LMFDB - Embedded newform 92.2.h.a.7.3

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			7.3
Character	$\chi$	$=$	92.7
Dual form			92.2.h.a.79.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25282 + 0.656083i) q^{2} +(1.27476 + 1.98356i) q^{3} +(1.13911 - 1.64391i) q^{4} +(2.16405 - 0.988288i) q^{5} +(-2.89842 - 1.64870i) q^{6} +(-2.09343 + 0.614686i) q^{7} +(-0.348560 + 2.80687i) q^{8} +(-1.06327 + 2.32823i) q^{9} +O(q^{10})$	\(q+(-1.25282 + 0.656083i) q^{2} +(1.27476 + 1.98356i) q^{3} +(1.13911 - 1.64391i) q^{4} +(2.16405 - 0.988288i) q^{5} +(-2.89842 - 1.64870i) q^{6} +(-2.09343 + 0.614686i) q^{7} +(-0.348560 + 2.80687i) q^{8} +(-1.06327 + 2.32823i) q^{9} +(-2.06276 + 2.65794i) q^{10} +(0.987339 + 1.13945i) q^{11} +(4.71288 + 0.163913i) q^{12} +(-5.49384 - 1.61314i) q^{13} +(2.21940 - 2.14355i) q^{14} +(4.71897 + 3.03270i) q^{15} +(-1.40486 - 3.74518i) q^{16} +(4.85453 + 0.697976i) q^{17} +(-0.195431 - 3.61444i) q^{18} +(-0.735682 - 5.11678i) q^{19} +(0.840437 - 4.68326i) 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} +(7.94113 - 1.58345i) q^{26} +(1.02800 - 0.147804i) q^{27} +(-1.37416 + 4.14159i) q^{28} +(0.103177 - 0.717609i) q^{29} +(-7.90172 - 0.703385i) q^{30} +(4.37054 - 6.80070i) q^{31} +(4.21718 + 3.77033i) q^{32} +(-1.00155 + 3.41097i) q^{33} +(-6.53978 + 2.31054i) q^{34} +(-3.92279 + 3.39912i) q^{35} +(2.61621 + 4.40002i) q^{36} +(5.44149 + 2.48504i) q^{37} +(4.27871 + 5.92773i) q^{38} +(-3.80356 - 12.9537i) q^{39} +(2.01969 + 6.41867i) q^{40} +(-0.631546 - 1.38289i) q^{41} +(7.08107 + 1.66981i) q^{42} +(-7.81415 + 5.02185i) q^{43} +(2.99784 - 0.325134i) q^{44} +6.08922i q^{45} +(6.47737 - 2.01088i) q^{46} -0.789926i q^{47} +(5.63795 - 7.56082i) q^{48} +(-1.88418 + 1.21089i) q^{49} +(-0.214169 + 0.908214i) q^{50} +(4.80387 + 10.5190i) q^{51} +(-8.90993 + 7.19381i) q^{52} +(0.108846 + 0.370694i) q^{53} +(-1.19092 + 0.859624i) q^{54} +(3.26275 + 1.49005i) q^{55} +(-0.995657 - 6.09023i) q^{56} +(9.21163 - 7.98192i) q^{57} +(0.341549 + 0.966726i) q^{58} +(-1.66397 + 5.66697i) q^{59} +(10.3609 - 4.30297i) q^{60} +(-5.54615 + 8.62998i) q^{61} +(-1.01368 + 11.3875i) q^{62} +(0.794742 - 5.52756i) q^{63} +(-7.75701 - 1.95672i) q^{64} +(-13.4832 + 1.93859i) q^{65} +(-0.983117 - 4.93043i) 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} +(-6.16442 - 3.79598i) q^{72} +(-1.67474 - 11.6480i) q^{73} +(-8.44760 + 0.456758i) q^{74} +(1.53993 + 0.221408i) q^{75} +(-9.24953 - 4.61918i) q^{76} +(-2.76732 - 1.77845i) q^{77} +(13.2639 + 13.7332i) q^{78} +(10.6017 + 3.11295i) q^{79} +(-6.74149 - 6.71635i) q^{80} +(6.63203 + 7.65378i) q^{81} +(1.69850 + 1.31817i) q^{82} +(-0.775283 + 1.69763i) q^{83} +(-9.96683 + 2.55380i) q^{84} +(11.1952 - 3.28722i) q^{85} +(6.49497 - 11.4182i) q^{86} +(1.55495 - 0.710120i) q^{87} +(-3.54243 + 2.37416i) q^{88} +(4.40465 + 6.85377i) q^{89} +(-3.99503 - 7.62868i) q^{90} +12.4925 q^{91} +(-6.79567 + 6.76896i) q^{92} +19.0610 q^{93} +(0.518257 + 0.989634i) q^{94} +(-6.64890 - 10.3459i) q^{95} +(-2.10280 + 13.1713i) q^{96} +(-5.23551 + 2.39098i) q^{97} +(1.56609 - 2.75320i) 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 $

$2$	−1.25282	+	0.656083i	−0.885877	+	0.463921i
$2$	−1.25282	+	0.656083i	−0.885877	+	0.463921i
$3$	1.27476	+	1.98356i	0.735982	+	1.14521i	0.984295	+	0.176531i	$0.0564875\pi$
$3$	1.27476	+	1.98356i	0.735982	+	1.14521i	−0.248313	+	0.968680i	$0.579876\pi$
$4$	1.13911	−	1.64391i	0.569555	−	0.821953i
$5$	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	$0.185089\pi$
$6$	−2.89842	−	1.64870i	−1.18328	−	0.673078i
$7$	−2.09343	+	0.614686i	−0.791241	+	0.232329i	−0.652290	−	0.757970i	$-0.726191\pi$
$7$	−2.09343	+	0.614686i	−0.791241	+	0.232329i	−0.138952	+	0.990299i	$0.544373\pi$
$8$	−0.348560	+	2.80687i	−0.123234	+	0.992378i
$9$	−1.06327	+	2.32823i	−0.354422	+	0.776077i
$10$	−2.06276	+	2.65794i	−0.652303	+	0.840515i
$11$	0.987339	+	1.13945i	0.297694	+	0.343557i	0.884815	−	0.465942i	$-0.154284\pi$
$11$	0.987339	+	1.13945i	0.297694	+	0.343557i	−0.587122	+	0.809499i	$0.699739\pi$
$12$	4.71288	+	0.163913i	1.36049	+	0.0473176i
$13$	−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	$0.882925\pi$
$14$	2.21940	−	2.14355i	0.593160	−	0.572888i
$15$	4.71897	+	3.03270i	1.21843	+	0.783039i
$16$	−1.40486	−	3.74518i	−0.351214	−	0.936295i
$17$	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	$0.342705\pi$
$18$	−0.195431	−	3.61444i	−0.0460636	−	0.851932i
$19$	−0.735682	−	5.11678i	−0.168777	−	1.17387i	−0.881417	−	0.472339i	$-0.843410\pi$
$19$	−0.735682	−	5.11678i	−0.168777	−	1.17387i	0.712640	−	0.701530i	$-0.247499\pi$
$20$	0.840437	−	4.68326i	0.187927	−	1.04721i
$21$	−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
$26$	7.94113	−	1.58345i	1.55738	−	0.310539i
$27$	1.02800	−	0.147804i	0.197839	−	0.0284449i
$28$	−1.37416	+	4.14159i	−0.259692	+	0.782688i
$29$	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	$0.0240118\pi$
$30$	−7.90172	−	0.703385i	−1.44265	−	0.128420i
$31$	4.37054	−	6.80070i	0.784972	−	1.22144i	−0.186071	−	0.982536i	$-0.559575\pi$
$31$	4.37054	−	6.80070i	0.784972	−	1.22144i	0.971043	−	0.238905i	$-0.0767883\pi$
$32$	4.21718	+	3.77033i	0.745499	+	0.666507i
$33$	−1.00155	+	3.41097i	−0.174348	+	0.593774i
$34$	−6.53978	+	2.31054i	−1.12156	+	0.396254i
$35$	−3.92279	+	3.39912i	−0.663073	+	0.574556i
$36$	2.61621	+	4.40002i	0.436036	+	0.733337i
$37$	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	$0.472731\pi$
$38$	4.27871	+	5.92773i	0.694098	+	0.961604i
$39$	−3.80356	−	12.9537i	−0.609056	−	2.07426i
$40$	2.01969	+	6.41867i	0.319342	+	1.01488i
$41$	−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	$0.901513\pi$
$42$	7.08107	+	1.66981i	1.09263	+	0.257657i
$43$	−7.81415	+	5.02185i	−1.19165	+	0.765825i	−0.977492	−	0.210975i	$-0.932336\pi$
$43$	−7.81415	+	5.02185i	−1.19165	+	0.765825i	−0.214155	+	0.976800i	$0.568700\pi$
$44$	2.99784	−	0.325134i	0.451941	−	0.0490158i
$45$			6.08922i			0.907727i
$46$	6.47737	−	2.01088i	0.955037	−	0.296488i
$47$		−	0.789926i		−	0.115223i	−0.998339	−	0.0576113i	$-0.981652\pi$
$47$		−	0.789926i		−	0.115223i	0.998339	−	0.0576113i	$-0.0183484\pi$
$48$	5.63795	−	7.56082i	0.813768	−	1.09131i
$49$	−1.88418	+	1.21089i	−0.269168	+	0.172984i
$50$	−0.214169	+	0.908214i	−0.0302880	+	0.128441i
$51$	4.80387	+	10.5190i	0.672677	+	1.47296i
$52$	−8.90993	+	7.19381i	−1.23558	+	0.997602i
$53$	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	$0.900644\pi$
$54$	−1.19092	+	0.859624i	−0.162064	+	0.116980i
$55$	3.26275	+	1.49005i	0.439949	+	0.200918i
$56$	−0.995657	−	6.09023i	−0.133050	−	0.813841i
$57$	9.21163	−	7.98192i	1.22011	−	1.05723i
$58$	0.341549	+	0.966726i	0.0448476	+	0.126937i
$59$	−1.66397	+	5.66697i	−0.216631	+	0.737776i	0.777432	+	0.628967i	$0.216522\pi$
$59$	−1.66397	+	5.66697i	−0.216631	+	0.737776i	−0.994063	+	0.108809i	$0.965296\pi$
$60$	10.3609	−	4.30297i	1.33759	−	0.555511i
$61$	−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	$0.953757\pi$
$62$	−1.01368	+	11.3875i	−0.128737	+	1.44621i
$63$	0.794742	−	5.52756i	0.100128	−	0.696407i
$64$	−7.75701	−	1.95672i	−0.969627	−	0.244590i
$65$	−13.4832	+	1.93859i	−1.67238	+	0.240452i
$66$	−0.983117	−	4.93043i	−0.121013	−	0.606894i
$67$	−0.0247864	+	0.0286050i	−0.00302814	+	0.00349466i	−0.757262	−	0.653112i	$-0.773463\pi$
$67$	−0.0247864	+	0.0286050i	−0.00302814	+	0.00349466i	0.754233	+	0.656606i	$0.228009\pi$
$68$	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	0.168418	−	0.985716i	$-0.446134\pi$
$71$	−6.60017	−	5.71908i	−0.783296	−	0.678730i	−0.951714	+	0.306985i	$0.900680\pi$
$72$	−6.16442	−	3.79598i	−0.726484	−	0.447360i
$73$	−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	$-0.287255\pi$
$74$	−8.44760	+	0.456758i	−0.982013	+	0.0530970i
$75$	1.53993	+	0.221408i	0.177816	+	0.0255660i
$76$	−9.24953	−	4.61918i	−1.06099	−	0.529856i
$77$	−2.76732	−	1.77845i	−0.315366	−	0.202673i
$78$	13.2639	+	13.7332i	1.50184	+	1.55498i
$79$	10.6017	+	3.11295i	1.19279	+	0.350235i	0.817092	−	0.576507i	$-0.195585\pi$
$79$	10.6017	+	3.11295i	1.19279	+	0.350235i	0.375698	+	0.926742i	$0.377403\pi$
$80$	−6.74149	−	6.71635i	−0.753722	−	0.750911i
$81$	6.63203	+	7.65378i	0.736893	+	0.850420i
$82$	1.69850	+	1.31817i	0.187568	+	0.145567i
$83$	−0.775283	+	1.69763i	−0.0850984	+	0.186340i	−0.947397	−	0.320060i	$-0.896297\pi$
$83$	−0.775283	+	1.69763i	−0.0850984	+	0.186340i	0.862299	+	0.506400i	$0.169024\pi$
$84$	−9.96683	+	2.55380i	−1.08747	+	0.278643i
$85$	11.1952	−	3.28722i	1.21429	−	0.356549i
$86$	6.49497	−	11.4182i	0.700370	−	1.23126i
$87$	1.55495	−	0.710120i	0.166708	−	0.0761329i
$88$	−3.54243	+	2.37416i	−0.377624	+	0.253087i
$89$	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	$0.676062\pi$
$90$	−3.99503	−	7.62868i	−0.421113	−	0.804134i
$91$	12.4925			1.30957
$92$	−6.79567	+	6.76896i	−0.708498	+	0.705713i
$93$	19.0610			1.97653
$94$	0.518257	+	0.989634i	0.0534541	+	0.102073i
$95$	−6.64890	−	10.3459i	−0.682163	−	1.06147i
$96$	−2.10280	+	13.1713i	−0.214616	+	1.34429i
$97$	−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	$0.458023\pi$
$98$	1.56609	−	2.75320i	0.158199	−	0.278115i
$99$	−3.70270	+	1.08721i	−0.372136	+	0.109269i
$100$	−0.327549	−	1.27834i	−0.0327549	−	0.127834i
$101$	−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	$0.258558\pi$
$102$	−12.9197	−	10.0267i	−1.27924	−	0.992789i
$103$	8.21311	+	9.47844i	0.809262	+	0.933938i	0.998851	−	0.0479253i	$-0.0152609\pi$
$103$	8.21311	+	9.47844i	0.809262	+	0.933938i	−0.189589	+	0.981864i	$0.560715\pi$
$104$	6.44279	−	14.8582i	0.631767	−	1.45697i
$105$	−11.7430	−	3.44805i	−1.14600	−	0.336495i
$106$	−0.379570	−	0.393001i	−0.0368671	−	0.0381716i
$107$	4.42938	+	2.84659i	0.428204	+	0.275190i	0.736941	−	0.675958i	$-0.236270\pi$
$107$	4.42938	+	2.84659i	0.428204	+	0.275190i	−0.308736	+	0.951148i	$0.599906\pi$
$108$	0.928028	−	1.85830i	0.0892996	−	0.178815i
$109$	−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	$0.617779\pi$
$110$	−5.06523	+	0.273875i	−0.482951	+	0.0261129i
$111$	2.00734	+	13.9614i	0.190528	+	1.32515i
$112$	5.24307	+	6.97672i	0.495424	+	0.659238i
$113$	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
$118$	−1.63335	−	8.19139i	−0.150362	−	0.754078i
$119$	−10.5916	+	1.52285i	−0.970934	+	0.139599i
$120$	−10.1572	+	12.1884i	−0.927223	+	1.11265i
$121$	1.24196	−	8.63799i	0.112905	−	0.785272i
$122$	1.28634	−	14.4505i	0.116460	−	1.30829i
$123$	1.93799	−	3.01556i	0.174742	−	0.271904i
$124$	−6.20118	−	14.9315i	−0.556882	−	1.34089i
$125$	−2.90902	+	9.90720i	−0.260190	+	0.886127i
$126$	2.63087	+	7.44644i	0.234376	+	0.663382i
$127$	0.525070	−	0.454976i	0.0465925	−	0.0403726i	−0.631253	−	0.775577i	$-0.717459\pi$
$127$	0.525070	−	0.454976i	0.0465925	−	0.0403726i	0.677846	+	0.735204i	$0.262914\pi$
$128$	11.0019	−	2.63783i	0.972440	−	0.233153i
$129$	−19.9223	−	9.09821i	−1.75406	−	0.801053i
$130$	15.6201	−	11.2748i	1.36997	−	0.988863i
$131$	4.86677	+	16.5747i	0.425211	+	1.44814i	0.842170	+	0.539212i	$0.181278\pi$
$131$	4.86677	+	16.5747i	0.425211	+	1.44814i	−0.416959	+	0.908925i	$0.636904\pi$
$132$	4.46644	+	5.53193i	0.388754	+	0.481492i
$133$	4.68531	+	10.2594i	0.406268	+	0.889602i
$134$	0.0122856	−	0.0520989i	0.00106131	−	0.00450066i
$135$	2.07857	−	1.33581i	0.178895	−	0.114969i
$136$	−3.65122	+	13.3827i	−0.313089	+	1.14756i
$137$		−	12.6245i		−	1.07859i	−0.842118	−	0.539294i	$-0.818691\pi$
$137$		−	12.6245i		−	1.07859i	0.842118	−	0.539294i	$-0.181309\pi$
$138$	12.2458	+	10.2849i	1.04243	+	0.875508i
$139$		−	4.60159i		−	0.390302i	−0.980773	−	0.195151i	$-0.937480\pi$
$139$		−	4.60159i		−	0.390302i	0.980773	−	0.195151i	$-0.0625196\pi$
$140$	1.11934	+	10.3207i	0.0946015	+	0.872256i
$141$	1.56687	−	1.00696i	0.131954	−	0.0848017i
$142$	12.0210	+	2.83471i	1.00878	+	0.237884i
$143$	−3.58619	−	7.85266i	−0.299892	−	0.656672i
$144$	10.2134	+	0.711299i	0.851115	+	0.0592749i
$145$	−0.485925	−	1.65491i	−0.0403539	−	0.137433i
$146$	9.74022	+	13.4941i	0.806107	+	1.11678i
$147$	−4.80374	−	2.19379i	−0.396205	−	0.180941i
$148$	10.2836	−	6.11456i	0.845310	−	0.502614i
$149$	−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	$0.345731\pi$
$150$	−2.07451	+	0.732936i	−0.169383	+	0.0598440i
$151$	1.25351	−	4.26906i	0.102009	−	0.347411i	−0.892634	−	0.450783i	$-0.851145\pi$
$151$	1.25351	−	4.26906i	0.102009	−	0.347411i	0.994643	+	0.103371i	$0.0329631\pi$
$152$	14.6185	−	0.281459i	1.18572	−	0.0228293i
$153$	−6.78671	+	10.5603i	−0.548673	+	0.853752i
$154$	4.63377	+	0.412483i	0.373400	+	0.0332388i
$155$	2.73702	−	19.0364i	0.219843	−	1.52904i
$156$	−25.6274	−	8.50303i	−2.05183	−	0.680787i
$157$	−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	$0.476164\pi$
$158$	−15.3244	+	3.05566i	−1.21915	+	0.243095i
$159$	−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	−0.0499432	−	0.998752i	$-0.515904\pi$
$163$	−13.3498	−	11.5677i	−1.04564	−	0.906050i	−0.995694	+	0.0927024i	$0.970449\pi$
$164$	−2.99275	−	0.537065i	−0.233694	−	0.0419377i
$165$	1.20361	+	8.37133i	0.0937013	+	0.651707i
$166$	−0.142499	−	2.63548i	−0.0110601	−	0.204553i
$167$	4.71723	+	0.678236i	0.365030	+	0.0524834i	0.322390	−	0.946607i	$-0.395514\pi$
$167$	4.71723	+	0.678236i	0.365030	+	0.0524834i	0.0426407	+	0.999090i	$0.486423\pi$
$168$	10.8111	−	9.73852i	0.834097	−	0.751343i
$169$	16.6437	+	10.6963i	1.28029	+	0.822790i
$170$	−11.8689	+	11.4633i	−0.910304	+	0.879195i
$171$	12.6953	+	3.72766i	0.970831	+	0.285062i
$172$	−0.645728	+	18.5662i	−0.0492363	+	1.41566i
$173$	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	$0.714025\pi$
$174$	−1.48217	+	1.90983i	−0.112363	+	0.144784i
$175$	−0.598030	+	1.30950i	−0.0452068	+	0.0989891i
$176$	2.88038	−	5.29852i	0.217116	−	0.399391i
$177$	−13.3619	+	3.92342i	−1.00435	+	0.294902i
$178$	−10.0149	−	5.69672i	−0.750647	−	0.426987i
$179$	−7.31079	+	3.33872i	−0.546434	+	0.249548i	−0.669451	−	0.742857i	$-0.733470\pi$
$179$	−7.31079	+	3.33872i	−0.546434	+	0.249548i	0.123017	+	0.992405i	$0.460743\pi$
$180$	10.0101	+	6.93629i	0.746109	+	0.517000i
$181$	−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	$-0.371667\pi$
$182$	−15.6509	+	8.19613i	−1.16012	+	0.607537i
$183$	−24.1881			−1.78804
$184$	4.07274	−	12.9388i	0.300246	−	0.953862i
$185$	14.2316			1.04633
$186$	−23.8800	+	12.5056i	−1.75096	+	0.916954i
$187$	3.99776	+	6.22063i	0.292345	+	0.454898i
$188$	−1.29856	−	0.899812i	−0.0947075	−	0.0656256i
$189$	−2.06119	+	0.941313i	−0.149929	+	0.0684705i
$190$	15.1176	+	8.59930i	1.09675	+	0.623858i
$191$	14.4587	−	4.24546i	1.04620	−	0.307191i	0.286917	−	0.957956i	$-0.407370\pi$
$191$	14.4587	−	4.24546i	1.04620	−	0.307191i	0.759279	+	0.650765i	$0.225552\pi$
$192$	−6.00704	−	17.8809i	−0.433521	−	1.29044i
$193$	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	$0.0939815\pi$
$194$	4.99047	−	6.43039i	0.358295	−	0.461675i
$195$	−21.0331	−	24.2735i	−1.50621	−	1.73826i
$196$	−0.155700	+	4.47674i	−0.0111214	+	0.319767i
$197$	−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	$0.744265\pi$
$198$	3.92552	−	3.79136i	0.278974	−	0.269440i
$199$	−2.39289	−	1.53782i	−0.169628	−	0.109013i	0.453072	−	0.891474i	$-0.350328\pi$
$199$	−2.39289	−	1.53782i	−0.169628	−	0.109013i	−0.622700	+	0.782461i	$0.713964\pi$
$200$	1.24906	+	1.38663i	0.0883217	+	0.0980495i
$201$	−0.0883366	−	0.0127009i	−0.00623078	−	0.000895851i
$202$	−0.574785	−	10.6305i	−0.0404417	−	0.747957i
$203$	0.225111	+	1.56568i	0.0157997	+	0.109889i
$204$	22.7644	+	4.08520i	1.59383	+	0.286021i
$205$	−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
$210$	16.9740	−	3.38459i	1.17132	−	0.233559i
$211$	10.6275	−	1.52800i	0.731627	−	0.105192i	0.233574	−	0.972339i	$-0.424958\pi$
$211$	10.6275	−	1.52800i	0.731627	−	0.105192i	0.498052	+	0.867147i	$0.334049\pi$
$212$	0.733374	+	0.243329i	0.0503683	+	0.0167119i
$213$	2.93053	−	20.3823i	0.200797	−	1.39657i
$214$	−7.41681	−	0.660220i	−0.507003	−	0.0451317i
$215$	−11.9472	+	18.5902i	−0.814790	+	1.26784i
$216$	0.0565472	+	2.93698i	0.00384755	+	0.199836i
$217$	−4.96912	+	16.9233i	−0.337326	+	1.14883i
$218$	6.27202	−	2.21594i	0.424794	−	0.150082i
$219$	20.9697	−	18.1704i	1.41700	−	1.22784i
$220$	6.16614	−	3.66633i	0.415721	−	0.247184i
$221$	−25.5441	−	11.6656i	−1.71828	−	0.784712i
$222$	−11.6746	−	16.1741i	−0.783551	−	1.08553i
$223$	0.990426	+	3.37308i	0.0663238	+	0.225878i	0.985985	−	0.166835i	$-0.0533547\pi$
$223$	0.990426	+	3.37308i	0.0663238	+	0.225878i	−0.919661	+	0.392713i	$0.871537\pi$
$224$	−11.1459	−	5.30067i	−0.744719	−	0.354166i
$225$	0.701563	+	1.53621i	0.0467709	+	0.102414i
$226$	−12.4556	−	2.93720i	−0.828536	−	0.195380i
$227$	18.5205	−	11.9024i	1.22925	−	0.789991i	0.245476	−	0.969403i	$-0.421056\pi$
$227$	18.5205	−	11.9024i	1.22925	−	0.789991i	0.983774	+	0.179412i	$0.0574194\pi$
$228$	−2.62847	−	24.2354i	−0.174075	−	1.60503i
$229$			3.82942i			0.253056i	0.991963	+	0.126528i	$0.0403833\pi$
$229$			3.82942i			0.253056i	−0.991963	+	0.126528i	$0.959617\pi$
$230$	12.0300	−	10.7532i	0.793236	−	0.709042i
$231$		−	7.75626i		−	0.510324i
$232$	1.97827	+	0.539732i	0.129880	+	0.0354352i
$233$	−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	$0.464476\pi$
$234$	−4.75692	+	20.1724i	−0.310969	+	1.31871i
$235$	−0.780674	−	1.70944i	−0.0509256	−	0.111511i
$236$	7.42052	+	9.19071i	0.483034	+	0.598264i
$237$	7.33993	+	24.9975i	0.476780	+	1.62376i
$238$	12.2703	−	8.85685i	0.795365	−	0.574104i
$239$	5.39620	+	2.46436i	0.349051	+	0.159406i	0.582223	−	0.813029i	$-0.302183\pi$
$239$	5.39620	+	2.46436i	0.349051	+	0.159406i	−0.233172	+	0.972436i	$0.574910\pi$
$240$	4.72853	−	21.9339i	0.305225	−	1.41583i
$241$	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	$0.0251901\pi$
$242$	4.11129	+	11.6367i	0.264284	+	0.748033i
$243$	−5.84971	+	19.9223i	−0.375259	+	1.27801i
$244$	7.86920	+	18.9479i	0.503774	+	1.21301i
$245$	−2.88074	+	4.48252i	−0.184044	+	0.286378i
$246$	−0.449484	+	5.04943i	−0.0286581	+	0.321940i
$247$	−4.21234	+	29.2975i	−0.268025	+	1.86415i
$248$	17.5653	+	14.6380i	1.11539	+	0.929513i
$249$	−4.35566	+	0.626250i	−0.276029	+	0.0396870i
$250$	−2.85548	−	14.3205i	−0.180596	−	0.905707i
$251$	−11.8946	+	13.7271i	−0.750779	+	0.866445i	−0.994644	−	0.103364i	$-0.967039\pi$
$251$	−11.8946	+	13.7271i	−0.750779	+	0.866445i	0.243864	+	0.969809i	$0.421585\pi$
$252$	−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
$256$	−12.0528	+	10.5229i	−0.753297	+	0.657680i
$257$	−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	$-0.188780\pi$
$258$	30.9282	−	1.67228i	1.92551	−	0.104111i
$259$	−12.9189	−	1.85745i	−0.802740	−	0.115417i
$260$	−12.1720	+	24.3733i	−0.754873	+	1.51157i
$261$	1.56105	+	1.00323i	0.0966268	+	0.0620983i
$262$	−16.9715	−	17.5721i	−1.04851	−	1.08561i
$263$	−13.3421	−	3.91760i	−0.822710	−	0.241569i	−0.156827	−	0.987626i	$-0.550127\pi$
$263$	−13.3421	−	3.91760i	−0.822710	−	0.241569i	−0.665883	+	0.746057i	$0.731945\pi$
$264$	−9.22504	−	4.00015i	−0.567762	−	0.246192i
$265$	0.601900	+	0.694629i	0.0369744	+	0.0426707i
$266$	−12.6009	−	9.77921i	−0.772608	−	0.599602i
$267$	−7.98002	+	17.4738i	−0.488369	+	1.06938i
$268$	0.0187896	+	0.0733308i	0.00114776	+	0.00447939i
$269$	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	$0.186386\pi$
$270$	−1.72766	+	3.03725i	−0.105142	+	0.184841i
$271$	−0.637765	+	0.291258i	−0.0387415	+	0.0176926i	−0.434692	−	0.900579i	$-0.643143\pi$
$271$	−0.637765	+	0.291258i	−0.0387415	+	0.0176926i	0.395950	+	0.918272i	$0.370415\pi$
$272$	−4.20587	−	19.1616i	−0.255018	−	1.16185i
$273$	15.9249	+	24.7797i	0.963821	+	1.49973i
$274$	8.28275	+	15.8163i	0.500379	+	0.955496i
$275$	0.994813			0.0599895
$276$	−22.0895	−	4.85084i	−1.32963	−	0.291987i
$277$	−18.6953			−1.12329			−0.561647	−	0.827377i	$-0.689832\pi$
$277$	−18.6953			−1.12329			−0.561647	+	0.827377i	$0.689832\pi$
$278$	3.01902	+	5.76496i	0.181069	+	0.345759i
$279$	11.1865	+	17.4066i	0.669720	+	1.04210i
$280$	−8.17355	−	12.1956i	−0.488463	−	0.728824i
$281$	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	$0.116145\pi$
$282$	−1.30235	+	2.28954i	−0.0775537	+	0.136340i
$283$	7.31305	−	2.14730i	0.434715	−	0.127644i	−0.0570507	−	0.998371i	$-0.518170\pi$
$283$	7.31305	−	2.14730i	0.434715	−	0.127644i	0.491766	+	0.870727i	$0.336351\pi$
$284$	−16.9200	+	4.33540i	−1.00401	+	0.257259i
$285$	12.0460	−	26.3770i	0.713542	−	1.56244i
$286$	9.64484	+	7.48512i	0.570311	+	0.442604i
$287$	2.17214	+	2.50678i	0.128217	+	0.147971i
$288$	−13.2622	+	5.80970i	−0.781482	+	0.342340i
$289$	6.76791	+	1.98724i	0.398112	+	0.116896i
$290$	1.69453	+	1.75449i	0.0995064	+	0.103027i
$291$	−11.4167	−	7.33705i	−0.669257	−	0.430105i
$292$	−21.0560	−	10.5153i	−1.23221	−	0.615361i
$293$	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	$0.433803\pi$
$294$	7.45752	−	0.403225i	0.434931	−	0.0235165i
$295$	1.99968	+	13.9081i	0.116426	+	0.809759i
$296$	−8.87187	+	14.4074i	−0.515667	+	0.837410i
$297$	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
$302$	1.23044	+	6.17077i	0.0708038	+	0.355088i
$303$	−17.5690	+	2.52604i	−1.00931	+	0.145117i
$304$	−18.1297	+	9.94360i	−1.03981	+	0.570304i
$305$	−3.47324	+	24.1569i	−0.198877	+	1.38322i
$306$	1.57407	−	17.6828i	0.0899834	−	1.01086i
$307$	7.88790	−	12.2738i	0.450186	−	0.700504i	−0.539780	−	0.841806i	$-0.681493\pi$
$307$	7.88790	−	12.2738i	0.450186	−	0.700504i	0.989966	+	0.141302i	$0.0451290\pi$
$308$	−6.07590	+	2.52337i	−0.346206	+	0.143782i
$309$	−8.33134	+	28.3739i	−0.473953	+	1.61414i
$310$	9.06046	+	25.6449i	0.514600	+	1.45653i
$311$	15.6718	−	13.5797i	0.888666	−	0.770034i	−0.0853882	−	0.996348i	$-0.527213\pi$
$311$	15.6718	−	13.5797i	0.888666	−	0.770034i	0.974054	+	0.226314i	$0.0726676\pi$
$312$	37.6852	−	6.16094i	2.13350	−	0.348794i
$313$	−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	$0.653898\pi$
$314$	1.95017	−	1.40765i	0.110054	−	0.0794385i
$315$	−3.74295	−	12.7473i	−0.210892	−	0.718231i
$316$	17.1940	−	13.8823i	0.967236	−	0.780940i
$317$	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	$0.848896\pi$
$318$	0.295682	−	1.25388i	0.0165810	−	0.0703142i
$319$	0.919549	−	0.590958i	0.0514848	−	0.0330873i
$320$	−18.7204	+	3.43172i	−1.04650	+	0.191839i
$321$			12.4147i			0.692919i
$322$	−12.3238	+	8.19118i	−0.686781	+	0.456477i
$323$		−	25.3530i		−	1.41068i
$324$	20.1367	−	2.18395i	1.11871	−	0.121331i
$325$	−3.17823	+	2.04252i	−0.176296	+	0.113299i
$326$	24.3142	+	5.73361i	1.34664	+	0.317556i
$327$	−4.60719	−	10.0883i	−0.254778	−	0.557886i
$328$	4.10173	−	1.29064i	0.226480	−	0.0712639i
$329$	0.485556	+	1.65365i	0.0267696	+	0.0911688i
$330$	−7.00020	−	9.69808i	−0.385348	−	0.533862i
$331$	−10.0083	−	4.57065i	−0.550107	−	0.251225i	0.120915	−	0.992663i	$-0.461417\pi$
$331$	−10.0083	−	4.57065i	−0.550107	−	0.251225i	−0.671022	+	0.741437i	$0.734144\pi$
$332$	1.90762	+	3.20828i	0.104694	+	0.176078i
$333$	−11.5715	+	10.0268i	−0.634115	+	0.549464i
$334$	−6.35482	+	2.24519i	−0.347720	+	0.122851i
$335$	−0.0253690	+	0.0863988i	−0.00138606	+	0.00472047i
$336$	−7.15511	+	19.2936i	−0.390343	+	1.05255i
$337$	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	$0.0201390\pi$
$338$	−27.8692	−	2.48083i	−1.51589	−	0.134939i
$339$	−3.03648	+	21.1192i	−0.164919	+	1.14704i
$340$	7.34873	−	22.1484i	0.398541	−	1.20117i
$341$	12.0643	−	1.73458i	0.653316	−	0.0939326i
$342$	−18.3505	+	3.65906i	−0.992282	+	0.197859i
$343$	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	0.865602	−	0.500733i	$-0.166936\pi$
$347$	9.18644	+	7.96010i	0.493154	+	0.427321i	−0.372448	+	0.928053i	$0.621481\pi$
$348$	0.603884	−	3.36509i	0.0323716	−	0.180388i
$349$	−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	$-0.153499\pi$
$350$	−0.109919	−	2.03293i	−0.00587544	−	0.108664i
$351$	−5.88609	−	0.846291i	−0.314176	−	0.0451717i
$352$	−0.132317	+	8.52786i	−0.00705252	+	0.454536i
$353$	−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	$0.997482\pi$
$354$	14.1660	−	13.6819i	0.752915	−	0.727184i
$355$	−19.9352	−	5.85350i	−1.05805	−	0.310672i
$356$	16.2843	+	0.566366i	0.863069	+	0.0300174i
$357$	−16.5224	−	19.0679i	−0.874461	−	1.00918i
$358$	6.96861	−	8.97930i	0.368302	−	0.474571i
$359$	1.38216	−	3.02652i	0.0729478	−	0.159733i	−0.869645	−	0.493677i	$-0.835652\pi$
$359$	1.38216	−	3.02652i	0.0729478	−	0.159733i	0.942593	+	0.333944i	$0.108380\pi$
$360$	−17.0916	−	2.12245i	−0.900808	−	0.111863i
$361$	−7.40982	+	2.17572i	−0.389990	+	0.114512i
$362$	18.5784	+	10.5679i	0.976461	+	0.555436i
$363$	18.7172	−	8.54785i	0.982398	−	0.448646i
$364$	14.2304	−	20.5365i	0.745873	−	1.07641i
$365$	−15.1358	−	23.5518i	−0.792245	−	1.23276i
$366$	30.3033	−	15.8694i	1.58398	−	0.829507i
$367$	10.9298			0.570533			0.285266	−	0.958448i	$-0.407918\pi$
$367$	10.9298			0.570533			0.285266	+	0.958448i	$0.407918\pi$
$368$	3.38653	+	18.8820i	0.176535	+	0.984294i
$369$	3.89119			0.202567
$370$	−17.8296	+	9.33710i	−0.926917	+	0.485413i
$371$	−0.455721	−	0.709115i	−0.0236598	−	0.0368154i
$372$	21.7126	−	31.3345i	1.12574	−	1.62462i
$373$	−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	$0.501009\pi$
$374$	−9.08971	−	5.17046i	−0.470018	−	0.267358i
$375$	−23.3598	+	6.85907i	−1.20630	+	0.354201i
$376$	2.21722	+	0.275336i	0.114344	+	0.0141994i
$377$	−1.72443	+	3.77599i	−0.0888129	+	0.194473i
$378$	1.96472	−	2.53161i	0.101054	−	0.130212i
$379$	−16.6381	−	19.2014i	−0.854642	−	0.986310i	0.145353	−	0.989380i	$-0.453568\pi$
$379$	−16.6381	−	19.2014i	−0.854642	−	0.986310i	−0.999995	+	0.00306989i	$0.999023\pi$
$380$	−24.5815	−	0.854939i	−1.26100	−	0.0438575i
$381$	1.57181	+	0.461525i	0.0805263	+	0.0236447i
$382$	−15.3288	+	14.8049i	−0.784288	+	0.757485i
$383$	12.9260	+	8.30703i	0.660487	+	0.424469i	0.827485	−	0.561488i	$-0.189771\pi$
$383$	12.9260	+	8.30703i	0.660487	+	0.424469i	−0.166998	+	0.985957i	$0.553407\pi$
$384$	19.2571	+	18.4604i	0.982708	+	0.942052i
$385$	−7.74625	−	1.11374i	−0.394785	−	0.0567616i
$386$	0.281638	+	5.20881i	0.0143350	+	0.265122i
$387$	−3.38349	−	23.5327i	−0.171993	−	1.19623i
$388$	−2.03328	+	11.3303i	−0.103224	+	0.575208i
$389$	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
$394$	18.0397	−	3.59709i	0.908829	−	0.181219i
$395$	26.0192	−	3.74100i	1.30917	−	0.188230i
$396$	−2.43051	+	7.32535i	−0.122138	+	0.368113i
$397$	−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	$0.630423\pi$
$398$	4.00680	+	0.356672i	0.200843	+	0.0178784i
$399$	−14.3775	+	22.3718i	−0.719776	+	1.11999i
$400$	−2.47459	−	0.917710i	−0.123729	−	0.0458855i
$401$	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	$-0.109995\pi$
$402$	0.119003	−	0.0420442i	0.00593531	−	0.00209698i
$403$	−34.9815	+	30.3116i	−1.74255	+	1.50993i
$404$	7.69457	+	12.9409i	0.382819	+	0.643836i
$405$	21.9162	+	10.0088i	1.08902	+	0.497340i
$406$	−1.30924	−	1.81382i	−0.0649765	−	0.0900186i
$407$	2.54101	+	8.65388i	0.125953	+	0.428957i
$408$	−31.1999	+	9.81733i	−1.54463	+	0.486030i
$409$	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	$0.537462\pi$
$410$	4.97837	+	1.17397i	0.245864	+	0.0579780i
$411$	25.0416	−	16.0932i	1.23521	−	0.793821i
$412$	24.9373	−	2.70460i	1.22857	−	0.133246i
$413$		−	12.8862i		−	0.634089i
$414$	−2.20538	+	17.2189i	−0.108389	+	0.846264i
$415$			4.43996i			0.217949i
$416$	−17.0864	−	27.5165i	−0.837731	−	1.34911i
$417$	9.12754	−	5.86591i	0.446977	−	0.287255i
$418$	−2.52981	+	10.7280i	−0.123737	+	0.524726i
$419$	−15.1366	−	33.1446i	−0.739472	−	1.61922i	−0.784421	−	0.620229i	$-0.787040\pi$
$419$	−15.1366	−	33.1446i	−0.739472	−	1.61922i	0.0449489	−	0.998989i	$-0.485687\pi$
$420$	−19.0448	+	15.3766i	−0.929292	+	0.750303i
$421$	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	$0.737049\pi$
$422$	−12.3118	+	8.88683i	−0.599330	+	0.432604i
$423$	1.83913	+	0.839902i	0.0894215	+	0.0408374i
$424$	−1.07843	+	0.176306i	−0.0523731	+	0.00856219i
$425$	2.44564	−	2.11916i	0.118631	−	0.102794i
$426$	9.70106	+	27.4580i	0.470018	+	1.33034i
$427$	6.30574	−	21.4754i	0.305156	−	1.03927i
$428$	9.72508	−	4.03891i	0.470079	−	0.195228i
$429$	11.0047	−	17.1237i	0.531313	−	0.826739i
$430$	2.77095	−	31.1284i	0.133627	−	1.50115i
$431$	−1.22660	+	8.53121i	−0.0590834	+	0.410934i	0.938720	+	0.344682i	$0.112013\pi$
$431$	−1.22660	+	8.53121i	−0.0590834	+	0.410934i	−0.997803	+	0.0662521i	$0.978896\pi$
$432$	−1.99774	−	3.64240i	−0.0961165	−	0.175245i
$433$	−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	$0.485863\pi$
$434$	−4.87766	−	24.4619i	−0.234135	−	1.17421i
$435$	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	0.842800	−	0.538227i	$-0.180906\pi$
$439$	9.00939	+	7.80668i	0.429994	+	0.372592i	−0.412806	+	0.910819i	$0.635451\pi$
$440$	−5.31963	+	8.63874i	−0.253604	+	0.411836i
$441$	−0.815839	−	5.67429i	−0.0388495	−	0.270204i
$442$	39.6557	−	2.14416i	1.88623	−	0.101987i
$443$	−22.4322	−	3.22526i	−1.06579	−	0.153237i	−0.412963	−	0.910748i	$-0.635506\pi$
$443$	−22.4322	−	3.22526i	−1.06579	−	0.153237i	−0.652823	+	0.757511i	$0.726415\pi$
$444$	25.2378	+	12.6037i	1.19773	+	0.598143i
$445$	16.3054	+	10.4788i	0.772949	+	0.496744i
$446$	−3.45384	−	3.57606i	−0.163544	−	0.169331i
$447$	−12.5563	−	3.68687i	−0.593893	−	0.174383i
$448$	17.4415	−	0.671871i	0.824034	−	0.0317429i
$449$	−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	$0.982868\pi$
$450$	−1.88681	−	1.46431i	−0.0889452	−	0.0690281i
$451$	0.952186	−	2.08500i	0.0448367	−	0.0981787i
$452$	17.5317	−	4.49215i	0.824621	−	0.211293i
$453$	10.0659	−	2.95561i	0.472936	−	0.138867i
$454$	−15.3939	+	27.0626i	−0.722471	+	1.27011i
$455$	27.0344	−	12.3462i	1.26739	−	0.578799i
$456$	19.1934	+	28.6380i	0.898814	+	1.34110i
$457$	−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	$0.857811\pi$
$458$	−2.51242	−	4.79758i	−0.117398	−	0.224176i
$459$	5.09362			0.237750
$460$	−8.01647	+	21.3644i	−0.373770	+	0.996122i
$461$	21.1419			0.984674			0.492337	−	0.870405i	$-0.336143\pi$
$461$	21.1419			0.984674			0.492337	+	0.870405i	$0.336143\pi$
$462$	5.08875	+	9.71719i	0.236750	+	0.452084i
$463$	−10.8887	−	16.9431i	−0.506039	−	0.787413i	0.490420	−	0.871486i	$-0.336843\pi$
$463$	−10.8887	−	16.9431i	−0.506039	−	0.787413i	−0.996460	+	0.0840736i	$0.973207\pi$
$464$	−2.83252	+	0.621722i	−0.131497	+	0.0288627i
$465$	41.2489	−	18.8377i	1.91287	−	0.873579i
$466$	9.46907	−	16.6467i	0.438646	−	0.771143i
$467$	16.5921	−	4.87189i	0.767792	−	0.225444i	0.125696	−	0.992069i	$-0.459884\pi$
$467$	16.5921	−	4.87189i	0.767792	−	0.225444i	0.642095	+	0.766625i	$0.278065\pi$
$468$	−7.27522	−	28.3933i	−0.336297	−	1.31248i
$469$	0.0343054	−	0.0751184i	0.00158408	−	0.00346865i
$470$	2.09958	+	1.62943i	0.0968462	+	0.0751599i
$471$	−2.62598	−	3.03054i	−0.120999	−	0.139640i
$472$	−15.3264	−	6.64582i	−0.705456	−	0.305899i
$473$	−13.4374	−	3.94556i	−0.617850	−	0.181417i
$474$	−25.5960	−	26.5017i	−1.17566	−	1.21726i
$475$	−2.86940	−	1.84405i	−0.131657	−	0.0846109i
$476$	−9.56163	+	19.1464i	−0.438256	+	0.877572i
$477$	−0.978793	−	0.140729i	−0.0448159	−	0.00644355i
$478$	−8.37729	+	0.452956i	−0.383168	+	0.0207177i
$479$	5.22142	+	36.3158i	0.238573	+	1.65931i	0.659118	+	0.752040i	$0.270930\pi$
$479$	5.22142	+	36.3158i	0.238573	+	1.65931i	−0.420545	+	0.907272i	$0.638161\pi$
$480$	8.46647	+	30.5815i	0.386440	+	1.39585i
$481$	−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
$486$	−5.74204	−	28.7969i	−0.260464	−	1.30625i
$487$	−26.4728	+	3.80622i	−1.19960	+	0.172476i	−0.713009	−	0.701155i	$-0.752668\pi$
$487$	−26.4728	+	3.80622i	−1.19960	+	0.172476i	−0.486589	+	0.873631i	$0.661759\pi$
$488$	−22.2901	−	18.5754i	−1.00902	−	0.840868i
$489$	5.92742	−	41.2261i	0.268047	−	1.86431i
$490$	0.668141	−	7.50580i	0.0301836	−	0.339077i
$491$	4.04450	−	6.29337i	0.182526	−	0.284016i	−0.737918	−	0.674890i	$-0.764191\pi$
$491$	4.04450	−	6.29337i	0.182526	−	0.284016i	0.920444	+	0.390874i	$0.127827\pi$
$492$	−2.74973	−	6.62093i	−0.123967	−	0.298494i
$493$	1.00175	−	3.41164i	0.0451164	−	0.153652i
$494$	−13.9443	−	39.4681i	−0.627383	−	1.77575i
$495$	−6.93835	+	6.01212i	−0.311856	+	0.270225i
$496$	−31.6098	−	6.81447i	−1.41932	−	0.305979i
$497$	17.3324	+	7.91545i	0.777465	+	0.355057i
$498$	5.04598	−	3.64225i	0.226116	−	0.163213i
$499$	3.15885	+	10.7580i	0.141409	+	0.481596i	0.999490	−	0.0319179i	$-0.0101615\pi$
$499$	3.15885	+	10.7580i	0.141409	+	0.481596i	−0.858081	+	0.513514i	$0.828343\pi$
$500$	12.9728	+	16.0675i	0.580162	+	0.718562i
$501$	4.66801	+	10.2215i	0.208551	+	0.456663i
$502$	5.89565	−	25.0014i	0.263136	−	1.11587i
$503$	−35.5200	+	22.8273i	−1.58376	+	1.01782i	−0.609388	+	0.792872i	$0.708585\pi$
$503$	−35.5200	+	22.8273i	−1.58376	+	1.01782i	−0.974371	+	0.224947i	$0.927779\pi$
$504$	15.2381	+	4.15742i	0.678759	+	0.185186i
$505$			17.9091i			0.796943i
$506$	8.68666	+	5.39522i	0.386169	+	0.239847i
$507$			46.6490i			2.07176i
$508$	−0.149825	−	1.38143i	−0.00664741	−	0.0612912i
$509$	−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	$0.394090\pi$
$510$	−37.8682	−	8.92981i	−1.67683	−	0.395419i
$511$	10.6658	+	23.3549i	0.471828	+	1.03316i
$512$	8.19604	−	21.0909i	0.362217	−	0.932094i
$513$	−1.51256	−	5.15131i	−0.0667811	−	0.227436i
$514$	11.5496	+	16.0008i	0.509431	+	0.705766i
$515$	27.1410	+	12.3949i	1.19598	+	0.546184i
$516$	−37.6503	+	22.3865i	−1.65746	+	0.985513i
$517$	0.900080	−	0.779924i	0.0395855	−	0.0343010i
$518$	17.4037	−	6.14881i	0.764673	−	0.270163i
$519$	−3.20440	+	10.9132i	−0.140658	+	0.479036i
$520$	−0.741669	−	38.5212i	−0.0325244	−	1.68927i
$521$	−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	$0.931679\pi$
$522$	−2.61392	−	0.232682i	−0.114408	−	0.0101842i
$523$	3.75821	−	26.1389i	0.164335	−	1.14298i	−0.726008	−	0.687686i	$-0.758627\pi$
$523$	3.75821	−	26.1389i	0.164335	−	1.14298i	0.890343	−	0.455290i	$-0.150464\pi$
$524$	32.7910	+	10.8799i	1.43248	+	0.475290i
$525$	−3.35982	+	0.483070i	−0.146635	+	0.0210829i
$526$	19.2855	−	3.84549i	0.840889	−	0.167672i
$527$	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
$532$	22.2026	+	3.98437i	0.962603	+	0.172744i
$533$	1.23882	+	8.61615i	0.0536591	+	0.373207i
$534$	−1.46675	−	27.1271i	−0.0634724	−	1.17390i
$535$	12.3986	+	1.78266i	0.536040	+	0.0770709i
$536$	−0.0716510	−	0.0795427i	−0.00309485	−	0.00343572i
$537$	−15.9421	−	10.2453i	−0.687950	−	0.442119i
$538$	−21.4871	+	20.7527i	−0.926373	+	0.894714i
$539$	−3.24006	−	0.951368i	−0.139559	−	0.0409783i
$540$	0.171764	−	4.93861i	0.00739154	−	0.212524i
$541$	−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	$0.821778\pi$
$542$	0.607915	−	0.783320i	0.0261122	−	0.0336465i
$543$	14.8036	−	32.4154i	0.635284	−	1.39108i
$544$	17.8408	+	21.2467i	0.764919	+	0.910944i
$545$	−10.7369	+	3.15263i	−0.459917	+	0.135044i
$546$	−36.2086	−	20.5964i	−1.54958	−	0.881444i
$547$	−22.4276	+	10.2424i	−0.958937	+	0.437932i	−0.832489	−	0.554041i	$-0.813085\pi$
$547$	−22.4276	+	10.2424i	−0.958937	+	0.437932i	−0.126448	+	0.991973i	$0.540358\pi$
$548$	−20.7536	−	14.3807i	−0.886549	−	0.614315i
$549$	−14.1955	−	22.0887i	−0.605851	−	0.942722i
$550$	−1.24632	+	0.652680i	−0.0531433	+	0.0278304i
$551$	−3.74775			−0.159659
$552$	30.8567	−	8.41532i	1.31335	−	0.358180i
$553$	−24.1075			−1.02515
$554$	23.4219	−	12.2657i	0.995099	−	0.521119i
$555$	18.1418	+	28.2292i	0.770078	+	1.19826i
$556$	−7.56458	−	5.24172i	−0.320810	−	0.222298i
$557$	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	$0.295879\pi$
$558$	−25.4349	−	14.4680i	−1.07674	−	0.612479i
$559$	51.0306	−	14.9839i	2.15836	−	0.633753i
$560$	18.2413	+	9.91629i	0.770834	+	0.419040i
$561$	−7.24284	+	15.8596i	−0.305793	+	0.669593i
$562$	−20.3923	+	26.2762i	−0.860198	+	1.10840i
$563$	26.8668	+	31.0059i	1.13230	+	1.30674i	0.945969	+	0.324257i	$0.105114\pi$
$563$	26.8668	+	31.0059i	1.13230	+	1.30674i	0.186331	+	0.982487i	$0.440340\pi$
$564$	0.129479	−	3.72283i	0.00545205	−	0.156759i
$565$	20.6559	+	6.06513i	0.869002	+	0.255162i
$566$	−7.75311	+	7.48815i	−0.325888	+	0.314750i
$567$	−18.5884	−	11.9460i	−0.780637	−	0.501685i
$568$	18.3533	−	16.5324i	0.770086	−	0.693683i
$569$	−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	$0.552176\pi$
$570$	2.21408	+	40.9488i	0.0927377	+	1.71516i
$571$	−4.09175	−	28.4588i	−0.171234	−	1.19096i	−0.876281	−	0.481801i	$-0.839983\pi$
$571$	−4.09175	−	28.4588i	−0.171234	−	1.19096i	0.705046	−	0.709161i	$-0.250926\pi$
$572$	−16.9941	−	3.04968i	−0.710559	−	0.127514i
$573$	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	$0.318778\pi$
$578$	−9.78276	+	1.95066i	−0.406909	+	0.0811369i
$579$	8.60862	−	1.23773i	0.357762	−	0.0514384i
$580$	−3.27404	−	1.08631i	−0.135947	−	0.0451065i
$581$	0.579488	−	4.03043i	0.0240412	−	0.167210i
$582$	19.1167	+	1.70171i	0.792414	+	0.0705381i
$583$	−0.314920	+	0.490025i	−0.0130426	+	0.0202947i
$584$	33.2783	−	0.640725i	1.37706	−	0.0265134i
$585$	9.82273	−	33.4531i	0.406120	−	1.38312i
$586$	−15.6858	+	5.54188i	−0.647975	+	0.228933i
$587$	−33.6765	+	29.1808i	−1.38998	+	1.20442i	−0.437725	+	0.899109i	$0.644215\pi$
$587$	−33.6765	+	29.1808i	−1.38998	+	1.20442i	−0.952252	+	0.305313i	$0.901239\pi$
$588$	−9.07837	+	5.39792i	−0.374386	+	0.222606i
$589$	−38.0130	−	17.3599i	−1.56630	−	0.715304i
$590$	−11.6301	−	16.1123i	−0.478803	−	0.663335i
$591$	−8.64048	−	29.4268i	−0.355422	−	1.21046i
$592$	1.66243	−	23.8705i	0.0683255	−	0.981071i
$593$	−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	$-0.287095\pi$
$594$	−2.15534	−	0.508258i	−0.0884349	−	0.0208541i
$595$	−21.4158	+	13.7631i	−0.877963	+	0.564232i
$596$	1.19687	+	11.0355i	0.0490256	+	0.452032i
$597$		−	6.70680i		−	0.274491i
$598$	−38.8294	+	0.598567i	−1.58785	+	0.0244772i
$599$		−	1.33089i		−	0.0543785i	−0.999630	−	0.0271893i	$-0.991344\pi$
$599$		−	1.33089i		−	0.0543785i	0.999630	−	0.0271893i	$-0.00865568\pi$
$600$	−1.15822	+	4.24520i	−0.0472841	+	0.173310i
$601$	−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	$0.362055\pi$
$602$	−6.57813	+	27.8955i	−0.268105	+	1.13694i
$603$	−0.0402445	−	0.0881233i	−0.00163888	−	0.00358866i
$604$	−5.59005	−	6.92359i	−0.227456	−	0.281717i
$605$	−5.84917	−	19.9204i	−0.237803	−	0.809881i
$606$	20.3535	−	14.6914i	0.826804	−	0.596797i
$607$	−17.9110	−	8.17968i	−0.726985	−	0.332003i	0.0173136	−	0.999850i	$-0.494489\pi$
$607$	−17.9110	−	8.17968i	−0.726985	−	0.332003i	−0.744298	+	0.667847i	$0.767216\pi$
$608$	16.1894	−	24.3521i	0.656569	−	0.987609i
$609$	−2.81867	+	2.44239i	−0.114218	+	0.0989706i
$610$	−11.4976	−	32.5429i	−0.465524	−	1.31763i
$611$	−1.27426	+	4.33972i	−0.0515509	+	0.175566i
$612$	9.62938	+	23.1861i	0.389245	+	0.937242i
$613$	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	$-0.0443002\pi$
$614$	−1.82947	+	20.5520i	−0.0738314	+	0.829411i
$615$	1.21365	−	8.44111i	0.0489390	−	0.340379i
$616$	5.95646	−	7.14762i	0.239992	−	0.287986i
$617$	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	$0.274065\pi$
$618$	−8.17800	−	41.0135i	−0.328967	−	1.64980i
$619$	−16.9786	+	19.5944i	−0.682429	+	0.787565i	−0.986267	−	0.165158i	$-0.947186\pi$
$619$	−16.9786	+	19.5944i	−0.682429	+	0.787565i	0.303838	+	0.952724i	$0.401732\pi$
$620$	−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
$624$	−43.1706	+	32.4431i	−1.72821	+	1.29876i
$625$	3.96542	+	27.5801i	0.158617	+	1.10320i
$626$	2.75114	−	0.148753i	0.109958	−	0.00594536i
$627$	18.1900	+	2.61533i	0.726439	+	0.104446i
$628$	−1.51967	+	3.04300i	−0.0606413	+	0.121429i
$629$	24.6814	+	15.8618i	0.984111	+	0.632449i
$630$	13.0526	+	13.5144i	0.520026	+	0.538427i
$631$	45.6117	+	13.3928i	1.81577	+	0.533159i	0.999038	−	0.0438540i	$-0.0139636\pi$
$631$	45.6117	+	13.3928i	1.81577	+	0.533159i	0.816735	+	0.577013i	$0.195782\pi$
$632$	−12.4330	+	28.6727i	−0.494558	+	1.14054i
$633$	16.5784	+	19.1325i	0.658931	+	0.760447i
$634$	−1.84160	−	1.42922i	−0.0731393	−	0.0567616i
$635$	0.686630	−	1.50351i	0.0272481	−	0.0596650i
$636$	0.452215	+	1.76488i	0.0179315	+	0.0699820i
$637$	12.3047	−	3.61298i	0.487529	−	0.143151i
$638$	−0.764310	+	1.34366i	−0.0302593	+	0.0531962i
$639$	20.3331	−	9.28581i	0.804364	−	0.367341i
$640$	21.2017	−	16.5814i	0.838072	−	0.655439i
$641$	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	$0.533478\pi$
$642$	−8.14505	−	15.5533i	−0.321459	−	0.613841i
$643$	22.3558			0.881625			0.440812	−	0.897599i	$-0.354690\pi$
$643$	22.3558			0.881625			0.440812	+	0.897599i	$0.354690\pi$
$644$	10.0655	−	18.3475i	0.396635	−	0.722994i
$645$	−52.1045			−2.05161
$646$	16.6337	+	31.7628i	0.654444	+	1.24969i
$647$	−7.86724	−	12.2417i	−0.309293	−	0.481270i	0.651457	−	0.758686i	$-0.274158\pi$
$647$	−7.86724	−	12.2417i	−0.309293	−	0.481270i	−0.960750	+	0.277416i	$0.910522\pi$
$648$	−23.7948	+	15.9474i	−0.934748	+	0.626475i
$649$	−8.10012	+	3.69920i	−0.317958	+	0.145206i
$650$	2.64168	−	4.64409i	0.103615	−	0.182156i
$651$	−39.9028	+	11.7165i	−1.56391	+	0.459207i
$652$	−34.2231	+	8.76897i	−1.34028	+	0.343420i
$653$	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	$0.0611727\pi$
$654$	12.3908	+	9.61615i	0.484517	+	0.376021i
$655$	26.9125	+	31.0587i	1.05156	+	1.21356i
$656$	−4.29195	+	4.30802i	−0.167573	+	0.168200i
$657$	28.9000	+	8.48581i	1.12750	+	0.331063i
$658$	−1.69325	−	1.75316i	−0.0660096	−	0.0683453i
$659$	−8.10663	−	5.20981i	−0.315789	−	0.202945i	0.373138	−	0.927776i	$-0.378282\pi$
$659$	−8.10663	−	5.20981i	−0.315789	−	0.202945i	−0.688927	+	0.724830i	$0.741918\pi$
$660$	15.1327	+	7.55723i	0.589041	+	0.294165i
$661$	−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	$0.733739\pi$
$662$	15.5373	−	0.840097i	0.603876	−	0.0326513i
$663$	−9.42309	−	65.5390i	−0.365963	−	2.54533i
$664$	−4.49480	−	2.76784i	−0.174432	−	0.107413i
$665$	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
$670$	−0.0249021	−	0.124886i	−0.000962050	−	0.00482478i
$671$	−15.3094	+	2.20115i	−0.591011	+	0.0849746i
$672$	−3.69415	−	28.8657i	−0.142505	−	1.11352i
$673$	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	$-0.0938000\pi$
$674$	−2.23916	+	25.1543i	−0.0862490	+	0.968908i
$675$	0.370484	−	0.576484i	0.0142599	−	0.0221889i
$676$	36.5427	−	15.1765i	1.40549	−	0.583711i
$677$	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	$-0.0893559\pi$
$678$	−10.0518	−	28.4507i	−0.386037	−	1.09264i
$679$	9.49046	−	8.22353i	0.364211	−	0.315590i
$680$	5.32458	+	32.5693i	0.204188	+	1.24898i
$681$	47.2184	+	21.5639i	1.80941	+	0.826331i
$682$	−13.9763	+	10.0883i	−0.535180	+	0.386300i
$683$	0.465604	+	1.58570i	0.0178159	+	0.0606752i	0.967921	−	0.251254i	$-0.0808430\pi$
$683$	0.465604	+	1.58570i	0.0178159	+	0.0606752i	−0.950105	+	0.311929i	$0.899025\pi$
$684$	20.5892	−	16.6236i	0.787249	−	0.635619i
$685$	−12.4767	−	27.3201i	−0.476710	−	1.04385i
$686$	−6.54345	+	27.7485i	−0.249830	+	1.05944i
$687$	−7.59590	+	4.88159i	−0.289802	+	0.186244i
$688$	29.7855	+	22.2104i	1.13556	+	0.846765i
$689$		−	2.21211i		−	0.0842749i
$690$	36.6649	+	10.1546i	1.39581	+	0.386580i
$691$			45.1426i			1.71730i	0.512559	+	0.858652i	$0.328697\pi$
$691$			45.1426i			1.71730i	−0.512559	+	0.858652i	$0.671303\pi$
$692$	9.59140	−	1.04025i	0.364610	−	0.0395442i
$693$	7.08305	−	4.55200i	0.269063	−	0.172916i
$694$	−16.7314	−	3.94549i	−0.635117	−	0.149769i
$695$	−4.54769	−	9.95806i	−0.172504	−	0.377731i
$696$	1.45122	+	4.61205i	0.0550084	+	0.174819i
$697$	−2.10063	−	7.15410i	−0.0795671	−	0.270981i
$698$	10.2966	+	14.2649i	0.389733	+	0.539936i
$699$	−29.0449	−	13.2644i	−1.09858	−	0.501704i
$700$	1.47148	+	2.47477i	0.0556166	+	0.0935376i
$701$	−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	$0.545353\pi$
$702$	7.92944	−	2.80151i	0.299277	−	0.105736i
$703$	8.71222	−	29.6711i	0.328588	−	1.11907i
$704$	−5.42921	−	10.7707i	−0.204621	−	0.405935i
$705$	2.39561	−	3.72764i	0.0902237	−	0.140391i
$706$	44.3014	+	3.94357i	1.66731	+	0.148418i
$707$	2.33743	−	16.2571i	0.0879079	−	0.611413i
$708$	−8.77099	+	26.4350i	−0.329634	+	0.993488i
$709$	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	$0.197179\pi$
$710$	28.8156	−	5.74577i	1.08143	−	0.215635i
$711$	−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
$716$	−2.83924	+	15.8214i	−0.106107	+	0.591274i
$717$	1.99063	+	13.8452i	0.0743416	+	0.517057i
$718$	0.254045	+	4.69849i	0.00948088	+	0.175346i
$719$	−8.62123	−	1.23955i	−0.321518	−	0.0462272i	−0.0203334	−	0.999793i	$-0.506473\pi$
$719$	−8.62123	−	1.23955i	−0.321518	−	0.0462272i	−0.301184	+	0.953566i	$0.597382\pi$
$720$	22.8052	−	8.55447i	0.849900	−	0.318806i
$721$	−23.0198	−	14.7939i	−0.857303	−	0.550955i
$722$	7.85571	−	7.58724i	0.292359	−	0.282368i
$723$	49.2831	+	14.4708i	1.83286	+	0.538176i
$724$	−30.2088	−	1.05066i	−1.12270	−	0.0390474i
$725$	−0.313259	−	0.361521i	−0.0116342	−	0.0134265i
$726$	−17.8411	+	22.9889i	−0.662147	+	0.853200i
$727$	−1.54895	+	3.39174i	−0.0574475	+	0.125792i	−0.936179	−	0.351525i	$-0.885663\pi$
$727$	−1.54895	+	3.39174i	−0.0574475	+	0.125792i	0.878731	+	0.477317i	$0.158391\pi$
$728$	−4.35439	+	35.0648i	−0.161384	+	1.29959i
$729$	−17.8225	+	5.23317i	−0.660094	+	0.193821i
$730$	34.4144	+	19.5758i	1.27373	+	0.724532i
$731$	−41.4392	+	18.9246i	−1.53268	+	0.699953i
$732$	−27.5529	+	39.7630i	−1.01839	+	1.46968i
$733$	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	$0.557755\pi$
$734$	−13.6931	+	7.17088i	−0.505422	+	0.264682i
$735$	−12.5636			−0.463416
$736$	−16.6309	−	21.4339i	−0.613023	−	0.790065i
$737$	−0.0570666			−0.00210207
$738$	−4.87496	+	2.55295i	−0.179450	+	0.0939752i
$739$	−14.2752	−	22.2127i	−0.525124	−	0.817108i	0.472823	−	0.881157i	$-0.343235\pi$
$739$	−14.2752	−	22.2127i	−0.525124	−	0.817108i	−0.997947	+	0.0640491i	$0.979599\pi$
$740$	16.2113	−	23.3954i	0.595941	−	0.860032i
$741$	−63.4831	+	28.9918i	−2.33211	+	1.06504i
$742$	1.03617	+	0.589402i	0.0380391	+	0.0216376i
$743$	−28.6055	+	8.39932i	−1.04943	+	0.308141i	−0.760588	−	0.649235i	$-0.775089\pi$
$743$	−28.6055	+	8.39932i	−1.04943	+	0.308141i	−0.288845	+	0.957376i	$0.593271\pi$
$744$	−6.64389	+	53.5017i	−0.243577	+	1.96147i
$745$	−5.48510	+	12.0107i	−0.200959	+	0.440038i
$746$	14.0093	−	18.0514i	0.512915	−	0.660910i
$747$	−3.12815	−	3.61008i	−0.114453	−	0.132086i
$748$	14.7800	+	0.514046i	0.540411	+	0.0187954i
$749$	−11.0223	−	3.23645i	−0.402748	−	0.118257i
$750$	24.7655	−	23.9192i	0.904309	−	0.873405i
$751$	−0.968913	−	0.622683i	−0.0353561	−	0.0227220i	0.522843	−	0.852429i	$-0.324871\pi$
$751$	−0.968913	−	0.622683i	−0.0353561	−	0.0227220i	−0.558200	+	0.829707i	$0.688508\pi$
$752$	−2.95841	+	1.10973i	−0.107882	+	0.0404678i
$753$	−42.3912	−	6.09494i	−1.54482	−	0.222112i
$754$	−0.316956	−	5.86200i	−0.0115428	−	0.213481i
$755$	−1.50641	−	10.4773i	−0.0548237	−	0.381308i
$756$	−0.800490	+	4.46066i	−0.0291135	+	0.162233i
$757$	−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	$0.152986\pi$
$762$	−2.27199	+	0.453031i	−0.0823057	+	0.0164116i
$763$	10.1580	−	1.46050i	0.367744	−	0.0528736i
$764$	9.49093	−	28.6048i	0.343370	−	1.03489i
$765$	−4.25013	+	29.5603i	−0.153664	+	1.06875i
$766$	−21.6440	−	1.92668i	−0.782031	−	0.0696138i
$767$	18.2832	−	28.4492i	0.660167	−	1.02724i
$768$	−36.2371	−	10.4933i	−1.30760	−	0.378643i
$769$	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	$-0.0443792\pi$
$770$	10.4354	−	3.68686i	0.376064	−	0.132865i
$771$	24.8651	−	21.5458i	0.895496	−	0.775952i
$772$	−3.77026	−	6.34092i	−0.135694	−	0.228215i
$773$	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	$0.563016\pi$
$774$	19.6783	+	27.2624i	0.707322	+	0.979926i
$775$	−1.50275	−	5.11791i	−0.0539805	−	0.183841i
$776$	−4.88627	−	15.5288i	−0.175407	−	0.557451i
$777$	−12.7841	−	27.9932i	−0.458626	−	1.00425i
$778$	−12.0519	−	2.84199i	−0.432080	−	0.101890i
$779$	−6.61134	+	4.24885i	−0.236876	+	0.152231i
$780$	−63.8623	+	6.92626i	−2.28664	+	0.248000i
$781$		−	13.1672i		−	0.471161i
$782$	32.8481	−	5.24083i	1.17465	−	0.187412i
$783$		−	0.752951i		−	0.0269083i
$784$	7.18198	+	5.35546i	0.256499	+	0.191266i
$785$	−3.40370	+	2.18742i	−0.121483	+	0.0780725i
$786$	13.2207	−	56.0643i	0.471566	−	1.99975i
$787$	9.86579	+	21.6031i	0.351677	+	0.770066i	0.999962	+	0.00866835i	$0.00275926\pi$
$787$	9.86579	+	21.6031i	0.351677	+	0.770066i	−0.648285	+	0.761398i	$0.724513\pi$
$788$	−20.2405	+	16.3421i	−0.721040	+	0.582162i
$789$	−9.23717	−	31.4589i	−0.328852	−	1.11997i
$790$	−30.1429	+	21.7575i	−1.07244	+	0.774099i
$791$	−17.9591	−	8.20163i	−0.638551	−	0.291616i
$792$	−1.76105	−	10.7720i	−0.0625761	−	0.382765i
$793$	44.3910	−	38.4650i	1.57637	−	1.36593i
$794$	−18.1087	−	51.2552i	−0.642655	−	1.81898i
$795$	−0.610564	+	2.07939i	−0.0216545	+	0.0737484i
$796$	−5.25380	+	2.18195i	−0.186216	+	0.0773371i
$797$	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	$0.122725\pi$
$798$	3.33463	−	37.4607i	0.118045	−	1.32609i
$799$	0.551349	−	3.83472i	0.0195053	−	0.135663i
$800$	3.70230	−	0.473809i	0.130896	−	0.0167517i
$801$	−20.6405	+	2.96765i	−0.729296	+	0.104857i
$802$	6.53556	+	32.7765i	0.230779	+	1.15738i
$803$	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
$808$	−18.1302	−	11.1644i	−0.637820	−	0.392762i
$809$	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	$0.835192\pi$
$810$	−34.0236	+	1.83964i	−1.19547	+	0.0646384i
$811$	47.1165	+	6.77433i	1.65449	+	0.237879i	0.905389	−	0.424583i	$-0.139579\pi$
$811$	47.1165	+	6.77433i	1.65449	+	0.237879i	0.749096	+	0.662462i	$0.230488\pi$
$812$	2.83026	+	1.41342i	0.0993227	+	0.0496014i
$813$	−1.39072	−	0.893764i	−0.0487748	−	0.0313457i
$814$	−8.86109	−	9.17463i	−0.310581	−	0.321571i
$815$	−40.3218	−	11.8395i	−1.41241	−	0.414721i
$816$	32.6469	−	32.7691i	1.14287	−	1.14715i
$817$	31.4444	+	36.2888i	1.10010	+	1.26958i
$818$	−38.6171	−	29.9697i	−1.35021	−	1.04787i
$819$	−13.2829	+	29.0854i	−0.464141	+	1.01633i
$820$	−7.00722	+	1.79546i	−0.244703	+	0.0627002i
$821$	−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	$0.705647\pi$
$822$	−20.8141	+	36.5913i	−0.725974	+	1.27627i
$823$	29.6714	−	13.5505i	1.03428	−	0.472339i	0.175389	−	0.984499i	$-0.443882\pi$
$823$	29.6714	−	13.5505i	1.03428	−	0.472339i	0.858890	+	0.512160i	$0.171154\pi$
$824$	−29.4675	+	19.7493i	−1.02655	+	0.688000i
$825$	1.26815	+	1.97327i	0.0441512	+	0.0687006i
$826$	8.45442	+	16.1441i	0.294167	+	0.561724i
$827$	−17.7933			−0.618733			−0.309366	−	0.950943i	$-0.600117\pi$
$827$	−17.7933			−0.618733			−0.309366	+	0.950943i	$0.600117\pi$
$828$	−8.53409	−	23.0191i	−0.296580	−	0.799969i
$829$	−15.0534			−0.522827			−0.261413	−	0.965227i	$-0.584189\pi$
$829$	−15.0534			−0.522827			−0.261413	+	0.965227i	$0.584189\pi$
$830$	−2.91299	−	5.56247i	−0.101111	−	0.193076i
$831$	−23.8320	−	37.0833i	−0.826724	−	1.28641i
$832$	39.4593	+	23.2630i	1.36800	+	0.806500i
$833$	−9.99195	+	4.56317i	−0.346201	+	0.158105i
$834$	−7.58663	+	13.3373i	−0.262703	+	0.461835i
$835$	10.8786	−	3.19425i	0.376470	−	0.110542i
$836$	−3.86909	−	15.1001i	−0.133815	−	0.522247i
$837$	3.48774	−	7.63709i	0.120554	−	0.263977i
$838$	40.7090	+	31.5933i	1.40627	+	1.09137i
$839$	−7.76009	−	8.95563i	−0.267908	−	0.309183i	0.605815	−	0.795605i	$-0.292847\pi$
$839$	−7.76009	−	8.95563i	−0.267908	−	0.309183i	−0.873724	+	0.486423i	$0.838302\pi$
$840$	13.7713	−	31.7591i	0.475156	−	1.09579i
$841$	27.3210	+	8.02216i	0.942103	+	0.276626i
$842$	−20.7452	−	21.4793i	−0.714927	−	0.740224i
$843$	46.6514	+	29.9810i	1.60676	+	1.03260i
$844$	9.59399	−	19.2112i	0.330239	−	0.661276i
$845$	46.5888	+	6.69846i	1.60270	+	0.230434i
$846$	−2.85514	+	0.154376i	−0.0981617	+	0.00530756i
$847$	2.70971	+	18.8464i	0.0931066	+	0.647571i
$848$	1.23540	−	0.928418i	0.0424239	−	0.0318820i
$849$	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	$-0.0176689\pi$
$854$	6.18968	+	31.0418i	0.211807	+	1.06223i
$855$	31.1572	−	4.47972i	1.06555	−	0.153203i
$856$	−9.53390	+	11.4405i	−0.325862	+	0.391027i
$857$	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	$-0.215526\pi$
$858$	−2.55236	+	28.6729i	−0.0871363	+	0.978875i
$859$	3.71977	−	5.78808i	0.126917	−	0.197487i	−0.771980	−	0.635647i	$-0.780733\pi$
$859$	3.71977	−	5.78808i	0.126917	−	0.197487i	0.898897	+	0.438160i	$0.144370\pi$
$860$	16.9513	+	40.8163i	0.578036	+	1.39182i
$861$	−2.20341	+	7.50412i	−0.0750919	+	0.255740i
$862$	−4.06047	−	11.4928i	−0.138300	−	0.391447i
$863$	−27.9293	+	24.2008i	−0.950723	+	0.823806i	−0.984457	−	0.175625i	$-0.943805\pi$
$863$	−27.9293	+	24.2008i	−0.950723	+	0.823806i	0.0337342	+	0.999431i	$0.489260\pi$
$864$	4.89253	+	3.25258i	0.166447	+	0.110655i
$865$	10.4390	+	4.76733i	0.354936	+	0.162094i
$866$	4.68768	−	3.38362i	0.159294	−	0.114980i
$867$	4.68564	+	15.9578i	0.159133	+	0.541956i
$868$	22.1599	+	27.4462i	0.752156	+	0.931586i
$869$	6.92046	+	15.1537i	0.234761	+	0.514054i
$870$	−1.32003	+	5.59777i	−0.0447531	+	0.189782i
$871$	0.182316	−	0.117168i	0.00617755	−	0.00397007i
$872$	3.50173	−	12.8348i	0.118583	−	0.434641i
$873$		−	14.7317i		−	0.498593i
$874$	−15.0545	−	31.6639i	−0.509226	−	1.07105i
$875$		−	22.5281i		−	0.761590i
$876$	−5.98357	−	55.1704i	−0.202166	−	1.86403i
$877$	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	$0.197600\pi$
$878$	−16.4090	−	3.86945i	−0.553775	−	0.130588i
$879$	11.5222	+	25.2301i	0.388635	+	0.850991i
$880$	0.996805	−	14.3129i	0.0336023	−	0.482488i
$881$	−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	$-0.224893\pi$
$882$	4.74490	+	6.57360i	0.159769	+	0.221345i
$883$	24.5116	+	11.1941i	0.824881	+	0.376711i	0.782700	−	0.622399i	$-0.213842\pi$
$883$	24.5116	+	11.1941i	0.824881	+	0.376711i	0.0421813	+	0.999110i	$0.486569\pi$
$884$	−48.2746	+	28.7037i	−1.62365	+	0.965409i
$885$	−25.0384	+	21.6959i	−0.841657	+	0.729300i
$886$	30.2195	−	10.6767i	1.01524	−	0.358691i
$887$	12.8650	−	43.8143i	0.431965	−	1.47114i	−0.400105	−	0.916469i	$-0.631026\pi$
$887$	12.8650	−	43.8143i	0.431965	−	1.47114i	0.832071	−	0.554670i	$-0.187155\pi$
$888$	−39.8874	+	0.767974i	−1.33853	+	0.0257715i
$889$	−0.819529	+	1.27521i	−0.0274861	+	0.0427693i
$890$	−27.3027	−	2.43040i	−0.915188	−	0.0814670i
$891$	−2.17303	+	15.1137i	−0.0727992	+	0.506329i
$892$	6.67323	+	2.21414i	0.223436	+	0.0741350i
$893$	−4.04187	+	0.581134i	−0.135256	+	0.0194469i
$894$	18.1497	−	3.61901i	0.607016	−	0.121038i
$895$	−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
$900$	3.32454	+	0.596607i	0.110818	+	0.0198869i
$901$	0.269659	+	1.87552i	0.00898363	+	0.0624825i
$902$	0.175014	+	3.23684i	0.00582734	+	0.107775i
$903$	47.2985	+	6.80049i	1.57399	+	0.226306i
$904$	−19.0168	+	17.1301i	−0.632490	+	0.569738i
$905$	−30.2479	−	19.4391i	−1.00547	−	0.646178i
$906$	−10.6716	+	10.3069i	−0.354540	+	0.342424i
$907$	−37.3788	−	10.9754i	−1.24114	−	0.364433i	−0.405699	−	0.914007i	$-0.632972\pi$
$907$	−37.3788	−	10.9754i	−1.24114	−	0.364433i	−0.835445	+	0.549574i	$0.814790\pi$
$908$	1.53046	−	44.0042i	0.0507899	−	1.46033i
$909$	−12.6177	−	14.5616i	−0.418503	−	0.482978i
$910$	−25.7691	+	33.2044i	−0.854237	+	1.10071i
$911$	−7.07107	+	15.4835i	−0.234275	+	0.512990i	−0.989858	−	0.142063i	$-0.954627\pi$
$911$	−7.07107	+	15.4835i	−0.234275	+	0.512990i	0.755583	+	0.655053i	$0.227354\pi$
$912$	−42.8348	−	23.2858i	−1.41840	−	0.771069i
$913$	−2.69983	+	0.792743i	−0.0893515	+	0.0262360i
$914$	6.52640	+	3.71238i	0.215874	+	0.122795i
$915$	−52.3442	+	23.9048i	−1.73045	+	0.790269i
$916$	6.29522	+	4.36214i	0.208000	+	0.144129i
$917$	−20.3764	−	31.7064i	−0.672890	−	1.04704i
$918$	−6.38138	+	3.34183i	−0.210617	+	0.110297i
$919$	−23.4063			−0.772104			−0.386052	−	0.922477i	$-0.626162\pi$
$919$	−23.4063			−0.772104			−0.386052	+	0.922477i	$0.626162\pi$
$920$	−3.97366	−	32.0253i	−0.131008	−	1.05584i
$921$	34.4011			1.13355
$922$	−26.4869	+	13.8708i	−0.872300	+	0.456811i
$923$	27.0346	+	42.0667i	0.889855	+	1.38464i
$924$	−12.7506	−	8.83523i	−0.419463	−	0.290658i
$925$	3.59039	−	1.63968i	0.118051	−	0.0539123i
$926$	24.7576	+	14.0828i	0.813585	+	0.462788i
$927$	−30.8007	+	9.04391i	−1.01163	+	0.297041i
$928$	3.14074	−	2.63727i	0.103100	−	0.0865728i
$929$	−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	$0.983927\pi$
$930$	−39.3183	+	50.6630i	−1.28930	+	1.66130i
$931$	7.58199	+	8.75008i	0.248490	+	0.286772i
$932$	−0.941412	+	27.0678i	−0.0308370	+	0.886635i
$933$	46.9139	+	13.7752i	1.53589	+	0.450979i
$934$	−17.5906	+	16.9894i	−0.575581	+	0.555910i
$935$	14.7991	+	9.51081i	0.483983	+	0.311037i
$936$	27.7429	+	30.7985i	0.906805	+	1.00668i
$937$	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	$0.530849\pi$
$938$	0.00630543	+	0.116617i	0.000205880	+	0.00380768i
$939$	−0.653734	−	4.54682i	−0.0213338	−	0.148380i
$940$	−3.69943	−	0.663883i	−0.120662	−	0.0216535i
$941$	−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
$946$	19.4232	−	3.87295i	0.631502	−	0.125920i
$947$	9.33745	−	1.34252i	0.303426	−	0.0436261i	0.0110800	−	0.999939i	$-0.496473\pi$
$947$	9.33745	−	1.34252i	0.303426	−	0.0436261i	0.292346	+	0.956312i	$0.405564\pi$
$948$	49.4545	+	16.4087i	1.60621	+	0.532931i
$949$	−9.58915	+	66.6940i	−0.311277	+	2.16498i
$950$	4.80469	+	0.427698i	0.155885	+	0.0138763i
$951$	−2.10126	+	3.26962i	−0.0681379	+	0.106025i
$952$	−0.582615	−	30.2601i	−0.0188827	−	0.980737i
$953$	−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	$0.124162\pi$
$954$	1.31858	−	0.465861i	0.0426906	−	0.0150828i
$955$	27.0936	−	23.4768i	0.876729	−	0.759690i
$956$	10.1980	−	6.06367i	0.329828	−	0.196113i
$957$	2.34440	+	1.07065i	0.0757838	+	0.0346093i
$958$	−30.3677	−	42.0714i	−0.981135	−	1.35927i
$959$	7.76013	+	26.4286i	0.250588	+	0.853423i
$960$	−30.6710	−	32.7584i	−0.989901	−	1.05727i
$961$	−14.2700	−	31.2469i	−0.460321	−	1.00796i
$962$	47.1465	+	11.1178i	1.52006	+	0.358451i
$963$	−11.3371	+	7.28593i	−0.365334	+	0.234786i
$964$	−4.69766	−	43.3139i	−0.151302	−	1.39505i
$965$		−	8.77524i		−	0.282485i
$966$	−31.9577	−	14.0034i	−1.02822	−	0.450550i
$967$			12.8467i			0.413123i	0.978434	+	0.206562i	$0.0662274\pi$
$967$			12.8467i			0.413123i	−0.978434	+	0.206562i	$0.933773\pi$
$968$	23.8128	+	6.49686i	0.765372	+	0.208817i
$969$	50.2893	−	32.3190i	1.61553	−	1.03824i
$970$	4.44454	−	18.8477i	0.142705	−	0.605163i
$971$	19.5925	+	42.9017i	0.628754	+	1.37678i	0.908977	+	0.416845i	$0.136864\pi$
$971$	19.5925	+	42.9017i	0.628754	+	1.37678i	−0.280223	+	0.959935i	$0.590408\pi$
$972$	26.0869	+	32.3100i	0.836737	+	1.03634i
$973$	2.82853	+	9.63309i	0.0906785	+	0.308823i
$974$	30.6685	−	22.1369i	0.982681	−	0.709311i
$975$	−8.10295	−	3.70049i	−0.259502	−	0.118511i
$976$	40.1124	+	8.64746i	1.28397	+	0.276798i
$977$	−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	$0.533359\pi$
$978$	19.6218	+	55.5378i	0.627435	+	1.77590i
$979$	−3.46065	+	11.7859i	−0.110603	+	0.376678i
$980$	4.08737	+	9.84176i	0.130566	+	0.314383i
$981$	6.50884	−	10.1279i	0.207811	−	0.323361i
$982$	−0.938057	+	10.5380i	−0.0299346	+	0.336281i
$983$	1.30074	−	9.04686i	0.0414872	−	0.288550i	−0.958507	−	0.285070i	$-0.907983\pi$
$983$	1.30074	−	9.04686i	0.0414872	−	0.288550i	0.999994	−	0.00348003i	$-0.00110773\pi$
$984$	7.78879	+	6.49077i	0.248297	+	0.206918i
$985$	−30.6295	+	4.40386i	−0.975937	+	0.140319i
$986$	0.983310	+	4.93139i	0.0313150	+	0.157048i
$987$	−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	0.426025	−	0.904711i	$-0.359914\pi$
$991$	−12.8706	−	11.1524i	−0.408848	−	0.354269i	−0.834873	+	0.550442i	$0.814459\pi$
$992$	44.0722	−	12.2014i	1.39929	−	0.387394i
$993$	−3.69203	−	25.6786i	−0.117163	−	0.814886i
$994$	−26.9076	+	1.45488i	−0.853457	+	0.0461460i
$995$	−6.69815	−	0.963048i	−0.212346	−	0.0305307i
$996$	−3.93208	+	7.87367i	−0.124593	+	0.249487i
$997$	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	$0.598246\pi$
$998$	−11.0156	−	11.4054i	−0.348694	−	0.361032i
$999$	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.7.3	✓	100
3.2	odd	2		828.2.u.a.559.8		100
4.3	odd	2	inner	92.2.h.a.7.4	yes	100
12.11	even	2		828.2.u.a.559.7		100
23.10	odd	22	inner	92.2.h.a.79.4	yes	100
69.56	even	22		828.2.u.a.631.7		100
92.79	even	22	inner	92.2.h.a.79.3	yes	100
276.263	odd	22		828.2.u.a.631.8		100

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

\(f(q)\)	\(=\)	\(q+(-1.25282 + 0.656083i) q^{2} +(1.27476 + 1.98356i) q^{3} +(1.13911 - 1.64391i) q^{4} +(2.16405 - 0.988288i) q^{5} +(-2.89842 - 1.64870i) q^{6} +(-2.09343 + 0.614686i) q^{7} +(-0.348560 + 2.80687i) q^{8} +(-1.06327 + 2.32823i) q^{9} +O(q^{10})\)	\(q+(-1.25282 + 0.656083i) q^{2} +(1.27476 + 1.98356i) q^{3} +(1.13911 - 1.64391i) q^{4} +(2.16405 - 0.988288i) q^{5} +(-2.89842 - 1.64870i) q^{6} +(-2.09343 + 0.614686i) q^{7} +(-0.348560 + 2.80687i) q^{8} +(-1.06327 + 2.32823i) q^{9} +(-2.06276 + 2.65794i) q^{10} +(0.987339 + 1.13945i) q^{11} +(4.71288 + 0.163913i) q^{12} +(-5.49384 - 1.61314i) q^{13} +(2.21940 - 2.14355i) q^{14} +(4.71897 + 3.03270i) q^{15} +(-1.40486 - 3.74518i) q^{16} +(4.85453 + 0.697976i) q^{17} +(-0.195431 - 3.61444i) q^{18} +(-0.735682 - 5.11678i) q^{19} +(0.840437 - 4.68326i) 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} +(7.94113 - 1.58345i) q^{26} +(1.02800 - 0.147804i) q^{27} +(-1.37416 + 4.14159i) q^{28} +(0.103177 - 0.717609i) q^{29} +(-7.90172 - 0.703385i) q^{30} +(4.37054 - 6.80070i) q^{31} +(4.21718 + 3.77033i) q^{32} +(-1.00155 + 3.41097i) q^{33} +(-6.53978 + 2.31054i) q^{34} +(-3.92279 + 3.39912i) q^{35} +(2.61621 + 4.40002i) q^{36} +(5.44149 + 2.48504i) q^{37} +(4.27871 + 5.92773i) q^{38} +(-3.80356 - 12.9537i) q^{39} +(2.01969 + 6.41867i) q^{40} +(-0.631546 - 1.38289i) q^{41} +(7.08107 + 1.66981i) q^{42} +(-7.81415 + 5.02185i) q^{43} +(2.99784 - 0.325134i) q^{44} +6.08922i q^{45} +(6.47737 - 2.01088i) q^{46} -0.789926i q^{47} +(5.63795 - 7.56082i) q^{48} +(-1.88418 + 1.21089i) q^{49} +(-0.214169 + 0.908214i) q^{50} +(4.80387 + 10.5190i) q^{51} +(-8.90993 + 7.19381i) q^{52} +(0.108846 + 0.370694i) q^{53} +(-1.19092 + 0.859624i) q^{54} +(3.26275 + 1.49005i) q^{55} +(-0.995657 - 6.09023i) q^{56} +(9.21163 - 7.98192i) q^{57} +(0.341549 + 0.966726i) q^{58} +(-1.66397 + 5.66697i) q^{59} +(10.3609 - 4.30297i) q^{60} +(-5.54615 + 8.62998i) q^{61} +(-1.01368 + 11.3875i) q^{62} +(0.794742 - 5.52756i) q^{63} +(-7.75701 - 1.95672i) q^{64} +(-13.4832 + 1.93859i) q^{65} +(-0.983117 - 4.93043i) 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} +(-6.16442 - 3.79598i) q^{72} +(-1.67474 - 11.6480i) q^{73} +(-8.44760 + 0.456758i) q^{74} +(1.53993 + 0.221408i) q^{75} +(-9.24953 - 4.61918i) q^{76} +(-2.76732 - 1.77845i) q^{77} +(13.2639 + 13.7332i) q^{78} +(10.6017 + 3.11295i) q^{79} +(-6.74149 - 6.71635i) q^{80} +(6.63203 + 7.65378i) q^{81} +(1.69850 + 1.31817i) q^{82} +(-0.775283 + 1.69763i) q^{83} +(-9.96683 + 2.55380i) q^{84} +(11.1952 - 3.28722i) q^{85} +(6.49497 - 11.4182i) q^{86} +(1.55495 - 0.710120i) q^{87} +(-3.54243 + 2.37416i) q^{88} +(4.40465 + 6.85377i) q^{89} +(-3.99503 - 7.62868i) q^{90} +12.4925 q^{91} +(-6.79567 + 6.76896i) q^{92} +19.0610 q^{93} +(0.518257 + 0.989634i) q^{94} +(-6.64890 - 10.3459i) q^{95} +(-2.10280 + 13.1713i) q^{96} +(-5.23551 + 2.39098i) q^{97} +(1.56609 - 2.75320i) 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