LMFDB - Embedded newform 950.2.h.d.191.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(191,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("950.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.h (of order $5$, degree $4$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			191.8
Character	$\chi$	$=$	950.191
Dual form			950.2.h.d.761.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(0.154308 + 0.474912i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.19349 - 1.89092i) q^{5} +(-0.154308 + 0.474912i) q^{6} -2.61594 q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.22532 - 1.61679i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(0.154308 + 0.474912i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.19349 - 1.89092i) q^{5} +(-0.154308 + 0.474912i) q^{6} -2.61594 q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.22532 - 1.61679i) q^{9} +(0.145902 - 2.23130i) q^{10} +(-1.39291 - 1.01201i) q^{11} +(-0.403984 + 0.293512i) q^{12} +(1.71827 - 1.24839i) q^{13} +(-2.11634 - 1.53761i) q^{14} +(0.713855 - 0.858587i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.79898 - 5.53669i) q^{17} +2.75065 q^{18} +(-0.309017 + 0.951057i) q^{19} +(1.42956 - 1.71940i) q^{20} +(-0.403661 - 1.24234i) q^{21} +(-0.532045 - 1.63747i) q^{22} +(-1.05116 - 0.763711i) q^{23} -0.499352 q^{24} +(-2.15116 + 4.51359i) q^{25} +2.12389 q^{26} +(2.32317 + 1.68788i) q^{27} +(-0.808371 - 2.48791i) q^{28} +(-2.90199 - 8.93142i) q^{29} +(1.08219 - 0.275018i) q^{30} +(1.91714 - 5.90034i) q^{31} -1.00000 q^{32} +(0.265678 - 0.817672i) q^{33} +(4.70979 - 3.42186i) q^{34} +(3.12210 + 4.94654i) q^{35} +(2.22532 + 1.61679i) q^{36} +(8.17597 - 5.94019i) q^{37} +(-0.809017 + 0.587785i) q^{38} +(0.858019 + 0.623388i) q^{39} +(2.16718 - 0.550750i) q^{40} +(-1.22240 + 0.888122i) q^{41} +(0.403661 - 1.24234i) q^{42} +5.61319 q^{43} +(0.532045 - 1.63747i) q^{44} +(-5.71312 - 2.27828i) q^{45} +(-0.401507 - 1.23571i) q^{46} +(1.36367 + 4.19693i) q^{47} +(-0.403984 - 0.293512i) q^{48} -0.156839 q^{49} +(-4.39335 + 2.38715i) q^{50} +2.90704 q^{51} +(1.71827 + 1.24839i) q^{52} +(0.544163 + 1.67476i) q^{53} +(0.887372 + 2.73105i) q^{54} +(-0.251204 + 3.84171i) q^{55} +(0.808371 - 2.48791i) q^{56} -0.499352 q^{57} +(2.90199 - 8.93142i) q^{58} +(-8.10594 + 5.88931i) q^{59} +(1.03716 + 0.413599i) q^{60} +(-4.45471 - 3.23654i) q^{61} +(5.01913 - 3.64661i) q^{62} +(-5.82131 + 4.22943i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-4.41135 - 1.75916i) q^{65} +(0.695553 - 0.505349i) q^{66} +(-1.28006 + 3.93962i) q^{67} +5.82162 q^{68} +(0.200493 - 0.617054i) q^{69} +(-0.381671 + 5.83696i) q^{70} +(-4.37105 - 13.4527i) q^{71} +(0.849997 + 2.61602i) q^{72} +(4.10763 + 2.98436i) q^{73} +10.1060 q^{74} +(-2.47550 - 0.325129i) q^{75} -1.00000 q^{76} +(3.64378 + 2.64736i) q^{77} +(0.327734 + 1.00866i) q^{78} +(2.92897 + 9.01443i) q^{79} +(2.07701 + 0.828271i) q^{80} +(2.10688 - 6.48431i) q^{81} -1.51096 q^{82} +(-1.73626 + 5.34365i) q^{83} +(1.05680 - 0.767810i) q^{84} +(-12.6165 + 3.20626i) q^{85} +(4.54117 + 3.29935i) q^{86} +(3.79384 - 2.75638i) q^{87} +(1.39291 - 1.01201i) q^{88} +(-1.00930 - 0.733300i) q^{89} +(-3.28287 - 5.20126i) q^{90} +(-4.49489 + 3.26573i) q^{91} +(0.401507 - 1.23571i) q^{92} +3.09797 q^{93} +(-1.36367 + 4.19693i) q^{94} +(2.16718 - 0.550750i) q^{95} +(-0.154308 - 0.474912i) q^{96} +(5.28061 + 16.2520i) q^{97} +(-0.126886 - 0.0921878i) q^{98} -4.73588 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 11 q^{5} + q^{6} - 10 q^{7} + 11 q^{8}+O(q^{10}) $ 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 11 * q^5 + q^6 - 10 * q^7 + 11 * q^8	\( 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 11 q^{5} + q^{6} - 10 q^{7} + 11 q^{8} - 4 q^{10} + 7 q^{11} + 4 q^{12} + 10 q^{13} - 5 q^{14} - 20 q^{15} - 11 q^{16} + 11 q^{17} - 50 q^{18} + 11 q^{19} + 4 q^{20} + 9 q^{21} + 8 q^{22} - 7 q^{23} + 6 q^{24} - 3 q^{25} + 10 q^{26} + 5 q^{27} - 20 q^{29} - 10 q^{30} - 11 q^{31} - 44 q^{32} - 2 q^{33} - q^{34} + 5 q^{35} + 43 q^{37} - 11 q^{38} - 33 q^{39} - 4 q^{40} - 32 q^{41} - 9 q^{42} - 74 q^{43} - 8 q^{44} + 10 q^{45} - 8 q^{46} - 19 q^{47} + 4 q^{48} + 54 q^{49} + 18 q^{50} + 34 q^{51} + 10 q^{52} + 23 q^{53} - 40 q^{54} + 2 q^{55} + 6 q^{57} + 20 q^{58} + 24 q^{59} - 35 q^{60} - 12 q^{61} + q^{62} - 44 q^{63} - 11 q^{64} + 43 q^{65} - 8 q^{66} + 35 q^{67} - 24 q^{68} + 29 q^{69} - 5 q^{70} - 2 q^{71} + 25 q^{72} + 22 q^{73} + 72 q^{74} + 7 q^{75} - 44 q^{76} - 3 q^{77} - 22 q^{78} - 19 q^{79} - q^{80} - 26 q^{81} - 58 q^{82} - 24 q^{83} - 21 q^{84} - 18 q^{85} - 6 q^{86} + 83 q^{87} - 7 q^{88} - 8 q^{89} + 60 q^{90} - 30 q^{91} + 8 q^{92} - 72 q^{93} + 19 q^{94} - 4 q^{95} + q^{96} - 16 q^{97} + q^{98} + 84 q^{99}+O(q^{100}) \) 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 11 * q^5 + q^6 - 10 * q^7 + 11 * q^8 - 4 * q^10 + 7 * q^11 + 4 * q^12 + 10 * q^13 - 5 * q^14 - 20 * q^15 - 11 * q^16 + 11 * q^17 - 50 * q^18 + 11 * q^19 + 4 * q^20 + 9 * q^21 + 8 * q^22 - 7 * q^23 + 6 * q^24 - 3 * q^25 + 10 * q^26 + 5 * q^27 - 20 * q^29 - 10 * q^30 - 11 * q^31 - 44 * q^32 - 2 * q^33 - q^34 + 5 * q^35 + 43 * q^37 - 11 * q^38 - 33 * q^39 - 4 * q^40 - 32 * q^41 - 9 * q^42 - 74 * q^43 - 8 * q^44 + 10 * q^45 - 8 * q^46 - 19 * q^47 + 4 * q^48 + 54 * q^49 + 18 * q^50 + 34 * q^51 + 10 * q^52 + 23 * q^53 - 40 * q^54 + 2 * q^55 + 6 * q^57 + 20 * q^58 + 24 * q^59 - 35 * q^60 - 12 * q^61 + q^62 - 44 * q^63 - 11 * q^64 + 43 * q^65 - 8 * q^66 + 35 * q^67 - 24 * q^68 + 29 * q^69 - 5 * q^70 - 2 * q^71 + 25 * q^72 + 22 * q^73 + 72 * q^74 + 7 * q^75 - 44 * q^76 - 3 * q^77 - 22 * q^78 - 19 * q^79 - q^80 - 26 * q^81 - 58 * q^82 - 24 * q^83 - 21 * q^84 - 18 * q^85 - 6 * q^86 + 83 * q^87 - 7 * q^88 - 8 * q^89 + 60 * q^90 - 30 * q^91 + 8 * q^92 - 72 * q^93 + 19 * q^94 - 4 * q^95 + q^96 - 16 * q^97 + q^98 + 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	0.154308	+	0.474912i	0.0890899	+	0.274190i	0.985668	−	0.168694i	$-0.0539551\pi$
$3$	0.154308	+	0.474912i	0.0890899	+	0.274190i	−0.896579	+	0.442885i	$0.853955\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−1.19349	−	1.89092i	−0.533745	−	0.845646i
$5$	−1.19349	−	1.89092i	−0.533745	−	0.845646i
$6$	−0.154308	+	0.474912i	−0.0629961	+	0.193882i
$7$	−2.61594			−0.988734			−0.494367	−	0.869253i	$-0.664600\pi$
$7$	−2.61594			−0.988734			−0.494367	+	0.869253i	$0.664600\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	2.22532	−	1.61679i	0.741774	−	0.538930i
$10$	0.145902	−	2.23130i	0.0461382	−	0.705600i
$11$	−1.39291	−	1.01201i	−0.419979	−	0.305132i	0.357650	−	0.933856i	$-0.383578\pi$
$11$	−1.39291	−	1.01201i	−0.419979	−	0.305132i	−0.777629	+	0.628723i	$0.783578\pi$
$12$	−0.403984	+	0.293512i	−0.116620	+	0.0847295i
$13$	1.71827	−	1.24839i	0.476561	−	0.346242i	−0.323432	−	0.946252i	$-0.604837\pi$
$13$	1.71827	−	1.24839i	0.476561	−	0.346242i	0.799993	+	0.600009i	$0.204837\pi$
$14$	−2.11634	−	1.53761i	−0.565616	−	0.410944i
$15$	0.713855	−	0.858587i	0.184317	−	0.221686i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	1.79898	−	5.53669i	0.436317	−	1.34284i	−0.455415	−	0.890279i	$-0.650509\pi$
$17$	1.79898	−	5.53669i	0.436317	−	1.34284i	0.891731	−	0.452565i	$-0.149491\pi$
$18$	2.75065			0.648334
$19$	−0.309017	+	0.951057i	−0.0708934	+	0.218187i
$19$	−0.309017	+	0.951057i	−0.0708934	+	0.218187i
$20$	1.42956	−	1.71940i	0.319660	−	0.384470i
$21$	−0.403661	−	1.24234i	−0.0880862	−	0.271101i
$22$	−0.532045	−	1.63747i	−0.113432	−	0.349109i
$23$	−1.05116	−	0.763711i	−0.219182	−	0.159245i	0.472777	−	0.881182i	$-0.343252\pi$
$23$	−1.05116	−	0.763711i	−0.219182	−	0.159245i	−0.691958	+	0.721938i	$0.743252\pi$
$24$	−0.499352			−0.101930
$25$	−2.15116	+	4.51359i	−0.430233	+	0.902718i
$26$	2.12389			0.416530
$27$	2.32317	+	1.68788i	0.447094	+	0.324833i
$28$	−0.808371	−	2.48791i	−0.152768	−	0.470171i
$29$	−2.90199	−	8.93142i	−0.538887	−	1.65852i	−0.735097	−	0.677961i	$-0.762864\pi$
$29$	−2.90199	−	8.93142i	−0.538887	−	1.65852i	0.196211	−	0.980562i	$-0.437136\pi$
$30$	1.08219	−	0.275018i	0.197579	−	0.0502112i
$31$	1.91714	−	5.90034i	0.344328	−	1.05973i	−0.617614	−	0.786481i	$-0.711901\pi$
$31$	1.91714	−	5.90034i	0.344328	−	1.05973i	0.961942	−	0.273252i	$-0.0880993\pi$
$32$	−1.00000			−0.176777
$33$	0.265678	−	0.817672i	0.0462485	−	0.142338i
$34$	4.70979	−	3.42186i	0.807722	−	0.586845i
$35$	3.12210	+	4.94654i	0.527732	+	0.836118i
$36$	2.22532	+	1.61679i	0.370887	+	0.269465i
$37$	8.17597	−	5.94019i	1.34412	−	0.976561i	0.344839	−	0.938662i	$-0.387934\pi$
$37$	8.17597	−	5.94019i	1.34412	−	0.976561i	0.999282	−	0.0378988i	$-0.0120664\pi$
$38$	−0.809017	+	0.587785i	−0.131240	+	0.0953514i
$39$	0.858019	+	0.623388i	0.137393	+	0.0998219i
$40$	2.16718	−	0.550750i	0.342661	−	0.0870812i
$41$	−1.22240	+	0.888122i	−0.190906	+	0.138701i	−0.679133	−	0.734015i	$-0.737644\pi$
$41$	−1.22240	+	0.888122i	−0.190906	+	0.138701i	0.488227	+	0.872717i	$0.337644\pi$
$42$	0.403661	−	1.24234i	0.0622863	−	0.191698i
$43$	5.61319			0.856003			0.428002	−	0.903778i	$-0.359218\pi$
$43$	5.61319			0.856003			0.428002	+	0.903778i	$0.359218\pi$
$44$	0.532045	−	1.63747i	0.0802088	−	0.246857i
$45$	−5.71312	−	2.27828i	−0.851662	−	0.339626i
$46$	−0.401507	−	1.23571i	−0.0591989	−	0.182196i
$47$	1.36367	+	4.19693i	0.198911	+	0.612185i	0.999909	+	0.0135176i	$0.00430292\pi$
$47$	1.36367	+	4.19693i	0.198911	+	0.612185i	−0.800998	+	0.598668i	$0.795697\pi$
$48$	−0.403984	−	0.293512i	−0.0583101	−	0.0423648i
$49$	−0.156839			−0.0224056
$50$	−4.39335	+	2.38715i	−0.621313	+	0.337594i
$51$	2.90704			0.407067
$52$	1.71827	+	1.24839i	0.238281	+	0.173121i
$53$	0.544163	+	1.67476i	0.0747465	+	0.230046i	0.981449	−	0.191726i	$-0.0614084\pi$
$53$	0.544163	+	1.67476i	0.0747465	+	0.230046i	−0.906702	+	0.421772i	$0.861408\pi$
$54$	0.887372	+	2.73105i	0.120756	+	0.371649i
$55$	−0.251204	+	3.84171i	−0.0338724	+	0.518016i
$56$	0.808371	−	2.48791i	0.108023	−	0.332461i
$57$	−0.499352			−0.0661408
$58$	2.90199	−	8.93142i	0.381051	−	1.17275i
$59$	−8.10594	+	5.88931i	−1.05530	+	0.766723i	−0.973214	−	0.229902i	$-0.926159\pi$
$59$	−8.10594	+	5.88931i	−1.05530	+	0.766723i	−0.0820896	+	0.996625i	$0.526159\pi$
$60$	1.03716	+	0.413599i	0.133897	+	0.0533954i
$61$	−4.45471	−	3.23654i	−0.570368	−	0.414396i	0.264871	−	0.964284i	$-0.414671\pi$
$61$	−4.45471	−	3.23654i	−0.570368	−	0.414396i	−0.835239	+	0.549887i	$0.814671\pi$
$62$	5.01913	−	3.64661i	0.637430	−	0.463120i
$63$	−5.82131	+	4.22943i	−0.733417	+	0.532858i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−4.41135	−	1.75916i	−0.547160	−	0.218197i
$66$	0.695553	−	0.505349i	0.0856167	−	0.0622042i
$67$	−1.28006	+	3.93962i	−0.156384	+	0.481301i	−0.998299	−	0.0583104i	$-0.981429\pi$
$67$	−1.28006	+	3.93962i	−0.156384	+	0.481301i	0.841914	+	0.539611i	$0.181429\pi$
$68$	5.82162			0.705975
$69$	0.200493	−	0.617054i	0.0241365	−	0.0742846i
$70$	−0.381671	+	5.83696i	−0.0456184	+	0.697650i
$71$	−4.37105	−	13.4527i	−0.518748	−	1.59654i	−0.776357	−	0.630294i	$-0.782935\pi$
$71$	−4.37105	−	13.4527i	−0.518748	−	1.59654i	0.257609	−	0.966249i	$-0.417065\pi$
$72$	0.849997	+	2.61602i	0.100173	+	0.308301i
$73$	4.10763	+	2.98436i	0.480761	+	0.349293i	0.801620	−	0.597833i	$-0.203972\pi$
$73$	4.10763	+	2.98436i	0.480761	+	0.349293i	−0.320859	+	0.947127i	$0.603972\pi$
$74$	10.1060			1.17480
$75$	−2.47550	−	0.325129i	−0.285846	−	0.0375427i
$76$	−1.00000			−0.114708
$77$	3.64378	+	2.64736i	0.415247	+	0.301695i
$78$	0.327734	+	1.00866i	0.0371086	+	0.114209i
$79$	2.92897	+	9.01443i	0.329535	+	1.01420i	0.969352	+	0.245676i	$0.0790100\pi$
$79$	2.92897	+	9.01443i	0.329535	+	1.01420i	−0.639817	+	0.768527i	$0.720990\pi$
$80$	2.07701	+	0.828271i	0.232217	+	0.0926036i
$81$	2.10688	−	6.48431i	0.234098	−	0.720479i
$82$	−1.51096			−0.166858
$83$	−1.73626	+	5.34365i	−0.190579	+	0.586541i	−1.00000		0.000687500i	$-0.999781\pi$
$83$	−1.73626	+	5.34365i	−0.190579	+	0.586541i	0.809421	+	0.587229i	$0.199781\pi$
$84$	1.05680	−	0.767810i	0.115306	−	0.0837749i
$85$	−12.6165	+	3.20626i	−1.36845	+	0.347767i
$86$	4.54117	+	3.29935i	0.489686	+	0.355778i
$87$	3.79384	−	2.75638i	0.406742	−	0.295515i
$88$	1.39291	−	1.01201i	0.148485	−	0.107881i
$89$	−1.00930	−	0.733300i	−0.106986	−	0.0777296i	0.533006	−	0.846111i	$-0.321062\pi$
$89$	−1.00930	−	0.733300i	−0.106986	−	0.0777296i	−0.639992	+	0.768382i	$0.721062\pi$
$90$	−3.28287	−	5.20126i	−0.346045	−	0.548261i
$91$	−4.49489	+	3.26573i	−0.471192	+	0.342341i
$92$	0.401507	−	1.23571i	0.0418600	−	0.128832i
$93$	3.09797			0.321245
$94$	−1.36367	+	4.19693i	−0.140651	+	0.432880i
$95$	2.16718	−	0.550750i	0.222348	−	0.0565057i
$96$	−0.154308	−	0.474912i	−0.0157490	−	0.0484705i
$97$	5.28061	+	16.2520i	0.536165	+	1.65014i	0.741119	+	0.671373i	$0.234295\pi$
$97$	5.28061	+	16.2520i	0.536165	+	1.65014i	−0.204955	+	0.978771i	$0.565705\pi$
$98$	−0.126886	−	0.0921878i	−0.0128174	−	0.00931237i
$99$	−4.73588			−0.475974
$100$	−4.95743	−	0.651102i	−0.495743	−	0.0651102i
$101$	9.45205			0.940514			0.470257	−	0.882530i	$-0.344161\pi$
$101$	9.45205			0.940514			0.470257	+	0.882530i	$0.344161\pi$
$102$	2.35184	+	1.70871i	0.232867	+	0.169188i
$103$	−1.17933	−	3.62959i	−0.116202	−	0.357634i	0.875993	−	0.482323i	$-0.160207\pi$
$103$	−1.17933	−	3.62959i	−0.116202	−	0.357634i	−0.992196	+	0.124689i	$0.960207\pi$
$104$	0.656319	+	2.01994i	0.0643574	+	0.198072i
$105$	−1.86741	+	2.24602i	−0.182240	+	0.219189i
$106$	−0.544163	+	1.67476i	−0.0528537	+	0.162667i
$107$	−7.13357			−0.689629			−0.344814	−	0.938671i	$-0.612058\pi$
$107$	−7.13357			−0.689629			−0.344814	+	0.938671i	$0.612058\pi$
$108$	−0.887372	+	2.73105i	−0.0853874	+	0.262795i
$109$	−12.1637	+	8.83747i	−1.16507	+	0.846476i	−0.990411	−	0.138152i	$-0.955884\pi$
$109$	−12.1637	+	8.83747i	−1.16507	+	0.846476i	−0.174664	+	0.984628i	$0.555884\pi$
$110$	−2.46133	+	2.96036i	−0.234679	+	0.282259i
$111$	4.08268	+	2.96624i	0.387511	+	0.281543i
$112$	2.11634	−	1.53761i	0.199976	−	0.145291i
$113$	−5.93039	+	4.30868i	−0.557884	+	0.405327i	−0.830684	−	0.556744i	$-0.812050\pi$
$113$	−5.93039	+	4.30868i	−0.557884	+	0.405327i	0.272800	+	0.962071i	$0.412050\pi$
$114$	−0.403984	−	0.293512i	−0.0378366	−	0.0274899i
$115$	−0.189571	+	2.89914i	−0.0176776	+	0.270346i
$116$	7.59752	−	5.51992i	0.705412	−	0.512512i
$117$	1.80530	−	5.55615i	0.166900	−	0.513667i
$118$	−10.0195			−0.922369
$119$	−4.70603	+	14.4837i	−0.431401	+	1.32772i
$120$	0.595971	+	0.944235i	0.0544045	+	0.0861964i
$121$	−2.48315	−	7.64234i	−0.225741	−	0.694758i
$122$	−1.70155	−	5.23683i	−0.154051	−	0.474120i
$123$	−0.610405	−	0.443485i	−0.0550384	−	0.0399877i
$124$	6.20399			0.557135
$125$	11.1022	−	1.31924i	0.993014	−	0.117997i
$126$	−7.19554			−0.641030
$127$	−4.73220	−	3.43814i	−0.419915	−	0.305086i	0.357689	−	0.933841i	$-0.383565\pi$
$127$	−4.73220	−	3.43814i	−0.419915	−	0.305086i	−0.777603	+	0.628755i	$0.783565\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	0.866161	+	2.66577i	0.0762612	+	0.234708i
$130$	−2.53485	−	4.01612i	−0.222321	−	0.352237i
$131$	5.96874	−	18.3699i	0.521492	−	1.60499i	−0.249659	−	0.968334i	$-0.580319\pi$
$131$	5.96874	−	18.3699i	0.521492	−	1.60499i	0.771151	−	0.636652i	$-0.219681\pi$
$132$	0.859751			0.0748317
$133$	0.808371	−	2.48791i	0.0700947	−	0.215729i
$134$	−3.35124	+	2.43482i	−0.289503	+	0.210336i
$135$	0.418971	−	6.40740i	0.0360593	−	0.551461i
$136$	4.70979	+	3.42186i	0.403861	+	0.293422i
$137$	2.19951	−	1.59804i	0.187917	−	0.136530i	−0.489849	−	0.871807i	$-0.662948\pi$
$137$	2.19951	−	1.59804i	0.187917	−	0.136530i	0.677766	+	0.735278i	$0.262948\pi$
$138$	0.524898	−	0.381361i	0.0446823	−	0.0324636i
$139$	11.7205	+	8.51542i	0.994118	+	0.722269i	0.960819	−	0.277177i	$-0.0893987\pi$
$139$	11.7205	+	8.51542i	0.994118	+	0.722269i	0.0332988	+	0.999445i	$0.489399\pi$
$140$	−3.73966	+	4.49786i	−0.316059	+	0.380139i
$141$	−1.78275	+	1.29524i	−0.150134	+	0.109079i
$142$	4.37105	−	13.4527i	0.366810	−	1.12893i
$143$	−3.65678			−0.305795
$144$	−0.849997	+	2.61602i	−0.0708331	+	0.218002i
$145$	−13.4251	+	16.1470i	−1.11489	+	1.34094i
$146$	1.56897	+	4.82880i	0.129849	+	0.399635i
$147$	−0.0242016	−	0.0744848i	−0.00199611	−	0.00614340i
$148$	8.17597	+	5.94019i	0.672060	+	0.488280i
$149$	13.3193			1.09116			0.545579	−	0.838060i	$-0.316310\pi$
$149$	13.3193			1.09116			0.545579	+	0.838060i	$0.316310\pi$
$150$	−1.81161	−	1.71810i	−0.147918	−	0.140282i
$151$	6.31286			0.513733			0.256867	−	0.966447i	$-0.417310\pi$
$151$	6.31286			0.513733			0.256867	+	0.966447i	$0.417310\pi$
$152$	−0.809017	−	0.587785i	−0.0656199	−	0.0476757i
$153$	−4.94836	−	15.2295i	−0.400051	−	1.23123i
$154$	1.39180	+	4.28352i	0.112154	+	0.345176i
$155$	−13.4452	+	3.41684i	−1.07994	+	0.274448i
$156$	−0.327734	+	1.00866i	−0.0262397	+	0.0807576i
$157$	−2.94220			−0.234814			−0.117407	−	0.993084i	$-0.537458\pi$
$157$	−2.94220			−0.234814			−0.117407	+	0.993084i	$0.537458\pi$
$158$	−2.92897	+	9.01443i	−0.233016	+	0.717150i
$159$	−0.711394	+	0.516858i	−0.0564173	+	0.0409895i
$160$	1.19349	+	1.89092i	0.0943537	+	0.149490i
$161$	2.74977	+	1.99783i	0.216712	+	0.157451i
$162$	5.51588	−	4.00752i	0.433369	−	0.314861i
$163$	9.46591	−	6.87739i	0.741427	−	0.538679i	−0.151730	−	0.988422i	$-0.548485\pi$
$163$	9.46591	−	6.87739i	0.741427	−	0.538679i	0.893158	+	0.449743i	$0.148485\pi$
$164$	−1.22240	−	0.888122i	−0.0954530	−	0.0693507i
$165$	−1.86324	+	0.473508i	−0.145053	+	0.0368625i
$166$	−4.54558	+	3.30256i	−0.352805	+	0.256328i
$167$	−4.27565	+	13.1591i	−0.330860	+	1.01828i	0.637866	+	0.770147i	$0.279817\pi$
$167$	−4.27565	+	13.1591i	−0.330860	+	1.01828i	−0.968726	+	0.248134i	$0.920183\pi$
$168$	1.30628			0.100781
$169$	−2.62327	+	8.07359i	−0.201790	+	0.621045i
$170$	−12.0916	−	4.82188i	−0.927380	−	0.369821i
$171$	0.849997	+	2.61602i	0.0650009	+	0.200052i
$172$	1.73457	+	5.33846i	0.132260	+	0.407054i
$173$	10.0685	+	7.31516i	0.765490	+	0.556161i	0.900589	−	0.434671i	$-0.143135\pi$
$173$	10.0685	+	7.31516i	0.765490	+	0.556161i	−0.135099	+	0.990832i	$0.543135\pi$
$174$	4.68944			0.355505
$175$	5.62732	−	11.8073i	0.425386	−	0.892548i
$176$	1.72173			0.129781
$177$	−4.04771	−	2.94084i	−0.304245	−	0.221047i
$178$	−0.385518	−	1.18650i	−0.0288958	−	0.0889322i
$179$	−6.46676	−	19.9026i	−0.483348	−	1.48759i	−0.834359	−	0.551221i	$-0.814162\pi$
$179$	−6.46676	−	19.9026i	−0.483348	−	1.48759i	0.351011	−	0.936371i	$-0.385838\pi$
$180$	0.401324	−	6.13753i	0.0299130	−	0.457464i
$181$	6.47344	−	19.9232i	0.481167	−	1.48088i	−0.356289	−	0.934376i	$-0.615958\pi$
$181$	6.47344	−	19.9232i	0.481167	−	1.48088i	0.837456	−	0.546504i	$-0.184042\pi$
$182$	−5.55599			−0.411837
$183$	0.849672	−	2.61502i	0.0628095	−	0.193308i
$184$	1.05116	−	0.763711i	0.0774924	−	0.0563015i
$185$	−20.9904	−	8.37055i	−1.54324	−	0.615415i
$186$	2.50631	+	1.82094i	0.183772	+	0.133518i
$187$	−8.10901	+	5.89154i	−0.592989	+	0.430832i
$188$	−3.57012	+	2.59385i	−0.260378	+	0.189176i
$189$	−6.07728	−	4.41540i	−0.442057	−	0.321173i
$190$	2.07701	+	0.828271i	0.150682	+	0.0600891i
$191$	−13.6934	+	9.94884i	−0.990820	+	0.719873i	−0.960101	−	0.279655i	$-0.909780\pi$
$191$	−13.6934	+	9.94884i	−0.990820	+	0.719873i	−0.0307197	+	0.999528i	$0.509780\pi$
$192$	0.154308	−	0.474912i	0.0111362	−	0.0342738i
$193$	−12.4940			−0.899338			−0.449669	−	0.893195i	$-0.648458\pi$
$193$	−12.4940			−0.899338			−0.449669	+	0.893195i	$0.648458\pi$
$194$	−5.28061	+	16.2520i	−0.379126	+	1.16683i
$195$	0.154739	−	2.36645i	0.0110811	−	0.169465i
$196$	−0.0484660	−	0.149163i	−0.00346185	−	0.0106545i
$197$	−2.19876	−	6.76710i	−0.156655	−	0.482136i	0.841669	−	0.539993i	$-0.181573\pi$
$197$	−2.19876	−	6.76710i	−0.156655	−	0.482136i	−0.998325	+	0.0578572i	$0.981573\pi$
$198$	−3.83141	−	2.78368i	−0.272287	−	0.197828i
$199$	−4.92316			−0.348994			−0.174497	−	0.984658i	$-0.555830\pi$
$199$	−4.92316			−0.348994			−0.174497	+	0.984658i	$0.555830\pi$
$200$	−3.62793	−	3.44065i	−0.256534	−	0.243291i
$201$	−2.06849			−0.145900
$202$	7.64687	+	5.55577i	0.538032	+	0.390903i
$203$	7.59145	+	23.3641i	0.532816	+	1.63984i
$204$	0.898324	+	2.76476i	0.0628952	+	0.193572i
$205$	3.13829	+	1.25149i	0.219187	+	0.0874077i
$206$	1.17933	−	3.62959i	0.0821675	−	0.252886i
$207$	−3.57393			−0.248405
$208$	−0.656319	+	2.01994i	−0.0455076	+	0.140058i
$209$	1.39291	−	1.01201i	0.0963498	−	0.0700022i
$210$	−2.83094	+	0.719431i	−0.195353	+	0.0496455i
$211$	−11.9910	−	8.71198i	−0.825496	−	0.599758i	0.0927857	−	0.995686i	$-0.470423\pi$
$211$	−11.9910	−	8.71198i	−0.825496	−	0.599758i	−0.918281	+	0.395928i	$0.870423\pi$
$212$	−1.42464	+	1.03506i	−0.0978444	+	0.0710881i
$213$	5.71436	−	4.15173i	0.391542	−	0.284472i
$214$	−5.77118	−	4.19301i	−0.394510	−	0.286628i
$215$	−6.69928	−	10.6141i	−0.456887	−	0.723875i
$216$	−2.32317	+	1.68788i	−0.158072	+	0.114846i
$217$	−5.01512	+	15.4350i	−0.340449	+	1.04779i
$218$	−15.0352			−1.01831
$219$	−0.783470	+	2.41127i	−0.0529420	+	0.162939i
$220$	−3.73131	+	0.948245i	−0.251565	+	0.0639306i
$221$	−3.82084	−	11.7593i	−0.257018	−	0.791019i
$222$	1.55945	+	4.79948i	0.104663	+	0.322120i
$223$	7.03861	+	5.11385i	0.471340	+	0.342449i	0.797963	−	0.602706i	$-0.205911\pi$
$223$	7.03861	+	5.11385i	0.471340	+	0.342449i	−0.326623	+	0.945155i	$0.605911\pi$
$224$	2.61594			0.174785
$225$	2.51050	+	13.5222i	0.167367	+	0.901478i
$226$	−7.33037			−0.487609
$227$	14.6305	+	10.6297i	0.971062	+	0.705518i	0.955693	−	0.294364i	$-0.0951077\pi$
$227$	14.6305	+	10.6297i	0.971062	+	0.705518i	0.0153689	+	0.999882i	$0.495108\pi$
$228$	−0.154308	−	0.474912i	−0.0102193	−	0.0314518i
$229$	5.13909	+	15.8165i	0.339601	+	1.04518i	0.964411	+	0.264407i	$0.0851763\pi$
$229$	5.13909	+	15.8165i	0.339601	+	1.04518i	−0.624810	+	0.780777i	$0.714824\pi$
$230$	−1.85744	+	2.23403i	−0.122476	+	0.147307i
$231$	−0.694998	+	2.13898i	−0.0457275	+	0.140735i
$232$	9.39105			0.616553
$233$	−4.28273	+	13.1809i	−0.280571	+	0.863509i	0.707120	+	0.707093i	$0.249994\pi$
$233$	−4.28273	+	13.1809i	−0.280571	+	0.863509i	−0.987691	+	0.156416i	$0.950006\pi$
$234$	4.72635	−	3.43389i	0.308971	−	0.224481i
$235$	6.30854	−	7.58758i	0.411524	−	0.494959i
$236$	−8.10594	−	5.88931i	−0.527652	−	0.383361i
$237$	−3.82910	+	2.78200i	−0.248727	+	0.180710i
$238$	−12.3205	+	8.95140i	−0.798622	+	0.580233i
$239$	21.1913	+	15.3964i	1.37075	+	0.995910i	0.997678	+	0.0681087i	$0.0216965\pi$
$239$	21.1913	+	15.3964i	1.37075	+	0.995910i	0.373075	+	0.927801i	$0.378304\pi$
$240$	−0.0728563	+	1.11421i	−0.00470286	+	0.0719216i
$241$	4.89327	−	3.55517i	0.315204	−	0.229009i	−0.418923	−	0.908022i	$-0.637592\pi$
$241$	4.89327	−	3.55517i	0.315204	−	0.229009i	0.734126	+	0.679013i	$0.237592\pi$
$242$	2.48315	−	7.64234i	0.159623	−	0.491268i
$243$	12.0194			0.771043
$244$	1.70155	−	5.23683i	0.108931	−	0.335254i
$245$	0.187186	+	0.296570i	0.0119589	+	0.0189472i
$246$	−0.233154	−	0.717574i	−0.0148654	−	0.0457509i
$247$	0.656319	+	2.01994i	0.0417606	+	0.128526i
$248$	5.01913	+	3.64661i	0.318715	+	0.231560i
$249$	−2.80568			−0.177803
$250$	9.75733	+	5.45844i	0.617108	+	0.345222i
$251$	−14.0017			−0.883777			−0.441889	−	0.897070i	$-0.645691\pi$
$251$	−14.0017			−0.883777			−0.441889	+	0.897070i	$0.645691\pi$
$252$	−5.82131	−	4.22943i	−0.366708	−	0.266429i
$253$	0.691288	+	2.12757i	0.0434609	+	0.133759i
$254$	−1.80754	−	5.56303i	−0.113415	−	0.349056i
$255$	−3.46952	−	5.49698i	−0.217270	−	0.344234i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	3.73737			0.233131			0.116565	−	0.993183i	$-0.462812\pi$
$257$	3.73737			0.233131			0.116565	+	0.993183i	$0.462812\pi$
$258$	−0.866161	+	2.66577i	−0.0539248	+	0.165964i
$259$	−21.3879	+	15.5392i	−1.32898	+	0.965558i
$260$	0.309880	−	4.73905i	0.0192179	−	0.293903i
$261$	−20.8981	−	15.1834i	−1.29356	−	0.939826i
$262$	15.6264	−	11.3532i	0.965401	−	0.701405i
$263$	9.80130	−	7.12106i	0.604374	−	0.439103i	−0.243055	−	0.970013i	$-0.578149\pi$
$263$	9.80130	−	7.12106i	0.604374	−	0.439103i	0.847429	+	0.530909i	$0.178149\pi$
$264$	0.695553	+	0.505349i	0.0428083	+	0.0311021i
$265$	2.51739	−	3.02778i	0.154642	−	0.185995i
$266$	2.11634	−	1.53761i	0.129761	−	0.0942771i
$267$	0.192509	−	0.592483i	0.0117814	−	0.0362594i
$268$	−4.14236			−0.253035
$269$	0.485845	−	1.49528i	0.0296225	−	0.0911687i	−0.935152	−	0.354246i	$-0.884737\pi$
$269$	0.485845	−	1.49528i	0.0296225	−	0.0911687i	0.964775	+	0.263077i	$0.0847375\pi$
$270$	4.10513	−	4.93743i	0.249830	−	0.300482i
$271$	4.86990	+	14.9880i	0.295826	+	0.910458i	0.982943	+	0.183911i	$0.0588759\pi$
$271$	4.86990	+	14.9880i	0.295826	+	0.910458i	−0.687117	+	0.726547i	$0.741124\pi$
$272$	1.79898	+	5.53669i	0.109079	+	0.335711i
$273$	−2.24453	−	1.63075i	−0.135845	−	0.0986973i
$274$	2.71875			0.164245
$275$	7.56418	−	4.11004i	0.456137	−	0.247844i
$276$	0.648809			0.0390537
$277$	18.3484	+	13.3309i	1.10245	+	0.800974i	0.981457	−	0.191680i	$-0.0613936\pi$
$277$	18.3484	+	13.3309i	1.10245	+	0.800974i	0.120989	+	0.992654i	$0.461394\pi$
$278$	4.47682	+	13.7782i	0.268502	+	0.826364i
$279$	−5.27337	−	16.2298i	−0.315708	−	0.971651i
$280$	−5.66922	+	1.44073i	−0.338801	+	0.0861001i
$281$	5.84683	−	17.9947i	0.348793	−	1.07347i	−0.610729	−	0.791839i	$-0.709124\pi$
$281$	5.84683	−	17.9947i	0.348793	−	1.07347i	0.959522	−	0.281634i	$-0.0908763\pi$
$282$	−2.20360			−0.131222
$283$	−1.18090	+	3.63443i	−0.0701971	+	0.216045i	−0.980001	−	0.198995i	$-0.936232\pi$
$283$	−1.18090	+	3.63443i	−0.0701971	+	0.216045i	0.909803	+	0.415040i	$0.136232\pi$
$284$	11.4436	−	8.31423i	0.679050	−	0.493359i
$285$	0.595971	+	0.944235i	0.0353023	+	0.0559316i
$286$	−2.95840	−	2.14940i	−0.174934	−	0.127097i
$287$	3.19772	−	2.32328i	0.188755	−	0.137139i
$288$	−2.22532	+	1.61679i	−0.131128	+	0.0952703i
$289$	−13.6653	−	9.92844i	−0.803842	−	0.584026i
$290$	−20.3521	+	5.17212i	−1.19512	+	0.303717i
$291$	−6.90344	+	5.01565i	−0.404687	+	0.294022i
$292$	−1.56897	+	4.82880i	−0.0918172	+	0.282584i
$293$	15.3121			0.894540			0.447270	−	0.894399i	$-0.352396\pi$
$293$	15.3121			0.894540			0.447270	+	0.894399i	$0.352396\pi$
$294$	0.0242016	−	0.0744848i	0.00141146	−	0.00434404i
$295$	20.8106	+	8.29886i	1.21164	+	0.483178i
$296$	3.12294	+	9.61142i	0.181517	+	0.558653i
$297$	−1.52782	−	4.70214i	−0.0886530	−	0.272846i
$298$	10.7755	+	7.82887i	0.624209	+	0.453514i
$299$	−2.75958			−0.159591
$300$	−0.455755	−	2.45481i	−0.0263130	−	0.141729i
$301$	−14.6838			−0.846359
$302$	5.10721	+	3.71061i	0.293887	+	0.213521i
$303$	1.45853	+	4.48889i	0.0837902	+	0.257880i
$304$	−0.309017	−	0.951057i	−0.0177233	−	0.0545468i
$305$	−0.803383	+	12.2863i	−0.0460016	+	0.703511i
$306$	4.94836	−	15.2295i	0.282879	−	0.870612i
$307$	15.8825			0.906460			0.453230	−	0.891394i	$-0.350272\pi$
$307$	15.8825			0.906460			0.453230	+	0.891394i	$0.350272\pi$
$308$	−1.39180	+	4.28352i	−0.0793052	+	0.244076i
$309$	1.54176	−	1.12015i	0.0877074	−	0.0637232i
$310$	−12.8857	−	5.13859i	−0.731861	−	0.291852i
$311$	5.87947	+	4.27168i	0.333394	+	0.242225i	0.741869	−	0.670544i	$-0.233939\pi$
$311$	5.87947	+	4.27168i	0.333394	+	0.242225i	−0.408475	+	0.912769i	$0.633939\pi$
$312$	−0.858019	+	0.623388i	−0.0485758	+	0.0352924i
$313$	4.10873	−	2.98517i	0.232239	−	0.168732i	−0.465579	−	0.885006i	$-0.654154\pi$
$313$	4.10873	−	2.98517i	0.232239	−	0.168732i	0.697819	+	0.716274i	$0.254154\pi$
$314$	−2.38029	−	1.72938i	−0.134328	−	0.0975948i
$315$	14.9452	+	5.95986i	0.842067	+	0.335800i
$316$	−7.66814	+	5.57123i	−0.431366	+	0.313406i
$317$	8.20520	−	25.2530i	0.460850	−	1.41835i	−0.403278	−	0.915077i	$-0.632129\pi$
$317$	8.20520	−	25.2530i	0.460850	−	1.41835i	0.864128	−	0.503272i	$-0.167871\pi$
$318$	−0.879332			−0.0493105
$319$	−4.99646	+	15.3775i	−0.279748	+	0.860977i
$320$	−0.145902	+	2.23130i	−0.00815616	+	0.124734i
$321$	−1.10077	−	3.38782i	−0.0614389	−	0.189090i
$322$	1.05032	+	3.23255i	0.0585320	+	0.180143i
$323$	4.70979	+	3.42186i	0.262060	+	0.190398i
$324$	6.81801			0.378778
$325$	1.93846	+	10.4410i	0.107527	+	0.579165i
$326$	11.7005			0.648031
$327$	−6.07398	−	4.41301i	−0.335892	−	0.244040i
$328$	−0.466913	−	1.43701i	−0.0257810	−	0.0793457i
$329$	−3.56727	−	10.9789i	−0.196670	−	0.605288i
$330$	−1.78571	−	0.712107i	−0.0983001	−	0.0392002i
$331$	−4.18887	+	12.8920i	−0.230241	+	0.708610i	0.767476	+	0.641078i	$0.221512\pi$
$331$	−4.18887	+	12.8920i	−0.230241	+	0.708610i	−0.997717	+	0.0675320i	$0.978488\pi$
$332$	−5.61864			−0.308363
$333$	8.59011	−	26.4376i	0.470735	−	1.44877i
$334$	−11.1938	+	8.13277i	−0.612497	+	0.445005i
$335$	8.97724	−	2.28140i	0.490479	−	0.124646i
$336$	1.05680	+	0.767810i	0.0576531	+	0.0418875i
$337$	−5.53012	+	4.01787i	−0.301245	+	0.218867i	−0.728131	−	0.685438i	$-0.759611\pi$
$337$	−5.53012	+	4.01787i	−0.301245	+	0.218867i	0.426886	+	0.904306i	$0.359611\pi$
$338$	−6.86780	+	4.98975i	−0.373559	+	0.271407i
$339$	−2.96135	−	2.15155i	−0.160839	−	0.116856i
$340$	−6.94805	−	11.0082i	−0.376811	−	0.597005i
$341$	−8.64161	+	6.27850i	−0.467970	+	0.340000i
$342$	−0.849997	+	2.61602i	−0.0459626	+	0.141458i
$343$	18.7219			1.01089
$344$	−1.73457	+	5.33846i	−0.0935218	+	0.287830i
$345$	−1.40609	+	0.357332i	−0.0757012	+	0.0192381i
$346$	3.84581	+	11.8362i	0.206752	+	0.636317i
$347$	−5.40466	−	16.6338i	−0.290137	−	0.892950i	−0.984812	−	0.173626i	$-0.944452\pi$
$347$	−5.40466	−	16.6338i	−0.290137	−	0.892950i	0.694675	−	0.719324i	$-0.255548\pi$
$348$	3.79384	+	2.75638i	0.203371	+	0.147758i
$349$	−16.6901			−0.893403			−0.446701	−	0.894683i	$-0.647401\pi$
$349$	−16.6901			−0.893403			−0.446701	+	0.894683i	$0.647401\pi$
$350$	11.4928	−	6.24465i	0.614314	−	0.333790i
$351$	6.09897			0.325539
$352$	1.39291	+	1.01201i	0.0742425	+	0.0539403i
$353$	8.46843	+	26.0632i	0.450729	+	1.38720i	0.876077	+	0.482172i	$0.160152\pi$
$353$	8.46843	+	26.0632i	0.450729	+	1.38720i	−0.425348	+	0.905030i	$0.639848\pi$
$354$	−1.54609	−	4.75837i	−0.0821737	−	0.252905i
$355$	−20.2212	+	24.3210i	−1.07323	+	1.29082i
$356$	0.385518	−	1.18650i	0.0204324	−	0.0628846i
$357$	−7.60464			−0.402480
$358$	6.46676	−	19.9026i	0.341779	−	1.05189i
$359$	25.2389	−	18.3371i	1.33206	−	0.967797i	0.332363	−	0.943152i	$-0.392154\pi$
$359$	25.2389	−	18.3371i	1.33206	−	0.967797i	0.999696	−	0.0246457i	$-0.00784577\pi$
$360$	3.93223	−	4.72947i	0.207247	−	0.249265i
$361$	−0.809017	−	0.587785i	−0.0425798	−	0.0309361i
$362$	16.9477	−	12.3132i	0.890751	−	0.647168i
$363$	3.24627	−	2.35855i	0.170385	−	0.123792i
$364$	−4.49489	−	3.26573i	−0.235596	−	0.171171i
$365$	0.740788	−	11.3290i	0.0387746	−	0.592987i
$366$	2.22447	−	1.61617i	0.116275	−	0.0844786i
$367$	0.429315	−	1.32129i	0.0224100	−	0.0689710i	−0.939226	−	0.343299i	$-0.888455\pi$
$367$	0.429315	−	1.32129i	0.0224100	−	0.0689710i	0.961636	+	0.274328i	$0.0884555\pi$
$368$	1.29930			0.0677309
$369$	−1.28431	+	3.95271i	−0.0668587	+	0.205770i
$370$	−12.0615	−	19.1097i	−0.627046	−	0.993468i
$371$	−1.42350	−	4.38108i	−0.0739044	−	0.227454i
$372$	0.957326	+	2.94635i	0.0496351	+	0.152761i
$373$	−12.6150	−	9.16536i	−0.653182	−	0.474564i	0.211172	−	0.977449i	$-0.432272\pi$
$373$	−12.6150	−	9.16536i	−0.653182	−	0.474564i	−0.864354	+	0.502885i	$0.832272\pi$
$374$	−10.0233			−0.518292
$375$	2.33969	+	5.06901i	0.120821	+	0.261763i
$376$	−4.41291			−0.227579
$377$	−16.1363	−	11.7237i	−0.831063	−	0.603803i
$378$	−2.32132	−	7.14427i	−0.119396	−	0.367462i
$379$	9.74712	+	29.9986i	0.500676	+	1.54092i	0.807921	+	0.589291i	$0.200593\pi$
$379$	9.74712	+	29.9986i	0.500676	+	1.54092i	−0.307245	+	0.951631i	$0.599407\pi$
$380$	1.19349	+	1.89092i	0.0612247	+	0.0970022i
$381$	0.902597	−	2.77791i	0.0462415	−	0.142317i
$382$	−16.9260			−0.866009
$383$	0.329965	−	1.01553i	0.0168604	−	0.0518910i	−0.942272	−	0.334847i	$-0.891315\pi$
$383$	0.329965	−	1.01553i	0.0168604	−	0.0518910i	0.959133	+	0.282956i	$0.0913152\pi$
$384$	0.403984	−	0.293512i	0.0206157	−	0.0149782i
$385$	0.657136	−	10.0497i	0.0334907	−	0.512180i
$386$	−10.1079	−	7.34379i	−0.514476	−	0.373789i
$387$	12.4911	−	9.07535i	0.634961	−	0.461326i
$388$	−13.8248	+	10.0443i	−0.701848	+	0.509923i
$389$	−23.9573	−	17.4060i	−1.21468	−	0.882519i	−0.219036	−	0.975717i	$-0.570291\pi$
$389$	−23.9573	−	17.4060i	−1.21468	−	0.882519i	−0.995648	+	0.0931974i	$0.970291\pi$
$390$	1.51615	−	1.82355i	0.0767734	−	0.0923389i
$391$	−6.11944	+	4.44604i	−0.309474	+	0.224846i
$392$	0.0484660	−	0.149163i	0.00244790	−	0.00753386i
$393$	9.64511			0.486531
$394$	2.19876	−	6.76710i	0.110772	−	0.340922i
$395$	13.5499	−	16.2971i	0.681769	−	0.819995i
$396$	−1.46347	−	4.50409i	−0.0735421	−	0.226339i
$397$	−8.92911	−	27.4810i	−0.448139	−	1.37923i	−0.879004	−	0.476815i	$-0.841791\pi$
$397$	−8.92911	−	27.4810i	−0.448139	−	1.37923i	0.430865	−	0.902417i	$-0.358209\pi$
$398$	−3.98292	−	2.89376i	−0.199646	−	0.145051i
$399$	1.30628			0.0653956
$400$	−0.912694	−	4.91599i	−0.0456347	−	0.245800i
$401$	21.7967			1.08848			0.544239	−	0.838930i	$-0.316819\pi$
$401$	21.7967			1.08848			0.544239	+	0.838930i	$0.316819\pi$
$402$	−1.67345	−	1.21583i	−0.0834639	−	0.0606401i
$403$	−4.07180	−	12.5317i	−0.202831	−	0.624249i
$404$	2.92084	+	8.98943i	0.145317	+	0.447241i
$405$	−14.7759	+	3.75501i	−0.734218	+	0.186588i
$406$	−7.59145	+	23.3641i	−0.376758	+	1.15954i
$407$	−17.3999			−0.862483
$408$	−0.898324	+	2.76476i	−0.0444736	+	0.136876i
$409$	−21.0508	+	15.2943i	−1.04090	+	0.756255i	−0.970460	−	0.241262i	$-0.922439\pi$
$409$	−21.0508	+	15.2943i	−1.04090	+	0.756255i	−0.0704351	+	0.997516i	$0.522439\pi$
$410$	1.80332	+	2.85711i	0.0890596	+	0.141103i
$411$	1.09833	+	0.797983i	0.0541766	+	0.0393616i
$412$	3.08752	−	2.24321i	0.152111	−	0.110515i
$413$	21.2047	−	15.4061i	1.04341	−	0.758085i
$414$	−2.89137	−	2.10070i	−0.142103	−	0.103244i
$415$	12.1766	−	3.09447i	0.597727	−	0.151901i
$416$	−1.71827	+	1.24839i	−0.0842449	+	0.0612075i
$417$	−2.23551	+	6.88019i	−0.109473	+	0.336924i
$418$	1.72173			0.0842128
$419$	−9.12826	+	28.0939i	−0.445945	+	1.37248i	0.435500	+	0.900189i	$0.356572\pi$
$419$	−9.12826	+	28.0939i	−0.445945	+	1.37248i	−0.881444	+	0.472288i	$0.843428\pi$
$420$	−2.71315	−	1.08195i	−0.132388	−	0.0527938i
$421$	7.30192	+	22.4730i	0.355874	+	1.09527i	0.955501	+	0.294987i	$0.0953154\pi$
$421$	7.30192	+	22.4730i	0.355874	+	1.09527i	−0.599628	+	0.800279i	$0.704685\pi$
$422$	−4.58016	−	14.0963i	−0.222959	−	0.686197i
$423$	9.82015	+	7.13475i	0.477472	+	0.346904i
$424$	−1.76095			−0.0855191
$425$	21.1204	+	20.0302i	1.02449	+	0.971607i
$426$	7.06334			0.342220
$427$	11.6533	+	8.46660i	0.563942	+	0.409728i
$428$	−2.20440	−	6.78443i	−0.106553	−	0.327938i
$429$	−0.564271	−	1.73665i	−0.0272433	−	0.0838462i
$430$	0.818974	−	12.5247i	0.0394945	−	0.603996i
$431$	3.22084	−	9.91273i	0.155142	−	0.477479i	−0.843033	−	0.537862i	$-0.819232\pi$
$431$	3.22084	−	9.91273i	0.155142	−	0.477479i	0.998175	+	0.0603827i	$0.0192321\pi$
$432$	−2.87160			−0.138160
$433$	−6.58137	+	20.2554i	−0.316280	+	0.973411i	0.658944	+	0.752192i	$0.271003\pi$
$433$	−6.58137	+	20.2554i	−0.316280	+	0.973411i	−0.975224	+	0.221219i	$0.928997\pi$
$434$	−13.1298	+	9.53933i	−0.630249	+	0.457903i
$435$	−9.74001	−	3.88413i	−0.466998	−	0.186230i
$436$	−12.1637	−	8.83747i	−0.582537	−	0.423238i
$437$	1.05116	−	0.763711i	0.0502837	−	0.0365333i
$438$	−2.05115	+	1.49025i	−0.0980077	+	0.0712068i
$439$	−8.11403	−	5.89519i	−0.387262	−	0.281362i	0.377071	−	0.926184i	$-0.376931\pi$
$439$	−8.11403	−	5.89519i	−0.387262	−	0.281362i	−0.764332	+	0.644822i	$0.776931\pi$
$440$	−3.57606	−	1.42606i	−0.170482	−	0.0679849i
$441$	−0.349017	+	0.253576i	−0.0166199	+	0.0120750i
$442$	3.82084	−	11.7593i	0.181739	−	0.559335i
$443$	33.6084			1.59678			0.798391	−	0.602140i	$-0.205685\pi$
$443$	33.6084			1.59678			0.798391	+	0.602140i	$0.205685\pi$
$444$	−1.55945	+	4.79948i	−0.0740080	+	0.227773i
$445$	−0.182022	+	2.78369i	−0.00862866	+	0.131960i
$446$	2.68851	+	8.27438i	0.127305	+	0.391803i
$447$	2.05527	+	6.32548i	0.0972111	+	0.299185i
$448$	2.11634	+	1.53761i	0.0999878	+	0.0726454i
$449$	15.4323			0.728294			0.364147	−	0.931342i	$-0.381361\pi$
$449$	15.4323			0.728294			0.364147	+	0.931342i	$0.381361\pi$
$450$	−5.91709	+	12.4153i	−0.278934	+	0.585263i
$451$	2.60148			0.122499
$452$	−5.93039	−	4.30868i	−0.278942	−	0.202663i
$453$	0.974126	+	2.99805i	0.0457684	+	0.140861i
$454$	5.58837	+	17.1992i	0.262275	+	0.807199i
$455$	11.5398	+	4.60187i	0.540996	+	0.215739i
$456$	0.154308	−	0.474912i	0.00722614	−	0.0222398i
$457$	29.2054			1.36617			0.683084	−	0.730339i	$-0.260638\pi$
$457$	29.2054			1.36617			0.683084	+	0.730339i	$0.260638\pi$
$458$	−5.13909	+	15.8165i	−0.240134	+	0.739057i
$459$	13.5246	−	9.82621i	0.631275	−	0.458648i
$460$	−2.81583	+	0.715591i	−0.131289	+	0.0333646i
$461$	−10.7923	−	7.84109i	−0.502649	−	0.365196i	0.307379	−	0.951587i	$-0.400548\pi$
$461$	−10.7923	−	7.84109i	−0.502649	−	0.365196i	−0.810028	+	0.586391i	$0.800548\pi$
$462$	−1.81953	+	1.32196i	−0.0846521	+	0.0615033i
$463$	−2.50960	+	1.82333i	−0.116631	+	0.0847375i	−0.644572	−	0.764544i	$-0.722964\pi$
$463$	−2.50960	+	1.82333i	−0.116631	+	0.0847375i	0.527941	+	0.849281i	$0.322964\pi$
$464$	7.59752	+	5.51992i	0.352706	+	0.256256i
$465$	−3.69740	−	5.85802i	−0.171463	−	0.271659i
$466$	−11.2123	+	8.14624i	−0.519402	+	0.377367i
$467$	−2.86270	+	8.81050i	−0.132470	+	0.407701i	−0.995188	−	0.0979845i	$-0.968760\pi$
$467$	−2.86270	+	8.81050i	−0.132470	+	0.407701i	0.862718	+	0.505686i	$0.168760\pi$
$468$	5.84209			0.270050
$469$	3.34856	−	10.3058i	0.154622	−	0.475878i
$470$	9.56358	−	2.43041i	0.441135	−	0.112106i
$471$	−0.454006	−	1.39729i	−0.0209195	−	0.0643836i
$472$	−3.09619	−	9.52910i	−0.142514	−	0.438612i
$473$	−7.81868	−	5.68060i	−0.359503	−	0.261194i
$474$	−4.73302			−0.217395
$475$	−3.62793	−	3.44065i	−0.166461	−	0.157868i
$476$	−15.2290			−0.698021
$477$	3.91867	+	2.84708i	0.179424	+	0.130359i
$478$	8.09436	+	24.9119i	0.370228	+	1.13944i
$479$	−8.15934	−	25.1119i	−0.372810	−	1.14739i	−0.944944	−	0.327231i	$-0.893885\pi$
$479$	−8.15934	−	25.1119i	−0.372810	−	1.14739i	0.572135	−	0.820160i	$-0.306115\pi$
$480$	−0.713855	+	0.858587i	−0.0325829	+	0.0391890i
$481$	6.63280	−	20.4136i	0.302429	−	0.930782i
$482$	6.04842			0.275498
$483$	−0.524479	+	1.61418i	−0.0238646	+	0.0734477i
$484$	6.50096	−	4.72323i	0.295498	−	0.214692i
$485$	24.4290	−	29.3819i	1.10926	−	1.33416i
$486$	9.72388	+	7.06481i	0.441084	+	0.320466i
$487$	28.7915	−	20.9182i	1.30467	−	0.947895i	0.304677	−	0.952456i	$-0.401452\pi$
$487$	28.7915	−	20.9182i	1.30467	−	0.947895i	0.999990	+	0.00456039i	$0.00145162\pi$
$488$	4.45471	−	3.23654i	0.201655	−	0.146511i
$489$	4.72682	+	3.43424i	0.213754	+	0.155301i
$490$	−0.0228831	+	0.349956i	−0.00103375	+	0.0158094i
$491$	34.5988	−	25.1375i	1.56142	−	1.13444i	0.626587	−	0.779352i	$-0.284451\pi$
$491$	34.5988	−	25.1375i	1.56142	−	1.13444i	0.934833	−	0.355087i	$-0.115549\pi$
$492$	0.233154	−	0.717574i	0.0105114	−	0.0323508i
$493$	−54.6711			−2.46226
$494$	−0.656319	+	2.01994i	−0.0295292	+	0.0908816i
$495$	5.65223	+	8.95518i	0.254049	+	0.402506i
$496$	1.91714	+	5.90034i	0.0860820	+	0.264933i
$497$	11.4344	+	35.1915i	0.512904	+	1.57856i
$498$	−2.26984	−	1.64914i	−0.101714	−	0.0738996i
$499$	26.1913			1.17249			0.586243	−	0.810135i	$-0.300606\pi$
$499$	26.1913			1.17249			0.586243	+	0.810135i	$0.300606\pi$
$500$	4.68545	+	10.1512i	0.209540	+	0.453975i
$501$	−6.90918			−0.308679
$502$	−11.3276	−	8.22997i	−0.505575	−	0.367322i
$503$	2.48653	+	7.65277i	0.110869	+	0.341220i	0.991063	−	0.133394i	$-0.0425876\pi$
$503$	2.48653	+	7.65277i	0.110869	+	0.341220i	−0.880194	+	0.474614i	$0.842588\pi$
$504$	−2.22354	−	6.84336i	−0.0990445	−	0.304828i
$505$	−11.2809	−	17.8731i	−0.501994	−	0.795341i
$506$	−0.691288	+	2.12757i	−0.0307315	+	0.0945818i
$507$	−4.23903			−0.188262
$508$	1.80754	−	5.56303i	0.0801965	−	0.246820i
$509$	21.9633	−	15.9573i	0.973505	−	0.707293i	0.0172574	−	0.999851i	$-0.494507\pi$
$509$	21.9633	−	15.9573i	0.973505	−	0.707293i	0.956248	+	0.292558i	$0.0945065\pi$
$510$	0.424142	−	6.48648i	0.0187813	−	0.287226i
$511$	−10.7453	−	7.80693i	−0.475345	−	0.345358i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−2.32317	+	1.68788i	−0.102570	+	0.0745218i
$514$	3.02360	+	2.19677i	0.133365	+	0.0968955i
$515$	−5.45576	+	6.56189i	−0.240409	+	0.289152i
$516$	−2.26764	+	1.64754i	−0.0998272	+	0.0725287i
$517$	2.34787	−	7.22600i	0.103259	−	0.317799i
$518$	−26.4369			−1.16157
$519$	−1.92041	+	5.91041i	−0.0842966	+	0.259438i
$520$	3.03624	−	3.65183i	0.133148	−	0.160143i
$521$	−1.88121	−	5.78976i	−0.0824171	−	0.253654i	0.901354	−	0.433084i	$-0.142575\pi$
$521$	−1.88121	−	5.78976i	−0.0824171	−	0.253654i	−0.983771	+	0.179430i	$0.942575\pi$
$522$	−7.98236	−	24.5672i	−0.349379	−	1.07528i
$523$	7.57690	+	5.50494i	0.331315	+	0.240714i	0.740988	−	0.671518i	$-0.234357\pi$
$523$	7.57690	+	5.50494i	0.331315	+	0.240714i	−0.409674	+	0.912232i	$0.634357\pi$
$524$	19.3153			0.843791
$525$	6.47577	+	0.850519i	0.282626	+	0.0371197i
$526$	12.1151			0.528242
$527$	−29.2195	−	21.2292i	−1.27282	−	0.924758i
$528$	0.265678	+	0.817672i	0.0115621	+	0.0355846i
$529$	−6.58571	−	20.2687i	−0.286335	−	0.881249i
$530$	3.81629	−	0.969841i	0.165769	−	0.0421272i
$531$	−8.51654	+	26.2112i	−0.369586	+	1.13747i
$532$	2.61594			0.113416
$533$	−0.991675	+	3.05206i	−0.0429542	+	0.132199i
$534$	0.503996	−	0.366174i	0.0218100	−	0.0158459i
$535$	8.51385	+	13.4890i	0.368086	+	0.583181i
$536$	−3.35124	−	2.43482i	−0.144751	−	0.105168i
$537$	8.45412	−	6.14228i	0.364822	−	0.265059i
$538$	1.27196	−	0.924133i	0.0548381	−	0.0398422i
$539$	0.218463	+	0.158723i	0.00940988	+	0.00683668i
$540$	6.22327	−	1.58153i	0.267807	−	0.0680582i
$541$	16.5850	−	12.0497i	0.713044	−	0.518057i	−0.171110	−	0.985252i	$-0.554735\pi$
$541$	16.5850	−	12.0497i	0.713044	−	0.518057i	0.884154	+	0.467195i	$0.154735\pi$
$542$	−4.86990	+	14.9880i	−0.209180	+	0.643791i
$543$	10.4607			0.448910
$544$	−1.79898	+	5.53669i	−0.0771306	+	0.237384i
$545$	31.2283	+	12.4532i	1.33767	+	0.533438i
$546$	−0.857334	−	2.63860i	−0.0366905	−	0.112922i
$547$	5.74657	+	17.6861i	0.245705	+	0.756203i	0.995520	+	0.0945550i	$0.0301428\pi$
$547$	5.74657	+	17.6861i	0.245705	+	0.756203i	−0.749814	+	0.661648i	$0.769857\pi$
$548$	2.19951	+	1.59804i	0.0939585	+	0.0682648i
$549$	−15.1460			−0.646414
$550$	8.53537	+	1.12102i	0.363949	+	0.0478007i
$551$	9.39105			0.400072
$552$	0.524898	+	0.381361i	0.0223411	+	0.0162318i
$553$	−7.66201	−	23.5813i	−0.325822	−	1.00278i
$554$	7.00845	+	21.5698i	0.297760	+	0.916413i
$555$	0.736290	−	11.2602i	0.0312538	−	0.477969i
$556$	−4.47682	+	13.7782i	−0.189860	+	0.584328i
$557$	4.12250			0.174676			0.0873379	−	0.996179i	$-0.472164\pi$
$557$	4.12250			0.174676			0.0873379	+	0.996179i	$0.472164\pi$
$558$	5.27337	−	16.2298i	0.223240	−	0.687061i
$559$	9.64496	−	7.00747i	0.407938	−	0.296384i
$560$	−5.43334	−	2.16671i	−0.229600	−	0.0915603i
$561$	−4.04925	−	2.94195i	−0.170959	−	0.124209i
$562$	15.3072	−	11.1213i	0.645695	−	0.469125i
$563$	13.9877	−	10.1626i	0.589509	−	0.428304i	−0.252630	−	0.967563i	$-0.581296\pi$
$563$	13.9877	−	10.1626i	0.589509	−	0.428304i	0.842140	+	0.539259i	$0.181296\pi$
$564$	−1.78275	−	1.29524i	−0.0750672	−	0.0545395i
$565$	15.2252	+	6.07154i	0.640531	+	0.255431i
$566$	−3.09163	+	2.24620i	−0.129951	+	0.0944149i
$567$	−5.51148	+	16.9626i	−0.231460	+	0.712362i
$568$	14.1450			0.593512
$569$	−12.2039	+	37.5599i	−0.511616	+	1.57459i	0.277741	+	0.960656i	$0.410414\pi$
$569$	−12.2039	+	37.5599i	−0.511616	+	1.57459i	−0.789356	+	0.613935i	$0.789586\pi$
$570$	−0.0728563	+	1.11421i	−0.00305162	+	0.0466689i
$571$	1.66713	+	5.13091i	0.0697674	+	0.214722i	0.979861	−	0.199681i	$-0.0639905\pi$
$571$	1.66713	+	5.13091i	0.0697674	+	0.214722i	−0.910094	+	0.414403i	$0.863991\pi$
$572$	−1.13001	−	3.47781i	−0.0472480	−	0.145414i
$573$	−6.83783	−	4.96797i	−0.285654	−	0.207540i
$574$	3.95260			0.164978
$575$	5.70829	−	3.10163i	0.238052	−	0.129347i
$576$	−2.75065			−0.114610
$577$	−8.50681	−	6.18056i	−0.354143	−	0.257300i	0.396462	−	0.918051i	$-0.370238\pi$
$577$	−8.50681	−	6.18056i	−0.354143	−	0.257300i	−0.750605	+	0.660751i	$0.770238\pi$
$578$	−5.21969	−	16.0645i	−0.217110	−	0.668197i
$579$	−1.92793	−	5.93355i	−0.0801219	−	0.246590i
$580$	−19.5053	−	7.77834i	−0.809913	−	0.322978i
$581$	4.54195	−	13.9787i	0.188432	−	0.579933i
$582$	−8.53313			−0.353709
$583$	0.936903	−	2.88349i	0.0388026	−	0.119422i
$584$	−4.10763	+	2.98436i	−0.169975	+	0.123494i
$585$	−12.6609	+	3.21753i	−0.523462	+	0.133028i
$586$	12.3877	+	9.00020i	0.511732	+	0.371795i
$587$	23.5588	−	17.1165i	0.972378	−	0.706474i	0.0163854	−	0.999866i	$-0.494784\pi$
$587$	23.5588	−	17.1165i	0.972378	−	0.706474i	0.955992	+	0.293392i	$0.0947841\pi$
$588$	0.0633605	−	0.0460341i	0.00261294	−	0.00189841i
$589$	5.01913	+	3.64661i	0.206810	+	0.150256i
$590$	11.9582	+	18.9461i	0.492310	+	0.779997i
$591$	2.87449	−	2.08844i	0.118241	−	0.0859068i
$592$	−3.12294	+	9.61142i	−0.128352	+	0.395027i
$593$	−30.0825			−1.23534			−0.617671	−	0.786437i	$-0.711924\pi$
$593$	−30.0825			−1.23534			−0.617671	+	0.786437i	$0.711924\pi$
$594$	1.52782	−	4.70214i	0.0626872	−	0.192931i
$595$	33.0041	−	8.38738i	1.35303	−	0.343849i
$596$	4.11588	+	12.6674i	0.168593	+	0.518876i
$597$	−0.759684	−	2.33807i	−0.0310918	−	0.0956907i
$598$	−2.23255	−	1.62204i	−0.0912957	−	0.0663302i
$599$	−12.1568			−0.496712			−0.248356	−	0.968669i	$-0.579890\pi$
$599$	−12.1568			−0.496712			−0.248356	+	0.968669i	$0.579890\pi$
$600$	1.07419	−	2.25387i	0.0438535	−	0.0920138i
$601$	24.7291			1.00872			0.504362	−	0.863493i	$-0.331728\pi$
$601$	24.7291			1.00872			0.504362	+	0.863493i	$0.331728\pi$
$602$	−11.8794	−	8.63091i	−0.484170	−	0.351770i
$603$	3.52099	+	10.8365i	0.143386	+	0.441296i
$604$	1.95078	+	6.00389i	0.0793762	+	0.244295i
$605$	−11.4874	+	13.8165i	−0.467031	+	0.561720i
$606$	−1.45853	+	4.48889i	−0.0592486	+	0.182349i
$607$	−19.9097			−0.808109			−0.404054	−	0.914735i	$-0.632399\pi$
$607$	−19.9097			−0.808109			−0.404054	+	0.914735i	$0.632399\pi$
$608$	0.309017	−	0.951057i	0.0125323	−	0.0385704i
$609$	−9.92446	+	7.21054i	−0.402159	+	0.292186i
$610$	−7.87165	+	9.46760i	−0.318714	+	0.383332i
$611$	7.58256	+	5.50905i	0.306758	+	0.222872i
$612$	12.9550	−	9.41234i	0.523674	−	0.380471i
$613$	23.3778	−	16.9849i	0.944219	−	0.686015i	−0.00521357	−	0.999986i	$-0.501660\pi$
$613$	23.3778	−	16.9849i	0.944219	−	0.686015i	0.949433	+	0.313971i	$0.101660\pi$
$614$	12.8492	+	9.33547i	0.518551	+	0.376749i
$615$	−0.110083	+	1.68352i	−0.00443899	+	0.0678862i
$616$	−3.64378	+	2.64736i	−0.146812	+	0.106665i
$617$	0.825876	−	2.54179i	0.0332485	−	0.102328i	−0.933055	−	0.359734i	$-0.882868\pi$
$617$	0.825876	−	2.54179i	0.0332485	−	0.102328i	0.966304	+	0.257405i	$0.0828675\pi$
$618$	1.90572			0.0766591
$619$	−8.07537	+	24.8534i	−0.324576	+	0.998944i	0.647055	+	0.762443i	$0.276000\pi$
$619$	−8.07537	+	24.8534i	−0.324576	+	0.998944i	−0.971631	+	0.236500i	$0.924000\pi$
$620$	−7.40440	−	11.7313i	−0.297368	−	0.471138i
$621$	−1.15297	−	3.54846i	−0.0462669	−	0.142395i
$622$	2.24576	+	6.91173i	0.0900466	+	0.277135i
$623$	2.64027	+	1.91827i	0.105780	+	0.0768539i
$624$	−1.06057			−0.0424568
$625$	−15.7450	−	19.4189i	−0.629800	−	0.776758i
$626$	5.07867			0.202985
$627$	0.695553	+	0.505349i	0.0277777	+	0.0201817i
$628$	−0.909191	−	2.79820i	−0.0362807	−	0.111660i
$629$	−18.1806	−	55.9541i	−0.724907	−	2.23103i
$630$	8.58780	+	13.6062i	0.342146	+	0.542084i
$631$	−12.5494	+	38.6230i	−0.499582	+	1.53756i	0.310110	+	0.950701i	$0.399634\pi$
$631$	−12.5494	+	38.6230i	−0.499582	+	1.53756i	−0.809692	+	0.586855i	$0.800366\pi$
$632$	−9.47834			−0.377028
$633$	2.28711	−	7.03901i	0.0909045	−	0.279775i
$634$	21.4815	−	15.6072i	0.853139	−	0.619842i
$635$	−0.853426	+	13.0516i	−0.0338672	+	0.517937i
$636$	−0.711394	−	0.516858i	−0.0282086	−	0.0204948i
$637$	−0.269492	+	0.195797i	−0.0106776	+	0.00775776i
$638$	−13.0809	+	9.50384i	−0.517878	+	0.376261i
$639$	−31.4772	−	22.8695i	−1.24522	−	0.904704i
$640$	−1.42956	+	1.71940i	−0.0565085	+	0.0679654i
$641$	2.83489	−	2.05967i	0.111971	−	0.0813520i	−0.530390	−	0.847753i	$-0.677955\pi$
$641$	2.83489	−	2.05967i	0.111971	−	0.0813520i	0.642362	+	0.766402i	$0.277955\pi$
$642$	1.10077	−	3.38782i	0.0434439	−	0.133707i
$643$	−36.6968			−1.44718			−0.723591	−	0.690229i	$-0.757510\pi$
$643$	−36.6968			−1.44718			−0.723591	+	0.690229i	$0.757510\pi$
$644$	−1.05032	+	3.23255i	−0.0413884	+	0.127380i
$645$	4.00701	−	4.81941i	0.157776	−	0.189764i
$646$	1.79898	+	5.53669i	0.0707799	+	0.217838i
$647$	−0.444747	−	1.36879i	−0.0174848	−	0.0538127i	0.941933	−	0.335800i	$-0.109007\pi$
$647$	−0.444747	−	1.36879i	−0.0174848	−	0.0538127i	−0.959418	+	0.281987i	$0.909007\pi$
$648$	5.51588	+	4.00752i	0.216684	+	0.157430i
$649$	17.2509			0.677157
$650$	−4.56884	+	9.58639i	−0.179205	+	0.376009i
$651$	−8.10412			−0.317626
$652$	9.46591	+	6.87739i	0.370714	+	0.269339i
$653$	−11.7058	−	36.0269i	−0.458085	−	1.40984i	−0.867474	−	0.497482i	$-0.834258\pi$
$653$	−11.7058	−	36.0269i	−0.458085	−	1.40984i	0.409389	−	0.912360i	$-0.365742\pi$
$654$	−2.32006	−	7.14040i	−0.0907214	−	0.279212i
$655$	−41.8597	+	10.6379i	−1.63559	+	0.415656i
$656$	0.466913	−	1.43701i	0.0182299	−	0.0561059i
$657$	13.9659			0.544861
$658$	3.56727	−	10.9789i	0.139067	−	0.428003i
$659$	−29.7595	+	21.6216i	−1.15927	+	0.842257i	−0.989685	−	0.143259i	$-0.954242\pi$
$659$	−29.7595	+	21.6216i	−1.15927	+	0.842257i	−0.169582	+	0.985516i	$0.554242\pi$
$660$	−1.02610	−	1.62572i	−0.0399411	−	0.0632811i
$661$	−11.0131	−	8.00145i	−0.428358	−	0.311220i	0.352634	−	0.935761i	$-0.385286\pi$
$661$	−11.0131	−	8.00145i	−0.428358	−	0.311220i	−0.780992	+	0.624541i	$0.785286\pi$
$662$	−10.9666	+	7.96771i	−0.426230	+	0.309674i
$663$	4.99506	−	3.62913i	0.193992	−	0.140944i
$664$	−4.54558	−	3.30256i	−0.176403	−	0.128164i
$665$	−5.66922	+	1.44073i	−0.219843	+	0.0558691i
$666$	22.4892	−	16.3394i	0.871439	−	0.633137i
$667$	−3.77057	+	11.6046i	−0.145997	+	0.449333i
$668$	−13.8363			−0.535342
$669$	−1.34251	+	4.13183i	−0.0519045	+	0.159746i
$670$	8.60371	+	3.43100i	0.332390	+	0.132551i
$671$	2.92962	+	9.01643i	0.113097	+	0.348075i
$672$	0.403661	+	1.24234i	0.0155716	+	0.0479244i
$673$	4.70903	+	3.42131i	0.181520	+	0.131882i	0.674835	−	0.737969i	$-0.264215\pi$
$673$	4.70903	+	3.42131i	0.181520	+	0.131882i	−0.493315	+	0.869851i	$0.664215\pi$
$674$	−6.83560			−0.263298
$675$	−12.6159	+	6.85493i	−0.485587	+	0.263846i
$676$	−8.48907			−0.326503
$677$	33.9783	+	24.6867i	1.30589	+	0.948787i	0.999995	−	0.00327670i	$-0.00104301\pi$
$677$	33.9783	+	24.6867i	1.30589	+	0.948787i	0.305899	+	0.952064i	$0.401043\pi$
$678$	−1.13114	−	3.48128i	−0.0434410	−	0.133698i
$679$	−13.8138	−	42.5144i	−0.530124	−	1.63155i
$680$	0.849385	−	12.9898i	0.0325724	−	0.498136i
$681$	−2.79056	+	8.58846i	−0.106934	+	0.329111i
$682$	−10.6816			−0.409020
$683$	1.98273	−	6.10220i	0.0758669	−	0.233494i	−0.905930	−	0.423427i	$-0.860827\pi$
$683$	1.98273	−	6.10220i	0.0758669	−	0.233494i	0.981797	+	0.189933i	$0.0608270\pi$
$684$	−2.22532	+	1.61679i	−0.0850873	+	0.0618195i
$685$	−5.64686	−	2.25186i	−0.215755	−	0.0860391i
$686$	15.1463	+	11.0044i	0.578289	+	0.420152i
$687$	−6.71844	+	4.88123i	−0.256324	+	0.186231i
$688$	−4.54117	+	3.29935i	−0.173130	+	0.125787i
$689$	3.02578	+	2.19836i	0.115273	+	0.0837507i
$690$	−1.34758	−	0.537390i	−0.0513016	−	0.0204581i
$691$	−8.24837	+	5.99279i	−0.313783	+	0.227977i	−0.733518	−	0.679670i	$-0.762123\pi$
$691$	−8.24837	+	5.99279i	−0.313783	+	0.227977i	0.419735	+	0.907647i	$0.362123\pi$
$692$	−3.84581	+	11.8362i	−0.146196	+	0.449944i
$693$	12.3888			0.470612
$694$	5.40466	−	16.6338i	0.205158	−	0.631411i
$695$	2.11372	−	32.3256i	0.0801781	−	1.22618i
$696$	1.44912	+	4.45992i	0.0549286	+	0.169053i
$697$	2.71819	+	8.36574i	0.102959	+	0.316875i
$698$	−13.5026	−	9.81022i	−0.511081	−	0.371322i
$699$	−6.92062			−0.261762
$700$	12.9683	+	1.70325i	0.490157	+	0.0643767i
$701$	−29.8902			−1.12894			−0.564469	−	0.825454i	$-0.690919\pi$
$701$	−29.8902			−1.12894			−0.564469	+	0.825454i	$0.690919\pi$
$702$	4.93417	+	3.58488i	0.186228	+	0.135303i
$703$	3.12294	+	9.61142i	0.117784	+	0.362502i
$704$	0.532045	+	1.63747i	0.0200522	+	0.0617143i
$705$	4.57689	+	1.82518i	0.172376	+	0.0687401i
$706$	−8.46843	+	26.0632i	−0.318714	+	0.980900i
$707$	−24.7260			−0.929918
$708$	1.54609	−	4.75837i	0.0581056	−	0.178831i
$709$	32.4793	−	23.5976i	1.21979	−	0.886226i	0.223703	−	0.974657i	$-0.428185\pi$
$709$	32.4793	−	23.5976i	1.21979	−	0.886226i	0.996082	+	0.0884315i	$0.0281854\pi$
$710$	−30.6548	+	7.79036i	−1.15045	+	0.292367i
$711$	21.0923	+	15.3245i	0.791025	+	0.574713i
$712$	1.00930	−	0.733300i	0.0378251	−	0.0274816i
$713$	−6.52137	+	4.73806i	−0.244227	+	0.177442i
$714$	−6.15229	−	4.46990i	−0.230244	−	0.167282i
$715$	4.36433	+	6.91468i	0.163217	+	0.258595i
$716$	16.9302	−	12.3005i	0.632711	−	0.459691i
$717$	−4.04193	+	12.4398i	−0.150949	+	0.464573i
$718$	31.1970			1.16426
$719$	2.09228	−	6.43937i	0.0780289	−	0.240148i	−0.904432	−	0.426618i	$-0.859705\pi$
$719$	2.09228	−	6.43937i	0.0780289	−	0.240148i	0.982461	+	0.186470i	$0.0597048\pi$
$720$	5.96115	−	1.51492i	0.222159	−	0.0564577i
$721$	3.08505	+	9.49481i	0.114893	+	0.353605i
$722$	−0.309017	−	0.951057i	−0.0115004	−	0.0353947i
$723$	2.44347	+	1.77528i	0.0908735	+	0.0660234i
$724$	20.9485			0.778545
$725$	46.5554	+	6.11453i	1.72903	+	0.227088i
$726$	4.01261			0.148922
$727$	−8.70848	−	6.32708i	−0.322980	−	0.234659i	0.414466	−	0.910065i	$-0.363968\pi$
$727$	−8.70848	−	6.32708i	−0.322980	−	0.234659i	−0.737446	+	0.675406i	$0.763968\pi$
$728$	−1.71689	−	5.28406i	−0.0636323	−	0.195840i
$729$	−4.46595	−	13.7448i	−0.165406	−	0.509066i
$730$	7.25833	−	8.72993i	0.268643	−	0.323109i
$731$	10.0980	−	31.0785i	0.373489	−	1.14948i
$732$	2.74960			0.101628
$733$	−12.9201	+	39.7640i	−0.477215	+	1.46872i	0.365731	+	0.930721i	$0.380819\pi$
$733$	−12.9201	+	39.7640i	−0.477215	+	1.46872i	−0.842946	+	0.537997i	$0.819181\pi$
$734$	1.12396	−	0.816605i	0.0414861	−	0.0301414i
$735$	−0.111960	+	0.134660i	−0.00412972	+	0.00496701i
$736$	1.05116	+	0.763711i	0.0387462	+	0.0281508i
$737$	5.76994	−	4.19211i	0.212538	−	0.154418i
$738$	−3.36238	+	2.44291i	−0.123771	+	0.0899248i
$739$	−25.4998	−	18.5267i	−0.938025	−	0.681515i	0.00991959	−	0.999951i	$-0.496842\pi$
$739$	−25.4998	−	18.5267i	−0.938025	−	0.681515i	−0.947944	+	0.318436i	$0.896842\pi$
$740$	1.47449	−	22.5497i	0.0542034	−	0.828942i
$741$	−0.858019	+	0.623388i	−0.0315201	+	0.0229007i
$742$	1.42350	−	4.38108i	0.0522583	−	0.160834i
$743$	22.9527			0.842051			0.421026	−	0.907049i	$-0.361670\pi$
$743$	22.9527			0.842051			0.421026	+	0.907049i	$0.361670\pi$
$744$	−0.957326	+	2.94635i	−0.0350973	+	0.108018i
$745$	−15.8964	−	25.1857i	−0.582400	−	0.922732i
$746$	−4.81852	−	14.8299i	−0.176418	−	0.542960i
$747$	4.77583	+	14.6985i	0.174738	+	0.537790i
$748$	−8.10901	−	5.89154i	−0.296495	−	0.215416i
$749$	18.6610			0.681859
$750$	−1.08664	+	5.47615i	−0.0396785	+	0.199961i
$751$	−17.1525			−0.625904			−0.312952	−	0.949769i	$-0.601318\pi$
$751$	−17.1525			−0.625904			−0.312952	+	0.949769i	$0.601318\pi$
$752$	−3.57012	−	2.59385i	−0.130189	−	0.0945878i
$753$	−2.16057	−	6.64956i	−0.0787356	−	0.242323i
$754$	−6.16353	−	18.9694i	−0.224463	−	0.690825i
$755$	−7.53434	−	11.9371i	−0.274203	−	0.434436i
$756$	2.32132	−	7.14427i	0.0844254	−	0.259835i
$757$	−44.1010			−1.60288			−0.801439	−	0.598077i	$-0.795932\pi$
$757$	−44.1010			−1.60288			−0.801439	+	0.598077i	$0.795932\pi$
$758$	−9.74712	+	29.9986i	−0.354031	+	1.08960i
$759$	−0.903734	+	0.656602i	−0.0328035	+	0.0238331i
$760$	−0.145902	+	2.23130i	−0.00529241	+	0.0809379i
$761$	22.8825	+	16.6251i	0.829490	+	0.602660i	0.919415	−	0.393289i	$-0.128663\pi$
$761$	22.8825	+	16.6251i	0.829490	+	0.602660i	−0.0899247	+	0.995949i	$0.528663\pi$
$762$	2.36303	−	1.71684i	0.0856036	−	0.0621946i
$763$	31.8197	−	23.1183i	1.15195	−	0.836940i
$764$	−13.6934	−	9.94884i	−0.495410	−	0.359937i
$765$	−22.8919	+	27.5332i	−0.827660	+	0.995465i
$766$	0.863858	−	0.627630i	0.0312125	−	0.0226772i
$767$	−6.57599	+	20.2388i	−0.237445	+	0.730781i
$768$	0.499352			0.0180188
$769$	−7.72720	+	23.7819i	−0.278650	+	0.857596i	0.709581	+	0.704624i	$0.248884\pi$
$769$	−7.72720	+	23.7819i	−0.278650	+	0.857596i	−0.988231	+	0.152972i	$0.951116\pi$
$770$	6.43870	−	7.74412i	0.232035	−	0.279079i
$771$	0.576707	+	1.77492i	0.0207696	+	0.0639222i
$772$	−3.86086	−	11.8825i	−0.138955	−	0.427661i
$773$	29.0602	+	21.1135i	1.04522	+	0.759400i	0.971299	−	0.237864i	$-0.0764471\pi$
$773$	29.0602	+	21.1135i	1.04522	+	0.759400i	0.0739260	+	0.997264i	$0.476447\pi$
$774$	15.4399			0.554976
$775$	22.5077	+	21.3458i	0.808499	+	0.766763i
$776$	−17.0884			−0.613438
$777$	−10.6801	−	7.75952i	−0.383145	−	0.278371i
$778$	−9.15088	−	28.1635i	−0.328075	−	1.00971i
$779$	−0.466913	−	1.43701i	−0.0167289	−	0.0514863i
$780$	2.29845	−	0.584109i	0.0822976	−	0.0209144i
$781$	−7.52579	+	23.1620i	−0.269294	+	0.828801i
$782$	−7.56405			−0.270490
$783$	8.33336	−	25.6474i	0.297810	−	0.916564i
$784$	0.126886	−	0.0921878i	0.00453163	−	0.00329242i
$785$	3.51149	+	5.56348i	0.125331	+	0.198569i
$786$	7.80306	+	5.66925i	0.278326	+	0.202216i
$787$	4.97781	−	3.61659i	0.177440	−	0.128918i	−0.495520	−	0.868596i	$-0.665023\pi$
$787$	4.97781	−	3.61659i	0.177440	−	0.128918i	0.672960	+	0.739679i	$0.265023\pi$
$788$	5.75644	−	4.18230i	0.205065	−	0.148988i
$789$	4.89430	+	3.55591i	0.174242	+	0.126594i
$790$	20.5413	−	5.22019i	0.730826	−	0.185726i
$791$	15.5136	−	11.2713i	0.551599	−	0.400760i
$792$	1.46347	−	4.50409i	0.0520021	−	0.160046i
$793$	−11.6949			−0.415297
$794$	8.92911	−	27.4810i	0.316882	−	0.975264i
$795$	1.82638	+	0.728325i	0.0647750	+	0.0258310i
$796$	−1.52134	−	4.68220i	−0.0539225	−	0.165956i
$797$	−1.20617	−	3.71221i	−0.0427247	−	0.131493i	0.927419	−	0.374024i	$-0.122022\pi$
$797$	−1.20617	−	3.71221i	−0.0427247	−	0.131493i	−0.970144	+	0.242531i	$0.922022\pi$
$798$	1.05680	+	0.767810i	0.0374103	+	0.0271802i
$799$	25.6903			0.908858
$800$	2.15116	−	4.51359i	0.0760551	−	0.159580i
$801$	−3.43161			−0.121250
$802$	17.6339	+	12.8118i	0.622676	+	0.452400i
$803$	−2.70136	−	8.31392i	−0.0953288	−	0.293392i
$804$	−0.639200	−	1.96725i	−0.0225428	−	0.0693797i
$805$	0.495906	−	7.58398i	0.0174784	−	0.267300i
$806$	4.07180	−	12.5317i	0.143423	−	0.441411i
$807$	0.785095			0.0276367
$808$	−2.92084	+	8.98943i	−0.102755	+	0.316247i
$809$	−8.28726	+	6.02104i	−0.291364	+	0.211689i	−0.723859	−	0.689948i	$-0.757633\pi$
$809$	−8.28726	+	6.02104i	−0.291364	+	0.211689i	0.432495	+	0.901637i	$0.357633\pi$
$810$	−14.1611	−	5.64716i	−0.497569	−	0.198421i
$811$	15.3500	+	11.1525i	0.539012	+	0.391615i	0.823718	−	0.566999i	$-0.191896\pi$
$811$	15.3500	+	11.1525i	0.539012	+	0.391615i	−0.284706	+	0.958615i	$0.591896\pi$
$812$	−19.8747	+	14.4398i	−0.697465	+	0.506738i
$813$	−6.36652	+	4.62555i	−0.223284	+	0.162225i
$814$	−14.0768	−	10.2274i	−0.493393	−	0.358471i
$815$	−24.3021	−	9.69120i	−0.851264	−	0.339468i
$816$	−2.35184	+	1.70871i	−0.0823309	+	0.0598169i
$817$	−1.73457	+	5.33846i	−0.0606850	+	0.186769i
$818$	−26.0202			−0.909776
$819$	−4.72257	+	14.5346i	−0.165020	+	0.507879i
$820$	−0.220452	+	3.37142i	−0.00769853	+	0.117735i
$821$	−12.4982	−	38.4656i	−0.436191	−	1.34246i	−0.891861	−	0.452310i	$-0.850600\pi$
$821$	−12.4982	−	38.4656i	−0.436191	−	1.34246i	0.455669	−	0.890149i	$-0.349400\pi$
$822$	0.419525	+	1.29116i	0.0146326	+	0.0450345i
$823$	−19.9911	−	14.5244i	−0.696847	−	0.506289i	0.182057	−	0.983288i	$-0.441725\pi$
$823$	−19.9911	−	14.5244i	−0.696847	−	0.506289i	−0.878904	+	0.476999i	$0.841725\pi$
$824$	3.81638			0.132950
$825$	3.11912	+	2.95811i	0.108594	+	0.102988i
$826$	26.2104			0.911977
$827$	−44.9835	−	32.6824i	−1.56423	−	1.13648i	−0.932432	−	0.361345i	$-0.882318\pi$
$827$	−44.9835	−	32.6824i	−1.56423	−	1.13648i	−0.631797	−	0.775134i	$-0.717682\pi$
$828$	−1.10440	−	3.39901i	−0.0383807	−	0.118124i
$829$	8.01057	+	24.6540i	0.278219	+	0.856269i	0.988350	+	0.152199i	$0.0486356\pi$
$829$	8.01057	+	24.6540i	0.278219	+	0.856269i	−0.710131	+	0.704069i	$0.751364\pi$
$830$	11.6700	+	4.65376i	0.405071	+	0.161534i
$831$	−3.49968	+	10.7709i	−0.121403	+	0.373639i
$832$	−2.12389			−0.0736328
$833$	−0.282150	+	0.868370i	−0.00977593	+	0.0300872i
$834$	−5.85264	+	4.25219i	−0.202660	+	0.147241i
$835$	29.9857	−	7.62033i	1.03770	−	0.263712i
$836$	1.39291	+	1.01201i	0.0481749	+	0.0350011i
$837$	14.4129	−	10.4716i	0.498183	−	0.361951i
$838$	−23.8981	+	17.3630i	−0.825546	+	0.599794i
$839$	−21.3958	−	15.5450i	−0.738665	−	0.536672i	0.153628	−	0.988129i	$-0.450904\pi$
$839$	−21.3958	−	15.5450i	−0.738665	−	0.536672i	−0.892293	+	0.451457i	$0.850904\pi$
$840$	−1.55903	−	2.47006i	−0.0537916	−	0.0852253i
$841$	−47.8872	+	34.7921i	−1.65128	+	1.19973i
$842$	−7.30192	+	22.4730i	−0.251641	+	0.774470i
$843$	9.44810			0.325410
$844$	4.58016	−	14.0963i	0.157656	−	0.485214i
$845$	18.3974	−	4.67535i	0.632888	−	0.160837i
$846$	3.75096	+	11.5443i	0.128961	+	0.396900i
$847$	6.49577	+	19.9919i	0.223197	+	0.686931i
$848$	−1.42464	−	1.03506i	−0.0489222	−	0.0355441i
$849$	−1.90826			−0.0654912
$850$	5.31336	+	28.6190i	0.182247	+	0.981625i
$851$	−13.1308			−0.450119
$852$	5.71436	+	4.15173i	0.195771	+	0.142236i
$853$	1.62674	+	5.00660i	0.0556986	+	0.171423i	0.975036	−	0.222048i	$-0.0712742\pi$
$853$	1.62674	+	5.00660i	0.0556986	+	0.171423i	−0.919337	+	0.393471i	$0.871274\pi$
$854$	4.45116	+	13.6993i	0.152315	+	0.468779i
$855$	3.93223	−	4.72947i	0.134479	−	0.161745i
$856$	2.20440	−	6.78443i	0.0753447	−	0.231887i
$857$	−42.2384			−1.44284			−0.721418	−	0.692500i	$-0.756509\pi$
$857$	−42.2384			−1.44284			−0.721418	+	0.692500i	$0.756509\pi$
$858$	0.564271	−	1.73665i	0.0192639	−	0.0592882i
$859$	25.3916	−	18.4480i	0.866349	−	0.629439i	−0.0632560	−	0.997997i	$-0.520148\pi$
$859$	25.3916	−	18.4480i	0.866349	−	0.629439i	0.929605	+	0.368558i	$0.120148\pi$
$860$	8.02441	−	9.65134i	0.273630	−	0.329108i
$861$	1.59679	+	1.16013i	0.0544183	+	0.0395372i
$862$	8.43227	−	6.12640i	0.287204	−	0.208666i
$863$	−31.6640	+	23.0052i	−1.07785	+	0.783107i	−0.977308	−	0.211825i	$-0.932059\pi$
$863$	−31.6640	+	23.0052i	−1.07785	+	0.783107i	−0.100547	+	0.994932i	$0.532059\pi$
$864$	−2.32317	−	1.68788i	−0.0790359	−	0.0574229i
$865$	1.81579	−	27.7692i	0.0617387	−	0.944181i
$866$	−17.2302	+	12.5185i	−0.585508	+	0.425396i
$867$	2.60646	−	8.02186i	0.0885200	−	0.272437i
$868$	−16.2293			−0.550858
$869$	5.04290	−	15.5205i	0.171069	−	0.526496i
$870$	−5.59680	−	8.86736i	−0.189749	−	0.300632i
$871$	2.71871	+	8.36733i	0.0921199	+	0.283516i
$872$	−4.64613	−	14.2993i	−0.157338	−	0.484236i
$873$	38.0272	+	27.6284i	1.28703	+	0.935079i
$874$	1.29930			0.0439496
$875$	−29.0428	+	3.45107i	−0.981826	+	0.116667i
$876$	−2.53536			−0.0856619
$877$	34.6937	+	25.2064i	1.17152	+	0.851160i	0.991190	−	0.132446i	$-0.0422830\pi$
$877$	34.6937	+	25.2064i	1.17152	+	0.851160i	0.180331	+	0.983606i	$0.442283\pi$
$878$	−3.09928	−	9.53862i	−0.104596	−	0.321913i
$879$	2.36278	+	7.27188i	0.0796944	+	0.245274i
$880$	−2.05487	−	3.25566i	−0.0692697	−	0.109748i
$881$	−0.804600	+	2.47630i	−0.0271077	+	0.0834288i	−0.963695	−	0.267005i	$-0.913966\pi$
$881$	−0.804600	+	2.47630i	−0.0271077	+	0.0834288i	0.936587	+	0.350434i	$0.113966\pi$
$882$	−0.431409			−0.0145263
$883$	15.5516	−	47.8628i	0.523352	−	1.61071i	−0.244200	−	0.969725i	$-0.578525\pi$
$883$	15.5516	−	47.8628i	0.523352	−	1.61071i	0.767552	−	0.640987i	$-0.221475\pi$
$884$	10.0031	−	7.26767i	0.336441	−	0.244438i
$885$	−0.729983	+	11.1638i	−0.0245381	+	0.375266i
$886$	27.1897	+	19.7545i	0.913457	+	0.663665i
$887$	−38.6882	+	28.1086i	−1.29902	+	0.943795i	−0.999946	−	0.0104335i	$-0.996679\pi$
$887$	−38.6882	+	28.1086i	−1.29902	+	0.943795i	−0.299077	+	0.954229i	$0.596679\pi$
$888$	−4.08268	+	2.96624i	−0.137006	+	0.0995406i
$889$	12.3792	+	8.99399i	0.415184	+	0.301649i
$890$	−1.78347	+	2.14506i	−0.0597821	+	0.0719027i
$891$	−9.49689	+	6.89989i	−0.318158	+	0.231155i
$892$	−2.68851	+	8.27438i	−0.0900179	+	0.277047i
$893$	−4.41291			−0.147673
$894$	−2.05527	+	6.32548i	−0.0687386	+	0.211556i
$895$	−29.9163	+	35.9817i	−0.999991	+	1.20274i
$896$	0.808371	+	2.48791i	0.0270058	+	0.0831152i
$897$	−0.425826	−	1.31056i	−0.0142179	−	0.0437583i
$898$	12.4850	+	9.07086i	0.416629	+	0.302699i
$899$	−58.2620			−1.94315
$900$	−12.0846	+	6.56621i	−0.402819	+	0.218874i
$901$	10.2516			0.341529
$902$	2.10464	+	1.52911i	0.0700768	+	0.0509138i
$903$	−2.26583	−	6.97350i	−0.0754021	−	0.232064i
$904$	−2.26521	−	6.97160i	−0.0753397	−	0.231872i
$905$	−45.3992	+	11.5374i	−1.50912	+	0.383515i
$906$	−0.974126	+	2.99805i	−0.0323632	+	0.0996036i
$907$	−15.2263			−0.505580			−0.252790	−	0.967521i	$-0.581348\pi$
$907$	−15.2263			−0.505580			−0.252790	+	0.967521i	$0.581348\pi$
$908$	−5.58837	+	17.1992i	−0.185456	+	0.570776i
$909$	21.0338	−	15.2820i	0.697648	−	0.506871i
$910$	6.63102	+	10.5059i	0.219816	+	0.348268i
$911$	−1.01436	−	0.736974i	−0.0336072	−	0.0244170i	0.570855	−	0.821051i	$-0.306612\pi$
$911$	−1.01436	−	0.736974i	−0.0336072	−	0.0244170i	−0.604462	+	0.796634i	$0.706612\pi$
$912$	0.403984	−	0.293512i	0.0133772	−	0.00971914i
$913$	7.82628	−	5.68612i	0.259012	−	0.188183i
$914$	23.6276	+	17.1665i	0.781532	+	0.567817i
$915$	−5.95887	+	1.51434i	−0.196994	+	0.0500625i
$916$	−13.4543	+	9.77514i	−0.444543	+	0.322980i
$917$	−15.6139	+	48.0546i	−0.515616	+	1.58690i
$918$	16.7173			0.551755
$919$	−13.2053	+	40.6417i	−0.435603	+	1.34065i	0.456865	+	0.889536i	$0.348972\pi$
$919$	−13.2053	+	40.6417i	−0.435603	+	1.34065i	−0.892468	+	0.451111i	$0.851028\pi$
$920$	−2.69866	−	1.07618i	−0.0889723	−	0.0354805i
$921$	2.45079	+	7.54277i	0.0807564	+	0.248543i
$922$	−4.12230	−	12.6871i	−0.135761	−	0.417829i
$923$	−24.3049	−	17.6585i	−0.800006	−	0.581238i
$924$	−2.24906			−0.0739886
$925$	9.22373	+	49.6813i	0.303274	+	1.63351i
$926$	−3.10204			−0.101939
$927$	−8.49267	−	6.17028i	−0.278936	−	0.202659i
$928$	2.90199	+	8.93142i	0.0952626	+	0.293188i
$929$	5.02925	+	15.4784i	0.165004	+	0.507831i	0.999037	−	0.0438844i	$-0.0139733\pi$
$929$	5.02925	+	15.4784i	0.165004	+	0.507831i	−0.834032	+	0.551716i	$0.813973\pi$
$930$	0.452000	−	6.91252i	0.0148217	−	0.226670i
$931$	0.0484660	−	0.149163i	0.00158841	−	0.00488862i
$932$	−13.8592			−0.453974
$933$	−1.12142	+	3.45138i	−0.0367137	+	0.112993i
$934$	−7.49466	+	5.44519i	−0.245233	+	0.178172i
$935$	20.8184	+	8.30200i	0.680836	+	0.271504i
$936$	4.72635	+	3.43389i	0.154485	+	0.112240i
$937$	−29.6619	+	21.5506i	−0.969012	+	0.704029i	−0.955226	−	0.295876i	$-0.904388\pi$
$937$	−29.6619	+	21.5506i	−0.969012	+	0.704029i	−0.0137862	+	0.999905i	$0.504388\pi$
$938$	8.76665	−	6.36934i	0.286241	−	0.207966i
$939$	2.05170	+	1.49065i	0.0669548	+	0.0486455i
$940$	9.16566	+	3.65509i	0.298951	+	0.119216i
$941$	9.66713	−	7.02358i	0.315140	−	0.228962i	−0.418959	−	0.908005i	$-0.637605\pi$
$941$	9.66713	−	7.02358i	0.315140	−	0.228962i	0.734099	+	0.679043i	$0.237605\pi$
$942$	0.454006	−	1.39729i	0.0147923	−	0.0455261i
$943$	1.96320			0.0639306
$944$	3.09619	−	9.52910i	0.100772	−	0.310146i
$945$	−1.09600	+	16.7614i	−0.0356530	+	0.545248i
$946$	−2.98647	−	9.19141i	−0.0970985	−	0.298839i
$947$	−7.50875	−	23.1096i	−0.244002	−	0.750960i	−0.995799	−	0.0915656i	$-0.970813\pi$
$947$	−7.50875	−	23.1096i	−0.244002	−	0.750960i	0.751797	−	0.659394i	$-0.229187\pi$
$948$	−3.82910	−	2.78200i	−0.124363	−	0.0903552i
$949$	10.7837			0.350052
$950$	−0.912694	−	4.91599i	−0.0296117	−	0.159496i
$951$	13.2591			0.429955
$952$	−12.3205	−	8.95140i	−0.399311	−	0.290117i
$953$	2.24857	+	6.92040i	0.0728384	+	0.224174i	0.980848	−	0.194777i	$-0.0623982\pi$
$953$	2.24857	+	6.92040i	0.0728384	+	0.224174i	−0.908009	+	0.418950i	$0.862398\pi$
$954$	1.49680	+	4.60668i	0.0484607	+	0.149147i
$955$	35.1554	+	14.0193i	1.13760	+	0.453654i
$956$	−8.09436	+	24.9119i	−0.261790	+	0.805708i
$957$	−8.07397			−0.260994
$958$	8.15934	−	25.1119i	0.263616	−	0.811328i
$959$	−5.75380	+	4.18038i	−0.185800	+	0.134991i
$960$	−1.08219	+	0.275018i	−0.0349274	+	0.00887616i
$961$	−6.05911	−	4.40220i	−0.195455	−	0.142007i
$962$	17.3649	−	12.6163i	0.559866	−	0.406767i
$963$	−15.8745	+	11.5335i	−0.511548	+	0.371662i
$964$	4.89327	+	3.55517i	0.157602	+	0.114504i
$965$	14.9115	+	23.6252i	0.480017	+	0.760521i
$966$	−1.37310	+	0.997618i	−0.0441789	+	0.0320978i
$967$	−5.60867	+	17.2617i	−0.180363	+	0.555099i	−0.999838	−	0.0180159i	$-0.994265\pi$
$967$	−5.60867	+	17.2617i	−0.180363	+	0.555099i	0.819475	+	0.573115i	$0.194265\pi$
$968$	8.03563			0.258275
$969$	−0.898324	+	2.76476i	−0.0288583	+	0.0888168i
$970$	37.0337	−	9.41143i	1.18908	−	0.302183i
$971$	6.60467	+	20.3271i	0.211954	+	0.652327i	0.999356	+	0.0358873i	$0.0114257\pi$
$971$	6.60467	+	20.3271i	0.211954	+	0.652327i	−0.787402	+	0.616440i	$0.788574\pi$
$972$	3.71419	+	11.4311i	0.119133	+	0.366653i
$973$	−30.6601	−	22.2759i	−0.982918	−	0.714132i
$974$	35.5882			1.14032
$975$	−4.65946	+	2.53174i	−0.149222	+	0.0810805i
$976$	5.50633			0.176253
$977$	−2.85512	−	2.07437i	−0.0913434	−	0.0663649i	0.541176	−	0.840909i	$-0.317979\pi$
$977$	−2.85512	−	2.07437i	−0.0913434	−	0.0663649i	−0.632520	+	0.774544i	$0.717979\pi$
$978$	1.80548	+	5.55671i	0.0577330	+	0.177684i
$979$	0.663760	+	2.04284i	0.0212139	+	0.0652896i
$980$	−0.224212	+	0.269670i	−0.00716218	+	0.00861428i
$981$	−12.7799	+	39.3324i	−0.408030	+	1.25579i
$982$	42.7664			1.36473
$983$	−14.5922	+	44.9101i	−0.465418	+	1.43241i	0.393039	+	0.919522i	$0.371424\pi$
$983$	−14.5922	+	44.9101i	−0.465418	+	1.43241i	−0.858456	+	0.512886i	$0.828576\pi$
$984$	0.610405	−	0.443485i	0.0194590	−	0.0141378i
$985$	−10.1718	+	12.2342i	−0.324102	+	0.389813i
$986$	−44.2299	−	32.1349i	−1.40857	−	1.02338i
$987$	4.66356	−	3.38828i	0.148443	−	0.107850i
$988$	−1.71827	+	1.24839i	−0.0546653	+	0.0397167i
$989$	−5.90035	−	4.28686i	−0.187620	−	0.136314i
$990$	−0.690974	+	10.5672i	−0.0219606	+	0.335847i
$991$	−8.72497	+	6.33906i	−0.277158	+	0.201367i	−0.717677	−	0.696376i	$-0.754794\pi$
$991$	−8.72497	+	6.33906i	−0.277158	+	0.201367i	0.440519	+	0.897743i	$0.354794\pi$
$992$	−1.91714	+	5.90034i	−0.0608692	+	0.187336i
$993$	−6.76895			−0.214806
$994$	−11.4344	+	35.1915i	−0.362678	+	1.11621i
$995$	5.87574	+	9.30931i	0.186274	+	0.295125i
$996$	−0.867003	−	2.66836i	−0.0274720	−	0.0845502i
$997$	11.7056	+	36.0261i	0.370720	+	1.14096i	0.946321	+	0.323228i	$0.104768\pi$
$997$	11.7056	+	36.0261i	0.370720	+	1.14096i	−0.575601	+	0.817730i	$0.695232\pi$
$998$	21.1892	+	15.3949i	0.670734	+	0.487317i
$999$	29.0205			0.918168

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.h.d.191.8	✓	44
25.11	even	5	inner	950.2.h.d.761.8	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.h.d.191.8	✓	44	1.1	even	1	trivial
950.2.h.d.761.8	yes	44	25.11	even	5	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.154308 + 0.474912i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.19349 - 1.89092i) q^{5} +(-0.154308 + 0.474912i) q^{6} -2.61594 q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.22532 - 1.61679i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.154308 + 0.474912i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.19349 - 1.89092i) q^{5} +(-0.154308 + 0.474912i) q^{6} -2.61594 q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.22532 - 1.61679i) q^{9} +(0.145902 - 2.23130i) q^{10} +(-1.39291 - 1.01201i) q^{11} +(-0.403984 + 0.293512i) q^{12} +(1.71827 - 1.24839i) q^{13} +(-2.11634 - 1.53761i) q^{14} +(0.713855 - 0.858587i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.79898 - 5.53669i) q^{17} +2.75065 q^{18} +(-0.309017 + 0.951057i) q^{19} +(1.42956 - 1.71940i) q^{20} +(-0.403661 - 1.24234i) q^{21} +(-0.532045 - 1.63747i) q^{22} +(-1.05116 - 0.763711i) q^{23} -0.499352 q^{24} +(-2.15116 + 4.51359i) q^{25} +2.12389 q^{26} +(2.32317 + 1.68788i) q^{27} +(-0.808371 - 2.48791i) q^{28} +(-2.90199 - 8.93142i) q^{29} +(1.08219 - 0.275018i) q^{30} +(1.91714 - 5.90034i) q^{31} -1.00000 q^{32} +(0.265678 - 0.817672i) q^{33} +(4.70979 - 3.42186i) q^{34} +(3.12210 + 4.94654i) q^{35} +(2.22532 + 1.61679i) q^{36} +(8.17597 - 5.94019i) q^{37} +(-0.809017 + 0.587785i) q^{38} +(0.858019 + 0.623388i) q^{39} +(2.16718 - 0.550750i) q^{40} +(-1.22240 + 0.888122i) q^{41} +(0.403661 - 1.24234i) q^{42} +5.61319 q^{43} +(0.532045 - 1.63747i) q^{44} +(-5.71312 - 2.27828i) q^{45} +(-0.401507 - 1.23571i) q^{46} +(1.36367 + 4.19693i) q^{47} +(-0.403984 - 0.293512i) q^{48} -0.156839 q^{49} +(-4.39335 + 2.38715i) q^{50} +2.90704 q^{51} +(1.71827 + 1.24839i) q^{52} +(0.544163 + 1.67476i) q^{53} +(0.887372 + 2.73105i) q^{54} +(-0.251204 + 3.84171i) q^{55} +(0.808371 - 2.48791i) q^{56} -0.499352 q^{57} +(2.90199 - 8.93142i) q^{58} +(-8.10594 + 5.88931i) q^{59} +(1.03716 + 0.413599i) q^{60} +(-4.45471 - 3.23654i) q^{61} +(5.01913 - 3.64661i) q^{62} +(-5.82131 + 4.22943i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-4.41135 - 1.75916i) q^{65} +(0.695553 - 0.505349i) q^{66} +(-1.28006 + 3.93962i) q^{67} +5.82162 q^{68} +(0.200493 - 0.617054i) q^{69} +(-0.381671 + 5.83696i) q^{70} +(-4.37105 - 13.4527i) q^{71} +(0.849997 + 2.61602i) q^{72} +(4.10763 + 2.98436i) q^{73} +10.1060 q^{74} +(-2.47550 - 0.325129i) q^{75} -1.00000 q^{76} +(3.64378 + 2.64736i) q^{77} +(0.327734 + 1.00866i) q^{78} +(2.92897 + 9.01443i) q^{79} +(2.07701 + 0.828271i) q^{80} +(2.10688 - 6.48431i) q^{81} -1.51096 q^{82} +(-1.73626 + 5.34365i) q^{83} +(1.05680 - 0.767810i) q^{84} +(-12.6165 + 3.20626i) q^{85} +(4.54117 + 3.29935i) q^{86} +(3.79384 - 2.75638i) q^{87} +(1.39291 - 1.01201i) q^{88} +(-1.00930 - 0.733300i) q^{89} +(-3.28287 - 5.20126i) q^{90} +(-4.49489 + 3.26573i) q^{91} +(0.401507 - 1.23571i) q^{92} +3.09797 q^{93} +(-1.36367 + 4.19693i) q^{94} +(2.16718 - 0.550750i) q^{95} +(-0.154308 - 0.474912i) q^{96} +(5.28061 + 16.2520i) q^{97} +(-0.126886 - 0.0921878i) q^{98} -4.73588 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 11 q^{5} + q^{6} - 10 q^{7} + 11 q^{8}+O(q^{10}) \) 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 11 * q^5 + q^6 - 10 * q^7 + 11 * q^8	\( 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 11 q^{5} + q^{6} - 10 q^{7} + 11 q^{8} - 4 q^{10} + 7 q^{11} + 4 q^{12} + 10 q^{13} - 5 q^{14} - 20 q^{15} - 11 q^{16} + 11 q^{17} - 50 q^{18} + 11 q^{19} + 4 q^{20} + 9 q^{21} + 8 q^{22} - 7 q^{23} + 6 q^{24} - 3 q^{25} + 10 q^{26} + 5 q^{27} - 20 q^{29} - 10 q^{30} - 11 q^{31} - 44 q^{32} - 2 q^{33} - q^{34} + 5 q^{35} + 43 q^{37} - 11 q^{38} - 33 q^{39} - 4 q^{40} - 32 q^{41} - 9 q^{42} - 74 q^{43} - 8 q^{44} + 10 q^{45} - 8 q^{46} - 19 q^{47} + 4 q^{48} + 54 q^{49} + 18 q^{50} + 34 q^{51} + 10 q^{52} + 23 q^{53} - 40 q^{54} + 2 q^{55} + 6 q^{57} + 20 q^{58} + 24 q^{59} - 35 q^{60} - 12 q^{61} + q^{62} - 44 q^{63} - 11 q^{64} + 43 q^{65} - 8 q^{66} + 35 q^{67} - 24 q^{68} + 29 q^{69} - 5 q^{70} - 2 q^{71} + 25 q^{72} + 22 q^{73} + 72 q^{74} + 7 q^{75} - 44 q^{76} - 3 q^{77} - 22 q^{78} - 19 q^{79} - q^{80} - 26 q^{81} - 58 q^{82} - 24 q^{83} - 21 q^{84} - 18 q^{85} - 6 q^{86} + 83 q^{87} - 7 q^{88} - 8 q^{89} + 60 q^{90} - 30 q^{91} + 8 q^{92} - 72 q^{93} + 19 q^{94} - 4 q^{95} + q^{96} - 16 q^{97} + q^{98} + 84 q^{99}+O(q^{100}) \) 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 11 * q^5 + q^6 - 10 * q^7 + 11 * q^8 - 4 * q^10 + 7 * q^11 + 4 * q^12 + 10 * q^13 - 5 * q^14 - 20 * q^15 - 11 * q^16 + 11 * q^17 - 50 * q^18 + 11 * q^19 + 4 * q^20 + 9 * q^21 + 8 * q^22 - 7 * q^23 + 6 * q^24 - 3 * q^25 + 10 * q^26 + 5 * q^27 - 20 * q^29 - 10 * q^30 - 11 * q^31 - 44 * q^32 - 2 * q^33 - q^34 + 5 * q^35 + 43 * q^37 - 11 * q^38 - 33 * q^39 - 4 * q^40 - 32 * q^41 - 9 * q^42 - 74 * q^43 - 8 * q^44 + 10 * q^45 - 8 * q^46 - 19 * q^47 + 4 * q^48 + 54 * q^49 + 18 * q^50 + 34 * q^51 + 10 * q^52 + 23 * q^53 - 40 * q^54 + 2 * q^55 + 6 * q^57 + 20 * q^58 + 24 * q^59 - 35 * q^60 - 12 * q^61 + q^62 - 44 * q^63 - 11 * q^64 + 43 * q^65 - 8 * q^66 + 35 * q^67 - 24 * q^68 + 29 * q^69 - 5 * q^70 - 2 * q^71 + 25 * q^72 + 22 * q^73 + 72 * q^74 + 7 * q^75 - 44 * q^76 - 3 * q^77 - 22 * q^78 - 19 * q^79 - q^80 - 26 * q^81 - 58 * q^82 - 24 * q^83 - 21 * q^84 - 18 * q^85 - 6 * q^86 + 83 * q^87 - 7 * q^88 - 8 * q^89 + 60 * q^90 - 30 * q^91 + 8 * q^92 - 72 * q^93 + 19 * q^94 - 4 * q^95 + q^96 - 16 * q^97 + q^98 + 84 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more