LMFDB - Embedded newform 920.2.bb.a.11.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(11,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 0, 9]))

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

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

chi := DirichletCharacter("920.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bb (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:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			11.14
Character	$\chi$	$=$	920.11
Dual form			920.2.bb.a.251.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.885153 - 1.10295i) q^{2} +(0.428448 - 2.97992i) q^{3} +(-0.433008 + 1.95256i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-3.66596 + 2.16513i) q^{6} +(2.08164 + 2.40234i) q^{7} +(2.53686 - 1.25073i) q^{8} +(-5.81789 - 1.70829i) q^{9} +(1.16004 + 0.808899i) q^{10} +(1.93917 - 3.01740i) q^{11} +(5.63297 + 2.12690i) q^{12} +(-3.34924 - 2.90214i) q^{13} +(0.807099 - 4.42239i) q^{14} +(0.428448 + 2.97992i) q^{15} +(-3.62501 - 1.69095i) q^{16} +(-6.03608 + 2.75658i) q^{17} +(3.26557 + 7.92895i) q^{18} +(-5.19606 - 2.37296i) q^{19} +(-0.134632 - 1.99546i) q^{20} +(8.05067 - 5.17385i) q^{21} +(-5.04451 + 0.532054i) q^{22} +(1.24098 + 4.63249i) q^{23} +(-2.64016 - 8.09553i) q^{24} +(0.841254 - 0.540641i) q^{25} +(-0.236325 + 6.26289i) q^{26} +(-3.83133 + 8.38944i) q^{27} +(-5.59210 + 3.02430i) q^{28} +(-2.39375 + 1.09319i) q^{29} +(2.90747 - 3.11025i) q^{30} +(1.22038 - 0.175464i) q^{31} +(1.34365 + 5.49496i) q^{32} +(-8.16080 - 7.07137i) q^{33} +(8.38324 + 4.21751i) q^{34} +(-2.67414 - 1.71857i) q^{35} +(5.85474 - 10.6201i) q^{36} +(-9.76872 - 2.86836i) q^{37} +(1.98205 + 7.83145i) q^{38} +(-10.0831 + 8.73707i) q^{39} +(-2.08173 + 1.91478i) q^{40} +(-0.570236 + 0.167436i) q^{41} +(-12.8326 - 4.29986i) q^{42} +(-9.49229 - 1.36479i) q^{43} +(5.05200 + 5.09291i) q^{44} +6.06351 q^{45} +(4.01096 - 5.46921i) q^{46} -2.34790i q^{47} +(-6.59204 + 10.0778i) q^{48} +(-0.441815 + 3.07289i) q^{49} +(-1.34094 - 0.449313i) q^{50} +(5.62826 + 19.1681i) q^{51} +(7.11685 - 5.28296i) q^{52} +(8.73607 + 10.0820i) q^{53} +(12.6445 - 3.20016i) q^{54} +(-1.01052 + 3.44150i) q^{55} +(8.28552 + 3.49084i) q^{56} +(-9.29749 + 14.4672i) q^{57} +(3.32457 + 1.67255i) q^{58} +(6.70259 - 7.73520i) q^{59} +(-6.00401 - 0.453759i) q^{60} +(-0.650622 - 4.52517i) q^{61} +(-1.27375 - 1.19071i) q^{62} +(-8.00688 - 17.5326i) q^{63} +(4.87135 - 6.34586i) q^{64} +(4.03120 + 1.84099i) q^{65} +(-0.575832 + 15.2602i) q^{66} +(-2.48603 - 3.86834i) q^{67} +(-2.76873 - 12.9795i) q^{68} +(14.3362 - 1.71325i) q^{69} +(0.471527 + 4.47064i) q^{70} +(-5.52515 - 8.59730i) q^{71} +(-16.8958 + 2.94292i) q^{72} +(6.95418 - 15.2275i) q^{73} +(5.48315 + 13.3134i) q^{74} +(-1.25063 - 2.73851i) q^{75} +(6.88330 - 9.11813i) q^{76} +(11.2855 - 1.62261i) q^{77} +(18.5617 + 3.38755i) q^{78} +(-5.58490 + 6.44532i) q^{79} +(3.95457 + 0.601175i) q^{80} +(8.05551 + 5.17696i) q^{81} +(0.689421 + 0.480737i) q^{82} +(-3.30843 + 11.2675i) q^{83} +(6.61627 + 17.9598i) q^{84} +(5.01496 - 4.34548i) q^{85} +(6.89684 + 11.6776i) q^{86} +(2.23202 + 7.60156i) q^{87} +(1.14545 - 10.0801i) q^{88} +(15.6366 + 2.24820i) q^{89} +(-5.36713 - 6.68776i) q^{90} -14.0872i q^{91} +(-9.58259 + 0.417190i) q^{92} -3.71182i q^{93} +(-2.58962 + 2.07825i) q^{94} +(5.65413 + 0.812941i) q^{95} +(16.9502 - 1.64965i) q^{96} +(1.23966 + 4.22190i) q^{97} +(3.78032 - 2.23268i) q^{98} +(-16.4365 + 14.2423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 2 q^{2} - 4 q^{4} - 48 q^{5} + 5 q^{6} - q^{8} - 48 q^{9} + 2 q^{10} + 3 q^{12} + 32 q^{16} + 7 q^{18} - 4 q^{20} + 8 q^{21} + 4 q^{23} + 2 q^{24} - 48 q^{25} + 7 q^{26} + 12 q^{27} + 5 q^{30}+ \cdots - 98 q^{98}+O(q^{100}) $ 480 * q + 2 * q^2 - 4 * q^4 - 48 * q^5 + 5 * q^6 - q^8 - 48 * q^9 + 2 * q^10 + 3 * q^12 + 32 * q^16 + 7 * q^18 - 4 * q^20 + 8 * q^21 + 4 * q^23 + 2 * q^24 - 48 * q^25 + 7 * q^26 + 12 * q^27 + 5 * q^30 - 118 * q^32 - 23 * q^34 + 54 * q^36 + 8 * q^37 - 65 * q^38 + 43 * q^40 - 10 * q^42 - q^44 + 480 * q^45 - 184 * q^46 - 44 * q^48 - 48 * q^49 - 9 * q^50 - 7 * q^52 + 32 * q^53 - 27 * q^54 + 67 * q^56 - 40 * q^58 - 12 * q^59 + 14 * q^60 - 8 * q^61 - 128 * q^62 + 59 * q^64 + 88 * q^66 + 10 * q^68 - 20 * q^69 + 3 * q^72 - 11 * q^74 + 110 * q^76 + 118 * q^78 - 144 * q^79 - q^80 - 56 * q^81 - 59 * q^82 - 162 * q^84 - 18 * q^86 - 76 * q^88 + 7 * q^90 - 149 * q^92 + 168 * q^94 + 65 * q^96 - 98 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$-1$	$e\left(\frac{9}{22}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.885153	−	1.10295i	−0.625898	−	0.779905i
$2$	−0.885153	−	1.10295i	−0.625898	−	0.779905i
$3$	0.428448	−	2.97992i	0.247365	−	1.72046i	−0.365962	−	0.930630i	$-0.619260\pi$
$3$	0.428448	−	2.97992i	0.247365	−	1.72046i	0.613327	−	0.789829i	$-0.289831\pi$
$4$	−0.433008	+	1.95256i	−0.216504	+	0.976282i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$6$	−3.66596	+	2.16513i	−1.49662	+	0.883910i
$7$	2.08164	+	2.40234i	0.786787	+	0.908000i	0.997580	−	0.0695303i	$-0.0221501\pi$
$7$	2.08164	+	2.40234i	0.786787	+	0.908000i	−0.210793	+	0.977531i	$0.567605\pi$
$8$	2.53686	−	1.25073i	0.896917	−	0.442200i
$9$	−5.81789	−	1.70829i	−1.93930	−	0.569429i
$10$	1.16004	+	0.808899i	0.366835	+	0.255796i
$11$	1.93917	−	3.01740i	0.584681	−	0.909781i	−0.415319	−	0.909676i	$-0.636330\pi$
$11$	1.93917	−	3.01740i	0.584681	−	0.909781i	1.00000		0.000105468i	$-3.35717e-5\pi$
$12$	5.63297	+	2.12690i	1.62610	+	0.613984i
$13$	−3.34924	−	2.90214i	−0.928913	−	0.804908i	0.0521416	−	0.998640i	$-0.483395\pi$
$13$	−3.34924	−	2.90214i	−0.928913	−	0.804908i	−0.981054	+	0.193732i	$0.937941\pi$
$14$	0.807099	−	4.42239i	0.215706	−	1.18193i
$15$	0.428448	+	2.97992i	0.110625	+	0.769413i
$16$	−3.62501	−	1.69095i	−0.906252	−	0.422738i
$17$	−6.03608	+	2.75658i	−1.46396	+	0.668570i	−0.978606	−	0.205745i	$-0.934038\pi$
$17$	−6.03608	+	2.75658i	−1.46396	+	0.668570i	−0.485359	+	0.874315i	$0.661311\pi$
$18$	3.26557	+	7.92895i	0.769701	+	1.86887i
$19$	−5.19606	−	2.37296i	−1.19206	−	0.544395i	−0.282217	−	0.959351i	$-0.591070\pi$
$19$	−5.19606	−	2.37296i	−1.19206	−	0.544395i	−0.909842	+	0.414955i	$0.863797\pi$
$20$	−0.134632	−	1.99546i	−0.0301047	−	0.446199i
$21$	8.05067	−	5.17385i	1.75680	−	1.12903i
$22$	−5.04451	+	0.532054i	−1.07549	+	0.113434i
$23$	1.24098	+	4.63249i	0.258763	+	0.965941i
$23$	1.24098	+	4.63249i	0.258763	+	0.965941i
$24$	−2.64016	−	8.09553i	−0.538921	−	1.65249i
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	−0.236325	+	6.26289i	−0.0463472	+	1.22825i
$27$	−3.83133	+	8.38944i	−0.737339	+	1.61455i
$28$	−5.59210	+	3.02430i	−1.05681	+	0.571540i
$29$	−2.39375	+	1.09319i	−0.444508	+	0.203000i	−0.625078	−	0.780562i	$-0.714933\pi$
$29$	−2.39375	+	1.09319i	−0.444508	+	0.203000i	0.180570	+	0.983562i	$0.442206\pi$
$30$	2.90747	−	3.11025i	0.530829	−	0.567851i
$31$	1.22038	−	0.175464i	0.219187	−	0.0315143i	−0.0318463	−	0.999493i	$-0.510139\pi$
$31$	1.22038	−	0.175464i	0.219187	−	0.0315143i	0.251033	+	0.967978i	$0.419230\pi$
$32$	1.34365	+	5.49496i	0.237525	+	0.971381i
$33$	−8.16080	−	7.07137i	−1.42061	−	1.23097i
$34$	8.38324	+	4.21751i	1.43771	+	0.723297i
$35$	−2.67414	−	1.71857i	−0.452012	−	0.290491i
$36$	5.85474	−	10.6201i	0.975789	−	1.77002i
$37$	−9.76872	−	2.86836i	−1.60597	−	0.471555i	−0.648769	−	0.760985i	$-0.724716\pi$
$37$	−9.76872	−	2.86836i	−1.60597	−	0.471555i	−0.957199	+	0.289431i	$0.906534\pi$
$38$	1.98205	+	7.83145i	0.321530	+	1.27043i
$39$	−10.0831	+	8.73707i	−1.61459	+	1.39905i
$40$	−2.08173	+	1.91478i	−0.329151	+	0.302754i
$41$	−0.570236	+	0.167436i	−0.0890560	+	0.0261492i	−0.325957	−	0.945385i	$-0.605686\pi$
$41$	−0.570236	+	0.167436i	−0.0890560	+	0.0261492i	0.236901	+	0.971534i	$0.423868\pi$
$42$	−12.8326	−	4.29986i	−1.98011	−	0.663482i
$43$	−9.49229	−	1.36479i	−1.44756	−	0.208128i	−0.626702	−	0.779259i	$-0.715596\pi$
$43$	−9.49229	−	1.36479i	−1.44756	−	0.208128i	−0.820859	+	0.571131i	$0.806505\pi$
$44$	5.05200	+	5.09291i	0.761617	+	0.767785i
$45$	6.06351			0.903894
$46$	4.01096	−	5.46921i	0.591383	−	0.806391i
$47$		−	2.34790i		−	0.342476i	−0.985230	−	0.171238i	$-0.945223\pi$
$47$		−	2.34790i		−	0.342476i	0.985230	−	0.171238i	$-0.0547767\pi$
$48$	−6.59204	+	10.0778i	−0.951478	+	1.45460i
$49$	−0.441815	+	3.07289i	−0.0631164	+	0.438984i
$50$	−1.34094	−	0.449313i	−0.189637	−	0.0635424i
$51$	5.62826	+	19.1681i	0.788114	+	2.68407i
$52$	7.11685	−	5.28296i	0.986930	−	0.732615i
$53$	8.73607	+	10.0820i	1.19999	+	1.38486i	0.902808	+	0.430044i	$0.141502\pi$
$53$	8.73607	+	10.0820i	1.19999	+	1.38486i	0.297184	+	0.954820i	$0.403953\pi$
$54$	12.6445	−	3.20016i	1.72069	−	0.435487i
$55$	−1.01052	+	3.44150i	−0.136258	+	0.464052i
$56$	8.28552	+	3.49084i	1.10720	+	0.466484i
$57$	−9.29749	+	14.4672i	−1.23148	+	1.91622i
$58$	3.32457	+	1.67255i	0.436537	+	0.219617i
$59$	6.70259	−	7.73520i	0.872603	−	1.00704i	−0.127282	−	0.991867i	$-0.540625\pi$
$59$	6.70259	−	7.73520i	0.872603	−	1.00704i	0.999885	−	0.0151707i	$-0.00482915\pi$
$60$	−6.00401	−	0.453759i	−0.775114	−	0.0585801i
$61$	−0.650622	−	4.52517i	−0.0833036	−	0.579389i	−0.988131	−	0.153611i	$-0.950910\pi$
$61$	−0.650622	−	4.52517i	−0.0833036	−	0.579389i	0.904828	−	0.425778i	$-0.139999\pi$
$62$	−1.27375	−	1.19071i	−0.161767	−	0.151220i
$63$	−8.00688	−	17.5326i	−1.00877	−	2.20890i
$64$	4.87135	−	6.34586i	0.608919	−	0.793233i
$65$	4.03120	+	1.84099i	0.500009	+	0.228346i
$66$	−0.575832	+	15.2602i	−0.0708800	+	1.87840i
$67$	−2.48603	−	3.86834i	−0.303717	−	0.472593i	0.655527	−	0.755172i	$-0.272446\pi$
$67$	−2.48603	−	3.86834i	−0.303717	−	0.472593i	−0.959244	+	0.282579i	$0.908810\pi$
$68$	−2.76873	−	12.9795i	−0.335758	−	1.57399i
$69$	14.3362	−	1.71325i	1.72587	−	0.206251i
$70$	0.471527	+	4.47064i	0.0563582	+	0.534344i
$71$	−5.52515	−	8.59730i	−0.655714	−	1.02031i	−0.996773	−	0.0802694i	$-0.974422\pi$
$71$	−5.52515	−	8.59730i	−0.655714	−	1.02031i	0.341059	−	0.940042i	$-0.389214\pi$
$72$	−16.8958	+	2.94292i	−1.99119	+	0.346826i
$73$	6.95418	−	15.2275i	0.813925	−	1.78225i	0.224400	−	0.974497i	$-0.427958\pi$
$73$	6.95418	−	15.2275i	0.813925	−	1.78225i	0.589525	−	0.807750i	$-0.299315\pi$
$74$	5.48315	+	13.3134i	0.637404	+	1.54765i
$75$	−1.25063	−	2.73851i	−0.144411	−	0.316216i
$76$	6.88330	−	9.11813i	0.789569	−	1.04592i
$77$	11.2855	−	1.62261i	1.28610	−	0.184913i
$78$	18.5617	+	3.38755i	2.10170	+	0.383565i
$79$	−5.58490	+	6.44532i	−0.628351	+	0.725156i	−0.977270	−	0.211997i	$-0.932003\pi$
$79$	−5.58490	+	6.44532i	−0.628351	+	0.725156i	0.348919	+	0.937153i	$0.386549\pi$
$80$	3.95457	+	0.601175i	0.442134	+	0.0672134i
$81$	8.05551	+	5.17696i	0.895056	+	0.575218i
$82$	0.689421	+	0.480737i	0.0761338	+	0.0530885i
$83$	−3.30843	+	11.2675i	−0.363147	+	1.23677i	0.552068	+	0.833799i	$0.313839\pi$
$83$	−3.30843	+	11.2675i	−0.363147	+	1.23677i	−0.915215	+	0.402966i	$0.867979\pi$
$84$	6.61627	+	17.9598i	0.721894	+	1.95957i
$85$	5.01496	−	4.34548i	0.543948	−	0.471334i
$86$	6.89684	+	11.6776i	0.743705	+	1.25923i
$87$	2.23202	+	7.60156i	0.239298	+	0.814973i
$88$	1.14545	−	10.0801i	0.122105	−	1.07454i
$89$	15.6366	+	2.24820i	1.65747	+	0.238309i	0.906556	−	0.422086i	$-0.138702\pi$
$89$	15.6366	+	2.24820i	1.65747	+	0.238309i	0.750919	+	0.660395i	$0.229611\pi$
$90$	−5.36713	−	6.68776i	−0.565745	−	0.704952i
$91$		−	14.0872i		−	1.47674i
$92$	−9.58259	+	0.417190i	−0.999054	+	0.0434951i
$93$		−	3.71182i		−	0.384898i
$94$	−2.58962	+	2.07825i	−0.267099	+	0.214355i
$95$	5.65413	+	0.812941i	0.580101	+	0.0834060i
$96$	16.9502	−	1.64965i	1.72998	−	0.168367i
$97$	1.23966	+	4.22190i	0.125869	+	0.428669i	0.998182	−	0.0602787i	$-0.0191989\pi$
$97$	1.23966	+	4.22190i	0.125869	+	0.428669i	−0.872313	+	0.488948i	$0.837381\pi$
$98$	3.78032	−	2.23268i	0.381870	−	0.225534i
$99$	−16.4365	+	14.2423i	−1.65193	+	1.43140i
$100$	0.691366	+	1.87670i	0.0691366	+	0.187670i
$101$	−0.157209	+	0.535404i	−0.0156429	+	0.0532747i	−0.966945	−	0.254987i	$-0.917929\pi$
$101$	−0.157209	+	0.535404i	−0.0156429	+	0.0532747i	0.951302	+	0.308261i	$0.0997471\pi$
$102$	16.1596	−	23.1744i	1.60004	−	2.29461i
$103$	0.338775	+	0.217717i	0.0333805	+	0.0214523i	0.557225	−	0.830362i	$-0.311866\pi$
$103$	0.338775	+	0.217717i	0.0333805	+	0.0214523i	−0.523844	+	0.851814i	$0.675503\pi$
$104$	−12.1264	−	3.17332i	−1.18909	−	0.311170i
$105$	−6.26692	+	7.23241i	−0.611589	+	0.705811i
$106$	3.38717	−	18.5596i	0.328991	−	1.80266i
$107$	7.70764	−	1.10819i	0.745126	−	0.107133i	0.240714	−	0.970596i	$-0.422618\pi$
$107$	7.70764	−	1.10819i	0.745126	−	0.107133i	0.504412	+	0.863463i	$0.331709\pi$
$108$	−14.7219	−	11.1136i	−1.41662	−	1.06941i
$109$	1.26997	+	2.78086i	0.121641	+	0.266358i	0.960651	−	0.277760i	$-0.0895919\pi$
$109$	1.26997	+	2.78086i	0.121641	+	0.266358i	−0.839009	+	0.544117i	$0.816865\pi$
$110$	4.69028	−	1.93171i	0.447200	−	0.184181i
$111$	−12.7329	+	27.8811i	−1.20855	+	2.64636i
$112$	−3.48372	−	12.2285i	−0.329181	−	1.15548i
$113$	−2.40461	−	3.74164i	−0.226207	−	0.351984i	0.709535	−	0.704670i	$-0.248905\pi$
$113$	−2.40461	−	3.74164i	−0.226207	−	0.351984i	−0.935742	+	0.352686i	$0.885269\pi$
$114$	24.1863	−	2.55098i	2.26526	−	0.238921i
$115$	−2.49584	−	4.09522i	−0.232738	−	0.381881i
$116$	−1.09801	−	5.14731i	−0.101947	−	0.477915i
$117$	14.5279	+	22.6058i	1.34310	+	2.08991i
$118$	−14.4644	−	0.545802i	−1.33155	−	0.0502451i
$119$	−19.1872	−	8.76251i	−1.75889	−	0.803258i
$120$	4.81399	+	7.02378i	0.439455	+	0.641181i
$121$	−0.774787	−	1.69655i	−0.0704352	−	0.154232i
$122$	−4.41515	+	4.72308i	−0.399729	+	0.427607i
$123$	0.254631	+	1.77100i	0.0229593	+	0.159686i
$124$	−0.185830	+	2.45885i	−0.0166880	+	0.220811i
$125$	−0.654861	+	0.755750i	−0.0585725	+	0.0675963i
$126$	−12.2503	+	24.3503i	−1.09135	+	2.16929i
$127$	−3.32644	+	5.17604i	−0.295174	+	0.459300i	−0.956888	−	0.290457i	$-0.906193\pi$
$127$	−3.32644	+	5.17604i	−0.295174	+	0.459300i	0.661714	+	0.749756i	$0.269829\pi$
$128$	−11.3111	+	0.244188i	−0.999767	+	0.0215834i
$129$	−8.13391	+	27.7015i	−0.716151	+	2.43899i
$130$	−1.53771	−	6.07578i	−0.134866	−	0.532881i
$131$	−4.22471	−	4.87557i	−0.369114	−	0.425981i	0.540558	−	0.841307i	$-0.318213\pi$
$131$	−4.22471	−	4.87557i	−0.369114	−	0.425981i	−0.909673	+	0.415326i	$0.863668\pi$
$132$	17.3410	−	12.8725i	1.50934	−	1.12041i
$133$	−5.11568	−	17.4224i	−0.443585	−	1.51071i
$134$	−2.06608	+	6.16604i	−0.178482	+	0.532665i
$135$	1.31255	−	9.12901i	0.112967	−	0.785700i
$136$	−11.8650	+	14.5426i	−1.01741	+	1.24702i
$137$		−	4.87600i		−	0.416585i	−0.978067	−	0.208293i	$-0.933209\pi$
$137$		−	4.87600i		−	0.416585i	0.978067	−	0.208293i	$-0.0667906\pi$
$138$	−14.5793	−	14.2956i	−1.24107	−	1.21692i
$139$	15.8762			1.34660			0.673300	−	0.739369i	$-0.264876\pi$
$139$	15.8762			1.34660			0.673300	+	0.739369i	$0.264876\pi$
$140$	4.51353	−	4.47727i	0.381463	−	0.378399i
$141$	−6.99656	−	1.00595i	−0.589216	−	0.0847165i
$142$	−4.59181	+	13.7039i	−0.385336	+	1.15001i
$143$	−15.2517	+	4.47829i	−1.27541	+	0.374493i
$144$	18.2013	+	16.0303i	1.51677	+	1.33586i
$145$	1.98880	−	1.72330i	0.165161	−	0.143113i
$146$	−22.9508	+	5.80856i	−1.89942	+	0.480720i
$147$	8.96767	+	2.63315i	0.739641	+	0.217178i
$148$	9.83058	−	17.8320i	0.808069	−	1.46578i
$149$	−14.9714	−	9.62152i	−1.22650	−	0.788226i	−0.243160	−	0.969986i	$-0.578184\pi$
$149$	−14.9714	−	9.62152i	−1.22650	−	0.788226i	−0.983343	+	0.181760i	$0.941820\pi$
$150$	−1.91344	+	3.80339i	−0.156232	+	0.310545i
$151$	−10.8286	−	9.38304i	−0.881220	−	0.763581i	0.0914415	−	0.995810i	$-0.470853\pi$
$151$	−10.8286	−	9.38304i	−0.881220	−	0.763581i	−0.972661	+	0.232229i	$0.925398\pi$
$152$	−16.1496	+	0.478989i	−1.30991	+	0.0388511i
$153$	39.8263	−	5.72616i	3.21977	−	0.462932i
$154$	−11.7790	−	11.0111i	−0.949183	−	0.887300i
$155$	−1.12151	+	0.512178i	−0.0900821	+	0.0411391i
$156$	−12.6936	−	23.4711i	−1.01630	−	1.87920i
$157$	−4.58543	+	10.0407i	−0.365957	+	0.801335i	0.633658	+	0.773613i	$0.281553\pi$
$157$	−4.58543	+	10.0407i	−0.365957	+	0.801335i	−0.999616	+	0.0277218i	$0.991175\pi$
$158$	12.0524	+	0.454787i	0.958836	+	0.0361809i
$159$	33.7864	−	21.7132i	2.67944	−	1.72197i
$160$	−2.83733	−	4.89383i	−0.224311	−	0.386891i
$161$	−8.54555	+	12.6245i	−0.673484	+	0.994946i
$162$	−1.42041	−	13.4672i	−0.111598	−	1.05809i
$163$	−14.0975	+	9.05992i	−1.10420	+	0.709628i	−0.960022	−	0.279924i	$-0.909691\pi$
$163$	−14.0975	+	9.05992i	−1.10420	+	0.709628i	−0.144180	+	0.989551i	$0.546055\pi$
$164$	−0.0800133	−	1.18592i	−0.00624799	−	0.0926051i
$165$	9.82246	+	4.48577i	0.764678	+	0.349217i
$166$	15.3559	−	6.32440i	1.19185	−	0.490868i
$167$	−5.72758	+	2.61570i	−0.443213	+	0.202409i	−0.624505	−	0.781021i	$-0.714699\pi$
$167$	−5.72758	+	2.61570i	−0.443213	+	0.202409i	0.181292	+	0.983429i	$0.441972\pi$
$168$	13.9524	−	23.1946i	1.07645	−	1.78950i
$169$	0.944945	+	6.57224i	0.0726881	+	0.505557i
$170$	−9.23187	−	1.68484i	−0.708052	−	0.129221i
$171$	26.1764	+	22.6820i	2.00176	+	1.73454i
$172$	6.77507	−	17.9433i	0.516594	−	1.36817i
$173$	0.934757	−	1.45451i	0.0710683	−	0.110584i	−0.803900	−	0.594764i	$-0.797246\pi$
$173$	0.934757	−	1.45451i	0.0710683	−	0.110584i	0.874969	+	0.484180i	$0.160882\pi$
$174$	6.40848	−	9.19035i	0.485826	−	0.696719i
$175$	3.04999	+	0.895559i	0.230558	+	0.0676979i
$176$	−12.1318	+	7.65907i	−0.914467	+	0.577324i
$177$	−20.1786	−	23.2873i	−1.51672	−	1.75038i
$178$	−11.3611	−	19.2364i	−0.851551	−	1.44183i
$179$	16.0036	−	4.69908i	1.19617	−	0.351226i	0.377780	−	0.925895i	$-0.376688\pi$
$179$	16.0036	−	4.69908i	1.19617	−	0.351226i	0.818385	+	0.574670i	$0.194869\pi$
$180$	−2.62555	+	11.8394i	−0.195697	+	0.882455i
$181$	1.16782	−	8.12235i	0.0868032	−	0.603729i	−0.899267	−	0.437400i	$-0.855899\pi$
$181$	1.16782	−	8.12235i	0.0868032	−	0.603729i	0.986070	−	0.166329i	$-0.0531915\pi$
$182$	−15.5376	+	12.4694i	−1.15172	+	0.924291i
$183$	−13.7634			−1.01742
$184$	8.94220	+	10.1999i	0.659227	+	0.751944i
$185$	10.1811			0.748531
$186$	−4.09396	+	3.28553i	−0.300184	+	0.240907i
$187$	−3.38724	+	23.5588i	−0.247699	+	1.72279i
$188$	4.58442	+	1.01666i	0.334353	+	0.0741475i
$189$	−28.1298	+	8.25964i	−2.04614	+	0.600801i
$190$	−4.10813	−	6.95581i	−0.298035	−	0.504628i
$191$	5.72946	+	6.61215i	0.414569	+	0.478438i	0.924175	−	0.381970i	$-0.124754\pi$
$191$	5.72946	+	6.61215i	0.414569	+	0.478438i	−0.509606	+	0.860408i	$0.670209\pi$
$192$	−16.8231	−	17.2351i	−1.21410	−	1.24384i
$193$	−7.95132	−	2.33472i	−0.572348	−	0.168057i	−0.0172643	−	0.999851i	$-0.505496\pi$
$193$	−7.95132	−	2.33472i	−0.572348	−	0.168057i	−0.555084	+	0.831794i	$0.687314\pi$
$194$	3.55927	−	5.10432i	0.255541	−	0.366469i
$195$	7.21316	−	11.2239i	0.516545	−	0.803760i
$196$	−5.80870	−	2.19326i	−0.414907	−	0.156661i
$197$	0.798313	+	0.691742i	0.0568775	+	0.0492846i	0.682836	−	0.730572i	$-0.260746\pi$
$197$	0.798313	+	0.691742i	0.0568775	+	0.0492846i	−0.625958	+	0.779857i	$0.715292\pi$
$198$	30.2573	+	5.52204i	2.15029	+	0.392434i
$199$	−1.16906	−	8.13099i	−0.0828724	−	0.576390i	−0.988373	−	0.152046i	$-0.951414\pi$
$199$	−1.16906	−	8.13099i	−0.0828724	−	0.576390i	0.905501	−	0.424344i	$-0.139495\pi$
$200$	1.45795	−	2.42371i	0.103093	−	0.171382i
$201$	−12.5925	+	5.75079i	−0.888205	+	0.405630i
$202$	0.729679	−	0.300521i	0.0513400	−	0.0211446i
$203$	−7.60914	−	3.47498i	−0.534057	−	0.243896i
$204$	−39.8640	+	2.68959i	−2.79104	+	0.188309i
$205$	0.499965	−	0.321308i	0.0349191	−	0.0224411i
$206$	−0.0597357	−	0.566366i	−0.00416198	−	0.0394606i
$207$	0.693721	−	29.0713i	0.0482169	−	2.02059i
$208$	7.23366	+	16.1837i	0.501564	+	1.12214i
$209$	−17.2362	+	11.0770i	−1.19225	+	0.766215i
$210$	13.5242	+	0.510325i	0.933258	+	0.0352158i
$211$	−4.67303	+	10.2325i	−0.321705	+	0.704435i	−0.999526	−	0.0307917i	$-0.990197\pi$
$211$	−4.67303	+	10.2325i	−0.321705	+	0.704435i	0.677821	+	0.735227i	$0.262924\pi$
$212$	−23.4685	+	12.6922i	−1.61182	+	0.871701i
$213$	−27.9865	+	12.7810i	−1.91760	+	0.875741i
$214$	−8.04473	−	7.52025i	−0.549926	−	0.514073i
$215$	9.49229	−	1.36479i	0.647369	−	0.0930776i
$216$	0.773363	+	26.0748i	0.0526207	+	1.77417i
$217$	2.96192	+	2.56652i	0.201068	+	0.174227i
$218$	1.94303	−	3.86220i	0.131599	−	0.261581i
$219$	−42.3973	−	27.2471i	−2.86495	−	1.84119i
$220$	−6.28219	−	3.46330i	−0.423545	−	0.233495i
$221$	28.2163	+	8.28505i	1.89803	+	0.557313i
$222$	42.0221	−	10.6353i	2.82034	−	0.713793i
$223$	7.19475	−	6.23428i	0.481796	−	0.417479i	−0.379804	−	0.925067i	$-0.624008\pi$
$223$	7.19475	−	6.23428i	0.481796	−	0.417479i	0.861600	+	0.507589i	$0.169463\pi$
$224$	−10.4038	+	14.6664i	−0.695133	+	0.979943i
$225$	−5.81789	+	1.70829i	−0.387860	+	0.113886i
$226$	−1.99841	+	5.96410i	−0.132932	+	0.396726i
$227$	3.37585	+	0.485373i	0.224063	+	0.0322154i	0.253432	−	0.967353i	$-0.418441\pi$
$227$	3.37585	+	0.485373i	0.224063	+	0.0322154i	−0.0293689	+	0.999569i	$0.509350\pi$
$228$	−24.2222	−	24.4184i	−1.60415	−	1.61714i
$229$	17.3702			1.14786			0.573928	−	0.818906i	$-0.305419\pi$
$229$	17.3702			1.14786			0.573928	+	0.818906i	$0.305419\pi$
$230$	−2.30763	+	6.37768i	−0.152161	+	0.420532i
$231$		−	34.3251i		−	2.25843i
$232$	−4.70533	+	5.76720i	−0.308920	+	0.378635i
$233$	2.55568	−	17.7752i	0.167428	−	1.16449i	−0.716746	−	0.697334i	$-0.754369\pi$
$233$	2.55568	−	17.7752i	0.167428	−	1.16449i	0.884175	−	0.467156i	$-0.154721\pi$
$234$	12.0737	−	36.0331i	0.789284	−	2.35556i
$235$	0.661479	+	2.25279i	0.0431502	+	0.146956i
$236$	12.2012	+	16.4366i	0.794230	+	1.06993i
$237$	16.8137	+	19.4041i	1.09217	+	1.26043i
$238$	7.31899	+	28.9188i	0.474420	+	1.87452i
$239$	4.63000	−	15.7683i	0.299490	−	1.01997i	−0.662993	−	0.748626i	$-0.730714\pi$
$239$	4.63000	−	15.7683i	0.299490	−	1.01997i	0.962483	−	0.271343i	$-0.0874677\pi$
$240$	3.48578	−	11.5267i	0.225006	−	0.744047i
$241$	5.07413	−	7.89551i	0.326854	−	0.508594i	−0.638471	−	0.769646i	$-0.720433\pi$
$241$	5.07413	−	7.89551i	0.326854	−	0.508594i	0.965325	+	0.261051i	$0.0840692\pi$
$242$	−1.18541	+	2.35626i	−0.0762007	+	0.151466i
$243$	0.759178	−	0.876138i	0.0487013	−	0.0562043i
$244$	9.11741	+	0.689058i	0.583683	+	0.0441124i
$245$	−0.441815	−	3.07289i	−0.0282265	−	0.196320i
$246$	1.72794	−	1.84845i	0.110169	−	0.117853i
$247$	10.5162	+	23.0273i	0.669131	+	1.46519i
$248$	2.87648	−	1.97150i	0.182657	−	0.125190i
$249$	32.1587	+	14.6864i	2.03797	+	0.930712i
$250$	1.41321	+	0.0533263i	0.0893791	+	0.00337265i
$251$	−3.84018	−	5.97544i	−0.242390	−	0.377167i	0.698649	−	0.715465i	$-0.253785\pi$
$251$	−3.84018	−	5.97544i	−0.242390	−	0.377167i	−0.941039	+	0.338298i	$0.890149\pi$
$252$	37.7006	−	8.04217i	2.37491	−	0.506609i
$253$	16.3846	+	5.23863i	1.03009	+	0.329350i
$254$	8.65334	−	0.912684i	0.542959	−	0.0572669i
$255$	−10.8006	−	16.8060i	−0.676357	−	1.05243i
$256$	10.2814	+	12.2594i	0.642585	+	0.766214i
$257$	3.26644	−	7.15251i	0.203755	−	0.446161i	−0.779976	−	0.625809i	$-0.784769\pi$
$257$	3.26644	−	7.15251i	0.203755	−	0.446161i	0.983731	+	0.179648i	$0.0574960\pi$
$258$	37.7532	−	15.5488i	2.35041	−	0.968026i
$259$	−13.4442	−	29.4387i	−0.835382	−	1.82923i
$260$	−5.34019	+	7.07401i	−0.331184	+	0.438712i
$261$	15.7941	−	2.27084i	0.977627	−	0.140562i
$262$	−1.63801	+	8.97528i	−0.101197	+	0.554494i
$263$	1.73322	−	2.00024i	0.106875	−	0.123340i	−0.699792	−	0.714347i	$-0.746724\pi$
$263$	1.73322	−	2.00024i	0.106875	−	0.123340i	0.806667	+	0.591007i	$0.201269\pi$
$264$	−29.5472	−	7.73215i	−1.81850	−	0.475881i
$265$	−11.2226	−	7.21234i	−0.689400	−	0.443050i
$266$	−14.6879	+	21.0638i	−0.900574	+	1.29151i
$267$	13.3989	−	45.6326i	0.820001	−	2.79267i
$268$	8.62965	−	3.17911i	0.527140	−	0.194195i
$269$	−12.6450	+	10.9569i	−0.770978	+	0.668056i	−0.948754	−	0.316015i	$-0.897655\pi$
$269$	−12.6450	+	10.9569i	−0.770978	+	0.668056i	0.177776	+	0.984071i	$0.443110\pi$
$270$	−11.2307	+	6.63289i	−0.683477	+	0.403665i
$271$	−6.37634	−	21.7158i	−0.387335	−	1.31914i	−0.890512	−	0.454959i	$-0.849654\pi$
$271$	−6.37634	−	21.7158i	−0.387335	−	1.31914i	0.503177	−	0.864183i	$-0.332164\pi$
$272$	26.5421	+	0.214083i	1.60935	+	0.0129807i
$273$	−41.9789	−	6.03565i	−2.54068	−	0.365294i
$274$	−5.37800	+	4.31601i	−0.324897	+	0.260740i
$275$		−	3.58679i		−	0.216292i
$276$	−2.86245	+	28.7341i	−0.172299	+	1.72959i
$277$		−	10.6374i		−	0.639139i	−0.947563	−	0.319570i	$-0.896462\pi$
$277$		−	10.6374i		−	0.639139i	0.947563	−	0.319570i	$-0.103538\pi$
$278$	−14.0529	−	17.5107i	−0.842834	−	1.05022i
$279$	−7.39979	−	1.06393i	−0.443014	−	0.0636958i
$280$	−8.93339	−	1.01514i	−0.533872	−	0.0606662i
$281$	−3.90688	−	13.3056i	−0.233065	−	0.793747i	−0.990099	−	0.140371i	$-0.955170\pi$
$281$	−3.90688	−	13.3056i	−0.233065	−	0.793747i	0.757034	−	0.653376i	$-0.226648\pi$
$282$	5.08350	+	8.60729i	0.302718	+	0.512557i
$283$	−5.11487	+	4.43206i	−0.304048	+	0.263459i	−0.793499	−	0.608572i	$-0.791743\pi$
$283$	−5.11487	+	4.43206i	−0.304048	+	0.263459i	0.489451	+	0.872031i	$0.337197\pi$
$284$	19.1792	−	7.06550i	1.13808	−	0.419260i
$285$	4.84500	−	16.5006i	0.286993	−	0.977409i
$286$	18.4394	+	12.8579i	1.09034	+	0.760302i
$287$	−1.58927	−	1.02136i	−0.0938115	−	0.0602890i
$288$	1.56979	−	34.2644i	0.0925007	−	2.01905i
$289$	17.7029	−	20.4302i	1.04134	−	1.20178i
$290$	−3.66111	−	0.668163i	−0.214988	−	0.0392359i
$291$	13.1121	−	1.88523i	0.768644	−	0.110514i
$292$	26.7215	+	20.1721i	1.56376	+	1.18048i
$293$	−5.84674	−	12.8026i	−0.341570	−	0.747934i	0.658419	−	0.752652i	$-0.271226\pi$
$293$	−5.84674	−	12.8026i	−0.341570	−	0.747934i	−0.999989	+	0.00471755i	$0.998498\pi$
$294$	−5.03353	−	12.2217i	−0.293561	−	0.712781i
$295$	−4.25183	+	9.31021i	−0.247551	+	0.542061i
$296$	−28.3694	+	4.94140i	−1.64894	+	0.287213i
$297$	17.8847	+	27.8292i	1.03778	+	1.61481i
$298$	2.63988	+	25.0292i	0.152924	+	1.44990i
$299$	9.28776	−	19.1168i	0.537125	−	1.10556i
$300$	5.88864	−	1.25615i	0.339981	−	0.0725236i
$301$	−16.4809	−	25.6447i	−0.949941	−	1.47814i
$302$	−0.764075	+	20.2489i	−0.0439676	+	1.16519i
$303$	1.52811	+	0.697863i	0.0877874	+	0.0400912i
$304$	14.8232	+	17.3883i	0.850169	+	0.997288i
$305$	1.89916	+	4.15857i	0.108745	+	0.238119i
$306$	−41.5680	−	38.8580i	−2.37629	−	2.22136i
$307$	0.466123	+	3.24196i	0.0266031	+	0.185028i	0.998790	−	0.0491777i	$-0.0156601\pi$
$307$	0.466123	+	3.24196i	0.0266031	+	0.185028i	−0.972187	+	0.234206i	$0.924751\pi$
$308$	−1.71847	+	22.7382i	−0.0979187	+	1.29563i
$309$	0.793929	−	0.916243i	0.0451650	−	0.0521232i
$310$	1.55762	+	0.783620i	0.0884668	+	0.0445066i
$311$	−4.61069	+	7.17438i	−0.261448	+	0.406822i	−0.947016	−	0.321188i	$-0.895918\pi$
$311$	−4.61069	+	7.17438i	−0.261448	+	0.406822i	0.685567	+	0.728009i	$0.259554\pi$
$312$	−14.6518	+	34.7760i	−0.829493	+	1.96880i
$313$	5.73645	−	19.5365i	0.324243	−	1.10427i	−0.622591	−	0.782548i	$-0.713920\pi$
$313$	5.73645	−	19.5365i	0.324243	−	1.10427i	0.946834	−	0.321723i	$-0.104262\pi$
$314$	15.1332	−	3.83004i	0.854017	−	0.216142i
$315$	12.6221	+	14.5666i	0.711172	+	0.820736i
$316$	−10.1666	−	13.6958i	−0.571915	−	0.770447i
$317$	3.16156	+	10.7673i	0.177571	+	0.604751i	0.999387	+	0.0349986i	$0.0111427\pi$
$317$	3.16156	+	10.7673i	0.177571	+	0.604751i	−0.821816	+	0.569752i	$0.807039\pi$
$318$	−53.8548	−	18.0453i	−3.02003	−	1.01193i
$319$	−1.34329	+	9.34278i	−0.0752097	+	0.523095i
$320$	−2.88619	+	7.46123i	−0.161343	+	0.417095i
$321$		−	23.4430i		−	1.30846i
$322$	21.4883	−	1.74924i	1.19750	−	0.0974812i
$323$	37.9051			2.10910
$324$	−13.5964	+	13.4872i	−0.755358	+	0.749290i
$325$	−4.38658	−	0.630694i	−0.243323	−	0.0349846i
$326$	22.4711	+	7.52947i	1.24456	+	0.417019i
$327$	8.83085	−	2.59297i	0.488347	−	0.143392i
$328$	−1.23719	+	1.13797i	−0.0683126	+	0.0628342i
$329$	5.64046	−	4.88748i	0.310969	−	0.269456i
$330$	−3.74679	−	14.8043i	−0.206254	−	0.814950i
$331$	−15.2399	−	4.47484i	−0.837661	−	0.245959i	−0.165356	−	0.986234i	$-0.552877\pi$
$331$	−15.2399	−	4.47484i	−0.837661	−	0.245959i	−0.672305	+	0.740275i	$0.734695\pi$
$332$	−20.5679	−	11.3388i	−1.12881	−	0.622299i
$333$	51.9334	+	33.3756i	2.84593	+	1.82897i
$334$	7.95477	+	4.00195i	0.435266	+	0.218977i
$335$	3.47516	+	3.01125i	0.189869	+	0.164522i
$336$	−37.9325	+	5.14195i	−2.06939	+	0.280516i
$337$	−27.0135	+	3.88396i	−1.47152	+	0.211573i	−0.830958	−	0.556335i	$-0.812207\pi$
$337$	−27.0135	+	3.88396i	−1.47152	+	0.211573i	−0.640561	+	0.767907i	$0.721298\pi$
$338$	6.41244	−	6.85966i	0.348791	−	0.373116i
$339$	−12.1801	+	5.56245i	−0.661530	+	0.302111i
$340$	6.31331	+	11.6736i	0.342388	+	0.633093i
$341$	1.83708	−	4.02264i	0.0994833	−	0.217838i
$342$	1.84703	−	48.9484i	0.0998760	−	2.64683i
$343$	10.4171	−	6.69469i	0.562473	−	0.361479i
$344$	−25.7876	+	8.41001i	−1.39038	+	0.453438i
$345$	−13.2728	+	5.68281i	−0.714582	+	0.305952i
$346$	−2.43166	+	0.256472i	−0.130727	+	0.0137880i
$347$	8.51815	−	5.47428i	0.457278	−	0.293875i	−0.291651	−	0.956525i	$-0.594205\pi$
$347$	8.51815	−	5.47428i	0.457278	−	0.293875i	0.748929	+	0.662650i	$0.230568\pi$
$348$	−15.8090	+	1.06662i	−0.847452	+	0.0571768i
$349$	3.33570	+	1.52336i	0.178556	+	0.0815437i	0.502687	−	0.864468i	$-0.332345\pi$
$349$	3.33570	+	1.52336i	0.178556	+	0.0815437i	−0.324131	+	0.946012i	$0.605072\pi$
$350$	−1.71195	−	4.15670i	−0.0915077	−	0.222185i
$351$	37.1793	−	16.9792i	1.98449	−	0.906284i
$352$	19.1861	+	6.60133i	1.02262	+	0.351852i
$353$	1.41708	+	9.85601i	0.0754236	+	0.524583i	0.992149	+	0.125064i	$0.0399136\pi$
$353$	1.41708	+	9.85601i	0.0754236	+	0.524583i	−0.916725	+	0.399519i	$0.869177\pi$
$354$	−7.82368	+	42.8689i	−0.415824	+	2.27845i
$355$	7.72348	+	6.69243i	0.409920	+	0.355197i
$356$	−11.1605	+	29.5579i	−0.591507	+	1.56657i
$357$	−34.3323	+	53.4221i	−1.81706	+	2.82740i
$358$	−19.3485	−	13.4918i	−1.02260	−	0.713064i
$359$	13.3031	+	3.90614i	0.702110	+	0.206158i	0.613253	−	0.789886i	$-0.289860\pi$
$359$	13.3031	+	3.90614i	0.702110	+	0.206158i	0.0888570	+	0.996044i	$0.471679\pi$
$360$	15.3823	−	7.58381i	0.810718	−	0.399702i
$361$	8.92578	+	10.3009i	0.469778	+	0.542152i
$362$	−9.99226	+	5.90147i	−0.525182	+	0.310175i
$363$	−5.38753	+	1.58192i	−0.282772	+	0.0830294i
$364$	27.5062	+	6.09989i	1.44172	+	0.319721i
$365$	−2.38240	+	16.5699i	−0.124700	+	0.867309i
$366$	12.1827	+	15.1804i	0.636802	+	0.793492i
$367$	−6.99093			−0.364924			−0.182462	−	0.983213i	$-0.558407\pi$
$367$	−6.99093			−0.364924			−0.182462	+	0.983213i	$0.558407\pi$
$368$	3.33475	−	18.8913i	0.173836	−	0.984775i
$369$	3.60360			0.187596
$370$	−9.01186	−	11.2293i	−0.468504	−	0.583784i
$371$	−6.03496	+	41.9741i	−0.313320	+	2.17919i
$372$	7.24756	+	1.60725i	0.375769	+	0.0833320i
$373$	−7.74246	+	2.27339i	−0.400889	+	0.117712i	−0.475961	−	0.879466i	$-0.657900\pi$
$373$	−7.74246	+	2.27339i	−0.400889	+	0.117712i	0.0750716	+	0.997178i	$0.476081\pi$
$374$	28.9824	−	17.1171i	1.49865	−	0.885107i
$375$	1.97150	+	2.27523i	0.101808	+	0.117493i
$376$	−2.93659	−	5.95630i	−0.151443	−	0.307173i
$377$	11.1898	+	3.28563i	0.576305	+	0.169219i
$378$	34.0091	+	23.7147i	1.74924	+	1.21975i
$379$	−8.08776	+	12.5848i	−0.415440	+	0.646438i	−0.984404	−	0.175925i	$-0.943708\pi$
$379$	−8.08776	+	12.5848i	−0.415440	+	0.646438i	0.568963	+	0.822363i	$0.307345\pi$
$380$	−4.03560	+	10.6880i	−0.207022	+	0.548285i
$381$	13.9990	+	12.1302i	0.717191	+	0.621449i
$382$	2.22144	−	12.1721i	0.113659	−	0.622778i
$383$	2.70759	+	18.8317i	0.138352	+	0.962257i	0.934197	+	0.356757i	$0.116118\pi$
$383$	2.70759	+	18.8317i	0.138352	+	0.962257i	−0.795846	+	0.605500i	$0.792973\pi$
$384$	−4.11855	+	33.8107i	−0.210174	+	1.72540i
$385$	−10.3712	+	4.73637i	−0.528566	+	0.241388i
$386$	4.46305	+	10.8365i	0.227163	+	0.551564i
$387$	52.8937	+	24.1557i	2.68874	+	1.22790i
$388$	−8.78032	+	0.592400i	−0.445753	+	0.0300746i
$389$	−1.36914	+	0.879892i	−0.0694181	+	0.0446123i	−0.574889	−	0.818231i	$-0.694955\pi$
$389$	−1.36914	+	0.879892i	−0.0694181	+	0.0446123i	0.505471	+	0.862843i	$0.331319\pi$
$390$	−18.7642	+	1.97909i	−0.950161	+	0.100215i
$391$	−20.2605	−	24.5412i	−1.02462	−	1.24110i
$392$	2.72253	+	8.34809i	0.137508	+	0.421642i
$393$	−16.3389	+	10.5004i	−0.824188	+	0.529674i
$394$	0.0563296	−	1.49280i	0.00283784	−	0.0752061i
$395$	3.54282	−	7.75769i	0.178259	−	0.390332i
$396$	−20.6918	−	38.2602i	−1.03980	−	1.92265i
$397$	15.1027	−	6.89716i	0.757981	−	0.346158i	0.00134883	−	0.999999i	$-0.499571\pi$
$397$	15.1027	−	6.89716i	0.757981	−	0.346158i	0.756632	+	0.653841i	$0.226843\pi$
$398$	−7.93330	+	8.48658i	−0.397660	+	0.425394i
$399$	−54.1092	+	7.77973i	−2.70885	+	0.389473i
$400$	−3.96375	+	0.537307i	−0.198187	+	0.0268654i
$401$	−16.4383	−	14.2438i	−0.820887	−	0.711303i	0.139424	−	0.990233i	$-0.455475\pi$
$401$	−16.4383	−	14.2438i	−0.820887	−	0.711303i	−0.960312	+	0.278930i	$0.910020\pi$
$402$	17.4891	+	8.79858i	0.872278	+	0.438833i
$403$	−4.59658	−	2.95404i	−0.228972	−	0.147151i
$404$	−0.977337	−	0.538794i	−0.0486244	−	0.0268060i
$405$	−9.18772	−	2.69776i	−0.456541	−	0.134053i
$406$	2.90252	+	11.4684i	0.144050	+	0.569168i
$407$	−27.5982	+	23.9139i	−1.36799	+	1.18537i
$408$	38.2522	+	41.5874i	1.89377	+	2.05888i
$409$	20.4959	−	6.01814i	1.01346	−	0.297578i	0.267490	−	0.963561i	$-0.413806\pi$
$409$	20.4959	−	6.01814i	1.01346	−	0.297578i	0.745967	+	0.665983i	$0.231988\pi$
$410$	−0.796934	−	0.267031i	−0.0393577	−	0.0131877i
$411$	−14.5301	−	2.08911i	−0.716718	−	0.103048i
$412$	−0.571800	+	0.567206i	−0.0281705	+	0.0279442i
$413$	32.5350			1.60094
$414$	−32.6783	+	24.9674i	−1.60605	+	1.22708i
$415$		−	11.7432i		−	0.576449i
$416$	11.4469	−	22.3034i	0.561232	−	1.09351i
$417$	6.80212	−	47.3098i	0.333101	−	2.31677i
$418$	27.4742	+	9.20585i	1.34380	+	0.450273i
$419$	−5.57184	−	18.9759i	−0.272202	−	0.927035i	−0.976207	−	0.216840i	$-0.930425\pi$
$419$	−5.57184	−	18.9759i	−0.272202	−	0.927035i	0.704005	−	0.710195i	$-0.251393\pi$
$420$	−11.4081	−	15.3683i	−0.556659	−	0.749894i
$421$	−2.17838	−	2.51398i	−0.106168	−	0.122524i	0.700179	−	0.713968i	$-0.253104\pi$
$421$	−2.17838	−	2.51398i	−0.106168	−	0.122524i	−0.806346	+	0.591444i	$0.798558\pi$
$422$	15.4223	−	3.90321i	0.750747	−	0.190005i
$423$	−4.01089	+	13.6598i	−0.195016	+	0.664163i
$424$	34.7720	+	14.6501i	1.68868	+	0.711472i
$425$	−3.58755	+	5.58234i	−0.174022	+	0.270783i
$426$	38.8692	+	19.5546i	1.88322	+	0.947426i
$427$	9.51666	−	10.9828i	0.460543	−	0.531495i
$428$	−1.17366	+	15.5295i	−0.0567310	+	0.750648i
$429$	6.81041	+	47.3675i	0.328810	+	2.28692i
$430$	−9.90742	−	9.26150i	−0.477778	−	0.446629i
$431$	4.48392	+	9.81842i	0.215983	+	0.472937i	0.986350	−	0.164664i	$-0.0526541\pi$
$431$	4.48392	+	9.81842i	0.215983	+	0.472937i	−0.770367	+	0.637601i	$0.779927\pi$
$432$	28.0747	−	23.9332i	1.35075	−	1.15149i
$433$	−3.26008	−	1.48883i	−0.156669	−	0.0715485i	0.335537	−	0.942027i	$-0.391082\pi$
$433$	−3.26008	−	1.48883i	−0.156669	−	0.0715485i	−0.492206	+	0.870479i	$0.663809\pi$
$434$	0.208996	−	5.53862i	0.0100321	−	0.265863i
$435$	−4.28321	−	6.66481i	−0.205364	−	0.319553i
$436$	−5.97971	+	1.27557i	−0.286376	+	0.0610888i
$437$	4.54450	−	27.0155i	0.217393	−	1.29233i
$438$	7.47586	+	70.8801i	0.357210	+	3.38678i
$439$	0.160247	+	0.249349i	0.00764817	+	0.0119008i	0.845057	−	0.534677i	$-0.179567\pi$
$439$	0.160247	+	0.249349i	0.00764817	+	0.0119008i	−0.837408	+	0.546578i	$0.815930\pi$
$440$	1.74085	+	9.99451i	0.0829917	+	0.476469i
$441$	7.81981	−	17.1230i	0.372372	−	0.815380i
$442$	−15.8377	−	38.4547i	−0.753323	−	1.82911i
$443$	−10.6769	−	23.3792i	−0.507276	−	1.11078i	−0.974036	−	0.226395i	$-0.927306\pi$
$443$	−10.6769	−	23.3792i	−0.507276	−	1.11078i	0.466760	−	0.884384i	$-0.345421\pi$
$444$	−48.9262	−	36.9345i	−2.32193	−	1.75283i
$445$	−15.6366	+	2.24820i	−0.741245	+	0.106575i
$446$	−13.2446	−	2.41717i	−0.627149	−	0.114456i
$447$	−35.0859	+	40.4912i	−1.65950	+	1.91517i
$448$	25.3853	−	1.50715i	1.19934	−	0.0712063i
$449$	15.5315	+	9.98151i	0.732978	+	0.471056i	0.853129	−	0.521699i	$-0.174702\pi$
$449$	15.5315	+	9.98151i	0.732978	+	0.471056i	−0.120152	+	0.992756i	$0.538338\pi$
$450$	7.03388	+	4.90476i	0.331581	+	0.231213i
$451$	−0.600560	+	2.04532i	−0.0282793	+	0.0963104i
$452$	8.34701	−	3.07499i	0.392610	−	0.144635i
$453$	−32.6002	+	28.2483i	−1.53169	+	1.32722i
$454$	−2.45280	−	4.15303i	−0.115115	−	0.194911i
$455$	3.96883	+	13.5166i	0.186062	+	0.633668i
$456$	−5.49194	+	48.3299i	−0.257183	+	2.26326i
$457$	−21.2187	−	3.05078i	−0.992567	−	0.142710i	−0.373150	−	0.927771i	$-0.621722\pi$
$457$	−21.2187	−	3.05078i	−0.992567	−	0.142710i	−0.619418	+	0.785062i	$0.712631\pi$
$458$	−15.3753	−	19.1585i	−0.718441	−	0.895219i
$459$		−	61.2007i		−	2.85660i
$460$	9.07689	−	3.10002i	0.423212	−	0.144539i
$461$		−	2.52025i		−	0.117380i	−0.998276	−	0.0586900i	$-0.981308\pi$
$461$		−	2.52025i		−	0.117380i	0.998276	−	0.0586900i	$-0.0186923\pi$
$462$	−37.8589	+	30.3830i	−1.76136	+	1.41354i
$463$	−13.2981	−	1.91198i	−0.618015	−	0.0888571i	−0.173805	−	0.984780i	$-0.555606\pi$
$463$	−13.2981	−	1.91198i	−0.618015	−	0.0888571i	−0.444210	+	0.895923i	$0.646515\pi$
$464$	10.5259	+	0.0848996i	0.488652	+	0.00394136i
$465$	1.04574	+	3.56147i	0.0484951	+	0.165159i
$466$	−21.8673	+	12.9149i	−1.01299	+	0.598273i
$467$	−19.5989	+	16.9826i	−0.906930	+	0.785860i	−0.977344	−	0.211658i	$-0.932114\pi$
$467$	−19.5989	+	16.9826i	−0.906930	+	0.785860i	0.0704134	+	0.997518i	$0.477568\pi$
$468$	−50.4299	+	18.5781i	−2.33112	+	0.858771i
$469$	4.11805	−	14.0248i	0.190154	−	0.647605i
$470$	1.89921	−	2.72365i	0.0876041	−	0.125632i
$471$	27.9559	+	17.9662i	1.28814	+	0.827837i
$472$	7.32891	−	28.0063i	0.337340	−	1.28909i
$473$	−22.5252	+	25.9955i	−1.03571	+	1.19528i
$474$	6.51905	−	35.7203i	0.299430	−	1.64069i
$475$	−5.65413	+	0.812941i	−0.259429	+	0.0373003i
$476$	25.4176	−	33.6700i	1.16501	−	1.54326i
$477$	−33.6026	−	73.5795i	−1.53856	−	3.36897i
$478$	−21.4900	+	8.85071i	−0.982929	+	0.404822i
$479$	−4.12549	+	9.03357i	−0.188499	+	0.412754i	−0.980161	−	0.198205i	$-0.936489\pi$
$479$	−4.12549	+	9.03357i	−0.188499	+	0.412754i	0.791662	+	0.610959i	$0.209216\pi$
$480$	−15.7989	+	6.35827i	−0.721117	+	0.290214i
$481$	24.3935	+	37.9570i	1.11225	+	1.73069i
$482$	−13.1998	+	1.39220i	−0.601232	+	0.0634131i
$483$	33.9586	+	30.8740i	1.54517	+	1.40482i
$484$	3.64810	−	0.778202i	0.165823	−	0.0353728i
$485$	−2.37890	−	3.70163i	−0.108020	−	0.168083i
$486$	−1.63833	−	0.0618210i	−0.0743161	−	0.00280426i
$487$	9.69876	+	4.42927i	0.439493	+	0.200710i	0.622857	−	0.782335i	$-0.285972\pi$
$487$	9.69876	+	4.42927i	0.439493	+	0.200710i	−0.183365	+	0.983045i	$0.558699\pi$
$488$	−7.31031	−	10.6660i	−0.330922	−	0.482827i
$489$	20.9578	+	45.8912i	0.947745	+	2.07527i
$490$	−2.99818	+	3.20728i	−0.135444	+	0.144890i
$491$	−1.82995	−	12.7276i	−0.0825844	−	0.574387i	−0.988534	−	0.151001i	$-0.951750\pi$
$491$	−1.82995	−	12.7276i	−0.0825844	−	0.574387i	0.905949	−	0.423386i	$-0.139159\pi$
$492$	−3.56824	−	0.269674i	−0.160869	−	0.0121578i
$493$	11.4354	−	13.1971i	0.515024	−	0.594369i
$494$	16.0896	−	31.9816i	0.723904	−	1.43892i
$495$	11.7582	−	18.2960i	0.528490	−	0.822346i
$496$	−4.72059	−	1.42755i	−0.211961	−	0.0640988i
$497$	9.15228	−	31.1698i	0.410536	−	1.39816i
$498$	−12.2670	−	48.4692i	−0.549697	−	2.17196i
$499$	12.6111	+	14.5540i	0.564551	+	0.651527i	0.964211	−	0.265137i	$-0.0854171\pi$
$499$	12.6111	+	14.5540i	0.564551	+	0.651527i	−0.399660	+	0.916664i	$0.630872\pi$
$500$	−1.19209	−	1.60590i	−0.0533118	−	0.0718182i
$501$	5.34061	+	18.1884i	0.238601	+	0.812599i
$502$	−3.19148	+	9.52472i	−0.142443	+	0.425109i
$503$	−2.35336	+	16.3680i	−0.104931	+	0.729812i	0.867638	+	0.497197i	$0.165637\pi$
$503$	−2.35336	+	16.3680i	−0.104931	+	0.729812i	−0.972569	+	0.232615i	$0.925272\pi$
$504$	−42.2409	−	34.4634i	−1.88156	−	1.53512i
$505$		−	0.558007i		−	0.0248310i
$506$	−8.72489	−	22.7084i	−0.387869	−	1.00951i
$507$	19.9896			0.887770
$508$	−8.66618	−	8.73636i	−0.384499	−	0.387613i
$509$	−30.1811	−	4.33938i	−1.33775	−	0.192340i	−0.563972	−	0.825794i	$-0.690727\pi$
$509$	−30.1811	−	4.33938i	−1.33775	−	0.192340i	−0.773780	+	0.633455i	$0.781636\pi$
$510$	−8.97607	+	26.7884i	−0.397467	+	1.18621i
$511$	51.0579	−	14.9919i	2.25867	−	0.663204i
$512$	4.42100	−	22.1913i	0.195382	−	0.980727i
$513$	39.8156	−	34.5005i	1.75790	−	1.52323i
$514$	−10.7802	+	2.72833i	−0.475493	+	0.120342i
$515$	−0.386390	−	0.113454i	−0.0170264	−	0.00499940i
$516$	−50.5670	−	27.8770i	−2.22609	−	1.22722i
$517$	−7.08456	−	4.55297i	−0.311578	−	0.200239i
$518$	−20.5693	+	40.8861i	−0.903764	+	1.79643i
$519$	−3.93383	−	3.40869i	−0.172676	−	0.149625i
$520$	12.5292	−	0.371608i	0.549441	−	0.0162961i
$521$	36.4733	−	5.24407i	1.59793	−	0.229747i	0.714953	−	0.699172i	$-0.246448\pi$
$521$	36.4733	−	5.24407i	1.59793	−	0.229747i	0.882972	+	0.469426i	$0.155539\pi$
$522$	−16.4848	−	15.4100i	−0.721519	−	0.674479i
$523$	21.0674	−	9.62117i	0.921214	−	0.420704i	0.102387	−	0.994745i	$-0.467352\pi$
$523$	21.0674	−	9.62117i	0.921214	−	0.420704i	0.818827	+	0.574040i	$0.194625\pi$
$524$	11.3492	−	6.13784i	0.495792	−	0.268133i
$525$	3.97546	−	8.70504i	0.173503	−	0.379919i
$526$	−3.74033	−	0.141139i	−0.163086	−	0.00615393i
$527$	−6.88264	+	4.42320i	−0.299812	+	0.192678i
$528$	17.6256	+	39.4333i	0.767055	+	1.71611i
$529$	−19.9199	+	11.4977i	−0.866084	+	0.499899i
$530$	1.97887	+	18.7620i	0.0859565	+	0.814971i
$531$	−52.2089	+	33.5526i	−2.26567	+	1.45606i
$532$	36.2335	−	2.44464i	1.57092	−	0.105989i
$533$	2.39578	+	1.09412i	0.103773	+	0.0473915i
$534$	−62.1907	+	25.6134i	−2.69125	+	1.10840i
$535$	−7.08322	+	3.23480i	−0.306234	+	0.139852i
$536$	−11.1450	−	6.70409i	−0.481389	−	0.289573i
$537$	−7.14618	−	49.7028i	−0.308381	−	2.14483i
$538$	23.2777	+	4.24825i	1.00357	+	0.183155i
$539$	8.41539	+	7.29198i	0.362476	+	0.314088i
$540$	17.2566	+	6.51579i	0.742607	+	0.280395i
$541$	21.2880	−	33.1248i	0.915244	−	1.42415i	0.00967199	−	0.999953i	$-0.496921\pi$
$541$	21.2880	−	33.1248i	0.915244	−	1.42415i	0.905572	−	0.424194i	$-0.139442\pi$
$542$	−18.3075	+	26.2546i	−0.786374	+	1.12773i
$543$	−23.7036	−	6.96001i	−1.01722	−	0.298683i
$544$	−23.2577	−	29.4642i	−0.997165	−	1.26327i
$545$	−2.00199	−	2.31042i	−0.0857558	−	0.0989674i
$546$	30.5007	+	51.6432i	1.30531	+	2.21012i
$547$	−27.6798	+	8.12752i	−1.18350	+	0.347507i	−0.813523	−	0.581533i	$-0.802453\pi$
$547$	−27.6798	+	8.12752i	−1.18350	+	0.347507i	−0.369979	+	0.929040i	$0.620635\pi$
$548$	9.52071	+	2.11135i	0.406704	+	0.0901924i
$549$	−3.94505	+	27.4384i	−0.168371	+	1.17104i
$550$	−3.95606	+	3.17486i	−0.168687	+	0.135377i
$551$	15.0322			0.640392
$552$	34.2261	−	22.2769i	1.45676	−	0.948170i
$553$	−27.1097			−1.15282
$554$	−11.7325	+	9.41572i	−0.498468	+	0.400036i
$555$	4.36209	−	30.3390i	0.185160	−	1.28782i
$556$	−6.87452	+	30.9993i	−0.291545	+	1.31466i
$557$	−24.3942	+	7.16280i	−1.03362	+	0.303497i	−0.754181	−	0.656667i	$-0.771966\pi$
$557$	−24.3942	+	7.16280i	−1.03362	+	0.303497i	−0.279436	+	0.960164i	$0.590148\pi$
$558$	5.37648	+	9.10336i	0.227605	+	0.385376i
$559$	27.8312	+	32.1189i	1.17713	+	1.35849i
$560$	6.78776	+	10.7517i	0.286835	+	0.454340i
$561$	68.7520	+	20.1874i	2.90271	+	0.852313i
$562$	−11.2173	+	16.0866i	−0.473172	+	0.678573i
$563$	−5.50535	+	8.56650i	−0.232023	+	0.361035i	−0.937669	−	0.347530i	$-0.887021\pi$
$563$	−5.50535	+	8.56650i	−0.232023	+	0.361035i	0.705646	+	0.708565i	$0.250657\pi$
$564$	4.99375	−	13.2256i	0.210275	−	0.556900i
$565$	3.36135	+	2.91262i	0.141413	+	0.122535i
$566$	9.41580	+	1.71841i	0.395776	+	0.0722301i
$567$	4.33185	+	30.1287i	0.181921	+	1.26528i
$568$	−24.7694	−	14.8997i	−1.03930	−	0.625178i
$569$	22.9999	−	10.5037i	0.964207	−	0.440339i	0.129832	−	0.991536i	$-0.458556\pi$
$569$	22.9999	−	10.5037i	0.964207	−	0.440339i	0.834375	+	0.551197i	$0.185829\pi$
$570$	−22.4879	+	9.26171i	−0.941915	+	0.387931i
$571$	−23.1710	−	10.5818i	−0.969676	−	0.442836i	−0.133350	−	0.991069i	$-0.542573\pi$
$571$	−23.1710	−	10.5818i	−0.969676	−	0.442836i	−0.836326	+	0.548233i	$0.815301\pi$
$572$	−2.14005	−	31.7190i	−0.0894800	−	1.32624i
$573$	22.1585	−	14.2404i	0.925683	−	0.594900i
$574$	0.280233	+	2.65695i	0.0116967	+	0.110899i
$575$	3.54849	+	3.22617i	0.147982	+	0.134541i
$576$	−39.1815	+	28.5979i	−1.63256	+	1.19158i
$577$	−10.1051	+	6.49415i	−0.420681	+	0.270355i	−0.733809	−	0.679356i	$-0.762259\pi$
$577$	−10.1051	+	6.49415i	−0.420681	+	0.270355i	0.313128	+	0.949711i	$0.398623\pi$
$578$	−38.2033	−	1.44157i	−1.58905	−	0.0599614i
$579$	−10.3640	+	22.6940i	−0.430713	+	0.943131i
$580$	2.50369	+	4.62946i	0.103960	+	0.192228i
$581$	−33.9553	+	15.5069i	−1.40870	+	0.643333i
$582$	−13.6855	−	12.7933i	−0.567283	−	0.530299i
$583$	47.3620	−	6.80963i	1.96154	−	0.282026i
$584$	−1.40372	−	47.3280i	−0.0580863	−	1.95844i
$585$	−20.3082	−	17.5971i	−0.839639	−	0.727551i
$586$	−8.94537	+	17.7809i	−0.369530	+	0.734523i
$587$	−11.6045	−	7.45777i	−0.478969	−	0.307815i	0.278786	−	0.960353i	$-0.410068\pi$
$587$	−11.6045	−	7.45777i	−0.478969	−	0.307815i	−0.757756	+	0.652538i	$0.773704\pi$
$588$	−9.02446	+	16.3698i	−0.372163	+	0.675078i
$589$	−6.75755	−	1.98420i	−0.278440	−	0.0817574i
$590$	14.0322	−	3.55139i	0.577698	−	0.146208i
$591$	2.40337	−	2.08254i	0.0988616	−	0.0856641i
$592$	30.5614	+	26.9163i	1.25607	+	1.10625i
$593$	37.0746	−	10.8861i	1.52247	−	0.447038i	0.589735	−	0.807597i	$-0.299232\pi$
$593$	37.0746	−	10.8861i	1.52247	−	0.447038i	0.932736	+	0.360559i	$0.117414\pi$
$594$	14.8635	−	44.3591i	0.609859	−	1.82008i
$595$	20.8787	+	3.00190i	0.855943	+	0.123066i
$596$	25.2694	−	25.0664i	1.03507	−	1.02676i
$597$	−24.7306			−1.01216
$598$	−29.3060	+	6.67736i	−1.19841	+	0.273058i
$599$			45.5875i			1.86266i	0.364181	+	0.931328i	$0.381349\pi$
$599$			45.5875i			1.86266i	−0.364181	+	0.931328i	$0.618651\pi$
$600$	−6.59782	−	5.38301i	−0.269355	−	0.219761i
$601$	−1.02920	+	7.15828i	−0.0419821	+	0.291992i	0.958004	+	0.286754i	$0.0925763\pi$
$601$	−1.02920	+	7.15828i	−0.0419821	+	0.291992i	−0.999986	+	0.00523782i	$0.998333\pi$
$602$	−13.6968	+	40.8771i	−0.558241	+	1.66603i
$603$	7.85522	+	26.7524i	0.319889	+	1.08944i
$604$	23.0099	−	17.0806i	0.936258	−	0.695000i
$605$	1.22137	+	1.40954i	0.0496560	+	0.0573060i
$606$	−0.582898	−	2.30314i	−0.0236786	−	0.0935588i
$607$	5.16295	−	17.5834i	0.209558	−	0.713687i	−0.785889	−	0.618367i	$-0.787794\pi$
$607$	5.16295	−	17.5834i	0.209558	−	0.713687i	0.995447	−	0.0953200i	$-0.0303874\pi$
$608$	6.05767	−	31.7406i	0.245671	−	1.28725i
$609$	−13.6153	+	21.1858i	−0.551719	+	0.858492i
$610$	2.90566	−	5.77565i	0.117647	−	0.233849i
$611$	−6.81392	+	7.86368i	−0.275662	+	0.318131i
$612$	−6.06444	+	80.2428i	−0.245140	+	3.24362i
$613$	−6.02289	−	41.8901i	−0.243262	−	1.69193i	−0.635532	−	0.772075i	$-0.719219\pi$
$613$	−6.02289	−	41.8901i	−0.243262	−	1.69193i	0.392270	−	0.919850i	$-0.371690\pi$
$614$	3.16314	−	3.38374i	0.127654	−	0.136557i
$615$	−0.743265	−	1.62752i	−0.0299713	−	0.0656280i
$616$	26.6003	−	18.2314i	1.07176	−	0.734565i
$617$	12.4283	+	5.67582i	0.500345	+	0.228500i	0.649568	−	0.760304i	$-0.274950\pi$
$617$	12.4283	+	5.67582i	0.500345	+	0.228500i	−0.149223	+	0.988804i	$0.547677\pi$
$618$	−1.71332	−	0.0646508i	−0.0689199	−	0.00260064i
$619$	8.39996	+	13.0706i	0.337623	+	0.525351i	0.968004	−	0.250934i	$-0.0807378\pi$
$619$	8.39996	+	13.0706i	0.337623	+	0.525351i	−0.630381	+	0.776286i	$0.717101\pi$
$620$	−0.514435	−	2.41160i	−0.0206602	−	0.0968523i
$621$	−43.6186	−	7.33744i	−1.75035	−	0.294441i
$622$	11.9942	−	1.26505i	0.480922	−	0.0507238i
$623$	27.1488	+	42.2444i	1.08769	+	1.69249i
$624$	51.3253	−	14.6219i	2.05466	−	0.585343i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	−26.6255	+	10.9658i	−1.06417	+	0.438282i
$627$	25.6239	+	56.1086i	1.02332	+	2.24076i
$628$	−17.6196	−	13.3011i	−0.703097	−	0.530770i
$629$	66.8716	−	9.61469i	2.66635	−	0.383363i
$630$	4.89385	−	26.8152i	0.194976	−	1.06834i
$631$	−18.4392	+	21.2799i	−0.734051	+	0.847140i	−0.992922	−	0.118772i	$-0.962104\pi$
$631$	−18.4392	+	21.2799i	−0.734051	+	0.847140i	0.258870	+	0.965912i	$0.416650\pi$
$632$	−6.10678	+	23.3361i	−0.242915	+	0.928261i
$633$	28.4899	+	18.3094i	1.13237	+	0.727732i
$634$	9.07734	−	13.0177i	0.360507	−	0.517001i
$635$	1.73344	−	5.90354i	0.0687893	−	0.234275i
$636$	27.7666	+	75.3721i	1.10102	+	2.98870i
$637$	10.3977	−	9.00964i	0.411971	−	0.356975i
$638$	11.4937	−	6.78820i	0.455038	−	0.268748i
$639$	17.4581	+	59.4567i	0.690630	+	2.35207i
$640$	10.7841	−	3.42099i	0.426279	−	0.135227i
$641$	7.87702	+	1.13254i	0.311124	+	0.0447328i	0.296108	−	0.955154i	$-0.404311\pi$
$641$	7.87702	+	1.13254i	0.311124	+	0.0447328i	0.0150155	+	0.999887i	$0.495220\pi$
$642$	−25.8565	+	20.7506i	−1.02047	+	0.818962i
$643$			9.38381i			0.370061i	0.982733	+	0.185031i	$0.0592384\pi$
$643$			9.38381i			0.370061i	−0.982733	+	0.185031i	$0.940762\pi$
$644$	−20.9497	−	22.1522i	−0.825536	−	0.872920i
$645$		−	28.8710i		−	1.13680i
$646$	−33.5518	−	41.8076i	−1.32008	−	1.64490i
$647$	−26.9425	−	3.87375i	−1.05922	−	0.152293i	−0.409380	−	0.912364i	$-0.634255\pi$
$647$	−26.9425	−	3.87375i	−1.05922	−	0.152293i	−0.649840	+	0.760071i	$0.725164\pi$
$648$	26.9107	+	3.05798i	1.05715	+	0.120129i
$649$	−10.3428	−	35.2243i	−0.405989	−	1.38267i
$650$	3.18716	+	5.39645i	0.125011	+	0.211666i
$651$	8.91707	−	7.72668i	0.349487	−	0.302833i
$652$	−11.5857	−	31.4493i	−0.453732	−	1.23165i
$653$	8.03178	−	27.3537i	0.314308	−	1.07043i	−0.639194	−	0.769046i	$-0.720732\pi$
$653$	8.03178	−	27.3537i	0.314308	−	1.07043i	0.953502	−	0.301388i	$-0.0974500\pi$
$654$	−10.6766	−	7.44483i	−0.417487	−	0.291116i
$655$	5.42718	+	3.48784i	0.212058	+	0.136281i
$656$	2.35024	+	0.357284i	0.0917614	+	0.0139496i
$657$	−66.4717	+	76.7124i	−2.59331	+	2.99283i
$658$	−10.3833	−	1.89499i	−0.404784	−	0.0738742i
$659$	−24.6513	+	3.54432i	−0.960277	+	0.138067i	−0.604589	−	0.796538i	$-0.706663\pi$
$659$	−24.6513	+	3.54432i	−0.960277	+	0.138067i	−0.355688	+	0.934605i	$0.615754\pi$
$660$	−13.0120	+	17.2366i	−0.506490	+	0.670934i
$661$	20.8752	+	45.7102i	0.811949	+	1.77792i	0.598794	+	0.800903i	$0.295647\pi$
$661$	20.8752	+	45.7102i	0.811949	+	1.77792i	0.213155	+	0.977018i	$0.431626\pi$
$662$	8.55411	+	20.7698i	0.332465	+	0.807241i
$663$	36.7780	−	80.5326i	1.42834	−	3.12763i
$664$	5.69953	+	32.7220i	0.221185	+	1.26986i
$665$	9.81691	+	15.2754i	0.380683	+	0.592355i
$666$	−9.15734	−	86.8226i	−0.354840	−	3.36431i
$667$	−8.03478	−	9.73239i	−0.311108	−	0.376840i
$668$	−2.62723	−	12.3161i	−0.101650	−	0.476523i
$669$	−15.4951	−	24.1109i	−0.599076	−	0.932180i
$670$	0.245210	−	6.49836i	0.00947330	−	0.251053i
$671$	−14.9159	−	6.81188i	−0.575823	−	0.262970i
$672$	39.2474	+	37.2863i	1.51400	+	1.43835i
$673$	4.55620	+	9.97668i	0.175629	+	0.384573i	0.976890	−	0.213741i	$-0.0685649\pi$
$673$	4.55620	+	9.97668i	0.175629	+	0.384573i	−0.801262	+	0.598314i	$0.795838\pi$
$674$	28.1949	+	26.3567i	1.08603	+	1.01522i
$675$	1.31255	+	9.12901i	0.0505202	+	0.351376i
$676$	−13.2419	−	1.00077i	−0.509303	−	0.0384911i
$677$	1.85226	−	2.13762i	0.0711882	−	0.0821555i	−0.719038	−	0.694970i	$-0.755417\pi$
$677$	1.85226	−	2.13762i	0.0711882	−	0.0821555i	0.790226	+	0.612815i	$0.209963\pi$
$678$	16.9163	+	8.51041i	0.649668	+	0.326840i
$679$	−7.56193	+	11.7666i	−0.290200	+	0.451560i
$680$	7.28723	−	17.2963i	0.279453	−	0.663281i
$681$	2.89275	−	9.85180i	0.110850	−	0.377522i
$682$	−6.06287	+	1.53444i	−0.232159	+	0.0587568i
$683$	−5.12648	−	5.91627i	−0.196159	−	0.226380i	0.649146	−	0.760664i	$-0.275127\pi$
$683$	−5.12648	−	5.91627i	−0.196159	−	0.226380i	−0.845305	+	0.534284i	$0.820581\pi$
$684$	−55.6227	+	41.2897i	−2.12679	+	1.57875i
$685$	1.37373	+	4.67849i	0.0524875	+	0.178756i
$686$	−16.6047	−	5.56379i	−0.633970	−	0.212426i
$687$	7.44224	−	51.7619i	0.283939	−	1.97484i
$688$	32.1018	+	20.9984i	1.22387	+	0.800555i
$689$		−	59.1202i		−	2.25230i
$690$	18.0163	+	9.60907i	0.685869	+	0.365811i
$691$	45.0991			1.71565			0.857825	−	0.513942i	$-0.171816\pi$
$691$	45.0991			1.71565			0.857825	+	0.513942i	$0.171816\pi$
$692$	2.43527	+	2.45499i	0.0925749	+	0.0933246i
$693$	−68.4297	−	9.83870i	−2.59943	−	0.373741i
$694$	−13.5777	−	4.54954i	−0.515404	−	0.172698i
$695$	−15.2331	+	4.47284i	−0.577824	+	0.169664i
$696$	15.1698	+	16.4925i	0.575011	+	0.625145i
$697$	2.98044	−	2.58256i	0.112892	−	0.0978216i
$698$	−1.27241	−	5.02752i	−0.0481613	−	0.190295i
$699$	−51.8737	−	15.2315i	−1.96204	−	0.576108i
$700$	−3.06931	+	5.56752i	−0.116009	+	0.210433i
$701$	−21.2853	−	13.6792i	−0.803933	−	0.516656i	0.0729642	−	0.997335i	$-0.476754\pi$
$701$	−21.2853	−	13.6792i	−0.803933	−	0.516656i	−0.876897	+	0.480678i	$0.840390\pi$
$702$	−51.6367	−	25.9778i	−1.94890	−	0.980469i
$703$	43.9524	+	38.0850i	1.65770	+	1.43640i
$704$	−9.70165	−	27.0045i	−0.365645	−	1.01777i
$705$	6.99656	−	1.00595i	0.263506	−	0.0378864i
$706$	9.61638	−	10.2871i	0.361917	−	0.387158i
$707$	−1.61348	+	0.736850i	−0.0606810	+	0.0277121i
$708$	54.2075	−	29.3164i	2.03724	−	1.10178i
$709$	8.31165	−	18.2000i	0.312150	−	0.683514i	−0.686915	−	0.726738i	$-0.741036\pi$
$709$	8.31165	−	18.2000i	0.312150	−	0.683514i	0.999065	+	0.0432237i	$0.0137628\pi$
$710$	0.544975	−	14.4425i	0.0204525	−	0.542016i
$711$	43.5028	−	27.9576i	1.63148	−	1.04849i
$712$	42.4798	−	13.8538i	1.59200	−	0.519192i
$713$	2.32731	+	5.43566i	0.0871584	+	0.203567i
$714$	89.3115	−	9.41985i	3.34240	−	0.352529i
$715$	13.3722	−	8.59378i	0.500091	−	0.321389i
$716$	2.24556	+	33.2828i	0.0839205	+	1.24384i
$717$	−45.0047	−	20.5530i	−1.68073	−	0.767564i
$718$	−7.46699	−	18.1302i	−0.278665	−	0.676614i
$719$	37.3098	−	17.0388i	1.39142	−	0.635440i	0.428084	−	0.903739i	$-0.359189\pi$
$719$	37.3098	−	17.0388i	1.39142	−	0.635440i	0.963336	+	0.268298i	$0.0864613\pi$
$720$	−21.9803	−	10.2531i	−0.819156	−	0.382111i
$721$	0.182176	+	1.26706i	0.00678460	+	0.0471879i
$722$	3.46072	−	18.9626i	0.128795	−	0.705714i
$723$	−21.3540	−	18.5033i	−0.794164	−	0.688147i
$724$	15.3537	+	5.79728i	0.570617	+	0.215454i
$725$	−1.42273	+	2.21381i	−0.0528388	+	0.0822187i
$726$	6.51358	+	4.54195i	0.241742	+	0.168568i
$727$	−15.3475	−	4.50642i	−0.569206	−	0.167134i	−0.0155495	−	0.999879i	$-0.504950\pi$
$727$	−15.3475	−	4.50642i	−0.569206	−	0.167134i	−0.553657	+	0.832745i	$0.686768\pi$
$728$	−17.6193	−	35.7374i	−0.653016	−	1.32452i
$729$	16.5265	+	19.0726i	0.612092	+	0.706392i
$730$	20.3846	−	12.0392i	0.754469	−	0.445593i
$731$	61.0584	−	17.9284i	2.25832	−	0.663104i
$732$	5.95968	−	26.8740i	0.220276	−	0.993290i
$733$	0.212840	−	1.48033i	0.00786141	−	0.0546773i	−0.985513	−	0.169599i	$-0.945753\pi$
$733$	0.212840	−	1.48033i	0.00786141	−	0.0546773i	0.993375	+	0.114922i	$0.0366618\pi$
$734$	6.18804	+	7.71066i	0.228405	+	0.284606i
$735$	−9.34626			−0.344742
$736$	−23.7879	+	13.0436i	−0.876834	+	0.480793i
$737$	−16.4932			−0.607533
$738$	−3.18974	−	3.97460i	−0.117416	−	0.146307i
$739$	−2.42772	+	16.8851i	−0.0893050	+	0.621130i	0.895186	+	0.445693i	$0.147043\pi$
$739$	−2.42772	+	16.8851i	−0.0893050	+	0.621130i	−0.984491	+	0.175436i	$0.943866\pi$
$740$	−4.40851	+	19.8793i	−0.162060	+	0.730778i
$741$	73.1253	−	21.4715i	2.68632	−	0.788776i
$742$	51.6373	−	30.4972i	1.89566	−	1.11959i
$743$	6.78609	+	7.83157i	0.248958	+	0.287312i	0.866449	−	0.499265i	$-0.166397\pi$
$743$	6.78609	+	7.83157i	0.248958	+	0.287312i	−0.617492	+	0.786577i	$0.711851\pi$
$744$	−4.64248	−	9.41638i	−0.170202	−	0.345221i
$745$	17.0756	+	5.01386i	0.625603	+	0.183694i
$746$	9.36071	+	6.52727i	0.342720	+	0.238980i
$747$	38.4962	−	59.9012i	1.40850	−	2.19167i
$748$	−44.5333	−	16.8149i	−1.62830	−	0.614815i
$749$	18.7068	+	16.2095i	0.683532	+	0.592284i
$750$	0.764395	−	4.18840i	0.0279117	−	0.152939i
$751$	2.82662	+	19.6596i	0.103145	+	0.717389i	0.974115	+	0.226053i	$0.0725821\pi$
$751$	2.82662	+	19.6596i	0.103145	+	0.717389i	−0.870970	+	0.491336i	$0.836509\pi$
$752$	−3.97019	+	8.51115i	−0.144778	+	0.310370i
$753$	−19.4517	+	8.88328i	−0.708858	+	0.323725i
$754$	−6.28081	−	15.2501i	−0.228734	−	0.555377i
$755$	13.0335	+	5.95219i	0.474337	+	0.216622i
$756$	−3.94705	−	58.5016i	−0.143553	−	2.12768i
$757$	33.6668	−	21.6363i	1.22364	−	0.786386i	0.240751	−	0.970587i	$-0.422606\pi$
$757$	33.6668	−	21.6363i	1.22364	−	0.786386i	0.982889	+	0.184201i	$0.0589698\pi$
$758$	21.0393	−	2.21906i	0.764183	−	0.0805998i
$759$	22.6306	−	46.5802i	0.821440	−	1.69076i
$760$	15.3605	−	5.00947i	0.557185	−	0.181712i
$761$	1.83316	−	1.17810i	0.0664519	−	0.0427061i	−0.506993	−	0.861950i	$-0.669243\pi$
$761$	1.83316	−	1.17810i	0.0664519	−	0.0427061i	0.573445	+	0.819244i	$0.305607\pi$
$762$	0.987781	−	26.1773i	0.0357835	−	0.948304i
$763$	−4.03694	+	8.83966i	−0.146147	+	0.320017i
$764$	−15.3915	+	8.32401i	−0.556846	+	0.301152i
$765$	−36.5998	+	16.7146i	−1.32327	+	0.604317i
$766$	18.3739	−	19.6553i	0.663875	−	0.710175i
$767$	−44.8972	+	6.45524i	−1.62114	+	0.233085i
$768$	40.9372	−	25.3851i	1.47719	−	0.916007i
$769$	−19.9741	−	17.3076i	−0.720283	−	0.624129i	0.215583	−	0.976486i	$-0.430835\pi$
$769$	−19.9741	−	17.3076i	−0.720283	−	0.624129i	−0.935866	+	0.352357i	$0.885380\pi$
$770$	14.4041	+	7.24654i	0.519088	+	0.261147i
$771$	−19.9144	−	12.7982i	−0.717200	−	0.460917i
$772$	8.00167	−	14.5145i	0.287986	−	0.522388i
$773$	26.2652	+	7.71216i	0.944694	+	0.277387i	0.717576	−	0.696480i	$-0.245251\pi$
$773$	26.2652	+	7.71216i	0.944694	+	0.277387i	0.227118	+	0.973867i	$0.427070\pi$
$774$	−20.1764	−	79.7207i	−0.725225	−	2.86550i
$775$	0.931787	−	0.807398i	0.0334708	−	0.0290026i
$776$	8.42531	+	9.15991i	0.302451	+	0.328822i
$777$	−93.4852	+	27.4497i	−3.35376	+	0.984754i
$778$	2.18238	+	0.731256i	0.0782419	+	0.0262168i
$779$	3.36031	+	0.483139i	0.120395	+	0.0173103i
$780$	18.7920	+	18.9442i	0.672862	+	0.678311i
$781$	−36.6557			−1.31164
$782$	−9.13412	+	44.0691i	−0.326635	+	1.57591i
$783$		−	24.2706i		−	0.867359i
$784$	6.79769	−	10.3922i	0.242775	−	0.371148i
$785$	1.57090	−	10.9258i	0.0560678	−	0.389960i
$786$	26.0438	+	8.72659i	0.928953	+	0.311267i
$787$	−2.17728	−	7.41513i	−0.0776115	−	0.264321i	0.911542	−	0.411208i	$-0.134893\pi$
$787$	−2.17728	−	7.41513i	−0.0776115	−	0.264321i	−0.989153	+	0.146887i	$0.953075\pi$
$788$	−1.69635	+	1.25923i	−0.0604299	+	0.0448581i
$789$	−5.21797	−	6.02185i	−0.185765	−	0.214384i
$790$	−11.6923	+	2.95918i	−0.415993	+	0.105283i
$791$	3.98318	−	13.5655i	0.141626	−	0.482332i
$792$	−23.8838	+	56.6883i	−0.848674	+	2.01433i
$793$	−10.9536	+	17.0441i	−0.388973	+	0.605254i
$794$	−20.9754	−	10.5525i	−0.744389	−	0.374494i
$795$	−26.3005	+	30.3524i	−0.932783	+	1.07649i
$796$	16.3825	+	1.23812i	0.580662	+	0.0438841i
$797$	5.35287	+	37.2301i	0.189609	+	1.31876i	0.833023	+	0.553238i	$0.186608\pi$
$797$	5.35287	+	37.2301i	0.189609	+	1.31876i	−0.643415	+	0.765518i	$0.722483\pi$
$798$	56.4756	+	52.7936i	1.99921	+	1.86887i
$799$	6.47218	+	14.1721i	0.228969	+	0.501373i
$800$	4.10115	+	3.89623i	0.144997	+	0.137752i
$801$	−87.1314	−	39.7916i	−3.07864	−	1.40597i
$802$	−1.15990	+	30.7386i	−0.0409574	+	1.08542i
$803$	−32.4623	−	50.5123i	−1.14557	−	1.78254i
$804$	−5.77614	−	27.0778i	−0.203709	−	0.954959i
$805$	4.64267	−	14.5206i	0.163633	−	0.511785i
$806$	0.810507	+	7.68458i	0.0285489	+	0.270678i
$807$	27.2331	+	42.3756i	0.958651	+	1.49169i
$808$	0.270828	+	1.55487i	0.00952771	+	0.0547002i
$809$	−10.0626	+	22.0340i	−0.353781	+	0.774673i	0.646153	+	0.763208i	$0.276377\pi$
$809$	−10.0626	+	22.0340i	−0.353781	+	0.774673i	−0.999934	+	0.0114651i	$0.996350\pi$
$810$	5.15704	+	12.5215i	0.181200	+	0.439962i
$811$	−18.1073	−	39.6495i	−0.635833	−	1.39228i	−0.903424	−	0.428748i	$-0.858955\pi$
$811$	−18.1073	−	39.6495i	−0.635833	−	1.39228i	0.267591	−	0.963533i	$-0.413773\pi$
$812$	10.0799	−	13.3526i	0.353736	−	0.468586i
$813$	−67.4434	+	9.69690i	−2.36534	+	0.340085i
$814$	50.8046	+	9.27197i	1.78070	+	0.324982i
$815$	10.9740	−	12.6647i	0.384402	−	0.443624i
$816$	12.0099	−	79.0016i	0.420429	−	2.76561i
$817$	46.0840	+	29.6164i	1.61227	+	1.03615i
$818$	−24.7797	−	17.2790i	−0.866403	−	0.604147i
$819$	−24.0651	+	81.9580i	−0.840901	+	2.86385i
$820$	0.410886	+	1.11534i	0.0143487	+	0.0389495i
$821$	10.1938	−	8.83294i	0.355765	−	0.308272i	−0.458580	−	0.888653i	$-0.651642\pi$
$821$	10.1938	−	8.83294i	0.355765	−	0.308272i	0.814345	+	0.580381i	$0.197096\pi$
$822$	10.5572	+	17.8752i	0.368224	+	0.623470i
$823$	5.54358	+	18.8797i	0.193237	+	0.658104i	0.997924	+	0.0644051i	$0.0205150\pi$
$823$	5.54358	+	18.8797i	0.193237	+	0.658104i	−0.804687	+	0.593699i	$0.797667\pi$
$824$	1.13173	+	0.128604i	0.0394257	+	0.00448012i
$825$	−10.6884	−	1.53676i	−0.372121	−	0.0535030i
$826$	−28.7984	−	35.8846i	−1.00203	−	1.24858i
$827$			35.6933i			1.24118i	0.784136	+	0.620590i	$0.213107\pi$
$827$			35.6933i			1.24118i	−0.784136	+	0.620590i	$0.786893\pi$
$828$	56.4631	+	13.9426i	1.96223	+	0.484540i
$829$		−	42.8868i		−	1.48952i	−0.667332	−	0.744760i	$-0.732564\pi$
$829$		−	42.8868i		−	1.48952i	0.667332	−	0.744760i	$-0.267436\pi$
$830$	−12.9521	+	10.3945i	−0.449575	+	0.360798i
$831$	−31.6986	−	4.55757i	−1.09961	−	0.158100i
$832$	−34.7319	+	7.11651i	−1.20411	+	0.246720i
$833$	−5.80385	−	19.7661i	−0.201091	−	0.684855i
$834$	−58.2014	+	34.3740i	−2.01535	+	1.19027i
$835$	4.75864	−	4.12339i	0.164680	−	0.142696i
$836$	−14.1652	−	38.4513i	−0.489914	−	1.32987i
$837$	−3.20363	+	10.9106i	−0.110734	+	0.377125i
$838$	−15.9976	+	22.9421i	−0.552629	+	0.792521i
$839$	−27.7816	−	17.8541i	−0.959127	−	0.616394i	−0.0353707	−	0.999374i	$-0.511261\pi$
$839$	−27.7816	−	17.8541i	−0.959127	−	0.616394i	−0.923756	+	0.382981i	$0.874898\pi$
$840$	−6.85253	+	26.1859i	−0.236435	+	0.903498i
$841$	−14.4560	+	16.6831i	−0.498482	+	0.575279i
$842$	−0.844605	+	4.62791i	−0.0291070	+	0.159488i
$843$	−41.3236	+	5.94144i	−1.42326	+	0.204634i
$844$	−17.9562	−	13.5552i	−0.618077	−	0.466588i
$845$	−2.75828	−	6.03979i	−0.0948877	−	0.207775i
$846$	18.6164	−	7.66722i	0.640044	−	0.263604i
$847$	2.46286	−	5.39291i	0.0846248	−	0.185302i
$848$	−14.6202	−	51.3195i	−0.502060	−	1.76232i
$849$	11.0157	+	17.1408i	0.378060	+	0.588272i
$850$	9.33258	−	0.984325i	0.320105	−	0.0337621i
$851$	1.16481	−	48.8131i	0.0399293	−	1.67329i
$852$	−12.8373	−	60.1797i	−0.439800	−	2.06172i
$853$	−4.54049	−	7.06514i	−0.155463	−	0.241906i	0.754781	−	0.655976i	$-0.227743\pi$
$853$	−4.54049	−	7.06514i	−0.155463	−	0.241906i	−0.910245	+	0.414071i	$0.864107\pi$
$854$	−20.5372	−	0.774956i	−0.702769	−	0.0265184i
$855$	−31.5064	−	14.3885i	−1.07750	−	0.492076i
$856$	18.1672	−	12.4515i	0.620942	−	0.425584i
$857$	11.6793	+	25.5740i	0.398956	+	0.873592i	0.997375	+	0.0724087i	$0.0230686\pi$
$857$	11.6793	+	25.5740i	0.398956	+	0.873592i	−0.598419	+	0.801183i	$0.704204\pi$
$858$	46.2158	−	49.4390i	1.57778	−	1.68782i
$859$	5.01109	+	34.8529i	0.170976	+	1.18917i	0.876827	+	0.480805i	$0.159656\pi$
$859$	5.01109	+	34.8529i	0.170976	+	1.18917i	−0.705851	+	0.708360i	$0.749435\pi$
$860$	−1.44541	+	19.1253i	−0.0492881	+	0.652166i
$861$	−3.72449	+	4.29830i	−0.126930	+	0.146486i
$862$	6.86029	−	13.6364i	0.233662	−	0.464456i
$863$	−20.2262	+	31.4726i	−0.688509	+	1.07134i	0.304409	+	0.952541i	$0.401541\pi$
$863$	−20.2262	+	31.4726i	−0.688509	+	1.07134i	−0.992918	+	0.118800i	$0.962095\pi$
$864$	−51.2476	−	9.78057i	−1.74348	−	0.332742i
$865$	−0.487110	+	1.65894i	−0.0165622	+	0.0564058i
$866$	1.24356	+	4.91355i	0.0422579	+	0.166969i
$867$	−53.2956	−	61.5064i	−1.81001	−	2.08887i
$868$	−6.29383	+	4.67202i	−0.213627	+	0.158579i
$869$	8.61807	+	29.3505i	0.292348	+	0.995646i
$870$	−3.55967	+	10.6236i	−0.120684	+	0.360172i
$871$	−2.90012	+	20.1708i	−0.0982669	+	0.683461i
$872$	6.69985	+	5.46626i	0.226886	+	0.185111i
$873$		−	26.6803i		−	0.902991i
$874$	−33.8194	+	18.9005i	−1.14396	+	0.639319i
$875$	−3.17876			−0.107462
$876$	71.5601	−	70.9853i	2.41779	−	2.39837i
$877$	−3.55618	−	0.511301i	−0.120084	−	0.0172654i	0.0820110	−	0.996631i	$-0.473866\pi$
$877$	−3.55618	−	0.511301i	−0.120084	−	0.0172654i	−0.202095	+	0.979366i	$0.564775\pi$
$878$	0.133177	−	0.397457i	0.00449451	−	0.0134135i
$879$	−40.6557	+	11.9376i	−1.37128	+	0.402645i
$880$	9.48255	−	10.7667i	0.319657	−	0.362947i
$881$	−16.4289	+	14.2358i	−0.553505	+	0.479615i	−0.886125	−	0.463446i	$-0.846613\pi$
$881$	−16.4289	+	14.2358i	−0.553505	+	0.479615i	0.332620	+	0.943061i	$0.392067\pi$
$882$	−25.8076	+	6.53159i	−0.868986	+	0.219930i
$883$	9.53703	+	2.80032i	0.320946	+	0.0942384i	0.438238	−	0.898859i	$-0.355603\pi$
$883$	9.53703	+	2.80032i	0.320946	+	0.0942384i	−0.117291	+	0.993098i	$0.537421\pi$
$884$	−28.3950	+	51.5066i	−0.955026	+	1.73235i
$885$	25.9220	+	16.6591i	0.871359	+	0.559988i
$886$	−16.3354	+	32.4703i	−0.548799	+	1.09086i
$887$	20.9816	+	18.1806i	0.704492	+	0.610446i	0.931626	−	0.363417i	$-0.118390\pi$
$887$	20.9816	+	18.1806i	0.704492	+	0.610446i	−0.227134	+	0.973863i	$0.572936\pi$
$888$	2.57016	+	86.6559i	0.0862490	+	2.90798i
$889$	−19.3591	+	2.78342i	−0.649283	+	0.0933528i
$890$	16.3204	+	15.2564i	0.547062	+	0.511396i
$891$	31.2419	−	14.2677i	1.04664	−	0.477987i
$892$	9.05745	+	16.7477i	0.303266	+	0.560754i
$893$	−5.57148	+	12.1998i	−0.186442	+	0.408252i
$894$	75.7162	+	2.85709i	2.53233	+	0.0955555i
$895$	−14.0315	+	9.01747i	−0.469020	+	0.301421i
$896$	−24.1322	−	26.6648i	−0.806201	−	0.890807i
$897$	−52.9874	−	35.8674i	−1.76920	−	1.19758i
$898$	−2.73865	−	25.9657i	−0.0913899	−	0.866486i
$899$	−2.72947	+	1.75412i	−0.0910329	+	0.0585033i
$900$	−0.816343	−	12.0995i	−0.0272114	−	0.403317i
$901$	−80.5234	−	36.7738i	−2.68262	−	1.22511i
$902$	2.78748	−	1.14803i	0.0928129	−	0.0382253i
$903$	−83.4805	+	38.1243i	−2.77806	+	1.26870i
$904$	−10.7799	−	6.48452i	−0.358536	−	0.215672i
$905$	1.16782	+	8.12235i	0.0388196	+	0.269996i
$906$	60.0127	+	10.9525i	1.99379	+	0.363872i
$907$	40.8454	+	35.3928i	1.35625	+	1.17520i	0.967210	+	0.253976i	$0.0817386\pi$
$907$	40.8454	+	35.3928i	1.35625	+	1.17520i	0.389040	+	0.921221i	$0.372807\pi$
$908$	−2.40949	+	6.38138i	−0.0799618	+	0.211774i
$909$	1.82925	−	2.84636i	0.0606723	−	0.0944080i
$910$	11.3951	−	16.3417i	0.377746	−	0.541722i
$911$	−24.0554	−	7.06330i	−0.796990	−	0.234017i	−0.142210	−	0.989837i	$-0.545421\pi$
$911$	−24.0554	−	7.06330i	−0.796990	−	0.234017i	−0.654781	+	0.755819i	$0.727239\pi$
$912$	58.1668	−	36.7220i	1.92609	−	1.21599i
$913$	27.5829	+	31.8324i	0.912861	+	1.05350i
$914$	15.4169	+	26.1036i	0.509946	+	0.863430i
$915$	13.2059	−	3.87761i	0.436574	−	0.128190i
$916$	−7.52145	+	33.9165i	−0.248516	+	1.12063i
$917$	2.91847	−	20.2984i	0.0963763	−	0.670312i
$918$	−67.5014	+	54.1720i	−2.22788	+	1.78794i
$919$	27.4420			0.905228			0.452614	−	0.891707i	$-0.350492\pi$
$919$	27.4420			0.905228			0.452614	+	0.891707i	$0.350492\pi$
$920$	−11.4536	−	7.26739i	−0.377614	−	0.239599i
$921$	9.86050			0.324914
$922$	−2.77972	+	2.23081i	−0.0915452	+	0.0734678i
$923$	−6.44546	+	44.8292i	−0.212155	+	1.47557i
$924$	67.0219	+	14.8631i	2.20486	+	0.488959i
$925$	−9.76872	+	2.86836i	−0.321194	+	0.0943109i
$926$	9.66203	+	16.3596i	0.317514	+	0.537609i
$927$	−1.59903	−	1.84538i	−0.0525191	−	0.0606103i
$928$	−9.22338	−	11.6847i	−0.302772	−	0.383569i
$929$	30.3331	+	8.90659i	0.995195	+	0.292216i	0.738483	−	0.674272i	$-0.235543\pi$
$929$	30.3331	+	8.90659i	0.995195	+	0.292216i	0.256712	+	0.966488i	$0.417361\pi$
$930$	3.00249	−	4.30584i	0.0984554	−	0.141194i
$931$	9.58755	−	14.9185i	0.314219	−	0.488935i
$932$	33.6005	+	12.6869i	1.10062	+	0.415574i
$933$	19.4036	+	16.8134i	0.635247	+	0.550445i
$934$	36.0790	+	6.58452i	1.18054	+	0.215452i
$935$	−3.38724	−	23.5588i	−0.110775	−	0.770454i
$936$	65.1289	+	39.1774i	2.12880	+	1.28055i
$937$	1.39518	−	0.637157i	0.0455785	−	0.0208150i	−0.392495	−	0.919754i	$-0.628388\pi$
$937$	1.39518	−	0.637157i	0.0455785	−	0.0208150i	0.438074	+	0.898939i	$0.355661\pi$
$938$	−19.1138	+	7.87207i	−0.624087	+	0.257032i
$939$	−55.7596	−	25.4646i	−1.81965	−	0.831005i
$940$	−4.68515	+	0.316103i	−0.152813	+	0.0103101i
$941$	43.9056	−	28.2164i	1.43128	−	0.919828i	0.431437	−	0.902143i	$-0.358007\pi$
$941$	43.9056	−	28.2164i	1.43128	−	0.919828i	0.999844	−	0.0176856i	$-0.00562979\pi$
$942$	−4.92942	−	46.7368i	−0.160609	−	1.52277i
$943$	−1.48330	−	2.43383i	−0.0483029	−	0.0792564i
$944$	−37.3768	+	16.7064i	−1.21651	+	0.543747i
$945$	24.6633	−	15.8501i	0.802297	−	0.515605i
$946$	48.6101	+	1.83426i	1.58045	+	0.0596371i
$947$	16.0177	−	35.0738i	0.520504	−	1.13974i	−0.448744	−	0.893660i	$-0.648129\pi$
$947$	16.0177	−	35.0738i	0.520504	−	1.13974i	0.969248	−	0.246084i	$-0.0791441\pi$
$948$	−45.1682	+	24.4277i	−1.46699	+	0.793376i
$949$	−67.4836	+	30.8187i	−2.19061	+	1.00042i
$950$	5.90140	+	5.51666i	0.191467	+	0.178984i
$951$	33.4402	−	4.80798i	1.08437	−	0.155909i
$952$	−59.6349	+	1.76873i	−1.93278	+	0.0573250i
$953$	23.5216	+	20.3816i	0.761941	+	0.660225i	0.946539	−	0.322589i	$-0.104553\pi$
$953$	23.5216	+	20.3816i	0.761941	+	0.660225i	−0.184598	+	0.982814i	$0.559098\pi$
$954$	−51.4112	+	102.191i	−1.66450	+	3.30856i
$955$	−7.36023	−	4.73013i	−0.238172	−	0.153064i
$956$	28.7838	+	15.8682i	0.930936	+	0.513214i
$957$	27.2652	+	8.00579i	0.881360	+	0.258791i
$958$	13.6153	−	3.44587i	0.439890	−	0.111331i
$959$	11.7138	−	10.1501i	0.378259	−	0.327764i
$960$	20.9973	+	11.7974i	0.677685	+	0.380759i
$961$	−28.2857	+	8.30544i	−0.912443	+	0.267917i
$962$	20.2728	−	60.5026i	0.653621	−	1.95068i
$963$	−46.7354	−	6.71953i	−1.50603	−	0.216534i
$964$	13.2193	+	13.3264i	0.425766	+	0.429214i
$965$	8.28700			0.266768
$966$	3.99403	−	64.7829i	0.128506	−	2.08436i
$967$		−	0.273814i		−	0.00880525i	−0.999990	−	0.00440263i	$-0.998599\pi$
$967$		−	0.273814i		−	0.00880525i	0.999990	−	0.00440263i	$-0.00140140\pi$
$968$	−4.08745	−	3.33486i	−0.131376	−	0.107186i
$969$	16.2404	−	112.954i	0.521716	−	3.62862i
$970$	−1.97704	+	5.90032i	−0.0634789	+	0.189448i
$971$	3.03927	+	10.3508i	0.0975347	+	0.332173i	0.993776	−	0.111393i	$-0.0355313\pi$
$971$	3.03927	+	10.3508i	0.0975347	+	0.332173i	−0.896242	+	0.443566i	$0.853713\pi$
$972$	1.38199	+	1.86172i	0.0443272	+	0.0597147i
$973$	33.0485	+	38.1400i	1.05949	+	1.22271i
$974$	−3.69960	−	14.6179i	−0.118543	−	0.468386i
$975$	−3.75884	+	12.8014i	−0.120379	+	0.409974i
$976$	−5.29335	+	17.5040i	−0.169436	+	0.560288i
$977$	6.20685	−	9.65804i	0.198575	−	0.308988i	−0.727658	−	0.685940i	$-0.759391\pi$
$977$	6.20685	−	9.65804i	0.198575	−	0.308988i	0.926233	+	0.376952i	$0.123028\pi$
$978$	32.0650	−	63.7362i	1.02532	−	2.03806i
$979$	37.1057	−	42.8222i	1.18590	−	1.36860i
$980$	6.19132	+	0.467915i	0.197774	+	0.0149470i
$981$	−2.63807	−	18.3482i	−0.0842272	−	0.585813i
$982$	−12.4181	+	13.2842i	−0.396278	+	0.423916i
$983$	−23.6209	−	51.7225i	−0.753389	−	1.64969i	−0.760177	−	0.649716i	$-0.774888\pi$
$983$	−23.6209	−	51.7225i	−0.753389	−	1.64969i	0.00678789	−	0.999977i	$-0.497839\pi$
$984$	2.86100	+	4.17431i	0.0912055	+	0.133072i
$985$	−0.960862	−	0.438811i	−0.0306156	−	0.0139817i
$986$	−24.6779	−	0.931201i	−0.785904	−	0.0296555i
$987$	−12.1477	−	18.9022i	−0.386665	−	0.601662i
$988$	−49.5159	+	10.5626i	−1.57531	+	0.336040i
$989$	−5.45741	−	45.6666i	−0.173536	−	1.45211i
$990$	−30.5874	+	3.22611i	−0.972132	+	0.102533i
$991$	−2.41034	−	3.75056i	−0.0765670	−	0.119141i	0.800858	−	0.598854i	$-0.204377\pi$
$991$	−2.41034	−	3.75056i	−0.0765670	−	0.119141i	−0.877425	+	0.479713i	$0.840741\pi$
$992$	2.60393	+	6.47019i	0.0826749	+	0.205429i
$993$	−19.8642	+	43.4965i	−0.630371	+	1.38032i
$994$	−42.4800	+	17.4955i	−1.34738	+	0.554924i
$995$	3.41247	+	7.47226i	0.108183	+	0.236887i
$996$	−42.6011	+	56.4326i	−1.34987	+	1.78813i
$997$	−49.5009	+	7.11716i	−1.56771	+	0.225403i	−0.870757	−	0.491713i	$-0.836371\pi$
$997$	−49.5009	+	7.11716i	−1.56771	+	0.225403i	−0.696954	+	0.717116i	$0.745462\pi$
$998$	4.88961	−	26.7920i	0.154778	−	0.848086i
$999$	61.4911	−	70.9645i	1.94549	−	2.24522i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bb.a.11.14	✓	480
8.3	odd	2		920.2.bb.b.11.33	yes	480
23.21	odd	22		920.2.bb.b.251.33	yes	480
184.67	even	22	inner	920.2.bb.a.251.14	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bb.a.11.14	✓	480	1.1	even	1	trivial
920.2.bb.a.251.14	yes	480	184.67	even	22	inner
920.2.bb.b.11.33	yes	480	8.3	odd	2
920.2.bb.b.251.33	yes	480	23.21	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:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.885153 - 1.10295i) q^{2} +(0.428448 - 2.97992i) q^{3} +(-0.433008 + 1.95256i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-3.66596 + 2.16513i) q^{6} +(2.08164 + 2.40234i) q^{7} +(2.53686 - 1.25073i) q^{8} +(-5.81789 - 1.70829i) q^{9} +(1.16004 + 0.808899i) q^{10} +(1.93917 - 3.01740i) q^{11} +(5.63297 + 2.12690i) q^{12} +(-3.34924 - 2.90214i) q^{13} +(0.807099 - 4.42239i) q^{14} +(0.428448 + 2.97992i) q^{15} +(-3.62501 - 1.69095i) q^{16} +(-6.03608 + 2.75658i) q^{17} +(3.26557 + 7.92895i) q^{18} +(-5.19606 - 2.37296i) q^{19} +(-0.134632 - 1.99546i) q^{20} +(8.05067 - 5.17385i) q^{21} +(-5.04451 + 0.532054i) q^{22} +(1.24098 + 4.63249i) q^{23} +(-2.64016 - 8.09553i) q^{24} +(0.841254 - 0.540641i) q^{25} +(-0.236325 + 6.26289i) q^{26} +(-3.83133 + 8.38944i) q^{27} +(-5.59210 + 3.02430i) q^{28} +(-2.39375 + 1.09319i) q^{29} +(2.90747 - 3.11025i) q^{30} +(1.22038 - 0.175464i) q^{31} +(1.34365 + 5.49496i) q^{32} +(-8.16080 - 7.07137i) q^{33} +(8.38324 + 4.21751i) q^{34} +(-2.67414 - 1.71857i) q^{35} +(5.85474 - 10.6201i) q^{36} +(-9.76872 - 2.86836i) q^{37} +(1.98205 + 7.83145i) q^{38} +(-10.0831 + 8.73707i) q^{39} +(-2.08173 + 1.91478i) q^{40} +(-0.570236 + 0.167436i) q^{41} +(-12.8326 - 4.29986i) q^{42} +(-9.49229 - 1.36479i) q^{43} +(5.05200 + 5.09291i) q^{44} +6.06351 q^{45} +(4.01096 - 5.46921i) q^{46} -2.34790i q^{47} +(-6.59204 + 10.0778i) q^{48} +(-0.441815 + 3.07289i) q^{49} +(-1.34094 - 0.449313i) q^{50} +(5.62826 + 19.1681i) q^{51} +(7.11685 - 5.28296i) q^{52} +(8.73607 + 10.0820i) q^{53} +(12.6445 - 3.20016i) q^{54} +(-1.01052 + 3.44150i) q^{55} +(8.28552 + 3.49084i) q^{56} +(-9.29749 + 14.4672i) q^{57} +(3.32457 + 1.67255i) q^{58} +(6.70259 - 7.73520i) q^{59} +(-6.00401 - 0.453759i) q^{60} +(-0.650622 - 4.52517i) q^{61} +(-1.27375 - 1.19071i) q^{62} +(-8.00688 - 17.5326i) q^{63} +(4.87135 - 6.34586i) q^{64} +(4.03120 + 1.84099i) q^{65} +(-0.575832 + 15.2602i) q^{66} +(-2.48603 - 3.86834i) q^{67} +(-2.76873 - 12.9795i) q^{68} +(14.3362 - 1.71325i) q^{69} +(0.471527 + 4.47064i) q^{70} +(-5.52515 - 8.59730i) q^{71} +(-16.8958 + 2.94292i) q^{72} +(6.95418 - 15.2275i) q^{73} +(5.48315 + 13.3134i) q^{74} +(-1.25063 - 2.73851i) q^{75} +(6.88330 - 9.11813i) q^{76} +(11.2855 - 1.62261i) q^{77} +(18.5617 + 3.38755i) q^{78} +(-5.58490 + 6.44532i) q^{79} +(3.95457 + 0.601175i) q^{80} +(8.05551 + 5.17696i) q^{81} +(0.689421 + 0.480737i) q^{82} +(-3.30843 + 11.2675i) q^{83} +(6.61627 + 17.9598i) q^{84} +(5.01496 - 4.34548i) q^{85} +(6.89684 + 11.6776i) q^{86} +(2.23202 + 7.60156i) q^{87} +(1.14545 - 10.0801i) q^{88} +(15.6366 + 2.24820i) q^{89} +(-5.36713 - 6.68776i) q^{90} -14.0872i q^{91} +(-9.58259 + 0.417190i) q^{92} -3.71182i q^{93} +(-2.58962 + 2.07825i) q^{94} +(5.65413 + 0.812941i) q^{95} +(16.9502 - 1.64965i) q^{96} +(1.23966 + 4.22190i) q^{97} +(3.78032 - 2.23268i) q^{98} +(-16.4365 + 14.2423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 2 q^{2} - 4 q^{4} - 48 q^{5} + 5 q^{6} - q^{8} - 48 q^{9} + 2 q^{10} + 3 q^{12} + 32 q^{16} + 7 q^{18} - 4 q^{20} + 8 q^{21} + 4 q^{23} + 2 q^{24} - 48 q^{25} + 7 q^{26} + 12 q^{27} + 5 q^{30}+ \cdots - 98 q^{98}+O(q^{100}) \) 480 * q + 2 * q^2 - 4 * q^4 - 48 * q^5 + 5 * q^6 - q^8 - 48 * q^9 + 2 * q^10 + 3 * q^12 + 32 * q^16 + 7 * q^18 - 4 * q^20 + 8 * q^21 + 4 * q^23 + 2 * q^24 - 48 * q^25 + 7 * q^26 + 12 * q^27 + 5 * q^30 - 118 * q^32 - 23 * q^34 + 54 * q^36 + 8 * q^37 - 65 * q^38 + 43 * q^40 - 10 * q^42 - q^44 + 480 * q^45 - 184 * q^46 - 44 * q^48 - 48 * q^49 - 9 * q^50 - 7 * q^52 + 32 * q^53 - 27 * q^54 + 67 * q^56 - 40 * q^58 - 12 * q^59 + 14 * q^60 - 8 * q^61 - 128 * q^62 + 59 * q^64 + 88 * q^66 + 10 * q^68 - 20 * q^69 + 3 * q^72 - 11 * q^74 + 110 * q^76 + 118 * q^78 - 144 * q^79 - q^80 - 56 * q^81 - 59 * q^82 - 162 * q^84 - 18 * q^86 - 76 * q^88 + 7 * q^90 - 149 * q^92 + 168 * q^94 + 65 * q^96 - 98 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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