0.942377i	0.454582	−	0.890705i	$-0.349789\pi$
$368$	1.99746	−	16.0457i	0.104125	−	0.836441i
$369$	9.99392	+	5.76999i	0.520263	+	0.300374i
$370$	5.17720	+	22.0281i	0.269150	+	1.14519i
$371$	−1.29284	+	13.9159i	−0.0671209	+	0.722480i
$372$	−8.01828	+	3.98938i	−0.415728	+	0.206840i
$373$	−14.0434	+	24.3239i	−0.727141	+	1.25944i	0.230946	+	0.972967i	$0.425818\pi$
$373$	−14.0434	+	24.3239i	−0.727141	+	1.25944i	−0.958087	+	0.286478i	$0.907515\pi$
$374$	3.50448	+	3.72850i	0.181212	+	0.192796i
$375$	4.97408	−	2.87179i	0.256860	−	0.148298i
$376$	−4.65779	−	27.3123i	−0.240207	−	1.40852i
$377$		−	6.95035i		−	0.357961i
$378$	9.28340	−	7.23168i	0.477487	−	0.371958i
$379$			11.4941i			0.590412i	0.955434	+	0.295206i	$0.0953883\pi$
$379$			11.4941i			0.590412i	−0.955434	+	0.295206i	$0.904612\pi$
$380$	−8.28472	−	0.513681i	−0.424997	−	0.0263513i
$381$	1.79799	−	1.03807i	0.0921139	−	0.0531820i
$382$	−19.7333	+	18.5476i	−1.00964	+	0.948979i
$383$	−4.63942	+	8.03571i	−0.237063	+	0.410606i	−0.959870	−	0.280444i	$-0.909518\pi$
$383$	−4.63942	+	8.03571i	−0.237063	+	0.410606i	0.722807	+	0.691050i	$0.242852\pi$
$384$	−0.281469	−	6.24160i	−0.0143636	−	0.318515i
$385$	−5.11311	−	3.62132i	−0.260588	−	0.184560i
$386$	−13.6580	+	3.20999i	−0.695174	+	0.163384i
$387$	0.715421	+	0.413049i	0.0363669	+	0.0209964i
$388$	−5.44312	+	8.20870i	−0.276332	+	0.416734i
$389$	9.61945	+	16.6614i	0.487726	+	0.844766i	0.999900	−	0.0141156i	$-0.00449329\pi$
$389$	9.61945	+	16.6614i	0.487726	+	0.844766i	−0.512175	+	0.858881i	$0.671160\pi$
$390$	−0.852608	+	2.82861i	−0.0431735	+	0.143232i
$391$	−14.6263			−0.739683
$392$	−16.9822	−	10.1787i	−0.857729	−	0.514102i
$393$	9.23837			0.466014
$394$	9.25779	−	30.7137i	0.466401	−	1.54733i
$395$	17.8264	+	30.8762i	0.896944	+	1.55355i
$396$	2.97873	−	4.49219i	0.149687	−	0.225741i
$397$	7.33685	+	4.23593i	0.368226	+	0.212595i	0.672683	−	0.739931i	$-0.265142\pi$
$397$	7.33685	+	4.23593i	0.368226	+	0.212595i	−0.304457	+	0.952526i	$0.598475\pi$
$398$	−21.0408	+	4.94515i	−1.05468	+	0.247878i
$399$	2.08963	+	1.47997i	0.104612	+	0.0740910i
$400$	−1.46751	+	1.94068i	−0.0733755	+	0.0970339i
$401$	4.65713	−	8.06639i	0.232566	−	0.402816i	−0.725997	−	0.687698i	$-0.758621\pi$
$401$	4.65713	−	8.06639i	0.232566	−	0.402816i	0.958563	+	0.284882i	$0.0919545\pi$
$402$	−5.04667	+	4.74345i	−0.251705	+	0.236582i
$403$	11.2169	−	6.47609i	0.558754	−	0.322597i
$404$	30.2766	+	1.87725i	1.50632	+	0.0933969i
$405$		−	15.0338i		−	0.747033i
$406$	−12.8437	+	10.0051i	−0.637422	+	0.496546i
$407$		−	6.75653i		−	0.334909i
$408$	−5.57118	+	0.950100i	−0.275815	+	0.0470370i
$409$	2.39217	−	1.38112i	0.118285	−	0.0682919i	−0.439690	−	0.898150i	$-0.644912\pi$
$409$	2.39217	−	1.38112i	0.118285	−	0.0682919i	0.557975	+	0.829858i	$0.311578\pi$
$410$	9.82166	+	10.4495i	0.485057	+	0.516064i
$411$	5.09543	−	8.82554i	0.251339	−	0.435332i
$412$	4.48688	−	2.23239i	0.221053	−	0.109982i
$413$	2.63459	−	28.3583i	0.129640	−	1.39542i
$414$	3.52500	+	14.9983i	0.173244	+	0.737125i
$415$	−10.8136	−	6.24322i	−0.530818	−	0.306468i
$416$	0.964899	+	8.98422i	0.0473081	+	0.440488i
$417$	0.536686	+	0.929568i	0.0262816	+	0.0455211i
$418$	2.37300	+	0.715277i	0.116067	+	0.0349853i
$419$	12.9306			0.631702			0.315851	−	0.948809i	$-0.397710\pi$
$419$	12.9306			0.631702			0.315851	+	0.948809i	$0.397710\pi$
$420$	6.45440	−	2.49628i	0.314942	−	0.121806i
$421$	−14.3913			−0.701388			−0.350694	−	0.936490i	$-0.614054\pi$
$421$	−14.3913			−0.701388			−0.350694	+	0.936490i	$0.614054\pi$
$422$	32.5897	+	9.82327i	1.58644	+	0.478189i
$423$	13.1999	+	22.8629i	0.641802	+	1.11163i
$424$	−14.0109	−	5.18888i	−0.680427	−	0.251994i
$425$	1.90599	+	1.10042i	0.0924541	+	0.0533784i
$426$	−1.22549	−	5.21426i	−0.0593752	−	0.252632i
$427$	2.47955	+	5.39286i	0.119994	+	0.260979i
$428$	−6.65155	−	13.3690i	−0.321515	−	0.646214i
$429$	0.441060	−	0.763939i	0.0212946	−	0.0368833i
$430$	0.703090	+	0.748034i	0.0339060	+	0.0360734i
$431$	32.9752	−	19.0382i	1.58836	−	0.917039i	0.594781	−	0.803888i	$-0.297239\pi$
$431$	32.9752	−	19.0382i	1.58836	−	0.917039i	0.993578	−	0.113151i	$-0.0360944\pi$
$432$	4.89607	+	11.5884i	0.235562	+	0.557545i
$433$		−	27.5947i		−	1.32612i	−0.748568	−	0.663058i	$-0.769258\pi$
$433$		−	27.5947i		−	1.32612i	0.748568	−	0.663058i	$-0.230742\pi$
$434$	−28.1142	−	11.4056i	−1.34952	−	0.547484i
$435$		−	5.69059i		−	0.272843i
$436$	0.263325	−	4.24694i	0.0126110	−	0.203392i
$437$	−6.13530	+	3.54222i	−0.293491	+	0.169447i
$438$	3.07008	−	2.88562i	0.146694	−	0.137880i
$439$	−8.61340	+	14.9189i	−0.411095	+	0.712038i	−0.995010	−	0.0997772i	$-0.968187\pi$
$439$	−8.61340	+	14.9189i	−0.411095	+	0.712038i	0.583915	+	0.811815i	$0.301520\pi$
$440$	5.15525	−	4.27663i	0.245767	−	0.203880i
$441$	18.5423	+	3.47529i	0.882967	+	0.165490i
$442$	7.95667	−	1.87003i	0.378460	−	0.0889483i
$443$	0.405292	+	0.233995i	0.0192560	+	0.0111175i	0.509597	−	0.860413i	$-0.329794\pi$
$443$	0.405292	+	0.233995i	0.0192560	+	0.0111175i	−0.490341	+	0.871531i	$0.663128\pi$
$444$	6.21944	+	4.12405i	0.295162	+	0.195719i
$445$	−12.1422	−	21.0309i	−0.575594	−	0.996959i
$446$	11.2508	−	37.3256i	0.532740	−	1.76742i
$447$	1.23083			0.0582163
$448$	15.2132	−	14.7160i	0.718754	−	0.695264i
$449$	−19.5997			−0.924967			−0.462484	−	0.886628i	$-0.653042\pi$
$449$	−19.5997			−0.924967			−0.462484	+	0.886628i	$0.653042\pi$
$450$	0.669058	−	2.21967i	0.0315397	−	0.104636i
$451$	−2.14098	−	3.70828i	−0.100815	−	0.174616i
$452$	31.6186	+	20.9660i	1.48721	+	0.986157i
$453$	−6.62535	−	3.82515i	−0.311286	−	0.179721i
$454$	13.3711	−	3.14257i	0.627537	−	0.147488i
$455$	−9.09316	+	4.18090i	−0.426294	+	0.196004i
$456$	−2.10685	+	1.74778i	−0.0986624	+	0.0818472i
$457$	16.7075	−	28.9382i	0.781542	−	1.35367i	−0.149501	−	0.988762i	$-0.547767\pi$
$457$	16.7075	−	28.9382i	0.781542	−	1.35367i	0.931043	−	0.364910i	$-0.118900\pi$
$458$	27.8221	−	26.1505i	1.30004	−	1.22193i
$459$	9.85494	−	5.68975i	0.459989	−	0.265575i
$460$	−1.18485	+	19.1095i	−0.0552441	+	0.890986i
$461$		−	32.9574i		−	1.53498i	−0.641060	−	0.767490i	$-0.721505\pi$
$461$		−	32.9574i		−	1.53498i	0.641060	−	0.767490i	$-0.278495\pi$
$462$	−2.04661	+	0.284656i	−0.0952170	+	0.0132434i
$463$			15.7228i			0.730702i	0.930870	+	0.365351i	$0.119051\pi$
$463$			15.7228i			0.730702i	−0.930870	+	0.365351i	$0.880949\pi$
$464$	−6.77378	−	16.0326i	−0.314465	−	0.744297i
$465$	9.18382	−	5.30228i	0.425890	−	0.245888i
$466$	11.0081	+	11.7118i	0.509942	+	0.542539i
$467$	3.93285	−	6.81189i	0.181991	−	0.315217i	−0.760568	−	0.649259i	$-0.775079\pi$
$467$	3.93285	−	6.81189i	0.181991	−	0.315217i	0.942558	+	0.334042i	$0.108413\pi$
$468$	−3.83518	−	7.70834i	−0.177281	−	0.356318i
$469$	−23.3624	−	2.17045i	−1.07878	−	0.100222i
$470$	7.50602	+	31.9369i	0.346227	+	1.47314i
$471$	8.68376	+	5.01357i	0.400127	+	0.231013i
$472$	28.5517	+	10.5741i	1.31420	+	0.486711i
$473$	−0.153263	−	0.265460i	−0.00704706	−	0.0122059i
$474$	11.2575	+	3.39327i	0.517075	+	0.155858i
$475$	1.06601			0.0489119
$476$	−14.9094	−	12.0114i	−0.683372	−	0.550540i
$477$	14.2362			0.651829
$478$	10.6389	+	3.20682i	0.486614	+	0.146676i
$479$	−4.16106	−	7.20717i	−0.190124	−	0.329304i	0.755167	−	0.655532i	$-0.227556\pi$
$479$	−4.16106	−	7.20717i	−0.190124	−	0.329304i	−0.945291	+	0.326228i	$0.894222\pi$
$480$	0.790009	+	7.35582i	0.0360588	+	0.335746i
$481$	−9.34653	−	5.39622i	−0.426165	−	0.246046i
$482$	−2.50238	−	10.6472i	−0.113980	−	0.484968i
$483$	3.41368	−	4.81994i	0.155328	−	0.219315i
$484$	−1.79062	+	0.890896i	−0.0813916	+	0.0404953i
$485$	5.83127	−	10.1001i	0.264784	−	0.458620i
$486$	−12.5341	−	13.3353i	−0.568559	−	0.604904i
$487$	24.5222	−	14.1579i	1.11121	−	0.641555i	0.172065	−	0.985086i	$-0.444956\pi$
$487$	24.5222	−	14.1579i	1.11121	−	0.641555i	0.939142	+	0.343530i	$0.111623\pi$
$488$	−6.25509	+	1.06673i	−0.283155	+	0.0482887i
$489$			11.4221i			0.516527i
$490$	20.8157	+	10.7850i	0.940358	+	0.487216i
$491$			5.32731i			0.240418i	0.992749	+	0.120209i	$0.0383565\pi$
$491$			5.32731i			0.240418i	−0.992749	+	0.120209i	$0.961644\pi$
$492$	4.72032	+	0.292675i	0.212808	+	0.0131948i
$493$	−13.6344	+	7.87185i	−0.614064	+	0.354530i
$494$	2.88471	−	2.71138i	0.129789	−	0.121991i
$495$	−3.19115	+	5.52723i	−0.143432	+	0.248431i
$496$	19.5629	−	25.8706i	0.878401	−	1.16162i
$497$	10.4875	−	14.8078i	0.470431	−	0.664223i
$498$	−4.00863	+	0.942136i	−0.179631	+	0.0422181i
$499$	−11.0319	−	6.36925i	−0.493854	−	0.285127i	0.232318	−	0.972640i	$-0.425369\pi$
$499$	−11.0319	−	6.36925i	−0.493854	−	0.285127i	−0.726172	+	0.687513i	$0.758702\pi$
$500$	−11.4953	+	17.3359i	−0.514084	+	0.775284i
$501$	6.12193	+	10.6035i	0.273508	+	0.473729i
$502$	9.10553	−	30.2085i	0.406400	−	1.34827i
$503$	−4.49059			−0.200225			−0.100113	−	0.994976i	$-0.531920\pi$
$503$	−4.49059			−0.200225			−0.100113	+	0.994976i	$0.531920\pi$
$504$	−8.72362	+	18.1834i	−0.388581	+	0.809952i
$505$	−35.9191			−1.59838
$506$	1.64985	−	5.47356i	0.0733450	−	0.243329i
$507$	2.88507	+	4.99709i	0.128131	+	0.221929i
$508$	−4.15522	+	6.26644i	−0.184358	+	0.278028i
$509$	9.33046	+	5.38695i	0.413566	+	0.238772i	0.692321	−	0.721590i	$-0.256588\pi$
$509$	9.33046	+	5.38695i	0.413566	+	0.238772i	−0.278755	+	0.960362i	$0.589922\pi$
$510$	6.51451	−	1.53109i	0.288467	−	0.0677976i
$511$	14.2122	+	1.32037i	0.628712	+	0.0584096i
$512$	10.9817	+	19.7839i	0.485329	+	0.874331i
$513$	2.75591	−	4.77337i	0.121676	−	0.210749i
$514$	3.31702	−	3.11773i	0.146308	−	0.137517i
$515$	−5.13910	+	2.96706i	−0.226456	+	0.130744i
$516$	0.337907	+	0.0209514i	0.0148755	+	0.000922332i
$517$		−	9.79576i		−	0.430817i
$518$	3.48267	+	25.0396i	0.153020	+	1.10018i
$519$		−	6.42300i		−	0.281938i
$520$	−1.79867	−	10.5470i	−0.0788769	−	0.462518i
$521$	−30.1645	+	17.4155i	−1.32153	+	0.762986i	−0.983973	−	0.178318i	$-0.942934\pi$
$521$	−30.1645	+	17.4155i	−1.32153	+	0.762986i	−0.337558	+	0.941305i	$0.609601\pi$
$522$	11.3580	+	12.0840i	0.497126	+	0.528904i
$523$	0.925359	−	1.60277i	0.0404631	−	0.0700842i	−0.845085	−	0.534633i	$-0.820450\pi$
$523$	0.925359	−	1.60277i	0.0404631	−	0.0700842i	0.885548	+	0.464548i	$0.153783\pi$
$524$	−29.9548	+	14.9036i	−1.30858	+	0.651066i
$525$	−0.807478	+	0.371266i	−0.0352412	+	0.0162034i
$526$	−0.820954	−	3.49302i	−0.0357953	−	0.152303i
$527$	−25.4082	−	14.6694i	−1.10680	−	0.639009i
$528$	0.272879	−	2.19206i	0.0118756	−	0.0953972i
$529$	−3.32953	−	5.76692i	−0.144762	−	0.250736i
$530$	16.9385	+	5.10565i	0.735762	+	0.221775i
$531$	−29.0109			−1.25896
$532$	−9.16300	−	1.42764i	−0.397266	−	0.0618958i
$533$	−6.83972			−0.296261
$534$	−7.66789	−	2.31127i	−0.331822	−	0.100019i
$535$	8.84056	+	15.3123i	0.382211	+	0.662009i
$536$	8.71122	−	23.5217i	0.376267	−	1.01598i
$537$	−5.36509	−	3.09754i	−0.231521	−	0.133669i
$538$	−0.931521	−	3.96347i	−0.0401607	−	0.170877i
$539$	−5.31367	−	4.55686i	−0.228876	−	0.196278i
$540$	−6.63543	−	13.3366i	−0.285543	−	0.573915i
$541$	8.51018	−	14.7401i	0.365881	−	0.633725i	−0.623036	−	0.782193i	$-0.714101\pi$
$541$	8.51018	−	14.7401i	0.365881	−	0.633725i	0.988917	+	0.148468i	$0.0474342\pi$
$542$	−0.915080	−	0.973575i	−0.0393061	−	0.0418186i
$543$	−7.44623	+	4.29908i	−0.319548	+	0.184491i
$544$	16.5314	−	12.0682i	0.708780	−	0.517420i
$545$			5.03841i			0.215822i
$546$	−1.24079	+	3.05849i	−0.0531008	+	0.130891i
$547$			3.32464i			0.142152i	0.997471	+	0.0710758i	$0.0226432\pi$
$547$			3.32464i			0.142152i	−0.997471	+	0.0710758i	$0.977357\pi$
$548$	−2.28397	+	36.8363i	−0.0975664	+	1.57357i
$549$	5.23609	−	3.02306i	0.223471	−	0.129021i
$550$	−0.626805	+	0.589145i	−0.0267271	+	0.0251212i
$551$	−3.81283	+	6.60402i	−0.162432	+	0.281341i
$552$	4.03142	+	4.85966i	0.171588	+	0.206841i
$553$	16.6395	+	36.1896i	0.707582	+	1.53894i
$554$	−6.62855	+	1.55789i	−0.281620	+	0.0661883i
$555$	−7.65245	−	4.41814i	−0.324828	−	0.187540i
$556$	−3.23977	−	2.14826i	−0.137397	−	0.0911065i
$557$	−10.0286	−	17.3700i	−0.424924	−	0.735990i	0.571490	−	0.820609i	$-0.306366\pi$
$557$	−10.0286	−	17.3700i	−0.424924	−	0.735990i	−0.996413	+	0.0846198i	$0.973032\pi$
$558$	−8.91901	+	29.5897i	−0.377572	+	1.25263i
$559$	−0.489626			−0.0207090
$560$	−16.9009	+	18.5064i	−0.714192	+	0.782038i
$561$	−1.99815			−0.0843619
$562$	−7.75870	+	25.7403i	−0.327281	+	1.08579i
$563$	−9.21452	−	15.9600i	−0.388346	−	0.672634i	0.603882	−	0.797074i	$-0.293620\pi$
$563$	−9.21452	−	15.9600i	−0.388346	−	0.672634i	−0.992227	+	0.124440i	$0.960287\pi$
$564$	9.01708	+	5.97914i	0.379688	+	0.251767i
$565$	−38.9038	−	22.4611i	−1.63669	−	0.944946i
$566$	−28.4916	+	6.69630i	−1.19759	+	0.281466i
$567$	1.55370	−	16.7238i	0.0652494	−	0.702335i
$568$	12.3853	+	14.9299i	0.519678	+	0.626444i
$569$	−13.8931	+	24.0636i	−0.582431	+	1.00880i	0.412760	+	0.910840i	$0.364565\pi$
$569$	−13.8931	+	24.0636i	−0.582431	+	1.00880i	−0.995190	+	0.0979594i	$0.968768\pi$
$570$	2.36185	−	2.21994i	0.0989269	−	0.0929831i
$571$	−0.216461	+	0.124974i	−0.00905861	+	0.00522999i	−0.504522	−	0.863399i	$-0.668331\pi$
$571$	−0.216461	+	0.124974i	−0.00905861	+	0.00522999i	0.495464	+	0.868629i	$0.334998\pi$
$572$	−0.197701	+	3.18855i	−0.00826628	+	0.133320i
$573$		−	10.5753i		−	0.441789i
$574$	9.84587	+	12.6393i	0.410959	+	0.527553i
$575$		−	2.45885i		−	0.102541i
$576$	−16.3593	−	14.0434i	−0.681636	−	0.585141i
$577$	33.7688	−	19.4964i	1.40581	−	0.811646i	0.410831	−	0.911711i	$-0.365239\pi$
$577$	33.7688	−	19.4964i	1.40581	−	0.811646i	0.994981	+	0.100065i	$0.0319052\pi$
$578$	3.78557	+	4.02756i	0.157459	+	0.167524i
$579$	2.73936	−	4.74471i	0.113844	−	0.197183i
$580$	9.18020	+	18.4513i	0.381187	+	0.766150i
$581$	−11.3840	−	8.06264i	−0.472288	−	0.334495i
$582$	−0.879971	−	3.74413i	−0.0364760	−	0.155199i
$583$	−4.57468	−	2.64119i	−0.189464	−	0.109387i
$584$	−5.29936	+	14.3092i	−0.219289	+	0.592117i
$585$	5.09733	+	8.82884i	0.210749	+	0.365028i
$586$	31.2589	+	9.42214i	1.29129	+	0.389225i
$587$	35.5786			1.46849			0.734244	−	0.678886i	$-0.237537\pi$
$587$	35.5786			1.46849			0.734244	+	0.678886i	$0.237537\pi$
$588$	7.43798	−	2.10986i	0.306737	−	0.0870091i
$589$	−14.2106			−0.585539
$590$	−34.5178	−	10.4045i	−1.42108	−	0.428345i
$591$	6.26328	+	10.8483i	0.257637	+	0.446241i
$592$	−26.8191	−	3.33859i	−1.10226	−	0.137215i
$593$	25.6808	+	14.8268i	1.05458	+	0.608863i	0.923929	−	0.382565i	$-0.124959\pi$
$593$	25.6808	+	14.8268i	1.05458	+	0.608863i	0.130654	+	0.991428i	$0.458292\pi$
$594$	1.01762	+	4.32980i	0.0417534	+	0.177654i
$595$	18.5004	+	13.1028i	0.758442	+	0.537161i
$596$	−3.99088	+	1.98561i	−0.163473	+	0.0813336i
$597$	4.22011	−	7.30945i	0.172718	−	0.299156i
$598$	−6.25407	−	6.65385i	−0.255748	−	0.272096i
$599$	7.68791	−	4.43862i	0.314120	−	0.181357i	−0.334649	−	0.942343i	$-0.608618\pi$
$599$	7.68791	−	4.43862i	0.314120	−	0.181357i	0.648768	+	0.760986i	$0.275284\pi$
$600$	−0.159723	−	0.936582i	−0.00652067	−	0.0382358i
$601$			28.9509i			1.18093i	0.807063	+	0.590465i	$0.201056\pi$
$601$			28.9509i			1.18093i	−0.807063	+	0.590465i	$0.798944\pi$
$602$	0.704823	+	0.904790i	0.0287264	+	0.0368765i
$603$			23.9000i			0.973282i
$604$	27.6530	+	1.71458i	1.12519	+	0.0697653i
$605$	2.05090	−	1.18409i	0.0833810	−	0.0481401i
$606$	−8.63141	+	8.11281i	−0.350627	+	0.329560i
$607$	12.9616	−	22.4501i	0.526095	−	0.911223i	−0.473443	−	0.880824i	$-0.656989\pi$
$607$	12.9616	−	22.4501i	0.526095	−	0.911223i	0.999538	−	0.0303986i	$-0.00967766\pi$
$608$	4.01176	−	9.06587i	0.162698	−	0.367670i
$609$	0.588109	−	6.33032i	0.0238314	−	0.256518i
$610$	7.31422	−	1.71904i	0.296144	−	0.0696018i
$611$	−13.5508	−	7.82356i	−0.548207	−	0.316507i
$612$	−10.7777	+	16.2538i	−0.435664	+	0.657020i
$613$	−6.09644	−	10.5593i	−0.246233	−	0.426488i	0.716245	−	0.697849i	$-0.245860\pi$
$613$	−6.09644	−	10.5593i	−0.246233	−	0.426488i	−0.962478	+	0.271361i	$0.912526\pi$
$614$	11.7471	−	38.9721i	0.474073	−	1.57278i
$615$	−5.60001			−0.225814
$616$	6.17678	−	4.22462i	0.248869	−	0.170215i
$617$	−14.7610			−0.594257			−0.297128	−	0.954838i	$-0.596029\pi$
$617$	−14.7610			−0.594257			−0.297128	+	0.954838i	$0.596029\pi$
$618$	−0.564783	+	1.87372i	−0.0227189	+	0.0753722i
$619$	−10.6621	−	18.4673i	−0.428547	−	0.742264i	0.568198	−	0.822892i	$-0.307641\pi$
$619$	−10.6621	−	18.4673i	−0.428547	−	0.742264i	−0.996744	+	0.0806276i	$0.974308\pi$
$620$	−21.2241	+	32.0079i	−0.852381	+	1.28547i
$621$	−11.0102	−	6.35676i	−0.441826	−	0.255088i
$622$	16.6115	−	3.90414i	0.666060	−	0.156542i
$623$	−11.3337	−	24.6500i	−0.454075	−	0.987582i
$624$	−2.81441	−	2.12821i	−0.112667	−	0.0851966i
$625$	13.8357	−	23.9641i	0.553427	−	0.958564i
$626$	0.372959	−	0.350550i	0.0149064	−	0.0140108i
$627$	−0.838165	+	0.483915i	−0.0334731	+	0.0193257i
$628$	−36.2445	−	2.24728i	−1.44631	−	0.0896763i
$629$			24.4467i			0.974752i
$630$	8.97732	−	22.1287i	0.357665	−	0.881629i
$631$			19.5060i			0.776523i	0.921549	+	0.388262i	$0.126924\pi$
$631$			19.5060i			0.776523i	−0.921549	+	0.388262i	$0.873076\pi$
$632$	−41.9758	+	7.15848i	−1.66971	+	0.284749i
$633$	−11.5110	+	6.64586i	−0.457520	+	0.264149i
$634$	−20.1420	−	21.4296i	−0.799941	−	0.851077i
$635$	4.45153	−	7.71028i	0.176654	−	0.305973i
$636$	5.22353	−	2.59890i	0.207126	−	0.103053i
$637$	−10.5475	+	3.71116i	−0.417907	+	0.147041i
$638$	−1.40789	−	5.99033i	−0.0557388	−	0.237159i
$639$	−16.0072	−	9.24174i	−0.633234	−	0.365598i
$640$	−14.4281	−	22.5762i	−0.570322	−	0.892404i
$641$	−16.8903	−	29.2548i	−0.667126	−	1.15550i	−0.978704	−	0.205276i	$-0.934191\pi$
$641$	−16.8903	−	29.2548i	−0.667126	−	1.15550i	0.311578	−	0.950221i	$-0.399142\pi$
$642$	5.58289	+	1.68281i	0.220339	+	0.0664152i
$643$	−18.8266			−0.742447			−0.371223	−	0.928544i	$-0.621062\pi$
$643$	−18.8266			−0.742447			−0.371223	+	0.928544i	$0.621062\pi$
$644$	−3.29298	+	21.1353i	−0.129761	+	0.832849i
$645$	−0.400880			−0.0157846
$646$	−8.58606	−	2.58803i	−0.337814	−	0.101825i
$647$	24.7139	+	42.8057i	0.971603	+	1.68287i	0.690718	+	0.723124i	$0.257295\pi$
$647$	24.7139	+	42.8057i	0.971603	+	1.68287i	0.280885	+	0.959741i	$0.409372\pi$
$648$	16.8379	+	6.23587i	0.661455	+	0.244968i
$649$	9.32241	+	5.38230i	0.365937	+	0.211274i
$650$	0.314374	+	1.33761i	0.0123308	+	0.0524654i
$651$	10.7642	−	4.94924i	0.421884	−	0.193976i
$652$	−18.4265	−	37.0354i	−0.721637	−	1.45042i
$653$	−10.1509	+	17.5819i	−0.397236	+	0.688032i	−0.993384	−	0.114842i	$-0.963364\pi$
$653$	−10.1509	+	17.5819i	−0.397236	+	0.688032i	0.596148	+	0.802875i	$0.296697\pi$
$654$	1.13799	+	1.21074i	0.0444990	+	0.0473436i
$655$	34.3090	−	19.8083i	1.34057	−	0.773976i
$656$	−15.7774	+	6.66596i	−0.616005	+	0.260262i
$657$		−	14.5393i		−	0.567231i
$658$	5.04924	+	36.3029i	0.196840	+	1.41524i
$659$		−	5.20139i		−	0.202617i	−0.994855	−	0.101309i	$-0.967697\pi$
$659$		−	5.20139i		−	0.202617i	0.994855	−	0.101309i	$-0.0323030\pi$
$660$	−0.161867	+	2.61062i	−0.00630066	+	0.101618i
$661$	−35.1500	+	20.2939i	−1.36718	+	0.789340i	−0.990567	−	0.137031i	$-0.956244\pi$
$661$	−35.1500	+	20.2939i	−1.36718	+	0.789340i	−0.376611	+	0.926372i	$0.622911\pi$
$662$	−12.3939	+	11.6492i	−0.481703	+	0.452761i
$663$	−1.59586	+	2.76410i	−0.0619779	+	0.107349i
$664$	11.4778	−	9.52164i	0.445426	−	0.369511i
$665$	10.9336	+	1.01577i	0.423988	+	0.0393899i
$666$	25.0684	−	5.89174i	0.971380	−	0.228300i
$667$	15.2328	+	8.79467i	0.589817	+	0.340531i
$668$	−36.9558	−	24.5050i	−1.42986	−	0.948128i
$669$	7.61162	+	13.1837i	0.294282	+	0.509712i
$670$	−8.57149	+	28.4368i	−0.331145	+	1.09861i
$671$	−2.24344			−0.0866069
$672$	0.118615	+	8.26440i	0.00457569	+	0.318806i
$673$	−0.730872			−0.0281730			−0.0140865	−	0.999901i	$-0.504484\pi$
$673$	−0.730872			−0.0281730			−0.0140865	+	0.999901i	$0.504484\pi$
$674$	10.2212	−	33.9099i	0.393706	−	1.30616i
$675$	0.956515	+	1.65673i	0.0368163	+	0.0637676i
$676$	−17.4161	−	11.5484i	−0.669849	−	0.444171i
$677$	9.59309	+	5.53857i	0.368692	+	0.212865i	0.672887	−	0.739745i	$-0.265054\pi$
$677$	9.59309	+	5.53857i	0.368692	+	0.212865i	−0.304195	+	0.952610i	$0.598387\pi$
$678$	−14.4218	+	3.38950i	−0.553865	+	0.130173i
$679$	7.53064	−	10.6329i	0.288999	−	0.408052i
$680$	−18.6529	+	15.4738i	−0.715304	+	0.593394i
$681$	−2.68182	+	4.64505i	−0.102768	+	0.177999i
$682$	8.35575	−	7.85371i	0.319958	−	0.300734i
$683$	−25.2358	+	14.5699i	−0.965619	+	0.557501i	−0.897898	−	0.440204i	$-0.854906\pi$
$683$	−25.2358	+	14.5699i	−0.965619	+	0.557501i	−0.0677214	+	0.997704i	$0.521573\pi$
$684$	−0.584577	+	9.42815i	−0.0223519	+	0.360494i
$685$		−	43.7012i		−	1.66974i
$686$	22.0412	+	14.1487i	0.841537	+	0.540199i
$687$			14.9102i			0.568860i
$688$	−1.12944	+	0.477187i	−0.0430594	+	0.0181926i
$689$	−7.30729	+	4.21887i	−0.278386	+	0.160726i
$690$	−5.12051	−	5.44783i	−0.194934	−	0.207395i
$691$	6.54391	−	11.3344i	0.248942	−	0.431180i	−0.714291	−	0.699849i	$-0.753251\pi$
$691$	6.54391	−	11.3344i	0.248942	−	0.431180i	0.963233	+	0.268669i	$0.0865838\pi$
$692$	10.3617	+	20.8261i	0.393894	+	0.791690i
$693$	−4.12112	+	5.81880i	−0.156549	+	0.221038i
$694$	11.1812	+	47.5740i	0.424432	+	1.80589i
$695$	3.98624	+	2.30146i	0.151207	+	0.0872992i
$696$	6.37349	+	2.36041i	0.241587	+	0.0894710i
$697$	7.74655	+	13.4174i	0.293421	+	0.508221i
$698$	12.6460	+	3.81180i	0.478659	+	0.144279i
$699$	−6.27650			−0.237399
$700$	2.01925	−	2.50645i	0.0763206	−	0.0947349i
$701$	14.8404			0.560516			0.280258	−	0.959925i	$-0.409580\pi$
$701$	14.8404			0.560516			0.280258	+	0.959925i	$0.409580\pi$
$702$	6.80229	+	2.05036i	0.256736	+	0.0773860i
$703$	5.92053	+	10.2547i	0.223297	+	0.386762i
$704$	2.65150	+	7.54782i	0.0999321	+	0.284469i
$705$	−11.0947	−	6.40552i	−0.417850	−	0.241246i
$706$	0.295623	+	1.25783i	0.0111259	+	0.0473390i
$707$	−39.9571	−	3.71215i	−1.50274	−	0.139610i
$708$	−10.6447	+	5.29611i	−0.400051	+	0.199040i
$709$	−14.0711	+	24.3719i	−0.528452	+	0.915306i	0.470998	+	0.882134i	$0.343894\pi$
$709$	−14.0711	+	24.3719i	−0.528452	+	0.915306i	−0.999450	+	0.0331712i	$0.989439\pi$
$710$	−15.7313	−	16.7369i	−0.590384	−	0.628123i
$711$	35.1377	−	20.2867i	1.31777	−	0.760812i
$712$	28.5912	−	4.87589i	1.07150	−	0.182732i
$713$			32.7782i			1.22755i
$714$	7.40510	−	1.02995i	0.277129	−	0.0385449i
$715$		−	3.78277i		−	0.141468i
$716$	22.3930	+	1.38844i	0.836864	+	0.0518884i
$717$	−3.75776	+	2.16955i	−0.140336	+	0.0810232i
$718$	−6.44664	+	6.05931i	−0.240586	+	0.226131i
$719$	10.5515	−	18.2758i	0.393506	−	0.681572i	−0.599404	−	0.800447i	$-0.704596\pi$
$719$	10.5515	−	18.2758i	0.393506	−	0.681572i	0.992909	+	0.118875i	$0.0379288\pi$
$720$	20.3628	+	15.3980i	0.758875	+	0.573849i
$721$	−6.02347	+	2.76950i	−0.224326	+	0.103142i
$722$	21.9290	−	5.15389i	0.816111	−	0.191808i
$723$	3.69879	+	2.13550i	0.137559	+	0.0794199i
$724$	17.2085	−	25.9519i	0.639548	−	0.964495i
$725$	−1.32335	−	2.29211i	−0.0491480	−	0.0851268i
$726$	0.225392	−	0.747762i	0.00836509	−	0.0277520i
$727$	−10.0292			−0.371962			−0.185981	−	0.982553i	$-0.559546\pi$
$727$	−10.0292			−0.371962			−0.185981	+	0.982553i	$0.559546\pi$
$728$	−0.910867	−	11.9186i	−0.0337590	−	0.441733i
$729$	−11.8981			−0.440672
$730$	5.21436	−	17.2992i	0.192992	−	0.640271i
$731$	0.554542	+	0.960494i	0.0205105	+	0.0355252i
$732$	1.36935	−	2.06510i	0.0506126	−	0.0763284i
$733$	−4.64857	−	2.68385i	−0.171699	−	0.0991304i	0.411688	−	0.911325i	$-0.364939\pi$
$733$	−4.64857	−	2.68385i	−0.171699	−	0.0991304i	−0.583387	+	0.812195i	$0.698273\pi$
$734$	−28.6990	+	6.74504i	−1.05930	+	0.248964i
$735$	−8.63575	+	3.03850i	−0.318534	+	0.112077i
$736$	−20.9113	−	9.25351i	−0.770801	−	0.341089i
$737$	4.43409	−	7.68007i	0.163332	−	0.282899i
$738$	11.8917	−	11.1772i	0.437739	−	0.411439i
$739$	−21.0840	+	12.1729i	−0.775588	+	0.447786i	−0.834865	−	0.550455i	$-0.814454\pi$
$739$	−21.0840	+	12.1729i	−0.775588	+	0.447786i	0.0592761	+	0.998242i	$0.481121\pi$
$740$	31.9400	+	1.98039i	1.17414	+	0.0728005i
$741$			1.54595i			0.0567918i
$742$	18.3151	+	7.43018i	0.672368	+	0.272771i
$743$			13.0820i			0.479931i	0.970781	+	0.239965i	$0.0771361\pi$
$743$			13.0820i			0.479931i	−0.970781	+	0.239965i	$0.922864\pi$
$744$	2.12922	+	12.4853i	0.0780609	+	0.457733i
$745$	4.57100	−	2.63907i	0.167468	−	0.0966880i
$746$	27.2039	+	28.9429i	0.996005	+	1.05967i
$747$	−7.10489	+	12.3060i	−0.259954	+	0.450254i
$748$	6.47885	−	3.22346i	0.236890	−	0.117862i
$749$	8.25192	+	17.9474i	0.301519	+	0.655782i
$750$	−1.85840	−	7.90719i	−0.0678592	−	0.288730i
$751$	−21.7529	−	12.5591i	−0.793776	−	0.458287i	0.0475140	−	0.998871i	$-0.484870\pi$
$751$	−21.7529	−	12.5591i	−0.793776	−	0.458287i	−0.841290	+	0.540584i	$0.818203\pi$
$752$	−38.8829	−	4.84035i	−1.41791	−	0.176510i
$753$	6.16027	+	10.6699i	0.224493	+	0.388833i
$754$	−9.41105	−	2.83670i	−0.342730	−	0.103307i
$755$	−32.8065			−1.19395
$756$	−6.00308	−	15.5216i	−0.218330	−	0.564516i
$757$	−19.1306			−0.695313			−0.347656	−	0.937622i	$-0.613022\pi$
$757$	−19.1306			−0.695313			−0.347656	+	0.937622i	$0.613022\pi$
$758$	15.5635	+	4.69118i	0.565290	+	0.170391i
$759$	1.11620	+	1.93331i	0.0405153	+	0.0701746i
$760$	−4.07686	+	11.0082i	−0.147883	+	0.399309i
$761$	22.1274	+	12.7752i	0.802116	+	0.463102i	0.844211	−	0.536012i	$-0.180070\pi$
$761$	22.1274	+	12.7752i	0.802116	+	0.463102i	−0.0420944	+	0.999114i	$0.513403\pi$
$762$	−0.671760	−	2.85823i	−0.0243353	−	0.103543i
$763$	−0.520708	+	5.60483i	−0.0188509	+	0.202908i
$764$	17.0603	+	34.2896i	0.617221	+	1.24055i
$765$	11.5463	−	19.9988i	0.417457	−	0.723058i
$766$	8.98715	+	9.56164i	0.324719	+	0.345476i
$767$	14.8910	−	8.59733i	0.537683	−	0.310432i
$768$	−8.56625	−	2.16631i	−0.309108	−	0.0781701i
$769$		−	18.4376i		−	0.664877i	−0.943125	−	0.332439i	$-0.892129\pi$
$769$		−	18.4376i		−	0.664877i	0.943125	−	0.332439i	$-0.107871\pi$
$770$	−6.99027	+	5.44535i	−0.251912	+	0.196237i
$771$			1.77763i			0.0640198i
$772$	−1.22789	+	19.8036i	−0.0441927	+	0.712747i
$773$	22.9033	−	13.2232i	0.823773	−	0.475606i	−0.0279428	−	0.999610i	$-0.508896\pi$
$773$	22.9033	−	13.2232i	0.823773	−	0.475606i	0.851716	+	0.524004i	$0.175562\pi$
$774$	0.851275	−	0.800128i	0.0305984	−	0.0287600i
$775$	2.46610	−	4.27141i	0.0885849	−	0.153434i
$776$	8.89337	+	10.7205i	0.319253	+	0.384843i
$777$	−8.05613	−	5.70569i	−0.289012	−	0.204691i
$778$	26.4862	−	6.22498i	0.949578	−	0.223176i
$779$	6.49890	+	3.75214i	0.232847	+	0.134434i
$780$	3.48207	+	2.30893i	0.124678	+	0.0826729i
$781$	3.42919	+	5.93952i	0.122706	+	0.212533i
$782$	−5.96955	+	19.8046i	−0.213471	+	0.708210i
$783$	−13.6848			−0.489055
$784$	−20.7134	+	18.8402i	−0.739766	+	0.672865i
$785$	42.9991			1.53471
$786$	3.77053	−	12.5091i	0.134490	−	0.446186i
$787$	−6.86328	−	11.8875i	−0.244649	−	0.423745i	0.717384	−	0.696678i	$-0.245340\pi$
$787$	−6.86328	−	11.8875i	−0.244649	−	0.423745i	−0.962033	+	0.272933i	$0.912006\pi$
$788$	−37.8091	−	25.0708i	−1.34689	−	0.893111i
$789$	1.21346	+	0.700589i	0.0432002	+	0.0249416i
$790$	49.0833	−	11.5359i	1.74631	−	0.410429i
$791$	−40.9560	−	29.0068i	−1.45623	−	1.03136i
$792$	−4.86687	−	5.86676i	−0.172937	−	0.208466i
$793$	−1.79176	+	3.10342i	−0.0636273	+	0.110206i
$794$	8.73007	−	8.20554i	0.309819	−	0.291204i
$795$	−5.98283	+	3.45419i	−0.212189	+	0.122507i
$796$	−1.89162	+	30.5084i	−0.0670467	+	1.08134i
$797$			8.49433i			0.300885i	0.988619	+	0.150442i	$0.0480698\pi$
$797$			8.49433i			0.300885i	−0.988619	+	0.150442i	$0.951930\pi$
$798$	2.85679	−	2.22541i	0.101129	−	0.0787788i
$799$			35.4433i			1.25389i
$800$	2.02881	+	2.77913i	0.0717292	+	0.0982571i
$801$	−23.9335	+	13.8180i	−0.845648	+	0.488235i
$802$	−9.02146	−	9.59814i	−0.318559	−	0.338922i
$803$	−2.69743	+	4.67208i	−0.0951901	+	0.164874i
$804$	4.36309	+	8.76938i	0.153874	+	0.309272i
$805$	2.34297	−	25.2195i	0.0825790	−	0.888869i
$806$	−4.19083	−	17.8313i	−0.147616	−	0.628080i
$807$	1.37689	+	0.794945i	0.0484687	+	0.0279834i
$808$	14.8989	−	40.2296i	0.524143	−	1.41527i
$809$	11.9326	+	20.6679i	0.419528	+	0.726643i	0.995892	−	0.0905495i	$-0.0288623\pi$
$809$	11.9326	+	20.6679i	0.419528	+	0.726643i	−0.576364	+	0.817193i	$0.695529\pi$
$810$	−20.3563	−	6.13585i	−0.715247	−	0.215592i
$811$	−3.01664			−0.105929			−0.0529643	−	0.998596i	$-0.516867\pi$
$811$	−3.01664			−0.105929			−0.0529643	+	0.998596i	$0.516867\pi$
$812$	8.30534	+	21.4744i	0.291460	+	0.753602i
$813$	0.521751			0.0182986
$814$	−9.14861	−	2.75760i	−0.320659	−	0.0966537i
$815$	24.4906	+	42.4190i	0.857869	+	1.48587i
$816$	−0.987340	+	7.93138i	−0.0345638	+	0.277654i
$817$	0.465228	+	0.268600i	0.0162763	+	0.00939711i
$818$	−0.893755	−	3.80278i	−0.0312494	−	0.132961i
$819$	4.75793	+	10.3482i	0.166256	+	0.361594i
$820$	18.1576	−	9.03408i	0.634092	−	0.315484i
$821$	13.4288	−	23.2593i	0.468668	−	0.811756i	−0.530691	−	0.847565i	$-0.678068\pi$
$821$	13.4288	−	23.2593i	0.468668	−	0.811756i	0.999359	+	0.0358093i	$0.0114009\pi$
$822$	−9.87049	−	10.5014i	−0.344273	−	0.366280i
$823$	−12.1310	+	7.00381i	−0.422859	+	0.244138i	−0.696300	−	0.717751i	$-0.745172\pi$
$823$	−12.1310	+	7.00381i	−0.422859	+	0.244138i	0.273441	+	0.961889i	$0.411838\pi$
$824$	−1.19147	−	6.98653i	−0.0415069	−	0.243387i
$825$		−	0.335912i		−	0.0116950i
$826$	−37.3230	−	15.1414i	−1.29863	−	0.526838i
$827$		−	23.4592i		−	0.815755i	−0.913037	−	0.407878i	$-0.866269\pi$
$827$		−	23.4592i		−	0.815755i	0.913037	−	0.407878i	$-0.133731\pi$
$828$	21.7469	+	1.34838i	0.755758	+	0.0468596i
$829$	30.6237	−	17.6806i	1.06361	−	0.614073i	0.137178	−	0.990546i	$-0.456197\pi$
$829$	30.6237	−	17.6806i	1.06361	−	0.614073i	0.926427	+	0.376473i	$0.122863\pi$
$830$	−12.8670	+	12.0939i	−0.446620	+	0.419786i
$831$	1.32948	−	2.30272i	0.0461190	−	0.0798805i
$832$	12.5588	+	2.36029i	0.435398	+	0.0818284i
$833$	19.2261	+	16.4877i	0.666143	+	0.571266i
$834$	1.47771	−	0.347302i	0.0511690	−	0.0120261i
$835$	45.4707	+	26.2525i	1.57358	+	0.908506i
$836$	1.93703	−	2.92121i	0.0669935	−	0.101032i
$837$	−12.7510	−	22.0854i	−0.440739	−	0.763382i
$838$	5.27748	−	17.5086i	0.182308	−	0.604824i
$839$	1.67014			0.0576598			0.0288299	−	0.999584i	$-0.490822\pi$
$839$	1.67014			0.0576598			0.0288299	+	0.999584i	$0.490822\pi$
$840$	−0.745771	−	9.75833i	−0.0257315	−	0.336695i
$841$	−10.0669			−0.347134
$842$	−5.87363	+	19.4863i	−0.202419	+	0.671544i
$843$	−5.24908	−	9.09168i	−0.180788	−	0.313134i
$844$	26.6022	−	40.1185i	0.915685	−	1.38094i
$845$	21.4289	+	12.3720i	0.737177	+	0.425609i
$846$	36.3447	−	8.54198i	1.24956	−	0.293679i
$847$	2.40384	−	1.10525i	0.0825968	−	0.0379768i
$848$	−12.7443	+	16.8535i	−0.437642	+	0.578750i
$849$	5.71452	−	9.89783i	0.196122	−	0.339693i
$850$	2.26792	−	2.13166i	0.0777891	−	0.0731153i
$851$	23.6534	−	13.6563i	0.810827	−	0.468131i
$852$	−7.56049	−	0.468776i	−0.259018	−	0.0160600i
$853$			45.5621i			1.56002i	0.625770	+	0.780008i	$0.284785\pi$
$853$			45.5621i			1.56002i	−0.625770	+	0.780008i	$0.715215\pi$
$854$	8.31414	−	1.15638i	0.284504	−	0.0395706i
$855$		−	11.1852i		−	0.382526i
$856$	−20.8169	+	3.55007i	−0.711506	+	0.121339i
$857$	24.6344	−	14.2227i	0.841495	−	0.485837i	−0.0162772	−	0.999868i	$-0.505181\pi$
$857$	24.6344	−	14.2227i	0.841495	−	0.485837i	0.857772	+	0.514030i	$0.171848\pi$
$858$	−0.854390	−	0.909005i	−0.0291684	−	0.0310329i
$859$	−11.4683	+	19.8637i	−0.391295	+	0.677742i	−0.992621	−	0.121262i	$-0.961306\pi$
$859$	−11.4683	+	19.8637i	−0.391295	+	0.677742i	0.601326	+	0.799004i	$0.294639\pi$
$860$	1.29983	−	0.646710i	0.0443237	−	0.0220526i
$861$	−6.22956	−	0.578747i	−0.212303	−	0.0197237i
$862$	−12.3201	−	52.4199i	−0.419624	−	1.78543i
$863$	5.18486	+	2.99348i	0.176495	+	0.101899i	0.585645	−	0.810568i	$-0.300841\pi$
$863$	5.18486	+	2.99348i	0.176495	+	0.101899i	−0.409150	+	0.912467i	$0.634175\pi$
$864$	17.6894	−	1.89982i	0.601804	−	0.0646334i
$865$	−13.7718	−	23.8534i	−0.468255	−	0.811041i
$866$	−37.3643	−	11.2624i	−1.26969	−	0.382714i
$867$	−2.15841			−0.0733036
$868$	−26.9180	+	33.4127i	−0.913658	+	1.13410i
$869$	−15.0550			−0.510704
$870$	−7.70528	−	2.32255i	−0.261234	−	0.0787417i
$871$	−7.08273	−	12.2676i	−0.239989	−	0.415673i
$872$	−5.64305	−	2.08989i	−0.191098	−	0.0707726i
$873$	−11.4940	−	6.63608i	−0.389014	−	0.224597i
$874$	2.29225	+	9.75316i	0.0775366	+	0.329906i
$875$	15.9039	−	22.4554i	0.537649	−	0.759132i
$876$	−2.65423	−	5.33475i	−0.0896781	−	0.180244i
$877$	1.88519	−	3.26525i	0.0636585	−	0.110260i	−0.832440	−	0.554116i	$-0.813056\pi$
$877$	1.88519	−	3.26525i	0.0636585	−	0.110260i	0.896098	+	0.443856i	$0.146390\pi$
$878$	16.6853	+	17.7518i	0.563100	+	0.599096i
$879$	−11.0409	+	6.37447i	−0.372401	+	0.215006i
$880$	−3.68667	−	8.72586i	−0.124278	−	0.294149i
$881$		−	13.9119i		−	0.468704i	−0.972152	−	0.234352i	$-0.924703\pi$
$881$		−	13.9119i		−	0.468704i	0.972152	−	0.234352i	$-0.0752969\pi$
$882$	12.2735	−	23.6886i	0.413270	−	0.797638i
$883$		−	21.3081i		−	0.717076i	−0.933515	−	0.358538i	$-0.883275\pi$
$883$		−	21.3081i		−	0.717076i	0.933515	−	0.358538i	$-0.116725\pi$
$884$	0.715325	−	11.5369i	0.0240590	−	0.388027i
$885$	12.1920	−	7.03905i	0.409829	−	0.236615i
$886$	0.482254	−	0.453279i	0.0162016	−	0.0152282i
$887$	−12.2069	+	21.1430i	−0.409868	+	0.709912i	−0.994875	−	0.101116i	$-0.967759\pi$
$887$	−12.2069	+	21.1430i	−0.409868	+	0.709912i	0.585006	+	0.811029i	$0.301092\pi$
$888$	8.12252	−	6.73818i	0.272574	−	0.226119i
$889$	5.74881	−	8.11701i	0.192809	−	0.272236i
$890$	−33.4323	+	7.85749i	−1.12065	+	0.263384i
$891$	5.49773	+	3.17412i	0.184181	+	0.106337i
$892$	−45.9484	−	30.4680i	−1.53847	−	1.02014i
$893$	8.58372	+	14.8674i	0.287243	+	0.497520i
$894$	0.502349	−	1.66659i	0.0168011	−	0.0557392i
$895$	−26.5662			−0.888009
$896$	−13.7169	−	26.6054i	−0.458251	−	0.888823i
$897$	3.56588			0.119061
$898$	−7.99939	+	26.5388i	−0.266943	+	0.885610i
$899$	17.6412	+	30.5554i	0.588366	+	1.01908i
$900$	−2.73245	−	1.81186i	−0.0910817	−	0.0603954i
$901$	16.5522	+	9.55643i	0.551434	+	0.318371i
$902$	−5.89498	+	1.38548i	−0.196281	+	0.0461314i
$903$	−0.445947	−	0.0414300i	−0.0148402	−	0.00137870i
$904$	41.2935	−	34.2558i	1.37340	−	1.13933i
$905$	−18.4356	+	31.9314i	−0.612821	+	1.06144i
$906$	−7.88346	+	7.40980i	−0.261910	+	0.246174i
$907$	0.571460	−	0.329933i	0.0189750	−	0.0109552i	−0.490482	−	0.871451i	$-0.663179\pi$
$907$	0.571460	−	0.329933i	0.0189750	−	0.0109552i	0.509458	+	0.860496i	$0.329846\pi$
$908$	1.20210	−	19.3876i	0.0398930	−	0.643401i
$909$			40.8765i			1.35579i
$910$	1.94984	+	14.0189i	0.0646365	+	0.464722i
$911$		−	1.88519i		−	0.0624592i	−0.999512	−	0.0312296i	$-0.990058\pi$
$911$		−	1.88519i		−	0.0624592i	0.999512	−	0.0312296i	$-0.00994231\pi$
$912$	1.50667	+	3.56610i	0.0498909	+	0.118085i
$913$	4.56620	−	2.63630i	0.151119	−	0.0872487i
$914$	−32.3645	−	34.4334i	−1.07052	−	1.13895i
$915$	−1.46700	+	2.54092i	−0.0484975	+	0.0840002i
$916$	−24.0535	−	48.3453i	−0.794751	−	1.59737i
$917$	40.2132	−	18.4894i	1.32796	−	0.610574i
$918$	−3.68197	−	15.6662i	−0.121523	−	0.517061i
$919$	45.8937	+	26.4968i	1.51389	+	0.874047i	0.999868	+	0.0162732i	$0.00518014\pi$
$919$	45.8937	+	26.4968i	1.51389	+	0.874047i	0.514027	+	0.857774i	$0.328153\pi$
$920$	25.3915	+	9.40366i	0.837131	+	0.310030i
$921$	7.94738	+	13.7653i	0.261875	+	0.453581i
$922$	−44.6257	−	13.4512i	−1.46967	−	0.442991i
$923$	10.9551			0.360592
$924$	−0.449865	+	2.88737i	−0.0147995	+	0.0949876i
$925$	−4.10977			−0.135128
$926$	21.2893	+	6.41709i	0.699611	+	0.210879i
$927$	3.37656	+	5.84838i	0.110901	+	0.192086i
$928$	−24.4735	+	2.62843i	−0.803381	+	0.0862825i
$929$	−39.5697	−	22.8456i	−1.29824	−	0.749539i	−0.318140	−	0.948044i	$-0.603058\pi$
$929$	−39.5697	−	22.8456i	−1.29824	−	0.749539i	−0.980100	+	0.198505i	$0.936391\pi$
$930$	−3.43123	−	14.5993i	−0.112515	−	0.478731i
$931$	12.0578	+	2.25993i	0.395178	+	0.0740662i
$932$	20.3511	−	10.1254i	0.666623	−	0.331669i
$933$	−3.33174	+	5.77074i	−0.109076	+	0.188925i
$934$	−7.61843	−	8.10543i	−0.249283	−	0.265218i
$935$	−7.42063	+	4.28430i	−0.242681	+	0.140112i
$936$	−12.0027	+	2.04692i	−0.392320	+	0.0669056i
$937$		−	5.84312i		−	0.190886i	−0.995435	−	0.0954432i	$-0.969573\pi$
$937$		−	5.84312i		−	0.190886i	0.995435	−	0.0954432i	$-0.0304268\pi$
$938$	−12.4740	+	30.7478i	−0.407289	+	1.00395i
$939$			0.199873i			0.00652261i
$940$	46.3073	+	2.87121i	1.51038	+	0.0936485i
$941$	−25.8593	+	14.9299i	−0.842989	+	0.486700i	−0.858279	−	0.513183i	$-0.828466\pi$
$941$	−25.8593	+	14.9299i	−0.842989	+	0.486700i	0.0152900	+	0.999883i	$0.495133\pi$
$942$	10.3328	−	9.71193i	0.336659	−	0.316432i
$943$	8.65468	−	14.9903i	0.281835	−	0.488153i
$944$	25.9707	−	34.3445i	0.845276	−	1.11782i
$945$	8.23193	+	17.9039i	0.267785	+	0.582413i
$946$	−0.421996	+	0.0991803i	−0.0137203	+	0.00322463i
$947$	33.6834	+	19.4471i	1.09457	+	0.631947i	0.934788	−	0.355206i	$-0.115589\pi$
$947$	33.6834	+	19.4471i	1.09457	+	0.631947i	0.159777	+	0.987153i	$0.448923\pi$
$948$	9.18925	−	13.8582i	0.298453	−	0.450094i
$949$	4.30869	+	7.46287i	0.139866	+	0.242255i
$950$	0.435079	−	1.44342i	0.0141158	−	0.0468307i
$951$	11.4844			0.372406
$952$	−22.3490	+	15.2856i	−0.724335	+	0.495410i
$953$	56.9618			1.84517			0.922586	−	0.385790i	$-0.126071\pi$
$953$	56.9618			1.84517			0.922586	+	0.385790i	$0.126071\pi$
$954$	5.81032	−	19.2763i	0.188116	−	0.624094i
$955$	−22.6749	−	39.2740i	−0.733741	−	1.27088i
$956$	8.68431	−	13.0967i	0.280871	−	0.423578i
$957$	2.08101	+	1.20147i	0.0672694	+	0.0388380i
$958$	−11.4571	+	2.69272i	−0.370162	+	0.0869979i
$959$	4.51641	−	48.6140i	0.145843	−	1.56983i
$960$	10.2825	+	1.93249i	0.331866	+	0.0623707i
$961$	−17.3748	+	30.0941i	−0.560478	+	0.970776i
$962$	−11.1214	+	10.4532i	−0.358567	+	0.337023i
$963$	17.4257	−	10.0607i	0.561534	−	0.324202i
$964$	−15.4381	−	0.957213i	−0.497227	−	0.0308298i
$965$		−	23.4942i		−	0.756306i
$966$	−5.13313	−	6.58946i	−0.165156	−	0.212012i
$967$		−	38.3384i		−	1.23288i	−0.787402	−	0.616440i	$-0.788574\pi$
$967$		−	38.3384i		−	1.23288i	0.787402	−	0.616440i	$-0.211426\pi$
$968$	0.475490	+	2.78817i	0.0152828	+	0.0896153i
$969$	3.03267	−	1.75091i	0.0974234	−	0.0562474i
$970$	−11.2959	−	12.0180i	−0.362690	−	0.385875i
$971$	−25.8479	+	44.7699i	−0.829500	+	1.43674i	0.0689318	+	0.997621i	$0.478041\pi$
$971$	−25.8479	+	44.7699i	−0.829500	+	1.43674i	−0.898431	+	0.439114i	$0.855292\pi$
$972$	−23.1722	+	11.5290i	−0.743250	+	0.369794i
$973$	4.19652	+	2.97215i	0.134534	+	0.0952828i
$974$	−9.16190	−	38.9824i	−0.293566	−	1.24908i
$975$	−0.464678	−	0.268282i	−0.0148816	−	0.00859191i
$976$	−1.10854	+	8.90502i	−0.0354836	+	0.285043i
$977$	1.89493	+	3.28211i	0.0606240	+	0.105004i	0.894745	−	0.446578i	$-0.147358\pi$
$977$	1.89493	+	3.28211i	0.0606240	+	0.105004i	−0.834120	+	0.551582i	$0.814024\pi$
$978$	15.4660	+	4.66181i	0.494549	+	0.149068i
$979$	10.2544			0.327734
$980$	23.0990	−	23.7835i	0.737870	−	0.759737i
$981$	5.73379			0.183066
$982$	7.21338	+	2.17428i	0.230188	+	0.0693840i
$983$	9.12289	+	15.8013i	0.290975	+	0.503983i	0.974041	−	0.226374i	$-0.0726870\pi$
$983$	9.12289	+	15.8013i	0.290975	+	0.503983i	−0.683066	+	0.730357i	$0.739354\pi$
$984$	2.32284	−	6.27204i	0.0740493	−	0.199945i
$985$	46.5206	+	26.8587i	1.48227	+	0.855788i
$986$	5.09406	+	21.6744i	0.162228	+	0.690253i
$987$	−11.6800	−	8.27224i	−0.371777	−	0.263308i
$988$	−2.49396	−	5.01262i	−0.0793435	−	0.159473i
$989$	0.619551	−	1.07309i	0.0197006	−	0.0341224i
$990$	6.18166	+	6.57682i	0.196466	+	0.209025i
$991$	5.26469	−	3.03957i	0.167238	−	0.0965552i	−0.414045	−	0.910257i	$-0.635884\pi$
$991$	5.26469	−	3.03957i	0.167238	−	0.0965552i	0.581283	+	0.813701i	$0.302551\pi$
$992$	−27.0454	−	37.0477i	−0.858693	−	1.17627i
$993$		−	6.64204i		−	0.210779i
$994$	−15.7700	−	20.2442i	−0.500195	−	0.642107i
$995$		−	36.1940i		−	1.14743i
$996$	−0.360386	+	5.81237i	−0.0114193	+	0.184172i
$997$	−33.5226	+	19.3543i	−1.06167	+	0.612956i	−0.925894	−	0.377784i	$-0.876686\pi$
$997$	−33.5226	+	19.3543i	−1.06167	+	0.612956i	−0.135776	+	0.990739i	$0.543353\pi$
$998$	−13.1267	+	12.3380i	−0.415519	+	0.390554i
$999$	−10.6248	+	18.4027i	−0.336154	+	0.582236i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.2.l.a.243.24	yes	80
4.3	odd	2	inner	308.2.l.a.243.30	yes	80
7.3	odd	6	inner	308.2.l.a.199.30	yes	80
28.3	even	6	inner	308.2.l.a.199.24	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.2.l.a.199.24	✓	80	28.3	even	6	inner
308.2.l.a.199.30	yes	80	7.3	odd	6	inner
308.2.l.a.243.24	yes	80	1.1	even	1	trivial
308.2.l.a.243.30	yes	80	4.3	odd	2	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:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	308.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.408138 - 1.35404i) q^{2} +(0.276123 + 0.478258i) q^{3} +(-1.66685 - 1.10527i) q^{4} +(2.05090 + 1.18409i) q^{5} +(0.760277 - 0.178685i) q^{6} +(2.15909 + 1.52916i) q^{7} +(-2.17688 + 1.80587i) q^{8} +(1.34751 - 2.33396i) q^{9} +O(q^{10})\)	\(q+(0.408138 - 1.35404i) q^{2} +(0.276123 + 0.478258i) q^{3} +(-1.66685 - 1.10527i) q^{4} +(2.05090 + 1.18409i) q^{5} +(0.760277 - 0.178685i) q^{6} +(2.15909 + 1.52916i) q^{7} +(-2.17688 + 1.80587i) q^{8} +(1.34751 - 2.33396i) q^{9} +(2.44035 - 2.29373i) q^{10} +(-0.866025 + 0.500000i) q^{11} +(0.0683509 - 1.10237i) q^{12} +1.59733i q^{13} +(2.95175 - 2.29939i) q^{14} +1.30781i q^{15} +(1.55675 + 3.68463i) q^{16} +(3.13348 - 1.80911i) q^{17} +(-2.61030 - 2.77716i) q^{18} +(0.876268 - 1.51774i) q^{19} +(-2.10980 - 4.24050i) q^{20} +(-0.135160 + 1.45484i) q^{21} +(0.323562 + 1.37670i) q^{22} +(-3.50081 - 2.02120i) q^{23} +(-1.46476 - 0.542470i) q^{24} +(0.304133 + 0.526774i) q^{25} +(2.16285 + 0.651933i) q^{26} +3.14505 q^{27} +(-1.90874 - 4.93525i) q^{28} -4.35122 q^{29} +(1.77083 + 0.533769i) q^{30} +(-4.05431 - 7.02227i) q^{31} +(5.62451 - 0.604068i) q^{32} +(-0.478258 - 0.276123i) q^{33} +(-1.17072 - 4.98122i) q^{34} +(2.61742 + 5.69271i) q^{35} +(-4.82575 + 2.40099i) q^{36} +(-3.37826 + 5.85133i) q^{37} +(-1.69744 - 1.80595i) q^{38} +(-0.763939 + 0.441060i) q^{39} +(-6.60289 + 1.12605i) q^{40} +4.28196i q^{41} +(1.91475 + 0.776787i) q^{42} +0.306527i q^{43} +(1.99617 + 0.123769i) q^{44} +(5.52723 - 3.19115i) q^{45} +(-4.16560 + 3.91531i) q^{46} +(-4.89788 + 8.48338i) q^{47} +(-1.33235 + 1.76194i) q^{48} +(2.32334 + 6.60319i) q^{49} +(0.837402 - 0.196812i) q^{50} +(1.73045 + 0.999074i) q^{51} +(1.76549 - 2.66251i) q^{52} +(2.64119 + 4.57468i) q^{53} +(1.28362 - 4.25852i) q^{54} -2.36818 q^{55} +(-7.46156 + 0.570242i) q^{56} +0.967830 q^{57} +(-1.77590 + 5.89172i) q^{58} +(-5.38230 - 9.32241i) q^{59} +(1.44549 - 2.17993i) q^{60} +(1.94287 + 1.12172i) q^{61} +(-11.1631 + 2.62364i) q^{62} +(6.47840 - 2.97867i) q^{63} +(1.47764 - 7.86235i) q^{64} +(-1.89139 + 3.27598i) q^{65} +(-0.569076 + 0.534885i) q^{66} +(-7.68007 + 4.43409i) q^{67} +(-7.22258 - 0.447824i) q^{68} -2.23239i q^{69} +(8.77643 - 1.22068i) q^{70} -6.85837i q^{71} +(1.28146 + 7.51420i) q^{72} +(4.67208 - 2.69743i) q^{73} +(6.54413 + 6.96245i) q^{74} +(-0.167956 + 0.290909i) q^{75} +(-3.13812 + 1.56133i) q^{76} +(-2.63441 - 0.244746i) q^{77} +(0.285420 + 1.21442i) q^{78} +(13.0380 + 7.52748i) q^{79} +(-1.17018 + 9.40016i) q^{80} +(-3.17412 - 5.49773i) q^{81} +(5.79794 + 1.74763i) q^{82} -5.27260 q^{83} +(1.83328 - 2.27560i) q^{84} +8.56860 q^{85} +(0.415049 + 0.125105i) q^{86} +(-1.20147 - 2.08101i) q^{87} +(0.982300 - 2.65237i) q^{88} +(-8.88061 - 5.12722i) q^{89} +(-2.06507 - 8.78652i) q^{90} +(-2.44258 + 3.44879i) q^{91} +(3.60135 + 7.23837i) q^{92} +(2.23897 - 3.87801i) q^{93} +(9.48782 + 10.0943i) q^{94} +(3.59428 - 2.07516i) q^{95} +(1.84195 + 2.52317i) q^{96} -4.92469i q^{97} +(9.88922 - 0.450887i) q^{98} +2.69503i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 12 q^{8} - 40 q^{9}+O(q^{10}) \) 80 * q + 12 * q^8 - 40 * q^9	\( 80 q + 12 q^{8} - 40 q^{9} - 18 q^{10} - 30 q^{12} - 4 q^{14} - 4 q^{16} - 10 q^{18} - 8 q^{21} + 40 q^{25} + 30 q^{26} + 16 q^{28} - 16 q^{29} + 36 q^{30} - 20 q^{32} - 20 q^{36} - 8 q^{37} - 12 q^{38} - 60 q^{40} + 4 q^{44} + 24 q^{45} - 10 q^{46} - 24 q^{49} - 64 q^{50} + 54 q^{52} - 30 q^{54} + 38 q^{56} + 80 q^{57} + 10 q^{58} - 12 q^{60} - 36 q^{64} - 16 q^{65} + 30 q^{66} + 60 q^{68} - 22 q^{70} - 38 q^{72} - 72 q^{73} + 28 q^{74} - 24 q^{78} + 42 q^{80} - 64 q^{81} - 90 q^{82} + 88 q^{84} - 2 q^{86} + 12 q^{88} - 120 q^{89} + 36 q^{92} + 8 q^{93} - 54 q^{94} - 42 q^{96} + 78 q^{98}+O(q^{100}) \) 80 * q + 12 * q^8 - 40 * q^9 - 18 * q^10 - 30 * q^12 - 4 * q^14 - 4 * q^16 - 10 * q^18 - 8 * q^21 + 40 * q^25 + 30 * q^26 + 16 * q^28 - 16 * q^29 + 36 * q^30 - 20 * q^32 - 20 * q^36 - 8 * q^37 - 12 * q^38 - 60 * q^40 + 4 * q^44 + 24 * q^45 - 10 * q^46 - 24 * q^49 - 64 * q^50 + 54 * q^52 - 30 * q^54 + 38 * q^56 + 80 * q^57 + 10 * q^58 - 12 * q^60 - 36 * q^64 - 16 * q^65 + 30 * q^66 + 60 * q^68 - 22 * q^70 - 38 * q^72 - 72 * q^73 + 28 * q^74 - 24 * q^78 + 42 * q^80 - 64 * q^81 - 90 * q^82 + 88 * q^84 - 2 * q^86 + 12 * q^88 - 120 * q^89 + 36 * q^92 + 8 * q^93 - 54 * q^94 - 42 * q^96 + 78 * q^98

Introduction

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