LMFDB - Embedded newform 855.2.k.k.676.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(406,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, 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("855.406");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.k (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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 13 x^{10} - 10 x^{9} + 44 x^{8} - 20 x^{7} + 119 x^{6} + 13 x^{5} + 83 x^{4} + \cdots + 4 $ x^12 - 3x^11 + 13x^10 - 10x^9 + 44x^8 - 20x^7 + 119x^6 + 13x^5 + 83x^4 + 14x^3 + 46x^2 + 12*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			676.5
Root			$-0.398236 + 0.689765i$ of defining polynomial
Character	$\chi$	$=$	855.676
Dual form			855.2.k.k.406.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.898236 - 1.55579i) q^{2} +(-0.613656 - 1.06288i) q^{4} +(0.500000 - 0.866025i) q^{5} -3.41478 q^{7} +1.38811 q^{8} +O(q^{10})$	\(q+(0.898236 - 1.55579i) q^{2} +(-0.613656 - 1.06288i) q^{4} +(0.500000 - 0.866025i) q^{5} -3.41478 q^{7} +1.38811 q^{8} +(-0.898236 - 1.55579i) q^{10} -4.35669 q^{11} +(-2.49135 - 4.31514i) q^{13} +(-3.06728 + 5.31268i) q^{14} +(2.47416 - 4.28538i) q^{16} +(0.0290433 - 0.0503046i) q^{17} +(-1.10304 - 4.21703i) q^{19} -1.22731 q^{20} +(-3.91334 + 6.77810i) q^{22} +(-0.216041 - 0.374194i) q^{23} +(-0.500000 - 0.866025i) q^{25} -8.95127 q^{26} +(2.09550 + 3.62951i) q^{28} +(-2.74750 - 4.75882i) q^{29} -0.592945 q^{31} +(-3.05666 - 5.29428i) q^{32} +(-0.0521756 - 0.0903707i) q^{34} +(-1.70739 + 2.95728i) q^{35} +6.62060 q^{37} +(-7.55160 - 2.07179i) q^{38} +(0.694056 - 1.20214i) q^{40} +(-0.0818718 + 0.141806i) q^{41} +(3.00242 - 5.20034i) q^{43} +(2.67351 + 4.63066i) q^{44} -0.776222 q^{46} +(5.54529 + 9.60473i) q^{47} +4.66070 q^{49} -1.79647 q^{50} +(-3.05766 + 5.29603i) q^{52} +(2.69971 + 4.67603i) q^{53} +(-2.17835 + 3.77300i) q^{55} -4.74009 q^{56} -9.87163 q^{58} +(1.72248 - 2.98342i) q^{59} +(-2.15698 - 3.73600i) q^{61} +(-0.532604 + 0.922498i) q^{62} -1.08574 q^{64} -4.98270 q^{65} +(3.39217 + 5.87541i) q^{67} -0.0712905 q^{68} +(3.06728 + 5.31268i) q^{70} +(-4.20501 + 7.28329i) q^{71} +(5.84804 - 10.1291i) q^{73} +(5.94686 - 10.3003i) q^{74} +(-3.80532 + 3.76021i) q^{76} +14.8771 q^{77} +(-3.64303 + 6.30991i) q^{79} +(-2.47416 - 4.28538i) q^{80} +(0.147080 + 0.254751i) q^{82} -16.1185 q^{83} +(-0.0290433 - 0.0503046i) q^{85} +(-5.39377 - 9.34228i) q^{86} -6.04757 q^{88} +(5.59024 + 9.68258i) q^{89} +(8.50740 + 14.7352i) q^{91} +(-0.265150 + 0.459252i) q^{92} +19.9239 q^{94} +(-4.20357 - 1.15325i) q^{95} +(-4.47355 + 7.74842i) q^{97} +(4.18641 - 7.25107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 5 q^{4} + 6 q^{5} + 4 q^{7} - 12 q^{8}+O(q^{10}) $ 12 * q + 3 * q^2 - 5 * q^4 + 6 * q^5 + 4 * q^7 - 12 * q^8	$ 12 q + 3 q^{2} - 5 q^{4} + 6 q^{5} + 4 q^{7} - 12 q^{8} - 3 q^{10} - 8 q^{13} + 10 q^{14} - 3 q^{16} + 4 q^{17} - 6 q^{19} - 10 q^{20} - 2 q^{23} - 6 q^{25} - 40 q^{26} - 26 q^{28} + 4 q^{29} + 24 q^{31} + 15 q^{32} + 7 q^{34} + 2 q^{35} - 29 q^{38} - 6 q^{40} + 12 q^{41} - 4 q^{43} + 6 q^{44} + 48 q^{46} + 6 q^{47} + 32 q^{49} - 6 q^{50} - 20 q^{52} + 26 q^{53} - 44 q^{56} - 20 q^{58} + 16 q^{59} + 20 q^{61} - 25 q^{62} + 28 q^{64} - 16 q^{65} - 12 q^{67} + 54 q^{68} - 10 q^{70} - 8 q^{71} - 4 q^{73} - 16 q^{74} - 66 q^{76} + 48 q^{77} - 12 q^{79} + 3 q^{80} + 26 q^{82} - 44 q^{83} - 4 q^{85} - 44 q^{86} - 32 q^{88} - 8 q^{89} + 2 q^{91} + 36 q^{92} - 14 q^{94} - 6 q^{95} + 30 q^{97} + 49 q^{98}+O(q^{100}) $ 12 * q + 3 * q^2 - 5 * q^4 + 6 * q^5 + 4 * q^7 - 12 * q^8 - 3 * q^10 - 8 * q^13 + 10 * q^14 - 3 * q^16 + 4 * q^17 - 6 * q^19 - 10 * q^20 - 2 * q^23 - 6 * q^25 - 40 * q^26 - 26 * q^28 + 4 * q^29 + 24 * q^31 + 15 * q^32 + 7 * q^34 + 2 * q^35 - 29 * q^38 - 6 * q^40 + 12 * q^41 - 4 * q^43 + 6 * q^44 + 48 * q^46 + 6 * q^47 + 32 * q^49 - 6 * q^50 - 20 * q^52 + 26 * q^53 - 44 * q^56 - 20 * q^58 + 16 * q^59 + 20 * q^61 - 25 * q^62 + 28 * q^64 - 16 * q^65 - 12 * q^67 + 54 * q^68 - 10 * q^70 - 8 * q^71 - 4 * q^73 - 16 * q^74 - 66 * q^76 + 48 * q^77 - 12 * q^79 + 3 * q^80 + 26 * q^82 - 44 * q^83 - 4 * q^85 - 44 * q^86 - 32 * q^88 - 8 * q^89 + 2 * q^91 + 36 * q^92 - 14 * q^94 - 6 * q^95 + 30 * q^97 + 49 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.898236	−	1.55579i	0.635149	−	1.10011i	−0.351335	−	0.936250i	$-0.614272\pi$
$2$	0.898236	−	1.55579i	0.635149	−	1.10011i	0.986484	−	0.163860i	$-0.0523946\pi$
$3$		0			0
$3$		0			0
$4$	−0.613656	−	1.06288i	−0.306828	−	0.531442i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	−3.41478			−1.29066			−0.645332	−	0.763902i	$-0.723281\pi$
$7$	−3.41478			−1.29066			−0.645332	+	0.763902i	$0.723281\pi$
$8$	1.38811			0.490771
$9$		0			0
$10$	−0.898236	−	1.55579i	−0.284047	−	0.491984i
$11$	−4.35669			−1.31359			−0.656796	−	0.754069i	$-0.728089\pi$
$11$	−4.35669			−1.31359			−0.656796	+	0.754069i	$0.728089\pi$
$12$		0			0
$13$	−2.49135	−	4.31514i	−0.690976	−	1.19680i	−0.971519	−	0.236963i	$-0.923848\pi$
$13$	−2.49135	−	4.31514i	−0.690976	−	1.19680i	0.280543	−	0.959841i	$-0.409485\pi$
$14$	−3.06728	+	5.31268i	−0.819764	+	1.41987i
$15$		0			0
$16$	2.47416	−	4.28538i	0.618541	−	1.07134i
$17$	0.0290433	−	0.0503046i	0.00704405	−	0.0122006i	−0.862482	−	0.506088i	$-0.831091\pi$
$17$	0.0290433	−	0.0503046i	0.00704405	−	0.0122006i	0.869526	+	0.493887i	$0.164424\pi$
$18$		0			0
$19$	−1.10304	−	4.21703i	−0.253054	−	0.967452i
$19$	−1.10304	−	4.21703i	−0.253054	−	0.967452i
$20$	−1.22731			−0.274435
$21$		0			0
$22$	−3.91334	+	6.77810i	−0.834326	+	1.44510i
$23$	−0.216041	−	0.374194i	−0.0450476	−	0.0780247i	0.842622	−	0.538505i	$-0.181011\pi$
$23$	−0.216041	−	0.374194i	−0.0450476	−	0.0780247i	−0.887670	+	0.460480i	$0.847677\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−8.95127			−1.75549
$27$		0			0
$28$	2.09550	+	3.62951i	0.396012	+	0.685913i
$29$	−2.74750	−	4.75882i	−0.510199	−	0.883690i	−0.999930	−	0.0118169i	$-0.996238\pi$
$29$	−2.74750	−	4.75882i	−0.510199	−	0.883690i	0.489731	−	0.871873i	$-0.337095\pi$
$30$		0			0
$31$	−0.592945			−0.106496			−0.0532480	−	0.998581i	$-0.516957\pi$
$31$	−0.592945			−0.106496			−0.0532480	+	0.998581i	$0.516957\pi$
$32$	−3.05666	−	5.29428i	−0.540346	−	0.935906i
$33$		0			0
$34$	−0.0521756	−	0.0903707i	−0.00894804	−	0.0154985i
$35$	−1.70739	+	2.95728i	−0.288601	+	0.499872i
$36$		0			0
$37$	6.62060			1.08842			0.544210	−	0.838949i	$-0.316830\pi$
$37$	6.62060			1.08842			0.544210	+	0.838949i	$0.316830\pi$
$38$	−7.55160	−	2.07179i	−1.22503	−	0.336089i
$39$		0			0
$40$	0.694056	−	1.20214i	0.109740	−	0.190075i
$41$	−0.0818718	+	0.141806i	−0.0127862	+	0.0221464i	−0.872348	−	0.488886i	$-0.837403\pi$
$41$	−0.0818718	+	0.141806i	−0.0127862	+	0.0221464i	0.859561	+	0.511032i	$0.170737\pi$
$42$		0			0
$43$	3.00242	−	5.20034i	0.457865	−	0.793045i	−0.540983	−	0.841033i	$-0.681948\pi$
$43$	3.00242	−	5.20034i	0.457865	−	0.793045i	0.998848	+	0.0479883i	$0.0152810\pi$
$44$	2.67351	+	4.63066i	0.403047	+	0.698098i
$45$		0			0
$46$	−0.776222			−0.114448
$47$	5.54529	+	9.60473i	0.808864	+	1.40099i	0.913651	+	0.406499i	$0.133250\pi$
$47$	5.54529	+	9.60473i	0.808864	+	1.40099i	−0.104788	+	0.994495i	$0.533416\pi$
$48$		0			0
$49$	4.66070			0.665814
$50$	−1.79647			−0.254060
$51$		0			0
$52$	−3.05766	+	5.29603i	−0.424022	+	0.734427i
$53$	2.69971	+	4.67603i	0.370834	+	0.642303i	0.989694	−	0.143198i	$-0.0457387\pi$
$53$	2.69971	+	4.67603i	0.370834	+	0.642303i	−0.618860	+	0.785501i	$0.712405\pi$
$54$		0			0
$55$	−2.17835	+	3.77300i	−0.293728	+	0.508752i
$56$	−4.74009			−0.633421
$57$		0			0
$58$	−9.87163			−1.29621
$59$	1.72248	−	2.98342i	0.224248	−	0.388408i	−0.731846	−	0.681470i	$-0.761341\pi$
$59$	1.72248	−	2.98342i	0.224248	−	0.388408i	0.956093	+	0.293062i	$0.0946742\pi$
$60$		0			0
$61$	−2.15698	−	3.73600i	−0.276173	−	0.478346i	0.694257	−	0.719727i	$-0.255733\pi$
$61$	−2.15698	−	3.73600i	−0.276173	−	0.478346i	−0.970430	+	0.241381i	$0.922400\pi$
$62$	−0.532604	+	0.922498i	−0.0676408	+	0.117157i
$63$		0			0
$64$	−1.08574			−0.135718
$65$	−4.98270			−0.618027
$66$		0			0
$67$	3.39217	+	5.87541i	0.414420	+	0.717796i	0.995367	−	0.0961450i	$-0.0306513\pi$
$67$	3.39217	+	5.87541i	0.414420	+	0.717796i	−0.580948	+	0.813941i	$0.697318\pi$
$68$	−0.0712905			−0.00864525
$69$		0			0
$70$	3.06728	+	5.31268i	0.366610	+	0.634986i
$71$	−4.20501	+	7.28329i	−0.499043	+	0.864368i	−0.999999	−	0.00110477i	$-0.999648\pi$
$71$	−4.20501	+	7.28329i	−0.499043	+	0.864368i	0.500956	+	0.865472i	$0.332982\pi$
$72$		0			0
$73$	5.84804	−	10.1291i	0.684461	−	1.18552i	−0.289145	−	0.957285i	$-0.593371\pi$
$73$	5.84804	−	10.1291i	0.684461	−	1.18552i	0.973606	−	0.228236i	$-0.0732958\pi$
$74$	5.94686	−	10.3003i	0.691309	−	1.19738i
$75$		0			0
$76$	−3.80532	+	3.76021i	−0.436501	+	0.431325i
$77$	14.8771			1.69541
$78$		0			0
$79$	−3.64303	+	6.30991i	−0.409873	+	0.709920i	−0.994875	−	0.101111i	$-0.967760\pi$
$79$	−3.64303	+	6.30991i	−0.409873	+	0.709920i	0.585003	+	0.811031i	$0.301094\pi$
$80$	−2.47416	−	4.28538i	−0.276620	−	0.479120i
$81$		0			0
$82$	0.147080	+	0.254751i	0.0162423	+	0.0281325i
$83$	−16.1185			−1.76923			−0.884617	−	0.466318i	$-0.845580\pi$
$83$	−16.1185			−1.76923			−0.884617	+	0.466318i	$0.845580\pi$
$84$		0			0
$85$	−0.0290433	−	0.0503046i	−0.00315019	−	0.00545629i
$86$	−5.39377	−	9.34228i	−0.581625	−	1.00740i
$87$		0			0
$88$	−6.04757			−0.644673
$89$	5.59024	+	9.68258i	0.592564	+	1.02635i	0.993886	+	0.110414i	$0.0352178\pi$
$89$	5.59024	+	9.68258i	0.592564	+	1.02635i	−0.401321	+	0.915937i	$0.631449\pi$
$90$		0			0
$91$	8.50740	+	14.7352i	0.891817	+	1.54467i
$92$	−0.265150	+	0.459252i	−0.0276438	+	0.0478804i
$93$		0			0
$94$	19.9239			2.05500
$95$	−4.20357	−	1.15325i	−0.431277	−	0.118321i
$96$		0			0
$97$	−4.47355	+	7.74842i	−0.454221	+	0.786733i	−0.998643	−	0.0520780i	$-0.983416\pi$
$97$	−4.47355	+	7.74842i	−0.454221	+	0.786733i	0.544422	+	0.838811i	$0.316749\pi$
$98$	4.18641	−	7.25107i	0.422891	−	0.732469i
$99$		0			0
$100$	−0.613656	+	1.06288i	−0.0613656	+	0.106288i
$101$	−1.09523	−	1.89700i	−0.108980	−	0.188758i	0.806377	−	0.591401i	$-0.201425\pi$
$101$	−1.09523	−	1.89700i	−0.108980	−	0.188758i	−0.915357	+	0.402643i	$0.868092\pi$
$102$		0			0
$103$	10.4903			1.03364			0.516818	−	0.856095i	$-0.327117\pi$
$103$	10.4903			1.03364			0.516818	+	0.856095i	$0.327117\pi$
$104$	−3.45827	−	5.98990i	−0.339111	−	0.587358i
$105$		0			0
$106$	9.69991			0.942138
$107$	13.6911			1.32357			0.661783	−	0.749696i	$-0.269800\pi$
$107$	13.6911			1.32357			0.661783	+	0.749696i	$0.269800\pi$
$108$		0			0
$109$	7.07679	−	12.2574i	0.677834	−	1.17404i	−0.297798	−	0.954629i	$-0.596252\pi$
$109$	7.07679	−	12.2574i	0.677834	−	1.17404i	0.975632	−	0.219413i	$-0.0704144\pi$
$110$	3.91334	+	6.77810i	0.373122	+	0.646266i
$111$		0			0
$112$	−8.44872	+	14.6336i	−0.798329	+	1.38275i
$113$	13.2851			1.24976			0.624879	−	0.780722i	$-0.285148\pi$
$113$	13.2851			1.24976			0.624879	+	0.780722i	$0.285148\pi$
$114$		0			0
$115$	−0.432081			−0.0402918
$116$	−3.37205	+	5.84056i	−0.313087	+	0.542282i
$117$		0			0
$118$	−3.09438	−	5.35963i	−0.284861	−	0.493394i
$119$	−0.0991765	+	0.171779i	−0.00909150	+	0.0157469i
$120$		0			0
$121$	7.98075			0.725523
$122$	−7.74991			−0.701644
$123$		0			0
$124$	0.363864	+	0.630231i	0.0326760	+	0.0565964i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−7.84813	−	13.5934i	−0.696409	−	1.20622i	−0.969703	−	0.244285i	$-0.921447\pi$
$127$	−7.84813	−	13.5934i	−0.696409	−	1.20622i	0.273295	−	0.961930i	$-0.411887\pi$
$128$	5.13806	−	8.89938i	0.454145	−	0.786602i
$129$		0			0
$130$	−4.47564	+	7.75203i	−0.392539	+	0.679898i
$131$	−5.86776	+	10.1633i	−0.512669	+	0.887968i	0.487223	+	0.873277i	$0.338010\pi$
$131$	−5.86776	+	10.1633i	−0.512669	+	0.887968i	−0.999892	+	0.0146910i	$0.995324\pi$
$132$		0			0
$133$	3.76663	+	14.4002i	0.326608	+	1.24866i
$134$	12.1879			1.05287
$135$		0			0
$136$	0.0403154	−	0.0698283i	0.00345702	−	0.00598773i
$137$	−5.12860	−	8.88300i	−0.438166	−	0.758926i	0.559382	−	0.828910i	$-0.311038\pi$
$137$	−5.12860	−	8.88300i	−0.438166	−	0.758926i	−0.997548	+	0.0699840i	$0.977705\pi$
$138$		0			0
$139$	−10.9044	−	18.8870i	−0.924899	−	1.60197i	−0.791723	−	0.610880i	$-0.790816\pi$
$139$	−10.9044	−	18.8870i	−0.924899	−	1.60197i	−0.133176	−	0.991092i	$-0.542518\pi$
$140$	4.19100			0.354204
$141$		0			0
$142$	7.55418	+	13.0842i	0.633933	+	1.09800i
$143$	10.8540	+	18.7997i	0.907660	+	1.57211i
$144$		0			0
$145$	−5.49501			−0.456336
$146$	−10.5058	−	18.1966i	−0.869469	−	1.50597i
$147$		0			0
$148$	−4.06277	−	7.03693i	−0.333958	−	0.578432i
$149$	10.3765	−	17.9727i	0.850079	−	1.47238i	−0.0310582	−	0.999518i	$-0.509888\pi$
$149$	10.3765	−	17.9727i	0.850079	−	1.47238i	0.881137	−	0.472862i	$-0.156779\pi$
$150$		0			0
$151$	−14.9510			−1.21669			−0.608346	−	0.793672i	$-0.708167\pi$
$151$	−14.9510			−1.21669			−0.608346	+	0.793672i	$0.708167\pi$
$152$	−1.53114	−	5.85370i	−0.124192	−	0.474798i
$153$		0			0
$154$	13.3632	−	23.1457i	1.07683	−	1.86513i
$155$	−0.296472	+	0.513505i	−0.0238132	+	0.0412457i
$156$		0			0
$157$	0.0399391	−	0.0691765i	0.00318749	−	0.00552089i	−0.864427	−	0.502758i	$-0.832319\pi$
$157$	0.0399391	−	0.0691765i	0.00318749	−	0.00552089i	0.867615	+	0.497237i	$0.165652\pi$
$158$	6.54460	+	11.3356i	0.520660	+	0.901810i
$159$		0			0
$160$	−6.11331			−0.483300
$161$	0.737731	+	1.27779i	0.0581413	+	0.100704i
$162$		0			0
$163$	18.4845			1.44782			0.723909	−	0.689896i	$-0.242344\pi$
$163$	18.4845			1.44782			0.723909	+	0.689896i	$0.242344\pi$
$164$	0.200965			0.0156927
$165$		0			0
$166$	−14.4782	+	25.0770i	−1.12373	+	1.94635i
$167$	9.34180	+	16.1805i	0.722890	+	1.25208i	0.959837	+	0.280560i	$0.0905201\pi$
$167$	9.34180	+	16.1805i	0.722890	+	1.25208i	−0.236946	+	0.971523i	$0.576147\pi$
$168$		0			0
$169$	−5.91363	+	10.2427i	−0.454894	+	0.787900i
$170$	−0.104351			−0.00800337
$171$		0			0
$172$	−7.36982			−0.561943
$173$	4.29860	−	7.44540i	0.326817	−	0.566063i	−0.655062	−	0.755575i	$-0.727357\pi$
$173$	4.29860	−	7.44540i	0.326817	−	0.566063i	0.981878	+	0.189512i	$0.0606907\pi$
$174$		0			0
$175$	1.70739	+	2.95728i	0.129066	+	0.223550i
$176$	−10.7792	+	18.6701i	−0.812510	+	1.40731i
$177$		0			0
$178$	20.0854			1.50547
$179$	−6.16587			−0.460859			−0.230429	−	0.973089i	$-0.574013\pi$
$179$	−6.16587			−0.460859			−0.230429	+	0.973089i	$0.574013\pi$
$180$		0			0
$181$	−10.0294	−	17.3715i	−0.745481	−	1.29121i	−0.949970	−	0.312343i	$-0.898886\pi$
$181$	−10.0294	−	17.3715i	−0.745481	−	1.29121i	0.204488	−	0.978869i	$-0.434447\pi$
$182$	30.5666			2.26575
$183$		0			0
$184$	−0.299889	−	0.519422i	−0.0221081	−	0.0382923i
$185$	3.31030	−	5.73361i	0.243378	−	0.421543i
$186$		0			0
$187$	−0.126533	+	0.219161i	−0.00925300	+	0.0160267i
$188$	6.80581	−	11.7880i	0.496364	−	0.859728i
$189$		0			0
$190$	−5.57002	+	5.50398i	−0.404092	+	0.399301i
$191$	17.0701			1.23515			0.617573	−	0.786513i	$-0.288116\pi$
$191$	17.0701			1.23515			0.617573	+	0.786513i	$0.288116\pi$
$192$		0			0
$193$	−3.63576	+	6.29733i	−0.261708	+	0.453292i	−0.966696	−	0.255928i	$-0.917619\pi$
$193$	−3.63576	+	6.29733i	−0.261708	+	0.453292i	0.704988	+	0.709219i	$0.250952\pi$
$194$	8.03662	+	13.9198i	0.576995	+	0.999385i
$195$		0			0
$196$	−2.86007	−	4.95378i	−0.204291	−	0.353842i
$197$	3.59854			0.256385			0.128193	−	0.991749i	$-0.459082\pi$
$197$	3.59854			0.256385			0.128193	+	0.991749i	$0.459082\pi$
$198$		0			0
$199$	−10.7918	−	18.6919i	−0.765008	−	1.32503i	−0.940242	−	0.340506i	$-0.889402\pi$
$199$	−10.7918	−	18.6919i	−0.765008	−	1.32503i	0.175234	−	0.984527i	$-0.443932\pi$
$200$	−0.694056	−	1.20214i	−0.0490771	−	0.0850041i
$201$		0			0
$202$	−3.93511			−0.276873
$203$	9.38211	+	16.2503i	0.658495	+	1.14055i
$204$		0			0
$205$	0.0818718	+	0.141806i	0.00571817	+	0.00990417i
$206$	9.42272	−	16.3206i	0.656512	−	1.13711i
$207$		0			0
$208$	−24.6560			−1.70959
$209$	4.80559	+	18.3723i	0.332410	+	1.27084i
$210$		0			0
$211$	−0.0351916	+	0.0609536i	−0.00242269	+	0.00419622i	−0.867234	−	0.497900i	$-0.834105\pi$
$211$	−0.0351916	+	0.0609536i	−0.00242269	+	0.00419622i	0.864812	+	0.502097i	$0.167438\pi$
$212$	3.31339	−	5.73896i	0.227564	−	0.394153i
$213$		0			0
$214$	12.2978	−	21.3004i	0.840661	−	1.45607i
$215$	−3.00242	−	5.20034i	−0.204763	−	0.354661i
$216$		0			0
$217$	2.02477			0.137451
$218$	−12.7133	−	22.0200i	−0.861051	−	1.49138i
$219$		0			0
$220$	5.34702			0.360496
$221$	−0.289428			−0.0194691
$222$		0			0
$223$	6.52703	−	11.3051i	0.437082	−	0.757049i	−0.560381	−	0.828235i	$-0.689345\pi$
$223$	6.52703	−	11.3051i	0.437082	−	0.757049i	0.997463	+	0.0711864i	$0.0226785\pi$
$224$	10.4378	+	18.0788i	0.697405	+	1.20794i
$225$		0			0
$226$	11.9332	−	20.6689i	0.793783	−	1.37487i
$227$	−7.75546			−0.514748			−0.257374	−	0.966312i	$-0.582857\pi$
$227$	−7.75546			−0.514748			−0.257374	+	0.966312i	$0.582857\pi$
$228$		0			0
$229$	19.0597			1.25950			0.629751	−	0.776797i	$-0.283157\pi$
$229$	19.0597			1.25950			0.629751	+	0.776797i	$0.283157\pi$
$230$	−0.388111	+	0.672228i	−0.0255913	+	0.0443254i
$231$		0			0
$232$	−3.81384	−	6.60577i	−0.250391	−	0.433690i
$233$	−6.26723	+	10.8552i	−0.410580	+	0.711145i	−0.994953	−	0.100340i	$-0.968007\pi$
$233$	−6.26723	+	10.8552i	−0.410580	+	0.711145i	0.584373	+	0.811485i	$0.301340\pi$
$234$		0			0
$235$	11.0906			0.723470
$236$	−4.22804			−0.275222
$237$		0			0
$238$	0.178168	+	0.308596i	0.0115489	+	0.0200033i
$239$	−15.7879			−1.02123			−0.510617	−	0.859808i	$-0.670583\pi$
$239$	−15.7879			−1.02123			−0.510617	+	0.859808i	$0.670583\pi$
$240$		0			0
$241$	−12.4166	−	21.5061i	−0.799822	−	1.38533i	−0.919732	−	0.392547i	$-0.871594\pi$
$241$	−12.4166	−	21.5061i	−0.799822	−	1.38533i	0.119910	−	0.992785i	$-0.461739\pi$
$242$	7.16860	−	12.4164i	0.460815	−	0.798155i
$243$		0			0
$244$	−2.64729	+	4.58524i	−0.169475	+	0.293540i
$245$	2.33035	−	4.03628i	0.148881	−	0.257869i
$246$		0			0
$247$	−15.4490	+	15.2658i	−0.982997	+	0.971342i
$248$	−0.823073			−0.0522652
$249$		0			0
$250$	−0.898236	+	1.55579i	−0.0568094	+	0.0983968i
$251$	1.65676	+	2.86958i	0.104573	+	0.181127i	0.913564	−	0.406695i	$-0.133319\pi$
$251$	1.65676	+	2.86958i	0.104573	+	0.181127i	−0.808990	+	0.587822i	$0.799986\pi$
$252$		0			0
$253$	0.941223	+	1.63025i	0.0591742	+	0.102493i
$254$	−28.1979			−1.76929
$255$		0			0
$256$	−10.3161	−	17.8681i	−0.644758	−	1.11675i
$257$	−12.4325	−	21.5337i	−0.775516	−	1.34323i	−0.934504	−	0.355952i	$-0.884157\pi$
$257$	−12.4325	−	21.5337i	−0.775516	−	1.34323i	0.158988	−	0.987280i	$-0.449177\pi$
$258$		0			0
$259$	−22.6079			−1.40478
$260$	3.05766	+	5.29603i	0.189628	+	0.328446i
$261$		0			0
$262$	10.5413	+	18.2580i	0.651242	+	1.12798i
$263$	−0.342686	+	0.593549i	−0.0211309	+	0.0365998i	−0.876397	−	0.481588i	$-0.840060\pi$
$263$	−0.342686	+	0.593549i	−0.0211309	+	0.0365998i	0.855267	+	0.518188i	$0.173393\pi$
$264$		0			0
$265$	5.39942			0.331684
$266$	25.7870	+	7.07470i	1.58110	+	0.433778i
$267$		0			0
$268$	4.16325	−	7.21097i	0.254311	−	0.440480i
$269$	5.58704	−	9.67704i	0.340648	−	0.590019i	−0.643905	−	0.765105i	$-0.722687\pi$
$269$	5.58704	−	9.67704i	0.340648	−	0.590019i	0.984553	+	0.175086i	$0.0560203\pi$
$270$		0			0
$271$	7.16308	−	12.4068i	0.435126	−	0.753661i	−0.562180	−	0.827015i	$-0.690037\pi$
$271$	7.16308	−	12.4068i	0.435126	−	0.753661i	0.997306	+	0.0733542i	$0.0233704\pi$
$272$	−0.143716	−	0.248923i	−0.00871406	−	0.0150932i
$273$		0			0
$274$	−18.4268			−1.11320
$275$	2.17835	+	3.77300i	0.131359	+	0.227521i
$276$		0			0
$277$	−15.3518			−0.922397			−0.461199	−	0.887297i	$-0.652580\pi$
$277$	−15.3518			−0.922397			−0.461199	+	0.887297i	$0.652580\pi$
$278$	−39.1789			−2.34979
$279$		0			0
$280$	−2.37004	+	4.10504i	−0.141637	+	0.245323i
$281$	4.80640	+	8.32493i	0.286726	+	0.496624i	0.973026	−	0.230694i	$-0.0740998\pi$
$281$	4.80640	+	8.32493i	0.286726	+	0.496624i	−0.686300	+	0.727318i	$0.740766\pi$
$282$		0			0
$283$	−2.86255	+	4.95809i	−0.170161	+	0.294728i	−0.938476	−	0.345344i	$-0.887762\pi$
$283$	−2.86255	+	4.95809i	−0.170161	+	0.294728i	0.768315	+	0.640072i	$0.221095\pi$
$284$	10.3217			0.612482
$285$		0			0
$286$	38.9979			2.30600
$287$	0.279574	−	0.484236i	0.0165027	−	0.0285836i
$288$		0			0
$289$	8.49831	+	14.7195i	0.499901	+	0.865854i
$290$	−4.93582	+	8.54908i	−0.289841	+	0.502019i
$291$		0			0
$292$	−14.3547			−0.840048
$293$	23.3141			1.36203			0.681013	−	0.732271i	$-0.261540\pi$
$293$	23.3141			1.36203			0.681013	+	0.732271i	$0.261540\pi$
$294$		0			0
$295$	−1.72248	−	2.98342i	−0.100287	−	0.173701i
$296$	9.19013			0.534165
$297$		0			0
$298$	−18.6412	−	32.2874i	−1.07985	−	1.87036i
$299$	−1.07647	+	1.86449i	−0.0622536	+	0.107826i
$300$		0			0
$301$	−10.2526	+	17.7580i	−0.590950	+	1.02356i
$302$	−13.4295	+	23.2606i	−0.772781	+	1.33850i
$303$		0			0
$304$	−20.8006	−	5.70668i	−1.19300	−	0.327301i
$305$	−4.31396			−0.247017
$306$		0			0
$307$	−4.24686	+	7.35577i	−0.242381	+	0.419816i	−0.961392	−	0.275183i	$-0.911262\pi$
$307$	−4.24686	+	7.35577i	−0.242381	+	0.419816i	0.719011	+	0.694999i	$0.244595\pi$
$308$	−9.12944	−	15.8127i	−0.520198	−	0.901010i
$309$		0			0
$310$	0.532604	+	0.922498i	0.0302499	+	0.0523943i
$311$	4.54326			0.257625			0.128812	−	0.991669i	$-0.458884\pi$
$311$	4.54326			0.257625			0.128812	+	0.991669i	$0.458884\pi$
$312$		0			0
$313$	9.43148	+	16.3358i	0.533099	+	0.923354i	0.999253	+	0.0386503i	$0.0123058\pi$
$313$	9.43148	+	16.3358i	0.533099	+	0.923354i	−0.466154	+	0.884703i	$0.654361\pi$
$314$	−0.0717495	−	0.124274i	−0.00404906	−	0.00701317i
$315$		0			0
$316$	8.94227			0.503042
$317$	−9.61822	−	16.6592i	−0.540213	−	0.935677i	−0.998891	−	0.0470741i	$-0.985010\pi$
$317$	−9.61822	−	16.6592i	−0.540213	−	0.935677i	0.458678	−	0.888602i	$-0.348323\pi$
$318$		0			0
$319$	11.9700	+	20.7327i	0.670193	+	1.16081i
$320$	−0.542870	+	0.940279i	−0.0303474	+	0.0525632i
$321$		0			0
$322$	2.65063			0.147714
$323$	−0.244172	−	0.0669888i	−0.0135861	−	0.00372735i
$324$		0			0
$325$	−2.49135	+	4.31514i	−0.138195	+	0.239361i
$326$	16.6034	−	28.7580i	0.919579	−	1.59276i
$327$		0			0
$328$	−0.113647	+	0.196843i	−0.00627511	+	0.0108688i
$329$	−18.9359	−	32.7980i	−1.04397	−	1.80821i
$330$		0			0
$331$	9.49306			0.521786			0.260893	−	0.965368i	$-0.415983\pi$
$331$	9.49306			0.521786			0.260893	+	0.965368i	$0.415983\pi$
$332$	9.89121	+	17.1321i	0.542851	+	0.940245i
$333$		0			0
$334$	33.5646			1.83657
$335$	6.78434			0.370668
$336$		0			0
$337$	−11.8854	+	20.5860i	−0.647437	+	1.12139i	0.336296	+	0.941756i	$0.390826\pi$
$337$	−11.8854	+	20.5860i	−0.647437	+	1.12139i	−0.983733	+	0.179637i	$0.942508\pi$
$338$	10.6237	+	18.4007i	0.577851	+	1.00087i
$339$		0			0
$340$	−0.0356453	+	0.0617394i	−0.00193314	+	0.00334829i
$341$	2.58328			0.139892
$342$		0			0
$343$	7.98819			0.431322
$344$	4.16769	−	7.21866i	0.224707	−	0.389204i
$345$		0			0
$346$	−7.72232	−	13.3755i	−0.415155	−	0.719069i
$347$	−14.0069	+	24.2607i	−0.751932	+	1.30238i	0.194953	+	0.980813i	$0.437545\pi$
$347$	−14.0069	+	24.2607i	−0.751932	+	1.30238i	−0.946885	+	0.321572i	$0.895789\pi$
$348$		0			0
$349$	0.00959659			0.000513694			0.000256847	−	1.00000i	$-0.499918\pi$
$349$	0.00959659			0.000513694			0.000256847		1.00000i	$0.499918\pi$
$350$	6.13455			0.327906
$351$		0			0
$352$	13.3169	+	23.0656i	0.709793	+	1.22940i
$353$	6.08582			0.323915			0.161958	−	0.986798i	$-0.448219\pi$
$353$	6.08582			0.323915			0.161958	+	0.986798i	$0.448219\pi$
$354$		0			0
$355$	4.20501	+	7.28329i	0.223179	+	0.386557i
$356$	6.86097	−	11.8836i	0.363631	−	0.629827i
$357$		0			0
$358$	−5.53841	+	9.59281i	−0.292714	+	0.506996i
$359$	8.91042	−	15.4333i	0.470274	−	0.814538i	−0.529148	−	0.848529i	$-0.677488\pi$
$359$	8.91042	−	15.4333i	0.470274	−	0.814538i	0.999422	+	0.0339910i	$0.0108218\pi$
$360$		0			0
$361$	−16.5666	+	9.30307i	−0.871927	+	0.489635i
$362$	−36.0352			−1.89397
$363$		0			0
$364$	10.4412	−	18.0848i	0.547269	−	0.947898i
$365$	−5.84804	−	10.1291i	−0.306100	−	0.530181i
$366$		0			0
$367$	2.45095	+	4.24517i	0.127938	+	0.221596i	0.922878	−	0.385093i	$-0.125831\pi$
$367$	2.45095	+	4.24517i	0.127938	+	0.221596i	−0.794939	+	0.606689i	$0.792497\pi$
$368$	−2.13808			−0.111455
$369$		0			0
$370$	−5.94686	−	10.3003i	−0.309163	−	0.535485i
$371$	−9.21891	−	15.9676i	−0.478622	−	0.828997i
$372$		0			0
$373$	−12.9995			−0.673090			−0.336545	−	0.941667i	$-0.609258\pi$
$373$	−12.9995			−0.673090			−0.336545	+	0.941667i	$0.609258\pi$
$374$	0.227313	+	0.393717i	0.0117541	+	0.0203586i
$375$		0			0
$376$	7.69748	+	13.3324i	0.396967	+	0.687567i
$377$	−13.6900	+	23.7117i	−0.705070	+	1.22122i
$378$		0			0
$379$	16.7313			0.859427			0.429713	−	0.902965i	$-0.358615\pi$
$379$	16.7313			0.859427			0.429713	+	0.902965i	$0.358615\pi$
$380$	1.35377	+	5.17561i	0.0694470	+	0.265503i
$381$		0			0
$382$	15.3330	−	26.5575i	0.784502	−	1.35880i
$383$	14.9461	−	25.8875i	0.763712	−	1.32279i	−0.177213	−	0.984172i	$-0.556708\pi$
$383$	14.9461	−	25.8875i	0.763712	−	1.32279i	0.940925	−	0.338615i	$-0.109958\pi$
$384$		0			0
$385$	7.43856	−	12.8840i	0.379104	−	0.656628i
$386$	6.53155	+	11.3130i	0.332447	+	0.575815i
$387$		0			0
$388$	10.9809			0.557471
$389$	15.8669	+	27.4822i	0.804483	+	1.39340i	0.916640	+	0.399714i	$0.130891\pi$
$389$	15.8669	+	27.4822i	0.804483	+	1.39340i	−0.112157	+	0.993691i	$0.535776\pi$
$390$		0			0
$391$	−0.0250982			−0.00126927
$392$	6.46957			0.326763
$393$		0			0
$394$	3.23234	−	5.59857i	0.162843	−	0.282052i
$395$	3.64303	+	6.30991i	0.183301	+	0.317486i
$396$		0			0
$397$	−16.9999	+	29.4447i	−0.853202	+	1.47779i	0.0251017	+	0.999685i	$0.492009\pi$
$397$	−16.9999	+	29.4447i	−0.853202	+	1.47779i	−0.878303	+	0.478104i	$0.841324\pi$
$398$	−38.7742			−1.94358
$399$		0			0
$400$	−4.94833			−0.247416
$401$	−4.55045	+	7.88161i	−0.227239	+	0.393589i	−0.956989	−	0.290125i	$-0.906303\pi$
$401$	−4.55045	+	7.88161i	−0.227239	+	0.393589i	0.729750	+	0.683714i	$0.239636\pi$
$402$		0			0
$403$	1.47723	+	2.55864i	0.0735861	+	0.127455i
$404$	−1.34419	+	2.32821i	−0.0668761	+	0.115833i
$405$		0			0
$406$	33.7094			1.67297
$407$	−28.8439			−1.42974
$408$		0			0
$409$	13.9425	+	24.1491i	0.689411	+	1.19409i	0.972029	+	0.234862i	$0.0754639\pi$
$409$	13.9425	+	24.1491i	0.689411	+	1.19409i	−0.282618	+	0.959233i	$0.591203\pi$
$410$	0.294161			0.0145276
$411$		0			0
$412$	−6.43741	−	11.1499i	−0.317148	−	0.549317i
$413$	−5.88188	+	10.1877i	−0.289428	+	0.501305i
$414$		0			0
$415$	−8.05924	+	13.9590i	−0.395613	+	0.685221i
$416$	−15.2304	+	26.3798i	−0.746731	+	1.29338i
$417$		0			0
$418$	32.9000	+	9.02615i	1.60919	+	0.441483i
$419$	−31.5961			−1.54357			−0.771785	−	0.635884i	$-0.780636\pi$
$419$	−31.5961			−1.54357			−0.771785	+	0.635884i	$0.780636\pi$
$420$		0			0
$421$	−6.42177	+	11.1228i	−0.312978	+	0.542094i	−0.979006	−	0.203833i	$-0.934660\pi$
$421$	−6.42177	+	11.1228i	−0.312978	+	0.542094i	0.666028	+	0.745927i	$0.267993\pi$
$422$	0.0632207	+	0.109502i	0.00307754	+	0.00533045i
$423$		0			0
$424$	3.74750	+	6.49086i	0.181995	+	0.315224i
$425$	−0.0580867			−0.00281762
$426$		0			0
$427$	7.36561	+	12.7576i	0.356447	+	0.617384i
$428$	−8.40161	−	14.5520i	−0.406107	−	0.703398i
$429$		0			0
$430$	−10.7875			−0.520221
$431$	16.6064	+	28.7630i	0.799900	+	1.38547i	0.919681	+	0.392667i	$0.128447\pi$
$431$	16.6064	+	28.7630i	0.799900	+	1.38547i	−0.119781	+	0.992800i	$0.538219\pi$
$432$		0			0
$433$	−3.66146	−	6.34183i	−0.175958	−	0.304769i	0.764534	−	0.644583i	$-0.222969\pi$
$433$	−3.66146	−	6.34183i	−0.175958	−	0.304769i	−0.940493	+	0.339814i	$0.889636\pi$
$434$	1.81872	−	3.15012i	0.0873016	−	0.151211i
$435$		0			0
$436$	−17.3709			−0.831914
$437$	−1.33968	+	1.32380i	−0.0640857	+	0.0633259i
$438$		0			0
$439$	−11.4327	+	19.8020i	−0.545651	+	0.945096i	0.452914	+	0.891554i	$0.350384\pi$
$439$	−11.4327	+	19.8020i	−0.545651	+	0.945096i	−0.998566	+	0.0535417i	$0.982949\pi$
$440$	−3.02379	+	5.23735i	−0.144153	+	0.249681i
$441$		0			0
$442$	−0.259975	+	0.450290i	−0.0123657	+	0.0214181i
$443$	7.40824	+	12.8315i	0.351976	+	0.609641i	0.986596	−	0.163184i	$-0.0521765\pi$
$443$	7.40824	+	12.8315i	0.351976	+	0.609641i	−0.634619	+	0.772825i	$0.718843\pi$
$444$		0			0
$445$	11.1805			0.530006
$446$	−11.7256	−	20.3094i	−0.555225	−	0.961677i
$447$		0			0
$448$	3.70756			0.175166
$449$	−41.8708			−1.97600			−0.988002	−	0.154441i	$-0.950642\pi$
$449$	−41.8708			−1.97600			−0.988002	+	0.154441i	$0.950642\pi$
$450$		0			0
$451$	0.356690	−	0.617805i	0.0167959	−	0.0290913i
$452$	−8.15249	−	14.1205i	−0.383461	−	0.664174i
$453$		0			0
$454$	−6.96623	+	12.0659i	−0.326942	+	0.566279i
$455$	17.0148			0.797666
$456$		0			0
$457$	38.4845			1.80023			0.900114	−	0.435655i	$-0.143483\pi$
$457$	38.4845			1.80023			0.900114	+	0.435655i	$0.143483\pi$
$458$	17.1201	−	29.6530i	0.799972	−	1.38559i
$459$		0			0
$460$	0.265150	+	0.459252i	0.0123627	+	0.0214128i
$461$	13.9830	−	24.2192i	0.651251	−	1.12800i	−0.331568	−	0.943431i	$-0.607578\pi$
$461$	13.9830	−	24.2192i	0.651251	−	1.12800i	0.982820	−	0.184569i	$-0.0590889\pi$
$462$		0			0
$463$	12.5403			0.582797			0.291399	−	0.956602i	$-0.405879\pi$
$463$	12.5403			0.582797			0.291399	+	0.956602i	$0.405879\pi$
$464$	−27.1911			−1.26232
$465$		0			0
$466$	11.2589	+	19.5010i	0.521559	+	0.903366i
$467$	−24.4525			−1.13153			−0.565764	−	0.824567i	$-0.691419\pi$
$467$	−24.4525			−1.13153			−0.565764	+	0.824567i	$0.691419\pi$
$468$		0			0
$469$	−11.5835	−	20.0632i	−0.534877	−	0.926434i
$470$	9.96196	−	17.2546i	0.459511	−	0.795896i
$471$		0			0
$472$	2.39099	−	4.14132i	0.110054	−	0.190620i
$473$	−13.0806	+	22.6563i	−0.601447	+	1.04174i
$474$		0			0
$475$	−3.10053	+	3.06377i	−0.142262	+	0.140575i
$476$	0.243441			0.0111581
$477$		0			0
$478$	−14.1813	+	24.5626i	−0.648635	+	1.12347i
$479$	−3.27876	−	5.67898i	−0.149810	−	0.259479i	0.781347	−	0.624097i	$-0.214533\pi$
$479$	−3.27876	−	5.67898i	−0.149810	−	0.259479i	−0.931157	+	0.364618i	$0.881200\pi$
$480$		0			0
$481$	−16.4942	−	28.5688i	−0.752071	−	1.30263i
$482$	−44.6121			−2.03202
$483$		0			0
$484$	−4.89744	−	8.48261i	−0.222611	−	0.385573i
$485$	4.47355	+	7.74842i	0.203134	+	0.351838i
$486$		0			0
$487$	−12.6305			−0.572341			−0.286170	−	0.958179i	$-0.592382\pi$
$487$	−12.6305			−0.572341			−0.286170	+	0.958179i	$0.592382\pi$
$488$	−2.99413	−	5.18598i	−0.135538	−	0.234758i
$489$		0			0
$490$	−4.18641	−	7.25107i	−0.189123	−	0.327570i
$491$	−6.46604	+	11.1995i	−0.291808	+	0.505427i	−0.974237	−	0.225525i	$-0.927590\pi$
$491$	−6.46604	+	11.1995i	−0.291808	+	0.505427i	0.682429	+	0.730952i	$0.260924\pi$
$492$		0			0
$493$	−0.319187			−0.0143755
$494$	9.87359	+	37.7478i	0.444234	+	1.69835i
$495$		0			0
$496$	−1.46704	+	2.54099i	−0.0658722	+	0.114094i
$497$	14.3592	−	24.8708i	0.644097	−	1.11561i
$498$		0			0
$499$	14.9627	−	25.9162i	0.669824	−	1.16017i	−0.308129	−	0.951345i	$-0.599703\pi$
$499$	14.9627	−	25.9162i	0.669824	−	1.16017i	0.977953	−	0.208825i	$-0.0669639\pi$
$500$	0.613656	+	1.06288i	0.0274435	+	0.0475336i
$501$		0			0
$502$	5.95263			0.265679
$503$	15.1592	+	26.2565i	0.675914	+	1.17072i	0.976201	+	0.216869i	$0.0695843\pi$
$503$	15.1592	+	26.2565i	0.675914	+	1.17072i	−0.300287	+	0.953849i	$0.597082\pi$
$504$		0			0
$505$	−2.19046			−0.0974744
$506$	3.38176			0.150338
$507$		0			0
$508$	−9.63211	+	16.6833i	−0.427356	+	0.740202i
$509$	−13.2252	−	22.9067i	−0.586197	−	1.01532i	−0.994725	−	0.102577i	$-0.967291\pi$
$509$	−13.2252	−	22.9067i	−0.586197	−	1.01532i	0.408528	−	0.912746i	$-0.366042\pi$
$510$		0			0
$511$	−19.9697	+	34.5886i	−0.883409	+	1.53011i
$512$	−16.5130			−0.729779
$513$		0			0
$514$	−44.6692			−1.97027
$515$	5.24513	−	9.08483i	0.231128	−	0.400325i
$516$		0			0
$517$	−24.1591	−	41.8448i	−1.06252	−	1.84033i
$518$	−20.3072	+	35.1731i	−0.892247	+	1.54542i
$519$		0			0
$520$	−6.91654			−0.303310
$521$	−3.32486			−0.145665			−0.0728324	−	0.997344i	$-0.523204\pi$
$521$	−3.32486			−0.145665			−0.0728324	+	0.997344i	$0.523204\pi$
$522$		0			0
$523$	−8.88844	−	15.3952i	−0.388664	−	0.673186i	0.603606	−	0.797283i	$-0.293730\pi$
$523$	−8.88844	−	15.3952i	−0.388664	−	0.673186i	−0.992270	+	0.124097i	$0.960397\pi$
$524$	14.4032			0.629205
$525$		0			0
$526$	0.615626	+	1.06630i	0.0268426	+	0.0464927i
$527$	−0.0172211	+	0.0298278i	−0.000750163	+	0.00129932i
$528$		0			0
$529$	11.4067	−	19.7569i	0.495941	−	0.858996i
$530$	4.84995	−	8.40037i	0.210669	−	0.364889i
$531$		0			0
$532$	12.9943	−	12.8403i	0.563376	−	0.556696i
$533$	0.815884			0.0353399
$534$		0			0
$535$	6.84553	−	11.8568i	0.295958	−	0.512615i
$536$	4.70871	+	8.15573i	0.203385	+	0.352274i
$537$		0			0
$538$	−10.0370	−	17.3845i	−0.432724	−	0.749500i
$539$	−20.3052			−0.874608
$540$		0			0
$541$	17.7241	+	30.6991i	0.762021	+	1.31986i	0.941808	+	0.336153i	$0.109126\pi$
$541$	17.7241	+	30.6991i	0.762021	+	1.31986i	−0.179787	+	0.983706i	$0.557541\pi$
$542$	−12.8683	−	22.2885i	−0.552740	−	0.957374i
$543$		0			0
$544$	−0.355102			−0.0152249
$545$	−7.07679	−	12.2574i	−0.303136	−	0.525048i
$546$		0			0
$547$	−9.90142	−	17.1498i	−0.423354	−	0.733271i	0.572911	−	0.819618i	$-0.305814\pi$
$547$	−9.90142	−	17.1498i	−0.423354	−	0.733271i	−0.996265	+	0.0863465i	$0.972481\pi$
$548$	−6.29440	+	10.9022i	−0.268883	+	0.465720i
$549$		0			0
$550$	7.82667			0.333730
$551$	−17.0375	+	16.8355i	−0.725820	+	0.717214i
$552$		0			0
$553$	12.4401	−	21.5469i	0.529008	−	0.916269i
$554$	−13.7895	+	23.8841i	−0.585860	+	1.01474i
$555$		0			0
$556$	−13.3831	+	23.1802i	−0.567570	+	0.983061i
$557$	13.6340	+	23.6148i	0.577692	+	1.00059i	0.995743	+	0.0921684i	$0.0293798\pi$
$557$	13.6340	+	23.6148i	0.577692	+	1.00059i	−0.418052	+	0.908423i	$0.637287\pi$
$558$		0			0
$559$	−29.9203			−1.26549
$560$	8.44872	+	14.6336i	0.357024	+	0.618383i
$561$		0			0
$562$	17.2691			0.728455
$563$	−28.6245			−1.20638			−0.603190	−	0.797598i	$-0.706104\pi$
$563$	−28.6245			−1.20638			−0.603190	+	0.797598i	$0.706104\pi$
$564$		0			0
$565$	6.64256	−	11.5052i	0.279454	−	0.484029i
$566$	5.14250	+	8.90706i	0.216155	+	0.374392i
$567$		0			0
$568$	−5.83702	+	10.1100i	−0.244916	+	0.424207i
$569$	32.2230			1.35086			0.675430	−	0.737424i	$-0.263958\pi$
$569$	32.2230			1.35086			0.675430	+	0.737424i	$0.263958\pi$
$570$		0			0
$571$	−7.39249			−0.309366			−0.154683	−	0.987964i	$-0.549436\pi$
$571$	−7.39249			−0.309366			−0.154683	+	0.987964i	$0.549436\pi$
$572$	13.3213	−	23.0731i	0.556991	−	0.964737i
$573$		0			0
$574$	−0.502247	−	0.869917i	−0.0209634	−	0.0363096i
$575$	−0.216041	+	0.374194i	−0.00900952	+	0.0156049i
$576$		0			0
$577$	3.03682			0.126425			0.0632123	−	0.998000i	$-0.479865\pi$
$577$	3.03682			0.126425			0.0632123	+	0.998000i	$0.479865\pi$
$578$	30.5340			1.27005
$579$		0			0
$580$	3.37205	+	5.84056i	0.140017	+	0.242516i
$581$	55.0410			2.28349
$582$		0			0
$583$	−11.7618	−	20.3720i	−0.487124	−	0.843723i
$584$	8.11773	−	14.0603i	0.335914	−	0.581820i
$585$		0			0
$586$	20.9416	−	36.2719i	0.865089	−	1.49838i
$587$	7.96968	−	13.8039i	0.328944	−	0.569748i	−0.653359	−	0.757048i	$-0.726641\pi$
$587$	7.96968	−	13.8039i	0.328944	−	0.569748i	0.982303	+	0.187301i	$0.0599740\pi$
$588$		0			0
$589$	0.654040	+	2.50046i	0.0269492	+	0.103030i
$590$	−6.18877			−0.254788
$591$		0			0
$592$	16.3804	−	28.3718i	0.673232	−	1.16607i
$593$	−13.2914	−	23.0213i	−0.545811	−	0.945373i	−0.998555	−	0.0537322i	$-0.982888\pi$
$593$	−13.2914	−	23.0213i	−0.545811	−	0.945373i	0.452744	−	0.891640i	$-0.350445\pi$
$594$		0			0
$595$	0.0991765	+	0.171779i	0.00406584	+	0.00704224i
$596$	−25.4705			−1.04331
$597$		0			0
$598$	1.93384	+	3.34951i	0.0790806	+	0.136972i
$599$	−18.8742	−	32.6911i	−0.771181	−	1.33572i	−0.936916	−	0.349554i	$-0.886333\pi$
$599$	−18.8742	−	32.6911i	−0.771181	−	1.33572i	0.165736	−	0.986170i	$-0.447000\pi$
$600$		0			0
$601$	−16.9222			−0.690269			−0.345134	−	0.938553i	$-0.612167\pi$
$601$	−16.9222			−0.690269			−0.345134	+	0.938553i	$0.612167\pi$
$602$	18.4185	+	31.9018i	0.750682	+	1.30022i
$603$		0			0
$604$	9.17476	+	15.8911i	0.373316	+	0.646601i
$605$	3.99037	−	6.91153i	0.162232	−	0.280994i
$606$		0			0
$607$	36.3712			1.47626			0.738131	−	0.674658i	$-0.235709\pi$
$607$	36.3712			1.47626			0.738131	+	0.674658i	$0.235709\pi$
$608$	−18.9545	+	18.7298i	−0.768708	+	0.759593i
$609$		0			0
$610$	−3.87496	+	6.71162i	−0.156892	+	0.271746i
$611$	27.6305	−	47.8574i	1.11781	−	1.93610i
$612$		0			0
$613$	−3.66105	+	6.34113i	−0.147869	+	0.256116i	−0.930439	−	0.366446i	$-0.880575\pi$
$613$	−3.66105	+	6.34113i	−0.147869	+	0.256116i	0.782571	+	0.622561i	$0.213908\pi$
$614$	7.62936	+	13.2144i	0.307896	+	0.533291i
$615$		0			0
$616$	20.6511			0.832057
$617$	−4.91459	−	8.51233i	−0.197854	−	0.342693i	0.749978	−	0.661462i	$-0.230064\pi$
$617$	−4.91459	−	8.51233i	−0.197854	−	0.342693i	−0.947832	+	0.318769i	$0.896731\pi$
$618$		0			0
$619$	8.29932			0.333578			0.166789	−	0.985993i	$-0.446660\pi$
$619$	8.29932			0.333578			0.166789	+	0.985993i	$0.446660\pi$
$620$	0.727729			0.0292263
$621$		0			0
$622$	4.08092	−	7.06836i	0.163630	−	0.283415i
$623$	−19.0894	−	33.0639i	−0.764802	−	1.32468i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	33.8868			1.35439
$627$		0			0
$628$	−0.0980355			−0.00391204
$629$	0.192284	−	0.333046i	0.00766688	−	0.0132794i
$630$		0			0
$631$	21.4448	+	37.1435i	0.853705	+	1.47866i	0.877841	+	0.478952i	$0.158983\pi$
$631$	21.4448	+	37.1435i	0.853705	+	1.47866i	−0.0241360	+	0.999709i	$0.507683\pi$
$632$	−5.05693	+	8.75885i	−0.201154	+	0.348409i
$633$		0			0
$634$	−34.5577			−1.37246
$635$	−15.6963			−0.622887
$636$		0			0
$637$	−11.6114	−	20.1116i	−0.460061	−	0.796850i
$638$	43.0076			1.70269
$639$		0			0
$640$	−5.13806	−	8.89938i	−0.203100	−	0.351779i
$641$	11.2034	−	19.4048i	0.442507	−	0.766444i	−0.555368	−	0.831605i	$-0.687423\pi$
$641$	11.2034	−	19.4048i	0.442507	−	0.766444i	0.997875	+	0.0651607i	$0.0207560\pi$
$642$		0			0
$643$	−2.71105	+	4.69568i	−0.106914	+	0.185180i	−0.914518	−	0.404544i	$-0.867430\pi$
$643$	−2.71105	+	4.69568i	−0.106914	+	0.185180i	0.807605	+	0.589724i	$0.200763\pi$
$644$	0.905427	−	1.56824i	0.0356788	−	0.0617975i
$645$		0			0
$646$	−0.323544	+	0.319708i	−0.0127297	+	0.0125787i
$647$	25.1940			0.990477			0.495238	−	0.868757i	$-0.335081\pi$
$647$	25.1940			0.990477			0.495238	+	0.868757i	$0.335081\pi$
$648$		0			0
$649$	−7.50430	+	12.9978i	−0.294570	+	0.510210i
$650$	4.47564	+	7.75203i	0.175549	+	0.304060i
$651$		0			0
$652$	−11.3431	−	19.6469i	−0.444231	−	0.769431i
$653$	8.11903			0.317722			0.158861	−	0.987301i	$-0.449218\pi$
$653$	8.11903			0.317722			0.158861	+	0.987301i	$0.449218\pi$
$654$		0			0
$655$	5.86776	+	10.1633i	0.229272	+	0.397112i
$656$	0.405129	+	0.701703i	0.0158176	+	0.0273969i
$657$		0			0
$658$	−68.0357			−2.65231
$659$	6.73290	+	11.6617i	0.262277	+	0.454277i	0.966847	−	0.255358i	$-0.0821934\pi$
$659$	6.73290	+	11.6617i	0.262277	+	0.454277i	−0.704570	+	0.709635i	$0.748860\pi$
$660$		0			0
$661$	−4.51947	−	7.82796i	−0.175787	−	0.304472i	0.764646	−	0.644450i	$-0.222914\pi$
$661$	−4.51947	−	7.82796i	−0.175787	−	0.304472i	−0.940433	+	0.339978i	$0.889580\pi$
$662$	8.52701	−	14.7692i	0.331412	−	0.574022i
$663$		0			0
$664$	−22.3743			−0.868289
$665$	14.3543	+	3.93811i	0.556634	+	0.152713i
$666$		0			0
$667$	−1.18715	+	2.05620i	−0.0459665	+	0.0796163i
$668$	11.4653	−	19.8585i	0.443606	−	0.768348i
$669$		0			0
$670$	6.09394	−	10.5550i	0.235429	−	0.407776i
$671$	9.39729	+	16.2766i	0.362779	+	0.628351i
$672$		0			0
$673$	13.6988			0.528048			0.264024	−	0.964516i	$-0.414950\pi$
$673$	13.6988			0.528048			0.264024	+	0.964516i	$0.414950\pi$
$674$	21.3517	+	36.9823i	0.822438	+	1.42450i
$675$		0			0
$676$	14.5157			0.558298
$677$	−11.6030			−0.445941			−0.222970	−	0.974825i	$-0.571575\pi$
$677$	−11.6030			−0.445941			−0.222970	+	0.974825i	$0.571575\pi$
$678$		0			0
$679$	15.2762	−	26.4591i	0.586246	−	1.01541i
$680$	−0.0403154	−	0.0698283i	−0.00154602	−	0.00267779i
$681$		0			0
$682$	2.32039	−	4.01904i	0.0888524	−	0.153897i
$683$	−25.5290			−0.976840			−0.488420	−	0.872609i	$-0.662426\pi$
$683$	−25.5290			−0.976840			−0.488420	+	0.872609i	$0.662426\pi$
$684$		0			0
$685$	−10.2572			−0.391908
$686$	7.17528	−	12.4279i	0.273953	−	0.474501i
$687$		0			0
$688$	−14.8570	−	25.7330i	−0.566416	−	0.981062i
$689$	13.4518	−	23.2993i	0.512474	−	0.887631i
$690$		0			0
$691$	−46.1415			−1.75530			−0.877652	−	0.479298i	$-0.840891\pi$
$691$	−46.1415			−1.75530			−0.877652	+	0.479298i	$0.840891\pi$
$692$	−10.5515			−0.401106
$693$		0			0
$694$	25.1631	+	43.5838i	0.955178	+	1.65442i
$695$	−21.8088			−0.827255
$696$		0			0
$697$	0.00475566	+	0.00823705i	0.000180134	+	0.000312000i
$698$	0.00862000	−	0.0149303i	0.000326272	−	0.000565119i
$699$		0			0
$700$	2.09550	−	3.62951i	0.0792024	−	0.137183i
$701$	−0.219837	+	0.380768i	−0.00830312	+	0.0143814i	−0.870147	−	0.492792i	$-0.835976\pi$
$701$	−0.219837	+	0.380768i	−0.00830312	+	0.0143814i	0.861844	+	0.507173i	$0.169310\pi$
$702$		0			0
$703$	−7.30277	−	27.9192i	−0.275429	−	1.05299i
$704$	4.73024			0.178277
$705$		0			0
$706$	5.46650	−	9.46826i	0.205735	−	0.356343i
$707$	3.73997	+	6.47782i	0.140656	+	0.243624i
$708$		0			0
$709$	19.4677	+	33.7191i	0.731125	+	1.26635i	0.956403	+	0.292051i	$0.0943377\pi$
$709$	19.4677	+	33.7191i	0.731125	+	1.26635i	−0.225278	+	0.974295i	$0.572329\pi$
$710$	15.1084			0.567007
$711$		0			0
$712$	7.75988	+	13.4405i	0.290814	+	0.503704i
$713$	0.128100	+	0.221876i	0.00479739	+	0.00830932i
$714$		0			0
$715$	21.7081			0.811835
$716$	3.78373	+	6.55361i	0.141404	+	0.244920i
$717$		0			0
$718$	−16.0073	−	27.7255i	−0.597388	−	1.03471i
$719$	11.5179	−	19.9496i	0.429546	−	0.743995i	−0.567287	−	0.823520i	$-0.692007\pi$
$719$	11.5179	−	19.9496i	0.429546	−	0.743995i	0.996833	+	0.0795252i	$0.0253404\pi$
$720$		0			0
$721$	−35.8219			−1.33408
$722$	−0.407100	+	34.1305i	−0.0151507	+	1.27021i
$723$		0			0
$724$	−12.3092	+	21.3202i	−0.457469	+	0.792360i
$725$	−2.74750	+	4.75882i	−0.102040	+	0.176738i
$726$		0			0
$727$	22.2700	−	38.5727i	0.825948	−	1.43058i	−0.0752445	−	0.997165i	$-0.523974\pi$
$727$	22.2700	−	38.5727i	0.825948	−	1.43058i	0.901193	−	0.433419i	$-0.142693\pi$
$728$	11.8092	+	20.4542i	0.437678	+	0.758081i
$729$		0			0
$730$	−21.0117			−0.777677
$731$	−0.174401	−	0.302071i	−0.00645044	−	0.0111725i
$732$		0			0
$733$	34.2392			1.26465			0.632326	−	0.774702i	$-0.282100\pi$
$733$	34.2392			1.26465			0.632326	+	0.774702i	$0.282100\pi$
$734$	8.80612			0.325040
$735$		0			0
$736$	−1.32072	+	2.28756i	−0.0486826	+	0.0843207i
$737$	−14.7786	−	25.5974i	−0.544378	−	0.942891i
$738$		0			0
$739$	2.42166	−	4.19444i	0.0890823	−	0.154295i	−0.818041	−	0.575160i	$-0.804940\pi$
$739$	2.42166	−	4.19444i	0.0890823	−	0.154295i	0.907123	+	0.420865i	$0.138273\pi$
$740$	−8.12555			−0.298701
$741$		0			0
$742$	−33.1230			−1.21598
$743$	−6.53384	+	11.3169i	−0.239703	+	0.415178i	−0.960629	−	0.277834i	$-0.910384\pi$
$743$	−6.53384	+	11.3169i	−0.239703	+	0.415178i	0.720926	+	0.693012i	$0.243717\pi$
$744$		0			0
$745$	−10.3765	−	17.9727i	−0.380167	−	0.658468i
$746$	−11.6766	+	20.2245i	−0.427512	+	0.740473i
$747$		0			0
$748$	0.310591			0.0113563
$749$	−46.7519			−1.70828
$750$		0			0
$751$	−4.24060	−	7.34493i	−0.154742	−	0.268020i	0.778223	−	0.627988i	$-0.216121\pi$
$751$	−4.24060	−	7.34493i	−0.154742	−	0.268020i	−0.932965	+	0.359967i	$0.882788\pi$
$752$	54.8798			2.00126
$753$		0			0
$754$	24.5937	+	42.5975i	0.895648	+	1.55131i
$755$	−7.47548	+	12.9479i	−0.272061	+	0.471223i
$756$		0			0
$757$	17.6798	−	30.6223i	0.642583	−	1.11299i	−0.342271	−	0.939601i	$-0.611196\pi$
$757$	17.6798	−	30.6223i	0.642583	−	1.11299i	0.984854	−	0.173386i	$-0.0554707\pi$
$758$	15.0286	−	26.0303i	0.545864	−	0.945464i
$759$		0			0
$760$	−5.83502	−	1.60085i	−0.211659	−	0.0580688i
$761$	19.8496			0.719547			0.359773	−	0.933040i	$-0.382854\pi$
$761$	19.8496			0.719547			0.359773	+	0.933040i	$0.382854\pi$
$762$		0			0
$763$	−24.1657	+	41.8562i	−0.874856	+	1.51529i
$764$	−10.4752	−	18.1435i	−0.378978	−	0.656409i
$765$		0			0
$766$	−26.8503	−	46.5061i	−0.970141	−	1.68033i
$767$	−17.1652			−0.619798
$768$		0			0
$769$	−2.82265	−	4.88897i	−0.101787	−	0.176301i	0.810634	−	0.585553i	$-0.199123\pi$
$769$	−2.82265	−	4.88897i	−0.101787	−	0.176301i	−0.912421	+	0.409253i	$0.865789\pi$
$770$	−13.3632	−	23.1457i	−0.481575	−	0.834113i
$771$		0			0
$772$	8.92444			0.321198
$773$	−24.6102	−	42.6260i	−0.885166	−	1.53315i	−0.845523	−	0.533938i	$-0.820711\pi$
$773$	−24.6102	−	42.6260i	−0.885166	−	1.53315i	−0.0396424	−	0.999214i	$-0.512622\pi$
$774$		0			0
$775$	0.296472	+	0.513505i	0.0106496	+	0.0184456i
$776$	−6.20979	+	10.7557i	−0.222918	+	0.386106i
$777$		0			0
$778$	57.0088			2.04387
$779$	0.688308	+	0.188838i	0.0246612	+	0.00676583i
$780$		0			0
$781$	18.3199	−	31.7310i	0.655539	−	1.13543i
$782$	−0.0225441	+	0.0390475i	−0.000806175	+	0.00139634i
$783$		0			0
$784$	11.5313	−	19.9729i	0.411834	−	0.713317i
$785$	−0.0399391	−	0.0691765i	−0.00142549	−	0.00246902i
$786$		0			0
$787$	3.44055			0.122642			0.0613211	−	0.998118i	$-0.480469\pi$
$787$	3.44055			0.122642			0.0613211	+	0.998118i	$0.480469\pi$
$788$	−2.20827	−	3.82483i	−0.0786662	−	0.136254i
$789$		0			0
$790$	13.0892			0.465693
$791$	−45.3657			−1.61302
$792$		0			0
$793$	−10.7476	+	18.6153i	−0.381658	+	0.661050i
$794$	30.5399	+	52.8966i	1.08382	+	1.87723i
$795$		0			0
$796$	−13.2449	+	22.9408i	−0.469452	+	0.813115i
$797$	18.2573			0.646709			0.323354	−	0.946278i	$-0.395189\pi$
$797$	18.2573			0.646709			0.323354	+	0.946278i	$0.395189\pi$
$798$		0			0
$799$	0.644215			0.0227907
$800$	−3.05666	+	5.29428i	−0.108069	+	0.187181i
$801$		0			0
$802$	8.17475	+	14.1591i	0.288661	+	0.499975i
$803$	−25.4781	+	44.1293i	−0.899102	+	1.55729i
$804$		0			0
$805$	1.47546			0.0520032
$806$	5.30761			0.186953
$807$		0			0
$808$	−1.52030	−	2.63324i	−0.0534841	−	0.0926372i
$809$	5.38593			0.189359			0.0946796	−	0.995508i	$-0.469817\pi$
$809$	5.38593			0.189359			0.0946796	+	0.995508i	$0.469817\pi$
$810$		0			0
$811$	12.3515	+	21.3935i	0.433721	+	0.751227i	0.997190	−	0.0749098i	$-0.0238669\pi$
$811$	12.3515	+	21.3935i	0.433721	+	0.751227i	−0.563469	+	0.826137i	$0.690534\pi$
$812$	11.5148	−	19.9442i	0.404090	−	0.699904i
$813$		0			0
$814$	−25.9086	+	44.8751i	−0.908097	+	1.57287i
$815$	9.24225	−	16.0080i	0.323742	−	0.560737i
$816$		0			0
$817$	−25.2418	−	6.92511i	−0.883098	−	0.242279i
$818$	50.0945			1.75151
$819$		0			0
$820$	0.100482	−	0.174040i	0.00350899	−	0.00607776i
$821$	−0.371028	−	0.642639i	−0.0129490	−	0.0224283i	0.859478	−	0.511172i	$-0.170789\pi$
$821$	−0.371028	−	0.642639i	−0.0129490	−	0.0224283i	−0.872427	+	0.488744i	$0.837455\pi$
$822$		0			0
$823$	18.4440	+	31.9459i	0.642916	+	1.11356i	0.984779	+	0.173813i	$0.0556088\pi$
$823$	18.4440	+	31.9459i	0.642916	+	1.11356i	−0.341863	+	0.939750i	$0.611058\pi$
$824$	14.5616			0.507279
$825$		0			0
$826$	10.5666	+	18.3019i	0.367660	+	0.636806i
$827$	14.3030	+	24.7736i	0.497365	+	0.861462i	0.999995	−	0.00303949i	$-0.000967501\pi$
$827$	14.3030	+	24.7736i	0.497365	+	0.861462i	−0.502630	+	0.864502i	$0.667634\pi$
$828$		0			0
$829$	−13.9492			−0.484477			−0.242238	−	0.970217i	$-0.577882\pi$
$829$	−13.9492			−0.484477			−0.242238	+	0.970217i	$0.577882\pi$
$830$	14.4782	+	25.0770i	0.502546	+	0.870435i
$831$		0			0
$832$	2.70496	+	4.68512i	0.0937775	+	0.162427i
$833$	0.135362	−	0.234454i	0.00469003	−	0.00812336i
$834$		0			0
$835$	18.6836			0.646573
$836$	16.5786	−	16.3821i	0.573383	−	0.566585i
$837$		0			0
$838$	−28.3807	+	49.1569i	−0.980396	+	1.69810i
$839$	−16.6964	+	28.9190i	−0.576424	+	0.998395i	0.419462	+	0.907773i	$0.362219\pi$
$839$	−16.6964	+	28.9190i	−0.576424	+	0.998395i	−0.995885	+	0.0906220i	$0.971114\pi$
$840$		0			0
$841$	−0.597562	+	1.03501i	−0.0206056	+	0.0356899i
$842$	11.5365	+	19.9819i	0.397575	+	0.688620i
$843$		0			0
$844$	0.0863822			0.00297340
$845$	5.91363	+	10.2427i	0.203435	+	0.352360i
$846$		0			0
$847$	−27.2525			−0.936406
$848$	26.7181			0.917503
$849$		0			0
$850$	−0.0521756	+	0.0903707i	−0.00178961	+	0.00309969i
$851$	−1.43032	−	2.47739i	−0.0490307	−	0.0849237i
$852$		0			0
$853$	25.2234	−	43.6882i	0.863633	−	1.49586i	−0.00476535	−	0.999989i	$-0.501517\pi$
$853$	25.2234	−	43.6882i	0.863633	−	1.49586i	0.868398	−	0.495867i	$-0.165150\pi$
$854$	26.4642			0.905587
$855$		0			0
$856$	19.0047			0.649568
$857$	−8.79337	+	15.2306i	−0.300376	+	0.520266i	−0.976221	−	0.216777i	$-0.930445\pi$
$857$	−8.79337	+	15.2306i	−0.300376	+	0.520266i	0.675845	+	0.737043i	$0.263779\pi$
$858$		0			0
$859$	−12.5285	−	21.7000i	−0.427467	−	0.740395i	0.569180	−	0.822213i	$-0.307261\pi$
$859$	−12.5285	−	21.7000i	−0.427467	−	0.740395i	−0.996647	+	0.0818181i	$0.973927\pi$
$860$	−3.68491	+	6.38245i	−0.125654	+	0.217640i
$861$		0			0
$862$	59.6657			2.03222
$863$	38.1452			1.29848			0.649239	−	0.760584i	$-0.275087\pi$
$863$	38.1452			1.29848			0.649239	+	0.760584i	$0.275087\pi$
$864$		0			0
$865$	−4.29860	−	7.44540i	−0.146157	−	0.253151i
$866$	−13.1554			−0.447039
$867$		0			0
$868$	−1.24252	−	2.15210i	−0.0421737	−	0.0730470i
$869$	15.8715	−	27.4903i	0.538405	−	0.932545i
$870$		0			0
$871$	16.9022	−	29.2754i	0.572708	−	0.991959i
$872$	9.82337	−	17.0146i	0.332661	−	0.576186i
$873$		0			0
$874$	0.856202	+	3.27335i	0.0289615	+	0.110723i
$875$	3.41478			0.115441
$876$		0			0
$877$	4.82308	−	8.35383i	0.162864	−	0.282089i	−0.773031	−	0.634369i	$-0.781260\pi$
$877$	4.82308	−	8.35383i	0.162864	−	0.282089i	0.935895	+	0.352280i	$0.114593\pi$
$878$	20.5385	+	35.5737i	0.693140	+	1.20055i
$879$		0			0
$880$	10.7792	+	18.6701i	0.363366	+	0.629368i
$881$	−20.0684			−0.676122			−0.338061	−	0.941124i	$-0.609771\pi$
$881$	−20.0684			−0.676122			−0.338061	+	0.941124i	$0.609771\pi$
$882$		0			0
$883$	8.84128	+	15.3135i	0.297533	+	0.515342i	0.975571	−	0.219685i	$-0.0705029\pi$
$883$	8.84128	+	15.3135i	0.297533	+	0.515342i	−0.678038	+	0.735027i	$0.737170\pi$
$884$	0.177610	+	0.307629i	0.00597365	+	0.0103467i
$885$		0			0
$886$	26.6174			0.894229
$887$	9.77257	+	16.9266i	0.328131	+	0.568339i	0.982141	−	0.188147i	$-0.0602480\pi$
$887$	9.77257	+	16.9266i	0.328131	+	0.568339i	−0.654010	+	0.756486i	$0.726915\pi$
$888$		0			0
$889$	26.7996	+	46.4183i	0.898830	+	1.55682i
$890$	10.0427	−	17.3945i	0.336633	−	0.583065i
$891$		0			0
$892$	−16.0214			−0.536437
$893$	34.3867	−	33.9790i	1.15071	−	1.13706i
$894$		0			0
$895$	−3.08294	+	5.33980i	−0.103051	+	0.178490i
$896$	−17.5453	+	30.3894i	−0.586148	+	1.01524i
$897$		0			0
$898$	−37.6098	+	65.1422i	−1.25506	+	2.17382i
$899$	1.62912	+	2.82172i	0.0543341	+	0.0941095i
$900$		0			0
$901$	0.313634			0.0104487
$902$	−0.640784	−	1.10987i	−0.0213358	−	0.0369546i
$903$		0			0
$904$	18.4412			0.613346
$905$	−20.0589			−0.666779
$906$		0			0
$907$	−12.3070	+	21.3163i	−0.408647	+	0.707797i	−0.994738	−	0.102448i	$-0.967333\pi$
$907$	−12.3070	+	21.3163i	−0.408647	+	0.707797i	0.586091	+	0.810245i	$0.300666\pi$
$908$	4.75919	+	8.24315i	0.157939	+	0.273559i
$909$		0			0
$910$	15.2833	−	26.4715i	0.506636	−	0.877520i
$911$	−36.8357			−1.22042			−0.610211	−	0.792239i	$-0.708915\pi$
$911$	−36.8357			−1.22042			−0.610211	+	0.792239i	$0.708915\pi$
$912$		0			0
$913$	70.2233			2.32405
$914$	34.5681	−	59.8738i	1.14341	−	1.98045i
$915$		0			0
$916$	−11.6961	−	20.2583i	−0.386451	−	0.669353i
$917$	20.0371	−	34.7053i	0.661683	−	1.14607i
$918$		0			0
$919$	1.06587			0.0351597			0.0175798	−	0.999845i	$-0.494404\pi$
$919$	1.06587			0.0351597			0.0175798	+	0.999845i	$0.494404\pi$
$920$	−0.599777			−0.0197741
$921$		0			0
$922$	−25.1200	−	43.5091i	−0.827283	−	1.43290i
$923$	41.9046			1.37931
$924$		0			0
$925$	−3.31030	−	5.73361i	−0.108842	−	0.188520i
$926$	11.2642	−	19.5101i	0.370163	−	0.641141i
$927$		0			0
$928$	−16.7964	+	29.0921i	−0.551367	+	0.954996i
$929$	20.5195	−	35.5409i	0.673224	−	1.16606i	−0.303760	−	0.952749i	$-0.598242\pi$
$929$	20.5195	−	35.5409i	0.673224	−	1.16606i	0.976984	−	0.213310i	$-0.0684245\pi$
$930$		0			0
$931$	−5.14093	−	19.6543i	−0.168487	−	0.644143i
$932$	15.3837			0.503910
$933$		0			0
$934$	−21.9641	+	38.0430i	−0.718689	+	1.24481i
$935$	0.126533	+	0.219161i	0.00413807	+	0.00716734i
$936$		0			0
$937$	4.86438	+	8.42536i	0.158912	+	0.275244i	0.934477	−	0.356024i	$-0.115868\pi$
$937$	4.86438	+	8.42536i	0.158912	+	0.275244i	−0.775564	+	0.631269i	$0.782535\pi$
$938$	−41.6189			−1.35891
$939$		0			0
$940$	−6.80581	−	11.7880i	−0.221981	−	0.384482i
$941$	−11.8693	−	20.5583i	−0.386929	−	0.670181i	0.605106	−	0.796145i	$-0.293131\pi$
$941$	−11.8693	−	20.5583i	−0.386929	−	0.670181i	−0.992035	+	0.125964i	$0.959797\pi$
$942$		0			0
$943$	0.0707506			0.00230396
$944$	−8.52339	−	14.7629i	−0.277413	−	0.480493i
$945$		0			0
$946$	23.4990	+	40.7014i	0.764017	+	1.32332i
$947$	−7.54677	+	13.0714i	−0.245237	+	0.424763i	−0.962198	−	0.272350i	$-0.912199\pi$
$947$	−7.54677	+	13.0714i	−0.245237	+	0.424763i	0.716961	+	0.697113i	$0.245532\pi$
$948$		0			0
$949$	−58.2780			−1.89178
$950$	1.98158	+	7.57577i	0.0642908	+	0.245790i
$951$		0			0
$952$	−0.137668	+	0.238448i	−0.00446185	+	0.00772815i
$953$	15.6549	−	27.1151i	0.507113	−	0.878345i	−0.492853	−	0.870113i	$-0.664046\pi$
$953$	15.6549	−	27.1151i	0.507113	−	0.878345i	0.999966	−	0.00823292i	$-0.00262065\pi$
$954$		0			0
$955$	8.53504	−	14.7831i	0.276187	−	0.478370i
$956$	9.68834	+	16.7807i	0.313343	+	0.542726i
$957$		0			0
$958$	−11.7804			−0.380608
$959$	17.5130	+	30.3335i	0.565525	+	0.979519i
$960$		0			0
$961$	−30.6484			−0.988659
$962$	−59.2628			−1.91071
$963$		0			0
$964$	−15.2390	+	26.3948i	−0.490816	+	0.850118i
$965$	3.63576	+	6.29733i	0.117039	+	0.202718i
$966$		0			0
$967$	8.84578	−	15.3213i	0.284461	−	0.492701i	−0.688017	−	0.725694i	$-0.741519\pi$
$967$	8.84578	−	15.3213i	0.284461	−	0.492701i	0.972478	+	0.232993i	$0.0748520\pi$
$968$	11.0782			0.356066
$969$		0			0
$970$	16.0732			0.516080
$971$	−8.85858	+	15.3435i	−0.284285	+	0.492397i	−0.972436	−	0.233172i	$-0.925090\pi$
$971$	−8.85858	+	15.3435i	−0.284285	+	0.492397i	0.688150	+	0.725568i	$0.258423\pi$
$972$		0			0
$973$	37.2361	+	64.4948i	1.19373	+	2.06761i
$974$	−11.3451	+	19.6504i	−0.363522	+	0.629638i
$975$		0			0
$976$	−21.3469			−0.683298
$977$	29.1094			0.931292			0.465646	−	0.884971i	$-0.345822\pi$
$977$	29.1094			0.931292			0.465646	+	0.884971i	$0.345822\pi$
$978$		0			0
$979$	−24.3549	−	42.1840i	−0.778388	−	1.34821i
$980$	−5.72014			−0.182723
$981$		0			0
$982$	11.6161	+	20.1196i	0.370683	+	0.642042i
$983$	20.2138	−	35.0113i	0.644719	−	1.11669i	−0.339648	−	0.940553i	$-0.610308\pi$
$983$	20.2138	−	35.0113i	0.644719	−	1.11669i	0.984366	−	0.176133i	$-0.0563588\pi$
$984$		0			0
$985$	1.79927	−	3.11643i	0.0573295	−	0.0992976i
$986$	−0.286705	+	0.496588i	−0.00913055	+	0.0158146i
$987$		0			0
$988$	25.7062	+	7.05253i	0.817823	+	0.224371i
$989$	−2.59458			−0.0825029
$990$		0			0
$991$	17.7942	−	30.8204i	0.565250	−	0.979042i	−0.431776	−	0.901981i	$-0.642113\pi$
$991$	17.7942	−	30.8204i	0.565250	−	0.979042i	0.997026	−	0.0770615i	$-0.0245538\pi$
$992$	1.81243	+	3.13922i	0.0575447	+	0.0996703i
$993$		0			0
$994$	−25.7959	−	44.6797i	−0.818195	−	1.41716i
$995$	−21.5835			−0.684244
$996$		0			0
$997$	−7.33443	−	12.7036i	−0.232284	−	0.402327i	0.726196	−	0.687488i	$-0.241286\pi$
$997$	−7.33443	−	12.7036i	−0.232284	−	0.402327i	−0.958480	+	0.285161i	$0.907953\pi$
$998$	−26.8801	−	46.5578i	−0.850876	−	1.47376i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.k.k.676.5	yes	12
3.2	odd	2		855.2.k.j.676.2	yes	12
19.7	even	3	inner	855.2.k.k.406.5	yes	12
57.26	odd	6		855.2.k.j.406.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
855.2.k.j.406.2	✓	12	57.26	odd	6
855.2.k.j.676.2	yes	12	3.2	odd	2
855.2.k.k.406.5	yes	12	19.7	even	3	inner
855.2.k.k.676.5	yes	12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.898236 - 1.55579i) q^{2} +(-0.613656 - 1.06288i) q^{4} +(0.500000 - 0.866025i) q^{5} -3.41478 q^{7} +1.38811 q^{8} +O(q^{10})\)	\(q+(0.898236 - 1.55579i) q^{2} +(-0.613656 - 1.06288i) q^{4} +(0.500000 - 0.866025i) q^{5} -3.41478 q^{7} +1.38811 q^{8} +(-0.898236 - 1.55579i) q^{10} -4.35669 q^{11} +(-2.49135 - 4.31514i) q^{13} +(-3.06728 + 5.31268i) q^{14} +(2.47416 - 4.28538i) q^{16} +(0.0290433 - 0.0503046i) q^{17} +(-1.10304 - 4.21703i) q^{19} -1.22731 q^{20} +(-3.91334 + 6.77810i) q^{22} +(-0.216041 - 0.374194i) q^{23} +(-0.500000 - 0.866025i) q^{25} -8.95127 q^{26} +(2.09550 + 3.62951i) q^{28} +(-2.74750 - 4.75882i) q^{29} -0.592945 q^{31} +(-3.05666 - 5.29428i) q^{32} +(-0.0521756 - 0.0903707i) q^{34} +(-1.70739 + 2.95728i) q^{35} +6.62060 q^{37} +(-7.55160 - 2.07179i) q^{38} +(0.694056 - 1.20214i) q^{40} +(-0.0818718 + 0.141806i) q^{41} +(3.00242 - 5.20034i) q^{43} +(2.67351 + 4.63066i) q^{44} -0.776222 q^{46} +(5.54529 + 9.60473i) q^{47} +4.66070 q^{49} -1.79647 q^{50} +(-3.05766 + 5.29603i) q^{52} +(2.69971 + 4.67603i) q^{53} +(-2.17835 + 3.77300i) q^{55} -4.74009 q^{56} -9.87163 q^{58} +(1.72248 - 2.98342i) q^{59} +(-2.15698 - 3.73600i) q^{61} +(-0.532604 + 0.922498i) q^{62} -1.08574 q^{64} -4.98270 q^{65} +(3.39217 + 5.87541i) q^{67} -0.0712905 q^{68} +(3.06728 + 5.31268i) q^{70} +(-4.20501 + 7.28329i) q^{71} +(5.84804 - 10.1291i) q^{73} +(5.94686 - 10.3003i) q^{74} +(-3.80532 + 3.76021i) q^{76} +14.8771 q^{77} +(-3.64303 + 6.30991i) q^{79} +(-2.47416 - 4.28538i) q^{80} +(0.147080 + 0.254751i) q^{82} -16.1185 q^{83} +(-0.0290433 - 0.0503046i) q^{85} +(-5.39377 - 9.34228i) q^{86} -6.04757 q^{88} +(5.59024 + 9.68258i) q^{89} +(8.50740 + 14.7352i) q^{91} +(-0.265150 + 0.459252i) q^{92} +19.9239 q^{94} +(-4.20357 - 1.15325i) q^{95} +(-4.47355 + 7.74842i) q^{97} +(4.18641 - 7.25107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 5 q^{4} + 6 q^{5} + 4 q^{7} - 12 q^{8}+O(q^{10}) \) 12 * q + 3 * q^2 - 5 * q^4 + 6 * q^5 + 4 * q^7 - 12 * q^8	\( 12 q + 3 q^{2} - 5 q^{4} + 6 q^{5} + 4 q^{7} - 12 q^{8} - 3 q^{10} - 8 q^{13} + 10 q^{14} - 3 q^{16} + 4 q^{17} - 6 q^{19} - 10 q^{20} - 2 q^{23} - 6 q^{25} - 40 q^{26} - 26 q^{28} + 4 q^{29} + 24 q^{31} + 15 q^{32} + 7 q^{34} + 2 q^{35} - 29 q^{38} - 6 q^{40} + 12 q^{41} - 4 q^{43} + 6 q^{44} + 48 q^{46} + 6 q^{47} + 32 q^{49} - 6 q^{50} - 20 q^{52} + 26 q^{53} - 44 q^{56} - 20 q^{58} + 16 q^{59} + 20 q^{61} - 25 q^{62} + 28 q^{64} - 16 q^{65} - 12 q^{67} + 54 q^{68} - 10 q^{70} - 8 q^{71} - 4 q^{73} - 16 q^{74} - 66 q^{76} + 48 q^{77} - 12 q^{79} + 3 q^{80} + 26 q^{82} - 44 q^{83} - 4 q^{85} - 44 q^{86} - 32 q^{88} - 8 q^{89} + 2 q^{91} + 36 q^{92} - 14 q^{94} - 6 q^{95} + 30 q^{97} + 49 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 - 5 * q^4 + 6 * q^5 + 4 * q^7 - 12 * q^8 - 3 * q^10 - 8 * q^13 + 10 * q^14 - 3 * q^16 + 4 * q^17 - 6 * q^19 - 10 * q^20 - 2 * q^23 - 6 * q^25 - 40 * q^26 - 26 * q^28 + 4 * q^29 + 24 * q^31 + 15 * q^32 + 7 * q^34 + 2 * q^35 - 29 * q^38 - 6 * q^40 + 12 * q^41 - 4 * q^43 + 6 * q^44 + 48 * q^46 + 6 * q^47 + 32 * q^49 - 6 * q^50 - 20 * q^52 + 26 * q^53 - 44 * q^56 - 20 * q^58 + 16 * q^59 + 20 * q^61 - 25 * q^62 + 28 * q^64 - 16 * q^65 - 12 * q^67 + 54 * q^68 - 10 * q^70 - 8 * q^71 - 4 * q^73 - 16 * q^74 - 66 * q^76 + 48 * q^77 - 12 * q^79 + 3 * q^80 + 26 * q^82 - 44 * q^83 - 4 * q^85 - 44 * q^86 - 32 * q^88 - 8 * q^89 + 2 * q^91 + 36 * q^92 - 14 * q^94 - 6 * q^95 + 30 * q^97 + 49 * q^98

Introduction

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