LMFDB - Embedded newform 1890.2.t.b.1151.2

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			1151.2
Character	$\chi$	$=$	1890.1151
Dual form			1890.2.t.b.1601.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-2.36047 - 1.19507i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-2.36047 - 1.19507i) q^{7} -1.00000i q^{8} +(-0.866025 - 0.500000i) q^{10} -3.17454i q^{11} +(-1.82400 - 1.05309i) q^{13} +(1.44669 + 2.21519i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.0900212 - 0.155921i) q^{17} +(-5.17571 + 2.98820i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-1.58727 + 2.74924i) q^{22} +0.789076i q^{23} +1.00000 q^{25} +(1.05309 + 1.82400i) q^{26} +(-0.145275 - 2.64176i) q^{28} +(6.84694 - 3.95308i) q^{29} +(-8.40319 + 4.85159i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.155921 + 0.0900212i) q^{34} +(-2.36047 - 1.19507i) q^{35} +(4.27097 + 7.39754i) q^{37} +5.97640 q^{38} -1.00000i q^{40} +(-5.85731 + 10.1452i) q^{41} +(-1.84922 - 3.20294i) q^{43} +(2.74924 - 1.58727i) q^{44} +(0.394538 - 0.683360i) q^{46} +(1.04181 - 1.80446i) q^{47} +(4.14362 + 5.64184i) q^{49} +(-0.866025 - 0.500000i) q^{50} -2.10618i q^{52} +(-0.613086 - 0.353965i) q^{53} -3.17454i q^{55} +(-1.19507 + 2.36047i) q^{56} -7.90616 q^{58} +(5.88665 + 10.1960i) q^{59} +(2.50805 + 1.44802i) q^{61} +9.70317 q^{62} -1.00000 q^{64} +(-1.82400 - 1.05309i) q^{65} +(-4.97848 - 8.62299i) q^{67} +0.180042 q^{68} +(1.44669 + 2.21519i) q^{70} +10.1885i q^{71} +(-5.09156 - 2.93961i) q^{73} -8.54194i q^{74} +(-5.17571 - 2.98820i) q^{76} +(-3.79380 + 7.49341i) q^{77} +(-5.50268 + 9.53091i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(10.1452 - 5.85731i) q^{82} +(-4.41475 - 7.64657i) q^{83} +(0.0900212 - 0.155921i) q^{85} +3.69843i q^{86} -3.17454 q^{88} +(-2.91136 - 5.04262i) q^{89} +(3.04699 + 4.66559i) q^{91} +(-0.683360 + 0.394538i) q^{92} +(-1.80446 + 1.04181i) q^{94} +(-5.17571 + 2.98820i) q^{95} +(-3.79334 + 2.19008i) q^{97} +(-0.767563 - 6.95779i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	−2.36047	−	1.19507i	−0.892173	−	0.451693i
$7$	−2.36047	−	1.19507i	−0.892173	−	0.451693i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−0.866025	−	0.500000i	−0.273861	−	0.158114i
$11$		−	3.17454i		−	0.957161i	−0.878044	−	0.478581i	$-0.841151\pi$
$11$		−	3.17454i		−	0.957161i	0.878044	−	0.478581i	$-0.158849\pi$
$12$		0			0
$13$	−1.82400	−	1.05309i	−0.505887	−	0.292074i	0.225254	−	0.974300i	$-0.427679\pi$
$13$	−1.82400	−	1.05309i	−0.505887	−	0.292074i	−0.731141	+	0.682226i	$0.761012\pi$
$14$	1.44669	+	2.21519i	0.386645	+	0.592035i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.0900212	−	0.155921i	0.0218333	−	0.0378165i	−0.854902	−	0.518789i	$-0.826383\pi$
$17$	0.0900212	−	0.155921i	0.0218333	−	0.0378165i	0.876736	+	0.480973i	$0.159716\pi$
$18$		0			0
$19$	−5.17571	+	2.98820i	−1.18739	+	0.685540i	−0.957713	−	0.287727i	$-0.907101\pi$
$19$	−5.17571	+	2.98820i	−1.18739	+	0.685540i	−0.229678	+	0.973267i	$0.573767\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$		0			0
$22$	−1.58727	+	2.74924i	−0.338408	+	0.586139i
$23$			0.789076i			0.164534i	0.996610	+	0.0822669i	$0.0262160\pi$
$23$			0.789076i			0.164534i	−0.996610	+	0.0822669i	$0.973784\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	1.05309	+	1.82400i	0.206528	+	0.357716i
$27$		0			0
$28$	−0.145275	−	2.64176i	−0.0274544	−	0.499246i
$29$	6.84694	−	3.95308i	1.27144	−	0.734069i	0.296185	−	0.955131i	$-0.404286\pi$
$29$	6.84694	−	3.95308i	1.27144	−	0.734069i	0.975260	+	0.221062i	$0.0709522\pi$
$30$		0			0
$31$	−8.40319	+	4.85159i	−1.50926	+	0.871370i	−0.509316	+	0.860579i	$0.670102\pi$
$31$	−8.40319	+	4.85159i	−1.50926	+	0.871370i	−0.999942	+	0.0107910i	$0.996565\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$	−0.155921	+	0.0900212i	−0.0267403	+	0.0154385i
$35$	−2.36047	−	1.19507i	−0.398992	−	0.202003i
$36$		0			0
$37$	4.27097	+	7.39754i	0.702143	+	1.21615i	0.967713	+	0.252056i	$0.0811068\pi$
$37$	4.27097	+	7.39754i	0.702143	+	1.21615i	−0.265569	+	0.964092i	$0.585560\pi$
$38$	5.97640			0.969500
$39$		0			0
$40$		−	1.00000i		−	0.158114i
$41$	−5.85731	+	10.1452i	−0.914758	+	1.58441i	−0.107502	+	0.994205i	$0.534285\pi$
$41$	−5.85731	+	10.1452i	−0.914758	+	1.58441i	−0.807256	+	0.590202i	$0.799048\pi$
$42$		0			0
$43$	−1.84922	−	3.20294i	−0.282003	−	0.488443i	0.689875	−	0.723929i	$-0.257665\pi$
$43$	−1.84922	−	3.20294i	−0.282003	−	0.488443i	−0.971878	+	0.235485i	$0.924332\pi$
$44$	2.74924	−	1.58727i	0.414463	−	0.239290i
$45$		0			0
$46$	0.394538	−	0.683360i	0.0581715	−	0.100756i
$47$	1.04181	−	1.80446i	0.151963	−	0.263207i	−0.779986	−	0.625797i	$-0.784774\pi$
$47$	1.04181	−	1.80446i	0.151963	−	0.263207i	0.931949	+	0.362589i	$0.118107\pi$
$48$		0			0
$49$	4.14362	+	5.64184i	0.591946	+	0.805977i
$50$	−0.866025	−	0.500000i	−0.122474	−	0.0707107i
$51$		0			0
$52$		−	2.10618i		−	0.292074i
$53$	−0.613086	−	0.353965i	−0.0842138	−	0.0486209i	0.457302	−	0.889312i	$-0.348816\pi$
$53$	−0.613086	−	0.353965i	−0.0842138	−	0.0486209i	−0.541516	+	0.840691i	$0.682149\pi$
$54$		0			0
$55$		−	3.17454i		−	0.428055i
$56$	−1.19507	+	2.36047i	−0.159698	+	0.315431i
$57$		0			0
$58$	−7.90616			−1.03813
$59$	5.88665	+	10.1960i	0.766377	+	1.32740i	0.939515	+	0.342506i	$0.111276\pi$
$59$	5.88665	+	10.1960i	0.766377	+	1.32740i	−0.173138	+	0.984898i	$0.555391\pi$
$60$		0			0
$61$	2.50805	+	1.44802i	0.321122	+	0.185400i	0.651893	−	0.758311i	$-0.273975\pi$
$61$	2.50805	+	1.44802i	0.321122	+	0.185400i	−0.330770	+	0.943711i	$0.607309\pi$
$62$	9.70317			1.23230
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−1.82400	−	1.05309i	−0.226240	−	0.130620i
$66$		0			0
$67$	−4.97848	−	8.62299i	−0.608219	−	1.05347i	−0.991534	−	0.129848i	$-0.958551\pi$
$67$	−4.97848	−	8.62299i	−0.608219	−	1.05347i	0.383315	−	0.923618i	$-0.374782\pi$
$68$	0.180042			0.0218333
$69$		0			0
$70$	1.44669	+	2.21519i	0.172913	+	0.264766i
$71$			10.1885i			1.20915i	0.796549	+	0.604574i	$0.206656\pi$
$71$			10.1885i			1.20915i	−0.796549	+	0.604574i	$0.793344\pi$
$72$		0			0
$73$	−5.09156	−	2.93961i	−0.595921	−	0.344055i	0.171514	−	0.985182i	$-0.445134\pi$
$73$	−5.09156	−	2.93961i	−0.595921	−	0.344055i	−0.767435	+	0.641126i	$0.778467\pi$
$74$		−	8.54194i		−	0.992981i
$75$		0			0
$76$	−5.17571	−	2.98820i	−0.593695	−	0.342770i
$77$	−3.79380	+	7.49341i	−0.432343	+	0.853953i
$78$		0			0
$79$	−5.50268	+	9.53091i	−0.619099	+	1.07231i	0.370551	+	0.928812i	$0.379169\pi$
$79$	−5.50268	+	9.53091i	−0.619099	+	1.07231i	−0.989650	+	0.143499i	$0.954164\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$		0			0
$82$	10.1452	−	5.85731i	1.12034	−	0.646831i
$83$	−4.41475	−	7.64657i	−0.484582	−	0.839320i	0.515261	−	0.857033i	$-0.327695\pi$
$83$	−4.41475	−	7.64657i	−0.484582	−	0.839320i	−0.999843	+	0.0177130i	$0.994361\pi$
$84$		0			0
$85$	0.0900212	−	0.155921i	0.00976417	−	0.0169120i
$86$			3.69843i			0.398812i
$87$		0			0
$88$	−3.17454			−0.338408
$89$	−2.91136	−	5.04262i	−0.308603	−	0.534516i	0.669454	−	0.742854i	$-0.266528\pi$
$89$	−2.91136	−	5.04262i	−0.308603	−	0.534516i	−0.978057	+	0.208337i	$0.933195\pi$
$90$		0			0
$91$	3.04699	+	4.66559i	0.319411	+	0.489087i
$92$	−0.683360	+	0.394538i	−0.0712452	+	0.0411335i
$93$		0			0
$94$	−1.80446	+	1.04181i	−0.186116	+	0.107454i
$95$	−5.17571	+	2.98820i	−0.531017	+	0.306583i
$96$		0			0
$97$	−3.79334	+	2.19008i	−0.385155	+	0.222369i	−0.680059	−	0.733158i	$-0.738046\pi$
$97$	−3.79334	+	2.19008i	−0.385155	+	0.222369i	0.294904	+	0.955527i	$0.404712\pi$
$98$	−0.767563	−	6.95779i	−0.0775355	−	0.702843i
$99$		0			0
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−16.9191			−1.68352			−0.841759	−	0.539854i	$-0.818479\pi$
$101$	−16.9191			−1.68352			−0.841759	+	0.539854i	$0.818479\pi$
$102$		0			0
$103$		−	5.31108i		−	0.523316i	−0.965161	−	0.261658i	$-0.915731\pi$
$103$		−	5.31108i		−	0.523316i	0.965161	−	0.261658i	$-0.0842693\pi$
$104$	−1.05309	+	1.82400i	−0.103264	+	0.178858i
$105$		0			0
$106$	0.353965	+	0.613086i	0.0343801	+	0.0595482i
$107$	−7.07344	+	4.08385i	−0.683816	+	0.394801i	−0.801291	−	0.598275i	$-0.795853\pi$
$107$	−7.07344	+	4.08385i	−0.683816	+	0.394801i	0.117476	+	0.993076i	$0.462520\pi$
$108$		0			0
$109$	−0.606828	+	1.05106i	−0.0581235	+	0.100673i	−0.893623	−	0.448818i	$-0.851845\pi$
$109$	−0.606828	+	1.05106i	−0.0581235	+	0.100673i	0.835500	+	0.549491i	$0.185178\pi$
$110$	−1.58727	+	2.74924i	−0.151340	+	0.262129i
$111$		0			0
$112$	2.21519	−	1.44669i	0.209316	−	0.136700i
$113$	1.23720	+	0.714296i	0.116386	+	0.0671953i	0.557063	−	0.830470i	$-0.311928\pi$
$113$	1.23720	+	0.714296i	0.116386	+	0.0671953i	−0.440677	+	0.897666i	$0.645262\pi$
$114$		0			0
$115$			0.789076i			0.0735818i
$116$	6.84694	+	3.95308i	0.635722	+	0.367034i
$117$		0			0
$118$		−	11.7733i		−	1.08382i
$119$	−0.398829	+	0.260466i	−0.0365606	+	0.0238769i
$120$		0			0
$121$	0.922270			0.0838427
$122$	−1.44802	−	2.50805i	−0.131098	−	0.227068i
$123$		0			0
$124$	−8.40319	−	4.85159i	−0.754629	−	0.435685i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−15.1021			−1.34010			−0.670048	−	0.742318i	$-0.733726\pi$
$127$	−15.1021			−1.34010			−0.670048	+	0.742318i	$0.733726\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	1.05309	+	1.82400i	0.0923620	+	0.159976i
$131$	8.38038			0.732197			0.366099	−	0.930576i	$-0.380693\pi$
$131$	8.38038			0.732197			0.366099	+	0.930576i	$0.380693\pi$
$132$		0			0
$133$	15.7882	−	0.868221i	1.36901	−	0.0752843i
$134$			9.95697i			0.860151i
$135$		0			0
$136$	−0.155921	−	0.0900212i	−0.0133701	−	0.00771925i
$137$			8.76324i			0.748694i	0.927289	+	0.374347i	$0.122133\pi$
$137$			8.76324i			0.748694i	−0.927289	+	0.374347i	$0.877867\pi$
$138$		0			0
$139$	2.76711	+	1.59759i	0.234704	+	0.135506i	0.612740	−	0.790285i	$-0.290067\pi$
$139$	2.76711	+	1.59759i	0.234704	+	0.135506i	−0.378036	+	0.925791i	$0.623401\pi$
$140$	−0.145275	−	2.64176i	−0.0122780	−	0.223269i
$141$		0			0
$142$	5.09423	−	8.82346i	0.427498	−	0.740448i
$143$	−3.34308	+	5.79038i	−0.279562	+	0.484216i
$144$		0			0
$145$	6.84694	−	3.95308i	0.568607	−	0.328286i
$146$	2.93961	+	5.09156i	0.243284	+	0.421380i
$147$		0			0
$148$	−4.27097	+	7.39754i	−0.351072	+	0.608074i
$149$		−	6.20523i		−	0.508353i	−0.967158	−	0.254176i	$-0.918196\pi$
$149$		−	6.20523i		−	0.508353i	0.967158	−	0.254176i	$-0.0818044\pi$
$150$		0			0
$151$	10.6607			0.867559			0.433779	−	0.901019i	$-0.357180\pi$
$151$	10.6607			0.867559			0.433779	+	0.901019i	$0.357180\pi$
$152$	2.98820	+	5.17571i	0.242375	+	0.419806i
$153$		0			0
$154$	7.03223	−	4.59259i	0.566673	−	0.370081i
$155$	−8.40319	+	4.85159i	−0.674961	+	0.389689i
$156$		0			0
$157$	−3.80928	+	2.19929i	−0.304014	+	0.175523i	−0.644245	−	0.764819i	$-0.722828\pi$
$157$	−3.80928	+	2.19929i	−0.304014	+	0.175523i	0.340231	+	0.940342i	$0.389495\pi$
$158$	9.53091	−	5.50268i	0.758239	−	0.437769i
$159$		0			0
$160$	0.866025	−	0.500000i	0.0684653	−	0.0395285i
$161$	0.943000	−	1.86259i	0.0743188	−	0.146793i
$162$		0			0
$163$	9.94559	+	17.2263i	0.778999	+	1.34927i	0.932519	+	0.361120i	$0.117606\pi$
$163$	9.94559	+	17.2263i	0.778999	+	1.34927i	−0.153520	+	0.988146i	$0.549061\pi$
$164$	−11.7146			−0.914758
$165$		0			0
$166$			8.82950i			0.685302i
$167$	−7.13831	+	12.3639i	−0.552379	+	0.956749i	0.445723	+	0.895171i	$0.352947\pi$
$167$	−7.13831	+	12.3639i	−0.552379	+	0.956749i	−0.998102	+	0.0615778i	$0.980387\pi$
$168$		0			0
$169$	−4.28201	−	7.41666i	−0.329385	−	0.570512i
$170$	−0.155921	+	0.0900212i	−0.0119586	+	0.00690431i
$171$		0			0
$172$	1.84922	−	3.20294i	0.141001	−	0.244222i
$173$	6.61430	−	11.4563i	0.502876	−	0.871007i	−0.497119	−	0.867683i	$-0.665609\pi$
$173$	6.61430	−	11.4563i	0.502876	−	0.871007i	0.999994	−	0.00332403i	$-0.00105807\pi$
$174$		0			0
$175$	−2.36047	−	1.19507i	−0.178435	−	0.0903387i
$176$	2.74924	+	1.58727i	0.207231	+	0.119645i
$177$		0			0
$178$			5.82271i			0.436431i
$179$	−3.52462	−	2.03494i	−0.263442	−	0.152098i	0.362462	−	0.931999i	$-0.381936\pi$
$179$	−3.52462	−	2.03494i	−0.263442	−	0.152098i	−0.625904	+	0.779900i	$0.715270\pi$
$180$		0			0
$181$			21.7339i			1.61547i	0.589546	+	0.807735i	$0.299307\pi$
$181$			21.7339i			1.61547i	−0.589546	+	0.807735i	$0.700693\pi$
$182$	−0.305975	−	5.56401i	−0.0226803	−	0.412432i
$183$		0			0
$184$	0.789076			0.0581715
$185$	4.27097	+	7.39754i	0.314008	+	0.543878i
$186$		0			0
$187$	−0.494979	−	0.285776i	−0.0361964	−	0.0208980i
$188$	2.08361			0.151963
$189$		0			0
$190$	5.97640			0.433574
$191$	−6.73693	−	3.88957i	−0.487467	−	0.281439i	0.236056	−	0.971739i	$-0.424145\pi$
$191$	−6.73693	−	3.88957i	−0.487467	−	0.281439i	−0.723523	+	0.690300i	$0.757478\pi$
$192$		0			0
$193$	−4.14681	−	7.18249i	−0.298494	−	0.517007i	0.677298	−	0.735709i	$-0.263151\pi$
$193$	−4.14681	−	7.18249i	−0.298494	−	0.517007i	−0.975792	+	0.218702i	$0.929818\pi$
$194$	4.38017			0.314478
$195$		0			0
$196$	−2.81417	+	6.40940i	−0.201012	+	0.457815i
$197$		−	13.3008i		−	0.947643i	−0.880621	−	0.473822i	$-0.842874\pi$
$197$		−	13.3008i		−	0.947643i	0.880621	−	0.473822i	$-0.157126\pi$
$198$		0			0
$199$	−16.1833	−	9.34343i	−1.14720	−	0.662338i	−0.198999	−	0.980000i	$-0.563769\pi$
$199$	−16.1833	−	9.34343i	−1.14720	−	0.662338i	−0.948204	+	0.317661i	$0.897102\pi$
$200$		−	1.00000i		−	0.0707107i
$201$		0			0
$202$	14.6524	+	8.45957i	1.03094	+	0.595213i
$203$	−20.8862	+	1.14857i	−1.46592	+	0.0806136i
$204$		0			0
$205$	−5.85731	+	10.1452i	−0.409092	+	0.708568i
$206$	−2.65554	+	4.59953i	−0.185020	+	0.320464i
$207$		0			0
$208$	1.82400	−	1.05309i	0.126472	−	0.0730185i
$209$	9.48617	+	16.4305i	0.656172	+	1.13652i
$210$		0			0
$211$	−12.1577	+	21.0578i	−0.836971	+	1.44968i	0.0554450	+	0.998462i	$0.482342\pi$
$211$	−12.1577	+	21.0578i	−0.836971	+	1.44968i	−0.892416	+	0.451214i	$0.850991\pi$
$212$		−	0.707930i		−	0.0486209i
$213$		0			0
$214$	8.16771			0.558333
$215$	−1.84922	−	3.20294i	−0.126116	−	0.218439i
$216$		0			0
$217$	25.6334	−	1.40963i	1.74011	−	0.0956917i
$218$	1.05106	−	0.606828i	0.0711865	−	0.0410996i
$219$		0			0
$220$	2.74924	−	1.58727i	0.185353	−	0.107014i
$221$	−0.328398	+	0.189601i	−0.0220904	+	0.0127539i
$222$		0			0
$223$	−14.5348	+	8.39165i	−0.973320	+	0.561946i	−0.900247	−	0.435380i	$-0.856614\pi$
$223$	−14.5348	+	8.39165i	−0.973320	+	0.561946i	−0.0730731	+	0.997327i	$0.523281\pi$
$224$	−2.64176	+	0.145275i	−0.176510	+	0.00970659i
$225$		0			0
$226$	−0.714296	−	1.23720i	−0.0475143	−	0.0822971i
$227$	−16.7913			−1.11448			−0.557240	−	0.830351i	$-0.688140\pi$
$227$	−16.7913			−1.11448			−0.557240	+	0.830351i	$0.688140\pi$
$228$		0			0
$229$			6.63136i			0.438213i	0.975701	+	0.219106i	$0.0703142\pi$
$229$			6.63136i			0.438213i	−0.975701	+	0.219106i	$0.929686\pi$
$230$	0.394538	−	0.683360i	0.0260151	−	0.0450594i
$231$		0			0
$232$	−3.95308	−	6.84694i	−0.259533	−	0.449524i
$233$	−6.79700	+	3.92425i	−0.445286	+	0.257086i	−0.705837	−	0.708374i	$-0.749429\pi$
$233$	−6.79700	+	3.92425i	−0.445286	+	0.257086i	0.260551	+	0.965460i	$0.416096\pi$
$234$		0			0
$235$	1.04181	−	1.80446i	0.0679599	−	0.117710i
$236$	−5.88665	+	10.1960i	−0.383189	+	0.663702i
$237$		0			0
$238$	0.475629	−	0.0261556i	0.0308304	−	0.00169542i
$239$	14.3341	+	8.27578i	0.927195	+	0.535316i	0.885923	−	0.463832i	$-0.153526\pi$
$239$	14.3341	+	8.27578i	0.927195	+	0.535316i	0.0412714	+	0.999148i	$0.486859\pi$
$240$		0			0
$241$			19.2604i			1.24067i	0.784336	+	0.620336i	$0.213004\pi$
$241$			19.2604i			1.24067i	−0.784336	+	0.620336i	$0.786996\pi$
$242$	−0.798709	−	0.461135i	−0.0513430	−	0.0296429i
$243$		0			0
$244$			2.89604i			0.185400i
$245$	4.14362	+	5.64184i	0.264726	+	0.360444i
$246$		0			0
$247$	12.5874			0.800914
$248$	4.85159	+	8.40319i	0.308076	+	0.533603i
$249$		0			0
$250$	−0.866025	−	0.500000i	−0.0547723	−	0.0316228i
$251$	22.0186			1.38980			0.694901	−	0.719105i	$-0.255448\pi$
$251$	22.0186			1.38980			0.694901	+	0.719105i	$0.255448\pi$
$252$		0			0
$253$	2.50496			0.157485
$254$	13.0788	+	7.55105i	0.820637	+	0.473795i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	20.8442			1.30022			0.650112	−	0.759839i	$-0.274722\pi$
$257$	20.8442			1.30022			0.650112	+	0.759839i	$0.274722\pi$
$258$		0			0
$259$	−1.24093	−	22.5658i	−0.0771076	−	1.40217i
$260$		−	2.10618i		−	0.130620i
$261$		0			0
$262$	−7.25762	−	4.19019i	−0.448377	−	0.258871i
$263$		−	22.5371i		−	1.38969i	−0.719157	−	0.694847i	$-0.755472\pi$
$263$		−	22.5371i		−	1.38969i	0.719157	−	0.694847i	$-0.244528\pi$
$264$		0			0
$265$	−0.613086	−	0.353965i	−0.0376616	−	0.0217439i
$266$	−14.1071	−	7.14221i	−0.864962	−	0.437917i
$267$		0			0
$268$	4.97848	−	8.62299i	0.304109	−	0.526733i
$269$	11.8691	−	20.5578i	0.723670	−	1.25343i	−0.235849	−	0.971790i	$-0.575787\pi$
$269$	11.8691	−	20.5578i	0.723670	−	1.25343i	0.959519	−	0.281643i	$-0.0908794\pi$
$270$		0			0
$271$	−10.2170	+	5.89877i	−0.620636	+	0.358325i	−0.777117	−	0.629356i	$-0.783319\pi$
$271$	−10.2170	+	5.89877i	−0.620636	+	0.358325i	0.156480	+	0.987681i	$0.449985\pi$
$272$	0.0900212	+	0.155921i	0.00545834	+	0.00945412i
$273$		0			0
$274$	4.38162	−	7.58919i	0.264703	−	0.458480i
$275$		−	3.17454i		−	0.191432i
$276$		0			0
$277$	−18.3064			−1.09993			−0.549963	−	0.835189i	$-0.685358\pi$
$277$	−18.3064			−1.09993			−0.549963	+	0.835189i	$0.685358\pi$
$278$	−1.59759	−	2.76711i	−0.0958173	−	0.165960i
$279$		0			0
$280$	−1.19507	+	2.36047i	−0.0714190	+	0.141065i
$281$	−18.8875	+	10.9047i	−1.12674	+	0.650521i	−0.943112	−	0.332475i	$-0.892116\pi$
$281$	−18.8875	+	10.9047i	−1.12674	+	0.650521i	−0.183624	+	0.982997i	$0.558783\pi$
$282$		0			0
$283$	1.31465	−	0.759014i	0.0781479	−	0.0451187i	−0.460417	−	0.887703i	$-0.652300\pi$
$283$	1.31465	−	0.759014i	0.0781479	−	0.0451187i	0.538565	+	0.842584i	$0.318967\pi$
$284$	−8.82346	+	5.09423i	−0.523576	+	0.302287i
$285$		0			0
$286$	5.79038	−	3.34308i	0.342392	−	0.197680i
$287$	25.9501	−	16.9474i	1.53179	−	1.00038i
$288$		0			0
$289$	8.48379	+	14.6944i	0.499047	+	0.864374i
$290$	−7.90616			−0.464266
$291$		0			0
$292$		−	5.87922i		−	0.344055i
$293$	−2.79327	+	4.83808i	−0.163184	+	0.282643i	−0.936009	−	0.351976i	$-0.885510\pi$
$293$	−2.79327	+	4.83808i	−0.163184	+	0.282643i	0.772825	+	0.634620i	$0.218843\pi$
$294$		0			0
$295$	5.88665	+	10.1960i	0.342734	+	0.593633i
$296$	7.39754	−	4.27097i	0.429973	−	0.248245i
$297$		0			0
$298$	−3.10262	+	5.37389i	−0.179730	+	0.311301i
$299$	0.830967	−	1.43928i	0.0480561	−	0.0832356i
$300$		0			0
$301$	0.537290	+	9.77038i	0.0309689	+	0.563155i
$302$	−9.23247	−	5.33037i	−0.531269	−	0.306728i
$303$		0			0
$304$		−	5.97640i		−	0.342770i
$305$	2.50805	+	1.44802i	0.143610	+	0.0829134i
$306$		0			0
$307$		−	22.8941i		−	1.30663i	−0.757085	−	0.653316i	$-0.773377\pi$
$307$		−	22.8941i		−	1.30663i	0.757085	−	0.653316i	$-0.226623\pi$
$308$	−8.38638	+	0.461181i	−0.477859	+	0.0262783i
$309$		0			0
$310$	9.70317			0.551103
$311$	−10.8658	−	18.8202i	−0.616146	−	1.06720i	−0.990182	−	0.139782i	$-0.955360\pi$
$311$	−10.8658	−	18.8202i	−0.616146	−	1.06720i	0.374037	−	0.927414i	$-0.377973\pi$
$312$		0			0
$313$	−2.71267	−	1.56616i	−0.153329	−	0.0885247i	0.421372	−	0.906888i	$-0.361549\pi$
$313$	−2.71267	−	1.56616i	−0.153329	−	0.0885247i	−0.574702	+	0.818363i	$0.694882\pi$
$314$	4.39858			0.248226
$315$		0			0
$316$	−11.0054			−0.619099
$317$	24.8434	+	14.3433i	1.39534	+	0.805602i	0.993900	−	0.110281i	$-0.0351752\pi$
$317$	24.8434	+	14.3433i	1.39534	+	0.805602i	0.401444	+	0.915884i	$0.368509\pi$
$318$		0			0
$319$	−12.5492	−	21.7359i	−0.702622	−	1.21698i
$320$	−1.00000			−0.0559017
$321$		0			0
$322$	−1.74796	+	1.14155i	−0.0974098	+	0.0636161i
$323$			1.07601i			0.0598705i
$324$		0			0
$325$	−1.82400	−	1.05309i	−0.101177	−	0.0584148i
$326$		−	19.8912i		−	1.10167i
$327$		0			0
$328$	10.1452	+	5.85731i	0.560172	+	0.323416i
$329$	−4.61560	+	3.01434i	−0.254466	+	0.166186i
$330$		0			0
$331$	2.85472	−	4.94451i	0.156909	−	0.271775i	−0.776843	−	0.629694i	$-0.783180\pi$
$331$	2.85472	−	4.94451i	0.156909	−	0.271775i	0.933753	+	0.357919i	$0.116514\pi$
$332$	4.41475	−	7.64657i	0.242291	−	0.419660i
$333$		0			0
$334$	12.3639	−	7.13831i	0.676523	−	0.390591i
$335$	−4.97848	−	8.62299i	−0.272004	−	0.471124i
$336$		0			0
$337$	5.41618	−	9.38110i	0.295038	−	0.511021i	−0.679956	−	0.733253i	$-0.738001\pi$
$337$	5.41618	−	9.38110i	0.295038	−	0.511021i	0.974994	+	0.222232i	$0.0713343\pi$
$338$			8.56402i			0.465821i
$339$		0			0
$340$	0.180042			0.00976417
$341$	15.4016	+	26.6763i	0.834042	+	1.44460i
$342$		0			0
$343$	−3.03851	−	18.2693i	−0.164064	−	0.986450i
$344$	−3.20294	+	1.84922i	−0.172691	+	0.0997031i
$345$		0			0
$346$	−11.4563	+	6.61430i	−0.615895	+	0.355587i
$347$	−16.7740	+	9.68446i	−0.900474	+	0.519889i	−0.877354	−	0.479844i	$-0.840693\pi$
$347$	−16.7740	+	9.68446i	−0.900474	+	0.519889i	−0.0231203	+	0.999733i	$0.507360\pi$
$348$		0			0
$349$	17.1942	−	9.92710i	0.920387	−	0.531385i	0.0366282	−	0.999329i	$-0.488338\pi$
$349$	17.1942	−	9.92710i	0.920387	−	0.531385i	0.883758	+	0.467944i	$0.155005\pi$
$350$	1.44669	+	2.21519i	0.0773289	+	0.118407i
$351$		0			0
$352$	−1.58727	−	2.74924i	−0.0846019	−	0.146535i
$353$	−11.4940			−0.611763			−0.305881	−	0.952070i	$-0.598951\pi$
$353$	−11.4940			−0.611763			−0.305881	+	0.952070i	$0.598951\pi$
$354$		0			0
$355$			10.1885i			0.540747i
$356$	2.91136	−	5.04262i	0.154302	−	0.267258i
$357$		0			0
$358$	2.03494	+	3.52462i	0.107550	+	0.186282i
$359$	19.1794	−	11.0732i	1.01225	−	0.584422i	0.100400	−	0.994947i	$-0.467988\pi$
$359$	19.1794	−	11.0732i	1.01225	−	0.584422i	0.911849	+	0.410525i	$0.134654\pi$
$360$		0			0
$361$	8.35868	−	14.4777i	0.439930	−	0.761982i
$362$	10.8670	−	18.8221i	0.571155	−	0.989269i
$363$		0			0
$364$	−2.51702	+	4.97156i	−0.131928	+	0.260581i
$365$	−5.09156	−	2.93961i	−0.266504	−	0.153866i
$366$		0			0
$367$		−	20.1428i		−	1.05144i	−0.850656	−	0.525722i	$-0.823795\pi$
$367$		−	20.1428i		−	1.05144i	0.850656	−	0.525722i	$-0.176205\pi$
$368$	−0.683360	−	0.394538i	−0.0356226	−	0.0205667i
$369$		0			0
$370$		−	8.54194i		−	0.444074i
$371$	1.02416	+	1.56820i	0.0531716	+	0.0814171i
$372$		0			0
$373$	27.2910			1.41308			0.706538	−	0.707675i	$-0.250256\pi$
$373$	27.2910			1.41308			0.706538	+	0.707675i	$0.250256\pi$
$374$	0.285776	+	0.494979i	0.0147771	+	0.0255948i
$375$		0			0
$376$	−1.80446	−	1.04181i	−0.0930579	−	0.0537270i
$377$	−16.6518			−0.857610
$378$		0			0
$379$	−19.6022			−1.00690			−0.503448	−	0.864026i	$-0.667935\pi$
$379$	−19.6022			−1.00690			−0.503448	+	0.864026i	$0.667935\pi$
$380$	−5.17571	−	2.98820i	−0.265509	−	0.153291i
$381$		0			0
$382$	3.88957	+	6.73693i	0.199008	+	0.344691i
$383$	3.97158			0.202938			0.101469	−	0.994839i	$-0.467646\pi$
$383$	3.97158			0.202938			0.101469	+	0.994839i	$0.467646\pi$
$384$		0			0
$385$	−3.79380	+	7.49341i	−0.193350	+	0.381900i
$386$			8.29363i			0.422134i
$387$		0			0
$388$	−3.79334	−	2.19008i	−0.192577	−	0.111185i
$389$		−	18.8926i		−	0.957891i	−0.877845	−	0.478945i	$-0.841019\pi$
$389$		−	18.8926i		−	0.957891i	0.877845	−	0.478945i	$-0.158981\pi$
$390$		0			0
$391$	0.123034	+	0.0710336i	0.00622209	+	0.00359232i
$392$	5.64184	−	4.14362i	0.284956	−	0.209285i
$393$		0			0
$394$	−6.65040	+	11.5188i	−0.335042	+	0.580311i
$395$	−5.50268	+	9.53091i	−0.276870	+	0.479552i
$396$		0			0
$397$	−30.5990	+	17.6664i	−1.53572	+	0.886649i	−0.536640	+	0.843812i	$0.680307\pi$
$397$	−30.5990	+	17.6664i	−1.53572	+	0.886649i	−0.999082	+	0.0428377i	$0.986360\pi$
$398$	9.34343	+	16.1833i	0.468344	+	0.811195i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$		−	0.623333i		−	0.0311278i	−0.999879	−	0.0155639i	$-0.995046\pi$
$401$		−	0.623333i		−	0.0311278i	0.999879	−	0.0155639i	$-0.00495434\pi$
$402$		0			0
$403$	20.4366			1.01802
$404$	−8.45957	−	14.6524i	−0.420879	−	0.728984i
$405$		0			0
$406$	18.6623	+	9.44841i	0.926192	+	0.468916i
$407$	23.4838	−	13.5584i	1.16405	−	0.672064i
$408$		0			0
$409$	1.20408	−	0.695174i	0.0595377	−	0.0343741i	−0.469936	−	0.882701i	$-0.655723\pi$
$409$	1.20408	−	0.695174i	0.0595377	−	0.0343741i	0.529473	+	0.848327i	$0.322390\pi$
$410$	10.1452	−	5.85731i	0.501033	−	0.289272i
$411$		0			0
$412$	4.59953	−	2.65554i	0.226603	−	0.130829i
$413$	−1.71037	−	31.1023i	−0.0841616	−	1.53044i
$414$		0			0
$415$	−4.41475	−	7.64657i	−0.216711	−	0.375355i
$416$	−2.10618			−0.103264
$417$		0			0
$418$		−	18.9723i		−	0.927968i
$419$	13.7784	−	23.8650i	0.673121	−	1.16588i	−0.303893	−	0.952706i	$-0.598287\pi$
$419$	13.7784	−	23.8650i	0.673121	−	1.16588i	0.977014	−	0.213174i	$-0.0683800\pi$
$420$		0			0
$421$	−17.1806	−	29.7576i	−0.837331	−	1.45030i	−0.892119	−	0.451801i	$-0.850782\pi$
$421$	−17.1806	−	29.7576i	−0.837331	−	1.45030i	0.0547882	−	0.998498i	$-0.482552\pi$
$422$	21.0578	−	12.1577i	1.02508	−	0.591828i
$423$		0			0
$424$	−0.353965	+	0.613086i	−0.0171901	+	0.0297741i
$425$	0.0900212	−	0.155921i	0.00436667	−	0.00756329i
$426$		0			0
$427$	−4.18968	−	6.41529i	−0.202753	−	0.310458i
$428$	−7.07344	−	4.08385i	−0.341908	−	0.197401i
$429$		0			0
$430$			3.69843i			0.178354i
$431$	−24.3620	−	14.0654i	−1.17348	−	0.677508i	−0.218981	−	0.975729i	$-0.570273\pi$
$431$	−24.3620	−	14.0654i	−1.17348	−	0.677508i	−0.954497	+	0.298221i	$0.903607\pi$
$432$		0			0
$433$			11.9782i			0.575635i	0.957685	+	0.287817i	$0.0929296\pi$
$433$			11.9782i			0.575635i	−0.957685	+	0.287817i	$0.907070\pi$
$434$	−22.9040	−	11.5960i	−1.09943	−	0.556623i
$435$		0			0
$436$	−1.21366			−0.0581235
$437$	−2.35792	−	4.08403i	−0.112795	−	0.195366i
$438$		0			0
$439$	9.40402	+	5.42941i	0.448829	+	0.259132i	0.707336	−	0.706878i	$-0.249897\pi$
$439$	9.40402	+	5.42941i	0.448829	+	0.259132i	−0.258506	+	0.966010i	$0.583230\pi$
$440$	−3.17454			−0.151340
$441$		0			0
$442$	0.379201			0.0180368
$443$	−1.83321	−	1.05840i	−0.0870983	−	0.0502862i	0.455818	−	0.890073i	$-0.349347\pi$
$443$	−1.83321	−	1.05840i	−0.0870983	−	0.0502862i	−0.542917	+	0.839787i	$0.682680\pi$
$444$		0			0
$445$	−2.91136	−	5.04262i	−0.138011	−	0.239043i
$446$	16.7833			0.794712
$447$		0			0
$448$	2.36047	+	1.19507i	0.111522	+	0.0564617i
$449$		−	12.2537i		−	0.578290i	−0.957285	−	0.289145i	$-0.906629\pi$
$449$		−	12.2537i		−	0.578290i	0.957285	−	0.289145i	$-0.0933710\pi$
$450$		0			0
$451$	32.2062	+	18.5943i	1.51653	+	0.875571i
$452$			1.42859i			0.0671953i
$453$		0			0
$454$	14.5417	+	8.39567i	0.682477	+	0.394028i
$455$	3.04699	+	4.66559i	0.142845	+	0.218726i
$456$		0			0
$457$	16.5567	−	28.6771i	0.774490	−	1.34146i	−0.160590	−	0.987021i	$-0.551340\pi$
$457$	16.5567	−	28.6771i	0.774490	−	1.34146i	0.935080	−	0.354435i	$-0.115327\pi$
$458$	3.31568	−	5.74293i	0.154932	−	0.268349i
$459$		0			0
$460$	−0.683360	+	0.394538i	−0.0318618	+	0.0183954i
$461$	−14.1222	−	24.4604i	−0.657737	−	1.13923i	−0.981200	−	0.192994i	$-0.938180\pi$
$461$	−14.1222	−	24.4604i	−0.657737	−	1.13923i	0.323463	−	0.946241i	$-0.395153\pi$
$462$		0			0
$463$	20.1122	−	34.8353i	0.934692	−	1.61893i	0.159511	−	0.987196i	$-0.449008\pi$
$463$	20.1122	−	34.8353i	0.934692	−	1.61893i	0.775181	−	0.631739i	$-0.217658\pi$
$464$			7.90616i			0.367034i
$465$		0			0
$466$	7.84850			0.363575
$467$	0.824539	+	1.42814i	0.0381551	+	0.0660866i	0.884472	−	0.466593i	$-0.154519\pi$
$467$	0.824539	+	1.42814i	0.0381551	+	0.0660866i	−0.846317	+	0.532679i	$0.821185\pi$
$468$		0			0
$469$	1.44650	+	26.3039i	0.0667930	+	1.21460i
$470$	−1.80446	+	1.04181i	−0.0832335	+	0.0480549i
$471$		0			0
$472$	10.1960	−	5.88665i	0.469308	−	0.270955i
$473$	−10.1679	+	5.87042i	−0.467519	+	0.269922i
$474$		0			0
$475$	−5.17571	+	2.98820i	−0.237478	+	0.137108i
$476$	−0.424984	−	0.215163i	−0.0194791	−	0.00986198i
$477$		0			0
$478$	−8.27578	−	14.3341i	−0.378526	−	0.655626i
$479$	−28.2535			−1.29093			−0.645467	−	0.763788i	$-0.723337\pi$
$479$	−28.2535			−1.29093			−0.645467	+	0.763788i	$0.723337\pi$
$480$		0			0
$481$		−	17.9908i		−	0.820312i
$482$	9.63020	−	16.6800i	0.438644	−	0.759753i
$483$		0			0
$484$	0.461135	+	0.798709i	0.0209607	+	0.0363050i
$485$	−3.79334	+	2.19008i	−0.172246	+	0.0994465i
$486$		0			0
$487$	−3.70797	+	6.42239i	−0.168024	+	0.291026i	−0.937725	−	0.347378i	$-0.887072\pi$
$487$	−3.70797	+	6.42239i	−0.168024	+	0.291026i	0.769701	+	0.638405i	$0.220405\pi$
$488$	1.44802	−	2.50805i	0.0655488	−	0.113534i
$489$		0			0
$490$	−0.767563	−	6.95779i	−0.0346749	−	0.314321i
$491$	−20.6718	−	11.9348i	−0.932904	−	0.538612i	−0.0451748	−	0.998979i	$-0.514384\pi$
$491$	−20.6718	−	11.9348i	−0.932904	−	0.538612i	−0.887729	+	0.460367i	$0.847718\pi$
$492$		0			0
$493$		−	1.42344i		−	0.0641087i
$494$	−10.9010	−	6.29368i	−0.490458	−	0.283166i
$495$		0			0
$496$		−	9.70317i		−	0.435685i
$497$	12.1759	−	24.0495i	0.546164	−	1.07877i
$498$		0			0
$499$	−7.96588			−0.356602			−0.178301	−	0.983976i	$-0.557060\pi$
$499$	−7.96588			−0.356602			−0.178301	+	0.983976i	$0.557060\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$		0			0
$502$	−19.0687	−	11.0093i	−0.851076	−	0.491369i
$503$	39.3978			1.75666			0.878332	−	0.478052i	$-0.158657\pi$
$503$	39.3978			1.75666			0.878332	+	0.478052i	$0.158657\pi$
$504$		0			0
$505$	−16.9191			−0.752892
$506$	−2.16936	−	1.25248i	−0.0964397	−	0.0556795i
$507$		0			0
$508$	−7.55105	−	13.0788i	−0.335024	−	0.580278i
$509$	−2.27010			−0.100620			−0.0503102	−	0.998734i	$-0.516021\pi$
$509$	−2.27010			−0.100620			−0.0503102	+	0.998734i	$0.516021\pi$
$510$		0			0
$511$	8.50542	+	13.0236i	0.376258	+	0.576131i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−18.0516	−	10.4221i	−0.796221	−	0.459698i
$515$		−	5.31108i		−	0.234034i
$516$		0			0
$517$	−5.72834	−	3.30726i	−0.251932	−	0.145453i
$518$	−10.2082	+	20.1630i	−0.448523	+	0.885911i
$519$		0			0
$520$	−1.05309	+	1.82400i	−0.0461810	+	0.0799878i
$521$	−9.24087	+	16.0057i	−0.404850	+	0.701221i	−0.994304	−	0.106581i	$-0.966010\pi$
$521$	−9.24087	+	16.0057i	−0.404850	+	0.701221i	0.589454	+	0.807802i	$0.299343\pi$
$522$		0			0
$523$	−30.9554	+	17.8721i	−1.35359	+	0.781493i	−0.988750	−	0.149578i	$-0.952208\pi$
$523$	−30.9554	+	17.8721i	−1.35359	+	0.781493i	−0.364836	+	0.931072i	$0.618875\pi$
$524$	4.19019	+	7.25762i	0.183049	+	0.317051i
$525$		0			0
$526$	−11.2685	+	19.5177i	−0.491331	+	0.851011i
$527$			1.74698i			0.0760997i
$528$		0			0
$529$	22.3774			0.972929
$530$	0.353965	+	0.613086i	0.0153753	+	0.0266307i
$531$		0			0
$532$	8.64601	+	13.2389i	0.374852	+	0.573978i
$533$	21.3675	−	12.3365i	0.925529	−	0.534354i
$534$		0			0
$535$	−7.07344	+	4.08385i	−0.305812	+	0.176560i
$536$	−8.62299	+	4.97848i	−0.372456	+	0.215038i
$537$		0			0
$538$	−20.5578	+	11.8691i	−0.886311	+	0.511712i
$539$	17.9103	−	13.1541i	0.771450	−	0.566588i
$540$		0			0
$541$	5.94967	+	10.3051i	0.255796	+	0.443052i	0.965111	−	0.261839i	$-0.0843291\pi$
$541$	5.94967	+	10.3051i	0.255796	+	0.443052i	−0.709315	+	0.704891i	$0.750996\pi$
$542$	11.7975			0.506748
$543$		0			0
$544$		−	0.180042i		−	0.00771925i
$545$	−0.606828	+	1.05106i	−0.0259936	+	0.0450223i
$546$		0			0
$547$	7.70794	+	13.3505i	0.329568	+	0.570828i	0.982426	−	0.186652i	$-0.0597637\pi$
$547$	7.70794	+	13.3505i	0.329568	+	0.570828i	−0.652858	+	0.757480i	$0.726430\pi$
$548$	−7.58919	+	4.38162i	−0.324194	+	0.187174i
$549$		0			0
$550$	−1.58727	+	2.74924i	−0.0676815	+	0.117228i
$551$	−23.6252	+	40.9200i	−1.00647	+	1.74325i
$552$		0			0
$553$	24.3790	−	15.9213i	1.03670	−	0.677045i
$554$	15.8538	+	9.15321i	0.673564	+	0.388883i
$555$		0			0
$556$			3.19519i			0.135506i
$557$	−14.4583	−	8.34752i	−0.612619	−	0.353696i	0.161371	−	0.986894i	$-0.448408\pi$
$557$	−14.4583	−	8.34752i	−0.612619	−	0.353696i	−0.773990	+	0.633198i	$0.781742\pi$
$558$		0			0
$559$			7.78956i			0.329463i
$560$	2.21519	−	1.44669i	0.0936090	−	0.0611339i
$561$		0			0
$562$	21.8094			0.919976
$563$	−14.7212	−	25.4979i	−0.620427	−	1.07461i	−0.989406	−	0.145173i	$-0.953626\pi$
$563$	−14.7212	−	25.4979i	−0.620427	−	1.07461i	0.368980	−	0.929437i	$-0.379707\pi$
$564$		0			0
$565$	1.23720	+	0.714296i	0.0520493	+	0.0300507i
$566$	−1.51803			−0.0638075
$567$		0			0
$568$	10.1885			0.427498
$569$	−4.93176	−	2.84736i	−0.206750	−	0.119367i	0.393050	−	0.919517i	$-0.371420\pi$
$569$	−4.93176	−	2.84736i	−0.206750	−	0.119367i	−0.599800	+	0.800150i	$0.704753\pi$
$570$		0			0
$571$	1.78017	+	3.08334i	0.0744976	+	0.129034i	0.900868	−	0.434094i	$-0.142931\pi$
$571$	1.78017	+	3.08334i	0.0744976	+	0.129034i	−0.826370	+	0.563127i	$0.809598\pi$
$572$	−6.68615			−0.279562
$573$		0			0
$574$	−30.9472	+	1.70184i	−1.29171	+	0.0710334i
$575$			0.789076i			0.0329068i
$576$		0			0
$577$	−5.31447	−	3.06831i	−0.221244	−	0.127735i	0.385282	−	0.922799i	$-0.374104\pi$
$577$	−5.31447	−	3.06831i	−0.221244	−	0.127735i	−0.606526	+	0.795064i	$0.707437\pi$
$578$		−	16.9676i		−	0.705758i
$579$		0			0
$580$	6.84694	+	3.95308i	0.284304	+	0.164143i
$581$	1.28270	+	23.3254i	0.0532155	+	0.967701i
$582$		0			0
$583$	−1.12368	+	1.94627i	−0.0465380	+	0.0806062i
$584$	−2.93961	+	5.09156i	−0.121642	+	0.210690i
$585$		0			0
$586$	4.83808	−	2.79327i	0.199859	−	0.115389i
$587$	1.76206	+	3.05198i	0.0727279	+	0.125969i	0.900096	−	0.435692i	$-0.143496\pi$
$587$	1.76206	+	3.05198i	0.0727279	+	0.125969i	−0.827368	+	0.561660i	$0.810163\pi$
$588$		0			0
$589$	28.9950	−	50.2208i	1.19472	−	2.06931i
$590$		−	11.7733i		−	0.484699i
$591$		0			0
$592$	−8.54194			−0.351072
$593$	20.0316	+	34.6957i	0.822598	+	1.42478i	0.903741	+	0.428079i	$0.140810\pi$
$593$	20.0316	+	34.6957i	0.822598	+	1.42478i	−0.0811430	+	0.996702i	$0.525857\pi$
$594$		0			0
$595$	−0.398829	+	0.260466i	−0.0163504	+	0.0106781i
$596$	5.37389	−	3.10262i	0.220123	−	0.127088i
$597$		0			0
$598$	−1.43928	+	0.830967i	−0.0588564	+	0.0339808i
$599$	−1.57658	+	0.910237i	−0.0644172	+	0.0371913i	−0.531863	−	0.846831i	$-0.678508\pi$
$599$	−1.57658	+	0.910237i	−0.0644172	+	0.0371913i	0.467446	+	0.884022i	$0.345174\pi$
$600$		0			0
$601$	−15.9038	+	9.18204i	−0.648728	+	0.374543i	−0.787969	−	0.615715i	$-0.788867\pi$
$601$	−15.9038	+	9.18204i	−0.648728	+	0.374543i	0.139241	+	0.990259i	$0.455534\pi$
$602$	4.41988	−	8.73004i	0.180141	−	0.355810i
$603$		0			0
$604$	5.33037	+	9.23247i	0.216890	+	0.375664i
$605$	0.922270			0.0374956
$606$		0			0
$607$		−	28.9070i		−	1.17330i	−0.809842	−	0.586649i	$-0.800447\pi$
$607$		−	28.9070i		−	1.17330i	0.809842	−	0.586649i	$-0.199553\pi$
$608$	−2.98820	+	5.17571i	−0.121188	+	0.209903i
$609$		0			0
$610$	−1.44802	−	2.50805i	−0.0586287	−	0.101548i
$611$	−3.80051	+	2.19423i	−0.153752	+	0.0887689i
$612$		0			0
$613$	20.0655	−	34.7545i	0.810439	−	1.40372i	−0.102119	−	0.994772i	$-0.532562\pi$
$613$	20.0655	−	34.7545i	0.810439	−	1.40372i	0.912557	−	0.408949i	$-0.134104\pi$
$614$	−11.4470	+	19.8268i	−0.461964	+	0.800146i
$615$		0			0
$616$	7.49341	+	3.79380i	0.301918	+	0.152856i
$617$	4.18249	+	2.41476i	0.168381	+	0.0972146i	0.581822	−	0.813316i	$-0.302340\pi$
$617$	4.18249	+	2.41476i	0.168381	+	0.0972146i	−0.413441	+	0.910531i	$0.635673\pi$
$618$		0			0
$619$		−	17.9309i		−	0.720705i	−0.932816	−	0.360352i	$-0.882656\pi$
$619$		−	17.9309i		−	0.720705i	0.932816	−	0.360352i	$-0.117344\pi$
$620$	−8.40319	−	4.85159i	−0.337480	−	0.194844i
$621$		0			0
$622$			21.7317i			0.871362i
$623$	0.845893	+	15.3822i	0.0338900	+	0.616275i
$624$		0			0
$625$	1.00000			0.0400000
$626$	1.56616	+	2.71267i	0.0625964	+	0.108420i
$627$		0			0
$628$	−3.80928	−	2.19929i	−0.152007	−	0.0877613i
$629$	1.53791			0.0613206
$630$		0			0
$631$	15.6119			0.621502			0.310751	−	0.950491i	$-0.399420\pi$
$631$	15.6119			0.621502			0.310751	+	0.950491i	$0.399420\pi$
$632$	9.53091	+	5.50268i	0.379119	+	0.218885i
$633$		0			0
$634$	−14.3433	−	24.8434i	−0.569647	−	0.986657i
$635$	−15.1021			−0.599309
$636$		0			0
$637$	−1.61662	−	14.6543i	−0.0640529	−	0.580626i
$638$			25.0985i			0.993658i
$639$		0			0
$640$	0.866025	+	0.500000i	0.0342327	+	0.0197642i
$641$			15.3319i			0.605572i	0.953059	+	0.302786i	$0.0979168\pi$
$641$			15.3319i			0.605572i	−0.953059	+	0.302786i	$0.902083\pi$
$642$		0			0
$643$	26.2575	+	15.1598i	1.03550	+	0.597844i	0.918554	−	0.395295i	$-0.129358\pi$
$643$	26.2575	+	15.1598i	1.03550	+	0.597844i	0.116941	+	0.993139i	$0.462691\pi$
$644$	2.08455	−	0.114633i	0.0821428	−	0.00451717i
$645$		0			0
$646$	0.538003	−	0.931848i	0.0211674	−	0.0366631i
$647$	−14.5503	+	25.2018i	−0.572030	+	0.990785i	0.424327	+	0.905509i	$0.360511\pi$
$647$	−14.5503	+	25.2018i	−0.572030	+	0.990785i	−0.996357	+	0.0852761i	$0.972823\pi$
$648$		0			0
$649$	32.3676	−	18.6874i	1.27054	−	0.733546i
$650$	1.05309	+	1.82400i	0.0413055	+	0.0715433i
$651$		0			0
$652$	−9.94559	+	17.2263i	−0.389500	+	0.674633i
$653$		−	3.29591i		−	0.128979i	−0.997918	−	0.0644895i	$-0.979458\pi$
$653$		−	3.29591i		−	0.128979i	0.997918	−	0.0644895i	$-0.0205419\pi$
$654$		0			0
$655$	8.38038			0.327449
$656$	−5.85731	−	10.1452i	−0.228689	−	0.396102i
$657$		0			0
$658$	5.50440	−	0.302696i	0.214584	−	0.0118003i
$659$	−5.58702	+	3.22567i	−0.217639	+	0.125654i	−0.604857	−	0.796334i	$-0.706770\pi$
$659$	−5.58702	+	3.22567i	−0.217639	+	0.125654i	0.387217	+	0.921988i	$0.373436\pi$
$660$		0			0
$661$	−32.5957	+	18.8191i	−1.26783	+	0.731979i	−0.974576	−	0.224057i	$-0.928070\pi$
$661$	−32.5957	+	18.8191i	−1.26783	+	0.731979i	−0.293249	+	0.956036i	$0.594737\pi$
$662$	−4.94451	+	2.85472i	−0.192174	+	0.110952i
$663$		0			0
$664$	−7.64657	+	4.41475i	−0.296744	+	0.171325i
$665$	15.7882	−	0.868221i	0.612241	−	0.0336682i
$666$		0			0
$667$	3.11928	+	5.40276i	0.120779	+	0.209196i
$668$	−14.2766			−0.552379
$669$		0			0
$670$			9.95697i			0.384671i
$671$	4.59681	−	7.96190i	0.177458	−	0.307366i
$672$		0			0
$673$	24.8051	+	42.9637i	0.956166	+	1.65613i	0.731676	+	0.681652i	$0.238738\pi$
$673$	24.8051	+	42.9637i	0.956166	+	1.65613i	0.224490	+	0.974476i	$0.427928\pi$
$674$	−9.38110	+	5.41618i	−0.361347	+	0.208624i
$675$		0			0
$676$	4.28201	−	7.41666i	0.164693	−	0.285256i
$677$	−3.63663	+	6.29882i	−0.139767	+	0.242083i	−0.927408	−	0.374050i	$-0.877969\pi$
$677$	−3.63663	+	6.29882i	−0.139767	+	0.242083i	0.787641	+	0.616134i	$0.211302\pi$
$678$		0			0
$679$	11.5713	−	0.636328i	0.444068	−	0.0244200i
$680$	−0.155921	−	0.0900212i	−0.00597931	−	0.00345215i
$681$		0			0
$682$		−	30.8031i		−	1.17951i
$683$	14.4216	+	8.32633i	0.551828	+	0.318598i	0.749859	−	0.661598i	$-0.230121\pi$
$683$	14.4216	+	8.32633i	0.551828	+	0.318598i	−0.198031	+	0.980196i	$0.563455\pi$
$684$		0			0
$685$			8.76324i			0.334826i
$686$	−6.50323	+	17.3409i	−0.248294	+	0.662080i
$687$		0			0
$688$	3.69843			0.141001
$689$	0.745513	+	1.29127i	0.0284018	+	0.0491934i
$690$		0			0
$691$	33.8682	+	19.5538i	1.28841	+	0.743863i	0.978370	−	0.206862i	$-0.0663250\pi$
$691$	33.8682	+	19.5538i	1.28841	+	0.743863i	0.310038	+	0.950724i	$0.399658\pi$
$692$	13.2286			0.502876
$693$		0			0
$694$	19.3689			0.735234
$695$	2.76711	+	1.59759i	0.104963	+	0.0606002i
$696$		0			0
$697$	1.05456	+	1.82656i	0.0399444	+	0.0691858i
$698$	−19.8542			−0.751492
$699$		0			0
$700$	−0.145275	−	2.64176i	−0.00549087	−	0.0998491i
$701$			38.2997i			1.44656i	0.690555	+	0.723280i	$0.257366\pi$
$701$			38.2997i			1.44656i	−0.690555	+	0.723280i	$0.742634\pi$
$702$		0			0
$703$	−44.2107	−	25.5250i	−1.66744	−	0.962695i
$704$			3.17454i			0.119645i
$705$		0			0
$706$	9.95408	+	5.74699i	0.374627	+	0.216291i
$707$	39.9371	+	20.2195i	1.50199	+	0.760434i
$708$		0			0
$709$	4.58548	−	7.94229i	0.172211	−	0.298279i	−0.766981	−	0.641670i	$-0.778242\pi$
$709$	4.58548	−	7.94229i	0.172211	−	0.298279i	0.939193	+	0.343390i	$0.111575\pi$
$710$	5.09423	−	8.82346i	0.191183	−	0.331139i
$711$		0			0
$712$	−5.04262	+	2.91136i	−0.188980	+	0.109108i
$713$	−3.82827	−	6.63076i	−0.143370	−	0.248324i
$714$		0			0
$715$	−3.34308	+	5.79038i	−0.125024	+	0.216548i
$716$		−	4.06988i		−	0.152098i
$717$		0			0
$718$	−22.1465			−0.826498
$719$	−16.5618	−	28.6858i	−0.617650	−	1.06980i	−0.989913	−	0.141674i	$-0.954752\pi$
$719$	−16.5618	−	28.6858i	−0.617650	−	1.06980i	0.372263	−	0.928127i	$-0.378582\pi$
$720$		0			0
$721$	−6.34710	+	12.5366i	−0.236378	+	0.466889i
$722$	−14.4777	+	8.35868i	−0.538802	+	0.311078i
$723$		0			0
$724$	−18.8221	+	10.8670i	−0.699519	+	0.403867i
$725$	6.84694	−	3.95308i	0.254289	−	0.146814i
$726$		0			0
$727$	−21.5870	+	12.4633i	−0.800617	+	0.462236i	−0.843687	−	0.536836i	$-0.819620\pi$
$727$	−21.5870	+	12.4633i	−0.800617	+	0.462236i	0.0430699	+	0.999072i	$0.486286\pi$
$728$	4.66559	−	3.04699i	0.172918	−	0.112929i
$729$		0			0
$730$	2.93961	+	5.09156i	0.108800	+	0.188447i
$731$	−0.665875			−0.0246283
$732$		0			0
$733$			14.7249i			0.543878i	0.962314	+	0.271939i	$0.0876649\pi$
$733$			14.7249i			0.543878i	−0.962314	+	0.271939i	$0.912335\pi$
$734$	−10.0714	+	17.4441i	−0.371742	+	0.643875i
$735$		0			0
$736$	0.394538	+	0.683360i	0.0145429	+	0.0251890i
$737$	−27.3740	+	15.8044i	−1.00834	+	0.582163i
$738$		0			0
$739$	13.3365	−	23.0995i	0.490590	−	0.849727i	−0.509351	−	0.860559i	$-0.670115\pi$
$739$	13.3365	−	23.0995i	0.490590	−	0.849727i	0.999941	+	0.0108315i	$0.00344786\pi$
$740$	−4.27097	+	7.39754i	−0.157004	+	0.271939i
$741$		0			0
$742$	−0.102845	−	1.87018i	−0.00377554	−	0.0686566i
$743$	−4.24232	−	2.44930i	−0.155636	−	0.0898562i	0.420160	−	0.907450i	$-0.361974\pi$
$743$	−4.24232	−	2.44930i	−0.155636	−	0.0898562i	−0.575795	+	0.817594i	$0.695307\pi$
$744$		0			0
$745$		−	6.20523i		−	0.227342i
$746$	−23.6347	−	13.6455i	−0.865329	−	0.499598i
$747$		0			0
$748$		−	0.571552i		−	0.0208980i
$749$	21.5771	−	1.18656i	0.788411	−	0.0433561i
$750$		0			0
$751$	−15.9206			−0.580949			−0.290475	−	0.956883i	$-0.593813\pi$
$751$	−15.9206			−0.580949			−0.290475	+	0.956883i	$0.593813\pi$
$752$	1.04181	+	1.80446i	0.0379907	+	0.0658019i
$753$		0			0
$754$	14.4209	+	8.32589i	0.525177	+	0.303211i
$755$	10.6607			0.387984
$756$		0			0
$757$	−27.4236			−0.996729			−0.498365	−	0.866968i	$-0.666066\pi$
$757$	−27.4236			−0.996729			−0.498365	+	0.866968i	$0.666066\pi$
$758$	16.9760	+	9.80108i	0.616595	+	0.355991i
$759$		0			0
$760$	2.98820	+	5.17571i	0.108393	+	0.187743i
$761$	1.54724			0.0560874			0.0280437	−	0.999607i	$-0.491072\pi$
$761$	1.54724			0.0560874			0.0280437	+	0.999607i	$0.491072\pi$
$762$		0			0
$763$	2.68848	−	1.75578i	0.0973296	−	0.0635637i
$764$		−	7.77914i		−	0.281439i
$765$		0			0
$766$	−3.43949	−	1.98579i	−0.124274	−	0.0717495i
$767$		−	24.7967i		−	0.895356i
$768$		0			0
$769$	2.38768	+	1.37853i	0.0861019	+	0.0497110i	0.542433	−	0.840099i	$-0.317503\pi$
$769$	2.38768	+	1.37853i	0.0861019	+	0.0497110i	−0.456331	+	0.889810i	$0.650837\pi$
$770$	7.03223	−	4.59259i	0.253424	−	0.165505i
$771$		0			0
$772$	4.14681	−	7.18249i	0.149247	−	0.258503i
$773$	−0.745114	+	1.29057i	−0.0267999	+	0.0464187i	−0.879114	−	0.476611i	$-0.841865\pi$
$773$	−0.745114	+	1.29057i	−0.0267999	+	0.0464187i	0.852314	+	0.523030i	$0.175198\pi$
$774$		0			0
$775$	−8.40319	+	4.85159i	−0.301852	+	0.174274i
$776$	2.19008	+	3.79334i	0.0786194	+	0.136173i
$777$		0			0
$778$	−9.44628	+	16.3614i	−0.338666	+	0.586586i
$779$		−	70.0112i		−	2.50841i
$780$		0			0
$781$	32.3437			1.15735
$782$	−0.0710336	−	0.123034i	−0.00254016	−	0.00439968i
$783$		0			0
$784$	−6.95779	+	0.767563i	−0.248493	+	0.0274130i
$785$	−3.80928	+	2.19929i	−0.135959	+	0.0784961i
$786$		0			0
$787$	−19.4311	+	11.2185i	−0.692643	+	0.399898i	−0.804602	−	0.593815i	$-0.797621\pi$
$787$	−19.4311	+	11.2185i	−0.692643	+	0.399898i	0.111958	+	0.993713i	$0.464288\pi$
$788$	11.5188	−	6.65040i	0.410341	−	0.236911i
$789$		0			0
$790$	9.53091	−	5.50268i	0.339095	−	0.195776i
$791$	−2.06673	−	3.16461i	−0.0734845	−	0.112520i
$792$		0			0
$793$	−3.04979	−	5.28239i	−0.108301	−	0.187583i
$794$	35.3327			1.25391
$795$		0			0
$796$		−	18.6869i		−	0.662338i
$797$	16.4080	−	28.4195i	0.581202	−	1.00667i	−0.414135	−	0.910216i	$-0.635916\pi$
$797$	16.4080	−	28.4195i	0.581202	−	1.00667i	0.995337	−	0.0964565i	$-0.0307509\pi$
$798$		0			0
$799$	−0.187569	−	0.324879i	−0.00663572	−	0.0114934i
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$		0			0
$802$	−0.311666	+	0.539822i	−0.0110053	+	0.0190618i
$803$	−9.33192	+	16.1634i	−0.329316	+	0.570393i
$804$		0			0
$805$	0.943000	−	1.86259i	0.0332364	−	0.0656477i
$806$	−17.6986	−	10.2183i	−0.623407	−	0.359924i
$807$		0			0
$808$			16.9191i			0.595213i
$809$	9.17296	+	5.29601i	0.322504	+	0.186198i	0.652508	−	0.757782i	$-0.273717\pi$
$809$	9.17296	+	5.29601i	0.322504	+	0.186198i	−0.330004	+	0.943980i	$0.607050\pi$
$810$		0			0
$811$		−	23.0365i		−	0.808921i	−0.914555	−	0.404461i	$-0.867459\pi$
$811$		−	23.0365i		−	0.808921i	0.914555	−	0.404461i	$-0.132541\pi$
$812$	−11.4378	−	17.5137i	−0.401387	−	0.614610i
$813$		0			0
$814$	−27.1168			−0.950442
$815$	9.94559	+	17.2263i	0.348379	+	0.603410i
$816$		0			0
$817$	19.1420	+	11.0517i	0.669695	+	0.386649i
$818$	−1.39035			−0.0486124
$819$		0			0
$820$	−11.7146			−0.409092
$821$	2.33352	+	1.34726i	0.0814404	+	0.0470196i	0.540167	−	0.841558i	$-0.318361\pi$
$821$	2.33352	+	1.34726i	0.0814404	+	0.0470196i	−0.458727	+	0.888577i	$0.651694\pi$
$822$		0			0
$823$	1.04054	+	1.80226i	0.0362708	+	0.0628229i	0.883591	−	0.468260i	$-0.155119\pi$
$823$	1.04054	+	1.80226i	0.0362708	+	0.0628229i	−0.847320	+	0.531082i	$0.821785\pi$
$824$	−5.31108			−0.185020
$825$		0			0
$826$	−14.0699	+	27.7905i	−0.489555	+	0.966956i
$827$		−	37.0830i		−	1.28950i	−0.764393	−	0.644751i	$-0.776961\pi$
$827$		−	37.0830i		−	1.28950i	0.764393	−	0.644751i	$-0.223039\pi$
$828$		0			0
$829$	−13.9461	−	8.05176i	−0.484367	−	0.279649i	0.237868	−	0.971298i	$-0.423551\pi$
$829$	−13.9461	−	8.05176i	−0.484367	−	0.279649i	−0.722234	+	0.691648i	$0.756885\pi$
$830$			8.82950i			0.306476i
$831$		0			0
$832$	1.82400	+	1.05309i	0.0632359	+	0.0365093i
$833$	1.25270	−	0.138194i	0.0434034	−	0.00478813i
$834$		0			0
$835$	−7.13831	+	12.3639i	−0.247031	+	0.427871i
$836$	−9.48617	+	16.4305i	−0.328086	+	0.568262i
$837$		0			0
$838$	−23.8650	+	13.7784i	−0.824402	+	0.475968i
$839$	9.48006	+	16.4199i	0.327288	+	0.566879i	0.981973	−	0.189023i	$-0.0605319\pi$
$839$	9.48006	+	16.4199i	0.327288	+	0.566879i	−0.654685	+	0.755902i	$0.727199\pi$
$840$		0			0
$841$	16.7537	−	29.0183i	0.577714	−	1.00063i
$842$			34.3612i			1.18416i
$843$		0			0
$844$	−24.3154			−0.836971
$845$	−4.28201	−	7.41666i	−0.147306	−	0.255141i
$846$		0			0
$847$	−2.17699	−	1.10218i	−0.0748022	−	0.0378712i
$848$	0.613086	−	0.353965i	0.0210535	−	0.0121552i
$849$		0			0
$850$	−0.155921	+	0.0900212i	−0.00534806	+	0.00308770i
$851$	−5.83722	+	3.37012i	−0.200097	+	0.115526i
$852$		0			0
$853$	−19.4322	+	11.2192i	−0.665347	+	0.384138i	−0.794311	−	0.607511i	$-0.792168\pi$
$853$	−19.4322	+	11.2192i	−0.665347	+	0.384138i	0.128964	+	0.991649i	$0.458835\pi$
$854$	0.420722	+	7.65065i	0.0143968	+	0.261800i
$855$		0			0
$856$	4.08385	+	7.07344i	0.139583	+	0.241765i
$857$	35.1457			1.20055			0.600277	−	0.799792i	$-0.295057\pi$
$857$	35.1457			1.20055			0.600277	+	0.799792i	$0.295057\pi$
$858$		0			0
$859$			32.5488i			1.11055i	0.831667	+	0.555275i	$0.187387\pi$
$859$			32.5488i			1.11055i	−0.831667	+	0.555275i	$0.812613\pi$
$860$	1.84922	−	3.20294i	0.0630578	−	0.109219i
$861$		0			0
$862$	14.0654	+	24.3620i	0.479070	+	0.829774i
$863$	−10.9055	+	6.29628i	−0.371227	+	0.214328i	−0.673994	−	0.738737i	$-0.735423\pi$
$863$	−10.9055	+	6.29628i	−0.371227	+	0.214328i	0.302768	+	0.953064i	$0.402089\pi$
$864$		0			0
$865$	6.61430	−	11.4563i	0.224893	−	0.389526i
$866$	5.98909	−	10.3734i	0.203518	−	0.352503i
$867$		0			0
$868$	14.0375	+	21.4944i	0.476464	+	0.729568i
$869$	30.2563	+	17.4685i	1.02637	+	0.592578i
$870$		0			0
$871$			20.9711i			0.710580i
$872$	1.05106	+	0.606828i	0.0355933	+	0.0205498i
$873$		0			0
$874$			4.71584i			0.159516i
$875$	−2.36047	−	1.19507i	−0.0797984	−	0.0404007i
$876$		0			0
$877$	−27.2268			−0.919383			−0.459691	−	0.888079i	$-0.652040\pi$
$877$	−27.2268			−0.919383			−0.459691	+	0.888079i	$0.652040\pi$
$878$	−5.42941	−	9.40402i	−0.183234	−	0.317370i
$879$		0			0
$880$	2.74924	+	1.58727i	0.0926767	+	0.0535069i
$881$	8.99478			0.303042			0.151521	−	0.988454i	$-0.451583\pi$
$881$	8.99478			0.303042			0.151521	+	0.988454i	$0.451583\pi$
$882$		0			0
$883$	−15.9491			−0.536730			−0.268365	−	0.963317i	$-0.586483\pi$
$883$	−15.9491			−0.536730			−0.268365	+	0.963317i	$0.586483\pi$
$884$	−0.328398	−	0.189601i	−0.0110452	−	0.00637696i
$885$		0			0
$886$	1.05840	+	1.83321i	0.0355577	+	0.0615878i
$887$	28.7064			0.963867			0.481934	−	0.876208i	$-0.339935\pi$
$887$	28.7064			0.963867			0.481934	+	0.876208i	$0.339935\pi$
$888$		0			0
$889$	35.6480	+	18.0480i	1.19560	+	0.605312i
$890$			5.82271i			0.195178i
$891$		0			0
$892$	−14.5348	−	8.39165i	−0.486660	−	0.280973i
$893$			12.4525i			0.416707i
$894$		0			0
$895$	−3.52462	−	2.03494i	−0.117815	−	0.0680205i
$896$	−1.44669	−	2.21519i	−0.0483306	−	0.0740044i
$897$		0			0
$898$	−6.12687	+	10.6121i	−0.204456	+	0.354129i
$899$	−38.3574	+	66.4370i	−1.27929	+	2.21580i
$900$		0			0
$901$	−0.110381	+	0.0637287i	−0.00367734	+	0.00212311i
$902$	−18.5943	−	32.2062i	−0.619122	−	1.07235i
$903$		0			0
$904$	0.714296	−	1.23720i	0.0237571	−	0.0411485i
$905$			21.7339i			0.722460i
$906$		0			0
$907$	−20.9291			−0.694938			−0.347469	−	0.937692i	$-0.612959\pi$
$907$	−20.9291			−0.694938			−0.347469	+	0.937692i	$0.612959\pi$
$908$	−8.39567	−	14.5417i	−0.278620	−	0.482584i
$909$		0			0
$910$	−0.305975	−	5.56401i	−0.0101430	−	0.184445i
$911$	48.9296	−	28.2495i	1.62111	−	0.935949i	0.634488	−	0.772933i	$-0.281211\pi$
$911$	48.9296	−	28.2495i	1.62111	−	0.935949i	0.986623	−	0.163017i	$-0.0521224\pi$
$912$		0			0
$913$	−24.2744	+	14.0148i	−0.803364	+	0.463823i
$914$	−28.6771	+	16.5567i	−0.948553	+	0.547647i
$915$		0			0
$916$	−5.74293	+	3.31568i	−0.189752	+	0.109553i
$917$	−19.7816	−	10.0151i	−0.653247	−	0.330729i
$918$		0			0
$919$	−7.93346	−	13.7412i	−0.261701	−	0.453279i	0.704993	−	0.709214i	$-0.250950\pi$
$919$	−7.93346	−	13.7412i	−0.261701	−	0.453279i	−0.966694	+	0.255935i	$0.917617\pi$
$920$	0.789076			0.0260151
$921$		0			0
$922$			28.2444i			0.930181i
$923$	10.7293	−	18.5838i	0.353161	−	0.611692i
$924$		0			0
$925$	4.27097	+	7.39754i	0.140429	+	0.243230i
$926$	−34.8353	+	20.1122i	−1.14476	+	0.660927i
$927$		0			0
$928$	3.95308	−	6.84694i	0.129766	−	0.224762i
$929$	−24.0288	+	41.6191i	−0.788359	+	1.36548i	0.138613	+	0.990347i	$0.455736\pi$
$929$	−24.0288	+	41.6191i	−0.788359	+	1.36548i	−0.926972	+	0.375131i	$0.877598\pi$
$930$		0			0
$931$	−38.3052	−	16.8186i	−1.25540	−	0.551207i
$932$	−6.79700	−	3.92425i	−0.222643	−	0.128543i
$933$		0			0
$934$		−	1.64908i		−	0.0539595i
$935$	−0.494979	−	0.285776i	−0.0161875	−	0.00934588i
$936$		0			0
$937$			8.04349i			0.262769i	0.991331	+	0.131385i	$0.0419423\pi$
$937$			8.04349i			0.262769i	−0.991331	+	0.131385i	$0.958058\pi$
$938$	11.8993	−	23.5031i	0.388524	−	0.767404i
$939$		0			0
$940$	2.08361			0.0679599
$941$	16.6440	+	28.8283i	0.542579	+	0.939775i	0.998755	+	0.0498854i	$0.0158856\pi$
$941$	16.6440	+	28.8283i	0.542579	+	0.939775i	−0.456175	+	0.889890i	$0.650781\pi$
$942$		0			0
$943$	−8.00530	−	4.62186i	−0.260689	−	0.150509i
$944$	−11.7733			−0.383189
$945$		0			0
$946$	11.7408			0.381728
$947$	27.0229	+	15.6017i	0.878128	+	0.506987i	0.870041	−	0.492980i	$-0.164092\pi$
$947$	27.0229	+	15.6017i	0.878128	+	0.506987i	0.00808714	+	0.999967i	$0.497426\pi$
$948$		0			0
$949$	6.19134	+	10.7237i	0.200979	+	0.348107i
$950$	5.97640			0.193900
$951$		0			0
$952$	0.260466	+	0.398829i	0.00844174	+	0.0129261i
$953$			10.1723i			0.329512i	0.986334	+	0.164756i	$0.0526837\pi$
$953$			10.1723i			0.329512i	−0.986334	+	0.164756i	$0.947316\pi$
$954$		0			0
$955$	−6.73693	−	3.88957i	−0.218002	−	0.125863i
$956$			16.5516i			0.535316i
$957$		0			0
$958$	24.4682	+	14.1267i	0.790533	+	0.456414i
$959$	10.4727	−	20.6853i	0.338180	−	0.667965i
$960$		0			0
$961$	31.5758	−	54.6908i	1.01857	−	1.76422i
$962$	−8.99542	+	15.5805i	−0.290024	+	0.502336i
$963$		0			0
$964$	−16.6800	+	9.63020i	−0.537227	+	0.310168i
$965$	−4.14681	−	7.18249i	−0.133491	−	0.231213i
$966$		0			0
$967$	−26.3617	+	45.6599i	−0.847737	+	1.46832i	0.0354867	+	0.999370i	$0.488702\pi$
$967$	−26.3617	+	45.6599i	−0.847737	+	1.46832i	−0.883223	+	0.468953i	$0.844631\pi$
$968$		−	0.922270i		−	0.0296429i
$969$		0			0
$970$	4.38017			0.140639
$971$	−4.76329	−	8.25026i	−0.152861	−	0.264763i	0.779417	−	0.626506i	$-0.215515\pi$
$971$	−4.76329	−	8.25026i	−0.152861	−	0.264763i	−0.932278	+	0.361742i	$0.882182\pi$
$972$		0			0
$973$	−4.62245	−	7.07796i	−0.148189	−	0.226909i
$974$	6.42239	−	3.70797i	0.205787	−	0.118811i
$975$		0			0
$976$	−2.50805	+	1.44802i	−0.0802806	+	0.0463500i
$977$	−26.6154	+	15.3664i	−0.851503	+	0.491616i	−0.861158	−	0.508338i	$-0.830260\pi$
$977$	−26.6154	+	15.3664i	−0.851503	+	0.491616i	0.00965461	+	0.999953i	$0.496927\pi$
$978$		0			0
$979$	−16.0080	+	9.24223i	−0.511618	+	0.295383i
$980$	−2.81417	+	6.40940i	−0.0898953	+	0.204741i
$981$		0			0
$982$	11.9348	+	20.6718i	0.380856	+	0.659662i
$983$	−10.3495			−0.330097			−0.165049	−	0.986285i	$-0.552778\pi$
$983$	−10.3495			−0.330097			−0.165049	+	0.986285i	$0.552778\pi$
$984$		0			0
$985$		−	13.3008i		−	0.423799i
$986$	−0.711722	+	1.23274i	−0.0226659	+	0.0392584i
$987$		0			0
$988$	6.29368	+	10.9010i	0.200229	+	0.346806i
$989$	2.52736	−	1.45917i	0.0803655	−	0.0463990i
$990$		0			0
$991$	−0.948097	+	1.64215i	−0.0301173	+	0.0521647i	−0.880691	−	0.473691i	$-0.842921\pi$
$991$	−0.948097	+	1.64215i	−0.0301173	+	0.0521647i	0.850574	+	0.525856i	$0.176255\pi$
$992$	−4.85159	+	8.40319i	−0.154038	+	0.266802i
$993$		0			0
$994$	−22.5694	+	14.7396i	−0.715858	+	0.467510i
$995$	−16.1833	−	9.34343i	−0.513045	−	0.296207i
$996$		0			0
$997$		−	28.6657i		−	0.907852i	−0.891039	−	0.453926i	$-0.850023\pi$
$997$		−	28.6657i		−	0.907852i	0.891039	−	0.453926i	$-0.149977\pi$
$998$	6.89865	+	3.98294i	0.218373	+	0.126078i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.t.b.1151.2		28
3.2	odd	2		630.2.t.b.311.11	✓	28
7.5	odd	6		1890.2.bk.b.341.4		28
9.2	odd	6		1890.2.bk.b.521.4		28
9.7	even	3		630.2.bk.b.101.8	yes	28
21.5	even	6		630.2.bk.b.131.1	yes	28
63.47	even	6	inner	1890.2.t.b.1601.2		28
63.61	odd	6		630.2.t.b.551.11	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.11	✓	28	3.2	odd	2
630.2.t.b.551.11	yes	28	63.61	odd	6
630.2.bk.b.101.8	yes	28	9.7	even	3
630.2.bk.b.131.1	yes	28	21.5	even	6
1890.2.t.b.1151.2		28	1.1	even	1	trivial
1890.2.t.b.1601.2		28	63.47	even	6	inner
1890.2.bk.b.341.4		28	7.5	odd	6
1890.2.bk.b.521.4		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)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-2.36047 - 1.19507i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-2.36047 - 1.19507i) q^{7} -1.00000i q^{8} +(-0.866025 - 0.500000i) q^{10} -3.17454i q^{11} +(-1.82400 - 1.05309i) q^{13} +(1.44669 + 2.21519i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.0900212 - 0.155921i) q^{17} +(-5.17571 + 2.98820i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-1.58727 + 2.74924i) q^{22} +0.789076i q^{23} +1.00000 q^{25} +(1.05309 + 1.82400i) q^{26} +(-0.145275 - 2.64176i) q^{28} +(6.84694 - 3.95308i) q^{29} +(-8.40319 + 4.85159i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.155921 + 0.0900212i) q^{34} +(-2.36047 - 1.19507i) q^{35} +(4.27097 + 7.39754i) q^{37} +5.97640 q^{38} -1.00000i q^{40} +(-5.85731 + 10.1452i) q^{41} +(-1.84922 - 3.20294i) q^{43} +(2.74924 - 1.58727i) q^{44} +(0.394538 - 0.683360i) q^{46} +(1.04181 - 1.80446i) q^{47} +(4.14362 + 5.64184i) q^{49} +(-0.866025 - 0.500000i) q^{50} -2.10618i q^{52} +(-0.613086 - 0.353965i) q^{53} -3.17454i q^{55} +(-1.19507 + 2.36047i) q^{56} -7.90616 q^{58} +(5.88665 + 10.1960i) q^{59} +(2.50805 + 1.44802i) q^{61} +9.70317 q^{62} -1.00000 q^{64} +(-1.82400 - 1.05309i) q^{65} +(-4.97848 - 8.62299i) q^{67} +0.180042 q^{68} +(1.44669 + 2.21519i) q^{70} +10.1885i q^{71} +(-5.09156 - 2.93961i) q^{73} -8.54194i q^{74} +(-5.17571 - 2.98820i) q^{76} +(-3.79380 + 7.49341i) q^{77} +(-5.50268 + 9.53091i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(10.1452 - 5.85731i) q^{82} +(-4.41475 - 7.64657i) q^{83} +(0.0900212 - 0.155921i) q^{85} +3.69843i q^{86} -3.17454 q^{88} +(-2.91136 - 5.04262i) q^{89} +(3.04699 + 4.66559i) q^{91} +(-0.683360 + 0.394538i) q^{92} +(-1.80446 + 1.04181i) q^{94} +(-5.17571 + 2.98820i) q^{95} +(-3.79334 + 2.19008i) q^{97} +(-0.767563 - 6.95779i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7}+O(q^{10}) \) 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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