LMFDB - Embedded newform 585.2.bu.c.361.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(316,585)]

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, 1]))

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

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

chi := DirichletCharacter("585.316");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bu (of order $6$, 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.22581504.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.4
Root			$1.20036 - 0.747754i$ of defining polynomial
Character	$\chi$	$=$	585.361
Dual form			585.2.bu.c.316.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.16117 - 1.24775i) q^{2} +(2.11378 - 3.66117i) q^{4} -1.00000i q^{5} +(-1.64996 - 0.952606i) q^{7} -5.55889i q^{8} +O(q^{10})$	\(q+(2.16117 - 1.24775i) q^{2} +(2.11378 - 3.66117i) q^{4} -1.00000i q^{5} +(-1.64996 - 0.952606i) q^{7} -5.55889i q^{8} +(-1.24775 - 2.16117i) q^{10} +(-0.926118 + 0.534695i) q^{11} +(1.40072 - 3.32235i) q^{13} -4.75447 q^{14} +(-2.70857 - 4.69138i) q^{16} +(-0.318632 + 0.551886i) q^{17} +(4.96410 + 2.86603i) q^{19} +(-3.66117 - 2.11378i) q^{20} +(-1.33433 + 2.31114i) q^{22} +(-1.90893 - 3.30636i) q^{23} -1.00000 q^{25} +(-1.11827 - 8.92792i) q^{26} +(-6.97531 + 4.02720i) q^{28} +(4.72756 + 8.18837i) q^{29} +1.46410i q^{31} +(-2.07908 - 1.20036i) q^{32} +1.59030i q^{34} +(-0.952606 + 1.64996i) q^{35} +(0.655970 - 0.378725i) q^{37} +14.3044 q^{38} -5.55889 q^{40} +(0.232051 - 0.133975i) q^{41} +(0.318632 - 0.551886i) q^{43} +4.52091i q^{44} +(-8.25104 - 4.76374i) q^{46} +9.44613i q^{47} +(-1.68508 - 2.91865i) q^{49} +(-2.16117 + 1.24775i) q^{50} +(-9.20287 - 12.1510i) q^{52} +6.99102 q^{53} +(0.534695 + 0.926118i) q^{55} +(-5.29543 + 9.17196i) q^{56} +(20.4341 + 11.7977i) q^{58} +(0.641756 + 0.370518i) q^{59} +(-2.09928 + 3.63606i) q^{61} +(1.82684 + 3.16418i) q^{62} +4.84325 q^{64} +(-3.32235 - 1.40072i) q^{65} +(-7.01029 + 4.04739i) q^{67} +(1.34703 + 2.33313i) q^{68} +4.75447i q^{70} +(-8.45663 - 4.88244i) q^{71} -3.71649i q^{73} +(0.945110 - 1.63698i) q^{74} +(20.9860 - 12.1163i) q^{76} +2.03741 q^{77} -9.31937 q^{79} +(-4.69138 + 2.70857i) q^{80} +(0.334335 - 0.579085i) q^{82} +5.11778i q^{83} +(0.551886 + 0.318632i) q^{85} -1.59030i q^{86} +(2.97231 + 5.14819i) q^{88} +(10.8932 - 6.28917i) q^{89} +(-5.47602 + 4.14741i) q^{91} -16.1402 q^{92} +(11.7864 + 20.4147i) q^{94} +(2.86603 - 4.96410i) q^{95} +(-3.65597 - 2.11078i) q^{97} +(-7.28351 - 4.20514i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} - 6 q^{7}+O(q^{10}) $ 8 * q + 2 * q^4 - 6 * q^7	$ 8 q + 2 q^{4} - 6 q^{7} - 2 q^{10} - 4 q^{14} - 2 q^{16} + 2 q^{17} + 12 q^{19} - 12 q^{20} - 12 q^{22} + 10 q^{23} - 8 q^{25} - 10 q^{26} - 18 q^{28} + 8 q^{29} - 6 q^{32} - 10 q^{35} + 6 q^{37} + 16 q^{38} - 12 q^{40} - 12 q^{41} - 2 q^{43} - 42 q^{46} + 12 q^{49} - 6 q^{52} + 24 q^{53} - 12 q^{56} + 36 q^{58} + 12 q^{59} - 28 q^{61} - 4 q^{62} - 8 q^{64} + 8 q^{65} + 6 q^{67} + 14 q^{68} - 10 q^{74} + 54 q^{76} + 36 q^{77} - 16 q^{79} + 4 q^{82} + 18 q^{85} - 18 q^{88} - 24 q^{89} + 28 q^{91} - 44 q^{92} + 32 q^{94} + 16 q^{95} - 30 q^{97} - 72 q^{98}+O(q^{100}) $ 8 * q + 2 * q^4 - 6 * q^7 - 2 * q^10 - 4 * q^14 - 2 * q^16 + 2 * q^17 + 12 * q^19 - 12 * q^20 - 12 * q^22 + 10 * q^23 - 8 * q^25 - 10 * q^26 - 18 * q^28 + 8 * q^29 - 6 * q^32 - 10 * q^35 + 6 * q^37 + 16 * q^38 - 12 * q^40 - 12 * q^41 - 2 * q^43 - 42 * q^46 + 12 * q^49 - 6 * q^52 + 24 * q^53 - 12 * q^56 + 36 * q^58 + 12 * q^59 - 28 * q^61 - 4 * q^62 - 8 * q^64 + 8 * q^65 + 6 * q^67 + 14 * q^68 - 10 * q^74 + 54 * q^76 + 36 * q^77 - 16 * q^79 + 4 * q^82 + 18 * q^85 - 18 * q^88 - 24 * q^89 + 28 * q^91 - 44 * q^92 + 32 * q^94 + 16 * q^95 - 30 * q^97 - 72 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	2.16117	−	1.24775i	1.52818	−	0.882295i	0.528742	−	0.848783i	$-0.322664\pi$
$2$	2.16117	−	1.24775i	1.52818	−	0.882295i	0.999438	−	0.0335125i	$-0.0106693\pi$
$3$		0			0
$3$		0			0
$4$	2.11378	−	3.66117i	1.05689	−	1.83059i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	−1.64996	−	0.952606i	−0.623627	−	0.360051i	0.154653	−	0.987969i	$-0.450574\pi$
$7$	−1.64996	−	0.952606i	−0.623627	−	0.360051i	−0.778280	+	0.627918i	$0.783907\pi$
$8$		−	5.55889i		−	1.96536i
$9$		0			0
$10$	−1.24775	−	2.16117i	−0.394574	−	0.683423i
$11$	−0.926118	+	0.534695i	−0.279235	+	0.161217i	−0.633077	−	0.774089i	$-0.718208\pi$
$11$	−0.926118	+	0.534695i	−0.279235	+	0.161217i	0.353842	+	0.935305i	$0.384875\pi$
$12$		0			0
$13$	1.40072	−	3.32235i	0.388490	−	0.921453i
$13$	1.40072	−	3.32235i	0.388490	−	0.921453i
$14$	−4.75447			−1.27069
$15$		0			0
$16$	−2.70857	−	4.69138i	−0.677142	−	1.17284i
$17$	−0.318632	+	0.551886i	−0.0772795	+	0.133852i	−0.902075	−	0.431579i	$-0.857957\pi$
$17$	−0.318632	+	0.551886i	−0.0772795	+	0.133852i	0.824796	+	0.565431i	$0.191290\pi$
$18$		0			0
$19$	4.96410	+	2.86603i	1.13884	+	0.657511i	0.946144	−	0.323747i	$-0.104943\pi$
$19$	4.96410	+	2.86603i	1.13884	+	0.657511i	0.192699	+	0.981258i	$0.438276\pi$
$20$	−3.66117	−	2.11378i	−0.818663	−	0.472655i
$21$		0			0
$22$	−1.33433	+	2.31114i	−0.284481	+	0.492736i
$23$	−1.90893	−	3.30636i	−0.398039	−	0.689423i	0.595445	−	0.803396i	$-0.296976\pi$
$23$	−1.90893	−	3.30636i	−0.398039	−	0.689423i	−0.993484	+	0.113973i	$0.963642\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−1.11827	−	8.92792i	−0.219311	−	1.75091i
$27$		0			0
$28$	−6.97531	+	4.02720i	−1.31821	+	0.761069i
$29$	4.72756	+	8.18837i	0.877886	+	1.52054i	0.853657	+	0.520836i	$0.174380\pi$
$29$	4.72756	+	8.18837i	0.877886	+	1.52054i	0.0242288	+	0.999706i	$0.492287\pi$
$30$		0			0
$31$			1.46410i			0.262960i	0.991319	+	0.131480i	$0.0419730\pi$
$31$			1.46410i			0.262960i	−0.991319	+	0.131480i	$0.958027\pi$
$32$	−2.07908	−	1.20036i	−0.367534	−	0.212196i
$33$		0			0
$34$			1.59030i			0.272733i
$35$	−0.952606	+	1.64996i	−0.161020	+	0.278895i
$36$		0			0
$37$	0.655970	−	0.378725i	0.107841	−	0.0622619i	−0.445110	−	0.895476i	$-0.646835\pi$
$37$	0.655970	−	0.378725i	0.107841	−	0.0622619i	0.552950	+	0.833214i	$0.313502\pi$
$38$	14.3044			2.32048
$39$		0			0
$40$	−5.55889			−0.878938
$41$	0.232051	−	0.133975i	0.0362402	−	0.0209233i	−0.481770	−	0.876297i	$-0.660006\pi$
$41$	0.232051	−	0.133975i	0.0362402	−	0.0209233i	0.518011	+	0.855374i	$0.326673\pi$
$42$		0			0
$43$	0.318632	−	0.551886i	0.0485909	−	0.0841618i	−0.840707	−	0.541490i	$-0.817860\pi$
$43$	0.318632	−	0.551886i	0.0485909	−	0.0841618i	0.889298	+	0.457328i	$0.151194\pi$
$44$			4.52091i			0.681552i
$45$		0			0
$46$	−8.25104	−	4.76374i	−1.21655	−	0.702375i
$47$			9.44613i			1.37786i	0.724828	+	0.688930i	$0.241919\pi$
$47$			9.44613i			1.37786i	−0.724828	+	0.688930i	$0.758081\pi$
$48$		0			0
$49$	−1.68508	−	2.91865i	−0.240726	−	0.416950i
$50$	−2.16117	+	1.24775i	−0.305636	+	0.176459i
$51$		0			0
$52$	−9.20287	−	12.1510i	−1.27621	−	1.68504i
$53$	6.99102			0.960290			0.480145	−	0.877189i	$-0.340584\pi$
$53$	6.99102			0.960290			0.480145	+	0.877189i	$0.340584\pi$
$54$		0			0
$55$	0.534695	+	0.926118i	0.0720982	+	0.124878i
$56$	−5.29543	+	9.17196i	−0.707632	+	1.22565i
$57$		0			0
$58$	20.4341	+	11.7977i	2.68313	+	1.54911i
$59$	0.641756	+	0.370518i	0.0835495	+	0.0482373i	0.541193	−	0.840899i	$-0.317973\pi$
$59$	0.641756	+	0.370518i	0.0835495	+	0.0482373i	−0.457643	+	0.889136i	$0.651306\pi$
$60$		0			0
$61$	−2.09928	+	3.63606i	−0.268785	+	0.465550i	−0.968548	−	0.248825i	$-0.919956\pi$
$61$	−2.09928	+	3.63606i	−0.268785	+	0.465550i	0.699763	+	0.714375i	$0.253289\pi$
$62$	1.82684	+	3.16418i	0.232009	+	0.401851i
$63$		0			0
$64$	4.84325			0.605406
$65$	−3.32235	−	1.40072i	−0.412086	−	0.173738i
$66$		0			0
$67$	−7.01029	+	4.04739i	−0.856443	+	0.494468i	−0.862820	−	0.505512i	$-0.831304\pi$
$67$	−7.01029	+	4.04739i	−0.856443	+	0.494468i	0.00637624	+	0.999980i	$0.497970\pi$
$68$	1.34703	+	2.33313i	0.163352	+	0.282934i
$69$		0			0
$70$			4.75447i			0.568268i
$71$	−8.45663	−	4.88244i	−1.00362	−	0.579439i	−0.0943010	−	0.995544i	$-0.530062\pi$
$71$	−8.45663	−	4.88244i	−1.00362	−	0.579439i	−0.909317	+	0.416105i	$0.863395\pi$
$72$		0			0
$73$		−	3.71649i		−	0.434982i	−0.976062	−	0.217491i	$-0.930213\pi$
$73$		−	3.71649i		−	0.434982i	0.976062	−	0.217491i	$-0.0697873\pi$
$74$	0.945110	−	1.63698i	0.109867	−	0.190295i
$75$		0			0
$76$	20.9860	−	12.1163i	2.40726	−	1.38983i
$77$	2.03741			0.232185
$78$		0			0
$79$	−9.31937			−1.04851			−0.524255	−	0.851561i	$-0.675656\pi$
$79$	−9.31937			−1.04851			−0.524255	+	0.851561i	$0.675656\pi$
$80$	−4.69138	+	2.70857i	−0.524512	+	0.302827i
$81$		0			0
$82$	0.334335	−	0.579085i	0.0369211	−	0.0639492i
$83$			5.11778i			0.561749i	0.959744	+	0.280875i	$0.0906245\pi$
$83$			5.11778i			0.561749i	−0.959744	+	0.280875i	$0.909376\pi$
$84$		0			0
$85$	0.551886	+	0.318632i	0.0598605	+	0.0345605i
$86$		−	1.59030i		−	0.171486i
$87$		0			0
$88$	2.97231	+	5.14819i	0.316849	+	0.548799i
$89$	10.8932	−	6.28917i	1.15467	−	0.666650i	0.204651	−	0.978835i	$-0.434394\pi$
$89$	10.8932	−	6.28917i	1.15467	−	0.666650i	0.950021	+	0.312185i	$0.101061\pi$
$90$		0			0
$91$	−5.47602	+	4.14741i	−0.574043	+	0.434767i
$92$	−16.1402			−1.68273
$93$		0			0
$94$	11.7864	+	20.4147i	1.21568	+	2.10562i
$95$	2.86603	−	4.96410i	0.294048	−	0.509306i
$96$		0			0
$97$	−3.65597	−	2.11078i	−0.371208	−	0.214317i	0.302778	−	0.953061i	$-0.402086\pi$
$97$	−3.65597	−	2.11078i	−0.371208	−	0.214317i	−0.673986	+	0.738744i	$0.735419\pi$
$98$	−7.28351	−	4.20514i	−0.735746	−	0.424783i
$99$		0			0
$100$	−2.11378	+	3.66117i	−0.211378	+	0.366117i
$101$	7.62379	+	13.2048i	0.758595	+	1.31393i	0.943567	+	0.331181i	$0.107447\pi$
$101$	7.62379	+	13.2048i	0.758595	+	1.31393i	−0.184972	+	0.982744i	$0.559219\pi$
$102$		0			0
$103$	13.5269			1.33285			0.666423	−	0.745574i	$-0.267824\pi$
$103$	13.5269			1.33285			0.666423	+	0.745574i	$0.267824\pi$
$104$	−18.4686	−	7.78645i	−1.81099	−	0.763524i
$105$		0			0
$106$	15.1088	−	8.72307i	1.46750	−	0.847259i
$107$	−3.68137	−	6.37632i	−0.355891	−	0.616422i	0.631379	−	0.775475i	$-0.282489\pi$
$107$	−3.68137	−	6.37632i	−0.355891	−	0.616422i	−0.987270	+	0.159053i	$0.949156\pi$
$108$		0			0
$109$		−	10.0760i		−	0.965103i	−0.875868	−	0.482551i	$-0.839710\pi$
$109$		−	10.0760i		−	0.965103i	0.875868	−	0.482551i	$-0.160290\pi$
$110$	2.31114	+	1.33433i	0.220358	+	0.127224i
$111$		0			0
$112$			10.3208i			0.975223i
$113$	−3.34403	+	5.79203i	−0.314580	+	0.544868i	−0.979348	−	0.202181i	$-0.935197\pi$
$113$	−3.34403	+	5.79203i	−0.314580	+	0.544868i	0.664768	+	0.747050i	$0.268530\pi$
$114$		0			0
$115$	−3.30636	+	1.90893i	−0.308320	+	0.178008i
$116$	39.9721			3.71131
$117$		0			0
$118$	1.84926			0.170238
$119$	1.05146	−	0.607061i	0.0963872	−	0.0556492i
$120$		0			0
$121$	−4.92820	+	8.53590i	−0.448018	+	0.775991i
$122$			10.4775i			0.948592i
$123$		0			0
$124$	5.36033	+	3.09479i	0.481372	+	0.277920i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	0.744750	+	1.28994i	0.0660859	+	0.114464i	0.897175	−	0.441675i	$-0.145616\pi$
$127$	0.744750	+	1.28994i	0.0660859	+	0.114464i	−0.831089	+	0.556139i	$0.812282\pi$
$128$	14.6253	−	8.44391i	1.29270	−	0.746343i
$129$		0			0
$130$	−8.92792	+	1.11827i	−0.783030	+	0.0980789i
$131$	−4.12676			−0.360557			−0.180278	−	0.983616i	$-0.557700\pi$
$131$	−4.12676			−0.360557			−0.180278	+	0.983616i	$0.557700\pi$
$132$		0			0
$133$	−5.46039	−	9.45767i	−0.473476	−	0.820084i
$134$	−10.1003	+	17.4942i	−0.872533	+	1.51127i
$135$		0			0
$136$	3.06787	+	1.77124i	0.263068	+	0.151882i
$137$	−17.4155	−	10.0548i	−1.48790	−	0.859041i	−0.487999	−	0.872844i	$-0.662273\pi$
$137$	−17.4155	−	10.0548i	−1.48790	−	0.859041i	−0.999905	+	0.0138029i	$0.995606\pi$
$138$		0			0
$139$	−10.4126	+	18.0352i	−0.883189	+	1.52973i	−0.0354130	+	0.999373i	$0.511275\pi$
$139$	−10.4126	+	18.0352i	−0.883189	+	1.52973i	−0.847776	+	0.530355i	$0.822059\pi$
$140$	4.02720	+	6.97531i	0.340360	+	0.589521i
$141$		0			0
$142$	−24.3683			−2.04494
$143$	0.479208	+	3.82584i	0.0400734	+	0.319933i
$144$		0			0
$145$	8.18837	−	4.72756i	0.680007	−	0.392602i
$146$	−4.63726	−	8.03198i	−0.383783	−	0.664731i
$147$		0			0
$148$		−	3.20216i		−	0.263216i
$149$	−11.5768	−	6.68388i	−0.948410	−	0.547565i	−0.0558233	−	0.998441i	$-0.517778\pi$
$149$	−11.5768	−	6.68388i	−0.948410	−	0.547565i	−0.892587	+	0.450876i	$0.851112\pi$
$150$		0			0
$151$			18.2984i			1.48910i	0.667567	+	0.744550i	$0.267336\pi$
$151$			18.2984i			1.48910i	−0.667567	+	0.744550i	$0.732664\pi$
$152$	15.9319	−	27.5949i	1.29225	−	2.23824i
$153$		0			0
$154$	4.40320	−	2.54219i	0.354820	−	0.204856i
$155$	1.46410			0.117599
$156$		0			0
$157$	2.42229			0.193320			0.0966599	−	0.995317i	$-0.469184\pi$
$157$	2.42229			0.193320			0.0966599	+	0.995317i	$0.469184\pi$
$158$	−20.1408	+	11.6283i	−1.60231	+	0.925096i
$159$		0			0
$160$	−1.20036	+	2.07908i	−0.0948968	+	0.164366i
$161$			7.27382i			0.573258i
$162$		0			0
$163$	−13.8416	−	7.99144i	−1.08416	−	0.625938i	−0.152142	−	0.988359i	$-0.548617\pi$
$163$	−13.8416	−	7.99144i	−1.08416	−	0.625938i	−0.932015	+	0.362421i	$0.881950\pi$
$164$		−	1.13277i		−	0.0884545i
$165$		0			0
$166$	6.38573	+	11.0604i	0.495629	+	0.858454i
$167$	12.4648	−	7.19658i	0.964558	−	0.556888i	0.0669853	−	0.997754i	$-0.478662\pi$
$167$	12.4648	−	7.19658i	0.964558	−	0.556888i	0.897573	+	0.440866i	$0.145329\pi$
$168$		0			0
$169$	−9.07597	−	9.30735i	−0.698151	−	0.715950i
$170$	1.59030			0.121970
$171$		0			0
$172$	−1.34703	−	2.33313i	−0.102710	−	0.177900i
$173$	12.1745	−	21.0868i	0.925608	−	1.60320i	0.135027	−	0.990842i	$-0.456888\pi$
$173$	12.1745	−	21.0868i	0.925608	−	1.60320i	0.790581	−	0.612358i	$-0.209779\pi$
$174$		0			0
$175$	1.64996	+	0.952606i	0.124725	+	0.0720103i
$176$	5.01691	+	2.89651i	0.378164	+	0.218333i
$177$		0			0
$178$	15.6947	−	27.1840i	1.17636	−	2.03752i
$179$	−1.89414	−	3.28075i	−0.141575	−	0.245215i	0.786515	−	0.617571i	$-0.211883\pi$
$179$	−1.89414	−	3.28075i	−0.141575	−	0.245215i	−0.928090	+	0.372356i	$0.878550\pi$
$180$		0			0
$181$	8.48794			0.630904			0.315452	−	0.948942i	$-0.397844\pi$
$181$	8.48794			0.630904			0.315452	+	0.948942i	$0.397844\pi$
$182$	−6.65968	+	15.7960i	−0.493649	+	1.17088i
$183$		0			0
$184$	−18.3797	+	10.6115i	−1.35497	+	0.782291i
$185$	−0.378725	−	0.655970i	−0.0278444	−	0.0482279i
$186$		0			0
$187$		−	0.681482i		−	0.0498349i
$188$	34.5839	+	19.9670i	2.52229	+	1.45625i
$189$		0			0
$190$		−	14.3044i		−	1.03775i
$191$	−2.72155	+	4.71386i	−0.196924	+	0.341083i	−0.947530	−	0.319668i	$-0.896429\pi$
$191$	−2.72155	+	4.71386i	−0.196924	+	0.341083i	0.750605	+	0.660751i	$0.229762\pi$
$192$		0			0
$193$	10.5288	−	6.07880i	0.757879	−	0.437562i	−0.0706548	−	0.997501i	$-0.522509\pi$
$193$	10.5288	−	6.07880i	0.757879	−	0.437562i	0.828534	+	0.559939i	$0.189176\pi$
$194$	−10.5349			−0.756363
$195$		0			0
$196$	−14.2476			−1.01768
$197$	−3.79172	+	2.18915i	−0.270149	+	0.155970i	−0.628955	−	0.777442i	$-0.716517\pi$
$197$	−3.79172	+	2.18915i	−0.270149	+	0.155970i	0.358807	+	0.933412i	$0.383184\pi$
$198$		0			0
$199$	10.4186	−	18.0456i	0.738558	−	1.27922i	−0.214586	−	0.976705i	$-0.568840\pi$
$199$	10.4186	−	18.0456i	0.738558	−	1.27922i	0.953144	−	0.302516i	$-0.0978265\pi$
$200$			5.55889i			0.393073i
$201$		0			0
$202$	32.9526	+	19.0252i	2.31854	+	1.33861i
$203$		−	18.0140i		−	1.26434i
$204$		0			0
$205$	−0.133975	−	0.232051i	−0.00935719	−	0.0162071i
$206$	29.2340	−	16.8783i	2.03683	−	1.17596i
$207$		0			0
$208$	−19.3803	+	2.42749i	−1.34378	+	0.168316i
$209$	−6.12979			−0.424007
$210$		0			0
$211$	5.32684	+	9.22635i	0.366715	+	0.635168i	0.989050	−	0.147583i	$-0.0471492\pi$
$211$	5.32684	+	9.22635i	0.366715	+	0.635168i	−0.622335	+	0.782751i	$0.713816\pi$
$212$	14.7775	−	25.5953i	1.01492	−	1.75789i
$213$		0			0
$214$	−15.9121	−	9.18688i	−1.08773	−	0.628002i
$215$	−0.551886	−	0.318632i	−0.0376383	−	0.0217305i
$216$		0			0
$217$	1.39471	−	2.41571i	0.0946792	−	0.163989i
$218$	−12.5723	−	21.7759i	−0.851505	−	1.47485i
$219$		0			0
$220$	4.52091			0.304799
$221$	1.38724	+	1.83164i	0.0933161	+	0.123210i
$222$		0			0
$223$	−18.4804	+	10.6697i	−1.23754	+	0.714494i	−0.968591	−	0.248661i	$-0.920010\pi$
$223$	−18.4804	+	10.6697i	−1.23754	+	0.714494i	−0.268949	+	0.963155i	$0.586676\pi$
$224$	2.28694	+	3.96110i	0.152803	+	0.264662i
$225$		0			0
$226$			16.6901i			1.11021i
$227$	−13.5842	−	7.84283i	−0.901613	−	0.520547i	−0.0238900	−	0.999715i	$-0.507605\pi$
$227$	−13.5842	−	7.84283i	−0.901613	−	0.520547i	−0.877723	+	0.479168i	$0.840938\pi$
$228$		0			0
$229$		−	7.62085i		−	0.503600i	−0.967779	−	0.251800i	$-0.918977\pi$
$229$		−	7.62085i		−	0.503600i	0.967779	−	0.251800i	$-0.0810225\pi$
$230$	−4.76374	+	8.25104i	−0.314112	+	0.544058i
$231$		0			0
$232$	45.5182	−	26.2800i	2.98842	−	1.72536i
$233$	−19.0550			−1.24833			−0.624166	−	0.781292i	$-0.714561\pi$
$233$	−19.0550			−1.24833			−0.624166	+	0.781292i	$0.714561\pi$
$234$		0			0
$235$	9.44613			0.616198
$236$	2.71306	−	1.56639i	0.176605	−	0.101963i
$237$		0			0
$238$	1.51493	−	2.62393i	0.0981980	−	0.170084i
$239$			12.7535i			0.824954i	0.910968	+	0.412477i	$0.135336\pi$
$239$			12.7535i			0.824954i	−0.910968	+	0.412477i	$0.864664\pi$
$240$		0			0
$241$	−22.4550	−	12.9644i	−1.44646	−	0.835111i	−0.448187	−	0.893940i	$-0.647930\pi$
$241$	−22.4550	−	12.9644i	−1.44646	−	0.835111i	−0.998268	+	0.0588285i	$0.981263\pi$
$242$			24.5967i			1.58114i
$243$		0			0
$244$	8.87483	+	15.3717i	0.568153	+	0.984069i
$245$	−2.91865	+	1.68508i	−0.186466	+	0.107656i
$246$		0			0
$247$	16.4752	−	12.4780i	1.04829	−	0.793954i
$248$	8.13878			0.516813
$249$		0			0
$250$	1.24775	+	2.16117i	0.0789149	+	0.136685i
$251$	−3.80593	+	6.59207i	−0.240228	+	0.416088i	−0.960779	−	0.277314i	$-0.910556\pi$
$251$	−3.80593	+	6.59207i	−0.240228	+	0.416088i	0.720551	+	0.693402i	$0.243889\pi$
$252$		0			0
$253$	3.53578	+	2.04139i	0.222293	+	0.128341i
$254$	3.21907	+	1.85853i	0.201982	+	0.116614i
$255$		0			0
$256$	16.2286	−	28.1087i	1.01429	−	1.75680i
$257$	−0.167891	−	0.290796i	−0.0104728	−	0.0181394i	0.860742	−	0.509042i	$-0.170000\pi$
$257$	−0.167891	−	0.290796i	−0.0104728	−	0.0181394i	−0.871214	+	0.490903i	$0.836667\pi$
$258$		0			0
$259$	−1.44310			−0.0896700
$260$	−12.1510	+	9.20287i	−0.753572	+	0.570738i
$261$		0			0
$262$	−8.91865	+	5.14918i	−0.550996	+	0.318118i
$263$	−2.68795	−	4.65566i	−0.165746	−	0.287080i	0.771174	−	0.636624i	$-0.219670\pi$
$263$	−2.68795	−	4.65566i	−0.165746	−	0.287080i	−0.936920	+	0.349544i	$0.886336\pi$
$264$		0			0
$265$		−	6.99102i		−	0.429455i
$266$	−23.6017	−	13.6264i	−1.44711	−	0.835491i
$267$		0			0
$268$			34.2212i			2.09039i
$269$	−0.655192	+	1.13483i	−0.0399478	+	0.0691916i	−0.885308	−	0.465005i	$-0.846052\pi$
$269$	−0.655192	+	1.13483i	−0.0399478	+	0.0691916i	0.845360	+	0.534197i	$0.179386\pi$
$270$		0			0
$271$	−10.0851	+	5.82266i	−0.612629	+	0.353701i	−0.773994	−	0.633194i	$-0.781744\pi$
$271$	−10.0851	+	5.82266i	−0.612629	+	0.353701i	0.161365	+	0.986895i	$0.448410\pi$
$272$	3.45214			0.209317
$273$		0			0
$274$	−50.1838			−3.03171
$275$	0.926118	−	0.534695i	0.0558470	−	0.0322433i
$276$		0			0
$277$	−10.1581	+	17.5943i	−0.610338	+	1.05714i	0.380845	+	0.924639i	$0.375633\pi$
$277$	−10.1581	+	17.5943i	−0.610338	+	1.05714i	−0.991183	+	0.132498i	$0.957700\pi$
$278$			51.9697i			3.11693i
$279$		0			0
$280$	9.17196	+	5.29543i	0.548129	+	0.316463i
$281$			11.8744i			0.708366i	0.935176	+	0.354183i	$0.115241\pi$
$281$			11.8744i			0.708366i	−0.935176	+	0.354183i	$0.884759\pi$
$282$		0			0
$283$	−11.3261	−	19.6173i	−0.673264	−	1.16613i	−0.976973	−	0.213363i	$-0.931558\pi$
$283$	−11.3261	−	19.6173i	−0.673264	−	1.16613i	0.303709	−	0.952765i	$-0.401775\pi$
$284$	−35.7509	+	20.6408i	−2.12143	+	1.22481i
$285$		0			0
$286$	5.80936	+	7.67038i	0.343515	+	0.453559i
$287$	−0.510500			−0.0301339
$288$		0			0
$289$	8.29695	+	14.3707i	0.488056	+	0.845337i
$290$	11.7977	−	20.4341i	0.692782	−	1.19993i
$291$		0			0
$292$	−13.6067	−	7.85584i	−0.796272	−	0.459728i
$293$	16.1191	+	9.30636i	0.941687	+	0.543683i	0.890489	−	0.455005i	$-0.150363\pi$
$293$	16.1191	+	9.30636i	0.941687	+	0.543683i	0.0511983	+	0.998689i	$0.483696\pi$
$294$		0			0
$295$	0.370518	−	0.641756i	0.0215724	−	0.0373645i
$296$	−2.10529	−	3.64647i	−0.122367	−	0.211946i
$297$		0			0
$298$	−33.3593			−1.93245
$299$	−13.6587	+	1.71083i	−0.789905	+	0.0989400i
$300$		0			0
$301$	−1.05146	+	0.607061i	−0.0606052	+	0.0349904i
$302$	22.8319	+	39.5459i	1.31383	+	2.27561i
$303$		0			0
$304$		−	31.0513i		−	1.78091i
$305$	3.63606	+	2.09928i	0.208200	+	0.120204i
$306$		0			0
$307$			3.14776i			0.179652i	0.995957	+	0.0898262i	$0.0286311\pi$
$307$			3.14776i			0.179652i	−0.995957	+	0.0898262i	$0.971369\pi$
$308$	4.30664	−	7.45932i	0.245394	−	0.425034i
$309$		0			0
$310$	3.16418	−	1.82684i	0.179713	−	0.103757i
$311$	−3.18059			−0.180355			−0.0901774	−	0.995926i	$-0.528743\pi$
$311$	−3.18059			−0.180355			−0.0901774	+	0.995926i	$0.528743\pi$
$312$		0			0
$313$	35.3533			1.99829			0.999144	−	0.0413596i	$-0.0131689\pi$
$313$	35.3533			1.99829			0.999144	+	0.0413596i	$0.0131689\pi$
$314$	5.23499	−	3.02242i	0.295427	−	0.170565i
$315$		0			0
$316$	−19.6991	+	34.1198i	−1.10816	+	1.91939i
$317$		−	13.6357i		−	0.765858i	−0.923778	−	0.382929i	$-0.874915\pi$
$317$		−	13.6357i		−	0.765858i	0.923778	−	0.382929i	$-0.125085\pi$
$318$		0			0
$319$	−8.75656	−	5.05560i	−0.490273	−	0.283059i
$320$		−	4.84325i		−	0.270746i
$321$		0			0
$322$	9.07594	+	15.7200i	0.505782	+	0.876041i
$323$	−3.16344	+	1.82641i	−0.176018	+	0.101624i
$324$		0			0
$325$	−1.40072	+	3.32235i	−0.0776980	+	0.184291i
$326$	−39.8854			−2.20905
$327$		0			0
$328$	−0.744750	−	1.28994i	−0.0411219	−	0.0712253i
$329$	8.99844	−	15.5858i	0.496100	−	0.859271i
$330$		0			0
$331$	−24.9380	−	14.3980i	−1.37072	−	0.791383i	−0.379698	−	0.925110i	$-0.623972\pi$
$331$	−24.9380	−	14.3980i	−1.37072	−	0.791383i	−0.991018	+	0.133727i	$0.957305\pi$
$332$	18.7371	+	10.8179i	1.02833	+	0.593707i
$333$		0			0
$334$	17.9591	−	31.1061i	0.982679	−	1.70205i
$335$	4.04739	+	7.01029i	0.221133	+	0.383013i
$336$		0			0
$337$	−11.7493			−0.640026			−0.320013	−	0.947413i	$-0.603687\pi$
$337$	−11.7493			−0.640026			−0.320013	+	0.947413i	$0.603687\pi$
$338$	−31.2280	−	8.79023i	−1.69858	−	0.478125i
$339$		0			0
$340$	2.33313	−	1.34703i	0.126532	−	0.0730532i
$341$	−0.782847	−	1.35593i	−0.0423936	−	0.0734278i
$342$		0			0
$343$			19.7574i			1.06680i
$344$	−3.06787	−	1.77124i	−0.165409	−	0.0954987i
$345$		0			0
$346$		−	60.7630i		−	3.26664i
$347$	0.949887	−	1.64525i	0.0509926	−	0.0883218i	−0.839402	−	0.543510i	$-0.817095\pi$
$347$	0.949887	−	1.64525i	0.0509926	−	0.0883218i	0.890395	+	0.455189i	$0.150428\pi$
$348$		0			0
$349$	−8.89329	+	5.13454i	−0.476047	+	0.274846i	−0.718768	−	0.695250i	$-0.755293\pi$
$349$	−8.89329	+	5.13454i	−0.476047	+	0.274846i	0.242721	+	0.970096i	$0.421960\pi$
$350$	4.75447			0.254137
$351$		0			0
$352$	2.56730			0.136838
$353$	0.693330	−	0.400294i	0.0369022	−	0.0213055i	−0.481435	−	0.876482i	$-0.659884\pi$
$353$	0.693330	−	0.400294i	0.0369022	−	0.0213055i	0.518338	+	0.855176i	$0.326551\pi$
$354$		0			0
$355$	−4.88244	+	8.45663i	−0.259133	+	0.448831i
$356$		−	53.1756i		−	2.81830i
$357$		0			0
$358$	−8.18714	−	4.72685i	−0.432704	−	0.249822i
$359$		−	8.13272i		−	0.429228i	−0.976699	−	0.214614i	$-0.931151\pi$
$359$		−	8.13272i		−	0.429228i	0.976699	−	0.214614i	$-0.0688494\pi$
$360$		0			0
$361$	6.92820	+	12.0000i	0.364642	+	0.631579i
$362$	18.3439	−	10.5909i	0.964135	−	0.556643i
$363$		0			0
$364$	3.60929	+	28.8154i	0.189178	+	1.51034i
$365$	−3.71649			−0.194530
$366$		0			0
$367$	10.2632	+	17.7765i	0.535737	+	0.927924i	0.999127	+	0.0417696i	$0.0132996\pi$
$367$	10.2632	+	17.7765i	0.535737	+	0.927924i	−0.463390	+	0.886154i	$0.653367\pi$
$368$	−10.3409	+	17.9110i	−0.539057	+	0.933675i
$369$		0			0
$370$	−1.63698	−	0.945110i	−0.0851025	−	0.0491339i
$371$	−11.5349	−	6.65968i	−0.598863	−	0.345754i
$372$		0			0
$373$	8.90292	−	15.4203i	0.460976	−	0.798433i	−0.538034	−	0.842923i	$-0.680833\pi$
$373$	8.90292	−	15.4203i	0.460976	−	0.798433i	0.999010	+	0.0444897i	$0.0141662\pi$
$374$	−0.850322	−	1.47280i	−0.0439691	−	0.0761568i
$375$		0			0
$376$	52.5100			2.70800
$377$	33.8266	−	4.23697i	1.74216	−	0.218215i
$378$		0			0
$379$	−1.77150	+	1.02277i	−0.0909956	+	0.0525363i	−0.544807	−	0.838561i	$-0.683397\pi$
$379$	−1.77150	+	1.02277i	−0.0909956	+	0.0525363i	0.453812	+	0.891098i	$0.350064\pi$
$380$	−12.1163	−	20.9860i	−0.621553	−	1.07656i
$381$		0			0
$382$			13.5833i			0.694982i
$383$	6.84611	+	3.95261i	0.349820	+	0.201969i	0.664606	−	0.747194i	$-0.268599\pi$
$383$	6.84611	+	3.95261i	0.349820	+	0.201969i	−0.314786	+	0.949163i	$0.601933\pi$
$384$		0			0
$385$		−	2.03741i		−	0.103836i
$386$	15.1697	−	26.2747i	0.772117	−	1.33735i
$387$		0			0
$388$	−15.4558	+	8.92343i	−0.784651	+	0.453018i
$389$	−9.21171			−0.467052			−0.233526	−	0.972351i	$-0.575026\pi$
$389$	−9.21171			−0.467052			−0.233526	+	0.972351i	$0.575026\pi$
$390$		0			0
$391$	2.43298			0.123041
$392$	−16.2244	+	9.36719i	−0.819458	+	0.473114i
$393$		0			0
$394$	−5.46304	+	9.46226i	−0.275224	+	0.476702i
$395$			9.31937i			0.468908i
$396$		0			0
$397$	5.50305	+	3.17719i	0.276190	+	0.159458i	0.631697	−	0.775215i	$-0.282359\pi$
$397$	5.50305	+	3.17719i	0.276190	+	0.159458i	−0.355507	+	0.934674i	$0.615692\pi$
$398$		−	51.9996i		−	2.60651i
$399$		0			0
$400$	2.70857	+	4.69138i	0.135428	+	0.234569i
$401$	−3.61063	+	2.08460i	−0.180306	+	0.104100i	−0.587437	−	0.809270i	$-0.699863\pi$
$401$	−3.61063	+	2.08460i	−0.180306	+	0.104100i	0.407130	+	0.913370i	$0.366530\pi$
$402$		0			0
$403$	4.86425	+	2.05080i	0.242306	+	0.102157i
$404$	64.4600			3.20701
$405$		0			0
$406$	−22.4770	−	38.9314i	−1.11552	−	1.93213i
$407$	−0.405004	+	0.701487i	−0.0200753	+	0.0347714i
$408$		0			0
$409$	8.80580	+	5.08403i	0.435419	+	0.251389i	0.701652	−	0.712519i	$-0.252446\pi$
$409$	8.80580	+	5.08403i	0.435419	+	0.251389i	−0.266234	+	0.963909i	$0.585779\pi$
$410$	−0.579085	−	0.334335i	−0.0285989	−	0.0165116i
$411$		0			0
$412$	28.5929	−	49.5244i	1.40867	−	2.43989i
$413$	−0.705915	−	1.22268i	−0.0347358	−	0.0601642i
$414$		0			0
$415$	5.11778			0.251222
$416$	−6.90023	+	5.22607i	−0.338311	+	0.256229i
$417$		0			0
$418$	−13.2475	+	7.64847i	−0.647959	+	0.374099i
$419$	14.2954	+	24.7604i	0.698378	+	1.20963i	0.969029	+	0.246948i	$0.0794277\pi$
$419$	14.2954	+	24.7604i	0.698378	+	1.20963i	−0.270651	+	0.962677i	$0.587239\pi$
$420$		0			0
$421$		−	2.01797i		−	0.0983498i	−0.998790	−	0.0491749i	$-0.984341\pi$
$421$		−	2.01797i		−	0.0983498i	0.998790	−	0.0491749i	$-0.0156592\pi$
$422$	23.0244	+	13.2932i	1.12081	+	0.647101i
$423$		0			0
$424$		−	38.8623i		−	1.88732i
$425$	0.318632	−	0.551886i	0.0154559	−	0.0267704i
$426$		0			0
$427$	6.92747	−	3.99957i	0.335244	−	0.193553i
$428$	−31.1264			−1.50455
$429$		0			0
$430$	−1.59030			−0.0766908
$431$	−17.8508	+	10.3061i	−0.859842	+	0.496430i	−0.863959	−	0.503562i	$-0.832023\pi$
$431$	−17.8508	+	10.3061i	−0.859842	+	0.496430i	0.00411765	+	0.999992i	$0.498689\pi$
$432$		0			0
$433$	14.7178	−	25.4920i	0.707292	−	1.22507i	−0.258566	−	0.965994i	$-0.583250\pi$
$433$	14.7178	−	25.4920i	0.707292	−	1.22507i	0.965858	−	0.259072i	$-0.0834168\pi$
$434$		−	6.96103i		−	0.334140i
$435$		0			0
$436$	−36.8899	−	21.2984i	−1.76670	−	1.02001i
$437$		−	21.8841i		−	1.04686i
$438$		0			0
$439$	8.47602	+	14.6809i	0.404538	+	0.700681i	0.994268	−	0.106920i	$-0.0340988\pi$
$439$	8.47602	+	14.6809i	0.404538	+	0.700681i	−0.589729	+	0.807601i	$0.700765\pi$
$440$	5.14819	−	2.97231i	0.245430	−	0.141699i
$441$		0			0
$442$	5.28351	+	2.22756i	0.251311	+	0.105954i
$443$	24.1399			1.14692			0.573461	−	0.819233i	$-0.305600\pi$
$443$	24.1399			1.14692			0.573461	+	0.819233i	$0.305600\pi$
$444$		0			0
$445$	−6.28917	−	10.8932i	−0.298135	−	0.516385i
$446$	−26.6262	+	46.1180i	−1.26079	+	2.18375i
$447$		0			0
$448$	−7.99118	−	4.61371i	−0.377548	−	0.217977i
$449$	−18.0679	−	10.4315i	−0.852676	−	0.492293i	0.00887706	−	0.999961i	$-0.497174\pi$
$449$	−18.0679	−	10.4315i	−0.852676	−	0.492293i	−0.861553	+	0.507668i	$0.830508\pi$
$450$		0			0
$451$	−0.143271	+	0.248153i	−0.00674637	+	0.0116851i
$452$	14.1371	+	24.4861i	0.664952	+	1.15173i
$453$		0			0
$454$	−39.1437			−1.83710
$455$	4.14741	+	5.47602i	0.194434	+	0.256720i
$456$		0			0
$457$	26.4708	−	15.2830i	1.23825	−	0.714906i	0.269517	−	0.962996i	$-0.413136\pi$
$457$	26.4708	−	15.2830i	1.23825	−	0.714906i	0.968737	+	0.248089i	$0.0798027\pi$
$458$	−9.50894	−	16.4700i	−0.444324	−	0.769591i
$459$		0			0
$460$			16.1402i			0.752541i
$461$	−4.05146	−	2.33911i	−0.188695	−	0.108943i	0.402676	−	0.915342i	$-0.368080\pi$
$461$	−4.05146	−	2.33911i	−0.188695	−	0.108943i	−0.591372	+	0.806399i	$0.701413\pi$
$462$		0			0
$463$		−	14.0011i		−	0.650688i	−0.945596	−	0.325344i	$-0.894520\pi$
$463$		−	14.0011i		−	0.650688i	0.945596	−	0.325344i	$-0.105480\pi$
$464$	25.6098	−	44.3575i	1.18891	−	2.05925i
$465$		0			0
$466$	−41.1811	+	23.7759i	−1.90768	+	1.10140i
$467$	−6.98506			−0.323230			−0.161615	−	0.986854i	$-0.551670\pi$
$467$	−6.98506			−0.323230			−0.161615	+	0.986854i	$0.551670\pi$
$468$		0			0
$469$	15.4223			0.712135
$470$	20.4147	−	11.7864i	0.941661	−	0.543668i
$471$		0			0
$472$	2.05967	−	3.56745i	0.0948039	−	0.164205i
$473$			0.681482i			0.0313346i
$474$		0			0
$475$	−4.96410	−	2.86603i	−0.227769	−	0.131502i
$476$		−	5.13277i		−	0.235260i
$477$		0			0
$478$	15.9132	+	27.5625i	0.727853	+	1.26068i
$479$	14.1065	−	8.14438i	0.644542	−	0.372126i	−0.141820	−	0.989892i	$-0.545296\pi$
$479$	14.1065	−	8.14438i	0.644542	−	0.372126i	0.786362	+	0.617766i	$0.211962\pi$
$480$		0			0
$481$	−0.339423	−	2.70985i	−0.0154764	−	0.123558i
$482$	−64.7056			−2.94726
$483$		0			0
$484$	20.8343	+	36.0860i	0.947012	+	1.64027i
$485$	−2.11078	+	3.65597i	−0.0958454	+	0.166009i
$486$		0			0
$487$	17.3559	+	10.0204i	0.786471	+	0.454069i	0.838719	−	0.544565i	$-0.183305\pi$
$487$	17.3559	+	10.0204i	0.786471	+	0.454069i	−0.0522474	+	0.998634i	$0.516638\pi$
$488$	20.2125	+	11.6697i	0.914975	+	0.528261i
$489$		0			0
$490$	−4.20514	+	7.28351i	−0.189969	+	0.329035i
$491$	7.89916	+	13.6818i	0.356484	+	0.617449i	0.987371	−	0.158426i	$-0.0506420\pi$
$491$	7.89916	+	13.6818i	0.356484	+	0.617449i	−0.630887	+	0.775875i	$0.717309\pi$
$492$		0			0
$493$	−6.02540			−0.271370
$494$	20.0364	−	47.5241i	0.901481	−	2.13821i
$495$		0			0
$496$	6.86865	−	3.96562i	0.308411	−	0.178061i
$497$	9.30208	+	16.1117i	0.417255	+	0.722708i
$498$		0			0
$499$		−	1.24651i		−	0.0558016i	−0.999611	−	0.0279008i	$-0.991118\pi$
$499$		−	1.24651i		−	0.0558016i	0.999611	−	0.0279008i	$-0.00888226\pi$
$500$	3.66117	+	2.11378i	0.163733	+	0.0945311i
$501$		0			0
$502$			18.9955i			0.847809i
$503$	−3.82672	+	6.62808i	−0.170625	+	0.295532i	−0.938639	−	0.344902i	$-0.887912\pi$
$503$	−3.82672	+	6.62808i	−0.170625	+	0.295532i	0.768013	+	0.640434i	$0.221245\pi$
$504$		0			0
$505$	13.2048	−	7.62379i	0.587605	−	0.339254i
$506$	10.1886			0.452938
$507$		0			0
$508$	6.29695			0.279382
$509$	22.2777	−	12.8621i	0.987444	−	0.570101i	0.0829345	−	0.996555i	$-0.473571\pi$
$509$	22.2777	−	12.8621i	0.987444	−	0.570101i	0.904509	+	0.426454i	$0.140237\pi$
$510$		0			0
$511$	−3.54035	+	6.13207i	−0.156616	+	0.271267i
$512$		−	47.2215i		−	2.08691i
$513$		0			0
$514$	−0.725685	−	0.418974i	−0.0320086	−	0.0184802i
$515$		−	13.5269i		−	0.596067i
$516$		0			0
$517$	−5.05080	−	8.74824i	−0.222134	−	0.384747i
$518$	−3.11879	+	1.80064i	−0.137032	+	0.0791154i
$519$		0			0
$520$	−7.78645	+	18.4686i	−0.341458	+	0.809900i
$521$	30.1519			1.32098			0.660490	−	0.750835i	$-0.270349\pi$
$521$	30.1519			1.32098			0.660490	+	0.750835i	$0.270349\pi$
$522$		0			0
$523$	−1.96876	−	3.41000i	−0.0860880	−	0.149109i	0.819766	−	0.572698i	$-0.194103\pi$
$523$	−1.96876	−	3.41000i	−0.0860880	−	0.149109i	−0.905854	+	0.423589i	$0.860770\pi$
$524$	−8.72307	+	15.1088i	−0.381069	+	0.660031i
$525$		0			0
$526$	−11.6182	−	6.70779i	−0.506579	−	0.292473i
$527$	−0.808017	−	0.466509i	−0.0351978	−	0.0203215i
$528$		0			0
$529$	4.21200	−	7.29539i	0.183130	−	0.317191i
$530$	−8.72307	−	15.1088i	−0.378906	−	0.656284i
$531$		0			0
$532$	−46.1682			−2.00165
$533$	−0.120072	−	0.958614i	−0.00520088	−	0.0415222i
$534$		0			0
$535$	−6.37632	+	3.68137i	−0.275672	+	0.159159i
$536$	22.4990	+	38.9694i	0.971809	+	1.68322i
$537$		0			0
$538$			3.27007i			0.140983i
$539$	3.12117	+	1.80201i	0.134438	+	0.0776180i
$540$		0			0
$541$		−	15.8881i		−	0.683083i	−0.939867	−	0.341541i	$-0.889051\pi$
$541$		−	15.8881i		−	0.683083i	0.939867	−	0.341541i	$-0.110949\pi$
$542$	−14.5305	+	25.1675i	−0.624138	+	1.08104i
$543$		0			0
$544$	1.32492	−	0.764945i	0.0568057	−	0.0327968i
$545$	−10.0760			−0.431607
$546$		0			0
$547$	−6.56107			−0.280531			−0.140266	−	0.990114i	$-0.544796\pi$
$547$	−6.56107			−0.280531			−0.140266	+	0.990114i	$0.544796\pi$
$548$	−73.6249	+	42.5074i	−3.14510	+	1.81582i
$549$		0			0
$550$	1.33433	−	2.31114i	0.0568962	−	0.0985471i
$551$			54.1972i			2.30888i
$552$		0			0
$553$	15.3766	+	8.87769i	0.653880	+	0.377518i
$554$			50.6990i			2.15399i
$555$		0			0
$556$	44.0200	+	76.2450i	1.86687	+	3.23351i
$557$	−6.79835	+	3.92503i	−0.288055	+	0.166309i	−0.637065	−	0.770810i	$-0.719852\pi$
$557$	−6.79835	+	3.92503i	−0.288055	+	0.166309i	0.349009	+	0.937119i	$0.386518\pi$
$558$		0			0
$559$	−1.38724	−	1.83164i	−0.0586741	−	0.0774702i
$560$	10.3208			0.436133
$561$		0			0
$562$	14.8163	+	25.6626i	0.624988	+	1.08251i
$563$	7.77976	−	13.4749i	0.327878	−	0.567901i	−0.654213	−	0.756310i	$-0.727000\pi$
$563$	7.77976	−	13.4749i	0.327878	−	0.567901i	0.982091	+	0.188410i	$0.0603333\pi$
$564$		0			0
$565$	5.79203	+	3.34403i	0.243673	+	0.140684i
$566$	−48.9552	−	28.2643i	−2.05774	−	1.18804i
$567$		0			0
$568$	−27.1409	+	47.0095i	−1.13881	+	1.97247i
$569$	−1.73957	−	3.01303i	−0.0729267	−	0.126313i	0.827256	−	0.561825i	$-0.189901\pi$
$569$	−1.73957	−	3.01303i	−0.0729267	−	0.126313i	−0.900183	+	0.435512i	$0.856567\pi$
$570$		0			0
$571$	21.5118			0.900240			0.450120	−	0.892968i	$-0.351381\pi$
$571$	21.5118			0.900240			0.450120	+	0.892968i	$0.351381\pi$
$572$	15.0200	+	6.33252i	0.628018	+	0.264776i
$573$		0			0
$574$	−1.10328	+	0.636978i	−0.0460500	+	0.0265870i
$575$	1.90893	+	3.30636i	0.0796078	+	0.137885i
$576$		0			0
$577$		−	9.97608i		−	0.415310i	−0.978202	−	0.207655i	$-0.933417\pi$
$577$		−	9.97608i		−	0.415310i	0.978202	−	0.207655i	$-0.0665831\pi$
$578$	35.8623	+	20.7051i	1.49167	+	0.861218i
$579$		0			0
$580$		−	39.9721i		−	1.65975i
$581$	4.87523	−	8.44414i	0.202259	−	0.350322i
$582$		0			0
$583$	−6.47451	+	3.73806i	−0.268147	+	0.154815i
$584$	−20.6595			−0.854898
$585$		0			0
$586$	46.4482			1.91876
$587$	−20.8341	+	12.0286i	−0.859915	+	0.496472i	−0.863984	−	0.503519i	$-0.832038\pi$
$587$	−20.8341	+	12.0286i	−0.859915	+	0.496472i	0.00406862	+	0.999992i	$0.498705\pi$
$588$		0			0
$589$	−4.19615	+	7.26795i	−0.172899	+	0.299471i
$590$		−	1.84926i		−	0.0761328i
$591$		0			0
$592$	−3.55348	−	2.05160i	−0.146047	−	0.0843203i
$593$		−	0.940219i		−	0.0386102i	−0.999814	−	0.0193051i	$-0.993855\pi$
$593$		−	0.940219i		−	0.0386102i	0.999814	−	0.0193051i	$-0.00614538\pi$
$594$		0			0
$595$	−0.607061	−	1.05146i	−0.0248871	−	0.0431057i
$596$	−48.9417	+	28.2565i	−2.00473	+	1.15743i
$597$		0			0
$598$	−27.3842	+	20.7401i	−1.11982	+	0.848128i
$599$	11.4270			0.466896			0.233448	−	0.972369i	$-0.424999\pi$
$599$	11.4270			0.466896			0.233448	+	0.972369i	$0.424999\pi$
$600$		0			0
$601$	18.0215	+	31.2142i	0.735114	+	1.27325i	0.954674	+	0.297655i	$0.0962045\pi$
$601$	18.0215	+	31.2142i	0.735114	+	1.27325i	−0.219560	+	0.975599i	$0.570462\pi$
$602$	−1.51493	+	2.62393i	−0.0617437	+	0.106943i
$603$		0			0
$604$	66.9935	+	38.6787i	2.72593	+	1.57381i
$605$	8.53590	+	4.92820i	0.347034	+	0.200360i
$606$		0			0
$607$	−19.9454	+	34.5464i	−0.809557	+	1.40219i	0.103614	+	0.994618i	$0.466959\pi$
$607$	−19.9454	+	34.5464i	−0.809557	+	1.40219i	−0.913171	+	0.407576i	$0.866374\pi$
$608$	−6.88052	−	11.9174i	−0.279042	−	0.483315i
$609$		0			0
$610$	10.4775			0.424223
$611$	31.3833	+	13.2314i	1.26963	+	0.535285i
$612$		0			0
$613$	0.299187	−	0.172736i	0.0120841	−	0.00697673i	−0.493946	−	0.869493i	$-0.664446\pi$
$613$	0.299187	−	0.172736i	0.0120841	−	0.00697673i	0.506030	+	0.862516i	$0.331113\pi$
$614$	3.92763	+	6.80286i	0.158506	+	0.274541i
$615$		0			0
$616$		−	11.3258i		−	0.456328i
$617$	−33.5022	−	19.3425i	−1.34875	−	0.778700i	−0.360676	−	0.932691i	$-0.617454\pi$
$617$	−33.5022	−	19.3425i	−1.34875	−	0.778700i	−0.988072	+	0.153991i	$0.950787\pi$
$618$		0			0
$619$			14.8971i			0.598764i	0.954133	+	0.299382i	$0.0967805\pi$
$619$			14.8971i			0.598764i	−0.954133	+	0.299382i	$0.903219\pi$
$620$	3.09479	−	5.36033i	0.124290	−	0.215276i
$621$		0			0
$622$	−6.87381	+	3.96859i	−0.275615	+	0.159126i
$623$	−23.9644			−0.960113
$624$		0			0
$625$	1.00000			0.0400000
$626$	76.4047	−	44.1123i	3.05374	−	1.76308i
$627$		0			0
$628$	5.12019	−	8.86842i	0.204318	−	0.353889i
$629$			0.482694i			0.0192463i
$630$		0			0
$631$	33.6408	+	19.4225i	1.33922	+	0.773198i	0.986691	−	0.162604i	$-0.0519893\pi$
$631$	33.6408	+	19.4225i	1.33922	+	0.773198i	0.352526	+	0.935802i	$0.385323\pi$
$632$			51.8053i			2.06071i
$633$		0			0
$634$	−17.0140	−	29.4691i	−0.675713	−	1.17037i
$635$	1.28994	−	0.744750i	0.0511899	−	0.0295545i
$636$		0			0
$637$	−12.0571	+	1.51022i	−0.477719	+	0.0598370i
$638$	−25.2326			−0.998967
$639$		0			0
$640$	−8.44391	−	14.6253i	−0.333775	−	0.578115i
$641$	−18.5908	+	32.2003i	−0.734293	+	1.27183i	0.220739	+	0.975333i	$0.429153\pi$
$641$	−18.5908	+	32.2003i	−0.734293	+	1.27183i	−0.955033	+	0.296501i	$0.904180\pi$
$642$		0			0
$643$	7.88410	+	4.55189i	0.310918	+	0.179509i	0.647337	−	0.762204i	$-0.275882\pi$
$643$	7.88410	+	4.55189i	0.310918	+	0.179509i	−0.336419	+	0.941712i	$0.609216\pi$
$644$	26.6307	+	15.3753i	1.04940	+	0.605870i
$645$		0			0
$646$	−4.55783	+	7.89439i	−0.179325	+	0.310601i
$647$	9.56118	+	16.5605i	0.375889	+	0.651059i	0.990460	−	0.137803i	$-0.0440041\pi$
$647$	9.56118	+	16.5605i	0.375889	+	0.651059i	−0.614571	+	0.788862i	$0.710671\pi$
$648$		0			0
$649$	−0.792455			−0.0311066
$650$	1.11827	+	8.92792i	0.0438622	+	0.350182i
$651$		0			0
$652$	−58.5161	+	33.7843i	−2.29167	+	1.32309i
$653$	17.3162	+	29.9926i	0.677636	+	1.17370i	0.975691	+	0.219152i	$0.0703289\pi$
$653$	17.3162	+	29.9926i	0.677636	+	1.17370i	−0.298055	+	0.954549i	$0.596338\pi$
$654$		0			0
$655$			4.12676i			0.161246i
$656$	−1.25705	−	0.725758i	−0.0490796	−	0.0283361i
$657$		0			0
$658$		−	44.9114i		−	1.75083i
$659$	−3.34926	+	5.80109i	−0.130469	+	0.225978i	−0.923857	−	0.382737i	$-0.874982\pi$
$659$	−3.34926	+	5.80109i	−0.130469	+	0.225978i	0.793389	+	0.608715i	$0.208315\pi$
$660$		0			0
$661$	5.22004	−	3.01379i	0.203036	−	0.117223i	−0.395035	−	0.918666i	$-0.629268\pi$
$661$	5.22004	−	3.01379i	0.203036	−	0.117223i	0.598071	+	0.801443i	$0.295934\pi$
$662$	−71.8604			−2.79294
$663$		0			0
$664$	28.4492			1.10404
$665$	−9.45767	+	5.46039i	−0.366753	+	0.211745i
$666$		0			0
$667$	18.0491	−	31.2620i	0.698865	−	1.21047i
$668$		−	60.8479i		−	2.35428i
$669$		0			0
$670$	17.4942	+	10.1003i	0.675861	+	0.390209i
$671$		−	4.48990i		−	0.173330i
$672$		0			0
$673$	11.6784	+	20.2276i	0.450169	+	0.779715i	0.998396	−	0.0566140i	$-0.0180304\pi$
$673$	11.6784	+	20.2276i	0.450169	+	0.779715i	−0.548227	+	0.836329i	$0.684697\pi$
$674$	−25.3923	+	14.6603i	−0.978075	+	0.564692i
$675$		0			0
$676$	−53.2604	+	13.5550i	−2.04848	+	0.521346i
$677$	45.4042			1.74503			0.872513	−	0.488590i	$-0.162489\pi$
$677$	45.4042			1.74503			0.872513	+	0.488590i	$0.162489\pi$
$678$		0			0
$679$	4.02148	+	6.96540i	0.154330	+	0.267308i
$680$	1.77124	−	3.06787i	0.0679239	−	0.117648i
$681$		0			0
$682$	−3.38374	−	1.95360i	−0.129570	−	0.0748073i
$683$	−22.0817	−	12.7489i	−0.844934	−	0.487823i	0.0140045	−	0.999902i	$-0.495542\pi$
$683$	−22.0817	−	12.7489i	−0.844934	−	0.487823i	−0.858938	+	0.512079i	$0.828875\pi$
$684$		0			0
$685$	−10.0548	+	17.4155i	−0.384175	+	0.665411i
$686$	24.6523	+	42.6991i	0.941230	+	1.63026i
$687$		0			0
$688$	−3.45214			−0.131612
$689$	9.79246	−	23.2266i	0.373063	−	0.884862i
$690$		0			0
$691$	5.71257	−	3.29815i	0.217316	−	0.125468i	−0.387391	−	0.921916i	$-0.626624\pi$
$691$	5.71257	−	3.29815i	0.217316	−	0.125468i	0.604707	+	0.796448i	$0.293290\pi$
$692$	−51.4683	−	89.1457i	−1.95653	−	3.38881i
$693$		0			0
$694$		−	4.74090i		−	0.179962i
$695$	18.0352	+	10.4126i	0.684115	+	0.394974i
$696$		0			0
$697$			0.170754i			0.00646778i
$698$	−12.8133	+	22.1933i	−0.484990	+	0.840028i
$699$		0			0
$700$	6.97531	−	4.02720i	0.263642	−	0.152214i
$701$	29.2474			1.10466			0.552329	−	0.833626i	$-0.313739\pi$
$701$	29.2474			1.10466			0.552329	+	0.833626i	$0.313739\pi$
$702$		0			0
$703$	4.34174			0.163752
$704$	−4.48542	+	2.58966i	−0.169051	+	0.0976015i
$705$		0			0
$706$	0.998937	−	1.73021i	0.0375955	−	0.0651173i
$707$		−	29.0499i		−	1.09253i
$708$		0			0
$709$	−9.46865	−	5.46673i	−0.355603	−	0.205307i	0.311548	−	0.950231i	$-0.399153\pi$
$709$	−9.46865	−	5.46673i	−0.355603	−	0.205307i	−0.667150	+	0.744923i	$0.732486\pi$
$710$			24.3683i			0.914527i
$711$		0			0
$712$	−34.9608	−	60.5538i	−1.31021	−	2.26935i
$713$	4.84084	−	2.79486i	0.181291	−	0.104668i
$714$		0			0
$715$	3.82584	−	0.479208i	0.143078	−	0.0179214i
$716$	−16.0152			−0.598516
$717$		0			0
$718$	−10.1476	−	17.5762i	−0.378706	−	0.655938i
$719$	−8.02989	+	13.9082i	−0.299464	+	0.518688i	−0.976014	−	0.217710i	$-0.930141\pi$
$719$	−8.02989	+	13.9082i	−0.299464	+	0.518688i	0.676549	+	0.736398i	$0.263475\pi$
$720$		0			0
$721$	−22.3189	−	12.8858i	−0.831199	−	0.479893i
$722$	29.9461	+	17.2894i	1.11448	+	0.643444i
$723$		0			0
$724$	17.9416	−	31.0758i	0.666796	−	1.15492i
$725$	−4.72756	−	8.18837i	−0.175577	−	0.304108i
$726$		0			0
$727$	−51.3754			−1.90541			−0.952704	−	0.303900i	$-0.901711\pi$
$727$	−51.3754			−1.90541			−0.952704	+	0.303900i	$0.901711\pi$
$728$	23.0550	+	30.4406i	0.854475	+	1.12820i
$729$		0			0
$730$	−8.03198	+	4.63726i	−0.297277	+	0.171633i
$731$	0.203052	+	0.351697i	0.00751016	+	0.0130080i
$732$		0			0
$733$			9.82358i			0.362842i	0.983406	+	0.181421i	$0.0580697\pi$
$733$			9.82358i			0.362842i	−0.983406	+	0.181421i	$0.941930\pi$
$734$	44.3613	+	25.6120i	1.63741	+	0.945357i
$735$		0			0
$736$			9.16560i			0.337848i
$737$	4.32824	−	7.49673i	0.159433	−	0.276146i
$738$		0			0
$739$	42.5082	−	24.5421i	1.56369	−	0.902797i	0.566811	−	0.823848i	$-0.308177\pi$
$739$	42.5082	−	24.5421i	1.56369	−	0.902797i	0.996879	−	0.0789487i	$-0.0251563\pi$
$740$	−3.20216			−0.117714
$741$		0			0
$742$	−33.2386			−1.22023
$743$	35.3663	−	20.4188i	1.29746	−	0.749091i	0.317499	−	0.948259i	$-0.397157\pi$
$743$	35.3663	−	20.4188i	1.29746	−	0.749091i	0.979966	+	0.199167i	$0.0638237\pi$
$744$		0			0
$745$	−6.68388	+	11.5768i	−0.244878	+	0.424142i
$746$		−	44.4346i		−	1.62687i
$747$		0			0
$748$	−2.49503	−	1.44050i	−0.0912272	−	0.0526700i
$749$			14.0276i			0.512557i
$750$		0			0
$751$	−1.36340	−	2.36148i	−0.0497512	−	0.0861716i	0.840077	−	0.542467i	$-0.182510\pi$
$751$	−1.36340	−	2.36148i	−0.0497512	−	0.0861716i	−0.889829	+	0.456295i	$0.849176\pi$
$752$	44.3154	−	25.5855i	1.61601	−	0.933006i
$753$		0			0
$754$	67.8184	−	51.3641i	2.46980	−	1.87057i
$755$	18.2984			0.665946
$756$		0			0
$757$	−7.40301	−	12.8224i	−0.269067	−	0.466038i	0.699554	−	0.714580i	$-0.253382\pi$
$757$	−7.40301	−	12.8224i	−0.269067	−	0.466038i	−0.968621	+	0.248542i	$0.920049\pi$
$758$	−2.55234	+	4.42078i	−0.0927051	+	0.160570i
$759$		0			0
$760$	−27.5949	−	15.9319i	−1.00097	−	0.577911i
$761$	−9.84575	−	5.68445i	−0.356908	−	0.206061i	0.310815	−	0.950470i	$-0.399398\pi$
$761$	−9.84575	−	5.68445i	−0.356908	−	0.206061i	−0.667724	+	0.744409i	$0.732731\pi$
$762$		0			0
$763$	−9.59843	+	16.6250i	−0.347486	+	0.601864i
$764$	11.5055	+	19.9281i	0.416255	+	0.720975i
$765$		0			0
$766$	19.7275			0.712784
$767$	2.12991	−	1.61314i	0.0769065	−	0.0582472i
$768$		0			0
$769$	18.2352	−	10.5281i	0.657579	−	0.379654i	−0.133775	−	0.991012i	$-0.542710\pi$
$769$	18.2352	−	10.5281i	0.657579	−	0.379654i	0.791354	+	0.611358i	$0.209377\pi$
$770$	−2.54219	−	4.40320i	−0.0916142	−	0.158680i
$771$		0			0
$772$		−	51.3970i		−	1.84982i
$773$	−12.1961	−	7.04144i	−0.438664	−	0.253263i	0.264367	−	0.964422i	$-0.414837\pi$
$773$	−12.1961	−	7.04144i	−0.438664	−	0.253263i	−0.703031	+	0.711159i	$0.748170\pi$
$774$		0			0
$775$		−	1.46410i		−	0.0525921i
$776$	−11.7336	+	20.3231i	−0.421210	+	0.729558i
$777$		0			0
$778$	−19.9081	+	11.4940i	−0.713740	+	0.412078i
$779$	1.53590			0.0550293
$780$		0			0
$781$	10.4425			0.373660
$782$	5.25809	−	3.03576i	0.188029	−	0.108558i
$783$		0			0
$784$	−9.12832	+	15.8107i	−0.326011	+	0.564668i
$785$		−	2.42229i		−	0.0864552i
$786$		0			0
$787$	−28.5998	−	16.5121i	−1.01947	−	0.588593i	−0.105522	−	0.994417i	$-0.533651\pi$
$787$	−28.5998	−	16.5121i	−1.01947	−	0.588593i	−0.913951	+	0.405823i	$0.866985\pi$
$788$			18.5095i			0.659374i
$789$		0			0
$790$	11.6283	+	20.1408i	0.413716	+	0.716576i
$791$	11.0350	−	6.37109i	0.392361	−	0.226530i
$792$		0			0
$793$	9.13974	+	12.0676i	0.324562	+	0.428534i
$794$	15.8574			0.562758
$795$		0			0
$796$	−44.0454	−	76.2890i	−1.56115	−	2.70399i
$797$	8.47079	−	14.6718i	0.300051	−	0.519703i	−0.676096	−	0.736813i	$-0.736330\pi$
$797$	8.47079	−	14.6718i	0.300051	−	0.519703i	0.976147	+	0.217110i	$0.0696630\pi$
$798$		0			0
$799$	−5.21319	−	3.00984i	−0.184429	−	0.106480i
$800$	2.07908	+	1.20036i	0.0735067	+	0.0424391i
$801$		0			0
$802$	−5.20213	+	9.01036i	−0.183694	+	0.318167i
$803$	1.98719	+	3.44191i	0.0701263	+	0.121462i
$804$		0			0
$805$	7.27382			0.256369
$806$	13.0714	−	1.63726i	0.460420	−	0.0576701i
$807$		0			0
$808$	73.4039	−	42.3798i	2.58234	−	1.49092i
$809$	−25.8818	−	44.8285i	−0.909954	−	1.57609i	−0.814125	−	0.580689i	$-0.802783\pi$
$809$	−25.8818	−	44.8285i	−0.909954	−	1.57609i	−0.0958292	−	0.995398i	$-0.530550\pi$
$810$		0			0
$811$		−	22.6699i		−	0.796047i	−0.917375	−	0.398023i	$-0.869696\pi$
$811$		−	22.6699i		−	0.796047i	0.917375	−	0.398023i	$-0.130304\pi$
$812$	−65.9524	−	38.0776i	−2.31448	−	1.33626i
$813$		0			0
$814$			2.02138i			0.0708494i
$815$	−7.99144	+	13.8416i	−0.279928	+	0.484849i
$816$		0			0
$817$	3.16344	−	1.82641i	0.110675	−	0.0638981i
$818$	25.3745			0.887198
$819$		0			0
$820$	−1.13277			−0.0395581
$821$	24.8230	−	14.3315i	0.866328	−	0.500174i	0.000201482	−	1.00000i	$-0.499936\pi$
$821$	24.8230	−	14.3315i	0.866328	−	0.500174i	0.866126	+	0.499826i	$0.166603\pi$
$822$		0			0
$823$	−12.9164	+	22.3718i	−0.450236	+	0.779831i	−0.998400	−	0.0565391i	$-0.981993\pi$
$823$	−12.9164	+	22.3718i	−0.450236	+	0.779831i	0.548165	+	0.836371i	$0.315327\pi$
$824$		−	75.1946i		−	2.61953i
$825$		0			0
$826$	−3.05121	−	1.76162i	−0.106165	−	0.0612945i
$827$			16.0820i			0.559227i	0.960113	+	0.279613i	$0.0902063\pi$
$827$			16.0820i			0.559227i	−0.960113	+	0.279613i	$0.909794\pi$
$828$		0			0
$829$	−11.2909	−	19.5564i	−0.392149	−	0.679222i	0.600584	−	0.799562i	$-0.294935\pi$
$829$	−11.2909	−	19.5564i	−0.392149	−	0.679222i	−0.992733	+	0.120340i	$0.961602\pi$
$830$	11.0604	−	6.38573i	0.383912	−	0.221652i
$831$		0			0
$832$	6.78404	−	16.0910i	0.235194	−	0.557854i
$833$	2.14768			0.0744128
$834$		0			0
$835$	−7.19658	−	12.4648i	−0.249048	−	0.431364i
$836$	−12.9570	+	22.4422i	−0.448128	+	0.776181i
$837$		0			0
$838$	61.7898	+	35.6744i	2.13449	+	1.23235i
$839$	−15.4533	−	8.92198i	−0.533508	−	0.308021i	0.208936	−	0.977929i	$-0.433000\pi$
$839$	−15.4533	−	8.92198i	−0.533508	−	0.308021i	−0.742444	+	0.669908i	$0.766333\pi$
$840$		0			0
$841$	−30.1996	+	52.3073i	−1.04137	+	1.80370i
$842$	−2.51793	−	4.36118i	−0.0867736	−	0.150296i
$843$		0			0
$844$	45.0390			1.55031
$845$	−9.30735	+	9.07597i	−0.320183	+	0.312223i
$846$		0			0
$847$	16.2627	−	9.38927i	0.558793	−	0.322619i
$848$	−18.9356	−	32.7975i	−0.650252	−	1.12627i
$849$		0			0
$850$		−	1.59030i		−	0.0545467i
$851$	−2.50440	−	1.44591i	−0.0858497	−	0.0495653i
$852$		0			0
$853$			19.7936i			0.677720i	0.940837	+	0.338860i	$0.110041\pi$
$853$			19.7936i			0.677720i	−0.940837	+	0.338860i	$0.889959\pi$
$854$	9.98097	−	17.2875i	0.341542	−	0.591568i
$855$		0			0
$856$	−35.4452	+	20.4643i	−1.21149	+	0.699456i
$857$	−11.7302			−0.400696			−0.200348	−	0.979725i	$-0.564207\pi$
$857$	−11.7302			−0.400696			−0.200348	+	0.979725i	$0.564207\pi$
$858$		0			0
$859$	5.37452			0.183376			0.0916882	−	0.995788i	$-0.470774\pi$
$859$	5.37452			0.183376			0.0916882	+	0.995788i	$0.470774\pi$
$860$	−2.33313	+	1.34703i	−0.0795591	+	0.0459335i
$861$		0			0
$862$	−25.7191	+	44.5467i	−0.875995	+	1.51727i
$863$		−	25.3234i		−	0.862017i	−0.902348	−	0.431008i	$-0.858158\pi$
$863$		−	25.3234i		−	0.862017i	0.902348	−	0.431008i	$-0.141842\pi$
$864$		0			0
$865$	−21.0868	−	12.1745i	−0.716973	−	0.413944i
$866$		−	73.4567i		−	2.49616i
$867$		0			0
$868$	−5.89623	−	10.2126i	−0.200131	−	0.346637i
$869$	8.63084	−	4.98302i	0.292781	−	0.169037i
$870$		0			0
$871$	3.62739	+	28.9599i	0.122909	+	0.981268i
$872$	−56.0112			−1.89678
$873$		0			0
$874$	−27.3060	−	47.2954i	−0.923640	−	1.59979i
$875$	0.952606	−	1.64996i	0.0322040	−	0.0557789i
$876$		0			0
$877$	17.9194	+	10.3458i	0.605095	+	0.349352i	0.771043	−	0.636783i	$-0.219735\pi$
$877$	17.9194	+	10.3458i	0.605095	+	0.349352i	−0.165949	+	0.986134i	$0.553069\pi$
$878$	36.6363	+	21.1520i	1.23642	+	0.713845i
$879$		0			0
$880$	2.89651	−	5.01691i	0.0976414	−	0.169120i
$881$	−24.1997	−	41.9150i	−0.815307	−	1.41215i	−0.909107	−	0.416562i	$-0.863235\pi$
$881$	−24.1997	−	41.9150i	−0.815307	−	1.41215i	0.0937999	−	0.995591i	$-0.470099\pi$
$882$		0			0
$883$	−45.8550			−1.54314			−0.771572	−	0.636142i	$-0.780529\pi$
$883$	−45.8550			−1.54314			−0.771572	+	0.636142i	$0.780529\pi$
$884$	9.63829	−	1.20725i	0.324171	−	0.0406042i
$885$		0			0
$886$	52.1705	−	30.1207i	1.75270	−	1.01192i
$887$	−0.541169	−	0.937332i	−0.0181707	−	0.0314725i	0.856797	−	0.515654i	$-0.172451\pi$
$887$	−0.541169	−	0.937332i	−0.0181707	−	0.0314725i	−0.874968	+	0.484181i	$0.839118\pi$
$888$		0			0
$889$		−	2.83781i		−	0.0951772i
$890$	−27.1840	−	15.6947i	−0.911208	−	0.526086i
$891$		0			0
$892$			90.2133i			3.02056i
$893$	−27.0729	+	46.8916i	−0.905959	+	1.56917i
$894$		0			0
$895$	−3.28075	+	1.89414i	−0.109663	+	0.0633142i
$896$	−32.1749			−1.07489
$897$		0			0
$898$	−52.0637			−1.73739
$899$	−11.9886	+	6.92163i	−0.399842	+	0.230849i
$900$		0			0
$901$	−2.22756	+	3.85824i	−0.0742107	+	0.128537i
$902$			0.715068i			0.0238092i
$903$		0			0
$904$	32.1973	+	18.5891i	1.07086	+	0.618264i
$905$		−	8.48794i		−	0.282149i
$906$		0			0
$907$	−22.7653	−	39.4307i	−0.755910	−	1.30928i	−0.944920	−	0.327300i	$-0.893861\pi$
$907$	−22.7653	−	39.4307i	−0.755910	−	1.30928i	0.189010	−	0.981975i	$-0.439472\pi$
$908$	−57.4279	+	33.1560i	−1.90581	+	1.10032i
$909$		0			0
$910$	15.7960	+	6.65968i	0.523632	+	0.220766i
$911$	−39.7417			−1.31670			−0.658350	−	0.752712i	$-0.728745\pi$
$911$	−39.7417			−1.31670			−0.658350	+	0.752712i	$0.728745\pi$
$912$		0			0
$913$	−2.73645	−	4.73967i	−0.0905632	−	0.156860i
$914$	38.1387	−	66.0582i	1.26152	−	2.18501i
$915$		0			0
$916$	−27.9012	−	16.1088i	−0.921883	−	0.532250i
$917$	6.80900	+	3.93118i	0.224853	+	0.129819i
$918$		0			0
$919$	−23.4969	+	40.6978i	−0.775091	+	1.34250i	0.159653	+	0.987173i	$0.448963\pi$
$919$	−23.4969	+	40.6978i	−0.775091	+	1.34250i	−0.934743	+	0.355323i	$0.884371\pi$
$920$	10.6115	+	18.3797i	0.349851	+	0.605960i
$921$		0			0
$922$	−11.6745			−0.384481
$923$	−28.0665	+	21.2569i	−0.923821	+	0.699680i
$924$		0			0
$925$	−0.655970	+	0.378725i	−0.0215682	+	0.0124524i
$926$	−17.4700	−	30.2589i	−0.574099	−	0.994369i
$927$		0			0
$928$		−	22.6991i		−	0.745134i
$929$	13.1821	+	7.61066i	0.432489	+	0.249698i	0.700406	−	0.713744i	$-0.253002\pi$
$929$	13.1821	+	7.61066i	0.432489	+	0.249698i	−0.267917	+	0.963442i	$0.586335\pi$
$930$		0			0
$931$		−	19.3180i		−	0.633121i
$932$	−40.2780	+	69.7635i	−1.31935	+	2.28518i
$933$		0			0
$934$	−15.0959	+	8.71564i	−0.493954	+	0.285184i
$935$	−0.681482			−0.0222869
$936$		0			0
$937$	6.07285			0.198392			0.0991958	−	0.995068i	$-0.468373\pi$
$937$	6.07285			0.198392			0.0991958	+	0.995068i	$0.468373\pi$
$938$	33.3302	−	19.2432i	1.08827	−	0.628313i
$939$		0			0
$940$	19.9670	−	34.5839i	0.651253	−	1.12800i
$941$		−	0.0496576i		−	0.00161879i	−1.00000		0.000809396i	$-0.999742\pi$
$941$		−	0.0496576i		−	0.00161879i	1.00000		0.000809396i	$-0.000257639\pi$
$942$		0			0
$943$	−0.885936	−	0.511495i	−0.0288500	−	0.0166566i
$944$		−	4.01429i		−	0.130654i
$945$		0			0
$946$	0.850322	+	1.47280i	0.0276464	+	0.0478849i
$947$	16.1584	−	9.32907i	0.525078	−	0.303154i	−0.213932	−	0.976849i	$-0.568627\pi$
$947$	16.1584	−	9.32907i	0.525078	−	0.303154i	0.739010	+	0.673695i	$0.235294\pi$
$948$		0			0
$949$	−12.3475	−	5.20576i	−0.400816	−	0.168986i
$950$	−14.3044			−0.464095
$951$		0			0
$952$	−3.37458	−	5.84495i	−0.109371	−	0.189436i
$953$	0.764764	−	1.32461i	0.0247731	−	0.0429083i	−0.853373	−	0.521301i	$-0.825447\pi$
$953$	0.764764	−	1.32461i	0.0247731	−	0.0429083i	0.878146	+	0.478392i	$0.158780\pi$
$954$		0			0
$955$	4.71386	+	2.72155i	0.152537	+	0.0880673i
$956$	46.6927	+	26.9581i	1.51015	+	0.871886i
$957$		0			0
$958$	20.3244	−	35.2028i	0.656650	−	1.13735i
$959$	19.1566	+	33.1802i	0.618598	+	1.07144i
$960$		0			0
$961$	28.8564			0.930852
$962$	−4.11477	−	5.43293i	−0.132666	−	0.175165i
$963$		0			0
$964$	−94.9299	+	54.8078i	−3.05749	+	1.76524i
$965$	−6.07880	−	10.5288i	−0.195683	−	0.338934i
$966$		0			0
$967$		−	32.1716i		−	1.03457i	−0.855813	−	0.517285i	$-0.826943\pi$
$967$		−	32.1716i		−	1.03457i	0.855813	−	0.517285i	$-0.173057\pi$
$968$	47.4501	+	27.3953i	1.52510	+	0.880519i
$969$		0			0
$970$			10.5349i			0.338256i
$971$	−8.62705	+	14.9425i	−0.276855	+	0.479527i	−0.970601	−	0.240692i	$-0.922626\pi$
$971$	−8.62705	+	14.9425i	−0.276855	+	0.479527i	0.693746	+	0.720219i	$0.255959\pi$
$972$		0			0
$973$	34.3609	−	19.8383i	1.10156	−	0.635986i
$974$	50.0122			1.60249
$975$		0			0
$976$	22.7442			0.728023
$977$	13.6164	−	7.86142i	0.435626	−	0.251509i	−0.266114	−	0.963942i	$-0.585740\pi$
$977$	13.6164	−	7.86142i	0.435626	−	0.251509i	0.701741	+	0.712432i	$0.252407\pi$
$978$		0			0
$979$	−6.72557	+	11.6490i	−0.214950	+	0.372304i
$980$			14.2476i			0.455122i
$981$		0			0
$982$	34.1429	+	19.7124i	1.08954	+	0.629049i
$983$		−	38.5356i		−	1.22910i	−0.788880	−	0.614548i	$-0.789338\pi$
$983$		−	38.5356i		−	1.22910i	0.788880	−	0.614548i	$-0.210662\pi$
$984$		0			0
$985$	2.18915	+	3.79172i	0.0697521	+	0.120814i
$986$	−13.0219	+	7.51821i	−0.414703	+	0.239429i
$987$		0			0
$988$	−10.8590	−	86.6944i	−0.345469	−	2.75812i
$989$	−2.43298			−0.0773642
$990$		0			0
$991$	−4.29571	−	7.44040i	−0.136458	−	0.236352i	0.789696	−	0.613499i	$-0.210238\pi$
$991$	−4.29571	−	7.44040i	−0.136458	−	0.236352i	−0.926153	+	0.377147i	$0.876905\pi$
$992$	1.75745	−	3.04399i	0.0557991	−	0.0966468i
$993$		0			0
$994$	40.2068	+	23.2134i	1.27528	+	0.736285i
$995$	−18.0456	−	10.4186i	−0.572085	−	0.330293i
$996$		0			0
$997$	10.2687	−	17.7859i	0.325213	−	0.563285i	−0.656343	−	0.754463i	$-0.727897\pi$
$997$	10.2687	−	17.7859i	0.325213	−	0.563285i	0.981555	+	0.191178i	$0.0612308\pi$
$998$	−1.55534	−	2.69393i	−0.0492335	−	0.0852750i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bu.c.361.4		8
3.2	odd	2		65.2.m.a.36.1	✓	8
12.11	even	2		1040.2.da.b.881.1		8
13.2	odd	12		7605.2.a.cj.1.4		4
13.4	even	6	inner	585.2.bu.c.316.4		8
13.11	odd	12		7605.2.a.cf.1.1		4
15.2	even	4		325.2.m.b.49.1		8
15.8	even	4		325.2.m.c.49.4		8
15.14	odd	2		325.2.n.d.101.4		8
39.2	even	12		845.2.a.l.1.1		4
39.5	even	4		845.2.e.n.146.4		8
39.8	even	4		845.2.e.m.146.1		8
39.11	even	12		845.2.a.m.1.4		4
39.17	odd	6		65.2.m.a.56.1	yes	8
39.20	even	12		845.2.e.m.191.1		8
39.23	odd	6		845.2.c.g.506.8		8
39.29	odd	6		845.2.c.g.506.1		8
39.32	even	12		845.2.e.n.191.4		8
39.35	odd	6		845.2.m.g.316.4		8
39.38	odd	2		845.2.m.g.361.4		8
156.95	even	6		1040.2.da.b.641.1		8
195.17	even	12		325.2.m.c.199.4		8
195.89	even	12		4225.2.a.bi.1.1		4
195.119	even	12		4225.2.a.bl.1.4		4
195.134	odd	6		325.2.n.d.251.4		8
195.173	even	12		325.2.m.b.199.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.1	✓	8	3.2	odd	2
65.2.m.a.56.1	yes	8	39.17	odd	6
325.2.m.b.49.1		8	15.2	even	4
325.2.m.b.199.1		8	195.173	even	12
325.2.m.c.49.4		8	15.8	even	4
325.2.m.c.199.4		8	195.17	even	12
325.2.n.d.101.4		8	15.14	odd	2
325.2.n.d.251.4		8	195.134	odd	6
585.2.bu.c.316.4		8	13.4	even	6	inner
585.2.bu.c.361.4		8	1.1	even	1	trivial
845.2.a.l.1.1		4	39.2	even	12
845.2.a.m.1.4		4	39.11	even	12
845.2.c.g.506.1		8	39.29	odd	6
845.2.c.g.506.8		8	39.23	odd	6
845.2.e.m.146.1		8	39.8	even	4
845.2.e.m.191.1		8	39.20	even	12
845.2.e.n.146.4		8	39.5	even	4
845.2.e.n.191.4		8	39.32	even	12
845.2.m.g.316.4		8	39.35	odd	6
845.2.m.g.361.4		8	39.38	odd	2
1040.2.da.b.641.1		8	156.95	even	6
1040.2.da.b.881.1		8	12.11	even	2
4225.2.a.bi.1.1		4	195.89	even	12
4225.2.a.bl.1.4		4	195.119	even	12
7605.2.a.cf.1.1		4	13.11	odd	12
7605.2.a.cj.1.4		4	13.2	odd	12

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.bu (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.16117 - 1.24775i) q^{2} +(2.11378 - 3.66117i) q^{4} -1.00000i q^{5} +(-1.64996 - 0.952606i) q^{7} -5.55889i q^{8} +O(q^{10})\)	\(q+(2.16117 - 1.24775i) q^{2} +(2.11378 - 3.66117i) q^{4} -1.00000i q^{5} +(-1.64996 - 0.952606i) q^{7} -5.55889i q^{8} +(-1.24775 - 2.16117i) q^{10} +(-0.926118 + 0.534695i) q^{11} +(1.40072 - 3.32235i) q^{13} -4.75447 q^{14} +(-2.70857 - 4.69138i) q^{16} +(-0.318632 + 0.551886i) q^{17} +(4.96410 + 2.86603i) q^{19} +(-3.66117 - 2.11378i) q^{20} +(-1.33433 + 2.31114i) q^{22} +(-1.90893 - 3.30636i) q^{23} -1.00000 q^{25} +(-1.11827 - 8.92792i) q^{26} +(-6.97531 + 4.02720i) q^{28} +(4.72756 + 8.18837i) q^{29} +1.46410i q^{31} +(-2.07908 - 1.20036i) q^{32} +1.59030i q^{34} +(-0.952606 + 1.64996i) q^{35} +(0.655970 - 0.378725i) q^{37} +14.3044 q^{38} -5.55889 q^{40} +(0.232051 - 0.133975i) q^{41} +(0.318632 - 0.551886i) q^{43} +4.52091i q^{44} +(-8.25104 - 4.76374i) q^{46} +9.44613i q^{47} +(-1.68508 - 2.91865i) q^{49} +(-2.16117 + 1.24775i) q^{50} +(-9.20287 - 12.1510i) q^{52} +6.99102 q^{53} +(0.534695 + 0.926118i) q^{55} +(-5.29543 + 9.17196i) q^{56} +(20.4341 + 11.7977i) q^{58} +(0.641756 + 0.370518i) q^{59} +(-2.09928 + 3.63606i) q^{61} +(1.82684 + 3.16418i) q^{62} +4.84325 q^{64} +(-3.32235 - 1.40072i) q^{65} +(-7.01029 + 4.04739i) q^{67} +(1.34703 + 2.33313i) q^{68} +4.75447i q^{70} +(-8.45663 - 4.88244i) q^{71} -3.71649i q^{73} +(0.945110 - 1.63698i) q^{74} +(20.9860 - 12.1163i) q^{76} +2.03741 q^{77} -9.31937 q^{79} +(-4.69138 + 2.70857i) q^{80} +(0.334335 - 0.579085i) q^{82} +5.11778i q^{83} +(0.551886 + 0.318632i) q^{85} -1.59030i q^{86} +(2.97231 + 5.14819i) q^{88} +(10.8932 - 6.28917i) q^{89} +(-5.47602 + 4.14741i) q^{91} -16.1402 q^{92} +(11.7864 + 20.4147i) q^{94} +(2.86603 - 4.96410i) q^{95} +(-3.65597 - 2.11078i) q^{97} +(-7.28351 - 4.20514i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} - 6 q^{7}+O(q^{10}) \) 8 * q + 2 * q^4 - 6 * q^7	\( 8 q + 2 q^{4} - 6 q^{7} - 2 q^{10} - 4 q^{14} - 2 q^{16} + 2 q^{17} + 12 q^{19} - 12 q^{20} - 12 q^{22} + 10 q^{23} - 8 q^{25} - 10 q^{26} - 18 q^{28} + 8 q^{29} - 6 q^{32} - 10 q^{35} + 6 q^{37} + 16 q^{38} - 12 q^{40} - 12 q^{41} - 2 q^{43} - 42 q^{46} + 12 q^{49} - 6 q^{52} + 24 q^{53} - 12 q^{56} + 36 q^{58} + 12 q^{59} - 28 q^{61} - 4 q^{62} - 8 q^{64} + 8 q^{65} + 6 q^{67} + 14 q^{68} - 10 q^{74} + 54 q^{76} + 36 q^{77} - 16 q^{79} + 4 q^{82} + 18 q^{85} - 18 q^{88} - 24 q^{89} + 28 q^{91} - 44 q^{92} + 32 q^{94} + 16 q^{95} - 30 q^{97} - 72 q^{98}+O(q^{100}) \) 8 * q + 2 * q^4 - 6 * q^7 - 2 * q^10 - 4 * q^14 - 2 * q^16 + 2 * q^17 + 12 * q^19 - 12 * q^20 - 12 * q^22 + 10 * q^23 - 8 * q^25 - 10 * q^26 - 18 * q^28 + 8 * q^29 - 6 * q^32 - 10 * q^35 + 6 * q^37 + 16 * q^38 - 12 * q^40 - 12 * q^41 - 2 * q^43 - 42 * q^46 + 12 * q^49 - 6 * q^52 + 24 * q^53 - 12 * q^56 + 36 * q^58 + 12 * q^59 - 28 * q^61 - 4 * q^62 - 8 * q^64 + 8 * q^65 + 6 * q^67 + 14 * q^68 - 10 * q^74 + 54 * q^76 + 36 * q^77 - 16 * q^79 + 4 * q^82 + 18 * q^85 - 18 * q^88 - 24 * q^89 + 28 * q^91 - 44 * q^92 + 32 * q^94 + 16 * q^95 - 30 * q^97 - 72 * q^98

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