LMFDB - Embedded newform 1890.2.t.b.1151.6

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			1151.6
Character	$\chi$	$=$	1890.1151
Dual form			1890.2.t.b.1601.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(2.64030 + 0.169721i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(2.64030 + 0.169721i) q^{7} -1.00000i q^{8} +(-0.866025 - 0.500000i) q^{10} -0.207763i q^{11} +(1.22567 + 0.707642i) q^{13} +(-2.20171 - 1.46713i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.680447 + 1.17857i) q^{17} +(5.73160 - 3.30914i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-0.103881 + 0.179928i) q^{22} -6.39482i q^{23} +1.00000 q^{25} +(-0.707642 - 1.22567i) q^{26} +(1.17317 + 2.37143i) q^{28} +(-6.11758 + 3.53199i) q^{29} +(4.10937 - 2.37255i) q^{31} +(0.866025 - 0.500000i) q^{32} +(1.17857 - 0.680447i) q^{34} +(2.64030 + 0.169721i) q^{35} +(1.32889 + 2.30171i) q^{37} -6.61828 q^{38} -1.00000i q^{40} +(1.41245 - 2.44643i) q^{41} +(1.06723 + 1.84849i) q^{43} +(0.179928 - 0.103881i) q^{44} +(-3.19741 + 5.53808i) q^{46} +(0.0573414 - 0.0993182i) q^{47} +(6.94239 + 0.896231i) q^{49} +(-0.866025 - 0.500000i) q^{50} +1.41528i q^{52} +(8.40507 + 4.85267i) q^{53} -0.207763i q^{55} +(0.169721 - 2.64030i) q^{56} +7.06398 q^{58} +(-4.34473 - 7.52530i) q^{59} +(-1.85102 - 1.06869i) q^{61} -4.74509 q^{62} -1.00000 q^{64} +(1.22567 + 0.707642i) q^{65} +(-0.0235223 - 0.0407418i) q^{67} -1.36089 q^{68} +(-2.20171 - 1.46713i) q^{70} -3.45539i q^{71} +(-11.5793 - 6.68529i) q^{73} -2.65778i q^{74} +(5.73160 + 3.30914i) q^{76} +(0.0352617 - 0.548556i) q^{77} +(-7.97657 + 13.8158i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-2.44643 + 1.41245i) q^{82} +(8.06016 + 13.9606i) q^{83} +(-0.680447 + 1.17857i) q^{85} -2.13446i q^{86} -0.207763 q^{88} +(1.40976 + 2.44178i) q^{89} +(3.11604 + 2.07641i) q^{91} +(5.53808 - 3.19741i) q^{92} +(-0.0993182 + 0.0573414i) q^{94} +(5.73160 - 3.30914i) q^{95} +(1.39248 - 0.803947i) q^{97} +(-5.56417 - 4.24735i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	2.64030	+	0.169721i	0.997940	+	0.0641486i
$7$	2.64030	+	0.169721i	0.997940	+	0.0641486i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−0.866025	−	0.500000i	−0.273861	−	0.158114i
$11$		−	0.207763i		−	0.0626428i	−0.999509	−	0.0313214i	$-0.990028\pi$
$11$		−	0.207763i		−	0.0626428i	0.999509	−	0.0313214i	$-0.00997154\pi$
$12$		0			0
$13$	1.22567	+	0.707642i	0.339940	+	0.196265i	0.660246	−	0.751050i	$-0.270452\pi$
$13$	1.22567	+	0.707642i	0.339940	+	0.196265i	−0.320305	+	0.947314i	$0.603786\pi$
$14$	−2.20171	−	1.46713i	−0.588431	−	0.392108i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.680447	+	1.17857i	−0.165033	+	0.285845i	−0.936667	−	0.350222i	$-0.886106\pi$
$17$	−0.680447	+	1.17857i	−0.165033	+	0.285845i	0.771634	+	0.636067i	$0.219440\pi$
$18$		0			0
$19$	5.73160	−	3.30914i	1.31492	−	0.759169i	0.332013	−	0.943275i	$-0.392272\pi$
$19$	5.73160	−	3.30914i	1.31492	−	0.759169i	0.982906	+	0.184106i	$0.0589389\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$		0			0
$22$	−0.103881	+	0.179928i	−0.0221476	+	0.0383607i
$23$		−	6.39482i		−	1.33341i	−0.745321	−	0.666706i	$-0.767704\pi$
$23$		−	6.39482i		−	1.33341i	0.745321	−	0.666706i	$-0.232296\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	−0.707642	−	1.22567i	−0.138780	−	0.240374i
$27$		0			0
$28$	1.17317	+	2.37143i	0.221708	+	0.448158i
$29$	−6.11758	+	3.53199i	−1.13601	+	0.655874i	−0.945439	−	0.325800i	$-0.894366\pi$
$29$	−6.11758	+	3.53199i	−1.13601	+	0.655874i	−0.190568	+	0.981674i	$0.561033\pi$
$30$		0			0
$31$	4.10937	−	2.37255i	0.738065	−	0.426122i	−0.0833006	−	0.996524i	$-0.526546\pi$
$31$	4.10937	−	2.37255i	0.738065	−	0.426122i	0.821365	+	0.570403i	$0.193213\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$	1.17857	−	0.680447i	0.202123	−	0.116696i
$35$	2.64030	+	0.169721i	0.446292	+	0.0286881i
$36$		0			0
$37$	1.32889	+	2.30171i	0.218468	+	0.378398i	0.954340	−	0.298723i	$-0.0965607\pi$
$37$	1.32889	+	2.30171i	0.218468	+	0.378398i	−0.735872	+	0.677121i	$0.763227\pi$
$38$	−6.61828			−1.07363
$39$		0			0
$40$		−	1.00000i		−	0.158114i
$41$	1.41245	−	2.44643i	0.220587	−	0.382068i	−0.734399	−	0.678718i	$-0.762536\pi$
$41$	1.41245	−	2.44643i	0.220587	−	0.382068i	0.954986	+	0.296650i	$0.0958693\pi$
$42$		0			0
$43$	1.06723	+	1.84849i	0.162751	+	0.281893i	0.935854	−	0.352387i	$-0.114630\pi$
$43$	1.06723	+	1.84849i	0.162751	+	0.281893i	−0.773103	+	0.634280i	$0.781297\pi$
$44$	0.179928	−	0.103881i	0.0271251	−	0.0156607i
$45$		0			0
$46$	−3.19741	+	5.53808i	−0.471432	+	0.816545i
$47$	0.0573414	−	0.0993182i	0.00836410	−	0.0144870i	−0.861813	−	0.507226i	$-0.830671\pi$
$47$	0.0573414	−	0.0993182i	0.00836410	−	0.0144870i	0.870177	+	0.492739i	$0.164004\pi$
$48$		0			0
$49$	6.94239	+	0.896231i	0.991770	+	0.128033i
$50$	−0.866025	−	0.500000i	−0.122474	−	0.0707107i
$51$		0			0
$52$			1.41528i			0.196265i
$53$	8.40507	+	4.85267i	1.15452	+	0.666565i	0.949986	−	0.312293i	$-0.101097\pi$
$53$	8.40507	+	4.85267i	1.15452	+	0.666565i	0.204539	+	0.978858i	$0.434430\pi$
$54$		0			0
$55$		−	0.207763i		−	0.0280147i
$56$	0.169721	−	2.64030i	0.0226800	−	0.352825i
$57$		0			0
$58$	7.06398			0.927546
$59$	−4.34473	−	7.52530i	−0.565636	−	0.979711i	−0.996990	−	0.0775280i	$-0.975297\pi$
$59$	−4.34473	−	7.52530i	−0.565636	−	0.979711i	0.431354	−	0.902183i	$-0.358036\pi$
$60$		0			0
$61$	−1.85102	−	1.06869i	−0.236999	−	0.136832i	0.376798	−	0.926296i	$-0.377025\pi$
$61$	−1.85102	−	1.06869i	−0.236999	−	0.136832i	−0.613797	+	0.789464i	$0.710359\pi$
$62$	−4.74509			−0.602627
$63$		0			0
$64$	−1.00000			−0.125000
$65$	1.22567	+	0.707642i	0.152026	+	0.0877722i
$66$		0			0
$67$	−0.0235223	−	0.0407418i	−0.00287371	−	0.00497740i	0.864585	−	0.502487i	$-0.167581\pi$
$67$	−0.0235223	−	0.0407418i	−0.00287371	−	0.00497740i	−0.867459	+	0.497509i	$0.834248\pi$
$68$	−1.36089			−0.165033
$69$		0			0
$70$	−2.20171	−	1.46713i	−0.263154	−	0.175356i
$71$		−	3.45539i		−	0.410079i	−0.978754	−	0.205040i	$-0.934268\pi$
$71$		−	3.45539i		−	0.410079i	0.978754	−	0.205040i	$-0.0657323\pi$
$72$		0			0
$73$	−11.5793	−	6.68529i	−1.35525	−	0.782454i	−0.366271	−	0.930508i	$-0.619366\pi$
$73$	−11.5793	−	6.68529i	−1.35525	−	0.782454i	−0.988979	+	0.148054i	$0.952699\pi$
$74$		−	2.65778i		−	0.308961i
$75$		0			0
$76$	5.73160	+	3.30914i	0.657460	+	0.379585i
$77$	0.0352617	−	0.548556i	0.00401845	−	0.0625138i
$78$		0			0
$79$	−7.97657	+	13.8158i	−0.897434	+	1.55440i	−0.0666713	+	0.997775i	$0.521238\pi$
$79$	−7.97657	+	13.8158i	−0.897434	+	1.55440i	−0.830763	+	0.556627i	$0.812095\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$		0			0
$82$	−2.44643	+	1.41245i	−0.270163	+	0.155979i
$83$	8.06016	+	13.9606i	0.884717	+	1.53237i	0.846038	+	0.533123i	$0.178982\pi$
$83$	8.06016	+	13.9606i	0.884717	+	1.53237i	0.0386794	+	0.999252i	$0.487685\pi$
$84$		0			0
$85$	−0.680447	+	1.17857i	−0.0738048	+	0.127834i
$86$		−	2.13446i		−	0.230164i
$87$		0			0
$88$	−0.207763			−0.0221476
$89$	1.40976	+	2.44178i	0.149435	+	0.258828i	0.931019	−	0.364972i	$-0.118921\pi$
$89$	1.40976	+	2.44178i	0.149435	+	0.258828i	−0.781584	+	0.623800i	$0.785588\pi$
$90$		0			0
$91$	3.11604	+	2.07641i	0.326650	+	0.217667i
$92$	5.53808	−	3.19741i	0.577384	−	0.333353i
$93$		0			0
$94$	−0.0993182	+	0.0573414i	−0.0102439	+	0.00591431i
$95$	5.73160	−	3.30914i	0.588050	−	0.339511i
$96$		0			0
$97$	1.39248	−	0.803947i	0.141385	−	0.0816284i	−0.427639	−	0.903950i	$-0.640655\pi$
$97$	1.39248	−	0.803947i	0.141385	−	0.0816284i	0.569024	+	0.822321i	$0.307321\pi$
$98$	−5.56417	−	4.24735i	−0.562066	−	0.429047i
$99$		0			0
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	6.10803			0.607772			0.303886	−	0.952708i	$-0.401716\pi$
$101$	6.10803			0.607772			0.303886	+	0.952708i	$0.401716\pi$
$102$		0			0
$103$			6.61641i			0.651934i	0.945381	+	0.325967i	$0.105690\pi$
$103$			6.61641i			0.651934i	−0.945381	+	0.325967i	$0.894310\pi$
$104$	0.707642	−	1.22567i	0.0693900	−	0.120187i
$105$		0			0
$106$	−4.85267	−	8.40507i	−0.471333	−	0.816372i
$107$	4.64917	−	2.68420i	0.449452	−	0.259491i	−0.258147	−	0.966106i	$-0.583112\pi$
$107$	4.64917	−	2.68420i	0.449452	−	0.259491i	0.707599	+	0.706614i	$0.249778\pi$
$108$		0			0
$109$	9.12274	−	15.8011i	0.873800	−	1.51347i	0.0157652	−	0.999876i	$-0.494982\pi$
$109$	9.12274	−	15.8011i	0.873800	−	1.51347i	0.858035	−	0.513591i	$-0.171685\pi$
$110$	−0.103881	+	0.179928i	−0.00990470	+	0.0171554i
$111$		0			0
$112$	−1.46713	+	2.20171i	−0.138631	+	0.208042i
$113$	3.64375	+	2.10372i	0.342775	+	0.197901i	0.661498	−	0.749947i	$-0.269921\pi$
$113$	3.64375	+	2.10372i	0.342775	+	0.197901i	−0.318723	+	0.947848i	$0.603254\pi$
$114$		0			0
$115$		−	6.39482i		−	0.596320i
$116$	−6.11758	−	3.53199i	−0.568003	−	0.327937i
$117$		0			0
$118$			8.68947i			0.799930i
$119$	−1.99661	+	2.99629i	−0.183029	+	0.274670i
$120$		0			0
$121$	10.9568			0.996076
$122$	1.06869	+	1.85102i	0.0967546	+	0.167584i
$123$		0			0
$124$	4.10937	+	2.37255i	0.369032	+	0.213061i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−14.9591			−1.32741			−0.663704	−	0.747995i	$-0.731017\pi$
$127$	−14.9591			−1.32741			−0.663704	+	0.747995i	$0.731017\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−0.707642	−	1.22567i	−0.0620643	−	0.107499i
$131$	16.7931			1.46722			0.733609	−	0.679572i	$-0.237834\pi$
$131$	16.7931			1.46722			0.733609	+	0.679572i	$0.237834\pi$
$132$		0			0
$133$	15.6948	−	7.76436i	1.36091	−	0.673255i
$134$			0.0470446i			0.00406403i
$135$		0			0
$136$	1.17857	+	0.680447i	0.101061	+	0.0583478i
$137$			3.39189i			0.289789i	0.989447	+	0.144894i	$0.0462842\pi$
$137$			3.39189i			0.289789i	−0.989447	+	0.144894i	$0.953716\pi$
$138$		0			0
$139$	5.07662	+	2.93099i	0.430593	+	0.248603i	0.699599	−	0.714535i	$-0.253362\pi$
$139$	5.07662	+	2.93099i	0.430593	+	0.248603i	−0.269006	+	0.963138i	$0.586695\pi$
$140$	1.17317	+	2.37143i	0.0991508	+	0.200422i
$141$		0			0
$142$	−1.72769	+	2.99245i	−0.144985	+	0.251121i
$143$	0.147022	−	0.254649i	0.0122946	−	0.0212948i
$144$		0			0
$145$	−6.11758	+	3.53199i	−0.508038	+	0.293316i
$146$	6.68529	+	11.5793i	0.553279	+	0.958307i
$147$		0			0
$148$	−1.32889	+	2.30171i	−0.109234	+	0.189199i
$149$		−	22.3632i		−	1.83207i	−0.401104	−	0.916033i	$-0.631373\pi$
$149$		−	22.3632i		−	1.83207i	0.401104	−	0.916033i	$-0.368627\pi$
$150$		0			0
$151$	12.6238			1.02731			0.513656	−	0.857996i	$-0.328291\pi$
$151$	12.6238			1.02731			0.513656	+	0.857996i	$0.328291\pi$
$152$	−3.30914	−	5.73160i	−0.268407	−	0.464894i
$153$		0			0
$154$	−0.304816	+	0.457433i	−0.0245627	+	0.0368610i
$155$	4.10937	−	2.37255i	0.330072	−	0.190567i
$156$		0			0
$157$	−5.02485	+	2.90110i	−0.401027	+	0.231533i	−0.686927	−	0.726727i	$-0.741041\pi$
$157$	−5.02485	+	2.90110i	−0.401027	+	0.231533i	0.285900	+	0.958259i	$0.407707\pi$
$158$	13.8158	−	7.97657i	1.09913	−	0.634582i
$159$		0			0
$160$	0.866025	−	0.500000i	0.0684653	−	0.0395285i
$161$	1.08534	−	16.8843i	0.0855365	−	1.33067i
$162$		0			0
$163$	8.98690	+	15.5658i	0.703908	+	1.21920i	0.967084	+	0.254457i	$0.0818967\pi$
$163$	8.98690	+	15.5658i	0.703908	+	1.21920i	−0.263176	+	0.964748i	$0.584770\pi$
$164$	2.82489			0.220587
$165$		0			0
$166$		−	16.1203i		−	1.25118i
$167$	5.00537	−	8.66956i	0.387327	−	0.670870i	−0.604762	−	0.796406i	$-0.706732\pi$
$167$	5.00537	−	8.66956i	0.387327	−	0.670870i	0.992089	+	0.125536i	$0.0400650\pi$
$168$		0			0
$169$	−5.49849	−	9.52366i	−0.422960	−	0.732589i
$170$	1.17857	−	0.680447i	0.0903921	−	0.0521879i
$171$		0			0
$172$	−1.06723	+	1.84849i	−0.0813754	+	0.140946i
$173$	−3.60215	+	6.23910i	−0.273866	+	0.474350i	−0.969848	−	0.243709i	$-0.921636\pi$
$173$	−3.60215	+	6.23910i	−0.273866	+	0.474350i	0.695982	+	0.718059i	$0.254969\pi$
$174$		0			0
$175$	2.64030	+	0.169721i	0.199588	+	0.0128297i
$176$	0.179928	+	0.103881i	0.0135626	+	0.00783035i
$177$		0			0
$178$		−	2.81953i		−	0.211333i
$179$	−12.7104	−	7.33833i	−0.950016	−	0.548492i	−0.0569303	−	0.998378i	$-0.518131\pi$
$179$	−12.7104	−	7.33833i	−0.950016	−	0.548492i	−0.893086	+	0.449886i	$0.851465\pi$
$180$		0			0
$181$		−	20.6504i		−	1.53493i	−0.641090	−	0.767465i	$-0.721518\pi$
$181$		−	20.6504i		−	1.53493i	0.641090	−	0.767465i	$-0.278482\pi$
$182$	−1.66037	−	3.35625i	−0.123075	−	0.248782i
$183$		0			0
$184$	−6.39482			−0.471432
$185$	1.32889	+	2.30171i	0.0977020	+	0.169225i
$186$		0			0
$187$	0.244863	+	0.141371i	0.0179061	+	0.0103381i
$188$	0.114683			0.00836410
$189$		0			0
$190$	−6.61828			−0.480141
$191$	19.0114	+	10.9763i	1.37562	+	0.794214i	0.991629	−	0.129124i	$-0.0412164\pi$
$191$	19.0114	+	10.9763i	1.37562	+	0.794214i	0.383990	+	0.923337i	$0.374550\pi$
$192$		0			0
$193$	−10.3050	−	17.8488i	−0.741772	−	1.28479i	−0.951688	−	0.307068i	$-0.900652\pi$
$193$	−10.3050	−	17.8488i	−0.741772	−	1.28479i	0.209915	−	0.977720i	$-0.432681\pi$
$194$	−1.60789			−0.115440
$195$		0			0
$196$	2.69504	+	6.46040i	0.192503	+	0.461457i
$197$			9.49837i			0.676731i	0.941015	+	0.338365i	$0.109874\pi$
$197$			9.49837i			0.676731i	−0.941015	+	0.338365i	$0.890126\pi$
$198$		0			0
$199$	1.57005	+	0.906467i	0.111298	+	0.0642578i	0.554616	−	0.832107i	$-0.312865\pi$
$199$	1.57005	+	0.906467i	0.111298	+	0.0642578i	−0.443318	+	0.896365i	$0.646199\pi$
$200$		−	1.00000i		−	0.0707107i
$201$		0			0
$202$	−5.28971	−	3.05401i	−0.372183	−	0.214880i
$203$	−16.7517	+	8.28723i	−1.17574	+	0.581650i
$204$		0			0
$205$	1.41245	−	2.44643i	0.0986496	−	0.170866i
$206$	3.30820	−	5.72998i	0.230493	−	0.399226i
$207$		0			0
$208$	−1.22567	+	0.707642i	−0.0849851	+	0.0490661i
$209$	−0.687516	−	1.19081i	−0.0475565	−	0.0823702i
$210$		0			0
$211$	11.3768	−	19.7053i	0.783214	−	1.35657i	−0.146847	−	0.989159i	$-0.546912\pi$
$211$	11.3768	−	19.7053i	0.783214	−	1.35657i	0.930060	−	0.367407i	$-0.119754\pi$
$212$			9.70533i			0.666565i
$213$		0			0
$214$	−5.36840			−0.366976
$215$	1.06723	+	1.84849i	0.0727844	+	0.126066i
$216$		0			0
$217$	11.2526	−	5.56679i	0.763879	−	0.377898i
$218$	−15.8011	+	9.12274i	−1.07018	+	0.617870i
$219$		0			0
$220$	0.179928	−	0.103881i	0.0121307	−	0.00700368i
$221$	−1.66801	+	0.963026i	−0.112202	+	0.0647801i
$222$		0			0
$223$	−8.80329	+	5.08258i	−0.589512	+	0.340355i	−0.764904	−	0.644144i	$-0.777214\pi$
$223$	−8.80329	+	5.08258i	−0.589512	+	0.340355i	0.175393	+	0.984499i	$0.443881\pi$
$224$	2.37143	−	1.17317i	0.158448	−	0.0783856i
$225$		0			0
$226$	−2.10372	−	3.64375i	−0.139937	−	0.242379i
$227$	−17.1927			−1.14112			−0.570560	−	0.821256i	$-0.693274\pi$
$227$	−17.1927			−1.14112			−0.570560	+	0.821256i	$0.693274\pi$
$228$		0			0
$229$			3.59285i			0.237423i	0.992929	+	0.118711i	$0.0378763\pi$
$229$			3.59285i			0.237423i	−0.992929	+	0.118711i	$0.962124\pi$
$230$	−3.19741	+	5.53808i	−0.210831	+	0.365170i
$231$		0			0
$232$	3.53199	+	6.11758i	0.231886	+	0.401639i
$233$	−18.4117	+	10.6300i	−1.20619	+	0.696396i	−0.961926	−	0.273312i	$-0.911881\pi$
$233$	−18.4117	+	10.6300i	−1.20619	+	0.696396i	−0.244268	+	0.969708i	$0.578548\pi$
$234$		0			0
$235$	0.0573414	−	0.0993182i	0.00374054	−	0.00647881i
$236$	4.34473	−	7.52530i	0.282818	−	0.489855i
$237$		0			0
$238$	3.22726	−	1.59656i	0.209192	−	0.103489i
$239$	4.18867	+	2.41833i	0.270943	+	0.156429i	0.629316	−	0.777150i	$-0.283335\pi$
$239$	4.18867	+	2.41833i	0.270943	+	0.156429i	−0.358373	+	0.933578i	$0.616669\pi$
$240$		0			0
$241$			1.60992i			0.103704i	0.998655	+	0.0518522i	$0.0165125\pi$
$241$			1.60992i			0.103704i	−0.998655	+	0.0518522i	$0.983488\pi$
$242$	−9.48890	−	5.47842i	−0.609969	−	0.352166i
$243$		0			0
$244$		−	2.13738i		−	0.136832i
$245$	6.94239	+	0.896231i	0.443533	+	0.0572581i
$246$		0			0
$247$	9.36675			0.595992
$248$	−2.37255	−	4.10937i	−0.150657	−	0.260945i
$249$		0			0
$250$	−0.866025	−	0.500000i	−0.0547723	−	0.0316228i
$251$	−2.86313			−0.180719			−0.0903596	−	0.995909i	$-0.528802\pi$
$251$	−2.86313			−0.180719			−0.0903596	+	0.995909i	$0.528802\pi$
$252$		0			0
$253$	−1.32860			−0.0835287
$254$	12.9550	+	7.47957i	0.812869	+	0.469310i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	31.4714			1.96313			0.981567	−	0.191118i	$-0.0612113\pi$
$257$	31.4714			1.96313			0.981567	+	0.191118i	$0.0612113\pi$
$258$		0			0
$259$	3.11802	+	6.30274i	0.193745	+	0.391633i
$260$			1.41528i			0.0877722i
$261$		0			0
$262$	−14.5432	−	8.39654i	−0.898484	−	0.518740i
$263$		−	3.29302i		−	0.203056i	−0.994833	−	0.101528i	$-0.967627\pi$
$263$		−	3.29302i		−	0.203056i	0.994833	−	0.101528i	$-0.0323732\pi$
$264$		0			0
$265$	8.40507	+	4.85267i	0.516319	+	0.298097i
$266$	−17.4743	−	1.12326i	−1.07142	−	0.0688717i
$267$		0			0
$268$	0.0235223	−	0.0407418i	0.00143685	−	0.00248870i
$269$	−9.44456	+	16.3585i	−0.575845	+	0.997393i	0.420104	+	0.907476i	$0.361994\pi$
$269$	−9.44456	+	16.3585i	−0.575845	+	0.997393i	−0.995949	+	0.0899173i	$0.971340\pi$
$270$		0			0
$271$	2.78962	−	1.61059i	0.169457	−	0.0978362i	−0.412873	−	0.910789i	$-0.635475\pi$
$271$	2.78962	−	1.61059i	0.169457	−	0.0978362i	0.582330	+	0.812953i	$0.302141\pi$
$272$	−0.680447	−	1.17857i	−0.0412582	−	0.0714612i
$273$		0			0
$274$	1.69594	−	2.93746i	0.102456	−	0.177459i
$275$		−	0.207763i		−	0.0125286i
$276$		0			0
$277$	0.118953			0.00714722			0.00357361	−	0.999994i	$-0.498862\pi$
$277$	0.118953			0.00714722			0.00357361	+	0.999994i	$0.498862\pi$
$278$	−2.93099	−	5.07662i	−0.175789	−	0.304475i
$279$		0			0
$280$	0.169721	−	2.64030i	0.0101428	−	0.157788i
$281$	11.3489	−	6.55231i	0.677021	−	0.390878i	−0.121711	−	0.992566i	$-0.538838\pi$
$281$	11.3489	−	6.55231i	0.677021	−	0.390878i	0.798732	+	0.601688i	$0.205505\pi$
$282$		0			0
$283$	−21.6963	+	12.5264i	−1.28971	+	0.744617i	−0.978603	−	0.205757i	$-0.934034\pi$
$283$	−21.6963	+	12.5264i	−1.28971	+	0.744617i	−0.311111	+	0.950374i	$0.600701\pi$
$284$	2.99245	−	1.72769i	0.177569	−	0.102520i
$285$		0			0
$286$	−0.254649	+	0.147022i	−0.0150577	+	0.00869357i
$287$	4.14450	−	6.21959i	0.244642	−	0.367131i
$288$		0			0
$289$	7.57398	+	13.1185i	0.445528	+	0.771678i
$290$	7.06398			0.414811
$291$		0			0
$292$		−	13.3706i		−	0.782454i
$293$	0.727716	−	1.26044i	0.0425136	−	0.0736358i	−0.843986	−	0.536366i	$-0.819797\pi$
$293$	0.727716	−	1.26044i	0.0425136	−	0.0736358i	0.886499	+	0.462730i	$0.153130\pi$
$294$		0			0
$295$	−4.34473	−	7.52530i	−0.252960	−	0.438140i
$296$	2.30171	−	1.32889i	0.133784	−	0.0772402i
$297$		0			0
$298$	−11.1816	+	19.3671i	−0.647733	+	1.12191i
$299$	4.52524	−	7.83795i	0.261702	−	0.453280i
$300$		0			0
$301$	2.50408	+	5.06171i	0.144333	+	0.291752i
$302$	−10.9325	−	6.31191i	−0.629097	−	0.363209i
$303$		0			0
$304$			6.61828i			0.379585i
$305$	−1.85102	−	1.06869i	−0.105989	−	0.0611930i
$306$		0			0
$307$			0.302317i			0.0172541i	0.999963	+	0.00862706i	$0.00274611\pi$
$307$			0.302317i			0.0172541i	−0.999963	+	0.00862706i	$0.997254\pi$
$308$	0.492694	−	0.243740i	0.0280739	−	0.0138884i
$309$		0			0
$310$	−4.74509			−0.269503
$311$	−0.158581	−	0.274670i	−0.00899228	−	0.0155751i	0.861494	−	0.507767i	$-0.169529\pi$
$311$	−0.158581	−	0.274670i	−0.00899228	−	0.0155751i	−0.870487	+	0.492192i	$0.836196\pi$
$312$		0			0
$313$	−18.3001	−	10.5656i	−1.03438	−	0.597201i	−0.116146	−	0.993232i	$-0.537054\pi$
$313$	−18.3001	−	10.5656i	−1.03438	−	0.597201i	−0.918237	+	0.396031i	$0.870387\pi$
$314$	5.80220			0.327437
$315$		0			0
$316$	−15.9531			−0.897434
$317$	−8.81472	−	5.08918i	−0.495084	−	0.285837i	0.231597	−	0.972812i	$-0.425605\pi$
$317$	−8.81472	−	5.08918i	−0.495084	−	0.285837i	−0.726681	+	0.686975i	$0.758938\pi$
$318$		0			0
$319$	0.733815	+	1.27101i	0.0410858	+	0.0711626i
$320$	−1.00000			−0.0559017
$321$		0			0
$322$	−9.38206	+	14.0795i	−0.522842	+	0.784621i
$323$			9.00678i			0.501151i
$324$		0			0
$325$	1.22567	+	0.707642i	0.0679880	+	0.0392529i
$326$		−	17.9738i		−	0.995476i
$327$		0			0
$328$	−2.44643	−	1.41245i	−0.135081	−	0.0779893i
$329$	0.168255	−	0.252498i	0.00927620	−	0.0139207i
$330$		0			0
$331$	11.0901	−	19.2086i	0.609566	−	1.05580i	−0.381746	−	0.924267i	$-0.624677\pi$
$331$	11.0901	−	19.2086i	0.609566	−	1.05580i	0.991312	−	0.131531i	$-0.0419894\pi$
$332$	−8.06016	+	13.9606i	−0.442359	+	0.766187i
$333$		0			0
$334$	−8.66956	+	5.00537i	−0.474377	+	0.273882i
$335$	−0.0235223	−	0.0407418i	−0.00128516	−	0.00222596i
$336$		0			0
$337$	−13.9347	+	24.1356i	−0.759070	+	1.31475i	0.184256	+	0.982878i	$0.441013\pi$
$337$	−13.9347	+	24.1356i	−0.759070	+	1.31475i	−0.943325	+	0.331869i	$0.892321\pi$
$338$			10.9970i			0.598156i
$339$		0			0
$340$	−1.36089			−0.0738048
$341$	−0.492926	−	0.853773i	−0.0266935	−	0.0462344i
$342$		0			0
$343$	18.1779	+	3.54459i	0.981514	+	0.191390i
$344$	1.84849	−	1.06723i	0.0996641	−	0.0575411i
$345$		0			0
$346$	6.23910	−	3.60215i	0.335416	−	0.193653i
$347$	−7.70036	+	4.44581i	−0.413377	+	0.238663i	−0.692240	−	0.721668i	$-0.743376\pi$
$347$	−7.70036	+	4.44581i	−0.413377	+	0.238663i	0.278863	+	0.960331i	$0.410043\pi$
$348$		0			0
$349$	−22.9898	+	13.2732i	−1.23062	+	0.710497i	−0.967159	−	0.254173i	$-0.918197\pi$
$349$	−22.9898	+	13.2732i	−1.23062	+	0.710497i	−0.263459	+	0.964671i	$0.584863\pi$
$350$	−2.20171	−	1.46713i	−0.117686	−	0.0784216i
$351$		0			0
$352$	−0.103881	−	0.179928i	−0.00553689	−	0.00959018i
$353$	−29.8048			−1.58635			−0.793175	−	0.608994i	$-0.791573\pi$
$353$	−29.8048			−1.58635			−0.793175	+	0.608994i	$0.791573\pi$
$354$		0			0
$355$		−	3.45539i		−	0.183393i
$356$	−1.40976	+	2.44178i	−0.0747173	+	0.129414i
$357$		0			0
$358$	7.33833	+	12.7104i	0.387843	+	0.671763i
$359$	−14.6722	+	8.47101i	−0.774370	+	0.447083i	−0.834431	−	0.551112i	$-0.814204\pi$
$359$	−14.6722	+	8.47101i	−0.774370	+	0.447083i	0.0600612	+	0.998195i	$0.480870\pi$
$360$		0			0
$361$	12.4008	−	21.4789i	0.652675	−	1.13047i
$362$	−10.3252	+	17.8838i	−0.542680	+	0.939949i
$363$		0			0
$364$	−0.240204	+	3.73678i	−0.0125901	+	0.195860i
$365$	−11.5793	−	6.68529i	−0.606086	−	0.349924i
$366$		0			0
$367$			21.0437i			1.09847i	0.835667	+	0.549236i	$0.185081\pi$
$367$			21.0437i			1.09847i	−0.835667	+	0.549236i	$0.814919\pi$
$368$	5.53808	+	3.19741i	0.288692	+	0.166677i
$369$		0			0
$370$		−	2.65778i		−	0.138171i
$371$	21.3683	+	14.2390i	1.10939	+	0.739253i
$372$		0			0
$373$	−11.2313			−0.581535			−0.290768	−	0.956794i	$-0.593911\pi$
$373$	−11.2313			−0.581535			−0.290768	+	0.956794i	$0.593911\pi$
$374$	−0.141371	−	0.244863i	−0.00731014	−	0.0126615i
$375$		0			0
$376$	−0.0993182	−	0.0573414i	−0.00512195	−	0.00295716i
$377$	−9.99753			−0.514899
$378$		0			0
$379$	2.41836			0.124223			0.0621113	−	0.998069i	$-0.480217\pi$
$379$	2.41836			0.124223			0.0621113	+	0.998069i	$0.480217\pi$
$380$	5.73160	+	3.30914i	0.294025	+	0.169755i
$381$		0			0
$382$	−10.9763	−	19.0114i	−0.561594	−	0.972709i
$383$	17.5017			0.894293			0.447146	−	0.894461i	$-0.352440\pi$
$383$	17.5017			0.894293			0.447146	+	0.894461i	$0.352440\pi$
$384$		0			0
$385$	0.0352617	−	0.548556i	0.00179710	−	0.0279570i
$386$			20.6101i			1.04902i
$387$		0			0
$388$	1.39248	+	0.803947i	0.0706923	+	0.0408142i
$389$		−	6.70962i		−	0.340191i	−0.985428	−	0.170096i	$-0.945592\pi$
$389$		−	6.70962i		−	0.340191i	0.985428	−	0.170096i	$-0.0544076\pi$
$390$		0			0
$391$	7.53673	+	4.35134i	0.381149	+	0.220057i
$392$	0.896231	−	6.94239i	0.0452665	−	0.350644i
$393$		0			0
$394$	4.74918	−	8.22583i	0.239260	−	0.414411i
$395$	−7.97657	+	13.8158i	−0.401345	+	0.695149i
$396$		0			0
$397$	6.02981	−	3.48131i	0.302628	−	0.174722i	−0.340995	−	0.940065i	$-0.610764\pi$
$397$	6.02981	−	3.48131i	0.302628	−	0.174722i	0.643623	+	0.765343i	$0.277431\pi$
$398$	−0.906467	−	1.57005i	−0.0454371	−	0.0786994i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$			11.5760i			0.578076i	0.957318	+	0.289038i	$0.0933354\pi$
$401$			11.5760i			0.578076i	−0.957318	+	0.289038i	$0.906665\pi$
$402$		0			0
$403$	6.71565			0.334530
$404$	3.05401	+	5.28971i	0.151943	+	0.263173i
$405$		0			0
$406$	18.6510	+	1.19891i	0.925635	+	0.0595008i
$407$	0.478209	−	0.276094i	0.0237039	−	0.0136855i
$408$		0			0
$409$	−31.4609	+	18.1640i	−1.55564	+	0.898151i	−0.557979	+	0.829855i	$0.688423\pi$
$409$	−31.4609	+	18.1640i	−1.55564	+	0.898151i	−0.997665	+	0.0682960i	$0.978244\pi$
$410$	−2.44643	+	1.41245i	−0.120821	+	0.0697558i
$411$		0			0
$412$	−5.72998	+	3.30820i	−0.282296	+	0.162983i
$413$	−10.1942	−	20.6065i	−0.501624	−	1.01398i
$414$		0			0
$415$	8.06016	+	13.9606i	0.395657	+	0.685299i
$416$	1.41528			0.0693900
$417$		0			0
$418$			1.37503i			0.0672550i
$419$	−16.0393	+	27.7808i	−0.783570	+	1.35718i	0.146280	+	0.989243i	$0.453270\pi$
$419$	−16.0393	+	27.7808i	−0.783570	+	1.35718i	−0.929850	+	0.367939i	$0.880063\pi$
$420$		0			0
$421$	−5.92162	−	10.2565i	−0.288602	−	0.499873i	0.684874	−	0.728661i	$-0.259857\pi$
$421$	−5.92162	−	10.2565i	−0.288602	−	0.499873i	−0.973476	+	0.228788i	$0.926524\pi$
$422$	−19.7053	+	11.3768i	−0.959237	+	0.553816i
$423$		0			0
$424$	4.85267	−	8.40507i	0.235666	−	0.408186i
$425$	−0.680447	+	1.17857i	−0.0330065	+	0.0571690i
$426$		0			0
$427$	−4.70588	−	3.13582i	−0.227734	−	0.151753i
$428$	4.64917	+	2.68420i	0.224726	+	0.129746i
$429$		0			0
$430$		−	2.13446i		−	0.102933i
$431$	−28.2466	−	16.3082i	−1.36059	−	0.785538i	−0.370890	−	0.928677i	$-0.620947\pi$
$431$	−28.2466	−	16.3082i	−1.36059	−	0.785538i	−0.989703	+	0.143139i	$0.954280\pi$
$432$		0			0
$433$		−	1.82172i		−	0.0875462i	−0.999041	−	0.0437731i	$-0.986062\pi$
$433$		−	1.82172i		−	0.0875462i	0.999041	−	0.0437731i	$-0.0139379\pi$
$434$	−12.5285	−	0.805343i	−0.601386	−	0.0386577i
$435$		0			0
$436$	18.2455			0.873800
$437$	−21.1614	−	36.6526i	−1.01229	−	1.75333i
$438$		0			0
$439$	20.6763	+	11.9375i	0.986825	+	0.569744i	0.904324	−	0.426847i	$-0.140376\pi$
$439$	20.6763	+	11.9375i	0.986825	+	0.569744i	0.0825012	+	0.996591i	$0.473709\pi$
$440$	−0.207763			−0.00990470
$441$		0			0
$442$	1.92605			0.0916129
$443$	20.4555	+	11.8100i	0.971868	+	0.561109i	0.899805	−	0.436292i	$-0.143708\pi$
$443$	20.4555	+	11.8100i	0.971868	+	0.561109i	0.0720631	+	0.997400i	$0.477042\pi$
$444$		0			0
$445$	1.40976	+	2.44178i	0.0668292	+	0.115752i
$446$	10.1652			0.481334
$447$		0			0
$448$	−2.64030	−	0.169721i	−0.124743	−	0.00801858i
$449$			33.6640i			1.58870i	0.607459	+	0.794351i	$0.292189\pi$
$449$			33.6640i			1.58870i	−0.607459	+	0.794351i	$0.707811\pi$
$450$		0			0
$451$	−0.508277	−	0.293454i	−0.0239338	−	0.0138182i
$452$			4.20744i			0.197901i
$453$		0			0
$454$	14.8893	+	8.59635i	0.698790	+	0.403447i
$455$	3.11604	+	2.07641i	0.146082	+	0.0973437i
$456$		0			0
$457$	−9.09952	+	15.7608i	−0.425658	+	0.737261i	−0.996482	−	0.0838116i	$-0.973291\pi$
$457$	−9.09952	+	15.7608i	−0.425658	+	0.737261i	0.570824	+	0.821073i	$0.306624\pi$
$458$	1.79643	−	3.11150i	0.0839415	−	0.145391i
$459$		0			0
$460$	5.53808	−	3.19741i	0.258214	−	0.149080i
$461$	7.33169	+	12.6989i	0.341471	+	0.591445i	0.984706	−	0.174224i	$-0.0557415\pi$
$461$	7.33169	+	12.6989i	0.341471	+	0.591445i	−0.643235	+	0.765669i	$0.722408\pi$
$462$		0			0
$463$	−3.20796	+	5.55635i	−0.149087	+	0.258226i	−0.930890	−	0.365299i	$-0.880967\pi$
$463$	−3.20796	+	5.55635i	−0.149087	+	0.258226i	0.781804	+	0.623525i	$0.214300\pi$
$464$		−	7.06398i		−	0.327937i
$465$		0			0
$466$	21.2600			0.984853
$467$	13.0712	+	22.6399i	0.604862	+	1.04765i	0.992073	+	0.125660i	$0.0401049\pi$
$467$	13.0712	+	22.6399i	0.604862	+	1.04765i	−0.387212	+	0.921991i	$0.626562\pi$
$468$		0			0
$469$	−0.0551912	−	0.111563i	−0.00254849	−	0.00515150i
$470$	−0.0993182	+	0.0573414i	−0.00458121	+	0.00264496i
$471$		0			0
$472$	−7.52530	+	4.34473i	−0.346380	+	0.199983i
$473$	0.384048	−	0.221730i	0.0176585	−	0.0101952i
$474$		0			0
$475$	5.73160	−	3.30914i	0.262984	−	0.151834i
$476$	−3.59317	−	0.230973i	−0.164693	−	0.0105866i
$477$		0			0
$478$	−2.41833	−	4.18867i	−0.110612	−	0.191585i
$479$	−33.7251			−1.54094			−0.770470	−	0.637476i	$-0.779979\pi$
$479$	−33.7251			−1.54094			−0.770470	+	0.637476i	$0.779979\pi$
$480$		0			0
$481$			3.76152i			0.171510i
$482$	0.804962	−	1.39424i	0.0366650	−	0.0635057i
$483$		0			0
$484$	5.47842	+	9.48890i	0.249019	+	0.431314i
$485$	1.39248	−	0.803947i	0.0632291	−	0.0365053i
$486$		0			0
$487$	3.38529	−	5.86349i	0.153402	−	0.265700i	−0.779074	−	0.626932i	$-0.784310\pi$
$487$	3.38529	−	5.86349i	0.153402	−	0.265700i	0.932476	+	0.361232i	$0.117644\pi$
$488$	−1.06869	+	1.85102i	−0.0483773	+	0.0837919i
$489$		0			0
$490$	−5.56417	−	4.24735i	−0.251364	−	0.191876i
$491$	7.86871	+	4.54300i	0.355110	+	0.205023i	0.666934	−	0.745117i	$-0.267607\pi$
$491$	7.86871	+	4.54300i	0.355110	+	0.205023i	−0.311824	+	0.950140i	$0.600940\pi$
$492$		0			0
$493$		−	9.61332i		−	0.432962i
$494$	−8.11184	−	4.68338i	−0.364969	−	0.210715i
$495$		0			0
$496$			4.74509i			0.213061i
$497$	0.586453	−	9.12327i	0.0263060	−	0.409234i
$498$		0			0
$499$	−42.0589			−1.88281			−0.941407	−	0.337274i	$-0.890495\pi$
$499$	−42.0589			−1.88281			−0.941407	+	0.337274i	$0.890495\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$		0			0
$502$	2.47954	+	1.43157i	0.110667	+	0.0638939i
$503$	19.9162			0.888021			0.444011	−	0.896021i	$-0.353555\pi$
$503$	19.9162			0.888021			0.444011	+	0.896021i	$0.353555\pi$
$504$		0			0
$505$	6.10803			0.271804
$506$	1.15061	+	0.664302i	0.0511506	+	0.0295318i
$507$		0			0
$508$	−7.47957	−	12.9550i	−0.331852	−	0.574785i
$509$	−24.0286			−1.06505			−0.532524	−	0.846415i	$-0.678756\pi$
$509$	−24.0286			−1.06505			−0.532524	+	0.846415i	$0.678756\pi$
$510$		0			0
$511$	−29.4381	−	19.6164i	−1.30227	−	0.867780i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−27.2551	−	15.7357i	−1.20217	−	0.694073i
$515$			6.61641i			0.291554i
$516$		0			0
$517$	−0.0206346	−	0.0119134i	−0.000907509	−	0.000523951i
$518$	0.451082	−	7.01735i	0.0198194	−	0.308324i
$519$		0			0
$520$	0.707642	−	1.22567i	0.0310322	−	0.0537493i
$521$	16.5020	−	28.5823i	0.722965	−	1.25221i	−0.236841	−	0.971548i	$-0.576112\pi$
$521$	16.5020	−	28.5823i	0.722965	−	1.25221i	0.959806	−	0.280663i	$-0.0905545\pi$
$522$		0			0
$523$	−26.4518	+	15.2720i	−1.15666	+	0.667797i	−0.950501	−	0.310722i	$-0.899429\pi$
$523$	−26.4518	+	15.2720i	−1.15666	+	0.667797i	−0.206157	+	0.978519i	$0.566096\pi$
$524$	8.39654	+	14.5432i	0.366805	+	0.635324i
$525$		0			0
$526$	−1.64651	+	2.85184i	−0.0717912	+	0.124346i
$527$			6.45757i			0.281296i
$528$		0			0
$529$	−17.8937			−0.777988
$530$	−4.85267	−	8.40507i	−0.210786	−	0.365093i
$531$		0			0
$532$	14.5715	+	9.70991i	0.631756	+	0.420978i
$533$	3.46239	−	1.99901i	0.149973	−	0.0865869i
$534$		0			0
$535$	4.64917	−	2.68420i	0.201001	−	0.116048i
$536$	−0.0407418	+	0.0235223i	−0.00175978	+	0.00101601i
$537$		0			0
$538$	16.3585	−	9.44456i	0.705264	−	0.407184i
$539$	0.186203	−	1.44237i	0.00802034	−	0.0621272i
$540$		0			0
$541$	−14.4385	−	25.0082i	−0.620760	−	1.07519i	−0.989345	−	0.145593i	$-0.953491\pi$
$541$	−14.4385	−	25.0082i	−0.620760	−	1.07519i	0.368585	−	0.929594i	$-0.379842\pi$
$542$	−3.22117			−0.138361
$543$		0			0
$544$			1.36089i			0.0583478i
$545$	9.12274	−	15.8011i	0.390775	−	0.676843i
$546$		0			0
$547$	14.0094	+	24.2650i	0.598999	+	1.03750i	0.992969	+	0.118374i	$0.0377681\pi$
$547$	14.0094	+	24.2650i	0.598999	+	1.03750i	−0.393970	+	0.919123i	$0.628899\pi$
$548$	−2.93746	+	1.69594i	−0.125482	+	0.0724472i
$549$		0			0
$550$	−0.103881	+	0.179928i	−0.00442951	+	0.00767214i
$551$	−23.3757	+	40.4879i	−0.995838	+	1.72484i
$552$		0			0
$553$	−23.4054	+	35.1242i	−0.995298	+	1.49363i
$554$	−0.103017	−	0.0594767i	−0.00437676	−	0.00252692i
$555$		0			0
$556$			5.86197i			0.248603i
$557$	−8.62658	−	4.98056i	−0.365520	−	0.211033i	0.305980	−	0.952038i	$-0.401016\pi$
$557$	−8.62658	−	4.98056i	−0.365520	−	0.211033i	−0.671499	+	0.741005i	$0.734349\pi$
$558$		0			0
$559$			3.02086i			0.127769i
$560$	−1.46713	+	2.20171i	−0.0619977	+	0.0930391i
$561$		0			0
$562$	−13.1046			−0.552785
$563$	19.2619	+	33.3626i	0.811794	+	1.40607i	0.911608	+	0.411062i	$0.134842\pi$
$563$	19.2619	+	33.3626i	0.811794	+	1.40607i	−0.0998141	+	0.995006i	$0.531825\pi$
$564$		0			0
$565$	3.64375	+	2.10372i	0.153294	+	0.0885041i
$566$	25.0528			1.05305
$567$		0			0
$568$	−3.45539			−0.144985
$569$	13.3337	+	7.69820i	0.558977	+	0.322725i	0.752735	−	0.658324i	$-0.228734\pi$
$569$	13.3337	+	7.69820i	0.558977	+	0.322725i	−0.193758	+	0.981049i	$0.562068\pi$
$570$		0			0
$571$	−2.32196	−	4.02175i	−0.0971709	−	0.168305i	0.813342	−	0.581786i	$-0.197646\pi$
$571$	−2.32196	−	4.02175i	−0.0971709	−	0.168305i	−0.910513	+	0.413481i	$0.864313\pi$
$572$	0.294043			0.0122946
$573$		0			0
$574$	−6.69903	+	3.31407i	−0.279612	+	0.138327i
$575$		−	6.39482i		−	0.266682i
$576$		0			0
$577$	−16.2075	−	9.35741i	−0.674727	−	0.389554i	0.123138	−	0.992390i	$-0.460704\pi$
$577$	−16.2075	−	9.35741i	−0.674727	−	0.389554i	−0.797865	+	0.602836i	$0.794037\pi$
$578$		−	15.1480i		−	0.630072i
$579$		0			0
$580$	−6.11758	−	3.53199i	−0.254019	−	0.146658i
$581$	18.9118	+	38.2282i	0.784595	+	1.58597i
$582$		0			0
$583$	1.00820	−	1.74626i	0.0417555	−	0.0723226i
$584$	−6.68529	+	11.5793i	−0.276639	+	0.479153i
$585$		0			0
$586$	−1.26044	+	0.727716i	−0.0520684	+	0.0300617i
$587$	−5.45638	−	9.45073i	−0.225209	−	0.390073i	0.731173	−	0.682192i	$-0.238973\pi$
$587$	−5.45638	−	9.45073i	−0.225209	−	0.390073i	−0.956382	+	0.292119i	$0.905640\pi$
$588$		0			0
$589$	15.7022	−	27.1970i	0.646997	−	1.12063i
$590$			8.68947i			0.357740i
$591$		0			0
$592$	−2.65778			−0.109234
$593$	9.60114	+	16.6297i	0.394272	+	0.682899i	0.993008	−	0.118048i	$-0.0376635\pi$
$593$	9.60114	+	16.6297i	0.394272	+	0.682899i	−0.598736	+	0.800946i	$0.704330\pi$
$594$		0			0
$595$	−1.99661	+	2.99629i	−0.0818532	+	0.122836i
$596$	19.3671	−	11.1816i	0.793307	−	0.458016i
$597$		0			0
$598$	−7.83795	+	4.52524i	−0.320518	+	0.185051i
$599$	−18.9751	+	10.9553i	−0.775301	+	0.447620i	−0.834762	−	0.550610i	$-0.814395\pi$
$599$	−18.9751	+	10.9553i	−0.775301	+	0.447620i	0.0594613	+	0.998231i	$0.481062\pi$
$600$		0			0
$601$	−38.2477	+	22.0823i	−1.56016	+	0.900756i	−0.562915	+	0.826515i	$0.690320\pi$
$601$	−38.2477	+	22.0823i	−1.56016	+	0.900756i	−0.997240	+	0.0742412i	$0.976347\pi$
$602$	0.362263	−	5.63561i	0.0147647	−	0.229690i
$603$		0			0
$604$	6.31191	+	10.9325i	0.256828	+	0.444839i
$605$	10.9568			0.445459
$606$		0			0
$607$			25.8388i			1.04876i	0.851483	+	0.524382i	$0.175704\pi$
$607$			25.8388i			1.04876i	−0.851483	+	0.524382i	$0.824296\pi$
$608$	3.30914	−	5.73160i	0.134203	−	0.232447i
$609$		0			0
$610$	1.06869	+	1.85102i	0.0432700	+	0.0749458i
$611$	0.140563	−	0.0811544i	0.00568659	−	0.00328315i
$612$		0			0
$613$	20.3696	−	35.2812i	0.822720	−	1.42499i	−0.0809298	−	0.996720i	$-0.525789\pi$
$613$	20.3696	−	35.2812i	0.822720	−	1.42499i	0.903650	−	0.428273i	$-0.140878\pi$
$614$	0.151158	−	0.261814i	0.00610025	−	0.0105659i
$615$		0			0
$616$	−0.548556	−	0.0352617i	−0.0221020	−	0.00142074i
$617$	−18.7258	−	10.8114i	−0.753874	−	0.435249i	0.0732181	−	0.997316i	$-0.476673\pi$
$617$	−18.7258	−	10.8114i	−0.753874	−	0.435249i	−0.827092	+	0.562067i	$0.810006\pi$
$618$		0			0
$619$		−	41.5576i		−	1.67034i	−0.549992	−	0.835170i	$-0.685369\pi$
$619$		−	41.5576i		−	1.67034i	0.549992	−	0.835170i	$-0.314631\pi$
$620$	4.10937	+	2.37255i	0.165036	+	0.0952837i
$621$		0			0
$622$			0.317161i			0.0127170i
$623$	3.30778	+	6.68631i	0.132523	+	0.267881i
$624$		0			0
$625$	1.00000			0.0400000
$626$	10.5656	+	18.3001i	0.422285	+	0.731419i
$627$		0			0
$628$	−5.02485	−	2.90110i	−0.200513	−	0.115766i
$629$	−3.61696			−0.144218
$630$		0			0
$631$	−24.7896			−0.986860			−0.493430	−	0.869785i	$-0.664257\pi$
$631$	−24.7896			−0.986860			−0.493430	+	0.869785i	$0.664257\pi$
$632$	13.8158	+	7.97657i	0.549564	+	0.317291i
$633$		0			0
$634$	5.08918	+	8.81472i	0.202117	+	0.350077i
$635$	−14.9591			−0.593635
$636$		0			0
$637$	7.87488	+	6.01121i	0.312014	+	0.238173i
$638$		−	1.46763i		−	0.0581040i
$639$		0			0
$640$	0.866025	+	0.500000i	0.0342327	+	0.0197642i
$641$		−	35.4280i		−	1.39932i	−0.714476	−	0.699660i	$-0.753335\pi$
$641$		−	35.4280i		−	1.39932i	0.714476	−	0.699660i	$-0.246665\pi$
$642$		0			0
$643$	−25.1223	−	14.5043i	−0.990726	−	0.571996i	−0.0852345	−	0.996361i	$-0.527164\pi$
$643$	−25.1223	−	14.5043i	−0.990726	−	0.571996i	−0.905491	+	0.424365i	$0.860497\pi$
$644$	15.1649	−	7.50220i	0.597579	−	0.295628i
$645$		0			0
$646$	4.50339	−	7.80010i	0.177184	−	0.306891i
$647$	−14.2851	+	24.7426i	−0.561607	+	0.972731i	0.435750	+	0.900068i	$0.356483\pi$
$647$	−14.2851	+	24.7426i	−0.561607	+	0.972731i	−0.997357	+	0.0726633i	$0.976850\pi$
$648$		0			0
$649$	−1.56348	+	0.902674i	−0.0613718	+	0.0354330i
$650$	−0.707642	−	1.22567i	−0.0277560	−	0.0480748i
$651$		0			0
$652$	−8.98690	+	15.5658i	−0.351954	+	0.609602i
$653$		−	23.3202i		−	0.912588i	−0.889829	−	0.456294i	$-0.849177\pi$
$653$		−	23.3202i		−	0.912588i	0.889829	−	0.456294i	$-0.150823\pi$
$654$		0			0
$655$	16.7931			0.656160
$656$	1.41245	+	2.44643i	0.0551468	+	0.0955170i
$657$		0			0
$658$	−0.271962	+	0.134542i	−0.0106022	+	0.00524500i
$659$	41.6998	−	24.0754i	1.62440	−	0.937845i	0.638670	−	0.769481i	$-0.279485\pi$
$659$	41.6998	−	24.0754i	1.62440	−	0.937845i	0.985725	−	0.168364i	$-0.0538485\pi$
$660$		0			0
$661$	−37.5132	+	21.6582i	−1.45909	+	0.842408i	−0.998967	−	0.0454452i	$-0.985529\pi$
$661$	−37.5132	+	21.6582i	−1.45909	+	0.842408i	−0.460127	+	0.887853i	$0.652196\pi$
$662$	−19.2086	+	11.0901i	−0.746562	+	0.431028i
$663$		0			0
$664$	13.9606	−	8.06016i	0.541776	−	0.312795i
$665$	15.6948	−	7.76436i	0.608618	−	0.301089i
$666$		0			0
$667$	22.5864	+	39.1208i	0.874550	+	1.51476i
$668$	10.0107			0.387327
$669$		0			0
$670$			0.0470446i			0.00181749i
$671$	−0.222034	+	0.384574i	−0.00857151	+	0.0148463i
$672$		0			0
$673$	−10.7910	−	18.6906i	−0.415964	−	0.720471i	0.579565	−	0.814926i	$-0.303222\pi$
$673$	−10.7910	−	18.6906i	−0.415964	−	0.720471i	−0.995529	+	0.0944550i	$0.969889\pi$
$674$	24.1356	−	13.9347i	0.929667	−	0.536743i
$675$		0			0
$676$	5.49849	−	9.52366i	0.211480	−	0.366294i
$677$	−18.2704	+	31.6452i	−0.702188	+	1.21623i	0.265509	+	0.964108i	$0.414460\pi$
$677$	−18.2704	+	31.6452i	−0.702188	+	1.21623i	−0.967697	+	0.252117i	$0.918873\pi$
$678$		0			0
$679$	3.81301	−	1.88633i	0.146330	−	0.0723907i
$680$	1.17857	+	0.680447i	0.0451960	+	0.0260940i
$681$		0			0
$682$			0.985853i			0.0377502i
$683$	−36.6115	−	21.1377i	−1.40090	−	0.808811i	−0.406416	−	0.913688i	$-0.633222\pi$
$683$	−36.6115	−	21.1377i	−1.40090	−	0.808811i	−0.994485	+	0.104878i	$0.966555\pi$
$684$		0			0
$685$			3.39189i			0.129597i
$686$	−13.9702	−	12.1587i	−0.533386	−	0.464220i
$687$		0			0
$688$	−2.13446			−0.0813754
$689$	6.86790	+	11.8956i	0.261646	+	0.453185i
$690$		0			0
$691$	−26.9067	−	15.5346i	−1.02358	−	0.590964i	−0.108441	−	0.994103i	$-0.534586\pi$
$691$	−26.9067	−	15.5346i	−1.02358	−	0.590964i	−0.915139	+	0.403139i	$0.867919\pi$
$692$	−7.20429			−0.273866
$693$		0			0
$694$	8.89161			0.337521
$695$	5.07662	+	2.93099i	0.192567	+	0.111179i
$696$		0			0
$697$	1.92219	+	3.32933i	0.0728081	+	0.126107i
$698$	26.5464			1.00480
$699$		0			0
$700$	1.17317	+	2.37143i	0.0443416	+	0.0896316i
$701$		−	27.7518i		−	1.04817i	−0.851666	−	0.524085i	$-0.824407\pi$
$701$		−	27.7518i		−	1.04817i	0.851666	−	0.524085i	$-0.175593\pi$
$702$		0			0
$703$	15.2333	+	8.79497i	0.574536	+	0.331709i
$704$			0.207763i			0.00783035i
$705$		0			0
$706$	25.8117	+	14.9024i	0.971437	+	0.560859i
$707$	16.1270	+	1.03666i	0.606520	+	0.0389877i
$708$		0			0
$709$	−7.10868	+	12.3126i	−0.266972	+	0.462409i	−0.968078	−	0.250648i	$-0.919356\pi$
$709$	−7.10868	+	12.3126i	−0.266972	+	0.462409i	0.701106	+	0.713057i	$0.252690\pi$
$710$	−1.72769	+	2.99245i	−0.0648392	+	0.112305i
$711$		0			0
$712$	2.44178	−	1.40976i	0.0915097	−	0.0528331i
$713$	−15.1720	−	26.2787i	−0.568196	−	0.984144i
$714$		0			0
$715$	0.147022	−	0.254649i	0.00549830	−	0.00952333i
$716$		−	14.6767i		−	0.548492i
$717$		0			0
$718$	16.9420			0.632271
$719$	−21.6234	−	37.4528i	−0.806415	−	1.39675i	−0.915332	−	0.402701i	$-0.868071\pi$
$719$	−21.6234	−	37.4528i	−0.806415	−	1.39675i	0.108916	−	0.994051i	$-0.465262\pi$
$720$		0			0
$721$	−1.12294	+	17.4693i	−0.0418207	+	0.650591i
$722$	−21.4789	+	12.4008i	−0.799361	+	0.461511i
$723$		0			0
$724$	17.8838	−	10.3252i	0.664645	−	0.383733i
$725$	−6.11758	+	3.53199i	−0.227201	+	0.131175i
$726$		0			0
$727$	−2.32159	+	1.34037i	−0.0861032	+	0.0497117i	−0.542433	−	0.840099i	$-0.682497\pi$
$727$	−2.32159	+	1.34037i	−0.0861032	+	0.0497117i	0.456330	+	0.889811i	$0.349164\pi$
$728$	2.07641	−	3.11604i	0.0769569	−	0.115488i
$729$		0			0
$730$	6.68529	+	11.5793i	0.247434	+	0.428568i
$731$	−2.90477			−0.107437
$732$		0			0
$733$		−	21.7022i		−	0.801588i	−0.916168	−	0.400794i	$-0.868734\pi$
$733$		−	21.7022i		−	0.801588i	0.916168	−	0.400794i	$-0.131266\pi$
$734$	10.5218	−	18.2244i	0.388368	−	0.672674i
$735$		0			0
$736$	−3.19741	−	5.53808i	−0.117858	−	0.204136i
$737$	−0.00846463	+	0.00488705i	−0.000311799	+	0.000180017i
$738$		0			0
$739$	−0.779082	+	1.34941i	−0.0286590	+	0.0496389i	−0.879999	−	0.474975i	$-0.842457\pi$
$739$	−0.779082	+	1.34941i	−0.0286590	+	0.0496389i	0.851340	+	0.524614i	$0.175790\pi$
$740$	−1.32889	+	2.30171i	−0.0488510	+	0.0846124i
$741$		0			0
$742$	−11.3860	−	23.0155i	−0.417993	−	0.844926i
$743$	5.56936	+	3.21547i	0.204320	+	0.117964i	0.598669	−	0.800997i	$-0.295697\pi$
$743$	5.56936	+	3.21547i	0.204320	+	0.117964i	−0.394349	+	0.918961i	$0.629030\pi$
$744$		0			0
$745$		−	22.3632i		−	0.819324i
$746$	9.72660	+	5.61566i	0.356116	+	0.205604i
$747$		0			0
$748$			0.282743i			0.0103381i
$749$	12.7308	−	6.29804i	0.465173	−	0.230125i
$750$		0			0
$751$	54.6839			1.99544			0.997722	−	0.0674569i	$-0.0214885\pi$
$751$	54.6839			1.99544			0.997722	+	0.0674569i	$0.0214885\pi$
$752$	0.0573414	+	0.0993182i	0.00209103	+	0.00362176i
$753$		0			0
$754$	8.65812	+	4.99877i	0.315310	+	0.182044i
$755$	12.6238			0.459427
$756$		0			0
$757$	6.88087			0.250089			0.125045	−	0.992151i	$-0.460093\pi$
$757$	6.88087			0.250089			0.125045	+	0.992151i	$0.460093\pi$
$758$	−2.09436	−	1.20918i	−0.0760705	−	0.0439193i
$759$		0			0
$760$	−3.30914	−	5.73160i	−0.120035	−	0.207907i
$761$	20.3654			0.738246			0.369123	−	0.929380i	$-0.379658\pi$
$761$	20.3654			0.738246			0.369123	+	0.929380i	$0.379658\pi$
$762$		0			0
$763$	26.7686	−	40.1712i	0.969087	−	1.45430i
$764$			21.9525i			0.794214i
$765$		0			0
$766$	−15.1569	−	8.75083i	−0.547640	−	0.316180i
$767$		−	12.2981i		−	0.444057i
$768$		0			0
$769$	17.8787	+	10.3223i	0.644721	+	0.372230i	0.786431	−	0.617678i	$-0.211927\pi$
$769$	17.8787	+	10.3223i	0.644721	+	0.372230i	−0.141710	+	0.989908i	$0.545260\pi$
$770$	−0.304816	+	0.457433i	−0.0109848	+	0.0164847i
$771$		0			0
$772$	10.3050	−	17.8488i	0.370886	−	0.642394i
$773$	13.4607	−	23.3145i	0.484146	−	0.838566i	−0.515688	−	0.856776i	$-0.672464\pi$
$773$	13.4607	−	23.3145i	0.484146	−	0.838566i	0.999834	+	0.0182107i	$0.00579695\pi$
$774$		0			0
$775$	4.10937	−	2.37255i	0.147613	−	0.0852244i
$776$	−0.803947	−	1.39248i	−0.0288600	−	0.0499870i
$777$		0			0
$778$	−3.35481	+	5.81070i	−0.120276	+	0.208324i
$779$		−	18.6959i		−	0.669852i
$780$		0			0
$781$	−0.717900			−0.0256885
$782$	−4.35134	−	7.53673i	−0.155603	−	0.269513i
$783$		0			0
$784$	−4.24735	+	5.56417i	−0.151691	+	0.198720i
$785$	−5.02485	+	2.90110i	−0.179345	+	0.103545i
$786$		0			0
$787$	23.5840	−	13.6162i	0.840677	−	0.485365i	−0.0168171	−	0.999859i	$-0.505353\pi$
$787$	23.5840	−	13.6162i	0.840677	−	0.485365i	0.857494	+	0.514493i	$0.172020\pi$
$788$	−8.22583	+	4.74918i	−0.293033	+	0.169183i
$789$		0			0
$790$	13.8158	−	7.97657i	0.491545	−	0.283794i
$791$	9.26355	+	6.17287i	0.329374	+	0.219482i
$792$		0			0
$793$	−1.51250	−	2.61972i	−0.0537104	−	0.0930291i
$794$	−6.96263			−0.247094
$795$		0			0
$796$			1.81293i			0.0642578i
$797$	12.9468	−	22.4246i	0.458601	−	0.794319i	−0.540287	−	0.841481i	$-0.681684\pi$
$797$	12.9468	−	22.4246i	0.458601	−	0.794319i	0.998887	+	0.0471616i	$0.0150176\pi$
$798$		0			0
$799$	0.0780356	+	0.135162i	0.00276070	+	0.00478167i
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$		0			0
$802$	5.78798	−	10.0251i	0.204381	−	0.353998i
$803$	−1.38895	+	2.40574i	−0.0490151	+	0.0848967i
$804$		0			0
$805$	1.08534	−	16.8843i	0.0382531	−	0.595092i
$806$	−5.81593	−	3.35783i	−0.204857	−	0.118274i
$807$		0			0
$808$		−	6.10803i		−	0.214880i
$809$	20.9833	+	12.1147i	0.737734	+	0.425931i	0.821245	−	0.570576i	$-0.193280\pi$
$809$	20.9833	+	12.1147i	0.737734	+	0.425931i	−0.0835110	+	0.996507i	$0.526613\pi$
$810$		0			0
$811$			26.9699i			0.947040i	0.880783	+	0.473520i	$0.157017\pi$
$811$			26.9699i			0.947040i	−0.880783	+	0.473520i	$0.842983\pi$
$812$	−15.5528	−	10.3638i	−0.545797	−	0.363698i
$813$		0			0
$814$	−0.552188			−0.0193542
$815$	8.98690	+	15.5658i	0.314797	+	0.545245i
$816$		0			0
$817$	12.2339	+	7.06322i	0.428008	+	0.247111i
$818$	36.3280			1.27018
$819$		0			0
$820$	2.82489			0.0986496
$821$	1.73135	+	0.999595i	0.0604245	+	0.0348861i	0.529908	−	0.848055i	$-0.322226\pi$
$821$	1.73135	+	0.999595i	0.0604245	+	0.0348861i	−0.469483	+	0.882941i	$0.655560\pi$
$822$		0			0
$823$	3.14423	+	5.44597i	0.109601	+	0.189835i	0.915609	−	0.402071i	$-0.131709\pi$
$823$	3.14423	+	5.44597i	0.109601	+	0.189835i	−0.806008	+	0.591905i	$0.798376\pi$
$824$	6.61641			0.230493
$825$		0			0
$826$	−1.47479	+	22.9428i	−0.0513144	+	0.798283i
$827$		−	43.5204i		−	1.51335i	−0.653789	−	0.756677i	$-0.726822\pi$
$827$		−	43.5204i		−	1.51335i	0.653789	−	0.756677i	$-0.273178\pi$
$828$		0			0
$829$	−28.3927	−	16.3926i	−0.986120	−	0.569337i	−0.0820080	−	0.996632i	$-0.526133\pi$
$829$	−28.3927	−	16.3926i	−0.986120	−	0.569337i	−0.904112	+	0.427295i	$0.859467\pi$
$830$		−	16.1203i		−	0.559544i
$831$		0			0
$832$	−1.22567	−	0.707642i	−0.0424925	−	0.0245331i
$833$	−5.78020	+	7.57225i	−0.200272	+	0.262363i
$834$		0			0
$835$	5.00537	−	8.66956i	0.173218	−	0.300022i
$836$	0.687516	−	1.19081i	0.0237782	−	0.0411851i
$837$		0			0
$838$	27.7808	−	16.0393i	0.959673	−	0.554067i
$839$	4.60486	+	7.97586i	0.158978	+	0.275357i	0.934500	−	0.355962i	$-0.115847\pi$
$839$	4.60486	+	7.97586i	0.158978	+	0.275357i	−0.775523	+	0.631320i	$0.782514\pi$
$840$		0			0
$841$	10.4499	−	18.0997i	0.360341	−	0.624128i
$842$			11.8432i			0.408145i
$843$		0			0
$844$	22.7537			0.783214
$845$	−5.49849	−	9.52366i	−0.189154	−	0.327624i
$846$		0			0
$847$	28.9294	+	1.85961i	0.994024	+	0.0638969i
$848$	−8.40507	+	4.85267i	−0.288631	+	0.166641i
$849$		0			0
$850$	1.17857	−	0.680447i	0.0404246	−	0.0233391i
$851$	14.7190	−	8.49802i	0.504561	−	0.291308i
$852$		0			0
$853$	−34.0668	+	19.6685i	−1.16642	+	0.673435i	−0.952835	−	0.303489i	$-0.901849\pi$
$853$	−34.0668	+	19.6685i	−1.16642	+	0.673435i	−0.213589	+	0.976924i	$0.568515\pi$
$854$	2.50750	+	5.06864i	0.0858050	+	0.173445i
$855$		0			0
$856$	−2.68420	−	4.64917i	−0.0917441	−	0.158905i
$857$	−32.4112			−1.10715			−0.553573	−	0.832801i	$-0.686736\pi$
$857$	−32.4112			−1.10715			−0.553573	+	0.832801i	$0.686736\pi$
$858$		0			0
$859$			26.4199i			0.901435i	0.892667	+	0.450717i	$0.148832\pi$
$859$			26.4199i			0.901435i	−0.892667	+	0.450717i	$0.851168\pi$
$860$	−1.06723	+	1.84849i	−0.0363922	+	0.0630331i
$861$		0			0
$862$	16.3082	+	28.2466i	0.555459	+	0.962084i
$863$	−24.4007	+	14.0878i	−0.830610	+	0.479553i	−0.854061	−	0.520172i	$-0.825868\pi$
$863$	−24.4007	+	14.0878i	−0.830610	+	0.479553i	0.0234518	+	0.999725i	$0.492534\pi$
$864$		0			0
$865$	−3.60215	+	6.23910i	−0.122477	+	0.212136i
$866$	−0.910860	+	1.57766i	−0.0309523	+	0.0536109i
$867$		0			0
$868$	10.4473	+	6.96168i	0.354605	+	0.236295i
$869$	2.87041	+	1.65723i	0.0973721	+	0.0562178i
$870$		0			0
$871$		−	0.0665815i		−	0.00225603i
$872$	−15.8011	−	9.12274i	−0.535091	−	0.308935i
$873$		0			0
$874$			42.3227i			1.43159i
$875$	2.64030	+	0.169721i	0.0892585	+	0.00573763i
$876$		0			0
$877$	36.3479			1.22738			0.613691	−	0.789546i	$-0.289684\pi$
$877$	36.3479			1.22738			0.613691	+	0.789546i	$0.289684\pi$
$878$	−11.9375	−	20.6763i	−0.402870	−	0.697791i
$879$		0			0
$880$	0.179928	+	0.103881i	0.00606536	+	0.00350184i
$881$	−0.589367			−0.0198563			−0.00992814	−	0.999951i	$-0.503160\pi$
$881$	−0.589367			−0.0198563			−0.00992814	+	0.999951i	$0.503160\pi$
$882$		0			0
$883$	55.1932			1.85740			0.928700	−	0.370833i	$-0.120928\pi$
$883$	55.1932			1.85740			0.928700	+	0.370833i	$0.120928\pi$
$884$	−1.66801	−	0.963026i	−0.0561012	−	0.0323901i
$885$		0			0
$886$	−11.8100	−	20.4555i	−0.396764	−	0.687215i
$887$	−50.8028			−1.70579			−0.852896	−	0.522082i	$-0.825156\pi$
$887$	−50.8028			−1.70579			−0.852896	+	0.522082i	$0.825156\pi$
$888$		0			0
$889$	−39.4966	−	2.53888i	−1.32467	−	0.0851514i
$890$		−	2.81953i		−	0.0945108i
$891$		0			0
$892$	−8.80329	−	5.08258i	−0.294756	−	0.170177i
$893$		−	0.759003i		−	0.0253991i
$894$		0			0
$895$	−12.7104	−	7.33833i	−0.424860	−	0.245293i
$896$	2.20171	+	1.46713i	0.0735539	+	0.0490135i
$897$		0			0
$898$	16.8320	−	29.1539i	0.561691	−	0.972878i
$899$	−16.7596	+	29.0285i	−0.558964	+	0.968154i
$900$		0			0
$901$	−11.4384	+	6.60397i	−0.381068	+	0.220010i
$902$	0.293454	+	0.508277i	0.00977094	+	0.0169238i
$903$		0			0
$904$	2.10372	−	3.64375i	0.0699687	−	0.121189i
$905$		−	20.6504i		−	0.686442i
$906$		0			0
$907$	−19.4956			−0.647340			−0.323670	−	0.946170i	$-0.604917\pi$
$907$	−19.4956			−0.647340			−0.323670	+	0.946170i	$0.604917\pi$
$908$	−8.59635	−	14.8893i	−0.285280	−	0.494119i
$909$		0			0
$910$	−1.66037	−	3.35625i	−0.0550406	−	0.111258i
$911$	−29.5749	+	17.0751i	−0.979860	+	0.565723i	−0.902228	−	0.431259i	$-0.858069\pi$
$911$	−29.5749	+	17.0751i	−0.979860	+	0.565723i	−0.0776324	+	0.996982i	$0.524736\pi$
$912$		0			0
$913$	2.90049	−	1.67460i	0.0959922	−	0.0554211i
$914$	15.7608	−	9.09952i	0.521322	−	0.300986i
$915$		0			0
$916$	−3.11150	+	1.79643i	−0.102807	+	0.0593556i
$917$	44.3388	+	2.85014i	1.46420	+	0.0941200i
$918$		0			0
$919$	−8.23460	−	14.2627i	−0.271634	−	0.470484i	0.697646	−	0.716442i	$-0.254231\pi$
$919$	−8.23460	−	14.2627i	−0.271634	−	0.470484i	−0.969280	+	0.245958i	$0.920897\pi$
$920$	−6.39482			−0.210831
$921$		0			0
$922$		−	14.6634i		−	0.482913i
$923$	2.44518	−	4.23517i	0.0804840	−	0.139402i
$924$		0			0
$925$	1.32889	+	2.30171i	0.0436937	+	0.0756796i
$926$	5.55635	−	3.20796i	0.182593	−	0.105420i
$927$		0			0
$928$	−3.53199	+	6.11758i	−0.115943	+	0.200820i
$929$	5.86104	−	10.1516i	0.192294	−	0.333064i	−0.753716	−	0.657200i	$-0.771740\pi$
$929$	5.86104	−	10.1516i	0.192294	−	0.333064i	0.946010	+	0.324137i	$0.105074\pi$
$930$		0			0
$931$	42.7568	−	17.8365i	1.40130	−	0.584568i
$932$	−18.4117	−	10.6300i	−0.603097	−	0.348198i
$933$		0			0
$934$		−	26.1423i		−	0.855403i
$935$	0.244863	+	0.141371i	0.00800786	+	0.00462334i
$936$		0			0
$937$		−	10.5888i		−	0.345922i	−0.984929	−	0.172961i	$-0.944667\pi$
$937$		−	10.5888i		−	0.345922i	0.984929	−	0.172961i	$-0.0553334\pi$
$938$	−0.00798447	+	0.124212i	−0.000260702	+	0.00405566i
$939$		0			0
$940$	0.114683			0.00374054
$941$	−5.81412	−	10.0704i	−0.189535	−	0.328284i	0.755560	−	0.655079i	$-0.227365\pi$
$941$	−5.81412	−	10.0704i	−0.189535	−	0.328284i	−0.945095	+	0.326795i	$0.894031\pi$
$942$		0			0
$943$	−15.6445	−	9.03234i	−0.509454	−	0.294134i
$944$	8.68947			0.282818
$945$		0			0
$946$	−0.443460			−0.0144181
$947$	1.79619	+	1.03703i	0.0583682	+	0.0336989i	0.528900	−	0.848684i	$-0.322605\pi$
$947$	1.79619	+	1.03703i	0.0583682	+	0.0336989i	−0.470532	+	0.882383i	$0.655938\pi$
$948$		0			0
$949$	−9.46159	−	16.3879i	−0.307136	−	0.531975i
$950$	−6.61828			−0.214725
$951$		0			0
$952$	2.99629	+	1.99661i	0.0971104	+	0.0647106i
$953$		−	28.8160i		−	0.933442i	−0.884405	−	0.466721i	$-0.845435\pi$
$953$		−	28.8160i		−	0.933442i	0.884405	−	0.466721i	$-0.154565\pi$
$954$		0			0
$955$	19.0114	+	10.9763i	0.615195	+	0.355183i
$956$			4.83666i			0.156429i
$957$		0			0
$958$	29.2068	+	16.8626i	0.943629	+	0.544805i
$959$	−0.575676	+	8.95561i	−0.0185895	+	0.289192i
$960$		0			0
$961$	−4.24206	+	7.34746i	−0.136840	+	0.237015i
$962$	1.88076	−	3.25757i	0.0606381	−	0.105028i
$963$		0			0
$964$	−1.39424	+	0.804962i	−0.0449053	+	0.0259261i
$965$	−10.3050	−	17.8488i	−0.331731	−	0.574574i
$966$		0			0
$967$	−9.12278	+	15.8011i	−0.293369	+	0.508130i	−0.974604	−	0.223935i	$-0.928110\pi$
$967$	−9.12278	+	15.8011i	−0.293369	+	0.508130i	0.681235	+	0.732065i	$0.261443\pi$
$968$		−	10.9568i		−	0.352166i
$969$		0			0
$970$	−1.60789			−0.0516263
$971$	1.09564	+	1.89770i	0.0351606	+	0.0609000i	0.883070	−	0.469241i	$-0.155472\pi$
$971$	1.09564	+	1.89770i	0.0351606	+	0.0609000i	−0.847910	+	0.530141i	$0.822139\pi$
$972$		0			0
$973$	12.9063	+	8.60030i	0.413759	+	0.275713i
$974$	−5.86349	+	3.38529i	−0.187878	+	0.108472i
$975$		0			0
$976$	1.85102	−	1.06869i	0.0592498	−	0.0342079i
$977$	0.216592	−	0.125049i	0.00692939	−	0.00400068i	−0.496531	−	0.868019i	$-0.665393\pi$
$977$	0.216592	−	0.125049i	0.00692939	−	0.00400068i	0.503461	+	0.864018i	$0.332060\pi$
$978$		0			0
$979$	0.507311	−	0.292896i	0.0162137	−	0.00936101i
$980$	2.69504	+	6.46040i	0.0860898	+	0.206370i
$981$		0			0
$982$	−4.54300	−	7.86871i	−0.144973	−	0.251101i
$983$	3.21720			0.102613			0.0513064	−	0.998683i	$-0.483661\pi$
$983$	3.21720			0.102613			0.0513064	+	0.998683i	$0.483661\pi$
$984$		0			0
$985$			9.49837i			0.302643i
$986$	−4.80666	+	8.32538i	−0.153075	+	0.265134i
$987$		0			0
$988$	4.68338	+	8.11184i	0.148998	+	0.258072i
$989$	11.8208	−	6.82473i	0.375879	−	0.217014i
$990$		0			0
$991$	−0.704168	+	1.21966i	−0.0223686	+	0.0387436i	−0.876993	−	0.480503i	$-0.840454\pi$
$991$	−0.704168	+	1.21966i	−0.0223686	+	0.0387436i	0.854624	+	0.519247i	$0.173787\pi$
$992$	2.37255	−	4.10937i	0.0753284	−	0.130473i
$993$		0			0
$994$	−5.06952	+	7.60775i	−0.160795	+	0.241303i
$995$	1.57005	+	0.906467i	0.0497739	+	0.0287369i
$996$		0			0
$997$		−	35.8484i		−	1.13533i	−0.823260	−	0.567664i	$-0.807847\pi$
$997$		−	35.8484i		−	1.13533i	0.823260	−	0.567664i	$-0.192153\pi$
$998$	36.4240	+	21.0294i	1.15298	+	0.665675i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.t.b.1151.6		28
3.2	odd	2		630.2.t.b.311.10	✓	28
7.5	odd	6		1890.2.bk.b.341.7		28
9.2	odd	6		1890.2.bk.b.521.7		28
9.7	even	3		630.2.bk.b.101.9	yes	28
21.5	even	6		630.2.bk.b.131.2	yes	28
63.47	even	6	inner	1890.2.t.b.1601.6		28
63.61	odd	6		630.2.t.b.551.10	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.10	✓	28	3.2	odd	2
630.2.t.b.551.10	yes	28	63.61	odd	6
630.2.bk.b.101.9	yes	28	9.7	even	3
630.2.bk.b.131.2	yes	28	21.5	even	6
1890.2.t.b.1151.6		28	1.1	even	1	trivial
1890.2.t.b.1601.6		28	63.47	even	6	inner
1890.2.bk.b.341.7		28	7.5	odd	6
1890.2.bk.b.521.7		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)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(2.64030 + 0.169721i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(2.64030 + 0.169721i) q^{7} -1.00000i q^{8} +(-0.866025 - 0.500000i) q^{10} -0.207763i q^{11} +(1.22567 + 0.707642i) q^{13} +(-2.20171 - 1.46713i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.680447 + 1.17857i) q^{17} +(5.73160 - 3.30914i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-0.103881 + 0.179928i) q^{22} -6.39482i q^{23} +1.00000 q^{25} +(-0.707642 - 1.22567i) q^{26} +(1.17317 + 2.37143i) q^{28} +(-6.11758 + 3.53199i) q^{29} +(4.10937 - 2.37255i) q^{31} +(0.866025 - 0.500000i) q^{32} +(1.17857 - 0.680447i) q^{34} +(2.64030 + 0.169721i) q^{35} +(1.32889 + 2.30171i) q^{37} -6.61828 q^{38} -1.00000i q^{40} +(1.41245 - 2.44643i) q^{41} +(1.06723 + 1.84849i) q^{43} +(0.179928 - 0.103881i) q^{44} +(-3.19741 + 5.53808i) q^{46} +(0.0573414 - 0.0993182i) q^{47} +(6.94239 + 0.896231i) q^{49} +(-0.866025 - 0.500000i) q^{50} +1.41528i q^{52} +(8.40507 + 4.85267i) q^{53} -0.207763i q^{55} +(0.169721 - 2.64030i) q^{56} +7.06398 q^{58} +(-4.34473 - 7.52530i) q^{59} +(-1.85102 - 1.06869i) q^{61} -4.74509 q^{62} -1.00000 q^{64} +(1.22567 + 0.707642i) q^{65} +(-0.0235223 - 0.0407418i) q^{67} -1.36089 q^{68} +(-2.20171 - 1.46713i) q^{70} -3.45539i q^{71} +(-11.5793 - 6.68529i) q^{73} -2.65778i q^{74} +(5.73160 + 3.30914i) q^{76} +(0.0352617 - 0.548556i) q^{77} +(-7.97657 + 13.8158i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-2.44643 + 1.41245i) q^{82} +(8.06016 + 13.9606i) q^{83} +(-0.680447 + 1.17857i) q^{85} -2.13446i q^{86} -0.207763 q^{88} +(1.40976 + 2.44178i) q^{89} +(3.11604 + 2.07641i) q^{91} +(5.53808 - 3.19741i) q^{92} +(-0.0993182 + 0.0573414i) q^{94} +(5.73160 - 3.30914i) q^{95} +(1.39248 - 0.803947i) q^{97} +(-5.56417 - 4.24735i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7}+O(q^{10}) \) 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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