LMFDB - Embedded newform 572.2.bn.a.95.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(95,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 21, 5]))

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

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

chi := DirichletCharacter("572.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bn (of order $30$, degree $8$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$80$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			95.18
Character	$\chi$	$=$	572.95
Dual form			572.2.bn.a.283.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.10180 - 0.886582i) q^{2} +(0.133436 - 0.120147i) q^{3} +(0.427944 + 1.95368i) q^{4} +(-1.12761 - 1.55202i) q^{5} +(-0.253541 + 0.0140758i) q^{6} +(-0.344634 - 0.310310i) q^{7} +(1.26059 - 2.53198i) q^{8} +(-0.310215 + 2.95150i) q^{9} +O(q^{10})$	\(q+(-1.10180 - 0.886582i) q^{2} +(0.133436 - 0.120147i) q^{3} +(0.427944 + 1.95368i) q^{4} +(-1.12761 - 1.55202i) q^{5} +(-0.253541 + 0.0140758i) q^{6} +(-0.344634 - 0.310310i) q^{7} +(1.26059 - 2.53198i) q^{8} +(-0.310215 + 2.95150i) q^{9} +(-0.133590 + 2.70974i) q^{10} +(3.24088 + 0.704759i) q^{11} +(0.291831 + 0.209276i) q^{12} +(1.86494 - 3.08577i) q^{13} +(0.104604 + 0.647448i) q^{14} +(-0.336934 - 0.0716175i) q^{15} +(-3.63373 + 1.67213i) q^{16} +(1.89955 - 4.26646i) q^{17} +(2.95855 - 2.97695i) q^{18} +(0.999847 + 4.70391i) q^{19} +(2.54960 - 2.86716i) q^{20} -0.0832695 q^{21} +(-2.94599 - 3.64981i) q^{22} +(-6.52912 - 3.76959i) q^{23} +(-0.136001 - 0.489313i) q^{24} +(0.407819 - 1.25514i) q^{25} +(-4.79059 + 1.74649i) q^{26} +(0.629841 + 0.866901i) q^{27} +(0.458762 - 0.806101i) q^{28} +(1.66009 - 7.81009i) q^{29} +(0.307740 + 0.377628i) q^{30} +(3.77004 + 2.73909i) q^{31} +(5.48614 + 1.37924i) q^{32} +(0.517126 - 0.295341i) q^{33} +(-5.87550 + 3.01670i) q^{34} +(-0.0929950 + 0.884788i) q^{35} +(-5.89904 + 0.657017i) q^{36} +(1.57034 - 7.38788i) q^{37} +(3.06877 - 6.06924i) q^{38} +(-0.121894 - 0.635821i) q^{39} +(-5.35113 + 0.898626i) q^{40} +(3.46433 + 3.84753i) q^{41} +(0.0917466 + 0.0738252i) q^{42} +(-0.871081 - 1.50876i) q^{43} +(0.0100441 + 6.63324i) q^{44} +(4.93059 - 2.84668i) q^{45} +(3.85176 + 9.94196i) q^{46} +(2.20364 - 6.78212i) q^{47} +(-0.283970 + 0.659703i) q^{48} +(-0.709219 - 6.74777i) q^{49} +(-1.56212 + 1.02135i) q^{50} +(-0.259132 - 0.797526i) q^{51} +(6.82670 + 2.32296i) q^{52} +(-3.68446 - 2.67692i) q^{53} +(0.0746182 - 1.51356i) q^{54} +(-2.56065 - 5.82461i) q^{55} +(-1.22014 + 0.481434i) q^{56} +(0.698575 + 0.507544i) q^{57} +(-8.75337 + 7.13338i) q^{58} +(7.98363 - 8.86672i) q^{59} +(-0.00427126 - 0.688909i) q^{60} +(-3.76828 + 8.46370i) q^{61} +(-1.72541 - 6.36039i) q^{62} +(1.02279 - 0.920926i) q^{63} +(-4.82184 - 6.38356i) q^{64} +(-6.89211 + 0.585119i) q^{65} +(-0.831615 - 0.133067i) q^{66} +(-5.36147 + 9.28633i) q^{67} +(9.14820 + 1.88531i) q^{68} +(-1.32413 + 0.281452i) q^{69} +(0.886900 - 0.892416i) q^{70} +(9.88188 + 4.39970i) q^{71} +(7.08209 + 4.50608i) q^{72} +(-1.28768 - 3.96307i) q^{73} +(-8.28017 + 6.74775i) q^{74} +(-0.0963827 - 0.216479i) q^{75} +(-8.76206 + 3.96639i) q^{76} +(-0.898226 - 1.24856i) q^{77} +(-0.429403 + 0.808619i) q^{78} +(-7.00894 - 5.09229i) q^{79} +(6.69261 + 3.75411i) q^{80} +(-8.52052 - 1.81109i) q^{81} +(-0.405863 - 7.31064i) q^{82} +(-0.377326 - 0.519345i) q^{83} +(-0.0356347 - 0.162682i) q^{84} +(-8.76359 + 1.86276i) q^{85} +(-0.377876 + 2.43464i) q^{86} +(-0.716840 - 1.24160i) q^{87} +(5.86985 - 7.31744i) q^{88} +(-3.48441 - 2.01173i) q^{89} +(-7.95636 - 1.23489i) q^{90} +(-1.60027 + 0.484754i) q^{91} +(4.57047 - 14.3690i) q^{92} +(0.832152 - 0.0874627i) q^{93} +(-8.44089 + 5.51885i) q^{94} +(6.17313 - 6.85596i) q^{95} +(0.897761 - 0.475101i) q^{96} +(-2.03271 - 0.213646i) q^{97} +(-5.20103 + 8.06350i) q^{98} +(-3.08547 + 9.34684i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q - 15 q^{2} - 3 q^{4} - 15 q^{6} - 78 q^{9}+O(q^{10}) $ 640 * q - 15 * q^2 - 3 * q^4 - 15 * q^6 - 78 * q^9	$ 640 q - 15 q^{2} - 3 q^{4} - 15 q^{6} - 78 q^{9} - 4 q^{12} - 20 q^{13} - 12 q^{14} - 19 q^{16} - 10 q^{17} - 45 q^{20} - 15 q^{22} - 15 q^{24} + 104 q^{25} - 20 q^{26} - 15 q^{28} - 10 q^{29} + 45 q^{30} - 24 q^{33} + 4 q^{36} - 18 q^{37} - 14 q^{38} - 20 q^{40} - 30 q^{41} - 13 q^{42} - 108 q^{45} - 15 q^{46} + 35 q^{48} - 74 q^{49} - 90 q^{50} + 15 q^{52} - 8 q^{53} + 50 q^{56} + 27 q^{58} - 10 q^{61} - 5 q^{62} - 84 q^{64} - 146 q^{66} - 70 q^{68} - 26 q^{69} - 15 q^{72} - 55 q^{74} + 44 q^{77} + 24 q^{78} - 39 q^{80} + 30 q^{81} - 29 q^{82} + 30 q^{84} - 30 q^{85} - 75 q^{88} - 24 q^{89} + 30 q^{90} + 14 q^{92} + 66 q^{93} - 5 q^{94} - 30 q^{97}+O(q^{100}) $ 640 * q - 15 * q^2 - 3 * q^4 - 15 * q^6 - 78 * q^9 - 4 * q^12 - 20 * q^13 - 12 * q^14 - 19 * q^16 - 10 * q^17 - 45 * q^20 - 15 * q^22 - 15 * q^24 + 104 * q^25 - 20 * q^26 - 15 * q^28 - 10 * q^29 + 45 * q^30 - 24 * q^33 + 4 * q^36 - 18 * q^37 - 14 * q^38 - 20 * q^40 - 30 * q^41 - 13 * q^42 - 108 * q^45 - 15 * q^46 + 35 * q^48 - 74 * q^49 - 90 * q^50 + 15 * q^52 - 8 * q^53 + 50 * q^56 + 27 * q^58 - 10 * q^61 - 5 * q^62 - 84 * q^64 - 146 * q^66 - 70 * q^68 - 26 * q^69 - 15 * q^72 - 55 * q^74 + 44 * q^77 + 24 * q^78 - 39 * q^80 + 30 * q^81 - 29 * q^82 + 30 * q^84 - 30 * q^85 - 75 * q^88 - 24 * q^89 + 30 * q^90 + 14 * q^92 + 66 * q^93 - 5 * q^94 - 30 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−1.10180	−	0.886582i	−0.779093	−	0.626908i
$2$	−1.10180	−	0.886582i	−0.779093	−	0.626908i
$3$	0.133436	−	0.120147i	0.0770395	−	0.0693667i	−0.629711	−	0.776829i	$-0.716827\pi$
$3$	0.133436	−	0.120147i	0.0770395	−	0.0693667i	0.706751	+	0.707463i	$0.250160\pi$
$4$	0.427944	+	1.95368i	0.213972	+	0.976840i
$5$	−1.12761	−	1.55202i	−0.504282	−	0.694085i	0.478660	−	0.878000i	$-0.341123\pi$
$5$	−1.12761	−	1.55202i	−0.504282	−	0.694085i	−0.982942	+	0.183916i	$0.941123\pi$
$6$	−0.253541	+	0.0140758i	−0.103507	+	0.00574640i
$7$	−0.344634	−	0.310310i	−0.130260	−	0.117286i	0.601426	−	0.798928i	$-0.294599\pi$
$7$	−0.344634	−	0.310310i	−0.130260	−	0.117286i	−0.731686	+	0.681642i	$0.761266\pi$
$8$	1.26059	−	2.53198i	0.445685	−	0.895190i
$9$	−0.310215	+	2.95150i	−0.103405	+	0.983834i
$10$	−0.133590	+	2.70974i	−0.0422447	+	0.856895i
$11$	3.24088	+	0.704759i	0.977163	+	0.212493i
$11$	3.24088	+	0.704759i	0.977163	+	0.212493i
$12$	0.291831	+	0.209276i	0.0842444	+	0.0604127i
$13$	1.86494	−	3.08577i	0.517242	−	0.855839i
$13$	1.86494	−	3.08577i	0.517242	−	0.855839i
$14$	0.104604	+	0.647448i	0.0279566	+	0.173038i
$15$	−0.336934	−	0.0716175i	−0.0869960	−	0.0184916i
$16$	−3.63373	+	1.67213i	−0.908432	+	0.418033i
$17$	1.89955	−	4.26646i	0.460709	−	1.03477i	−0.522559	−	0.852603i	$-0.675023\pi$
$17$	1.89955	−	4.26646i	0.460709	−	1.03477i	0.983268	−	0.182166i	$-0.0583108\pi$
$18$	2.95855	−	2.97695i	0.697336	−	0.701673i
$19$	0.999847	+	4.70391i	0.229381	+	1.07915i	0.930552	+	0.366159i	$0.119327\pi$
$19$	0.999847	+	4.70391i	0.229381	+	1.07915i	−0.701172	+	0.712993i	$0.747339\pi$
$20$	2.54960	−	2.86716i	0.570107	−	0.641118i
$21$	−0.0832695			−0.0181709
$22$	−2.94599	−	3.64981i	−0.628087	−	0.778143i
$23$	−6.52912	−	3.76959i	−1.36142	−	0.786014i	−0.371604	−	0.928391i	$-0.621192\pi$
$23$	−6.52912	−	3.76959i	−1.36142	−	0.786014i	−0.989812	+	0.142377i	$0.954525\pi$
$24$	−0.136001	−	0.489313i	−0.0277610	−	0.0998807i
$25$	0.407819	−	1.25514i	0.0815638	−	0.251028i
$26$	−4.79059	+	1.74649i	−0.939512	+	0.342516i
$27$	0.629841	+	0.866901i	0.121213	+	0.166835i
$28$	0.458762	−	0.806101i	0.0866980	−	0.152339i
$29$	1.66009	−	7.81009i	0.308270	−	1.45030i	−0.502320	−	0.864682i	$-0.667520\pi$
$29$	1.66009	−	7.81009i	0.308270	−	1.45030i	0.810590	−	0.585615i	$-0.199147\pi$
$30$	0.307740	+	0.377628i	0.0561855	+	0.0689452i
$31$	3.77004	+	2.73909i	0.677118	+	0.491955i	0.872400	−	0.488792i	$-0.162562\pi$
$31$	3.77004	+	2.73909i	0.677118	+	0.491955i	−0.195282	+	0.980747i	$0.562562\pi$
$32$	5.48614	+	1.37924i	0.969821	+	0.243817i
$33$	0.517126	−	0.295341i	0.0900200	−	0.0514122i
$34$	−5.87550	+	3.01670i	−1.00764	+	0.517359i
$35$	−0.0929950	+	0.884788i	−0.0157190	+	0.149557i
$36$	−5.89904	+	0.657017i	−0.983174	+	0.109503i
$37$	1.57034	−	7.38788i	0.258163	−	1.21456i	−0.637720	−	0.770268i	$-0.720122\pi$
$37$	1.57034	−	7.38788i	0.258163	−	1.21456i	0.895883	−	0.444291i	$-0.146544\pi$
$38$	3.06877	−	6.06924i	0.497820	−	0.984560i
$39$	−0.121894	−	0.635821i	−0.0195187	−	0.101813i
$40$	−5.35113	+	0.898626i	−0.846088	+	0.142085i
$41$	3.46433	+	3.84753i	0.541038	+	0.600883i	0.950224	−	0.311567i	$-0.100854\pi$
$41$	3.46433	+	3.84753i	0.541038	+	0.600883i	−0.409186	+	0.912451i	$0.634187\pi$
$42$	0.0917466	+	0.0738252i	0.0141568	+	0.0113915i
$43$	−0.871081	−	1.50876i	−0.132839	−	0.230083i	0.791931	−	0.610610i	$-0.209076\pi$
$43$	−0.871081	−	1.50876i	−0.132839	−	0.230083i	−0.924770	+	0.380527i	$0.875743\pi$
$44$	0.0100441	+	6.63324i	0.00151420	+	0.999999i
$45$	4.93059	−	2.84668i	0.735009	−	0.424358i
$46$	3.85176	+	9.94196i	0.567911	+	1.46586i
$47$	2.20364	−	6.78212i	0.321434	−	0.989273i	−0.651590	−	0.758571i	$-0.725898\pi$
$47$	2.20364	−	6.78212i	0.321434	−	0.989273i	0.973024	−	0.230702i	$-0.0741023\pi$
$48$	−0.283970	+	0.659703i	−0.0409876	+	0.0952199i
$49$	−0.709219	−	6.74777i	−0.101317	−	0.963967i
$50$	−1.56212	+	1.02135i	−0.220917	+	0.144441i
$51$	−0.259132	−	0.797526i	−0.0362857	−	0.111676i
$52$	6.82670	+	2.32296i	0.946693	+	0.322136i
$53$	−3.68446	−	2.67692i	−0.506100	−	0.367703i	0.305242	−	0.952275i	$-0.401263\pi$
$53$	−3.68446	−	2.67692i	−0.506100	−	0.367703i	−0.811342	+	0.584572i	$0.801263\pi$
$54$	0.0746182	−	1.51356i	0.0101543	−	0.205970i
$55$	−2.56065	−	5.82461i	−0.345278	−	0.785390i
$56$	−1.22014	+	0.481434i	−0.163048	+	0.0643344i
$57$	0.698575	+	0.507544i	0.0925285	+	0.0672259i
$58$	−8.75337	+	7.13338i	−1.14937	+	0.936659i
$59$	7.98363	−	8.86672i	1.03938	−	1.15435i	0.0515729	−	0.998669i	$-0.483577\pi$
$59$	7.98363	−	8.86672i	1.03938	−	1.15435i	0.987808	−	0.155680i	$-0.0497568\pi$
$60$	−0.00427126	−	0.688909i	−0.000551417	−	0.0889378i
$61$	−3.76828	+	8.46370i	−0.482479	+	1.08367i	0.494275	+	0.869305i	$0.335433\pi$
$61$	−3.76828	+	8.46370i	−0.482479	+	1.08367i	−0.976755	+	0.214361i	$0.931233\pi$
$62$	−1.72541	−	6.36039i	−0.219127	−	0.807770i
$63$	1.02279	−	0.920926i	0.128860	−	0.116026i
$64$	−4.82184	−	6.38356i	−0.602730	−	0.797945i
$65$	−6.89211	+	0.585119i	−0.854861	+	0.0725751i
$66$	−0.831615	−	0.133067i	−0.102365	−	0.0163794i
$67$	−5.36147	+	9.28633i	−0.655007	+	1.13451i	0.326885	+	0.945064i	$0.394001\pi$
$67$	−5.36147	+	9.28633i	−0.655007	+	1.13451i	−0.981892	+	0.189442i	$0.939332\pi$
$68$	9.14820	+	1.88531i	1.10938	+	0.228627i
$69$	−1.32413	+	0.281452i	−0.159406	+	0.0338828i
$70$	0.886900	−	0.892416i	0.106005	−	0.106664i
$71$	9.88188	+	4.39970i	1.17276	+	0.522148i	0.898271	−	0.439442i	$-0.144824\pi$
$71$	9.88188	+	4.39970i	1.17276	+	0.522148i	0.274492	+	0.961589i	$0.411490\pi$
$72$	7.08209	+	4.50608i	0.834632	+	0.531047i
$73$	−1.28768	−	3.96307i	−0.150712	−	0.463843i	0.846990	−	0.531610i	$-0.178413\pi$
$73$	−1.28768	−	3.96307i	−0.150712	−	0.463843i	−0.997701	+	0.0677668i	$0.978413\pi$
$74$	−8.28017	+	6.74775i	−0.962550	+	0.784411i
$75$	−0.0963827	−	0.216479i	−0.0111293	−	0.0249969i
$76$	−8.76206	+	3.96639i	−1.00508	+	0.454977i
$77$	−0.898226	−	1.24856i	−0.102362	−	0.142287i
$78$	−0.429403	+	0.808619i	−0.0486204	+	0.0915581i
$79$	−7.00894	−	5.09229i	−0.788567	−	0.572928i	0.118971	−	0.992898i	$-0.462041\pi$
$79$	−7.00894	−	5.09229i	−0.788567	−	0.572928i	−0.907538	+	0.419970i	$0.862041\pi$
$80$	6.69261	+	3.75411i	0.748256	+	0.419722i
$81$	−8.52052	−	1.81109i	−0.946725	−	0.201233i
$82$	−0.405863	−	7.31064i	−0.0448201	−	0.807325i
$83$	−0.377326	−	0.519345i	−0.0414170	−	0.0570055i	0.787806	−	0.615923i	$-0.211217\pi$
$83$	−0.377326	−	0.519345i	−0.0414170	−	0.0570055i	−0.829223	+	0.558918i	$0.811217\pi$
$84$	−0.0356347	−	0.162682i	−0.00388806	−	0.0177500i
$85$	−8.76359	+	1.86276i	−0.950545	+	0.202044i
$86$	−0.377876	+	2.43464i	−0.0407474	+	0.262534i
$87$	−0.716840	−	1.24160i	−0.0768533	−	0.133114i
$88$	5.86985	−	7.31744i	0.625728	−	0.780041i
$89$	−3.48441	−	2.01173i	−0.369347	−	0.213243i	0.303826	−	0.952727i	$-0.401736\pi$
$89$	−3.48441	−	2.01173i	−0.369347	−	0.213243i	−0.673173	+	0.739485i	$0.735069\pi$
$90$	−7.95636	−	1.23489i	−0.838674	−	0.130169i
$91$	−1.60027	+	0.484754i	−0.167754	+	0.0508160i
$92$	4.57047	−	14.3690i	0.476505	−	1.49807i
$93$	0.832152	−	0.0874627i	0.0862902	−	0.00906946i
$94$	−8.44089	+	5.51885i	−0.870611	+	0.569226i
$95$	6.17313	−	6.85596i	0.633350	−	0.703406i
$96$	0.897761	−	0.475101i	0.0916273	−	0.0484898i
$97$	−2.03271	−	0.213646i	−0.206390	−	0.0216925i	0.000769181	−	1.00000i	$-0.499755\pi$
$97$	−2.03271	−	0.213646i	−0.206390	−	0.0216925i	−0.207159	+	0.978307i	$0.566422\pi$
$98$	−5.20103	+	8.06350i	−0.525383	+	0.814536i
$99$	−3.08547	+	9.34684i	−0.310101	+	0.939393i
$100$	2.62666	+	0.259619i	0.262666	+	0.0259619i
$101$	2.61750	+	5.87901i	0.260451	+	0.584983i	0.995682	−	0.0928344i	$-0.0295927\pi$
$101$	2.61750	+	5.87901i	0.260451	+	0.584983i	−0.735230	+	0.677817i	$0.762926\pi$
$102$	−0.421560	+	1.10846i	−0.0417406	+	0.109754i
$103$	−8.12693	+	2.64060i	−0.800771	+	0.260186i	−0.680684	−	0.732577i	$-0.738317\pi$
$103$	−8.12693	+	2.64060i	−0.800771	+	0.260186i	−0.120087	+	0.992763i	$0.538317\pi$
$104$	−5.46220	−	8.61188i	−0.535612	−	0.844464i
$105$	0.0938954	+	0.129236i	0.00916325	+	0.0126121i
$106$	1.68625	+	6.21602i	0.163783	+	0.603753i
$107$	10.4402	+	11.5951i	1.00930	+	1.12094i	0.992643	+	0.121075i	$0.0386343\pi$
$107$	10.4402	+	11.5951i	1.00930	+	1.12094i	0.0166526	+	0.999861i	$0.494699\pi$
$108$	−1.42411	+	1.60149i	−0.137035	+	0.154104i
$109$	20.0863			1.92392			0.961959	−	0.273195i	$-0.0880804\pi$
$109$	20.0863			1.92392			0.961959	+	0.273195i	$0.0880804\pi$
$110$	−2.34266	+	8.68780i	−0.223364	+	0.828349i
$111$	−0.678088	−	1.17448i	−0.0643612	−	0.111477i
$112$	1.77119	+	0.551309i	0.167361	+	0.0520938i
$113$	12.4027	−	2.63628i	1.16675	−	0.248001i	0.416489	−	0.909141i	$-0.363260\pi$
$113$	12.4027	−	2.63628i	1.16675	−	0.248001i	0.750263	+	0.661140i	$0.229927\pi$
$114$	−0.319713	−	1.17856i	−0.0299439	−	0.110382i
$115$	1.51182	+	14.3840i	0.140977	+	1.34131i
$116$	15.9688	−	0.0990072i	1.48267	−	0.00919259i
$117$	8.52913	+	6.46163i	0.788519	+	0.597378i
$118$	−16.6575	+	2.69124i	−1.53345	+	0.247749i
$119$	−1.97858	+	0.880920i	−0.181376	+	0.0807538i
$120$	−0.606069	+	0.762830i	−0.0553262	+	0.0696365i
$121$	10.0066	+	4.56808i	0.909694	+	0.415280i
$122$	11.6557	−	5.98445i	1.05526	−	0.541806i
$123$	0.924536	+	0.0971726i	0.0833626	+	0.00876176i
$124$	−3.73794	+	8.53762i	−0.335677	+	0.766701i
$125$	−11.5304	+	3.74646i	−1.03131	+	0.335093i
$126$	−1.94339	+	0.107891i	−0.173131	+	0.00961169i
$127$	1.01566	+	9.66333i	0.0901250	+	0.857482i	0.942423	+	0.334425i	$0.108542\pi$
$127$	1.01566	+	9.66333i	0.0901250	+	0.857482i	−0.852298	+	0.523057i	$0.824791\pi$
$128$	−0.346825	+	11.3084i	−0.0306552	+	0.999530i
$129$	−0.297506	−	0.0966655i	−0.0261939	−	0.00851092i
$130$	8.11251	+	5.46573i	0.711514	+	0.479376i
$131$	15.9643			1.39481			0.697405	−	0.716677i	$-0.254338\pi$
$131$	15.9643			1.39481			0.697405	+	0.716677i	$0.254338\pi$
$132$	0.798302	+	0.883909i	0.0694833	+	0.0769344i
$133$	1.11509	−	1.93139i	0.0966906	−	0.167473i
$134$	14.1404	−	5.47834i	1.22154	−	0.473256i
$135$	0.635235	−	1.95505i	0.0546723	−	0.168264i
$136$	−8.40805	−	10.1879i	−0.720984	−	0.873603i
$137$	−0.00595685	+	0.0133793i	−0.000508928	+	0.00114307i	−0.913800	−	0.406165i	$-0.866866\pi$
$137$	−0.00595685	+	0.0133793i	−0.000508928	+	0.00114307i	0.913291	+	0.407308i	$0.133532\pi$
$138$	1.70846	+	0.863842i	0.145434	+	0.0735351i
$139$	−3.33145	+	3.69995i	−0.282570	+	0.313826i	−0.867675	−	0.497132i	$-0.834387\pi$
$139$	−3.33145	+	3.69995i	−0.282570	+	0.313826i	0.585105	+	0.810957i	$0.301053\pi$
$140$	−1.76839	+	0.196958i	−0.149456	+	0.0166460i
$141$	−0.520802	−	1.16974i	−0.0438595	−	0.0985100i
$142$	−6.98720	−	13.6087i	−0.586353	−	1.14202i
$143$	8.21878	−	8.68629i	0.687289	−	0.726384i
$144$	−3.80806	−	11.2437i	−0.317339	−	0.936973i
$145$	−13.9933	+	6.23024i	−1.16208	+	0.517393i
$146$	−2.09482	+	5.50817i	−0.173368	+	0.455859i
$147$	−0.905357	−	0.815187i	−0.0746726	−	0.0672355i
$148$	15.1056	−	0.0936549i	1.24167	−	0.00769839i
$149$	−3.56761	−	1.58840i	−0.292270	−	0.130127i	0.255364	−	0.966845i	$-0.417805\pi$
$149$	−3.56761	−	1.58840i	−0.292270	−	0.130127i	−0.547634	+	0.836718i	$0.684471\pi$
$150$	−0.0857317	+	0.323969i	−0.00699996	+	0.0264519i
$151$	7.59895	+	2.46905i	0.618394	+	0.200928i	0.601427	−	0.798928i	$-0.294599\pi$
$151$	7.59895	+	2.46905i	0.618394	+	0.200928i	0.0169667	+	0.999856i	$0.494599\pi$
$152$	13.1706	+	3.39810i	1.06828	+	0.275622i
$153$	12.0032	+	6.93005i	0.970401	+	0.560261i
$154$	−0.117285	+	2.17202i	−0.00945109	+	0.175027i
$155$		−	8.93980i		−	0.718062i
$156$	1.19003	−	0.510238i	0.0952783	−	0.0408518i
$157$	−7.41227	+	22.8126i	−0.591564	+	1.82065i	−0.0204263	+	0.999791i	$0.506502\pi$
$157$	−7.41227	+	22.8126i	−0.591564	+	1.82065i	−0.571137	+	0.820854i	$0.693498\pi$
$158$	3.20774	+	11.8247i	0.255194	+	0.940723i
$159$	−0.813263	+	0.0854774i	−0.0644960	+	0.00677880i
$160$	−4.04561	−	10.0698i	−0.319834	−	0.796091i
$161$	1.08042	+	3.32519i	0.0851489	+	0.262061i
$162$	7.78226	+	9.54961i	0.611432	+	0.750288i
$163$	−0.574388	+	5.46493i	−0.0449895	+	0.428047i	0.948725	+	0.316103i	$0.102374\pi$
$163$	−0.574388	+	5.46493i	−0.0449895	+	0.428047i	−0.993715	+	0.111944i	$0.964292\pi$
$164$	−6.03430	+	8.41473i	−0.471200	+	0.657080i
$165$	−1.04149	−	0.469561i	−0.0810799	−	0.0365553i
$166$	−0.0447025	+	0.906748i	−0.00346958	+	0.0703773i
$167$	−3.04869	−	6.84746i	−0.235914	−	0.529873i	0.756328	−	0.654193i	$-0.226992\pi$
$167$	−3.04869	−	6.84746i	−0.235914	−	0.529873i	−0.992242	+	0.124320i	$0.960325\pi$
$168$	−0.104968	+	0.210837i	−0.00809849	+	0.0162664i
$169$	−6.04399	−	11.5096i	−0.464922	−	0.885351i
$170$	11.3072	+	5.71725i	0.867226	+	0.438493i
$171$	−14.1938	+	1.49183i	−1.08542	+	0.114083i
$172$	2.57485	−	2.34748i	0.196331	−	0.178993i
$173$	1.17277	+	5.51743i	0.0891637	+	0.419482i	0.999978	+	0.00666553i	$0.00212172\pi$
$173$	1.17277	+	5.51743i	0.0891637	+	0.419482i	−0.910814	+	0.412817i	$0.864545\pi$
$174$	−0.310966	+	2.00354i	−0.0235743	+	0.151888i
$175$	−0.530031	+	0.306013i	−0.0400666	+	0.0231324i
$176$	−12.9549	+	2.85828i	−0.976515	+	0.215451i
$177$		−	2.14235i		−	0.161029i
$178$	2.05558	+	5.30575i	0.154072	+	0.397682i
$179$	−17.5277	+	15.7820i	−1.31008	+	1.17960i	−0.339016	+	0.940780i	$0.610094\pi$
$179$	−17.5277	+	15.7820i	−1.31008	+	1.17960i	−0.971064	+	0.238821i	$0.923239\pi$
$180$	7.67152	+	8.41458i	0.571801	+	0.627186i
$181$	3.04789	−	2.21442i	0.226548	−	0.164596i	−0.468721	−	0.883346i	$-0.655285\pi$
$181$	3.04789	−	2.21442i	0.226548	−	0.164596i	0.695269	+	0.718750i	$0.255285\pi$
$182$	2.19296	+	0.884667i	0.162553	+	0.0655759i
$183$	0.514059	+	1.58211i	0.0380004	+	0.116953i
$184$	−17.7751	+	11.7797i	−1.31039	+	0.868412i
$185$	−13.2369	+	5.89343i	−0.973194	+	0.433294i
$186$	−0.994411	−	0.641404i	−0.0729138	−	0.0470301i
$187$	9.16305	−	12.4884i	0.670068	−	0.913240i
$188$	14.1931	+	1.40284i	1.03514	+	0.102313i
$189$	0.0519436	−	0.494210i	0.00377834	−	0.0359485i
$190$	−12.8799	+	2.08093i	−0.934410	+	0.150967i
$191$	−7.66025	−	6.89732i	−0.554277	−	0.499073i	0.343722	−	0.939072i	$-0.388312\pi$
$191$	−7.66025	−	6.89732i	−0.554277	−	0.499073i	−0.897998	+	0.439999i	$0.854979\pi$
$192$	−1.41037	−	0.272471i	−0.101785	−	0.0196639i
$193$	−1.06597	−	10.1420i	−0.0767299	−	0.730036i	−0.963479	−	0.267785i	$-0.913708\pi$
$193$	−1.06597	−	10.1420i	−0.0767299	−	0.730036i	0.886749	−	0.462252i	$-0.152958\pi$
$194$	2.05023	+	2.03756i	0.147198	+	0.146288i
$195$	−0.849357	+	0.906139i	−0.0608237	+	0.0648900i
$196$	12.8795	−	4.27325i	0.919962	−	0.305232i
$197$	−10.6966	+	18.5271i	−0.762104	+	1.32000i	0.179660	+	0.983729i	$0.442500\pi$
$197$	−10.6966	+	18.5271i	−0.762104	+	1.32000i	−0.941764	+	0.336274i	$0.890833\pi$
$198$	11.6863	−	7.56287i	0.830511	−	0.537470i
$199$	10.8718	−	6.27682i	0.770679	−	0.444952i	−0.0624377	−	0.998049i	$-0.519887\pi$
$199$	10.8718	−	6.27682i	0.770679	−	0.444952i	0.833117	+	0.553097i	$0.186554\pi$
$200$	−2.66389	−	2.61480i	−0.188366	−	0.184894i
$201$	0.400307	+	1.88330i	0.0282355	+	0.132837i
$202$	2.32825	−	8.79814i	0.163815	−	0.619035i
$203$	−2.99567	+	2.17648i	−0.210255	+	0.152759i
$204$	1.44722	−	0.847557i	0.101325	−	0.0593409i
$205$	2.06504	−	9.71523i	0.144228	−	0.678541i
$206$	11.2954	+	4.29577i	0.786988	+	0.299300i
$207$	13.1514	−	18.1013i	0.914085	−	1.25813i
$208$	−1.61687	+	14.3313i	−0.112110	+	0.993696i
$209$	−0.0747358	+	15.9495i	−0.00516958	+	1.10325i
$210$	0.0111239	−	0.225639i	0.000767625	−	0.0155705i
$211$	−6.98411	+	3.10953i	−0.480806	+	0.214069i	−0.632804	−	0.774312i	$-0.718096\pi$
$211$	−6.98411	+	3.10953i	−0.480806	+	0.214069i	0.151998	+	0.988381i	$0.451429\pi$
$212$	3.65310	−	8.34383i	0.250896	−	0.573056i
$213$	1.84721	−	0.600195i	0.126569	−	0.0411247i
$214$	−1.22312	−	22.0316i	−0.0836111	−	1.50605i
$215$	−1.35938	+	3.05322i	−0.0927091	+	0.208228i
$216$	2.98894	−	0.501939i	0.203372	−	0.0341527i
$217$	−0.449316	−	2.11387i	−0.0305016	−	0.143499i
$218$	−22.1312	−	17.8081i	−1.49891	−	1.20612i
$219$	−0.647973	−	0.374108i	−0.0437860	−	0.0252798i
$220$	10.2836	−	7.49529i	0.693320	−	0.505332i
$221$	−9.62278	−	13.8183i	−0.647299	−	0.929518i
$222$	−0.294155	+	1.89523i	−0.0197424	+	0.127199i
$223$	6.47424	+	7.19037i	0.433547	+	0.481503i	0.919840	−	0.392293i	$-0.128318\pi$
$223$	6.47424	+	7.19037i	0.433547	+	0.481503i	−0.486293	+	0.873796i	$0.661651\pi$
$224$	−1.46272	−	2.17774i	−0.0977322	−	0.145506i
$225$	3.57803	+	1.59304i	0.238535	+	0.106203i
$226$	−16.0027	−	8.09138i	−1.06448	−	0.538231i
$227$	−15.0649	−	13.5645i	−0.999891	−	0.900306i	−0.00487167	−	0.999988i	$-0.501551\pi$
$227$	−15.0649	−	13.5645i	−0.999891	−	0.900306i	−0.995019	+	0.0996822i	$0.968217\pi$
$228$	−0.692628	+	1.58199i	−0.0458704	+	0.104770i
$229$	6.32261	−	8.70232i	0.417810	−	0.575065i	−0.547292	−	0.836942i	$-0.684341\pi$
$229$	6.32261	−	8.70232i	0.417810	−	0.575065i	0.965101	+	0.261876i	$0.0843413\pi$
$230$	11.0868	−	17.1887i	0.731044	−	1.13339i
$231$	−0.269867	−	0.0586849i	−0.0177559	−	0.00386118i
$232$	−17.6823	−	14.0486i	−1.16090	−	0.922335i
$233$	−10.3304	+	14.2185i	−0.676764	+	0.931486i	−0.999889	−	0.0148700i	$-0.995267\pi$
$233$	−10.3304	+	14.2185i	−0.676764	+	0.931486i	0.323125	+	0.946356i	$0.395267\pi$
$234$	−3.66867	−	14.6812i	−0.239828	−	0.959742i
$235$	−13.0108	+	4.22748i	−0.848733	+	0.275770i
$236$	20.7393	+	11.8030i	1.35001	+	0.768310i
$237$	−1.54707	+	0.162603i	−0.100493	+	0.0105622i
$238$	2.96101	+	0.783571i	0.191934	+	0.0507914i
$239$	3.28035	+	1.06585i	0.212188	+	0.0689440i	0.413182	−	0.910648i	$-0.364417\pi$
$239$	3.28035	+	1.06585i	0.212188	+	0.0689440i	−0.200994	+	0.979592i	$0.564417\pi$
$240$	1.34408	−	0.303159i	0.0867600	−	0.0195689i
$241$	4.85550	+	8.40998i	0.312771	+	0.541734i	0.978961	−	0.204047i	$-0.0654096\pi$
$241$	4.85550	+	8.40998i	0.312771	+	0.541734i	−0.666191	+	0.745782i	$0.732076\pi$
$242$	−6.97537	−	13.9048i	−0.448394	−	0.893836i
$243$	−4.13851	+	2.38937i	−0.265485	+	0.153278i
$244$	−18.1480	−	3.74002i	−1.16181	−	0.239431i
$245$	−9.67295	+	8.70956i	−0.617982	+	0.556434i
$246$	−0.932506	−	0.926742i	−0.0594544	−	0.0590869i
$247$	16.3799	+	5.68721i	1.04223	+	0.361869i
$248$	11.6878	−	6.09279i	0.742175	−	0.386893i
$249$	−0.112747	−	0.0239650i	−0.00714503	−	0.00151872i
$250$	16.0258	+	6.09479i	1.01356	+	0.385469i
$251$	−21.8000	−	2.29128i	−1.37601	−	0.144624i	−0.612523	−	0.790453i	$-0.709845\pi$
$251$	−21.8000	−	2.29128i	−1.37601	−	0.144624i	−0.763482	+	0.645829i	$0.776512\pi$
$252$	2.23689	+	1.60410i	0.140911	+	0.101049i
$253$	−18.5035	−	16.8183i	−1.16330	−	1.05735i
$254$	7.44828	−	11.5476i	0.467347	−	0.724558i
$255$	−0.945577	+	1.30148i	−0.0592143	+	0.0815015i
$256$	10.4080	−	12.1521i	0.650497	−	0.759509i
$257$	4.98458	+	1.05950i	0.310929	+	0.0660901i	0.360734	−	0.932669i	$-0.382526\pi$
$257$	4.98458	+	1.05950i	0.310929	+	0.0660901i	−0.0498041	+	0.998759i	$0.515860\pi$
$258$	0.242091	+	0.370270i	0.0150719	+	0.0230520i
$259$	−2.83373	+	2.05882i	−0.176079	+	0.127929i
$260$	−4.09257	−	13.2146i	−0.253811	−	0.819533i
$261$	22.5365	+	7.32255i	1.39497	+	0.453255i
$262$	−17.5896	−	14.1537i	−1.08669	−	0.874418i
$263$	9.33673	−	16.1717i	0.575727	−	0.997189i	−0.420235	−	0.907415i	$-0.638052\pi$
$263$	9.33673	−	16.1717i	0.575727	−	0.997189i	0.995962	−	0.0897738i	$-0.0286144\pi$
$264$	−0.0959145	−	1.68165i	−0.00590313	−	0.103499i
$265$			8.73687i			0.536702i
$266$	−2.94095	+	1.13940i	−0.180321	+	0.0698609i
$267$	−0.706649	+	0.150203i	−0.0432462	+	0.00919227i
$268$	−20.4369	−	6.50055i	−1.24838	−	0.397084i
$269$	−12.1735	−	5.41998i	−0.742230	−	0.330462i	0.000548149	−	1.00000i	$-0.499826\pi$
$269$	−12.1735	−	5.41998i	−0.742230	−	0.330462i	−0.742778	+	0.669538i	$0.766492\pi$
$270$	−2.43322	+	1.59090i	−0.148081	+	0.0968188i
$271$	−0.00317810	+	0.0149518i	−0.000193056	+	0.000908257i	−0.978244	−	0.207458i	$-0.933481\pi$
$271$	−0.00317810	+	0.0149518i	−0.000193056	+	0.000908257i	0.978051	+	0.208366i	$0.0668144\pi$
$272$	0.231635	+	18.6795i	0.0140450	+	1.13261i
$273$	−0.155293	+	0.256951i	−0.00939874	+	0.0155514i
$274$	0.0184251	−	0.00946013i	0.00111310	−	0.000571507i
$275$	2.20626	−	3.78034i	0.133043	−	0.227963i
$276$	−1.11652	−	2.46647i	−0.0672065	−	0.148464i
$277$	24.1595	+	2.53926i	1.45160	+	0.152570i	0.797263	−	0.603632i	$-0.206280\pi$
$277$	24.1595	+	2.53926i	1.45160	+	0.152570i	0.654339	+	0.756201i	$0.272947\pi$
$278$	6.95091	−	1.12302i	0.416888	−	0.0673540i
$279$	−9.25395	+	10.2776i	−0.554020	+	0.615301i
$280$	2.12304	+	1.35081i	0.126876	+	0.0807266i
$281$	24.8079	−	18.0240i	1.47992	−	1.07522i	0.502332	−	0.864675i	$-0.332475\pi$
$281$	24.8079	−	18.0240i	1.47992	−	1.07522i	0.977584	−	0.210547i	$-0.0675246\pi$
$282$	−0.463249	+	1.75056i	−0.0275861	+	0.104244i
$283$	−21.0373	−	23.3642i	−1.25053	−	1.38886i	−0.889902	−	0.456152i	$-0.849227\pi$
$283$	−21.0373	−	23.3642i	−1.25053	−	1.38886i	−0.360633	−	0.932708i	$-0.617439\pi$
$284$	−4.36670	+	21.1888i	−0.259116	+	1.25733i
$285$		−	1.65651i		−	0.0981234i
$286$	−16.7566	+	2.28397i	−0.990838	+	0.135054i
$287$		−	2.40101i		−	0.141727i
$288$	−5.77270	+	15.7645i	−0.340160	+	0.928931i
$289$	−3.21918	−	3.57527i	−0.189364	−	0.210310i
$290$	20.9415	+	5.54175i	1.22973	+	0.325423i
$291$	−0.296906	+	0.215715i	−0.0174049	+	0.0126454i
$292$	7.19152	−	4.21169i	0.420852	−	0.246471i
$293$	−9.22182	+	10.2419i	−0.538744	+	0.598336i	−0.949639	−	0.313347i	$-0.898550\pi$
$293$	−9.22182	+	10.2419i	−0.538744	+	0.598336i	0.410895	+	0.911683i	$0.365216\pi$
$294$	0.274796	+	1.70085i	0.0160264	+	0.0991955i
$295$	−22.7638	−	2.39257i	−1.32536	−	0.139301i
$296$	−16.7264	−	13.2891i	−0.972202	−	0.772415i
$297$	1.43028	+	3.25341i	0.0829934	+	0.188782i
$298$	2.52256	+	4.91309i	0.146128	+	0.284608i
$299$	−23.8085	+	13.1173i	−1.37688	+	0.758595i
$300$	0.381684	−	0.280942i	0.0220366	−	0.0162202i
$301$	−0.167978	+	0.790275i	−0.00968210	+	0.0455507i
$302$	−6.18354	−	9.45750i	−0.355823	−	0.544218i
$303$	1.05561	+	0.469989i	0.0606433	+	0.0270002i
$304$	−11.4987	−	15.4209i	−0.659498	−	0.884447i
$305$	17.3850	−	3.69529i	0.995461	−	0.211592i
$306$	−7.08112	−	18.2774i	−0.404800	−	1.04485i
$307$			18.8191i			1.07407i	0.843561	+	0.537033i	$0.180455\pi$
$307$			18.8191i			1.07407i	−0.843561	+	0.537033i	$0.819545\pi$
$308$	2.05490	−	2.28916i	0.117089	−	0.130437i
$309$	−0.767169	+	1.32878i	−0.0436427	+	0.0755914i
$310$	−7.92586	+	9.84990i	−0.450159	+	0.559437i
$311$	−26.8385	−	8.72037i	−1.52187	−	0.494487i	−0.575567	−	0.817755i	$-0.695219\pi$
$311$	−26.8385	−	8.72037i	−1.52187	−	0.494487i	−0.946308	+	0.323268i	$0.895219\pi$
$312$	−1.76354	−	0.492873i	−0.0998410	−	0.0279034i
$313$	−10.8354	+	7.87236i	−0.612451	+	0.444972i	−0.850277	−	0.526336i	$-0.823565\pi$
$313$	−10.8354	+	7.87236i	−0.612451	+	0.444972i	0.237825	+	0.971308i	$0.423565\pi$
$314$	28.3921	−	18.5635i	1.60226	−	1.04760i
$315$	−2.58261	−	0.548950i	−0.145513	−	0.0309298i
$316$	6.94927	−	15.8724i	0.390927	−	0.892894i
$317$	7.29908	−	10.0463i	0.409957	−	0.564258i	−0.553251	−	0.833015i	$-0.686613\pi$
$317$	7.29908	−	10.0463i	0.409957	−	0.564258i	0.963208	+	0.268757i	$0.0866129\pi$
$318$	0.971840	+	0.626845i	0.0544981	+	0.0351517i
$319$	10.8844	−	24.1416i	0.609407	−	1.35167i
$320$	−4.47026	+	14.6818i	−0.249895	+	0.820735i
$321$	2.78621	+	0.292843i	0.155511	+	0.0163449i
$322$	1.75764	−	4.62158i	0.0979495	−	0.257551i
$323$	21.9683	+	4.66951i	1.22235	+	0.259819i
$324$	−0.108013	−	17.4214i	−0.00600074	−	0.967856i
$325$	−3.11251	−	3.59920i	−0.172651	−	0.199647i
$326$	5.47798	−	5.51204i	0.303397	−	0.305284i
$327$	2.68024	−	2.41330i	0.148218	−	0.133456i
$328$	14.1090	−	3.92147i	0.779037	−	0.216527i
$329$	−2.86401	+	1.65354i	−0.157898	+	0.0911625i
$330$	0.731214	+	1.44073i	0.0402520	+	0.0793096i
$331$	−6.45645	−	11.1829i	−0.354879	−	0.614668i	0.632219	−	0.774790i	$-0.282144\pi$
$331$	−6.45645	−	11.1829i	−0.354879	−	0.614668i	−0.987097	+	0.160122i	$0.948811\pi$
$332$	0.853160	−	0.959426i	0.0468232	−	0.0526553i
$333$	21.3182	+	6.92670i	1.16823	+	0.379581i
$334$	−2.71178	+	10.2475i	−0.148382	+	0.560717i
$335$	20.4582	−	2.15024i	1.11775	−	0.117480i
$336$	0.302579	−	0.139238i	0.0165070	−	0.00759603i
$337$	15.9896	−	5.19534i	0.871010	−	0.283008i	0.160790	−	0.986989i	$-0.448596\pi$
$337$	15.9896	−	5.19534i	0.871010	−	0.283008i	0.710219	+	0.703980i	$0.248596\pi$
$338$	−3.54488	+	18.0398i	−0.192816	+	0.981235i
$339$	1.33824	−	1.84192i	0.0726830	−	0.100040i
$340$	−7.38956	−	16.3241i	−0.400755	−	0.885298i
$341$	10.2878	+	11.5340i	0.557118	+	0.624603i
$342$	16.9614	+	10.9402i	0.917166	+	0.591581i
$343$	−3.75758	+	5.17187i	−0.202890	+	0.279255i
$344$	−4.91821	+	0.303641i	−0.265172	+	0.0163712i
$345$	1.92992	+	1.73770i	0.103903	+	0.0935548i
$346$	3.59950	−	7.11888i	0.193510	−	0.382713i
$347$	13.9363	+	6.20486i	0.748142	+	0.333094i	0.745146	−	0.666901i	$-0.232380\pi$
$347$	13.9363	+	6.20486i	0.748142	+	0.333094i	0.00299569	+	0.999996i	$0.499046\pi$
$348$	2.11893	−	1.93181i	0.113586	−	0.103556i
$349$	12.5915	+	13.9843i	0.674010	+	0.748564i	0.979015	−	0.203787i	$-0.0653250\pi$
$349$	12.5915	+	13.9843i	0.674010	+	0.748564i	−0.305005	+	0.952351i	$0.598658\pi$
$350$	0.855296	+	0.132749i	0.0457175	+	0.00709573i
$351$	3.84968	−	0.326826i	0.205480	−	0.0174447i
$352$	16.8079	+	8.33635i	0.895864	+	0.444329i
$353$	1.03187	+	0.595748i	0.0549206	+	0.0317084i	0.527209	−	0.849736i	$-0.323239\pi$
$353$	1.03187	+	0.595748i	0.0549206	+	0.0317084i	−0.472288	+	0.881444i	$0.656572\pi$
$354$	−1.89937	+	2.36045i	−0.100950	+	0.125456i
$355$	−4.31448	−	20.2980i	−0.228989	−	1.07731i
$356$	2.43913	−	7.66833i	0.129274	−	0.406421i
$357$	−0.158175	+	0.355266i	−0.00837149	+	0.0188027i
$358$	33.3041	−	1.84894i	1.76018	−	0.0977193i
$359$	1.74493	−	0.566961i	0.0920937	−	0.0299231i	−0.262608	−	0.964903i	$-0.584583\pi$
$359$	1.74493	−	0.566961i	0.0920937	−	0.0299231i	0.354701	+	0.934980i	$0.384583\pi$
$360$	−0.992294	−	16.0726i	−0.0522985	−	0.847103i
$361$	−3.76973	+	1.67839i	−0.198407	+	0.0883364i
$362$	−5.32144	−	0.262346i	−0.279689	−	0.0137886i
$363$	1.88409	−	0.592715i	0.0988889	−	0.0311095i
$364$	−1.63188	−	2.91897i	−0.0855337	−	0.152995i
$365$	−4.69877	+	6.46730i	−0.245945	+	0.338514i
$366$	0.836279	−	2.19893i	0.0437130	−	0.114940i
$367$	−0.826224	+	3.88708i	−0.0431286	+	0.202904i	−0.994436	−	0.105338i	$-0.966407\pi$
$367$	−0.826224	+	3.88708i	−0.0431286	+	0.202904i	0.951308	+	0.308242i	$0.0997408\pi$
$368$	30.0283	+	2.78011i	1.56533	+	0.144923i
$369$	−12.4307	+	9.03142i	−0.647116	+	0.470157i
$370$	19.8094	+	5.24216i	1.02984	+	0.272527i
$371$	0.439117	+	2.06588i	0.0227978	+	0.107255i
$372$	0.526989	+	1.58833i	0.0273231	+	0.0823510i
$373$	−19.1804	+	11.0738i	−0.993122	+	0.573379i	−0.906206	−	0.422836i	$-0.861035\pi$
$373$	−19.1804	+	11.0738i	−0.993122	+	0.573379i	−0.0869161	+	0.996216i	$0.527701\pi$
$374$	−21.1679	+	5.63595i	−1.09456	+	0.291428i
$375$	−1.08845	+	1.88525i	−0.0562074	+	0.0973540i
$376$	−14.3943	−	14.1290i	−0.742329	−	0.728649i
$377$	−21.0042	−	19.6880i	−1.08177	−	1.01398i
$378$	−0.495389	+	0.498470i	−0.0254801	+	0.0256385i
$379$	3.86325	+	36.7564i	0.198442	+	1.88805i	0.412096	+	0.911140i	$0.364797\pi$
$379$	3.86325	+	36.7564i	0.198442	+	1.88805i	−0.213654	+	0.976909i	$0.568536\pi$
$380$	16.0361	+	9.12635i	0.822634	+	0.468172i
$381$	1.29654	+	1.16741i	0.0664238	+	0.0598083i
$382$	2.32506	+	14.3909i	0.118960	+	0.736305i
$383$	−0.0489616	+	0.465838i	−0.00250182	+	0.0238032i	−0.995702	−	0.0926194i	$-0.970476\pi$
$383$	−0.0489616	+	0.465838i	−0.00250182	+	0.0238032i	0.993200	+	0.116423i	$0.0371427\pi$
$384$	1.31239	+	1.55062i	0.0669724	+	0.0791297i
$385$	−0.924948	+	2.80196i	−0.0471397	+	0.142801i
$386$	−7.81722	+	12.1196i	−0.397886	+	0.616869i
$387$	4.72332	−	2.10296i	0.240100	−	0.106899i
$388$	−0.452489	−	4.06269i	−0.0229717	−	0.206252i
$389$	−10.3706	−	31.9173i	−0.525809	−	1.61827i	−0.762711	−	0.646739i	$-0.776132\pi$
$389$	−10.3706	−	31.9173i	−0.525809	−	1.61827i	0.236903	−	0.971533i	$-0.423868\pi$
$390$	1.73919	−	0.245363i	0.0880674	−	0.0124244i
$391$	−28.4852	+	20.6957i	−1.44056	+	1.04663i
$392$	−17.9792	−	6.71042i	−0.908089	−	0.338927i
$393$	2.13022	−	1.91806i	0.107455	−	0.0967533i
$394$	28.2114	−	10.9298i	1.42127	−	0.550636i
$395$			16.6201i			0.836250i
$396$	−19.5811	−	2.02809i	−0.983989	−	0.101915i
$397$	−14.9726	+	8.64445i	−0.751454	+	0.433852i	−0.826219	−	0.563349i	$-0.809513\pi$
$397$	−14.9726	+	8.64445i	−0.751454	+	0.433852i	0.0747649	+	0.997201i	$0.476179\pi$
$398$	−17.5435	−	2.72289i	−0.879375	−	0.136486i
$399$	−0.0832568	−	0.391692i	−0.00416805	−	0.0196091i
$400$	0.616853	+	5.24276i	0.0308427	+	0.262138i
$401$	−14.2725	+	1.50010i	−0.712732	+	0.0749112i	−0.453953	−	0.891025i	$-0.649987\pi$
$401$	−14.2725	+	1.50010i	−0.712732	+	0.0749112i	−0.258779	+	0.965937i	$0.583320\pi$
$402$	1.22864	−	2.42993i	0.0612788	−	0.121194i
$403$	15.4831	−	6.52523i	0.771268	−	0.325045i
$404$	−10.3655	+	7.62965i	−0.515705	+	0.379589i
$405$	6.79696	+	15.2662i	0.337744	+	0.758585i
$406$	5.23028	+	0.257851i	0.259574	+	0.0127970i
$407$	10.2960	−	22.8365i	0.510352	−	1.13196i
$408$	−2.34598	−	0.349234i	−0.116143	−	0.0172896i
$409$	2.00489	−	19.0753i	0.0991355	−	0.943211i	−0.826025	−	0.563634i	$-0.809403\pi$
$409$	2.00489	−	19.0753i	0.0991355	−	0.943211i	0.925160	−	0.379577i	$-0.123930\pi$
$410$	−10.8886	+	8.87345i	−0.537750	+	0.438229i
$411$	0.000812617		0.00250098i	4.00835e−5		0.000123364i
$412$	−8.63676	−	14.7474i	−0.425503	−	0.726552i
$413$	−5.50287	+	0.578375i	−0.270779	+	0.0284600i
$414$	−30.5386	+	8.28434i	−1.50089	+	0.407153i
$415$	−0.380558	+	1.17124i	−0.0186809	+	0.0574937i
$416$	14.4873	−	14.3568i	0.710300	−	0.703899i
$417$			0.893970i			0.0437779i
$418$	14.2229	−	17.5069i	0.695663	−	0.856292i
$419$	−4.55876	−	2.63200i	−0.222710	−	0.128582i	0.384494	−	0.923127i	$-0.374376\pi$
$419$	−4.55876	−	2.63200i	−0.222710	−	0.128582i	−0.607204	+	0.794546i	$0.707709\pi$
$420$	−0.212304	+	0.238747i	−0.0103594	+	0.0116497i
$421$	6.39508	+	2.07789i	0.311677	+	0.101270i	0.460679	−	0.887567i	$-0.347606\pi$
$421$	6.39508	+	2.07789i	0.311677	+	0.101270i	−0.149002	+	0.988837i	$0.547606\pi$
$422$	10.4520	+	2.76590i	0.508794	+	0.134642i
$423$	19.3338	+	8.60797i	0.940043	+	0.418534i
$424$	−11.4225	+	5.95449i	−0.554725	+	0.289176i
$425$	−4.58033	−	4.12414i	−0.222178	−	0.200050i
$426$	−2.56739	−	0.976406i	−0.124390	−	0.0473070i
$427$	3.92505	−	1.74755i	0.189947	−	0.0845697i
$428$	−18.1852	+	25.3589i	−0.879014	+	1.22577i
$429$	0.0530549	−	2.14653i	0.00256152	−	0.103635i
$430$	4.20471	−	2.15885i	0.202769	−	0.104109i
$431$	−8.92675	−	20.0498i	−0.429986	−	0.965765i	−0.990486	−	0.137611i	$-0.956058\pi$
$431$	−8.92675	−	20.0498i	−0.429986	−	0.965765i	0.560500	−	0.828154i	$-0.310609\pi$
$432$	−3.73824	−	2.09691i	−0.179856	−	0.100887i
$433$	−7.20883	+	8.00622i	−0.346434	+	0.384754i	−0.891030	−	0.453944i	$-0.850016\pi$
$433$	−7.20883	+	8.00622i	−0.346434	+	0.384754i	0.544596	+	0.838699i	$0.316683\pi$
$434$	−1.37906	+	2.72742i	−0.0661969	+	0.130920i
$435$	−1.11868	+	2.51259i	−0.0536365	+	0.120470i
$436$	8.59581	+	39.2422i	0.411665	+	1.87936i
$437$	11.2037	−	34.4814i	0.535946	−	1.64947i
$438$	0.382263	+	0.986675i	0.0182652	+	0.0471451i
$439$	−12.6762	+	21.9559i	−0.605004	+	1.04790i	0.387047	+	0.922060i	$0.373495\pi$
$439$	−12.6762	+	21.9559i	−0.605004	+	1.04790i	−0.992051	+	0.125838i	$0.959838\pi$
$440$	−17.9757	−	0.858915i	−0.856958	−	0.0409472i
$441$	20.1361			0.958860
$442$	−1.64862	+	23.7564i	−0.0784169	+	1.12998i
$443$	−6.75091	−	2.19350i	−0.320745	−	0.104216i	0.144219	−	0.989546i	$-0.453933\pi$
$443$	−6.75091	−	2.19350i	−0.320745	−	0.104216i	−0.464965	+	0.885329i	$0.653933\pi$
$444$	2.00438	−	1.82738i	0.0951236	−	0.0867236i
$445$	0.806814	+	7.67632i	0.0382466	+	0.363892i
$446$	−0.758488	−	13.6623i	−0.0359155	−	0.646930i
$447$	−0.666890	+	0.216686i	−0.0315428	+	0.0102489i
$448$	−0.319111	+	3.69626i	−0.0150766	+	0.174632i
$449$	−11.2678	−	1.18429i	−0.531760	−	0.0558903i	−0.165156	−	0.986267i	$-0.552813\pi$
$449$	−11.2678	−	1.18429i	−0.531760	−	0.0558903i	−0.366604	+	0.930377i	$0.619480\pi$
$450$	−2.52993	−	4.92744i	−0.119262	−	0.232282i
$451$	8.51591	+	14.9109i	0.400999	+	0.702127i
$452$	10.4581	+	23.1028i	0.491909	+	1.08666i
$453$	1.31062	−	0.583527i	0.0615785	−	0.0274165i
$454$	4.57252	+	28.3016i	0.214599	+	1.32826i
$455$	2.55683	+	1.93704i	0.119866	+	0.0908098i
$456$	2.16571	−	1.12897i	0.101419	−	0.0528691i
$457$	−0.0663979	−	0.631734i	−0.00310596	−	0.0295513i	0.992859	−	0.119293i	$-0.0380626\pi$
$457$	−0.0663979	−	0.631734i	−0.00310596	−	0.0295513i	−0.995965	+	0.0897413i	$0.971396\pi$
$458$	−14.6816	+	3.98274i	−0.686026	+	0.186101i
$459$	4.89502	−	1.04047i	0.228480	−	0.0485649i
$460$	−27.4547	+	9.10914i	−1.28008	+	0.424716i
$461$	5.47936	+	9.49053i	0.255199	+	0.442018i	0.964950	−	0.262435i	$-0.0845256\pi$
$461$	5.47936	+	9.49053i	0.255199	+	0.442018i	−0.709750	+	0.704453i	$0.751192\pi$
$462$	0.245311	+	0.303918i	0.0114129	+	0.0141396i
$463$	13.4823			0.626575			0.313288	−	0.949658i	$-0.398570\pi$
$463$	13.4823			0.626575			0.313288	+	0.949658i	$0.398570\pi$
$464$	7.02720	+	31.1556i	0.326229	+	1.44636i
$465$	−1.07409	−	1.19289i	−0.0498096	−	0.0553191i
$466$	23.9879	−	6.50731i	1.11122	−	0.301445i
$467$	17.6966	+	24.3573i	0.818902	+	1.12712i	0.989888	+	0.141849i	$0.0453047\pi$
$467$	17.6966	+	24.3573i	0.818902	+	1.12712i	−0.170986	+	0.985273i	$0.554695\pi$
$468$	−8.97396	+	19.4284i	−0.414822	+	0.898078i
$469$	4.72939	−	1.53667i	0.218383	−	0.0709569i
$470$	18.0834	+	6.87732i	0.834125	+	0.317227i
$471$	1.75179	+	3.93459i	0.0807184	+	0.181296i
$472$	−12.3863	−	31.3917i	−0.570126	−	1.44492i
$473$	−1.75976	−	5.50360i	−0.0809139	−	0.253056i
$474$	1.84873	+	1.19245i	0.0849149	+	0.0547709i
$475$	6.31182	+	0.663399i	0.289606	+	0.0304388i
$476$	−2.56776	−	3.48852i	−0.117693	−	0.159896i
$477$	9.04390	−	10.0443i	0.414092	−	0.459896i
$478$	−2.66934	−	4.08265i	−0.122093	−	0.186736i
$479$	−27.1022	+	2.84856i	−1.23833	+	0.130154i	−0.700966	−	0.713194i	$-0.747248\pi$
$479$	−27.1022	+	2.84856i	−1.23833	+	0.130154i	−0.537367	+	0.843349i	$0.680581\pi$
$480$	−1.74969	−	0.857615i	−0.0798620	−	0.0391446i
$481$	−19.8687	−	18.6237i	−0.905935	−	0.849166i
$482$	2.10632	−	13.5710i	0.0959404	−	0.618140i
$483$	0.543677	+	0.313892i	0.0247382	+	0.0142826i
$484$	−4.64228	+	21.5046i	−0.211013	+	0.977483i
$485$	1.96051	+	3.39571i	0.0890224	+	0.154191i
$486$	6.67820	+	1.03651i	0.302929	+	0.0470171i
$487$	11.8150	−	2.51135i	0.535387	−	0.113800i	0.0677192	−	0.997704i	$-0.478428\pi$
$487$	11.8150	−	2.51135i	0.535387	−	0.113800i	0.467668	+	0.883904i	$0.345094\pi$
$488$	16.6797	+	20.2104i	0.755053	+	0.914884i
$489$	0.579949	+	0.798231i	0.0262262	+	0.0360973i
$490$	18.3794	−	1.02037i	0.830298	−	0.0460955i
$491$	3.49513	+	0.742913i	0.157733	+	0.0335272i	0.286101	−	0.958199i	$-0.407641\pi$
$491$	3.49513	+	0.742913i	0.157733	+	0.0335272i	−0.128368	+	0.991727i	$0.540974\pi$
$492$	0.205806	+	1.84783i	0.00927843	+	0.0833067i
$493$	−30.1680	−	21.9184i	−1.35870	−	0.987153i
$494$	−13.0052	−	20.7883i	−0.585132	−	0.935309i
$495$	17.9857	−	5.75087i	0.808397	−	0.258482i
$496$	−18.2794	−	3.64911i	−0.820769	−	0.163850i
$497$	−2.04036	−	4.58273i	−0.0915229	−	0.205564i
$498$	0.102978	+	0.126364i	0.00461454	+	0.00566250i
$499$	−0.433505	−	1.33419i	−0.0194064	−	0.0597267i	0.940884	−	0.338728i	$-0.109997\pi$
$499$	−0.433505	−	1.33419i	−0.0194064	−	0.0597267i	−0.960291	+	0.279001i	$0.909997\pi$
$500$	−12.2537	−	20.9234i	−0.548004	−	0.935725i
$501$	−1.22950	−	0.547411i	−0.0549302	−	0.0244565i
$502$	21.9880	+	21.8521i	0.981371	+	0.975305i
$503$	3.93650	−	0.836729i	0.175520	−	0.0373079i	−0.119313	−	0.992857i	$-0.538069\pi$
$503$	3.93650	−	0.836729i	0.175520	−	0.0373079i	0.294833	+	0.955549i	$0.404736\pi$
$504$	−1.04245	−	3.75060i	−0.0464343	−	0.167065i
$505$	6.17282	−	10.6916i	0.274687	−	0.475772i
$506$	5.47643	+	34.9353i	0.243457	+	1.55306i
$507$	−2.18932	−	0.809629i	−0.0972313	−	0.0359569i
$508$	−18.4444	+	6.11963i	−0.818338	+	0.271515i
$509$	−7.20498	+	6.48739i	−0.319355	+	0.287549i	−0.813179	−	0.582013i	$-0.802265\pi$
$509$	−7.20498	+	6.48739i	−0.319355	+	0.287549i	0.493824	+	0.869562i	$0.335599\pi$
$510$	2.19570	−	0.595639i	0.0972275	−	0.0263753i
$511$	−0.786003	+	1.76539i	−0.0347707	+	0.0780964i
$512$	−22.2414	+	4.16178i	−0.982940	+	0.183926i
$513$	−3.44808	+	3.82948i	−0.152237	+	0.169076i
$514$	−4.55269	−	5.58660i	−0.200811	−	0.246415i
$515$	13.2623	+	9.63560i	0.584405	+	0.424595i
$516$	0.0615375	−	0.622598i	0.00270904	−	0.0274084i
$517$	11.9215	−	20.4270i	0.524307	−	0.898378i
$518$	4.94753	+	0.243912i	0.217382	+	0.0107169i
$519$	0.819390	+	0.595322i	0.0359672	+	0.0261317i
$520$	−7.20659	+	18.1883i	−0.316030	+	0.797608i
$521$	13.8048	+	42.4869i	0.604800	+	1.86138i	0.498159	+	0.867086i	$0.334010\pi$
$521$	13.8048	+	42.4869i	0.604800	+	1.86138i	0.106641	+	0.994298i	$0.465990\pi$
$522$	−18.3388	−	28.0485i	−0.802666	−	1.22765i
$523$	−2.33985	−	22.2622i	−0.102315	−	0.973459i	−0.918434	−	0.395575i	$-0.870545\pi$
$523$	−2.33985	−	22.2622i	−0.102315	−	0.973459i	0.816119	−	0.577884i	$-0.196121\pi$
$524$	6.83184	+	31.1892i	0.298450	+	1.36251i
$525$	−0.0339589	+	0.104515i	−0.00148209	+	0.00456140i
$526$	−24.6248	+	9.54026i	−1.07369	+	0.415975i
$527$	18.8476	−	10.8817i	0.821015	−	0.474013i
$528$	−1.38525	+	1.93789i	−0.0602851	+	0.0843358i
$529$	16.9196	+	29.3057i	0.735637	+	1.27416i
$530$	7.74596	−	9.62632i	0.336463	−	0.418141i
$531$	23.6935	+	26.3143i	1.02821	+	1.14194i
$532$	4.25052	+	1.35200i	0.184283	+	0.0586167i
$533$	18.3334	−	3.51473i	0.794107	−	0.152240i
$534$	0.911756	+	0.461008i	0.0394556	+	0.0199498i
$535$	6.22326	−	29.2782i	0.269055	−	1.26581i
$536$	16.7542	+	25.2813i	0.723672	+	1.09199i
$537$	−0.442676	+	4.21178i	−0.0191029	+	0.181752i
$538$	8.60753	+	16.7645i	0.371097	+	0.722771i
$539$	2.45705	−	22.3685i	0.105833	−	0.963481i
$540$	4.09139	+	0.404392i	0.176065	+	0.0174023i
$541$	22.2464	+	16.1630i	0.956449	+	0.694901i	0.952323	−	0.305090i	$-0.0986867\pi$
$541$	22.2464	+	16.1630i	0.956449	+	0.694901i	0.00412599	+	0.999991i	$0.498687\pi$
$542$	0.0167577	−	0.0136563i	0.000719803	−	0.000586589i
$543$	0.140644	−	0.661677i	0.00603560	−	0.0283953i
$544$	16.3057	−	20.7865i	0.699099	−	0.891213i
$545$	−22.6495	−	31.1743i	−0.970197	−	1.33536i
$546$	0.398910	−	0.145430i	0.0170718	−	0.00622381i
$547$	−7.87580	+	24.2392i	−0.336745	+	1.03639i	0.629111	+	0.777315i	$0.283419\pi$
$547$	−7.87580	+	24.2392i	−0.336745	+	1.03639i	−0.965856	+	0.259079i	$0.916581\pi$
$548$	−0.0286881	−	0.00591218i	−0.00122549	−	0.000252556i
$549$	−23.8117	−	13.7477i	−1.01626	−	0.586736i
$550$	−5.78245	+	2.20916i	−0.246565	+	0.0941989i
$551$	38.3978			1.63580
$552$	−0.956546	+	3.70745i	−0.0407133	+	0.157800i
$553$	0.835331	+	3.92992i	0.0355219	+	0.167117i
$554$	−24.3677	−	24.2171i	−1.03529	−	1.02889i
$555$	−1.05820	+	2.37676i	−0.0449182	+	0.100888i
$556$	−8.65419	−	4.92521i	−0.367019	−	0.208876i
$557$	20.4429	+	4.34527i	0.866193	+	0.184115i	0.619517	−	0.784983i	$-0.287328\pi$
$557$	20.4429	+	4.34527i	0.866193	+	0.184115i	0.246676	+	0.969098i	$0.420662\pi$
$558$	19.3079	−	3.11946i	0.817370	−	0.132057i
$559$	−6.28019	−	0.125783i	−0.265624	−	0.00532006i
$560$	−1.14156	−	3.37058i	−0.0482399	−	0.142433i
$561$	−0.277752	−	2.76731i	−0.0117267	−	0.116836i
$562$	−43.3132	−	2.13533i	−1.82706	−	0.0900736i
$563$	0.372905	−	3.54796i	0.0157161	−	0.149529i	−0.983850	−	0.178997i	$-0.942715\pi$
$563$	0.372905	−	3.54796i	0.0157161	−	0.149529i	0.999566	+	0.0294684i	$0.00938143\pi$
$564$	2.06242	−	1.51806i	0.0868437	−	0.0639220i
$565$	−18.0770	−	16.2766i	−0.760506	−	0.684762i
$566$	2.46462	+	44.3941i	0.103596	+	1.86602i
$567$	2.37446	+	3.26817i	0.0997181	+	0.137250i
$568$	23.5969	−	19.4745i	0.990104	−	0.817133i
$569$	−7.88000	+	7.09518i	−0.330347	+	0.297445i	−0.817567	−	0.575834i	$-0.804678\pi$
$569$	−7.88000	+	7.09518i	−0.330347	+	0.297445i	0.487220	+	0.873279i	$0.338011\pi$
$570$	−1.46864	+	1.82515i	−0.0615144	+	0.0764473i
$571$	30.2617			1.26641			0.633206	−	0.773983i	$-0.281738\pi$
$571$	30.2617			1.26641			0.633206	+	0.773983i	$0.281738\pi$
$572$	20.4874	+	12.3396i	0.856622	+	0.515945i
$573$	−1.85085			−0.0773202
$574$	−2.12869	+	2.64544i	−0.0888499	+	0.110419i
$575$	−7.39406	+	6.65764i	−0.308354	+	0.277643i
$576$	20.3369	−	12.2514i	0.847371	−	0.510475i
$577$	9.01110	+	12.4027i	0.375137	+	0.516332i	0.954288	−	0.298888i	$-0.0966158\pi$
$577$	9.01110	+	12.4027i	0.375137	+	0.516332i	−0.579151	+	0.815220i	$0.696616\pi$
$578$	0.377143	+	6.79332i	0.0156871	+	0.282565i
$579$	−1.36076	−	1.22524i	−0.0565514	−	0.0509191i
$580$	−18.1603	−	24.6723i	−0.754064	−	1.02446i
$581$	−0.0311185	+	0.296073i	−0.00129101	+	0.0122832i
$582$	0.518381	+	0.0255561i	0.0214876	+	0.00105933i
$583$	−10.0543	−	11.2722i	−0.416407	−	0.466848i
$584$	−11.6577	−	1.73542i	−0.482397	−	0.0718121i
$585$	0.411058	−	20.5236i	0.0169951	−	0.848546i
$586$	19.2409	−	3.10863i	0.794834	−	0.128416i
$587$	−28.9608	−	6.15581i	−1.19534	−	0.254077i	−0.433084	−	0.901353i	$-0.642575\pi$
$587$	−28.9608	−	6.15581i	−1.19534	−	0.254077i	−0.762256	+	0.647276i	$0.775908\pi$
$588$	1.20517	−	2.11763i	0.0497004	−	0.0873297i
$589$	−9.11498	+	20.4726i	−0.375576	+	0.843558i
$590$	22.9600	+	22.8181i	0.945248	+	0.939405i
$591$	0.798651	+	3.75736i	0.0328521	+	0.154557i
$592$	6.64731	+	29.4713i	0.273203	+	1.21126i
$593$	20.5751			0.844920			0.422460	−	0.906382i	$-0.361167\pi$
$593$	20.5751			0.844920			0.422460	+	0.906382i	$0.361167\pi$
$594$	1.30852	−	4.85268i	0.0536894	−	0.199108i
$595$	3.59827	+	2.07746i	0.147515	+	0.0851676i
$596$	1.57649	−	7.64972i	0.0645756	−	0.313345i
$597$	0.696550	−	2.14376i	0.0285079	−	0.0877383i
$598$	37.8619	+	6.65549i	1.54829	+	0.272163i
$599$	2.05817	+	2.83282i	0.0840944	+	0.115746i	0.848992	−	0.528406i	$-0.177210\pi$
$599$	2.05817	+	2.83282i	0.0840944	+	0.115746i	−0.764897	+	0.644152i	$0.777210\pi$
$600$	−0.669620	−	0.0288516i	−0.0273371	−	0.00117786i
$601$	1.05030	−	4.94127i	0.0428426	−	0.201559i	−0.951521	−	0.307585i	$-0.900479\pi$
$601$	1.05030	−	4.94127i	0.0428426	−	0.201559i	0.994363	+	0.106026i	$0.0338126\pi$
$602$	0.885722	−	0.721802i	0.0360994	−	0.0294184i
$603$	−25.7454	−	18.7051i	−1.04843	−	0.761732i
$604$	−1.57180	+	15.9025i	−0.0639557	+	0.647065i
$605$	−4.19381	−	20.6815i	−0.170503	−	0.840823i
$606$	−0.746394	−	1.45372i	−0.0303202	−	0.0590534i
$607$	4.86635	−	46.3002i	0.197519	−	1.87927i	−0.227064	−	0.973880i	$-0.572913\pi$
$607$	4.86635	−	46.3002i	0.197519	−	1.87927i	0.424583	−	0.905389i	$-0.360421\pi$
$608$	−1.00251	+	27.1853i	−0.0406570	+	1.10251i
$609$	−0.138234	+	0.650342i	−0.00560154	+	0.0263532i
$610$	−22.4310	−	11.3417i	−0.908206	−	0.459213i
$611$	−16.8184	−	19.4482i	−0.680400	−	0.786789i
$612$	−8.40240	+	26.4161i	−0.339647	+	1.06781i
$613$	10.0533	+	11.1653i	0.406050	+	0.450964i	0.911137	−	0.412105i	$-0.135206\pi$
$613$	10.0533	+	11.1653i	0.406050	+	0.450964i	−0.505087	+	0.863069i	$0.668540\pi$
$614$	16.6847	−	20.7350i	0.673341	−	0.836797i
$615$	−0.891701	−	1.54447i	−0.0359568	−	0.0622791i
$616$	−4.29363	+	0.700367i	−0.172995	+	0.0282186i
$617$	−27.7447	+	16.0184i	−1.11696	+	0.644878i	−0.940623	−	0.339452i	$-0.889758\pi$
$617$	−27.7447	+	16.0184i	−1.11696	+	0.644878i	−0.176337	+	0.984330i	$0.556425\pi$
$618$	2.02334	−	0.783892i	0.0813906	−	0.0315328i
$619$	−9.12508	+	28.0841i	−0.366768	+	1.12880i	0.582099	+	0.813118i	$0.302232\pi$
$619$	−9.12508	+	28.0841i	−0.366768	+	1.12880i	−0.948867	+	0.315678i	$0.897768\pi$
$620$	17.4655	−	3.82573i	0.701431	−	0.153645i
$621$	−0.844444	−	8.03435i	−0.0338864	−	0.322407i
$622$	21.8395	+	33.4027i	0.875684	+	1.33933i
$623$	0.576589	+	1.77456i	0.0231006	+	0.0710962i
$624$	1.50611	+	2.10658i	0.0602925	+	0.0843305i
$625$	13.4779	+	9.79230i	0.539118	+	0.391692i
$626$	18.9179	+	0.932651i	0.756113	+	0.0372762i
$627$	1.90630	+	2.13722i	0.0761304	+	0.0853523i
$628$	−47.7406	−	4.71867i	−1.90506	−	0.188295i
$629$	−28.5371	−	20.7335i	−1.13785	−	0.826697i
$630$	2.35884	+	2.89453i	0.0939783	+	0.115321i
$631$	8.19208	−	9.09823i	0.326122	−	0.362195i	−0.557681	−	0.830056i	$-0.688309\pi$
$631$	8.19208	−	9.09823i	0.326122	−	0.362195i	0.883802	+	0.467861i	$0.154975\pi$
$632$	−21.7290	+	11.3272i	−0.864331	+	0.450572i
$633$	−0.558335	+	1.25404i	−0.0221918	+	0.0498437i
$634$	−16.9490	+	4.59784i	−0.673133	+	0.182604i
$635$	13.8524	−	12.4728i	0.549717	−	0.494967i
$636$	−0.515027	−	1.55228i	−0.0204221	−	0.0615518i
$637$	−22.1447	−	10.3957i	−0.877406	−	0.411892i
$638$	−33.3960	+	16.9494i	−1.32216	+	0.671035i
$639$	−16.0512	+	27.8015i	−0.634976	+	1.09981i
$640$	17.9419	−	12.2132i	0.709217	−	0.482768i
$641$	7.78145	−	1.65400i	0.307349	−	0.0653290i	−0.0516554	−	0.998665i	$-0.516450\pi$
$641$	7.78145	−	1.65400i	0.307349	−	0.0653290i	0.359004	+	0.933336i	$0.383116\pi$
$642$	−2.81023	−	2.79286i	−0.110911	−	0.110226i
$643$	21.9867	+	9.78910i	0.867070	+	0.386044i	0.791553	−	0.611100i	$-0.209273\pi$
$643$	21.9867	+	9.78910i	0.867070	+	0.386044i	0.0755166	+	0.997145i	$0.475939\pi$
$644$	−6.03399	+	3.53378i	−0.237772	+	0.139251i
$645$	0.185443	+	0.570736i	0.00730183	+	0.0224727i
$646$	−20.0649	−	24.6216i	−0.789442	−	0.968724i
$647$	16.0836	+	36.1243i	0.632311	+	1.42019i	0.890897	+	0.454205i	$0.150077\pi$
$647$	16.0836	+	36.1243i	0.632311	+	1.42019i	−0.258587	+	0.965988i	$0.583257\pi$
$648$	−15.3265	+	19.2907i	−0.602082	+	0.757812i
$649$	32.1229	−	23.1095i	1.26093	−	0.907126i
$650$	0.238397	+	6.72511i	0.00935070	+	0.263780i
$651$	−0.313929	−	0.228083i	−0.0123038	−	0.00893927i
$652$	−10.9225	+	1.21652i	−0.427760	+	0.0476425i
$653$	−14.5234	−	3.08705i	−0.568345	−	0.120805i	−0.0852284	−	0.996361i	$-0.527162\pi$
$653$	−14.5234	−	3.08705i	−0.568345	−	0.120805i	−0.483117	+	0.875556i	$0.660495\pi$
$654$	−5.09269	+	0.282730i	−0.199140	+	0.0110556i
$655$	−18.0015	−	24.7770i	−0.703378	−	0.968116i
$656$	−19.0220	−	8.18806i	−0.742685	−	0.319690i
$657$	12.0965	−	2.57119i	0.471929	−	0.100312i
$658$	4.62158	+	0.717307i	0.180168	+	0.0279635i
$659$	−4.34775	−	7.53053i	−0.169364	−	0.293348i	0.768832	−	0.639451i	$-0.220838\pi$
$659$	−4.34775	−	7.53053i	−0.169364	−	0.293348i	−0.938197	+	0.346103i	$0.887505\pi$
$660$	0.471672	−	2.23568i	0.0183598	−	0.0870239i
$661$	−21.8504	−	12.6153i	−0.849883	−	0.490680i	0.0107284	−	0.999942i	$-0.496585\pi$
$661$	−21.8504	−	12.6153i	−0.849883	−	0.490680i	−0.860611	+	0.509262i	$0.829918\pi$
$662$	−2.80082	+	18.0455i	−0.108857	+	0.701360i
$663$	−2.94425	−	0.687716i	−0.114345	−	0.0267087i
$664$	−1.79062	+	0.300703i	−0.0694897	+	0.0116695i
$665$	−4.25495	+	0.447213i	−0.165000	+	0.0173422i
$666$	−17.3474	−	26.5322i	−0.672197	−	1.02810i
$667$	−40.2797	+	44.7352i	−1.55964	+	1.73215i
$668$	12.0731	−	8.88649i	0.467121	−	0.343829i
$669$	1.72780	+	0.181599i	0.0668005	+	0.00702101i
$670$	−24.4473	−	15.7687i	−0.944482	−	0.609199i
$671$	−18.1774	+	24.7741i	−0.701732	+	0.956395i
$672$	−0.456828	−	0.114848i	−0.0176225	−	0.00443037i
$673$	−2.87916	−	6.46671i	−0.110984	−	0.249273i	0.849511	−	0.527570i	$-0.176897\pi$
$673$	−2.87916	−	6.46671i	−0.110984	−	0.249273i	−0.960495	+	0.278297i	$0.910230\pi$
$674$	−22.2235	−	8.45186i	−0.856018	−	0.325553i
$675$	1.34494	−	0.436998i	0.0517668	−	0.0168201i
$676$	19.8995	−	16.7335i	0.765366	−	0.643595i
$677$	4.76345	+	6.55633i	0.183074	+	0.251980i	0.890684	−	0.454624i	$-0.150226\pi$
$677$	4.76345	+	6.55633i	0.183074	+	0.251980i	−0.707609	+	0.706604i	$0.750226\pi$
$678$	−3.10749	+	0.842983i	−0.119342	+	0.0323746i
$679$	0.634244	+	0.704399i	0.0243401	+	0.0270324i
$680$	−6.33080	+	24.5374i	−0.242775	+	0.940966i
$681$	−3.63993			−0.139482
$682$	−1.10931	−	21.8293i	−0.0424779	−	0.835886i
$683$	11.1714	+	19.3495i	0.427463	+	0.740388i	0.996647	−	0.0818223i	$-0.0260740\pi$
$683$	11.1714	+	19.3495i	0.427463	+	0.740388i	−0.569184	+	0.822210i	$0.692741\pi$
$684$	−8.98869	−	27.0917i	−0.343691	−	1.03588i
$685$	0.0274819	−	0.00584147i	0.00105003	−	0.000223191i
$686$	8.72541	−	2.36698i	0.333138	−	0.0903717i
$687$	−0.201889	−	1.92085i	−0.00770254	−	0.0732848i
$688$	5.68811	+	4.02585i	0.216857	+	0.153484i
$689$	−15.1317	+	6.37712i	−0.576470	+	0.242949i
$690$	−0.585771	−	3.62564i	−0.0222999	−	0.138026i
$691$	28.3517	−	12.6230i	1.07855	−	0.480201i	0.210965	−	0.977494i	$-0.432339\pi$
$691$	28.3517	−	12.6230i	1.07855	−	0.480201i	0.867583	+	0.497293i	$0.165673\pi$
$692$	−10.2774	+	4.65236i	−0.390689	+	0.176856i
$693$	3.96378	−	2.26379i	0.150572	−	0.0859943i
$694$	−9.85400	−	19.1922i	−0.374053	−	0.728528i
$695$	9.49897	+	0.998382i	0.360316	+	0.0378708i
$696$	−4.04735	+	0.249876i	−0.153414	+	0.00947151i
$697$	22.9960	−	7.47186i	0.871037	−	0.283017i
$698$	−1.47516	−	26.5714i	−0.0558356	−	1.00574i
$699$	0.329862	+	3.13843i	0.0124765	+	0.118706i
$700$	−0.824676	−	0.904554i	−0.0311698	−	0.0341889i
$701$	39.7105	+	12.9027i	1.49984	+	0.487329i	0.939972	−	0.341251i	$-0.110851\pi$
$701$	39.7105	+	12.9027i	1.49984	+	0.487329i	0.559871	+	0.828580i	$0.310851\pi$
$702$	−4.53135	−	3.05296i	−0.171025	−	0.115226i
$703$	36.3220			1.36991
$704$	−11.1282	−	24.0866i	−0.419408	−	0.907798i
$705$	−1.22820	+	2.12731i	−0.0462567	+	0.0801190i
$706$	−0.608734	−	1.57123i	−0.0229100	−	0.0591340i
$707$	0.922234	−	2.83835i	0.0346842	−	0.106747i
$708$	4.18546	−	0.916806i	0.157299	−	0.0344557i
$709$	−9.06271	+	20.3552i	−0.340357	+	0.764454i	0.659561	+	0.751651i	$0.270742\pi$
$709$	−9.06271	+	20.3552i	−0.340357	+	0.764454i	−0.999918	+	0.0128034i	$0.995924\pi$
$710$	−13.2421	+	26.1896i	−0.496969	+	0.982877i
$711$	17.2042	−	19.1072i	0.645208	−	0.716576i
$712$	−9.48605	+	6.28651i	−0.355505	+	0.235597i
$713$	−14.2898	−	32.0954i	−0.535156	−	1.20198i
$714$	0.489250	−	0.251199i	0.0183097	−	0.00940088i
$715$	−22.7489	−	2.96097i	−0.850760	−	0.110734i
$716$	−38.3338	−	27.4897i	−1.43260	−	1.02734i
$717$	0.565775	−	0.251899i	0.0211293	−	0.00940736i
$718$	−2.42522	−	0.922341i	−0.0905086	−	0.0344215i
$719$	−14.3759	−	12.9441i	−0.536129	−	0.482733i	0.356017	−	0.934479i	$-0.384134\pi$
$719$	−14.3759	−	12.9441i	−0.536129	−	0.482733i	−0.892146	+	0.451747i	$0.850801\pi$
$720$	−13.1564	+	18.5887i	−0.490310	+	0.692758i
$721$	3.62023	+	1.61183i	0.134824	+	0.0600276i
$722$	5.64153	+	1.49292i	0.209956	+	0.0555606i
$723$	1.65833	+	0.538825i	0.0616740	+	0.0200391i
$724$	5.63059	+	5.00695i	0.209259	+	0.186082i
$725$	−9.12572	−	5.26874i	−0.338921	−	0.195676i
$726$	−2.60139	−	1.01734i	−0.0965465	−	0.0377571i
$727$		−	5.98628i		−	0.222019i	−0.993819	−	0.111009i	$-0.964592\pi$
$727$		−	5.98628i		−	0.222019i	0.993819	−	0.111009i	$-0.0354084\pi$
$728$	−0.789893	+	4.66292i	−0.0292754	+	0.172819i
$729$	7.81027	−	24.0375i	0.289269	−	0.890280i
$730$	10.9109	−	2.95986i	0.403831	−	0.109549i
$731$	−8.09172	+	0.850474i	−0.299283	+	0.0314559i
$732$	−2.87095	+	1.68136i	−0.106113	+	0.0621449i
$733$	6.08099	+	18.7154i	0.224607	+	0.691268i	0.998331	+	0.0577461i	$0.0183914\pi$
$733$	6.08099	+	18.7154i	0.224607	+	0.691268i	−0.773725	+	0.633522i	$0.781609\pi$
$734$	4.35655	−	3.55028i	0.160803	−	0.131043i
$735$	−0.244298	+	2.32434i	−0.00901108	+	0.0857347i
$736$	−30.6205	−	29.6857i	−1.12869	−	1.09423i
$737$	−23.9205	+	26.3174i	−0.881123	+	0.969412i
$738$	21.7033	+	1.06997i	0.798909	+	0.0393860i
$739$	−5.33328	−	11.9787i	−0.196188	−	0.440645i	0.788486	−	0.615053i	$-0.210866\pi$
$739$	−5.33328	−	11.9787i	−0.196188	−	0.440645i	−0.984673	+	0.174408i	$0.944199\pi$
$740$	−17.1785	−	23.3385i	−0.631495	−	0.857942i
$741$	2.86897	−	1.20910i	0.105394	−	0.0444175i
$742$	1.34775	−	2.66551i	0.0494776	−	0.0978540i
$743$	19.3849	−	2.03744i	0.711165	−	0.0747464i	0.257963	−	0.966155i	$-0.416949\pi$
$743$	19.3849	−	2.03744i	0.711165	−	0.0747464i	0.453201	+	0.891408i	$0.350282\pi$
$744$	0.827546	−	2.21725i	0.0303393	−	0.0812882i
$745$	1.55764	+	7.32810i	0.0570674	+	0.268481i
$746$	30.9508	+	4.80383i	1.13319	+	0.175881i
$747$	1.64990	−	0.952571i	0.0603667	−	0.0348527i
$748$	28.3196	+	12.5573i	1.03547	+	0.459142i
$749$		−	7.23577i		−	0.264389i
$750$	2.87069	−	1.11218i	0.104823	−	0.0406110i
$751$	7.80322	−	7.02605i	0.284744	−	0.256384i	−0.514364	−	0.857572i	$-0.671972\pi$
$751$	7.80322	−	7.02605i	0.284744	−	0.256384i	0.799108	+	0.601187i	$0.205305\pi$
$752$	3.33315	+	28.3291i	0.121548	+	1.03306i
$753$	−3.18420	+	2.31346i	−0.116039	+	0.0843072i
$754$	5.68748	+	40.3143i	0.207126	+	1.46816i
$755$	−4.73663	−	14.5778i	−0.172384	−	0.530542i
$756$	0.987757	−	0.110013i	0.0359244	−	0.00400114i
$757$	22.1805	−	9.87539i	0.806164	−	0.358927i	0.0380785	−	0.999275i	$-0.487876\pi$
$757$	22.1805	−	9.87539i	0.806164	−	0.358927i	0.768085	+	0.640347i	$0.221210\pi$
$758$	28.3310	−	43.9235i	1.02903	−	1.59537i
$759$	−4.48969	−	0.0210377i	−0.162965	−	0.000763621i
$760$	−9.57738	−	24.2728i	−0.347408	−	0.880466i
$761$	2.53113	−	24.0821i	0.0917533	−	0.872974i	−0.847741	−	0.530410i	$-0.822038\pi$
$761$	2.53113	−	24.0821i	0.0917533	−	0.872974i	0.939494	−	0.342564i	$-0.111295\pi$
$762$	−0.393529	−	2.43575i	−0.0142560	−	0.0882379i
$763$	−6.92243	−	6.23298i	−0.250609	−	0.225649i
$764$	10.1970	−	17.9174i	0.368915	−	0.648227i
$765$	−2.77933	−	26.4436i	−0.100487	−	0.956070i
$766$	0.466950	−	0.469854i	0.0168716	−	0.0169765i
$767$	−12.4717	−	41.1716i	−0.450327	−	1.48662i
$768$	−0.0712401	−	2.87202i	−0.00257065	−	0.103635i
$769$	−2.84075	+	4.92032i	−0.102440	+	0.177431i	−0.912689	−	0.408654i	$-0.865998\pi$
$769$	−2.84075	+	4.92032i	−0.102440	+	0.177431i	0.810249	+	0.586085i	$0.199332\pi$
$770$	3.50328	−	2.26716i	0.126249	−	0.0817029i
$771$	0.792420	−	0.457504i	0.0285383	−	0.0164766i
$772$	19.3580	−	6.42276i	0.696710	−	0.231160i
$773$	2.44222	+	11.4898i	0.0878407	+	0.413258i	0.999994	+	0.00340929i	$0.00108521\pi$
$773$	2.44222	+	11.4898i	0.0878407	+	0.413258i	−0.912153	+	0.409849i	$0.865581\pi$
$774$	−7.06862	−	1.87056i	−0.254076	−	0.0672360i
$775$	4.97543	−	3.61486i	0.178723	−	0.129850i
$776$	−3.10335	+	4.87745i	−0.111404	+	0.175090i
$777$	−0.130762	+	0.615185i	−0.00469104	+	0.0220696i
$778$	−16.8710	+	44.3610i	−0.604854	+	1.59042i
$779$	−14.6346	+	20.1429i	−0.524341	+	0.721693i
$780$	−2.13378	−	1.27159i	−0.0764017	−	0.0455304i
$781$	28.9253	+	21.2232i	1.03503	+	0.759427i
$782$	49.7336	+	2.45186i	1.77847	+	0.0876782i
$783$	7.81616	−	3.47998i	0.279327	−	0.124364i
$784$	13.8603	+	23.3336i	0.495009	+	0.833344i
$785$	43.7638	−	14.2197i	1.56200	−	0.507524i
$786$	−4.04760	+	0.224710i	−0.144373	+	0.00801514i
$787$	−21.2962	+	47.8320i	−0.759127	+	1.70503i	−0.0512558	+	0.998686i	$0.516322\pi$
$787$	−21.2962	+	47.8320i	−0.759127	+	1.70503i	−0.707871	+	0.706342i	$0.750344\pi$
$788$	−40.7736	−	12.9692i	−1.45250	−	0.462010i
$789$	−0.697115	−	3.27967i	−0.0248179	−	0.116759i
$790$	14.7351	−	18.3121i	0.524252	−	0.651516i
$791$	−5.09248	−	2.94014i	−0.181068	−	0.104540i
$792$	19.7765	+	19.5948i	0.702728	+	0.696273i
$793$	19.0894	+	27.4124i	0.677886	+	0.973442i
$794$	24.1609	+	3.74997i	0.857438	+	0.133082i
$795$	1.04971	+	1.16582i	0.0372292	+	0.0413472i
$796$	16.9154	+	18.5538i	0.599550	+	0.657623i
$797$	−38.0769	−	16.9529i	−1.34875	−	0.600503i	−0.399997	−	0.916516i	$-0.630989\pi$
$797$	−38.0769	−	16.9529i	−1.34875	−	0.600503i	−0.948755	+	0.316013i	$0.897656\pi$
$798$	−0.255535	+	0.505382i	−0.00904583	+	0.0178903i
$799$	−24.7497	−	22.2847i	−0.875582	−	0.788377i
$800$	3.96848	−	6.32338i	0.140307	−	0.223565i
$801$	7.01853	−	9.66018i	0.247988	−	0.341326i
$802$	17.0554	+	11.0009i	0.602247	+	0.388455i
$803$	−1.38021	−	13.7514i	−0.0487066	−	0.485275i
$804$	−3.50805	+	1.58802i	−0.123719	+	0.0560050i
$805$	3.94247	−	5.42634i	0.138954	−	0.191253i
$806$	−22.8445	−	6.53752i	−0.804663	−	0.230274i
$807$	−2.27558	+	0.739379i	−0.0801041	+	0.0260274i
$808$	18.1851	+	0.783534i	0.639750	+	0.0275646i
$809$	−1.03589	+	0.108876i	−0.0364199	+	0.00382789i	−0.122721	−	0.992441i	$-0.539162\pi$
$809$	−1.03589	+	0.108876i	−0.0364199	+	0.00382789i	0.0863010	+	0.996269i	$0.472495\pi$
$810$	6.04584	−	22.8465i	0.212429	−	0.802743i
$811$	−2.23079	−	0.724828i	−0.0783337	−	0.0254521i	0.269588	−	0.962976i	$-0.413112\pi$
$811$	−2.23079	−	0.724828i	−0.0783337	−	0.0254521i	−0.347922	+	0.937524i	$0.613112\pi$
$812$	−5.53413	−	4.92117i	−0.194210	−	0.172699i
$813$	0.00137233	+	0.00237695i	4.81299e−5	+	8.33634e-5i
$814$	−31.5906	+	16.0332i	−1.10725	+	0.561962i
$815$	9.12937	−	5.27085i	0.319788	−	0.184630i
$816$	2.27518	+	2.46469i	0.0796473	+	0.0862814i
$817$	6.22611	−	5.60601i	0.217824	−	0.196130i
$818$	−19.1208	+	19.2397i	−0.668542	+	0.672700i
$819$	−0.934323	−	4.87358i	−0.0326479	−	0.170297i
$820$	19.8642	−	0.123158i	0.693687	−	0.00430088i
$821$	2.55103	+	0.542239i	0.0890317	+	0.0189243i	0.252212	−	0.967672i	$-0.418842\pi$
$821$	2.55103	+	0.542239i	0.0890317	+	0.0189243i	−0.163180	+	0.986596i	$0.552175\pi$
$822$	0.00132198	−	0.00347604i	4.61093e−5	−	0.000121241i
$823$	22.0410	+	2.31661i	0.768302	+	0.0807518i	0.480567	−	0.876958i	$-0.340431\pi$
$823$	22.0410	+	2.31661i	0.768302	+	0.0807518i	0.287735	+	0.957710i	$0.407098\pi$
$824$	−3.55876	+	23.9059i	−0.123975	+	0.832803i
$825$	−0.159799	−	0.769510i	−0.00556350	−	0.0267909i
$826$	6.57586	+	4.24149i	0.228803	+	0.147580i
$827$	−8.74356	+	12.0345i	−0.304043	+	0.418480i	−0.933512	−	0.358546i	$-0.883273\pi$
$827$	−8.74356	+	12.0345i	−0.304043	+	0.418480i	0.629469	+	0.777026i	$0.283273\pi$
$828$	40.9923	+	17.9472i	1.42458	+	0.623710i
$829$	42.4022	+	9.01286i	1.47269	+	0.313029i	0.873203	−	0.487357i	$-0.162039\pi$
$829$	42.4022	+	9.01286i	1.47269	+	0.313029i	0.599485	+	0.800386i	$0.295372\pi$
$830$	1.45770	−	0.953078i	0.0505974	−	0.0330818i
$831$	3.52884	−	2.56385i	0.122414	−	0.0889389i
$832$	−28.6907	+	2.97415i	−0.994670	+	0.103110i
$833$	−30.1363	−	9.79187i	−1.04416	−	0.339268i
$834$	0.792578	−	0.984980i	0.0274447	−	0.0341071i
$835$	−7.18968	+	12.4529i	−0.248809	+	0.430950i
$836$	−31.1921	+	6.67948i	−1.07880	+	0.231014i
$837$			4.99344i			0.172598i
$838$	2.68938	+	6.94167i	0.0929029	+	0.239796i
$839$	2.57588	−	0.547519i	0.0889291	−	0.0189025i	−0.163232	−	0.986588i	$-0.552192\pi$
$839$	2.57588	−	0.547519i	0.0889291	−	0.0189025i	0.252161	+	0.967685i	$0.418859\pi$
$840$	0.445586	−	0.0748282i	0.0153742	−	0.00258182i
$841$	−31.7487	−	14.1355i	−1.09478	−	0.487429i
$842$	−5.20390	−	7.95918i	−0.179338	−	0.274292i
$843$	1.14475	−	5.38564i	0.0394274	−	0.185491i
$844$	−9.06383	−	12.3140i	−0.311990	−	0.423866i
$845$	−11.0478	+	22.3587i	−0.380057	+	0.769162i
$846$	−13.6704	−	26.6253i	−0.469998	−	0.915397i
$847$	−2.03111	−	4.67948i	−0.0697897	−	0.160789i
$848$	17.8645	+	3.56628i	0.613469	+	0.122467i
$849$	−5.61427	−	0.590083i	−0.192681	−	0.0202516i
$850$	1.39023	+	8.60484i	0.0476845	+	0.295143i
$851$	−38.1022	+	42.3168i	−1.30613	+	1.45060i
$852$	1.96309	+	3.35201i	0.0672544	+	0.114838i
$853$	−8.74629	+	6.35455i	−0.299467	+	0.217576i	−0.727364	−	0.686252i	$-0.759255\pi$
$853$	−8.74629	+	6.35455i	−0.299467	+	0.217576i	0.427897	+	0.903828i	$0.359255\pi$
$854$	−5.87398	−	1.55443i	−0.201004	−	0.0531915i
$855$	18.3204	+	20.3468i	0.626543	+	0.695847i
$856$	42.5193	−	11.8179i	1.45328	−	0.403927i
$857$			18.4900i			0.631606i	0.948825	+	0.315803i	$0.102274\pi$
$857$			18.4900i			0.631606i	−0.948825	+	0.315803i	$0.897726\pi$
$858$	−1.96153	+	2.31801i	−0.0669654	+	0.0791357i
$859$		−	15.1548i		−	0.517075i	−0.966001	−	0.258537i	$-0.916759\pi$
$859$		−	15.1548i		−	0.517075i	0.966001	−	0.258537i	$-0.0832405\pi$
$860$	−6.54676	−	1.34919i	−0.223243	−	0.0460069i
$861$	−0.288473	−	0.320382i	−0.00983114	−	0.0109186i
$862$	−7.94027	+	30.0052i	−0.270447	+	1.02198i
$863$	−39.8923	+	28.9834i	−1.35795	+	0.986608i	−0.359377	+	0.933192i	$0.617011\pi$
$863$	−39.8923	+	28.9834i	−1.35795	+	0.986608i	−0.998572	+	0.0534155i	$0.982989\pi$
$864$	2.25973	+	5.62464i	0.0768776	+	0.191354i
$865$	7.24074	−	8.04166i	0.246193	−	0.273425i
$866$	15.0409	−	2.43006i	0.511110	−	0.0825769i
$867$	−0.859112	−	0.0902964i	−0.0291770	−	0.00306663i
$868$	3.93753	−	1.78244i	0.133649	−	0.0604998i
$869$	−19.1263	−	21.4431i	−0.648815	−	0.727408i
$870$	3.46018	−	1.77658i	0.117311	−	0.0602318i
$871$	18.6567	+	33.8627i	0.632158	+	1.14739i
$872$	25.3205	−	50.8581i	0.857461	−	1.72227i
$873$	1.26115	−	5.93326i	0.0426836	−	0.200810i
$874$	−42.9149	+	28.0588i	−1.45162	+	0.949103i
$875$	5.13634	+	2.28685i	0.173640	+	0.0773095i
$876$	0.453590	−	1.42603i	0.0153254	−	0.0481811i
$877$	27.2020	−	5.78196i	0.918545	−	0.195243i	0.275704	−	0.961242i	$-0.411089\pi$
$877$	27.2020	−	5.78196i	0.918545	−	0.195243i	0.642841	+	0.766000i	$0.277756\pi$
$878$	33.4324	−	12.9526i	1.12829	−	0.437128i
$879$			2.47461i			0.0834664i
$880$	19.0442	+	16.8833i	0.641980	+	0.569136i
$881$	23.4796	−	40.6679i	0.791048	−	1.37014i	−0.134270	−	0.990945i	$-0.542869\pi$
$881$	23.4796	−	40.6679i	0.791048	−	1.37014i	0.925318	−	0.379191i	$-0.123798\pi$
$882$	−22.1860	−	17.8523i	−0.747041	−	0.601117i
$883$	49.3498	+	16.0347i	1.66075	+	0.539611i	0.981030	−	0.193858i	$-0.0621000\pi$
$883$	49.3498	+	16.0347i	1.66075	+	0.539611i	0.679723	+	0.733469i	$0.262100\pi$
$884$	22.8785	−	24.7133i	0.769487	−	0.831198i
$885$	−3.32497	+	2.41573i	−0.111768	+	0.0812040i
$886$	5.49345	+	8.40204i	0.184556	+	0.282272i
$887$	−17.2153	−	3.65922i	−0.578032	−	0.122864i	−0.0903872	−	0.995907i	$-0.528810\pi$
$887$	−17.2153	−	3.65922i	−0.578032	−	0.122864i	−0.487645	+	0.873042i	$0.662144\pi$
$888$	−3.82855	+	0.236367i	−0.128478	+	0.00793197i
$889$	2.64860	−	3.64548i	0.0888312	−	0.122266i
$890$	5.91674	−	9.17311i	0.198329	−	0.307483i
$891$	−26.3376	−	11.8744i	−0.882343	−	0.397809i
$892$	−11.2771	+	15.7257i	−0.377584	+	0.526534i
$893$	34.1058	+	3.58466i	1.14131	+	0.119956i
$894$	0.926892	+	0.352508i	0.0309999	+	0.0117896i
$895$	44.2583	+	9.40740i	1.47939	+	0.314455i
$896$	3.62864	−	3.78964i	0.121224	−	0.126603i
$897$	−1.60092	+	4.61084i	−0.0534532	+	0.153952i
$898$	11.3649	+	11.2947i	0.379253	+	0.376909i
$899$	27.6511	−	24.8972i	0.922216	−	0.830367i
$900$	−1.58110	+	7.67206i	−0.0527032	+	0.255735i
$901$	−18.4198	+	10.6347i	−0.613652	+	0.354292i
$902$	3.83688	−	23.9790i	0.127754	−	0.798412i
$903$	0.0725345	+	0.125633i	0.00241380	+	0.00418082i
$904$	8.95972	−	34.7268i	0.297996	−	1.15500i
$905$	−6.87365	−	2.23338i	−0.228488	−	0.0742402i
$906$	−1.96140	−	0.519043i	−0.0651630	−	0.0172440i
$907$	19.5059	−	2.05016i	0.647684	−	0.0680743i	0.225010	−	0.974356i	$-0.427758\pi$
$907$	19.5059	−	2.05016i	0.647684	−	0.0680743i	0.422674	+	0.906282i	$0.361092\pi$
$908$	20.0537	−	35.2368i	0.665506	−	1.16937i
$909$	−18.1639	+	5.90180i	−0.602458	+	0.195750i
$910$	−1.09978	−	4.40107i	−0.0364572	−	0.145894i
$911$	−29.1530	+	40.1257i	−0.965882	+	1.32942i	−0.0217823	+	0.999763i	$0.506934\pi$
$911$	−29.1530	+	40.1257i	−0.965882	+	1.32942i	−0.944100	+	0.329660i	$0.893066\pi$
$912$	−3.38711	−	0.676169i	−0.112158	−	0.0223902i
$913$	−0.856857	−	1.94906i	−0.0283578	−	0.0645045i
$914$	−0.486927	+	0.754914i	−0.0161061	+	0.0249703i
$915$	1.87581	−	2.58183i	0.0620124	−	0.0853528i
$916$	19.7073	+	8.62824i	0.651146	+	0.285085i
$917$	−5.50186	−	4.95389i	−0.181687	−	0.163592i
$918$	−6.31581	−	3.19344i	−0.208453	−	0.105399i
$919$	6.49550	+	2.89198i	0.214267	+	0.0953976i	0.511063	−	0.859543i	$-0.329252\pi$
$919$	6.49550	+	2.89198i	0.214267	+	0.0953976i	−0.296797	+	0.954941i	$0.595918\pi$
$920$	38.3257	+	14.3043i	1.26356	+	0.471600i
$921$	2.26106	+	2.51116i	0.0745044	+	0.0827455i
$922$	2.37695	−	15.3146i	0.0782807	−	0.504359i
$923$	32.0056	−	22.2881i	1.05348	−	0.733620i
$924$	−0.000836364	−	0.552347i	−2.75143e−5	−	0.0181709i
$925$	−8.63239	−	4.98391i	−0.283831	−	0.163870i
$926$	−14.8548	−	11.9532i	−0.488160	−	0.392805i
$927$	−5.27264	−	24.8058i	−0.173176	−	0.814730i
$928$	19.8794	−	40.5576i	0.652574	−	1.33137i
$929$	5.51272	−	12.3818i	0.180866	−	0.406233i	−0.800246	−	0.599672i	$-0.795298\pi$
$929$	5.51272	−	12.3818i	0.180866	−	0.406233i	0.981112	+	0.193440i	$0.0619643\pi$
$930$	0.125834	+	2.26660i	0.00412627	+	0.0743248i
$931$	31.0318	−	10.0828i	1.01703	−	0.330452i
$932$	−32.1993	−	14.0975i	−1.05472	−	0.461778i
$933$	−4.62896	+	2.06095i	−0.151545	+	0.0674723i
$934$	2.09655	−	42.5265i	0.0686011	−	1.39151i
$935$	−29.7145	−	0.139236i	−0.971770	−	0.00455350i
$936$	27.1124	−	13.4501i	0.886197	−	0.439632i
$937$	−6.36791	+	8.76468i	−0.208031	+	0.286329i	−0.900264	−	0.435344i	$-0.856627\pi$
$937$	−6.36791	+	8.76468i	−0.208031	+	0.286329i	0.692234	+	0.721673i	$0.256627\pi$
$938$	−6.57325	−	2.49988i	−0.214624	−	0.0816240i
$939$	−0.499995	+	2.35229i	−0.0163167	+	0.0767641i
$940$	−13.8270	−	23.6099i	−0.450988	−	0.770069i
$941$	−1.93048	+	1.40257i	−0.0629318	+	0.0457226i	−0.618806	−	0.785544i	$-0.712383\pi$
$941$	−1.93048	+	1.40257i	−0.0629318	+	0.0457226i	0.555875	+	0.831266i	$0.312383\pi$
$942$	1.55821	−	5.88826i	0.0507691	−	0.191850i
$943$	−8.11544	−	38.1801i	−0.264275	−	1.24332i
$944$	−14.1840	+	45.5689i	−0.461650	+	1.48314i
$945$	−0.825596	+	0.476658i	−0.0268566	+	0.0155057i
$946$	−2.94048	+	7.62407i	−0.0956034	+	0.247880i
$947$	−6.27494	+	10.8685i	−0.203908	+	0.353179i	−0.949784	−	0.312905i	$-0.898698\pi$
$947$	−6.27494	+	10.8685i	−0.203908	+	0.353179i	0.745876	+	0.666085i	$0.232031\pi$
$948$	−0.979734	−	2.95289i	−0.0318203	−	0.0959054i
$949$	−14.6306	−	3.41741i	−0.474929	−	0.110934i
$950$	−6.36623	−	6.32688i	−0.206548	−	0.205271i
$951$	−0.233069	−	2.21750i	−0.00755778	−	0.0719075i
$952$	−0.263698	+	6.12019i	−0.00854651	+	0.198357i
$953$	−14.8726	−	13.3914i	−0.481771	−	0.433789i	0.392117	−	0.919915i	$-0.371743\pi$
$953$	−14.8726	−	13.3914i	−0.481771	−	0.433789i	−0.873888	+	0.486127i	$0.838409\pi$
$954$	−18.8697	+	3.04866i	−0.610928	+	0.0987039i
$955$	−2.06702	+	19.6664i	−0.0668871	+	0.636388i
$956$	−0.678522	+	6.86487i	−0.0219450	+	0.222026i
$957$	−1.44816	−	4.52909i	−0.0468124	−	0.146405i
$958$	32.3868	+	20.8898i	1.04637	+	0.674919i
$959$	0.00620467	−	0.00276250i	0.000200359	−	8.92057e-5i
$960$	1.16747	+	2.49617i	0.0376799	+	0.0805634i
$961$	−2.86898	−	8.82981i	−0.0925477	−	0.284833i
$962$	5.38002	+	38.1349i	0.173459	+	1.22952i
$963$	−37.4616	+	27.2174i	−1.20718	+	0.877069i
$964$	−14.3525	+	13.0851i	−0.462264	+	0.421443i
$965$	−14.5386	+	13.0906i	−0.468014	+	0.421401i
$966$	−0.320734	−	0.827862i	−0.0103195	−	0.0266360i
$967$			36.6171i			1.17753i	0.808306	+	0.588763i	$0.200385\pi$
$967$			36.6171i			1.17753i	−0.808306	+	0.588763i	$0.799615\pi$
$968$	24.1805	−	19.5781i	0.777191	−	0.629265i
$969$	3.49240	−	2.01634i	0.112192	−	0.0647741i
$970$	0.850474	−	5.47957i	0.0273071	−	0.175938i
$971$	−4.20880	−	19.8009i	−0.135067	−	0.635440i	−0.992643	−	0.121082i	$-0.961364\pi$
$971$	−4.20880	−	19.8009i	−0.135067	−	0.635440i	0.857576	−	0.514358i	$-0.171970\pi$
$972$	−6.43911	−	7.06280i	−0.206535	−	0.226540i
$973$	2.29626	−	0.241347i	0.0736149	−	0.00773723i
$974$	−15.2443	−	7.70792i	−0.488458	−	0.246978i
$975$	−0.847754	−	0.106306i	−0.0271498	−	0.00340450i
$976$	−0.459512	−	37.0558i	−0.0147086	−	1.18613i
$977$	10.5719	+	23.7449i	0.338225	+	0.759665i	0.999951	+	0.00991954i	$0.00315754\pi$
$977$	10.5719	+	23.7449i	0.338225	+	0.759665i	−0.661726	+	0.749746i	$0.730176\pi$
$978$	0.0687075	−	1.39367i	0.00219702	−	0.0445646i
$979$	−9.87479	−	8.97544i	−0.315600	−	0.286856i
$980$	−21.1552	−	15.1706i	−0.675777	−	0.484608i
$981$	−6.23107	+	59.2847i	−0.198943	+	1.89282i
$982$	−3.19229	−	3.91726i	−0.101870	−	0.125005i
$983$	−7.09990	−	21.8513i	−0.226452	−	0.696947i	−0.998141	−	0.0609471i	$-0.980588\pi$
$983$	−7.09990	−	21.8513i	−0.226452	−	0.696947i	0.771689	−	0.636000i	$-0.219412\pi$
$984$	1.41150	−	2.21841i	0.0449969	−	0.0707204i
$985$	40.8161	−	4.28995i	1.30051	−	0.136689i
$986$	13.8068	+	50.8962i	0.439699	+	1.62086i
$987$	−0.183496	+	0.564743i	−0.00584075	+	0.0179760i
$988$	−4.10133	+	34.4348i	−0.130481	+	1.09552i
$989$			13.1345i			0.417652i
$990$	−24.9153	−	9.60946i	−0.791861	−	0.305409i
$991$	−39.8200	−	22.9901i	−1.26493	−	0.730305i	−0.290902	−	0.956753i	$-0.593955\pi$
$991$	−39.8200	−	22.9901i	−1.26493	−	0.730305i	−0.974023	+	0.226448i	$0.927289\pi$
$992$	16.9051	+	20.2268i	0.536737	+	0.642202i
$993$	−2.20511	−	0.716484i	−0.0699771	−	0.0227369i
$994$	−1.81489	+	6.85823i	−0.0575648	+	0.217530i
$995$	−22.0009	−	9.79541i	−0.697474	−	0.310535i
$996$	−0.00142927	−	0.230526i	−4.52882e−5	−	0.00730451i
$997$	8.99792	+	8.10176i	0.284967	+	0.256585i	0.799200	−	0.601065i	$-0.205257\pi$
$997$	8.99792	+	8.10176i	0.284967	+	0.256585i	−0.514233	+	0.857650i	$0.671923\pi$
$998$	−0.705233	+	1.85436i	−0.0223238	+	0.0586986i
$999$	7.39362	−	3.29185i	0.233924	−	0.104150i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bn.a.95.18	✓	640
4.3	odd	2	inner	572.2.bn.a.95.39	yes	640
11.8	odd	10	inner	572.2.bn.a.459.65	yes	640
13.10	even	6	inner	572.2.bn.a.491.10	yes	640
44.19	even	10	inner	572.2.bn.a.459.10	yes	640
52.23	odd	6	inner	572.2.bn.a.491.65	yes	640
143.140	odd	30	inner	572.2.bn.a.283.39	yes	640
572.283	even	30	inner	572.2.bn.a.283.18	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bn.a.95.18	✓	640	1.1	even	1	trivial
572.2.bn.a.95.39	yes	640	4.3	odd	2	inner
572.2.bn.a.283.18	yes	640	572.283	even	30	inner
572.2.bn.a.283.39	yes	640	143.140	odd	30	inner
572.2.bn.a.459.10	yes	640	44.19	even	10	inner
572.2.bn.a.459.65	yes	640	11.8	odd	10	inner
572.2.bn.a.491.10	yes	640	13.10	even	6	inner
572.2.bn.a.491.65	yes	640	52.23	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bn (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.10180 - 0.886582i) q^{2} +(0.133436 - 0.120147i) q^{3} +(0.427944 + 1.95368i) q^{4} +(-1.12761 - 1.55202i) q^{5} +(-0.253541 + 0.0140758i) q^{6} +(-0.344634 - 0.310310i) q^{7} +(1.26059 - 2.53198i) q^{8} +(-0.310215 + 2.95150i) q^{9} +O(q^{10})\)	\(q+(-1.10180 - 0.886582i) q^{2} +(0.133436 - 0.120147i) q^{3} +(0.427944 + 1.95368i) q^{4} +(-1.12761 - 1.55202i) q^{5} +(-0.253541 + 0.0140758i) q^{6} +(-0.344634 - 0.310310i) q^{7} +(1.26059 - 2.53198i) q^{8} +(-0.310215 + 2.95150i) q^{9} +(-0.133590 + 2.70974i) q^{10} +(3.24088 + 0.704759i) q^{11} +(0.291831 + 0.209276i) q^{12} +(1.86494 - 3.08577i) q^{13} +(0.104604 + 0.647448i) q^{14} +(-0.336934 - 0.0716175i) q^{15} +(-3.63373 + 1.67213i) q^{16} +(1.89955 - 4.26646i) q^{17} +(2.95855 - 2.97695i) q^{18} +(0.999847 + 4.70391i) q^{19} +(2.54960 - 2.86716i) q^{20} -0.0832695 q^{21} +(-2.94599 - 3.64981i) q^{22} +(-6.52912 - 3.76959i) q^{23} +(-0.136001 - 0.489313i) q^{24} +(0.407819 - 1.25514i) q^{25} +(-4.79059 + 1.74649i) q^{26} +(0.629841 + 0.866901i) q^{27} +(0.458762 - 0.806101i) q^{28} +(1.66009 - 7.81009i) q^{29} +(0.307740 + 0.377628i) q^{30} +(3.77004 + 2.73909i) q^{31} +(5.48614 + 1.37924i) q^{32} +(0.517126 - 0.295341i) q^{33} +(-5.87550 + 3.01670i) q^{34} +(-0.0929950 + 0.884788i) q^{35} +(-5.89904 + 0.657017i) q^{36} +(1.57034 - 7.38788i) q^{37} +(3.06877 - 6.06924i) q^{38} +(-0.121894 - 0.635821i) q^{39} +(-5.35113 + 0.898626i) q^{40} +(3.46433 + 3.84753i) q^{41} +(0.0917466 + 0.0738252i) q^{42} +(-0.871081 - 1.50876i) q^{43} +(0.0100441 + 6.63324i) q^{44} +(4.93059 - 2.84668i) q^{45} +(3.85176 + 9.94196i) q^{46} +(2.20364 - 6.78212i) q^{47} +(-0.283970 + 0.659703i) q^{48} +(-0.709219 - 6.74777i) q^{49} +(-1.56212 + 1.02135i) q^{50} +(-0.259132 - 0.797526i) q^{51} +(6.82670 + 2.32296i) q^{52} +(-3.68446 - 2.67692i) q^{53} +(0.0746182 - 1.51356i) q^{54} +(-2.56065 - 5.82461i) q^{55} +(-1.22014 + 0.481434i) q^{56} +(0.698575 + 0.507544i) q^{57} +(-8.75337 + 7.13338i) q^{58} +(7.98363 - 8.86672i) q^{59} +(-0.00427126 - 0.688909i) q^{60} +(-3.76828 + 8.46370i) q^{61} +(-1.72541 - 6.36039i) q^{62} +(1.02279 - 0.920926i) q^{63} +(-4.82184 - 6.38356i) q^{64} +(-6.89211 + 0.585119i) q^{65} +(-0.831615 - 0.133067i) q^{66} +(-5.36147 + 9.28633i) q^{67} +(9.14820 + 1.88531i) q^{68} +(-1.32413 + 0.281452i) q^{69} +(0.886900 - 0.892416i) q^{70} +(9.88188 + 4.39970i) q^{71} +(7.08209 + 4.50608i) q^{72} +(-1.28768 - 3.96307i) q^{73} +(-8.28017 + 6.74775i) q^{74} +(-0.0963827 - 0.216479i) q^{75} +(-8.76206 + 3.96639i) q^{76} +(-0.898226 - 1.24856i) q^{77} +(-0.429403 + 0.808619i) q^{78} +(-7.00894 - 5.09229i) q^{79} +(6.69261 + 3.75411i) q^{80} +(-8.52052 - 1.81109i) q^{81} +(-0.405863 - 7.31064i) q^{82} +(-0.377326 - 0.519345i) q^{83} +(-0.0356347 - 0.162682i) q^{84} +(-8.76359 + 1.86276i) q^{85} +(-0.377876 + 2.43464i) q^{86} +(-0.716840 - 1.24160i) q^{87} +(5.86985 - 7.31744i) q^{88} +(-3.48441 - 2.01173i) q^{89} +(-7.95636 - 1.23489i) q^{90} +(-1.60027 + 0.484754i) q^{91} +(4.57047 - 14.3690i) q^{92} +(0.832152 - 0.0874627i) q^{93} +(-8.44089 + 5.51885i) q^{94} +(6.17313 - 6.85596i) q^{95} +(0.897761 - 0.475101i) q^{96} +(-2.03271 - 0.213646i) q^{97} +(-5.20103 + 8.06350i) q^{98} +(-3.08547 + 9.34684i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 15 q^{2} - 3 q^{4} - 15 q^{6} - 78 q^{9}+O(q^{10}) \) 640 * q - 15 * q^2 - 3 * q^4 - 15 * q^6 - 78 * q^9	\( 640 q - 15 q^{2} - 3 q^{4} - 15 q^{6} - 78 q^{9} - 4 q^{12} - 20 q^{13} - 12 q^{14} - 19 q^{16} - 10 q^{17} - 45 q^{20} - 15 q^{22} - 15 q^{24} + 104 q^{25} - 20 q^{26} - 15 q^{28} - 10 q^{29} + 45 q^{30} - 24 q^{33} + 4 q^{36} - 18 q^{37} - 14 q^{38} - 20 q^{40} - 30 q^{41} - 13 q^{42} - 108 q^{45} - 15 q^{46} + 35 q^{48} - 74 q^{49} - 90 q^{50} + 15 q^{52} - 8 q^{53} + 50 q^{56} + 27 q^{58} - 10 q^{61} - 5 q^{62} - 84 q^{64} - 146 q^{66} - 70 q^{68} - 26 q^{69} - 15 q^{72} - 55 q^{74} + 44 q^{77} + 24 q^{78} - 39 q^{80} + 30 q^{81} - 29 q^{82} + 30 q^{84} - 30 q^{85} - 75 q^{88} - 24 q^{89} + 30 q^{90} + 14 q^{92} + 66 q^{93} - 5 q^{94} - 30 q^{97}+O(q^{100}) \) 640 * q - 15 * q^2 - 3 * q^4 - 15 * q^6 - 78 * q^9 - 4 * q^12 - 20 * q^13 - 12 * q^14 - 19 * q^16 - 10 * q^17 - 45 * q^20 - 15 * q^22 - 15 * q^24 + 104 * q^25 - 20 * q^26 - 15 * q^28 - 10 * q^29 + 45 * q^30 - 24 * q^33 + 4 * q^36 - 18 * q^37 - 14 * q^38 - 20 * q^40 - 30 * q^41 - 13 * q^42 - 108 * q^45 - 15 * q^46 + 35 * q^48 - 74 * q^49 - 90 * q^50 + 15 * q^52 - 8 * q^53 + 50 * q^56 + 27 * q^58 - 10 * q^61 - 5 * q^62 - 84 * q^64 - 146 * q^66 - 70 * q^68 - 26 * q^69 - 15 * q^72 - 55 * q^74 + 44 * q^77 + 24 * q^78 - 39 * q^80 + 30 * q^81 - 29 * q^82 + 30 * q^84 - 30 * q^85 - 75 * q^88 - 24 * q^89 + 30 * q^90 + 14 * q^92 + 66 * q^93 - 5 * q^94 - 30 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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