LMFDB - Embedded newform 585.2.j.e.451.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(406,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("585.406");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.j (of order $3$, degree $2$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			451.1
Root			$-0.309017 + 0.535233i$ of defining polynomial
Character	$\chi$	$=$	585.451
Dual form			585.2.j.e.406.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.535233i) q^{2} +(0.809017 + 1.40126i) q^{4} -1.00000 q^{5} +(-2.11803 - 3.66854i) q^{7} -2.23607 q^{8} +O(q^{10})$	\(q+(-0.309017 + 0.535233i) q^{2} +(0.809017 + 1.40126i) q^{4} -1.00000 q^{5} +(-2.11803 - 3.66854i) q^{7} -2.23607 q^{8} +(0.309017 - 0.535233i) q^{10} +(-0.118034 + 0.204441i) q^{11} +(-1.00000 - 3.46410i) q^{13} +2.61803 q^{14} +(-0.927051 + 1.60570i) q^{16} +(-1.73607 - 3.00696i) q^{17} +(-2.11803 - 3.66854i) q^{19} +(-0.809017 - 1.40126i) q^{20} +(-0.0729490 - 0.126351i) q^{22} +(1.88197 - 3.25966i) q^{23} +1.00000 q^{25} +(2.16312 + 0.535233i) q^{26} +(3.42705 - 5.93583i) q^{28} +(-3.73607 + 6.47106i) q^{29} +(-2.80902 - 4.86536i) q^{32} +2.14590 q^{34} +(2.11803 + 3.66854i) q^{35} +(-1.50000 + 2.59808i) q^{37} +2.61803 q^{38} +2.23607 q^{40} +(5.97214 - 10.3440i) q^{41} +(3.11803 + 5.40059i) q^{43} -0.381966 q^{44} +(1.16312 + 2.01458i) q^{46} +4.94427 q^{47} +(-5.47214 + 9.47802i) q^{49} +(-0.309017 + 0.535233i) q^{50} +(4.04508 - 4.20378i) q^{52} -6.00000 q^{53} +(0.118034 - 0.204441i) q^{55} +(4.73607 + 8.20311i) q^{56} +(-2.30902 - 3.99933i) q^{58} +(-0.354102 - 0.613323i) q^{59} +(-7.20820 - 12.4850i) q^{61} -0.236068 q^{64} +(1.00000 + 3.46410i) q^{65} +(1.35410 - 2.34537i) q^{67} +(2.80902 - 4.86536i) q^{68} -2.61803 q^{70} +(-3.11803 - 5.40059i) q^{71} -6.00000 q^{73} +(-0.927051 - 1.60570i) q^{74} +(3.42705 - 5.93583i) q^{76} +1.00000 q^{77} +(0.927051 - 1.60570i) q^{80} +(3.69098 + 6.39297i) q^{82} -8.94427 q^{83} +(1.73607 + 3.00696i) q^{85} -3.85410 q^{86} +(0.263932 - 0.457144i) q^{88} +(-4.50000 + 7.79423i) q^{89} +(-10.5902 + 11.0056i) q^{91} +6.09017 q^{92} +(-1.52786 + 2.64634i) q^{94} +(2.11803 + 3.66854i) q^{95} +(1.73607 + 3.00696i) q^{97} +(-3.38197 - 5.85774i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + q^{4} - 4 q^{5} - 4 q^{7}+O(q^{10}) $ 4 * q + q^2 + q^4 - 4 * q^5 - 4 * q^7	$ 4 q + q^{2} + q^{4} - 4 q^{5} - 4 q^{7} - q^{10} + 4 q^{11} - 4 q^{13} + 6 q^{14} + 3 q^{16} + 2 q^{17} - 4 q^{19} - q^{20} - 7 q^{22} + 12 q^{23} + 4 q^{25} - 7 q^{26} + 7 q^{28} - 6 q^{29} - 9 q^{32} + 22 q^{34} + 4 q^{35} - 6 q^{37} + 6 q^{38} + 6 q^{41} + 8 q^{43} - 6 q^{44} - 11 q^{46} - 16 q^{47} - 4 q^{49} + q^{50} + 5 q^{52} - 24 q^{53} - 4 q^{55} + 10 q^{56} - 7 q^{58} + 12 q^{59} - 2 q^{61} + 8 q^{64} + 4 q^{65} - 8 q^{67} + 9 q^{68} - 6 q^{70} - 8 q^{71} - 24 q^{73} + 3 q^{74} + 7 q^{76} + 4 q^{77} - 3 q^{80} + 17 q^{82} - 2 q^{85} - 2 q^{86} + 10 q^{88} - 18 q^{89} - 20 q^{91} + 2 q^{92} - 24 q^{94} + 4 q^{95} - 2 q^{97} - 18 q^{98}+O(q^{100}) $ 4 * q + q^2 + q^4 - 4 * q^5 - 4 * q^7 - q^10 + 4 * q^11 - 4 * q^13 + 6 * q^14 + 3 * q^16 + 2 * q^17 - 4 * q^19 - q^20 - 7 * q^22 + 12 * q^23 + 4 * q^25 - 7 * q^26 + 7 * q^28 - 6 * q^29 - 9 * q^32 + 22 * q^34 + 4 * q^35 - 6 * q^37 + 6 * q^38 + 6 * q^41 + 8 * q^43 - 6 * q^44 - 11 * q^46 - 16 * q^47 - 4 * q^49 + q^50 + 5 * q^52 - 24 * q^53 - 4 * q^55 + 10 * q^56 - 7 * q^58 + 12 * q^59 - 2 * q^61 + 8 * q^64 + 4 * q^65 - 8 * q^67 + 9 * q^68 - 6 * q^70 - 8 * q^71 - 24 * q^73 + 3 * q^74 + 7 * q^76 + 4 * q^77 - 3 * q^80 + 17 * q^82 - 2 * q^85 - 2 * q^86 + 10 * q^88 - 18 * q^89 - 20 * q^91 + 2 * q^92 - 24 * q^94 + 4 * q^95 - 2 * q^97 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.309017	+	0.535233i	−0.218508	+	0.378467i	−0.954352	−	0.298684i	$-0.903452\pi$
$2$	−0.309017	+	0.535233i	−0.218508	+	0.378467i	0.735844	+	0.677151i	$0.236786\pi$
$3$		0			0
$3$		0			0
$4$	0.809017	+	1.40126i	0.404508	+	0.700629i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	−2.11803	−	3.66854i	−0.800542	−	1.38658i	−0.919260	−	0.393651i	$-0.871212\pi$
$7$	−2.11803	−	3.66854i	−0.800542	−	1.38658i	0.118718	−	0.992928i	$-0.462121\pi$
$8$	−2.23607			−0.790569
$9$		0			0
$10$	0.309017	−	0.535233i	0.0977198	−	0.169256i
$11$	−0.118034	+	0.204441i	−0.0355886	+	0.0616412i	−0.883271	−	0.468863i	$-0.844664\pi$
$11$	−0.118034	+	0.204441i	−0.0355886	+	0.0616412i	0.847683	+	0.530504i	$0.177997\pi$
$12$		0			0
$13$	−1.00000	−	3.46410i	−0.277350	−	0.960769i
$13$	−1.00000	−	3.46410i	−0.277350	−	0.960769i
$14$	2.61803			0.699699
$15$		0			0
$16$	−0.927051	+	1.60570i	−0.231763	+	0.401425i
$17$	−1.73607	−	3.00696i	−0.421058	−	0.729294i	0.574985	−	0.818164i	$-0.305008\pi$
$17$	−1.73607	−	3.00696i	−0.421058	−	0.729294i	−0.996043	+	0.0888696i	$0.971675\pi$
$18$		0			0
$19$	−2.11803	−	3.66854i	−0.485910	−	0.841621i	0.513959	−	0.857815i	$-0.328179\pi$
$19$	−2.11803	−	3.66854i	−0.485910	−	0.841621i	−0.999869	+	0.0161937i	$0.994845\pi$
$20$	−0.809017	−	1.40126i	−0.180902	−	0.313331i
$21$		0			0
$22$	−0.0729490	−	0.126351i	−0.0155528	−	0.0269382i
$23$	1.88197	−	3.25966i	0.392417	−	0.679686i	−0.600351	−	0.799737i	$-0.704972\pi$
$23$	1.88197	−	3.25966i	0.392417	−	0.679686i	0.992768	+	0.120051i	$0.0383057\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	2.16312	+	0.535233i	0.424223	+	0.104968i
$27$		0			0
$28$	3.42705	−	5.93583i	0.647652	−	1.12177i
$29$	−3.73607	+	6.47106i	−0.693770	+	1.20165i	0.276823	+	0.960921i	$0.410718\pi$
$29$	−3.73607	+	6.47106i	−0.693770	+	1.20165i	−0.970593	+	0.240725i	$0.922615\pi$
$30$		0			0
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	−2.80902	−	4.86536i	−0.496569	−	0.860082i
$33$		0			0
$34$	2.14590			0.368018
$35$	2.11803	+	3.66854i	0.358013	+	0.620097i
$36$		0			0
$37$	−1.50000	+	2.59808i	−0.246598	+	0.427121i	−0.962580	−	0.270998i	$-0.912646\pi$
$37$	−1.50000	+	2.59808i	−0.246598	+	0.427121i	0.715981	+	0.698119i	$0.245980\pi$
$38$	2.61803			0.424701
$39$		0			0
$40$	2.23607			0.353553
$41$	5.97214	−	10.3440i	0.932691	−	1.61547i	0.153990	−	0.988072i	$-0.450788\pi$
$41$	5.97214	−	10.3440i	0.932691	−	1.61547i	0.778701	−	0.627396i	$-0.215879\pi$
$42$		0			0
$43$	3.11803	+	5.40059i	0.475496	+	0.823583i	0.999606	−	0.0280676i	$-0.00893538\pi$
$43$	3.11803	+	5.40059i	0.475496	+	0.823583i	−0.524110	+	0.851650i	$0.675602\pi$
$44$	−0.381966			−0.0575835
$45$		0			0
$46$	1.16312	+	2.01458i	0.171493	+	0.297034i
$47$	4.94427			0.721196			0.360598	−	0.932721i	$-0.382573\pi$
$47$	4.94427			0.721196			0.360598	+	0.932721i	$0.382573\pi$
$48$		0			0
$49$	−5.47214	+	9.47802i	−0.781734	+	1.35400i
$50$	−0.309017	+	0.535233i	−0.0437016	+	0.0756934i
$51$		0			0
$52$	4.04508	−	4.20378i	0.560952	−	0.582959i
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$		0			0
$55$	0.118034	−	0.204441i	0.0159157	−	0.0275668i
$56$	4.73607	+	8.20311i	0.632884	+	1.09619i
$57$		0			0
$58$	−2.30902	−	3.99933i	−0.303189	−	0.525138i
$59$	−0.354102	−	0.613323i	−0.0461001	−	0.0798478i	0.842055	−	0.539392i	$-0.181346\pi$
$59$	−0.354102	−	0.613323i	−0.0461001	−	0.0798478i	−0.888155	+	0.459545i	$0.848013\pi$
$60$		0			0
$61$	−7.20820	−	12.4850i	−0.922916	−	1.59854i	−0.794879	−	0.606768i	$-0.792466\pi$
$61$	−7.20820	−	12.4850i	−0.922916	−	1.59854i	−0.128037	−	0.991769i	$-0.540868\pi$
$62$		0			0
$63$		0			0
$64$	−0.236068			−0.0295085
$65$	1.00000	+	3.46410i	0.124035	+	0.429669i
$66$		0			0
$67$	1.35410	−	2.34537i	0.165430	−	0.286533i	−0.771378	−	0.636377i	$-0.780432\pi$
$67$	1.35410	−	2.34537i	0.165430	−	0.286533i	0.936808	+	0.349844i	$0.113766\pi$
$68$	2.80902	−	4.86536i	0.340643	−	0.590012i
$69$		0			0
$70$	−2.61803			−0.312915
$71$	−3.11803	−	5.40059i	−0.370043	−	0.640933i	0.619529	−	0.784974i	$-0.287324\pi$
$71$	−3.11803	−	5.40059i	−0.370043	−	0.640933i	−0.989572	+	0.144041i	$0.953990\pi$
$72$		0			0
$73$	−6.00000			−0.702247			−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000			−0.702247			−0.351123	+	0.936329i	$0.614200\pi$
$74$	−0.927051	−	1.60570i	−0.107767	−	0.186659i
$75$		0			0
$76$	3.42705	−	5.93583i	0.393110	−	0.680886i
$77$	1.00000			0.113961
$78$		0			0
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$	0.927051	−	1.60570i	0.103647	−	0.179523i
$81$		0			0
$82$	3.69098	+	6.39297i	0.407601	+	0.705985i
$83$	−8.94427			−0.981761			−0.490881	−	0.871227i	$-0.663325\pi$
$83$	−8.94427			−0.981761			−0.490881	+	0.871227i	$0.663325\pi$
$84$		0			0
$85$	1.73607	+	3.00696i	0.188303	+	0.326150i
$86$	−3.85410			−0.415599
$87$		0			0
$88$	0.263932	−	0.457144i	0.0281352	−	0.0487317i
$89$	−4.50000	+	7.79423i	−0.476999	+	0.826187i	−0.999653	−	0.0263586i	$-0.991609\pi$
$89$	−4.50000	+	7.79423i	−0.476999	+	0.826187i	0.522654	+	0.852545i	$0.324942\pi$
$90$		0			0
$91$	−10.5902	+	11.0056i	−1.11015	+	1.15370i
$92$	6.09017			0.634944
$93$		0			0
$94$	−1.52786	+	2.64634i	−0.157587	+	0.272949i
$95$	2.11803	+	3.66854i	0.217306	+	0.376385i
$96$		0			0
$97$	1.73607	+	3.00696i	0.176271	+	0.305310i	0.940600	−	0.339516i	$-0.110263\pi$
$97$	1.73607	+	3.00696i	0.176271	+	0.305310i	−0.764329	+	0.644826i	$0.776930\pi$
$98$	−3.38197	−	5.85774i	−0.341630	−	0.591721i
$99$		0			0
$100$	0.809017	+	1.40126i	0.0809017	+	0.140126i
$101$	0.263932	−	0.457144i	0.0262622	−	0.0454875i	−0.852596	−	0.522571i	$-0.824973\pi$
$101$	0.263932	−	0.457144i	0.0262622	−	0.0454875i	0.878858	+	0.477084i	$0.158306\pi$
$102$		0			0
$103$	12.9443			1.27544			0.637719	−	0.770270i	$-0.279878\pi$
$103$	12.9443			1.27544			0.637719	+	0.770270i	$0.279878\pi$
$104$	2.23607	+	7.74597i	0.219265	+	0.759555i
$105$		0			0
$106$	1.85410	−	3.21140i	0.180086	−	0.311919i
$107$	−2.88197	+	4.99171i	−0.278610	+	0.482567i	−0.971040	−	0.238919i	$-0.923207\pi$
$107$	−2.88197	+	4.99171i	−0.278610	+	0.482567i	0.692429	+	0.721486i	$0.256540\pi$
$108$		0			0
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$	0.0729490	+	0.126351i	0.00695542	+	0.0120471i
$111$		0			0
$112$	7.85410			0.742143
$113$	0.736068	+	1.27491i	0.0692435	+	0.119933i	0.898568	−	0.438833i	$-0.144608\pi$
$113$	0.736068	+	1.27491i	0.0692435	+	0.119933i	−0.829325	+	0.558766i	$0.811275\pi$
$114$		0			0
$115$	−1.88197	+	3.25966i	−0.175494	+	0.303965i
$116$	−12.0902			−1.12254
$117$		0			0
$118$	0.437694			0.0402930
$119$	−7.35410	+	12.7377i	−0.674149	+	1.16766i
$120$		0			0
$121$	5.47214	+	9.47802i	0.497467	+	0.861638i
$122$	8.90983			0.806658
$123$		0			0
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	2.11803	−	3.66854i	0.187945	−	0.325531i	−0.756620	−	0.653855i	$-0.773151\pi$
$127$	2.11803	−	3.66854i	0.187945	−	0.325531i	0.944565	+	0.328325i	$0.106484\pi$
$128$	5.69098	−	9.85707i	0.503017	−	0.871250i
$129$		0			0
$130$	−2.16312	−	0.535233i	−0.189718	−	0.0469431i
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$		0			0
$133$	−8.97214	+	15.5402i	−0.777983	+	1.34751i
$134$	0.836881	+	1.44952i	0.0722955	+	0.125219i
$135$		0			0
$136$	3.88197	+	6.72376i	0.332876	+	0.576558i
$137$	0.736068	+	1.27491i	0.0628865	+	0.108923i	0.895755	−	0.444549i	$-0.146636\pi$
$137$	0.736068	+	1.27491i	0.0628865	+	0.108923i	−0.832868	+	0.553472i	$0.813303\pi$
$138$		0			0
$139$	8.35410	+	14.4697i	0.708586	+	1.22731i	0.965382	+	0.260841i	$0.0839998\pi$
$139$	8.35410	+	14.4697i	0.708586	+	1.22731i	−0.256796	+	0.966466i	$0.582667\pi$
$140$	−3.42705	+	5.93583i	−0.289639	+	0.501669i
$141$		0			0
$142$	3.85410			0.323429
$143$	0.826238	+	0.204441i	0.0690935	+	0.0170962i
$144$		0			0
$145$	3.73607	−	6.47106i	0.310264	−	0.537392i
$146$	1.85410	−	3.21140i	0.153447	−	0.265777i
$147$		0			0
$148$	−4.85410			−0.399005
$149$	2.26393	+	3.92125i	0.185469	+	0.321241i	0.943734	−	0.330705i	$-0.107286\pi$
$149$	2.26393	+	3.92125i	0.185469	+	0.321241i	−0.758266	+	0.651946i	$0.773953\pi$
$150$		0			0
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$	4.73607	+	8.20311i	0.384146	+	0.665360i
$153$		0			0
$154$	−0.309017	+	0.535233i	−0.0249013	+	0.0431303i
$155$		0			0
$156$		0			0
$157$	−18.0000			−1.43656			−0.718278	−	0.695756i	$-0.755069\pi$
$157$	−18.0000			−1.43656			−0.718278	+	0.695756i	$0.755069\pi$
$158$		0			0
$159$		0			0
$160$	2.80902	+	4.86536i	0.222072	+	0.384640i
$161$	−15.9443			−1.25658
$162$		0			0
$163$	−7.35410	−	12.7377i	−0.576018	−	0.997692i	−0.995930	−	0.0901274i	$-0.971273\pi$
$163$	−7.35410	−	12.7377i	−0.576018	−	0.997692i	0.419913	−	0.907565i	$-0.362061\pi$
$164$	19.3262			1.50913
$165$		0			0
$166$	2.76393	−	4.78727i	0.214523	−	0.371564i
$167$	−8.59017	+	14.8786i	−0.664727	+	1.15134i	0.314632	+	0.949214i	$0.398119\pi$
$167$	−8.59017	+	14.8786i	−0.664727	+	1.15134i	−0.979359	+	0.202128i	$0.935214\pi$
$168$		0			0
$169$	−11.0000	+	6.92820i	−0.846154	+	0.532939i
$170$	−2.14590			−0.164583
$171$		0			0
$172$	−5.04508	+	8.73834i	−0.384684	+	0.666292i
$173$	−9.44427	−	16.3580i	−0.718035	−	1.24367i	−0.961777	−	0.273833i	$-0.911709\pi$
$173$	−9.44427	−	16.3580i	−0.718035	−	1.24367i	0.243743	−	0.969840i	$-0.421625\pi$
$174$		0			0
$175$	−2.11803	−	3.66854i	−0.160108	−	0.277316i
$176$	−0.218847	−	0.379054i	−0.0164962	−	0.0285723i
$177$		0			0
$178$	−2.78115	−	4.81710i	−0.208456	−	0.361057i
$179$	−4.11803	+	7.13264i	−0.307796	+	0.533119i	−0.977880	−	0.209167i	$-0.932925\pi$
$179$	−4.11803	+	7.13264i	−0.307796	+	0.533119i	0.670084	+	0.742286i	$0.266258\pi$
$180$		0			0
$181$	6.00000			0.445976			0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000			0.445976			0.222988	+	0.974821i	$0.428419\pi$
$182$	−2.61803	−	9.06914i	−0.194062	−	0.672249i
$183$		0			0
$184$	−4.20820	+	7.28882i	−0.310233	+	0.537339i
$185$	1.50000	−	2.59808i	0.110282	−	0.191014i
$186$		0			0
$187$	0.819660			0.0599395
$188$	4.00000	+	6.92820i	0.291730	+	0.505291i
$189$		0			0
$190$	−2.61803			−0.189932
$191$	−13.5902	−	23.5389i	−0.983350	−	1.70321i	−0.649050	−	0.760746i	$-0.724833\pi$
$191$	−13.5902	−	23.5389i	−0.983350	−	1.70321i	−0.334300	−	0.942467i	$-0.608500\pi$
$192$		0			0
$193$	1.73607	−	3.00696i	0.124965	−	0.216446i	−0.796754	−	0.604303i	$-0.793452\pi$
$193$	1.73607	−	3.00696i	0.124965	−	0.216446i	0.921719	+	0.387858i	$0.126785\pi$
$194$	−2.14590			−0.154067
$195$		0			0
$196$	−17.7082			−1.26487
$197$	1.50000	−	2.59808i	0.106871	−	0.185105i	−0.807630	−	0.589689i	$-0.799250\pi$
$197$	1.50000	−	2.59808i	0.106871	−	0.185105i	0.914501	+	0.404584i	$0.132584\pi$
$198$		0			0
$199$	0.645898	+	1.11873i	0.0457865	+	0.0793045i	0.888010	−	0.459823i	$-0.152087\pi$
$199$	0.645898	+	1.11873i	0.0457865	+	0.0793045i	−0.842224	+	0.539128i	$0.818754\pi$
$200$	−2.23607			−0.158114
$201$		0			0
$202$	0.163119	+	0.282530i	0.0114770	+	0.0198788i
$203$	31.6525			2.22157
$204$		0			0
$205$	−5.97214	+	10.3440i	−0.417112	+	0.722459i
$206$	−4.00000	+	6.92820i	−0.278693	+	0.482711i
$207$		0			0
$208$	6.48936	+	1.60570i	0.449956	+	0.111335i
$209$	1.00000			0.0691714
$210$		0			0
$211$	6.59017	−	11.4145i	0.453686	−	0.785807i	−0.544926	−	0.838484i	$-0.683442\pi$
$211$	6.59017	−	11.4145i	0.453686	−	0.785807i	0.998612	+	0.0526772i	$0.0167754\pi$
$212$	−4.85410	−	8.40755i	−0.333381	−	0.577433i
$213$		0			0
$214$	−1.78115	−	3.08505i	−0.121757	−	0.210889i
$215$	−3.11803	−	5.40059i	−0.212648	−	0.368317i
$216$		0			0
$217$		0			0
$218$	0.618034	−	1.07047i	0.0418585	−	0.0725011i
$219$		0			0
$220$	0.381966			0.0257521
$221$	−8.68034	+	9.02087i	−0.583903	+	0.606810i
$222$		0			0
$223$	−0.354102	+	0.613323i	−0.0237124	+	0.0410711i	−0.877638	−	0.479324i	$-0.840882\pi$
$223$	−0.354102	+	0.613323i	−0.0237124	+	0.0410711i	0.853926	+	0.520395i	$0.174215\pi$
$224$	−11.8992	+	20.6100i	−0.795048	+	1.37706i
$225$		0			0
$226$	−0.909830			−0.0605210
$227$	−3.11803	−	5.40059i	−0.206951	−	0.358450i	0.743801	−	0.668401i	$-0.233021\pi$
$227$	−3.11803	−	5.40059i	−0.206951	−	0.358450i	−0.950753	+	0.309951i	$0.899687\pi$
$228$		0			0
$229$	15.8885			1.04994			0.524972	−	0.851119i	$-0.324076\pi$
$229$	15.8885			1.04994			0.524972	+	0.851119i	$0.324076\pi$
$230$	−1.16312	−	2.01458i	−0.0766938	−	0.132838i
$231$		0			0
$232$	8.35410	−	14.4697i	0.548474	−	0.949984i
$233$	15.8885			1.04089			0.520447	−	0.853894i	$-0.325765\pi$
$233$	15.8885			1.04089			0.520447	+	0.853894i	$0.325765\pi$
$234$		0			0
$235$	−4.94427			−0.322529
$236$	0.572949	−	0.992377i	0.0372958	−	0.0645982i
$237$		0			0
$238$	−4.54508	−	7.87232i	−0.294614	−	0.510287i
$239$	25.8885			1.67459			0.837295	−	0.546751i	$-0.184136\pi$
$239$	25.8885			1.67459			0.837295	+	0.546751i	$0.184136\pi$
$240$		0			0
$241$	−7.50000	−	12.9904i	−0.483117	−	0.836784i	0.516695	−	0.856170i	$-0.327162\pi$
$241$	−7.50000	−	12.9904i	−0.483117	−	0.836784i	−0.999812	+	0.0193858i	$0.993829\pi$
$242$	−6.76393			−0.434802
$243$		0			0
$244$	11.6631	−	20.2011i	0.746655	−	1.29324i
$245$	5.47214	−	9.47802i	0.349602	−	0.605528i
$246$		0			0
$247$	−10.5902	+	11.0056i	−0.673836	+	0.700271i
$248$		0			0
$249$		0			0
$250$	0.309017	−	0.535233i	0.0195440	−	0.0338511i
$251$	10.1180	+	17.5249i	0.638645	+	1.10616i	0.985730	+	0.168332i	$0.0538379\pi$
$251$	10.1180	+	17.5249i	0.638645	+	1.10616i	−0.347086	+	0.937833i	$0.612829\pi$
$252$		0			0
$253$	0.444272	+	0.769502i	0.0279311	+	0.0483781i
$254$	1.30902	+	2.26728i	0.0821350	+	0.142262i
$255$		0			0
$256$	3.28115	+	5.68312i	0.205072	+	0.355195i
$257$	8.73607	−	15.1313i	0.544941	−	0.943865i	−0.453670	−	0.891170i	$-0.649885\pi$
$257$	8.73607	−	15.1313i	0.544941	−	0.943865i	0.998611	−	0.0526955i	$-0.0167813\pi$
$258$		0			0
$259$	12.7082			0.789649
$260$	−4.04508	+	4.20378i	−0.250866	+	0.260707i
$261$		0			0
$262$	−3.70820	+	6.42280i	−0.229094	+	0.396802i
$263$	1.88197	−	3.25966i	0.116047	−	0.200999i	−0.802151	−	0.597122i	$-0.796311\pi$
$263$	1.88197	−	3.25966i	0.116047	−	0.200999i	0.918198	+	0.396122i	$0.129644\pi$
$264$		0			0
$265$	6.00000			0.368577
$266$	−5.54508	−	9.60437i	−0.339991	−	0.588882i
$267$		0			0
$268$	4.38197			0.267671
$269$	−3.26393	−	5.65330i	−0.199005	−	0.344688i	0.749201	−	0.662343i	$-0.230438\pi$
$269$	−3.26393	−	5.65330i	−0.199005	−	0.344688i	−0.948206	+	0.317655i	$0.897104\pi$
$270$		0			0
$271$	−0.645898	+	1.11873i	−0.0392355	+	0.0679579i	−0.884976	−	0.465636i	$-0.845826\pi$
$271$	−0.645898	+	1.11873i	−0.0392355	+	0.0679579i	0.845741	+	0.533594i	$0.179159\pi$
$272$	6.43769			0.390343
$273$		0			0
$274$	−0.909830			−0.0549648
$275$	−0.118034	+	0.204441i	−0.00711772	+	0.0123282i
$276$		0			0
$277$	−8.44427	−	14.6259i	−0.507367	−	0.878786i	−0.999964	−	0.00852782i	$-0.997285\pi$
$277$	−8.44427	−	14.6259i	−0.507367	−	0.878786i	0.492597	−	0.870258i	$-0.336048\pi$
$278$	−10.3262			−0.619327
$279$		0			0
$280$	−4.73607	−	8.20311i	−0.283034	−	0.490230i
$281$	15.8885			0.947831			0.473916	−	0.880570i	$-0.342840\pi$
$281$	15.8885			0.947831			0.473916	+	0.880570i	$0.342840\pi$
$282$		0			0
$283$	5.35410	−	9.27358i	0.318268	−	0.551257i	−0.661859	−	0.749629i	$-0.730232\pi$
$283$	5.35410	−	9.27358i	0.318268	−	0.551257i	0.980127	+	0.198372i	$0.0635654\pi$
$284$	5.04508	−	8.73834i	0.299371	−	0.518525i
$285$		0			0
$286$	−0.364745	+	0.379054i	−0.0215678	+	0.0224139i
$287$	−50.5967			−2.98663
$288$		0			0
$289$	2.47214	−	4.28187i	0.145420	−	0.251874i
$290$	2.30902	+	3.99933i	0.135590	+	0.234849i
$291$		0			0
$292$	−4.85410	−	8.40755i	−0.284065	−	0.492015i
$293$	−14.9721	−	25.9325i	−0.874682	−	1.51499i	−0.857102	−	0.515147i	$-0.827737\pi$
$293$	−14.9721	−	25.9325i	−0.874682	−	1.51499i	−0.0175799	−	0.999845i	$-0.505596\pi$
$294$		0			0
$295$	0.354102	+	0.613323i	0.0206166	+	0.0357090i
$296$	3.35410	−	5.80948i	0.194953	−	0.337669i
$297$		0			0
$298$	−2.79837			−0.162105
$299$	−13.1738	−	3.25966i	−0.761858	−	0.188511i
$300$		0			0
$301$	13.2082	−	22.8773i	0.761308	−	1.31862i
$302$	−2.47214	+	4.28187i	−0.142255	+	0.246394i
$303$		0			0
$304$	7.85410			0.450464
$305$	7.20820	+	12.4850i	0.412741	+	0.714888i
$306$		0			0
$307$	24.9443			1.42364			0.711822	−	0.702360i	$-0.247870\pi$
$307$	24.9443			1.42364			0.711822	+	0.702360i	$0.247870\pi$
$308$	0.809017	+	1.40126i	0.0460980	+	0.0798441i
$309$		0			0
$310$		0			0
$311$	24.0000			1.36092			0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000			1.36092			0.680458	+	0.732787i	$0.261781\pi$
$312$		0			0
$313$	3.88854			0.219793			0.109897	−	0.993943i	$-0.464948\pi$
$313$	3.88854			0.219793			0.109897	+	0.993943i	$0.464948\pi$
$314$	5.56231	−	9.63420i	0.313899	−	0.543689i
$315$		0			0
$316$		0			0
$317$	11.8885			0.667727			0.333864	−	0.942621i	$-0.391648\pi$
$317$	11.8885			0.667727			0.333864	+	0.942621i	$0.391648\pi$
$318$		0			0
$319$	−0.881966	−	1.52761i	−0.0493806	−	0.0855297i
$320$	0.236068			0.0131966
$321$		0			0
$322$	4.92705	−	8.53390i	0.274574	−	0.475576i
$323$	−7.35410	+	12.7377i	−0.409193	+	0.708743i
$324$		0			0
$325$	−1.00000	−	3.46410i	−0.0554700	−	0.192154i
$326$	9.09017			0.503458
$327$		0			0
$328$	−13.3541	+	23.1300i	−0.737357	+	1.27714i
$329$	−10.4721	−	18.1383i	−0.577348	−	0.999995i
$330$		0			0
$331$	2.82624	+	4.89519i	0.155344	+	0.269064i	0.933184	−	0.359398i	$-0.117018\pi$
$331$	2.82624	+	4.89519i	0.155344	+	0.269064i	−0.777840	+	0.628462i	$0.783685\pi$
$332$	−7.23607	−	12.5332i	−0.397131	−	0.687851i
$333$		0			0
$334$	−5.30902	−	9.19549i	−0.290496	−	0.503155i
$335$	−1.35410	+	2.34537i	−0.0739825	+	0.128141i
$336$		0			0
$337$	−7.88854			−0.429716			−0.214858	−	0.976645i	$-0.568929\pi$
$337$	−7.88854			−0.429716			−0.214858	+	0.976645i	$0.568929\pi$
$338$	−0.309017	−	8.02850i	−0.0168083	−	0.436693i
$339$		0			0
$340$	−2.80902	+	4.86536i	−0.152340	+	0.263861i
$341$		0			0
$342$		0			0
$343$	16.7082			0.902158
$344$	−6.97214	−	12.0761i	−0.375912	−	0.651099i
$345$		0			0
$346$	11.6738			0.627585
$347$	15.3541	+	26.5941i	0.824251	+	1.42765i	0.902490	+	0.430711i	$0.141737\pi$
$347$	15.3541	+	26.5941i	0.824251	+	1.42765i	−0.0782387	+	0.996935i	$0.524930\pi$
$348$		0			0
$349$	−1.20820	+	2.09267i	−0.0646737	+	0.112018i	−0.896549	−	0.442944i	$-0.853934\pi$
$349$	−1.20820	+	2.09267i	−0.0646737	+	0.112018i	0.831876	+	0.554962i	$0.187267\pi$
$350$	2.61803			0.139940
$351$		0			0
$352$	1.32624			0.0706887
$353$	−9.73607	+	16.8634i	−0.518199	+	0.897546i	0.481578	+	0.876403i	$0.340064\pi$
$353$	−9.73607	+	16.8634i	−0.518199	+	0.897546i	−0.999776	+	0.0211430i	$0.993269\pi$
$354$		0			0
$355$	3.11803	+	5.40059i	0.165488	+	0.286634i
$356$	−14.5623			−0.771801
$357$		0			0
$358$	−2.54508	−	4.40822i	−0.134512	−	0.232981i
$359$	−17.8885			−0.944121			−0.472061	−	0.881566i	$-0.656490\pi$
$359$	−17.8885			−0.944121			−0.472061	+	0.881566i	$0.656490\pi$
$360$		0			0
$361$	0.527864	−	0.914287i	0.0277823	−	0.0481204i
$362$	−1.85410	+	3.21140i	−0.0974494	+	0.168787i
$363$		0			0
$364$	−23.9894	−	5.93583i	−1.25738	−	0.311122i
$365$	6.00000			0.314054
$366$		0			0
$367$	−2.82624	+	4.89519i	−0.147528	+	0.255527i	−0.930313	−	0.366766i	$-0.880465\pi$
$367$	−2.82624	+	4.89519i	−0.147528	+	0.255527i	0.782785	+	0.622292i	$0.213798\pi$
$368$	3.48936	+	6.04374i	0.181895	+	0.315052i
$369$		0			0
$370$	0.927051	+	1.60570i	0.0481951	+	0.0834763i
$371$	12.7082	+	22.0113i	0.659777	+	1.14277i
$372$		0			0
$373$	−13.9721	−	24.2004i	−0.723450	−	1.25305i	−0.959609	−	0.281337i	$-0.909222\pi$
$373$	−13.9721	−	24.2004i	−0.723450	−	1.25305i	0.236159	−	0.971714i	$-0.424111\pi$
$374$	−0.253289	+	0.438709i	−0.0130973	+	0.0226851i
$375$		0			0
$376$	−11.0557			−0.570156
$377$	26.1525	+	6.47106i	1.34692	+	0.333277i
$378$		0			0
$379$	−5.40983	+	9.37010i	−0.277884	+	0.481310i	−0.970859	−	0.239652i	$-0.922967\pi$
$379$	−5.40983	+	9.37010i	−0.277884	+	0.481310i	0.692974	+	0.720962i	$0.256300\pi$
$380$	−3.42705	+	5.93583i	−0.175804	+	0.304501i
$381$		0			0
$382$	16.7984			0.859480
$383$	2.11803	+	3.66854i	0.108226	+	0.187454i	0.915052	−	0.403336i	$-0.132149\pi$
$383$	2.11803	+	3.66854i	0.108226	+	0.187454i	−0.806825	+	0.590790i	$0.798816\pi$
$384$		0			0
$385$	−1.00000			−0.0509647
$386$	1.07295	+	1.85840i	0.0546117	+	0.0945902i
$387$		0			0
$388$	−2.80902	+	4.86536i	−0.142606	+	0.247001i
$389$	0.111456			0.00565105			0.00282553	−	0.999996i	$-0.499101\pi$
$389$	0.111456			0.00565105			0.00282553	+	0.999996i	$0.499101\pi$
$390$		0			0
$391$	−13.0689			−0.660922
$392$	12.2361	−	21.1935i	0.618015	−	1.07043i
$393$		0			0
$394$	0.927051	+	1.60570i	0.0467042	+	0.0808940i
$395$		0			0
$396$		0			0
$397$	−13.9721	−	24.2004i	−0.701241	−	1.21459i	−0.968031	−	0.250831i	$-0.919296\pi$
$397$	−13.9721	−	24.2004i	−0.701241	−	1.21459i	0.266790	−	0.963755i	$-0.414037\pi$
$398$	−0.798374			−0.0400189
$399$		0			0
$400$	−0.927051	+	1.60570i	−0.0463525	+	0.0802850i
$401$	4.44427	−	7.69770i	0.221936	−	0.384405i	−0.733460	−	0.679733i	$-0.762096\pi$
$401$	4.44427	−	7.69770i	0.221936	−	0.384405i	0.955396	+	0.295328i	$0.0954289\pi$
$402$		0			0
$403$		0			0
$404$	0.854102			0.0424932
$405$		0			0
$406$	−9.78115	+	16.9415i	−0.485430	+	0.840790i
$407$	−0.354102	−	0.613323i	−0.0175522	−	0.0304013i
$408$		0			0
$409$	−12.4443	−	21.5541i	−0.615330	−	1.06578i	−0.990327	−	0.138756i	$-0.955690\pi$
$409$	−12.4443	−	21.5541i	−0.615330	−	1.06578i	0.374997	−	0.927026i	$-0.377644\pi$
$410$	−3.69098	−	6.39297i	−0.182285	−	0.315726i
$411$		0			0
$412$	10.4721	+	18.1383i	0.515925	+	0.893609i
$413$	−1.50000	+	2.59808i	−0.0738102	+	0.127843i
$414$		0			0
$415$	8.94427			0.439057
$416$	−14.0451	+	14.5961i	−0.688617	+	0.715632i
$417$		0			0
$418$	−0.309017	+	0.535233i	−0.0151145	+	0.0261791i
$419$	8.82624	−	15.2875i	0.431190	−	0.746843i	−0.565786	−	0.824552i	$-0.691427\pi$
$419$	8.82624	−	15.2875i	0.431190	−	0.746843i	0.996976	+	0.0777091i	$0.0247606\pi$
$420$		0			0
$421$	6.00000			0.292422			0.146211	−	0.989253i	$-0.453292\pi$
$421$	6.00000			0.292422			0.146211	+	0.989253i	$0.453292\pi$
$422$	4.07295	+	7.05455i	0.198268	+	0.343410i
$423$		0			0
$424$	13.4164			0.651558
$425$	−1.73607	−	3.00696i	−0.0842117	−	0.145859i
$426$		0			0
$427$	−30.5344	+	52.8872i	−1.47767	+	2.55939i
$428$	−9.32624			−0.450801
$429$		0			0
$430$	3.85410			0.185861
$431$	13.5902	−	23.5389i	0.654615	−	1.13383i	−0.327375	−	0.944895i	$-0.606164\pi$
$431$	13.5902	−	23.5389i	0.654615	−	1.13383i	0.981990	−	0.188933i	$-0.0605028\pi$
$432$		0			0
$433$	7.26393	+	12.5815i	0.349082	+	0.604628i	0.986087	−	0.166232i	$-0.0531600\pi$
$433$	7.26393	+	12.5815i	0.349082	+	0.604628i	−0.637004	+	0.770860i	$0.719827\pi$
$434$		0			0
$435$		0			0
$436$	−1.61803	−	2.80252i	−0.0774898	−	0.134216i
$437$	−15.9443			−0.762718
$438$		0			0
$439$	11.3541	−	19.6659i	0.541902	−	0.938601i	−0.456893	−	0.889522i	$-0.651038\pi$
$439$	11.3541	−	19.6659i	0.541902	−	0.938601i	0.998795	−	0.0490797i	$-0.0156288\pi$
$440$	−0.263932	+	0.457144i	−0.0125825	+	0.0217935i
$441$		0			0
$442$	−2.14590	−	7.43361i	−0.102070	−	0.353581i
$443$	−0.944272			−0.0448637			−0.0224319	−	0.999748i	$-0.507141\pi$
$443$	−0.944272			−0.0448637			−0.0224319	+	0.999748i	$0.507141\pi$
$444$		0			0
$445$	4.50000	−	7.79423i	0.213320	−	0.369482i
$446$	−0.218847	−	0.379054i	−0.0103627	−	0.0179487i
$447$		0			0
$448$	0.500000	+	0.866025i	0.0236228	+	0.0409159i
$449$	1.97214	+	3.41584i	0.0930709	+	0.161203i	0.908802	−	0.417228i	$-0.136998\pi$
$449$	1.97214	+	3.41584i	0.0930709	+	0.161203i	−0.815731	+	0.578431i	$0.803665\pi$
$450$		0			0
$451$	1.40983	+	2.44190i	0.0663863	+	0.114984i
$452$	−1.19098	+	2.06284i	−0.0560191	+	0.0970280i
$453$		0			0
$454$	3.85410			0.180882
$455$	10.5902	−	11.0056i	0.496475	−	0.515952i
$456$		0			0
$457$	0.791796	−	1.37143i	0.0370387	−	0.0641528i	−0.846912	−	0.531733i	$-0.821541\pi$
$457$	0.791796	−	1.37143i	0.0370387	−	0.0641528i	0.883950	+	0.467580i	$0.154874\pi$
$458$	−4.90983	+	8.50408i	−0.229421	+	0.397369i
$459$		0			0
$460$	−6.09017			−0.283956
$461$	−0.791796	−	1.37143i	−0.0368776	−	0.0638739i	0.846998	−	0.531597i	$-0.178408\pi$
$461$	−0.791796	−	1.37143i	−0.0368776	−	0.0638739i	−0.883875	+	0.467723i	$0.845075\pi$
$462$		0			0
$463$	11.0557			0.513803			0.256902	−	0.966438i	$-0.417298\pi$
$463$	11.0557			0.513803			0.256902	+	0.966438i	$0.417298\pi$
$464$	−6.92705	−	11.9980i	−0.321580	−	0.556993i
$465$		0			0
$466$	−4.90983	+	8.50408i	−0.227443	+	0.393944i
$467$	−8.94427			−0.413892			−0.206946	−	0.978352i	$-0.566352\pi$
$467$	−8.94427			−0.413892			−0.206946	+	0.978352i	$0.566352\pi$
$468$		0			0
$469$	−11.4721			−0.529734
$470$	1.52786	−	2.64634i	0.0704751	−	0.122066i
$471$		0			0
$472$	0.791796	+	1.37143i	0.0364454	+	0.0631252i
$473$	−1.47214			−0.0676889
$474$		0			0
$475$	−2.11803	−	3.66854i	−0.0971821	−	0.168324i
$476$	−23.7984			−1.09080
$477$		0			0
$478$	−8.00000	+	13.8564i	−0.365911	+	0.633777i
$479$	16.0623	−	27.8207i	0.733905	−	1.27116i	−0.221296	−	0.975207i	$-0.571029\pi$
$479$	16.0623	−	27.8207i	0.733905	−	1.27116i	0.955202	−	0.295955i	$-0.0956378\pi$
$480$		0			0
$481$	10.5000	+	2.59808i	0.478759	+	0.118462i
$482$	9.27051			0.422260
$483$		0			0
$484$	−8.85410	+	15.3358i	−0.402459	+	0.697080i
$485$	−1.73607	−	3.00696i	−0.0788308	−	0.136539i
$486$		0			0
$487$	−7.06231	−	12.2323i	−0.320024	−	0.554297i	0.660469	−	0.750853i	$-0.270358\pi$
$487$	−7.06231	−	12.2323i	−0.320024	−	0.554297i	−0.980493	+	0.196556i	$0.937024\pi$
$488$	16.1180	+	27.9173i	0.729629	+	1.26375i
$489$		0			0
$490$	3.38197	+	5.85774i	0.152782	+	0.264626i
$491$	−0.118034	+	0.204441i	−0.00532680	+	0.00922629i	−0.868677	−	0.495380i	$-0.835029\pi$
$491$	−0.118034	+	0.204441i	−0.00532680	+	0.00922629i	0.863350	+	0.504606i	$0.168362\pi$
$492$		0			0
$493$	25.9443			1.16847
$494$	−2.61803	−	9.06914i	−0.117791	−	0.408040i
$495$		0			0
$496$		0			0
$497$	−13.2082	+	22.8773i	−0.592469	+	1.02619i
$498$		0			0
$499$	−21.8885			−0.979866			−0.489933	−	0.871760i	$-0.662979\pi$
$499$	−21.8885			−0.979866			−0.489933	+	0.871760i	$0.662979\pi$
$500$	−0.809017	−	1.40126i	−0.0361803	−	0.0626662i
$501$		0			0
$502$	−12.5066			−0.558196
$503$	4.59017	+	7.95041i	0.204666	+	0.354491i	0.950026	−	0.312170i	$-0.101056\pi$
$503$	4.59017	+	7.95041i	0.204666	+	0.354491i	−0.745361	+	0.666662i	$0.767723\pi$
$504$		0			0
$505$	−0.263932	+	0.457144i	−0.0117448	+	0.0203426i
$506$	−0.549150			−0.0244127
$507$		0			0
$508$	6.85410			0.304102
$509$	−16.6803	+	28.8912i	−0.739343	+	1.28058i	0.213448	+	0.976954i	$0.431530\pi$
$509$	−16.6803	+	28.8912i	−0.739343	+	1.28058i	−0.952791	+	0.303625i	$0.901803\pi$
$510$		0			0
$511$	12.7082	+	22.0113i	0.562178	+	0.973721i
$512$	18.7082			0.826794
$513$		0			0
$514$	5.39919	+	9.35167i	0.238148	+	0.412484i
$515$	−12.9443			−0.570393
$516$		0			0
$517$	−0.583592	+	1.01081i	−0.0256664	+	0.0444554i
$518$	−3.92705	+	6.80185i	−0.172545	+	0.298856i
$519$		0			0
$520$	−2.23607	−	7.74597i	−0.0980581	−	0.339683i
$521$	−29.7771			−1.30456			−0.652279	−	0.757979i	$-0.726187\pi$
$521$	−29.7771			−1.30456			−0.652279	+	0.757979i	$0.726187\pi$
$522$		0			0
$523$	−2.64590	+	4.58283i	−0.115697	+	0.200393i	−0.918058	−	0.396446i	$-0.870244\pi$
$523$	−2.64590	+	4.58283i	−0.115697	+	0.200393i	0.802361	+	0.596839i	$0.203577\pi$
$524$	9.70820	+	16.8151i	0.424105	+	0.734571i
$525$		0			0
$526$	1.16312	+	2.01458i	0.0507144	+	0.0878399i
$527$		0			0
$528$		0			0
$529$	4.41641	+	7.64944i	0.192018	+	0.332584i
$530$	−1.85410	+	3.21140i	−0.0805370	+	0.139494i
$531$		0			0
$532$	−29.0344			−1.25880
$533$	−41.8050	−	10.3440i	−1.81077	−	0.448050i
$534$		0			0
$535$	2.88197	−	4.99171i	0.124598	−	0.215811i
$536$	−3.02786	+	5.24441i	−0.130784	+	0.226524i
$537$		0			0
$538$	4.03444			0.173937
$539$	−1.29180	−	2.23746i	−0.0556416	−	0.0963741i
$540$		0			0
$541$	−27.8885			−1.19902			−0.599511	−	0.800366i	$-0.704638\pi$
$541$	−27.8885			−1.19902			−0.599511	+	0.800366i	$0.704638\pi$
$542$	−0.399187	−	0.691412i	−0.0171465	−	0.0296987i
$543$		0			0
$544$	−9.75329	+	16.8932i	−0.418169	+	0.724290i
$545$	2.00000			0.0856706
$546$		0			0
$547$	18.8328			0.805233			0.402617	−	0.915369i	$-0.368101\pi$
$547$	18.8328			0.805233			0.402617	+	0.915369i	$0.368101\pi$
$548$	−1.19098	+	2.06284i	−0.0508763	+	0.0881203i
$549$		0			0
$550$	−0.0729490	−	0.126351i	−0.00311056	−	0.00538764i
$551$	31.6525			1.34844
$552$		0			0
$553$		0			0
$554$	10.4377			0.443455
$555$		0			0
$556$	−13.5172	+	23.4125i	−0.573258	+	0.992912i
$557$	−4.97214	+	8.61199i	−0.210676	+	0.364902i	−0.951926	−	0.306327i	$-0.900900\pi$
$557$	−4.97214	+	8.61199i	−0.210676	+	0.364902i	0.741250	+	0.671229i	$0.234233\pi$
$558$		0			0
$559$	15.5902	−	16.2018i	0.659394	−	0.685262i
$560$	−7.85410			−0.331896
$561$		0			0
$562$	−4.90983	+	8.50408i	−0.207109	+	0.358723i
$563$	15.3541	+	26.5941i	0.647098	+	1.12081i	0.983813	+	0.179200i	$0.0573510\pi$
$563$	15.3541	+	26.5941i	0.647098	+	1.12081i	−0.336714	+	0.941607i	$0.609316\pi$
$564$		0			0
$565$	−0.736068	−	1.27491i	−0.0309666	−	0.0536357i
$566$	3.30902	+	5.73139i	0.139088	+	0.240908i
$567$		0			0
$568$	6.97214	+	12.0761i	0.292544	+	0.506702i
$569$	8.44427	−	14.6259i	0.354002	−	0.613150i	−0.632944	−	0.774197i	$-0.718154\pi$
$569$	8.44427	−	14.6259i	0.354002	−	0.613150i	0.986947	+	0.161047i	$0.0514872\pi$
$570$		0			0
$571$	28.0000			1.17176			0.585882	−	0.810397i	$-0.300748\pi$
$571$	28.0000			1.17176			0.585882	+	0.810397i	$0.300748\pi$
$572$	0.381966	+	1.32317i	0.0159708	+	0.0553245i
$573$		0			0
$574$	15.6353	−	27.0811i	0.652603	−	1.13034i
$575$	1.88197	−	3.25966i	0.0784834	−	0.135937i
$576$		0			0
$577$	27.8885			1.16102			0.580508	−	0.814255i	$-0.302854\pi$
$577$	27.8885			1.16102			0.580508	+	0.814255i	$0.302854\pi$
$578$	1.52786	+	2.64634i	0.0635508	+	0.110073i
$579$		0			0
$580$	12.0902			0.502017
$581$	18.9443	+	32.8124i	0.785941	+	1.36129i
$582$		0			0
$583$	0.708204	−	1.22665i	0.0293308	−	0.0508025i
$584$	13.4164			0.555175
$585$		0			0
$586$	18.5066			0.764500
$587$	5.11803	−	8.86469i	0.211244	−	0.365885i	−0.740860	−	0.671659i	$-0.765582\pi$
$587$	5.11803	−	8.86469i	0.211244	−	0.365885i	0.952104	+	0.305774i	$0.0989152\pi$
$588$		0			0
$589$		0			0
$590$	−0.437694			−0.0180196
$591$		0			0
$592$	−2.78115	−	4.81710i	−0.114305	−	0.197982i
$593$	7.88854			0.323944			0.161972	−	0.986795i	$-0.448215\pi$
$593$	7.88854			0.323944			0.161972	+	0.986795i	$0.448215\pi$
$594$		0			0
$595$	7.35410	−	12.7377i	0.301489	−	0.522194i
$596$	−3.66312	+	6.34471i	−0.150047	+	0.259889i
$597$		0			0
$598$	5.81559	−	6.04374i	0.237817	−	0.247147i
$599$	24.0000			0.980613			0.490307	−	0.871550i	$-0.336885\pi$
$599$	24.0000			0.980613			0.490307	+	0.871550i	$0.336885\pi$
$600$		0			0
$601$	−21.9721	+	38.0569i	−0.896262	+	1.55237i	−0.0640274	+	0.997948i	$0.520394\pi$
$601$	−21.9721	+	38.0569i	−0.896262	+	1.55237i	−0.832235	+	0.554423i	$0.812939\pi$
$602$	8.16312	+	14.1389i	0.332704	+	0.576260i
$603$		0			0
$604$	6.47214	+	11.2101i	0.263347	+	0.456131i
$605$	−5.47214	−	9.47802i	−0.222474	−	0.385336i
$606$		0			0
$607$	0.354102	+	0.613323i	0.0143726	+	0.0248940i	0.873122	−	0.487501i	$-0.162092\pi$
$607$	0.354102	+	0.613323i	0.0143726	+	0.0248940i	−0.858750	+	0.512395i	$0.828758\pi$
$608$	−11.8992	+	20.6100i	−0.482576	+	0.835846i
$609$		0			0
$610$	−8.90983			−0.360748
$611$	−4.94427	−	17.1275i	−0.200024	−	0.692903i
$612$		0			0
$613$	−19.9721	+	34.5928i	−0.806667	+	1.39719i	0.108493	+	0.994097i	$0.465398\pi$
$613$	−19.9721	+	34.5928i	−0.806667	+	1.39719i	−0.915160	+	0.403091i	$0.867936\pi$
$614$	−7.70820	+	13.3510i	−0.311078	+	0.538803i
$615$		0			0
$616$	−2.23607			−0.0900937
$617$	−20.2082	−	35.0016i	−0.813552	−	1.40911i	−0.910363	−	0.413810i	$-0.864198\pi$
$617$	−20.2082	−	35.0016i	−0.813552	−	1.40911i	0.0968116	−	0.995303i	$-0.469136\pi$
$618$		0			0
$619$	12.0000			0.482321			0.241160	−	0.970485i	$-0.422472\pi$
$619$	12.0000			0.482321			0.241160	+	0.970485i	$0.422472\pi$
$620$		0			0
$621$		0			0
$622$	−7.41641	+	12.8456i	−0.297371	+	0.515061i
$623$	38.1246			1.52743
$624$		0			0
$625$	1.00000			0.0400000
$626$	−1.20163	+	2.08128i	−0.0480266	+	0.0831846i
$627$		0			0
$628$	−14.5623	−	25.2227i	−0.581099	−	1.00649i
$629$	10.4164			0.415329
$630$		0			0
$631$	8.06231	+	13.9643i	0.320955	+	0.555911i	0.980685	−	0.195592i	$-0.0626627\pi$
$631$	8.06231	+	13.9643i	0.320955	+	0.555911i	−0.659730	+	0.751503i	$0.729329\pi$
$632$		0			0
$633$		0			0
$634$	−3.67376	+	6.36314i	−0.145904	+	0.252713i
$635$	−2.11803	+	3.66854i	−0.0840516	+	0.145582i
$636$		0			0
$637$	38.3050	+	9.47802i	1.51770	+	0.375533i
$638$	1.09017			0.0431602
$639$		0			0
$640$	−5.69098	+	9.85707i	−0.224956	+	0.389635i
$641$	4.44427	+	7.69770i	0.175538	+	0.304041i	0.940347	−	0.340216i	$-0.110500\pi$
$641$	4.44427	+	7.69770i	0.175538	+	0.304041i	−0.764809	+	0.644257i	$0.777167\pi$
$642$		0			0
$643$	8.64590	+	14.9751i	0.340961	+	0.590562i	0.984611	−	0.174758i	$-0.0559143\pi$
$643$	8.64590	+	14.9751i	0.340961	+	0.590562i	−0.643650	+	0.765320i	$0.722581\pi$
$644$	−12.8992	−	22.3420i	−0.508299	−	0.880400i
$645$		0			0
$646$	−4.54508	−	7.87232i	−0.178824	−	0.309732i
$647$	1.29837	−	2.24885i	0.0510443	−	0.0884114i	−0.839374	−	0.543554i	$-0.817078\pi$
$647$	1.29837	−	2.24885i	0.0510443	−	0.0884114i	0.890419	+	0.455142i	$0.150412\pi$
$648$		0			0
$649$	0.167184			0.00656256
$650$	2.16312	+	0.535233i	0.0848445	+	0.0209936i
$651$		0			0
$652$	11.8992	−	20.6100i	0.466008	−	0.807150i
$653$	−10.5000	+	18.1865i	−0.410897	+	0.711694i	−0.994988	−	0.0999939i	$-0.968118\pi$
$653$	−10.5000	+	18.1865i	−0.410897	+	0.711694i	0.584091	+	0.811688i	$0.301451\pi$
$654$		0			0
$655$	−12.0000			−0.468879
$656$	11.0729	+	19.1789i	0.432326	+	0.748811i
$657$		0			0
$658$	12.9443			0.504620
$659$	−21.8820	−	37.9007i	−0.852400	−	1.47640i	−0.879036	−	0.476756i	$-0.841813\pi$
$659$	−21.8820	−	37.9007i	−0.852400	−	1.47640i	0.0266355	−	0.999645i	$-0.491521\pi$
$660$		0			0
$661$	20.6803	−	35.8194i	0.804372	−	1.39321i	−0.112342	−	0.993670i	$-0.535835\pi$
$661$	20.6803	−	35.8194i	0.804372	−	1.39321i	0.916714	−	0.399544i	$-0.130831\pi$
$662$	−3.49342			−0.135776
$663$		0			0
$664$	20.0000			0.776151
$665$	8.97214	−	15.5402i	0.347925	−	0.602623i
$666$		0			0
$667$	14.0623	+	24.3566i	0.544495	+	0.943092i
$668$	−27.7984			−1.07555
$669$		0			0
$670$	−0.836881	−	1.44952i	−0.0323315	−	0.0559999i
$671$	3.40325			0.131381
$672$		0			0
$673$	4.79180	−	8.29963i	0.184710	−	0.319927i	−0.758769	−	0.651360i	$-0.774199\pi$
$673$	4.79180	−	8.29963i	0.184710	−	0.319927i	0.943479	+	0.331433i	$0.107532\pi$
$674$	2.43769	−	4.22221i	0.0938965	−	0.162633i
$675$		0			0
$676$	−18.6074	−	9.80881i	−0.715669	−	0.377262i
$677$	−12.1115			−0.465481			−0.232741	−	0.972539i	$-0.574769\pi$
$677$	−12.1115			−0.465481			−0.232741	+	0.972539i	$0.574769\pi$
$678$		0			0
$679$	7.35410	−	12.7377i	0.282225	−	0.488827i
$680$	−3.88197	−	6.72376i	−0.148867	−	0.257845i
$681$		0			0
$682$		0			0
$683$	12.8820	+	22.3122i	0.492915	+	0.853753i	0.999967	−	0.00816213i	$-0.00259812\pi$
$683$	12.8820	+	22.3122i	0.492915	+	0.853753i	−0.507052	+	0.861915i	$0.669265\pi$
$684$		0			0
$685$	−0.736068	−	1.27491i	−0.0281237	−	0.0487117i
$686$	−5.16312	+	8.94278i	−0.197129	+	0.341437i
$687$		0			0
$688$	−11.5623			−0.440809
$689$	6.00000	+	20.7846i	0.228582	+	0.791831i
$690$		0			0
$691$	−19.2984	+	33.4258i	−0.734145	+	1.27158i	0.220953	+	0.975284i	$0.429083\pi$
$691$	−19.2984	+	33.4258i	−0.734145	+	1.27158i	−0.955098	+	0.296291i	$0.904250\pi$
$692$	15.2812	−	26.4677i	0.580902	−	1.00615i
$693$		0			0
$694$	−18.9787			−0.720422
$695$	−8.35410	−	14.4697i	−0.316889	−	0.548868i
$696$		0			0
$697$	−41.4721			−1.57087
$698$	−0.746711	−	1.29334i	−0.0282634	−	0.0489537i
$699$		0			0
$700$	3.42705	−	5.93583i	0.129530	−	0.224353i
$701$	−7.88854			−0.297946			−0.148973	−	0.988841i	$-0.547597\pi$
$701$	−7.88854			−0.297946			−0.148973	+	0.988841i	$0.547597\pi$
$702$		0			0
$703$	12.7082			0.479299
$704$	0.0278640	−	0.0482619i	0.00105017	−	0.00181894i
$705$		0			0
$706$	−6.01722	−	10.4221i	−0.226461	−	0.392242i
$707$	−2.23607			−0.0840960
$708$		0			0
$709$	−12.1525	−	21.0487i	−0.456396	−	0.790501i	0.542371	−	0.840139i	$-0.317527\pi$
$709$	−12.1525	−	21.0487i	−0.456396	−	0.790501i	−0.998767	+	0.0496381i	$0.984193\pi$
$710$	−3.85410			−0.144642
$711$		0			0
$712$	10.0623	−	17.4284i	0.377101	−	0.653158i
$713$		0			0
$714$		0			0
$715$	−0.826238	−	0.204441i	−0.0308995	−	0.00764565i
$716$	−13.3262			−0.498025
$717$		0			0
$718$	5.52786	−	9.57454i	0.206298	−	0.357319i
$719$	−16.0623	−	27.8207i	−0.599023	−	1.03754i	−0.992966	−	0.118403i	$-0.962222\pi$
$719$	−16.0623	−	27.8207i	−0.599023	−	1.03754i	0.393943	−	0.919135i	$-0.371111\pi$
$720$		0			0
$721$	−27.4164	−	47.4866i	−1.02104	−	1.76849i
$722$	0.326238	+	0.565061i	0.0121413	+	0.0210294i
$723$		0			0
$724$	4.85410	+	8.40755i	0.180401	+	0.312464i
$725$	−3.73607	+	6.47106i	−0.138754	+	0.240329i
$726$		0			0
$727$	28.9443			1.07348			0.536742	−	0.843747i	$-0.319655\pi$
$727$	28.9443			1.07348			0.536742	+	0.843747i	$0.319655\pi$
$728$	23.6803	−	24.6093i	0.877652	−	0.912082i
$729$		0			0
$730$	−1.85410	+	3.21140i	−0.0686234	+	0.118859i
$731$	10.8262	−	18.7516i	0.400423	−	0.693553i
$732$		0			0
$733$	−43.8885			−1.62106			−0.810530	−	0.585697i	$-0.800821\pi$
$733$	−43.8885			−1.62106			−0.810530	+	0.585697i	$0.800821\pi$
$734$	−1.74671	−	3.02539i	−0.0644723	−	0.111669i
$735$		0			0
$736$	−21.1459			−0.779448
$737$	0.319660	+	0.553668i	0.0117748	+	0.0203946i
$738$		0			0
$739$	−13.7705	+	23.8512i	−0.506556	+	0.877381i	0.493415	+	0.869794i	$0.335748\pi$
$739$	−13.7705	+	23.8512i	−0.506556	+	0.877381i	−0.999971	+	0.00758729i	$0.997585\pi$
$740$	4.85410			0.178440
$741$		0			0
$742$	−15.7082			−0.576666
$743$	−19.0623	+	33.0169i	−0.699328	+	1.21127i	0.269372	+	0.963036i	$0.413184\pi$
$743$	−19.0623	+	33.0169i	−0.699328	+	1.21127i	−0.968700	+	0.248236i	$0.920149\pi$
$744$		0			0
$745$	−2.26393	−	3.92125i	−0.0829441	−	0.143663i
$746$	17.2705			0.632318
$747$		0			0
$748$	0.663119	+	1.14856i	0.0242460	+	0.0419954i
$749$	24.4164			0.892156
$750$		0			0
$751$	15.3541	−	26.5941i	0.560279	−	0.970432i	−0.437193	−	0.899368i	$-0.644027\pi$
$751$	15.3541	−	26.5941i	0.560279	−	0.970432i	0.997472	−	0.0710640i	$-0.0226395\pi$
$752$	−4.58359	+	7.93901i	−0.167146	+	0.289506i
$753$		0			0
$754$	−11.5451	+	11.9980i	−0.420447	+	0.436942i
$755$	−8.00000			−0.291150
$756$		0			0
$757$	3.44427	−	5.96565i	0.125184	−	0.216825i	−0.796621	−	0.604479i	$-0.793381\pi$
$757$	3.44427	−	5.96565i	0.125184	−	0.216825i	0.921805	+	0.387654i	$0.126714\pi$
$758$	−3.34346	−	5.79104i	−0.121440	−	0.210340i
$759$		0			0
$760$	−4.73607	−	8.20311i	−0.171795	−	0.297558i
$761$	−18.9721	−	32.8607i	−0.687739	−	1.19120i	−0.972567	−	0.232621i	$-0.925270\pi$
$761$	−18.9721	−	32.8607i	−0.687739	−	1.19120i	0.284828	−	0.958579i	$-0.408063\pi$
$762$		0			0
$763$	4.23607	+	7.33708i	0.153356	+	0.265620i
$764$	21.9894	−	38.0867i	0.795547	−	1.37793i
$765$		0			0
$766$	−2.61803			−0.0945934
$767$	−1.77051	+	1.83997i	−0.0639294	+	0.0664374i
$768$		0			0
$769$	−14.9164	+	25.8360i	−0.537899	+	0.931669i	0.461118	+	0.887339i	$0.347449\pi$
$769$	−14.9164	+	25.8360i	−0.537899	+	0.931669i	−0.999017	+	0.0443301i	$0.985885\pi$
$770$	0.309017	−	0.535233i	0.0111362	−	0.0192885i
$771$		0			0
$772$	5.61803			0.202197
$773$	−10.0279	−	17.3688i	−0.360677	−	0.624711i	0.627395	−	0.778701i	$-0.284121\pi$
$773$	−10.0279	−	17.3688i	−0.360677	−	0.624711i	−0.988072	+	0.153990i	$0.950788\pi$
$774$		0			0
$775$		0			0
$776$	−3.88197	−	6.72376i	−0.139354	−	0.241369i
$777$		0			0
$778$	−0.0344419	+	0.0596550i	−0.00123480	+	0.00213874i
$779$	−50.5967			−1.81282
$780$		0			0
$781$	1.47214			0.0526772
$782$	4.03851	−	6.99490i	0.144417	−	0.250137i
$783$		0			0
$784$	−10.1459	−	17.5732i	−0.362354	−	0.627615i
$785$	18.0000			0.642448
$786$		0			0
$787$	−14.7705	−	25.5833i	−0.526512	−	0.911945i	−0.999523	−	0.0308887i	$-0.990166\pi$
$787$	−14.7705	−	25.5833i	−0.526512	−	0.911945i	0.473011	−	0.881057i	$-0.343167\pi$
$788$	4.85410			0.172920
$789$		0			0
$790$		0			0
$791$	3.11803	−	5.40059i	0.110865	−	0.192023i
$792$		0			0
$793$	−36.0410	+	37.4549i	−1.27985	+	1.33006i
$794$	17.2705			0.612907
$795$		0			0
$796$	−1.04508	+	1.81014i	−0.0370421	+	0.0641587i
$797$	26.9164	+	46.6206i	0.953428	+	1.65139i	0.737925	+	0.674883i	$0.235806\pi$
$797$	26.9164	+	46.6206i	0.953428	+	1.65139i	0.215503	+	0.976503i	$0.430861\pi$
$798$		0			0
$799$	−8.58359	−	14.8672i	−0.303666	−	0.525964i
$800$	−2.80902	−	4.86536i	−0.0993137	−	0.172016i
$801$		0			0
$802$	2.74671	+	4.75744i	0.0969897	+	0.167991i
$803$	0.708204	−	1.22665i	0.0249920	−	0.0432874i
$804$		0			0
$805$	15.9443			0.561962
$806$		0			0
$807$		0			0
$808$	−0.590170	+	1.02220i	−0.0207621	+	0.0359610i
$809$	−1.44427	+	2.50155i	−0.0507779	+	0.0879499i	−0.890297	−	0.455380i	$-0.849503\pi$
$809$	−1.44427	+	2.50155i	−0.0507779	+	0.0879499i	0.839519	+	0.543330i	$0.182837\pi$
$810$		0			0
$811$	31.7771			1.11584			0.557922	−	0.829893i	$-0.311599\pi$
$811$	31.7771			1.11584			0.557922	+	0.829893i	$0.311599\pi$
$812$	25.6074	+	44.3533i	0.898643	+	1.55650i
$813$		0			0
$814$	0.437694			0.0153412
$815$	7.35410	+	12.7377i	0.257603	+	0.446181i
$816$		0			0
$817$	13.2082	−	22.8773i	0.462097	−	0.800375i
$818$	15.3820			0.537818
$819$		0			0
$820$	−19.3262			−0.674902
$821$	−12.6803	+	21.9630i	−0.442547	+	0.766514i	−0.997878	−	0.0651158i	$-0.979258\pi$
$821$	−12.6803	+	21.9630i	−0.442547	+	0.766514i	0.555331	+	0.831630i	$0.312592\pi$
$822$		0			0
$823$	13.2984	+	23.0335i	0.463552	+	0.802896i	0.999135	−	0.0415869i	$-0.0132413\pi$
$823$	13.2984	+	23.0335i	0.463552	+	0.802896i	−0.535583	+	0.844483i	$0.679908\pi$
$824$	−28.9443			−1.00832
$825$		0			0
$826$	−0.927051	−	1.60570i	−0.0322562	−	0.0558694i
$827$	8.94427			0.311023			0.155511	−	0.987834i	$-0.450297\pi$
$827$	8.94427			0.311023			0.155511	+	0.987834i	$0.450297\pi$
$828$		0			0
$829$	21.6246	−	37.4549i	0.751054	−	1.30086i	−0.196259	−	0.980552i	$-0.562879\pi$
$829$	21.6246	−	37.4549i	0.751054	−	1.30086i	0.947312	−	0.320311i	$-0.103787\pi$
$830$	−2.76393	+	4.78727i	−0.0959375	+	0.166169i
$831$		0			0
$832$	0.236068	+	0.817763i	0.00818418	+	0.0283508i
$833$	38.0000			1.31662
$834$		0			0
$835$	8.59017	−	14.8786i	0.297275	−	0.514896i
$836$	0.809017	+	1.40126i	0.0279804	+	0.0484635i
$837$		0			0
$838$	5.45492	+	9.44819i	0.188437	+	0.326382i
$839$	15.3541	+	26.5941i	0.530082	+	0.918130i	0.999384	+	0.0350918i	$0.0111724\pi$
$839$	15.3541	+	26.5941i	0.530082	+	0.918130i	−0.469302	+	0.883038i	$0.655494\pi$
$840$		0			0
$841$	−13.4164	−	23.2379i	−0.462635	−	0.801307i
$842$	−1.85410	+	3.21140i	−0.0638966	+	0.110672i
$843$		0			0
$844$	21.3262			0.734079
$845$	11.0000	−	6.92820i	0.378412	−	0.238337i
$846$		0			0
$847$	23.1803	−	40.1495i	0.796486	−	1.37955i
$848$	5.56231	−	9.63420i	0.191010	−	0.330840i
$849$		0			0
$850$	2.14590			0.0736037
$851$	5.64590	+	9.77898i	0.193539	+	0.335219i
$852$		0			0
$853$	6.00000			0.205436			0.102718	−	0.994711i	$-0.467246\pi$
$853$	6.00000			0.205436			0.102718	+	0.994711i	$0.467246\pi$
$854$	−18.8713	−	32.6861i	−0.645763	−	1.11849i
$855$		0			0
$856$	6.44427	−	11.1618i	0.220261	−	0.381503i
$857$	−35.8885			−1.22593			−0.612965	−	0.790110i	$-0.710023\pi$
$857$	−35.8885			−1.22593			−0.612965	+	0.790110i	$0.710023\pi$
$858$		0			0
$859$	21.8885			0.746827			0.373414	−	0.927665i	$-0.378187\pi$
$859$	21.8885			0.746827			0.373414	+	0.927665i	$0.378187\pi$
$860$	5.04508	−	8.73834i	0.172036	−	0.297975i
$861$		0			0
$862$	8.39919	+	14.5478i	0.286077	+	0.495501i
$863$	−14.8328			−0.504915			−0.252457	−	0.967608i	$-0.581239\pi$
$863$	−14.8328			−0.504915			−0.252457	+	0.967608i	$0.581239\pi$
$864$		0			0
$865$	9.44427	+	16.3580i	0.321115	+	0.556187i
$866$	−8.97871			−0.305109
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−9.47871	−	2.34537i	−0.321174	−	0.0794699i
$872$	4.47214			0.151446
$873$		0			0
$874$	4.92705	−	8.53390i	0.166660	−	0.288664i
$875$	2.11803	+	3.66854i	0.0716026	+	0.124019i
$876$		0			0
$877$	16.8607	+	29.2036i	0.569345	+	0.986134i	0.996631	+	0.0820175i	$0.0261363\pi$
$877$	16.8607	+	29.2036i	0.569345	+	0.986134i	−0.427286	+	0.904116i	$0.640530\pi$
$878$	7.01722	+	12.1542i	0.236820	+	0.410184i
$879$		0			0
$880$	0.218847	+	0.379054i	0.00737733	+	0.0127779i
$881$	7.50000	−	12.9904i	0.252681	−	0.437657i	−0.711582	−	0.702603i	$-0.752021\pi$
$881$	7.50000	−	12.9904i	0.252681	−	0.437657i	0.964263	+	0.264946i	$0.0853542\pi$
$882$		0			0
$883$	−42.8328			−1.44144			−0.720720	−	0.693227i	$-0.756188\pi$
$883$	−42.8328			−1.44144			−0.720720	+	0.693227i	$0.756188\pi$
$884$	−19.6631	−	4.86536i	−0.661342	−	0.163640i
$885$		0			0
$886$	0.291796	−	0.505406i	0.00980308	−	0.0169794i
$887$	22.2426	−	38.5254i	0.746835	−	1.29356i	−0.202498	−	0.979283i	$-0.564906\pi$
$887$	22.2426	−	38.5254i	0.746835	−	1.29356i	0.949333	−	0.314273i	$-0.101761\pi$
$888$		0			0
$889$	−17.9443			−0.601832
$890$	2.78115	+	4.81710i	0.0932245	+	0.161469i
$891$		0			0
$892$	−1.14590			−0.0383675
$893$	−10.4721	−	18.1383i	−0.350437	−	0.606974i
$894$		0			0
$895$	4.11803	−	7.13264i	0.137651	−	0.238418i
$896$	−48.2148			−1.61074
$897$		0			0
$898$	−2.43769			−0.0813469
$899$		0			0
$900$		0			0
$901$	10.4164	+	18.0417i	0.347021	+	0.601058i
$902$	−1.74265			−0.0580238
$903$		0			0
$904$	−1.64590	−	2.85078i	−0.0547418	−	0.0948155i
$905$	−6.00000			−0.199447
$906$		0			0
$907$	−10.0623	+	17.4284i	−0.334113	+	0.578701i	−0.983314	−	0.181916i	$-0.941770\pi$
$907$	−10.0623	+	17.4284i	−0.334113	+	0.578701i	0.649201	+	0.760617i	$0.275104\pi$
$908$	5.04508	−	8.73834i	0.167427	−	0.289992i
$909$		0			0
$910$	2.61803	+	9.06914i	0.0867870	+	0.300639i
$911$	−48.0000			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$912$		0			0
$913$	1.05573	−	1.82857i	0.0349395	−	0.0605170i
$914$	0.489357	+	0.847591i	0.0161865	+	0.0280358i
$915$		0			0
$916$	12.8541	+	22.2640i	0.424711	+	0.735622i
$917$	−25.4164	−	44.0225i	−0.839324	−	1.45375i
$918$		0			0
$919$	−23.3541	−	40.4505i	−0.770381	−	1.33434i	−0.937354	−	0.348377i	$-0.886733\pi$
$919$	−23.3541	−	40.4505i	−0.770381	−	1.33434i	0.166974	−	0.985961i	$-0.446601\pi$
$920$	4.20820	−	7.28882i	0.138740	−	0.240305i
$921$		0			0
$922$	0.978714			0.0322322
$923$	−15.5902	+	16.2018i	−0.513157	+	0.533288i
$924$		0			0
$925$	−1.50000	+	2.59808i	−0.0493197	+	0.0854242i
$926$	−3.41641	+	5.91739i	−0.112270	+	0.194458i
$927$		0			0
$928$	41.9787			1.37802
$929$	9.97214	+	17.2722i	0.327175	+	0.566684i	0.981950	−	0.189140i	$-0.0605699\pi$
$929$	9.97214	+	17.2722i	0.327175	+	0.566684i	−0.654775	+	0.755824i	$0.727237\pi$
$930$		0			0
$931$	46.3607			1.51941
$932$	12.8541	+	22.2640i	0.421050	+	0.729280i
$933$		0			0
$934$	2.76393	−	4.78727i	0.0904386	−	0.156644i
$935$	−0.819660			−0.0268058
$936$		0			0
$937$	−6.00000			−0.196011			−0.0980057	−	0.995186i	$-0.531246\pi$
$937$	−6.00000			−0.196011			−0.0980057	+	0.995186i	$0.531246\pi$
$938$	3.54508	−	6.14027i	0.115751	−	0.200487i
$939$		0			0
$940$	−4.00000	−	6.92820i	−0.130466	−	0.225973i
$941$	11.8885			0.387555			0.193778	−	0.981045i	$-0.437926\pi$
$941$	11.8885			0.387555			0.193778	+	0.981045i	$0.437926\pi$
$942$		0			0
$943$	−22.4787	−	38.9343i	−0.732008	−	1.26787i
$944$	1.31308			0.0427372
$945$		0			0
$946$	0.454915	−	0.787936i	0.0147906	−	0.0256180i
$947$	19.5902	−	33.9312i	0.636595	−	1.10261i	−0.349580	−	0.936907i	$-0.613676\pi$
$947$	19.5902	−	33.9312i	0.636595	−	1.10261i	0.986175	−	0.165708i	$-0.0529910\pi$
$948$		0			0
$949$	6.00000	+	20.7846i	0.194768	+	0.674697i
$950$	2.61803			0.0849402
$951$		0			0
$952$	16.4443	−	28.4823i	0.532962	−	0.923117i
$953$	21.0967	+	36.5406i	0.683391	+	1.18367i	0.973940	+	0.226807i	$0.0728288\pi$
$953$	21.0967	+	36.5406i	0.683391	+	1.18367i	−0.290549	+	0.956860i	$0.593838\pi$
$954$		0			0
$955$	13.5902	+	23.5389i	0.439768	+	0.761700i
$956$	20.9443	+	36.2765i	0.677386	+	1.17327i
$957$		0			0
$958$	9.92705	+	17.1942i	0.320728	+	0.555518i
$959$	3.11803	−	5.40059i	0.100687	−	0.174394i
$960$		0			0
$961$	−31.0000			−1.00000
$962$	−4.63525	+	4.81710i	−0.149447	+	0.155309i
$963$		0			0
$964$	12.1353	−	21.0189i	0.390850	−	0.676972i
$965$	−1.73607	+	3.00696i	−0.0558860	+	0.0967974i
$966$		0			0
$967$	−54.8328			−1.76330			−0.881652	−	0.471900i	$-0.843568\pi$
$967$	−54.8328			−1.76330			−0.881652	+	0.471900i	$0.843568\pi$
$968$	−12.2361	−	21.1935i	−0.393282	−	0.681185i
$969$		0			0
$970$	2.14590			0.0689006
$971$	−5.88197	−	10.1879i	−0.188761	−	0.326944i	0.756076	−	0.654484i	$-0.227114\pi$
$971$	−5.88197	−	10.1879i	−0.188761	−	0.326944i	−0.944838	+	0.327539i	$0.893781\pi$
$972$		0			0
$973$	35.3885	−	61.2948i	1.13450	−	1.96502i
$974$	8.72949			0.279711
$975$		0			0
$976$	26.7295			0.855590
$977$	3.79180	−	6.56758i	0.121310	−	0.210116i	−0.798974	−	0.601365i	$-0.794624\pi$
$977$	3.79180	−	6.56758i	0.121310	−	0.210116i	0.920285	+	0.391250i	$0.127957\pi$
$978$		0			0
$979$	−1.06231	−	1.83997i	−0.0339514	−	0.0588056i
$980$	17.7082			0.565668
$981$		0			0
$982$	−0.0729490	−	0.126351i	−0.00232790	−	0.00403204i
$983$	−38.8328			−1.23857			−0.619287	−	0.785165i	$-0.712578\pi$
$983$	−38.8328			−1.23857			−0.619287	+	0.785165i	$0.712578\pi$
$984$		0			0
$985$	−1.50000	+	2.59808i	−0.0477940	+	0.0827816i
$986$	−8.01722	+	13.8862i	−0.255320	+	0.442228i
$987$		0			0
$988$	−23.9894	−	5.93583i	−0.763203	−	0.188844i
$989$	23.4721			0.746371
$990$		0			0
$991$	23.3541	−	40.4505i	0.741867	−	1.28495i	−0.209777	−	0.977749i	$-0.567274\pi$
$991$	23.3541	−	40.4505i	0.741867	−	1.28495i	0.951644	−	0.307203i	$-0.0993930\pi$
$992$		0			0
$993$		0			0
$994$	−8.16312	−	14.1389i	−0.258918	−	0.448460i
$995$	−0.645898	−	1.11873i	−0.0204763	−	0.0354661i
$996$		0			0
$997$	9.44427	+	16.3580i	0.299103	+	0.518062i	0.975931	−	0.218080i	$-0.0699792\pi$
$997$	9.44427	+	16.3580i	0.299103	+	0.518062i	−0.676828	+	0.736141i	$0.736646\pi$
$998$	6.76393	−	11.7155i	0.214109	−	0.370847i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.j.e.451.1		4
3.2	odd	2		65.2.e.a.61.2	yes	4
12.11	even	2		1040.2.q.n.321.2		4
13.3	even	3	inner	585.2.j.e.406.1		4
13.4	even	6		7605.2.a.bf.1.1		2
13.9	even	3		7605.2.a.ba.1.2		2
15.2	even	4		325.2.o.a.74.3		8
15.8	even	4		325.2.o.a.74.2		8
15.14	odd	2		325.2.e.b.126.1		4
39.2	even	12		845.2.m.e.361.3		8
39.5	even	4		845.2.m.e.316.2		8
39.8	even	4		845.2.m.e.316.3		8
39.11	even	12		845.2.m.e.361.2		8
39.17	odd	6		845.2.a.b.1.2		2
39.20	even	12		845.2.c.c.506.2		4
39.23	odd	6		845.2.e.g.146.1		4
39.29	odd	6		65.2.e.a.16.2	✓	4
39.32	even	12		845.2.c.c.506.3		4
39.35	odd	6		845.2.a.e.1.1		2
39.38	odd	2		845.2.e.g.191.1		4
156.107	even	6		1040.2.q.n.81.2		4
195.29	odd	6		325.2.e.b.276.1		4
195.68	even	12		325.2.o.a.224.3		8
195.74	odd	6		4225.2.a.u.1.2		2
195.107	even	12		325.2.o.a.224.2		8
195.134	odd	6		4225.2.a.y.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.e.a.16.2	✓	4	39.29	odd	6
65.2.e.a.61.2	yes	4	3.2	odd	2
325.2.e.b.126.1		4	15.14	odd	2
325.2.e.b.276.1		4	195.29	odd	6
325.2.o.a.74.2		8	15.8	even	4
325.2.o.a.74.3		8	15.2	even	4
325.2.o.a.224.2		8	195.107	even	12
325.2.o.a.224.3		8	195.68	even	12
585.2.j.e.406.1		4	13.3	even	3	inner
585.2.j.e.451.1		4	1.1	even	1	trivial
845.2.a.b.1.2		2	39.17	odd	6
845.2.a.e.1.1		2	39.35	odd	6
845.2.c.c.506.2		4	39.20	even	12
845.2.c.c.506.3		4	39.32	even	12
845.2.e.g.146.1		4	39.23	odd	6
845.2.e.g.191.1		4	39.38	odd	2
845.2.m.e.316.2		8	39.5	even	4
845.2.m.e.316.3		8	39.8	even	4
845.2.m.e.361.2		8	39.11	even	12
845.2.m.e.361.3		8	39.2	even	12
1040.2.q.n.81.2		4	156.107	even	6
1040.2.q.n.321.2		4	12.11	even	2
4225.2.a.u.1.2		2	195.74	odd	6
4225.2.a.y.1.1		2	195.134	odd	6
7605.2.a.ba.1.2		2	13.9	even	3
7605.2.a.bf.1.1		2	13.4	even	6

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.535233i) q^{2} +(0.809017 + 1.40126i) q^{4} -1.00000 q^{5} +(-2.11803 - 3.66854i) q^{7} -2.23607 q^{8} +O(q^{10})\)	\(q+(-0.309017 + 0.535233i) q^{2} +(0.809017 + 1.40126i) q^{4} -1.00000 q^{5} +(-2.11803 - 3.66854i) q^{7} -2.23607 q^{8} +(0.309017 - 0.535233i) q^{10} +(-0.118034 + 0.204441i) q^{11} +(-1.00000 - 3.46410i) q^{13} +2.61803 q^{14} +(-0.927051 + 1.60570i) q^{16} +(-1.73607 - 3.00696i) q^{17} +(-2.11803 - 3.66854i) q^{19} +(-0.809017 - 1.40126i) q^{20} +(-0.0729490 - 0.126351i) q^{22} +(1.88197 - 3.25966i) q^{23} +1.00000 q^{25} +(2.16312 + 0.535233i) q^{26} +(3.42705 - 5.93583i) q^{28} +(-3.73607 + 6.47106i) q^{29} +(-2.80902 - 4.86536i) q^{32} +2.14590 q^{34} +(2.11803 + 3.66854i) q^{35} +(-1.50000 + 2.59808i) q^{37} +2.61803 q^{38} +2.23607 q^{40} +(5.97214 - 10.3440i) q^{41} +(3.11803 + 5.40059i) q^{43} -0.381966 q^{44} +(1.16312 + 2.01458i) q^{46} +4.94427 q^{47} +(-5.47214 + 9.47802i) q^{49} +(-0.309017 + 0.535233i) q^{50} +(4.04508 - 4.20378i) q^{52} -6.00000 q^{53} +(0.118034 - 0.204441i) q^{55} +(4.73607 + 8.20311i) q^{56} +(-2.30902 - 3.99933i) q^{58} +(-0.354102 - 0.613323i) q^{59} +(-7.20820 - 12.4850i) q^{61} -0.236068 q^{64} +(1.00000 + 3.46410i) q^{65} +(1.35410 - 2.34537i) q^{67} +(2.80902 - 4.86536i) q^{68} -2.61803 q^{70} +(-3.11803 - 5.40059i) q^{71} -6.00000 q^{73} +(-0.927051 - 1.60570i) q^{74} +(3.42705 - 5.93583i) q^{76} +1.00000 q^{77} +(0.927051 - 1.60570i) q^{80} +(3.69098 + 6.39297i) q^{82} -8.94427 q^{83} +(1.73607 + 3.00696i) q^{85} -3.85410 q^{86} +(0.263932 - 0.457144i) q^{88} +(-4.50000 + 7.79423i) q^{89} +(-10.5902 + 11.0056i) q^{91} +6.09017 q^{92} +(-1.52786 + 2.64634i) q^{94} +(2.11803 + 3.66854i) q^{95} +(1.73607 + 3.00696i) q^{97} +(-3.38197 - 5.85774i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + q^{4} - 4 q^{5} - 4 q^{7}+O(q^{10}) \) 4 * q + q^2 + q^4 - 4 * q^5 - 4 * q^7	\( 4 q + q^{2} + q^{4} - 4 q^{5} - 4 q^{7} - q^{10} + 4 q^{11} - 4 q^{13} + 6 q^{14} + 3 q^{16} + 2 q^{17} - 4 q^{19} - q^{20} - 7 q^{22} + 12 q^{23} + 4 q^{25} - 7 q^{26} + 7 q^{28} - 6 q^{29} - 9 q^{32} + 22 q^{34} + 4 q^{35} - 6 q^{37} + 6 q^{38} + 6 q^{41} + 8 q^{43} - 6 q^{44} - 11 q^{46} - 16 q^{47} - 4 q^{49} + q^{50} + 5 q^{52} - 24 q^{53} - 4 q^{55} + 10 q^{56} - 7 q^{58} + 12 q^{59} - 2 q^{61} + 8 q^{64} + 4 q^{65} - 8 q^{67} + 9 q^{68} - 6 q^{70} - 8 q^{71} - 24 q^{73} + 3 q^{74} + 7 q^{76} + 4 q^{77} - 3 q^{80} + 17 q^{82} - 2 q^{85} - 2 q^{86} + 10 q^{88} - 18 q^{89} - 20 q^{91} + 2 q^{92} - 24 q^{94} + 4 q^{95} - 2 q^{97} - 18 q^{98}+O(q^{100}) \) 4 * q + q^2 + q^4 - 4 * q^5 - 4 * q^7 - q^10 + 4 * q^11 - 4 * q^13 + 6 * q^14 + 3 * q^16 + 2 * q^17 - 4 * q^19 - q^20 - 7 * q^22 + 12 * q^23 + 4 * q^25 - 7 * q^26 + 7 * q^28 - 6 * q^29 - 9 * q^32 + 22 * q^34 + 4 * q^35 - 6 * q^37 + 6 * q^38 + 6 * q^41 + 8 * q^43 - 6 * q^44 - 11 * q^46 - 16 * q^47 - 4 * q^49 + q^50 + 5 * q^52 - 24 * q^53 - 4 * q^55 + 10 * q^56 - 7 * q^58 + 12 * q^59 - 2 * q^61 + 8 * q^64 + 4 * q^65 - 8 * q^67 + 9 * q^68 - 6 * q^70 - 8 * q^71 - 24 * q^73 + 3 * q^74 + 7 * q^76 + 4 * q^77 - 3 * q^80 + 17 * q^82 - 2 * q^85 - 2 * q^86 + 10 * q^88 - 18 * q^89 - 20 * q^91 + 2 * q^92 - 24 * q^94 + 4 * q^95 - 2 * q^97 - 18 * q^98

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