LMFDB - Embedded newform 1890.2.t.b.1151.12

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			1151.12
Character	$\chi$	$=$	1890.1151
Dual form			1890.2.t.b.1601.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.82075 + 1.91960i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.82075 + 1.91960i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{10} +3.07697i q^{11} +(-0.449846 - 0.259719i) q^{13} +(-2.53662 + 0.752047i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.44423 - 4.23353i) q^{17} +(0.713627 - 0.412013i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-1.53849 + 2.66474i) q^{22} +8.94137i q^{23} +1.00000 q^{25} +(-0.259719 - 0.449846i) q^{26} +(-2.57280 - 0.617016i) q^{28} +(-5.55412 + 3.20667i) q^{29} +(-0.784474 + 0.452916i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(4.23353 - 2.44423i) q^{34} +(-1.82075 + 1.91960i) q^{35} +(2.53840 + 4.39664i) q^{37} +0.824025 q^{38} +1.00000i q^{40} +(-2.18596 + 3.78619i) q^{41} +(-1.84515 - 3.19589i) q^{43} +(-2.66474 + 1.53849i) q^{44} +(-4.47068 + 7.74345i) q^{46} +(-1.89222 + 3.27742i) q^{47} +(-0.369732 - 6.99023i) q^{49} +(0.866025 + 0.500000i) q^{50} -0.519437i q^{52} +(-4.69700 - 2.71181i) q^{53} +3.07697i q^{55} +(-1.91960 - 1.82075i) q^{56} -6.41334 q^{58} +(5.29109 + 9.16443i) q^{59} +(-8.24872 - 4.76240i) q^{61} -0.905833 q^{62} -1.00000 q^{64} +(-0.449846 - 0.259719i) q^{65} +(-3.95287 - 6.84657i) q^{67} +4.88846 q^{68} +(-2.53662 + 0.752047i) q^{70} +10.6760i q^{71} +(5.78211 + 3.33830i) q^{73} +5.07681i q^{74} +(0.713627 + 0.412013i) q^{76} +(-5.90656 - 5.60240i) q^{77} +(-1.73049 + 2.99730i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-3.78619 + 2.18596i) q^{82} +(3.32033 + 5.75098i) q^{83} +(2.44423 - 4.23353i) q^{85} -3.69030i q^{86} -3.07697 q^{88} +(-0.771960 - 1.33707i) q^{89} +(1.31761 - 0.390641i) q^{91} +(-7.74345 + 4.47068i) q^{92} +(-3.27742 + 1.89222i) q^{94} +(0.713627 - 0.412013i) q^{95} +(1.93786 - 1.11882i) q^{97} +(3.17492 - 6.23858i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	−1.82075	+	1.91960i	−0.688179	+	0.725541i
$7$	−1.82075	+	1.91960i	−0.688179	+	0.725541i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$			3.07697i			0.927743i	0.885903	+	0.463871i	$0.153540\pi$
$11$			3.07697i			0.927743i	−0.885903	+	0.463871i	$0.846460\pi$
$12$		0			0
$13$	−0.449846	−	0.259719i	−0.124765	−	0.0720330i	0.436319	−	0.899792i	$-0.356282\pi$
$13$	−0.449846	−	0.259719i	−0.124765	−	0.0720330i	−0.561084	+	0.827759i	$0.689615\pi$
$14$	−2.53662	+	0.752047i	−0.677939	+	0.200993i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.44423	−	4.23353i	0.592813	−	1.02678i	−0.401039	−	0.916061i	$-0.631351\pi$
$17$	2.44423	−	4.23353i	0.592813	−	1.02678i	0.993852	−	0.110721i	$-0.0353160\pi$
$18$		0			0
$19$	0.713627	−	0.412013i	0.163717	−	0.0945222i	−0.415903	−	0.909409i	$-0.636534\pi$
$19$	0.713627	−	0.412013i	0.163717	−	0.0945222i	0.579620	+	0.814887i	$0.303201\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$		0			0
$22$	−1.53849	+	2.66474i	−0.328007	+	0.568124i
$23$			8.94137i			1.86440i	0.361939	+	0.932202i	$0.382115\pi$
$23$			8.94137i			1.86440i	−0.361939	+	0.932202i	$0.617885\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	−0.259719	−	0.449846i	−0.0509350	−	0.0882220i
$27$		0			0
$28$	−2.57280	−	0.617016i	−0.486213	−	0.116605i
$29$	−5.55412	+	3.20667i	−1.03137	+	0.595464i	−0.917378	−	0.398017i	$-0.869698\pi$
$29$	−5.55412	+	3.20667i	−1.03137	+	0.595464i	−0.113996	+	0.993481i	$0.536365\pi$
$30$		0			0
$31$	−0.784474	+	0.452916i	−0.140896	+	0.0813462i	−0.568791	−	0.822482i	$-0.692589\pi$
$31$	−0.784474	+	0.452916i	−0.140896	+	0.0813462i	0.427895	+	0.903828i	$0.359255\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$	4.23353	−	2.44423i	0.726045	−	0.419182i
$35$	−1.82075	+	1.91960i	−0.307763	+	0.324472i
$36$		0			0
$37$	2.53840	+	4.39664i	0.417311	+	0.722804i	0.995668	−	0.0929800i	$-0.0296392\pi$
$37$	2.53840	+	4.39664i	0.417311	+	0.722804i	−0.578357	+	0.815784i	$0.696306\pi$
$38$	0.824025			0.133675
$39$		0			0
$40$			1.00000i			0.158114i
$41$	−2.18596	+	3.78619i	−0.341389	+	0.591304i	−0.984691	−	0.174309i	$-0.944231\pi$
$41$	−2.18596	+	3.78619i	−0.341389	+	0.591304i	0.643302	+	0.765613i	$0.277564\pi$
$42$		0			0
$43$	−1.84515	−	3.19589i	−0.281383	−	0.487369i	0.690343	−	0.723482i	$-0.257460\pi$
$43$	−1.84515	−	3.19589i	−0.281383	−	0.487369i	−0.971726	+	0.236113i	$0.924126\pi$
$44$	−2.66474	+	1.53849i	−0.401724	+	0.231936i
$45$		0			0
$46$	−4.47068	+	7.74345i	−0.659166	+	1.14171i
$47$	−1.89222	+	3.27742i	−0.276008	+	0.478060i	−0.970389	−	0.241547i	$-0.922345\pi$
$47$	−1.89222	+	3.27742i	−0.276008	+	0.478060i	0.694381	+	0.719608i	$0.255678\pi$
$48$		0			0
$49$	−0.369732	−	6.99023i	−0.0528188	−	0.998604i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$		0			0
$52$		−	0.519437i		−	0.0720330i
$53$	−4.69700	−	2.71181i	−0.645182	−	0.372496i	0.141426	−	0.989949i	$-0.454831\pi$
$53$	−4.69700	−	2.71181i	−0.645182	−	0.372496i	−0.786608	+	0.617453i	$0.788165\pi$
$54$		0			0
$55$			3.07697i			0.414899i
$56$	−1.91960	−	1.82075i	−0.256517	−	0.243308i
$57$		0			0
$58$	−6.41334			−0.842113
$59$	5.29109	+	9.16443i	0.688841	+	1.19311i	0.972213	+	0.234097i	$0.0752134\pi$
$59$	5.29109	+	9.16443i	0.688841	+	1.19311i	−0.283372	+	0.959010i	$0.591453\pi$
$60$		0			0
$61$	−8.24872	−	4.76240i	−1.05614	−	0.609763i	−0.131779	−	0.991279i	$-0.542069\pi$
$61$	−8.24872	−	4.76240i	−1.05614	−	0.609763i	−0.924362	+	0.381516i	$0.875402\pi$
$62$	−0.905833			−0.115041
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−0.449846	−	0.259719i	−0.0557965	−	0.0322141i
$66$		0			0
$67$	−3.95287	−	6.84657i	−0.482920	−	0.836442i	0.516888	−	0.856053i	$-0.327090\pi$
$67$	−3.95287	−	6.84657i	−0.482920	−	0.836442i	−0.999808	+	0.0196114i	$0.993757\pi$
$68$	4.88846			0.592813
$69$		0			0
$70$	−2.53662	+	0.752047i	−0.303184	+	0.0898868i
$71$			10.6760i			1.26701i	0.773741	+	0.633503i	$0.218383\pi$
$71$			10.6760i			1.26701i	−0.773741	+	0.633503i	$0.781617\pi$
$72$		0			0
$73$	5.78211	+	3.33830i	0.676744	+	0.390719i	0.798627	−	0.601826i	$-0.205560\pi$
$73$	5.78211	+	3.33830i	0.676744	+	0.390719i	−0.121883	+	0.992544i	$0.538893\pi$
$74$			5.07681i			0.590167i
$75$		0			0
$76$	0.713627	+	0.412013i	0.0818586	+	0.0472611i
$77$	−5.90656	−	5.60240i	−0.673115	−	0.638453i
$78$		0			0
$79$	−1.73049	+	2.99730i	−0.194696	+	0.337223i	−0.946801	−	0.321820i	$-0.895705\pi$
$79$	−1.73049	+	2.99730i	−0.194696	+	0.337223i	0.752105	+	0.659043i	$0.229039\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$		0			0
$82$	−3.78619	+	2.18596i	−0.418115	+	0.241399i
$83$	3.32033	+	5.75098i	0.364454	+	0.631252i	0.988688	−	0.149985i	$-0.0479224\pi$
$83$	3.32033	+	5.75098i	0.364454	+	0.631252i	−0.624235	+	0.781237i	$0.714589\pi$
$84$		0			0
$85$	2.44423	−	4.23353i	0.265114	−	0.459191i
$86$		−	3.69030i		−	0.397935i
$87$		0			0
$88$	−3.07697			−0.328007
$89$	−0.771960	−	1.33707i	−0.0818276	−	0.141729i	0.822207	−	0.569188i	$-0.192742\pi$
$89$	−0.771960	−	1.33707i	−0.0818276	−	0.141729i	−0.904035	+	0.427459i	$0.859409\pi$
$90$		0			0
$91$	1.31761	−	0.390641i	0.138123	−	0.0409503i
$92$	−7.74345	+	4.47068i	−0.807310	+	0.466101i
$93$		0			0
$94$	−3.27742	+	1.89222i	−0.338040	+	0.195167i
$95$	0.713627	−	0.412013i	0.0732166	−	0.0422716i
$96$		0			0
$97$	1.93786	−	1.11882i	0.196759	−	0.113599i	−0.398384	−	0.917219i	$-0.630429\pi$
$97$	1.93786	−	1.11882i	0.196759	−	0.113599i	0.595143	+	0.803620i	$0.297095\pi$
$98$	3.17492	−	6.23858i	0.320715	−	0.630192i
$99$		0			0
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	4.19679			0.417597			0.208798	−	0.977959i	$-0.433045\pi$
$101$	4.19679			0.417597			0.208798	+	0.977959i	$0.433045\pi$
$102$		0			0
$103$		−	0.701137i		−	0.0690851i	−0.999403	−	0.0345426i	$-0.989003\pi$
$103$		−	0.701137i		−	0.0690851i	0.999403	−	0.0345426i	$-0.0109974\pi$
$104$	0.259719	−	0.449846i	0.0254675	−	0.0441110i
$105$		0			0
$106$	−2.71181	−	4.69700i	−0.263395	−	0.456213i
$107$	17.8959	−	10.3322i	1.73006	−	0.998851i	0.841072	−	0.540924i	$-0.181925\pi$
$107$	17.8959	−	10.3322i	1.73006	−	0.998851i	0.888990	−	0.457927i	$-0.151408\pi$
$108$		0			0
$109$	−0.903287	+	1.56454i	−0.0865192	+	0.149856i	−0.906038	−	0.423197i	$-0.860908\pi$
$109$	−0.903287	+	1.56454i	−0.0865192	+	0.149856i	0.819518	+	0.573053i	$0.194241\pi$
$110$	−1.53849	+	2.66474i	−0.146689	+	0.254073i
$111$		0			0
$112$	−0.752047	−	2.53662i	−0.0710618	−	0.239688i
$113$	16.2514	+	9.38276i	1.52881	+	0.882656i	0.999412	+	0.0342794i	$0.0109136\pi$
$113$	16.2514	+	9.38276i	1.52881	+	0.882656i	0.529393	+	0.848377i	$0.322420\pi$
$114$		0			0
$115$			8.94137i			0.833787i
$116$	−5.55412	−	3.20667i	−0.515687	−	0.297732i
$117$		0			0
$118$			10.5822i			0.974168i
$119$	3.67635	+	12.4002i	0.337011	+	1.13672i
$120$		0			0
$121$	1.53223			0.139293
$122$	−4.76240	−	8.24872i	−0.431168	−	0.746804i
$123$		0			0
$124$	−0.784474	−	0.452916i	−0.0704479	−	0.0406731i
$125$	1.00000			0.0894427
$126$		0			0
$127$	1.53891			0.136556			0.0682779	−	0.997666i	$-0.478250\pi$
$127$	1.53891			0.136556			0.0682779	+	0.997666i	$0.478250\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	−0.259719	−	0.449846i	−0.0227788	−	0.0394541i
$131$	−10.5223			−0.919335			−0.459668	−	0.888091i	$-0.652031\pi$
$131$	−10.5223			−0.919335			−0.459668	+	0.888091i	$0.652031\pi$
$132$		0			0
$133$	−0.508437	+	2.12005i	−0.0440871	+	0.183832i
$134$		−	7.90574i		−	0.682952i
$135$		0			0
$136$	4.23353	+	2.44423i	0.363022	+	0.209591i
$137$		−	0.00335499i		−	0.000286636i	−1.00000		0.000143318i	$-0.999954\pi$
$137$		−	0.00335499i		−	0.000286636i	1.00000		0.000143318i	$-4.56196e-5\pi$
$138$		0			0
$139$	16.6324	+	9.60272i	1.41074	+	0.814492i	0.995458	−	0.0951995i	$-0.0303489\pi$
$139$	16.6324	+	9.60272i	1.41074	+	0.814492i	0.415284	+	0.909692i	$0.363682\pi$
$140$	−2.57280	−	0.617016i	−0.217441	−	0.0521474i
$141$		0			0
$142$	−5.33799	+	9.24567i	−0.447954	+	0.775879i
$143$	0.799148	−	1.38416i	0.0668281	−	0.115750i
$144$		0			0
$145$	−5.55412	+	3.20667i	−0.461244	+	0.266300i
$146$	3.33830	+	5.78211i	0.276280	+	0.478530i
$147$		0			0
$148$	−2.53840	+	4.39664i	−0.208655	+	0.361402i
$149$		−	12.0662i		−	0.988502i	−0.869319	−	0.494251i	$-0.835442\pi$
$149$		−	12.0662i		−	0.988502i	0.869319	−	0.494251i	$-0.164558\pi$
$150$		0			0
$151$	−14.6605			−1.19305			−0.596527	−	0.802593i	$-0.703453\pi$
$151$	−14.6605			−1.19305			−0.596527	+	0.802593i	$0.703453\pi$
$152$	0.412013	+	0.713627i	0.0334186	+	0.0578828i
$153$		0			0
$154$	−2.31403	−	7.80511i	−0.186470	−	0.628953i
$155$	−0.784474	+	0.452916i	−0.0630105	+	0.0363791i
$156$		0			0
$157$	−0.502653	+	0.290207i	−0.0401161	+	0.0231610i	−0.519924	−	0.854213i	$-0.674040\pi$
$157$	−0.502653	+	0.290207i	−0.0401161	+	0.0231610i	0.479808	+	0.877374i	$0.340706\pi$
$158$	−2.99730	+	1.73049i	−0.238453	+	0.137671i
$159$		0			0
$160$	−0.866025	+	0.500000i	−0.0684653	+	0.0395285i
$161$	−17.1638	−	16.2800i	−1.35270	−	1.28304i
$162$		0			0
$163$	0.0642633	+	0.111307i	0.00503349	+	0.00871827i	0.868531	−	0.495635i	$-0.165064\pi$
$163$	0.0642633	+	0.111307i	0.00503349	+	0.00871827i	−0.863498	+	0.504353i	$0.831731\pi$
$164$	−4.37192			−0.341389
$165$		0			0
$166$			6.64066i			0.515415i
$167$	12.6749	−	21.9535i	0.980811	−	1.69881i	0.321564	−	0.946888i	$-0.395791\pi$
$167$	12.6749	−	21.9535i	0.980811	−	1.69881i	0.659247	−	0.751927i	$-0.270875\pi$
$168$		0			0
$169$	−6.36509	−	11.0247i	−0.489622	−	0.848051i
$170$	4.23353	−	2.44423i	0.324697	−	0.187464i
$171$		0			0
$172$	1.84515	−	3.19589i	0.140691	−	0.243685i
$173$	−2.36631	+	4.09857i	−0.179907	+	0.311609i	−0.941849	−	0.336037i	$-0.890913\pi$
$173$	−2.36631	+	4.09857i	−0.179907	+	0.311609i	0.761941	+	0.647646i	$0.224246\pi$
$174$		0			0
$175$	−1.82075	+	1.91960i	−0.137636	+	0.145108i
$176$	−2.66474	−	1.53849i	−0.200862	−	0.115968i
$177$		0			0
$178$		−	1.54392i		−	0.115722i
$179$	6.52127	+	3.76505i	0.487422	+	0.281413i	0.723504	−	0.690320i	$-0.242530\pi$
$179$	6.52127	+	3.76505i	0.487422	+	0.281413i	−0.236082	+	0.971733i	$0.575863\pi$
$180$		0			0
$181$			12.3791i			0.920133i	0.887884	+	0.460067i	$0.152175\pi$
$181$			12.3791i			0.920133i	−0.887884	+	0.460067i	$0.847825\pi$
$182$	1.33641	+	0.320501i	0.0990611	+	0.0237571i
$183$		0			0
$184$	−8.94137			−0.659166
$185$	2.53840	+	4.39664i	0.186627	+	0.323248i
$186$		0			0
$187$	13.0265	+	7.52084i	0.952590	+	0.549978i
$188$	−3.78444			−0.276008
$189$		0			0
$190$	0.824025			0.0597811
$191$	−16.6514	−	9.61366i	−1.20485	−	0.695620i	−0.243220	−	0.969971i	$-0.578204\pi$
$191$	−16.6514	−	9.61366i	−1.20485	−	0.695620i	−0.961630	+	0.274351i	$0.911537\pi$
$192$		0			0
$193$	−11.8348	−	20.4985i	−0.851889	−	1.47551i	−0.879502	−	0.475896i	$-0.842124\pi$
$193$	−11.8348	−	20.4985i	−0.851889	−	1.47551i	0.0276128	−	0.999619i	$-0.491209\pi$
$194$	2.23764			0.160653
$195$		0			0
$196$	5.86885	−	3.81531i	0.419204	−	0.272522i
$197$			5.93788i			0.423057i	0.977372	+	0.211528i	$0.0678441\pi$
$197$			5.93788i			0.423057i	−0.977372	+	0.211528i	$0.932156\pi$
$198$		0			0
$199$	−14.4039	−	8.31608i	−1.02106	−	0.589511i	−0.106652	−	0.994296i	$-0.534013\pi$
$199$	−14.4039	−	8.31608i	−1.02106	−	0.589511i	−0.914412	+	0.404785i	$0.867346\pi$
$200$			1.00000i			0.0707107i
$201$		0			0
$202$	3.63453	+	2.09840i	0.255725	+	0.147643i
$203$	3.95714	−	16.5002i	0.277737	−	1.15809i
$204$		0			0
$205$	−2.18596	+	3.78619i	−0.152674	+	0.264439i
$206$	0.350569	−	0.607203i	0.0244253	−	0.0423058i
$207$		0			0
$208$	0.449846	−	0.259719i	0.0311912	−	0.0180082i
$209$	1.26775	+	2.19581i	0.0876923	+	0.151888i
$210$		0			0
$211$	10.7108	−	18.5516i	0.737360	−	1.27714i	−0.216320	−	0.976322i	$-0.569406\pi$
$211$	10.7108	−	18.5516i	0.737360	−	1.27714i	0.953680	−	0.300822i	$-0.0972611\pi$
$212$		−	5.42363i		−	0.372496i
$213$		0			0
$214$	20.6644			1.41259
$215$	−1.84515	−	3.19589i	−0.125838	−	0.217958i
$216$		0			0
$217$	0.558914	−	2.33053i	0.0379415	−	0.158206i
$218$	−1.56454	+	0.903287i	−0.105964	+	0.0611783i
$219$		0			0
$220$	−2.66474	+	1.53849i	−0.179657	+	0.103725i
$221$	−2.19905	+	1.26962i	−0.147924	+	0.0854042i
$222$		0			0
$223$	23.0028	−	13.2807i	1.54038	−	0.889340i	0.541569	−	0.840657i	$-0.317831\pi$
$223$	23.0028	−	13.2807i	1.54038	−	0.889340i	0.998814	−	0.0486838i	$-0.0155027\pi$
$224$	0.617016	−	2.57280i	0.0412261	−	0.171902i
$225$		0			0
$226$	9.38276	+	16.2514i	0.624132	+	1.08103i
$227$	26.7377			1.77464			0.887321	−	0.461152i	$-0.152564\pi$
$227$	26.7377			1.77464			0.887321	+	0.461152i	$0.152564\pi$
$228$		0			0
$229$			7.93372i			0.524275i	0.965031	+	0.262137i	$0.0844274\pi$
$229$			7.93372i			0.524275i	−0.965031	+	0.262137i	$0.915573\pi$
$230$	−4.47068	+	7.74345i	−0.294788	+	0.510588i
$231$		0			0
$232$	−3.20667	−	5.55412i	−0.210528	−	0.364646i
$233$	−24.2871	+	14.0222i	−1.59110	+	0.918623i	−0.597983	+	0.801509i	$0.704031\pi$
$233$	−24.2871	+	14.0222i	−1.59110	+	0.918623i	−0.993118	+	0.117114i	$0.962636\pi$
$234$		0			0
$235$	−1.89222	+	3.27742i	−0.123435	+	0.213795i
$236$	−5.29109	+	9.16443i	−0.344420	+	0.596554i
$237$		0			0
$238$	−3.01626	+	12.5770i	−0.195515	+	0.815247i
$239$	24.5540	+	14.1762i	1.58826	+	0.916985i	0.993593	+	0.113016i	$0.0360512\pi$
$239$	24.5540	+	14.1762i	1.58826	+	0.916985i	0.594671	+	0.803969i	$0.297282\pi$
$240$		0			0
$241$		−	0.954238i		−	0.0614679i	−0.999528	−	0.0307339i	$-0.990216\pi$
$241$		−	0.954238i		−	0.0614679i	0.999528	−	0.0307339i	$-0.00978446\pi$
$242$	1.32695	+	0.766113i	0.0852994	+	0.0492476i
$243$		0			0
$244$		−	9.52480i		−	0.609763i
$245$	−0.369732	−	6.99023i	−0.0236213	−	0.446589i
$246$		0			0
$247$	−0.428029			−0.0272349
$248$	−0.452916	−	0.784474i	−0.0287602	−	0.0498142i
$249$		0			0
$250$	0.866025	+	0.500000i	0.0547723	+	0.0316228i
$251$	−6.84608			−0.432121			−0.216060	−	0.976380i	$-0.569321\pi$
$251$	−6.84608			−0.432121			−0.216060	+	0.976380i	$0.569321\pi$
$252$		0			0
$253$	−27.5124			−1.72969
$254$	1.33273	+	0.769453i	0.0836230	+	0.0482798i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	26.4342			1.64892			0.824459	−	0.565922i	$-0.191479\pi$
$257$	26.4342			1.64892			0.824459	+	0.565922i	$0.191479\pi$
$258$		0			0
$259$	−13.0616	−	3.13247i	−0.811608	−	0.194642i
$260$		−	0.519437i		−	0.0322141i
$261$		0			0
$262$	−9.11256	−	5.26114i	−0.562976	−	0.325034i
$263$			25.7323i			1.58672i	0.608750	+	0.793362i	$0.291671\pi$
$263$			25.7323i			1.58672i	−0.608750	+	0.793362i	$0.708329\pi$
$264$		0			0
$265$	−4.69700	−	2.71181i	−0.288534	−	0.166585i
$266$	−1.50035	+	1.58180i	−0.0919921	+	0.0969864i
$267$		0			0
$268$	3.95287	−	6.84657i	0.241460	−	0.418221i
$269$	4.44806	−	7.70427i	0.271203	−	0.469738i	−0.697967	−	0.716130i	$-0.745912\pi$
$269$	4.44806	−	7.70427i	0.271203	−	0.469738i	0.969170	+	0.246392i	$0.0792451\pi$
$270$		0			0
$271$	19.2172	−	11.0951i	1.16736	−	0.673978i	0.214306	−	0.976767i	$-0.431251\pi$
$271$	19.2172	−	11.0951i	1.16736	−	0.673978i	0.953058	+	0.302789i	$0.0979176\pi$
$272$	2.44423	+	4.23353i	0.148203	+	0.256696i
$273$		0			0
$274$	0.00167750	−	0.00290551i	0.000101341	−	0.000175528i
$275$			3.07697i			0.185549i
$276$		0			0
$277$	12.6086			0.757576			0.378788	−	0.925484i	$-0.376341\pi$
$277$	12.6086			0.757576			0.378788	+	0.925484i	$0.376341\pi$
$278$	9.60272	+	16.6324i	0.575933	+	0.997545i
$279$		0			0
$280$	−1.91960	−	1.82075i	−0.114718	−	0.108811i
$281$	6.81401	−	3.93407i	0.406490	−	0.234687i	−0.282791	−	0.959182i	$-0.591260\pi$
$281$	6.81401	−	3.93407i	0.406490	−	0.234687i	0.689280	+	0.724495i	$0.257927\pi$
$282$		0			0
$283$	−25.5885	+	14.7735i	−1.52108	+	0.878193i	−0.521385	+	0.853322i	$0.674584\pi$
$283$	−25.5885	+	14.7735i	−1.52108	+	0.878193i	−0.999691	+	0.0248719i	$0.992082\pi$
$284$	−9.24567	+	5.33799i	−0.548629	+	0.316751i
$285$		0			0
$286$	1.38416	−	0.799148i	0.0818474	−	0.0472546i
$287$	−3.28789	−	11.0899i	−0.194078	−	0.654615i
$288$		0			0
$289$	−3.44853	−	5.97302i	−0.202854	−	0.351354i
$290$	−6.41334			−0.376605
$291$		0			0
$292$			6.67660i			0.390719i
$293$	3.97830	−	6.89061i	0.232415	−	0.402554i	−0.726104	−	0.687585i	$-0.758671\pi$
$293$	3.97830	−	6.89061i	0.232415	−	0.402554i	0.958518	+	0.285031i	$0.0920040\pi$
$294$		0			0
$295$	5.29109	+	9.16443i	0.308059	+	0.533574i
$296$	−4.39664	+	2.53840i	−0.255550	+	0.147542i
$297$		0			0
$298$	6.03310	−	10.4496i	0.349488	−	0.605332i
$299$	2.32224	−	4.02224i	0.134299	−	0.232612i
$300$		0			0
$301$	9.49440	+	2.27698i	0.547248	+	0.131243i
$302$	−12.6964	−	7.33025i	−0.730593	−	0.421808i
$303$		0			0
$304$			0.824025i			0.0472611i
$305$	−8.24872	−	4.76240i	−0.472320	−	0.272694i
$306$		0			0
$307$		−	33.8175i		−	1.93006i	−0.262132	−	0.965032i	$-0.584426\pi$
$307$		−	33.8175i		−	1.93006i	0.262132	−	0.965032i	$-0.415574\pi$
$308$	1.89854	−	7.91644i	0.108180	−	0.451081i
$309$		0			0
$310$	−0.905833			−0.0514479
$311$	11.6897	+	20.2471i	0.662861	+	1.14811i	0.979860	+	0.199684i	$0.0639914\pi$
$311$	11.6897	+	20.2471i	0.662861	+	1.14811i	−0.316999	+	0.948426i	$0.602675\pi$
$312$		0			0
$313$	14.9966	+	8.65830i	0.847659	+	0.489396i	0.859860	−	0.510529i	$-0.170551\pi$
$313$	14.9966	+	8.65830i	0.847659	+	0.489396i	−0.0122014	+	0.999926i	$0.503884\pi$
$314$	−0.580414			−0.0327546
$315$		0			0
$316$	−3.46099			−0.194696
$317$	−13.8006	−	7.96781i	−0.775121	−	0.447517i	0.0595771	−	0.998224i	$-0.481025\pi$
$317$	−13.8006	−	7.96781i	−0.775121	−	0.447517i	−0.834699	+	0.550707i	$0.814358\pi$
$318$		0			0
$319$	−9.86685	−	17.0899i	−0.552437	−	0.956850i
$320$	−1.00000			−0.0559017
$321$		0			0
$322$	−6.72433	−	22.6808i	−0.374732	−	1.26395i
$323$		−	4.02822i		−	0.224136i
$324$		0			0
$325$	−0.449846	−	0.259719i	−0.0249530	−	0.0144066i
$326$			0.128527i			0.00711843i
$327$		0			0
$328$	−3.78619	−	2.18596i	−0.209057	−	0.120699i
$329$	−2.84607	−	9.59966i	−0.156909	−	0.529247i
$330$		0			0
$331$	−4.20318	+	7.28013i	−0.231028	+	0.400152i	−0.958111	−	0.286398i	$-0.907542\pi$
$331$	−4.20318	+	7.28013i	−0.231028	+	0.400152i	0.727083	+	0.686550i	$0.240876\pi$
$332$	−3.32033	+	5.75098i	−0.182227	+	0.315626i
$333$		0			0
$334$	21.9535	−	12.6749i	1.20124	−	0.693538i
$335$	−3.95287	−	6.84657i	−0.215968	−	0.374068i
$336$		0			0
$337$	7.68218	−	13.3059i	0.418475	−	0.724820i	−0.577311	−	0.816524i	$-0.695898\pi$
$337$	7.68218	−	13.3059i	0.418475	−	0.724820i	0.995786	+	0.0917044i	$0.0292315\pi$
$338$		−	12.7302i		−	0.692431i
$339$		0			0
$340$	4.88846			0.265114
$341$	−1.39361	−	2.41381i	−0.0754684	−	0.130715i
$342$		0			0
$343$	14.0916	+	12.0177i	0.760877	+	0.648896i
$344$	3.19589	−	1.84515i	0.172311	−	0.0994838i
$345$		0			0
$346$	−4.09857	+	2.36631i	−0.220341	+	0.127214i
$347$	9.56913	−	5.52474i	0.513698	−	0.296584i	−0.220654	−	0.975352i	$-0.570819\pi$
$347$	9.56913	−	5.52474i	0.513698	−	0.296584i	0.734352	+	0.678768i	$0.237486\pi$
$348$		0			0
$349$	13.7644	−	7.94687i	0.736791	−	0.425386i	−0.0841107	−	0.996456i	$-0.526805\pi$
$349$	13.7644	−	7.94687i	0.736791	−	0.425386i	0.820901	+	0.571070i	$0.193472\pi$
$350$	−2.53662	+	0.752047i	−0.135588	+	0.0401986i
$351$		0			0
$352$	−1.53849	−	2.66474i	−0.0820017	−	0.142031i
$353$	11.9879			0.638053			0.319026	−	0.947746i	$-0.396644\pi$
$353$	11.9879			0.638053			0.319026	+	0.947746i	$0.396644\pi$
$354$		0			0
$355$			10.6760i			0.566622i
$356$	0.771960	−	1.33707i	0.0409138	−	0.0708647i
$357$		0			0
$358$	3.76505	+	6.52127i	0.198989	+	0.344660i
$359$	11.7767	−	6.79925i	0.621548	−	0.358851i	−0.155923	−	0.987769i	$-0.549835\pi$
$359$	11.7767	−	6.79925i	0.621548	−	0.358851i	0.777471	+	0.628918i	$0.216502\pi$
$360$		0			0
$361$	−9.16049	+	15.8664i	−0.482131	+	0.835076i
$362$	−6.18956	+	10.7206i	−0.325316	+	0.563464i
$363$		0			0
$364$	0.997112	+	0.945766i	0.0522629	+	0.0495716i
$365$	5.78211	+	3.33830i	0.302649	+	0.174735i
$366$		0			0
$367$		−	5.63278i		−	0.294029i	−0.989134	−	0.147014i	$-0.953034\pi$
$367$		−	5.63278i		−	0.294029i	0.989134	−	0.147014i	$-0.0469664\pi$
$368$	−7.74345	−	4.47068i	−0.403655	−	0.233050i
$369$		0			0
$370$			5.07681i			0.263931i
$371$	13.7577	−	4.07882i	0.714262	−	0.211762i
$372$		0			0
$373$	5.72999			0.296687			0.148344	−	0.988936i	$-0.452606\pi$
$373$	5.72999			0.296687			0.148344	+	0.988936i	$0.452606\pi$
$374$	7.52084	+	13.0265i	0.388893	+	0.673583i
$375$		0			0
$376$	−3.27742	−	1.89222i	−0.169020	−	0.0975837i
$377$	3.33133			0.171572
$378$		0			0
$379$	−12.0397			−0.618437			−0.309219	−	0.950991i	$-0.600067\pi$
$379$	−12.0397			−0.618437			−0.309219	+	0.950991i	$0.600067\pi$
$380$	0.713627	+	0.412013i	0.0366083	+	0.0211358i
$381$		0			0
$382$	−9.61366	−	16.6514i	−0.491878	−	0.851957i
$383$	−20.5060			−1.04781			−0.523903	−	0.851778i	$-0.675525\pi$
$383$	−20.5060			−1.04781			−0.523903	+	0.851778i	$0.675525\pi$
$384$		0			0
$385$	−5.90656	−	5.60240i	−0.301026	−	0.285525i
$386$		−	23.6696i		−	1.20475i
$387$		0			0
$388$	1.93786	+	1.11882i	0.0983797	+	0.0567995i
$389$		−	25.8396i		−	1.31012i	−0.755577	−	0.655060i	$-0.772643\pi$
$389$		−	25.8396i		−	1.31012i	0.755577	−	0.655060i	$-0.227357\pi$
$390$		0			0
$391$	37.8536	+	21.8548i	1.91434	+	1.10524i
$392$	6.99023	−	0.369732i	0.353060	−	0.0186743i
$393$		0			0
$394$	−2.96894	+	5.14236i	−0.149573	+	0.259068i
$395$	−1.73049	+	2.99730i	−0.0870706	+	0.150811i
$396$		0			0
$397$	5.58453	−	3.22423i	0.280279	−	0.161819i	−0.353271	−	0.935521i	$-0.614930\pi$
$397$	5.58453	−	3.22423i	0.280279	−	0.161819i	0.633550	+	0.773702i	$0.281597\pi$
$398$	−8.31608	−	14.4039i	−0.416848	−	0.722001i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$			12.1434i			0.606413i	0.952925	+	0.303206i	$0.0980571\pi$
$401$			12.1434i			0.606413i	−0.952925	+	0.303206i	$0.901943\pi$
$402$		0			0
$403$	0.470523			0.0234384
$404$	2.09840	+	3.63453i	0.104399	+	0.180825i
$405$		0			0
$406$	11.6771	−	12.3111i	0.579525	−	0.610988i
$407$	−13.5284	+	7.81060i	−0.670576	+	0.387157i
$408$		0			0
$409$	19.2077	−	11.0896i	0.949761	−	0.548345i	0.0567546	−	0.998388i	$-0.481925\pi$
$409$	19.2077	−	11.0896i	0.949761	−	0.548345i	0.893007	+	0.450043i	$0.148591\pi$
$410$	−3.78619	+	2.18596i	−0.186987	+	0.107957i
$411$		0			0
$412$	0.607203	−	0.350569i	0.0299147	−	0.0172713i
$413$	−27.2258	−	6.52937i	−1.33969	−	0.321289i
$414$		0			0
$415$	3.32033	+	5.75098i	0.162989	+	0.282305i
$416$	0.519437			0.0254675
$417$		0			0
$418$			2.53551i			0.124016i
$419$	7.31349	−	12.6673i	0.357287	−	0.618840i	−0.630219	−	0.776417i	$-0.717035\pi$
$419$	7.31349	−	12.6673i	0.357287	−	0.618840i	0.987507	+	0.157577i	$0.0503684\pi$
$420$		0			0
$421$	17.6810	+	30.6243i	0.861717	+	1.49254i	0.870270	+	0.492575i	$0.163944\pi$
$421$	17.6810	+	30.6243i	0.861717	+	1.49254i	−0.00855262	+	0.999963i	$0.502722\pi$
$422$	18.5516	−	10.7108i	0.903078	−	0.521392i
$423$		0			0
$424$	2.71181	−	4.69700i	0.131697	−	0.228106i
$425$	2.44423	−	4.23353i	0.118563	−	0.205356i
$426$		0			0
$427$	24.1608	−	7.16310i	1.16922	−	0.346647i
$428$	17.8959	+	10.3322i	0.865031	+	0.499426i
$429$		0			0
$430$		−	3.69030i		−	0.177962i
$431$	−14.2396	−	8.22125i	−0.685898	−	0.396003i	0.116175	−	0.993229i	$-0.462937\pi$
$431$	−14.2396	−	8.22125i	−0.685898	−	0.396003i	−0.802074	+	0.597225i	$0.796270\pi$
$432$		0			0
$433$		−	22.0355i		−	1.05896i	−0.848323	−	0.529479i	$-0.822388\pi$
$433$		−	22.0355i		−	1.05896i	0.848323	−	0.529479i	$-0.177612\pi$
$434$	1.64930	−	1.73884i	0.0791687	−	0.0834669i
$435$		0			0
$436$	−1.80657			−0.0865192
$437$	3.68396	+	6.38080i	0.176228	+	0.305235i
$438$		0			0
$439$	21.4924	+	12.4087i	1.02578	+	0.592233i	0.915772	−	0.401697i	$-0.131580\pi$
$439$	21.4924	+	12.4087i	1.02578	+	0.592233i	0.110006	+	0.993931i	$0.464913\pi$
$440$	−3.07697			−0.146689
$441$		0			0
$442$	−2.53925			−0.120780
$443$	14.3967	+	8.31193i	0.684007	+	0.394912i	0.801363	−	0.598178i	$-0.204109\pi$
$443$	14.3967	+	8.31193i	0.684007	+	0.394912i	−0.117356	+	0.993090i	$0.537442\pi$
$444$		0			0
$445$	−0.771960	−	1.33707i	−0.0365944	−	0.0633834i
$446$	26.5614			1.25772
$447$		0			0
$448$	1.82075	−	1.91960i	0.0860224	−	0.0906926i
$449$		−	12.5154i		−	0.590638i	−0.955399	−	0.295319i	$-0.904574\pi$
$449$		−	12.5154i		−	0.590638i	0.955399	−	0.295319i	$-0.0954260\pi$
$450$		0			0
$451$	−11.6500	−	6.72614i	−0.548578	−	0.316721i
$452$			18.7655i			0.882656i
$453$		0			0
$454$	23.1555	+	13.3688i	1.08674	+	0.627431i
$455$	1.31761	−	0.390641i	0.0617707	−	0.0183135i
$456$		0			0
$457$	16.3501	−	28.3193i	0.764827	−	1.32472i	−0.175511	−	0.984478i	$-0.556158\pi$
$457$	16.3501	−	28.3193i	0.764827	−	1.32472i	0.940338	−	0.340242i	$-0.110509\pi$
$458$	−3.96686	+	6.87080i	−0.185359	+	0.321051i
$459$		0			0
$460$	−7.74345	+	4.47068i	−0.361040	+	0.208447i
$461$	−2.69005	−	4.65931i	−0.125288	−	0.217006i	0.796557	−	0.604563i	$-0.206652\pi$
$461$	−2.69005	−	4.65931i	−0.125288	−	0.217006i	−0.921846	+	0.387557i	$0.873319\pi$
$462$		0			0
$463$	5.41835	−	9.38485i	0.251812	−	0.436151i	−0.712213	−	0.701964i	$-0.752307\pi$
$463$	5.41835	−	9.38485i	0.251812	−	0.436151i	0.964025	+	0.265813i	$0.0856402\pi$
$464$		−	6.41334i		−	0.297732i
$465$		0			0
$466$	−28.0443			−1.29913
$467$	2.76713	+	4.79281i	0.128048	+	0.221785i	0.922920	−	0.384992i	$-0.125796\pi$
$467$	2.76713	+	4.79281i	0.128048	+	0.221785i	−0.794872	+	0.606777i	$0.792462\pi$
$468$		0			0
$469$	20.3399	+	4.87797i	0.939208	+	0.225244i
$470$	−3.27742	+	1.89222i	−0.151176	+	0.0872815i
$471$		0			0
$472$	−9.16443	+	5.29109i	−0.421827	+	0.243542i
$473$	9.83368	−	5.67748i	0.452153	−	0.261051i
$474$		0			0
$475$	0.713627	−	0.412013i	0.0327434	−	0.0189044i
$476$	−8.90067	+	9.38389i	−0.407962	+	0.430110i
$477$		0			0
$478$	14.1762	+	24.5540i	0.648406	+	1.12307i
$479$	−39.8255			−1.81968			−0.909838	−	0.414964i	$-0.863794\pi$
$479$	−39.8255			−1.81968			−0.909838	+	0.414964i	$0.863794\pi$
$480$		0			0
$481$		−	2.63708i		−	0.120241i
$482$	0.477119	−	0.826394i	0.0217322	−	0.0376412i
$483$		0			0
$484$	0.766113	+	1.32695i	0.0348233	+	0.0603158i
$485$	1.93786	−	1.11882i	0.0879935	−	0.0508031i
$486$		0			0
$487$	19.7936	−	34.2835i	0.896934	−	1.55354i	0.0655411	−	0.997850i	$-0.479123\pi$
$487$	19.7936	−	34.2835i	0.896934	−	1.55354i	0.831393	−	0.555685i	$-0.187544\pi$
$488$	4.76240	−	8.24872i	0.215584	−	0.373402i
$489$		0			0
$490$	3.17492	−	6.23858i	0.143428	−	0.281830i
$491$	−27.1823	−	15.6937i	−1.22672	−	0.708247i	−0.260377	−	0.965507i	$-0.583847\pi$
$491$	−27.1823	−	15.6937i	−1.22672	−	0.708247i	−0.966342	+	0.257260i	$0.917180\pi$
$492$		0			0
$493$			31.3514i			1.41200i
$494$	−0.370684	−	0.214015i	−0.0166779	−	0.00962898i
$495$		0			0
$496$		−	0.905833i		−	0.0406731i
$497$	−20.4936	−	19.4383i	−0.919264	−	0.871927i
$498$		0			0
$499$	−29.6748			−1.32843			−0.664214	−	0.747542i	$-0.731234\pi$
$499$	−29.6748			−1.32843			−0.664214	+	0.747542i	$0.731234\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$		0			0
$502$	−5.92888	−	3.42304i	−0.264619	−	0.152778i
$503$	31.4939			1.40424			0.702121	−	0.712058i	$-0.252236\pi$
$503$	31.4939			1.40424			0.702121	+	0.712058i	$0.252236\pi$
$504$		0			0
$505$	4.19679			0.186755
$506$	−23.8264	−	13.7562i	−1.05921	−	0.611537i
$507$		0			0
$508$	0.769453	+	1.33273i	0.0341390	+	0.0591304i
$509$	−12.4151			−0.550290			−0.275145	−	0.961403i	$-0.588726\pi$
$509$	−12.4151			−0.550290			−0.275145	+	0.961403i	$0.588726\pi$
$510$		0			0
$511$	−16.9360	+	5.02112i	−0.749204	+	0.222121i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	22.8927	+	13.2171i	1.00975	+	0.582981i
$515$		−	0.701137i		−	0.0308958i
$516$		0			0
$517$	−10.0845	−	5.82231i	−0.443517	−	0.256065i
$518$	−9.74544	−	9.24360i	−0.428190	−	0.406141i
$519$		0			0
$520$	0.259719	−	0.449846i	0.0113894	−	0.0197270i
$521$	−20.9931	+	36.3610i	−0.919722	+	1.59301i	−0.119886	+	0.992788i	$0.538253\pi$
$521$	−20.9931	+	36.3610i	−0.919722	+	1.59301i	−0.799836	+	0.600218i	$0.795080\pi$
$522$		0			0
$523$	−20.1026	+	11.6062i	−0.879024	+	0.507505i	−0.870337	−	0.492457i	$-0.836099\pi$
$523$	−20.1026	+	11.6062i	−0.879024	+	0.507505i	−0.00868774	+	0.999962i	$0.502765\pi$
$524$	−5.26114	−	9.11256i	−0.229834	−	0.398084i
$525$		0			0
$526$	−12.8662	+	22.2849i	−0.560992	+	0.971666i
$527$			4.42813i			0.192892i
$528$		0			0
$529$	−56.9480			−2.47600
$530$	−2.71181	−	4.69700i	−0.117794	−	0.204025i
$531$		0			0
$532$	−2.09024	+	0.619706i	−0.0906233	+	0.0268677i
$533$	1.96669	−	1.13547i	0.0851867	−	0.0491826i
$534$		0			0
$535$	17.8959	−	10.3322i	0.773707	−	0.446700i
$536$	6.84657	−	3.95287i	0.295727	−	0.170738i
$537$		0			0
$538$	7.70427	−	4.44806i	0.332155	−	0.191770i
$539$	21.5088	−	1.13766i	0.926448	−	0.0490023i
$540$		0			0
$541$	3.91386	+	6.77900i	0.168270	+	0.291452i	0.937812	−	0.347145i	$-0.112849\pi$
$541$	3.91386	+	6.77900i	0.168270	+	0.291452i	−0.769542	+	0.638596i	$0.779515\pi$
$542$	22.1902			0.953149
$543$		0			0
$544$			4.88846i			0.209591i
$545$	−0.903287	+	1.56454i	−0.0386926	+	0.0670175i
$546$		0			0
$547$	20.3459	+	35.2402i	0.869930	+	1.50676i	0.862068	+	0.506793i	$0.169169\pi$
$547$	20.3459	+	35.2402i	0.869930	+	1.50676i	0.00786205	+	0.999969i	$0.497497\pi$
$548$	0.00290551	−	0.00167750i	0.000124117	−	7.16591e-5i
$549$		0			0
$550$	−1.53849	+	2.66474i	−0.0656013	+	0.113625i
$551$	−2.64238	+	4.57674i	−0.112569	+	0.194975i
$552$		0			0
$553$	−2.60283	−	8.77920i	−0.110683	−	0.373330i
$554$	10.9193	+	6.30428i	0.463918	+	0.267843i
$555$		0			0
$556$			19.2054i			0.814492i
$557$	−26.3951	−	15.2392i	−1.11840	−	0.645707i	−0.177406	−	0.984138i	$-0.556771\pi$
$557$	−26.3951	−	15.2392i	−1.11840	−	0.645707i	−0.940991	+	0.338430i	$0.890104\pi$
$558$		0			0
$559$			1.91688i			0.0810754i
$560$	−0.752047	−	2.53662i	−0.0317798	−	0.107192i
$561$		0			0
$562$	7.86814			0.331898
$563$	−4.87559	−	8.44476i	−0.205481	−	0.355904i	0.744805	−	0.667283i	$-0.232543\pi$
$563$	−4.87559	−	8.44476i	−0.205481	−	0.355904i	−0.950286	+	0.311378i	$0.899209\pi$
$564$		0			0
$565$	16.2514	+	9.38276i	0.683703	+	0.394736i
$566$	−29.5470			−1.24195
$567$		0			0
$568$	−10.6760			−0.447954
$569$	−28.8139	−	16.6357i	−1.20794	−	0.697405i	−0.245632	−	0.969363i	$-0.578996\pi$
$569$	−28.8139	−	16.6357i	−1.20794	−	0.697405i	−0.962309	+	0.271958i	$0.912329\pi$
$570$		0			0
$571$	18.9605	+	32.8406i	0.793473	+	1.37434i	0.923804	+	0.382865i	$0.125062\pi$
$571$	18.9605	+	32.8406i	0.793473	+	1.37434i	−0.130332	+	0.991470i	$0.541604\pi$
$572$	1.59830			0.0668281
$573$		0			0
$574$	2.69754	−	11.2481i	0.112593	−	0.469485i
$575$			8.94137i			0.372881i
$576$		0			0
$577$	−11.5550	−	6.67129i	−0.481042	−	0.277730i	0.239809	−	0.970820i	$-0.422915\pi$
$577$	−11.5550	−	6.67129i	−0.481042	−	0.277730i	−0.720850	+	0.693091i	$0.756249\pi$
$578$		−	6.89705i		−	0.286880i
$579$		0			0
$580$	−5.55412	−	3.20667i	−0.230622	−	0.133150i
$581$	−17.0851	−	4.09740i	−0.708809	−	0.169989i
$582$		0			0
$583$	8.34418	−	14.4525i	0.345581	−	0.598563i
$584$	−3.33830	+	5.78211i	−0.138140	+	0.239265i
$585$		0			0
$586$	6.89061	−	3.97830i	0.284649	−	0.164342i
$587$	8.76612	+	15.1834i	0.361817	+	0.626685i	0.988260	−	0.152782i	$-0.0488233\pi$
$587$	8.76612	+	15.1834i	0.361817	+	0.626685i	−0.626443	+	0.779467i	$0.715490\pi$
$588$		0			0
$589$	−0.373215	+	0.646427i	−0.0153780	+	0.0266356i
$590$			10.5822i			0.435661i
$591$		0			0
$592$	−5.07681			−0.208655
$593$	13.1868	+	22.8403i	0.541519	+	0.937938i	0.998817	+	0.0486245i	$0.0154838\pi$
$593$	13.1868	+	22.8403i	0.541519	+	0.937938i	−0.457298	+	0.889313i	$0.651183\pi$
$594$		0			0
$595$	3.67635	+	12.4002i	0.150716	+	0.508357i
$596$	10.4496	−	6.03310i	0.428034	−	0.247126i
$597$		0			0
$598$	4.02224	−	2.32224i	0.164481	−	0.0949634i
$599$	−24.1184	+	13.9248i	−0.985452	+	0.568951i	−0.903912	−	0.427719i	$-0.859317\pi$
$599$	−24.1184	+	13.9248i	−0.985452	+	0.568951i	−0.0815405	+	0.996670i	$0.525984\pi$
$600$		0			0
$601$	−23.8076	+	13.7453i	−0.971131	+	0.560683i	−0.899581	−	0.436754i	$-0.856128\pi$
$601$	−23.8076	+	13.7453i	−0.971131	+	0.560683i	−0.0715503	+	0.997437i	$0.522795\pi$
$602$	7.08390	+	6.71912i	0.288718	+	0.273851i
$603$		0			0
$604$	−7.33025	−	12.6964i	−0.298263	−	0.516607i
$605$	1.53223			0.0622938
$606$		0			0
$607$			39.3814i			1.59844i	0.601037	+	0.799221i	$0.294754\pi$
$607$			39.3814i			1.59844i	−0.601037	+	0.799221i	$0.705246\pi$
$608$	−0.412013	+	0.713627i	−0.0167093	+	0.0289414i
$609$		0			0
$610$	−4.76240	−	8.24872i	−0.192824	−	0.333981i
$611$	1.70241	−	0.982888i	0.0688722	−	0.0397634i
$612$		0			0
$613$	−0.989576	+	1.71400i	−0.0399686	+	0.0692277i	−0.885318	−	0.464987i	$-0.846059\pi$
$613$	−0.989576	+	1.71400i	−0.0399686	+	0.0692277i	0.845349	+	0.534214i	$0.179392\pi$
$614$	16.9087	−	29.2868i	0.682381	−	1.18192i
$615$		0			0
$616$	5.60240	−	5.90656i	0.225727	−	0.237982i
$617$	33.1061	+	19.1138i	1.33280	+	0.769493i	0.985728	−	0.168346i	$-0.0538425\pi$
$617$	33.1061	+	19.1138i	1.33280	+	0.769493i	0.347072	+	0.937838i	$0.387176\pi$
$618$		0			0
$619$		−	26.6725i		−	1.07206i	−0.844200	−	0.536028i	$-0.819924\pi$
$619$		−	26.6725i		−	1.07206i	0.844200	−	0.536028i	$-0.180076\pi$
$620$	−0.784474	−	0.452916i	−0.0315052	−	0.0181896i
$621$		0			0
$622$			23.3794i			0.937427i
$623$	3.97219	+	0.952623i	0.159143	+	0.0381661i
$624$		0			0
$625$	1.00000			0.0400000
$626$	8.65830	+	14.9966i	0.346055	+	0.599385i
$627$		0			0
$628$	−0.502653	−	0.290207i	−0.0200580	−	0.0115805i
$629$	24.8178			0.989549
$630$		0			0
$631$	8.55537			0.340584			0.170292	−	0.985394i	$-0.445529\pi$
$631$	8.55537			0.340584			0.170292	+	0.985394i	$0.445529\pi$
$632$	−2.99730	−	1.73049i	−0.119226	−	0.0688353i
$633$		0			0
$634$	−7.96781	−	13.8006i	−0.316442	−	0.548094i
$635$	1.53891			0.0610696
$636$		0			0
$637$	−1.64917	+	3.24055i	−0.0653425	+	0.128395i
$638$		−	19.7337i		−	0.781265i
$639$		0			0
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$			24.1197i			0.952672i	0.879263	+	0.476336i	$0.158035\pi$
$641$			24.1197i			0.952672i	−0.879263	+	0.476336i	$0.841965\pi$
$642$		0			0
$643$	13.4384	+	7.75864i	0.529957	+	0.305971i	0.740999	−	0.671506i	$-0.234352\pi$
$643$	13.4384	+	7.75864i	0.529957	+	0.305971i	−0.211042	+	0.977477i	$0.567686\pi$
$644$	5.51697	−	23.0043i	0.217399	−	0.906498i
$645$		0			0
$646$	2.01411	−	3.48854i	0.0792440	−	0.137255i
$647$	3.88442	−	6.72802i	0.152712	−	0.264506i	−0.779511	−	0.626388i	$-0.784533\pi$
$647$	3.88442	−	6.72802i	0.152712	−	0.264506i	0.932224	+	0.361883i	$0.117866\pi$
$648$		0			0
$649$	−28.1987	+	16.2805i	−1.10690	+	0.639067i
$650$	−0.259719	−	0.449846i	−0.0101870	−	0.0176444i
$651$		0			0
$652$	−0.0642633	+	0.111307i	−0.00251675	+	0.00435913i
$653$		−	17.3302i		−	0.678184i	−0.940753	−	0.339092i	$-0.889880\pi$
$653$		−	17.3302i		−	0.678184i	0.940753	−	0.339092i	$-0.110120\pi$
$654$		0			0
$655$	−10.5223			−0.411139
$656$	−2.18596	−	3.78619i	−0.0853473	−	0.147826i
$657$		0			0
$658$	2.33506	−	9.73659i	0.0910301	−	0.379572i
$659$	−3.46721	+	2.00179i	−0.135063	+	0.0779787i	−0.566009	−	0.824399i	$-0.691513\pi$
$659$	−3.46721	+	2.00179i	−0.135063	+	0.0779787i	0.430946	+	0.902378i	$0.358180\pi$
$660$		0			0
$661$	−33.8131	+	19.5220i	−1.31518	+	0.759317i	−0.982948	−	0.183882i	$-0.941134\pi$
$661$	−33.8131	+	19.5220i	−1.31518	+	0.759317i	−0.332228	+	0.943199i	$0.607800\pi$
$662$	−7.28013	+	4.20318i	−0.282950	+	0.163361i
$663$		0			0
$664$	−5.75098	+	3.32033i	−0.223181	+	0.128854i
$665$	−0.508437	+	2.12005i	−0.0197163	+	0.0822121i
$666$		0			0
$667$	−28.6720	−	49.6614i	−1.11019	−	1.92290i
$668$	25.3497			0.980811
$669$		0			0
$670$		−	7.90574i		−	0.305425i
$671$	14.6538	−	25.3811i	0.565703	−	0.979827i
$672$		0			0
$673$	5.02582	+	8.70498i	0.193731	+	0.335552i	0.946484	−	0.322751i	$-0.104608\pi$
$673$	5.02582	+	8.70498i	0.193731	+	0.335552i	−0.752753	+	0.658303i	$0.771274\pi$
$674$	13.3059	−	7.68218i	0.512525	−	0.295906i
$675$		0			0
$676$	6.36509	−	11.0247i	0.244811	−	0.424026i
$677$	11.3646	−	19.6840i	0.436776	−	0.756519i	−0.560663	−	0.828044i	$-0.689453\pi$
$677$	11.3646	−	19.6840i	0.436776	−	0.756519i	0.997439	+	0.0715258i	$0.0227868\pi$
$678$		0			0
$679$	−1.38066	+	5.75700i	−0.0529849	+	0.220933i
$680$	4.23353	+	2.44423i	0.162349	+	0.0937320i
$681$		0			0
$682$		−	2.78723i		−	0.106728i
$683$	6.28399	+	3.62806i	0.240450	+	0.138824i	0.615384	−	0.788228i	$-0.289001\pi$
$683$	6.28399	+	3.62806i	0.240450	+	0.138824i	−0.374933	+	0.927052i	$0.622334\pi$
$684$		0			0
$685$		−	0.00335499i		−	0.000128188i
$686$	6.19485	+	17.4535i	0.236520	+	0.666377i
$687$		0			0
$688$	3.69030			0.140691
$689$	1.40862	+	2.43980i	0.0536640	+	0.0929488i
$690$		0			0
$691$	−8.38246	−	4.83962i	−0.318884	−	0.184108i	0.332011	−	0.943275i	$-0.392273\pi$
$691$	−8.38246	−	4.83962i	−0.318884	−	0.184108i	−0.650895	+	0.759168i	$0.725606\pi$
$692$	−4.73262			−0.179907
$693$		0			0
$694$	11.0495			0.419433
$695$	16.6324	+	9.60272i	0.630903	+	0.364252i
$696$		0			0
$697$	10.6860	+	18.5086i	0.404760	+	0.701065i
$698$	15.8937			0.601587
$699$		0			0
$700$	−2.57280	−	0.617016i	−0.0972426	−	0.0233210i
$701$		−	5.56860i		−	0.210323i	−0.994455	−	0.105162i	$-0.966464\pi$
$701$		−	5.56860i		−	0.210323i	0.994455	−	0.105162i	$-0.0335360\pi$
$702$		0			0
$703$	3.62295	+	2.09171i	0.136642	+	0.0788903i
$704$		−	3.07697i		−	0.115968i
$705$		0			0
$706$	10.3818	+	5.99396i	0.390726	+	0.225586i
$707$	−7.64132	+	8.05617i	−0.287381	+	0.302983i
$708$		0			0
$709$	−12.6267	+	21.8702i	−0.474207	+	0.821351i	−0.999564	−	0.0295310i	$-0.990599\pi$
$709$	−12.6267	+	21.8702i	−0.474207	+	0.821351i	0.525357	+	0.850882i	$0.323932\pi$
$710$	−5.33799	+	9.24567i	−0.200331	+	0.346984i
$711$		0			0
$712$	1.33707	−	0.771960i	0.0501089	−	0.0289304i
$713$	−4.04969	−	7.01427i	−0.151662	−	0.262687i
$714$		0			0
$715$	0.799148	−	1.38416i	0.0298864	−	0.0517648i
$716$			7.53011i			0.281413i
$717$		0			0
$718$	13.5985			0.507492
$719$	3.56765	+	6.17935i	0.133051	+	0.230451i	0.924851	−	0.380329i	$-0.124189\pi$
$719$	3.56765	+	6.17935i	0.133051	+	0.230451i	−0.791800	+	0.610780i	$0.790856\pi$
$720$		0			0
$721$	1.34590	+	1.27660i	0.0501241	+	0.0475429i
$722$	−15.8664	+	9.16049i	−0.590488	+	0.340918i
$723$		0			0
$724$	−10.7206	+	6.18956i	−0.398429	+	0.230033i
$725$	−5.55412	+	3.20667i	−0.206275	+	0.119093i
$726$		0			0
$727$	−7.48124	+	4.31930i	−0.277464	+	0.160194i	−0.632275	−	0.774744i	$-0.717879\pi$
$727$	−7.48124	+	4.31930i	−0.277464	+	0.160194i	0.354811	+	0.934938i	$0.384545\pi$
$728$	0.390641	+	1.31761i	0.0144781	+	0.0488340i
$729$		0			0
$730$	3.33830	+	5.78211i	0.123556	+	0.214005i
$731$	−18.0399			−0.667229
$732$		0			0
$733$		−	36.2890i		−	1.34037i	−0.742196	−	0.670183i	$-0.766216\pi$
$733$		−	36.2890i		−	1.34037i	0.742196	−	0.670183i	$-0.233784\pi$
$734$	2.81639	−	4.87813i	0.103955	−	0.180055i
$735$		0			0
$736$	−4.47068	−	7.74345i	−0.164792	−	0.285427i
$737$	21.0667	−	12.1629i	0.776003	−	0.448025i
$738$		0			0
$739$	5.37054	−	9.30205i	0.197558	−	0.342181i	−0.750178	−	0.661236i	$-0.770032\pi$
$739$	5.37054	−	9.30205i	0.197558	−	0.342181i	0.947736	+	0.319055i	$0.103365\pi$
$740$	−2.53840	+	4.39664i	−0.0933136	+	0.161624i
$741$		0			0
$742$	13.9539	+	3.34647i	0.512264	+	0.122853i
$743$	−9.06518	−	5.23379i	−0.332569	−	0.192009i	0.324412	−	0.945916i	$-0.394834\pi$
$743$	−9.06518	−	5.23379i	−0.332569	−	0.192009i	−0.656981	+	0.753907i	$0.728167\pi$
$744$		0			0
$745$		−	12.0662i		−	0.442072i
$746$	4.96231	+	2.86499i	0.181683	+	0.104895i
$747$		0			0
$748$			15.0417i			0.549978i
$749$	−12.7503	+	53.1653i	−0.465885	+	1.94262i
$750$		0			0
$751$	18.5461			0.676758			0.338379	−	0.941010i	$-0.390121\pi$
$751$	18.5461			0.676758			0.338379	+	0.941010i	$0.390121\pi$
$752$	−1.89222	−	3.27742i	−0.0690021	−	0.119515i
$753$		0			0
$754$	2.88502	+	1.66566i	0.105066	+	0.0606599i
$755$	−14.6605			−0.533550
$756$		0			0
$757$	−8.57410			−0.311631			−0.155816	−	0.987786i	$-0.549801\pi$
$757$	−8.57410			−0.311631			−0.155816	+	0.987786i	$0.549801\pi$
$758$	−10.4267	−	6.01984i	−0.378714	−	0.218651i
$759$		0			0
$760$	0.412013	+	0.713627i	0.0149453	+	0.0258860i
$761$	3.68978			0.133755			0.0668773	−	0.997761i	$-0.478696\pi$
$761$	3.68978			0.133755			0.0668773	+	0.997761i	$0.478696\pi$
$762$		0			0
$763$	−1.35863	−	4.58259i	−0.0491857	−	0.165901i
$764$		−	19.2273i		−	0.695620i
$765$		0			0
$766$	−17.7587	−	10.2530i	−0.641648	−	0.370456i
$767$		−	5.49677i		−	0.198477i
$768$		0			0
$769$	−1.09328	−	0.631204i	−0.0394246	−	0.0227618i	0.480158	−	0.877182i	$-0.340579\pi$
$769$	−1.09328	−	0.631204i	−0.0394246	−	0.0227618i	−0.519583	+	0.854420i	$0.673913\pi$
$770$	−2.31403	−	7.80511i	−0.0833919	−	0.281276i
$771$		0			0
$772$	11.8348	−	20.4985i	0.425944	−	0.737757i
$773$	1.80204	−	3.12123i	0.0648150	−	0.112263i	−0.831797	−	0.555080i	$-0.812688\pi$
$773$	1.80204	−	3.12123i	0.0648150	−	0.112263i	0.896612	+	0.442817i	$0.146021\pi$
$774$		0			0
$775$	−0.784474	+	0.452916i	−0.0281791	+	0.0162692i
$776$	1.11882	+	1.93786i	0.0401633	+	0.0695649i
$777$		0			0
$778$	12.9198	−	22.3778i	0.463197	−	0.802282i
$779$			3.60257i			0.129075i
$780$		0			0
$781$	−32.8497			−1.17546
$782$	21.8548	+	37.8536i	0.781525	+	1.35364i
$783$		0			0
$784$	6.23858	+	3.17492i	0.222806	+	0.113390i
$785$	−0.502653	+	0.290207i	−0.0179405	+	0.0103579i
$786$		0			0
$787$	−12.5305	+	7.23448i	−0.446664	+	0.257882i	−0.706420	−	0.707793i	$-0.749691\pi$
$787$	−12.5305	+	7.23448i	−0.446664	+	0.257882i	0.259756	+	0.965674i	$0.416358\pi$
$788$	−5.14236	+	2.96894i	−0.183189	+	0.105764i
$789$		0			0
$790$	−2.99730	+	1.73049i	−0.106639	+	0.0615682i
$791$	−47.6010	+	14.1126i	−1.69249	+	0.501785i
$792$		0			0
$793$	2.47377	+	4.28469i	0.0878461	+	0.152154i
$794$	6.44846			0.228847
$795$		0			0
$796$		−	16.6322i		−	0.589511i
$797$	13.9972	−	24.2439i	0.495808	−	0.858764i	−0.504180	−	0.863598i	$-0.668205\pi$
$797$	13.9972	−	24.2439i	0.495808	−	0.858764i	0.999988	+	0.00483393i	$0.00153869\pi$
$798$		0			0
$799$	9.25003	+	16.0215i	0.327243	+	0.566801i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$		0			0
$802$	−6.07170	+	10.5165i	−0.214399	+	0.371350i
$803$	−10.2719	+	17.7914i	−0.362486	+	0.627845i
$804$		0			0
$805$	−17.1638	−	16.2800i	−0.604946	−	0.573795i
$806$	0.407485	+	0.235262i	0.0143531	+	0.00828674i
$807$		0			0
$808$			4.19679i			0.147643i
$809$	−37.0756	−	21.4056i	−1.30351	−	0.752582i	−0.322505	−	0.946568i	$-0.604525\pi$
$809$	−37.0756	−	21.4056i	−1.30351	−	0.752582i	−0.981004	+	0.193986i	$0.937858\pi$
$810$		0			0
$811$		−	7.75794i		−	0.272418i	−0.990680	−	0.136209i	$-0.956508\pi$
$811$		−	7.75794i		−	0.272418i	0.990680	−	0.136209i	$-0.0434919\pi$
$812$	16.2682	−	4.82314i	0.570902	−	0.169259i
$813$		0			0
$814$	−15.6212			−0.547523
$815$	0.0642633	+	0.111307i	0.00225105	+	0.00389893i
$816$		0			0
$817$	−2.63350	−	1.52045i	−0.0921344	−	0.0531938i
$818$	22.1792			0.775477
$819$		0			0
$820$	−4.37192			−0.152674
$821$	21.1360	+	12.2029i	0.737650	+	0.425883i	0.821214	−	0.570620i	$-0.193297\pi$
$821$	21.1360	+	12.2029i	0.737650	+	0.425883i	−0.0835640	+	0.996502i	$0.526630\pi$
$822$		0			0
$823$	−11.5997	−	20.0913i	−0.404342	−	0.700340i	0.589903	−	0.807474i	$-0.299166\pi$
$823$	−11.5997	−	20.0913i	−0.404342	−	0.700340i	−0.994245	+	0.107134i	$0.965833\pi$
$824$	0.701137			0.0244253
$825$		0			0
$826$	−20.3135	−	19.2675i	−0.706799	−	0.670402i
$827$			29.3259i			1.01976i	0.860245	+	0.509881i	$0.170311\pi$
$827$			29.3259i			1.01976i	−0.860245	+	0.509881i	$0.829689\pi$
$828$		0			0
$829$	26.1269	+	15.0844i	0.907424	+	0.523901i	0.879601	−	0.475712i	$-0.157809\pi$
$829$	26.1269	+	15.0844i	0.907424	+	0.523901i	0.0278223	+	0.999613i	$0.491143\pi$
$830$			6.64066i			0.230501i
$831$		0			0
$832$	0.449846	+	0.259719i	0.0155956	+	0.00900412i
$833$	−30.4971	−	15.5205i	−1.05666	−	0.537752i
$834$		0			0
$835$	12.6749	−	21.9535i	0.438632	−	0.759733i
$836$	−1.26775	+	2.19581i	−0.0438461	+	0.0759438i
$837$		0			0
$838$	12.6673	−	7.31349i	0.437586	−	0.252640i
$839$	18.2437	+	31.5990i	0.629843	+	1.09092i	0.987583	+	0.157098i	$0.0502139\pi$
$839$	18.2437	+	31.5990i	0.629843	+	1.09092i	−0.357740	+	0.933821i	$0.616453\pi$
$840$		0			0
$841$	6.06549	−	10.5057i	0.209155	−	0.362267i
$842$			35.3619i			1.21865i
$843$		0			0
$844$	21.4215			0.737360
$845$	−6.36509	−	11.0247i	−0.218966	−	0.379260i
$846$		0			0
$847$	−2.78980	+	2.94126i	−0.0958587	+	0.101063i
$848$	4.69700	−	2.71181i	0.161296	−	0.0931241i
$849$		0			0
$850$	4.23353	−	2.44423i	0.145209	−	0.0838364i
$851$	−39.3120	+	22.6968i	−1.34760	+	0.778036i
$852$		0			0
$853$	−2.99449	+	1.72887i	−0.102530	+	0.0591954i	−0.550388	−	0.834909i	$-0.685520\pi$
$853$	−2.99449	+	1.72887i	−0.102530	+	0.0591954i	0.447858	+	0.894104i	$0.352187\pi$
$854$	24.5054	+	5.87696i	0.838558	+	0.201105i
$855$		0			0
$856$	10.3322	+	17.8959i	0.353147	+	0.611669i
$857$	26.1122			0.891977			0.445989	−	0.895039i	$-0.352852\pi$
$857$	26.1122			0.891977			0.445989	+	0.895039i	$0.352852\pi$
$858$		0			0
$859$			26.6217i			0.908319i	0.890920	+	0.454160i	$0.150060\pi$
$859$			26.6217i			0.908319i	−0.890920	+	0.454160i	$0.849940\pi$
$860$	1.84515	−	3.19589i	0.0629191	−	0.108979i
$861$		0			0
$862$	−8.22125	−	14.2396i	−0.280017	−	0.485003i
$863$	−20.3839	+	11.7687i	−0.693877	+	0.400610i	−0.805063	−	0.593189i	$-0.797869\pi$
$863$	−20.3839	+	11.7687i	−0.693877	+	0.400610i	0.111186	+	0.993800i	$0.464535\pi$
$864$		0			0
$865$	−2.36631	+	4.09857i	−0.0804570	+	0.139356i
$866$	11.0177	−	19.0833i	0.374398	−	0.648476i
$867$		0			0
$868$	2.29775	−	0.681229i	0.0779908	−	0.0231224i
$869$	−9.22263	−	5.32469i	−0.312856	−	0.180628i
$870$		0			0
$871$			4.10653i			0.139145i
$872$	−1.56454	−	0.903287i	−0.0529820	−	0.0305892i
$873$		0			0
$874$			7.36791i			0.249223i
$875$	−1.82075	+	1.91960i	−0.0615526	+	0.0648943i
$876$		0			0
$877$	7.21212			0.243536			0.121768	−	0.992559i	$-0.461144\pi$
$877$	7.21212			0.243536			0.121768	+	0.992559i	$0.461144\pi$
$878$	12.4087	+	21.4924i	0.418772	+	0.725335i
$879$		0			0
$880$	−2.66474	−	1.53849i	−0.0898283	−	0.0518624i
$881$	57.4455			1.93539			0.967694	−	0.252129i	$-0.0811307\pi$
$881$	57.4455			1.93539			0.967694	+	0.252129i	$0.0811307\pi$
$882$		0			0
$883$	15.0734			0.507262			0.253631	−	0.967301i	$-0.418375\pi$
$883$	15.0734			0.507262			0.253631	+	0.967301i	$0.418375\pi$
$884$	−2.19905	−	1.26962i	−0.0739622	−	0.0427021i
$885$		0			0
$886$	8.31193	+	14.3967i	0.279245	+	0.483666i
$887$	−35.1323			−1.17963			−0.589814	−	0.807539i	$-0.700799\pi$
$887$	−35.1323			−1.17963			−0.589814	+	0.807539i	$0.700799\pi$
$888$		0			0
$889$	−2.80197	+	2.95409i	−0.0939749	+	0.0990768i
$890$		−	1.54392i		−	0.0517523i
$891$		0			0
$892$	23.0028	+	13.2807i	0.770191	+	0.444670i
$893$			3.11847i			0.104356i
$894$		0			0
$895$	6.52127	+	3.76505i	0.217982	+	0.125852i
$896$	2.53662	−	0.752047i	0.0847424	−	0.0251241i
$897$		0			0
$898$	6.25770	−	10.8387i	0.208822	−	0.361691i
$899$	2.90471	−	5.03110i	0.0968775	−	0.167797i
$900$		0			0
$901$	−22.9611	+	13.2566i	−0.764945	+	0.441641i
$902$	−6.72614	−	11.6500i	−0.223956	−	0.387903i
$903$		0			0
$904$	−9.38276	+	16.2514i	−0.312066	+	0.540514i
$905$			12.3791i			0.411496i
$906$		0			0
$907$	9.56489			0.317597			0.158799	−	0.987311i	$-0.449238\pi$
$907$	9.56489			0.317597			0.158799	+	0.987311i	$0.449238\pi$
$908$	13.3688	+	23.1555i	0.443661	+	0.768443i
$909$		0			0
$910$	1.33641	+	0.320501i	0.0443015	+	0.0106245i
$911$	10.5695	−	6.10232i	0.350184	−	0.202179i	−0.314582	−	0.949230i	$-0.601864\pi$
$911$	10.5695	−	6.10232i	0.350184	−	0.202179i	0.664766	+	0.747051i	$0.268531\pi$
$912$		0			0
$913$	−17.6956	+	10.2166i	−0.585640	+	0.338119i
$914$	28.3193	−	16.3501i	0.936718	−	0.540814i
$915$		0			0
$916$	−6.87080	+	3.96686i	−0.227018	+	0.131069i
$917$	19.1584	−	20.1986i	0.632668	−	0.667015i
$918$		0			0
$919$	−5.75745	−	9.97219i	−0.189921	−	0.328952i	0.755303	−	0.655376i	$-0.227490\pi$
$919$	−5.75745	−	9.97219i	−0.189921	−	0.328952i	−0.945224	+	0.326424i	$0.894156\pi$
$920$	−8.94137			−0.294788
$921$		0			0
$922$		−	5.38010i		−	0.177184i
$923$	2.77275	−	4.80254i	0.0912662	−	0.158078i
$924$		0			0
$925$	2.53840	+	4.39664i	0.0834622	+	0.144561i
$926$	9.38485	−	5.41835i	0.308405	−	0.178058i
$927$		0			0
$928$	3.20667	−	5.55412i	0.105264	−	0.182323i
$929$	7.79341	−	13.4986i	0.255694	−	0.442874i	−0.709390	−	0.704816i	$-0.751030\pi$
$929$	7.79341	−	13.4986i	0.255694	−	0.442874i	0.965084	+	0.261942i	$0.0843629\pi$
$930$		0			0
$931$	−3.14391	−	4.83608i	−0.103038	−	0.158496i
$932$	−24.2871	−	14.0222i	−0.795551	−	0.459311i
$933$		0			0
$934$			5.53426i			0.181087i
$935$	13.0265	+	7.52084i	0.426011	+	0.245958i
$936$		0			0
$937$		−	52.6446i		−	1.71982i	−0.510442	−	0.859912i	$-0.670518\pi$
$937$		−	52.6446i		−	1.71982i	0.510442	−	0.859912i	$-0.329482\pi$
$938$	15.1759	+	14.3944i	0.495509	+	0.469993i
$939$		0			0
$940$	−3.78444			−0.123435
$941$	−1.60723	−	2.78380i	−0.0523942	−	0.0907494i	0.838639	−	0.544688i	$-0.183352\pi$
$941$	−1.60723	−	2.78380i	−0.0523942	−	0.0907494i	−0.891033	+	0.453939i	$0.850019\pi$
$942$		0			0
$943$	−33.8537	−	19.5454i	−1.10243	−	0.636487i
$944$	−10.5822			−0.344420
$945$		0			0
$946$	11.3550			0.369182
$947$	−3.02017	−	1.74370i	−0.0981423	−	0.0566625i	0.450126	−	0.892965i	$-0.351379\pi$
$947$	−3.02017	−	1.74370i	−0.0981423	−	0.0566625i	−0.548268	+	0.836303i	$0.684713\pi$
$948$		0			0
$949$	−1.73404	−	3.00344i	−0.0562892	−	0.0974958i
$950$	0.824025			0.0267349
$951$		0			0
$952$	−12.4002	+	3.67635i	−0.401891	+	0.119151i
$953$		−	45.7759i		−	1.48283i	−0.671049	−	0.741413i	$-0.734156\pi$
$953$		−	45.7759i		−	1.48283i	0.671049	−	0.741413i	$-0.265844\pi$
$954$		0			0
$955$	−16.6514	−	9.61366i	−0.538825	−	0.311091i
$956$			28.3525i			0.916985i
$957$		0			0
$958$	−34.4899	−	19.9128i	−1.11432	−	0.643353i
$959$	0.00644025	+	0.00610861i	0.000207966	+	0.000197257i
$960$		0			0
$961$	−15.0897	+	26.1362i	−0.486766	+	0.843103i
$962$	1.31854	−	2.28378i	0.0425115	−	0.0736320i
$963$		0			0
$964$	0.826394	−	0.477119i	0.0266164	−	0.0153670i
$965$	−11.8348	−	20.4985i	−0.380976	−	0.659870i
$966$		0			0
$967$	−25.9697	+	44.9808i	−0.835129	+	1.44649i	0.0587965	+	0.998270i	$0.481274\pi$
$967$	−25.9697	+	44.9808i	−0.835129	+	1.44649i	−0.893925	+	0.448216i	$0.852060\pi$
$968$			1.53223i			0.0492476i
$969$		0			0
$970$	2.23764			0.0718464
$971$	13.0616	+	22.6234i	0.419167	+	0.726019i	0.995856	−	0.0909448i	$-0.0289887\pi$
$971$	13.0616	+	22.6234i	0.419167	+	0.726019i	−0.576688	+	0.816964i	$0.695655\pi$
$972$		0			0
$973$	−48.7169	+	14.4434i	−1.56179	+	0.463034i
$974$	34.2835	−	19.7936i	1.09852	−	0.634228i
$975$		0			0
$976$	8.24872	−	4.76240i	0.264035	−	0.152441i
$977$	−35.7603	+	20.6462i	−1.14407	+	0.660532i	−0.947436	−	0.319944i	$-0.896336\pi$
$977$	−35.7603	+	20.6462i	−1.14407	+	0.660532i	−0.196638	+	0.980476i	$0.563002\pi$
$978$		0			0
$979$	4.11414	−	2.37530i	0.131489	−	0.0759149i
$980$	5.86885	−	3.81531i	0.187474	−	0.121876i
$981$		0			0
$982$	−15.6937	−	27.1823i	−0.500806	−	0.867422i
$983$	−15.2552			−0.486567			−0.243283	−	0.969955i	$-0.578224\pi$
$983$	−15.2552			−0.486567			−0.243283	+	0.969955i	$0.578224\pi$
$984$		0			0
$985$			5.93788i			0.189197i
$986$	−15.6757	+	27.1511i	−0.499216	+	0.864667i
$987$		0			0
$988$	−0.214015	−	0.370684i	−0.00680872	−	0.0117930i
$989$	28.5757	−	16.4982i	0.908653	−	0.524611i
$990$		0			0
$991$	1.36395	−	2.36244i	0.0433274	−	0.0750453i	−0.843548	−	0.537053i	$-0.819537\pi$
$991$	1.36395	−	2.36244i	0.0433274	−	0.0750453i	0.886876	+	0.462008i	$0.152871\pi$
$992$	0.452916	−	0.784474i	0.0143801	−	0.0249071i
$993$		0			0
$994$	−8.02884	−	27.0809i	−0.254659	−	0.858953i
$995$	−14.4039	−	8.31608i	−0.456634	−	0.263638i
$996$		0			0
$997$		−	0.196236i		−	0.00621485i	−0.999995	−	0.00310743i	$-0.999011\pi$
$997$		−	0.196236i		−	0.00621485i	0.999995	−	0.00310743i	$-0.000989126\pi$
$998$	−25.6992	−	14.8374i	−0.813493	−	0.469670i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.t.b.1151.12		28
3.2	odd	2		630.2.t.b.311.3	✓	28
7.5	odd	6		1890.2.bk.b.341.11		28
9.2	odd	6		1890.2.bk.b.521.11		28
9.7	even	3		630.2.bk.b.101.5	yes	28
21.5	even	6		630.2.bk.b.131.12	yes	28
63.47	even	6	inner	1890.2.t.b.1601.12		28
63.61	odd	6		630.2.t.b.551.3	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.3	✓	28	3.2	odd	2
630.2.t.b.551.3	yes	28	63.61	odd	6
630.2.bk.b.101.5	yes	28	9.7	even	3
630.2.bk.b.131.12	yes	28	21.5	even	6
1890.2.t.b.1151.12		28	1.1	even	1	trivial
1890.2.t.b.1601.12		28	63.47	even	6	inner
1890.2.bk.b.341.11		28	7.5	odd	6
1890.2.bk.b.521.11		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)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.82075 + 1.91960i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.82075 + 1.91960i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{10} +3.07697i q^{11} +(-0.449846 - 0.259719i) q^{13} +(-2.53662 + 0.752047i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.44423 - 4.23353i) q^{17} +(0.713627 - 0.412013i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-1.53849 + 2.66474i) q^{22} +8.94137i q^{23} +1.00000 q^{25} +(-0.259719 - 0.449846i) q^{26} +(-2.57280 - 0.617016i) q^{28} +(-5.55412 + 3.20667i) q^{29} +(-0.784474 + 0.452916i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(4.23353 - 2.44423i) q^{34} +(-1.82075 + 1.91960i) q^{35} +(2.53840 + 4.39664i) q^{37} +0.824025 q^{38} +1.00000i q^{40} +(-2.18596 + 3.78619i) q^{41} +(-1.84515 - 3.19589i) q^{43} +(-2.66474 + 1.53849i) q^{44} +(-4.47068 + 7.74345i) q^{46} +(-1.89222 + 3.27742i) q^{47} +(-0.369732 - 6.99023i) q^{49} +(0.866025 + 0.500000i) q^{50} -0.519437i q^{52} +(-4.69700 - 2.71181i) q^{53} +3.07697i q^{55} +(-1.91960 - 1.82075i) q^{56} -6.41334 q^{58} +(5.29109 + 9.16443i) q^{59} +(-8.24872 - 4.76240i) q^{61} -0.905833 q^{62} -1.00000 q^{64} +(-0.449846 - 0.259719i) q^{65} +(-3.95287 - 6.84657i) q^{67} +4.88846 q^{68} +(-2.53662 + 0.752047i) q^{70} +10.6760i q^{71} +(5.78211 + 3.33830i) q^{73} +5.07681i q^{74} +(0.713627 + 0.412013i) q^{76} +(-5.90656 - 5.60240i) q^{77} +(-1.73049 + 2.99730i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-3.78619 + 2.18596i) q^{82} +(3.32033 + 5.75098i) q^{83} +(2.44423 - 4.23353i) q^{85} -3.69030i q^{86} -3.07697 q^{88} +(-0.771960 - 1.33707i) q^{89} +(1.31761 - 0.390641i) q^{91} +(-7.74345 + 4.47068i) q^{92} +(-3.27742 + 1.89222i) q^{94} +(0.713627 - 0.412013i) q^{95} +(1.93786 - 1.11882i) q^{97} +(3.17492 - 6.23858i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7}+O(q^{10}) \) 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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