LMFDB - Embedded newform 1890.2.t.b.1151.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(1151,1890)]

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([5, 0, 1]))

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

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

chi := DirichletCharacter("1890.1151");

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.t (of order $6$, 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:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1151.9
Character	$\chi$	$=$	1890.1151
Dual form			1890.2.t.b.1601.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(2.05946 + 1.66090i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(2.05946 + 1.66090i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{10} +3.95684i q^{11} +(-2.82686 - 1.63209i) q^{13} +(0.953096 + 2.46812i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.497322 + 0.861388i) q^{17} +(-4.90846 + 2.83390i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-1.97842 + 3.42673i) q^{22} +7.70987i q^{23} +1.00000 q^{25} +(-1.63209 - 2.82686i) q^{26} +(-0.408654 + 2.61400i) q^{28} +(4.10273 - 2.36871i) q^{29} +(-4.83278 + 2.79020i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-0.861388 + 0.497322i) q^{34} +(2.05946 + 1.66090i) q^{35} +(-5.05548 - 8.75634i) q^{37} -5.66780 q^{38} +1.00000i q^{40} +(5.16567 - 8.94721i) q^{41} +(5.10292 + 8.83852i) q^{43} +(-3.42673 + 1.97842i) q^{44} +(-3.85494 + 6.67695i) q^{46} +(2.36963 - 4.10432i) q^{47} +(1.48279 + 6.84115i) q^{49} +(0.866025 + 0.500000i) q^{50} -3.26418i q^{52} +(8.82289 + 5.09390i) q^{53} +3.95684i q^{55} +(-1.66090 + 2.05946i) q^{56} +4.73743 q^{58} +(1.70360 + 2.95072i) q^{59} +(5.45543 + 3.14969i) q^{61} -5.58041 q^{62} -1.00000 q^{64} +(-2.82686 - 1.63209i) q^{65} +(-4.61095 - 7.98640i) q^{67} -0.994645 q^{68} +(0.953096 + 2.46812i) q^{70} -2.74965i q^{71} +(-12.7539 - 7.36348i) q^{73} -10.1110i q^{74} +(-4.90846 - 2.83390i) q^{76} +(-6.57194 + 8.14898i) q^{77} +(0.920736 - 1.59476i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(8.94721 - 5.16567i) q^{82} +(-0.789829 - 1.36802i) q^{83} +(-0.497322 + 0.861388i) q^{85} +10.2058i q^{86} -3.95684 q^{88} +(6.92781 + 11.9993i) q^{89} +(-3.11107 - 8.05637i) q^{91} +(-6.67695 + 3.85494i) q^{92} +(4.10432 - 2.36963i) q^{94} +(-4.90846 + 2.83390i) q^{95} +(0.776974 - 0.448586i) q^{97} +(-2.13644 + 6.66600i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7}+O(q^{10}) $ 28 * q + 14 * q^4 + 28 * q^5 - 4 * q^7	$ 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7} - 6 q^{14} - 14 q^{16} + 6 q^{17} - 6 q^{19} + 14 q^{20} - 6 q^{22} + 28 q^{25} - 12 q^{26} - 8 q^{28} - 12 q^{31} - 4 q^{35} + 4 q^{37} + 12 q^{38} - 18 q^{41} + 28 q^{43} - 18 q^{46} - 30 q^{47} - 14 q^{49} + 42 q^{53} - 6 q^{56} - 12 q^{58} + 24 q^{59} + 24 q^{61} + 12 q^{62} - 28 q^{64} - 40 q^{67} + 12 q^{68} - 6 q^{70} + 6 q^{73} - 6 q^{76} + 24 q^{77} + 2 q^{79} - 14 q^{80} + 24 q^{82} + 18 q^{83} + 6 q^{85} - 12 q^{88} - 6 q^{89} + 66 q^{91} + 30 q^{92} + 42 q^{94} - 6 q^{95} - 72 q^{97} + 24 q^{98}+O(q^{100}) $ 28 * q + 14 * q^4 + 28 * q^5 - 4 * q^7 - 6 * q^14 - 14 * q^16 + 6 * q^17 - 6 * q^19 + 14 * q^20 - 6 * q^22 + 28 * q^25 - 12 * q^26 - 8 * q^28 - 12 * q^31 - 4 * q^35 + 4 * q^37 + 12 * q^38 - 18 * q^41 + 28 * q^43 - 18 * q^46 - 30 * q^47 - 14 * q^49 + 42 * q^53 - 6 * q^56 - 12 * q^58 + 24 * q^59 + 24 * q^61 + 12 * q^62 - 28 * q^64 - 40 * q^67 + 12 * q^68 - 6 * q^70 + 6 * q^73 - 6 * q^76 + 24 * q^77 + 2 * q^79 - 14 * q^80 + 24 * q^82 + 18 * q^83 + 6 * q^85 - 12 * q^88 - 6 * q^89 + 66 * q^91 + 30 * q^92 + 42 * q^94 - 6 * q^95 - 72 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$757$	$1081$	$1541$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	2.05946	+	1.66090i	0.778404	+	0.627763i
$7$	2.05946	+	1.66090i	0.778404	+	0.627763i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$			3.95684i			1.19303i	0.802601	+	0.596516i	$0.203449\pi$
$11$			3.95684i			1.19303i	−0.802601	+	0.596516i	$0.796551\pi$
$12$		0			0
$13$	−2.82686	−	1.63209i	−0.784030	−	0.452660i	0.0538267	−	0.998550i	$-0.482858\pi$
$13$	−2.82686	−	1.63209i	−0.784030	−	0.452660i	−0.837857	+	0.545890i	$0.816191\pi$
$14$	0.953096	+	2.46812i	0.254726	+	0.659632i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.497322	+	0.861388i	−0.120618	+	0.208917i	−0.920012	−	0.391891i	$-0.871821\pi$
$17$	−0.497322	+	0.861388i	−0.120618	+	0.208917i	0.799393	+	0.600808i	$0.205154\pi$
$18$		0			0
$19$	−4.90846	+	2.83390i	−1.12608	+	0.650141i	−0.942945	−	0.332947i	$-0.891957\pi$
$19$	−4.90846	+	2.83390i	−1.12608	+	0.650141i	−0.183132	+	0.983088i	$0.558624\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$		0			0
$22$	−1.97842	+	3.42673i	−0.421801	+	0.730580i
$23$			7.70987i			1.60762i	0.594886	+	0.803810i	$0.297197\pi$
$23$			7.70987i			1.60762i	−0.594886	+	0.803810i	$0.702803\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	−1.63209	−	2.82686i	−0.320079	−	0.554393i
$27$		0			0
$28$	−0.408654	+	2.61400i	−0.0772283	+	0.494000i
$29$	4.10273	−	2.36871i	0.761858	−	0.439859i	−0.0681041	−	0.997678i	$-0.521695\pi$
$29$	4.10273	−	2.36871i	0.761858	−	0.439859i	0.829963	+	0.557819i	$0.188362\pi$
$30$		0			0
$31$	−4.83278	+	2.79020i	−0.867992	+	0.501135i	−0.866680	−	0.498864i	$-0.833751\pi$
$31$	−4.83278	+	2.79020i	−0.867992	+	0.501135i	−0.00131164	+	0.999999i	$0.500418\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$	−0.861388	+	0.497322i	−0.147727	+	0.0852901i
$35$	2.05946	+	1.66090i	0.348113	+	0.280744i
$36$		0			0
$37$	−5.05548	−	8.75634i	−0.831115	−	1.43953i	−0.897155	−	0.441717i	$-0.854370\pi$
$37$	−5.05548	−	8.75634i	−0.831115	−	1.43953i	0.0660393	−	0.997817i	$-0.478964\pi$
$38$	−5.66780			−0.919438
$39$		0			0
$40$			1.00000i			0.158114i
$41$	5.16567	−	8.94721i	0.806743	−	1.39732i	−0.108365	−	0.994111i	$-0.534562\pi$
$41$	5.16567	−	8.94721i	0.806743	−	1.39732i	0.915108	−	0.403208i	$-0.132105\pi$
$42$		0			0
$43$	5.10292	+	8.83852i	0.778188	+	1.34786i	0.932985	+	0.359915i	$0.117194\pi$
$43$	5.10292	+	8.83852i	0.778188	+	1.34786i	−0.154797	+	0.987946i	$0.549472\pi$
$44$	−3.42673	+	1.97842i	−0.516598	+	0.298258i
$45$		0			0
$46$	−3.85494	+	6.67695i	−0.568379	+	0.984462i
$47$	2.36963	−	4.10432i	0.345646	−	0.598677i	−0.639825	−	0.768521i	$-0.720993\pi$
$47$	2.36963	−	4.10432i	0.345646	−	0.598677i	0.985471	+	0.169844i	$0.0543264\pi$
$48$		0			0
$49$	1.48279	+	6.84115i	0.211827	+	0.977307i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$		0			0
$52$		−	3.26418i		−	0.452660i
$53$	8.82289	+	5.09390i	1.21192	+	0.699701i	0.963177	−	0.268869i	$-0.0866500\pi$
$53$	8.82289	+	5.09390i	1.21192	+	0.699701i	0.248741	+	0.968570i	$0.419983\pi$
$54$		0			0
$55$			3.95684i			0.533540i
$56$	−1.66090	+	2.05946i	−0.221948	+	0.275208i
$57$		0			0
$58$	4.73743			0.622055
$59$	1.70360	+	2.95072i	0.221790	+	0.384152i	0.955352	−	0.295471i	$-0.0954767\pi$
$59$	1.70360	+	2.95072i	0.221790	+	0.384152i	−0.733562	+	0.679623i	$0.762143\pi$
$60$		0			0
$61$	5.45543	+	3.14969i	0.698496	+	0.403277i	0.806787	−	0.590842i	$-0.201204\pi$
$61$	5.45543	+	3.14969i	0.698496	+	0.403277i	−0.108291	+	0.994119i	$0.534538\pi$
$62$	−5.58041			−0.708713
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−2.82686	−	1.63209i	−0.350629	−	0.202436i
$66$		0			0
$67$	−4.61095	−	7.98640i	−0.563317	−	0.975694i	−0.997204	−	0.0747267i	$-0.976192\pi$
$67$	−4.61095	−	7.98640i	−0.563317	−	0.975694i	0.433887	−	0.900967i	$-0.357142\pi$
$68$	−0.994645			−0.120618
$69$		0			0
$70$	0.953096	+	2.46812i	0.113917	+	0.294997i
$71$		−	2.74965i		−	0.326324i	−0.986599	−	0.163162i	$-0.947831\pi$
$71$		−	2.74965i		−	0.326324i	0.986599	−	0.163162i	$-0.0521693\pi$
$72$		0			0
$73$	−12.7539	−	7.36348i	−1.49273	−	0.861830i	−0.492767	−	0.870161i	$-0.664015\pi$
$73$	−12.7539	−	7.36348i	−1.49273	−	0.861830i	−0.999965	+	0.00833139i	$0.997348\pi$
$74$		−	10.1110i		−	1.17537i
$75$		0			0
$76$	−4.90846	−	2.83390i	−0.563039	−	0.325071i
$77$	−6.57194	+	8.14898i	−0.748942	+	0.928662i
$78$		0			0
$79$	0.920736	−	1.59476i	0.103591	−	0.179425i	−0.809571	−	0.587022i	$-0.800300\pi$
$79$	0.920736	−	1.59476i	0.103591	−	0.179425i	0.913162	+	0.407598i	$0.133633\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$		0			0
$82$	8.94721	−	5.16567i	0.988054	−	0.570453i
$83$	−0.789829	−	1.36802i	−0.0866950	−	0.150160i	0.819417	−	0.573198i	$-0.194297\pi$
$83$	−0.789829	−	1.36802i	−0.0866950	−	0.150160i	−0.906112	+	0.423037i	$0.860964\pi$
$84$		0			0
$85$	−0.497322	+	0.861388i	−0.0539422	+	0.0934306i
$86$			10.2058i			1.10052i
$87$		0			0
$88$	−3.95684			−0.421801
$89$	6.92781	+	11.9993i	0.734347	+	1.27193i	0.955009	+	0.296576i	$0.0958447\pi$
$89$	6.92781	+	11.9993i	0.734347	+	1.27193i	−0.220663	+	0.975350i	$0.570822\pi$
$90$		0			0
$91$	−3.11107	−	8.05637i	−0.326129	−	0.844537i
$92$	−6.67695	+	3.85494i	−0.696120	+	0.401905i
$93$		0			0
$94$	4.10432	−	2.36963i	0.423329	−	0.244409i
$95$	−4.90846	+	2.83390i	−0.503597	+	0.290752i
$96$		0			0
$97$	0.776974	−	0.448586i	0.0788897	−	0.0455470i	−0.460036	−	0.887900i	$-0.652164\pi$
$97$	0.776974	−	0.448586i	0.0788897	−	0.0455470i	0.538926	+	0.842353i	$0.318830\pi$
$98$	−2.13644	+	6.66600i	−0.215813	+	0.673368i
$99$		0			0
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	0.215695			0.0214624			0.0107312	−	0.999942i	$-0.496584\pi$
$101$	0.215695			0.0214624			0.0107312	+	0.999942i	$0.496584\pi$
$102$		0			0
$103$			11.3535i			1.11869i	0.828934	+	0.559346i	$0.188948\pi$
$103$			11.3535i			1.11869i	−0.828934	+	0.559346i	$0.811052\pi$
$104$	1.63209	−	2.82686i	0.160039	−	0.277196i
$105$		0			0
$106$	5.09390	+	8.82289i	0.494763	+	0.856955i
$107$	5.53564	−	3.19600i	0.535151	−	0.308969i	−0.207961	−	0.978137i	$-0.566683\pi$
$107$	5.53564	−	3.19600i	0.535151	−	0.308969i	0.743111	+	0.669168i	$0.233349\pi$
$108$		0			0
$109$	0.615666	−	1.06636i	0.0589701	−	0.102139i	−0.835033	−	0.550199i	$-0.814552\pi$
$109$	0.615666	−	1.06636i	0.0589701	−	0.102139i	0.894003	+	0.448060i	$0.147885\pi$
$110$	−1.97842	+	3.42673i	−0.188635	+	0.326725i
$111$		0			0
$112$	−2.46812	+	0.953096i	−0.233215	+	0.0900591i
$113$	7.32005	+	4.22623i	0.688612	+	0.397571i	0.803092	−	0.595855i	$-0.203187\pi$
$113$	7.32005	+	4.22623i	0.688612	+	0.397571i	−0.114480	+	0.993426i	$0.536520\pi$
$114$		0			0
$115$			7.70987i			0.718949i
$116$	4.10273	+	2.36871i	0.380929	+	0.219930i
$117$		0			0
$118$			3.40720i			0.313658i
$119$	−2.45490	+	0.947992i	−0.225040	+	0.0869023i
$120$		0			0
$121$	−4.65660			−0.423327
$122$	3.14969	+	5.45543i	0.285160	+	0.493911i
$123$		0			0
$124$	−4.83278	−	2.79020i	−0.433996	−	0.250568i
$125$	1.00000			0.0894427
$126$		0			0
$127$	20.5777			1.82598			0.912988	−	0.407985i	$-0.133769\pi$
$127$	20.5777			1.82598			0.912988	+	0.407985i	$0.133769\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	−1.63209	−	2.82686i	−0.143144	−	0.247932i
$131$	−5.00917			−0.437654			−0.218827	−	0.975764i	$-0.570223\pi$
$131$	−5.00917			−0.437654			−0.218827	+	0.975764i	$0.570223\pi$
$132$		0			0
$133$	−14.8156	−	2.31617i	−1.28468	−	0.200837i
$134$		−	9.22190i		−	0.796651i
$135$		0			0
$136$	−0.861388	−	0.497322i	−0.0738634	−	0.0426450i
$137$			9.23672i			0.789147i	0.918864	+	0.394573i	$0.129108\pi$
$137$			9.23672i			0.789147i	−0.918864	+	0.394573i	$0.870892\pi$
$138$		0			0
$139$	−11.2919	−	6.51936i	−0.957763	−	0.552965i	−0.0622791	−	0.998059i	$-0.519837\pi$
$139$	−11.2919	−	6.51936i	−0.957763	−	0.552965i	−0.895484	+	0.445094i	$0.853170\pi$
$140$	−0.408654	+	2.61400i	−0.0345375	+	0.220923i
$141$		0			0
$142$	1.37483	−	2.38127i	0.115373	−	0.199832i
$143$	6.45792	−	11.1854i	0.540038	−	0.935373i
$144$		0			0
$145$	4.10273	−	2.36871i	0.340713	−	0.196711i
$146$	−7.36348	−	12.7539i	−0.609406	−	1.05552i
$147$		0			0
$148$	5.05548	−	8.75634i	0.415558	−	0.719767i
$149$			22.0661i			1.80773i	0.427821	+	0.903863i	$0.359281\pi$
$149$			22.0661i			1.80773i	−0.427821	+	0.903863i	$0.640719\pi$
$150$		0			0
$151$	5.53782			0.450661			0.225331	−	0.974282i	$-0.427654\pi$
$151$	5.53782			0.450661			0.225331	+	0.974282i	$0.427654\pi$
$152$	−2.83390	−	4.90846i	−0.229860	−	0.398128i
$153$		0			0
$154$	−9.76595	+	3.77125i	−0.786963	+	0.303896i
$155$	−4.83278	+	2.79020i	−0.388178	+	0.224115i
$156$		0			0
$157$	14.5468	−	8.39860i	1.16096	−	0.670281i	0.209427	−	0.977824i	$-0.432840\pi$
$157$	14.5468	−	8.39860i	1.16096	−	0.670281i	0.951534	+	0.307543i	$0.0995068\pi$
$158$	1.59476	−	0.920736i	0.126872	−	0.0732498i
$159$		0			0
$160$	−0.866025	+	0.500000i	−0.0684653	+	0.0395285i
$161$	−12.8054	+	15.8782i	−1.00920	+	1.25138i
$162$		0			0
$163$	0.864749	+	1.49779i	0.0677324	+	0.117316i	0.897903	−	0.440194i	$-0.145090\pi$
$163$	0.864749	+	1.49779i	0.0677324	+	0.117316i	−0.830170	+	0.557510i	$0.811757\pi$
$164$	10.3313			0.806743
$165$		0			0
$166$		−	1.57966i		−	0.122605i
$167$	0.371022	−	0.642629i	0.0287105	−	0.0497281i	−0.851313	−	0.524658i	$-0.824193\pi$
$167$	0.371022	−	0.642629i	0.0287105	−	0.0497281i	0.880024	+	0.474930i	$0.157527\pi$
$168$		0			0
$169$	−1.17257	−	2.03096i	−0.0901981	−	0.156228i
$170$	−0.861388	+	0.497322i	−0.0660654	+	0.0381429i
$171$		0			0
$172$	−5.10292	+	8.83852i	−0.389094	+	0.673930i
$173$	−0.482119	+	0.835055i	−0.0366548	+	0.0634881i	−0.883771	−	0.467920i	$-0.845004\pi$
$173$	−0.482119	+	0.835055i	−0.0366548	+	0.0634881i	0.847116	+	0.531408i	$0.178337\pi$
$174$		0			0
$175$	2.05946	+	1.66090i	0.155681	+	0.125553i
$176$	−3.42673	−	1.97842i	−0.258299	−	0.149129i
$177$		0			0
$178$			13.8556i			1.03852i
$179$	0.186006	+	0.107391i	0.0139028	+	0.00802676i	0.506935	−	0.861984i	$-0.330778\pi$
$179$	0.186006	+	0.107391i	0.0139028	+	0.00802676i	−0.493033	+	0.870011i	$0.664112\pi$
$180$		0			0
$181$		−	11.1757i		−	0.830681i	−0.909666	−	0.415341i	$-0.863662\pi$
$181$		−	11.1757i		−	0.830681i	0.909666	−	0.415341i	$-0.136338\pi$
$182$	1.33392	−	8.53256i	0.0988765	−	0.632476i
$183$		0			0
$184$	−7.70987			−0.568379
$185$	−5.05548	−	8.75634i	−0.371686	−	0.643779i
$186$		0			0
$187$	−3.40837	−	1.96783i	−0.249245	−	0.143902i
$188$	4.73926			0.345646
$189$		0			0
$190$	−5.66780			−0.411185
$191$	−16.3524	−	9.44109i	−1.18322	−	0.683133i	−0.226464	−	0.974020i	$-0.572716\pi$
$191$	−16.3524	−	9.44109i	−1.18322	−	0.683133i	−0.956758	+	0.290886i	$0.906050\pi$
$192$		0			0
$193$	2.94509	+	5.10105i	0.211992	+	0.367181i	0.952338	−	0.305045i	$-0.0986715\pi$
$193$	2.94509	+	5.10105i	0.211992	+	0.367181i	−0.740346	+	0.672226i	$0.765338\pi$
$194$	0.897172			0.0644132
$195$		0			0
$196$	−5.18322	+	4.70471i	−0.370230	+	0.336051i
$197$		−	24.0786i		−	1.71553i	−0.514043	−	0.857764i	$-0.671853\pi$
$197$		−	24.0786i		−	1.71553i	0.514043	−	0.857764i	$-0.328147\pi$
$198$		0			0
$199$	13.1750	+	7.60658i	0.933950	+	0.539216i	0.888059	−	0.459730i	$-0.152054\pi$
$199$	13.1750	+	7.60658i	0.933950	+	0.539216i	0.0458914	+	0.998946i	$0.485387\pi$
$200$			1.00000i			0.0707107i
$201$		0			0
$202$	0.186797	+	0.107847i	0.0131430	+	0.00758812i
$203$	12.3836	+	1.93597i	0.869161	+	0.135878i
$204$		0			0
$205$	5.16567	−	8.94721i	0.360786	−	0.624900i
$206$	−5.67674	+	9.83240i	−0.395517	+	0.685056i
$207$		0			0
$208$	2.82686	−	1.63209i	0.196007	−	0.113165i
$209$	−11.2133	−	19.4220i	−0.775640	−	1.34345i
$210$		0			0
$211$	−3.11109	+	5.38856i	−0.214176	+	0.370964i	−0.953017	−	0.302916i	$-0.902040\pi$
$211$	−3.11109	+	5.38856i	−0.214176	+	0.370964i	0.738841	+	0.673879i	$0.235373\pi$
$212$			10.1878i			0.699701i
$213$		0			0
$214$	6.39201			0.436949
$215$	5.10292	+	8.83852i	0.348016	+	0.602782i
$216$		0			0
$217$	−14.5872	−	2.28045i	−0.990243	−	0.154807i
$218$	1.06636	−	0.615666i	0.0722233	−	0.0416982i
$219$		0			0
$220$	−3.42673	+	1.97842i	−0.231030	+	0.133385i
$221$	2.81172	−	1.62335i	0.189137	−	0.109198i
$222$		0			0
$223$	−4.37102	+	2.52361i	−0.292705	+	0.168994i	−0.639161	−	0.769073i	$-0.720718\pi$
$223$	−4.37102	+	2.52361i	−0.292705	+	0.168994i	0.346456	+	0.938066i	$0.387385\pi$
$224$	−2.61400	−	0.408654i	−0.174655	−	0.0273043i
$225$		0			0
$226$	4.22623	+	7.32005i	0.281125	+	0.486922i
$227$	5.07962			0.337146			0.168573	−	0.985689i	$-0.446084\pi$
$227$	5.07962			0.337146			0.168573	+	0.985689i	$0.446084\pi$
$228$		0			0
$229$		−	29.6559i		−	1.95972i	−0.199692	−	0.979859i	$-0.563994\pi$
$229$		−	29.6559i		−	1.95972i	0.199692	−	0.979859i	$-0.436006\pi$
$230$	−3.85494	+	6.67695i	−0.254187	+	0.440265i
$231$		0			0
$232$	2.36871	+	4.10273i	0.155514	+	0.269358i
$233$	15.8420	−	9.14639i	1.03784	−	0.599200i	0.118622	−	0.992939i	$-0.462152\pi$
$233$	15.8420	−	9.14639i	1.03784	−	0.599200i	0.919222	+	0.393740i	$0.128819\pi$
$234$		0			0
$235$	2.36963	−	4.10432i	0.154578	−	0.267737i
$236$	−1.70360	+	2.95072i	−0.110895	+	0.192076i
$237$		0			0
$238$	−2.60000	−	0.406465i	−0.168533	−	0.0263472i
$239$	−6.05638	−	3.49665i	−0.391755	−	0.226180i	0.291165	−	0.956673i	$-0.405957\pi$
$239$	−6.05638	−	3.49665i	−0.391755	−	0.226180i	−0.682920	+	0.730493i	$0.739290\pi$
$240$		0			0
$241$			5.51586i			0.355308i	0.984093	+	0.177654i	$0.0568507\pi$
$241$			5.51586i			0.355308i	−0.984093	+	0.177654i	$0.943149\pi$
$242$	−4.03273	−	2.32830i	−0.259234	−	0.149669i
$243$		0			0
$244$			6.29939i			0.403277i
$245$	1.48279	+	6.84115i	0.0947319	+	0.437065i
$246$		0			0
$247$	18.5007			1.17717
$248$	−2.79020	−	4.83278i	−0.177178	−	0.306882i
$249$		0			0
$250$	0.866025	+	0.500000i	0.0547723	+	0.0316228i
$251$	−0.276363			−0.0174439			−0.00872195	−	0.999962i	$-0.502776\pi$
$251$	−0.276363			−0.0174439			−0.00872195	+	0.999962i	$0.502776\pi$
$252$		0			0
$253$	−30.5068			−1.91794
$254$	17.8208	+	10.2889i	1.11818	+	0.645580i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	16.4912			1.02870			0.514348	−	0.857582i	$-0.328034\pi$
$257$	16.4912			1.02870			0.514348	+	0.857582i	$0.328034\pi$
$258$		0			0
$259$	4.13188	−	26.4300i	0.256742	−	1.64228i
$260$		−	3.26418i		−	0.202436i
$261$		0			0
$262$	−4.33807	−	2.50459i	−0.268007	−	0.154734i
$263$		−	2.50928i		−	0.154729i	−0.997003	−	0.0773646i	$-0.975349\pi$
$263$		−	2.50928i		−	0.154729i	0.997003	−	0.0773646i	$-0.0246505\pi$
$264$		0			0
$265$	8.82289	+	5.09390i	0.541986	+	0.312916i
$266$	−11.6726	−	9.41368i	−0.715695	−	0.577189i
$267$		0			0
$268$	4.61095	−	7.98640i	0.281659	−	0.487847i
$269$	13.3603	−	23.1408i	0.814594	−	1.41092i	−0.0950245	−	0.995475i	$-0.530293\pi$
$269$	13.3603	−	23.1408i	0.814594	−	1.41092i	0.909619	−	0.415444i	$-0.136374\pi$
$270$		0			0
$271$	12.9500	−	7.47668i	0.786656	−	0.454176i	−0.0521278	−	0.998640i	$-0.516600\pi$
$271$	12.9500	−	7.47668i	0.786656	−	0.454176i	0.838784	+	0.544464i	$0.183267\pi$
$272$	−0.497322	−	0.861388i	−0.0301546	−	0.0522293i
$273$		0			0
$274$	−4.61836	+	7.99924i	−0.279005	+	0.483252i
$275$			3.95684i			0.238607i
$276$		0			0
$277$	−14.2293			−0.854956			−0.427478	−	0.904026i	$-0.640598\pi$
$277$	−14.2293			−0.854956			−0.427478	+	0.904026i	$0.640598\pi$
$278$	−6.51936	−	11.2919i	−0.391005	−	0.677241i
$279$		0			0
$280$	−1.66090	+	2.05946i	−0.0992581	+	0.123077i
$281$	−21.5588	+	12.4470i	−1.28609	+	0.742524i	−0.977954	−	0.208819i	$-0.933038\pi$
$281$	−21.5588	+	12.4470i	−1.28609	+	0.742524i	−0.308135	+	0.951343i	$0.599705\pi$
$282$		0			0
$283$	14.8780	−	8.58983i	0.884407	−	0.510612i	0.0122977	−	0.999924i	$-0.496085\pi$
$283$	14.8780	−	8.58983i	0.884407	−	0.510612i	0.872109	+	0.489312i	$0.162752\pi$
$284$	2.38127	−	1.37483i	0.141302	−	0.0815810i
$285$		0			0
$286$	11.1854	−	6.45792i	0.661409	−	0.381865i
$287$	25.4990	−	9.84677i	1.50516	−	0.581236i
$288$		0			0
$289$	8.00534	+	13.8657i	0.470902	+	0.815627i
$290$	4.73743			0.278191
$291$		0			0
$292$		−	14.7270i		−	0.861830i
$293$	3.98706	−	6.90578i	0.232926	−	0.403440i	−0.725742	−	0.687967i	$-0.758503\pi$
$293$	3.98706	−	6.90578i	0.232926	−	0.403440i	0.958668	+	0.284527i	$0.0918366\pi$
$294$		0			0
$295$	1.70360	+	2.95072i	0.0991875	+	0.171798i
$296$	8.75634	−	5.05548i	0.508952	−	0.293844i
$297$		0			0
$298$	−11.0331	+	19.1098i	−0.639128	+	1.10700i
$299$	12.5832	−	21.7947i	0.727705	−	1.26042i
$300$		0			0
$301$	−4.17065	+	26.6781i	−0.240392	+	1.53770i
$302$	4.79589	+	2.76891i	0.275973	+	0.159333i
$303$		0			0
$304$		−	5.66780i		−	0.325071i
$305$	5.45543	+	3.14969i	0.312377	+	0.180351i
$306$		0			0
$307$		−	15.5665i		−	0.888429i	−0.895920	−	0.444215i	$-0.853483\pi$
$307$		−	15.5665i		−	0.888429i	0.895920	−	0.444215i	$-0.146517\pi$
$308$	−10.3432	−	1.61698i	−0.589358	−	0.0921358i
$309$		0			0
$310$	−5.58041			−0.316946
$311$	10.0834	+	17.4650i	0.571779	+	0.990350i	0.996383	+	0.0849714i	$0.0270799\pi$
$311$	10.0834	+	17.4650i	0.571779	+	0.990350i	−0.424604	+	0.905379i	$0.639587\pi$
$312$		0			0
$313$	−5.77815	−	3.33602i	−0.326600	−	0.188563i	0.327730	−	0.944771i	$-0.393716\pi$
$313$	−5.77815	−	3.33602i	−0.326600	−	0.188563i	−0.654331	+	0.756209i	$0.727050\pi$
$314$	16.7972			0.947921
$315$		0			0
$316$	1.84147			0.103591
$317$	−22.1197	−	12.7708i	−1.24236	−	0.717279i	−0.272789	−	0.962074i	$-0.587946\pi$
$317$	−22.1197	−	12.7708i	−1.24236	−	0.717279i	−0.969575	+	0.244795i	$0.921279\pi$
$318$		0			0
$319$	9.37263	+	16.2339i	0.524766	+	0.908922i
$320$	−1.00000			−0.0559017
$321$		0			0
$322$	−19.0289	+	7.34825i	−1.06044	+	0.409502i
$323$		−	5.63745i		−	0.313676i
$324$		0			0
$325$	−2.82686	−	1.63209i	−0.156806	−	0.0905320i
$326$			1.72950i			0.0957881i
$327$		0			0
$328$	8.94721	+	5.16567i	0.494027	+	0.285227i
$329$	11.6971	−	4.51697i	0.644880	−	0.249029i
$330$		0			0
$331$	−0.906390	+	1.56991i	−0.0498197	+	0.0862903i	−0.889860	−	0.456234i	$-0.849198\pi$
$331$	−0.906390	+	1.56991i	−0.0498197	+	0.0862903i	0.840040	+	0.542524i	$0.182531\pi$
$332$	0.789829	−	1.36802i	0.0433475	−	0.0750801i
$333$		0			0
$334$	0.642629	−	0.371022i	0.0351631	−	0.0203014i
$335$	−4.61095	−	7.98640i	−0.251923	−	0.436344i
$336$		0			0
$337$	7.15488	−	12.3926i	0.389751	−	0.675069i	−0.602665	−	0.797995i	$-0.705894\pi$
$337$	7.15488	−	12.3926i	0.389751	−	0.675069i	0.992416	+	0.122926i	$0.0392277\pi$
$338$		−	2.34515i		−	0.127559i
$339$		0			0
$340$	−0.994645			−0.0539422
$341$	−11.0404	−	19.1225i	−0.597871	−	1.03554i
$342$		0			0
$343$	−8.30875	+	16.5519i	−0.448630	+	0.893717i
$344$	−8.83852	+	5.10292i	−0.476541	+	0.275131i
$345$		0			0
$346$	−0.835055	+	0.482119i	−0.0448928	+	0.0259189i
$347$	5.20049	−	3.00250i	0.279177	−	0.161183i	−0.353874	−	0.935293i	$-0.615136\pi$
$347$	5.20049	−	3.00250i	0.279177	−	0.161183i	0.633051	+	0.774110i	$0.281802\pi$
$348$		0			0
$349$	−11.6157	+	6.70633i	−0.621775	+	0.358982i	−0.777560	−	0.628809i	$-0.783543\pi$
$349$	−11.6157	+	6.70633i	−0.621775	+	0.358982i	0.155785	+	0.987791i	$0.450209\pi$
$350$	0.953096	+	2.46812i	0.0509451	+	0.131926i
$351$		0			0
$352$	−1.97842	−	3.42673i	−0.105450	−	0.182645i
$353$	0.505383			0.0268988			0.0134494	−	0.999910i	$-0.495719\pi$
$353$	0.505383			0.0268988			0.0134494	+	0.999910i	$0.495719\pi$
$354$		0			0
$355$		−	2.74965i		−	0.145937i
$356$	−6.92781	+	11.9993i	−0.367173	+	0.635963i
$357$		0			0
$358$	0.107391	+	0.186006i	0.00567578	+	0.00983073i
$359$	−11.2748	+	6.50952i	−0.595062	+	0.343559i	−0.767097	−	0.641532i	$-0.778299\pi$
$359$	−11.2748	+	6.50952i	−0.595062	+	0.343559i	0.172034	+	0.985091i	$0.444966\pi$
$360$		0			0
$361$	6.56197	−	11.3657i	0.345367	−	0.598193i
$362$	5.58784	−	9.67842i	0.293690	−	0.508686i
$363$		0			0
$364$	5.42149	−	6.72246i	0.284163	−	0.352352i
$365$	−12.7539	−	7.36348i	−0.667570	−	0.385422i
$366$		0			0
$367$		−	32.0287i		−	1.67188i	−0.548819	−	0.835942i	$-0.684922\pi$
$367$		−	32.0287i		−	1.67188i	0.548819	−	0.835942i	$-0.315078\pi$
$368$	−6.67695	−	3.85494i	−0.348060	−	0.200952i
$369$		0			0
$370$		−	10.1110i		−	0.525643i
$371$	9.70995	+	25.1447i	0.504116	+	1.30545i
$372$		0			0
$373$	6.80077			0.352130			0.176065	−	0.984379i	$-0.443663\pi$
$373$	6.80077			0.352130			0.176065	+	0.984379i	$0.443663\pi$
$374$	−1.96783	−	3.40837i	−0.101754	−	0.176243i
$375$		0			0
$376$	4.10432	+	2.36963i	0.211664	+	0.122204i
$377$	−15.4638			−0.796426
$378$		0			0
$379$	2.14646			0.110256			0.0551281	−	0.998479i	$-0.482443\pi$
$379$	2.14646			0.110256			0.0551281	+	0.998479i	$0.482443\pi$
$380$	−4.90846	−	2.83390i	−0.251799	−	0.145376i
$381$		0			0
$382$	−9.44109	−	16.3524i	−0.483048	−	0.836664i
$383$	−0.710547			−0.0363072			−0.0181536	−	0.999835i	$-0.505779\pi$
$383$	−0.710547			−0.0363072			−0.0181536	+	0.999835i	$0.505779\pi$
$384$		0			0
$385$	−6.57194	+	8.14898i	−0.334937	+	0.415310i
$386$			5.89018i			0.299802i
$387$		0			0
$388$	0.776974	+	0.448586i	0.0394449	+	0.0227735i
$389$			19.6149i			0.994517i	0.867603	+	0.497258i	$0.165660\pi$
$389$			19.6149i			0.994517i	−0.867603	+	0.497258i	$0.834340\pi$
$390$		0			0
$391$	−6.64119	−	3.83429i	−0.335859	−	0.193908i
$392$	−6.84115	+	1.48279i	−0.345530	+	0.0748922i
$393$		0			0
$394$	12.0393	−	20.8527i	0.606531	−	1.05054i
$395$	0.920736	−	1.59476i	0.0463273	−	0.0802412i
$396$		0			0
$397$	20.7322	−	11.9697i	1.04052	−	0.600743i	0.120538	−	0.992709i	$-0.461538\pi$
$397$	20.7322	−	11.9697i	1.04052	−	0.600743i	0.919980	+	0.391965i	$0.128205\pi$
$398$	7.60658	+	13.1750i	0.381284	+	0.660402i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$		−	0.675625i		−	0.0337391i	−0.999858	−	0.0168696i	$-0.994630\pi$
$401$		−	0.675625i		−	0.0337391i	0.999858	−	0.0168696i	$-0.00537000\pi$
$402$		0			0
$403$	18.2154			0.907376
$404$	0.107847	+	0.186797i	0.00536561	+	0.00929351i
$405$		0			0
$406$	9.75657	+	7.86842i	0.484210	+	0.390503i
$407$	34.6475	−	20.0037i	1.71741	−	0.991548i
$408$		0			0
$409$	−26.2888	+	15.1779i	−1.29990	+	0.750497i	−0.980386	−	0.197085i	$-0.936853\pi$
$409$	−26.2888	+	15.1779i	−1.29990	+	0.750497i	−0.319513	+	0.947582i	$0.603519\pi$
$410$	8.94721	−	5.16567i	0.441871	−	0.255114i
$411$		0			0
$412$	−9.83240	+	5.67674i	−0.484408	+	0.279673i
$413$	−1.39237	+	8.90643i	−0.0685138	+	0.438257i
$414$		0			0
$415$	−0.789829	−	1.36802i	−0.0387712	−	0.0671537i
$416$	3.26418			0.160039
$417$		0			0
$418$		−	22.4266i		−	1.09692i
$419$	5.87786	−	10.1808i	0.287152	−	0.497363i	−0.685976	−	0.727624i	$-0.740625\pi$
$419$	5.87786	−	10.1808i	0.287152	−	0.497363i	0.973129	+	0.230261i	$0.0739581\pi$
$420$		0			0
$421$	14.4557	+	25.0380i	0.704526	+	1.22028i	0.966862	+	0.255299i	$0.0821739\pi$
$421$	14.4557	+	25.0380i	0.704526	+	1.22028i	−0.262336	+	0.964977i	$0.584493\pi$
$422$	−5.38856	+	3.11109i	−0.262311	+	0.151445i
$423$		0			0
$424$	−5.09390	+	8.82289i	−0.247382	+	0.428477i
$425$	−0.497322	+	0.861388i	−0.0241237	+	0.0417834i
$426$		0			0
$427$	6.00392	+	15.5476i	0.290550	+	0.752402i
$428$	5.53564	+	3.19600i	0.267575	+	0.154485i
$429$		0			0
$430$			10.2058i			0.492169i
$431$	17.2762	+	9.97444i	0.832167	+	0.480452i	0.854594	−	0.519297i	$-0.173806\pi$
$431$	17.2762	+	9.97444i	0.832167	+	0.480452i	−0.0224273	+	0.999748i	$0.507139\pi$
$432$		0			0
$433$		−	28.8157i		−	1.38479i	−0.721517	−	0.692397i	$-0.756555\pi$
$433$		−	28.8157i		−	1.38479i	0.721517	−	0.692397i	$-0.243445\pi$
$434$	−11.4927	−	9.26853i	−0.551665	−	0.444904i
$435$		0			0
$436$	1.23133			0.0589701
$437$	−21.8490	−	37.8436i	−1.04518	−	1.81030i
$438$		0			0
$439$	7.07993	+	4.08760i	0.337907	+	0.195091i	0.659346	−	0.751840i	$-0.270833\pi$
$439$	7.07993	+	4.08760i	0.337907	+	0.195091i	−0.321439	+	0.946930i	$0.604167\pi$
$440$	−3.95684			−0.188635
$441$		0			0
$442$	3.24670			0.154430
$443$	22.7505	+	13.1350i	1.08091	+	0.624063i	0.931141	−	0.364659i	$-0.118814\pi$
$443$	22.7505	+	13.1350i	1.08091	+	0.624063i	0.149767	+	0.988721i	$0.452148\pi$
$444$		0			0
$445$	6.92781	+	11.9993i	0.328410	+	0.568822i
$446$	−5.04722			−0.238993
$447$		0			0
$448$	−2.05946	−	1.66090i	−0.0973006	−	0.0784704i
$449$		−	6.39690i		−	0.301888i	−0.988542	−	0.150944i	$-0.951769\pi$
$449$		−	6.39690i		−	0.301888i	0.988542	−	0.150944i	$-0.0482314\pi$
$450$		0			0
$451$	35.4027	+	20.4398i	1.66705	+	0.962471i
$452$			8.45246i			0.397571i
$453$		0			0
$454$	4.39908	+	2.53981i	0.206459	+	0.119199i
$455$	−3.11107	−	8.05637i	−0.145849	−	0.377689i
$456$		0			0
$457$	5.16337	−	8.94322i	0.241532	−	0.418346i	−0.719619	−	0.694369i	$-0.755683\pi$
$457$	5.16337	−	8.94322i	0.241532	−	0.418346i	0.961151	+	0.276023i	$0.0890167\pi$
$458$	14.8280	−	25.6828i	0.692865	−	1.20008i
$459$		0			0
$460$	−6.67695	+	3.85494i	−0.311314	+	0.179737i
$461$	−4.00379	−	6.93476i	−0.186475	−	0.322984i	0.757598	−	0.652722i	$-0.226373\pi$
$461$	−4.00379	−	6.93476i	−0.186475	−	0.322984i	−0.944073	+	0.329738i	$0.893040\pi$
$462$		0			0
$463$	15.2865	−	26.4770i	0.710425	−	1.23049i	−0.254273	−	0.967132i	$-0.581836\pi$
$463$	15.2865	−	26.4770i	0.710425	−	1.23049i	0.964698	−	0.263359i	$-0.0848304\pi$
$464$			4.73743i			0.219930i
$465$		0			0
$466$	18.2928			0.847396
$467$	−3.61017	−	6.25300i	−0.167059	−	0.289354i	0.770326	−	0.637651i	$-0.220094\pi$
$467$	−3.61017	−	6.25300i	−0.167059	−	0.289354i	−0.937385	+	0.348296i	$0.886760\pi$
$468$		0			0
$469$	3.76856	−	24.1061i	0.174016	−	1.11311i
$470$	4.10432	−	2.36963i	0.189318	−	0.109303i
$471$		0			0
$472$	−2.95072	+	1.70360i	−0.135818	+	0.0784146i
$473$	−34.9726	+	20.1914i	−1.60804	+	0.928404i
$474$		0			0
$475$	−4.90846	+	2.83390i	−0.225215	+	0.130028i
$476$	−2.04844	−	1.65201i	−0.0938899	−	0.0757198i
$477$		0			0
$478$	−3.49665	−	6.05638i	−0.159933	−	0.277012i
$479$	−18.2719			−0.834864			−0.417432	−	0.908708i	$-0.637070\pi$
$479$	−18.2719			−0.834864			−0.417432	+	0.908708i	$0.637070\pi$
$480$		0			0
$481$			33.0039i			1.50485i
$482$	−2.75793	+	4.77687i	−0.125620	+	0.217581i
$483$		0			0
$484$	−2.32830	−	4.03273i	−0.105832	−	0.183306i
$485$	0.776974	−	0.448586i	0.0352806	−	0.0203692i
$486$		0			0
$487$	−19.2868	+	33.4057i	−0.873967	+	1.51375i	−0.0161074	+	0.999870i	$0.505127\pi$
$487$	−19.2868	+	33.4057i	−0.873967	+	1.51375i	−0.857859	+	0.513885i	$0.828206\pi$
$488$	−3.14969	+	5.45543i	−0.142580	+	0.246956i
$489$		0			0
$490$	−2.13644	+	6.66600i	−0.0965146	+	0.301139i
$491$	−21.3449	−	12.3235i	−0.963282	−	0.556151i	−0.0661005	−	0.997813i	$-0.521056\pi$
$491$	−21.3449	−	12.3235i	−0.963282	−	0.556151i	−0.897182	+	0.441662i	$0.854389\pi$
$492$		0			0
$493$			4.71206i			0.212220i
$494$	16.0221	+	9.25035i	0.720867	+	0.416193i
$495$		0			0
$496$		−	5.58041i		−	0.250568i
$497$	4.56691	−	5.66282i	0.204854	−	0.254012i
$498$		0			0
$499$	10.5180			0.470850			0.235425	−	0.971893i	$-0.424352\pi$
$499$	10.5180			0.470850			0.235425	+	0.971893i	$0.424352\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$		0			0
$502$	−0.239338	−	0.138182i	−0.0106822	−	0.00616735i
$503$	−19.4315			−0.866406			−0.433203	−	0.901296i	$-0.642617\pi$
$503$	−19.4315			−0.866406			−0.433203	+	0.901296i	$0.642617\pi$
$504$		0			0
$505$	0.215695			0.00959830
$506$	−26.4196	−	15.2534i	−1.17450	−	0.678095i
$507$		0			0
$508$	10.2889	+	17.8208i	0.456494	+	0.790671i
$509$	−23.3328			−1.03421			−0.517105	−	0.855922i	$-0.672990\pi$
$509$	−23.3328			−1.03421			−0.517105	+	0.855922i	$0.672990\pi$
$510$		0			0
$511$	−14.0362	−	36.3479i	−0.620925	−	1.60793i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	14.2818	+	8.24562i	0.629945	+	0.363699i
$515$			11.3535i			0.500294i
$516$		0			0
$517$	16.2402	+	9.37626i	0.714241	+	0.412367i
$518$	16.7933	−	20.8232i	0.737857	−	0.914917i
$519$		0			0
$520$	1.63209	−	2.82686i	0.0715718	−	0.123966i
$521$	11.8637	−	20.5486i	0.519759	−	0.900249i	−0.479977	−	0.877281i	$-0.659355\pi$
$521$	11.8637	−	20.5486i	0.519759	−	0.900249i	0.999736	−	0.0229682i	$-0.00731164\pi$
$522$		0			0
$523$	15.7239	−	9.07818i	0.687556	−	0.396961i	−0.115140	−	0.993349i	$-0.536732\pi$
$523$	15.7239	−	9.07818i	0.687556	−	0.396961i	0.802696	+	0.596388i	$0.203398\pi$
$524$	−2.50459	−	4.33807i	−0.109413	−	0.189510i
$525$		0			0
$526$	1.25464	−	2.17310i	0.0547050	−	0.0947519i
$527$		−	5.55052i		−	0.241785i
$528$		0			0
$529$	−36.4421			−1.58444
$530$	5.09390	+	8.82289i	0.221265	+	0.383242i
$531$		0			0
$532$	−5.40196	−	13.9888i	−0.234205	−	0.606491i
$533$	−29.2053	+	16.8617i	−1.26502	+	0.730360i
$534$		0			0
$535$	5.53564	−	3.19600i	0.239327	−	0.138175i
$536$	7.98640	−	4.61095i	0.344960	−	0.199163i
$537$		0			0
$538$	23.1408	−	13.3603i	0.997670	−	0.576005i
$539$	−27.0694	+	5.86716i	−1.16596	+	0.252717i
$540$		0			0
$541$	5.56494	+	9.63875i	0.239255	+	0.414402i	0.960501	−	0.278277i	$-0.0897634\pi$
$541$	5.56494	+	9.63875i	0.239255	+	0.414402i	−0.721245	+	0.692680i	$0.756430\pi$
$542$	14.9534			0.642302
$543$		0			0
$544$		−	0.994645i		−	0.0426450i
$545$	0.615666	−	1.06636i	0.0263722	−	0.0456781i
$546$		0			0
$547$	−15.8512	−	27.4550i	−0.677747	−	1.17389i	−0.975658	−	0.219299i	$-0.929623\pi$
$547$	−15.8512	−	27.4550i	−0.677747	−	1.17389i	0.297911	−	0.954594i	$-0.403710\pi$
$548$	−7.99924	+	4.61836i	−0.341711	+	0.197287i
$549$		0			0
$550$	−1.97842	+	3.42673i	−0.0843602	+	0.146116i
$551$	−13.4254	+	23.2535i	−0.571941	+	0.990631i
$552$		0			0
$553$	4.54497	−	1.75510i	0.193272	−	0.0746345i
$554$	−12.3229	−	7.11465i	−0.523552	−	0.302273i
$555$		0			0
$556$		−	13.0387i		−	0.552965i
$557$	28.2949	+	16.3360i	1.19889	+	0.692181i	0.960308	−	0.278941i	$-0.0899835\pi$
$557$	28.2949	+	16.3360i	1.19889	+	0.692181i	0.238584	+	0.971122i	$0.423317\pi$
$558$		0			0
$559$		−	33.3137i		−	1.40902i
$560$	−2.46812	+	0.953096i	−0.104297	+	0.0402757i
$561$		0			0
$562$	−24.8939			−1.05009
$563$	12.2498	+	21.2172i	0.516267	+	0.894200i	0.999822	+	0.0188863i	$0.00601207\pi$
$563$	12.2498	+	21.2172i	0.516267	+	0.894200i	−0.483555	+	0.875314i	$0.660655\pi$
$564$		0			0
$565$	7.32005	+	4.22623i	0.307957	+	0.177799i
$566$	17.1797			0.722115
$567$		0			0
$568$	2.74965			0.115373
$569$	−18.5002	−	10.6811i	−0.775567	−	0.447774i	0.0592899	−	0.998241i	$-0.481116\pi$
$569$	−18.5002	−	10.6811i	−0.775567	−	0.447774i	−0.834857	+	0.550467i	$0.814450\pi$
$570$		0			0
$571$	8.22432	+	14.2449i	0.344177	+	0.596132i	0.985204	−	0.171386i	$-0.0548246\pi$
$571$	8.22432	+	14.2449i	0.344177	+	0.596132i	−0.641027	+	0.767518i	$0.721491\pi$
$572$	12.9158			0.540038
$573$		0			0
$574$	27.0062	+	4.22194i	1.12722	+	0.176220i
$575$			7.70987i			0.321524i
$576$		0			0
$577$	17.2606	+	9.96542i	0.718569	+	0.414866i	0.814226	−	0.580549i	$-0.197162\pi$
$577$	17.2606	+	9.96542i	0.718569	+	0.414866i	−0.0956570	+	0.995414i	$0.530495\pi$
$578$			16.0107i			0.665957i
$579$		0			0
$580$	4.10273	+	2.36871i	0.170357	+	0.0983555i
$581$	0.645533	−	4.12923i	0.0267812	−	0.171309i
$582$		0			0
$583$	−20.1558	+	34.9108i	−0.834766	+	1.44586i
$584$	7.36348	−	12.7539i	0.304703	−	0.527761i
$585$		0			0
$586$	6.90578	−	3.98706i	0.285275	−	0.164704i
$587$	−1.94532	−	3.36939i	−0.0802918	−	0.139070i	0.823083	−	0.567920i	$-0.192252\pi$
$587$	−1.94532	−	3.36939i	−0.0802918	−	0.139070i	−0.903375	+	0.428851i	$0.858919\pi$
$588$		0			0
$589$	15.8143	−	27.3912i	0.651618	−	1.12863i
$590$			3.40720i			0.140272i
$591$		0			0
$592$	10.1110			0.415558
$593$	7.52066	+	13.0262i	0.308836	+	0.534920i	0.978108	−	0.208097i	$-0.0667271\pi$
$593$	7.52066	+	13.0262i	0.308836	+	0.534920i	−0.669272	+	0.743018i	$0.733394\pi$
$594$		0			0
$595$	−2.45490	+	0.947992i	−0.100641	+	0.0388639i
$596$	−19.1098	+	11.0331i	−0.782769	+	0.451932i
$597$		0			0
$598$	21.7947	−	12.5832i	0.891253	−	0.514565i
$599$	−23.6663	+	13.6638i	−0.966979	+	0.558286i	−0.898314	−	0.439354i	$-0.855207\pi$
$599$	−23.6663	+	13.6638i	−0.966979	+	0.558286i	−0.0686653	+	0.997640i	$0.521874\pi$
$600$		0			0
$601$	−10.2307	+	5.90670i	−0.417319	+	0.240939i	−0.693930	−	0.720043i	$-0.744122\pi$
$601$	−10.2307	+	5.90670i	−0.417319	+	0.240939i	0.276610	+	0.960982i	$0.410789\pi$
$602$	−16.9509	+	21.0186i	−0.690868	+	0.856653i
$603$		0			0
$604$	2.76891	+	4.79589i	0.112665	+	0.195142i
$605$	−4.65660			−0.189318
$606$		0			0
$607$		−	0.740209i		−	0.0300441i	−0.999887	−	0.0150221i	$-0.995218\pi$
$607$		−	0.740209i		−	0.0300441i	0.999887	−	0.0150221i	$-0.00478185\pi$
$608$	2.83390	−	4.90846i	0.114930	−	0.199064i
$609$		0			0
$610$	3.14969	+	5.45543i	0.127527	+	0.220884i
$611$	−13.3972	+	7.73490i	−0.541994	+	0.312920i
$612$		0			0
$613$	8.29710	−	14.3710i	0.335117	−	0.580439i	−0.648390	−	0.761308i	$-0.724558\pi$
$613$	8.29710	−	14.3710i	0.335117	−	0.580439i	0.983507	+	0.180869i	$0.0578909\pi$
$614$	7.78327	−	13.4810i	0.314107	−	0.544050i
$615$		0			0
$616$	−8.14898	−	6.57194i	−0.328332	−	0.264791i
$617$	40.0027	+	23.0956i	1.61045	+	0.929793i	0.989266	+	0.146128i	$0.0466813\pi$
$617$	40.0027	+	23.0956i	1.61045	+	0.929793i	0.621184	+	0.783665i	$0.286652\pi$
$618$		0			0
$619$			18.0967i			0.727366i	0.931523	+	0.363683i	$0.118481\pi$
$619$			18.0967i			0.727366i	−0.931523	+	0.363683i	$0.881519\pi$
$620$	−4.83278	−	2.79020i	−0.194089	−	0.112057i
$621$		0			0
$622$			20.1669i			0.808618i
$623$	−5.66215	+	36.2186i	−0.226849	+	1.45107i
$624$		0			0
$625$	1.00000			0.0400000
$626$	−3.33602	−	5.77815i	−0.133334	−	0.230941i
$627$		0			0
$628$	14.5468	+	8.39860i	0.580481	+	0.335141i
$629$	10.0568			0.400991
$630$		0			0
$631$	8.36756			0.333107			0.166554	−	0.986032i	$-0.446736\pi$
$631$	8.36756			0.333107			0.166554	+	0.986032i	$0.446736\pi$
$632$	1.59476	+	0.920736i	0.0634362	+	0.0366249i
$633$		0			0
$634$	−12.7708	−	22.1197i	−0.507193	−	0.878484i
$635$	20.5777			0.816602
$636$		0			0
$637$	6.97372	−	21.7590i	0.276309	−	0.862124i
$638$			18.7453i			0.742132i
$639$		0			0
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$			17.2032i			0.679485i	0.940518	+	0.339743i	$0.110340\pi$
$641$			17.2032i			0.679485i	−0.940518	+	0.339743i	$0.889660\pi$
$642$		0			0
$643$	−33.1046	−	19.1129i	−1.30552	−	0.753740i	−0.324172	−	0.945998i	$-0.605086\pi$
$643$	−33.1046	−	19.1129i	−1.30552	−	0.753740i	−0.981344	+	0.192258i	$0.938419\pi$
$644$	−20.1536	−	3.15067i	−0.794164	−	0.124154i
$645$		0			0
$646$	2.81872	−	4.88217i	0.110901	−	0.192086i
$647$	7.26184	−	12.5779i	0.285492	−	0.494487i	−0.687236	−	0.726434i	$-0.741176\pi$
$647$	7.26184	−	12.5779i	0.285492	−	0.494487i	0.972728	+	0.231947i	$0.0745096\pi$
$648$		0			0
$649$	−11.6755	+	6.74088i	−0.458305	+	0.264603i
$650$	−1.63209	−	2.82686i	−0.0640158	−	0.110879i
$651$		0			0
$652$	−0.864749	+	1.49779i	−0.0338662	+	0.0586580i
$653$		−	20.8516i		−	0.815987i	−0.912985	−	0.407994i	$-0.866229\pi$
$653$		−	20.8516i		−	0.815987i	0.912985	−	0.407994i	$-0.133771\pi$
$654$		0			0
$655$	−5.00917			−0.195725
$656$	5.16567	+	8.94721i	0.201686	+	0.349330i
$657$		0			0
$658$	12.3884	+	1.93672i	0.482952	+	0.0755011i
$659$	19.3743	−	11.1857i	0.754715	−	0.435735i	−0.0726801	−	0.997355i	$-0.523155\pi$
$659$	19.3743	−	11.1857i	0.754715	−	0.435735i	0.827395	+	0.561621i	$0.189822\pi$
$660$		0			0
$661$	−38.5676	+	22.2670i	−1.50011	+	0.866086i	−0.500106	+	0.865964i	$0.666705\pi$
$661$	−38.5676	+	22.2670i	−1.50011	+	0.866086i	−1.00000		0.000121967i	$0.999961\pi$
$662$	−1.56991	+	0.906390i	−0.0610164	+	0.0352279i
$663$		0			0
$664$	1.36802	−	0.789829i	0.0530896	−	0.0306513i
$665$	−14.8156	−	2.31617i	−0.574526	−	0.0898171i
$666$		0			0
$667$	18.2625	+	31.6316i	0.707126	+	1.22478i
$668$	0.742044			0.0287105
$669$		0			0
$670$		−	9.22190i		−	0.356273i
$671$	−12.4628	+	21.5863i	−0.481123	+	0.833329i
$672$		0			0
$673$	−2.10536	−	3.64659i	−0.0811557	−	0.140566i	0.822591	−	0.568634i	$-0.192528\pi$
$673$	−2.10536	−	3.64659i	−0.0811557	−	0.140566i	−0.903747	+	0.428068i	$0.859194\pi$
$674$	12.3926	−	7.15488i	0.477346	−	0.275596i
$675$		0			0
$676$	1.17257	−	2.03096i	0.0450990	−	0.0781138i
$677$	19.8282	−	34.3434i	0.762059	−	1.31992i	−0.179729	−	0.983716i	$-0.557522\pi$
$677$	19.8282	−	34.3434i	0.762059	−	1.31992i	0.941788	−	0.336209i	$-0.109145\pi$
$678$		0			0
$679$	2.34521	+	0.366633i	0.0900009	+	0.0140701i
$680$	−0.861388	−	0.497322i	−0.0330327	−	0.0190714i
$681$		0			0
$682$		−	22.0808i		−	0.845517i
$683$	−39.4682	−	22.7869i	−1.51021	−	0.871918i	−0.999929	−	0.0119087i	$-0.996209\pi$
$683$	−39.4682	−	22.7869i	−1.51021	−	0.871918i	−0.510278	−	0.860010i	$-0.670457\pi$
$684$		0			0
$685$			9.23672i			0.352917i
$686$	−15.4715	+	10.1800i	−0.590706	+	0.388673i
$687$		0			0
$688$	−10.2058			−0.389094
$689$	−16.6274	−	28.7995i	−0.633453	−	1.09717i
$690$		0			0
$691$	−17.0955	−	9.87010i	−0.650344	−	0.375476i	0.138244	−	0.990398i	$-0.455854\pi$
$691$	−17.0955	−	9.87010i	−0.650344	−	0.375476i	−0.788588	+	0.614922i	$0.789187\pi$
$692$	−0.964238			−0.0366548
$693$		0			0
$694$	6.00500			0.227947
$695$	−11.2919	−	6.51936i	−0.428325	−	0.247293i
$696$		0			0
$697$	5.13801	+	8.89930i	0.194616	+	0.337085i
$698$	−13.4127			−0.507677
$699$		0			0
$700$	−0.408654	+	2.61400i	−0.0154457	+	0.0988000i
$701$			13.6845i			0.516855i	0.966031	+	0.258427i	$0.0832043\pi$
$701$			13.6845i			0.516855i	−0.966031	+	0.258427i	$0.916796\pi$
$702$		0			0
$703$	49.6292	+	28.6534i	1.87180	+	1.08068i
$704$		−	3.95684i		−	0.149129i
$705$		0			0
$706$	0.437675	+	0.252692i	0.0164721	+	0.00951017i
$707$	0.444216	+	0.358249i	0.0167065	+	0.0134733i
$708$		0			0
$709$	3.49061	−	6.04592i	0.131093	−	0.227059i	−0.793005	−	0.609215i	$-0.791485\pi$
$709$	3.49061	−	6.04592i	0.131093	−	0.227059i	0.924098	+	0.382155i	$0.124818\pi$
$710$	1.37483	−	2.38127i	0.0515963	−	0.0893675i
$711$		0			0
$712$	−11.9993	+	6.92781i	−0.449694	+	0.259631i
$713$	−21.5121	−	37.2601i	−0.805635	−	1.39540i
$714$		0			0
$715$	6.45792	−	11.1854i	0.241512	−	0.418312i
$716$			0.214781i			0.00802676i
$717$		0			0
$718$	−13.0190			−0.485866
$719$	7.49920	+	12.9890i	0.279673	+	0.484408i	0.971303	−	0.237844i	$-0.0764406\pi$
$719$	7.49920	+	12.9890i	0.279673	+	0.484408i	−0.691630	+	0.722252i	$0.743107\pi$
$720$		0			0
$721$	−18.8571	+	23.3821i	−0.702273	+	0.870795i
$722$	11.3657	−	6.56197i	0.422986	−	0.244211i
$723$		0			0
$724$	9.67842	−	5.58784i	0.359696	−	0.207670i
$725$	4.10273	−	2.36871i	0.152372	−	0.0879718i
$726$		0			0
$727$	22.4642	−	12.9697i	0.833152	−	0.481020i	−0.0217788	−	0.999763i	$-0.506933\pi$
$727$	22.4642	−	12.9697i	0.833152	−	0.481020i	0.854931	+	0.518742i	$0.173600\pi$
$728$	8.05637	−	3.11107i	0.298589	−	0.115304i
$729$		0			0
$730$	−7.36348	−	12.7539i	−0.272534	−	0.472044i
$731$	−10.1512			−0.375455
$732$		0			0
$733$			22.7143i			0.838973i	0.907762	+	0.419486i	$0.137790\pi$
$733$			22.7143i			0.838973i	−0.907762	+	0.419486i	$0.862210\pi$
$734$	16.0143	−	27.7376i	0.591100	−	1.02382i
$735$		0			0
$736$	−3.85494	−	6.67695i	−0.142095	−	0.246116i
$737$	31.6009	−	18.2448i	1.16404	−	0.672056i
$738$		0			0
$739$	−6.74623	+	11.6848i	−0.248164	+	0.429833i	−0.963016	−	0.269443i	$-0.913161\pi$
$739$	−6.74623	+	11.6848i	−0.248164	+	0.429833i	0.714852	+	0.699275i	$0.246494\pi$
$740$	5.05548	−	8.75634i	0.185843	−	0.321890i
$741$		0			0
$742$	−4.16328	+	26.6309i	−0.152839	+	0.977652i
$743$	32.3371	+	18.6698i	1.18633	+	0.684930i	0.957471	−	0.288529i	$-0.0931662\pi$
$743$	32.3371	+	18.6698i	1.18633	+	0.684930i	0.228862	+	0.973459i	$0.426500\pi$
$744$		0			0
$745$			22.0661i			0.808440i
$746$	5.88964	+	3.40038i	0.215635	+	0.124497i
$747$		0			0
$748$		−	3.93565i		−	0.143902i
$749$	16.7087	+	2.61212i	0.610523	+	0.0954447i
$750$		0			0
$751$	−30.6698			−1.11916			−0.559579	−	0.828777i	$-0.689037\pi$
$751$	−30.6698			−1.11916			−0.559579	+	0.828777i	$0.689037\pi$
$752$	2.36963	+	4.10432i	0.0864116	+	0.149669i
$753$		0			0
$754$	−13.3920	−	7.73190i	−0.487710	−	0.281579i
$755$	5.53782			0.201542
$756$		0			0
$757$	−22.5697			−0.820308			−0.410154	−	0.912016i	$-0.634525\pi$
$757$	−22.5697			−0.820308			−0.410154	+	0.912016i	$0.634525\pi$
$758$	1.85889	+	1.07323i	0.0675179	+	0.0389815i
$759$		0			0
$760$	−2.83390	−	4.90846i	−0.102796	−	0.178048i
$761$	−20.2312			−0.733382			−0.366691	−	0.930343i	$-0.619509\pi$
$761$	−20.2312			−0.733382			−0.366691	+	0.930343i	$0.619509\pi$
$762$		0			0
$763$	3.03907	−	1.17358i	0.110022	−	0.0424864i
$764$		−	18.8822i		−	0.683133i
$765$		0			0
$766$	−0.615351	−	0.355273i	−0.0222335	−	0.0128365i
$767$		−	11.1217i		−	0.401582i
$768$		0			0
$769$	−29.9888	−	17.3140i	−1.08142	−	0.624359i	−0.150143	−	0.988664i	$-0.547973\pi$
$769$	−29.9888	−	17.3140i	−1.08142	−	0.624359i	−0.931280	+	0.364305i	$0.881307\pi$
$770$	−9.76595	+	3.77125i	−0.351941	+	0.135906i
$771$		0			0
$772$	−2.94509	+	5.10105i	−0.105996	+	0.183591i
$773$	−9.02636	+	15.6341i	−0.324656	+	0.562320i	−0.981443	−	0.191756i	$-0.938582\pi$
$773$	−9.02636	+	15.6341i	−0.324656	+	0.562320i	0.656787	+	0.754076i	$0.271915\pi$
$774$		0			0
$775$	−4.83278	+	2.79020i	−0.173598	+	0.100227i
$776$	0.448586	+	0.776974i	0.0161033	+	0.0278917i
$777$		0			0
$778$	−9.80747	+	16.9870i	−0.351615	+	0.609015i
$779$			58.5560i			2.09799i
$780$		0			0
$781$	10.8799			0.389315
$782$	−3.83429	−	6.64119i	−0.137114	−	0.237488i
$783$		0			0
$784$	−6.66600	−	2.13644i	−0.238072	−	0.0763015i
$785$	14.5468	−	8.39860i	0.519198	−	0.299759i
$786$		0			0
$787$	1.54781	−	0.893627i	0.0551734	−	0.0318544i	−0.472160	−	0.881513i	$-0.656525\pi$
$787$	1.54781	−	0.893627i	0.0551734	−	0.0318544i	0.527333	+	0.849659i	$0.323192\pi$
$788$	20.8527	−	12.0393i	0.742846	−	0.428882i
$789$		0			0
$790$	1.59476	−	0.920736i	0.0567391	−	0.0327583i
$791$	8.05601	+	20.8617i	0.286439	+	0.741756i
$792$		0			0
$793$	−10.2812	−	17.8075i	−0.365094	−	0.632362i
$794$	23.9395			0.849580
$795$		0			0
$796$			15.2132i			0.539216i
$797$	−21.5468	+	37.3202i	−0.763227	+	1.32195i	0.177951	+	0.984039i	$0.443053\pi$
$797$	−21.5468	+	37.3202i	−0.763227	+	1.32195i	−0.941179	+	0.337909i	$0.890280\pi$
$798$		0			0
$799$	2.35694	+	4.08234i	0.0833826	+	0.144423i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$		0			0
$802$	0.337812	−	0.585108i	0.0119286	−	0.0206609i
$803$	29.1361	−	50.4652i	1.02819	−	1.78088i
$804$		0			0
$805$	−12.8054	+	15.8782i	−0.451330	+	0.559633i
$806$	15.7750	+	9.10772i	0.555652	+	0.320806i
$807$		0			0
$808$			0.215695i			0.00758812i
$809$	31.6514	+	18.2739i	1.11280	+	0.642478i	0.939554	−	0.342400i	$-0.111240\pi$
$809$	31.6514	+	18.2739i	1.11280	+	0.642478i	0.173250	+	0.984878i	$0.444573\pi$
$810$		0			0
$811$		−	0.856906i		−	0.0300900i	−0.999887	−	0.0150450i	$-0.995211\pi$
$811$		−	0.856906i		−	0.0300900i	0.999887	−	0.0150450i	$-0.00478916\pi$
$812$	4.51523	+	11.6925i	0.158453	+	0.410327i
$813$		0			0
$814$	40.0074			1.40226
$815$	0.864749	+	1.49779i	0.0302908	+	0.0524653i
$816$		0			0
$817$	−50.0949	−	28.9223i	−1.75260	−	1.01186i
$818$	−30.3557			−1.06136
$819$		0			0
$820$	10.3313			0.360786
$821$	11.7056	+	6.75824i	0.408529	+	0.235864i	0.690157	−	0.723659i	$-0.257541\pi$
$821$	11.7056	+	6.75824i	0.408529	+	0.235864i	−0.281629	+	0.959523i	$0.590875\pi$
$822$		0			0
$823$	7.48663	+	12.9672i	0.260968	+	0.452009i	0.966499	−	0.256669i	$-0.0826251\pi$
$823$	7.48663	+	12.9672i	0.260968	+	0.452009i	−0.705532	+	0.708678i	$0.749292\pi$
$824$	−11.3535			−0.395517
$825$		0			0
$826$	−5.65904	+	7.01701i	−0.196903	+	0.244153i
$827$		−	14.6192i		−	0.508361i	−0.967157	−	0.254180i	$-0.918194\pi$
$827$		−	14.6192i		−	0.508361i	0.967157	−	0.254180i	$-0.0818057\pi$
$828$		0			0
$829$	3.40972	+	1.96860i	0.118425	+	0.0683724i	0.558042	−	0.829813i	$-0.311553\pi$
$829$	3.40972	+	1.96860i	0.118425	+	0.0683724i	−0.439618	+	0.898185i	$0.644886\pi$
$830$		−	1.57966i		−	0.0548308i
$831$		0			0
$832$	2.82686	+	1.63209i	0.0980037	+	0.0565825i
$833$	−6.63031	−	2.12500i	−0.229726	−	0.0736269i
$834$		0			0
$835$	0.371022	−	0.642629i	0.0128397	−	0.0222391i
$836$	11.2133	−	19.4220i	0.387820	−	0.671724i
$837$		0			0
$838$	10.1808	−	5.87786i	0.351688	−	0.203047i
$839$	16.9706	+	29.3940i	0.585891	+	1.01479i	0.994764	+	0.102202i	$0.0325888\pi$
$839$	16.9706	+	29.3940i	0.585891	+	1.01479i	−0.408872	+	0.912592i	$0.634078\pi$
$840$		0			0
$841$	−3.27839	+	5.67833i	−0.113048	+	0.195804i
$842$			28.9113i			0.996351i
$843$		0			0
$844$	−6.22217			−0.214176
$845$	−1.17257	−	2.03096i	−0.0403378	−	0.0698671i
$846$		0			0
$847$	−9.59010	−	7.73417i	−0.329520	−	0.265749i
$848$	−8.82289	+	5.09390i	−0.302979	+	0.174925i
$849$		0			0
$850$	−0.861388	+	0.497322i	−0.0295453	+	0.0170580i
$851$	67.5103	−	38.9771i	2.31422	−	1.33612i
$852$		0			0
$853$	−27.7997	+	16.0501i	−0.951843	+	0.549547i	−0.893653	−	0.448759i	$-0.851866\pi$
$853$	−27.7997	+	16.0501i	−0.951843	+	0.549547i	−0.0581898	+	0.998306i	$0.518533\pi$
$854$	−2.57427	+	16.4666i	−0.0880896	+	0.563476i
$855$		0			0
$856$	3.19600	+	5.53564i	0.109237	+	0.189204i
$857$	14.7405			0.503525			0.251763	−	0.967789i	$-0.418990\pi$
$857$	14.7405			0.503525			0.251763	+	0.967789i	$0.418990\pi$
$858$		0			0
$859$			1.58168i			0.0539661i	0.999636	+	0.0269831i	$0.00859002\pi$
$859$			1.58168i			0.0539661i	−0.999636	+	0.0269831i	$0.991410\pi$
$860$	−5.10292	+	8.83852i	−0.174008	+	0.301391i
$861$		0			0
$862$	9.97444	+	17.2762i	0.339731	+	0.588431i
$863$	5.03980	−	2.90973i	0.171557	−	0.0990483i	−0.411763	−	0.911291i	$-0.635087\pi$
$863$	5.03980	−	2.90973i	0.171557	−	0.0990483i	0.583320	+	0.812243i	$0.301753\pi$
$864$		0			0
$865$	−0.482119	+	0.835055i	−0.0163925	+	0.0283927i
$866$	14.4078	−	24.9551i	0.489598	−	0.848009i
$867$		0			0
$868$	−5.31867	−	13.7731i	−0.180527	−	0.467490i
$869$	6.31022	+	3.64321i	0.214060	+	0.123587i
$870$		0			0
$871$			30.1019i			1.01996i
$872$	1.06636	+	0.615666i	0.0361117	+	0.0208491i
$873$		0			0
$874$		−	43.6980i		−	1.47811i
$875$	2.05946	+	1.66090i	0.0696226	+	0.0561488i
$876$		0			0
$877$	−48.1745			−1.62674			−0.813369	−	0.581748i	$-0.802369\pi$
$877$	−48.1745			−1.62674			−0.813369	+	0.581748i	$0.802369\pi$
$878$	4.08760	+	7.07993i	0.137950	+	0.238936i
$879$		0			0
$880$	−3.42673	−	1.97842i	−0.115515	−	0.0666926i
$881$	−53.9354			−1.81713			−0.908566	−	0.417742i	$-0.862822\pi$
$881$	−53.9354			−1.81713			−0.908566	+	0.417742i	$0.862822\pi$
$882$		0			0
$883$	−42.9089			−1.44400			−0.722000	−	0.691893i	$-0.756777\pi$
$883$	−42.9089			−1.44400			−0.722000	+	0.691893i	$0.756777\pi$
$884$	2.81172	+	1.62335i	0.0945684	+	0.0545991i
$885$		0			0
$886$	13.1350	+	22.7505i	0.441279	+	0.764317i
$887$	−19.1085			−0.641600			−0.320800	−	0.947147i	$-0.603952\pi$
$887$	−19.1085			−0.641600			−0.320800	+	0.947147i	$0.603952\pi$
$888$		0			0
$889$	42.3791	+	34.1776i	1.42135	+	1.14628i
$890$			13.8556i			0.464442i
$891$		0			0
$892$	−4.37102	−	2.52361i	−0.146353	−	0.0844968i
$893$			26.8612i			0.898876i
$894$		0			0
$895$	0.186006	+	0.107391i	0.00621750	+	0.00358968i
$896$	−0.953096	−	2.46812i	−0.0318407	−	0.0824540i
$897$		0			0
$898$	3.19845	−	5.53988i	0.106734	−	0.184868i
$899$	−13.2184	+	22.8949i	−0.440858	+	0.763589i
$900$		0			0
$901$	−8.77564	+	5.06662i	−0.292359	+	0.168794i
$902$	20.4398	+	35.4027i	0.680570	+	1.17878i
$903$		0			0
$904$	−4.22623	+	7.32005i	−0.140562	+	0.243461i
$905$		−	11.1757i		−	0.371492i
$906$		0			0
$907$	−27.0455			−0.898032			−0.449016	−	0.893524i	$-0.648225\pi$
$907$	−27.0455			−0.898032			−0.449016	+	0.893524i	$0.648225\pi$
$908$	2.53981	+	4.39908i	0.0842865	+	0.145989i
$909$		0			0
$910$	1.33392	−	8.53256i	0.0442189	−	0.282852i
$911$	−4.11941	+	2.37834i	−0.136482	+	0.0787979i	−0.566686	−	0.823934i	$-0.691775\pi$
$911$	−4.11941	+	2.37834i	−0.136482	+	0.0787979i	0.430204	+	0.902732i	$0.358442\pi$
$912$		0			0
$913$	5.41306	−	3.12523i	0.179146	−	0.103430i
$914$	8.94322	−	5.16337i	0.295815	−	0.170789i
$915$		0			0
$916$	25.6828	−	14.8280i	0.848582	−	0.489929i
$917$	−10.3162	−	8.31976i	−0.340671	−	0.274743i
$918$		0			0
$919$	−17.3173	−	29.9945i	−0.571245	−	0.989426i	−0.996438	−	0.0843232i	$-0.973127\pi$
$919$	−17.3173	−	29.9945i	−0.571245	−	0.989426i	0.425193	−	0.905103i	$-0.360206\pi$
$920$	−7.70987			−0.254187
$921$		0			0
$922$		−	8.00758i		−	0.263715i
$923$	−4.48768	+	7.77289i	−0.147714	+	0.255848i
$924$		0			0
$925$	−5.05548	−	8.75634i	−0.166223	−	0.287907i
$926$	26.4770	−	15.2865i	0.870089	−	0.502346i
$927$		0			0
$928$	−2.36871	+	4.10273i	−0.0777569	+	0.134679i
$929$	14.6395	−	25.3564i	0.480307	−	0.831917i	−0.519437	−	0.854509i	$-0.673858\pi$
$929$	14.6395	−	25.3564i	0.480307	−	0.831917i	0.999745	+	0.0225917i	$0.00719178\pi$
$930$		0			0
$931$	−26.6653	−	29.3774i	−0.873921	−	0.962806i
$932$	15.8420	+	9.14639i	0.518922	+	0.299600i
$933$		0			0
$934$		−	7.22034i		−	0.236257i
$935$	−3.40837	−	1.96783i	−0.111466	−	0.0643548i
$936$		0			0
$937$			25.3740i			0.828932i	0.910065	+	0.414466i	$0.136032\pi$
$937$			25.3740i			0.828932i	−0.910065	+	0.414466i	$0.863968\pi$
$938$	15.3167	−	18.9922i	0.500108	−	0.620117i
$939$		0			0
$940$	4.73926			0.154578
$941$	6.09522	+	10.5572i	0.198699	+	0.344156i	0.948107	−	0.317952i	$-0.102995\pi$
$941$	6.09522	+	10.5572i	0.198699	+	0.344156i	−0.749408	+	0.662108i	$0.769662\pi$
$942$		0			0
$943$	68.9819	+	39.8267i	2.24636	+	1.29694i
$944$	−3.40720			−0.110895
$945$		0			0
$946$	−40.3829			−1.31296
$947$	−14.1104	−	8.14666i	−0.458527	−	0.264731i	0.252898	−	0.967493i	$-0.418616\pi$
$947$	−14.1104	−	8.14666i	−0.458527	−	0.264731i	−0.711425	+	0.702762i	$0.751950\pi$
$948$		0			0
$949$	24.0357	+	41.6310i	0.780231	+	1.35140i
$950$	−5.66780			−0.183888
$951$		0			0
$952$	−0.947992	−	2.45490i	−0.0307246	−	0.0795638i
$953$		−	58.2513i		−	1.88695i	−0.331449	−	0.943473i	$-0.607538\pi$
$953$		−	58.2513i		−	1.88695i	0.331449	−	0.943473i	$-0.392462\pi$
$954$		0			0
$955$	−16.3524	−	9.44109i	−0.529153	−	0.305506i
$956$		−	6.99331i		−	0.226180i
$957$		0			0
$958$	−15.8239	−	9.13594i	−0.511248	−	0.295169i
$959$	−15.3413	+	19.0227i	−0.495397	+	0.614275i
$960$		0			0
$961$	0.0704801	−	0.122075i	0.00227355	−	0.00393791i
$962$	−16.5020	+	28.5822i	−0.532045	+	0.921529i
$963$		0			0
$964$	−4.77687	+	2.75793i	−0.153853	+	0.0888269i
$965$	2.94509	+	5.10105i	0.0948058	+	0.164209i
$966$		0			0
$967$	5.61342	−	9.72273i	0.180515	−	0.312662i	−0.761541	−	0.648117i	$-0.775557\pi$
$967$	5.61342	−	9.72273i	0.180515	−	0.312662i	0.942056	+	0.335455i	$0.108890\pi$
$968$		−	4.65660i		−	0.149669i
$969$		0			0
$970$	0.897172			0.0288065
$971$	8.18607	+	14.1787i	0.262704	+	0.455016i	0.966959	−	0.254930i	$-0.0820525\pi$
$971$	8.18607	+	14.1787i	0.262704	+	0.455016i	−0.704256	+	0.709946i	$0.748719\pi$
$972$		0			0
$973$	−12.4272	−	32.1811i	−0.398396	−	1.03168i
$974$	−33.4057	+	19.2868i	−1.07039	+	0.617988i
$975$		0			0
$976$	−5.45543	+	3.14969i	−0.174624	+	0.100819i
$977$	50.6299	−	29.2312i	1.61979	−	0.935189i	0.632823	−	0.774297i	$-0.281896\pi$
$977$	50.6299	−	29.2312i	1.61979	−	0.935189i	0.986972	−	0.160892i	$-0.0514371\pi$
$978$		0			0
$979$	−47.4794	+	27.4123i	−1.51745	+	0.876100i
$980$	−5.18322	+	4.70471i	−0.165572	+	0.150286i
$981$		0			0
$982$	−12.3235	−	21.3449i	−0.393258	−	0.681143i
$983$	25.3666			0.809070			0.404535	−	0.914522i	$-0.367433\pi$
$983$	25.3666			0.809070			0.404535	+	0.914522i	$0.367433\pi$
$984$		0			0
$985$		−	24.0786i		−	0.767208i
$986$	−2.35603	+	4.08076i	−0.0750312	+	0.129958i
$987$		0			0
$988$	9.25035	+	16.0221i	0.294293	+	0.509730i
$989$	−68.1438	+	39.3429i	−2.16685	+	1.25103i
$990$		0			0
$991$	−11.2022	+	19.4028i	−0.355850	+	0.616349i	−0.987263	−	0.159097i	$-0.949142\pi$
$991$	−11.2022	+	19.4028i	−0.355850	+	0.616349i	0.631413	+	0.775446i	$0.282475\pi$
$992$	2.79020	−	4.83278i	0.0885891	−	0.153441i
$993$		0			0
$994$	6.78647	−	2.62069i	0.215254	−	0.0831231i
$995$	13.1750	+	7.60658i	0.417675	+	0.241145i
$996$		0			0
$997$			24.3980i			0.772693i	0.922354	+	0.386346i	$0.126263\pi$
$997$			24.3980i			0.772693i	−0.922354	+	0.386346i	$0.873737\pi$
$998$	9.10884	+	5.25899i	0.288335	+	0.166470i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.t.b.1151.9		28
3.2	odd	2		630.2.t.b.311.2	✓	28
7.5	odd	6		1890.2.bk.b.341.12		28
9.2	odd	6		1890.2.bk.b.521.12		28
9.7	even	3		630.2.bk.b.101.1	yes	28
21.5	even	6		630.2.bk.b.131.8	yes	28
63.47	even	6	inner	1890.2.t.b.1601.9		28
63.61	odd	6		630.2.t.b.551.2	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.2	✓	28	3.2	odd	2
630.2.t.b.551.2	yes	28	63.61	odd	6
630.2.bk.b.101.1	yes	28	9.7	even	3
630.2.bk.b.131.8	yes	28	21.5	even	6
1890.2.t.b.1151.9		28	1.1	even	1	trivial
1890.2.t.b.1601.9		28	63.47	even	6	inner
1890.2.bk.b.341.12		28	7.5	odd	6
1890.2.bk.b.521.12		28	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(2.05946 + 1.66090i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(2.05946 + 1.66090i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{10} +3.95684i q^{11} +(-2.82686 - 1.63209i) q^{13} +(0.953096 + 2.46812i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.497322 + 0.861388i) q^{17} +(-4.90846 + 2.83390i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-1.97842 + 3.42673i) q^{22} +7.70987i q^{23} +1.00000 q^{25} +(-1.63209 - 2.82686i) q^{26} +(-0.408654 + 2.61400i) q^{28} +(4.10273 - 2.36871i) q^{29} +(-4.83278 + 2.79020i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-0.861388 + 0.497322i) q^{34} +(2.05946 + 1.66090i) q^{35} +(-5.05548 - 8.75634i) q^{37} -5.66780 q^{38} +1.00000i q^{40} +(5.16567 - 8.94721i) q^{41} +(5.10292 + 8.83852i) q^{43} +(-3.42673 + 1.97842i) q^{44} +(-3.85494 + 6.67695i) q^{46} +(2.36963 - 4.10432i) q^{47} +(1.48279 + 6.84115i) q^{49} +(0.866025 + 0.500000i) q^{50} -3.26418i q^{52} +(8.82289 + 5.09390i) q^{53} +3.95684i q^{55} +(-1.66090 + 2.05946i) q^{56} +4.73743 q^{58} +(1.70360 + 2.95072i) q^{59} +(5.45543 + 3.14969i) q^{61} -5.58041 q^{62} -1.00000 q^{64} +(-2.82686 - 1.63209i) q^{65} +(-4.61095 - 7.98640i) q^{67} -0.994645 q^{68} +(0.953096 + 2.46812i) q^{70} -2.74965i q^{71} +(-12.7539 - 7.36348i) q^{73} -10.1110i q^{74} +(-4.90846 - 2.83390i) q^{76} +(-6.57194 + 8.14898i) q^{77} +(0.920736 - 1.59476i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(8.94721 - 5.16567i) q^{82} +(-0.789829 - 1.36802i) q^{83} +(-0.497322 + 0.861388i) q^{85} +10.2058i q^{86} -3.95684 q^{88} +(6.92781 + 11.9993i) q^{89} +(-3.11107 - 8.05637i) q^{91} +(-6.67695 + 3.85494i) q^{92} +(4.10432 - 2.36963i) q^{94} +(-4.90846 + 2.83390i) q^{95} +(0.776974 - 0.448586i) q^{97} +(-2.13644 + 6.66600i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7}+O(q^{10}) \) 28 * q + 14 * q^4 + 28 * q^5 - 4 * q^7	\( 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7} - 6 q^{14} - 14 q^{16} + 6 q^{17} - 6 q^{19} + 14 q^{20} - 6 q^{22} + 28 q^{25} - 12 q^{26} - 8 q^{28} - 12 q^{31} - 4 q^{35} + 4 q^{37} + 12 q^{38} - 18 q^{41} + 28 q^{43} - 18 q^{46} - 30 q^{47} - 14 q^{49} + 42 q^{53} - 6 q^{56} - 12 q^{58} + 24 q^{59} + 24 q^{61} + 12 q^{62} - 28 q^{64} - 40 q^{67} + 12 q^{68} - 6 q^{70} + 6 q^{73} - 6 q^{76} + 24 q^{77} + 2 q^{79} - 14 q^{80} + 24 q^{82} + 18 q^{83} + 6 q^{85} - 12 q^{88} - 6 q^{89} + 66 q^{91} + 30 q^{92} + 42 q^{94} - 6 q^{95} - 72 q^{97} + 24 q^{98}+O(q^{100}) \) 28 * q + 14 * q^4 + 28 * q^5 - 4 * q^7 - 6 * q^14 - 14 * q^16 + 6 * q^17 - 6 * q^19 + 14 * q^20 - 6 * q^22 + 28 * q^25 - 12 * q^26 - 8 * q^28 - 12 * q^31 - 4 * q^35 + 4 * q^37 + 12 * q^38 - 18 * q^41 + 28 * q^43 - 18 * q^46 - 30 * q^47 - 14 * q^49 + 42 * q^53 - 6 * q^56 - 12 * q^58 + 24 * q^59 + 24 * q^61 + 12 * q^62 - 28 * q^64 - 40 * q^67 + 12 * q^68 - 6 * q^70 + 6 * q^73 - 6 * q^76 + 24 * q^77 + 2 * q^79 - 14 * q^80 + 24 * q^82 + 18 * q^83 + 6 * q^85 - 12 * q^88 - 6 * q^89 + 66 * q^91 + 30 * q^92 + 42 * q^94 - 6 * q^95 - 72 * q^97 + 24 * q^98

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