LMFDB - Embedded newform 1890.2.t.b.1601.6

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			1601.6
Character	$\chi$	$=$	1890.1601
Dual form			1890.2.t.b.1151.6

$q$-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 $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

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

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	$0.00997154\pi$
$11$			0.207763i			0.0626428i	−0.999509	+	0.0313214i	$0.990028\pi$
$12$		0			0
$13$	1.22567	−	0.707642i	0.339940	−	0.196265i	−0.320305	−	0.947314i	$-0.603786\pi$
$13$	1.22567	−	0.707642i	0.339940	−	0.196265i	0.660246	+	0.751050i	$0.270452\pi$
$14$	−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	0.771634	−	0.636067i	$-0.219440\pi$
$17$	−0.680447	−	1.17857i	−0.165033	−	0.285845i	−0.936667	+	0.350222i	$0.886106\pi$
$18$		0			0
$19$	5.73160	+	3.30914i	1.31492	+	0.759169i	0.982906	−	0.184106i	$-0.0589389\pi$
$19$	5.73160	+	3.30914i	1.31492	+	0.759169i	0.332013	+	0.943275i	$0.392272\pi$
$20$	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	$0.232296\pi$
$23$			6.39482i			1.33341i	−0.745321	+	0.666706i	$0.767704\pi$
$24$		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	−0.190568	−	0.981674i	$-0.561033\pi$
$29$	−6.11758	−	3.53199i	−1.13601	−	0.655874i	−0.945439	+	0.325800i	$0.894366\pi$
$30$		0			0
$31$	4.10937	+	2.37255i	0.738065	+	0.426122i	0.821365	−	0.570403i	$-0.193213\pi$
$31$	4.10937	+	2.37255i	0.738065	+	0.426122i	−0.0833006	+	0.996524i	$0.526546\pi$
$32$	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	−0.735872	−	0.677121i	$-0.763227\pi$
$37$	1.32889	−	2.30171i	0.218468	−	0.378398i	0.954340	+	0.298723i	$0.0965607\pi$
$38$	−6.61828			−1.07363
$39$		0			0
$40$			1.00000i			0.158114i
$41$	1.41245	+	2.44643i	0.220587	+	0.382068i	0.954986	−	0.296650i	$-0.0958693\pi$
$41$	1.41245	+	2.44643i	0.220587	+	0.382068i	−0.734399	+	0.678718i	$0.762536\pi$
$42$		0			0
$43$	1.06723	−	1.84849i	0.162751	−	0.281893i	−0.773103	−	0.634280i	$-0.781297\pi$
$43$	1.06723	−	1.84849i	0.162751	−	0.281893i	0.935854	+	0.352387i	$0.114630\pi$
$44$	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	0.870177	−	0.492739i	$-0.164004\pi$
$47$	0.0573414	+	0.0993182i	0.00836410	+	0.0144870i	−0.861813	+	0.507226i	$0.830671\pi$
$48$		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	0.204539	−	0.978858i	$-0.434430\pi$
$53$	8.40507	−	4.85267i	1.15452	−	0.666565i	0.949986	+	0.312293i	$0.101097\pi$
$54$		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	0.431354	+	0.902183i	$0.358036\pi$
$59$	−4.34473	+	7.52530i	−0.565636	+	0.979711i	−0.996990	+	0.0775280i	$0.975297\pi$
$60$		0			0
$61$	−1.85102	+	1.06869i	−0.236999	+	0.136832i	−0.613797	−	0.789464i	$-0.710359\pi$
$61$	−1.85102	+	1.06869i	−0.236999	+	0.136832i	0.376798	+	0.926296i	$0.377025\pi$
$62$	−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	−0.867459	−	0.497509i	$-0.834248\pi$
$67$	−0.0235223	+	0.0407418i	−0.00287371	+	0.00497740i	0.864585	+	0.502487i	$0.167581\pi$
$68$	−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	$0.0657323\pi$
$71$			3.45539i			0.410079i	−0.978754	+	0.205040i	$0.934268\pi$
$72$		0			0
$73$	−11.5793	+	6.68529i	−1.35525	+	0.782454i	−0.988979	−	0.148054i	$-0.952699\pi$
$73$	−11.5793	+	6.68529i	−1.35525	+	0.782454i	−0.366271	+	0.930508i	$0.619366\pi$
$74$			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	−0.830763	−	0.556627i	$-0.812095\pi$
$79$	−7.97657	−	13.8158i	−0.897434	−	1.55440i	−0.0666713	−	0.997775i	$-0.521238\pi$
$80$	−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	0.0386794	−	0.999252i	$-0.487685\pi$
$83$	8.06016	−	13.9606i	0.884717	−	1.53237i	0.846038	−	0.533123i	$-0.178982\pi$
$84$		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	−0.781584	−	0.623800i	$-0.785588\pi$
$89$	1.40976	−	2.44178i	0.149435	−	0.258828i	0.931019	+	0.364972i	$0.118921\pi$
$90$		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	0.569024	−	0.822321i	$-0.307321\pi$
$97$	1.39248	+	0.803947i	0.141385	+	0.0816284i	−0.427639	+	0.903950i	$0.640655\pi$
$98$	−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	$-0.894310\pi$
$103$		−	6.61641i		−	0.651934i	0.945381	−	0.325967i	$-0.105690\pi$
$104$	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	0.707599	−	0.706614i	$-0.249778\pi$
$107$	4.64917	+	2.68420i	0.449452	+	0.259491i	−0.258147	+	0.966106i	$0.583112\pi$
$108$		0			0
$109$	9.12274	+	15.8011i	0.873800	+	1.51347i	0.858035	+	0.513591i	$0.171685\pi$
$109$	9.12274	+	15.8011i	0.873800	+	1.51347i	0.0157652	+	0.999876i	$0.494982\pi$
$110$	−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	−0.318723	−	0.947848i	$-0.603254\pi$
$113$	3.64375	−	2.10372i	0.342775	−	0.197901i	0.661498	+	0.749947i	$0.269921\pi$
$114$		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	$-0.953716\pi$
$137$		−	3.39189i		−	0.289789i	0.989447	−	0.144894i	$-0.0462842\pi$
$138$		0			0
$139$	5.07662	−	2.93099i	0.430593	−	0.248603i	−0.269006	−	0.963138i	$-0.586695\pi$
$139$	5.07662	−	2.93099i	0.430593	−	0.248603i	0.699599	+	0.714535i	$0.253362\pi$
$140$	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	$0.368627\pi$
$149$			22.3632i			1.83207i	−0.401104	+	0.916033i	$0.631373\pi$
$150$		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	0.285900	−	0.958259i	$-0.407707\pi$
$157$	−5.02485	−	2.90110i	−0.401027	−	0.231533i	−0.686927	+	0.726727i	$0.741041\pi$
$158$	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	−0.263176	−	0.964748i	$-0.584770\pi$
$163$	8.98690	−	15.5658i	0.703908	−	1.21920i	0.967084	−	0.254457i	$-0.0818967\pi$
$164$	2.82489			0.220587
$165$		0			0
$166$			16.1203i			1.25118i
$167$	5.00537	+	8.66956i	0.387327	+	0.670870i	0.992089	−	0.125536i	$-0.0400650\pi$
$167$	5.00537	+	8.66956i	0.387327	+	0.670870i	−0.604762	+	0.796406i	$0.706732\pi$
$168$		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	0.695982	−	0.718059i	$-0.254969\pi$
$173$	−3.60215	−	6.23910i	−0.273866	−	0.474350i	−0.969848	+	0.243709i	$0.921636\pi$
$174$		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	−0.893086	−	0.449886i	$-0.851465\pi$
$179$	−12.7104	+	7.33833i	−0.950016	+	0.548492i	−0.0569303	+	0.998378i	$0.518131\pi$
$180$		0			0
$181$			20.6504i			1.53493i	0.641090	+	0.767465i	$0.278482\pi$
$181$			20.6504i			1.53493i	−0.641090	+	0.767465i	$0.721518\pi$
$182$	−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	0.383990	−	0.923337i	$-0.374550\pi$
$191$	19.0114	−	10.9763i	1.37562	−	0.794214i	0.991629	+	0.129124i	$0.0412164\pi$
$192$		0			0
$193$	−10.3050	+	17.8488i	−0.741772	+	1.28479i	0.209915	+	0.977720i	$0.432681\pi$
$193$	−10.3050	+	17.8488i	−0.741772	+	1.28479i	−0.951688	+	0.307068i	$0.900652\pi$
$194$	−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	$-0.890126\pi$
$197$		−	9.49837i		−	0.676731i	0.941015	−	0.338365i	$-0.109874\pi$
$198$		0			0
$199$	1.57005	−	0.906467i	0.111298	−	0.0642578i	−0.443318	−	0.896365i	$-0.646199\pi$
$199$	1.57005	−	0.906467i	0.111298	−	0.0642578i	0.554616	+	0.832107i	$0.312865\pi$
$200$			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	0.930060	+	0.367407i	$0.119754\pi$
$211$	11.3768	+	19.7053i	0.783214	+	1.35657i	−0.146847	+	0.989159i	$0.546912\pi$
$212$		−	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	0.175393	−	0.984499i	$-0.443881\pi$
$223$	−8.80329	−	5.08258i	−0.589512	−	0.340355i	−0.764904	+	0.644144i	$0.777214\pi$
$224$	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	$-0.962124\pi$
$229$		−	3.59285i		−	0.237423i	0.992929	−	0.118711i	$-0.0378763\pi$
$230$	−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	−0.244268	−	0.969708i	$-0.578548\pi$
$233$	−18.4117	−	10.6300i	−1.20619	−	0.696396i	−0.961926	+	0.273312i	$0.911881\pi$
$234$		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	−0.358373	−	0.933578i	$-0.616669\pi$
$239$	4.18867	−	2.41833i	0.270943	−	0.156429i	0.629316	+	0.777150i	$0.283335\pi$
$240$		0			0
$241$		−	1.60992i		−	0.103704i	−0.998655	−	0.0518522i	$-0.983488\pi$
$241$		−	1.60992i		−	0.103704i	0.998655	−	0.0518522i	$-0.0165125\pi$
$242$	−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	$0.0323732\pi$
$263$			3.29302i			0.203056i	−0.994833	+	0.101528i	$0.967627\pi$
$264$		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	−0.995949	−	0.0899173i	$-0.971340\pi$
$269$	−9.44456	−	16.3585i	−0.575845	−	0.997393i	0.420104	−	0.907476i	$-0.361994\pi$
$270$		0			0
$271$	2.78962	+	1.61059i	0.169457	+	0.0978362i	0.582330	−	0.812953i	$-0.302141\pi$
$271$	2.78962	+	1.61059i	0.169457	+	0.0978362i	−0.412873	+	0.910789i	$0.635475\pi$
$272$	−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	0.798732	−	0.601688i	$-0.205505\pi$
$281$	11.3489	+	6.55231i	0.677021	+	0.390878i	−0.121711	+	0.992566i	$0.538838\pi$
$282$		0			0
$283$	−21.6963	−	12.5264i	−1.28971	−	0.744617i	−0.311111	−	0.950374i	$-0.600701\pi$
$283$	−21.6963	−	12.5264i	−1.28971	−	0.744617i	−0.978603	+	0.205757i	$0.934034\pi$
$284$	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	0.886499	−	0.462730i	$-0.153130\pi$
$293$	0.727716	+	1.26044i	0.0425136	+	0.0736358i	−0.843986	+	0.536366i	$0.819797\pi$
$294$		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	$-0.997254\pi$
$307$		−	0.302317i		−	0.0172541i	0.999963	−	0.00862706i	$-0.00274611\pi$
$308$	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	−0.870487	−	0.492192i	$-0.836196\pi$
$311$	−0.158581	+	0.274670i	−0.00899228	+	0.0155751i	0.861494	+	0.507767i	$0.169529\pi$
$312$		0			0
$313$	−18.3001	+	10.5656i	−1.03438	+	0.597201i	−0.918237	−	0.396031i	$-0.870387\pi$
$313$	−18.3001	+	10.5656i	−1.03438	+	0.597201i	−0.116146	+	0.993232i	$0.537054\pi$
$314$	5.80220			0.327437
$315$		0			0
$316$	−15.9531			−0.897434
$317$	−8.81472	+	5.08918i	−0.495084	+	0.285837i	−0.726681	−	0.686975i	$-0.758938\pi$
$317$	−8.81472	+	5.08918i	−0.495084	+	0.285837i	0.231597	+	0.972812i	$0.425605\pi$
$318$		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	0.991312	+	0.131531i	$0.0419894\pi$
$331$	11.0901	+	19.2086i	0.609566	+	1.05580i	−0.381746	+	0.924267i	$0.624677\pi$
$332$	−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	−0.943325	−	0.331869i	$-0.892321\pi$
$337$	−13.9347	−	24.1356i	−0.759070	−	1.31475i	0.184256	−	0.982878i	$-0.441013\pi$
$338$		−	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	0.278863	−	0.960331i	$-0.410043\pi$
$347$	−7.70036	−	4.44581i	−0.413377	−	0.238663i	−0.692240	+	0.721668i	$0.743376\pi$
$348$		0			0
$349$	−22.9898	−	13.2732i	−1.23062	−	0.710497i	−0.263459	−	0.964671i	$-0.584863\pi$
$349$	−22.9898	−	13.2732i	−1.23062	−	0.710497i	−0.967159	+	0.254173i	$0.918197\pi$
$350$	−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	0.0600612	−	0.998195i	$-0.480870\pi$
$359$	−14.6722	−	8.47101i	−0.774370	−	0.447083i	−0.834431	+	0.551112i	$0.814204\pi$
$360$		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	$-0.814919\pi$
$367$		−	21.0437i		−	1.09847i	0.835667	−	0.549236i	$-0.185081\pi$
$368$	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	$0.0544076\pi$
$389$			6.70962i			0.340191i	−0.985428	+	0.170096i	$0.945592\pi$
$390$		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	0.643623	−	0.765343i	$-0.277431\pi$
$397$	6.02981	+	3.48131i	0.302628	+	0.174722i	−0.340995	+	0.940065i	$0.610764\pi$
$398$	−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	$-0.906665\pi$
$401$		−	11.5760i		−	0.578076i	0.957318	−	0.289038i	$-0.0933354\pi$
$402$		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	−0.997665	−	0.0682960i	$-0.978244\pi$
$409$	−31.4609	−	18.1640i	−1.55564	−	0.898151i	−0.557979	−	0.829855i	$-0.688423\pi$
$410$	−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	−0.929850	−	0.367939i	$-0.880063\pi$
$419$	−16.0393	−	27.7808i	−0.783570	−	1.35718i	0.146280	−	0.989243i	$-0.453270\pi$
$420$		0			0
$421$	−5.92162	+	10.2565i	−0.288602	+	0.499873i	−0.973476	−	0.228788i	$-0.926524\pi$
$421$	−5.92162	+	10.2565i	−0.288602	+	0.499873i	0.684874	+	0.728661i	$0.259857\pi$
$422$	−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	−0.989703	−	0.143139i	$-0.954280\pi$
$431$	−28.2466	+	16.3082i	−1.36059	+	0.785538i	−0.370890	+	0.928677i	$0.620947\pi$
$432$		0			0
$433$			1.82172i			0.0875462i	0.999041	+	0.0437731i	$0.0139379\pi$
$433$			1.82172i			0.0875462i	−0.999041	+	0.0437731i	$0.986062\pi$
$434$	−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	0.0825012	−	0.996591i	$-0.473709\pi$
$439$	20.6763	−	11.9375i	0.986825	−	0.569744i	0.904324	+	0.426847i	$0.140376\pi$
$440$	−0.207763			−0.00990470
$441$		0			0
$442$	1.92605			0.0916129
$443$	20.4555	−	11.8100i	0.971868	−	0.561109i	0.0720631	−	0.997400i	$-0.477042\pi$
$443$	20.4555	−	11.8100i	0.971868	−	0.561109i	0.899805	+	0.436292i	$0.143708\pi$
$444$		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	$-0.707811\pi$
$449$		−	33.6640i		−	1.58870i	0.607459	−	0.794351i	$-0.292189\pi$
$450$		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	0.570824	−	0.821073i	$-0.306624\pi$
$457$	−9.09952	−	15.7608i	−0.425658	−	0.737261i	−0.996482	+	0.0838116i	$0.973291\pi$
$458$	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	−0.643235	−	0.765669i	$-0.722408\pi$
$461$	7.33169	−	12.6989i	0.341471	−	0.591445i	0.984706	+	0.174224i	$0.0557415\pi$
$462$		0			0
$463$	−3.20796	−	5.55635i	−0.149087	−	0.258226i	0.781804	−	0.623525i	$-0.214300\pi$
$463$	−3.20796	−	5.55635i	−0.149087	−	0.258226i	−0.930890	+	0.365299i	$0.880967\pi$
$464$			7.06398i			0.327937i
$465$		0			0
$466$	21.2600			0.984853
$467$	13.0712	−	22.6399i	0.604862	−	1.04765i	−0.387212	−	0.921991i	$-0.626562\pi$
$467$	13.0712	−	22.6399i	0.604862	−	1.04765i	0.992073	−	0.125660i	$-0.0401049\pi$
$468$		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	0.932476	−	0.361232i	$-0.117644\pi$
$487$	3.38529	+	5.86349i	0.153402	+	0.265700i	−0.779074	+	0.626932i	$0.784310\pi$
$488$	−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	−0.311824	−	0.950140i	$-0.600940\pi$
$491$	7.86871	−	4.54300i	0.355110	−	0.205023i	0.666934	+	0.745117i	$0.267607\pi$
$492$		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	0.959806	+	0.280663i	$0.0905545\pi$
$521$	16.5020	+	28.5823i	0.722965	+	1.25221i	−0.236841	+	0.971548i	$0.576112\pi$
$522$		0			0
$523$	−26.4518	−	15.2720i	−1.15666	−	0.667797i	−0.206157	−	0.978519i	$-0.566096\pi$
$523$	−26.4518	−	15.2720i	−1.15666	−	0.667797i	−0.950501	+	0.310722i	$0.899429\pi$
$524$	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	0.368585	+	0.929594i	$0.379842\pi$
$541$	−14.4385	+	25.0082i	−0.620760	+	1.07519i	−0.989345	+	0.145593i	$0.953491\pi$
$542$	−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	−0.393970	−	0.919123i	$-0.628899\pi$
$547$	14.0094	−	24.2650i	0.598999	−	1.03750i	0.992969	−	0.118374i	$-0.0377681\pi$
$548$	−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	−0.671499	−	0.741005i	$-0.734349\pi$
$557$	−8.62658	+	4.98056i	−0.365520	+	0.211033i	0.305980	+	0.952038i	$0.401016\pi$
$558$		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	−0.0998141	−	0.995006i	$-0.531825\pi$
$563$	19.2619	−	33.3626i	0.811794	−	1.40607i	0.911608	−	0.411062i	$-0.134842\pi$
$564$		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	−0.193758	−	0.981049i	$-0.562068\pi$
$569$	13.3337	−	7.69820i	0.558977	−	0.322725i	0.752735	+	0.658324i	$0.228734\pi$
$570$		0			0
$571$	−2.32196	+	4.02175i	−0.0971709	+	0.168305i	−0.910513	−	0.413481i	$-0.864313\pi$
$571$	−2.32196	+	4.02175i	−0.0971709	+	0.168305i	0.813342	+	0.581786i	$0.197646\pi$
$572$	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	−0.797865	−	0.602836i	$-0.794037\pi$
$577$	−16.2075	+	9.35741i	−0.674727	+	0.389554i	0.123138	+	0.992390i	$0.460704\pi$
$578$			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	−0.956382	−	0.292119i	$-0.905640\pi$
$587$	−5.45638	+	9.45073i	−0.225209	+	0.390073i	0.731173	+	0.682192i	$0.238973\pi$
$588$		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	−0.598736	−	0.800946i	$-0.704330\pi$
$593$	9.60114	−	16.6297i	0.394272	−	0.682899i	0.993008	+	0.118048i	$0.0376635\pi$
$594$		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	0.0594613	−	0.998231i	$-0.481062\pi$
$599$	−18.9751	−	10.9553i	−0.775301	−	0.447620i	−0.834762	+	0.550610i	$0.814395\pi$
$600$		0			0
$601$	−38.2477	−	22.0823i	−1.56016	−	0.900756i	−0.997240	−	0.0742412i	$-0.976347\pi$
$601$	−38.2477	−	22.0823i	−1.56016	−	0.900756i	−0.562915	−	0.826515i	$-0.690320\pi$
$602$	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	$-0.824296\pi$
$607$		−	25.8388i		−	1.04876i	0.851483	−	0.524382i	$-0.175704\pi$
$608$	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	0.903650	+	0.428273i	$0.140878\pi$
$613$	20.3696	+	35.2812i	0.822720	+	1.42499i	−0.0809298	+	0.996720i	$0.525789\pi$
$614$	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	−0.827092	−	0.562067i	$-0.810006\pi$
$617$	−18.7258	+	10.8114i	−0.753874	+	0.435249i	0.0732181	+	0.997316i	$0.476673\pi$
$618$		0			0
$619$			41.5576i			1.67034i	0.549992	+	0.835170i	$0.314631\pi$
$619$			41.5576i			1.67034i	−0.549992	+	0.835170i	$0.685369\pi$
$620$	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	$0.246665\pi$
$641$			35.4280i			1.39932i	−0.714476	+	0.699660i	$0.753335\pi$
$642$		0			0
$643$	−25.1223	+	14.5043i	−0.990726	+	0.571996i	−0.905491	−	0.424365i	$-0.860497\pi$
$643$	−25.1223	+	14.5043i	−0.990726	+	0.571996i	−0.0852345	+	0.996361i	$0.527164\pi$
$644$	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	−0.997357	−	0.0726633i	$-0.976850\pi$
$647$	−14.2851	−	24.7426i	−0.561607	−	0.972731i	0.435750	−	0.900068i	$-0.356483\pi$
$648$		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	$0.150823\pi$
$653$			23.3202i			0.912588i	−0.889829	+	0.456294i	$0.849177\pi$
$654$		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	0.985725	+	0.168364i	$0.0538485\pi$
$659$	41.6998	+	24.0754i	1.62440	+	0.937845i	0.638670	+	0.769481i	$0.279485\pi$
$660$		0			0
$661$	−37.5132	−	21.6582i	−1.45909	−	0.842408i	−0.460127	−	0.887853i	$-0.652196\pi$
$661$	−37.5132	−	21.6582i	−1.45909	−	0.842408i	−0.998967	+	0.0454452i	$0.985529\pi$
$662$	−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	−0.995529	−	0.0944550i	$-0.969889\pi$
$673$	−10.7910	+	18.6906i	−0.415964	+	0.720471i	0.579565	+	0.814926i	$0.303222\pi$
$674$	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	−0.967697	−	0.252117i	$-0.918873\pi$
$677$	−18.2704	−	31.6452i	−0.702188	−	1.21623i	0.265509	−	0.964108i	$-0.414460\pi$
$678$		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	−0.994485	−	0.104878i	$-0.966555\pi$
$683$	−36.6115	+	21.1377i	−1.40090	+	0.808811i	−0.406416	+	0.913688i	$0.633222\pi$
$684$		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	−0.915139	−	0.403139i	$-0.867919\pi$
$691$	−26.9067	+	15.5346i	−1.02358	+	0.590964i	−0.108441	+	0.994103i	$0.534586\pi$
$692$	−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	$0.175593\pi$
$701$			27.7518i			1.04817i	−0.851666	+	0.524085i	$0.824407\pi$
$702$		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	0.701106	−	0.713057i	$-0.252690\pi$
$709$	−7.10868	−	12.3126i	−0.266972	−	0.462409i	−0.968078	+	0.250648i	$0.919356\pi$
$710$	−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	0.108916	+	0.994051i	$0.465262\pi$
$719$	−21.6234	+	37.4528i	−0.806415	+	1.39675i	−0.915332	+	0.402701i	$0.868071\pi$
$720$		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	0.456330	−	0.889811i	$-0.349164\pi$
$727$	−2.32159	−	1.34037i	−0.0861032	−	0.0497117i	−0.542433	+	0.840099i	$0.682497\pi$
$728$	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	$0.131266\pi$
$733$			21.7022i			0.801588i	−0.916168	+	0.400794i	$0.868734\pi$
$734$	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	0.851340	−	0.524614i	$-0.175790\pi$
$739$	−0.779082	−	1.34941i	−0.0286590	−	0.0496389i	−0.879999	+	0.474975i	$0.842457\pi$
$740$	−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	−0.394349	−	0.918961i	$-0.629030\pi$
$743$	5.56936	−	3.21547i	0.204320	−	0.117964i	0.598669	+	0.800997i	$0.295697\pi$
$744$		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	−0.141710	−	0.989908i	$-0.545260\pi$
$769$	17.8787	−	10.3223i	0.644721	−	0.372230i	0.786431	+	0.617678i	$0.211927\pi$
$770$	−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	0.999834	−	0.0182107i	$-0.00579695\pi$
$773$	13.4607	+	23.3145i	0.484146	+	0.838566i	−0.515688	+	0.856776i	$0.672464\pi$
$774$		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	0.857494	−	0.514493i	$-0.172020\pi$
$787$	23.5840	+	13.6162i	0.840677	+	0.485365i	−0.0168171	+	0.999859i	$0.505353\pi$
$788$	−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	0.998887	−	0.0471616i	$-0.0150176\pi$
$797$	12.9468	+	22.4246i	0.458601	+	0.794319i	−0.540287	+	0.841481i	$0.681684\pi$
$798$		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	−0.0835110	−	0.996507i	$-0.526613\pi$
$809$	20.9833	−	12.1147i	0.737734	−	0.425931i	0.821245	+	0.570576i	$0.193280\pi$
$810$		0			0
$811$		−	26.9699i		−	0.947040i	−0.880783	−	0.473520i	$-0.842983\pi$
$811$		−	26.9699i		−	0.947040i	0.880783	−	0.473520i	$-0.157017\pi$
$812$	−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	−0.469483	−	0.882941i	$-0.655560\pi$
$821$	1.73135	−	0.999595i	0.0604245	−	0.0348861i	0.529908	+	0.848055i	$0.322226\pi$
$822$		0			0
$823$	3.14423	−	5.44597i	0.109601	−	0.189835i	−0.806008	−	0.591905i	$-0.798376\pi$
$823$	3.14423	−	5.44597i	0.109601	−	0.189835i	0.915609	+	0.402071i	$0.131709\pi$
$824$	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	$0.273178\pi$
$827$			43.5204i			1.51335i	−0.653789	+	0.756677i	$0.726822\pi$
$828$		0			0
$829$	−28.3927	+	16.3926i	−0.986120	+	0.569337i	−0.904112	−	0.427295i	$-0.859467\pi$
$829$	−28.3927	+	16.3926i	−0.986120	+	0.569337i	−0.0820080	+	0.996632i	$0.526133\pi$
$830$			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	−0.775523	−	0.631320i	$-0.782514\pi$
$839$	4.60486	−	7.97586i	0.158978	−	0.275357i	0.934500	+	0.355962i	$0.115847\pi$
$840$		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	−0.213589	−	0.976924i	$-0.568515\pi$
$853$	−34.0668	−	19.6685i	−1.16642	−	0.673435i	−0.952835	+	0.303489i	$0.901849\pi$
$854$	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	$-0.851168\pi$
$859$		−	26.4199i		−	0.901435i	0.892667	−	0.450717i	$-0.148832\pi$
$860$	−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	0.0234518	−	0.999725i	$-0.492534\pi$
$863$	−24.4007	−	14.0878i	−0.830610	−	0.479553i	−0.854061	+	0.520172i	$0.825868\pi$
$864$		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	−0.0776324	−	0.996982i	$-0.524736\pi$
$911$	−29.5749	−	17.0751i	−0.979860	−	0.565723i	−0.902228	+	0.431259i	$0.858069\pi$
$912$		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	−0.969280	−	0.245958i	$-0.920897\pi$
$919$	−8.23460	+	14.2627i	−0.271634	+	0.470484i	0.697646	+	0.716442i	$0.254231\pi$
$920$	−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	0.946010	−	0.324137i	$-0.105074\pi$
$929$	5.86104	+	10.1516i	0.192294	+	0.333064i	−0.753716	+	0.657200i	$0.771740\pi$
$930$		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	$0.0553334\pi$
$937$			10.5888i			0.345922i	−0.984929	+	0.172961i	$0.944667\pi$
$938$	−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	−0.945095	−	0.326795i	$-0.894031\pi$
$941$	−5.81412	+	10.0704i	−0.189535	+	0.328284i	0.755560	+	0.655079i	$0.227365\pi$
$942$		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	−0.470532	−	0.882383i	$-0.655938\pi$
$947$	1.79619	−	1.03703i	0.0583682	−	0.0336989i	0.528900	+	0.848684i	$0.322605\pi$
$948$		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	$0.154565\pi$
$953$			28.8160i			0.933442i	−0.884405	+	0.466721i	$0.845435\pi$
$954$		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	0.681235	−	0.732065i	$-0.261443\pi$
$967$	−9.12278	−	15.8011i	−0.293369	−	0.508130i	−0.974604	+	0.223935i	$0.928110\pi$
$968$			10.9568i			0.352166i
$969$		0			0
$970$	−1.60789			−0.0516263
$971$	1.09564	−	1.89770i	0.0351606	−	0.0609000i	−0.847910	−	0.530141i	$-0.822139\pi$
$971$	1.09564	−	1.89770i	0.0351606	−	0.0609000i	0.883070	+	0.469241i	$0.155472\pi$
$972$		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	0.503461	−	0.864018i	$-0.332060\pi$
$977$	0.216592	+	0.125049i	0.00692939	+	0.00400068i	−0.496531	+	0.868019i	$0.665393\pi$
$978$		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	0.854624	−	0.519247i	$-0.173787\pi$
$991$	−0.704168	−	1.21966i	−0.0223686	−	0.0387436i	−0.876993	+	0.480503i	$0.840454\pi$
$992$	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	$0.192153\pi$
$997$			35.8484i			1.13533i	−0.823260	+	0.567664i	$0.807847\pi$
$998$	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.1601.6		28
3.2	odd	2		630.2.t.b.551.10	yes	28
7.3	odd	6		1890.2.bk.b.521.7		28
9.4	even	3		630.2.bk.b.131.2	yes	28
9.5	odd	6		1890.2.bk.b.341.7		28
21.17	even	6		630.2.bk.b.101.9	yes	28
63.31	odd	6		630.2.t.b.311.10	✓	28
63.59	even	6	inner	1890.2.t.b.1151.6		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.10	✓	28	63.31	odd	6
630.2.t.b.551.10	yes	28	3.2	odd	2
630.2.bk.b.101.9	yes	28	21.17	even	6
630.2.bk.b.131.2	yes	28	9.4	even	3
1890.2.t.b.1151.6		28	63.59	even	6	inner
1890.2.t.b.1601.6		28	1.1	even	1	trivial
1890.2.bk.b.341.7		28	9.5	odd	6
1890.2.bk.b.521.7		28	7.3	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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