LMFDB - Embedded newform 855.2.k.i.406.4

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:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 9x^{8} - 2x^{7} + 56x^{6} - 18x^{5} + 125x^{4} + x^{3} + 189x^{2} - 52x + 16 $ x^10 - x^9 + 9x^8 - 2x^7 + 56x^6 - 18x^5 + 125x^4 + x^3 + 189x^2 - 52*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 285)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			406.4
Root			$-0.690702 + 1.19633i$ of defining polynomial
Character	$\chi$	$=$	855.406
Dual form			855.2.k.i.676.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.690702 + 1.19633i) q^{2} +(0.0458624 - 0.0794360i) q^{4} +(0.500000 + 0.866025i) q^{5} -4.36264 q^{7} +2.88952 q^{8} +(-0.690702 + 1.19633i) q^{10} +4.31625 q^{11} +(3.18132 - 5.51021i) q^{13} +(-3.01329 - 5.21916i) q^{14} +(1.90407 + 3.29794i) q^{16} +(2.85821 + 4.95056i) q^{17} +(2.97100 + 3.18954i) q^{19} +0.0917248 q^{20} +(2.98124 + 5.16366i) q^{22} +(-0.289678 + 0.501738i) q^{23} +(-0.500000 + 0.866025i) q^{25} +8.78938 q^{26} +(-0.200081 + 0.346551i) q^{28} +(-1.77672 + 3.07737i) q^{29} +1.18345 q^{31} +(0.259229 - 0.448998i) q^{32} +(-3.94834 + 6.83872i) q^{34} +(-2.18132 - 3.77816i) q^{35} -6.54609 q^{37} +(-1.76367 + 5.75732i) q^{38} +(1.44476 + 2.50239i) q^{40} +(-0.381403 - 0.660610i) q^{41} +(3.18132 + 5.51021i) q^{43} +(0.197954 - 0.342866i) q^{44} -0.800326 q^{46} +(-1.36632 + 2.36653i) q^{47} +12.0327 q^{49} -1.38140 q^{50} +(-0.291806 - 0.505423i) q^{52} +(2.56853 - 4.44882i) q^{53} +(2.15812 + 3.73798i) q^{55} -12.6059 q^{56} -4.90874 q^{58} +(1.91484 + 3.31660i) q^{59} +(6.01053 - 10.4105i) q^{61} +(0.817411 + 1.41580i) q^{62} +8.33247 q^{64} +6.36264 q^{65} +(2.00213 - 3.46779i) q^{67} +0.524337 q^{68} +(3.01329 - 5.21916i) q^{70} +(1.53953 + 2.66654i) q^{71} +(-4.04320 - 7.00303i) q^{73} +(-4.52140 - 7.83129i) q^{74} +(0.389622 - 0.0897246i) q^{76} -18.8303 q^{77} +(-5.66836 - 9.81790i) q^{79} +(-1.90407 + 3.29794i) q^{80} +(0.526872 - 0.912569i) q^{82} -7.67889 q^{83} +(-2.85821 + 4.95056i) q^{85} +(-4.39469 + 7.61182i) q^{86} +12.4719 q^{88} +(4.92093 - 8.52330i) q^{89} +(-13.8790 + 24.0391i) q^{91} +(0.0265707 + 0.0460218i) q^{92} -3.77487 q^{94} +(-1.27672 + 4.16773i) q^{95} +(-1.00000 - 1.73205i) q^{97} +(8.31098 + 14.3950i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - 7 q^{4} + 5 q^{5} + 4 q^{7} + 12 q^{8} + q^{10} - 10 q^{11} + 8 q^{13} - 4 q^{14} - 7 q^{16} + 10 q^{17} + 5 q^{19} - 14 q^{20} - 2 q^{22} - 2 q^{23} - 5 q^{25} + 4 q^{26} - 10 q^{28} - 7 q^{29}+ \cdots + 21 q^{98}+O(q^{100}) $ 10 * q - q^2 - 7 * q^4 + 5 * q^5 + 4 * q^7 + 12 * q^8 + q^10 - 10 * q^11 + 8 * q^13 - 4 * q^14 - 7 * q^16 + 10 * q^17 + 5 * q^19 - 14 * q^20 - 2 * q^22 - 2 * q^23 - 5 * q^25 + 4 * q^26 - 10 * q^28 - 7 * q^29 - 18 * q^31 - 23 * q^32 - 25 * q^34 + 2 * q^35 + 12 * q^37 + 37 * q^38 + 6 * q^40 + 12 * q^41 + 8 * q^43 + 16 * q^44 - 40 * q^46 + 6 * q^47 + 30 * q^49 + 2 * q^50 + 4 * q^52 + 8 * q^53 - 5 * q^55 - 72 * q^56 + 76 * q^58 - q^59 - 7 * q^61 + 15 * q^62 + 28 * q^64 + 16 * q^65 + 14 * q^67 + 2 * q^68 + 4 * q^70 - 27 * q^71 - 26 * q^73 - 18 * q^74 - 56 * q^76 - 28 * q^77 - 23 * q^79 + 7 * q^80 + 36 * q^82 + 24 * q^83 - 10 * q^85 - 2 * q^86 - 9 * q^89 - 46 * q^91 - 52 * q^92 + 90 * q^94 - 2 * q^95 - 10 * q^97 + 21 * q^98

Character values

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

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

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 $

$2$	0.690702	+	1.19633i	0.488400	+	0.845933i	0.999911	−	0.0133433i	$-0.00424744\pi$
$2$	0.690702	+	1.19633i	0.488400	+	0.845933i	−0.511511	+	0.859277i	$0.670914\pi$
$3$		0			0
$3$		0			0
$4$	0.0458624	−	0.0794360i	0.0229312	−	0.0397180i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−4.36264			−1.64892			−0.824462	−	0.565917i	$-0.808522\pi$
$7$	−4.36264			−1.64892			−0.824462	+	0.565917i	$0.808522\pi$
$8$	2.88952			1.02160
$9$		0			0
$10$	−0.690702	+	1.19633i	−0.218419	+	0.378313i
$11$	4.31625			1.30140			0.650699	−	0.759336i	$-0.274476\pi$
$11$	4.31625			1.30140			0.650699	+	0.759336i	$0.274476\pi$
$12$		0			0
$13$	3.18132	−	5.51021i	0.882340	−	1.52826i	0.0336075	−	0.999435i	$-0.489300\pi$
$13$	3.18132	−	5.51021i	0.882340	−	1.52826i	0.848732	−	0.528823i	$-0.177366\pi$
$14$	−3.01329	−	5.21916i	−0.805334	−	1.39488i
$15$		0			0
$16$	1.90407	+	3.29794i	0.476017	+	0.824486i
$17$	2.85821	+	4.95056i	0.693217	+	1.20069i	0.970778	+	0.239979i	$0.0771405\pi$
$17$	2.85821	+	4.95056i	0.693217	+	1.20069i	−0.277561	+	0.960708i	$0.589526\pi$
$18$		0			0
$19$	2.97100	+	3.18954i	0.681594	+	0.731730i
$19$	2.97100	+	3.18954i	0.681594	+	0.731730i
$20$	0.0917248			0.0205103
$21$		0			0
$22$	2.98124	+	5.16366i	0.635603	+	1.10090i
$23$	−0.289678	+	0.501738i	−0.0604021	+	0.104620i	−0.894645	−	0.446777i	$-0.852572\pi$
$23$	−0.289678	+	0.501738i	−0.0604021	+	0.104620i	0.834243	+	0.551397i	$0.185905\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	8.78938			1.72374
$27$		0			0
$28$	−0.200081	+	0.346551i	−0.0378118	+	0.0654920i
$29$	−1.77672	+	3.07737i	−0.329929	+	0.571454i	−0.982497	−	0.186276i	$-0.940358\pi$
$29$	−1.77672	+	3.07737i	−0.329929	+	0.571454i	0.652569	+	0.757730i	$0.273691\pi$
$30$		0			0
$31$	1.18345			0.212554			0.106277	−	0.994337i	$-0.466107\pi$
$31$	1.18345			0.212554			0.106277	+	0.994337i	$0.466107\pi$
$32$	0.259229	−	0.448998i	0.0458257	−	0.0793724i
$33$		0			0
$34$	−3.94834	+	6.83872i	−0.677134	+	1.17283i
$35$	−2.18132	−	3.77816i	−0.368711	−	0.638626i
$36$		0			0
$37$	−6.54609			−1.07617			−0.538086	−	0.842890i	$-0.680852\pi$
$37$	−6.54609			−1.07617			−0.538086	+	0.842890i	$0.680852\pi$
$38$	−1.76367	+	5.75732i	−0.286105	+	0.933960i
$39$		0			0
$40$	1.44476	+	2.50239i	0.228436	+	0.395663i
$41$	−0.381403	−	0.660610i	−0.0595652	−	0.103170i	0.834705	−	0.550697i	$-0.185638\pi$
$41$	−0.381403	−	0.660610i	−0.0595652	−	0.103170i	−0.894270	+	0.447527i	$0.852305\pi$
$42$		0			0
$43$	3.18132	+	5.51021i	0.485147	+	0.840299i	0.999854	−	0.0170666i	$-0.00543274\pi$
$43$	3.18132	+	5.51021i	0.485147	+	0.840299i	−0.514707	+	0.857366i	$0.672099\pi$
$44$	0.197954	−	0.342866i	0.0298426	−	0.0516890i
$45$		0			0
$46$	−0.800326			−0.118002
$47$	−1.36632	+	2.36653i	−0.199298	+	0.345194i	−0.948301	−	0.317372i	$-0.897200\pi$
$47$	−1.36632	+	2.36653i	−0.199298	+	0.345194i	0.749003	+	0.662567i	$0.230533\pi$
$48$		0			0
$49$	12.0327			1.71895
$50$	−1.38140			−0.195360
$51$		0			0
$52$	−0.291806	−	0.505423i	−0.0404662	−	0.0700896i
$53$	2.56853	−	4.44882i	0.352814	−	0.611092i	−0.633927	−	0.773393i	$-0.718558\pi$
$53$	2.56853	−	4.44882i	0.352814	−	0.611092i	0.986741	+	0.162300i	$0.0518914\pi$
$54$		0			0
$55$	2.15812	+	3.73798i	0.291001	+	0.504029i
$56$	−12.6059			−1.68454
$57$		0			0
$58$	−4.90874			−0.644549
$59$	1.91484	+	3.31660i	0.249291	+	0.431785i	0.963329	−	0.268322i	$-0.0864691\pi$
$59$	1.91484	+	3.31660i	0.249291	+	0.431785i	−0.714038	+	0.700107i	$0.753136\pi$
$60$		0			0
$61$	6.01053	−	10.4105i	0.769569	−	1.33293i	−0.168227	−	0.985748i	$-0.553804\pi$
$61$	6.01053	−	10.4105i	0.769569	−	1.33293i	0.937797	−	0.347185i	$-0.112862\pi$
$62$	0.817411	+	1.41580i	0.103811	+	0.179806i
$63$		0			0
$64$	8.33247			1.04156
$65$	6.36264			0.789189
$66$		0			0
$67$	2.00213	−	3.46779i	0.244599	−	0.423658i	−0.717420	−	0.696641i	$-0.754677\pi$
$67$	2.00213	−	3.46779i	0.244599	−	0.423658i	0.962019	+	0.272983i	$0.0880104\pi$
$68$	0.524337			0.0635852
$69$		0			0
$70$	3.01329	−	5.21916i	0.360156	−	0.623809i
$71$	1.53953	+	2.66654i	0.182708	+	0.316460i	0.942802	−	0.333354i	$-0.108180\pi$
$71$	1.53953	+	2.66654i	0.182708	+	0.316460i	−0.760094	+	0.649814i	$0.774847\pi$
$72$		0			0
$73$	−4.04320	−	7.00303i	−0.473221	−	0.819643i	0.526309	−	0.850293i	$-0.323575\pi$
$73$	−4.04320	−	7.00303i	−0.473221	−	0.819643i	−0.999530	+	0.0306504i	$0.990242\pi$
$74$	−4.52140	−	7.83129i	−0.525602	−	0.910369i
$75$		0			0
$76$	0.389622	−	0.0897246i	0.0446927	−	0.0102921i
$77$	−18.8303			−2.14591
$78$		0			0
$79$	−5.66836	−	9.81790i	−0.637741	−	1.10460i	−0.985927	−	0.167174i	$-0.946536\pi$
$79$	−5.66836	−	9.81790i	−0.637741	−	1.10460i	0.348187	−	0.937425i	$-0.386798\pi$
$80$	−1.90407	+	3.29794i	−0.212881	+	0.368721i
$81$		0			0
$82$	0.526872	−	0.912569i	0.0581833	−	0.100776i
$83$	−7.67889			−0.842868			−0.421434	−	0.906859i	$-0.638473\pi$
$83$	−7.67889			−0.842868			−0.421434	+	0.906859i	$0.638473\pi$
$84$		0			0
$85$	−2.85821	+	4.95056i	−0.310016	+	0.536963i
$86$	−4.39469	+	7.61182i	−0.473891	+	0.820804i
$87$		0			0
$88$	12.4719			1.32951
$89$	4.92093	−	8.52330i	0.521618	−	0.903468i	−0.478066	−	0.878324i	$-0.658662\pi$
$89$	4.92093	−	8.52330i	0.521618	−	0.903468i	0.999684	−	0.0251445i	$-0.00800458\pi$
$90$		0			0
$91$	−13.8790	+	24.0391i	−1.45491	+	2.51998i
$92$	0.0265707	+	0.0460218i	0.00277019	+	0.00479811i
$93$		0			0
$94$	−3.77487			−0.389348
$95$	−1.27672	+	4.16773i	−0.130989	+	0.427600i
$96$		0			0
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	0.810782	−	0.585348i	$-0.199042\pi$
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	−0.912317	+	0.409484i	$0.865709\pi$
$98$	8.31098	+	14.3950i	0.839536	+	1.45412i
$99$		0			0
$100$	0.0458624	+	0.0794360i	0.00458624	+	0.00794360i
$101$	−2.24985	+	3.89685i	−0.223868	+	0.387751i	−0.955979	−	0.293434i	$-0.905202\pi$
$101$	−2.24985	+	3.89685i	−0.223868	+	0.387751i	0.732111	+	0.681185i	$0.238535\pi$
$102$		0			0
$103$	−16.0717			−1.58359			−0.791796	−	0.610785i	$-0.790854\pi$
$103$	−16.0717			−1.58359			−0.791796	+	0.610785i	$0.790854\pi$
$104$	9.19248	−	15.9218i	0.901397	−	1.56127i
$105$		0			0
$106$	7.09634			0.689258
$107$	−13.6789			−1.32239			−0.661194	−	0.750215i	$-0.729950\pi$
$107$	−13.6789			−1.32239			−0.661194	+	0.750215i	$0.729950\pi$
$108$		0			0
$109$	4.48337	+	7.76542i	0.429429	+	0.743792i	0.996823	−	0.0796541i	$-0.0253816\pi$
$109$	4.48337	+	7.76542i	0.429429	+	0.743792i	−0.567394	+	0.823447i	$0.692048\pi$
$110$	−2.98124	+	5.16366i	−0.284250	+	0.492336i
$111$		0			0
$112$	−8.30677	−	14.3878i	−0.784916	−	1.35951i
$113$	−6.42952			−0.604838			−0.302419	−	0.953175i	$-0.597794\pi$
$113$	−6.42952			−0.604838			−0.302419	+	0.953175i	$0.597794\pi$
$114$		0			0
$115$	−0.579357			−0.0540253
$116$	0.162969	+	0.282271i	0.0151313	+	0.0262082i
$117$		0			0
$118$	−2.64517	+	4.58156i	−0.243507	+	0.421767i
$119$	−12.4693	−	21.5975i	−1.14306	−	1.97984i
$120$		0			0
$121$	7.63001			0.693637
$122$	16.6059			1.50343
$123$		0			0
$124$	0.0542759	−	0.0940086i	0.00487412	−	0.00844222i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	3.09172	−	5.35502i	0.274346	−	0.475182i	−0.695624	−	0.718406i	$-0.744872\pi$
$127$	3.09172	−	5.35502i	0.274346	−	0.475182i	0.969970	+	0.243225i	$0.0782052\pi$
$128$	5.23680	+	9.07040i	0.462872	+	0.801717i
$129$		0			0
$130$	4.39469	+	7.61182i	0.385440	+	0.667601i
$131$	8.69872	+	15.0666i	0.760010	+	1.31638i	0.942845	+	0.333233i	$0.108140\pi$
$131$	8.69872	+	15.0666i	0.760010	+	1.31638i	−0.182834	+	0.983144i	$0.558527\pi$
$132$		0			0
$133$	−12.9614	−	13.9148i	−1.12390	−	1.20657i
$134$	5.53149			0.477848
$135$		0			0
$136$	8.25883	+	14.3047i	0.708189	+	1.22662i
$137$	7.85821	−	13.6108i	0.671372	−	1.16285i	−0.306143	−	0.951985i	$-0.599039\pi$
$137$	7.85821	−	13.6108i	0.671372	−	1.16285i	0.977515	−	0.210865i	$-0.0676280\pi$
$138$		0			0
$139$	−3.27672	+	5.67545i	−0.277928	+	0.481385i	−0.970870	−	0.239608i	$-0.922981\pi$
$139$	−3.27672	+	5.67545i	−0.277928	+	0.481385i	0.692942	+	0.720994i	$0.256314\pi$
$140$	−0.400163			−0.0338199
$141$		0			0
$142$	−2.12671	+	3.68357i	−0.178469	+	0.309118i
$143$	13.7314	−	23.7834i	1.14828	−	1.98887i
$144$		0			0
$145$	−3.55344			−0.295097
$146$	5.58529	−	9.67401i	0.462242	−	0.800627i
$147$		0			0
$148$	−0.300220	+	0.519996i	−0.0246779	+	0.0427434i
$149$	2.87560	+	4.98069i	0.235578	+	0.408034i	0.959441	−	0.281911i	$-0.0909682\pi$
$149$	2.87560	+	4.98069i	0.235578	+	0.408034i	−0.723862	+	0.689945i	$0.757635\pi$
$150$		0			0
$151$	−12.6673			−1.03085			−0.515425	−	0.856935i	$-0.672366\pi$
$151$	−12.6673			−1.03085			−0.515425	+	0.856935i	$0.672366\pi$
$152$	8.58475	+	9.21622i	0.696315	+	0.747534i
$153$		0			0
$154$	−13.0061	−	22.5272i	−1.04806	−	1.81529i
$155$	0.591725	+	1.02490i	0.0475285	+	0.0823217i
$156$		0			0
$157$	−0.689434	−	1.19414i	−0.0550228	−	0.0953024i	0.837202	−	0.546894i	$-0.184190\pi$
$157$	−0.689434	−	1.19414i	−0.0550228	−	0.0953024i	−0.892225	+	0.451591i	$0.850856\pi$
$158$	7.83030	−	13.5625i	0.622945	−	1.07897i
$159$		0			0
$160$	0.518458			0.0409877
$161$	1.26376	−	2.18890i	0.0995986	−	0.172510i
$162$		0			0
$163$	−11.6120			−0.909523			−0.454762	−	0.890613i	$-0.650276\pi$
$163$	−11.6120			−0.909523			−0.454762	+	0.890613i	$0.650276\pi$
$164$	−0.0699683			−0.00546361
$165$		0			0
$166$	−5.30382	−	9.18649i	−0.411657	−	0.713010i
$167$	−10.1557	+	17.5902i	−0.785871	+	1.36117i	0.142606	+	0.989780i	$0.454452\pi$
$167$	−10.1557	+	17.5902i	−0.785871	+	1.36117i	−0.928477	+	0.371390i	$0.878881\pi$
$168$		0			0
$169$	−13.7416	−	23.8012i	−1.05705	−	1.83086i
$170$	−7.89667			−0.605647
$171$		0			0
$172$	0.583613			0.0445000
$173$	−6.12545	−	10.6096i	−0.465709	−	0.806632i	0.533524	−	0.845785i	$-0.320867\pi$
$173$	−6.12545	−	10.6096i	−0.465709	−	0.806632i	−0.999233	+	0.0391527i	$0.987534\pi$
$174$		0			0
$175$	2.18132	−	3.77816i	0.164892	−	0.285602i
$176$	8.21843	+	14.2347i	0.619488	+	1.07298i
$177$		0			0
$178$	13.5956			1.01903
$179$	19.1840			1.43388			0.716941	−	0.697134i	$-0.245542\pi$
$179$	19.1840			1.43388			0.716941	+	0.697134i	$0.245542\pi$
$180$		0			0
$181$	1.61492	−	2.79713i	0.120036	−	0.207909i	−0.799746	−	0.600339i	$-0.795032\pi$
$181$	1.61492	−	2.79713i	0.120036	−	0.207909i	0.919782	+	0.392430i	$0.128366\pi$
$182$	−38.3449			−2.84231
$183$		0			0
$184$	−0.837031	+	1.44978i	−0.0617067	+	0.106879i
$185$	−3.27305	−	5.66908i	−0.240639	−	0.416799i
$186$		0			0
$187$	12.3367	+	21.3678i	0.902151	+	1.56257i
$188$	0.125325	+	0.217070i	0.00914029	+	0.0158314i
$189$		0			0
$190$	−5.86782	+	1.35128i	−0.425696	+	0.0980320i
$191$	−27.5509			−1.99352			−0.996758	−	0.0804642i	$-0.974360\pi$
$191$	−27.5509			−1.99352			−0.996758	+	0.0804642i	$0.974360\pi$
$192$		0			0
$193$	−11.1233	−	19.2662i	−0.800674	−	1.38681i	−0.919173	−	0.393854i	$-0.871141\pi$
$193$	−11.1233	−	19.2662i	−0.800674	−	1.38681i	0.118499	−	0.992954i	$-0.462192\pi$
$194$	1.38140	−	2.39266i	0.0991790	−	0.171783i
$195$		0			0
$196$	0.551847	−	0.955827i	0.0394176	−	0.0682734i
$197$	−12.6627			−0.902178			−0.451089	−	0.892479i	$-0.648964\pi$
$197$	−12.6627			−0.902178			−0.451089	+	0.892479i	$0.648964\pi$
$198$		0			0
$199$	4.38478	−	7.59466i	0.310829	−	0.538371i	−0.667713	−	0.744418i	$-0.732727\pi$
$199$	4.38478	−	7.59466i	0.310829	−	0.538371i	0.978542	+	0.206048i	$0.0660602\pi$
$200$	−1.44476	+	2.50239i	−0.102160	+	0.176946i
$201$		0			0
$202$	−6.21590			−0.437349
$203$	7.75120	−	13.4255i	0.544028	−	0.942284i
$204$		0			0
$205$	0.381403	−	0.660610i	0.0266384	−	0.0461390i
$206$	−11.1008	−	19.2271i	−0.773426	−	1.33961i
$207$		0			0
$208$	24.2298			1.68004
$209$	12.8236	+	13.7668i	0.887025	+	0.952272i
$210$		0			0
$211$	−3.93389	−	6.81369i	−0.270820	−	0.469074i	0.698252	−	0.715852i	$-0.253962\pi$
$211$	−3.93389	−	6.81369i	−0.270820	−	0.469074i	−0.969072	+	0.246778i	$0.920628\pi$
$212$	−0.235598	−	0.408067i	−0.0161809	−	0.0280262i
$213$		0			0
$214$	−9.44803	−	16.3645i	−0.645854	−	1.11865i
$215$	−3.18132	+	5.51021i	−0.216964	+	0.375793i
$216$		0			0
$217$	−5.16297			−0.350485
$218$	−6.19334	+	10.7272i	−0.419466	+	0.726536i
$219$		0			0
$220$	0.395907			0.0266921
$221$	36.3715			2.44661
$222$		0			0
$223$	13.6768	+	23.6889i	0.915864	+	1.58632i	0.805631	+	0.592417i	$0.201826\pi$
$223$	13.6768	+	23.6889i	0.915864	+	1.58632i	0.110232	+	0.993906i	$0.464840\pi$
$224$	−1.13092	+	1.95882i	−0.0755631	+	0.130879i
$225$		0			0
$226$	−4.44088	−	7.69183i	−0.295403	−	0.511653i
$227$	25.0922			1.66543			0.832713	−	0.553704i	$-0.186786\pi$
$227$	25.0922			1.66543			0.832713	+	0.553704i	$0.186786\pi$
$228$		0			0
$229$	4.98530			0.329438			0.164719	−	0.986341i	$-0.447328\pi$
$229$	4.98530			0.329438			0.164719	+	0.986341i	$0.447328\pi$
$230$	−0.400163	−	0.693102i	−0.0263860	−	0.0457018i
$231$		0			0
$232$	−5.13386	+	8.89211i	−0.337055	+	0.583796i
$233$	6.39821	+	11.0820i	0.419161	+	0.726007i	0.995855	−	0.0909523i	$-0.0289911\pi$
$233$	6.39821	+	11.0820i	0.419161	+	0.726007i	−0.576695	+	0.816960i	$0.695658\pi$
$234$		0			0
$235$	−2.73264			−0.178258
$236$	0.351277			0.0228662
$237$		0			0
$238$	17.2252	−	29.8349i	1.11654	−	1.93391i
$239$	−12.8049			−0.828283			−0.414142	−	0.910212i	$-0.635918\pi$
$239$	−12.8049			−0.828283			−0.414142	+	0.910212i	$0.635918\pi$
$240$		0			0
$241$	0.546395	−	0.946383i	0.0351964	−	0.0609619i	−0.847891	−	0.530171i	$-0.822128\pi$
$241$	0.546395	−	0.946383i	0.0351964	−	0.0609619i	0.883087	+	0.469209i	$0.155461\pi$
$242$	5.27006	+	9.12801i	0.338772	+	0.586771i
$243$		0			0
$244$	−0.551315	−	0.954905i	−0.0352943	−	0.0611315i
$245$	6.01633	+	10.4206i	0.384369	+	0.665747i
$246$		0			0
$247$	27.0267	−	6.22389i	1.71967	−	0.396017i
$248$	3.41960			0.217145
$249$		0			0
$250$	−0.690702	−	1.19633i	−0.0436838	−	0.0756626i
$251$	3.04764	−	5.27867i	0.192365	−	0.333187i	−0.753668	−	0.657255i	$-0.771717\pi$
$251$	3.04764	−	5.27867i	0.192365	−	0.333187i	0.946034	+	0.324068i	$0.105051\pi$
$252$		0			0
$253$	−1.25032	+	2.16563i	−0.0786072	+	0.136152i
$254$	8.54184			0.535963
$255$		0			0
$256$	1.09835	−	1.90239i	0.0686467	−	0.118900i
$257$	2.31016	−	4.00131i	0.144104	−	0.249595i	−0.784934	−	0.619579i	$-0.787303\pi$
$257$	2.31016	−	4.00131i	0.144104	−	0.249595i	0.929038	+	0.369984i	$0.120637\pi$
$258$		0			0
$259$	28.5583			1.77452
$260$	0.291806	−	0.505423i	0.0180971	−	0.0313450i
$261$		0			0
$262$	−12.0164	+	20.8131i	−0.742378	+	1.28584i
$263$	−15.0247	−	26.0236i	−0.926465	−	1.60468i	−0.789189	−	0.614151i	$-0.789499\pi$
$263$	−15.0247	−	26.0236i	−0.926465	−	1.60468i	−0.137276	−	0.990533i	$-0.543835\pi$
$264$		0			0
$265$	5.13706			0.315567
$266$	7.69425	−	25.1171i	0.471765	−	1.54003i
$267$		0			0
$268$	−0.183645	−	0.318082i	−0.0112179	−	0.0194300i
$269$	−0.105639	−	0.182973i	−0.00644095	−	0.0111561i	0.862787	−	0.505568i	$-0.168717\pi$
$269$	−0.105639	−	0.182973i	−0.00644095	−	0.0111561i	−0.869228	+	0.494412i	$0.835384\pi$
$270$		0			0
$271$	3.70364	+	6.41489i	0.224980	+	0.389677i	0.956313	−	0.292343i	$-0.0944350\pi$
$271$	3.70364	+	6.41489i	0.224980	+	0.389677i	−0.731333	+	0.682020i	$0.761102\pi$
$272$	−10.8844	+	18.8524i	−0.659966	+	1.14309i
$273$		0			0
$274$	21.7107			1.31159
$275$	−2.15812	+	3.73798i	−0.130140	+	0.225409i
$276$		0			0
$277$	−29.0668			−1.74646			−0.873229	−	0.487310i	$-0.837978\pi$
$277$	−29.0668			−1.74646			−0.873229	+	0.487310i	$0.837978\pi$
$278$	−9.05295			−0.542960
$279$		0			0
$280$	−6.30296	−	10.9171i	−0.376674	−	0.652419i
$281$	5.73796	−	9.93843i	0.342298	−	0.592877i	−0.642561	−	0.766234i	$-0.722128\pi$
$281$	5.73796	−	9.93843i	0.342298	−	0.592877i	0.984859	+	0.173357i	$0.0554615\pi$
$282$		0			0
$283$	13.6662	+	23.6706i	0.812373	+	1.40707i	0.911199	+	0.411966i	$0.135158\pi$
$283$	13.6662	+	23.6706i	0.812373	+	1.40707i	−0.0988265	+	0.995105i	$0.531509\pi$
$284$	0.282426			0.0167589
$285$		0			0
$286$	37.9371			2.24327
$287$	1.66393	+	2.88201i	0.0982185	+	0.170119i
$288$		0			0
$289$	−7.83868	+	13.5770i	−0.461099	+	0.798647i
$290$	−2.45437	−	4.25109i	−0.144125	−	0.249633i
$291$		0			0
$292$	−0.741724			−0.0434061
$293$	−13.0211			−0.760698			−0.380349	−	0.924843i	$-0.624196\pi$
$293$	−13.0211			−0.760698			−0.380349	+	0.924843i	$0.624196\pi$
$294$		0			0
$295$	−1.91484	+	3.31660i	−0.111486	+	0.193100i
$296$	−18.9150			−1.09941
$297$		0			0
$298$	−3.97236	+	6.88034i	−0.230113	+	0.398567i
$299$	1.84312	+	3.19238i	0.106590	+	0.184620i
$300$		0			0
$301$	−13.8790	−	24.0391i	−0.799971	−	1.38559i
$302$	−8.74932	−	15.1543i	−0.503467	−	0.872030i
$303$		0			0
$304$	−4.86193	+	15.8713i	−0.278851	+	0.910281i
$305$	12.0211			0.688324
$306$		0			0
$307$	−2.01267	−	3.48604i	−0.114869	−	0.198959i	0.802858	−	0.596170i	$-0.203312\pi$
$307$	−2.01267	−	3.48604i	−0.114869	−	0.198959i	−0.917727	+	0.397211i	$0.869978\pi$
$308$	−0.863601	+	1.49580i	−0.0492082	+	0.0852312i
$309$		0			0
$310$	−0.817411	+	1.41580i	−0.0464258	+	0.0804119i
$311$	−15.3578			−0.870860			−0.435430	−	0.900223i	$-0.643404\pi$
$311$	−15.3578			−0.870860			−0.435430	+	0.900223i	$0.643404\pi$
$312$		0			0
$313$	−10.9800	+	19.0179i	−0.620625	+	1.07495i	0.368744	+	0.929531i	$0.379788\pi$
$313$	−10.9800	+	19.0179i	−0.620625	+	1.07495i	−0.989369	+	0.145424i	$0.953546\pi$
$314$	0.952387	−	1.64958i	0.0537463	−	0.0930913i
$315$		0			0
$316$	−1.03986			−0.0584967
$317$	−12.0640	+	20.8954i	−0.677580	+	1.17360i	0.298127	+	0.954526i	$0.403638\pi$
$317$	−12.0640	+	20.8954i	−0.677580	+	1.17360i	−0.975708	+	0.219077i	$0.929695\pi$
$318$		0			0
$319$	−7.66877	+	13.2827i	−0.429369	+	0.743689i
$320$	4.16624	+	7.21613i	0.232900	+	0.403394i
$321$		0			0
$322$	3.49154			0.194576
$323$	−7.29826	+	23.8245i	−0.406086	+	1.32563i
$324$		0			0
$325$	3.18132	+	5.51021i	0.176468	+	0.305652i
$326$	−8.02044	−	13.8918i	−0.444211	−	0.769396i
$327$		0			0
$328$	−1.10207	−	1.90884i	−0.0608517	−	0.105398i
$329$	5.96076	−	10.3243i	0.328627	−	0.569199i
$330$		0			0
$331$	−24.8416			−1.36542			−0.682710	−	0.730690i	$-0.739199\pi$
$331$	−24.8416			−1.36542			−0.682710	+	0.730690i	$0.739199\pi$
$332$	−0.352173	+	0.609981i	−0.0193280	+	0.0334771i
$333$		0			0
$334$	−28.0582			−1.53528
$335$	4.00426			0.218776
$336$		0			0
$337$	−0.284651	−	0.493031i	−0.0155059	−	0.0268571i	0.858168	−	0.513368i	$-0.171603\pi$
$337$	−0.284651	−	0.493031i	−0.0155059	−	0.0268571i	−0.873674	+	0.486511i	$0.838269\pi$
$338$	18.9827	−	32.8790i	1.03252	−	1.78838i
$339$		0			0
$340$	0.262168	+	0.454089i	0.0142181	+	0.0246264i
$341$	5.10806			0.276617
$342$		0			0
$343$	−21.9557			−1.18550
$344$	9.19248	+	15.9218i	0.495625	+	0.858448i
$345$		0			0
$346$	8.46172	−	14.6561i	0.454905	−	0.787918i
$347$	4.68682	+	8.11782i	0.251602	+	0.435787i	0.963967	−	0.266022i	$-0.0857093\pi$
$347$	4.68682	+	8.11782i	0.251602	+	0.435787i	−0.712365	+	0.701809i	$0.752376\pi$
$348$		0			0
$349$	14.8297			0.793815			0.396907	−	0.917859i	$-0.370083\pi$
$349$	14.8297			0.793815			0.396907	+	0.917859i	$0.370083\pi$
$350$	6.02657			0.322134
$351$		0			0
$352$	1.11890	−	1.93799i	0.0596375	−	0.103295i
$353$	−31.2650			−1.66407			−0.832034	−	0.554725i	$-0.812824\pi$
$353$	−31.2650			−1.66407			−0.832034	+	0.554725i	$0.812824\pi$
$354$		0			0
$355$	−1.53953	+	2.66654i	−0.0817097	+	0.141525i
$356$	−0.451372	−	0.781799i	−0.0239226	−	0.0414352i
$357$		0			0
$358$	13.2504	+	22.9504i	0.700307	+	1.21297i
$359$	5.43561	+	9.41475i	0.286880	+	0.496892i	0.973063	−	0.230537i	$-0.0740484\pi$
$359$	5.43561	+	9.41475i	0.286880	+	0.496892i	−0.686183	+	0.727429i	$0.740715\pi$
$360$		0			0
$361$	−1.34631	+	18.9522i	−0.0708586	+	0.997486i
$362$	4.46172			0.234503
$363$		0			0
$364$	1.27305	+	2.20498i	0.0667258	+	0.115572i
$365$	4.04320	−	7.00303i	0.211631	−	0.366555i
$366$		0			0
$367$	9.36477	−	16.2203i	0.488837	−	0.846691i	−0.511080	−	0.859533i	$-0.670755\pi$
$367$	9.36477	−	16.2203i	0.488837	−	0.846691i	0.999918	+	0.0128422i	$0.00408791\pi$
$368$	−2.20627			−0.115010
$369$		0			0
$370$	4.52140	−	7.83129i	0.235056	−	0.407129i
$371$	−11.2056	+	19.4086i	−0.581764	+	1.00765i
$372$		0			0
$373$	29.3275			1.51852			0.759259	−	0.650788i	$-0.225561\pi$
$373$	29.3275			1.51852			0.759259	+	0.650788i	$0.225561\pi$
$374$	−17.0420	+	29.5176i	−0.881221	+	1.52632i
$375$		0			0
$376$	−3.94800	+	6.83813i	−0.203602	+	0.352650i
$377$	11.3046	+	19.5802i	0.582219	+	1.00843i
$378$		0			0
$379$	−10.6486			−0.546980			−0.273490	−	0.961875i	$-0.588178\pi$
$379$	−10.6486			−0.546980			−0.273490	+	0.961875i	$0.588178\pi$
$380$	0.272515	+	0.292560i	0.0139797	+	0.0150080i
$381$		0			0
$382$	−19.0295	−	32.9600i	−0.973632	−	1.68638i
$383$	4.63977	+	8.03632i	0.237081	+	0.410637i	0.959876	−	0.280426i	$-0.0904759\pi$
$383$	4.63977	+	8.03632i	0.237081	+	0.410637i	−0.722794	+	0.691063i	$0.757143\pi$
$384$		0			0
$385$	−9.41513	−	16.3075i	−0.479839	−	0.831106i
$386$	15.3658	−	26.6143i	0.782098	−	1.35463i
$387$		0			0
$388$	−0.183450			−0.00931325
$389$	0.666237	−	1.15396i	0.0337796	−	0.0585079i	−0.848641	−	0.528969i	$-0.822579\pi$
$389$	0.666237	−	1.15396i	0.0337796	−	0.0585079i	0.882421	+	0.470461i	$0.155912\pi$
$390$		0			0
$391$	−3.31184			−0.167487
$392$	34.7686			1.75608
$393$		0			0
$394$	−8.74613	−	15.1487i	−0.440623	−	0.763182i
$395$	5.66836	−	9.81790i	0.285206	−	0.493992i
$396$		0			0
$397$	15.8324	+	27.4225i	0.794605	+	1.37630i	0.923090	+	0.384584i	$0.125655\pi$
$397$	15.8324	+	27.4225i	0.794605	+	1.37630i	−0.128485	+	0.991711i	$0.541011\pi$
$398$	12.1143			0.607235
$399$		0			0
$400$	−3.80814			−0.190407
$401$	−2.44425	−	4.23356i	−0.122060	−	0.211414i	0.798520	−	0.601968i	$-0.205617\pi$
$401$	−2.44425	−	4.23356i	−0.122060	−	0.211414i	−0.920580	+	0.390554i	$0.872283\pi$
$402$		0			0
$403$	3.76493	−	6.52106i	0.187545	−	0.324837i
$404$	0.206367	+	0.357438i	0.0102671	+	0.0177832i
$405$		0			0
$406$	21.4151			1.06281
$407$	−28.2546			−1.40053
$408$		0			0
$409$	11.3941	−	19.7351i	0.563400	−	0.975837i	−0.433797	−	0.901011i	$-0.642826\pi$
$409$	11.3941	−	19.7351i	0.563400	−	0.975837i	0.997197	−	0.0748266i	$-0.0238403\pi$
$410$	1.05374			0.0520407
$411$		0			0
$412$	−0.737087	+	1.27667i	−0.0363137	+	0.0628972i
$413$	−8.35377	−	14.4692i	−0.411062	−	0.711980i
$414$		0			0
$415$	−3.83945	−	6.65012i	−0.188471	−	0.326441i
$416$	−1.64938	−	2.85682i	−0.0808677	−	0.140067i
$417$		0			0
$418$	−7.61243	+	24.8500i	−0.372336	+	1.21545i
$419$	−30.8809			−1.50863			−0.754316	−	0.656512i	$-0.772031\pi$
$419$	−30.8809			−1.50863			−0.754316	+	0.656512i	$0.772031\pi$
$420$		0			0
$421$	−13.2891	−	23.0174i	−0.647671	−	1.12180i	−0.983678	−	0.179939i	$-0.942410\pi$
$421$	−13.2891	−	23.0174i	−0.647671	−	1.12180i	0.336007	−	0.941859i	$-0.390923\pi$
$422$	5.43429	−	9.41246i	0.264537	−	0.458191i
$423$		0			0
$424$	7.42180	−	12.8549i	0.360434	−	0.624291i
$425$	−5.71641			−0.277287
$426$		0			0
$427$	−26.2218	+	45.4175i	−1.26896	+	2.19791i
$428$	−0.627347	+	1.08660i	−0.0303240	+	0.0525227i
$429$		0			0
$430$	−8.78938			−0.423861
$431$	8.23718	−	14.2672i	0.396771	−	0.687228i	−0.596554	−	0.802573i	$-0.703464\pi$
$431$	8.23718	−	14.2672i	0.396771	−	0.687228i	0.993325	+	0.115345i	$0.0367974\pi$
$432$		0			0
$433$	18.4021	−	31.8733i	0.884346	−	1.53173i	0.0378851	−	0.999282i	$-0.487938\pi$
$433$	18.4021	−	31.8733i	0.884346	−	1.53173i	0.846461	−	0.532450i	$-0.178729\pi$
$434$	−3.56607	−	6.17662i	−0.171177	−	0.296487i
$435$		0			0
$436$	0.822473			0.0393893
$437$	−2.46095	+	0.566723i	−0.117723	+	0.0271100i
$438$		0			0
$439$	−4.79140	−	8.29895i	−0.228681	−	0.396087i	0.728736	−	0.684794i	$-0.240108\pi$
$439$	−4.79140	−	8.29895i	−0.228681	−	0.396087i	−0.957417	+	0.288707i	$0.906775\pi$
$440$	6.23593	+	10.8010i	0.297287	+	0.514915i
$441$		0			0
$442$	25.1219	+	43.5123i	1.19492	+	2.06967i
$443$	−11.1218	+	19.2635i	−0.528412	+	0.915236i	0.471040	+	0.882112i	$0.343879\pi$
$443$	−11.1218	+	19.2635i	−0.528412	+	0.915236i	−0.999451	+	0.0331236i	$0.989454\pi$
$444$		0			0
$445$	9.84186			0.466549
$446$	−18.8931	+	32.7239i	−0.894616	+	1.54952i
$447$		0			0
$448$	−36.3516			−1.71745
$449$	0.491188			0.0231806			0.0115903	−	0.999933i	$-0.496311\pi$
$449$	0.491188			0.0231806			0.0115903	+	0.999933i	$0.496311\pi$
$450$		0			0
$451$	−1.64623	−	2.85136i	−0.0775180	−	0.134265i
$452$	−0.294873	+	0.510736i	−0.0138697	+	0.0240230i
$453$		0			0
$454$	17.3312	+	30.0185i	0.813394	+	1.40884i
$455$	−27.7579			−1.30131
$456$		0			0
$457$	13.2607			0.620311			0.310156	−	0.950686i	$-0.399619\pi$
$457$	13.2607			0.620311			0.310156	+	0.950686i	$0.399619\pi$
$458$	3.44336	+	5.96407i	0.160897	+	0.278683i
$459$		0			0
$460$	−0.0265707	+	0.0460218i	−0.00123887	+	0.00214578i
$461$	11.6867	+	20.2420i	0.544305	+	0.942763i	0.998650	+	0.0519379i	$0.0165398\pi$
$461$	11.6867	+	20.2420i	0.544305	+	0.942763i	−0.454346	+	0.890825i	$0.650127\pi$
$462$		0			0
$463$	−0.981649			−0.0456211			−0.0228105	−	0.999740i	$-0.507261\pi$
$463$	−0.981649			−0.0456211			−0.0228105	+	0.999740i	$0.507261\pi$
$464$	−13.5320			−0.628207
$465$		0			0
$466$	−8.83851	+	15.3087i	−0.409436	+	0.709164i
$467$	18.8498			0.872264			0.436132	−	0.899883i	$-0.356348\pi$
$467$	18.8498			0.872264			0.436132	+	0.899883i	$0.356348\pi$
$468$		0			0
$469$	−8.73457	+	15.1287i	−0.403325	+	0.698579i
$470$	−1.88744	−	3.26914i	−0.0870610	−	0.150794i
$471$		0			0
$472$	5.53296	+	9.58337i	0.254675	+	0.441110i
$473$	13.7314	+	23.7834i	0.631369	+	1.09356i
$474$		0			0
$475$	−4.24772	+	0.978193i	−0.194899	+	0.0448826i
$476$	−2.28750			−0.104847
$477$		0			0
$478$	−8.84440	−	15.3189i	−0.404533	−	0.700672i
$479$	10.0795	−	17.4583i	0.460546	−	0.797688i	−0.538443	−	0.842662i	$-0.680987\pi$
$479$	10.0795	−	17.4583i	0.460546	−	0.797688i	0.998988	+	0.0449739i	$0.0143205\pi$
$480$		0			0
$481$	−20.8252	+	36.0704i	−0.949549	+	1.64467i
$482$	1.50958			0.0687596
$483$		0			0
$484$	0.349931	−	0.606098i	0.0159059	−	0.0275499i
$485$	1.00000	−	1.73205i	0.0454077	−	0.0786484i
$486$		0			0
$487$	2.79159			0.126499			0.0632494	−	0.997998i	$-0.479854\pi$
$487$	2.79159			0.126499			0.0632494	+	0.997998i	$0.479854\pi$
$488$	17.3675	−	30.0814i	0.786190	−	1.36172i
$489$		0			0
$490$	−8.31098	+	14.3950i	−0.375452	+	0.650302i
$491$	2.88904	+	5.00397i	0.130381	+	0.225826i	0.923823	−	0.382819i	$-0.125047\pi$
$491$	2.88904	+	5.00397i	0.130381	+	0.225826i	−0.793443	+	0.608645i	$0.791713\pi$
$492$		0			0
$493$	−20.3129			−0.914849
$494$	26.1132	+	28.0341i	1.17489	+	1.26131i
$495$		0			0
$496$	2.25337	+	3.90295i	0.101179	+	0.175248i
$497$	−6.71641	−	11.6332i	−0.301272	−	0.521819i
$498$		0			0
$499$	−6.39792	−	11.0815i	−0.286410	−	0.496077i	0.686540	−	0.727092i	$-0.259129\pi$
$499$	−6.39792	−	11.0815i	−0.286410	−	0.496077i	−0.972950	+	0.231015i	$0.925795\pi$
$500$	−0.0458624	+	0.0794360i	−0.00205103	+	0.00355249i
$501$		0			0
$502$	8.42004			0.375805
$503$	15.8339	−	27.4252i	0.706000	−	1.22283i	−0.260329	−	0.965520i	$-0.583831\pi$
$503$	15.8339	−	27.4252i	0.706000	−	1.22283i	0.966329	−	0.257308i	$-0.0828356\pi$
$504$		0			0
$505$	−4.49970			−0.200234
$506$	−3.45440			−0.153567
$507$		0			0
$508$	−0.283588	−	0.491189i	−0.0125822	−	0.0217930i
$509$	−2.74405	+	4.75283i	−0.121628	+	0.210665i	−0.920410	−	0.390955i	$-0.872145\pi$
$509$	−2.74405	+	4.75283i	−0.121628	+	0.210665i	0.798782	+	0.601621i	$0.205478\pi$
$510$		0			0
$511$	17.6391	+	30.5517i	0.780306	+	1.35153i
$512$	23.9817			1.05985
$513$		0			0
$514$	6.38252			0.281521
$515$	−8.03585	−	13.9185i	−0.354102	−	0.613323i
$516$		0			0
$517$	−5.89737	+	10.2145i	−0.259366	+	0.449235i
$518$	19.7252	+	34.1651i	0.866678	+	1.50113i
$519$		0			0
$520$	18.3850			0.806234
$521$	−8.28086			−0.362791			−0.181396	−	0.983410i	$-0.558061\pi$
$521$	−8.28086			−0.362791			−0.181396	+	0.983410i	$0.558061\pi$
$522$		0			0
$523$	−5.77584	+	10.0040i	−0.252560	+	0.437446i	−0.964230	−	0.265067i	$-0.914606\pi$
$523$	−5.77584	+	10.0040i	−0.252560	+	0.437446i	0.711670	+	0.702514i	$0.247939\pi$
$524$	1.59578			0.0697118
$525$		0			0
$526$	20.7552	−	35.9491i	0.904970	−	1.56745i
$527$	3.38254	+	5.85874i	0.147346	+	0.255211i
$528$		0			0
$529$	11.3322	+	19.6279i	0.492703	+	0.853387i
$530$	3.54817	+	6.14561i	0.154123	+	0.266948i
$531$		0			0
$532$	−1.69978	+	0.391436i	−0.0736948	+	0.0169709i
$533$	−4.85347			−0.210227
$534$		0			0
$535$	−6.83945	−	11.8463i	−0.295695	−	0.512159i
$536$	5.78518	−	10.0202i	0.249882	−	0.432808i
$537$		0			0
$538$	0.145931	−	0.252759i	0.00629152	−	0.0108972i
$539$	51.9360			2.23704
$540$		0			0
$541$	12.9374	−	22.4083i	0.556224	−	0.963409i	−0.441583	−	0.897220i	$-0.645583\pi$
$541$	12.9374	−	22.4083i	0.556224	−	0.963409i	0.997807	−	0.0661881i	$-0.0210837\pi$
$542$	−5.11622	+	8.86155i	−0.219760	+	0.380636i
$543$		0			0
$544$	2.96372			0.127069
$545$	−4.48337	+	7.76542i	−0.192046	+	0.332634i
$546$		0			0
$547$	−3.20287	+	5.54753i	−0.136945	+	0.237195i	−0.926339	−	0.376692i	$-0.877062\pi$
$547$	−3.20287	+	5.54753i	−0.136945	+	0.237195i	0.789394	+	0.613887i	$0.210395\pi$
$548$	−0.720793	−	1.24845i	−0.0307907	−	0.0533311i
$549$		0			0
$550$	−5.96248			−0.254241
$551$	−15.0940	+	3.47595i	−0.643028	+	0.148080i
$552$		0			0
$553$	24.7291	+	42.8320i	1.05159	+	1.82140i
$554$	−20.0765	−	34.7736i	−0.852970	−	1.47739i
$555$		0			0
$556$	0.300557	+	0.520580i	0.0127464	+	0.0220775i
$557$	−1.76281	+	3.05327i	−0.0746925	+	0.129371i	−0.900953	−	0.433918i	$-0.857131\pi$
$557$	−1.76281	+	3.05327i	−0.0746925	+	0.129371i	0.826260	+	0.563289i	$0.190464\pi$
$558$		0			0
$559$	40.4832			1.71226
$560$	8.30677	−	14.3878i	0.351025	−	0.607993i
$561$		0			0
$562$	15.8529			0.668713
$563$	30.7179			1.29461			0.647303	−	0.762232i	$-0.275897\pi$
$563$	30.7179			1.29461			0.647303	+	0.762232i	$0.275897\pi$
$564$		0			0
$565$	−3.21476	−	5.56813i	−0.135246	−	0.234253i
$566$	−18.8786	+	32.6986i	−0.793525	+	1.37443i
$567$		0			0
$568$	4.44849	+	7.70501i	0.186654	+	0.323295i
$569$	−9.17896			−0.384802			−0.192401	−	0.981316i	$-0.561627\pi$
$569$	−9.17896			−0.384802			−0.192401	+	0.981316i	$0.561627\pi$
$570$		0			0
$571$	−7.49001			−0.313447			−0.156724	−	0.987643i	$-0.550093\pi$
$571$	−7.49001			−0.313447			−0.156724	+	0.987643i	$0.550093\pi$
$572$	−1.25951	−	2.18153i	−0.0526627	−	0.0912145i
$573$		0			0
$574$	−2.29855	+	3.98121i	−0.0959398	+	0.166173i
$575$	−0.289678	−	0.501738i	−0.0120804	−	0.0209239i
$576$		0			0
$577$	32.6093			1.35754			0.678771	−	0.734350i	$-0.262513\pi$
$577$	32.6093			1.35754			0.678771	+	0.734350i	$0.262513\pi$
$578$	−21.6568			−0.900803
$579$		0			0
$580$	−0.162969	+	0.282271i	−0.00676694	+	0.0117207i
$581$	33.5003			1.38983
$582$		0			0
$583$	11.0864	−	19.2022i	0.459152	−	0.795275i
$584$	−11.6829	−	20.2354i	−0.483442	−	0.837346i
$585$		0			0
$586$	−8.99367	−	15.5775i	−0.371525	−	0.643500i
$587$	−9.19474	−	15.9258i	−0.379508	−	0.657326i	0.611483	−	0.791258i	$-0.290573\pi$
$587$	−9.19474	−	15.9258i	−0.379508	−	0.657326i	−0.990991	+	0.133931i	$0.957240\pi$
$588$		0			0
$589$	3.51603	+	3.77466i	0.144875	+	0.155532i
$590$	−5.29033			−0.217800
$591$		0			0
$592$	−12.4642	−	21.5886i	−0.512276	−	0.887288i
$593$	0.208669	−	0.361425i	0.00856900	−	0.0148419i	−0.861709	−	0.507403i	$-0.830606\pi$
$593$	0.208669	−	0.361425i	0.00856900	−	0.0148419i	0.870278	+	0.492561i	$0.163939\pi$
$594$		0			0
$595$	12.4693	−	21.5975i	0.511193	−	0.885412i
$596$	0.527528			0.0216084
$597$		0			0
$598$	−2.54609	+	4.40996i	−0.104118	+	0.180337i
$599$	−19.4828	+	33.7452i	−0.796045	+	1.37879i	0.126129	+	0.992014i	$0.459745\pi$
$599$	−19.4828	+	33.7452i	−0.796045	+	1.37879i	−0.922174	+	0.386776i	$0.873589\pi$
$600$		0			0
$601$	10.0358			0.409367			0.204683	−	0.978828i	$-0.434383\pi$
$601$	10.0358			0.409367			0.204683	+	0.978828i	$0.434383\pi$
$602$	19.1725	−	33.2077i	0.781411	−	1.35344i
$603$		0			0
$604$	−0.580953	+	1.00624i	−0.0236386	+	0.0409433i
$605$	3.81500	+	6.60778i	0.155102	+	0.268644i
$606$		0			0
$607$	−6.25423			−0.253851			−0.126926	−	0.991912i	$-0.540511\pi$
$607$	−6.25423			−0.253851			−0.126926	+	0.991912i	$0.540511\pi$
$608$	2.20227	−	0.507152i	0.0893137	−	0.0205677i
$609$		0			0
$610$	8.30296	+	14.3812i	0.336177	+	0.582276i
$611$	8.69340	+	15.0574i	0.351697	+	0.609157i
$612$		0			0
$613$	−14.9371	−	25.8719i	−0.603306	−	1.04496i	−0.992317	−	0.123723i	$-0.960517\pi$
$613$	−14.9371	−	25.8719i	−0.603306	−	1.04496i	0.389011	−	0.921233i	$-0.372817\pi$
$614$	2.78031	−	4.81563i	0.112204	−	0.194343i
$615$		0			0
$616$	−54.4103			−2.19225
$617$	−15.3197	+	26.5346i	−0.616749	+	1.06824i	0.373326	+	0.927700i	$0.378217\pi$
$617$	−15.3197	+	26.5346i	−0.616749	+	1.06824i	−0.990075	+	0.140540i	$0.955116\pi$
$618$		0			0
$619$	21.1480			0.850011			0.425006	−	0.905191i	$-0.360272\pi$
$619$	21.1480			0.850011			0.425006	+	0.905191i	$0.360272\pi$
$620$	0.108552			0.00435954
$621$		0			0
$622$	−10.6076	−	18.3730i	−0.425328	−	0.736690i
$623$	−21.4683	+	37.1841i	−0.860108	+	1.48975i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−30.3356			−1.21245
$627$		0			0
$628$	−0.126476			−0.00504696
$629$	−18.7101	−	32.4068i	−0.746020	−	1.29214i
$630$		0			0
$631$	13.0124	−	22.5381i	0.518014	−	0.897227i	−0.481767	−	0.876299i	$-0.660005\pi$
$631$	13.0124	−	22.5381i	0.518014	−	0.897227i	0.999781	−	0.0209274i	$-0.00666189\pi$
$632$	−16.3788	−	28.3690i	−0.651515	−	1.12846i
$633$		0			0
$634$	−33.3304			−1.32372
$635$	6.18345			0.245383
$636$		0			0
$637$	38.2798	−	66.3025i	1.51670	−	2.62700i
$638$	−21.1873			−0.838815
$639$		0			0
$640$	−5.23680	+	9.07040i	−0.207003	+	0.358539i
$641$	−9.59982	−	16.6274i	−0.379170	−	0.656742i	0.611771	−	0.791035i	$-0.290457\pi$
$641$	−9.59982	−	16.6274i	−0.379170	−	0.656742i	−0.990942	+	0.134292i	$0.957124\pi$
$642$		0			0
$643$	−4.27305	−	7.40113i	−0.168513	−	0.291872i	0.769385	−	0.638786i	$-0.220563\pi$
$643$	−4.27305	−	7.40113i	−0.168513	−	0.291872i	−0.937897	+	0.346914i	$0.887230\pi$
$644$	−0.115919	−	0.200777i	−0.00456783	−	0.00791172i
$645$		0			0
$646$	−33.5429	+	7.72446i	−1.31973	+	0.303915i
$647$	21.6966			0.852983			0.426492	−	0.904492i	$-0.359749\pi$
$647$	21.6966			0.852983			0.426492	+	0.904492i	$0.359749\pi$
$648$		0			0
$649$	8.26493	+	14.3153i	0.324427	+	0.561924i
$650$	−4.39469	+	7.61182i	−0.172374	+	0.298560i
$651$		0			0
$652$	−0.532555	+	0.922413i	−0.0208565	+	0.0361245i
$653$	4.39011			0.171798			0.0858991	−	0.996304i	$-0.472624\pi$
$653$	4.39011			0.171798			0.0858991	+	0.996304i	$0.472624\pi$
$654$		0			0
$655$	−8.69872	+	15.0666i	−0.339887	+	0.588702i
$656$	1.45244	−	2.51569i	0.0567081	−	0.0982213i
$657$		0			0
$658$	16.4684			0.642006
$659$	−7.57327	+	13.1173i	−0.295013	+	0.510977i	−0.974988	−	0.222258i	$-0.928657\pi$
$659$	−7.57327	+	13.1173i	−0.295013	+	0.510977i	0.679975	+	0.733235i	$0.261991\pi$
$660$		0			0
$661$	−3.65794	+	6.33574i	−0.142277	+	0.246432i	−0.928354	−	0.371698i	$-0.878776\pi$
$661$	−3.65794	+	6.33574i	−0.142277	+	0.246432i	0.786076	+	0.618129i	$0.212109\pi$
$662$	−17.1582	−	29.7188i	−0.666871	−	1.15505i
$663$		0			0
$664$	−22.1883			−0.861072
$665$	5.56988	−	18.1823i	0.215991	−	0.705080i
$666$		0			0
$667$	−1.02936	−	1.78290i	−0.0398568	−	0.0690340i
$668$	0.931530	+	1.61346i	0.0360420	+	0.0624265i
$669$		0			0
$670$	2.76575	+	4.79041i	0.106850	+	0.185070i
$671$	25.9429	−	44.9345i	1.00152	−	1.73468i
$672$		0			0
$673$	39.7027			1.53043			0.765213	−	0.643777i	$-0.222634\pi$
$673$	39.7027			1.53043			0.765213	+	0.643777i	$0.222634\pi$
$674$	0.393218	−	0.681074i	0.0151462	−	0.0262340i
$675$		0			0
$676$	−2.52090			−0.0969575
$677$	9.45197			0.363269			0.181634	−	0.983366i	$-0.441861\pi$
$677$	9.45197			0.363269			0.181634	+	0.983366i	$0.441861\pi$
$678$		0			0
$679$	4.36264	+	7.55632i	0.167423	+	0.289985i
$680$	−8.25883	+	14.3047i	−0.316712	+	0.548561i
$681$		0			0
$682$	3.52815	+	6.11093i	0.135100	+	0.234000i
$683$	6.27600			0.240145			0.120072	−	0.992765i	$-0.461687\pi$
$683$	6.27600			0.240145			0.120072	+	0.992765i	$0.461687\pi$
$684$		0			0
$685$	15.7164			0.600493
$686$	−15.1648	−	26.2663i	−0.578996	−	1.00285i
$687$		0			0
$688$	−12.1149	+	20.9836i	−0.461877	+	0.799994i
$689$	−16.3426	−	28.3063i	−0.622604	−	1.07838i
$690$		0			0
$691$	−33.8913			−1.28929			−0.644643	−	0.764483i	$-0.722994\pi$
$691$	−33.8913			−1.28929			−0.644643	+	0.764483i	$0.722994\pi$
$692$	−1.12371			−0.0427171
$693$		0			0
$694$	−6.47439	+	11.2140i	−0.245765	+	0.425677i
$695$	−6.55344			−0.248586
$696$		0			0
$697$	2.18026	−	3.77632i	0.0825832	−	0.143038i
$698$	10.2429	+	17.7412i	0.387699	+	0.671514i
$699$		0			0
$700$	−0.200081	−	0.346551i	−0.00756237	−	0.0130984i
$701$	20.1520	+	34.9043i	0.761131	+	1.31832i	0.942268	+	0.334860i	$0.108689\pi$
$701$	20.1520	+	34.9043i	0.761131	+	1.31832i	−0.181136	+	0.983458i	$0.557978\pi$
$702$		0			0
$703$	−19.4484	−	20.8790i	−0.733512	−	0.787467i
$704$	35.9650			1.35548
$705$		0			0
$706$	−21.5948	−	37.4033i	−0.812730	−	1.40769i
$707$	9.81529	−	17.0006i	0.369142	−	0.639373i
$708$		0			0
$709$	2.63706	−	4.56751i	0.0990367	−	0.171537i	−0.812249	−	0.583310i	$-0.801757\pi$
$709$	2.63706	−	4.56751i	0.0990367	−	0.171537i	0.911286	+	0.411774i	$0.135091\pi$
$710$	−4.25342			−0.159628
$711$		0			0
$712$	14.2191	−	24.6282i	0.532884	−	0.922981i
$713$	−0.342820	+	0.593782i	−0.0128387	+	0.0222373i
$714$		0			0
$715$	27.4628			1.02705
$716$	0.879826	−	1.52390i	0.0328806	−	0.0569509i
$717$		0			0
$718$	−7.50877	+	13.0056i	−0.280225	+	0.485364i
$719$	11.8834	+	20.5827i	0.443176	+	0.767604i	0.997923	−	0.0644151i	$-0.0205182\pi$
$719$	11.8834	+	20.5827i	0.443176	+	0.767604i	−0.554747	+	0.832019i	$0.687185\pi$
$720$		0			0
$721$	70.1151			2.61122
$722$	−23.6030	+	11.4797i	−0.878414	+	0.427231i
$723$		0			0
$724$	−0.148128	−	0.256566i	−0.00550515	−	0.00953520i
$725$	−1.77672	−	3.07737i	−0.0659858	−	0.114291i
$726$		0			0
$727$	16.9225	+	29.3106i	0.627620	+	1.08707i	0.988028	+	0.154275i	$0.0493040\pi$
$727$	16.9225	+	29.3106i	0.627620	+	1.08707i	−0.360408	+	0.932795i	$0.617363\pi$
$728$	−40.1035	+	69.4613i	−1.48634	+	2.57441i
$729$		0			0
$730$	11.1706			0.413442
$731$	−18.1857	+	31.4986i	−0.672624	+	1.16502i
$732$		0			0
$733$	24.6249			0.909542			0.454771	−	0.890608i	$-0.349721\pi$
$733$	24.6249			0.909542			0.454771	+	0.890608i	$0.349721\pi$
$734$	25.8731			0.954992
$735$		0			0
$736$	0.150186	+	0.260130i	0.00553594	+	0.00958853i
$737$	8.64168	−	14.9678i	0.318320	−	0.551347i
$738$		0			0
$739$	−9.22966	−	15.9862i	−0.339518	−	0.588063i	0.644824	−	0.764331i	$-0.276931\pi$
$739$	−9.22966	−	15.9862i	−0.339518	−	0.588063i	−0.984342	+	0.176268i	$0.943597\pi$
$740$	−0.600439			−0.0220726
$741$		0			0
$742$	−30.9588			−1.13653
$743$	−4.47864	−	7.75723i	−0.164305	−	0.284585i	0.772103	−	0.635497i	$-0.219205\pi$
$743$	−4.47864	−	7.75723i	−0.164305	−	0.284585i	−0.936408	+	0.350912i	$0.885872\pi$
$744$		0			0
$745$	−2.87560	+	4.98069i	−0.105354	+	0.182478i
$746$	20.2565	+	35.0853i	0.741644	+	1.28457i
$747$		0			0
$748$	2.26317			0.0827497
$749$	59.6761			2.18052
$750$		0			0
$751$	14.6128	−	25.3101i	0.533228	−	0.923578i	−0.466019	−	0.884775i	$-0.654312\pi$
$751$	14.6128	−	25.3101i	0.533228	−	0.923578i	0.999247	−	0.0388032i	$-0.0123545\pi$
$752$	−10.4063			−0.379477
$753$		0			0
$754$	−15.6163	+	27.0482i	−0.568711	+	0.985037i
$755$	−6.33364	−	10.9702i	−0.230505	−	0.399246i
$756$		0			0
$757$	−9.33886	−	16.1754i	−0.339427	−	0.587904i	0.644898	−	0.764268i	$-0.276900\pi$
$757$	−9.33886	−	16.1754i	−0.339427	−	0.587904i	−0.984325	+	0.176364i	$0.943566\pi$
$758$	−7.35499	−	12.7392i	−0.267145	−	0.462709i
$759$		0			0
$760$	−3.68911	+	12.0427i	−0.133818	+	0.436836i
$761$	−41.5952			−1.50782			−0.753912	−	0.656975i	$-0.771836\pi$
$761$	−41.5952			−1.50782			−0.753912	+	0.656975i	$0.771836\pi$
$762$		0			0
$763$	−19.5593	−	33.8778i	−0.708096	−	1.22646i
$764$	−1.26355	+	2.18854i	−0.0457137	+	0.0791785i
$765$		0			0
$766$	−6.40940	+	11.1014i	−0.231581	+	0.401110i
$767$	24.3669			0.879838
$768$		0			0
$769$	−17.6255	+	30.5282i	−0.635590	+	1.10087i	0.350800	+	0.936450i	$0.385910\pi$
$769$	−17.6255	+	30.5282i	−0.635590	+	1.10087i	−0.986390	+	0.164424i	$0.947424\pi$
$770$	13.0061	−	22.5272i	0.468707	−	0.811824i
$771$		0			0
$772$	−2.04057			−0.0734417
$773$	23.9762	−	41.5280i	0.862364	−	1.49366i	−0.00727780	−	0.999974i	$-0.502317\pi$
$773$	23.9762	−	41.5280i	0.862364	−	1.49366i	0.869641	−	0.493684i	$-0.164350\pi$
$774$		0			0
$775$	−0.591725	+	1.02490i	−0.0212554	+	0.0368154i
$776$	−2.88952	−	5.00479i	−0.103728	−	0.179661i
$777$		0			0
$778$	1.84068			0.0659917
$779$	0.973891	−	3.17917i	0.0348933	−	0.113906i
$780$		0			0
$781$	6.64499	+	11.5095i	0.237776	+	0.411841i
$782$	−2.28750	−	3.96206i	−0.0818007	−	0.141683i
$783$		0			0
$784$	22.9110	+	39.6830i	0.818250	+	1.41725i
$785$	0.689434	−	1.19414i	0.0246070	−	0.0426205i
$786$		0			0
$787$	−5.26074			−0.187525			−0.0937626	−	0.995595i	$-0.529889\pi$
$787$	−5.26074			−0.187525			−0.0937626	+	0.995595i	$0.529889\pi$
$788$	−0.580741	+	1.00587i	−0.0206880	+	0.0358327i
$789$		0			0
$790$	15.6606			0.557179
$791$	28.0497			0.997333
$792$		0			0
$793$	−38.2429	−	66.2386i	−1.35804	−	2.35220i
$794$	−21.8709	+	37.8815i	−0.776170	+	1.34437i
$795$		0			0
$796$	−0.402193	−	0.696619i	−0.0142554	−	0.0246910i
$797$	21.0174			0.744474			0.372237	−	0.928138i	$-0.378591\pi$
$797$	21.0174			0.744474			0.372237	+	0.928138i	$0.378591\pi$
$798$		0			0
$799$	−15.6209			−0.552627
$800$	0.259229	+	0.448998i	0.00916514	+	0.0158745i
$801$		0			0
$802$	3.37649	−	5.84825i	0.119228	−	0.206509i
$803$	−17.4515	−	30.2268i	−0.615849	−	1.06668i
$804$		0			0
$805$	2.52753			0.0890837
$806$	10.4018			0.366387
$807$		0			0
$808$	−6.50098	+	11.2600i	−0.228704	+	0.396126i
$809$	−35.3856			−1.24409			−0.622046	−	0.782981i	$-0.713698\pi$
$809$	−35.3856			−1.24409			−0.622046	+	0.782981i	$0.713698\pi$
$810$		0			0
$811$	−2.67523	+	4.63364i	−0.0939401	+	0.162709i	−0.909166	−	0.416434i	$-0.863280\pi$
$811$	−2.67523	+	4.63364i	−0.0939401	+	0.162709i	0.815226	+	0.579143i	$0.196613\pi$
$812$	−0.710978	−	1.23145i	−0.0249504	−	0.0432154i
$813$		0			0
$814$	−19.5155	−	33.8018i	−0.684017	−	1.18475i
$815$	−5.80601	−	10.0563i	−0.203376	−	0.352257i
$816$		0			0
$817$	−8.12332	+	26.5178i	−0.284199	+	0.927740i
$818$	31.4796			1.10066
$819$		0			0
$820$	−0.0349842	−	0.0605943i	−0.00122170	−	0.00211605i
$821$	3.81886	−	6.61446i	0.133279	−	0.230846i	−0.791660	−	0.610962i	$-0.790783\pi$
$821$	3.81886	−	6.61446i	0.133279	−	0.230846i	0.924939	+	0.380116i	$0.124116\pi$
$822$		0			0
$823$	−13.7866	+	23.8791i	−0.480570	+	0.832372i	−0.999752	−	0.0222919i	$-0.992904\pi$
$823$	−13.7866	+	23.8791i	−0.480570	+	0.832372i	0.519181	+	0.854664i	$0.326237\pi$
$824$	−46.4394			−1.61779
$825$		0			0
$826$	11.5399	−	19.9877i	0.401525	−	0.695462i
$827$	−9.51585	+	16.4819i	−0.330898	+	0.573133i	−0.982688	−	0.185267i	$-0.940685\pi$
$827$	−9.51585	+	16.4819i	−0.330898	+	0.573133i	0.651790	+	0.758400i	$0.274018\pi$
$828$		0			0
$829$	−13.7455			−0.477402			−0.238701	−	0.971093i	$-0.576722\pi$
$829$	−13.7455			−0.477402			−0.238701	+	0.971093i	$0.576722\pi$
$830$	5.30382	−	9.18649i	0.184098	−	0.318868i
$831$		0			0
$832$	26.5083	−	45.9137i	0.919009	−	1.59177i
$833$	34.3918	+	59.5684i	1.19161	+	2.06392i
$834$		0			0
$835$	−20.3114			−0.702905
$836$	1.68170	−	0.387274i	0.0581629	−	0.0133941i
$837$		0			0
$838$	−21.3295	−	36.9438i	−0.736815	−	1.27620i
$839$	17.1800	+	29.7566i	0.593118	+	1.02731i	0.993809	+	0.111098i	$0.0354367\pi$
$839$	17.1800	+	29.7566i	0.593118	+	1.02731i	−0.400691	+	0.916213i	$0.631230\pi$
$840$		0			0
$841$	8.18652	+	14.1795i	0.282294	+	0.488947i
$842$	18.3576	−	31.7963i	0.632644	−	1.09577i
$843$		0			0
$844$	−0.721671			−0.0248409
$845$	13.7416	−	23.8012i	0.472726	−	0.818786i
$846$		0			0
$847$	−33.2870			−1.14375
$848$	19.5626			0.671783
$849$		0			0
$850$	−3.94834	−	6.83872i	−0.135427	−	0.234566i
$851$	1.89626	−	3.28442i	0.0650030	−	0.112589i
$852$		0			0
$853$	−22.7147	−	39.3431i	−0.777738	−	1.34708i	−0.933243	−	0.359247i	$-0.883034\pi$
$853$	−22.7147	−	39.3431i	−0.777738	−	1.34708i	0.155505	−	0.987835i	$-0.450300\pi$
$854$	−72.4457			−2.47904
$855$		0			0
$856$	−39.5254			−1.35095
$857$	6.94674	+	12.0321i	0.237296	+	0.411009i	0.959937	−	0.280214i	$-0.0904055\pi$
$857$	6.94674	+	12.0321i	0.237296	+	0.411009i	−0.722641	+	0.691223i	$0.757072\pi$
$858$		0			0
$859$	1.60333	−	2.77705i	0.0547049	−	0.0947517i	−0.837376	−	0.546627i	$-0.815912\pi$
$859$	1.60333	−	2.77705i	0.0547049	−	0.0947517i	0.892081	+	0.451875i	$0.149245\pi$
$860$	0.291806	+	0.505423i	0.00995051	+	0.0172348i
$861$		0			0
$862$	22.7577			0.775132
$863$	−51.7277			−1.76083			−0.880416	−	0.474201i	$-0.842737\pi$
$863$	−51.7277			−1.76083			−0.880416	+	0.474201i	$0.842737\pi$
$864$		0			0
$865$	6.12545	−	10.6096i	0.208272	−	0.360737i
$866$	50.8413			1.72766
$867$		0			0
$868$	−0.236786	+	0.410126i	−0.00803705	+	0.0139206i
$869$	−24.4661	−	42.3765i	−0.829955	−	1.43752i
$870$		0			0
$871$	−12.7388	−	22.0643i	−0.431639	−	0.747620i
$872$	12.9548	+	22.4383i	0.438704	+	0.759857i
$873$		0			0
$874$	−2.37777	−	2.55267i	−0.0804292	−	0.0863453i
$875$	4.36264			0.147484
$876$		0			0
$877$	−8.51355	−	14.7459i	−0.287482	−	0.497933i	0.685726	−	0.727860i	$-0.259485\pi$
$877$	−8.51355	−	14.7459i	−0.287482	−	0.497933i	−0.973208	+	0.229926i	$0.926151\pi$
$878$	6.61885	−	11.4642i	0.223376	−	0.386898i
$879$		0			0
$880$	−8.21843	+	14.2347i	−0.277043	+	0.479853i
$881$	−12.9112			−0.434990			−0.217495	−	0.976061i	$-0.569789\pi$
$881$	−12.9112			−0.434990			−0.217495	+	0.976061i	$0.569789\pi$
$882$		0			0
$883$	−12.5102	+	21.6684i	−0.421003	+	0.729199i	−0.996038	−	0.0889302i	$-0.971655\pi$
$883$	−12.5102	+	21.6684i	−0.421003	+	0.729199i	0.575035	+	0.818129i	$0.304989\pi$
$884$	1.66808	−	2.88921i	0.0561038	−	0.0971746i
$885$		0			0
$886$	−30.7273			−1.03230
$887$	5.03634	−	8.72319i	0.169104	−	0.292896i	−0.769001	−	0.639247i	$-0.779246\pi$
$887$	5.03634	−	8.72319i	0.169104	−	0.292896i	0.938105	+	0.346351i	$0.112579\pi$
$888$		0			0
$889$	−13.4881	+	23.3621i	−0.452376	+	0.783539i
$890$	6.79779	+	11.7741i	0.227862	+	0.394669i
$891$		0			0
$892$	2.50900			0.0840075
$893$	−11.6075	+	2.67304i	−0.388430	+	0.0894500i
$894$		0			0
$895$	9.59201	+	16.6139i	0.320626	+	0.555340i
$896$	−22.8463	−	39.5709i	−0.763240	−	1.32197i
$897$		0			0
$898$	0.339264	+	0.587623i	0.0113214	+	0.0196092i
$899$	−2.10266	+	3.64191i	−0.0701276	+	0.121465i
$900$		0			0
$901$	29.3655			0.978307
$902$	2.27411	−	3.93887i	0.0757196	−	0.131150i
$903$		0			0
$904$	−18.5782			−0.617902
$905$	3.22984			0.107364
$906$		0			0
$907$	3.93231	+	6.81096i	0.130570	+	0.226154i	0.923897	−	0.382642i	$-0.124986\pi$
$907$	3.93231	+	6.81096i	0.130570	+	0.226154i	−0.793326	+	0.608797i	$0.791653\pi$
$908$	1.15079	−	1.99322i	0.0381903	−	0.0661475i
$909$		0			0
$910$	−19.1725	−	33.2077i	−0.635561	−	1.10082i
$911$	52.2665			1.73167			0.865833	−	0.500333i	$-0.166789\pi$
$911$	52.2665			1.73167			0.865833	+	0.500333i	$0.166789\pi$
$912$		0			0
$913$	−33.1440			−1.09691
$914$	9.15922	+	15.8642i	0.302960	+	0.524742i
$915$		0			0
$916$	0.228638	−	0.396013i	0.00755441	−	0.0130846i
$917$	−37.9494	−	65.7303i	−1.25320	−	2.17061i
$918$		0			0
$919$	24.2225			0.799026			0.399513	−	0.916728i	$-0.369179\pi$
$919$	24.2225			0.799026			0.399513	+	0.916728i	$0.369179\pi$
$920$	−1.67406			−0.0551922
$921$		0			0
$922$	−16.1441	+	27.9623i	−0.531677	+	0.920891i
$923$	19.5909			0.644844
$924$		0			0
$925$	3.27305	−	5.66908i	0.107617	−	0.186398i
$926$	−0.678026	−	1.17438i	−0.0222813	−	0.0385924i
$927$		0			0
$928$	0.921156	+	1.59549i	0.0302384	+	0.0523745i
$929$	−21.3993	−	37.0647i	−0.702089	−	1.21605i	−0.967732	−	0.251983i	$-0.918917\pi$
$929$	−21.3993	−	37.0647i	−0.702089	−	1.21605i	0.265642	−	0.964072i	$-0.414416\pi$
$930$		0			0
$931$	35.7490	+	38.3786i	1.17163	+	1.25781i
$932$	1.17375			0.0384474
$933$		0			0
$934$	13.0196	+	22.5506i	0.426014	+	0.737877i
$935$	−12.3367	+	21.3678i	−0.403454	+	0.698803i
$936$		0			0
$937$	−5.67783	+	9.83429i	−0.185487	+	0.321272i	−0.943740	−	0.330687i	$-0.892719\pi$
$937$	−5.67783	+	9.83429i	−0.185487	+	0.321272i	0.758254	+	0.651960i	$0.226053\pi$
$938$	−24.1319			−0.787935
$939$		0			0
$940$	−0.125325	+	0.217070i	−0.00408766	+	0.00708004i
$941$	22.0711	−	38.2283i	0.719498	−	1.24621i	−0.241701	−	0.970351i	$-0.577705\pi$
$941$	22.0711	−	38.2283i	0.719498	−	1.24621i	0.961199	−	0.275856i	$-0.0889613\pi$
$942$		0			0
$943$	0.441937			0.0143915
$944$	−7.29198	+	12.6301i	−0.237334	+	0.411074i
$945$		0			0
$946$	−18.9686	+	32.8545i	−0.616721	+	1.06819i
$947$	−18.6191	−	32.2492i	−0.605038	−	1.04796i	−0.992045	−	0.125880i	$-0.959825\pi$
$947$	−18.6191	−	32.2492i	−0.605038	−	1.04796i	0.387007	−	0.922077i	$-0.373509\pi$
$948$		0			0
$949$	−51.4509			−1.67017
$950$	−4.10415	−	4.40604i	−0.133156	−	0.142951i
$951$		0			0
$952$	−36.0303	−	62.4064i	−1.16775	−	2.02260i
$953$	−19.6433	−	34.0232i	−0.636310	−	1.10212i	−0.986236	−	0.165344i	$-0.947127\pi$
$953$	−19.6433	−	34.0232i	−0.636310	−	1.10212i	0.349926	−	0.936777i	$-0.386207\pi$
$954$		0			0
$955$	−13.7755	−	23.8598i	−0.445764	−	0.772085i
$956$	−0.587266	+	1.01717i	−0.0189935	+	0.0328978i
$957$		0			0
$958$	27.8478			0.899721
$959$	−34.2826	+	59.3791i	−1.10704	+	1.91745i
$960$		0			0
$961$	−29.5994			−0.954821
$962$	−57.5361			−1.85504
$963$		0			0
$964$	−0.0501180	−	0.0868069i	−0.00161419	−	0.00279586i
$965$	11.1233	−	19.2662i	0.358072	−	0.620200i
$966$		0			0
$967$	−10.5429	−	18.2608i	−0.339037	−	0.587229i	0.645215	−	0.764001i	$-0.276768\pi$
$967$	−10.5429	−	18.2608i	−0.339037	−	0.587229i	−0.984252	+	0.176772i	$0.943434\pi$
$968$	22.0470			0.708618
$969$		0			0
$970$	2.76281			0.0887084
$971$	−12.1226	−	20.9969i	−0.389031	−	0.673822i	0.603288	−	0.797523i	$-0.293857\pi$
$971$	−12.1226	−	20.9969i	−0.389031	−	0.673822i	−0.992319	+	0.123701i	$0.960523\pi$
$972$		0			0
$973$	14.2952	−	24.7600i	0.458282	−	0.793768i
$974$	1.92815	+	3.33966i	0.0617820	+	0.107010i
$975$		0			0
$976$	45.7778			1.46531
$977$	51.4540			1.64616			0.823080	−	0.567926i	$-0.192254\pi$
$977$	51.4540			1.64616			0.823080	+	0.567926i	$0.192254\pi$
$978$		0			0
$979$	21.2400	−	36.7887i	0.678832	−	1.17577i
$980$	1.10369			0.0352562
$981$		0			0
$982$	−3.99093	+	6.91249i	−0.127356	+	0.220587i
$983$	4.56746	+	7.91108i	0.145679	+	0.252324i	0.929626	−	0.368504i	$-0.120130\pi$
$983$	4.56746	+	7.91108i	0.145679	+	0.252324i	−0.783947	+	0.620828i	$0.786797\pi$
$984$		0			0
$985$	−6.33133	−	10.9662i	−0.201733	−	0.349412i
$986$	−14.0302	−	24.3010i	−0.446812	−	0.773901i
$987$		0			0
$988$	0.745111	−	2.43234i	0.0237051	−	0.0773830i
$989$	−3.68624			−0.117216
$990$		0			0
$991$	8.87713	+	15.3756i	0.281991	+	0.488424i	0.971875	−	0.235497i	$-0.0756717\pi$
$991$	8.87713	+	15.3756i	0.281991	+	0.488424i	−0.689884	+	0.723920i	$0.742338\pi$
$992$	0.306785	−	0.531367i	0.00974042	−	0.0168709i
$993$		0			0
$994$	9.27807	−	16.0701i	0.294283	−	0.509712i
$995$	8.76955			0.278014
$996$		0			0
$997$	28.1217	−	48.7081i	0.890622	−	1.54260i	0.0514903	−	0.998673i	$-0.483603\pi$
$997$	28.1217	−	48.7081i	0.890622	−	1.54260i	0.839131	−	0.543929i	$-0.183064\pi$
$998$	8.83810	−	15.3080i	0.279765	−	0.484568i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.k.i.406.4		10
3.2	odd	2		285.2.i.f.121.2	yes	10
19.11	even	3	inner	855.2.k.i.676.4		10
57.11	odd	6		285.2.i.f.106.2	✓	10
57.26	odd	6		5415.2.a.y.1.4		5
57.50	even	6		5415.2.a.z.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.i.f.106.2	✓	10	57.11	odd	6
285.2.i.f.121.2	yes	10	3.2	odd	2
855.2.k.i.406.4		10	1.1	even	1	trivial
855.2.k.i.676.4		10	19.11	even	3	inner
5415.2.a.y.1.4		5	57.26	odd	6
5415.2.a.z.1.2		5	57.50	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.690702 + 1.19633i) q^{2} +(0.0458624 - 0.0794360i) q^{4} +(0.500000 + 0.866025i) q^{5} -4.36264 q^{7} +2.88952 q^{8} +(-0.690702 + 1.19633i) q^{10} +4.31625 q^{11} +(3.18132 - 5.51021i) q^{13} +(-3.01329 - 5.21916i) q^{14} +(1.90407 + 3.29794i) q^{16} +(2.85821 + 4.95056i) q^{17} +(2.97100 + 3.18954i) q^{19} +0.0917248 q^{20} +(2.98124 + 5.16366i) q^{22} +(-0.289678 + 0.501738i) q^{23} +(-0.500000 + 0.866025i) q^{25} +8.78938 q^{26} +(-0.200081 + 0.346551i) q^{28} +(-1.77672 + 3.07737i) q^{29} +1.18345 q^{31} +(0.259229 - 0.448998i) q^{32} +(-3.94834 + 6.83872i) q^{34} +(-2.18132 - 3.77816i) q^{35} -6.54609 q^{37} +(-1.76367 + 5.75732i) q^{38} +(1.44476 + 2.50239i) q^{40} +(-0.381403 - 0.660610i) q^{41} +(3.18132 + 5.51021i) q^{43} +(0.197954 - 0.342866i) q^{44} -0.800326 q^{46} +(-1.36632 + 2.36653i) q^{47} +12.0327 q^{49} -1.38140 q^{50} +(-0.291806 - 0.505423i) q^{52} +(2.56853 - 4.44882i) q^{53} +(2.15812 + 3.73798i) q^{55} -12.6059 q^{56} -4.90874 q^{58} +(1.91484 + 3.31660i) q^{59} +(6.01053 - 10.4105i) q^{61} +(0.817411 + 1.41580i) q^{62} +8.33247 q^{64} +6.36264 q^{65} +(2.00213 - 3.46779i) q^{67} +0.524337 q^{68} +(3.01329 - 5.21916i) q^{70} +(1.53953 + 2.66654i) q^{71} +(-4.04320 - 7.00303i) q^{73} +(-4.52140 - 7.83129i) q^{74} +(0.389622 - 0.0897246i) q^{76} -18.8303 q^{77} +(-5.66836 - 9.81790i) q^{79} +(-1.90407 + 3.29794i) q^{80} +(0.526872 - 0.912569i) q^{82} -7.67889 q^{83} +(-2.85821 + 4.95056i) q^{85} +(-4.39469 + 7.61182i) q^{86} +12.4719 q^{88} +(4.92093 - 8.52330i) q^{89} +(-13.8790 + 24.0391i) q^{91} +(0.0265707 + 0.0460218i) q^{92} -3.77487 q^{94} +(-1.27672 + 4.16773i) q^{95} +(-1.00000 - 1.73205i) q^{97} +(8.31098 + 14.3950i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - 7 q^{4} + 5 q^{5} + 4 q^{7} + 12 q^{8} + q^{10} - 10 q^{11} + 8 q^{13} - 4 q^{14} - 7 q^{16} + 10 q^{17} + 5 q^{19} - 14 q^{20} - 2 q^{22} - 2 q^{23} - 5 q^{25} + 4 q^{26} - 10 q^{28} - 7 q^{29}+ \cdots + 21 q^{98}+O(q^{100}) \) 10 * q - q^2 - 7 * q^4 + 5 * q^5 + 4 * q^7 + 12 * q^8 + q^10 - 10 * q^11 + 8 * q^13 - 4 * q^14 - 7 * q^16 + 10 * q^17 + 5 * q^19 - 14 * q^20 - 2 * q^22 - 2 * q^23 - 5 * q^25 + 4 * q^26 - 10 * q^28 - 7 * q^29 - 18 * q^31 - 23 * q^32 - 25 * q^34 + 2 * q^35 + 12 * q^37 + 37 * q^38 + 6 * q^40 + 12 * q^41 + 8 * q^43 + 16 * q^44 - 40 * q^46 + 6 * q^47 + 30 * q^49 + 2 * q^50 + 4 * q^52 + 8 * q^53 - 5 * q^55 - 72 * q^56 + 76 * q^58 - q^59 - 7 * q^61 + 15 * q^62 + 28 * q^64 + 16 * q^65 + 14 * q^67 + 2 * q^68 + 4 * q^70 - 27 * q^71 - 26 * q^73 - 18 * q^74 - 56 * q^76 - 28 * q^77 - 23 * q^79 + 7 * q^80 + 36 * q^82 + 24 * q^83 - 10 * q^85 - 2 * q^86 - 9 * q^89 - 46 * q^91 - 52 * q^92 + 90 * q^94 - 2 * q^95 - 10 * q^97 + 21 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more