LMFDB - Embedded newform 104.2.u.a.19.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [104,2,Mod(11,104)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("104.11"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(104, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 6, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 104 = 2^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	104.u (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.830444181021$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.5
Character	$\chi$	$=$	104.19
Dual form			104.2.u.a.11.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.376293 + 1.36323i) q^{2} +(1.11333 - 1.92835i) q^{3} +(-1.71681 - 1.02595i) q^{4} +(0.0693382 + 0.0693382i) q^{5} +(2.20985 + 2.24336i) q^{6} +(3.36551 + 0.901786i) q^{7} +(2.04463 - 1.95435i) q^{8} +(-0.979029 - 1.69573i) q^{9} +(-0.120616 + 0.0684326i) q^{10} +(-0.305781 + 0.0819339i) q^{11} +(-3.88978 + 2.16838i) q^{12} +(-3.13155 - 1.78702i) q^{13} +(-2.49576 + 4.24864i) q^{14} +(0.210905 - 0.0565119i) q^{15} +(1.89485 + 3.52272i) q^{16} +(-5.48889 + 3.16901i) q^{17} +(2.68007 - 0.696553i) q^{18} +(-0.397336 - 0.106466i) q^{19} +(-0.0479027 - 0.190178i) q^{20} +(5.48590 - 5.48590i) q^{21} +(0.00336858 - 0.447683i) q^{22} +(-3.68562 + 6.38369i) q^{23} +(-1.49231 - 6.11862i) q^{24} -4.99038i q^{25} +(3.61450 - 3.59658i) q^{26} +2.32006 q^{27} +(-4.85274 - 5.00104i) q^{28} +(-3.16915 - 1.82971i) q^{29} +(-0.00232339 + 0.308778i) q^{30} +(1.12080 + 1.12080i) q^{31} +(-5.51530 + 1.25755i) q^{32} +(-0.182440 + 0.680874i) q^{33} +(-2.25467 - 8.67511i) q^{34} +(0.170830 + 0.295887i) q^{35} +(-0.0589301 + 3.91567i) q^{36} +(0.804964 + 3.00417i) q^{37} +(0.294652 - 0.501598i) q^{38} +(-6.93245 + 4.04918i) q^{39} +(0.277282 + 0.00626016i) q^{40} +(1.85187 + 6.91129i) q^{41} +(5.41425 + 9.54287i) q^{42} +(4.88743 - 2.82176i) q^{43} +(0.609028 + 0.173052i) q^{44} +(0.0496946 - 0.185463i) q^{45} +(-7.31557 - 7.42650i) q^{46} +(6.15946 - 6.15946i) q^{47} +(8.90264 + 0.268027i) q^{48} +(4.45127 + 2.56994i) q^{49} +(6.80306 + 1.87785i) q^{50} +14.1127i q^{51} +(3.54287 + 6.28077i) q^{52} -3.89384i q^{53} +(-0.873024 + 3.16278i) q^{54} +(-0.0268835 - 0.0155212i) q^{55} +(8.64364 - 4.73356i) q^{56} +(-0.647671 + 0.647671i) q^{57} +(3.68685 - 3.63178i) q^{58} +(-2.51467 + 9.38488i) q^{59} +(-0.420062 - 0.119358i) q^{60} +(-11.9231 + 6.88378i) q^{61} +(-1.94966 + 1.10616i) q^{62} +(-1.76575 - 6.58987i) q^{63} +(0.361046 - 7.99185i) q^{64} +(-0.0932273 - 0.341044i) q^{65} +(-0.859539 - 0.504916i) q^{66} +(-3.16917 - 11.8275i) q^{67} +(12.6746 + 0.190751i) q^{68} +(8.20666 + 14.2144i) q^{69} +(-0.467645 + 0.121541i) q^{70} +(1.81764 - 6.78351i) q^{71} +(-5.31580 - 1.55378i) q^{72} +(1.49582 + 1.49582i) q^{73} +(-4.39828 - 0.0330948i) q^{74} +(-9.62322 - 5.55597i) q^{75} +(0.572920 + 0.590428i) q^{76} -1.10300 q^{77} +(-2.91133 - 10.9742i) q^{78} -10.3044i q^{79} +(-0.112874 + 0.375645i) q^{80} +(5.52009 - 9.56108i) q^{81} +(-10.1185 - 0.0761368i) q^{82} +(2.53771 - 2.53771i) q^{83} +(-15.0465 + 3.78997i) q^{84} +(-0.600323 - 0.160856i) q^{85} +(2.00761 + 7.72451i) q^{86} +(-7.05665 + 4.07416i) q^{87} +(-0.465083 + 0.765128i) q^{88} +(0.110536 - 0.0296181i) q^{89} +(0.234129 + 0.137534i) q^{90} +(-8.92775 - 8.83821i) q^{91} +(12.8768 - 7.17829i) q^{92} +(3.40912 - 0.913470i) q^{93} +(6.07901 + 10.7145i) q^{94} +(-0.0201684 - 0.0349327i) q^{95} +(-3.71539 + 12.0355i) q^{96} +(6.28973 + 1.68533i) q^{97} +(-5.17841 + 5.10107i) q^{98} +(0.438306 + 0.438306i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{2} - 4 q^{3} - 6 q^{4} - 6 q^{6} - 10 q^{8} - 20 q^{9} - 6 q^{10} - 8 q^{11} + 8 q^{14} - 10 q^{16} - 12 q^{17} - 6 q^{18} - 8 q^{19} + 10 q^{20} - 20 q^{22} + 46 q^{24} - 2 q^{26} + 8 q^{27}+ \cdots + 168 q^{99}+O(q^{100}) $ 48 * q - 4 * q^2 - 4 * q^3 - 6 * q^4 - 6 * q^6 - 10 * q^8 - 20 * q^9 - 6 * q^10 - 8 * q^11 + 8 * q^14 - 10 * q^16 - 12 * q^17 - 6 * q^18 - 8 * q^19 + 10 * q^20 - 20 * q^22 + 46 * q^24 - 2 * q^26 + 8 * q^27 + 12 * q^28 - 54 * q^30 + 16 * q^32 + 4 * q^33 - 46 * q^34 - 4 * q^35 + 30 * q^36 - 32 * q^40 - 16 * q^42 - 12 * q^43 - 16 * q^44 + 34 * q^46 + 46 * q^48 - 60 * q^49 + 86 * q^50 + 12 * q^52 + 32 * q^54 + 48 * q^56 + 36 * q^57 + 30 * q^58 - 64 * q^59 + 80 * q^60 + 42 * q^62 - 16 * q^65 + 8 * q^66 - 8 * q^67 - 32 * q^68 + 36 * q^70 - 24 * q^72 - 12 * q^73 + 38 * q^74 + 24 * q^75 - 94 * q^76 + 40 * q^78 - 108 * q^80 - 8 * q^81 + 54 * q^82 - 48 * q^83 - 72 * q^84 + 80 * q^86 - 108 * q^88 + 12 * q^89 + 104 * q^91 - 20 * q^92 + 26 * q^94 - 32 * q^96 + 4 * q^97 - 16 * q^98 + 168 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/104\mathbb{Z}\right)^\times$.

$n$	$41$	$53$	$79$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$-1$	$-1$

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 $

$2$	−0.376293	+	1.36323i	−0.266080	+	0.963951i
$2$	−0.376293	+	1.36323i	−0.266080	+	0.963951i
$3$	1.11333	−	1.92835i	0.642784	−	1.11333i	−0.342024	−	0.939691i	$-0.611113\pi$
$3$	1.11333	−	1.92835i	0.642784	−	1.11333i	0.984809	−	0.173644i	$-0.0555541\pi$
$4$	−1.71681	−	1.02595i	−0.858403	−	0.512975i
$5$	0.0693382	+	0.0693382i	0.0310090	+	0.0310090i	0.722441	−	0.691432i	$-0.243020\pi$
$5$	0.0693382	+	0.0693382i	0.0310090	+	0.0310090i	−0.691432	+	0.722441i	$0.743020\pi$
$6$	2.20985	+	2.24336i	0.902169	+	0.915848i
$7$	3.36551	+	0.901786i	1.27204	+	0.340843i	0.830814	−	0.556551i	$-0.187876\pi$
$7$	3.36551	+	0.901786i	1.27204	+	0.340843i	0.441230	+	0.897394i	$0.354542\pi$
$8$	2.04463	−	1.95435i	0.722887	−	0.690966i
$9$	−0.979029	−	1.69573i	−0.326343	−	0.565243i
$10$	−0.120616	+	0.0684326i	−0.0381420	+	0.0216403i
$11$	−0.305781	+	0.0819339i	−0.0921966	+	0.0247040i	−0.304622	−	0.952473i	$-0.598530\pi$
$11$	−0.305781	+	0.0819339i	−0.0921966	+	0.0247040i	0.212426	+	0.977177i	$0.431864\pi$
$12$	−3.88978	+	2.16838i	−1.12288	+	0.625958i
$13$	−3.13155	−	1.78702i	−0.868534	−	0.495629i
$13$	−3.13155	−	1.78702i	−0.868534	−	0.495629i
$14$	−2.49576	+	4.24864i	−0.667021	+	1.13550i
$15$	0.210905	−	0.0565119i	0.0544555	−	0.0145913i
$16$	1.89485	+	3.52272i	0.473712	+	0.880680i
$17$	−5.48889	+	3.16901i	−1.33125	+	0.768598i	−0.985491	−	0.169725i	$-0.945712\pi$
$17$	−5.48889	+	3.16901i	−1.33125	+	0.768598i	−0.345760	+	0.938323i	$0.612379\pi$
$18$	2.68007	−	0.696553i	0.631699	−	0.164179i
$19$	−0.397336	−	0.106466i	−0.0911550	−	0.0244249i	0.212953	−	0.977062i	$-0.431692\pi$
$19$	−0.397336	−	0.106466i	−0.0911550	−	0.0244249i	−0.304108	+	0.952637i	$0.598358\pi$
$20$	−0.0479027	−	0.190178i	−0.0107114	−	0.0425251i
$21$	5.48590	−	5.48590i	1.19712	−	1.19712i
$22$	0.00336858	−	0.447683i	0.000718183	−	0.0954462i
$23$	−3.68562	+	6.38369i	−0.768505	+	1.33109i	0.169868	+	0.985467i	$0.445666\pi$
$23$	−3.68562	+	6.38369i	−0.768505	+	1.33109i	−0.938373	+	0.345624i	$0.887667\pi$
$24$	−1.49231	−	6.11862i	−0.304617	−	1.24896i
$25$		−	4.99038i		−	0.998077i
$26$	3.61450	−	3.59658i	0.708861	−	0.705348i
$27$	2.32006			0.446496
$28$	−4.85274	−	5.00104i	−0.917082	−	0.945108i
$29$	−3.16915	−	1.82971i	−0.588496	−	0.339768i	0.176006	−	0.984389i	$-0.443682\pi$
$29$	−3.16915	−	1.82971i	−0.588496	−	0.339768i	−0.764503	+	0.644621i	$0.777015\pi$
$30$	−0.00232339	+	0.308778i	−0.000424192	+	0.0563749i
$31$	1.12080	+	1.12080i	0.201301	+	0.201301i	0.800557	−	0.599256i	$-0.204537\pi$
$31$	1.12080	+	1.12080i	0.201301	+	0.201301i	−0.599256	+	0.800557i	$0.704537\pi$
$32$	−5.51530	+	1.25755i	−0.974977	+	0.222305i
$33$	−0.182440	+	0.680874i	−0.0317587	+	0.118525i
$34$	−2.25467	−	8.67511i	−0.386672	−	1.48777i
$35$	0.170830	+	0.295887i	0.0288756	+	0.0500140i
$36$	−0.0589301	+	3.91567i	−0.00982169	+	0.652612i
$37$	0.804964	+	3.00417i	0.132335	+	0.493882i	0.999995	−	0.00327710i	$-0.00104314\pi$
$37$	0.804964	+	3.00417i	0.132335	+	0.493882i	−0.867659	+	0.497159i	$0.834376\pi$
$38$	0.294652	−	0.501598i	0.0477989	−	0.0813700i
$39$	−6.93245	+	4.04918i	−1.11008	+	0.648387i
$40$	0.277282	+	0.00626016i	0.0438422	+	0.000989819i
$41$	1.85187	+	6.91129i	0.289214	+	1.07936i	0.945705	+	0.325027i	$0.105373\pi$
$41$	1.85187	+	6.91129i	0.289214	+	1.07936i	−0.656491	+	0.754334i	$0.727960\pi$
$42$	5.41425	+	9.54287i	0.835437	+	1.47250i
$43$	4.88743	−	2.82176i	0.745326	−	0.430314i	−0.0786766	−	0.996900i	$-0.525069\pi$
$43$	4.88743	−	2.82176i	0.745326	−	0.430314i	0.824003	+	0.566586i	$0.191736\pi$
$44$	0.609028	+	0.173052i	0.0918144	+	0.0260886i
$45$	0.0496946	−	0.185463i	0.00740804	−	0.0276472i
$46$	−7.31557	−	7.42650i	−1.07862	−	1.09498i
$47$	6.15946	−	6.15946i	0.898449	−	0.898449i	−0.0968500	−	0.995299i	$-0.530877\pi$
$47$	6.15946	−	6.15946i	0.898449	−	0.898449i	0.995299	+	0.0968500i	$0.0308767\pi$
$48$	8.90264	+	0.268027i	1.28499	+	0.0386864i
$49$	4.45127	+	2.56994i	0.635896	+	0.367135i
$50$	6.80306	+	1.87785i	0.962097	+	0.265568i
$51$			14.1127i			1.97617i
$52$	3.54287	+	6.28077i	0.491307	+	0.870986i
$53$		−	3.89384i		−	0.534861i	−0.963577	−	0.267430i	$-0.913825\pi$
$53$		−	3.89384i		−	0.534861i	0.963577	−	0.267430i	$-0.0861745\pi$
$54$	−0.873024	+	3.16278i	−0.118803	+	0.430400i
$55$	−0.0268835	−	0.0155212i	−0.00362497	−	0.00209288i
$56$	8.64364	−	4.73356i	1.15505	−	0.632549i
$57$	−0.647671	+	0.647671i	−0.0857861	+	0.0857861i
$58$	3.68685	−	3.63178i	0.484107	−	0.476876i
$59$	−2.51467	+	9.38488i	−0.327382	+	1.22181i	0.584513	+	0.811385i	$0.301286\pi$
$59$	−2.51467	+	9.38488i	−0.327382	+	1.22181i	−0.911895	+	0.410423i	$0.865381\pi$
$60$	−0.420062	−	0.119358i	−0.0542298	−	0.0154091i
$61$	−11.9231	+	6.88378i	−1.52659	+	0.881378i	−0.527089	+	0.849810i	$0.676717\pi$
$61$	−11.9231	+	6.88378i	−1.52659	+	0.881378i	−0.999502	+	0.0315679i	$0.989950\pi$
$62$	−1.94966	+	1.10616i	−0.247607	+	0.140482i
$63$	−1.76575	−	6.58987i	−0.222463	−	0.830245i
$64$	0.361046	−	7.99185i	0.0451307	−	0.998981i
$65$	−0.0932273	−	0.341044i	−0.0115634	−	0.0423013i
$66$	−0.859539	−	0.504916i	−0.105802	−	0.0621509i
$67$	−3.16917	−	11.8275i	−0.387176	−	1.44496i	−0.834708	−	0.550693i	$-0.814363\pi$
$67$	−3.16917	−	11.8275i	−0.387176	−	1.44496i	0.447532	−	0.894268i	$-0.352303\pi$
$68$	12.6746	+	0.190751i	1.53702	+	0.0231319i
$69$	8.20666	+	14.2144i	0.987966	+	1.71121i
$70$	−0.467645	+	0.121541i	−0.0558943	+	0.0145270i
$71$	1.81764	−	6.78351i	0.215714	−	0.805055i	−0.770200	−	0.637802i	$-0.779844\pi$
$71$	1.81764	−	6.78351i	0.215714	−	0.805055i	0.985914	−	0.167253i	$-0.0534896\pi$
$72$	−5.31580	−	1.55378i	−0.626473	−	0.183114i
$73$	1.49582	+	1.49582i	0.175072	+	0.175072i	0.789204	−	0.614131i	$-0.210494\pi$
$73$	1.49582	+	1.49582i	0.175072	+	0.175072i	−0.614131	+	0.789204i	$0.710494\pi$
$74$	−4.39828	−	0.0330948i	−0.511290	−	0.00384719i
$75$	−9.62322	−	5.55597i	−1.11119	−	0.641548i
$76$	0.572920	+	0.590428i	0.0657184	+	0.0677267i
$77$	−1.10300			−0.125698
$78$	−2.91133	−	10.9742i	−0.329644	−	1.24259i
$79$		−	10.3044i		−	1.15933i	−0.814854	−	0.579667i	$-0.803183\pi$
$79$		−	10.3044i		−	1.15933i	0.814854	−	0.579667i	$-0.196817\pi$
$80$	−0.112874	+	0.375645i	−0.0126196	+	0.0419983i
$81$	5.52009	−	9.56108i	0.613344	−	1.06234i
$82$	−10.1185	−	0.0761368i	−1.11741	−	0.00840790i
$83$	2.53771	−	2.53771i	0.278550	−	0.278550i	−0.553980	−	0.832530i	$-0.686892\pi$
$83$	2.53771	−	2.53771i	0.278550	−	0.278550i	0.832530	+	0.553980i	$0.186892\pi$
$84$	−15.0465	+	3.78997i	−1.64171	+	0.413519i
$85$	−0.600323	−	0.160856i	−0.0651142	−	0.0174473i
$86$	2.00761	+	7.72451i	0.216486	+	0.832956i
$87$	−7.05665	+	4.07416i	−0.756552	+	0.436796i
$88$	−0.465083	+	0.765128i	−0.0495781	+	0.0815629i
$89$	0.110536	−	0.0296181i	0.0117168	−	0.00313951i	−0.252956	−	0.967478i	$-0.581403\pi$
$89$	0.110536	−	0.0296181i	0.0117168	−	0.00313951i	0.264673	+	0.964338i	$0.414736\pi$
$90$	0.234129	+	0.137534i	0.0246794	+	0.0144973i
$91$	−8.92775	−	8.83821i	−0.935882	−	0.926496i
$92$	12.8768	−	7.17829i	1.34250	−	0.748388i
$93$	3.40912	−	0.913470i	0.353509	−	0.0947224i
$94$	6.07901	+	10.7145i	0.627002	+	1.10512i
$95$	−0.0201684	−	0.0349327i	−0.00206923	−	0.00358402i
$96$	−3.71539	+	12.0355i	−0.379200	+	1.22837i
$97$	6.28973	+	1.68533i	0.638626	+	0.171119i	0.563581	−	0.826061i	$-0.309423\pi$
$97$	6.28973	+	1.68533i	0.638626	+	0.171119i	0.0750449	+	0.997180i	$0.476090\pi$
$98$	−5.17841	+	5.10107i	−0.523099	+	0.515286i
$99$	0.438306	+	0.438306i	0.0440515	+	0.0440515i
$100$	−5.11989	+	8.56752i	−0.511989	+	0.856752i
$101$	3.22024	−	5.57761i	0.320425	−	0.554993i	−0.660150	−	0.751133i	$-0.729507\pi$
$101$	3.22024	−	5.57761i	0.320425	−	0.554993i	0.980576	+	0.196140i	$0.0628408\pi$
$102$	−19.2389	−	5.31051i	−1.90493	−	0.525819i
$103$	15.5401			1.53121			0.765604	−	0.643312i	$-0.222440\pi$
$103$	15.5401			1.53121			0.765604	+	0.643312i	$0.222440\pi$
$104$	−9.89531	+	2.46634i	−0.970315	+	0.241844i
$105$	0.760766			0.0742431
$106$	5.30822	+	1.46523i	0.515579	+	0.142315i
$107$	−0.865163	+	1.49851i	−0.0836385	+	0.144866i	−0.904810	−	0.425815i	$-0.859987\pi$
$107$	−0.865163	+	1.49851i	−0.0836385	+	0.144866i	0.821172	+	0.570681i	$0.193321\pi$
$108$	−3.98310	−	2.38027i	−0.383274	−	0.229042i
$109$	13.2174	+	13.2174i	1.26599	+	1.26599i	0.948140	+	0.317853i	$0.102962\pi$
$109$	13.2174	+	13.2174i	1.26599	+	1.26599i	0.317853	+	0.948140i	$0.397038\pi$
$110$	0.0312751	−	0.0308079i	0.00298196	−	0.00293742i
$111$	6.68929	+	1.79239i	0.634919	+	0.170126i
$112$	3.20040	+	13.5645i	0.302409	+	1.28172i
$113$	−6.88323	−	11.9221i	−0.647520	−	1.12154i	−0.983713	−	0.179744i	$-0.942473\pi$
$113$	−6.88323	−	11.9221i	−0.647520	−	1.12154i	0.336193	−	0.941793i	$-0.390860\pi$
$114$	−0.639212	−	1.12664i	−0.0598677	−	0.105520i
$115$	−0.698188	+	0.187079i	−0.0651064	+	0.0174452i
$116$	3.56362	+	6.39265i	0.330874	+	0.593542i
$117$	0.0355813	+	7.05979i	0.00328949	+	0.652678i
$118$	−11.8475	−	6.95955i	−1.09065	−	0.640679i
$119$	−21.3307	+	5.71554i	−1.95538	+	0.523943i
$120$	0.320780	−	0.527728i	0.0292831	−	0.0481748i
$121$	−9.43949	+	5.44989i	−0.858135	+	0.495445i
$122$	−4.89763	−	18.8442i	−0.443410	−	1.70608i
$123$	15.3891	+	4.12351i	1.38759	+	0.371804i
$124$	−0.774310	−	3.07408i	−0.0695351	−	0.276060i
$125$	0.692716	−	0.692716i	0.0619584	−	0.0619584i
$126$	9.64796	+	0.0725959i	0.859509	+	0.00646736i
$127$	4.23231	−	7.33057i	0.375557	−	0.650483i	−0.614853	−	0.788641i	$-0.710785\pi$
$127$	4.23231	−	7.33057i	0.375557	−	0.650483i	0.990410	+	0.138158i	$0.0441182\pi$
$128$	10.7589	+	3.49947i	0.950961	+	0.309312i
$129$		−	12.5662i		−	1.10640i
$130$	0.500004	+	0.00124220i	0.0438532	+	0.000108948i
$131$	−13.5858			−1.18700			−0.593499	−	0.804835i	$-0.702254\pi$
$131$	−13.5858			−1.18700			−0.593499	+	0.804835i	$0.702254\pi$
$132$	1.01176	−	0.981755i	0.0880622	−	0.0854508i
$133$	−1.24123	−	0.716623i	−0.107628	−	0.0621391i
$134$	17.3162	+	0.130295i	1.49589	+	0.0112558i
$135$	0.160869	+	0.160869i	0.0138454	+	0.0138454i
$136$	−5.02941	+	17.2067i	−0.431268	+	1.47546i
$137$	3.19234	−	11.9140i	0.272740	−	1.01788i	−0.684601	−	0.728918i	$-0.740024\pi$
$137$	3.19234	−	11.9140i	0.272740	−	1.01788i	0.957341	−	0.288961i	$-0.0933097\pi$
$138$	−22.4656	+	5.83882i	−1.91240	+	0.497034i
$139$	5.36196	+	9.28718i	0.454795	+	0.787729i	0.998676	−	0.0514337i	$-0.0163791\pi$
$139$	5.36196	+	9.28718i	0.454795	+	0.787729i	−0.543881	+	0.839162i	$0.683046\pi$
$140$	0.0102827	−	0.683244i	0.000869047	−	0.0577447i
$141$	−5.02007	−	18.7351i	−0.422766	−	1.57778i
$142$	8.56354	+	5.03045i	0.718636	+	0.422146i
$143$	1.10399	+	0.289857i	0.0923199	+	0.0242390i
$144$	4.11846	−	6.66199i	0.343205	−	0.555166i
$145$	−0.0928744	−	0.346612i	−0.00771280	−	0.0287846i
$146$	−2.60202	+	1.47628i	−0.215344	+	0.122178i
$147$	9.91151	−	5.72241i	0.817488	−	0.471977i
$148$	1.70016	−	5.98343i	0.139752	−	0.491835i
$149$	2.96712	−	11.0734i	0.243076	−	0.907172i	−0.731265	−	0.682094i	$-0.761070\pi$
$149$	2.96712	−	11.0734i	0.243076	−	0.907172i	0.974341	−	0.225078i	$-0.0722637\pi$
$150$	11.1952	−	11.0280i	0.914087	−	0.900434i
$151$	−7.63837	+	7.63837i	−0.621602	+	0.621602i	−0.945941	−	0.324339i	$-0.894858\pi$
$151$	−7.63837	+	7.63837i	−0.621602	+	0.621602i	0.324339	+	0.945941i	$0.394858\pi$
$152$	−1.02048	+	0.558849i	−0.0827716	+	0.0453286i
$153$	10.7476	+	6.20511i	0.868889	+	0.501653i
$154$	0.415051	−	1.50364i	0.0334458	−	0.121167i
$155$			0.155428i			0.0124843i
$156$	16.0559	+	0.160705i	1.28550	+	0.0128667i
$157$			0.295631i			0.0235940i	0.999930	+	0.0117970i	$0.00375518\pi$
$157$			0.295631i			0.0235940i	−0.999930	+	0.0117970i	$0.996245\pi$
$158$	14.0473	+	3.87747i	1.11754	+	0.308475i
$159$	−7.50870	−	4.33515i	−0.595479	−	0.343800i
$160$	−0.469617	−	0.295225i	−0.0371265	−	0.0233396i
$161$	−18.1607	+	18.1607i	−1.43127	+	1.43127i
$162$	10.9568	+	11.1229i	0.860848	+	0.873901i
$163$	−0.643966	+	2.40331i	−0.0504393	+	0.188242i	−0.986549	−	0.163466i	$-0.947732\pi$
$163$	−0.643966	+	2.40331i	−0.0504393	+	0.188242i	0.936110	+	0.351708i	$0.114399\pi$
$164$	3.91133	−	13.7653i	0.305424	−	1.07489i
$165$	−0.0598607	+	0.0345606i	−0.00466015	+	0.00269054i
$166$	2.50456	+	4.41441i	0.194392	+	0.342625i
$167$	2.40443	+	8.97345i	0.186060	+	0.694386i	0.994401	+	0.105672i	$0.0336992\pi$
$167$	2.40443	+	8.97345i	0.186060	+	0.694386i	−0.808341	+	0.588715i	$0.799634\pi$
$168$	0.495292	−	21.9380i	0.0382126	−	1.69255i
$169$	6.61315	+	11.1922i	0.508704	+	0.860942i
$170$	0.445182	−	0.757851i	0.0341439	−	0.0581246i
$171$	0.208466	+	0.778006i	0.0159418	+	0.0594956i
$172$	−11.2858	−	0.169849i	−0.860531	−	0.0129508i
$173$	1.48266	+	2.56803i	0.112724	+	0.195244i	0.916868	−	0.399191i	$-0.130709\pi$
$173$	1.48266	+	2.56803i	0.112724	+	0.195244i	−0.804144	+	0.594435i	$0.797376\pi$
$174$	−2.89865	−	11.1529i	−0.219746	−	0.845502i
$175$	4.50026	−	16.7952i	0.340188	−	1.26960i
$176$	−0.868040	−	0.921930i	−0.0654310	−	0.0694931i
$177$	15.2977	+	15.2977i	1.14984	+	1.14984i
$178$	−0.00121770	+	0.161832i	−9.12705e−5	+	0.0121298i
$179$	5.42364	+	3.13134i	0.405382	+	0.234047i	0.688803	−	0.724948i	$-0.258136\pi$
$179$	5.42364	+	3.13134i	0.405382	+	0.234047i	−0.283422	+	0.958995i	$0.591470\pi$
$180$	−0.275592	+	0.267420i	−0.0205414	+	0.0199323i
$181$	−19.6735			−1.46232			−0.731160	−	0.682206i	$-0.761021\pi$
$181$	−19.6735			−1.46232			−0.731160	+	0.682206i	$0.761021\pi$
$182$	15.4080	−	8.84484i	1.14212	−	0.655623i
$183$			30.6558i			2.26614i
$184$	4.94020	+	20.2553i	0.364196	+	1.49324i
$185$	−0.152489	+	0.264119i	−0.0112112	+	0.0194184i
$186$	−0.0375558	+	4.99115i	−0.00275373	+	0.365969i
$187$	1.41875	−	1.41875i	0.103749	−	0.103749i
$188$	−16.8939	+	4.25530i	−1.23211	+	0.310349i
$189$	7.80819	+	2.09220i	0.567963	+	0.152185i
$190$	0.0552106	−	0.0143493i	0.00400540	−	0.00104101i
$191$	6.98944	−	4.03535i	0.505738	−	0.291988i	−0.225342	−	0.974280i	$-0.572350\pi$
$191$	6.98944	−	4.03535i	0.505738	−	0.291988i	0.731080	+	0.682292i	$0.239017\pi$
$192$	−15.0091	−	9.59383i	−1.08319	−	0.692375i
$193$	3.79172	−	1.01599i	0.272934	−	0.0731325i	−0.119756	−	0.992803i	$-0.538211\pi$
$193$	3.79172	−	1.01599i	0.272934	−	0.0731325i	0.392690	+	0.919671i	$0.371545\pi$
$194$	−4.66428	+	7.94019i	−0.334876	+	0.570073i
$195$	−0.761447	−	0.199921i	−0.0545283	−	0.0143167i
$196$	−5.00534	−	8.97888i	−0.357524	−	0.641349i
$197$	−17.9395	+	4.80687i	−1.27813	+	0.342475i	−0.833142	−	0.553059i	$-0.813460\pi$
$197$	−17.9395	+	4.80687i	−1.27813	+	0.342475i	−0.444993	+	0.895534i	$0.646794\pi$
$198$	−0.762445	+	0.432582i	−0.0541846	+	0.0307423i
$199$	0.747531	+	1.29476i	0.0529911	+	0.0917833i	0.891304	−	0.453406i	$-0.149791\pi$
$199$	0.747531	+	1.29476i	0.0529911	+	0.0917833i	−0.838313	+	0.545189i	$0.816458\pi$
$200$	−9.75295	−	10.2035i	−0.689638	−	0.721497i
$201$	−26.3360	−	7.05670i	−1.85760	−	0.497741i
$202$	6.39183	+	6.48875i	0.449727	+	0.456547i
$203$	−9.01580	−	9.01580i	−0.632785	−	0.632785i
$204$	14.4789	−	24.2287i	1.01373	−	1.69635i
$205$	−0.350811	+	0.607622i	−0.0245017	+	0.0424382i
$206$	−5.84762	+	21.1847i	−0.407423	+	1.47601i
$207$	14.4333			1.00319
$208$	0.361345	−	14.4177i	0.0250548	−	0.999686i
$209$	0.130221			0.00900758
$210$	−0.286271	+	1.03710i	−0.0197546	+	0.0715667i
$211$	−5.13613	+	8.89604i	−0.353586	+	0.612429i	−0.986875	−	0.161487i	$-0.948371\pi$
$211$	−5.13613	+	8.89604i	−0.353586	+	0.612429i	0.633289	+	0.773915i	$0.281704\pi$
$212$	−3.99489	+	6.68498i	−0.274370	+	0.459126i
$213$	−11.0574	−	11.0574i	−0.757638	−	0.757638i
$214$	−1.71726	−	1.74330i	−0.117389	−	0.119169i
$215$	0.534542	+	0.143230i	0.0364554	+	0.00976820i
$216$	4.74367	−	4.53421i	0.322766	−	0.308514i
$217$	2.76134	+	4.78278i	0.187452	+	0.324676i
$218$	−22.9919	+	13.0447i	−1.55721	+	0.883500i
$219$	4.54982	−	1.21912i	0.307448	−	0.0823805i
$220$	0.0302298	+	0.0542280i	0.00203809	+	0.00365605i
$221$	22.8518	−	0.115173i	1.53718	−	0.00774737i
$222$	−4.96058	+	8.44459i	−0.332932	+	0.566764i
$223$	−4.08977	+	1.09585i	−0.273871	+	0.0733836i	−0.393141	−	0.919478i	$-0.628611\pi$
$223$	−4.08977	+	1.09585i	−0.273871	+	0.0733836i	0.119269	+	0.992862i	$0.461945\pi$
$224$	−19.6959	−	0.741341i	−1.31598	−	0.0495330i
$225$	−8.46233	+	4.88573i	−0.564155	+	0.325715i
$226$	18.8427	−	4.89724i	1.25340	−	0.325759i
$227$	20.5241	+	5.49942i	1.36223	+	0.365009i	0.864636	−	0.502399i	$-0.167549\pi$
$227$	20.5241	+	5.49942i	1.36223	+	0.365009i	0.497598	+	0.867408i	$0.334216\pi$
$228$	1.77640	−	0.447447i	0.117645	−	0.0296329i
$229$	−2.65946	+	2.65946i	−0.175742	+	0.175742i	−0.789497	−	0.613755i	$-0.789658\pi$
$229$	−2.65946	+	2.65946i	−0.175742	+	0.175742i	0.613755	+	0.789497i	$0.289658\pi$
$230$	0.00769145	−	1.02219i	0.000507159	−	0.0674012i
$231$	−1.22801	+	2.12697i	−0.0807969	+	0.139944i
$232$	−10.0556	+	2.45254i	−0.660185	+	0.161017i
$233$		−	12.9659i		−	0.849423i	−0.905329	−	0.424711i	$-0.860376\pi$
$233$		−	12.9659i		−	0.849423i	0.905329	−	0.424711i	$-0.139624\pi$
$234$	−9.63752	−	2.60805i	−0.630024	−	0.170493i
$235$	0.854172			0.0557200
$236$	13.9456	−	13.5321i	0.907783	−	0.880865i
$237$	−19.8705	−	11.4722i	−1.29073	−	0.745201i
$238$	0.234985	−	31.2294i	0.0152318	−	2.02430i
$239$	−2.00711	−	2.00711i	−0.129829	−	0.129829i	0.639206	−	0.769035i	$-0.279263\pi$
$239$	−2.00711	−	2.00711i	−0.129829	−	0.129829i	−0.769035	+	0.639206i	$0.779263\pi$
$240$	0.598709	+	0.635878i	0.0386465	+	0.0410458i
$241$	−2.01768	+	7.53010i	−0.129970	+	0.485056i	−0.999968	−	0.00799977i	$-0.997454\pi$
$241$	−2.01768	+	7.53010i	−0.129970	+	0.485056i	0.869998	+	0.493056i	$0.164120\pi$
$242$	−3.87745	−	14.9190i	−0.249252	−	0.959028i
$243$	−8.81133	−	15.2617i	−0.565247	−	0.979036i
$244$	27.5320	+	0.414352i	1.76256	+	0.0265261i
$245$	0.130448	+	0.486839i	0.00833402	+	0.0311030i
$246$	−11.4121	+	19.4273i	−0.727611	+	1.23864i
$247$	1.05402	+	1.04345i	0.0670656	+	0.0663929i
$248$	4.48205	+	0.101191i	0.284610	+	0.00642561i
$249$	−2.06828	−	7.71891i	−0.131072	−	0.489166i
$250$	0.683668	+	1.20500i	0.0432390	+	0.0762107i
$251$	−8.49344	+	4.90369i	−0.536101	+	0.309518i	−0.743497	−	0.668739i	$-0.766834\pi$
$251$	−8.49344	+	4.90369i	−0.536101	+	0.309518i	0.207396	+	0.978257i	$0.433501\pi$
$252$	−3.72943	+	13.1251i	−0.234932	+	0.826803i
$253$	0.603955	−	2.25399i	0.0379703	−	0.141707i
$254$	8.40069	+	8.52807i	0.527106	+	0.535099i
$255$	−0.978548	+	0.978548i	−0.0612791	+	0.0612791i
$256$	−8.81909	+	13.3500i	−0.551193	+	0.834378i
$257$	8.22290	+	4.74749i	0.512930	+	0.296140i	0.734037	−	0.679109i	$-0.237634\pi$
$257$	8.22290	+	4.74749i	0.512930	+	0.296140i	−0.221107	+	0.975250i	$0.570967\pi$
$258$	17.1307	+	4.72860i	1.06651	+	0.294390i
$259$			10.8365i			0.673345i
$260$	−0.189841	+	0.681154i	−0.0117735	+	0.0422434i
$261$			7.16535i			0.443524i
$262$	5.11225	−	18.5206i	0.315836	−	1.14421i
$263$	0.383169	+	0.221223i	0.0236272	+	0.0136412i	0.511767	−	0.859124i	$-0.328991\pi$
$263$	0.383169	+	0.221223i	0.0236272	+	0.0136412i	−0.488140	+	0.872765i	$0.662324\pi$
$264$	0.957643	+	1.74869i	0.0589389	+	0.107624i
$265$	0.269992	−	0.269992i	0.0165855	−	0.0165855i
$266$	1.44399	−	1.42242i	0.0885367	−	0.0872143i
$267$	0.0659497	−	0.246128i	0.00403606	−	0.0150628i
$268$	−6.69359	+	23.5570i	−0.408876	+	1.43897i
$269$	12.2972	−	7.09981i	0.749776	−	0.432883i	−0.0758371	−	0.997120i	$-0.524163\pi$
$269$	12.2972	−	7.09981i	0.749776	−	0.432883i	0.825613	+	0.564237i	$0.190830\pi$
$270$	−0.279836	+	0.158768i	−0.0170303	+	0.00966231i
$271$	1.28851	+	4.80880i	0.0782717	+	0.292114i	0.993955	−	0.109786i	$-0.0350166\pi$
$271$	1.28851	+	4.80880i	0.0782717	+	0.292114i	−0.915684	+	0.401900i	$0.868350\pi$
$272$	−21.5642	−	13.3310i	−1.30752	−	0.808311i
$273$	−26.9827	+	7.37596i	−1.63307	+	0.446413i
$274$	15.0402	+	8.83504i	0.908614	+	0.533744i
$275$	0.408882	+	1.52597i	0.0246565	+	0.0920193i
$276$	0.493979	−	32.8229i	0.0297341	−	1.97571i
$277$	−5.99110	−	10.3769i	−0.359970	−	0.623487i	0.627985	−	0.778225i	$-0.283880\pi$
$277$	−5.99110	−	10.3769i	−0.359970	−	0.623487i	−0.987955	+	0.154739i	$0.950546\pi$
$278$	−14.6783	+	3.81489i	−0.880344	+	0.228802i
$279$	0.803275	−	2.99786i	0.0480908	−	0.179477i
$280$	0.927551	+	0.271118i	0.0554318	+	0.0162024i
$281$	−5.12419	−	5.12419i	−0.305684	−	0.305684i	0.537549	−	0.843233i	$-0.319350\pi$
$281$	−5.12419	−	5.12419i	−0.305684	−	0.305684i	−0.843233	+	0.537549i	$0.819350\pi$
$282$	27.4294	+	0.206392i	1.63340	+	0.0122905i
$283$	−10.7351	−	6.19789i	−0.638133	−	0.368426i	0.145762	−	0.989320i	$-0.453437\pi$
$283$	−10.7351	−	6.19789i	−0.638133	−	0.368426i	−0.783895	+	0.620893i	$0.786770\pi$
$284$	−10.0801	+	9.78117i	−0.598143	+	0.580406i
$285$	−0.0898167			−0.00532028
$286$	−0.810564	+	1.39592i	−0.0479297	+	0.0825424i
$287$			24.9300i			1.47157i
$288$	7.53210	+	8.12128i	0.443833	+	0.478551i
$289$	11.5853	−	20.0663i	0.681486	−	1.18037i
$290$	0.507461	+	0.00381838i	0.0297991	+	0.000224223i
$291$	10.2525	−	10.2525i	0.601012	−	0.601012i
$292$	−1.03340	−	4.10267i	−0.0604749	−	0.240091i
$293$	2.75972	+	0.739465i	0.161225	+	0.0432000i	0.338528	−	0.940956i	$-0.390071\pi$
$293$	2.75972	+	0.739465i	0.161225	+	0.0432000i	−0.177304	+	0.984156i	$0.556738\pi$
$294$	4.07135	+	15.6650i	0.237446	+	0.913602i
$295$	−0.825094	+	0.476368i	−0.0480388	+	0.0277352i
$296$	7.51705	+	4.56924i	0.436919	+	0.265582i
$297$	−0.709432	+	0.190092i	−0.0411654	+	0.0110302i
$298$	13.9792	+	8.21174i	0.809792	+	0.475693i
$299$	22.9494	−	13.4045i	1.32720	−	0.775204i
$300$	10.8211	+	19.4115i	0.624754	+	1.12072i
$301$	18.9933	−	5.08925i	1.09476	−	0.293339i
$302$	−7.53861	−	13.2871i	−0.433798	−	0.764589i
$303$	−7.17040	−	12.4195i	−0.411929	−	0.713481i
$304$	−0.377842	−	1.60144i	−0.0216707	−	0.0918488i
$305$	−1.30403	−	0.349415i	−0.0746687	−	0.0200074i
$306$	−12.5032	+	12.3165i	−0.714763	+	0.704086i
$307$	1.31454	+	1.31454i	0.0750248	+	0.0750248i	0.743623	−	0.668599i	$-0.233106\pi$
$307$	1.31454	+	1.31454i	0.0750248	+	0.0750248i	−0.668599	+	0.743623i	$0.733106\pi$
$308$	1.89363	+	1.13162i	0.107900	+	0.0644801i
$309$	17.3013	−	29.9667i	0.984236	−	1.70475i
$310$	−0.211885	−	0.0584867i	−0.0120343	−	0.00332182i
$311$	−26.3976			−1.49687			−0.748436	−	0.663207i	$-0.769195\pi$
$311$	−26.3976			−1.49687			−0.748436	+	0.663207i	$0.769195\pi$
$312$	−6.26082	+	21.8275i	−0.354449	+	1.23574i
$313$	23.0930			1.30529			0.652647	−	0.757662i	$-0.273658\pi$
$313$	23.0930			1.30529			0.652647	+	0.757662i	$0.273658\pi$
$314$	−0.403014	−	0.111244i	−0.0227434	−	0.00627787i
$315$	0.334496	−	0.579364i	0.0188467	−	0.0326434i
$316$	−10.5718	+	17.6906i	−0.594710	+	0.995176i
$317$	13.9691	+	13.9691i	0.784583	+	0.784583i	0.980600	−	0.196018i	$-0.0628010\pi$
$317$	13.9691	+	13.9691i	0.784583	+	0.784583i	−0.196018	+	0.980600i	$0.562801\pi$
$318$	8.73530	−	8.60482i	0.489851	−	0.482534i
$319$	1.11898	+	0.299830i	0.0626510	+	0.0167873i
$320$	0.579175	−	0.529106i	0.0323769	−	0.0295779i
$321$	1.92643	+	3.33668i	0.107523	+	0.186235i
$322$	−17.9235	−	31.5911i	−0.998839	−	1.76050i
$323$	2.51832	−	0.674782i	0.140123	−	0.0375459i
$324$	−19.2861	+	10.7512i	−1.07145	+	0.597288i
$325$	−8.91789	+	15.6276i	−0.494676	+	0.866864i
$326$	−3.03395	−	1.78223i	−0.168035	−	0.0987084i
$327$	40.2031	−	10.7724i	2.22323	−	0.595714i
$328$	17.2935	+	10.5118i	0.954872	+	0.580419i
$329$	26.2842	−	15.1752i	1.44910	−	0.836636i
$330$	−0.0245889	−	0.0946089i	−0.00135358	−	0.00520805i
$331$	8.82798	+	2.36545i	0.485229	+	0.130017i	0.493137	−	0.869952i	$-0.335850\pi$
$331$	8.82798	+	2.36545i	0.485229	+	0.130017i	−0.00790714	+	0.999969i	$0.502517\pi$
$332$	−6.96032	+	1.75319i	−0.381997	+	0.0962188i
$333$	4.30617	−	4.30617i	0.235976	−	0.235976i
$334$	−13.1377	−	0.0988542i	−0.718861	−	0.00540906i
$335$	0.600354	−	1.03984i	0.0328009	−	0.0568127i
$336$	29.7203	+	8.93033i	1.62137	+	0.487189i
$337$			8.38992i			0.457028i	0.973541	+	0.228514i	$0.0733867\pi$
$337$			8.38992i			0.457028i	−0.973541	+	0.228514i	$0.926613\pi$
$338$	−17.7461	+	4.80370i	−0.965261	+	0.261287i
$339$	−30.6534			−1.66486
$340$	0.865609	+	0.892061i	0.0469442	+	0.0483788i
$341$	−0.434551	−	0.250888i	−0.0235322	−	0.0135863i
$342$	−1.13905	−	0.00857074i	−0.0615926	−	0.000463453i
$343$	−4.58281	−	4.58281i	−0.247448	−	0.247448i
$344$	4.47830	−	15.3212i	0.241454	−	0.826064i
$345$	−0.416563	+	1.55463i	−0.0224270	+	0.0836987i
$346$	−4.05874	+	1.05487i	−0.218199	+	0.0567102i
$347$	1.54479	+	2.67566i	0.0829287	+	0.143637i	0.904507	−	0.426459i	$-0.140239\pi$
$347$	1.54479	+	2.67566i	0.0829287	+	0.143637i	−0.821578	+	0.570096i	$0.806906\pi$
$348$	16.2948	+	0.245234i	0.873492	+	0.0131459i
$349$	7.75487	+	28.9416i	0.415109	+	1.54921i	0.784618	+	0.619980i	$0.212859\pi$
$349$	7.75487	+	28.9416i	0.415109	+	1.54921i	−0.369509	+	0.929227i	$0.620474\pi$
$350$	21.2023	+	12.4548i	1.13331	+	0.665738i
$351$	−7.26538	−	4.14599i	−0.387797	−	0.221296i
$352$	1.58344	−	0.836424i	0.0843978	−	0.0445816i
$353$	−6.52845	−	24.3645i	−0.347474	−	1.29679i	−0.889695	−	0.456556i	$-0.849083\pi$
$353$	−6.52845	−	24.3645i	−0.347474	−	1.29679i	0.542220	−	0.840236i	$-0.317584\pi$
$354$	−26.6107	+	15.0979i	−1.41434	+	0.802444i
$355$	0.596389	−	0.344325i	0.0316530	−	0.0182749i
$356$	−0.220156	−	0.0625562i	−0.0116682	−	0.00331547i
$357$	−12.7266	+	47.4964i	−0.673564	+	2.51378i
$358$	−6.30962	+	6.21538i	−0.333474	+	0.328493i
$359$	−9.78353	+	9.78353i	−0.516355	+	0.516355i	−0.916467	−	0.400111i	$-0.868971\pi$
$359$	−9.78353	+	9.78353i	−0.516355	+	0.516355i	0.400111	+	0.916467i	$0.368971\pi$
$360$	−0.260852	−	0.476324i	−0.0137481	−	0.0251045i
$361$	−16.3079	−	9.41539i	−0.858313	−	0.495547i
$362$	7.40301	−	26.8196i	0.389093	−	1.40960i
$363$			24.2702i			1.27386i
$364$	6.25965	+	24.3329i	0.328095	+	1.27539i
$365$			0.207435i			0.0108576i
$366$	−41.7910	−	11.5356i	−2.18445	−	0.602974i
$367$	7.32432	+	4.22870i	0.382327	+	0.220736i	0.678830	−	0.734295i	$-0.262487\pi$
$367$	7.32432	+	4.22870i	0.382327	+	0.220736i	−0.296504	+	0.955032i	$0.595821\pi$
$368$	−29.4716	−	0.887286i	−1.53631	−	0.0462530i
$369$	9.90662	−	9.90662i	0.515718	−	0.515718i
$370$	−0.302674	−	0.307264i	−0.0157353	−	0.0159739i
$371$	3.51141	−	13.1048i	0.182304	−	0.680366i
$372$	−6.78997	−	1.92934i	−0.352044	−	0.100031i
$373$	8.98736	−	5.18886i	0.465348	−	0.268669i	−0.248942	−	0.968518i	$-0.580083\pi$
$373$	8.98736	−	5.18886i	0.465348	−	0.268669i	0.714290	+	0.699850i	$0.246750\pi$
$374$	1.40022	+	2.46795i	0.0724037	+	0.127615i
$375$	−0.564575	−	2.10702i	−0.0291546	−	0.108806i
$376$	0.556103	−	24.6315i	0.0286788	−	1.27028i
$377$	6.65461	+	11.3931i	0.342730	+	0.586776i
$378$	−5.79033	+	9.85710i	−0.297822	+	0.506995i
$379$	1.21827	+	4.54665i	0.0625784	+	0.233546i	0.990131	−	0.140148i	$-0.0447578\pi$
$379$	1.21827	+	4.54665i	0.0625784	+	0.233546i	−0.927552	+	0.373694i	$0.878091\pi$
$380$	−0.00121399	+	0.0806645i	−6.22761e−5	+	0.00413800i
$381$	−9.42395	−	16.3228i	−0.482804	−	0.836241i
$382$	2.87105	+	11.0467i	0.146895	+	0.565198i
$383$	5.80376	−	21.6599i	0.296558	−	1.10677i	−0.643414	−	0.765519i	$-0.722482\pi$
$383$	5.80376	−	21.6599i	0.296558	−	1.10677i	0.939972	−	0.341252i	$-0.110851\pi$
$384$	18.7265	−	16.8509i	0.955630	−	0.859916i
$385$	−0.0764799	−	0.0764799i	−0.00389778	−	0.00389778i
$386$	−0.0417707	+	5.55131i	−0.00212607	+	0.282554i
$387$	−9.56987	−	5.52517i	−0.486464	−	0.280860i
$388$	−9.06919	−	9.34634i	−0.460418	−	0.474489i
$389$	0.255974			0.0129784			0.00648920	−	0.999979i	$-0.497934\pi$
$389$	0.255974			0.0129784			0.00648920	+	0.999979i	$0.497934\pi$
$390$	0.559067	−	0.962800i	0.0283094	−	0.0487533i
$391$		−	46.7191i		−	2.36269i
$392$	14.1238	−	3.44475i	0.713359	−	0.173986i
$393$	−15.1255	+	26.1982i	−0.762983	+	1.32153i
$394$	0.197627	−	26.2645i	0.00995628	−	1.32319i
$395$	0.714488	−	0.714488i	0.0359498	−	0.0359498i
$396$	−0.302807	−	1.20217i	−0.0152166	−	0.0604112i
$397$	−29.9538	−	8.02610i	−1.50334	−	0.402818i	−0.589122	−	0.808044i	$-0.700526\pi$
$397$	−29.9538	−	8.02610i	−1.50334	−	0.402818i	−0.914217	+	0.405226i	$0.867193\pi$
$398$	−2.04635	+	0.531849i	−0.102574	+	0.0266592i
$399$	−2.76380	+	1.59568i	−0.138363	+	0.0798841i
$400$	17.5797	−	9.45603i	0.878986	−	0.472801i
$401$	20.6707	−	5.53870i	1.03225	−	0.276590i	0.297350	−	0.954769i	$-0.403897\pi$
$401$	20.6707	−	5.53870i	1.03225	−	0.276590i	0.734897	+	0.678179i	$0.237231\pi$
$402$	19.5300	−	33.2467i	0.974067	−	1.65819i
$403$	−1.50695	−	5.51271i	−0.0750663	−	0.274608i
$404$	−11.2509	+	6.27188i	−0.559752	+	0.312038i
$405$	1.04570	−	0.280195i	0.0519613	−	0.0139230i
$406$	15.6832	−	8.89805i	0.778345	−	0.441603i
$407$	−0.492286	−	0.852665i	−0.0244017	−	0.0422650i
$408$	27.5811	+	28.8553i	1.36547	+	1.42855i
$409$	−31.2652	−	8.37750i	−1.54597	−	0.414241i	−0.617779	−	0.786352i	$-0.711967\pi$
$409$	−31.2652	−	8.37750i	−1.54597	−	0.414241i	−0.928188	+	0.372112i	$0.878634\pi$
$410$	−0.696322	−	0.706881i	−0.0343889	−	0.0349104i
$411$	−19.4202	−	19.4202i	−0.957927	−	0.957927i
$412$	−26.6793	−	15.9433i	−1.31439	−	0.785472i
$413$	−16.9263	+	29.3172i	−0.832889	+	1.44261i
$414$	−5.43116	+	19.6760i	−0.266927	+	0.967021i
$415$	0.351920			0.0172751
$416$	19.5187	+	5.91787i	0.956982	+	0.290148i
$417$	23.8786			1.16934
$418$	−0.0490013	+	0.177522i	−0.00239673	+	0.00868286i
$419$	−10.4525	+	18.1043i	−0.510640	+	0.884454i	0.489284	+	0.872125i	$0.337258\pi$
$419$	−10.4525	+	18.1043i	−0.510640	+	0.884454i	−0.999924	+	0.0123300i	$0.996075\pi$
$420$	−1.30609	−	0.780508i	−0.0637305	−	0.0380849i
$421$	8.42426	+	8.42426i	0.410573	+	0.410573i	0.881938	−	0.471365i	$-0.156239\pi$
$421$	8.42426	+	8.42426i	0.410573	+	0.410573i	−0.471365	+	0.881938i	$0.656239\pi$
$422$	−10.1947	−	10.3493i	−0.496269	−	0.503794i
$423$	−16.4750	−	4.41447i	−0.801044	−	0.214639i
$424$	−7.60993	−	7.96148i	−0.369571	−	0.386644i
$425$	15.8146	+	27.3917i	0.767120	+	1.32869i
$426$	19.2346	−	10.9129i	0.931918	−	0.528734i
$427$	−46.3349	+	12.4154i	−2.24230	+	0.600823i
$428$	3.02271	−	1.68503i	0.146108	−	0.0814491i
$429$	1.78805	−	1.80617i	0.0863279	−	0.0872025i
$430$	−0.396400	+	0.674808i	−0.0191161	+	0.0325421i
$431$	21.5916	−	5.78544i	1.04003	−	0.278675i	0.301904	−	0.953338i	$-0.402378\pi$
$431$	21.5916	−	5.78544i	1.04003	−	0.278675i	0.738125	+	0.674663i	$0.235711\pi$
$432$	4.39617	+	8.17292i	0.211511	+	0.393220i
$433$	−12.3592	+	7.13560i	−0.593946	+	0.342915i	−0.766656	−	0.642058i	$-0.778081\pi$
$433$	−12.3592	+	7.13560i	−0.593946	+	0.342915i	0.172710	+	0.984973i	$0.444748\pi$
$434$	−7.55911	+	1.96462i	−0.362849	+	0.0943047i
$435$	−0.771790	−	0.206801i	−0.0370045	−	0.00991533i
$436$	−9.13129	−	36.2520i	−0.437309	−	1.73616i
$437$	2.14407	−	2.14407i	0.102565	−	0.102565i
$438$	−0.0501221	+	6.66120i	−0.00239493	+	0.318285i
$439$	1.78605	−	3.09353i	0.0852434	−	0.147646i	−0.820251	−	0.572003i	$-0.806167\pi$
$439$	1.78605	−	3.09353i	0.0852434	−	0.147646i	0.905495	+	0.424357i	$0.139500\pi$
$440$	−0.0853007	+	0.0208046i	−0.00406655	+	0.000991819i
$441$		−	10.0642i		−	0.479247i
$442$	−8.44196	+	31.1956i	−0.401543	+	1.48382i
$443$	8.73925			0.415214			0.207607	−	0.978212i	$-0.433432\pi$
$443$	8.73925			0.415214			0.207607	+	0.978212i	$0.433432\pi$
$444$	−9.64531	−	9.94007i	−0.457746	−	0.471735i
$445$	0.00971805	+	0.00561072i	0.000460680	+	0.000265974i
$446$	0.0450541	−	5.98767i	0.00213337	−	0.283524i
$447$	−18.0501	−	18.0501i	−0.853740	−	0.853740i
$448$	8.42204	−	26.5711i	0.397904	−	1.25537i
$449$	−6.78232	+	25.3120i	−0.320077	+	1.19455i	0.599091	+	0.800681i	$0.295529\pi$
$449$	−6.78232	+	25.3120i	−0.320077	+	1.19455i	−0.919169	+	0.393864i	$0.871138\pi$
$450$	−3.47607	−	13.3746i	−0.163863	−	0.630484i
$451$	−1.13254	−	1.96161i	−0.0533291	−	0.0923687i
$452$	−0.414319	+	27.5298i	−0.0194879	+	1.29489i
$453$	6.22541	+	23.2335i	0.292495	+	1.09161i
$454$	−15.2201	+	25.9098i	−0.714314	+	1.21601i
$455$	−0.00620857	−	1.23186i	−0.000291062	−	0.0577505i
$456$	−0.0584746	+	2.59002i	−0.00273832	+	0.121289i
$457$	8.37320	+	31.2492i	0.391682	+	1.46178i	0.827359	+	0.561674i	$0.189842\pi$
$457$	8.37320	+	31.2492i	0.391682	+	1.46178i	−0.435677	+	0.900103i	$0.643491\pi$
$458$	−2.62473	−	4.62620i	−0.122645	−	0.216168i
$459$	−12.7346	+	7.35230i	−0.594398	+	0.343176i
$460$	1.39059	+	0.395128i	0.0648365	+	0.0184230i
$461$	−4.21669	+	15.7369i	−0.196391	+	0.732941i	0.795511	+	0.605939i	$0.207202\pi$
$461$	−4.21669	+	15.7369i	−0.196391	+	0.732941i	−0.991902	+	0.127003i	$0.959464\pi$
$462$	−2.43746	−	2.47442i	−0.113401	−	0.115121i
$463$	−24.8178	+	24.8178i	−1.15338	+	1.15338i	−0.167509	+	0.985871i	$0.553572\pi$
$463$	−24.8178	+	24.8178i	−1.15338	+	1.15338i	−0.985871	+	0.167509i	$0.946428\pi$
$464$	0.440489	−	14.6310i	0.0204492	−	0.679229i
$465$	0.299721	+	0.173044i	0.0138992	+	0.00802471i
$466$	17.6755	+	4.87897i	0.818802	+	0.226014i
$467$		−	10.5453i		−	0.487976i	−0.969778	−	0.243988i	$-0.921544\pi$
$467$		−	10.5453i		−	0.487976i	0.969778	−	0.243988i	$-0.0784558\pi$
$468$	7.18191	−	12.1568i	0.331984	−	0.561948i
$469$		−	42.6636i		−	1.97002i
$470$	−0.321419	+	1.16443i	−0.0148260	+	0.0537114i
$471$	0.570082	+	0.329137i	0.0262680	+	0.0151658i
$472$	13.1997	+	24.1032i	0.607568	+	1.10944i
$473$	−1.26329	+	1.26329i	−0.0580860	+	0.0580860i
$474$	23.1164	−	22.7712i	1.06177	−	1.04591i
$475$	−0.531305	+	1.98286i	−0.0243779	+	0.0909797i
$476$	42.4845	+	12.0718i	1.94728	+	0.553308i
$477$	−6.60290	+	3.81219i	−0.302326	+	0.174548i
$478$	3.49143	−	1.98090i	0.159694	−	0.0906042i
$479$	2.68034	+	10.0032i	0.122468	+	0.457057i	0.999737	−	0.0229425i	$-0.00730348\pi$
$479$	2.68034	+	10.0032i	0.122468	+	0.457057i	−0.877269	+	0.480000i	$0.840637\pi$
$480$	−1.09214	+	0.576903i	−0.0498492	+	0.0263319i
$481$	2.84771	−	10.8462i	0.129845	−	0.494543i
$482$	−9.50603	−	5.58410i	−0.432988	−	0.254349i
$483$	14.8013	+	55.2392i	0.673483	+	2.51347i
$484$	21.7971	+	0.328042i	0.990777	+	0.0149110i
$485$	0.319261	+	0.552977i	0.0144969	+	0.0251094i
$486$	24.1208	−	6.26903i	1.09414	−	0.284369i
$487$	−6.29726	+	23.5017i	−0.285356	+	1.06496i	0.663222	+	0.748422i	$0.269188\pi$
$487$	−6.29726	+	23.5017i	−0.285356	+	1.06496i	−0.948579	+	0.316541i	$0.897478\pi$
$488$	−10.9250	+	37.3766i	−0.494550	+	1.69196i
$489$	3.91748	+	3.91748i	0.177155	+	0.177155i
$490$	−0.712761	−	0.00536316i	−0.0321993	−	0.000242283i
$491$	28.1909	+	16.2760i	1.27224	+	0.734525i	0.975408	−	0.220406i	$-0.0707382\pi$
$491$	28.1909	+	16.2760i	1.27224	+	0.734525i	0.296827	+	0.954931i	$0.404072\pi$
$492$	−22.1897	−	22.8678i	−1.00039	−	1.03096i
$493$	23.1935			1.04458
$494$	−1.81908	+	1.04423i	−0.0818443	+	0.0469821i
$495$			0.0607828i			0.00273198i
$496$	−1.82451	+	6.07200i	−0.0819230	+	0.272641i
$497$	12.2346	−	21.1909i	0.548795	−	0.950541i
$498$	11.3010	+	0.0850338i	0.506408	+	0.00381046i
$499$	20.4541	−	20.4541i	0.915653	−	0.915653i	−0.0810563	−	0.996710i	$-0.525829\pi$
$499$	20.4541	−	20.4541i	0.915653	−	0.915653i	0.996710	+	0.0810563i	$0.0258294\pi$
$500$	−1.89995	+	0.478567i	−0.0849684	+	0.0214021i
$501$	19.9809	+	5.35387i	0.892681	+	0.239193i
$502$	−3.48885	−	13.4238i	−0.155715	−	0.599132i
$503$	22.7444	−	13.1315i	1.01412	−	0.585504i	0.101726	−	0.994812i	$-0.467563\pi$
$503$	22.7444	−	13.1315i	1.01412	−	0.585504i	0.912396	+	0.409309i	$0.134230\pi$
$504$	−16.4892	−	10.0230i	−0.734487	−	0.446458i
$505$	0.610027	−	0.163456i	0.0271459	−	0.00727371i
$506$	2.84545	+	1.67149i	0.126496	+	0.0743069i
$507$	28.9452	−	0.291775i	1.28550	−	0.0129582i
$508$	−14.7869	+	8.24304i	−0.656061	+	0.365726i
$509$	−13.3661	+	3.58144i	−0.592443	+	0.158745i	−0.542569	−	0.840011i	$-0.682548\pi$
$509$	−13.3661	+	3.58144i	−0.592443	+	0.158745i	−0.0498735	+	0.998756i	$0.515882\pi$
$510$	−0.965768	−	1.70221i	−0.0427649	−	0.0753752i
$511$	3.68529	+	6.38311i	0.163028	+	0.282372i
$512$	−14.8806	−	17.0460i	−0.657638	−	0.753334i
$513$	−0.921843	−	0.247007i	−0.0407004	−	0.0109056i
$514$	−9.56616	+	9.42327i	−0.421945	+	0.415643i
$515$	1.07752	+	1.07752i	0.0474812	+	0.0474812i
$516$	−12.8924	+	21.5738i	−0.567554	+	0.949734i
$517$	−1.37878	+	2.38812i	−0.0606386	+	0.105029i
$518$	−14.7726	−	4.07769i	−0.649072	−	0.179163i
$519$	6.60277			0.289829
$520$	−0.857135	−	0.515112i	−0.0375879	−	0.0225891i
$521$	0.605870			0.0265437			0.0132718	−	0.999912i	$-0.495775\pi$
$521$	0.605870			0.0265437			0.0132718	+	0.999912i	$0.495775\pi$
$522$	−9.76804	−	2.69627i	−0.427536	−	0.118013i
$523$	6.97171	−	12.0753i	0.304851	−	0.528018i	−0.672377	−	0.740209i	$-0.734727\pi$
$523$	6.97171	−	12.0753i	0.304851	−	0.528018i	0.977228	+	0.212191i	$0.0680599\pi$
$524$	23.3242	+	13.9384i	1.01892	+	0.608900i
$525$	−27.3768	−	27.3768i	−1.19482	−	1.19482i
$526$	−0.445762	+	0.439104i	−0.0194362	+	0.0191458i
$527$	−9.70376	−	2.60011i	−0.422702	−	0.113263i
$528$	−2.74422	+	0.647471i	−0.119427	+	0.0281775i
$529$	−15.6676	−	27.1371i	−0.681201	−	1.17987i
$530$	0.266466	+	0.469659i	0.0115745	+	0.0204007i
$531$	18.3761	−	4.92387i	0.797457	−	0.213678i
$532$	1.39573	+	2.50374i	0.0605125	+	0.108551i
$533$	6.55135	−	24.9523i	0.283770	−	1.08081i
$534$	0.310713	+	0.182521i	0.0134459	+	0.00789846i
$535$	−0.163893	+	0.0439149i	−0.00708570	+	0.00189861i
$536$	−29.5949	−	17.9893i	−1.27830	−	0.777018i
$537$	12.0766	−	6.97245i	0.521146	−	0.300884i
$538$	5.05133	+	19.4356i	0.217778	+	0.837929i
$539$	−1.57168	−	0.421131i	−0.0676971	−	0.0181394i
$540$	−0.111137	−	0.441225i	−0.00478259	−	0.0189873i
$541$	−8.59605	+	8.59605i	−0.369573	+	0.369573i	−0.867321	−	0.497748i	$-0.834160\pi$
$541$	−8.59605	+	8.59605i	−0.369573	+	0.369573i	0.497748	+	0.867321i	$0.334160\pi$
$542$	−7.04037	−	0.0529752i	−0.302410	−	0.00227548i
$543$	−21.9032	+	37.9374i	−0.939956	+	1.62805i
$544$	26.2877	−	24.3806i	1.12708	−	1.04531i
$545$			1.83294i			0.0785144i
$546$	0.0982807	−	39.5593i	0.00420602	−	1.69298i
$547$	8.02828			0.343264			0.171632	−	0.985161i	$-0.445096\pi$
$547$	8.02828			0.343264			0.171632	+	0.985161i	$0.445096\pi$
$548$	−17.7038	+	17.1788i	−0.756267	+	0.733841i
$549$	23.3460	+	13.4788i	0.996384	+	0.575263i
$550$	−2.23411	−	0.0168105i	−0.0952627	−	0.000716802i
$551$	1.06441	+	1.06441i	0.0453456	+	0.0453456i
$552$	44.5594	+	13.0245i	1.89657	+	0.554358i
$553$	9.29235	−	34.6795i	0.395151	−	1.47472i
$554$	16.4005	−	4.26251i	0.696791	−	0.181097i
$555$	0.339542	+	0.588105i	0.0144128	+	0.0249637i
$556$	0.322749	−	21.4454i	0.0136876	−	0.909488i
$557$	−9.27198	−	34.6035i	−0.392866	−	1.46620i	−0.825384	−	0.564572i	$-0.809041\pi$
$557$	−9.27198	−	34.6035i	−0.392866	−	1.46620i	0.432517	−	0.901626i	$-0.357625\pi$
$558$	3.78452	+	2.22313i	0.160211	+	0.0941124i
$559$	−20.3477	+	0.102553i	−0.860617	+	0.00433751i
$560$	−0.718628	+	1.16245i	−0.0303676	+	0.0491224i
$561$	−1.15631	−	4.31540i	−0.0488193	−	0.182196i
$562$	8.91366	−	5.05726i	0.376000	−	0.213328i
$563$	−5.28880	+	3.05349i	−0.222897	+	0.128689i	−0.607291	−	0.794480i	$-0.707744\pi$
$563$	−5.28880	+	3.05349i	−0.222897	+	0.128689i	0.384394	+	0.923169i	$0.374410\pi$
$564$	−10.6029	+	37.3150i	−0.446461	+	1.57124i
$565$	0.349387	−	1.30393i	0.0146988	−	0.0548567i
$566$	12.4887	−	12.3022i	0.524939	−	0.517098i
$567$	27.2000	−	27.2000i	1.14229	−	1.14229i
$568$	−9.54095	−	17.4221i	−0.400329	−	0.731015i
$569$	−16.0840	−	9.28610i	−0.674276	−	0.389293i	0.123419	−	0.992355i	$-0.460614\pi$
$569$	−16.0840	−	9.28610i	−0.674276	−	0.389293i	−0.797695	+	0.603061i	$0.793947\pi$
$570$	0.0337974	−	0.122441i	0.00141562	−	0.00512849i
$571$		−	30.2053i		−	1.26405i	−0.774947	−	0.632026i	$-0.782223\pi$
$571$		−	30.2053i		−	1.26405i	0.774947	−	0.632026i	$-0.217777\pi$
$572$	−1.59795	−	1.63026i	−0.0668137	−	0.0681647i
$573$		−	17.9708i		−	0.750741i
$574$	−33.9854	−	9.38100i	−1.41852	−	0.391555i
$575$	31.8570	+	18.3927i	1.32853	+	0.767027i
$576$	−13.9055	+	7.21201i	−0.579395	+	0.300501i
$577$	−26.5827	+	26.5827i	−1.10665	+	1.10665i	−0.113063	+	0.993588i	$0.536066\pi$
$577$	−26.5827	+	26.5827i	−1.10665	+	1.10665i	−0.993588	+	0.113063i	$0.963934\pi$
$578$	22.9955	+	23.3442i	0.956488	+	0.970991i
$579$	2.26227	−	8.44291i	0.0940168	−	0.350875i
$580$	−0.196159	+	0.690350i	−0.00814508	+	0.0286652i
$581$	10.8292	−	6.25222i	0.449269	−	0.259386i
$582$	10.1186	+	17.8345i	0.419429	+	0.739263i
$583$	0.319038	+	1.19067i	0.0132132	+	0.0493123i
$584$	5.98175	+	0.135049i	0.247527	+	0.00558838i
$585$	−0.487046	+	0.491980i	−0.0201369	+	0.0203409i
$586$	−2.04653	+	3.48388i	−0.0845412	+	0.143918i
$587$	−9.64475	−	35.9947i	−0.398081	−	1.48566i	−0.816468	−	0.577391i	$-0.804071\pi$
$587$	−9.64475	−	35.9947i	−0.398081	−	1.48566i	0.418387	−	0.908269i	$-0.362596\pi$
$588$	−22.8871	−	0.344446i	−0.943847	−	0.0142047i
$589$	−0.326006	−	0.564659i	−0.0134329	−	0.0232664i
$590$	−0.338923	−	1.30405i	−0.0139533	−	0.0536869i
$591$	−10.7033	+	39.9453i	−0.440275	+	1.64313i
$592$	−9.05755	+	8.52811i	−0.372263	+	0.350503i
$593$	11.5292	+	11.5292i	0.473447	+	0.473447i	0.903028	−	0.429581i	$-0.141339\pi$
$593$	11.5292	+	11.5292i	0.473447	+	0.473447i	−0.429581	+	0.903028i	$0.641339\pi$
$594$	0.00781531	−	1.03865i	0.000320666	−	0.0426164i
$595$	−1.87534	−	1.08273i	−0.0768814	−	0.0443875i
$596$	−16.4548	+	15.9668i	−0.674014	+	0.654027i
$597$	3.32901			0.136247
$598$	9.63778	+	36.3295i	0.394118	+	1.48562i
$599$			16.7701i			0.685208i	0.939480	+	0.342604i	$0.111309\pi$
$599$			16.7701i			0.685208i	−0.939480	+	0.342604i	$0.888691\pi$
$600$	−30.5342	+	7.44721i	−1.24656	+	0.304031i
$601$	−8.91511	+	15.4414i	−0.363655	+	0.629869i	−0.988559	−	0.150832i	$-0.951805\pi$
$601$	−8.91511	+	15.4414i	−0.363655	+	0.629869i	0.624904	+	0.780701i	$0.285138\pi$
$602$	−0.209236	+	27.8074i	−0.00852782	+	1.13334i
$603$	−16.9535	+	16.9535i	−0.690401	+	0.690401i
$604$	20.9502	−	5.27701i	0.852451	−	0.214719i
$605$	−1.03240	−	0.276632i	−0.0419732	−	0.0112467i
$606$	19.6288	−	5.10155i	0.797367	−	0.207236i
$607$	−7.27664	+	4.20117i	−0.295350	+	0.170520i	−0.640352	−	0.768082i	$-0.721211\pi$
$607$	−7.27664	+	4.20117i	−0.295350	+	0.170520i	0.345002	+	0.938602i	$0.387878\pi$
$608$	2.32531	+	0.0875235i	0.0943038	+	0.00354955i
$609$	−27.4232	+	7.34804i	−1.11125	+	0.297757i
$610$	0.967032	−	1.64622i	0.0391540	−	0.0666534i
$611$	−30.2957	+	8.28157i	−1.22563	+	0.335037i
$612$	−12.0853	−	21.6794i	−0.488521	−	0.876339i
$613$	28.9567	−	7.75893i	1.16955	−	0.313380i	0.378776	−	0.925488i	$-0.376345\pi$
$613$	28.9567	−	7.75893i	1.16955	−	0.313380i	0.790774	+	0.612108i	$0.209678\pi$
$614$	−2.28668	+	1.29737i	−0.0922828	+	0.0523577i
$615$	0.781140	+	1.35297i	0.0314986	+	0.0545572i
$616$	−2.25523	+	2.15564i	−0.0908656	+	0.0868533i
$617$	−29.7623	−	7.97479i	−1.19819	−	0.321053i	−0.396069	−	0.918221i	$-0.629626\pi$
$617$	−29.7623	−	7.97479i	−1.19819	−	0.321053i	−0.802116	+	0.597168i	$0.796293\pi$
$618$	34.3412	+	34.8620i	1.38141	+	1.40235i
$619$	16.2444	+	16.2444i	0.652916	+	0.652916i	0.953694	−	0.300778i	$-0.0972463\pi$
$619$	16.2444	+	16.2444i	0.652916	+	0.652916i	−0.300778	+	0.953694i	$0.597246\pi$
$620$	0.159462	−	0.266840i	0.00640414	−	0.0107166i
$621$	−8.55087	+	14.8105i	−0.343135	+	0.594327i
$622$	9.93326	−	35.9861i	0.398287	−	1.44291i
$623$	0.398720			0.0159744
$624$	−27.4001	−	16.7485i	−1.09688	−	0.670477i
$625$	−24.8559			−0.994234
$626$	−8.68975	+	31.4812i	−0.347312	+	1.25824i
$627$	0.144980	−	0.251112i	0.00578993	−	0.0100284i
$628$	0.303303	−	0.507542i	0.0121031	−	0.0202531i
$629$	−13.9386	−	13.9386i	−0.555768	−	0.555768i
$630$	0.663939	+	0.674006i	0.0264520	+	0.0268530i
$631$	18.9019	+	5.06474i	0.752472	+	0.201624i	0.614614	−	0.788828i	$-0.289312\pi$
$631$	18.9019	+	5.06474i	0.752472	+	0.201624i	0.137858	+	0.990452i	$0.455978\pi$
$632$	−20.1384	−	21.0687i	−0.801061	−	0.838067i
$633$	11.4365	+	19.8085i	0.454559	+	0.787319i
$634$	−24.2996	+	13.7866i	−0.965061	+	0.547538i
$635$	0.801750	−	0.214828i	0.0318165	−	0.00852520i
$636$	8.44334	+	15.1462i	0.334800	+	0.600585i
$637$	−9.34683	−	16.0024i	−0.370335	−	0.634038i
$638$	−0.829804	+	1.41261i	−0.0328523	+	0.0559257i
$639$	−13.2825	+	3.55904i	−0.525448	+	0.140793i
$640$	0.503355	+	0.988649i	0.0198969	+	0.0390798i
$641$	15.3793	−	8.87927i	0.607448	−	0.350710i	−0.164518	−	0.986374i	$-0.552607\pi$
$641$	15.3793	−	8.87927i	0.607448	−	0.350710i	0.771966	+	0.635664i	$0.219274\pi$
$642$	−5.27358	+	1.37061i	−0.208131	+	0.0540935i
$643$	−32.3334	−	8.66372i	−1.27511	−	0.341664i	−0.443121	−	0.896462i	$-0.646129\pi$
$643$	−32.3334	−	8.66372i	−1.27511	−	0.341664i	−0.831985	+	0.554798i	$0.812796\pi$
$644$	49.8105	−	12.5464i	1.96281	−	0.494399i
$645$	0.871322	−	0.871322i	0.0343083	−	0.0343083i
$646$	−0.0277426	+	3.68697i	−0.00109152	+	0.145062i
$647$	13.7124	−	23.7505i	0.539089	−	0.933730i	−0.459864	−	0.887989i	$-0.652102\pi$
$647$	13.7124	−	23.7505i	0.539089	−	0.933730i	0.998953	−	0.0457408i	$-0.0145648\pi$
$648$	−7.39912	−	30.3371i	−0.290665	−	1.19175i
$649$		−	3.07576i		−	0.120734i
$650$	−17.9483	−	18.0377i	−0.703991	−	0.707498i
$651$	12.2972			0.481964
$652$	3.57125	−	3.46535i	0.139861	−	0.135713i
$653$	15.1849	+	8.76701i	0.594232	+	0.343080i	0.766769	−	0.641923i	$-0.221863\pi$
$653$	15.1849	+	8.76701i	0.594232	+	0.343080i	−0.172537	+	0.985003i	$0.555197\pi$
$654$	−0.442889	+	58.8597i	−0.0173183	+	2.30160i
$655$	−0.942016	−	0.942016i	−0.0368076	−	0.0368076i
$656$	−20.8375	+	19.6195i	−0.813567	+	0.766012i
$657$	1.07205	−	4.00095i	0.0418247	−	0.156092i
$658$	10.7968	+	41.5419i	0.420901	+	1.61947i
$659$	−1.44190	−	2.49744i	−0.0561684	−	0.0972865i	0.836574	−	0.547854i	$-0.184555\pi$
$659$	−1.44190	−	2.49744i	−0.0561684	−	0.0972865i	−0.892742	+	0.450567i	$0.851222\pi$
$660$	0.138227	+	0.00208029i	0.00538047	+	8.09750e-5i
$661$	−10.3684	−	38.6953i	−0.403283	−	1.50507i	−0.807200	−	0.590278i	$-0.799018\pi$
$661$	−10.3684	−	38.6953i	−0.403283	−	1.50507i	0.403917	−	0.914796i	$-0.367649\pi$
$662$	−6.54657	+	11.1445i	−0.254440	+	0.433143i
$663$	25.2196	−	44.1945i	0.979447	−	1.71637i
$664$	0.229115	−	10.1482i	0.00889141	−	0.393828i
$665$	−0.0363752	−	0.135754i	−0.00141057	−	0.00526431i
$666$	4.24993	+	7.49069i	0.164681	+	0.290258i
$667$	23.3606	−	13.4872i	0.904525	−	0.522228i
$668$	5.07838	−	17.8725i	0.196488	−	0.691508i
$669$	−2.44010	+	9.10656i	−0.0943396	+	0.352080i
$670$	1.19164	+	1.20971i	0.0460371	+	0.0467351i
$671$	3.08184	−	3.08184i	0.118973	−	0.118973i
$672$	−23.3577	+	37.1552i	−0.901041	+	1.43329i
$673$	6.34609	+	3.66391i	0.244624	+	0.141234i	0.617300	−	0.786728i	$-0.288226\pi$
$673$	6.34609	+	3.66391i	0.244624	+	0.141234i	−0.372676	+	0.927961i	$0.621560\pi$
$674$	−11.4374	−	3.15707i	−0.440553	−	0.121606i
$675$		−	11.5780i		−	0.445637i
$676$	0.129187	−	25.9997i	0.00496875	−	0.999988i
$677$			45.6313i			1.75376i	0.480714	+	0.876878i	$0.340378\pi$
$677$			45.6313i			1.75376i	−0.480714	+	0.876878i	$0.659622\pi$
$678$	11.5347	−	41.7877i	0.442986	−	1.60485i
$679$	19.6484	+	11.3440i	0.754035	+	0.435342i
$680$	−1.54181	+	0.844349i	−0.0591257	+	0.0323793i
$681$	33.4550	−	33.4550i	1.28200	−	1.28200i
$682$	0.505537	−	0.497986i	0.0193580	−	0.0190689i
$683$	5.80580	−	21.6676i	0.222153	−	0.829086i	−0.761372	−	0.648315i	$-0.775474\pi$
$683$	5.80580	−	21.6676i	0.222153	−	0.829086i	0.983525	−	0.180771i	$-0.0578593\pi$
$684$	0.440300	−	1.54956i	0.0168353	−	0.0592490i
$685$	1.04744	−	0.604742i	0.0400208	−	0.0231060i
$686$	7.97192	−	4.52295i	0.304369	−	0.172687i
$687$	2.16751	+	8.08925i	0.0826956	+	0.308624i
$688$	19.2012	+	11.8702i	0.732039	+	0.452548i
$689$	−6.95836	+	12.1937i	−0.265092	+	0.464545i
$690$	−1.96258	−	1.15287i	−0.0747141	−	0.0438890i
$691$	−1.10893	−	4.13859i	−0.0421857	−	0.157439i	0.941620	−	0.336678i	$-0.109303\pi$
$691$	−1.10893	−	4.13859i	−0.0421857	−	0.157439i	−0.983806	+	0.179238i	$0.942637\pi$
$692$	0.0892447	−	5.92995i	0.00339257	−	0.225423i
$693$	1.07987	+	1.87038i	0.0410207	+	0.0710500i
$694$	−4.22884	+	1.09908i	−0.160524	+	0.0417204i
$695$	−0.272168	+	1.01575i	−0.0103239	+	0.0385294i
$696$	−6.46593	+	22.1213i	−0.245090	+	0.838506i
$697$	−32.0667	−	32.0667i	−1.21461	−	1.21461i
$698$	−42.3722	−	0.318829i	−1.60381	−	0.0120679i
$699$	−25.0028	−	14.4354i	−0.945692	−	0.545995i
$700$	−24.9571	+	24.2171i	−0.943291	+	0.915319i
$701$	−36.4870			−1.37810			−0.689048	−	0.724716i	$-0.741971\pi$
$701$	−36.4870			−1.37810			−0.689048	+	0.724716i	$0.741971\pi$
$702$	8.38586	−	8.34429i	0.316504	−	0.314935i
$703$		−	1.27936i		−	0.0482521i
$704$	0.544402	+	2.47334i	0.0205179	+	0.0932176i
$705$	0.950979	−	1.64714i	0.0358159	−	0.0620350i
$706$	35.6711	+	0.268407i	1.34250	+	0.0101016i
$707$	15.8676	−	15.8676i	0.596761	−	0.596761i
$708$	−10.5685	−	41.9579i	−0.397188	−	1.57687i
$709$	−14.8664	−	3.98345i	−0.558321	−	0.149602i	−0.0313862	−	0.999507i	$-0.509992\pi$
$709$	−14.8664	−	3.98345i	−0.558321	−	0.149602i	−0.526935	+	0.849906i	$0.676659\pi$
$710$	0.244978	+	0.942584i	0.00919387	+	0.0353745i
$711$	−17.4734	+	10.0883i	−0.655305	+	0.378340i
$712$	0.168122	−	0.276584i	0.00630064	−	0.0103654i
$713$	−11.2857	+	3.02398i	−0.422651	+	0.113249i
$714$	−59.9597	−	35.2219i	−2.24394	−	1.31815i
$715$	0.0564503	+	0.0966466i	0.00211112	+	0.00361438i
$716$	−6.09873	−	10.9403i	−0.227920	−	0.408858i
$717$	−6.10501	+	1.63583i	−0.227996	+	0.0610913i
$718$	−9.65575	−	17.0187i	−0.360350	−	0.635133i
$719$	11.9512	+	20.7000i	0.445703	+	0.771980i	0.998101	−	0.0616005i	$-0.0196205\pi$
$719$	11.9512	+	20.7000i	0.445703	+	0.771980i	−0.552398	+	0.833580i	$0.686287\pi$
$720$	0.747497	−	0.176364i	0.0278576	−	0.00657270i
$721$	52.3002	+	14.0138i	1.94776	+	0.521902i
$722$	18.9719	−	18.6886i	0.706063	−	0.695517i
$723$	12.2743	+	12.2743i	0.456487	+	0.456487i
$724$	33.7756	+	20.1840i	1.25526	+	0.750134i
$725$	−9.13095	+	15.8153i	−0.339115	+	0.587364i
$726$	−33.0860	−	9.13272i	−1.22793	−	0.338947i
$727$	21.0545			0.780868			0.390434	−	0.920631i	$-0.372325\pi$
$727$	21.0545			0.780868			0.390434	+	0.920631i	$0.372325\pi$
$728$	−35.5269	−	0.622959i	−1.31671	−	0.0230884i
$729$	−6.11928			−0.226640
$730$	−0.282782	−	0.0780564i	−0.0104662	−	0.00288900i
$731$	−17.8844	+	30.9766i	−0.661477	+	1.14571i
$732$	31.4514	−	52.6301i	1.16248	−	1.94526i
$733$	2.18046	+	2.18046i	0.0805370	+	0.0805370i	0.746228	−	0.665691i	$-0.231863\pi$
$733$	2.18046	+	2.18046i	0.0805370	+	0.0805370i	−0.665691	+	0.746228i	$0.731863\pi$
$734$	−8.52080	+	8.39352i	−0.314508	+	0.309811i
$735$	1.08403	+	0.290465i	0.0399850	+	0.0107140i
$736$	12.2996	−	39.8428i	0.453368	−	1.46863i
$737$	1.93815	+	3.35697i	0.0713926	+	0.123656i
$738$	9.77723	+	17.2328i	0.359905	+	0.634349i
$739$	45.3273	−	12.1454i	1.66739	−	0.446776i	0.702985	−	0.711204i	$-0.251850\pi$
$739$	45.3273	−	12.1454i	1.66739	−	0.446776i	0.964405	+	0.264429i	$0.0851833\pi$
$740$	0.532767	−	0.296994i	0.0195849	−	0.0109177i
$741$	3.18561	−	0.870813i	0.117026	−	0.0319901i
$742$	16.5435	+	9.71812i	0.607332	+	0.356763i
$743$	−41.4704	+	11.1120i	−1.52140	+	0.407658i	−0.920203	−	0.391442i	$-0.871976\pi$
$743$	−41.4704	+	11.1120i	−1.52140	+	0.407658i	−0.601198	+	0.799100i	$0.705310\pi$
$744$	5.18515	−	8.53031i	0.190097	−	0.312736i
$745$	0.973548	−	0.562078i	0.0356680	−	0.0205929i
$746$	3.69173	+	14.2044i	0.135164	+	0.520060i
$747$	−6.78775	−	1.81877i	−0.248351	−	0.0665454i
$748$	−3.89129	+	0.980152i	−0.142280	+	0.0358379i
$749$	−4.26305	+	4.26305i	−0.155768	+	0.155768i
$750$	3.08481	+	0.0232116i	0.112641	+	0.000847568i
$751$	−3.78589	+	6.55735i	−0.138149	+	0.239281i	−0.926796	−	0.375565i	$-0.877449\pi$
$751$	−3.78589	+	6.55735i	−0.138149	+	0.239281i	0.788647	+	0.614846i	$0.210782\pi$
$752$	33.3693	+	10.0268i	1.21685	+	0.365639i
$753$			21.8378i			0.795814i
$754$	−18.0356	+	4.78463i	−0.656817	+	0.174246i
$755$	−1.05926			−0.0385505
$756$	−11.2587	−	11.6027i	−0.409474	−	0.421987i
$757$	18.5122	+	10.6880i	0.672836	+	0.388462i	0.797151	−	0.603781i	$-0.206340\pi$
$757$	18.5122	+	10.6880i	0.672836	+	0.388462i	−0.124314	+	0.992243i	$0.539673\pi$
$758$	−6.65657	−	0.0500872i	−0.241777	−	0.00181925i
$759$	−3.67408	−	3.67408i	−0.133361	−	0.133361i
$760$	−0.109508	−	0.0320084i	−0.00397226	−	0.00116107i
$761$	0.991139	−	3.69898i	0.0359288	−	0.134088i	−0.945632	−	0.325239i	$-0.894555\pi$
$761$	0.991139	−	3.69898i	0.0359288	−	0.134088i	0.981561	+	0.191151i	$0.0612220\pi$
$762$	25.7979	−	6.70489i	0.934559	−	0.242893i
$763$	32.5639	+	56.4024i	1.17889	+	2.04190i
$764$	−16.1396	−	0.242898i	−0.583910	−	0.00878773i
$765$	0.314966	+	1.17547i	0.0113876	+	0.0424991i
$766$	27.3436	+	16.0624i	0.987965	+	0.580357i
$767$	24.6457	−	24.8954i	0.889906	−	0.898922i
$768$	15.9250	+	31.8694i	0.574644	+	1.14999i
$769$	4.33512	+	16.1789i	0.156329	+	0.583426i	0.998988	+	0.0449792i	$0.0143221\pi$
$769$	4.33512	+	16.1789i	0.156329	+	0.583426i	−0.842659	+	0.538447i	$0.819011\pi$
$770$	0.133039	−	0.0754811i	0.00479439	−	0.00272015i
$771$	18.3097	−	10.5711i	0.659407	−	0.380709i
$772$	−7.55201	−	2.14586i	−0.271803	−	0.0772313i
$773$	6.29416	−	23.4901i	0.226385	−	0.844882i	−0.755459	−	0.655195i	$-0.772586\pi$
$773$	6.29416	−	23.4901i	0.226385	−	0.844882i	0.981845	−	0.189686i	$-0.0607471\pi$
$774$	11.1332	−	10.9669i	0.400173	−	0.394196i
$775$	5.59321	−	5.59321i	0.200914	−	0.200914i
$776$	16.1539	−	8.84645i	0.579892	−	0.317569i
$777$	20.8965	+	12.0646i	0.749659	+	0.432816i
$778$	−0.0963214	+	0.348952i	−0.00345329	+	0.0125105i
$779$		−	2.94326i		−	0.105453i
$780$	1.10215	+	1.12443i	0.0394632	+	0.0402612i
$781$			2.22320i			0.0795523i
$782$	63.6890	+	17.5801i	2.27751	+	0.628663i
$783$	−7.35262	−	4.24504i	−0.262761	−	0.151705i
$784$	−0.618695	+	20.5502i	−0.0220962	+	0.733937i
$785$	−0.0204986	+	0.0204986i	−0.000731625	+	0.000731625i
$786$	−30.0226	−	30.4779i	−1.07087	−	1.08711i
$787$	−9.30815	+	34.7385i	−0.331800	+	1.23829i	0.575498	+	0.817803i	$0.304808\pi$
$787$	−9.30815	+	34.7385i	−0.331800	+	1.23829i	−0.907297	+	0.420490i	$0.861858\pi$
$788$	35.7302	+	10.1526i	1.27284	+	0.361670i
$789$	0.853191	−	0.492590i	0.0303744	−	0.0175367i
$790$	0.705156	+	1.24287i	0.0250883	+	0.0442193i
$791$	−12.4144	−	46.3312i	−0.441405	−	1.64735i
$792$	1.75278	+	0.0395722i	0.0622823	+	0.00140614i
$793$	49.6390	−	0.250181i	1.76273	−	0.00888417i
$794$	22.2129	−	37.8138i	0.788305	−	1.34196i
$795$	−0.220048	−	0.821232i	−0.00780431	−	0.0291261i
$796$	0.0449957	−	2.98979i	0.00159483	−	0.105970i
$797$	5.36008	+	9.28393i	0.189864	+	0.328854i	0.945205	−	0.326478i	$-0.105862\pi$
$797$	5.36008	+	9.28393i	0.189864	+	0.328854i	−0.755341	+	0.655332i	$0.772529\pi$
$798$	−1.13529	−	4.36815i	−0.0401887	−	0.154631i
$799$	−14.2892	+	53.3280i	−0.505515	+	1.88661i
$800$	6.27563	+	27.5235i	0.221877	+	0.973102i
$801$	−0.158442	−	0.158442i	−0.00559829	−	0.00559829i
$802$	−0.227715	+	30.2632i	−0.00804089	+	1.06863i
$803$	−0.579952	−	0.334836i	−0.0204661	−	0.0118161i
$804$	37.9739	+	39.1344i	1.33924	+	1.38016i
$805$	−2.51847			−0.0887642
$806$	8.08216	+	0.0200792i	0.284682	+	0.000707261i
$807$		−	31.6179i		−	1.11300i
$808$	−4.31640	−	17.6976i	−0.151850	−	0.622600i
$809$	−19.6641	+	34.0593i	−0.691355	+	1.19746i	0.280040	+	0.959988i	$0.409652\pi$
$809$	−19.6641	+	34.0593i	−0.691355	+	1.19746i	−0.971394	+	0.237473i	$0.923681\pi$
$810$	−0.0115198	+	1.53097i	−0.000404763	+	0.0537928i
$811$	−38.2641	+	38.2641i	−1.34364	+	1.34364i	−0.451226	+	0.892410i	$0.649013\pi$
$811$	−38.2641	+	38.2641i	−1.34364	+	1.34364i	−0.892410	+	0.451226i	$0.850987\pi$
$812$	6.22862	+	24.7282i	0.218582	+	0.867788i
$813$	10.7076	+	2.86910i	0.375532	+	0.100624i
$814$	1.34762	−	0.350249i	0.0472342	−	0.0122762i
$815$	−0.211293	+	0.121990i	−0.00740127	+	0.00427312i
$816$	−49.7150	+	26.7414i	−1.74037	+	0.936137i
$817$	−2.24237	+	0.600841i	−0.0784506	+	0.0210208i
$818$	23.1854	−	39.4694i	0.810658	−	1.38002i
$819$	−6.24667	+	23.7919i	−0.218276	+	0.831356i
$820$	1.22566	−	0.683255i	0.0428021	−	0.0238603i
$821$	−19.9781	+	5.35310i	−0.697239	+	0.186825i	−0.589993	−	0.807408i	$-0.700870\pi$
$821$	−19.9781	+	5.35310i	−0.697239	+	0.186825i	−0.107245	+	0.994233i	$0.534203\pi$
$822$	33.7819	−	19.1665i	1.17828	−	0.668510i
$823$	−11.8141	−	20.4626i	−0.411813	−	0.713281i	0.583275	−	0.812275i	$-0.301771\pi$
$823$	−11.8141	−	20.4626i	−0.411813	−	0.713281i	−0.995088	+	0.0989937i	$0.968438\pi$
$824$	31.7737	−	30.3707i	1.10689	−	1.05801i
$825$	3.39782	+	0.910444i	0.118297	+	0.0316976i
$826$	−33.5970	−	34.1064i	−1.16899	−	1.18671i
$827$	−17.7598	−	17.7598i	−0.617568	−	0.617568i	0.327339	−	0.944907i	$-0.393848\pi$
$827$	−17.7598	−	17.7598i	−0.617568	−	0.617568i	−0.944907	+	0.327339i	$0.893848\pi$
$828$	−24.7792	−	14.8079i	−0.861137	−	0.514609i
$829$	16.4735	−	28.5329i	0.572147	−	0.990988i	−0.424198	−	0.905569i	$-0.639444\pi$
$829$	16.4735	−	28.5329i	0.572147	−	0.990988i	0.996345	−	0.0854184i	$-0.0272227\pi$
$830$	−0.132425	+	0.479749i	−0.00459655	+	0.0166523i
$831$	−26.6804			−0.925533
$832$	−15.4122	+	24.3816i	−0.534322	+	0.845281i
$833$	−32.5767			−1.12872
$834$	−8.98537	+	32.5521i	−0.311138	+	1.12719i
$835$	−0.455484	+	0.788922i	−0.0157627	+	0.0273018i
$836$	−0.223564	−	0.133600i	−0.00773213	−	0.00462066i
$837$	2.60032	+	2.60032i	0.0898802	+	0.0898802i
$838$	−20.7472	−	21.0618i	−0.716700	−	0.727567i
$839$	−42.5633	−	11.4048i	−1.46945	−	0.393737i	−0.566706	−	0.823920i	$-0.691782\pi$
$839$	−42.5633	−	11.4048i	−1.46945	−	0.393737i	−0.902742	+	0.430183i	$0.858449\pi$
$840$	1.55549	−	1.48680i	0.0536694	−	0.0512995i
$841$	−7.80433	−	13.5175i	−0.269115	−	0.466121i
$842$	−14.6542	+	8.31423i	−0.505018	+	0.286527i
$843$	−15.5862	+	4.17630i	−0.536817	+	0.143840i
$844$	17.9446	−	10.0034i	0.617680	−	0.344330i
$845$	−0.317506	+	1.23459i	−0.0109225	+	0.0424713i
$846$	12.2174	−	20.7982i	0.420043	−	0.715056i
$847$	−36.6834	+	9.82927i	−1.26045	+	0.337738i
$848$	13.7169	−	7.37825i	0.471041	−	0.253370i
$849$	−23.9034	+	13.8007i	−0.820364	+	0.473637i
$850$	−43.2921	+	11.2517i	−1.48491	+	0.385929i
$851$	−22.1445	−	5.93359i	−0.759102	−	0.203401i
$852$	7.63904	+	30.3277i	0.261709	+	1.03901i
$853$	0.463907	−	0.463907i	0.0158839	−	0.0158839i	−0.699120	−	0.715004i	$-0.746425\pi$
$853$	0.463907	−	0.463907i	0.0158839	−	0.0158839i	0.715004	+	0.699120i	$0.246425\pi$
$854$	0.510439	−	67.8371i	0.0174669	−	2.32134i
$855$	−0.0394909	+	0.0684002i	−0.00135056	+	0.00233924i
$856$	1.15966	+	4.75473i	0.0396365	+	0.162513i
$857$			33.1382i			1.13198i	0.824412	+	0.565990i	$0.191506\pi$
$857$			33.1382i			1.13198i	−0.824412	+	0.565990i	$0.808494\pi$
$858$	1.78939	+	3.11718i	0.0610889	+	0.106419i
$859$	21.3046			0.726903			0.363451	−	0.931613i	$-0.381598\pi$
$859$	21.3046			0.726903			0.363451	+	0.931613i	$0.381598\pi$
$860$	−0.770757	−	0.794311i	−0.0262826	−	0.0270858i
$861$	48.0738	+	27.7554i	1.63835	+	0.945903i
$862$	−0.237859	+	31.6114i	−0.00810151	+	1.07669i
$863$	27.2032	+	27.2032i	0.926008	+	0.926008i	0.997445	−	0.0714372i	$-0.0227585\pi$
$863$	27.2032	+	27.2032i	0.926008	+	0.926008i	−0.0714372	+	0.997445i	$0.522759\pi$
$864$	−12.7958	+	2.91758i	−0.435324	+	0.0992582i
$865$	−0.0752583	+	0.280868i	−0.00255886	+	0.00954979i
$866$	−5.07679	−	19.5336i	−0.172516	−	0.663777i
$867$	−25.7966	−	44.6809i	−0.876097	−	1.51744i
$868$	0.166212	−	11.0441i	0.00564159	−	0.374861i
$869$	0.844278	+	3.15089i	0.0286402	+	0.106887i
$870$	0.572337	−	0.974312i	0.0194040	−	0.0330323i
$871$	−11.2115	+	42.7018i	−0.379889	+	1.44689i
$872$	52.8560	+	1.19332i	1.78993	+	0.0404110i
$873$	−3.29997	−	12.3157i	−0.111687	−	0.416822i
$874$	2.11607	+	3.72967i	0.0715771	+	0.126158i
$875$	2.95602	−	1.70666i	0.0999318	−	0.0576957i
$876$	−9.06191	−	2.57490i	−0.306174	−	0.0869976i
$877$	4.86299	−	18.1489i	0.164212	−	0.612846i	−0.833928	−	0.551874i	$-0.813913\pi$
$877$	4.86299	−	18.1489i	0.164212	−	0.612846i	0.998139	−	0.0609726i	$-0.0194202\pi$
$878$	3.54512	+	3.59887i	0.119642	+	0.121456i
$879$	4.49844	−	4.49844i	0.151729	−	0.151729i
$880$	0.00373661	−	0.124113i	0.000125961	−	0.00418386i
$881$	−10.8962	−	6.29091i	−0.367101	−	0.211946i	0.305090	−	0.952324i	$-0.401313\pi$
$881$	−10.8962	−	6.29091i	−0.367101	−	0.211946i	−0.672191	+	0.740377i	$0.734647\pi$
$882$	13.7198	+	3.78709i	0.461971	+	0.127518i
$883$			44.2186i			1.48807i	0.668139	+	0.744036i	$0.267091\pi$
$883$			44.2186i			1.48807i	−0.668139	+	0.744036i	$0.732909\pi$
$884$	−39.3502	−	23.2471i	−1.32349	−	0.781884i
$885$			2.12143i			0.0713111i
$886$	−3.28852	+	11.9136i	−0.110480	+	0.400246i
$887$	−5.54684	−	3.20247i	−0.186245	−	0.107528i	0.403979	−	0.914768i	$-0.367627\pi$
$887$	−5.54684	−	3.20247i	−0.186245	−	0.107528i	−0.590223	+	0.807240i	$0.700960\pi$
$888$	17.1801	−	9.40842i	0.576526	−	0.315726i
$889$	20.8545	−	20.8545i	0.699437	−	0.699437i
$890$	−0.0113056	+	0.0111367i	−0.000378963	+	0.000373303i
$891$	−0.904565	+	3.37588i	−0.0303041	+	0.113096i
$892$	8.14563	+	2.31454i	0.272736	+	0.0774965i
$893$	−3.10314	+	1.79160i	−0.103843	+	0.0599536i
$894$	31.3986	−	17.8144i	1.05013	−	0.595801i
$895$	0.158944	+	0.593187i	0.00531291	+	0.0198280i
$896$	33.0534	+	21.4797i	1.10424	+	0.717587i
$897$	−0.298259	−	59.1783i	−0.00995857	−	1.97591i
$898$	−31.9539	−	18.7706i	−1.06632	−	0.626383i
$899$	−1.50124	−	5.60271i	−0.0500692	−	0.186861i
$900$	19.5407	+	0.294084i	0.651357	+	0.00980280i
$901$	12.3396	+	21.3729i	0.411093	+	0.712034i
$902$	3.10030	−	0.805770i	0.103229	−	0.0268292i
$903$	11.3321	−	42.2919i	0.377108	−	1.40738i
$904$	−37.3736	−	10.9241i	−1.24303	−	0.363330i
$905$	−1.36413	−	1.36413i	−0.0453451	−	0.0453451i
$906$	−34.0153	−	0.255947i	−1.13008	−	0.00850328i
$907$	11.0865	+	6.40082i	0.368123	+	0.212536i	0.672638	−	0.739972i	$-0.265161\pi$
$907$	11.0865	+	6.40082i	0.368123	+	0.212536i	−0.304515	+	0.952507i	$0.598494\pi$
$908$	−29.5938	−	30.4982i	−0.982105	−	1.01212i
$909$	−12.6108			−0.418274
$910$	1.68165	+	0.455077i	0.0557461	+	0.0150857i
$911$			4.52483i			0.149914i	0.997187	+	0.0749572i	$0.0238820\pi$
$911$			4.52483i			0.149914i	−0.997187	+	0.0749572i	$0.976118\pi$
$912$	−3.50880	−	1.05432i	−0.116188	−	0.0349121i
$913$	−0.568060	+	0.983909i	−0.0188000	+	0.0325626i
$914$	−45.7507	−	0.344251i	−1.51330	−	0.0113868i
$915$	−2.12562	+	2.12562i	−0.0702708	+	0.0702708i
$916$	7.29426	−	1.83730i	0.241009	−	0.0607063i
$917$	−45.7232	−	12.2515i	−1.50991	−	0.404580i
$918$	−5.23097	−	20.1268i	−0.172648	−	0.664283i
$919$	44.0101	−	25.4093i	1.45176	−	0.838174i	0.453179	−	0.891420i	$-0.350290\pi$
$919$	44.0101	−	25.4093i	1.45176	−	0.838174i	0.998581	+	0.0532452i	$0.0169565\pi$
$920$	−1.06192	+	1.74701i	−0.0350105	+	0.0575972i
$921$	3.99842	−	1.07137i	0.131753	−	0.0353030i
$922$	−19.8664	−	11.6700i	−0.654264	−	0.384332i
$923$	−17.8143	+	17.9947i	−0.586363	+	0.592304i
$924$	4.29041	−	2.39172i	0.141144	−	0.0786818i
$925$	14.9920	−	4.01708i	0.492932	−	0.132081i
$926$	−24.4936	−	43.1712i	−0.804911	−	1.41869i
$927$	−15.2142	−	26.3517i	−0.499699	−	0.865504i
$928$	19.7798	+	6.10605i	0.649303	+	0.200441i
$929$	58.1272	+	15.5751i	1.90709	+	0.511003i	0.994851	+	0.101347i	$0.0323152\pi$
$929$	58.1272	+	15.5751i	1.90709	+	0.511003i	0.912240	+	0.409657i	$0.134351\pi$
$930$	−0.348682	+	0.343474i	−0.0114337	+	0.0112629i
$931$	−1.49504	−	1.49504i	−0.0489979	−	0.0489979i
$932$	−13.3023	+	22.2599i	−0.435733	+	0.729147i
$933$	−29.3894	+	50.9040i	−0.962166	+	1.66652i
$934$	14.3756	+	3.96811i	0.470385	+	0.129841i
$935$	0.196747			0.00643433
$936$	13.8700	+	14.3651i	0.453356	+	0.469539i
$937$	−31.3424			−1.02391			−0.511956	−	0.859012i	$-0.671079\pi$
$937$	−31.3424			−1.02391			−0.511956	+	0.859012i	$0.671079\pi$
$938$	58.1604	+	16.0540i	1.89900	+	0.524182i
$939$	25.7103	−	44.5315i	0.839023	−	1.45323i
$940$	−1.46645	−	0.876338i	−0.0478302	−	0.0285830i
$941$	22.8653	+	22.8653i	0.745387	+	0.745387i	0.973609	−	0.228222i	$-0.0732912\pi$
$941$	22.8653	+	22.8653i	0.745387	+	0.745387i	−0.228222	+	0.973609i	$0.573291\pi$
$942$	−0.663208	+	0.653302i	−0.0216085	+	0.0212857i
$943$	−50.9448	−	13.6506i	−1.65899	−	0.444525i
$944$	−37.8252	+	8.92446i	−1.23111	+	0.290466i
$945$	0.396337	+	0.686476i	0.0128928	+	0.0223311i
$946$	−1.24679	−	2.19752i	−0.0405366	−	0.0714476i
$947$	−20.0408	+	5.36992i	−0.651239	+	0.174499i	−0.569289	−	0.822138i	$-0.692781\pi$
$947$	−20.0408	+	5.36992i	−0.651239	+	0.174499i	−0.0819499	+	0.996636i	$0.526115\pi$
$948$	22.3438	+	40.0817i	0.725694	+	1.30179i
$949$	−2.01117	−	7.35728i	−0.0652855	−	0.238827i
$950$	−2.50317	−	1.47043i	−0.0812135	−	0.0477070i
$951$	42.4896	−	11.3851i	1.37782	−	0.369186i
$952$	−32.4433	+	53.3738i	−1.05149	+	1.72985i
$953$	2.83553	−	1.63710i	0.0918520	−	0.0530308i	−0.453370	−	0.891322i	$-0.649779\pi$
$953$	2.83553	−	1.63710i	0.0918520	−	0.0530308i	0.545222	+	0.838291i	$0.316445\pi$
$954$	−2.71227	−	10.4358i	−0.0878129	−	0.337871i
$955$	0.764439	+	0.204831i	0.0247367	+	0.00662817i
$956$	1.38663	+	5.50503i	0.0448467	+	0.178045i
$957$	1.82398	−	1.82398i	0.0589609	−	0.0589609i
$958$	−14.6453	−	0.110198i	−0.473167	−	0.00356034i
$959$	21.4877	−	37.2178i	0.693874	−	1.20182i
$960$	−0.375488	−	1.70593i	−0.0121188	−	0.0550585i
$961$		−	28.4876i		−	0.918956i
$962$	13.7143	+	7.96344i	0.442166	+	0.256752i
$963$	3.38808			0.109179
$964$	11.1895	−	10.8577i	0.360389	−	0.349702i
$965$	0.333358	+	0.192464i	0.0107312	+	0.00619565i
$966$	−80.8736	−	0.608532i	−2.60206	−	0.0195792i
$967$	15.9826	+	15.9826i	0.513966	+	0.513966i	0.915739	−	0.401773i	$-0.131606\pi$
$967$	15.9826	+	15.9826i	0.513966	+	0.513966i	−0.401773	+	0.915739i	$0.631606\pi$
$968$	−8.64930	+	29.5911i	−0.277999	+	0.951093i
$969$	1.50252	−	5.60747i	0.0482678	−	0.180138i
$970$	−0.873972	+	0.227146i	−0.0280616	+	0.00729322i
$971$	12.5870	+	21.8014i	0.403938	+	0.699640i	0.994197	−	0.107573i	$-0.0343080\pi$
$971$	12.5870	+	21.8014i	0.403938	+	0.699640i	−0.590260	+	0.807213i	$0.700975\pi$
$972$	−0.530375	+	35.2413i	−0.0170118	+	1.13037i
$973$	9.67068	+	36.0915i	0.310028	+	1.15704i
$974$	−29.6687	−	17.4282i	−0.950645	−	0.558435i
$975$	20.2069	+	34.5956i	0.647140	+	1.10795i
$976$	−46.8420	−	28.9578i	−1.49938	−	0.926918i
$977$	−5.42229	−	20.2363i	−0.173475	−	0.647416i	−0.996806	−	0.0798556i	$-0.974554\pi$
$977$	−5.42229	−	20.2363i	−0.173475	−	0.647416i	0.823332	−	0.567560i	$-0.192113\pi$
$978$	−6.81457	+	3.86632i	−0.217906	+	0.123631i
$979$	−0.0313732	+	0.0181133i	−0.00100269	+	0.000578905i
$980$	0.275519	−	0.969641i	0.00880112	−	0.0309740i
$981$	9.47286	−	35.3532i	0.302445	−	1.12874i
$982$	−32.7960	+	32.3061i	−1.04656	+	1.03093i
$983$	14.2586	−	14.2586i	0.454777	−	0.454777i	−0.442159	−	0.896937i	$-0.645787\pi$
$983$	14.2586	−	14.2586i	0.454777	−	0.454777i	0.896937	+	0.442159i	$0.145787\pi$
$984$	39.5239	−	21.6447i	1.25998	−	0.690008i
$985$	−1.57719	−	0.910592i	−0.0502535	−	0.0290139i
$986$	−8.72755	+	31.6181i	−0.277942	+	1.00693i
$987$		−	67.5804i		−	2.15111i
$988$	−0.739020	−	2.87277i	−0.0235114	−	0.0913949i
$989$			41.5997i			1.32280i
$990$	−0.0828611	−	0.0228722i	−0.00263350	−	0.000726925i
$991$	−23.1803	−	13.3832i	−0.736348	−	0.425131i	0.0843920	−	0.996433i	$-0.473105\pi$
$991$	−23.1803	−	13.3832i	−0.736348	−	0.425131i	−0.820740	+	0.571302i	$0.806439\pi$
$992$	−7.59100	−	4.77209i	−0.241014	−	0.151514i
$993$	14.3899	−	14.3899i	0.456650	−	0.456650i
$994$	24.2843	+	24.6525i	0.770251	+	0.781931i
$995$	−0.0379440	+	0.141609i	−0.00120291	+	0.00448931i
$996$	−4.36840	+	15.3738i	−0.138418	+	0.487139i
$997$	−31.1545	+	17.9870i	−0.986672	+	0.569655i	−0.904278	−	0.426944i	$-0.859590\pi$
$997$	−31.1545	+	17.9870i	−0.986672	+	0.569655i	−0.0823942	+	0.996600i	$0.526257\pi$
$998$	20.1870	+	35.5805i	0.639008	+	1.12628i
$999$	1.86757	+	6.96985i	0.0590872	+	0.220516i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	104.2.u.a.19.5	yes	48
3.2	odd	2		936.2.ed.d.19.8		48
4.3	odd	2		416.2.bk.a.175.2		48
8.3	odd	2	inner	104.2.u.a.19.11	yes	48
8.5	even	2		416.2.bk.a.175.1		48
13.11	odd	12	inner	104.2.u.a.11.11	yes	48
24.11	even	2		936.2.ed.d.19.2		48
39.11	even	12		936.2.ed.d.739.2		48
52.11	even	12		416.2.bk.a.271.1		48
104.11	even	12	inner	104.2.u.a.11.5	✓	48
104.37	odd	12		416.2.bk.a.271.2		48
312.11	odd	12		936.2.ed.d.739.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.u.a.11.5	✓	48	104.11	even	12	inner
104.2.u.a.11.11	yes	48	13.11	odd	12	inner
104.2.u.a.19.5	yes	48	1.1	even	1	trivial
104.2.u.a.19.11	yes	48	8.3	odd	2	inner
416.2.bk.a.175.1		48	8.5	even	2
416.2.bk.a.175.2		48	4.3	odd	2
416.2.bk.a.271.1		48	52.11	even	12
416.2.bk.a.271.2		48	104.37	odd	12
936.2.ed.d.19.2		48	24.11	even	2
936.2.ed.d.19.8		48	3.2	odd	2
936.2.ed.d.739.2		48	39.11	even	12
936.2.ed.d.739.8		48	312.11	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	104.u (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.376293 + 1.36323i) q^{2} +(1.11333 - 1.92835i) q^{3} +(-1.71681 - 1.02595i) q^{4} +(0.0693382 + 0.0693382i) q^{5} +(2.20985 + 2.24336i) q^{6} +(3.36551 + 0.901786i) q^{7} +(2.04463 - 1.95435i) q^{8} +(-0.979029 - 1.69573i) q^{9} +(-0.120616 + 0.0684326i) q^{10} +(-0.305781 + 0.0819339i) q^{11} +(-3.88978 + 2.16838i) q^{12} +(-3.13155 - 1.78702i) q^{13} +(-2.49576 + 4.24864i) q^{14} +(0.210905 - 0.0565119i) q^{15} +(1.89485 + 3.52272i) q^{16} +(-5.48889 + 3.16901i) q^{17} +(2.68007 - 0.696553i) q^{18} +(-0.397336 - 0.106466i) q^{19} +(-0.0479027 - 0.190178i) q^{20} +(5.48590 - 5.48590i) q^{21} +(0.00336858 - 0.447683i) q^{22} +(-3.68562 + 6.38369i) q^{23} +(-1.49231 - 6.11862i) q^{24} -4.99038i q^{25} +(3.61450 - 3.59658i) q^{26} +2.32006 q^{27} +(-4.85274 - 5.00104i) q^{28} +(-3.16915 - 1.82971i) q^{29} +(-0.00232339 + 0.308778i) q^{30} +(1.12080 + 1.12080i) q^{31} +(-5.51530 + 1.25755i) q^{32} +(-0.182440 + 0.680874i) q^{33} +(-2.25467 - 8.67511i) q^{34} +(0.170830 + 0.295887i) q^{35} +(-0.0589301 + 3.91567i) q^{36} +(0.804964 + 3.00417i) q^{37} +(0.294652 - 0.501598i) q^{38} +(-6.93245 + 4.04918i) q^{39} +(0.277282 + 0.00626016i) q^{40} +(1.85187 + 6.91129i) q^{41} +(5.41425 + 9.54287i) q^{42} +(4.88743 - 2.82176i) q^{43} +(0.609028 + 0.173052i) q^{44} +(0.0496946 - 0.185463i) q^{45} +(-7.31557 - 7.42650i) q^{46} +(6.15946 - 6.15946i) q^{47} +(8.90264 + 0.268027i) q^{48} +(4.45127 + 2.56994i) q^{49} +(6.80306 + 1.87785i) q^{50} +14.1127i q^{51} +(3.54287 + 6.28077i) q^{52} -3.89384i q^{53} +(-0.873024 + 3.16278i) q^{54} +(-0.0268835 - 0.0155212i) q^{55} +(8.64364 - 4.73356i) q^{56} +(-0.647671 + 0.647671i) q^{57} +(3.68685 - 3.63178i) q^{58} +(-2.51467 + 9.38488i) q^{59} +(-0.420062 - 0.119358i) q^{60} +(-11.9231 + 6.88378i) q^{61} +(-1.94966 + 1.10616i) q^{62} +(-1.76575 - 6.58987i) q^{63} +(0.361046 - 7.99185i) q^{64} +(-0.0932273 - 0.341044i) q^{65} +(-0.859539 - 0.504916i) q^{66} +(-3.16917 - 11.8275i) q^{67} +(12.6746 + 0.190751i) q^{68} +(8.20666 + 14.2144i) q^{69} +(-0.467645 + 0.121541i) q^{70} +(1.81764 - 6.78351i) q^{71} +(-5.31580 - 1.55378i) q^{72} +(1.49582 + 1.49582i) q^{73} +(-4.39828 - 0.0330948i) q^{74} +(-9.62322 - 5.55597i) q^{75} +(0.572920 + 0.590428i) q^{76} -1.10300 q^{77} +(-2.91133 - 10.9742i) q^{78} -10.3044i q^{79} +(-0.112874 + 0.375645i) q^{80} +(5.52009 - 9.56108i) q^{81} +(-10.1185 - 0.0761368i) q^{82} +(2.53771 - 2.53771i) q^{83} +(-15.0465 + 3.78997i) q^{84} +(-0.600323 - 0.160856i) q^{85} +(2.00761 + 7.72451i) q^{86} +(-7.05665 + 4.07416i) q^{87} +(-0.465083 + 0.765128i) q^{88} +(0.110536 - 0.0296181i) q^{89} +(0.234129 + 0.137534i) q^{90} +(-8.92775 - 8.83821i) q^{91} +(12.8768 - 7.17829i) q^{92} +(3.40912 - 0.913470i) q^{93} +(6.07901 + 10.7145i) q^{94} +(-0.0201684 - 0.0349327i) q^{95} +(-3.71539 + 12.0355i) q^{96} +(6.28973 + 1.68533i) q^{97} +(-5.17841 + 5.10107i) q^{98} +(0.438306 + 0.438306i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{2} - 4 q^{3} - 6 q^{4} - 6 q^{6} - 10 q^{8} - 20 q^{9} - 6 q^{10} - 8 q^{11} + 8 q^{14} - 10 q^{16} - 12 q^{17} - 6 q^{18} - 8 q^{19} + 10 q^{20} - 20 q^{22} + 46 q^{24} - 2 q^{26} + 8 q^{27}+ \cdots + 168 q^{99}+O(q^{100}) \) 48 * q - 4 * q^2 - 4 * q^3 - 6 * q^4 - 6 * q^6 - 10 * q^8 - 20 * q^9 - 6 * q^10 - 8 * q^11 + 8 * q^14 - 10 * q^16 - 12 * q^17 - 6 * q^18 - 8 * q^19 + 10 * q^20 - 20 * q^22 + 46 * q^24 - 2 * q^26 + 8 * q^27 + 12 * q^28 - 54 * q^30 + 16 * q^32 + 4 * q^33 - 46 * q^34 - 4 * q^35 + 30 * q^36 - 32 * q^40 - 16 * q^42 - 12 * q^43 - 16 * q^44 + 34 * q^46 + 46 * q^48 - 60 * q^49 + 86 * q^50 + 12 * q^52 + 32 * q^54 + 48 * q^56 + 36 * q^57 + 30 * q^58 - 64 * q^59 + 80 * q^60 + 42 * q^62 - 16 * q^65 + 8 * q^66 - 8 * q^67 - 32 * q^68 + 36 * q^70 - 24 * q^72 - 12 * q^73 + 38 * q^74 + 24 * q^75 - 94 * q^76 + 40 * q^78 - 108 * q^80 - 8 * q^81 + 54 * q^82 - 48 * q^83 - 72 * q^84 + 80 * q^86 - 108 * q^88 + 12 * q^89 + 104 * q^91 - 20 * q^92 + 26 * q^94 - 32 * q^96 + 4 * q^97 - 16 * q^98 + 168 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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