LMFDB - Embedded newform 92.2.h.a.7.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [92,2,Mod(7,92)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(92, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 19]))

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

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

chi := DirichletCharacter("92.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 92 = 2^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	92.h (of order $22$, degree $10$, 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:	$0.734623698596$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			7.4
Character	$\chi$	$=$	92.7
Dual form			92.2.h.a.79.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.471110 + 1.33344i) q^{2} +(-1.27476 - 1.98356i) q^{3} +(-1.55611 - 1.25639i) q^{4} +(2.16405 - 0.988288i) q^{5} +(3.24551 - 0.765333i) q^{6} +(2.09343 - 0.614686i) q^{7} +(2.40842 - 1.48308i) q^{8} +(-1.06327 + 2.32823i) q^{9} +O(q^{10})$	\(q+(-0.471110 + 1.33344i) q^{2} +(-1.27476 - 1.98356i) q^{3} +(-1.55611 - 1.25639i) q^{4} +(2.16405 - 0.988288i) q^{5} +(3.24551 - 0.765333i) q^{6} +(2.09343 - 0.614686i) q^{7} +(2.40842 - 1.48308i) q^{8} +(-1.06327 + 2.32823i) q^{9} +(0.298314 + 3.35122i) q^{10} +(-0.987339 - 1.13945i) q^{11} +(-0.508468 + 4.68824i) q^{12} +(-5.49384 - 1.61314i) q^{13} +(-0.166590 + 3.08104i) q^{14} +(-4.71897 - 3.03270i) q^{15} +(0.842957 + 3.91017i) q^{16} +(4.85453 + 0.697976i) q^{17} +(-2.60363 - 2.51465i) q^{18} +(0.735682 + 5.11678i) q^{19} +(-4.60917 - 1.18101i) q^{20} +(-3.88788 - 3.36887i) q^{21} +(1.98453 - 0.779748i) q^{22} +(4.71714 + 0.865213i) q^{23} +(-6.01193 - 2.88669i) q^{24} +(0.432089 - 0.498658i) q^{25} +(4.73922 - 6.56572i) q^{26} +(-1.02800 + 0.147804i) q^{27} +(-4.02989 - 1.67365i) q^{28} +(0.103177 - 0.717609i) q^{29} +(6.26707 - 4.86371i) q^{30} +(-4.37054 + 6.80070i) q^{31} +(-5.61109 - 0.718090i) q^{32} +(-1.00155 + 3.41097i) q^{33} +(-3.21773 + 6.14439i) q^{34} +(3.92279 - 3.39912i) q^{35} +(4.57973 - 2.28710i) q^{36} +(5.44149 + 2.48504i) q^{37} +(-7.16949 - 1.42958i) q^{38} +(3.80356 + 12.9537i) q^{39} +(3.74623 - 5.58966i) q^{40} +(-0.631546 - 1.38289i) q^{41} +(6.32380 - 3.59714i) q^{42} +(7.81415 - 5.02185i) q^{43} +(0.104812 + 3.01359i) q^{44} +6.08922i q^{45} +(-3.37600 + 5.88240i) q^{46} +0.789926i q^{47} +(6.68150 - 6.65658i) q^{48} +(-1.88418 + 1.21089i) q^{49} +(0.461367 + 0.811087i) q^{50} +(-4.80387 - 10.5190i) q^{51} +(6.52228 + 9.41263i) q^{52} +(0.108846 + 0.370694i) q^{53} +(0.287214 - 1.44040i) q^{54} +(-3.26275 - 1.49005i) q^{55} +(4.13023 - 4.58513i) q^{56} +(9.21163 - 7.98192i) q^{57} +(0.908278 + 0.475652i) q^{58} +(1.66397 - 5.66697i) q^{59} +(3.53298 + 10.6481i) q^{60} +(-5.54615 + 8.62998i) q^{61} +(-7.00929 - 9.03172i) q^{62} +(-0.794742 + 5.52756i) q^{63} +(3.60097 - 7.14374i) q^{64} +(-13.4832 + 1.93859i) q^{65} +(-4.07647 - 2.94245i) q^{66} +(0.0247864 - 0.0286050i) q^{67} +(-6.67725 - 7.18532i) q^{68} +(-4.29701 - 10.4597i) q^{69} +(2.68444 + 6.83216i) q^{70} +(6.60017 + 5.71908i) q^{71} +(0.892149 + 7.18426i) q^{72} +(-1.67474 - 11.6480i) q^{73} +(-5.87719 + 6.08515i) q^{74} +(-1.53993 - 0.221408i) q^{75} +(5.28388 - 8.88657i) q^{76} +(-2.76732 - 1.77845i) q^{77} +(-19.0649 - 1.03083i) q^{78} +(-10.6017 - 3.11295i) q^{79} +(5.68857 + 7.62871i) q^{80} +(6.63203 + 7.65378i) q^{81} +(2.14153 - 0.190632i) q^{82} +(0.775283 - 1.69763i) q^{83} +(1.81735 + 10.1270i) q^{84} +(11.1952 - 3.28722i) q^{85} +(3.01500 + 12.7855i) q^{86} +(-1.55495 + 0.710120i) q^{87} +(-4.06782 - 1.27997i) q^{88} +(4.40465 + 6.85377i) q^{89} +(-8.11959 - 2.86869i) q^{90} -12.4925 q^{91} +(-6.25334 - 7.27294i) q^{92} +19.0610 q^{93} +(-1.05332 - 0.372142i) q^{94} +(6.64890 + 10.3459i) q^{95} +(5.72841 + 12.0453i) q^{96} +(-5.23551 + 2.39098i) q^{97} +(-0.726986 - 3.08289i) q^{98} +(3.70270 - 1.08721i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 7 q^{2} - 11 q^{4} - 22 q^{5} - 12 q^{6} - 10 q^{8} - 12 q^{9}+O(q^{10}) $ 100 * q - 7 * q^2 - 11 * q^4 - 22 * q^5 - 12 * q^6 - 10 * q^8 - 12 * q^9	$ 100 q - 7 q^{2} - 11 q^{4} - 22 q^{5} - 12 q^{6} - 10 q^{8} - 12 q^{9} - 11 q^{10} - 18 q^{12} - 18 q^{13} - 11 q^{14} + 5 q^{16} - 22 q^{17} - 24 q^{18} - 11 q^{20} - 22 q^{21} - 30 q^{24} - 16 q^{25} + 12 q^{26} - 11 q^{28} - 42 q^{29} - 11 q^{30} - 27 q^{32} - 22 q^{33} + 11 q^{34} + 77 q^{36} - 22 q^{37} + 44 q^{38} + 77 q^{40} - 10 q^{41} + 99 q^{42} + 66 q^{44} + 65 q^{46} + 38 q^{48} - 8 q^{49} + 30 q^{50} + 96 q^{52} - 22 q^{53} + 48 q^{54} + 44 q^{56} - 22 q^{57} + 79 q^{58} + 11 q^{60} - 22 q^{61} - 36 q^{62} + 10 q^{64} - 22 q^{65} - 44 q^{66} - 10 q^{69} + 34 q^{70} - 21 q^{72} - 18 q^{73} - 22 q^{74} - 66 q^{76} + 122 q^{77} - 66 q^{78} - 110 q^{80} + 8 q^{81} - 122 q^{82} - 165 q^{84} + 54 q^{85} - 121 q^{86} - 99 q^{88} + 22 q^{89} - 198 q^{90} - 86 q^{92} + 212 q^{93} - 61 q^{94} - 147 q^{96} + 22 q^{97} - 71 q^{98}+O(q^{100}) $ 100 * q - 7 * q^2 - 11 * q^4 - 22 * q^5 - 12 * q^6 - 10 * q^8 - 12 * q^9 - 11 * q^10 - 18 * q^12 - 18 * q^13 - 11 * q^14 + 5 * q^16 - 22 * q^17 - 24 * q^18 - 11 * q^20 - 22 * q^21 - 30 * q^24 - 16 * q^25 + 12 * q^26 - 11 * q^28 - 42 * q^29 - 11 * q^30 - 27 * q^32 - 22 * q^33 + 11 * q^34 + 77 * q^36 - 22 * q^37 + 44 * q^38 + 77 * q^40 - 10 * q^41 + 99 * q^42 + 66 * q^44 + 65 * q^46 + 38 * q^48 - 8 * q^49 + 30 * q^50 + 96 * q^52 - 22 * q^53 + 48 * q^54 + 44 * q^56 - 22 * q^57 + 79 * q^58 + 11 * q^60 - 22 * q^61 - 36 * q^62 + 10 * q^64 - 22 * q^65 - 44 * q^66 - 10 * q^69 + 34 * q^70 - 21 * q^72 - 18 * q^73 - 22 * q^74 - 66 * q^76 + 122 * q^77 - 66 * q^78 - 110 * q^80 + 8 * q^81 - 122 * q^82 - 165 * q^84 + 54 * q^85 - 121 * q^86 - 99 * q^88 + 22 * q^89 - 198 * q^90 - 86 * q^92 + 212 * q^93 - 61 * q^94 - 147 * q^96 + 22 * q^97 - 71 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$e\left(\frac{19}{22}\right)$	$-1$

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 $

$2$	−0.471110	+	1.33344i	−0.333125	+	0.942883i
$2$	−0.471110	+	1.33344i	−0.333125	+	0.942883i
$3$	−1.27476	−	1.98356i	−0.735982	−	1.14521i	−0.984295	−	0.176531i	$-0.943513\pi$
$3$	−1.27476	−	1.98356i	−0.735982	−	1.14521i	0.248313	−	0.968680i	$-0.420124\pi$
$4$	−1.55611	−	1.25639i	−0.778055	−	0.628196i
$5$	2.16405	−	0.988288i	0.967792	−	0.441976i	0.132138	−	0.991231i	$-0.457816\pi$
$5$	2.16405	−	0.988288i	0.967792	−	0.441976i	0.835654	+	0.549256i	$0.185089\pi$
$6$	3.24551	−	0.765333i	1.32497	−	0.312446i
$7$	2.09343	−	0.614686i	0.791241	−	0.232329i	0.138952	−	0.990299i	$-0.455627\pi$
$7$	2.09343	−	0.614686i	0.791241	−	0.232329i	0.652290	+	0.757970i	$0.273809\pi$
$8$	2.40842	−	1.48308i	0.851505	−	0.524347i
$9$	−1.06327	+	2.32823i	−0.354422	+	0.776077i
$10$	0.298314	+	3.35122i	0.0943353	+	1.05975i
$11$	−0.987339	−	1.13945i	−0.297694	−	0.343557i	0.587122	−	0.809499i	$-0.300261\pi$
$11$	−0.987339	−	1.13945i	−0.297694	−	0.343557i	−0.884815	+	0.465942i	$0.845716\pi$
$12$	−0.508468	+	4.68824i	−0.146782	+	1.35338i
$13$	−5.49384	−	1.61314i	−1.52372	−	0.447403i	−0.590595	−	0.806968i	$-0.701107\pi$
$13$	−5.49384	−	1.61314i	−1.52372	−	0.447403i	−0.933120	+	0.359564i	$0.882925\pi$
$14$	−0.166590	+	3.08104i	−0.0445231	+	0.823442i
$15$	−4.71897	−	3.03270i	−1.21843	−	0.783039i
$16$	0.842957	+	3.91017i	0.210739	+	0.977542i
$17$	4.85453	+	0.697976i	1.17740	+	0.169284i	0.703106	−	0.711085i	$-0.251796\pi$
$17$	4.85453	+	0.697976i	1.17740	+	0.169284i	0.474290	+	0.880369i	$0.342705\pi$
$18$	−2.60363	−	2.51465i	−0.613682	−	0.592709i
$19$	0.735682	+	5.11678i	0.168777	+	1.17387i	0.881417	+	0.472339i	$0.156590\pi$
$19$	0.735682	+	5.11678i	0.168777	+	1.17387i	−0.712640	+	0.701530i	$0.752501\pi$
$20$	−4.60917	−	1.18101i	−1.03064	−	0.264082i
$21$	−3.88788	−	3.36887i	−0.848405	−	0.735147i
$22$	1.98453	−	0.779748i	0.423103	−	0.166243i
$23$	4.71714	+	0.865213i	0.983592	+	0.180409i
$23$	4.71714	+	0.865213i	0.983592	+	0.180409i
$24$	−6.01193	−	2.88669i	−1.22718	−	0.589243i
$25$	0.432089	−	0.498658i	0.0864178	−	0.0997315i
$26$	4.73922	−	6.56572i	0.929437	−	1.28764i
$27$	−1.02800	+	0.147804i	−0.197839	+	0.0284449i
$28$	−4.02989	−	1.67365i	−0.761578	−	0.316290i
$29$	0.103177	−	0.717609i	0.0191594	−	0.133257i	−0.977997	−	0.208620i	$-0.933103\pi$
$29$	0.103177	−	0.717609i	0.0191594	−	0.133257i	0.997156	+	0.0753638i	$0.0240118\pi$
$30$	6.26707	−	4.86371i	1.14420	−	0.887989i
$31$	−4.37054	+	6.80070i	−0.784972	+	1.22144i	0.186071	+	0.982536i	$0.440425\pi$
$31$	−4.37054	+	6.80070i	−0.784972	+	1.22144i	−0.971043	+	0.238905i	$0.923212\pi$
$32$	−5.61109	−	0.718090i	−0.991910	−	0.126942i
$33$	−1.00155	+	3.41097i	−0.174348	+	0.593774i
$34$	−3.21773	+	6.14439i	−0.551836	+	1.05375i
$35$	3.92279	−	3.39912i	0.663073	−	0.574556i
$36$	4.57973	−	2.28710i	0.763288	−	0.381184i
$37$	5.44149	+	2.48504i	0.894575	+	0.408539i	0.809011	−	0.587794i	$-0.200003\pi$
$37$	5.44149	+	2.48504i	0.894575	+	0.408539i	0.0855645	+	0.996333i	$0.472731\pi$
$38$	−7.16949	−	1.42958i	−1.16304	−	0.231909i
$39$	3.80356	+	12.9537i	0.609056	+	2.07426i
$40$	3.74623	−	5.58966i	0.592331	−	0.883803i
$41$	−0.631546	−	1.38289i	−0.0986309	−	0.215971i	0.853884	−	0.520463i	$-0.174241\pi$
$41$	−0.631546	−	1.38289i	−0.0986309	−	0.215971i	−0.952515	+	0.304492i	$0.901513\pi$
$42$	6.32380	−	3.59714i	0.975783	−	0.555050i
$43$	7.81415	−	5.02185i	1.19165	−	0.765825i	0.214155	−	0.976800i	$-0.431300\pi$
$43$	7.81415	−	5.02185i	1.19165	−	0.765825i	0.977492	+	0.210975i	$0.0676637\pi$
$44$	0.104812	+	3.01359i	0.0158010	+	0.454316i
$45$			6.08922i			0.907727i
$46$	−3.37600	+	5.88240i	−0.497764	+	0.867312i
$47$			0.789926i			0.115223i	0.998339	+	0.0576113i	$0.0183484\pi$
$47$			0.789926i			0.115223i	−0.998339	+	0.0576113i	$0.981652\pi$
$48$	6.68150	−	6.65658i	0.964391	−	0.960794i
$49$	−1.88418	+	1.21089i	−0.269168	+	0.172984i
$50$	0.461367	+	0.811087i	0.0652471	+	0.114705i
$51$	−4.80387	−	10.5190i	−0.672677	−	1.47296i
$52$	6.52228	+	9.41263i	0.904478	+	1.30530i
$53$	0.108846	+	0.370694i	0.0149511	+	0.0509187i	0.966631	−	0.256174i	$-0.0824620\pi$
$53$	0.108846	+	0.370694i	0.0149511	+	0.0509187i	−0.951680	+	0.307093i	$0.900644\pi$
$54$	0.287214	−	1.44040i	0.0390848	−	0.196014i
$55$	−3.26275	−	1.49005i	−0.439949	−	0.200918i
$56$	4.13023	−	4.58513i	0.551925	−	0.612714i
$57$	9.21163	−	7.98192i	1.22011	−	1.05723i
$58$	0.908278	+	0.475652i	0.119263	+	0.0624562i
$59$	1.66397	−	5.66697i	0.216631	−	0.737776i	−0.777432	−	0.628967i	$-0.783478\pi$
$59$	1.66397	−	5.66697i	0.216631	−	0.737776i	0.994063	−	0.108809i	$-0.0347038\pi$
$60$	3.53298	+	10.6481i	0.456106	+	1.37466i
$61$	−5.54615	+	8.62998i	−0.710112	+	1.10496i	0.279354	+	0.960188i	$0.409880\pi$
$61$	−5.54615	+	8.62998i	−0.710112	+	1.10496i	−0.989466	+	0.144768i	$0.953757\pi$
$62$	−7.00929	−	9.03172i	−0.890181	−	1.14703i
$63$	−0.794742	+	5.52756i	−0.100128	+	0.696407i
$64$	3.60097	−	7.14374i	0.450121	−	0.892967i
$65$	−13.4832	+	1.93859i	−1.67238	+	0.240452i
$66$	−4.07647	−	2.94245i	−0.501779	−	0.362190i
$67$	0.0247864	−	0.0286050i	0.00302814	−	0.00349466i	−0.754233	−	0.656606i	$-0.771991\pi$
$67$	0.0247864	−	0.0286050i	0.00302814	−	0.00349466i	0.757262	+	0.653112i	$0.226537\pi$
$68$	−6.67725	−	7.18532i	−0.809736	−	0.871348i
$69$	−4.29701	−	10.4597i	−0.517299	−	1.25920i
$70$	2.68444	+	6.83216i	0.320852	+	0.816599i
$71$	6.60017	+	5.71908i	0.783296	+	0.678730i	0.951714	−	0.306985i	$-0.0993203\pi$
$71$	6.60017	+	5.71908i	0.783296	+	0.678730i	−0.168418	+	0.985716i	$0.553866\pi$
$72$	0.892149	+	7.18426i	0.105141	+	0.846673i
$73$	−1.67474	−	11.6480i	−0.196013	−	1.36330i	−0.815711	−	0.578460i	$-0.803654\pi$
$73$	−1.67474	−	11.6480i	−0.196013	−	1.36330i	0.619698	−	0.784840i	$-0.287255\pi$
$74$	−5.87719	+	6.08515i	−0.683210	+	0.707385i
$75$	−1.53993	−	0.221408i	−0.177816	−	0.0255660i
$76$	5.28388	−	8.88657i	0.606102	−	1.01936i
$77$	−2.76732	−	1.77845i	−0.315366	−	0.202673i
$78$	−19.0649	−	1.03083i	−2.15867	−	0.116718i
$79$	−10.6017	−	3.11295i	−1.19279	−	0.350235i	−0.375698	−	0.926742i	$-0.622597\pi$
$79$	−10.6017	−	3.11295i	−1.19279	−	0.350235i	−0.817092	+	0.576507i	$0.804415\pi$
$80$	5.68857	+	7.62871i	0.636002	+	0.852916i
$81$	6.63203	+	7.65378i	0.736893	+	0.850420i
$82$	2.14153	−	0.190632i	0.236492	−	0.0210518i
$83$	0.775283	−	1.69763i	0.0850984	−	0.186340i	−0.862299	−	0.506400i	$-0.830976\pi$
$83$	0.775283	−	1.69763i	0.0850984	−	0.186340i	0.947397	+	0.320060i	$0.103703\pi$
$84$	1.81735	+	10.1270i	0.198289	+	1.10495i
$85$	11.1952	−	3.28722i	1.21429	−	0.356549i
$86$	3.01500	+	12.7855i	0.325115	+	1.37870i
$87$	−1.55495	+	0.710120i	−0.166708	+	0.0761329i
$88$	−4.06782	−	1.27997i	−0.433631	−	0.136446i
$89$	4.40465	+	6.85377i	0.466892	+	0.726499i	0.992233	−	0.124393i	$-0.0396985\pi$
$89$	4.40465	+	6.85377i	0.466892	+	0.726499i	−0.525341	+	0.850892i	$0.676062\pi$
$90$	−8.11959	−	2.86869i	−0.855880	−	0.302387i
$91$	−12.4925			−1.30957
$92$	−6.25334	−	7.27294i	−0.651956	−	0.758257i
$93$	19.0610			1.97653
$94$	−1.05332	−	0.372142i	−0.108641	−	0.0383835i
$95$	6.64890	+	10.3459i	0.682163	+	1.06147i
$96$	5.72841	+	12.0453i	0.584653	+	1.22937i
$97$	−5.23551	+	2.39098i	−0.531586	+	0.242767i	−0.663078	−	0.748550i	$-0.730750\pi$
$97$	−5.23551	+	2.39098i	−0.531586	+	0.242767i	0.131493	+	0.991317i	$0.458023\pi$
$98$	−0.726986	−	3.08289i	−0.0734367	−	0.311419i
$99$	3.70270	−	1.08721i	0.372136	−	0.109269i
$100$	−1.29889	+	0.233093i	−0.129889	+	0.0233093i
$101$	−3.12719	+	6.84758i	−0.311167	+	0.681360i	−0.999009	−	0.0444999i	$-0.985831\pi$
$101$	−3.12719	+	6.84758i	−0.311167	+	0.681360i	0.687843	+	0.725860i	$0.258558\pi$
$102$	16.2896	−	1.45005i	1.61291	−	0.143576i
$103$	−8.21311	−	9.47844i	−0.809262	−	0.933938i	0.189589	−	0.981864i	$-0.439285\pi$
$103$	−8.21311	−	9.47844i	−0.809262	−	0.933938i	−0.998851	+	0.0479253i	$0.984739\pi$
$104$	−15.6239	+	4.26267i	−1.53205	+	0.417989i
$105$	−11.7430	−	3.44805i	−1.14600	−	0.336495i
$106$	−0.545576	−	0.0294990i	−0.0529910	−	0.00286520i
$107$	−4.42938	−	2.84659i	−0.428204	−	0.275190i	0.308736	−	0.951148i	$-0.400094\pi$
$107$	−4.42938	−	2.84659i	−0.428204	−	0.275190i	−0.736941	+	0.675958i	$0.763730\pi$
$108$	1.78538	+	1.06157i	0.171798	+	0.102150i
$109$	−4.65577	−	0.669398i	−0.445942	−	0.0641167i	−0.0843138	−	0.996439i	$-0.526870\pi$
$109$	−4.65577	−	0.669398i	−0.445942	−	0.0641167i	−0.361628	+	0.932323i	$0.617779\pi$
$110$	3.52400	−	3.64870i	0.336001	−	0.347890i
$111$	−2.00734	−	13.9614i	−0.190528	−	1.32515i
$112$	4.16820	+	7.66750i	0.393857	+	0.724511i
$113$	6.83880	+	5.92585i	0.643340	+	0.557457i	0.914252	−	0.405147i	$-0.132780\pi$
$113$	6.83880	+	5.92585i	0.643340	+	0.557457i	−0.270912	+	0.962604i	$0.587325\pi$
$114$	6.30370	+	16.0435i	0.590396	+	1.50261i
$115$	11.0632	−	2.78953i	1.03165	−	0.260125i
$116$	−1.06215	+	0.987048i	−0.0986183	+	0.0916451i
$117$	9.59716	−	11.0757i	0.887258	−	1.02395i
$118$	6.77263	+	4.88857i	0.623471	+	0.450029i
$119$	10.5916	−	1.52285i	0.970934	−	0.139599i
$120$	−15.8630	−	0.305419i	−1.44809	−	0.0278808i
$121$	1.24196	−	8.63799i	0.112905	−	0.785272i
$122$	−8.89469	−	11.4611i	−0.805287	−	1.03764i
$123$	−1.93799	+	3.01556i	−0.174742	+	0.271904i
$124$	15.3454	−	5.09152i	1.37806	−	0.457232i
$125$	−2.90902	+	9.90720i	−0.260190	+	0.886127i
$126$	−6.99624	−	3.66383i	−0.623274	−	0.326400i
$127$	−0.525070	+	0.454976i	−0.0465925	+	0.0403726i	−0.677846	−	0.735204i	$-0.737086\pi$
$127$	−0.525070	+	0.454976i	−0.0465925	+	0.0403726i	0.631253	+	0.775577i	$0.282541\pi$
$128$	7.82927	+	8.16716i	0.692016	+	0.721882i
$129$	−19.9223	−	9.09821i	−1.75406	−	0.801053i
$130$	3.76708	−	18.8922i	0.330394	−	1.65696i
$131$	−4.86677	−	16.5747i	−0.425211	−	1.44814i	−0.842170	−	0.539212i	$-0.818722\pi$
$131$	−4.86677	−	16.5747i	−0.425211	−	1.44814i	0.416959	−	0.908925i	$-0.363096\pi$
$132$	5.84404	−	4.04950i	0.508658	−	0.352464i
$133$	4.68531	+	10.2594i	0.406268	+	0.889602i
$134$	0.0264659	+	0.0465273i	0.00228631	+	0.00401934i
$135$	−2.07857	+	1.33581i	−0.178895	+	0.114969i
$136$	12.7269	−	5.51862i	1.09132	−	0.473218i
$137$		−	12.6245i		−	1.07859i	−0.842118	−	0.539294i	$-0.818691\pi$
$137$		−	12.6245i		−	1.07859i	0.842118	−	0.539294i	$-0.181309\pi$
$138$	15.9717	−	0.802130i	1.35960	−	0.0682819i
$139$			4.60159i			0.390302i	0.980773	+	0.195151i	$0.0625196\pi$
$139$			4.60159i			0.390302i	−0.980773	+	0.195151i	$0.937480\pi$
$140$	−10.3749	+	0.360838i	−0.876841	+	0.0304963i
$141$	1.56687	−	1.00696i	0.131954	−	0.0848017i
$142$	−10.7354	+	6.10660i	−0.900899	+	0.512454i
$143$	3.58619	+	7.85266i	0.299892	+	0.656672i
$144$	−10.0001	−	2.19496i	−0.833338	−	0.182913i
$145$	−0.485925	−	1.65491i	−0.0403539	−	0.137433i
$146$	16.3209	+	3.25436i	1.35073	+	0.269333i
$147$	4.80374	+	2.19379i	0.396205	+	0.180941i
$148$	−5.34536	−	10.7036i	−0.439386	−	0.879834i
$149$	−4.19449	+	3.63455i	−0.343626	+	0.297754i	−0.809526	−	0.587084i	$-0.800276\pi$
$149$	−4.19449	+	3.63455i	−0.343626	+	0.297754i	0.465900	+	0.884837i	$0.345731\pi$
$150$	1.02071	−	1.94909i	0.0833406	−	0.159142i
$151$	−1.25351	+	4.26906i	−0.102009	+	0.347411i	−0.994643	−	0.103371i	$-0.967037\pi$
$151$	−1.25351	+	4.26906i	−0.102009	+	0.347411i	0.892634	+	0.450783i	$0.148855\pi$
$152$	9.36040	+	11.2323i	0.759229	+	0.911058i
$153$	−6.78671	+	10.5603i	−0.548673	+	0.853752i
$154$	3.67517	−	2.85221i	0.296154	−	0.229837i
$155$	−2.73702	+	19.0364i	−0.219843	+	1.52904i
$156$	10.3562	−	24.9362i	0.829160	−	1.99649i
$157$	−1.68337	+	0.242032i	−0.134348	+	0.0193163i	−0.209161	−	0.977881i	$-0.567073\pi$
$157$	−1.68337	+	0.242032i	−0.134348	+	0.0193163i	0.0748129	+	0.997198i	$0.476164\pi$
$158$	9.14552	−	12.6702i	0.727579	−	1.00799i
$159$	0.596543	−	0.688447i	0.0473089	−	0.0545974i
$160$	−12.8524	+	3.99139i	−1.01607	+	0.315547i
$161$	10.4068	−	1.08830i	0.820173	−	0.0857700i
$162$	−13.3303	+	5.23763i	−1.04732	+	0.411507i
$163$	13.3498	+	11.5677i	1.04564	+	0.906050i	0.995694	−	0.0927024i	$-0.0295505\pi$
$163$	13.3498	+	11.5677i	1.04564	+	0.906050i	0.0499432	+	0.998752i	$0.484096\pi$
$164$	−0.754700	+	2.94540i	−0.0589322	+	0.229997i
$165$	1.20361	+	8.37133i	0.0937013	+	0.651707i
$166$	1.89844	+	1.83356i	0.147348	+	0.142312i
$167$	−4.71723	−	0.678236i	−0.365030	−	0.0524834i	−0.0426407	−	0.999090i	$-0.513577\pi$
$167$	−4.71723	−	0.678236i	−0.365030	−	0.0524834i	−0.322390	+	0.946607i	$0.604486\pi$
$168$	−14.3599	−	2.34763i	−1.10789	−	0.181123i
$169$	16.6437	+	10.6963i	1.28029	+	0.822790i
$170$	−0.890893	+	16.4768i	−0.0683283	+	1.26371i
$171$	−12.6953	−	3.72766i	−0.970831	−	0.285062i
$172$	−18.4691	−	2.00309i	−1.40826	−	0.152734i
$173$	3.15893	+	3.64560i	0.240169	+	0.277170i	0.863019	−	0.505171i	$-0.168571\pi$
$173$	3.15893	+	3.64560i	0.240169	+	0.277170i	−0.622850	+	0.782341i	$0.714025\pi$
$174$	−0.214350	−	2.40797i	−0.0162498	−	0.182548i
$175$	0.598030	−	1.30950i	0.0452068	−	0.0989891i
$176$	3.62316	−	4.82117i	0.273106	−	0.363409i
$177$	−13.3619	+	3.92342i	−1.00435	+	0.294902i
$178$	−11.2142	+	2.64445i	−0.840537	+	0.198210i
$179$	7.31079	−	3.33872i	0.546434	−	0.249548i	−0.123017	−	0.992405i	$-0.539257\pi$
$179$	7.31079	−	3.33872i	0.546434	−	0.249548i	0.669451	+	0.742857i	$0.266530\pi$
$180$	7.65044	−	9.47549i	0.570230	−	0.706261i
$181$	−8.17100	−	12.7143i	−0.607346	−	0.945049i	−0.999682	−	0.0252268i	$-0.991969\pi$
$181$	−8.17100	−	12.7143i	−0.607346	−	0.945049i	0.392336	−	0.919822i	$-0.371667\pi$
$182$	5.88535	−	16.6580i	0.436251	−	1.23477i
$183$	24.1881			1.78804
$184$	12.6440	−	4.91208i	0.932130	−	0.362123i
$185$	14.2316			1.04633
$186$	−8.97983	+	25.4166i	−0.658433	+	1.86364i
$187$	−3.99776	−	6.22063i	−0.292345	−	0.454898i
$188$	0.992456	−	1.22921i	0.0723823	−	0.0896495i
$189$	−2.06119	+	0.941313i	−0.149929	+	0.0684705i
$190$	−16.9280	+	3.99184i	−1.22808	+	0.289598i
$191$	−14.4587	+	4.24546i	−1.04620	+	0.307191i	−0.759279	−	0.650765i	$-0.774448\pi$
$191$	−14.4587	+	4.24546i	−1.04620	+	0.307191i	−0.286917	+	0.957956i	$0.592630\pi$
$192$	−18.7604	+	1.96379i	−1.35392	+	0.141724i
$193$	1.53229	−	3.35524i	0.110296	−	0.241515i	−0.846433	−	0.532496i	$-0.821254\pi$
$193$	1.53229	−	3.35524i	0.110296	−	0.241515i	0.956729	+	0.290980i	$0.0939815\pi$
$194$	−0.721716	−	8.10764i	−0.0518162	−	0.582095i
$195$	21.0331	+	24.2735i	1.50621	+	1.73826i
$196$	4.45333	+	0.482991i	0.318095	+	0.0344994i
$197$	−12.4803	−	3.66454i	−0.889182	−	0.261087i	−0.194928	−	0.980818i	$-0.562447\pi$
$197$	−12.4803	−	3.66454i	−0.889182	−	0.261087i	−0.694254	+	0.719730i	$0.744265\pi$
$198$	−0.294653	+	5.44952i	−0.0209401	+	0.387281i
$199$	2.39289	+	1.53782i	0.169628	+	0.109013i	0.622700	−	0.782461i	$-0.286036\pi$
$199$	2.39289	+	1.53782i	0.169628	+	0.109013i	−0.453072	+	0.891474i	$0.649672\pi$
$200$	0.301105	−	1.84180i	0.0212914	−	0.130235i
$201$	−0.0883366	−	0.0127009i	−0.00623078	−	0.000895851i
$202$	−7.65757	−	7.39587i	−0.538785	−	0.520372i
$203$	−0.225111	−	1.56568i	−0.0157997	−	0.109889i
$204$	−5.74065	+	22.4043i	−0.401926	+	1.56861i
$205$	−2.73339	−	2.36850i	−0.190908	−	0.165423i
$206$	16.5082	−	6.48628i	1.15018	−	0.451921i
$207$	−7.02999	+	10.0626i	−0.488618	+	0.699401i
$208$	1.67656	−	22.8416i	0.116249	−	1.58378i
$209$	5.10394	−	5.89026i	0.353047	−	0.407438i
$210$	10.1300	−	14.0341i	0.699036	−	0.968446i
$211$	−10.6275	+	1.52800i	−0.731627	+	0.105192i	−0.498052	−	0.867147i	$-0.665951\pi$
$211$	−10.6275	+	1.52800i	−0.731627	+	0.105192i	−0.233574	+	0.972339i	$0.575042\pi$
$212$	0.296361	−	0.713594i	0.0203542	−	0.0490098i
$213$	2.93053	−	20.3823i	0.200797	−	1.39657i
$214$	5.88247	−	4.56524i	0.402118	−	0.312073i
$215$	11.9472	−	18.5902i	0.814790	−	1.26784i
$216$	−2.25665	+	1.88057i	−0.153545	+	0.127957i
$217$	−4.96912	+	16.9233i	−0.337326	+	1.14883i
$218$	3.08598	−	5.89281i	0.209009	−	0.399112i
$219$	−20.9697	+	18.1704i	−1.41700	+	1.22784i
$220$	3.20512	+	6.41798i	0.216089	+	0.432700i
$221$	−25.5441	−	11.6656i	−1.71828	−	0.784712i
$222$	19.5623	+	3.90068i	1.31293	+	0.261796i
$223$	−0.990426	−	3.37308i	−0.0663238	−	0.225878i	0.919661	−	0.392713i	$-0.128463\pi$
$223$	−0.990426	−	3.37308i	−0.0663238	−	0.225878i	−0.985985	+	0.166835i	$0.946645\pi$
$224$	−12.1878	+	1.94579i	−0.814332	+	0.130008i
$225$	0.701563	+	1.53621i	0.0467709	+	0.102414i
$226$	−11.1236	+	6.32738i	−0.739930	+	0.420891i
$227$	−18.5205	+	11.9024i	−1.22925	+	0.789991i	−0.983774	−	0.179412i	$-0.942581\pi$
$227$	−18.5205	+	11.9024i	−1.22925	+	0.789991i	−0.245476	+	0.969403i	$0.578944\pi$
$228$	−24.3627	+	0.847331i	−1.61346	+	0.0561159i
$229$			3.82942i			0.253056i	0.991963	+	0.126528i	$0.0403833\pi$
$229$			3.82942i			0.253056i	−0.991963	+	0.126528i	$0.959617\pi$
$230$	−1.49232	+	16.0663i	−0.0984009	+	1.05938i
$231$			7.75626i			0.510324i
$232$	−0.815776	−	1.88132i	−0.0535583	−	0.123515i
$233$	−11.3923	+	7.32140i	−0.746336	+	0.479641i	−0.857708	−	0.514138i	$-0.828112\pi$
$233$	−11.3923	+	7.32140i	−0.746336	+	0.479641i	0.111372	+	0.993779i	$0.464476\pi$
$234$	10.2475	+	18.0151i	0.669897	+	1.17768i
$235$	0.780674	+	1.70944i	0.0509256	+	0.111511i
$236$	−9.70926	+	6.72782i	−0.632019	+	0.437944i
$237$	7.33993	+	24.9975i	0.476780	+	1.62376i
$238$	−2.95921	+	14.8407i	−0.191817	+	0.961981i
$239$	−5.39620	−	2.46436i	−0.349051	−	0.159406i	0.233172	−	0.972436i	$-0.425090\pi$
$239$	−5.39620	−	2.46436i	−0.349051	−	0.159406i	−0.582223	+	0.813029i	$0.697817\pi$
$240$	7.88047	−	21.0084i	0.508682	−	1.35609i
$241$	16.4632	−	14.2655i	1.06049	−	0.918920i	0.0636195	−	0.997974i	$-0.479736\pi$
$241$	16.4632	−	14.2655i	1.06049	−	0.918920i	0.996870	+	0.0790546i	$0.0251901\pi$
$242$	10.9331	+	5.72552i	0.702808	+	0.368050i
$243$	5.84971	−	19.9223i	0.375259	−	1.27801i
$244$	19.4731	−	6.46106i	1.24664	−	0.413627i
$245$	−2.88074	+	4.48252i	−0.184044	+	0.286378i
$246$	−3.10806	−	4.00485i	−0.198163	−	0.255340i
$247$	4.21234	−	29.2975i	0.268025	−	1.86415i
$248$	−0.440151	+	22.8608i	−0.0279496	+	1.45166i
$249$	−4.35566	+	0.626250i	−0.276029	+	0.0396870i
$250$	−11.8402	−	8.54638i	−0.748838	−	0.540520i
$251$	11.8946	−	13.7271i	0.750779	−	0.866445i	−0.243864	−	0.969809i	$-0.578415\pi$
$251$	11.8946	−	13.7271i	0.750779	−	0.866445i	0.994644	+	0.103364i	$0.0329606\pi$
$252$	8.18148	−	7.60298i	0.515385	−	0.478942i
$253$	−3.67155	−	6.22920i	−0.230828	−	0.391626i
$254$	−0.359316	−	0.914492i	−0.0225455	−	0.0573804i
$255$	−20.7916	−	18.0160i	−1.30202	−	1.12821i
$256$	−14.5788	+	6.59221i	−0.911178	+	0.412013i
$257$	−1.98584	−	13.8118i	−0.123873	−	0.861558i	−0.953102	−	0.302648i	$-0.902129\pi$
$257$	−1.98584	−	13.8118i	−0.123873	−	0.861558i	0.829229	−	0.558909i	$-0.188780\pi$
$258$	21.5175	−	22.2789i	1.33962	−	1.38702i
$259$	12.9189	+	1.85745i	0.802740	+	0.115417i
$260$	23.4169	+	13.9235i	1.45226	+	0.863498i
$261$	1.56105	+	1.00323i	0.0966268	+	0.0620983i
$262$	24.3941	+	1.31898i	1.50707	+	0.0814867i
$263$	13.3421	+	3.91760i	0.822710	+	0.241569i	0.665883	−	0.746057i	$-0.268055\pi$
$263$	13.3421	+	3.91760i	0.822710	+	0.241569i	0.156827	+	0.987626i	$0.449873\pi$
$264$	2.64657	+	9.70043i	0.162885	+	0.597020i
$265$	0.601900	+	0.694629i	0.0369744	+	0.0426707i
$266$	−15.8875	+	1.41426i	−0.974128	+	0.0867137i
$267$	7.98002	−	17.4738i	0.488369	−	1.06938i
$268$	−0.0745095	+	0.0133711i	−0.00455139	+	0.000816773i
$269$	20.2675	−	5.95106i	1.23573	−	0.362843i	0.402320	−	0.915499i	$-0.368204\pi$
$269$	20.2675	−	5.95106i	1.23573	−	0.362843i	0.833409	+	0.552656i	$0.186386\pi$
$270$	−0.801990	−	3.40095i	−0.0488075	−	0.206975i
$271$	0.637765	−	0.291258i	0.0387415	−	0.0176926i	−0.395950	−	0.918272i	$-0.629585\pi$
$271$	0.637765	−	0.291258i	0.0387415	−	0.0176926i	0.434692	+	0.900579i	$0.356857\pi$
$272$	1.36296	+	19.5704i	0.0826414	+	1.18663i
$273$	15.9249	+	24.7797i	0.963821	+	1.49973i
$274$	16.8340	+	5.94755i	1.01698	+	0.359305i
$275$	−0.994813			−0.0599895
$276$	−6.45484	+	21.6751i	−0.388536	+	1.30469i
$277$	−18.6953			−1.12329			−0.561647	−	0.827377i	$-0.689832\pi$
$277$	−18.6953			−1.12329			−0.561647	+	0.827377i	$0.689832\pi$
$278$	−6.13593	−	2.16786i	−0.368009	−	0.130019i
$279$	−11.1865	−	17.4066i	−0.669720	−	1.04210i
$280$	4.40658	−	14.0043i	0.263343	−	0.836917i
$281$	21.3936	−	9.77015i	1.27624	−	0.582838i	0.342070	−	0.939674i	$-0.388872\pi$
$281$	21.3936	−	9.77015i	1.27624	−	0.582838i	0.934167	+	0.356836i	$0.116145\pi$
$282$	0.604557	+	2.56371i	0.0360008	+	0.152667i
$283$	−7.31305	+	2.14730i	−0.434715	+	0.127644i	−0.491766	−	0.870727i	$-0.663649\pi$
$283$	−7.31305	+	2.14730i	−0.434715	+	0.127644i	0.0570507	+	0.998371i	$0.481830\pi$
$284$	−3.08519	−	17.1919i	−0.183072	−	1.02015i
$285$	12.0460	−	26.3770i	0.713542	−	1.56244i
$286$	−12.1605	+	1.08249i	−0.719066	+	0.0640089i
$287$	−2.17214	−	2.50678i	−0.128217	−	0.147971i
$288$	7.63797	−	12.3004i	0.450072	−	0.724807i
$289$	6.76791	+	1.98724i	0.398112	+	0.116896i
$290$	2.43564	+	0.131694i	0.143026	+	0.00773333i
$291$	11.4167	+	7.33705i	0.669257	+	0.430105i
$292$	−12.0284	+	20.2298i	−0.703911	+	1.18386i
$293$	11.6437	+	1.67411i	0.680233	+	0.0978027i	0.473766	−	0.880651i	$-0.342894\pi$
$293$	11.6437	+	1.67411i	0.680233	+	0.0978027i	0.206467	+	0.978454i	$0.433803\pi$
$294$	−5.18837	+	5.37196i	−0.302592	+	0.313299i
$295$	−1.99968	−	13.9081i	−0.116426	−	0.809759i
$296$	16.7909	−	2.08511i	0.975951	−	0.121195i
$297$	1.18340	+	1.02542i	0.0686677	+	0.0595009i
$298$	−2.87037	−	7.30536i	−0.166276	−	0.423188i
$299$	−24.5195	−	12.3627i	−1.41800	−	0.714955i
$300$	2.11812	+	2.27929i	0.122290	+	0.131595i
$301$	13.2715	−	15.3161i	0.764957	−	0.882807i
$302$	−5.10199	−	3.68268i	−0.293586	−	0.211914i
$303$	17.5690	−	2.52604i	1.00931	−	0.145117i
$304$	−19.3873	+	7.18986i	−1.11194	+	0.412367i
$305$	−3.47324	+	24.1569i	−0.198877	+	1.38322i
$306$	−10.8842	−	14.0247i	−0.622211	−	0.801741i
$307$	−7.88790	+	12.2738i	−0.450186	+	0.700504i	−0.989966	−	0.141302i	$-0.954871\pi$
$307$	−7.88790	+	12.2738i	−0.450186	+	0.700504i	0.539780	+	0.841806i	$0.318507\pi$
$308$	2.07183	+	6.24431i	0.118053	+	0.355803i
$309$	−8.33134	+	28.3739i	−0.473953	+	1.61414i
$310$	−24.0944	−	12.6179i	−1.36847	−	0.716648i
$311$	−15.6718	+	13.5797i	−0.888666	+	0.770034i	−0.974054	−	0.226314i	$-0.927332\pi$
$311$	−15.6718	+	13.5797i	−0.888666	+	0.770034i	0.0853882	+	0.996348i	$0.472787\pi$
$312$	28.3719	+	25.5570i	1.60624	+	1.44688i
$313$	−1.77214	−	0.809308i	−0.100167	−	0.0457448i	0.364701	−	0.931125i	$-0.381171\pi$
$313$	−1.77214	−	0.809308i	−0.100167	−	0.0457448i	−0.464868	+	0.885380i	$0.653898\pi$
$314$	0.470319	−	2.35869i	0.0265416	−	0.133109i
$315$	3.74295	+	12.7473i	0.210892	+	0.718231i
$316$	12.5864	+	18.1641i	0.708040	+	1.02181i
$317$	0.684752	+	1.49940i	0.0384595	+	0.0842146i	0.927887	−	0.372862i	$-0.121624\pi$
$317$	0.684752	+	1.49940i	0.0384595	+	0.0842146i	−0.889427	+	0.457077i	$0.848896\pi$
$318$	0.636964	+	1.11979i	0.0357192	+	0.0627946i
$319$	−0.919549	+	0.590958i	−0.0514848	+	0.0330873i
$320$	0.732607	−	19.0182i	0.0409540	−	1.06315i
$321$			12.4147i			0.692919i
$322$	−3.45158	+	14.3896i	−0.192349	+	0.801899i
$323$			25.3530i			1.41068i
$324$	−0.704032	−	20.2426i	−0.0391129	−	1.12459i
$325$	−3.17823	+	2.04252i	−0.176296	+	0.113299i
$326$	−21.7140	+	12.3515i	−1.20263	+	0.684085i
$327$	4.60719	+	10.0883i	0.254778	+	0.557886i
$328$	−3.57196	−	2.39395i	−0.197229	−	0.132184i
$329$	0.485556	+	1.65365i	0.0267696	+	0.0911688i
$330$	−11.7297	−	2.33887i	−0.645697	−	0.128751i
$331$	10.0083	+	4.57065i	0.550107	+	0.251225i	0.671022	−	0.741437i	$-0.265856\pi$
$331$	10.0083	+	4.57065i	0.550107	+	0.251225i	−0.120915	+	0.992663i	$0.538583\pi$
$332$	−3.33932	+	1.66765i	−0.183269	+	0.0915239i
$333$	−11.5715	+	10.0268i	−0.634115	+	0.549464i
$334$	3.12672	−	5.97061i	0.171087	−	0.326697i
$335$	0.0253690	−	0.0863988i	0.00138606	−	0.00472047i
$336$	9.89553	−	18.0421i	0.539845	−	0.984277i
$337$	9.65429	−	15.0224i	0.525903	−	0.818321i	−0.472097	−	0.881547i	$-0.656503\pi$
$337$	9.65429	−	15.0224i	0.525903	−	0.818321i	0.997999	+	0.0632263i	$0.0201390\pi$
$338$	−22.1038	+	17.1542i	−1.20229	+	0.933067i
$339$	3.03648	−	21.1192i	0.164919	−	1.14704i
$340$	−21.5511	−	8.95034i	−1.16877	−	0.485400i
$341$	12.0643	−	1.73458i	0.653316	−	0.0939326i
$342$	10.9515	−	15.1722i	0.592188	−	0.820418i
$343$	−13.2015	+	15.2354i	−0.712815	+	0.822633i
$344$	11.3720	−	23.6837i	0.613136	−	1.27694i
$345$	−19.6361	−	18.3886i	−1.05717	−	0.990007i
$346$	−6.34939	+	2.49476i	−0.341345	+	0.134119i
$347$	−9.18644	−	7.96010i	−0.493154	−	0.427321i	0.372448	−	0.928053i	$-0.378519\pi$
$347$	−9.18644	−	7.96010i	−0.493154	−	0.427321i	−0.865602	+	0.500733i	$0.833064\pi$
$348$	3.31186	+	0.848597i	0.177534	+	0.0454896i
$349$	−1.77040	−	12.3134i	−0.0947674	−	0.659122i	−0.980730	−	0.195366i	$-0.937411\pi$
$349$	−1.77040	−	12.3134i	−0.0947674	−	0.659122i	0.885963	−	0.463756i	$-0.153499\pi$
$350$	1.46440	+	1.41436i	0.0782755	+	0.0756005i
$351$	5.88609	+	0.846291i	0.314176	+	0.0451717i
$352$	4.72182	+	7.10255i	0.251674	+	0.378567i
$353$	−26.4572	−	17.0030i	−1.40817	−	0.904978i	−0.408205	−	0.912890i	$-0.633845\pi$
$353$	−26.4572	−	17.0030i	−1.40817	−	0.904978i	−0.999969	+	0.00791181i	$0.997482\pi$
$354$	1.06331	−	19.6657i	0.0565145	−	1.04522i
$355$	19.9352	+	5.85350i	1.05805	+	0.310672i
$356$	1.75690	−	16.1992i	0.0931157	−	0.858556i
$357$	−16.5224	−	19.0679i	−0.874461	−	1.00918i
$358$	1.00779	+	11.3214i	0.0532635	+	0.598354i
$359$	−1.38216	+	3.02652i	−0.0729478	+	0.159733i	−0.942593	−	0.333944i	$-0.891620\pi$
$359$	−1.38216	+	3.02652i	−0.0729478	+	0.159733i	0.869645	+	0.493677i	$0.164348\pi$
$360$	9.03077	+	14.6654i	0.475963	+	0.772934i
$361$	−7.40982	+	2.17572i	−0.389990	+	0.114512i
$362$	20.8032	−	4.90567i	1.09339	−	0.257836i
$363$	−18.7172	+	8.54785i	−0.982398	+	0.448646i
$364$	19.4397	+	15.6955i	1.01892	+	0.822668i
$365$	−15.1358	−	23.5518i	−0.792245	−	1.23276i
$366$	−11.3953	+	32.2533i	−0.595640	+	1.68591i
$367$	−10.9298			−0.570533			−0.285266	−	0.958448i	$-0.592082\pi$
$367$	−10.9298			−0.570533			−0.285266	+	0.958448i	$0.592082\pi$
$368$	0.593220	+	19.1742i	0.0309237	+	0.999522i
$369$	3.89119			0.202567
$370$	−6.70465	+	18.9769i	−0.348558	+	0.986563i
$371$	0.455721	+	0.709115i	0.0236598	+	0.0368154i
$372$	−29.6610	−	23.9481i	−1.53785	−	1.24165i
$373$	−14.6971	+	6.71196i	−0.760990	+	0.347532i	−0.757821	−	0.652463i	$-0.773736\pi$
$373$	−14.6971	+	6.71196i	−0.760990	+	0.347532i	−0.00316870	+	0.999995i	$0.501009\pi$
$374$	10.1782	−	2.40015i	0.526302	−	0.124109i
$375$	23.3598	−	6.85907i	1.20630	−	0.354201i
$376$	1.17152	+	1.90247i	0.0604165	+	0.0981125i
$377$	−1.72443	+	3.77599i	−0.0888129	+	0.194473i
$378$	−0.284135	−	3.19193i	−0.0146143	−	0.164175i
$379$	16.6381	+	19.2014i	0.854642	+	0.986310i	0.999995	−	0.00306989i	$-0.000977179\pi$
$379$	16.6381	+	19.2014i	0.854642	+	0.986310i	−0.145353	+	0.989380i	$0.546432\pi$
$380$	2.65208	−	24.4530i	0.136049	−	1.25441i
$381$	1.57181	+	0.461525i	0.0805263	+	0.0236447i
$382$	1.15059	−	21.2799i	0.0588695	−	1.08877i
$383$	−12.9260	−	8.30703i	−0.660487	−	0.424469i	0.166998	−	0.985957i	$-0.446593\pi$
$383$	−12.9260	−	8.30703i	−0.660487	−	0.424469i	−0.827485	+	0.561488i	$0.810229\pi$
$384$	6.21964	−	25.9410i	0.317395	−	1.32380i
$385$	−7.74625	−	1.11374i	−0.394785	−	0.0567616i
$386$	3.75213	+	3.62390i	0.190978	+	0.184451i
$387$	3.38349	+	23.5327i	0.171993	+	1.19623i
$388$	11.1510	+	2.85723i	0.566108	+	0.145054i
$389$	6.61711	+	5.73376i	0.335501	+	0.290713i	0.806275	−	0.591541i	$-0.201480\pi$
$389$	6.61711	+	5.73376i	0.335501	+	0.290713i	−0.470775	+	0.882254i	$0.656026\pi$
$390$	−42.2761	+	16.6108i	−2.14073	+	0.841121i
$391$	22.2956	+	7.49265i	1.12754	+	0.378920i
$392$	−2.74205	+	5.71070i	−0.138494	+	0.288434i
$393$	−26.6730	+	30.7823i	−1.34547	+	1.55276i
$394$	10.7660	−	14.9152i	0.542384	−	0.751419i
$395$	−26.0192	+	3.74100i	−1.30917	+	0.188230i
$396$	−7.12778	−	2.96023i	−0.358184	−	0.148757i
$397$	−5.47035	+	38.0471i	−0.274549	+	1.90953i	0.123817	+	0.992305i	$0.460486\pi$
$397$	−5.47035	+	38.0471i	−0.274549	+	1.90953i	−0.398366	+	0.917226i	$0.630423\pi$
$398$	−3.17790	+	2.46629i	−0.159294	+	0.123624i
$399$	14.3775	−	22.3718i	0.719776	−	1.11999i
$400$	2.31407	+	1.26919i	0.115703	+	0.0634597i
$401$	6.65811	−	22.6754i	0.332490	−	1.13236i	−0.608396	−	0.793634i	$-0.708187\pi$
$401$	6.65811	−	22.6754i	0.332490	−	1.13236i	0.940886	−	0.338723i	$-0.109995\pi$
$402$	0.0585521	−	0.111808i	0.00292031	−	0.00557647i
$403$	34.9815	−	30.3116i	1.74255	−	1.50993i
$404$	13.4695	−	6.72662i	0.670132	−	0.334662i
$405$	21.9162	+	10.0088i	1.08902	+	0.497340i
$406$	2.19379	+	0.437438i	0.108876	+	0.0217097i
$407$	−2.54101	−	8.65388i	−0.125953	−	0.428957i
$408$	−27.1702	−	18.2097i	−1.34513	−	0.901514i
$409$	14.3588	+	31.4413i	0.709996	+	1.55467i	0.827415	+	0.561592i	$0.189811\pi$
$409$	14.3588	+	31.4413i	0.709996	+	1.55467i	−0.117419	+	0.993082i	$0.537462\pi$
$410$	4.44597	−	2.52898i	0.219571	−	0.124898i
$411$	−25.0416	+	16.0932i	−1.23521	+	0.793821i
$412$	0.871873	+	25.0684i	0.0429541	+	1.23503i
$413$		−	12.8862i		−	0.634089i
$414$	−10.1060	−	14.1147i	−0.496682	−	0.693698i
$415$		−	4.43996i		−	0.217949i
$416$	29.6680	+	12.9965i	1.45460	+	0.637207i
$417$	9.12754	−	5.86591i	0.446977	−	0.287255i
$418$	5.44978	+	9.58075i	0.266557	+	0.468610i
$419$	15.1366	+	33.1446i	0.739472	+	1.61922i	0.784421	+	0.620229i	$0.212960\pi$
$419$	15.1366	+	33.1446i	0.739472	+	1.61922i	−0.0449489	+	0.998989i	$0.514313\pi$
$420$	13.9413	+	20.1193i	0.680264	+	0.981723i
$421$	5.94890	+	20.2601i	0.289932	+	0.987417i	0.967692	+	0.252134i	$0.0811324\pi$
$421$	5.94890	+	20.2601i	0.289932	+	0.987417i	−0.677761	+	0.735283i	$0.737049\pi$
$422$	2.96923	−	14.8910i	0.144540	−	0.724880i
$423$	−1.83913	−	0.839902i	−0.0894215	−	0.0408374i
$424$	0.811913	+	0.731361i	0.0394300	+	0.0355180i
$425$	2.44564	−	2.11916i	0.118631	−	0.102794i
$426$	25.7979	+	13.5100i	1.24991	+	0.654561i
$427$	−6.30574	+	21.4754i	−0.305156	+	1.03927i
$428$	3.31617	+	9.99464i	0.160293	+	0.483109i
$429$	11.0047	−	17.1237i	0.531313	−	0.826739i
$430$	19.1604	+	24.6888i	0.923995	+	1.19060i
$431$	1.22660	−	8.53121i	0.0590834	−	0.410934i	−0.938720	−	0.344682i	$-0.887987\pi$
$431$	1.22660	−	8.53121i	0.0590834	−	0.410934i	0.997803	−	0.0662521i	$-0.0211042\pi$
$432$	−1.44450	−	3.89506i	−0.0694984	−	0.187401i
$433$	−4.04637	+	0.581781i	−0.194456	+	0.0279586i	−0.238855	−	0.971055i	$-0.576772\pi$
$433$	−4.04637	+	0.581781i	−0.194456	+	0.0279586i	0.0443984	+	0.999014i	$0.485863\pi$
$434$	−20.2251	−	14.5987i	−0.970837	−	0.700762i
$435$	−2.66318	+	3.07347i	−0.127690	+	0.147362i
$436$	6.40386	+	6.89113i	0.306689	+	0.330025i
$437$	−0.956787	+	24.7731i	−0.0457693	+	1.18506i
$438$	−14.3500	−	36.5221i	−0.685670	−	1.74509i
$439$	−9.00939	−	7.80668i	−0.429994	−	0.372592i	0.412806	−	0.910819i	$-0.364549\pi$
$439$	−9.00939	−	7.80668i	−0.429994	−	0.372592i	−0.842800	+	0.538227i	$0.819094\pi$
$440$	−10.0679	+	1.25025i	−0.479970	+	0.0596031i
$441$	−0.815839	−	5.67429i	−0.0388495	−	0.270204i
$442$	27.5894	−	28.5656i	1.31229	−	1.35873i
$443$	22.4322	+	3.22526i	1.06579	+	0.153237i	0.652823	−	0.757511i	$-0.273585\pi$
$443$	22.4322	+	3.22526i	1.06579	+	0.153237i	0.412963	+	0.910748i	$0.364494\pi$
$444$	−14.4173	+	24.2474i	−0.684215	+	1.15073i
$445$	16.3054	+	10.4788i	0.772949	+	0.496744i
$446$	4.96439	+	0.268422i	0.235071	+	0.0127102i
$447$	12.5563	+	3.68687i	0.593893	+	0.174383i
$448$	3.14722	−	17.1684i	0.148692	−	0.811129i
$449$	−17.0194	−	19.6414i	−0.803194	−	0.926936i	0.195358	−	0.980732i	$-0.437413\pi$
$449$	−17.0194	−	19.6414i	−0.803194	−	0.926936i	−0.998552	+	0.0537965i	$0.982868\pi$
$450$	−2.37895	+	0.211767i	−0.112145	+	0.00998277i
$451$	−0.952186	+	2.08500i	−0.0448367	+	0.0981787i
$452$	−3.19673	−	17.8135i	−0.150361	−	0.837876i
$453$	10.0659	−	2.95561i	0.472936	−	0.138867i
$454$	−7.14592	−	30.3033i	−0.335374	−	1.42220i
$455$	−27.0344	+	12.3462i	−1.26739	+	0.578799i
$456$	10.3477	−	32.8854i	0.484574	−	1.54000i
$457$	−2.87038	−	4.46640i	−0.134271	−	0.208929i	0.767607	−	0.640921i	$-0.221447\pi$
$457$	−2.87038	−	4.46640i	−0.134271	−	0.208929i	−0.901878	+	0.431992i	$0.857811\pi$
$458$	−5.10630	−	1.80408i	−0.238602	−	0.0842992i
$459$	−5.09362			−0.237750
$460$	−20.7203	−	9.55890i	−0.966089	−	0.445686i
$461$	21.1419			0.984674			0.492337	−	0.870405i	$-0.336143\pi$
$461$	21.1419			0.984674			0.492337	+	0.870405i	$0.336143\pi$
$462$	−10.3425	−	3.65405i	−0.481176	−	0.170002i
$463$	10.8887	+	16.9431i	0.506039	+	0.787413i	0.996460	−	0.0840736i	$-0.0267931\pi$
$463$	10.8887	+	16.9431i	0.506039	+	0.787413i	−0.490420	+	0.871486i	$0.663157\pi$
$464$	2.89294	−	0.201476i	0.134302	−	0.00935327i
$465$	41.2489	−	18.8377i	1.91287	−	0.873579i
$466$	−4.39559	−	18.6401i	−0.203622	−	0.863488i
$467$	−16.5921	+	4.87189i	−0.767792	+	0.225444i	−0.642095	−	0.766625i	$-0.721935\pi$
$467$	−16.5921	+	4.87189i	−0.767792	+	0.225444i	−0.125696	+	0.992069i	$0.540116\pi$
$468$	−28.8497	+	5.17723i	−1.33358	+	0.239318i
$469$	0.0343054	−	0.0751184i	0.00158408	−	0.00346865i
$470$	−2.64721	+	0.235646i	−0.122107	+	0.0108695i
$471$	2.62598	+	3.03054i	0.120999	+	0.139640i
$472$	−4.39700	−	16.1162i	−0.202388	−	0.741810i
$473$	−13.4374	−	3.94556i	−0.617850	−	0.181417i
$474$	−36.7905	−	1.98925i	−1.68984	−	0.0913691i
$475$	2.86940	+	1.84405i	0.131657	+	0.0846109i
$476$	−18.3951	−	10.9375i	−0.843136	−	0.501321i
$477$	−0.978793	−	0.140729i	−0.0448159	−	0.00644355i
$478$	5.82828	−	6.03451i	0.266579	−	0.276012i
$479$	−5.22142	−	36.3158i	−0.238573	−	1.65931i	−0.659118	−	0.752040i	$-0.729070\pi$
$479$	−5.22142	−	36.3158i	−0.238573	−	1.65931i	0.420545	−	0.907272i	$-0.361839\pi$
$480$	24.3008	+	20.4054i	1.10918	+	0.931374i
$481$	−25.8859	−	22.4303i	−1.18030	−	1.02273i
$482$	11.2661	+	28.6733i	0.513157	+	1.30603i
$483$	−15.4249	−	19.2553i	−0.701857	−	0.876145i
$484$	−12.7853	+	11.8813i	−0.581151	+	0.540058i
$485$	−8.96693	+	10.3484i	−0.407167	+	0.469896i
$486$	23.8092	+	17.1858i	1.08001	+	0.779564i
$487$	26.4728	−	3.80622i	1.19960	−	0.172476i	0.486589	−	0.873631i	$-0.338241\pi$
$487$	26.4728	−	3.80622i	1.19960	−	0.172476i	0.713009	+	0.701155i	$0.247332\pi$
$488$	−0.558545	+	29.0100i	−0.0252841	+	1.31322i
$489$	5.92742	−	41.2261i	0.268047	−	1.86431i
$490$	−4.62002	−	5.95305i	−0.208711	−	0.268932i
$491$	−4.04450	+	6.29337i	−0.182526	+	0.284016i	−0.920444	−	0.390874i	$-0.872173\pi$
$491$	−4.04450	+	6.29337i	−0.182526	+	0.284016i	0.737918	+	0.674890i	$0.235809\pi$
$492$	6.80445	−	2.25768i	0.306768	−	0.101784i
$493$	1.00175	−	3.41164i	0.0451164	−	0.153652i
$494$	37.0819	+	19.4192i	1.66839	+	0.873713i
$495$	6.93835	−	6.01212i	0.311856	−	0.270225i
$496$	−30.2760	−	11.3569i	−1.35943	−	0.509938i
$497$	17.3324	+	7.91545i	0.777465	+	0.355057i
$498$	1.21693	−	6.10303i	0.0545321	−	0.273484i
$499$	−3.15885	−	10.7580i	−0.141409	−	0.481596i	0.858081	−	0.513514i	$-0.171657\pi$
$499$	−3.15885	−	10.7580i	−0.141409	−	0.481596i	−0.999490	+	0.0319179i	$0.989838\pi$
$500$	16.9741	−	11.7618i	0.759104	−	0.526005i
$501$	4.66801	+	10.2215i	0.208551	+	0.456663i
$502$	12.7005	+	22.3276i	0.566853	+	0.996532i
$503$	35.5200	−	22.8273i	1.58376	−	1.01782i	0.609388	−	0.792872i	$-0.291415\pi$
$503$	35.5200	−	22.8273i	1.58376	−	1.01782i	0.974371	−	0.224947i	$-0.0722210\pi$
$504$	6.28371	+	14.4913i	0.279899	+	0.645495i
$505$			17.9091i			0.796943i
$506$	10.0360	−	1.96114i	0.446152	−	0.0871832i
$507$		−	46.6490i		−	2.07176i
$508$	1.38870	−	0.0482985i	0.0616134	−	0.00214290i
$509$	−8.96660	+	5.76248i	−0.397437	+	0.255417i	−0.724060	−	0.689738i	$-0.757726\pi$
$509$	−8.96660	+	5.76248i	−0.397437	+	0.255417i	0.326622	+	0.945155i	$0.394090\pi$
$510$	33.8184	−	19.2368i	1.49750	−	0.851819i
$511$	−10.6658	−	23.3549i	−0.471828	−	1.03316i
$512$	−1.92206	−	22.5456i	−0.0849437	−	0.996386i
$513$	−1.51256	−	5.15131i	−0.0667811	−	0.227436i
$514$	19.3527	+	3.85890i	0.853613	+	0.170209i
$515$	−27.1410	−	12.3949i	−1.19598	−	0.546184i
$516$	19.5704	+	39.1881i	0.861538	+	1.72516i
$517$	0.900080	−	0.779924i	0.0395855	−	0.0343010i
$518$	−8.56302	+	16.3515i	−0.376237	+	0.718442i
$519$	3.20440	−	10.9132i	0.140658	−	0.479036i
$520$	−29.5981	+	24.6655i	−1.29796	+	1.08165i
$521$	−17.4595	+	27.1676i	−0.764916	+	1.19023i	0.212138	+	0.977240i	$0.431958\pi$
$521$	−17.4595	+	27.1676i	−0.764916	+	1.19023i	−0.977054	+	0.212993i	$0.931679\pi$
$522$	−2.07317	+	1.60894i	−0.0907402	+	0.0704212i
$523$	−3.75821	+	26.1389i	−0.164335	+	1.14298i	0.726008	+	0.687686i	$0.241373\pi$
$523$	−3.75821	+	26.1389i	−0.164335	+	1.14298i	−0.890343	+	0.455290i	$0.849536\pi$
$524$	−13.2511	+	31.9066i	−0.578876	+	1.39385i
$525$	−3.35982	+	0.483070i	−0.146635	+	0.0210829i
$526$	−11.5095	+	15.9453i	−0.501837	+	0.695246i
$527$	−25.9636	+	29.9636i	−1.13099	+	1.30524i
$528$	−14.1817	−	1.04093i	−0.617181	−	0.0453008i
$529$	21.5028	+	8.16266i	0.934905	+	0.354898i
$530$	−1.20981	+	0.475348i	−0.0525506	+	0.0206478i
$531$	11.4248	+	9.89961i	0.495792	+	0.429606i
$532$	5.59896	−	21.8513i	0.242746	−	0.947375i
$533$	1.23882	+	8.61615i	0.0536591	+	0.373207i
$534$	19.5408	+	18.8730i	0.845611	+	0.816713i
$535$	−12.3986	−	1.78266i	−0.536040	−	0.0770709i
$536$	0.0172726	−	0.105653i	0.000746064	−	0.00456352i
$537$	−15.9421	−	10.2453i	−0.687950	−	0.442119i
$538$	−1.61284	+	29.8290i	−0.0695345	+	1.28602i
$539$	3.24006	+	0.951368i	0.139559	+	0.0409783i
$540$	4.91279	+	0.532822i	0.211413	+	0.0229290i
$541$	−4.67578	−	5.39614i	−0.201028	−	0.231998i	0.646280	−	0.763100i	$-0.276324\pi$
$541$	−4.67578	−	5.39614i	−0.201028	−	0.231998i	−0.847308	+	0.531102i	$0.821778\pi$
$542$	0.0879160	+	0.987634i	0.00377631	+	0.0424225i
$543$	−14.8036	+	32.4154i	−0.635284	+	1.39108i
$544$	−26.7380	−	7.40240i	−1.14638	−	0.317375i
$545$	−10.7369	+	3.15263i	−0.459917	+	0.135044i
$546$	−40.5446	+	9.56094i	−1.73515	+	0.409170i
$547$	22.4276	−	10.2424i	0.958937	−	0.437932i	0.126448	−	0.991973i	$-0.459642\pi$
$547$	22.4276	−	10.2424i	0.958937	−	0.437932i	0.832489	+	0.554041i	$0.186915\pi$
$548$	−15.8614	+	19.6452i	−0.677565	+	0.839201i
$549$	−14.1955	−	22.0887i	−0.605851	−	0.942722i
$550$	0.468667	−	1.32652i	0.0199840	−	0.0565631i
$551$	3.74775			0.159659
$552$	−25.8615	−	18.8185i	−1.10074	−	0.800969i
$553$	−24.1075			−1.02515
$554$	8.80756	−	24.9290i	0.374197	−	1.05913i
$555$	−18.1418	−	28.2292i	−0.770078	−	1.19826i
$556$	5.78140	−	7.16058i	0.245186	−	0.303676i
$557$	9.07079	−	4.14249i	0.384342	−	0.175523i	−0.213868	−	0.976863i	$-0.568606\pi$
$557$	9.07079	−	4.14249i	0.384342	−	0.175523i	0.598210	+	0.801340i	$0.295879\pi$
$558$	28.4807	−	6.71612i	1.20568	−	0.284316i
$559$	−51.0306	+	14.9839i	−2.15836	+	0.633753i
$560$	16.5979	+	12.4735i	0.701388	+	0.527100i
$561$	−7.24284	+	15.8596i	−0.305793	+	0.669593i
$562$	2.94911	+	33.1299i	0.124401	+	1.39750i
$563$	−26.8668	−	31.0059i	−1.13230	−	1.30674i	−0.945969	−	0.324257i	$-0.894886\pi$
$563$	−26.8668	−	31.0059i	−1.13230	−	1.30674i	−0.186331	−	0.982487i	$-0.559660\pi$
$564$	−3.70336	−	0.401652i	−0.155940	−	0.0169126i
$565$	20.6559	+	6.06513i	0.869002	+	0.255162i
$566$	0.581956	−	10.7631i	0.0244614	−	0.452407i
$567$	18.5884	+	11.9460i	0.780637	+	0.501685i
$568$	24.3778	+	3.98539i	1.02287	+	0.167223i
$569$	−0.997069	−	0.143357i	−0.0417993	−	0.00600983i	0.121383	−	0.992606i	$-0.461267\pi$
$569$	−0.997069	−	0.143357i	−0.0417993	−	0.00600983i	−0.163183	+	0.986596i	$0.552176\pi$
$570$	29.4971	+	28.4890i	1.23550	+	1.19327i
$571$	4.09175	+	28.4588i	0.171234	+	1.19096i	0.876281	+	0.481801i	$0.160017\pi$
$571$	4.09175	+	28.4588i	0.171234	+	1.19096i	−0.705046	+	0.709161i	$0.749074\pi$
$572$	4.28551	−	16.7253i	0.179186	−	0.699318i
$573$	26.8525	+	23.2678i	1.12178	+	0.972028i
$574$	4.36595	−	1.71544i	0.182231	−	0.0716011i
$575$	2.46967	−	1.97839i	0.102992	−	0.0825045i
$576$	12.8035	+	15.9796i	0.533478	+	0.665816i
$577$	−8.92001	+	10.2942i	−0.371345	+	0.428555i	−0.910409	−	0.413710i	$-0.864233\pi$
$577$	−8.92001	+	10.2942i	−0.371345	+	0.428555i	0.539064	+	0.842265i	$0.318778\pi$
$578$	−5.83829	+	8.08838i	−0.242841	+	0.336432i
$579$	−8.60862	+	1.23773i	−0.357762	+	0.0514384i
$580$	−1.32306	+	3.18573i	−0.0549371	+	0.132280i
$581$	0.579488	−	4.03043i	0.0240412	−	0.167210i
$582$	−15.1620	+	11.7669i	−0.628485	+	0.487752i
$583$	0.314920	−	0.490025i	0.0130426	−	0.0202947i
$584$	−21.3084	−	25.5696i	−0.881748	−	1.05808i
$585$	9.82273	−	33.4531i	0.406120	−	1.38312i
$586$	−7.71780	+	14.7375i	−0.318819	+	0.608799i
$587$	33.6765	−	29.1808i	1.38998	−	1.20442i	0.437725	−	0.899109i	$-0.355785\pi$
$587$	33.6765	−	29.1808i	1.38998	−	1.20442i	0.952252	−	0.305313i	$-0.0987609\pi$
$588$	−4.71888	−	9.44916i	−0.194603	−	0.389677i
$589$	−38.0130	−	17.3599i	−1.56630	−	0.715304i
$590$	19.4876	+	3.88579i	0.802292	+	0.159975i
$591$	8.64048	+	29.4268i	0.355422	+	1.21046i
$592$	−5.13000	+	23.3719i	−0.210842	+	0.960580i
$593$	−9.22653	−	20.2033i	−0.378888	−	0.829649i	−0.998982	−	0.0451211i	$-0.985633\pi$
$593$	−9.22653	−	20.2033i	−0.378888	−	0.829649i	0.620093	−	0.784528i	$-0.287095\pi$
$594$	−1.92484	+	1.09490i	−0.0789773	+	0.0449243i
$595$	21.4158	−	13.7631i	0.877963	−	0.564232i
$596$	11.0935	−	0.385830i	0.454408	−	0.0158042i
$597$		−	6.70680i		−	0.274491i
$598$	28.0363	−	26.8710i	1.14649	−	1.09884i
$599$			1.33089i			0.0543785i	0.999630	+	0.0271893i	$0.00865568\pi$
$599$			1.33089i			0.0543785i	−0.999630	+	0.0271893i	$0.991344\pi$
$600$	−4.03716	+	1.75059i	−0.164816	+	0.0714674i
$601$	−5.66720	+	3.64209i	−0.231170	+	0.148564i	−0.651098	−	0.758993i	$-0.725692\pi$
$601$	−5.66720	+	3.64209i	−0.231170	+	0.148564i	0.419929	+	0.907557i	$0.362055\pi$
$602$	14.1708	+	24.9123i	0.577557	+	1.01535i
$603$	0.0402445	+	0.0881233i	0.00163888	+	0.00358866i
$604$	7.31422	−	5.06823i	0.297611	−	0.206223i
$605$	−5.84917	−	19.9204i	−0.237803	−	0.809881i
$606$	−4.90862	+	24.6172i	−0.199399	+	1.00001i
$607$	17.9110	+	8.17968i	0.726985	+	0.332003i	0.744298	−	0.667847i	$-0.232784\pi$
$607$	17.9110	+	8.17968i	0.726985	+	0.332003i	−0.0173136	+	0.999850i	$0.505511\pi$
$608$	−0.453668	−	29.2390i	−0.0183987	−	1.18580i
$609$	−2.81867	+	2.44239i	−0.114218	+	0.0989706i
$610$	−30.5754	−	16.0119i	−1.23796	−	0.648303i
$611$	1.27426	−	4.33972i	0.0515509	−	0.175566i
$612$	23.8288	−	7.90626i	0.963221	−	0.319592i
$613$	17.4580	−	27.1651i	0.705121	−	1.09719i	−0.285210	−	0.958465i	$-0.592063\pi$
$613$	17.4580	−	27.1651i	0.705121	−	1.09719i	0.990331	−	0.138724i	$-0.0443002\pi$
$614$	−12.6503	−	16.3003i	−0.510524	−	0.657828i
$615$	−1.21365	+	8.44111i	−0.0489390	+	0.340379i
$616$	−9.30246	−	0.179105i	−0.374807	−	0.00721636i
$617$	26.4111	−	3.79734i	1.06327	−	0.152875i	0.411590	−	0.911369i	$-0.364974\pi$
$617$	26.4111	−	3.79734i	1.06327	−	0.152875i	0.651680	+	0.758494i	$0.274065\pi$
$618$	−33.9099	−	24.4766i	−1.36406	−	0.984592i
$619$	16.9786	−	19.5944i	0.682429	−	0.787565i	−0.303838	−	0.952724i	$-0.598268\pi$
$619$	16.9786	−	19.5944i	0.682429	−	0.787565i	0.986267	+	0.165158i	$0.0528135\pi$
$620$	28.1763	−	26.1839i	1.13159	−	1.05157i
$621$	−4.97710	−	0.192226i	−0.199724	−	0.00771375i
$622$	−10.7245	−	27.2949i	−0.430014	−	1.09443i
$623$	13.4337	+	11.6404i	0.538211	+	0.466363i
$624$	−47.4450	+	25.7920i	−1.89932	+	1.03251i
$625$	3.96542	+	27.5801i	0.158617	+	1.10320i
$626$	1.91403	−	1.98176i	0.0765002	−	0.0792071i
$627$	−18.1900	−	2.61533i	−0.726439	−	0.104446i
$628$	2.92360	+	1.73834i	0.116664	+	0.0693675i
$629$	24.6814	+	15.8618i	0.984111	+	0.632449i
$630$	−18.7611	−	1.01440i	−0.747461	−	0.0404149i
$631$	−45.6117	−	13.3928i	−1.81577	−	0.533159i	−0.816735	−	0.577013i	$-0.804218\pi$
$631$	−45.6117	−	13.3928i	−1.81577	−	0.533159i	−0.999038	+	0.0438540i	$0.986036\pi$
$632$	−30.1502	+	8.22590i	−1.19931	+	0.327209i
$633$	16.5784	+	19.1325i	0.658931	+	0.760447i
$634$	−2.32195	+	0.206692i	−0.0922163	+	0.00820879i
$635$	−0.686630	+	1.50351i	−0.0272481	+	0.0596650i
$636$	−1.79325	+	0.321808i	−0.0711069	+	0.0127605i
$637$	12.3047	−	3.61298i	0.487529	−	0.143151i
$638$	−0.354797	−	1.50457i	−0.0140465	−	0.0595664i
$639$	−20.3331	+	9.28581i	−0.804364	+	0.367341i
$640$	25.0144	+	9.93655i	0.988782	+	0.392777i
$641$	21.3490	+	33.2197i	0.843236	+	1.31210i	0.948216	+	0.317626i	$0.102886\pi$
$641$	21.3490	+	33.2197i	0.843236	+	1.31210i	−0.104980	+	0.994474i	$0.533478\pi$
$642$	−16.5542	−	5.84868i	−0.653341	−	0.230829i
$643$	−22.3558			−0.881625			−0.440812	−	0.897599i	$-0.645310\pi$
$643$	−22.3558			−0.881625			−0.440812	+	0.897599i	$0.645310\pi$
$644$	−17.5615	−	11.3815i	−0.692020	−	0.448495i
$645$	−52.1045			−2.05161
$646$	−33.8067	−	11.9441i	−1.33011	−	0.469933i
$647$	7.86724	+	12.2417i	0.309293	+	0.481270i	0.960750	−	0.277416i	$-0.0894781\pi$
$647$	7.86724	+	12.2417i	0.309293	+	0.481270i	−0.651457	+	0.758686i	$0.725842\pi$
$648$	27.3239	+	8.59769i	1.07338	+	0.337749i
$649$	−8.10012	+	3.69920i	−0.317958	+	0.145206i
$650$	−1.22628	−	5.20022i	−0.0480987	−	0.203970i
$651$	39.9028	−	11.7165i	1.56391	−	0.459207i
$652$	−6.24023	−	34.7731i	−0.244386	−	1.36182i
$653$	4.96864	−	10.8798i	0.194438	−	0.425760i	−0.787152	−	0.616759i	$-0.788445\pi$
$653$	4.96864	−	10.8798i	0.194438	−	0.425760i	0.981590	+	0.190999i	$0.0611727\pi$
$654$	−15.6226	+	1.39068i	−0.610894	+	0.0543798i
$655$	−26.9125	−	31.0587i	−1.05156	−	1.21356i
$656$	4.87498	−	3.63517i	0.190336	−	0.141930i
$657$	28.9000	+	8.48581i	1.12750	+	0.331063i
$658$	−2.43379	−	0.131594i	−0.0948791	−	0.00513007i
$659$	8.10663	+	5.20981i	0.315789	+	0.202945i	0.688927	−	0.724830i	$-0.258082\pi$
$659$	8.10663	+	5.20981i	0.315789	+	0.202945i	−0.373138	+	0.927776i	$0.621718\pi$
$660$	8.64471	−	14.5389i	0.336495	−	0.565927i
$661$	−28.3807	−	4.08053i	−1.10388	−	0.158714i	−0.433805	−	0.901007i	$-0.642829\pi$
$661$	−28.3807	−	4.08053i	−1.10388	−	0.158714i	−0.670076	+	0.742292i	$0.733739\pi$
$662$	−10.8097	+	11.1922i	−0.420131	+	0.434997i
$663$	9.42309	+	65.5390i	0.365963	+	2.54533i
$664$	−0.650512	−	5.23842i	−0.0252448	−	0.203290i
$665$	20.2785	+	17.5714i	0.786365	+	0.681389i
$666$	−7.91861	−	20.1536i	−0.306840	−	0.780936i
$667$	1.10758	−	3.29579i	0.0428857	−	0.127614i
$668$	6.48840	+	6.98210i	0.251044	+	0.270146i
$669$	−5.42816	+	6.26443i	−0.209865	+	0.242197i
$670$	0.103256	+	0.0745313i	0.00398912	+	0.00287940i
$671$	15.3094	−	2.20115i	0.591011	−	0.0849746i
$672$	19.3961	+	21.6949i	0.748221	+	0.836898i
$673$	3.12827	−	21.7576i	0.120586	−	0.838694i	−0.836309	−	0.548259i	$-0.815291\pi$
$673$	3.12827	−	21.7576i	0.120586	−	0.838694i	0.956895	−	0.290435i	$-0.0938000\pi$
$674$	15.4832	+	19.9506i	0.596389	+	0.768468i
$675$	−0.370484	+	0.576484i	−0.0142599	+	0.0221889i
$676$	−12.4608	−	37.5556i	−0.479260	−	1.44445i
$677$	7.86602	−	26.7892i	0.302316	−	1.02959i	−0.658541	−	0.752545i	$-0.728826\pi$
$677$	7.86602	−	26.7892i	0.302316	−	1.02959i	0.960856	−	0.277047i	$-0.0893559\pi$
$678$	26.7306	+	13.9984i	1.02658	+	0.537607i
$679$	−9.49046	+	8.22353i	−0.364211	+	0.315590i
$680$	22.0876	−	24.5204i	0.847022	−	0.940314i
$681$	47.2184	+	21.5639i	1.80941	+	0.826331i
$682$	−3.37064	+	16.9041i	−0.129069	+	0.647292i
$683$	−0.465604	−	1.58570i	−0.0178159	−	0.0606752i	0.950105	−	0.311929i	$-0.100975\pi$
$683$	−0.465604	−	1.58570i	−0.0178159	−	0.0606752i	−0.967921	+	0.251254i	$0.919157\pi$
$684$	15.0718	+	21.7509i	0.576285	+	0.831666i
$685$	−12.4767	−	27.3201i	−0.476710	−	1.04385i
$686$	−14.0960	−	24.7809i	−0.538189	−	0.946141i
$687$	7.59590	−	4.88159i	0.289802	−	0.186244i
$688$	26.2233	+	26.3214i	0.999753	+	1.00350i
$689$		−	2.21211i		−	0.0842749i
$690$	33.7708	−	17.5205i	1.28563	−	0.666993i
$691$		−	45.1426i		−	1.71730i	−0.512559	−	0.858652i	$-0.671303\pi$
$691$		−	45.1426i		−	1.71730i	0.512559	−	0.858652i	$-0.328697\pi$
$692$	−0.335340	−	9.64182i	−0.0127477	−	0.366527i
$693$	7.08305	−	4.55200i	0.269063	−	0.172916i
$694$	14.9421	−	8.49946i	0.567195	−	0.322635i
$695$	4.54769	+	9.95806i	0.172504	+	0.377731i
$696$	−2.69180	+	4.01637i	−0.102032	+	0.152240i
$697$	−2.10063	−	7.15410i	−0.0795671	−	0.270981i
$698$	17.2532	+	3.44026i	0.653044	+	0.130216i
$699$	29.0449	+	13.2644i	1.09858	+	0.501704i
$700$	−2.57585	+	1.28637i	−0.0973579	+	0.0486202i
$701$	−30.2360	+	26.1997i	−1.14200	+	0.989548i	−1.00000		0.000318374i	$-0.999899\pi$
$701$	−30.2360	+	26.1997i	−1.14200	+	0.989548i	−0.142000	+	0.989867i	$0.545353\pi$
$702$	−3.90147	+	7.45003i	−0.147252	+	0.281183i
$703$	−8.71222	+	29.6711i	−0.328588	+	1.11907i
$704$	−11.6953	+	2.95016i	−0.440783	+	0.111188i
$705$	2.39561	−	3.72764i	0.0902237	−	0.140391i
$706$	35.1367	−	27.2687i	1.32239	−	1.02627i
$707$	−2.33743	+	16.2571i	−0.0879079	+	0.611413i
$708$	25.7220	+	10.6826i	0.966692	+	0.401475i
$709$	38.1255	−	5.48162i	1.43183	−	0.205867i	0.617641	−	0.786460i	$-0.288089\pi$
$709$	38.1255	−	5.48162i	1.43183	−	0.205867i	0.814194	+	0.580594i	$0.197179\pi$
$710$	−17.1970	+	23.8247i	−0.645390	+	0.894125i
$711$	18.5202	−	21.3734i	0.694560	−	0.801565i
$712$	20.7729	+	9.97433i	0.778498	+	0.373804i
$713$	−26.5005	+	28.2984i	−0.992452	+	1.05978i
$714$	33.2098	−	13.0486i	1.24284	−	0.488330i
$715$	15.5214	+	13.4493i	0.580466	+	0.502977i
$716$	−15.5711	−	3.98979i	−0.581921	−	0.149106i
$717$	1.99063	+	13.8452i	0.0743416	+	0.517057i
$718$	−3.38452	−	3.26885i	−0.126309	−	0.121992i
$719$	8.62123	+	1.23955i	0.321518	+	0.0462272i	0.301184	−	0.953566i	$-0.402618\pi$
$719$	8.62123	+	1.23955i	0.321518	+	0.0462272i	0.0203334	+	0.999793i	$0.493527\pi$
$720$	−23.8099	+	5.13295i	−0.887341	+	0.191294i
$721$	−23.0198	−	14.7939i	−0.857303	−	0.550955i
$722$	0.589657	−	10.9055i	0.0219448	−	0.405862i
$723$	−49.2831	−	14.4708i	−1.83286	−	0.538176i
$724$	−3.25920	+	30.0509i	−0.121127	+	1.11683i
$725$	−0.313259	−	0.361521i	−0.0116342	−	0.0134265i
$726$	−2.58017	−	28.9852i	−0.0957589	−	1.07574i
$727$	1.54895	−	3.39174i	0.0574475	−	0.125792i	−0.878731	−	0.477317i	$-0.841609\pi$
$727$	1.54895	−	3.39174i	0.0574475	−	0.125792i	0.936179	+	0.351525i	$0.114337\pi$
$728$	−30.0872	+	18.5274i	−1.11511	+	0.686669i
$729$	−17.8225	+	5.23317i	−0.660094	+	0.193821i
$730$	38.5355	−	9.08718i	1.42626	−	0.336332i
$731$	41.4392	−	18.9246i	1.53268	−	0.699953i
$732$	−37.6394	−	30.3898i	−1.39119	−	1.12324i
$733$	21.3671	+	33.2479i	0.789213	+	1.22804i	0.969661	+	0.244454i	$0.0786088\pi$
$733$	21.3671	+	33.2479i	0.789213	+	1.22804i	−0.180448	+	0.983584i	$0.557755\pi$
$734$	5.14916	−	14.5742i	0.190059	−	0.537945i
$735$	12.5636			0.463416
$736$	−25.8470	−	8.24212i	−0.952733	−	0.303809i
$737$	−0.0570666			−0.00210207
$738$	−1.83318	+	5.18866i	−0.0674803	+	0.190997i
$739$	14.2752	+	22.2127i	0.525124	+	0.817108i	0.997947	−	0.0640491i	$-0.0204014\pi$
$739$	14.2752	+	22.2127i	0.525124	+	0.817108i	−0.472823	+	0.881157i	$0.656765\pi$
$740$	−22.1459	−	17.8805i	−0.814100	−	0.657298i
$741$	−63.4831	+	28.9918i	−2.33211	+	1.06504i
$742$	−1.16026	+	0.273603i	−0.0425943	+	0.0100443i
$743$	28.6055	−	8.39932i	1.04943	−	0.308141i	0.288845	−	0.957376i	$-0.406729\pi$
$743$	28.6055	−	8.39932i	1.04943	−	0.308141i	0.760588	+	0.649235i	$0.224911\pi$
$744$	45.9069	−	28.2689i	1.68303	−	1.03639i
$745$	−5.48510	+	12.0107i	−0.200959	+	0.440038i
$746$	−2.02600	−	22.7598i	−0.0741772	−	0.833296i
$747$	3.12815	+	3.61008i	0.114453	+	0.132086i
$748$	−1.59460	+	14.7027i	−0.0583044	+	0.537585i
$749$	−11.0223	−	3.23645i	−0.402748	−	0.118257i
$750$	−1.85893	+	34.3803i	−0.0678784	+	1.25539i
$751$	0.968913	+	0.622683i	0.0353561	+	0.0227220i	0.558200	−	0.829707i	$-0.311492\pi$
$751$	0.968913	+	0.622683i	0.0353561	+	0.0227220i	−0.522843	+	0.852429i	$0.675129\pi$
$752$	−3.08874	+	0.665874i	−0.112635	+	0.0242819i
$753$	−42.3912	−	6.09494i	−1.54482	−	0.222112i
$754$	−4.22264	−	4.07833i	−0.153780	−	0.148524i
$755$	1.50641	+	10.4773i	0.0548237	+	0.381308i
$756$	4.39009	+	1.12487i	0.159666	+	0.0409113i
$757$	−19.1497	−	16.5933i	−0.696007	−	0.603093i	0.233299	−	0.972405i	$-0.425048\pi$
$757$	−19.1497	−	16.5933i	−0.696007	−	0.603093i	−0.929305	+	0.369312i	$0.879593\pi$
$758$	−33.4423	+	13.1399i	−1.21468	+	0.477263i
$759$	−7.67567	+	15.2235i	−0.278609	+	0.552577i
$760$	31.3571	+	15.0564i	1.13744	+	0.546154i
$761$	8.35572	−	9.64301i	0.302895	−	0.349559i	−0.583814	−	0.811887i	$-0.698440\pi$
$761$	8.35572	−	9.64301i	0.302895	−	0.349559i	0.886709	+	0.462328i	$0.152986\pi$
$762$	−1.35591	+	1.87848i	−0.0491195	+	0.0680502i
$763$	−10.1580	+	1.46050i	−0.367744	+	0.0528736i
$764$	27.8333	+	11.5594i	1.00697	+	0.418205i
$765$	−4.25013	+	29.5603i	−0.153664	+	1.06875i
$766$	17.1665	−	13.3225i	0.620250	−	0.481360i
$767$	−18.2832	+	28.4492i	−0.660167	+	1.02724i
$768$	31.6606	+	20.5146i	1.14245	+	0.740256i
$769$	6.44296	−	21.9427i	0.232339	−	0.791274i	−0.757958	−	0.652304i	$-0.773803\pi$
$769$	6.44296	−	21.9427i	0.232339	−	0.791274i	0.990297	−	0.138970i	$-0.0443792\pi$
$770$	5.13444	−	9.80444i	0.185032	−	0.353327i
$771$	−24.8651	+	21.5458i	−0.895496	+	0.775952i
$772$	−6.59990	+	3.29597i	−0.237536	+	0.118625i
$773$	11.5523	+	5.27576i	0.415508	+	0.189756i	0.612189	−	0.790712i	$-0.290289\pi$
$773$	11.5523	+	5.27576i	0.415508	+	0.189756i	−0.196681	+	0.980467i	$0.563016\pi$
$774$	−32.9734	−	6.57483i	−1.18520	−	0.236327i
$775$	1.50275	+	5.11791i	0.0539805	+	0.183841i
$776$	−9.06331	+	13.5231i	−0.325354	+	0.485452i
$777$	−12.7841	−	27.9932i	−0.458626	−	1.00425i
$778$	−10.7630	+	6.12227i	−0.385872	+	0.219494i
$779$	6.61134	−	4.24885i	0.236876	−	0.152231i
$780$	−2.23279	−	64.1980i	−0.0799468	−	2.29866i
$781$		−	13.1672i		−	0.471161i
$782$	−20.4947	+	26.1999i	−0.732888	+	0.936907i
$783$			0.752951i			0.0269083i
$784$	−6.32305	−	6.34672i	−0.225823	−	0.226669i
$785$	−3.40370	+	2.18742i	−0.121483	+	0.0780725i
$786$	−28.4803	−	50.0686i	−1.01586	−	1.78589i
$787$	−9.86579	−	21.6031i	−0.351677	−	0.770066i	−0.999962	−	0.00866835i	$-0.997241\pi$
$787$	−9.86579	−	21.6031i	−0.351677	−	0.770066i	0.648285	−	0.761398i	$-0.275487\pi$
$788$	14.8166	+	21.3825i	0.527818	+	0.761721i
$789$	−9.23717	−	31.4589i	−0.328852	−	1.11997i
$790$	7.26953	−	36.4574i	0.258638	−	1.29710i
$791$	17.9591	+	8.20163i	0.638551	+	0.291616i
$792$	7.30525	−	8.10986i	0.259581	−	0.288171i
$793$	44.3910	−	38.4650i	1.57637	−	1.36593i
$794$	−48.1563	−	25.2188i	−1.70900	−	0.894981i
$795$	0.610564	−	2.07939i	0.0216545	−	0.0737484i
$796$	−1.79150	−	5.39943i	−0.0634981	−	0.191378i
$797$	5.63454	−	8.76752i	0.199586	−	0.310562i	−0.727005	−	0.686632i	$-0.759088\pi$
$797$	5.63454	−	8.76752i	0.199586	−	0.310562i	0.926591	+	0.376070i	$0.122725\pi$
$798$	23.0581	+	29.7111i	0.816246	+	1.05176i
$799$	−0.551349	+	3.83472i	−0.0195053	+	0.135663i
$800$	−2.78257	+	2.48773i	−0.0983788	+	0.0879547i
$801$	−20.6405	+	2.96765i	−0.729296	+	0.104857i
$802$	27.0996	+	19.5608i	0.956919	+	0.690716i
$803$	−11.6188	+	13.4088i	−0.410019	+	0.473188i
$804$	0.121504	+	0.130749i	0.00428512	+	0.00461117i
$805$	21.4453	−	12.6401i	0.755848	−	0.445504i
$806$	23.9385	+	60.9257i	0.843198	+	2.14602i
$807$	−37.6404	−	32.6156i	−1.32501	−	1.14812i
$808$	2.62391	+	21.1297i	0.0923087	+	0.743340i
$809$	2.96494	+	20.6216i	0.104242	+	0.725017i	0.973171	+	0.230081i	$0.0738993\pi$
$809$	2.96494	+	20.6216i	0.104242	+	0.725017i	−0.868930	+	0.494936i	$0.835192\pi$
$810$	−23.6710	+	24.5086i	−0.831715	+	0.861145i
$811$	−47.1165	−	6.77433i	−1.65449	−	0.237879i	−0.749096	−	0.662462i	$-0.769512\pi$
$811$	−47.1165	−	6.77433i	−1.65449	−	0.237879i	−0.905389	+	0.424583i	$0.860421\pi$
$812$	−1.61681	+	2.71920i	−0.0567390	+	0.0954253i
$813$	−1.39072	−	0.893764i	−0.0487748	−	0.0313457i
$814$	12.7365	+	0.688657i	0.446414	+	0.0241374i
$815$	40.3218	+	11.8395i	1.41241	+	0.414721i
$816$	37.0817	−	27.6510i	1.29812	−	0.967980i
$817$	31.4444	+	36.2888i	1.10010	+	1.26958i
$818$	−48.6896	+	4.33419i	−1.70239	+	0.151541i
$819$	13.2829	−	29.0854i	0.464141	−	1.01633i
$820$	1.27770	+	7.11985i	0.0446191	+	0.248636i
$821$	−44.1314	+	12.9582i	−1.54020	+	0.452243i	−0.938153	−	0.346220i	$-0.887465\pi$
$821$	−44.1314	+	12.9582i	−1.54020	+	0.452243i	−0.602044	+	0.798463i	$0.705647\pi$
$822$	−9.66199	−	40.9731i	−0.337000	−	1.42910i
$823$	−29.6714	+	13.5505i	−1.03428	+	0.472339i	−0.858890	−	0.512160i	$-0.828846\pi$
$823$	−29.6714	+	13.5505i	−1.03428	+	0.472339i	−0.175389	+	0.984499i	$0.556118\pi$
$824$	−33.8379	−	10.6474i	−1.17880	−	0.370919i
$825$	1.26815	+	1.97327i	0.0441512	+	0.0687006i
$826$	17.1829	+	6.07082i	0.597871	+	0.211231i
$827$	17.7933			0.618733			0.309366	−	0.950943i	$-0.399883\pi$
$827$	17.7933			0.618733			0.309366	+	0.950943i	$0.399883\pi$
$828$	23.5821	−	6.82614i	0.819533	−	0.237225i
$829$	−15.0534			−0.522827			−0.261413	−	0.965227i	$-0.584189\pi$
$829$	−15.0534			−0.522827			−0.261413	+	0.965227i	$0.584189\pi$
$830$	5.92041	+	2.09171i	0.205501	+	0.0726044i
$831$	23.8320	+	37.0833i	0.826724	+	1.28641i
$832$	−31.3070	+	33.4377i	−1.08537	+	1.15924i
$833$	−9.99195	+	4.56317i	−0.346201	+	0.158105i
$834$	3.52175	+	14.9345i	0.121948	+	0.517139i
$835$	−10.8786	+	3.19425i	−0.376470	+	0.110542i
$836$	−15.3428	+	2.75335i	−0.530641	+	0.0952264i
$837$	3.48774	−	7.63709i	0.120554	−	0.263977i
$838$	−51.3272	+	4.56898i	−1.77307	+	0.157833i
$839$	7.76009	+	8.95563i	0.267908	+	0.309183i	0.873724	−	0.486423i	$-0.161698\pi$
$839$	7.76009	+	8.95563i	0.267908	+	0.309183i	−0.605815	+	0.795605i	$0.707153\pi$
$840$	−33.3957	+	9.11138i	−1.15226	+	0.314372i
$841$	27.3210	+	8.02216i	0.942103	+	0.276626i
$842$	−29.8182	−	1.61225i	−1.02760	−	0.0555620i
$843$	−46.6514	−	29.9810i	−1.60676	−	1.03260i
$844$	18.4573	+	10.9746i	0.635327	+	0.377760i
$845$	46.5888	+	6.69846i	1.60270	+	0.230434i
$846$	1.98639	−	2.05668i	0.0682935	−	0.0707100i
$847$	−2.70971	−	18.8464i	−0.0931066	−	0.647571i
$848$	−1.35772	+	0.738084i	−0.0466244	+	0.0253459i
$849$	13.5817	+	11.7686i	0.466122	+	0.403897i
$850$	1.67360	+	4.25947i	0.0574040	+	0.146099i
$851$	23.5182	+	16.4303i	0.806193	+	0.563225i
$852$	−30.1684	+	28.0352i	−1.03355	+	0.960471i
$853$	26.6150	−	30.7153i	0.911279	−	1.05167i	−0.0871805	−	0.996193i	$-0.527786\pi$
$853$	26.6150	−	30.7153i	0.911279	−	1.05167i	0.998460	−	0.0554798i	$-0.0176689\pi$
$854$	−25.6654	−	18.5256i	−0.878251	−	0.633932i
$855$	−31.1572	+	4.47972i	−1.06555	+	0.153203i
$856$	−14.8895	−	0.286676i	−0.508913	−	0.00979838i
$857$	6.09160	−	42.3680i	0.208085	−	1.44726i	−0.571311	−	0.820734i	$-0.693565\pi$
$857$	6.09160	−	42.3680i	0.208085	−	1.44726i	0.779396	−	0.626531i	$-0.215526\pi$
$858$	17.6489	+	22.7412i	0.602524	+	0.776373i
$859$	−3.71977	+	5.78808i	−0.126917	+	0.197487i	−0.898897	−	0.438160i	$-0.855630\pi$
$859$	−3.71977	+	5.78808i	−0.126917	+	0.197487i	0.771980	+	0.635647i	$0.219267\pi$
$860$	−41.9476	+	13.9180i	−1.43040	+	0.474600i
$861$	−2.20341	+	7.50412i	−0.0750919	+	0.255740i
$862$	10.7980	+	5.65474i	0.367780	+	0.192601i
$863$	27.9293	−	24.2008i	0.950723	−	0.823806i	−0.0337342	−	0.999431i	$-0.510740\pi$
$863$	27.9293	−	24.2008i	0.950723	−	0.823806i	0.984457	+	0.175625i	$0.0561945\pi$
$864$	5.87433	−	0.0911453i	0.199849	−	0.00310083i
$865$	10.4390	+	4.76733i	0.354936	+	0.162094i
$866$	1.13052	−	5.66967i	0.0384166	−	0.192663i
$867$	−4.68564	−	15.9578i	−0.159133	−	0.541956i
$868$	28.9948	−	20.0913i	0.984146	−	0.681943i
$869$	6.92046	+	15.1537i	0.234761	+	0.514054i
$870$	−2.84363	−	4.99912i	−0.0964081	−	0.169486i
$871$	−0.182316	+	0.117168i	−0.00617755	+	0.00397007i
$872$	−12.2058	+	5.29267i	−0.413341	+	0.179232i
$873$		−	14.7317i		−	0.498593i
$874$	−32.5826	−	12.9467i	−1.10212	−	0.437928i
$875$			22.5281i			0.761590i
$876$	55.4604	−	1.92890i	1.87383	−	0.0651715i
$877$	18.4268	−	11.8422i	0.622230	−	0.399883i	−0.191195	−	0.981552i	$-0.561236\pi$
$877$	18.4268	−	11.8422i	0.622230	−	0.399883i	0.813426	+	0.581669i	$0.197600\pi$
$878$	14.6541	−	8.33564i	0.494553	−	0.281314i
$879$	−11.5222	−	25.2301i	−0.388635	−	0.850991i
$880$	3.07598	−	14.0140i	0.103691	−	0.472411i
$881$	−6.83372	−	23.2735i	−0.230234	−	0.784104i	−0.990858	−	0.134911i	$-0.956925\pi$
$881$	−6.83372	−	23.2735i	−0.230234	−	0.784104i	0.760624	−	0.649193i	$-0.224893\pi$
$882$	7.95066	+	1.58534i	0.267713	+	0.0533813i
$883$	−24.5116	−	11.1941i	−0.824881	−	0.376711i	−0.0421813	−	0.999110i	$-0.513431\pi$
$883$	−24.5116	−	11.1941i	−0.824881	−	0.376711i	−0.782700	+	0.622399i	$0.786158\pi$
$884$	25.0928	+	50.2463i	0.843963	+	1.68997i
$885$	−25.0384	+	21.6959i	−0.841657	+	0.729300i
$886$	−14.8687	+	28.3925i	−0.499525	+	0.953864i
$887$	−12.8650	+	43.8143i	−0.431965	+	1.47114i	0.400105	+	0.916469i	$0.368974\pi$
$887$	−12.8650	+	43.8143i	−0.431965	+	1.47114i	−0.832071	+	0.554670i	$0.812845\pi$
$888$	−25.5403	−	30.6478i	−0.857076	−	1.02847i
$889$	−0.819529	+	1.27521i	−0.0274861	+	0.0427693i
$890$	−21.6545	+	16.8055i	−0.725861	+	0.563322i
$891$	2.17303	−	15.1137i	0.0727992	−	0.506329i
$892$	−2.69670	+	6.49325i	−0.0902922	+	0.217410i
$893$	−4.04187	+	0.581134i	−0.135256	+	0.0194469i
$894$	−10.8316	+	15.0061i	−0.362263	+	0.501880i
$895$	12.5213	−	14.4503i	0.418540	−	0.483021i
$896$	21.4103	+	12.2848i	0.715266	+	0.410407i
$897$	6.73418	+	64.3954i	0.224848	+	2.15010i
$898$	34.2086	−	13.4410i	1.14156	−	0.448532i
$899$	4.42930	+	3.83801i	0.147725	+	0.128005i
$900$	0.838372	−	3.27195i	0.0279457	−	0.109065i
$901$	0.269659	+	1.87552i	0.00898363	+	0.0624825i
$902$	−2.33163	−	2.25194i	−0.0776347	−	0.0749815i
$903$	−47.2985	−	6.80049i	−1.57399	−	0.226306i
$904$	25.2592	+	4.12948i	0.840108	+	0.137345i
$905$	−30.2479	−	19.4391i	−1.00547	−	0.646178i
$906$	−0.801020	+	14.8146i	−0.0266121	+	0.492183i
$907$	37.3788	+	10.9754i	1.24114	+	0.364433i	0.835445	−	0.549574i	$-0.185210\pi$
$907$	37.3788	+	10.9754i	1.24114	+	0.364433i	0.405699	+	0.914007i	$0.367028\pi$
$908$	43.7741	+	4.74757i	1.45269	+	0.157554i
$909$	−12.6177	−	14.5616i	−0.418503	−	0.482978i
$910$	−3.72670	−	41.8651i	−0.123539	−	1.38782i
$911$	7.07107	−	15.4835i	0.234275	−	0.512990i	−0.755583	−	0.655053i	$-0.772646\pi$
$911$	7.07107	−	15.4835i	0.234275	−	0.512990i	0.989858	+	0.142063i	$0.0453735\pi$
$912$	38.9757	+	29.2906i	1.29061	+	0.969909i
$913$	−2.69983	+	0.792743i	−0.0893515	+	0.0262360i
$914$	7.30793	−	1.72331i	0.241725	−	0.0570019i
$915$	52.3442	−	23.9048i	1.73045	−	0.790269i
$916$	4.81126	−	5.95901i	0.158968	−	0.196891i
$917$	−20.3764	−	31.7064i	−0.672890	−	1.04704i
$918$	2.39966	−	6.79202i	0.0792004	−	0.224170i
$919$	23.4063			0.772104			0.386052	−	0.922477i	$-0.373838\pi$
$919$	23.4063			0.772104			0.386052	+	0.922477i	$0.373838\pi$
$920$	22.5077	−	23.1259i	0.742058	−	0.762439i
$921$	34.4011			1.13355
$922$	−9.96015	+	28.1913i	−0.328020	+	0.928432i
$923$	−27.0346	−	42.0667i	−0.889855	−	1.38464i
$924$	9.74490	−	12.0696i	0.320584	−	0.397060i
$925$	3.59039	−	1.63968i	0.118051	−	0.0539123i
$926$	−27.7223	+	6.53729i	−0.911012	+	0.214829i
$927$	30.8007	−	9.04391i	1.01163	−	0.297041i
$928$	−1.09424	+	3.95248i	−0.0359202	+	0.129746i
$929$	−11.6689	+	25.5514i	−0.382845	+	0.838314i	0.615880	+	0.787840i	$0.288801\pi$
$929$	−11.6689	+	25.5514i	−0.382845	+	0.838314i	−0.998725	+	0.0504744i	$0.983927\pi$
$930$	5.68616	+	63.8775i	0.186457	+	2.09463i
$931$	−7.58199	−	8.75008i	−0.248490	−	0.286772i
$932$	26.9263	+	2.92032i	0.881999	+	0.0956582i
$933$	46.9139	+	13.7752i	1.53589	+	0.450979i
$934$	1.32036	−	24.4197i	0.0432036	−	0.799038i
$935$	−14.7991	−	9.51081i	−0.483983	−	0.311037i
$936$	6.68787	−	40.9083i	0.218600	−	1.33713i
$937$	2.77947	+	0.399628i	0.0908014	+	0.0130553i	0.187566	−	0.982252i	$-0.439940\pi$
$937$	2.77947	+	0.399628i	0.0908014	+	0.0130553i	−0.0967643	+	0.995307i	$0.530849\pi$
$938$	0.0840041	+	0.0811332i	0.00274283	+	0.00264909i
$939$	0.653734	+	4.54682i	0.0213338	+	0.148380i
$940$	0.932909	−	3.64091i	0.0304281	−	0.118753i
$941$	−12.4974	−	10.8291i	−0.407404	−	0.353017i	0.426923	−	0.904288i	$-0.359598\pi$
$941$	−12.4974	−	10.8291i	−0.407404	−	0.353017i	−0.834326	+	0.551271i	$0.814143\pi$
$942$	−5.27816	+	2.07386i	−0.171972	+	0.0675699i
$943$	−1.78259	−	7.06972i	−0.0580492	−	0.230222i
$944$	23.5615	+	1.72940i	0.766860	+	0.0562871i
$945$	−3.53022	+	4.07409i	−0.114838	+	0.132530i
$946$	11.5916	−	16.0591i	0.376877	−	0.522126i
$947$	−9.33745	+	1.34252i	−0.303426	+	0.0436261i	−0.292346	−	0.956312i	$-0.594436\pi$
$947$	−9.33745	+	1.34252i	−0.303426	+	0.0436261i	−0.0110800	+	0.999939i	$0.503527\pi$
$948$	19.9849	−	48.1207i	0.649080	−	1.56289i
$949$	−9.58915	+	66.6940i	−0.311277	+	2.16498i
$950$	−3.81073	+	2.95741i	−0.123636	+	0.0959512i
$951$	2.10126	−	3.26962i	0.0681379	−	0.106025i
$952$	23.2506	−	19.3759i	0.753557	−	0.627975i
$953$	−1.81384	+	6.17738i	−0.0587561	+	0.200105i	−0.983640	−	0.180144i	$-0.942344\pi$
$953$	−1.81384	+	6.17738i	−0.0587561	+	0.200105i	0.924884	+	0.380249i	$0.124162\pi$
$954$	0.648773	−	1.23886i	0.0210048	−	0.0401096i
$955$	−27.0936	+	23.4768i	−0.876729	+	0.759690i
$956$	5.30088	+	10.6146i	0.171443	+	0.343299i
$957$	2.34440	+	1.07065i	0.0757838	+	0.0346093i
$958$	50.8847	+	10.1463i	1.64401	+	0.327812i
$959$	−7.76013	−	26.4286i	−0.250588	−	0.853423i
$960$	−38.6577	+	22.7904i	−1.24767	+	0.735558i
$961$	−14.2700	−	31.2469i	−0.460321	−	1.00796i
$962$	42.1045	−	23.9501i	1.35750	−	0.772183i
$963$	11.3371	−	7.28593i	0.365334	−	0.234786i
$964$	−43.5416	+	1.51437i	−1.40238	+	0.0487745i
$965$		−	8.77524i		−	0.282485i
$966$	32.9425	−	11.4968i	1.05991	−	0.369903i
$967$		−	12.8467i		−	0.413123i	−0.978434	−	0.206562i	$-0.933773\pi$
$967$		−	12.8467i		−	0.413123i	0.978434	−	0.206562i	$-0.0662274\pi$
$968$	−9.81965	−	22.6458i	−0.315615	−	0.727864i
$969$	50.2893	−	32.3190i	1.61553	−	1.03824i
$970$	−9.57451	−	16.8321i	−0.307419	−	0.540445i
$971$	−19.5925	−	42.9017i	−0.628754	−	1.37678i	−0.908977	−	0.416845i	$-0.863136\pi$
$971$	−19.5925	−	42.9017i	−0.628754	−	1.37678i	0.280223	−	0.959935i	$-0.409592\pi$
$972$	−34.1330	+	23.6517i	−1.09482	+	0.758629i
$973$	2.82853	+	9.63309i	0.0906785	+	0.308823i
$974$	−7.39627	+	37.0930i	−0.236992	+	1.18854i
$975$	8.10295	+	3.70049i	0.259502	+	0.118511i
$976$	−38.4199	−	14.4117i	−1.22979	−	0.461307i
$977$	−34.5042	+	29.8981i	−1.10389	+	0.956525i	−0.999278	−	0.0379886i	$-0.987905\pi$
$977$	−34.5042	+	29.8981i	−1.10389	+	0.956525i	−0.104610	+	0.994513i	$0.533359\pi$
$978$	52.1800	+	27.3259i	1.66853	+	0.873786i
$979$	3.46065	−	11.7859i	0.110603	−	0.376678i
$980$	10.1146	−	3.35596i	0.323098	−	0.107202i
$981$	6.50884	−	10.1279i	0.207811	−	0.323361i
$982$	−6.48641	−	8.35797i	−0.206990	−	0.266713i
$983$	−1.30074	+	9.04686i	−0.0414872	+	0.288550i	0.958507	+	0.285070i	$0.0920168\pi$
$983$	−1.30074	+	9.04686i	−0.0414872	+	0.288550i	−0.999994	+	0.00348003i	$0.998892\pi$
$984$	−0.195172	+	10.1369i	−0.00622185	+	0.323153i
$985$	−30.6295	+	4.40386i	−0.975937	+	0.140319i
$986$	4.07727	+	2.94302i	0.129847	+	0.0937250i
$987$	2.66116	−	3.07114i	0.0847055	−	0.0977554i
$988$	−43.3640	+	40.2978i	−1.37959	+	1.28204i
$989$	41.2054	−	16.9279i	1.31026	−	0.538275i
$990$	4.74805	+	12.0842i	0.150903	+	0.384062i
$991$	12.8706	+	11.1524i	0.408848	+	0.354269i	0.834873	−	0.550442i	$-0.185541\pi$
$991$	12.8706	+	11.1524i	0.408848	+	0.354269i	−0.426025	+	0.904711i	$0.640086\pi$
$992$	29.4070	−	35.0209i	0.933674	−	1.11191i
$993$	−3.69203	−	25.6786i	−0.117163	−	0.814886i
$994$	−18.7202	+	19.3826i	−0.593770	+	0.614780i
$995$	6.69815	+	0.963048i	0.212346	+	0.0305307i
$996$	7.56470	+	4.49791i	0.239697	+	0.142522i
$997$	13.7885	+	8.86131i	0.436685	+	0.280640i	0.740456	−	0.672105i	$-0.234609\pi$
$997$	13.7885	+	8.86131i	0.436685	+	0.280640i	−0.303771	+	0.952745i	$0.598246\pi$
$998$	15.8333	+	0.856102i	0.501196	+	0.0270994i
$999$	−5.96114	−	1.75035i	−0.188602	−	0.0553786i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.2.h.a.7.4	yes	100
3.2	odd	2		828.2.u.a.559.7		100
4.3	odd	2	inner	92.2.h.a.7.3	✓	100
12.11	even	2		828.2.u.a.559.8		100
23.10	odd	22	inner	92.2.h.a.79.3	yes	100
69.56	even	22		828.2.u.a.631.8		100
92.79	even	22	inner	92.2.h.a.79.4	yes	100
276.263	odd	22		828.2.u.a.631.7		100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.2.h.a.7.3	✓	100	4.3	odd	2	inner
92.2.h.a.7.4	yes	100	1.1	even	1	trivial
92.2.h.a.79.3	yes	100	23.10	odd	22	inner
92.2.h.a.79.4	yes	100	92.79	even	22	inner
828.2.u.a.559.7		100	3.2	odd	2
828.2.u.a.559.8		100	12.11	even	2
828.2.u.a.631.7		100	276.263	odd	22
828.2.u.a.631.8		100	69.56	even	22

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:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	92.h (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.471110 + 1.33344i) q^{2} +(-1.27476 - 1.98356i) q^{3} +(-1.55611 - 1.25639i) q^{4} +(2.16405 - 0.988288i) q^{5} +(3.24551 - 0.765333i) q^{6} +(2.09343 - 0.614686i) q^{7} +(2.40842 - 1.48308i) q^{8} +(-1.06327 + 2.32823i) q^{9} +O(q^{10})\)	\(q+(-0.471110 + 1.33344i) q^{2} +(-1.27476 - 1.98356i) q^{3} +(-1.55611 - 1.25639i) q^{4} +(2.16405 - 0.988288i) q^{5} +(3.24551 - 0.765333i) q^{6} +(2.09343 - 0.614686i) q^{7} +(2.40842 - 1.48308i) q^{8} +(-1.06327 + 2.32823i) q^{9} +(0.298314 + 3.35122i) q^{10} +(-0.987339 - 1.13945i) q^{11} +(-0.508468 + 4.68824i) q^{12} +(-5.49384 - 1.61314i) q^{13} +(-0.166590 + 3.08104i) q^{14} +(-4.71897 - 3.03270i) q^{15} +(0.842957 + 3.91017i) q^{16} +(4.85453 + 0.697976i) q^{17} +(-2.60363 - 2.51465i) q^{18} +(0.735682 + 5.11678i) q^{19} +(-4.60917 - 1.18101i) q^{20} +(-3.88788 - 3.36887i) q^{21} +(1.98453 - 0.779748i) q^{22} +(4.71714 + 0.865213i) q^{23} +(-6.01193 - 2.88669i) q^{24} +(0.432089 - 0.498658i) q^{25} +(4.73922 - 6.56572i) q^{26} +(-1.02800 + 0.147804i) q^{27} +(-4.02989 - 1.67365i) q^{28} +(0.103177 - 0.717609i) q^{29} +(6.26707 - 4.86371i) q^{30} +(-4.37054 + 6.80070i) q^{31} +(-5.61109 - 0.718090i) q^{32} +(-1.00155 + 3.41097i) q^{33} +(-3.21773 + 6.14439i) q^{34} +(3.92279 - 3.39912i) q^{35} +(4.57973 - 2.28710i) q^{36} +(5.44149 + 2.48504i) q^{37} +(-7.16949 - 1.42958i) q^{38} +(3.80356 + 12.9537i) q^{39} +(3.74623 - 5.58966i) q^{40} +(-0.631546 - 1.38289i) q^{41} +(6.32380 - 3.59714i) q^{42} +(7.81415 - 5.02185i) q^{43} +(0.104812 + 3.01359i) q^{44} +6.08922i q^{45} +(-3.37600 + 5.88240i) q^{46} +0.789926i q^{47} +(6.68150 - 6.65658i) q^{48} +(-1.88418 + 1.21089i) q^{49} +(0.461367 + 0.811087i) q^{50} +(-4.80387 - 10.5190i) q^{51} +(6.52228 + 9.41263i) q^{52} +(0.108846 + 0.370694i) q^{53} +(0.287214 - 1.44040i) q^{54} +(-3.26275 - 1.49005i) q^{55} +(4.13023 - 4.58513i) q^{56} +(9.21163 - 7.98192i) q^{57} +(0.908278 + 0.475652i) q^{58} +(1.66397 - 5.66697i) q^{59} +(3.53298 + 10.6481i) q^{60} +(-5.54615 + 8.62998i) q^{61} +(-7.00929 - 9.03172i) q^{62} +(-0.794742 + 5.52756i) q^{63} +(3.60097 - 7.14374i) q^{64} +(-13.4832 + 1.93859i) q^{65} +(-4.07647 - 2.94245i) q^{66} +(0.0247864 - 0.0286050i) q^{67} +(-6.67725 - 7.18532i) q^{68} +(-4.29701 - 10.4597i) q^{69} +(2.68444 + 6.83216i) q^{70} +(6.60017 + 5.71908i) q^{71} +(0.892149 + 7.18426i) q^{72} +(-1.67474 - 11.6480i) q^{73} +(-5.87719 + 6.08515i) q^{74} +(-1.53993 - 0.221408i) q^{75} +(5.28388 - 8.88657i) q^{76} +(-2.76732 - 1.77845i) q^{77} +(-19.0649 - 1.03083i) q^{78} +(-10.6017 - 3.11295i) q^{79} +(5.68857 + 7.62871i) q^{80} +(6.63203 + 7.65378i) q^{81} +(2.14153 - 0.190632i) q^{82} +(0.775283 - 1.69763i) q^{83} +(1.81735 + 10.1270i) q^{84} +(11.1952 - 3.28722i) q^{85} +(3.01500 + 12.7855i) q^{86} +(-1.55495 + 0.710120i) q^{87} +(-4.06782 - 1.27997i) q^{88} +(4.40465 + 6.85377i) q^{89} +(-8.11959 - 2.86869i) q^{90} -12.4925 q^{91} +(-6.25334 - 7.27294i) q^{92} +19.0610 q^{93} +(-1.05332 - 0.372142i) q^{94} +(6.64890 + 10.3459i) q^{95} +(5.72841 + 12.0453i) q^{96} +(-5.23551 + 2.39098i) q^{97} +(-0.726986 - 3.08289i) q^{98} +(3.70270 - 1.08721i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 7 q^{2} - 11 q^{4} - 22 q^{5} - 12 q^{6} - 10 q^{8} - 12 q^{9}+O(q^{10}) \) 100 * q - 7 * q^2 - 11 * q^4 - 22 * q^5 - 12 * q^6 - 10 * q^8 - 12 * q^9	\( 100 q - 7 q^{2} - 11 q^{4} - 22 q^{5} - 12 q^{6} - 10 q^{8} - 12 q^{9} - 11 q^{10} - 18 q^{12} - 18 q^{13} - 11 q^{14} + 5 q^{16} - 22 q^{17} - 24 q^{18} - 11 q^{20} - 22 q^{21} - 30 q^{24} - 16 q^{25} + 12 q^{26} - 11 q^{28} - 42 q^{29} - 11 q^{30} - 27 q^{32} - 22 q^{33} + 11 q^{34} + 77 q^{36} - 22 q^{37} + 44 q^{38} + 77 q^{40} - 10 q^{41} + 99 q^{42} + 66 q^{44} + 65 q^{46} + 38 q^{48} - 8 q^{49} + 30 q^{50} + 96 q^{52} - 22 q^{53} + 48 q^{54} + 44 q^{56} - 22 q^{57} + 79 q^{58} + 11 q^{60} - 22 q^{61} - 36 q^{62} + 10 q^{64} - 22 q^{65} - 44 q^{66} - 10 q^{69} + 34 q^{70} - 21 q^{72} - 18 q^{73} - 22 q^{74} - 66 q^{76} + 122 q^{77} - 66 q^{78} - 110 q^{80} + 8 q^{81} - 122 q^{82} - 165 q^{84} + 54 q^{85} - 121 q^{86} - 99 q^{88} + 22 q^{89} - 198 q^{90} - 86 q^{92} + 212 q^{93} - 61 q^{94} - 147 q^{96} + 22 q^{97} - 71 q^{98}+O(q^{100}) \) 100 * q - 7 * q^2 - 11 * q^4 - 22 * q^5 - 12 * q^6 - 10 * q^8 - 12 * q^9 - 11 * q^10 - 18 * q^12 - 18 * q^13 - 11 * q^14 + 5 * q^16 - 22 * q^17 - 24 * q^18 - 11 * q^20 - 22 * q^21 - 30 * q^24 - 16 * q^25 + 12 * q^26 - 11 * q^28 - 42 * q^29 - 11 * q^30 - 27 * q^32 - 22 * q^33 + 11 * q^34 + 77 * q^36 - 22 * q^37 + 44 * q^38 + 77 * q^40 - 10 * q^41 + 99 * q^42 + 66 * q^44 + 65 * q^46 + 38 * q^48 - 8 * q^49 + 30 * q^50 + 96 * q^52 - 22 * q^53 + 48 * q^54 + 44 * q^56 - 22 * q^57 + 79 * q^58 + 11 * q^60 - 22 * q^61 - 36 * q^62 + 10 * q^64 - 22 * q^65 - 44 * q^66 - 10 * q^69 + 34 * q^70 - 21 * q^72 - 18 * q^73 - 22 * q^74 - 66 * q^76 + 122 * q^77 - 66 * q^78 - 110 * q^80 + 8 * q^81 - 122 * q^82 - 165 * q^84 + 54 * q^85 - 121 * q^86 - 99 * q^88 + 22 * q^89 - 198 * q^90 - 86 * q^92 + 212 * q^93 - 61 * q^94 - 147 * q^96 + 22 * q^97 - 71 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more