LMFDB - Embedded newform 1890.2.i.e.991.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(991,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 4]))

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

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

chi := DirichletCharacter("1890.991");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.i (of order $3$, degree $2$, not 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:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			991.2
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1890.991
Dual form			1890.2.i.e.1171.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.62132 + 2.09077i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.62132 + 2.09077i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{10} +(-2.12132 - 3.67423i) q^{11} +(-1.00000 - 1.73205i) q^{13} +(-1.62132 - 2.09077i) q^{14} +1.00000 q^{16} +(1.12132 + 1.94218i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(2.12132 + 3.67423i) q^{22} +(-4.24264 + 7.34847i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(1.00000 + 1.73205i) q^{26} +(1.62132 + 2.09077i) q^{28} +(0.621320 - 1.07616i) q^{29} +6.24264 q^{31} -1.00000 q^{32} +(-2.62132 + 0.358719i) q^{35} +(4.12132 + 7.13834i) q^{37} +(-1.12132 - 1.94218i) q^{38} +(0.500000 - 0.866025i) q^{40} +(4.50000 + 7.79423i) q^{41} +(0.500000 - 0.866025i) q^{43} +(-2.12132 - 3.67423i) q^{44} +(4.24264 - 7.34847i) q^{46} -1.24264 q^{47} +(-1.74264 + 6.77962i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-1.00000 - 1.73205i) q^{52} +(0.878680 - 1.52192i) q^{53} +4.24264 q^{55} +(-1.62132 - 2.09077i) q^{56} +(-0.621320 + 1.07616i) q^{58} -1.75736 q^{59} -12.4853 q^{61} -6.24264 q^{62} +1.00000 q^{64} +2.00000 q^{65} -6.48528 q^{67} +(2.62132 - 0.358719i) q^{70} -4.24264 q^{71} +(-2.24264 + 3.88437i) q^{73} +(-4.12132 - 7.13834i) q^{74} +(1.12132 + 1.94218i) q^{76} +(4.24264 - 10.3923i) q^{77} -10.7279 q^{79} +(-0.500000 + 0.866025i) q^{80} +(-4.50000 - 7.79423i) q^{82} +(-4.50000 + 7.79423i) q^{83} +(-0.500000 + 0.866025i) q^{86} +(2.12132 + 3.67423i) q^{88} +(2.00000 - 4.89898i) q^{91} +(-4.24264 + 7.34847i) q^{92} +1.24264 q^{94} -2.24264 q^{95} +(3.24264 - 5.61642i) q^{97} +(1.74264 - 6.77962i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{4} - 2 q^{5} - 2 q^{7} - 4 q^{8}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^4 - 2 * q^5 - 2 * q^7 - 4 * q^8	$ 4 q - 4 q^{2} + 4 q^{4} - 2 q^{5} - 2 q^{7} - 4 q^{8} + 2 q^{10} - 4 q^{13} + 2 q^{14} + 4 q^{16} - 4 q^{19} - 2 q^{20} - 2 q^{25} + 4 q^{26} - 2 q^{28} - 6 q^{29} + 8 q^{31} - 4 q^{32} - 2 q^{35} + 8 q^{37} + 4 q^{38} + 2 q^{40} + 18 q^{41} + 2 q^{43} + 12 q^{47} + 10 q^{49} + 2 q^{50} - 4 q^{52} + 12 q^{53} + 2 q^{56} + 6 q^{58} - 24 q^{59} - 16 q^{61} - 8 q^{62} + 4 q^{64} + 8 q^{65} + 8 q^{67} + 2 q^{70} + 8 q^{73} - 8 q^{74} - 4 q^{76} + 8 q^{79} - 2 q^{80} - 18 q^{82} - 18 q^{83} - 2 q^{86} + 8 q^{91} - 12 q^{94} + 8 q^{95} - 4 q^{97} - 10 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 + 4 * q^4 - 2 * q^5 - 2 * q^7 - 4 * q^8 + 2 * q^10 - 4 * q^13 + 2 * q^14 + 4 * q^16 - 4 * q^19 - 2 * q^20 - 2 * q^25 + 4 * q^26 - 2 * q^28 - 6 * q^29 + 8 * q^31 - 4 * q^32 - 2 * q^35 + 8 * q^37 + 4 * q^38 + 2 * q^40 + 18 * q^41 + 2 * q^43 + 12 * q^47 + 10 * q^49 + 2 * q^50 - 4 * q^52 + 12 * q^53 + 2 * q^56 + 6 * q^58 - 24 * q^59 - 16 * q^61 - 8 * q^62 + 4 * q^64 + 8 * q^65 + 8 * q^67 + 2 * q^70 + 8 * q^73 - 8 * q^74 - 4 * q^76 + 8 * q^79 - 2 * q^80 - 18 * q^82 - 18 * q^83 - 2 * q^86 + 8 * q^91 - 12 * q^94 + 8 * q^95 - 4 * q^97 - 10 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	1.62132	+	2.09077i	0.612801	+	0.790237i
$7$	1.62132	+	2.09077i	0.612801	+	0.790237i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−2.12132	−	3.67423i	−0.639602	−	1.10782i	−0.985520	−	0.169559i	$-0.945766\pi$
$11$	−2.12132	−	3.67423i	−0.639602	−	1.10782i	0.345918	−	0.938265i	$-0.387568\pi$
$12$		0			0
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	−1.62132	−	2.09077i	−0.433316	−	0.558782i
$15$		0			0
$16$	1.00000			0.250000
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$		0			0
$19$	1.12132	+	1.94218i	0.257249	+	0.445568i	0.965504	−	0.260389i	$-0.0838508\pi$
$19$	1.12132	+	1.94218i	0.257249	+	0.445568i	−0.708255	+	0.705956i	$0.750517\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$		0			0
$22$	2.12132	+	3.67423i	0.452267	+	0.783349i
$23$	−4.24264	+	7.34847i	−0.884652	+	1.53226i	−0.0385394	+	0.999257i	$0.512271\pi$
$23$	−4.24264	+	7.34847i	−0.884652	+	1.53226i	−0.846112	+	0.533005i	$0.821063\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	1.00000	+	1.73205i	0.196116	+	0.339683i
$27$		0			0
$28$	1.62132	+	2.09077i	0.306401	+	0.395118i
$29$	0.621320	−	1.07616i	0.115376	−	0.199838i	−0.802554	−	0.596580i	$-0.796526\pi$
$29$	0.621320	−	1.07616i	0.115376	−	0.199838i	0.917930	+	0.396742i	$0.129859\pi$
$30$		0			0
$31$	6.24264			1.12121			0.560606	−	0.828083i	$-0.310568\pi$
$31$	6.24264			1.12121			0.560606	+	0.828083i	$0.310568\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$		0			0
$35$	−2.62132	+	0.358719i	−0.443084	+	0.0606347i
$36$		0			0
$37$	4.12132	+	7.13834i	0.677541	+	1.17354i	0.975719	+	0.219025i	$0.0702877\pi$
$37$	4.12132	+	7.13834i	0.677541	+	1.17354i	−0.298178	+	0.954510i	$0.596379\pi$
$38$	−1.12132	−	1.94218i	−0.181902	−	0.315064i
$39$		0			0
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	0.967486	+	0.252924i	$0.0813924\pi$
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	−0.264704	+	0.964330i	$0.585274\pi$
$42$		0			0
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	−0.825380	−	0.564578i	$-0.809039\pi$
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	0.901629	+	0.432511i	$0.142372\pi$
$44$	−2.12132	−	3.67423i	−0.319801	−	0.553912i
$45$		0			0
$46$	4.24264	−	7.34847i	0.625543	−	1.08347i
$47$	−1.24264			−0.181258			−0.0906289	−	0.995885i	$-0.528888\pi$
$47$	−1.24264			−0.181258			−0.0906289	+	0.995885i	$0.528888\pi$
$48$		0			0
$49$	−1.74264	+	6.77962i	−0.248949	+	0.968517i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$		0			0
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	0.878680	−	1.52192i	0.120696	−	0.209051i	−0.799346	−	0.600871i	$-0.794821\pi$
$53$	0.878680	−	1.52192i	0.120696	−	0.209051i	0.920042	+	0.391819i	$0.128154\pi$
$54$		0			0
$55$	4.24264			0.572078
$56$	−1.62132	−	2.09077i	−0.216658	−	0.279391i
$57$		0			0
$58$	−0.621320	+	1.07616i	−0.0815834	+	0.141307i
$59$	−1.75736			−0.228789			−0.114394	−	0.993435i	$-0.536493\pi$
$59$	−1.75736			−0.228789			−0.114394	+	0.993435i	$0.536493\pi$
$60$		0			0
$61$	−12.4853			−1.59858			−0.799288	−	0.600948i	$-0.794790\pi$
$61$	−12.4853			−1.59858			−0.799288	+	0.600948i	$0.794790\pi$
$62$	−6.24264			−0.792816
$63$		0			0
$64$	1.00000			0.125000
$65$	2.00000			0.248069
$66$		0			0
$67$	−6.48528			−0.792303			−0.396152	−	0.918185i	$-0.629655\pi$
$67$	−6.48528			−0.792303			−0.396152	+	0.918185i	$0.629655\pi$
$68$		0			0
$69$		0			0
$70$	2.62132	−	0.358719i	0.313308	−	0.0428752i
$71$	−4.24264			−0.503509			−0.251754	−	0.967791i	$-0.581008\pi$
$71$	−4.24264			−0.503509			−0.251754	+	0.967791i	$0.581008\pi$
$72$		0			0
$73$	−2.24264	+	3.88437i	−0.262481	+	0.454631i	−0.966901	−	0.255153i	$-0.917874\pi$
$73$	−2.24264	+	3.88437i	−0.262481	+	0.454631i	0.704419	+	0.709784i	$0.251207\pi$
$74$	−4.12132	−	7.13834i	−0.479094	−	0.829815i
$75$		0			0
$76$	1.12132	+	1.94218i	0.128624	+	0.222784i
$77$	4.24264	−	10.3923i	0.483494	−	1.18431i
$78$		0			0
$79$	−10.7279			−1.20699			−0.603493	−	0.797368i	$-0.706225\pi$
$79$	−10.7279			−1.20699			−0.603493	+	0.797368i	$0.706225\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$		0			0
$82$	−4.50000	−	7.79423i	−0.496942	−	0.860729i
$83$	−4.50000	+	7.79423i	−0.493939	+	0.855528i	−0.999976	−	0.00698436i	$-0.997777\pi$
$83$	−4.50000	+	7.79423i	−0.493939	+	0.855528i	0.506036	+	0.862512i	$0.331110\pi$
$84$		0			0
$85$		0			0
$86$	−0.500000	+	0.866025i	−0.0539164	+	0.0933859i
$87$		0			0
$88$	2.12132	+	3.67423i	0.226134	+	0.391675i
$89$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$89$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$90$		0			0
$91$	2.00000	−	4.89898i	0.209657	−	0.513553i
$92$	−4.24264	+	7.34847i	−0.442326	+	0.766131i
$93$		0			0
$94$	1.24264			0.128169
$95$	−2.24264			−0.230090
$96$		0			0
$97$	3.24264	−	5.61642i	0.329240	−	0.570261i	−0.653121	−	0.757254i	$-0.726541\pi$
$97$	3.24264	−	5.61642i	0.329240	−	0.570261i	0.982361	+	0.186993i	$0.0598741\pi$
$98$	1.74264	−	6.77962i	0.176033	−	0.684845i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−6.62132	−	11.4685i	−0.658846	−	1.14115i	−0.980915	−	0.194438i	$-0.937712\pi$
$101$	−6.62132	−	11.4685i	−0.658846	−	1.14115i	0.322069	−	0.946716i	$-0.395622\pi$
$102$		0			0
$103$	−1.62132	+	2.80821i	−0.159753	+	0.276701i	−0.934780	−	0.355228i	$-0.884403\pi$
$103$	−1.62132	+	2.80821i	−0.159753	+	0.276701i	0.775026	+	0.631929i	$0.217737\pi$
$104$	1.00000	+	1.73205i	0.0980581	+	0.169842i
$105$		0			0
$106$	−0.878680	+	1.52192i	−0.0853449	+	0.147822i
$107$	7.50000	+	12.9904i	0.725052	+	1.25583i	0.958952	+	0.283567i	$0.0915178\pi$
$107$	7.50000	+	12.9904i	0.725052	+	1.25583i	−0.233900	+	0.972261i	$0.575149\pi$
$108$		0			0
$109$	−8.86396	+	15.3528i	−0.849013	+	1.47053i	0.0330761	+	0.999453i	$0.489470\pi$
$109$	−8.86396	+	15.3528i	−0.849013	+	1.47053i	−0.882090	+	0.471082i	$0.843864\pi$
$110$	−4.24264			−0.404520
$111$		0			0
$112$	1.62132	+	2.09077i	0.153200	+	0.197559i
$113$	6.36396	+	11.0227i	0.598671	+	1.03693i	0.993018	+	0.117967i	$0.0376377\pi$
$113$	6.36396	+	11.0227i	0.598671	+	1.03693i	−0.394346	+	0.918962i	$0.629029\pi$
$114$		0			0
$115$	−4.24264	−	7.34847i	−0.395628	−	0.685248i
$116$	0.621320	−	1.07616i	0.0576881	−	0.0999188i
$117$		0			0
$118$	1.75736			0.161778
$119$		0			0
$120$		0			0
$121$	−3.50000	+	6.06218i	−0.318182	+	0.551107i
$122$	12.4853			1.13036
$123$		0			0
$124$	6.24264			0.560606
$125$	1.00000			0.0894427
$126$		0			0
$127$	6.75736			0.599619			0.299809	−	0.953999i	$-0.403077\pi$
$127$	6.75736			0.599619			0.299809	+	0.953999i	$0.403077\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	−2.00000			−0.175412
$131$	1.75736	−	3.04384i	0.153541	−	0.265941i	−0.778986	−	0.627042i	$-0.784266\pi$
$131$	1.75736	−	3.04384i	0.153541	−	0.265941i	0.932527	+	0.361101i	$0.117599\pi$
$132$		0			0
$133$	−2.24264	+	5.49333i	−0.194462	+	0.476332i
$134$	6.48528			0.560243
$135$		0			0
$136$		0			0
$137$	9.36396	+	16.2189i	0.800017	+	1.38567i	0.919604	+	0.392847i	$0.128510\pi$
$137$	9.36396	+	16.2189i	0.800017	+	1.38567i	−0.119587	+	0.992824i	$0.538157\pi$
$138$		0			0
$139$	7.12132	+	12.3345i	0.604023	+	1.04620i	0.992205	+	0.124615i	$0.0397696\pi$
$139$	7.12132	+	12.3345i	0.604023	+	1.04620i	−0.388183	+	0.921582i	$0.626897\pi$
$140$	−2.62132	+	0.358719i	−0.221542	+	0.0303173i
$141$		0			0
$142$	4.24264			0.356034
$143$	−4.24264	+	7.34847i	−0.354787	+	0.614510i
$144$		0			0
$145$	0.621320	+	1.07616i	0.0515978	+	0.0893701i
$146$	2.24264	−	3.88437i	0.185602	−	0.321473i
$147$		0			0
$148$	4.12132	+	7.13834i	0.338770	+	0.586768i
$149$	7.24264	−	12.5446i	0.593340	−	1.02770i	−0.400439	−	0.916324i	$-0.631142\pi$
$149$	7.24264	−	12.5446i	0.593340	−	1.02770i	0.993779	−	0.111372i	$-0.0355245\pi$
$150$		0			0
$151$	−0.121320	−	0.210133i	−0.00987291	−	0.0171004i	0.861047	−	0.508526i	$-0.169809\pi$
$151$	−0.121320	−	0.210133i	−0.00987291	−	0.0171004i	−0.870920	+	0.491425i	$0.836476\pi$
$152$	−1.12132	−	1.94218i	−0.0909511	−	0.157532i
$153$		0			0
$154$	−4.24264	+	10.3923i	−0.341882	+	0.837436i
$155$	−3.12132	+	5.40629i	−0.250710	+	0.434243i
$156$		0			0
$157$	−16.7279			−1.33503			−0.667517	−	0.744595i	$-0.732643\pi$
$157$	−16.7279			−1.33503			−0.667517	+	0.744595i	$0.732643\pi$
$158$	10.7279			0.853468
$159$		0			0
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−22.2426	+	3.04384i	−1.75297	+	0.239888i
$162$		0			0
$163$	7.48528	+	12.9649i	0.586292	+	1.01549i	0.994713	+	0.102694i	$0.0327464\pi$
$163$	7.48528	+	12.9649i	0.586292	+	1.01549i	−0.408420	+	0.912794i	$0.633920\pi$
$164$	4.50000	+	7.79423i	0.351391	+	0.608627i
$165$		0			0
$166$	4.50000	−	7.79423i	0.349268	−	0.604949i
$167$	10.2426	+	17.7408i	0.792599	+	1.37282i	0.924352	+	0.381540i	$0.124606\pi$
$167$	10.2426	+	17.7408i	0.792599	+	1.37282i	−0.131753	+	0.991283i	$0.542061\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$		0			0
$171$		0			0
$172$	0.500000	−	0.866025i	0.0381246	−	0.0660338i
$173$	10.2426			0.778734			0.389367	−	0.921083i	$-0.372694\pi$
$173$	10.2426			0.778734			0.389367	+	0.921083i	$0.372694\pi$
$174$		0			0
$175$	1.00000	−	2.44949i	0.0755929	−	0.185164i
$176$	−2.12132	−	3.67423i	−0.159901	−	0.276956i
$177$		0			0
$178$		0			0
$179$	0.878680	−	1.52192i	0.0656756	−	0.113753i	−0.831318	−	0.555797i	$-0.812413\pi$
$179$	0.878680	−	1.52192i	0.0656756	−	0.113753i	0.896993	+	0.442044i	$0.145746\pi$
$180$		0			0
$181$	−23.2426			−1.72761			−0.863806	−	0.503825i	$-0.831926\pi$
$181$	−23.2426			−1.72761			−0.863806	+	0.503825i	$0.831926\pi$
$182$	−2.00000	+	4.89898i	−0.148250	+	0.363137i
$183$		0			0
$184$	4.24264	−	7.34847i	0.312772	−	0.541736i
$185$	−8.24264			−0.606011
$186$		0			0
$187$		0			0
$188$	−1.24264			−0.0906289
$189$		0			0
$190$	2.24264			0.162698
$191$	−14.4853			−1.04812			−0.524059	−	0.851682i	$-0.675583\pi$
$191$	−14.4853			−1.04812			−0.524059	+	0.851682i	$0.675583\pi$
$192$		0			0
$193$	0.242641			0.0174657			0.00873283	−	0.999962i	$-0.497220\pi$
$193$	0.242641			0.0174657			0.00873283	+	0.999962i	$0.497220\pi$
$194$	−3.24264	+	5.61642i	−0.232808	+	0.403235i
$195$		0			0
$196$	−1.74264	+	6.77962i	−0.124474	+	0.484258i
$197$	−27.2132			−1.93886			−0.969430	−	0.245367i	$-0.921091\pi$
$197$	−27.2132			−1.93886			−0.969430	+	0.245367i	$0.921091\pi$
$198$		0			0
$199$	−2.24264	+	3.88437i	−0.158977	+	0.275356i	−0.934500	−	0.355963i	$-0.884153\pi$
$199$	−2.24264	+	3.88437i	−0.158977	+	0.275356i	0.775523	+	0.631319i	$0.217486\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$		0			0
$202$	6.62132	+	11.4685i	0.465874	+	0.806918i
$203$	3.25736	−	0.445759i	0.228622	−	0.0312862i
$204$		0			0
$205$	−9.00000			−0.628587
$206$	1.62132	−	2.80821i	0.112963	−	0.195657i
$207$		0			0
$208$	−1.00000	−	1.73205i	−0.0693375	−	0.120096i
$209$	4.75736	−	8.23999i	0.329073	−	0.569972i
$210$		0			0
$211$	−1.87868	−	3.25397i	−0.129334	−	0.224012i	0.794085	−	0.607807i	$-0.207950\pi$
$211$	−1.87868	−	3.25397i	−0.129334	−	0.224012i	−0.923419	+	0.383794i	$0.874617\pi$
$212$	0.878680	−	1.52192i	0.0603480	−	0.104526i
$213$		0			0
$214$	−7.50000	−	12.9904i	−0.512689	−	0.888004i
$215$	0.500000	+	0.866025i	0.0340997	+	0.0590624i
$216$		0			0
$217$	10.1213	+	13.0519i	0.687080	+	0.886023i
$218$	8.86396	−	15.3528i	0.600343	−	1.03982i
$219$		0			0
$220$	4.24264			0.286039
$221$		0			0
$222$		0			0
$223$	−5.86396	+	10.1567i	−0.392680	+	0.680141i	−0.992802	−	0.119767i	$-0.961785\pi$
$223$	−5.86396	+	10.1567i	−0.392680	+	0.680141i	0.600122	+	0.799908i	$0.295119\pi$
$224$	−1.62132	−	2.09077i	−0.108329	−	0.139695i
$225$		0			0
$226$	−6.36396	−	11.0227i	−0.423324	−	0.733219i
$227$	−9.00000	−	15.5885i	−0.597351	−	1.03464i	−0.993210	−	0.116331i	$-0.962887\pi$
$227$	−9.00000	−	15.5885i	−0.597351	−	1.03464i	0.395860	−	0.918311i	$-0.370447\pi$
$228$		0			0
$229$	14.6213	−	25.3249i	0.966204	−	1.67351i	0.259859	−	0.965646i	$-0.416324\pi$
$229$	14.6213	−	25.3249i	0.966204	−	1.67351i	0.706345	−	0.707868i	$-0.250343\pi$
$230$	4.24264	+	7.34847i	0.279751	+	0.484544i
$231$		0			0
$232$	−0.621320	+	1.07616i	−0.0407917	+	0.0706533i
$233$	9.87868	+	17.1104i	0.647174	+	1.12094i	0.983795	+	0.179298i	$0.0573825\pi$
$233$	9.87868	+	17.1104i	0.647174	+	1.12094i	−0.336621	+	0.941640i	$0.609284\pi$
$234$		0			0
$235$	0.621320	−	1.07616i	0.0405305	−	0.0702008i
$236$	−1.75736			−0.114394
$237$		0			0
$238$		0			0
$239$	11.1213	+	19.2627i	0.719378	+	1.24600i	0.961246	+	0.275691i	$0.0889066\pi$
$239$	11.1213	+	19.2627i	0.719378	+	1.24600i	−0.241868	+	0.970309i	$0.577760\pi$
$240$		0			0
$241$	−3.74264	−	6.48244i	−0.241085	−	0.417571i	0.719939	−	0.694037i	$-0.244170\pi$
$241$	−3.74264	−	6.48244i	−0.241085	−	0.417571i	−0.961024	+	0.276467i	$0.910836\pi$
$242$	3.50000	−	6.06218i	0.224989	−	0.389692i
$243$		0			0
$244$	−12.4853			−0.799288
$245$	−5.00000	−	4.89898i	−0.319438	−	0.312984i
$246$		0			0
$247$	2.24264	−	3.88437i	0.142696	−	0.247156i
$248$	−6.24264			−0.396408
$249$		0			0
$250$	−1.00000			−0.0632456
$251$	9.51472			0.600564			0.300282	−	0.953851i	$-0.402919\pi$
$251$	9.51472			0.600564			0.300282	+	0.953851i	$0.402919\pi$
$252$		0			0
$253$	36.0000			2.26330
$254$	−6.75736			−0.423994
$255$		0			0
$256$	1.00000			0.0625000
$257$	8.48528	−	14.6969i	0.529297	−	0.916770i	−0.470119	−	0.882603i	$-0.655789\pi$
$257$	8.48528	−	14.6969i	0.529297	−	0.916770i	0.999416	−	0.0341667i	$-0.0108777\pi$
$258$		0			0
$259$	−8.24264	+	20.1903i	−0.512173	+	1.25456i
$260$	2.00000			0.124035
$261$		0			0
$262$	−1.75736	+	3.04384i	−0.108570	+	0.188049i
$263$	−7.86396	−	13.6208i	−0.484913	−	0.839893i	0.514937	−	0.857228i	$-0.327815\pi$
$263$	−7.86396	−	13.6208i	−0.484913	−	0.839893i	−0.999850	+	0.0173347i	$0.994482\pi$
$264$		0			0
$265$	0.878680	+	1.52192i	0.0539769	+	0.0934907i
$266$	2.24264	−	5.49333i	0.137505	−	0.336817i
$267$		0			0
$268$	−6.48528			−0.396152
$269$	−11.4853	+	19.8931i	−0.700270	+	1.21290i	0.268102	+	0.963391i	$0.413604\pi$
$269$	−11.4853	+	19.8931i	−0.700270	+	1.21290i	−0.968372	+	0.249513i	$0.919730\pi$
$270$		0			0
$271$	−10.3640	−	17.9509i	−0.629566	−	1.09044i	−0.987639	−	0.156746i	$-0.949899\pi$
$271$	−10.3640	−	17.9509i	−0.629566	−	1.09044i	0.358073	−	0.933694i	$-0.383434\pi$
$272$		0			0
$273$		0			0
$274$	−9.36396	−	16.2189i	−0.565698	−	0.979817i
$275$	−2.12132	+	3.67423i	−0.127920	+	0.221565i
$276$		0			0
$277$	−4.87868	−	8.45012i	−0.293131	−	0.507719i	0.681417	−	0.731895i	$-0.261364\pi$
$277$	−4.87868	−	8.45012i	−0.293131	−	0.507719i	−0.974548	+	0.224177i	$0.928031\pi$
$278$	−7.12132	−	12.3345i	−0.427108	−	0.739773i
$279$		0			0
$280$	2.62132	−	0.358719i	0.156654	−	0.0214376i
$281$	3.98528	−	6.90271i	0.237742	−	0.411781i	−0.722324	−	0.691555i	$-0.756926\pi$
$281$	3.98528	−	6.90271i	0.237742	−	0.411781i	0.960066	+	0.279774i	$0.0902594\pi$
$282$		0			0
$283$	1.48528			0.0882908			0.0441454	−	0.999025i	$-0.485944\pi$
$283$	1.48528			0.0882908			0.0441454	+	0.999025i	$0.485944\pi$
$284$	−4.24264			−0.251754
$285$		0			0
$286$	4.24264	−	7.34847i	0.250873	−	0.434524i
$287$	−9.00000	+	22.0454i	−0.531253	+	1.30130i
$288$		0			0
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	−0.621320	−	1.07616i	−0.0364852	−	0.0631942i
$291$		0			0
$292$	−2.24264	+	3.88437i	−0.131241	+	0.227315i
$293$	10.2426	+	17.7408i	0.598381	+	1.03643i	0.993060	+	0.117608i	$0.0375226\pi$
$293$	10.2426	+	17.7408i	0.598381	+	1.03643i	−0.394679	+	0.918819i	$0.629144\pi$
$294$		0			0
$295$	0.878680	−	1.52192i	0.0511587	−	0.0886095i
$296$	−4.12132	−	7.13834i	−0.239547	−	0.414907i
$297$		0			0
$298$	−7.24264	+	12.5446i	−0.419555	+	0.726690i
$299$	16.9706			0.981433
$300$		0			0
$301$	2.62132	−	0.358719i	0.151090	−	0.0206762i
$302$	0.121320	+	0.210133i	0.00698120	+	0.0120918i
$303$		0			0
$304$	1.12132	+	1.94218i	0.0643121	+	0.111392i
$305$	6.24264	−	10.8126i	0.357453	−	0.619126i
$306$		0			0
$307$	−29.9706			−1.71051			−0.855255	−	0.518207i	$-0.826600\pi$
$307$	−29.9706			−1.71051			−0.855255	+	0.518207i	$0.826600\pi$
$308$	4.24264	−	10.3923i	0.241747	−	0.592157i
$309$		0			0
$310$	3.12132	−	5.40629i	0.177279	−	0.307056i
$311$	−24.7279			−1.40219			−0.701096	−	0.713067i	$-0.747306\pi$
$311$	−24.7279			−1.40219			−0.701096	+	0.713067i	$0.747306\pi$
$312$		0			0
$313$	17.2132			0.972948			0.486474	−	0.873695i	$-0.338283\pi$
$313$	17.2132			0.972948			0.486474	+	0.873695i	$0.338283\pi$
$314$	16.7279			0.944011
$315$		0			0
$316$	−10.7279			−0.603493
$317$	31.4558			1.76674			0.883368	−	0.468680i	$-0.155270\pi$
$317$	31.4558			1.76674			0.883368	+	0.468680i	$0.155270\pi$
$318$		0			0
$319$	−5.27208			−0.295180
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$		0			0
$322$	22.2426	−	3.04384i	1.23953	−	0.169626i
$323$		0			0
$324$		0			0
$325$	−1.00000	+	1.73205i	−0.0554700	+	0.0960769i
$326$	−7.48528	−	12.9649i	−0.414571	−	0.718059i
$327$		0			0
$328$	−4.50000	−	7.79423i	−0.248471	−	0.430364i
$329$	−2.01472	−	2.59808i	−0.111075	−	0.143237i
$330$		0			0
$331$	−4.00000			−0.219860			−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000			−0.219860			−0.109930	+	0.993939i	$0.535063\pi$
$332$	−4.50000	+	7.79423i	−0.246970	+	0.427764i
$333$		0			0
$334$	−10.2426	−	17.7408i	−0.560452	−	0.970732i
$335$	3.24264	−	5.61642i	0.177164	−	0.306858i
$336$		0			0
$337$	−5.24264	−	9.08052i	−0.285585	−	0.494647i	0.687166	−	0.726500i	$-0.258855\pi$
$337$	−5.24264	−	9.08052i	−0.285585	−	0.494647i	−0.972751	+	0.231853i	$0.925521\pi$
$338$	−4.50000	+	7.79423i	−0.244768	+	0.423950i
$339$		0			0
$340$		0			0
$341$	−13.2426	−	22.9369i	−0.717129	−	1.24210i
$342$		0			0
$343$	−17.0000	+	7.34847i	−0.917914	+	0.396780i
$344$	−0.500000	+	0.866025i	−0.0269582	+	0.0466930i
$345$		0			0
$346$	−10.2426			−0.550648
$347$	9.00000			0.483145			0.241573	−	0.970383i	$-0.422337\pi$
$347$	9.00000			0.483145			0.241573	+	0.970383i	$0.422337\pi$
$348$		0			0
$349$	−13.0000	+	22.5167i	−0.695874	+	1.20529i	0.274011	+	0.961727i	$0.411649\pi$
$349$	−13.0000	+	22.5167i	−0.695874	+	1.20529i	−0.969885	+	0.243563i	$0.921684\pi$
$350$	−1.00000	+	2.44949i	−0.0534522	+	0.130931i
$351$		0			0
$352$	2.12132	+	3.67423i	0.113067	+	0.195837i
$353$	−0.878680	−	1.52192i	−0.0467674	−	0.0810035i	0.841694	−	0.539955i	$-0.181559\pi$
$353$	−0.878680	−	1.52192i	−0.0467674	−	0.0810035i	−0.888462	+	0.458951i	$0.848225\pi$
$354$		0			0
$355$	2.12132	−	3.67423i	0.112588	−	0.195008i
$356$		0			0
$357$		0			0
$358$	−0.878680	+	1.52192i	−0.0464397	+	0.0804359i
$359$	5.12132	+	8.87039i	0.270293	+	0.468161i	0.968937	−	0.247309i	$-0.0795461\pi$
$359$	5.12132	+	8.87039i	0.270293	+	0.468161i	−0.698644	+	0.715470i	$0.746213\pi$
$360$		0			0
$361$	6.98528	−	12.0989i	0.367646	−	0.636782i
$362$	23.2426			1.22161
$363$		0			0
$364$	2.00000	−	4.89898i	0.104828	−	0.256776i
$365$	−2.24264	−	3.88437i	−0.117385	−	0.203317i
$366$		0			0
$367$	15.8640	+	27.4772i	0.828092	+	1.43430i	0.899533	+	0.436853i	$0.143907\pi$
$367$	15.8640	+	27.4772i	0.828092	+	1.43430i	−0.0714411	+	0.997445i	$0.522760\pi$
$368$	−4.24264	+	7.34847i	−0.221163	+	0.383065i
$369$		0			0
$370$	8.24264			0.428514
$371$	4.60660	−	0.630399i	0.239163	−	0.0327287i
$372$		0			0
$373$	16.8492	−	29.1837i	0.872421	−	1.51108i	0.0129355	−	0.999916i	$-0.495882\pi$
$373$	16.8492	−	29.1837i	0.872421	−	1.51108i	0.859485	−	0.511161i	$-0.170784\pi$
$374$		0			0
$375$		0			0
$376$	1.24264			0.0640843
$377$	−2.48528			−0.127999
$378$		0			0
$379$	34.4853			1.77139			0.885695	−	0.464268i	$-0.153682\pi$
$379$	34.4853			1.77139			0.885695	+	0.464268i	$0.153682\pi$
$380$	−2.24264			−0.115045
$381$		0			0
$382$	14.4853			0.741131
$383$	4.13604	−	7.16383i	0.211342	−	0.366055i	−0.740793	−	0.671733i	$-0.765550\pi$
$383$	4.13604	−	7.16383i	0.211342	−	0.366055i	0.952135	+	0.305679i	$0.0988834\pi$
$384$		0			0
$385$	6.87868	+	8.87039i	0.350570	+	0.452077i
$386$	−0.242641			−0.0123501
$387$		0			0
$388$	3.24264	−	5.61642i	0.164620	−	0.285130i
$389$	15.1066	+	26.1654i	0.765935	+	1.32664i	0.939751	+	0.341860i	$0.111057\pi$
$389$	15.1066	+	26.1654i	0.765935	+	1.32664i	−0.173816	+	0.984778i	$0.555610\pi$
$390$		0			0
$391$		0			0
$392$	1.74264	−	6.77962i	0.0880166	−	0.342422i
$393$		0			0
$394$	27.2132			1.37098
$395$	5.36396	−	9.29065i	0.269890	−	0.467463i
$396$		0			0
$397$	−15.1213	−	26.1909i	−0.758917	−	1.31448i	−0.943403	−	0.331648i	$-0.892395\pi$
$397$	−15.1213	−	26.1909i	−0.758917	−	1.31448i	0.184486	−	0.982835i	$-0.440938\pi$
$398$	2.24264	−	3.88437i	0.112413	−	0.194706i
$399$		0			0
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−3.25736	+	5.64191i	−0.162665	+	0.281744i	−0.935824	−	0.352469i	$-0.885342\pi$
$401$	−3.25736	+	5.64191i	−0.162665	+	0.281744i	0.773159	+	0.634213i	$0.218676\pi$
$402$		0			0
$403$	−6.24264	−	10.8126i	−0.310968	−	0.538613i
$404$	−6.62132	−	11.4685i	−0.329423	−	0.570577i
$405$		0			0
$406$	−3.25736	+	0.445759i	−0.161660	+	0.0221227i
$407$	17.4853	−	30.2854i	0.866713	−	1.50119i
$408$		0			0
$409$	1.48528			0.0734424			0.0367212	−	0.999326i	$-0.488309\pi$
$409$	1.48528			0.0734424			0.0367212	+	0.999326i	$0.488309\pi$
$410$	9.00000			0.444478
$411$		0			0
$412$	−1.62132	+	2.80821i	−0.0798767	+	0.138351i
$413$	−2.84924	−	3.67423i	−0.140202	−	0.180797i
$414$		0			0
$415$	−4.50000	−	7.79423i	−0.220896	−	0.382604i
$416$	1.00000	+	1.73205i	0.0490290	+	0.0849208i
$417$		0			0
$418$	−4.75736	+	8.23999i	−0.232690	+	0.403031i
$419$	−17.4853	−	30.2854i	−0.854212	−	1.47954i	−0.877374	−	0.479807i	$-0.840707\pi$
$419$	−17.4853	−	30.2854i	−0.854212	−	1.47954i	0.0231623	−	0.999732i	$-0.492627\pi$
$420$		0			0
$421$	20.1066	−	34.8257i	0.979936	−	1.69730i	0.317357	−	0.948306i	$-0.397204\pi$
$421$	20.1066	−	34.8257i	0.979936	−	1.69730i	0.662578	−	0.748993i	$-0.269462\pi$
$422$	1.87868	+	3.25397i	0.0914527	+	0.158401i
$423$		0			0
$424$	−0.878680	+	1.52192i	−0.0426725	+	0.0739109i
$425$		0			0
$426$		0			0
$427$	−20.2426	−	26.1039i	−0.979610	−	1.26325i
$428$	7.50000	+	12.9904i	0.362526	+	0.627914i
$429$		0			0
$430$	−0.500000	−	0.866025i	−0.0241121	−	0.0417635i
$431$	−7.24264	+	12.5446i	−0.348866	+	0.604253i	−0.986048	−	0.166460i	$-0.946766\pi$
$431$	−7.24264	+	12.5446i	−0.348866	+	0.604253i	0.637183	+	0.770713i	$0.280100\pi$
$432$		0			0
$433$	27.4558			1.31944			0.659722	−	0.751510i	$-0.270674\pi$
$433$	27.4558			1.31944			0.659722	+	0.751510i	$0.270674\pi$
$434$	−10.1213	−	13.0519i	−0.485839	−	0.626513i
$435$		0			0
$436$	−8.86396	+	15.3528i	−0.424507	+	0.735267i
$437$	−19.0294			−0.910301
$438$		0			0
$439$	13.2721			0.633442			0.316721	−	0.948519i	$-0.397418\pi$
$439$	13.2721			0.633442			0.316721	+	0.948519i	$0.397418\pi$
$440$	−4.24264			−0.202260
$441$		0			0
$442$		0			0
$443$	−12.5147			−0.594592			−0.297296	−	0.954785i	$-0.596085\pi$
$443$	−12.5147			−0.594592			−0.297296	+	0.954785i	$0.596085\pi$
$444$		0			0
$445$		0			0
$446$	5.86396	−	10.1567i	0.277667	−	0.480933i
$447$		0			0
$448$	1.62132	+	2.09077i	0.0766002	+	0.0987796i
$449$	−9.00000			−0.424736			−0.212368	−	0.977190i	$-0.568118\pi$
$449$	−9.00000			−0.424736			−0.212368	+	0.977190i	$0.568118\pi$
$450$		0			0
$451$	19.0919	−	33.0681i	0.899002	−	1.55712i
$452$	6.36396	+	11.0227i	0.299336	+	0.518464i
$453$		0			0
$454$	9.00000	+	15.5885i	0.422391	+	0.731603i
$455$	3.24264	+	4.18154i	0.152017	+	0.196034i
$456$		0			0
$457$	18.9706			0.887405			0.443703	−	0.896174i	$-0.353665\pi$
$457$	18.9706			0.887405			0.443703	+	0.896174i	$0.353665\pi$
$458$	−14.6213	+	25.3249i	−0.683209	+	1.18335i
$459$		0			0
$460$	−4.24264	−	7.34847i	−0.197814	−	0.342624i
$461$	15.1066	−	26.1654i	0.703585	−	1.21864i	−0.263615	−	0.964628i	$-0.584915\pi$
$461$	15.1066	−	26.1654i	0.703585	−	1.21864i	0.967200	−	0.254016i	$-0.0817517\pi$
$462$		0			0
$463$	−2.86396	−	4.96053i	−0.133100	−	0.230535i	0.791770	−	0.610819i	$-0.209160\pi$
$463$	−2.86396	−	4.96053i	−0.133100	−	0.230535i	−0.924870	+	0.380284i	$0.875826\pi$
$464$	0.621320	−	1.07616i	0.0288441	−	0.0499594i
$465$		0			0
$466$	−9.87868	−	17.1104i	−0.457621	−	0.792623i
$467$	0.985281	+	1.70656i	0.0455934	+	0.0789701i	0.887921	−	0.459995i	$-0.152149\pi$
$467$	0.985281	+	1.70656i	0.0455934	+	0.0789701i	−0.842328	+	0.538965i	$0.818815\pi$
$468$		0			0
$469$	−10.5147	−	13.5592i	−0.485525	−	0.626107i
$470$	−0.621320	+	1.07616i	−0.0286594	+	0.0496395i
$471$		0			0
$472$	1.75736			0.0808890
$473$	−4.24264			−0.195077
$474$		0			0
$475$	1.12132	−	1.94218i	0.0514497	−	0.0891135i
$476$		0			0
$477$		0			0
$478$	−11.1213	−	19.2627i	−0.508677	−	0.881055i
$479$	7.24264	+	12.5446i	0.330925	+	0.573178i	0.982693	−	0.185239i	$-0.0593061\pi$
$479$	7.24264	+	12.5446i	0.330925	+	0.573178i	−0.651769	+	0.758418i	$0.725973\pi$
$480$		0			0
$481$	8.24264	−	14.2767i	0.375832	−	0.650960i
$482$	3.74264	+	6.48244i	0.170473	+	0.295267i
$483$		0			0
$484$	−3.50000	+	6.06218i	−0.159091	+	0.275554i
$485$	3.24264	+	5.61642i	0.147241	+	0.255028i
$486$		0			0
$487$	−6.48528	+	11.2328i	−0.293876	+	0.509008i	−0.974723	−	0.223418i	$-0.928279\pi$
$487$	−6.48528	+	11.2328i	−0.293876	+	0.509008i	0.680847	+	0.732426i	$0.261612\pi$
$488$	12.4853			0.565182
$489$		0			0
$490$	5.00000	+	4.89898i	0.225877	+	0.221313i
$491$	11.1213	+	19.2627i	0.501898	+	0.869313i	0.999998	+	0.00219320i	$0.000698117\pi$
$491$	11.1213	+	19.2627i	0.501898	+	0.869313i	−0.498099	+	0.867120i	$0.665969\pi$
$492$		0			0
$493$		0			0
$494$	−2.24264	+	3.88437i	−0.100901	+	0.174766i
$495$		0			0
$496$	6.24264			0.280303
$497$	−6.87868	−	8.87039i	−0.308551	−	0.397891i
$498$		0			0
$499$	−12.8492	+	22.2555i	−0.575211	+	0.996295i	0.420808	+	0.907150i	$0.361747\pi$
$499$	−12.8492	+	22.2555i	−0.575211	+	0.996295i	−0.996019	+	0.0891449i	$0.971587\pi$
$500$	1.00000			0.0447214
$501$		0			0
$502$	−9.51472			−0.424663
$503$	−4.75736			−0.212120			−0.106060	−	0.994360i	$-0.533824\pi$
$503$	−4.75736			−0.212120			−0.106060	+	0.994360i	$0.533824\pi$
$504$		0			0
$505$	13.2426			0.589290
$506$	−36.0000			−1.60040
$507$		0			0
$508$	6.75736			0.299809
$509$	15.6213	−	27.0569i	0.692403	−	1.19928i	−0.278646	−	0.960394i	$-0.589885\pi$
$509$	15.6213	−	27.0569i	0.692403	−	1.19928i	0.971048	−	0.238883i	$-0.0767812\pi$
$510$		0			0
$511$	−11.7574	+	1.60896i	−0.520115	+	0.0711761i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−8.48528	+	14.6969i	−0.374270	+	0.648254i
$515$	−1.62132	−	2.80821i	−0.0714439	−	0.123744i
$516$		0			0
$517$	2.63604	+	4.56575i	0.115933	+	0.200802i
$518$	8.24264	−	20.1903i	0.362161	−	0.887109i
$519$		0			0
$520$	−2.00000			−0.0877058
$521$	17.2279	−	29.8396i	0.754769	−	1.30730i	−0.190720	−	0.981644i	$-0.561082\pi$
$521$	17.2279	−	29.8396i	0.754769	−	1.30730i	0.945489	−	0.325654i	$-0.105584\pi$
$522$		0			0
$523$	−1.25736	−	2.17781i	−0.0549805	−	0.0952290i	0.837225	−	0.546858i	$-0.184176\pi$
$523$	−1.25736	−	2.17781i	−0.0549805	−	0.0952290i	−0.892206	+	0.451629i	$0.850843\pi$
$524$	1.75736	−	3.04384i	0.0767706	−	0.132971i
$525$		0			0
$526$	7.86396	+	13.6208i	0.342885	+	0.593894i
$527$		0			0
$528$		0			0
$529$	−24.5000	−	42.4352i	−1.06522	−	1.84501i
$530$	−0.878680	−	1.52192i	−0.0381674	−	0.0661079i
$531$		0			0
$532$	−2.24264	+	5.49333i	−0.0972308	+	0.238166i
$533$	9.00000	−	15.5885i	0.389833	−	0.675211i
$534$		0			0
$535$	−15.0000			−0.648507
$536$	6.48528			0.280121
$537$		0			0
$538$	11.4853	−	19.8931i	0.495166	−	0.857652i
$539$	28.6066	−	7.97887i	1.23217	−	0.343674i
$540$		0			0
$541$	−10.7279	−	18.5813i	−0.461229	−	0.798873i	0.537793	−	0.843077i	$-0.319258\pi$
$541$	−10.7279	−	18.5813i	−0.461229	−	0.798873i	−0.999023	+	0.0442041i	$0.985925\pi$
$542$	10.3640	+	17.9509i	0.445170	+	0.771057i
$543$		0			0
$544$		0			0
$545$	−8.86396	−	15.3528i	−0.379690	−	0.657643i
$546$		0			0
$547$	−6.22792	+	10.7871i	−0.266287	+	0.461222i	−0.967900	−	0.251336i	$-0.919130\pi$
$547$	−6.22792	+	10.7871i	−0.266287	+	0.461222i	0.701613	+	0.712558i	$0.252463\pi$
$548$	9.36396	+	16.2189i	0.400009	+	0.692835i
$549$		0			0
$550$	2.12132	−	3.67423i	0.0904534	−	0.156670i
$551$	2.78680			0.118722
$552$		0			0
$553$	−17.3934	−	22.4296i	−0.739643	−	0.953804i
$554$	4.87868	+	8.45012i	0.207275	+	0.359011i
$555$		0			0
$556$	7.12132	+	12.3345i	0.302011	+	0.523099i
$557$	20.4853	−	35.4815i	0.867989	−	1.50340i	0.00394110	−	0.999992i	$-0.498746\pi$
$557$	20.4853	−	35.4815i	0.867989	−	1.50340i	0.864048	−	0.503409i	$-0.167921\pi$
$558$		0			0
$559$	−2.00000			−0.0845910
$560$	−2.62132	+	0.358719i	−0.110771	+	0.0151587i
$561$		0			0
$562$	−3.98528	+	6.90271i	−0.168109	+	0.291173i
$563$	4.97056			0.209484			0.104742	−	0.994499i	$-0.466598\pi$
$563$	4.97056			0.209484			0.104742	+	0.994499i	$0.466598\pi$
$564$		0			0
$565$	−12.7279			−0.535468
$566$	−1.48528			−0.0624310
$567$		0			0
$568$	4.24264			0.178017
$569$	−4.97056			−0.208377			−0.104188	−	0.994558i	$-0.533224\pi$
$569$	−4.97056			−0.208377			−0.104188	+	0.994558i	$0.533224\pi$
$570$		0			0
$571$	26.0000			1.08807			0.544033	−	0.839064i	$-0.316897\pi$
$571$	26.0000			1.08807			0.544033	+	0.839064i	$0.316897\pi$
$572$	−4.24264	+	7.34847i	−0.177394	+	0.307255i
$573$		0			0
$574$	9.00000	−	22.0454i	0.375653	−	0.920158i
$575$	8.48528			0.353861
$576$		0			0
$577$	−18.4853	+	32.0174i	−0.769552	+	1.33290i	0.168254	+	0.985744i	$0.446187\pi$
$577$	−18.4853	+	32.0174i	−0.769552	+	1.33290i	−0.937806	+	0.347160i	$0.887146\pi$
$578$	−8.50000	−	14.7224i	−0.353553	−	0.612372i
$579$		0			0
$580$	0.621320	+	1.07616i	0.0257989	+	0.0446850i
$581$	−23.5919	+	3.22848i	−0.978756	+	0.133940i
$582$		0			0
$583$	−7.45584			−0.308790
$584$	2.24264	−	3.88437i	0.0928011	−	0.160736i
$585$		0			0
$586$	−10.2426	−	17.7408i	−0.423120	−	0.732865i
$587$	2.22792	−	3.85887i	0.0919562	−	0.159273i	−0.816378	−	0.577518i	$-0.804021\pi$
$587$	2.22792	−	3.85887i	0.0919562	−	0.159273i	0.908334	+	0.418245i	$0.137355\pi$
$588$		0			0
$589$	7.00000	+	12.1244i	0.288430	+	0.499575i
$590$	−0.878680	+	1.52192i	−0.0361747	+	0.0626564i
$591$		0			0
$592$	4.12132	+	7.13834i	0.169385	+	0.293384i
$593$	−4.75736	−	8.23999i	−0.195361	−	0.338376i	0.751658	−	0.659554i	$-0.229255\pi$
$593$	−4.75736	−	8.23999i	−0.195361	−	0.338376i	−0.947019	+	0.321178i	$0.895921\pi$
$594$		0			0
$595$		0			0
$596$	7.24264	−	12.5446i	0.296670	−	0.513848i
$597$		0			0
$598$	−16.9706			−0.693978
$599$	33.9411			1.38680			0.693398	−	0.720554i	$-0.256113\pi$
$599$	33.9411			1.38680			0.693398	+	0.720554i	$0.256113\pi$
$600$		0			0
$601$	8.00000	−	13.8564i	0.326327	−	0.565215i	−0.655453	−	0.755236i	$-0.727522\pi$
$601$	8.00000	−	13.8564i	0.326327	−	0.565215i	0.981780	+	0.190021i	$0.0608557\pi$
$602$	−2.62132	+	0.358719i	−0.106837	+	0.0146203i
$603$		0			0
$604$	−0.121320	−	0.210133i	−0.00493645	−	0.00855019i
$605$	−3.50000	−	6.06218i	−0.142295	−	0.246463i
$606$		0			0
$607$	−22.6213	+	39.1813i	−0.918171	+	1.59032i	−0.115980	+	0.993252i	$0.537001\pi$
$607$	−22.6213	+	39.1813i	−0.918171	+	1.59032i	−0.802191	+	0.597067i	$0.796332\pi$
$608$	−1.12132	−	1.94218i	−0.0454755	−	0.0787660i
$609$		0			0
$610$	−6.24264	+	10.8126i	−0.252757	+	0.437788i
$611$	1.24264	+	2.15232i	0.0502719	+	0.0870734i
$612$		0			0
$613$	5.00000	−	8.66025i	0.201948	−	0.349784i	−0.747208	−	0.664590i	$-0.768606\pi$
$613$	5.00000	−	8.66025i	0.201948	−	0.349784i	0.949156	+	0.314806i	$0.101939\pi$
$614$	29.9706			1.20951
$615$		0			0
$616$	−4.24264	+	10.3923i	−0.170941	+	0.418718i
$617$	−1.75736	−	3.04384i	−0.0707486	−	0.122540i	0.828481	−	0.560017i	$-0.189205\pi$
$617$	−1.75736	−	3.04384i	−0.0707486	−	0.122540i	−0.899230	+	0.437477i	$0.855872\pi$
$618$		0			0
$619$	18.2426	+	31.5972i	0.733234	+	1.27000i	0.955494	+	0.295011i	$0.0953232\pi$
$619$	18.2426	+	31.5972i	0.733234	+	1.27000i	−0.222260	+	0.974987i	$0.571343\pi$
$620$	−3.12132	+	5.40629i	−0.125355	+	0.217122i
$621$		0			0
$622$	24.7279			0.991499
$623$		0			0
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−17.2132			−0.687978
$627$		0			0
$628$	−16.7279			−0.667517
$629$		0			0
$630$		0			0
$631$	−7.51472			−0.299156			−0.149578	−	0.988750i	$-0.547792\pi$
$631$	−7.51472			−0.299156			−0.149578	+	0.988750i	$0.547792\pi$
$632$	10.7279			0.426734
$633$		0			0
$634$	−31.4558			−1.24927
$635$	−3.37868	+	5.85204i	−0.134079	+	0.232231i
$636$		0			0
$637$	13.4853	−	3.76127i	0.534306	−	0.149027i
$638$	5.27208			0.208724
$639$		0			0
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−5.48528	−	9.50079i	−0.216656	−	0.375258i	0.737128	−	0.675753i	$-0.236182\pi$
$641$	−5.48528	−	9.50079i	−0.216656	−	0.375258i	−0.953783	+	0.300495i	$0.902848\pi$
$642$		0			0
$643$	−18.2279	−	31.5717i	−0.718839	−	1.24507i	−0.961460	−	0.274945i	$-0.911340\pi$
$643$	−18.2279	−	31.5717i	−0.718839	−	1.24507i	0.242621	−	0.970121i	$-0.421993\pi$
$644$	−22.2426	+	3.04384i	−0.876483	+	0.119944i
$645$		0			0
$646$		0			0
$647$	7.13604	−	12.3600i	0.280547	−	0.485921i	−0.690973	−	0.722881i	$-0.742818\pi$
$647$	7.13604	−	12.3600i	0.280547	−	0.485921i	0.971519	+	0.236960i	$0.0761509\pi$
$648$		0			0
$649$	3.72792	+	6.45695i	0.146334	+	0.253457i
$650$	1.00000	−	1.73205i	0.0392232	−	0.0679366i
$651$		0			0
$652$	7.48528	+	12.9649i	0.293146	+	0.507744i
$653$	18.7279	−	32.4377i	0.732880	−	1.26939i	−0.222767	−	0.974872i	$-0.571509\pi$
$653$	18.7279	−	32.4377i	0.732880	−	1.26939i	0.955647	−	0.294514i	$-0.0951578\pi$
$654$		0			0
$655$	1.75736	+	3.04384i	0.0686657	+	0.118932i
$656$	4.50000	+	7.79423i	0.175695	+	0.304314i
$657$		0			0
$658$	2.01472	+	2.59808i	0.0785419	+	0.101284i
$659$	−11.8492	+	20.5235i	−0.461581	+	0.799482i	−0.999040	−	0.0438082i	$-0.986051\pi$
$659$	−11.8492	+	20.5235i	−0.461581	+	0.799482i	0.537459	+	0.843290i	$0.319384\pi$
$660$		0			0
$661$	−5.24264			−0.203915			−0.101958	−	0.994789i	$-0.532511\pi$
$661$	−5.24264			−0.203915			−0.101958	+	0.994789i	$0.532511\pi$
$662$	4.00000			0.155464
$663$		0			0
$664$	4.50000	−	7.79423i	0.174634	−	0.302475i
$665$	−3.63604	−	4.68885i	−0.141000	−	0.181826i
$666$		0			0
$667$	5.27208	+	9.13151i	0.204136	+	0.353573i
$668$	10.2426	+	17.7408i	0.396300	+	0.686411i
$669$		0			0
$670$	−3.24264	+	5.61642i	−0.125274	+	0.216981i
$671$	26.4853	+	45.8739i	1.02245	+	1.77094i
$672$		0			0
$673$	−13.3640	+	23.1471i	−0.515143	+	0.892254i	0.484703	+	0.874679i	$0.338928\pi$
$673$	−13.3640	+	23.1471i	−0.515143	+	0.892254i	−0.999846	+	0.0175746i	$0.994406\pi$
$674$	5.24264	+	9.08052i	0.201939	+	0.349769i
$675$		0			0
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	0.727922			0.0279763			0.0139882	−	0.999902i	$-0.495547\pi$
$677$	0.727922			0.0279763			0.0139882	+	0.999902i	$0.495547\pi$
$678$		0			0
$679$	17.0000	−	2.32640i	0.652400	−	0.0892789i
$680$		0			0
$681$		0			0
$682$	13.2426	+	22.9369i	0.507087	+	0.878300i
$683$	−17.7426	+	30.7312i	−0.678903	+	1.17589i	0.296408	+	0.955061i	$0.404211\pi$
$683$	−17.7426	+	30.7312i	−0.678903	+	1.17589i	−0.975311	+	0.220834i	$0.929122\pi$
$684$		0			0
$685$	−18.7279			−0.715557
$686$	17.0000	−	7.34847i	0.649063	−	0.280566i
$687$		0			0
$688$	0.500000	−	0.866025i	0.0190623	−	0.0330169i
$689$	−3.51472			−0.133900
$690$		0			0
$691$	0.970563			0.0369219			0.0184610	−	0.999830i	$-0.494123\pi$
$691$	0.970563			0.0369219			0.0184610	+	0.999830i	$0.494123\pi$
$692$	10.2426			0.389367
$693$		0			0
$694$	−9.00000			−0.341635
$695$	−14.2426			−0.540254
$696$		0			0
$697$		0			0
$698$	13.0000	−	22.5167i	0.492057	−	0.852268i
$699$		0			0
$700$	1.00000	−	2.44949i	0.0377964	−	0.0925820i
$701$	20.6985			0.781771			0.390885	−	0.920439i	$-0.372169\pi$
$701$	20.6985			0.781771			0.390885	+	0.920439i	$0.372169\pi$
$702$		0			0
$703$	−9.24264	+	16.0087i	−0.348593	+	0.603780i
$704$	−2.12132	−	3.67423i	−0.0799503	−	0.138478i
$705$		0			0
$706$	0.878680	+	1.52192i	0.0330695	+	0.0572781i
$707$	13.2426	−	32.4377i	0.498041	−	1.21995i
$708$		0			0
$709$	18.9706			0.712454			0.356227	−	0.934399i	$-0.384063\pi$
$709$	18.9706			0.712454			0.356227	+	0.934399i	$0.384063\pi$
$710$	−2.12132	+	3.67423i	−0.0796117	+	0.137892i
$711$		0			0
$712$		0			0
$713$	−26.4853	+	45.8739i	−0.991882	+	1.71799i
$714$		0			0
$715$	−4.24264	−	7.34847i	−0.158666	−	0.274817i
$716$	0.878680	−	1.52192i	0.0328378	−	0.0568767i
$717$		0			0
$718$	−5.12132	−	8.87039i	−0.191126	−	0.331040i
$719$	−16.2426	−	28.1331i	−0.605748	−	1.04919i	−0.991933	−	0.126765i	$-0.959541\pi$
$719$	−16.2426	−	28.1331i	−0.605748	−	1.04919i	0.386184	−	0.922422i	$-0.373793\pi$
$720$		0			0
$721$	−8.50000	+	1.16320i	−0.316557	+	0.0433198i
$722$	−6.98528	+	12.0989i	−0.259965	+	0.450273i
$723$		0			0
$724$	−23.2426			−0.863806
$725$	−1.24264			−0.0461505
$726$		0			0
$727$	−3.48528	+	6.03668i	−0.129262	+	0.223888i	−0.923391	−	0.383861i	$-0.874594\pi$
$727$	−3.48528	+	6.03668i	−0.129262	+	0.223888i	0.794129	+	0.607749i	$0.207927\pi$
$728$	−2.00000	+	4.89898i	−0.0741249	+	0.181568i
$729$		0			0
$730$	2.24264	+	3.88437i	0.0830039	+	0.143767i
$731$		0			0
$732$		0			0
$733$	4.12132	−	7.13834i	0.152224	−	0.263660i	−0.779820	−	0.626003i	$-0.784690\pi$
$733$	4.12132	−	7.13834i	0.152224	−	0.263660i	0.932045	+	0.362343i	$0.118023\pi$
$734$	−15.8640	−	27.4772i	−0.585549	−	1.01420i
$735$		0			0
$736$	4.24264	−	7.34847i	0.156386	−	0.270868i
$737$	13.7574	+	23.8284i	0.506759	+	0.877732i
$738$		0			0
$739$	16.4853	−	28.5533i	0.606421	−	1.05035i	−0.385404	−	0.922748i	$-0.625938\pi$
$739$	16.4853	−	28.5533i	0.606421	−	1.05035i	0.991825	−	0.127604i	$-0.0407286\pi$
$740$	−8.24264			−0.303005
$741$		0			0
$742$	−4.60660	+	0.630399i	−0.169114	+	0.0231427i
$743$	5.37868	+	9.31615i	0.197325	+	0.341776i	0.947660	−	0.319281i	$-0.103441\pi$
$743$	5.37868	+	9.31615i	0.197325	+	0.341776i	−0.750335	+	0.661057i	$0.770108\pi$
$744$		0			0
$745$	7.24264	+	12.5446i	0.265350	+	0.459599i
$746$	−16.8492	+	29.1837i	−0.616895	+	1.06849i
$747$		0			0
$748$		0			0
$749$	−15.0000	+	36.7423i	−0.548088	+	1.34254i
$750$		0			0
$751$	−2.75736	+	4.77589i	−0.100617	+	0.174275i	−0.911939	−	0.410325i	$-0.865415\pi$
$751$	−2.75736	+	4.77589i	−0.100617	+	0.174275i	0.811322	+	0.584600i	$0.198748\pi$
$752$	−1.24264			−0.0453144
$753$		0			0
$754$	2.48528			0.0905086
$755$	0.242641			0.00883060
$756$		0			0
$757$	4.78680			0.173979			0.0869895	−	0.996209i	$-0.472275\pi$
$757$	4.78680			0.173979			0.0869895	+	0.996209i	$0.472275\pi$
$758$	−34.4853			−1.25256
$759$		0			0
$760$	2.24264			0.0813491
$761$	7.50000	−	12.9904i	0.271875	−	0.470901i	−0.697467	−	0.716617i	$-0.745690\pi$
$761$	7.50000	−	12.9904i	0.271875	−	0.470901i	0.969342	+	0.245716i	$0.0790230\pi$
$762$		0			0
$763$	−46.4706	+	6.35935i	−1.68235	+	0.230224i
$764$	−14.4853			−0.524059
$765$		0			0
$766$	−4.13604	+	7.16383i	−0.149441	+	0.258840i
$767$	1.75736	+	3.04384i	0.0634546	+	0.109907i
$768$		0			0
$769$	4.74264	+	8.21449i	0.171024	+	0.296222i	0.938778	−	0.344522i	$-0.111959\pi$
$769$	4.74264	+	8.21449i	0.171024	+	0.296222i	−0.767754	+	0.640745i	$0.778626\pi$
$770$	−6.87868	−	8.87039i	−0.247890	−	0.319667i
$771$		0			0
$772$	0.242641			0.00873283
$773$	−4.75736	+	8.23999i	−0.171110	+	0.296372i	−0.938808	−	0.344440i	$-0.888069\pi$
$773$	−4.75736	+	8.23999i	−0.171110	+	0.296372i	0.767698	+	0.640812i	$0.221402\pi$
$774$		0			0
$775$	−3.12132	−	5.40629i	−0.112121	−	0.194200i
$776$	−3.24264	+	5.61642i	−0.116404	+	0.201618i
$777$		0			0
$778$	−15.1066	−	26.1654i	−0.541598	−	0.938075i
$779$	−10.0919	+	17.4797i	−0.361579	+	0.626274i
$780$		0			0
$781$	9.00000	+	15.5885i	0.322045	+	0.557799i
$782$		0			0
$783$		0			0
$784$	−1.74264	+	6.77962i	−0.0622372	+	0.242129i
$785$	8.36396	−	14.4868i	0.298523	−	0.517056i
$786$		0			0
$787$	20.5147			0.731271			0.365635	−	0.930758i	$-0.380852\pi$
$787$	20.5147			0.731271			0.365635	+	0.930758i	$0.380852\pi$
$788$	−27.2132			−0.969430
$789$		0			0
$790$	−5.36396	+	9.29065i	−0.190841	+	0.330547i
$791$	−12.7279	+	31.1769i	−0.452553	+	1.10852i
$792$		0			0
$793$	12.4853	+	21.6251i	0.443365	+	0.767931i
$794$	15.1213	+	26.1909i	0.536636	+	0.929480i
$795$		0			0
$796$	−2.24264	+	3.88437i	−0.0794883	+	0.137678i
$797$	−1.24264	−	2.15232i	−0.0440166	−	0.0762390i	0.843178	−	0.537635i	$-0.180682\pi$
$797$	−1.24264	−	2.15232i	−0.0440166	−	0.0762390i	−0.887194	+	0.461396i	$0.847349\pi$
$798$		0			0
$799$		0			0
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$		0			0
$802$	3.25736	−	5.64191i	0.115021	−	0.199223i
$803$	19.0294			0.671534
$804$		0			0
$805$	8.48528	−	20.7846i	0.299067	−	0.732561i
$806$	6.24264	+	10.8126i	0.219888	+	0.380857i
$807$		0			0
$808$	6.62132	+	11.4685i	0.232937	+	0.403459i
$809$	9.98528	−	17.2950i	0.351064	−	0.608060i	−0.635372	−	0.772206i	$-0.719153\pi$
$809$	9.98528	−	17.2950i	0.351064	−	0.608060i	0.986436	+	0.164146i	$0.0524867\pi$
$810$		0			0
$811$	27.4558			0.964105			0.482053	−	0.876142i	$-0.339891\pi$
$811$	27.4558			0.964105			0.482053	+	0.876142i	$0.339891\pi$
$812$	3.25736	−	0.445759i	0.114311	−	0.0156431i
$813$		0			0
$814$	−17.4853	+	30.2854i	−0.612859	+	1.06150i
$815$	−14.9706			−0.524396
$816$		0			0
$817$	2.24264			0.0784601
$818$	−1.48528			−0.0519316
$819$		0			0
$820$	−9.00000			−0.314294
$821$	−32.6985			−1.14118			−0.570592	−	0.821233i	$-0.693286\pi$
$821$	−32.6985			−1.14118			−0.570592	+	0.821233i	$0.693286\pi$
$822$		0			0
$823$	30.7574			1.07213			0.536067	−	0.844175i	$-0.319909\pi$
$823$	30.7574			1.07213			0.536067	+	0.844175i	$0.319909\pi$
$824$	1.62132	−	2.80821i	0.0564814	−	0.0978286i
$825$		0			0
$826$	2.84924	+	3.67423i	0.0991378	+	0.127843i
$827$	36.9411			1.28457			0.642284	−	0.766466i	$-0.277987\pi$
$827$	36.9411			1.28457			0.642284	+	0.766466i	$0.277987\pi$
$828$		0			0
$829$	6.86396	−	11.8887i	0.238395	−	0.412913i	−0.721859	−	0.692040i	$-0.756712\pi$
$829$	6.86396	−	11.8887i	0.238395	−	0.412913i	0.960254	+	0.279128i	$0.0900453\pi$
$830$	4.50000	+	7.79423i	0.156197	+	0.270542i
$831$		0			0
$832$	−1.00000	−	1.73205i	−0.0346688	−	0.0600481i
$833$		0			0
$834$		0			0
$835$	−20.4853			−0.708922
$836$	4.75736	−	8.23999i	0.164537	−	0.284986i
$837$		0			0
$838$	17.4853	+	30.2854i	0.604019	+	1.04619i
$839$	−25.0919	+	43.4604i	−0.866268	+	1.50042i	−0.000485409		1.00000i	$0.500155\pi$
$839$	−25.0919	+	43.4604i	−0.866268	+	1.50042i	−0.865783	+	0.500420i	$0.833179\pi$
$840$		0			0
$841$	13.7279	+	23.7775i	0.473377	+	0.819912i
$842$	−20.1066	+	34.8257i	−0.692919	+	1.20017i
$843$		0			0
$844$	−1.87868	−	3.25397i	−0.0646668	−	0.112006i
$845$	4.50000	+	7.79423i	0.154805	+	0.268130i
$846$		0			0
$847$	−18.3492	+	2.51104i	−0.630487	+	0.0862802i
$848$	0.878680	−	1.52192i	0.0301740	−	0.0522629i
$849$		0			0
$850$		0			0
$851$	−69.9411			−2.39755
$852$		0			0
$853$	1.27208	−	2.20330i	0.0435551	−	0.0754397i	−0.843426	−	0.537245i	$-0.819465\pi$
$853$	1.27208	−	2.20330i	0.0435551	−	0.0754397i	0.886981	+	0.461806i	$0.152798\pi$
$854$	20.2426	+	26.1039i	0.692689	+	0.893256i
$855$		0			0
$856$	−7.50000	−	12.9904i	−0.256345	−	0.444002i
$857$	−19.0919	−	33.0681i	−0.652166	−	1.12959i	−0.982596	−	0.185755i	$-0.940527\pi$
$857$	−19.0919	−	33.0681i	−0.652166	−	1.12959i	0.330430	−	0.943831i	$-0.392806\pi$
$858$		0			0
$859$	−0.636039	+	1.10165i	−0.0217014	+	0.0375879i	−0.876672	−	0.481088i	$-0.840242\pi$
$859$	−0.636039	+	1.10165i	−0.0217014	+	0.0375879i	0.854971	+	0.518676i	$0.173575\pi$
$860$	0.500000	+	0.866025i	0.0170499	+	0.0295312i
$861$		0			0
$862$	7.24264	−	12.5446i	0.246685	−	0.427272i
$863$	−25.9706	−	44.9823i	−0.884048	−	1.53122i	−0.846801	−	0.531910i	$-0.821474\pi$
$863$	−25.9706	−	44.9823i	−0.884048	−	1.53122i	−0.0372476	−	0.999306i	$-0.511859\pi$
$864$		0			0
$865$	−5.12132	+	8.87039i	−0.174130	+	0.301602i
$866$	−27.4558			−0.932988
$867$		0			0
$868$	10.1213	+	13.0519i	0.343540	+	0.443011i
$869$	22.7574	+	39.4169i	0.771991	+	1.33713i
$870$		0			0
$871$	6.48528	+	11.2328i	0.219745	+	0.380610i
$872$	8.86396	−	15.3528i	0.300172	−	0.519912i
$873$		0			0
$874$	19.0294			0.643680
$875$	1.62132	+	2.09077i	0.0548106	+	0.0706809i
$876$		0			0
$877$	−12.8492	+	22.2555i	−0.433888	+	0.751516i	−0.997204	−	0.0747253i	$-0.976192\pi$
$877$	−12.8492	+	22.2555i	−0.433888	+	0.751516i	0.563316	+	0.826241i	$0.309525\pi$
$878$	−13.2721			−0.447911
$879$		0			0
$880$	4.24264			0.143019
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$		0			0
$883$	26.9411			0.906641			0.453321	−	0.891348i	$-0.350239\pi$
$883$	26.9411			0.906641			0.453321	+	0.891348i	$0.350239\pi$
$884$		0			0
$885$		0			0
$886$	12.5147			0.420440
$887$	−0.621320	+	1.07616i	−0.0208619	+	0.0361339i	−0.876268	−	0.481824i	$-0.839974\pi$
$887$	−0.621320	+	1.07616i	−0.0208619	+	0.0361339i	0.855406	+	0.517958i	$0.173308\pi$
$888$		0			0
$889$	10.9558	+	14.1281i	0.367447	+	0.473841i
$890$		0			0
$891$		0			0
$892$	−5.86396	+	10.1567i	−0.196340	+	0.340071i
$893$	−1.39340	−	2.41344i	−0.0466283	−	0.0807626i
$894$		0			0
$895$	0.878680	+	1.52192i	0.0293710	+	0.0508721i
$896$	−1.62132	−	2.09077i	−0.0541645	−	0.0698477i
$897$		0			0
$898$	9.00000			0.300334
$899$	3.87868	−	6.71807i	0.129361	−	0.224060i
$900$		0			0
$901$		0			0
$902$	−19.0919	+	33.0681i	−0.635690	+	1.10105i
$903$		0			0
$904$	−6.36396	−	11.0227i	−0.211662	−	0.366610i
$905$	11.6213	−	20.1287i	0.386306	−	0.669101i
$906$		0			0
$907$	25.2279	+	43.6960i	0.837679	+	1.45090i	0.891830	+	0.452371i	$0.149422\pi$
$907$	25.2279	+	43.6960i	0.837679	+	1.45090i	−0.0541507	+	0.998533i	$0.517245\pi$
$908$	−9.00000	−	15.5885i	−0.298675	−	0.517321i
$909$		0			0
$910$	−3.24264	−	4.18154i	−0.107492	−	0.138617i
$911$	−23.3345	+	40.4166i	−0.773107	+	1.33906i	0.162745	+	0.986668i	$0.447965\pi$
$911$	−23.3345	+	40.4166i	−0.773107	+	1.33906i	−0.935852	+	0.352393i	$0.885368\pi$
$912$		0			0
$913$	38.1838			1.26370
$914$	−18.9706			−0.627490
$915$		0			0
$916$	14.6213	−	25.3249i	0.483102	−	0.836757i
$917$	9.21320	−	1.26080i	0.304247	−	0.0416352i
$918$		0			0
$919$	4.12132	+	7.13834i	0.135950	+	0.235472i	0.925960	−	0.377622i	$-0.123258\pi$
$919$	4.12132	+	7.13834i	0.135950	+	0.235472i	−0.790010	+	0.613094i	$0.789925\pi$
$920$	4.24264	+	7.34847i	0.139876	+	0.242272i
$921$		0			0
$922$	−15.1066	+	26.1654i	−0.497509	+	0.861712i
$923$	4.24264	+	7.34847i	0.139648	+	0.241878i
$924$		0			0
$925$	4.12132	−	7.13834i	0.135508	−	0.234707i
$926$	2.86396	+	4.96053i	0.0941156	+	0.163013i
$927$		0			0
$928$	−0.621320	+	1.07616i	−0.0203958	+	0.0353266i
$929$	−53.9117			−1.76879			−0.884393	−	0.466744i	$-0.845427\pi$
$929$	−53.9117			−1.76879			−0.884393	+	0.466744i	$0.845427\pi$
$930$		0			0
$931$	−15.1213	+	4.21759i	−0.495581	+	0.138226i
$932$	9.87868	+	17.1104i	0.323587	+	0.560469i
$933$		0			0
$934$	−0.985281	−	1.70656i	−0.0322394	−	0.0558403i
$935$		0			0
$936$		0			0
$937$	−2.24264			−0.0732639			−0.0366319	−	0.999329i	$-0.511663\pi$
$937$	−2.24264			−0.0732639			−0.0366319	+	0.999329i	$0.511663\pi$
$938$	10.5147	+	13.5592i	0.343318	+	0.442725i
$939$		0			0
$940$	0.621320	−	1.07616i	0.0202652	−	0.0351004i
$941$	−13.2426			−0.431698			−0.215849	−	0.976427i	$-0.569252\pi$
$941$	−13.2426			−0.431698			−0.215849	+	0.976427i	$0.569252\pi$
$942$		0			0
$943$	−76.3675			−2.48687
$944$	−1.75736			−0.0571972
$945$		0			0
$946$	4.24264			0.137940
$947$	−14.4853			−0.470708			−0.235354	−	0.971910i	$-0.575625\pi$
$947$	−14.4853			−0.470708			−0.235354	+	0.971910i	$0.575625\pi$
$948$		0			0
$949$	8.97056			0.291197
$950$	−1.12132	+	1.94218i	−0.0363804	+	0.0630128i
$951$		0			0
$952$		0			0
$953$	−50.1838			−1.62561			−0.812806	−	0.582535i	$-0.802061\pi$
$953$	−50.1838			−1.62561			−0.812806	+	0.582535i	$0.802061\pi$
$954$		0			0
$955$	7.24264	−	12.5446i	0.234366	−	0.405934i
$956$	11.1213	+	19.2627i	0.359689	+	0.623000i
$957$		0			0
$958$	−7.24264	−	12.5446i	−0.233999	−	0.405298i
$959$	−18.7279	+	45.8739i	−0.604756	+	1.48134i
$960$		0			0
$961$	7.97056			0.257115
$962$	−8.24264	+	14.2767i	−0.265753	+	0.460298i
$963$		0			0
$964$	−3.74264	−	6.48244i	−0.120542	−	0.208785i
$965$	−0.121320	+	0.210133i	−0.00390544	+	0.00676442i
$966$		0			0
$967$	−21.4853	−	37.2136i	−0.690920	−	1.19671i	−0.971537	−	0.236889i	$-0.923872\pi$
$967$	−21.4853	−	37.2136i	−0.690920	−	1.19671i	0.280617	−	0.959820i	$-0.409461\pi$
$968$	3.50000	−	6.06218i	0.112494	−	0.194846i
$969$		0			0
$970$	−3.24264	−	5.61642i	−0.104115	−	0.180332i
$971$	−4.75736	−	8.23999i	−0.152671	−	0.264434i	0.779538	−	0.626355i	$-0.215454\pi$
$971$	−4.75736	−	8.23999i	−0.152671	−	0.264434i	−0.932209	+	0.361922i	$0.882121\pi$
$972$		0			0
$973$	−14.2426	+	34.8872i	−0.456598	+	1.11843i
$974$	6.48528	−	11.2328i	0.207802	−	0.359923i
$975$		0			0
$976$	−12.4853			−0.399644
$977$	39.5147			1.26419			0.632094	−	0.774892i	$-0.282196\pi$
$977$	39.5147			1.26419			0.632094	+	0.774892i	$0.282196\pi$
$978$		0			0
$979$		0			0
$980$	−5.00000	−	4.89898i	−0.159719	−	0.156492i
$981$		0			0
$982$	−11.1213	−	19.2627i	−0.354896	−	0.614697i
$983$	−1.86396	−	3.22848i	−0.0594511	−	0.102972i	0.834768	−	0.550602i	$-0.185602\pi$
$983$	−1.86396	−	3.22848i	−0.0594511	−	0.102972i	−0.894219	+	0.447629i	$0.852268\pi$
$984$		0			0
$985$	13.6066	−	23.5673i	0.433542	−	0.750917i
$986$		0			0
$987$		0			0
$988$	2.24264	−	3.88437i	0.0713479	−	0.123578i
$989$	4.24264	+	7.34847i	0.134908	+	0.233668i
$990$		0			0
$991$	−3.12132	+	5.40629i	−0.0991520	+	0.171736i	−0.911334	−	0.411668i	$-0.864946\pi$
$991$	−3.12132	+	5.40629i	−0.0991520	+	0.171736i	0.812182	+	0.583404i	$0.198280\pi$
$992$	−6.24264			−0.198204
$993$		0			0
$994$	6.87868	+	8.87039i	0.218178	+	0.281352i
$995$	−2.24264	−	3.88437i	−0.0710965	−	0.123143i
$996$		0			0
$997$	−22.3640	−	38.7355i	−0.708274	−	1.22677i	−0.965497	−	0.260414i	$-0.916141\pi$
$997$	−22.3640	−	38.7355i	−0.708274	−	1.22677i	0.257223	−	0.966352i	$-0.417192\pi$
$998$	12.8492	−	22.2555i	0.406736	−	0.704487i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.i.e.991.2		4
3.2	odd	2		630.2.i.e.151.2	yes	4
7.2	even	3		1890.2.l.e.1801.1		4
9.4	even	3		1890.2.l.e.361.1		4
9.5	odd	6		630.2.l.e.571.1	yes	4
21.2	odd	6		630.2.l.e.331.1	yes	4
63.23	odd	6		630.2.i.e.121.2	✓	4
63.58	even	3	inner	1890.2.i.e.1171.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.e.121.2	✓	4	63.23	odd	6
630.2.i.e.151.2	yes	4	3.2	odd	2
630.2.l.e.331.1	yes	4	21.2	odd	6
630.2.l.e.571.1	yes	4	9.5	odd	6
1890.2.i.e.991.2		4	1.1	even	1	trivial
1890.2.i.e.1171.2		4	63.58	even	3	inner
1890.2.l.e.361.1		4	9.4	even	3
1890.2.l.e.1801.1		4	7.2	even	3

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:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.62132 + 2.09077i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.62132 + 2.09077i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{10} +(-2.12132 - 3.67423i) q^{11} +(-1.00000 - 1.73205i) q^{13} +(-1.62132 - 2.09077i) q^{14} +1.00000 q^{16} +(1.12132 + 1.94218i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(2.12132 + 3.67423i) q^{22} +(-4.24264 + 7.34847i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(1.00000 + 1.73205i) q^{26} +(1.62132 + 2.09077i) q^{28} +(0.621320 - 1.07616i) q^{29} +6.24264 q^{31} -1.00000 q^{32} +(-2.62132 + 0.358719i) q^{35} +(4.12132 + 7.13834i) q^{37} +(-1.12132 - 1.94218i) q^{38} +(0.500000 - 0.866025i) q^{40} +(4.50000 + 7.79423i) q^{41} +(0.500000 - 0.866025i) q^{43} +(-2.12132 - 3.67423i) q^{44} +(4.24264 - 7.34847i) q^{46} -1.24264 q^{47} +(-1.74264 + 6.77962i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-1.00000 - 1.73205i) q^{52} +(0.878680 - 1.52192i) q^{53} +4.24264 q^{55} +(-1.62132 - 2.09077i) q^{56} +(-0.621320 + 1.07616i) q^{58} -1.75736 q^{59} -12.4853 q^{61} -6.24264 q^{62} +1.00000 q^{64} +2.00000 q^{65} -6.48528 q^{67} +(2.62132 - 0.358719i) q^{70} -4.24264 q^{71} +(-2.24264 + 3.88437i) q^{73} +(-4.12132 - 7.13834i) q^{74} +(1.12132 + 1.94218i) q^{76} +(4.24264 - 10.3923i) q^{77} -10.7279 q^{79} +(-0.500000 + 0.866025i) q^{80} +(-4.50000 - 7.79423i) q^{82} +(-4.50000 + 7.79423i) q^{83} +(-0.500000 + 0.866025i) q^{86} +(2.12132 + 3.67423i) q^{88} +(2.00000 - 4.89898i) q^{91} +(-4.24264 + 7.34847i) q^{92} +1.24264 q^{94} -2.24264 q^{95} +(3.24264 - 5.61642i) q^{97} +(1.74264 - 6.77962i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{4} - 2 q^{5} - 2 q^{7} - 4 q^{8}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^4 - 2 * q^5 - 2 * q^7 - 4 * q^8	\( 4 q - 4 q^{2} + 4 q^{4} - 2 q^{5} - 2 q^{7} - 4 q^{8} + 2 q^{10} - 4 q^{13} + 2 q^{14} + 4 q^{16} - 4 q^{19} - 2 q^{20} - 2 q^{25} + 4 q^{26} - 2 q^{28} - 6 q^{29} + 8 q^{31} - 4 q^{32} - 2 q^{35} + 8 q^{37} + 4 q^{38} + 2 q^{40} + 18 q^{41} + 2 q^{43} + 12 q^{47} + 10 q^{49} + 2 q^{50} - 4 q^{52} + 12 q^{53} + 2 q^{56} + 6 q^{58} - 24 q^{59} - 16 q^{61} - 8 q^{62} + 4 q^{64} + 8 q^{65} + 8 q^{67} + 2 q^{70} + 8 q^{73} - 8 q^{74} - 4 q^{76} + 8 q^{79} - 2 q^{80} - 18 q^{82} - 18 q^{83} - 2 q^{86} + 8 q^{91} - 12 q^{94} + 8 q^{95} - 4 q^{97} - 10 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^4 - 2 * q^5 - 2 * q^7 - 4 * q^8 + 2 * q^10 - 4 * q^13 + 2 * q^14 + 4 * q^16 - 4 * q^19 - 2 * q^20 - 2 * q^25 + 4 * q^26 - 2 * q^28 - 6 * q^29 + 8 * q^31 - 4 * q^32 - 2 * q^35 + 8 * q^37 + 4 * q^38 + 2 * q^40 + 18 * q^41 + 2 * q^43 + 12 * q^47 + 10 * q^49 + 2 * q^50 - 4 * q^52 + 12 * q^53 + 2 * q^56 + 6 * q^58 - 24 * q^59 - 16 * q^61 - 8 * q^62 + 4 * q^64 + 8 * q^65 + 8 * q^67 + 2 * q^70 + 8 * q^73 - 8 * q^74 - 4 * q^76 + 8 * q^79 - 2 * q^80 - 18 * q^82 - 18 * q^83 - 2 * q^86 + 8 * q^91 - 12 * q^94 + 8 * q^95 - 4 * q^97 - 10 * q^98

Introduction

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