LMFDB - Embedded newform 1890.2.bk.b.341.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(341,1890)]

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, 5]))

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

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

chi := DirichletCharacter("1890.341");

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.bk (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			341.4
Character	$\chi$	$=$	1890.341
Dual form			1890.2.bk.b.521.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.145275 - 2.64176i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.145275 - 2.64176i) q^{7} -1.00000i q^{8} +(-0.866025 + 0.500000i) q^{10} +(2.74924 + 1.58727i) q^{11} +(1.82400 + 1.05309i) q^{13} +(2.64176 + 0.145275i) q^{14} +1.00000 q^{16} +(-0.0900212 - 0.155921i) q^{17} +(-5.17571 - 2.98820i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-1.58727 + 2.74924i) q^{22} +(0.683360 - 0.394538i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-1.05309 + 1.82400i) q^{26} +(-0.145275 + 2.64176i) q^{28} +(6.84694 - 3.95308i) q^{29} +9.70317i q^{31} +1.00000i q^{32} +(0.155921 - 0.0900212i) q^{34} +(2.36047 - 1.19507i) q^{35} +(4.27097 - 7.39754i) q^{37} +(2.98820 - 5.17571i) q^{38} +(0.866025 - 0.500000i) q^{40} +(5.85731 - 10.1452i) q^{41} +(-1.84922 - 3.20294i) q^{43} +(-2.74924 - 1.58727i) q^{44} +(0.394538 + 0.683360i) q^{46} +2.08361 q^{47} +(-6.95779 - 0.767563i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(-1.82400 - 1.05309i) q^{52} +(0.613086 - 0.353965i) q^{53} +3.17454i q^{55} +(-2.64176 - 0.145275i) q^{56} +(3.95308 + 6.84694i) q^{58} +11.7733 q^{59} +2.89604i q^{61} -9.70317 q^{62} -1.00000 q^{64} +2.10618i q^{65} +9.95697 q^{67} +(0.0900212 + 0.155921i) q^{68} +(1.19507 + 2.36047i) q^{70} +10.1885i q^{71} +(-5.09156 + 2.93961i) q^{73} +(7.39754 + 4.27097i) q^{74} +(5.17571 + 2.98820i) q^{76} +(4.59259 - 7.03223i) q^{77} +11.0054 q^{79} +(0.500000 + 0.866025i) q^{80} +(10.1452 + 5.85731i) q^{82} +(4.41475 + 7.64657i) q^{83} +(0.0900212 - 0.155921i) q^{85} +(3.20294 - 1.84922i) q^{86} +(1.58727 - 2.74924i) q^{88} +(2.91136 - 5.04262i) q^{89} +(3.04699 - 4.66559i) q^{91} +(-0.683360 + 0.394538i) q^{92} +2.08361i q^{94} -5.97640i q^{95} +(3.79334 - 2.19008i) q^{97} +(0.767563 - 6.95779i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{4} + 14 q^{5} + 8 q^{7}+O(q^{10}) $ 28 * q - 28 * q^4 + 14 * q^5 + 8 * q^7	$ 28 q - 28 q^{4} + 14 q^{5} + 8 q^{7} + 28 q^{16} - 6 q^{17} - 6 q^{19} - 14 q^{20} - 6 q^{22} - 30 q^{23} - 14 q^{25} + 12 q^{26} - 8 q^{28} + 4 q^{35} + 4 q^{37} + 6 q^{38} + 18 q^{41} + 28 q^{43} - 18 q^{46} - 60 q^{47} - 20 q^{49} - 42 q^{53} + 6 q^{58} + 48 q^{59} - 12 q^{62} - 28 q^{64} + 80 q^{67} + 6 q^{68} + 6 q^{70} + 6 q^{73} + 6 q^{76} + 18 q^{77} - 4 q^{79} + 14 q^{80} + 24 q^{82} - 18 q^{83} + 6 q^{85} + 96 q^{86} + 6 q^{88} + 6 q^{89} + 66 q^{91} + 30 q^{92} + 72 q^{97} - 24 q^{98}+O(q^{100}) $ 28 * q - 28 * q^4 + 14 * q^5 + 8 * q^7 + 28 * q^16 - 6 * q^17 - 6 * q^19 - 14 * q^20 - 6 * q^22 - 30 * q^23 - 14 * q^25 + 12 * q^26 - 8 * q^28 + 4 * q^35 + 4 * q^37 + 6 * q^38 + 18 * q^41 + 28 * q^43 - 18 * q^46 - 60 * q^47 - 20 * q^49 - 42 * q^53 + 6 * q^58 + 48 * q^59 - 12 * q^62 - 28 * q^64 + 80 * q^67 + 6 * q^68 + 6 * q^70 + 6 * q^73 + 6 * q^76 + 18 * q^77 - 4 * q^79 + 14 * q^80 + 24 * q^82 - 18 * q^83 + 6 * q^85 + 96 * q^86 + 6 * q^88 + 6 * q^89 + 66 * q^91 + 30 * q^92 + 72 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	0.145275	−	2.64176i	0.0549087	−	0.998491i
$7$	0.145275	−	2.64176i	0.0549087	−	0.998491i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−0.866025	+	0.500000i	−0.273861	+	0.158114i
$11$	2.74924	+	1.58727i	0.828926	+	0.478581i	0.853485	−	0.521118i	$-0.174485\pi$
$11$	2.74924	+	1.58727i	0.828926	+	0.478581i	−0.0245589	+	0.999698i	$0.507818\pi$
$12$		0			0
$13$	1.82400	+	1.05309i	0.505887	+	0.292074i	0.731141	−	0.682226i	$-0.238988\pi$
$13$	1.82400	+	1.05309i	0.505887	+	0.292074i	−0.225254	+	0.974300i	$0.572321\pi$
$14$	2.64176	+	0.145275i	0.706040	+	0.0388263i
$15$		0			0
$16$	1.00000			0.250000
$17$	−0.0900212	−	0.155921i	−0.0218333	−	0.0378165i	0.854902	−	0.518789i	$-0.173617\pi$
$17$	−0.0900212	−	0.155921i	−0.0218333	−	0.0378165i	−0.876736	+	0.480973i	$0.840284\pi$
$18$		0			0
$19$	−5.17571	−	2.98820i	−1.18739	−	0.685540i	−0.229678	−	0.973267i	$-0.573767\pi$
$19$	−5.17571	−	2.98820i	−1.18739	−	0.685540i	−0.957713	+	0.287727i	$0.907101\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$		0			0
$22$	−1.58727	+	2.74924i	−0.338408	+	0.586139i
$23$	0.683360	−	0.394538i	0.142490	−	0.0822669i	−0.427060	−	0.904223i	$-0.640451\pi$
$23$	0.683360	−	0.394538i	0.142490	−	0.0822669i	0.569550	+	0.821956i	$0.307117\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−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
$31$			9.70317i			1.74274i	0.490626	+	0.871370i	$0.336768\pi$
$31$			9.70317i			1.74274i	−0.490626	+	0.871370i	$0.663232\pi$
$32$			1.00000i			0.176777i
$33$		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	−0.265569	−	0.964092i	$-0.585560\pi$
$37$	4.27097	−	7.39754i	0.702143	−	1.21615i	0.967713	−	0.252056i	$-0.0811068\pi$
$38$	2.98820	−	5.17571i	0.484750	−	0.839612i
$39$		0			0
$40$	0.866025	−	0.500000i	0.136931	−	0.0790569i
$41$	5.85731	−	10.1452i	0.914758	−	1.58441i	0.107502	−	0.994205i	$-0.465715\pi$
$41$	5.85731	−	10.1452i	0.914758	−	1.58441i	0.807256	−	0.590202i	$-0.200952\pi$
$42$		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
$47$	2.08361			0.303926			0.151963	−	0.988386i	$-0.451441\pi$
$47$	2.08361			0.303926			0.151963	+	0.988386i	$0.451441\pi$
$48$		0			0
$49$	−6.95779	−	0.767563i	−0.993970	−	0.109652i
$50$	−0.866025	−	0.500000i	−0.122474	−	0.0707107i
$51$		0			0
$52$	−1.82400	−	1.05309i	−0.252944	−	0.146037i
$53$	0.613086	−	0.353965i	0.0842138	−	0.0486209i	−0.457302	−	0.889312i	$-0.651184\pi$
$53$	0.613086	−	0.353965i	0.0842138	−	0.0486209i	0.541516	+	0.840691i	$0.317851\pi$
$54$		0			0
$55$			3.17454i			0.428055i
$56$	−2.64176	−	0.145275i	−0.353020	−	0.0194132i
$57$		0			0
$58$	3.95308	+	6.84694i	0.519065	+	0.899047i
$59$	11.7733			1.53275			0.766377	−	0.642391i	$-0.222057\pi$
$59$	11.7733			1.53275			0.766377	+	0.642391i	$0.222057\pi$
$60$		0			0
$61$			2.89604i			0.370800i	0.982663	+	0.185400i	$0.0593581\pi$
$61$			2.89604i			0.370800i	−0.982663	+	0.185400i	$0.940642\pi$
$62$	−9.70317			−1.23230
$63$		0			0
$64$	−1.00000			−0.125000
$65$			2.10618i			0.261239i
$66$		0			0
$67$	9.95697			1.21644			0.608219	−	0.793770i	$-0.291884\pi$
$67$	9.95697			1.21644			0.608219	+	0.793770i	$0.291884\pi$
$68$	0.0900212	+	0.155921i	0.0109167	+	0.0189082i
$69$		0			0
$70$	1.19507	+	2.36047i	0.142838	+	0.282130i
$71$			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	−0.767435	−	0.641126i	$-0.778467\pi$
$73$	−5.09156	+	2.93961i	−0.595921	+	0.344055i	0.171514	+	0.985182i	$0.445134\pi$
$74$	7.39754	+	4.27097i	0.859947	+	0.496490i
$75$		0			0
$76$	5.17571	+	2.98820i	0.593695	+	0.342770i
$77$	4.59259	−	7.03223i	0.523374	−	0.801397i
$78$		0			0
$79$	11.0054			1.23820			0.619099	−	0.785313i	$-0.287498\pi$
$79$	11.0054			1.23820			0.619099	+	0.785313i	$0.287498\pi$
$80$	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	0.999843	−	0.0177130i	$-0.00563853\pi$
$83$	4.41475	+	7.64657i	0.484582	+	0.839320i	−0.515261	+	0.857033i	$0.672305\pi$
$84$		0			0
$85$	0.0900212	−	0.155921i	0.00976417	−	0.0169120i
$86$	3.20294	−	1.84922i	0.345382	−	0.199406i
$87$		0			0
$88$	1.58727	−	2.74924i	0.169204	−	0.293070i
$89$	2.91136	−	5.04262i	0.308603	−	0.534516i	−0.669454	−	0.742854i	$-0.733472\pi$
$89$	2.91136	−	5.04262i	0.308603	−	0.534516i	0.978057	+	0.208337i	$0.0668052\pi$
$90$		0			0
$91$	3.04699	−	4.66559i	0.319411	−	0.489087i
$92$	−0.683360	+	0.394538i	−0.0712452	+	0.0411335i
$93$		0			0
$94$			2.08361i			0.214908i
$95$		−	5.97640i		−	0.613166i
$96$		0			0
$97$	3.79334	−	2.19008i	0.385155	−	0.222369i	−0.294904	−	0.955527i	$-0.595288\pi$
$97$	3.79334	−	2.19008i	0.385155	−	0.222369i	0.680059	+	0.733158i	$0.261954\pi$
$98$	0.767563	−	6.95779i	0.0775355	−	0.702843i
$99$		0			0
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	−8.45957	+	14.6524i	−0.841759	+	1.45797i	0.0466478	+	0.998911i	$0.485146\pi$
$101$	−8.45957	+	14.6524i	−0.841759	+	1.45797i	−0.888407	+	0.459057i	$0.848187\pi$
$102$		0			0
$103$	4.59953	−	2.65554i	0.453205	−	0.261658i	−0.255978	−	0.966683i	$-0.582397\pi$
$103$	4.59953	−	2.65554i	0.453205	−	0.261658i	0.709183	+	0.705025i	$0.249064\pi$
$104$	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	$-0.204147\pi$
$107$	7.07344	+	4.08385i	0.683816	+	0.394801i	−0.117476	+	0.993076i	$0.537480\pi$
$108$		0			0
$109$	−0.606828	−	1.05106i	−0.0581235	−	0.100673i	0.835500	−	0.549491i	$-0.185178\pi$
$109$	−0.606828	−	1.05106i	−0.0581235	−	0.100673i	−0.893623	+	0.448818i	$0.851845\pi$
$110$	−3.17454			−0.302681
$111$		0			0
$112$	0.145275	−	2.64176i	0.0137272	−	0.249623i
$113$	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
$115$	0.683360	+	0.394538i	0.0637237	+	0.0367909i
$116$	−6.84694	+	3.95308i	−0.635722	+	0.367034i
$117$		0			0
$118$			11.7733i			1.08382i
$119$	−0.424984	+	0.215163i	−0.0389583	+	0.0197240i
$120$		0			0
$121$	−0.461135	−	0.798709i	−0.0419214	−	0.0726099i
$122$	−2.89604			−0.262195
$123$		0			0
$124$		−	9.70317i		−	0.871370i
$125$	−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	$0.733726\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	−2.10618			−0.184724
$131$	4.19019	+	7.25762i	0.366099	+	0.634101i	0.988952	−	0.148237i	$-0.0473599\pi$
$131$	4.19019	+	7.25762i	0.366099	+	0.634101i	−0.622853	+	0.782339i	$0.714027\pi$
$132$		0			0
$133$	−8.64601	+	13.2389i	−0.749704	+	1.14796i
$134$			9.95697i			0.860151i
$135$		0			0
$136$	−0.155921	+	0.0900212i	−0.0133701	+	0.00771925i
$137$	−7.58919	−	4.38162i	−0.648388	−	0.374347i	0.139450	−	0.990229i	$-0.455466\pi$
$137$	−7.58919	−	4.38162i	−0.648388	−	0.374347i	−0.787838	+	0.615882i	$0.788800\pi$
$138$		0			0
$139$	−2.76711	−	1.59759i	−0.234704	−	0.135506i	0.378036	−	0.925791i	$-0.376599\pi$
$139$	−2.76711	−	1.59759i	−0.234704	−	0.135506i	−0.612740	+	0.790285i	$0.709933\pi$
$140$	−2.36047	+	1.19507i	−0.199496	+	0.101002i
$141$		0			0
$142$	−10.1885			−0.854996
$143$	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
$149$	−5.37389	+	3.10262i	−0.440246	+	0.254176i	−0.703702	−	0.710495i	$-0.748471\pi$
$149$	−5.37389	+	3.10262i	−0.440246	+	0.254176i	0.263456	+	0.964671i	$0.415138\pi$
$150$		0			0
$151$	−5.33037	+	9.23247i	−0.433779	+	0.751328i	−0.997195	−	0.0748455i	$-0.976154\pi$
$151$	−5.33037	+	9.23247i	−0.433779	+	0.751328i	0.563416	+	0.826174i	$0.309487\pi$
$152$	−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
$157$			4.39858i			0.351045i	0.984475	+	0.175523i	$0.0561615\pi$
$157$			4.39858i			0.351045i	−0.984475	+	0.175523i	$0.943839\pi$
$158$			11.0054i			0.875539i
$159$		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	−0.153520	−	0.988146i	$-0.549061\pi$
$163$	9.94559	−	17.2263i	0.778999	−	1.34927i	0.932519	−	0.361120i	$-0.117606\pi$
$164$	−5.85731	+	10.1452i	−0.457379	+	0.792203i
$165$		0			0
$166$	−7.64657	+	4.41475i	−0.593489	+	0.342651i
$167$	7.13831	−	12.3639i	0.552379	−	0.956749i	−0.445723	−	0.895171i	$-0.647053\pi$
$167$	7.13831	−	12.3639i	0.552379	−	0.956749i	0.998102	−	0.0615778i	$-0.0196132\pi$
$168$		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
$173$	13.2286			1.00575			0.502876	−	0.864359i	$-0.332275\pi$
$173$	13.2286			1.00575			0.502876	+	0.864359i	$0.332275\pi$
$174$		0			0
$175$	2.21519	+	1.44669i	0.167453	+	0.109360i
$176$	2.74924	+	1.58727i	0.207231	+	0.119645i
$177$		0			0
$178$	5.04262	+	2.91136i	0.377960	+	0.218215i
$179$	3.52462	−	2.03494i	0.263442	−	0.152098i	−0.362462	−	0.931999i	$-0.618064\pi$
$179$	3.52462	−	2.03494i	0.263442	−	0.152098i	0.625904	+	0.779900i	$0.284730\pi$
$180$		0			0
$181$		−	21.7339i		−	1.61547i	−0.589546	−	0.807735i	$-0.700693\pi$
$181$		−	21.7339i		−	1.61547i	0.589546	−	0.807735i	$-0.299307\pi$
$182$	4.66559	+	3.04699i	0.345837	+	0.225858i
$183$		0			0
$184$	−0.394538	−	0.683360i	−0.0290857	−	0.0503780i
$185$	8.54194			0.628016
$186$		0			0
$187$		−	0.571552i		−	0.0417961i
$188$	−2.08361			−0.151963
$189$		0			0
$190$	5.97640			0.433574
$191$			7.77914i			0.562878i	0.959579	+	0.281439i	$0.0908118\pi$
$191$			7.77914i			0.562878i	−0.959579	+	0.281439i	$0.909188\pi$
$192$		0			0
$193$	8.29363			0.596988			0.298494	−	0.954411i	$-0.403516\pi$
$193$	8.29363			0.596988			0.298494	+	0.954411i	$0.403516\pi$
$194$	2.19008	+	3.79334i	0.157239	+	0.272346i
$195$		0			0
$196$	6.95779	+	0.767563i	0.496985	+	0.0548259i
$197$		−	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	−0.948204	−	0.317661i	$-0.897102\pi$
$199$	−16.1833	+	9.34343i	−1.14720	+	0.662338i	−0.198999	+	0.980000i	$0.563769\pi$
$200$	0.866025	+	0.500000i	0.0612372	+	0.0353553i
$201$		0			0
$202$	−14.6524	−	8.45957i	−1.03094	−	0.595213i
$203$	−9.44841	−	18.6623i	−0.663148	−	1.30983i
$204$		0			0
$205$	11.7146			0.818184
$206$	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	$0.850991\pi$
$212$	−0.613086	+	0.353965i	−0.0421069	+	0.0243104i
$213$		0			0
$214$	−4.08385	+	7.07344i	−0.279167	+	0.483531i
$215$	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
$220$		−	3.17454i		−	0.214028i
$221$		−	0.379201i		−	0.0255078i
$222$		0			0
$223$	14.5348	−	8.39165i	0.973320	−	0.561946i	0.0730731	−	0.997327i	$-0.476719\pi$
$223$	14.5348	−	8.39165i	0.973320	−	0.561946i	0.900247	+	0.435380i	$0.143386\pi$
$224$	2.64176	+	0.145275i	0.176510	+	0.00970659i
$225$		0			0
$226$	−0.714296	+	1.23720i	−0.0475143	+	0.0822971i
$227$	−8.39567	+	14.5417i	−0.557240	+	0.965168i	0.440485	+	0.897760i	$0.354806\pi$
$227$	−8.39567	+	14.5417i	−0.557240	+	0.965168i	−0.997725	+	0.0674083i	$0.978527\pi$
$228$		0			0
$229$	−5.74293	+	3.31568i	−0.379503	+	0.219106i	−0.677602	−	0.735429i	$-0.736981\pi$
$229$	−5.74293	+	3.31568i	−0.379503	+	0.219106i	0.298099	+	0.954535i	$0.403648\pi$
$230$	−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	$-0.250571\pi$
$233$	6.79700	+	3.92425i	0.445286	+	0.257086i	−0.260551	+	0.965460i	$0.583904\pi$
$234$		0			0
$235$	1.04181	+	1.80446i	0.0679599	+	0.117710i
$236$	−11.7733			−0.766377
$237$		0			0
$238$	−0.215163	−	0.424984i	−0.0139469	−	0.0275476i
$239$	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
$241$	16.6800	+	9.63020i	1.07445	+	0.620336i	0.929395	−	0.369087i	$-0.120330\pi$
$241$	16.6800	+	9.63020i	1.07445	+	0.620336i	0.145058	+	0.989423i	$0.453663\pi$
$242$	0.798709	−	0.461135i	0.0513430	−	0.0296429i
$243$		0			0
$244$		−	2.89604i		−	0.185400i
$245$	−2.81417	−	6.40940i	−0.179791	−	0.409482i
$246$		0			0
$247$	−6.29368	−	10.9010i	−0.400457	−	0.693612i
$248$	9.70317			0.616152
$249$		0			0
$250$		−	1.00000i		−	0.0632456i
$251$	−22.0186			−1.38980			−0.694901	−	0.719105i	$-0.744552\pi$
$251$	−22.0186			−1.38980			−0.694901	+	0.719105i	$0.744552\pi$
$252$		0			0
$253$	2.50496			0.157485
$254$		−	15.1021i		−	0.947590i
$255$		0			0
$256$	1.00000			0.0625000
$257$	10.4221	+	18.0516i	0.650112	+	1.12603i	0.983095	+	0.183094i	$0.0586112\pi$
$257$	10.4221	+	18.0516i	0.650112	+	1.12603i	−0.332984	+	0.942933i	$0.608055\pi$
$258$		0			0
$259$	−18.9221	−	12.3576i	−1.17576	−	0.767861i
$260$		−	2.10618i		−	0.130620i
$261$		0			0
$262$	−7.25762	+	4.19019i	−0.448377	+	0.258871i
$263$	19.5177	+	11.2685i	1.20351	+	0.694847i	0.961334	−	0.275385i	$-0.0888052\pi$
$263$	19.5177	+	11.2685i	1.20351	+	0.694847i	0.242177	+	0.970232i	$0.422139\pi$
$264$		0			0
$265$	0.613086	+	0.353965i	0.0376616	+	0.0217439i
$266$	−13.2389	−	8.64601i	−0.811728	−	0.530121i
$267$		0			0
$268$	−9.95697			−0.608219
$269$	−11.8691	−	20.5578i	−0.723670	−	1.25343i	−0.959519	−	0.281643i	$-0.909121\pi$
$269$	−11.8691	−	20.5578i	−0.723670	−	1.25343i	0.235849	−	0.971790i	$-0.424213\pi$
$270$		0			0
$271$	−10.2170	−	5.89877i	−0.620636	−	0.358325i	0.156480	−	0.987681i	$-0.449985\pi$
$271$	−10.2170	−	5.89877i	−0.620636	−	0.358325i	−0.777117	+	0.629356i	$0.783319\pi$
$272$	−0.0900212	−	0.155921i	−0.00545834	−	0.00945412i
$273$		0			0
$274$	4.38162	−	7.58919i	0.264703	−	0.458480i
$275$	−2.74924	+	1.58727i	−0.165785	+	0.0957161i
$276$		0			0
$277$	9.15321	−	15.8538i	0.549963	−	0.952564i	−0.448313	−	0.893876i	$-0.647975\pi$
$277$	9.15321	−	15.8538i	0.549963	−	0.952564i	0.998276	−	0.0586874i	$-0.0186915\pi$
$278$	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
$283$		−	1.51803i		−	0.0902374i	−0.998982	−	0.0451187i	$-0.985633\pi$
$283$		−	1.51803i		−	0.0902374i	0.998982	−	0.0451187i	$-0.0143666\pi$
$284$		−	10.1885i		−	0.604574i
$285$		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
$290$	−3.95308	+	6.84694i	−0.232133	+	0.402066i
$291$		0			0
$292$	5.09156	−	2.93961i	0.297961	−	0.172028i
$293$	2.79327	−	4.83808i	0.163184	−	0.282643i	−0.772825	−	0.634620i	$-0.781157\pi$
$293$	2.79327	−	4.83808i	0.163184	−	0.282643i	0.936009	+	0.351976i	$0.114490\pi$
$294$		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
$299$	1.66193			0.0961121
$300$		0			0
$301$	−8.73004	+	4.41988i	−0.503191	+	0.254758i
$302$	−9.23247	−	5.33037i	−0.531269	−	0.306728i
$303$		0			0
$304$	−5.17571	−	2.98820i	−0.296848	−	0.171385i
$305$	−2.50805	+	1.44802i	−0.143610	+	0.0829134i
$306$		0			0
$307$			22.8941i			1.30663i	0.757085	+	0.653316i	$0.226623\pi$
$307$			22.8941i			1.30663i	−0.757085	+	0.653316i	$0.773377\pi$
$308$	−4.59259	+	7.03223i	−0.261687	+	0.400698i
$309$		0			0
$310$	−4.85159	−	8.40319i	−0.275552	−	0.477269i
$311$	−21.7317			−1.23229			−0.616146	−	0.787632i	$-0.711307\pi$
$311$	−21.7317			−1.23229			−0.616146	+	0.787632i	$0.711307\pi$
$312$		0			0
$313$		−	3.13232i		−	0.177049i	−0.996074	−	0.0885247i	$-0.971785\pi$
$313$		−	3.13232i		−	0.177049i	0.996074	−	0.0885247i	$-0.0282152\pi$
$314$	−4.39858			−0.248226
$315$		0			0
$316$	−11.0054			−0.619099
$317$		−	28.6867i		−	1.61120i	−0.592457	−	0.805602i	$-0.701842\pi$
$317$		−	28.6867i		−	1.61120i	0.592457	−	0.805602i	$-0.298158\pi$
$318$		0			0
$319$	25.0985			1.40524
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$		0			0
$322$	1.86259	−	0.943000i	0.103798	−	0.0525513i
$323$			1.07601i			0.0598705i
$324$		0			0
$325$	−1.82400	+	1.05309i	−0.101177	+	0.0584148i
$326$	17.2263	+	9.94559i	0.954075	+	0.550836i
$327$		0			0
$328$	−10.1452	−	5.85731i	−0.560172	−	0.323416i
$329$	0.302696	−	5.50440i	0.0166882	−	0.303467i
$330$		0			0
$331$	−5.70943			−0.313819			−0.156909	−	0.987613i	$-0.550153\pi$
$331$	−5.70943			−0.313819			−0.156909	+	0.987613i	$0.550153\pi$
$332$	−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	$0.0713343\pi$
$338$	7.41666	−	4.28201i	0.403413	−	0.232911i
$339$		0			0
$340$	−0.0900212	+	0.155921i	−0.00488208	+	0.00845602i
$341$	−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
$346$			13.2286i			0.711174i
$347$		−	19.3689i		−	1.03978i	−0.854234	−	0.519889i	$-0.825973\pi$
$347$		−	19.3689i		−	1.03978i	0.854234	−	0.519889i	$-0.174027\pi$
$348$		0			0
$349$	−17.1942	+	9.92710i	−0.920387	+	0.531385i	−0.883758	−	0.467944i	$-0.844995\pi$
$349$	−17.1942	+	9.92710i	−0.920387	+	0.531385i	−0.0366282	+	0.999329i	$0.511662\pi$
$350$	−1.44669	+	2.21519i	−0.0773289	+	0.118407i
$351$		0			0
$352$	−1.58727	+	2.74924i	−0.0846019	+	0.146535i
$353$	−5.74699	+	9.95408i	−0.305881	+	0.529802i	−0.977457	−	0.211134i	$-0.932284\pi$
$353$	−5.74699	+	9.95408i	−0.305881	+	0.529802i	0.671576	+	0.740936i	$0.265618\pi$
$354$		0			0
$355$	−8.82346	+	5.09423i	−0.468301	+	0.270374i
$356$	−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	$-0.532012\pi$
$359$	−19.1794	−	11.0732i	−1.01225	−	0.584422i	−0.911849	+	0.410525i	$0.865346\pi$
$360$		0			0
$361$	8.35868	+	14.4777i	0.439930	+	0.761982i
$362$	21.7339			1.14231
$363$		0			0
$364$	−3.04699	+	4.66559i	−0.159706	+	0.244543i
$365$	−5.09156	−	2.93961i	−0.266504	−	0.153866i
$366$		0			0
$367$	−17.4441	−	10.0714i	−0.910577	−	0.525722i	−0.0299604	−	0.999551i	$-0.509538\pi$
$367$	−17.4441	−	10.0714i	−0.910577	−	0.525722i	−0.880617	+	0.473829i	$0.842871\pi$
$368$	0.683360	−	0.394538i	0.0356226	−	0.0205667i
$369$		0			0
$370$			8.54194i			0.444074i
$371$	−0.846025	−	1.67105i	−0.0439234	−	0.0867565i
$372$		0			0
$373$	−13.6455	−	23.6347i	−0.706538	−	1.22376i	−0.966134	−	0.258042i	$-0.916923\pi$
$373$	−13.6455	−	23.6347i	−0.706538	−	1.22376i	0.259596	−	0.965717i	$-0.416411\pi$
$374$	0.571552			0.0295543
$375$		0			0
$376$		−	2.08361i		−	0.107454i
$377$	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	$0.667935\pi$
$380$			5.97640i			0.306583i
$381$		0			0
$382$	−7.77914			−0.398015
$383$	1.98579	+	3.43949i	0.101469	+	0.175750i	0.912290	−	0.409544i	$-0.134312\pi$
$383$	1.98579	+	3.43949i	0.101469	+	0.175750i	−0.810821	+	0.585294i	$0.800979\pi$
$384$		0			0
$385$	8.38638	+	0.461181i	0.427410	+	0.0235040i
$386$			8.29363i			0.422134i
$387$		0			0
$388$	−3.79334	+	2.19008i	−0.192577	+	0.111185i
$389$	16.3614	+	9.44628i	0.829558	+	0.478945i	0.853701	−	0.520763i	$-0.174353\pi$
$389$	16.3614	+	9.44628i	0.829558	+	0.478945i	−0.0241434	+	0.999709i	$0.507686\pi$
$390$		0			0
$391$	−0.123034	−	0.0710336i	−0.00622209	−	0.00359232i
$392$	−0.767563	+	6.95779i	−0.0387678	+	0.351421i
$393$		0			0
$394$	13.3008			0.670085
$395$	5.50268	+	9.53091i	0.276870	+	0.479552i
$396$		0			0
$397$	−30.5990	−	17.6664i	−1.53572	−	0.886649i	−0.999082	−	0.0428377i	$-0.986360\pi$
$397$	−30.5990	−	17.6664i	−1.53572	−	0.886649i	−0.536640	−	0.843812i	$-0.680307\pi$
$398$	−9.34343	−	16.1833i	−0.468344	−	0.811195i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−0.539822	+	0.311666i	−0.0269574	+	0.0155639i	−0.513418	−	0.858139i	$-0.671621\pi$
$401$	−0.539822	+	0.311666i	−0.0269574	+	0.0155639i	0.486461	+	0.873702i	$0.338288\pi$
$402$		0			0
$403$	−10.2183	+	17.6986i	−0.509010	+	0.881630i
$404$	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
$409$		−	1.39035i		−	0.0687483i	−0.999409	−	0.0343741i	$-0.989056\pi$
$409$		−	1.39035i		−	0.0687483i	0.999409	−	0.0343741i	$-0.0109438\pi$
$410$			11.7146i			0.578544i
$411$		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
$416$	−1.05309	+	1.82400i	−0.0516319	+	0.0894291i
$417$		0			0
$418$	16.4305	−	9.48617i	0.803644	−	0.463984i
$419$	−13.7784	+	23.8650i	−0.673121	+	1.16588i	0.303893	+	0.952706i	$0.401713\pi$
$419$	−13.7784	+	23.8650i	−0.673121	+	1.16588i	−0.977014	+	0.213174i	$0.931620\pi$
$420$		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
$425$	0.180042			0.00873334
$426$		0			0
$427$	7.65065	+	0.420722i	0.370241	+	0.0203602i
$428$	−7.07344	−	4.08385i	−0.341908	−	0.197401i
$429$		0			0
$430$	3.20294	+	1.84922i	0.154459	+	0.0891772i
$431$	24.3620	−	14.0654i	1.17348	−	0.677508i	0.218981	−	0.975729i	$-0.429727\pi$
$431$	24.3620	−	14.0654i	1.17348	−	0.677508i	0.954497	+	0.298221i	$0.0963933\pi$
$432$		0			0
$433$		−	11.9782i		−	0.575635i	−0.957685	−	0.287817i	$-0.907070\pi$
$433$		−	11.9782i		−	0.575635i	0.957685	−	0.287817i	$-0.0929296\pi$
$434$	−1.40963	+	25.6334i	−0.0676643	+	1.23044i
$435$		0			0
$436$	0.606828	+	1.05106i	0.0290618	+	0.0503365i
$437$	−4.71584			−0.225589
$438$		0			0
$439$			10.8588i			0.518264i	0.965842	+	0.259132i	$0.0834364\pi$
$439$			10.8588i			0.518264i	−0.965842	+	0.259132i	$0.916564\pi$
$440$	3.17454			0.151340
$441$		0			0
$442$	0.379201			0.0180368
$443$			2.11680i			0.100572i	0.998735	+	0.0502862i	$0.0160134\pi$
$443$			2.11680i			0.100572i	−0.998735	+	0.0502862i	$0.983987\pi$
$444$		0			0
$445$	5.82271			0.276023
$446$	8.39165	+	14.5348i	0.397356	+	0.688241i
$447$		0			0
$448$	−0.145275	+	2.64176i	−0.00686359	+	0.124811i
$449$		−	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
$452$	−1.23720	−	0.714296i	−0.0581928	−	0.0335976i
$453$		0			0
$454$	−14.5417	−	8.39567i	−0.682477	−	0.394028i
$455$	5.56401	+	0.305975i	0.260845	+	0.0143443i
$456$		0			0
$457$	−33.1134			−1.54898			−0.774490	−	0.632586i	$-0.781994\pi$
$457$	−33.1134			−1.54898			−0.774490	+	0.632586i	$0.781994\pi$
$458$	−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	$0.0618196\pi$
$461$	14.1222	+	24.4604i	0.657737	+	1.13923i	−0.323463	+	0.946241i	$0.604847\pi$
$462$		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	$-0.217658\pi$
$464$	6.84694	−	3.95308i	0.317861	−	0.183517i
$465$		0			0
$466$	−3.92425	+	6.79700i	−0.181787	+	0.314865i
$467$	−0.824539	+	1.42814i	−0.0381551	+	0.0660866i	−0.884472	−	0.466593i	$-0.845481\pi$
$467$	−0.824539	+	1.42814i	−0.0381551	+	0.0660866i	0.846317	+	0.532679i	$0.178815\pi$
$468$		0			0
$469$	1.44650	−	26.3039i	0.0667930	−	1.21460i
$470$	−1.80446	+	1.04181i	−0.0832335	+	0.0480549i
$471$		0			0
$472$		−	11.7733i		−	0.541910i
$473$		−	11.7408i		−	0.539845i
$474$		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
$479$	−14.1267	+	24.4682i	−0.645467	+	1.11798i	0.338726	+	0.940885i	$0.390004\pi$
$479$	−14.1267	+	24.4682i	−0.645467	+	1.11798i	−0.984193	+	0.177097i	$0.943329\pi$
$480$		0			0
$481$	15.5805	−	8.99542i	0.710411	−	0.410156i
$482$	−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	0.769701	−	0.638405i	$-0.220405\pi$
$487$	−3.70797	−	6.42239i	−0.168024	−	0.291026i	−0.937725	+	0.347378i	$0.887072\pi$
$488$	2.89604			0.131098
$489$		0			0
$490$	6.40940	−	2.81417i	0.289547	−	0.127131i
$491$	−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
$493$	−1.23274	−	0.711722i	−0.0555198	−	0.0320544i
$494$	10.9010	−	6.29368i	0.490458	−	0.283166i
$495$		0			0
$496$			9.70317i			0.435685i
$497$	26.9155	+	1.48013i	1.20732	+	0.0663927i
$498$		0			0
$499$	3.98294	+	6.89865i	0.178301	+	0.308826i	0.941299	−	0.337575i	$-0.109607\pi$
$499$	3.98294	+	6.89865i	0.178301	+	0.308826i	−0.762998	+	0.646401i	$0.776273\pi$
$500$	1.00000			0.0447214
$501$		0			0
$502$		−	22.0186i		−	0.982738i
$503$	−39.3978			−1.75666			−0.878332	−	0.478052i	$-0.841343\pi$
$503$	−39.3978			−1.75666			−0.878332	+	0.478052i	$0.841343\pi$
$504$		0			0
$505$	−16.9191			−0.752892
$506$			2.50496i			0.111359i
$507$		0			0
$508$	15.1021			0.670048
$509$	−1.13505	−	1.96596i	−0.0503102	−	0.0871399i	0.839774	−	0.542937i	$-0.182688\pi$
$509$	−1.13505	−	1.96596i	−0.0503102	−	0.0871399i	−0.890084	+	0.455797i	$0.849354\pi$
$510$		0			0
$511$	7.02607	+	13.8777i	0.310815	+	0.613914i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−18.0516	+	10.4221i	−0.796221	+	0.459698i
$515$	4.59953	+	2.65554i	0.202679	+	0.117017i
$516$		0			0
$517$	5.72834	+	3.30726i	0.251932	+	0.145453i
$518$	12.3576	−	18.9221i	0.542960	−	0.831388i
$519$		0			0
$520$	2.10618			0.0923620
$521$	9.24087	+	16.0057i	0.404850	+	0.701221i	0.994304	−	0.106581i	$-0.0339904\pi$
$521$	9.24087	+	16.0057i	0.404850	+	0.701221i	−0.589454	+	0.807802i	$0.700657\pi$
$522$		0			0
$523$	−30.9554	−	17.8721i	−1.35359	−	0.781493i	−0.364836	−	0.931072i	$-0.618875\pi$
$523$	−30.9554	−	17.8721i	−1.35359	−	0.781493i	−0.988750	+	0.149578i	$0.952208\pi$
$524$	−4.19019	−	7.25762i	−0.183049	−	0.317051i
$525$		0			0
$526$	−11.2685	+	19.5177i	−0.491331	+	0.851011i
$527$	1.51293	−	0.873491i	0.0659043	−	0.0380499i
$528$		0			0
$529$	−11.1887	+	19.3794i	−0.486464	+	0.842581i
$530$	−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
$535$			8.16771i			0.353121i
$536$		−	9.95697i		−	0.430075i
$537$		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	−0.709315	−	0.704891i	$-0.750996\pi$
$541$	5.94967	−	10.3051i	0.255796	−	0.443052i	0.965111	+	0.261839i	$0.0843291\pi$
$542$	5.89877	−	10.2170i	0.253374	−	0.438856i
$543$		0			0
$544$	0.155921	−	0.0900212i	0.00668507	−	0.00385963i
$545$	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
$551$	−47.2504			−2.01293
$552$		0			0
$553$	1.59880	−	29.0735i	0.0679879	−	1.23633i
$554$	15.8538	+	9.15321i	0.673564	+	0.388883i
$555$		0			0
$556$	2.76711	+	1.59759i	0.117352	+	0.0677531i
$557$	14.4583	−	8.34752i	0.612619	−	0.353696i	−0.161371	−	0.986894i	$-0.551592\pi$
$557$	14.4583	−	8.34752i	0.612619	−	0.353696i	0.773990	+	0.633198i	$0.218258\pi$
$558$		0			0
$559$		−	7.78956i		−	0.329463i
$560$	2.36047	−	1.19507i	0.0997480	−	0.0505008i
$561$		0			0
$562$	−10.9047	−	18.8875i	−0.459988	−	0.796723i
$563$	−29.4425			−1.24085			−0.620427	−	0.784265i	$-0.713041\pi$
$563$	−29.4425			−1.24085			−0.620427	+	0.784265i	$0.713041\pi$
$564$		0			0
$565$			1.42859i			0.0601013i
$566$	1.51803			0.0638075
$567$		0			0
$568$	10.1885			0.427498
$569$			5.69471i			0.238735i	0.992850	+	0.119367i	$0.0380866\pi$
$569$			5.69471i			0.238735i	−0.992850	+	0.119367i	$0.961913\pi$
$570$		0			0
$571$	−3.56033			−0.148995			−0.0744976	−	0.997221i	$-0.523735\pi$
$571$	−3.56033			−0.148995			−0.0744976	+	0.997221i	$0.523735\pi$
$572$	−3.34308	−	5.79038i	−0.139781	−	0.242108i
$573$		0			0
$574$	16.9474	−	25.9501i	0.707372	−	1.08314i
$575$			0.789076i			0.0329068i
$576$		0			0
$577$	−5.31447	+	3.06831i	−0.221244	+	0.127735i	−0.606526	−	0.795064i	$-0.707437\pi$
$577$	−5.31447	+	3.06831i	−0.221244	+	0.127735i	0.385282	+	0.922799i	$0.374104\pi$
$578$	14.6944	+	8.48379i	0.611205	+	0.352879i
$579$		0			0
$580$	−6.84694	−	3.95308i	−0.284304	−	0.164143i
$581$	20.8418	−	10.5519i	0.864662	−	0.437765i
$582$		0			0
$583$	2.24736			0.0930760
$584$	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	0.827368	−	0.561660i	$-0.189837\pi$
$587$	−1.76206	−	3.05198i	−0.0727279	−	0.125969i	−0.900096	+	0.435692i	$0.856504\pi$
$588$		0			0
$589$	28.9950	−	50.2208i	1.19472	−	2.06931i
$590$	−10.1960	+	5.88665i	−0.419762	+	0.242350i
$591$		0			0
$592$	4.27097	−	7.39754i	0.175536	−	0.304037i
$593$	−20.0316	+	34.6957i	−0.822598	+	1.42478i	0.0811430	+	0.996702i	$0.474143\pi$
$593$	−20.0316	+	34.6957i	−0.822598	+	1.42478i	−0.903741	+	0.428079i	$0.859190\pi$
$594$		0			0
$595$	−0.398829	−	0.260466i	−0.0163504	−	0.0106781i
$596$	5.37389	−	3.10262i	0.220123	−	0.127088i
$597$		0			0
$598$			1.66193i			0.0679616i
$599$		−	1.82047i		−	0.0743825i	−0.999308	−	0.0371913i	$-0.988159\pi$
$599$		−	1.82047i		−	0.0743825i	0.999308	−	0.0371913i	$-0.0118411\pi$
$600$		0			0
$601$	15.9038	−	9.18204i	0.648728	−	0.374543i	−0.139241	−	0.990259i	$-0.544466\pi$
$601$	15.9038	−	9.18204i	0.648728	−	0.374543i	0.787969	+	0.615715i	$0.211133\pi$
$602$	−4.41988	−	8.73004i	−0.180141	−	0.355810i
$603$		0			0
$604$	5.33037	−	9.23247i	0.216890	−	0.375664i
$605$	0.461135	−	0.798709i	0.0187478	−	0.0324721i
$606$		0			0
$607$	25.0342	−	14.4535i	1.01611	−	0.586649i	0.103132	−	0.994668i	$-0.467114\pi$
$607$	25.0342	−	14.4535i	1.01611	−	0.586649i	0.912973	+	0.408019i	$0.133780\pi$
$608$	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	0.912557	+	0.408949i	$0.134104\pi$
$613$	20.0655	+	34.7545i	0.810439	+	1.40372i	−0.102119	+	0.994772i	$0.532562\pi$
$614$	−22.8941			−0.923929
$615$		0			0
$616$	−7.03223	−	4.59259i	−0.283337	−	0.185041i
$617$	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
$619$	−15.5286	−	8.96546i	−0.624149	−	0.360352i	0.154334	−	0.988019i	$-0.450677\pi$
$619$	−15.5286	−	8.96546i	−0.624149	−	0.360352i	−0.778482	+	0.627666i	$0.784010\pi$
$620$	8.40319	−	4.85159i	0.337480	−	0.194844i
$621$		0			0
$622$		−	21.7317i		−	0.871362i
$623$	−12.8984	−	8.42367i	−0.516765	−	0.337487i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	3.13232			0.125193
$627$		0			0
$628$		−	4.39858i		−	0.175523i
$629$	−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	$0.399420\pi$
$632$		−	11.0054i		−	0.437769i
$633$		0			0
$634$	28.6867			1.13929
$635$	−7.55105	−	13.0788i	−0.299654	−	0.519017i
$636$		0			0
$637$	−11.8827	−	8.72720i	−0.470810	−	0.345784i
$638$			25.0985i			0.993658i
$639$		0			0
$640$	0.866025	−	0.500000i	0.0342327	−	0.0197642i
$641$	−13.2778	−	7.66593i	−0.524441	−	0.302786i	0.214309	−	0.976766i	$-0.431250\pi$
$641$	−13.2778	−	7.66593i	−0.524441	−	0.302786i	−0.738750	+	0.673980i	$0.764583\pi$
$642$		0			0
$643$	−26.2575	−	15.1598i	−1.03550	−	0.597844i	−0.116941	−	0.993139i	$-0.537309\pi$
$643$	−26.2575	−	15.1598i	−1.03550	−	0.597844i	−0.918554	+	0.395295i	$0.870642\pi$
$644$	0.943000	+	1.86259i	0.0371594	+	0.0733963i
$645$		0			0
$646$	−1.07601			−0.0423349
$647$	14.5503	+	25.2018i	0.572030	+	0.990785i	0.996357	+	0.0852761i	$0.0271772\pi$
$647$	14.5503	+	25.2018i	0.572030	+	0.990785i	−0.424327	+	0.905509i	$0.639489\pi$
$648$		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
$653$	−2.85434	+	1.64796i	−0.111699	+	0.0644895i	−0.554809	−	0.831978i	$-0.687209\pi$
$653$	−2.85434	+	1.64796i	−0.111699	+	0.0644895i	0.443110	+	0.896467i	$0.353875\pi$
$654$		0			0
$655$	−4.19019	+	7.25762i	−0.163724	+	0.283579i
$656$	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
$661$			37.6383i			1.46396i	0.681327	+	0.731979i	$0.261403\pi$
$661$			37.6383i			1.46396i	−0.681327	+	0.731979i	$0.738597\pi$
$662$		−	5.70943i		−	0.221903i
$663$		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
$668$	−7.13831	+	12.3639i	−0.276190	+	0.478374i
$669$		0			0
$670$	−8.62299	+	4.97848i	−0.333135	+	0.192336i
$671$	−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
$677$	−7.27326			−0.279534			−0.139767	−	0.990184i	$-0.544635\pi$
$677$	−7.27326			−0.279534			−0.139767	+	0.990184i	$0.544635\pi$
$678$		0			0
$679$	−5.23460	−	10.3392i	−0.200885	−	0.396784i
$680$	−0.155921	−	0.0900212i	−0.00597931	−	0.00345215i
$681$		0			0
$682$	−26.6763	−	15.4016i	−1.02149	−	0.589757i
$683$	−14.4216	+	8.32633i	−0.551828	+	0.318598i	−0.749859	−	0.661598i	$-0.769879\pi$
$683$	−14.4216	+	8.32633i	−0.551828	+	0.318598i	0.198031	+	0.980196i	$0.436545\pi$
$684$		0			0
$685$		−	8.76324i		−	0.334826i
$686$	−18.2693	−	3.03851i	−0.697525	−	0.116011i
$687$		0			0
$688$	−1.84922	−	3.20294i	−0.0705007	−	0.122111i
$689$	1.49103			0.0568036
$690$		0			0
$691$			39.1077i			1.48773i	0.668332	+	0.743863i	$0.267008\pi$
$691$			39.1077i			1.48773i	−0.668332	+	0.743863i	$0.732992\pi$
$692$	−13.2286			−0.502876
$693$		0			0
$694$	19.3689			0.735234
$695$		−	3.19519i		−	0.121200i
$696$		0			0
$697$	−2.10913			−0.0798889
$698$	−9.92710	−	17.1942i	−0.375746	−	0.650812i
$699$		0			0
$700$	−2.21519	−	1.44669i	−0.0837265	−	0.0546798i
$701$			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
$704$	−2.74924	−	1.58727i	−0.103616	−	0.0598226i
$705$		0			0
$706$	−9.95408	−	5.74699i	−0.374627	−	0.216291i
$707$	37.4792	+	24.4768i	1.40955	+	0.920544i
$708$		0			0
$709$	−9.17097			−0.344423			−0.172211	−	0.985060i	$-0.555091\pi$
$709$	−9.17097			−0.344423			−0.172211	+	0.985060i	$0.555091\pi$
$710$	−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
$716$	−3.52462	+	2.03494i	−0.131721	+	0.0760492i
$717$		0			0
$718$	11.0732	−	19.1794i	0.413249	−	0.715768i
$719$	16.5618	−	28.6858i	0.617650	−	1.06980i	−0.372263	−	0.928127i	$-0.621418\pi$
$719$	16.5618	−	28.6858i	0.617650	−	1.06980i	0.989913	−	0.141674i	$-0.0452485\pi$
$720$		0			0
$721$	−6.34710	−	12.5366i	−0.236378	−	0.466889i
$722$	−14.4777	+	8.35868i	−0.538802	+	0.311078i
$723$		0			0
$724$			21.7339i			0.807735i
$725$			7.90616i			0.293628i
$726$		0			0
$727$	21.5870	−	12.4633i	0.800617	−	0.462236i	−0.0430699	−	0.999072i	$-0.513714\pi$
$727$	21.5870	−	12.4633i	0.800617	−	0.462236i	0.843687	+	0.536836i	$0.180380\pi$
$728$	−4.66559	−	3.04699i	−0.172918	−	0.112929i
$729$		0			0
$730$	2.93961	−	5.09156i	0.108800	−	0.188447i
$731$	−0.332937	+	0.576665i	−0.0123141	+	0.0213287i
$732$		0			0
$733$	−12.7522	+	7.36247i	−0.471012	+	0.271939i	−0.716663	−	0.697419i	$-0.754332\pi$
$733$	−12.7522	+	7.36247i	−0.471012	+	0.271939i	0.245651	+	0.969358i	$0.420998\pi$
$734$	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	0.999941	−	0.0108315i	$-0.00344786\pi$
$739$	13.3365	+	23.0995i	0.490590	+	0.849727i	−0.509351	+	0.860559i	$0.670115\pi$
$740$	−8.54194			−0.314008
$741$		0			0
$742$	1.67105	−	0.846025i	0.0613461	−	0.0310586i
$743$	−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
$745$	−5.37389	−	3.10262i	−0.196884	−	0.113671i
$746$	23.6347	−	13.6455i	0.865329	−	0.499598i
$747$		0			0
$748$			0.571552i			0.0208980i
$749$	11.8162	−	18.0931i	0.431753	−	0.661106i
$750$		0			0
$751$	7.96028	+	13.7876i	0.290475	+	0.503117i	0.973922	−	0.226883i	$-0.0728535\pi$
$751$	7.96028	+	13.7876i	0.290475	+	0.503117i	−0.683447	+	0.730000i	$0.739520\pi$
$752$	2.08361			0.0759815
$753$		0			0
$754$			16.6518i			0.606422i
$755$	−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	$0.666066\pi$
$758$		−	19.6022i		−	0.711983i
$759$		0			0
$760$	−5.97640			−0.216787
$761$	0.773619	+	1.33995i	0.0280437	+	0.0485731i	0.879707	−	0.475517i	$-0.157739\pi$
$761$	0.773619	+	1.33995i	0.0280437	+	0.0485731i	−0.851663	+	0.524090i	$0.824406\pi$
$762$		0			0
$763$	−2.86480	+	1.45040i	−0.103713	+	0.0525080i
$764$		−	7.77914i		−	0.281439i
$765$		0			0
$766$	−3.43949	+	1.98579i	−0.124274	+	0.0717495i
$767$	21.4745	+	12.3983i	0.775401	+	0.447678i
$768$		0			0
$769$	−2.38768	−	1.37853i	−0.0861019	−	0.0497110i	0.456331	−	0.889810i	$-0.349163\pi$
$769$	−2.38768	−	1.37853i	−0.0861019	−	0.0497110i	−0.542433	+	0.840099i	$0.682497\pi$
$770$	−0.461181	+	8.38638i	−0.0166198	+	0.302224i
$771$		0			0
$772$	−8.29363			−0.298494
$773$	0.745114	+	1.29057i	0.0267999	+	0.0464187i	0.879114	−	0.476611i	$-0.158135\pi$
$773$	0.745114	+	1.29057i	0.0267999	+	0.0464187i	−0.852314	+	0.523030i	$0.824802\pi$
$774$		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
$779$	−60.6315	+	35.0056i	−2.17235	+	1.25421i
$780$		0			0
$781$	−16.1718	+	28.0105i	−0.578674	+	1.00229i
$782$	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
$787$			22.4371i			0.799796i	0.916560	+	0.399898i	$0.130954\pi$
$787$			22.4371i			0.799796i	−0.916560	+	0.399898i	$0.869046\pi$
$788$			13.3008i			0.473822i
$789$		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
$794$	17.6664	−	30.5990i	0.626956	−	1.08592i
$795$		0			0
$796$	16.1833	−	9.34343i	0.573602	−	0.331169i
$797$	−16.4080	+	28.4195i	−0.581202	+	1.00667i	0.414135	+	0.910216i	$0.364084\pi$
$797$	−16.4080	+	28.4195i	−0.581202	+	1.00667i	−0.995337	+	0.0964565i	$0.969249\pi$
$798$		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
$803$	−18.6638			−0.658633
$804$		0			0
$805$	1.14155	−	1.74796i	0.0402344	−	0.0616074i
$806$	−17.6986	−	10.2183i	−0.623407	−	0.359924i
$807$		0			0
$808$	14.6524	+	8.45957i	0.515470	+	0.297607i
$809$	−9.17296	+	5.29601i	−0.322504	+	0.186198i	−0.652508	−	0.757782i	$-0.726283\pi$
$809$	−9.17296	+	5.29601i	−0.322504	+	0.186198i	0.330004	+	0.943980i	$0.392950\pi$
$810$		0			0
$811$			23.0365i			0.808921i	0.914555	+	0.404461i	$0.132541\pi$
$811$			23.0365i			0.808921i	−0.914555	+	0.404461i	$0.867459\pi$
$812$	9.44841	+	18.6623i	0.331574	+	0.654917i
$813$		0			0
$814$	13.5584	+	23.4838i	0.475221	+	0.823107i
$815$	19.8912			0.696758
$816$		0			0
$817$			22.1033i			0.773297i
$818$	1.39035			0.0486124
$819$		0			0
$820$	−11.7146			−0.409092
$821$		−	2.69452i		−	0.0940392i	−0.998894	−	0.0470196i	$-0.985028\pi$
$821$		−	2.69452i		−	0.0940392i	0.998894	−	0.0470196i	$-0.0149723\pi$
$822$		0			0
$823$	−2.08107			−0.0725417			−0.0362708	−	0.999342i	$-0.511548\pi$
$823$	−2.08107			−0.0725417			−0.0362708	+	0.999342i	$0.511548\pi$
$824$	−2.65554	−	4.59953i	−0.0925101	−	0.160232i
$825$		0			0
$826$	31.1023	+	1.71037i	1.08219	+	0.0595112i
$827$		−	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	−0.722234	−	0.691648i	$-0.756885\pi$
$829$	−13.9461	+	8.05176i	−0.484367	+	0.279649i	0.237868	+	0.971298i	$0.423551\pi$
$830$	−7.64657	−	4.41475i	−0.265416	−	0.153238i
$831$		0			0
$832$	−1.82400	−	1.05309i	−0.0632359	−	0.0365093i
$833$	0.506669	+	1.15396i	0.0175550	+	0.0399825i
$834$		0			0
$835$	14.2766			0.494063
$836$	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	0.654685	−	0.755902i	$-0.272801\pi$
$839$	−9.48006	−	16.4199i	−0.327288	−	0.566879i	−0.981973	+	0.189023i	$0.939468\pi$
$840$		0			0
$841$	16.7537	−	29.0183i	0.577714	−	1.00063i
$842$	29.7576	−	17.1806i	1.02552	−	0.592082i
$843$		0			0
$844$	12.1577	−	21.0578i	0.418485	−	0.724838i
$845$	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
$850$			0.180042i			0.00617540i
$851$		−	6.74025i		−	0.231053i
$852$		0			0
$853$	19.4322	−	11.2192i	0.665347	−	0.384138i	−0.128964	−	0.991649i	$-0.541165\pi$
$853$	19.4322	−	11.2192i	0.665347	−	0.384138i	0.794311	+	0.607511i	$0.207832\pi$
$854$	−0.420722	+	7.65065i	−0.0143968	+	0.261800i
$855$		0			0
$856$	4.08385	−	7.07344i	0.139583	−	0.241765i
$857$	17.5728	−	30.4371i	0.600277	−	1.03971i	−0.392502	−	0.919751i	$-0.628390\pi$
$857$	17.5728	−	30.4371i	0.600277	−	1.03971i	0.992779	−	0.119959i	$-0.0382762\pi$
$858$		0			0
$859$	−28.1881	+	16.2744i	−0.961764	+	0.555275i	−0.896716	−	0.442607i	$-0.854054\pi$
$859$	−28.1881	+	16.2744i	−0.961764	+	0.555275i	−0.0650488	+	0.997882i	$0.520720\pi$
$860$	−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	$-0.264577\pi$
$863$	10.9055	+	6.29628i	0.371227	+	0.214328i	−0.302768	+	0.953064i	$0.597911\pi$
$864$		0			0
$865$	6.61430	+	11.4563i	0.224893	+	0.389526i
$866$	11.9782			0.407035
$867$		0			0
$868$	−25.6334	−	1.40963i	−0.870056	−	0.0478459i
$869$	30.2563	+	17.4685i	1.02637	+	0.592578i
$870$		0			0
$871$	18.1615	+	10.4856i	0.615380	+	0.355290i
$872$	−1.05106	+	0.606828i	−0.0355933	+	0.0205498i
$873$		0			0
$874$		−	4.71584i		−	0.159516i
$875$	−0.145275	+	2.64176i	−0.00491119	+	0.0893078i
$876$		0			0
$877$	13.6134	+	23.5791i	0.459691	+	0.796209i	0.998944	−	0.0459350i	$-0.0146267\pi$
$877$	13.6134	+	23.5791i	0.459691	+	0.796209i	−0.539253	+	0.842144i	$0.681293\pi$
$878$	−10.8588			−0.366468
$879$		0			0
$880$			3.17454i			0.107014i
$881$	−8.99478			−0.303042			−0.151521	−	0.988454i	$-0.548417\pi$
$881$	−8.99478			−0.303042			−0.151521	+	0.988454i	$0.548417\pi$
$882$		0			0
$883$	−15.9491			−0.536730			−0.268365	−	0.963317i	$-0.586483\pi$
$883$	−15.9491			−0.536730			−0.268365	+	0.963317i	$0.586483\pi$
$884$			0.379201i			0.0127539i
$885$		0			0
$886$	−2.11680			−0.0711154
$887$	14.3532	+	24.8605i	0.481934	+	0.834734i	0.999785	−	0.0207370i	$-0.00660127\pi$
$887$	14.3532	+	24.8605i	0.481934	+	0.834734i	−0.517851	+	0.855471i	$0.673268\pi$
$888$		0			0
$889$	−2.19396	+	39.8961i	−0.0735829	+	1.33807i
$890$			5.82271i			0.195178i
$891$		0			0
$892$	−14.5348	+	8.39165i	−0.486660	+	0.280973i
$893$	−10.7842	−	6.22624i	−0.360879	−	0.208353i
$894$		0			0
$895$	3.52462	+	2.03494i	0.117815	+	0.0680205i
$896$	−2.64176	−	0.145275i	−0.0882550	−	0.00485329i
$897$		0			0
$898$	12.2537			0.408913
$899$	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
$905$	18.8221	−	10.8670i	0.625669	−	0.361230i
$906$		0			0
$907$	10.4645	−	18.1251i	0.347469	−	0.601834i	−0.638330	−	0.769763i	$-0.720375\pi$
$907$	10.4645	−	18.1251i	0.347469	−	0.601834i	0.985799	+	0.167929i	$0.0537079\pi$
$908$	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
$913$			28.0296i			0.927645i
$914$		−	33.1134i		−	1.09529i
$915$		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	−0.966694	−	0.255935i	$-0.917617\pi$
$919$	−7.93346	+	13.7412i	−0.261701	+	0.453279i	0.704993	+	0.709214i	$0.250950\pi$
$920$	0.394538	−	0.683360i	0.0130075	−	0.0225297i
$921$		0			0
$922$	−24.4604	+	14.1222i	−0.805560	+	0.465091i
$923$	−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
$929$	−48.0576			−1.57672			−0.788359	−	0.615216i	$-0.789069\pi$
$929$	−48.0576			−1.57672			−0.788359	+	0.615216i	$0.789069\pi$
$930$		0			0
$931$	33.7179	+	24.7640i	1.10506	+	0.811606i
$932$	−6.79700	−	3.92425i	−0.222643	−	0.128543i
$933$		0			0
$934$	−1.42814	−	0.824539i	−0.0467303	−	0.0269797i
$935$	0.494979	−	0.285776i	0.0161875	−	0.00934588i
$936$		0			0
$937$		−	8.04349i		−	0.262769i	−0.991331	−	0.131385i	$-0.958058\pi$
$937$		−	8.04349i		−	0.262769i	0.991331	−	0.131385i	$-0.0419423\pi$
$938$	26.3039	+	1.44650i	0.858853	+	0.0472298i
$939$		0			0
$940$	−1.04181	−	1.80446i	−0.0339799	−	0.0588550i
$941$	33.2880			1.08516			0.542579	−	0.840004i	$-0.317448\pi$
$941$	33.2880			1.08516			0.542579	+	0.840004i	$0.317448\pi$
$942$		0			0
$943$		−	9.24373i		−	0.301017i
$944$	11.7733			0.383189
$945$		0			0
$946$	11.7408			0.381728
$947$		−	31.2034i		−	1.01397i	−0.861954	−	0.506987i	$-0.830759\pi$
$947$		−	31.2034i		−	1.01397i	0.861954	−	0.506987i	$-0.169241\pi$
$948$		0			0
$949$	−12.3827			−0.401959
$950$	2.98820	+	5.17571i	0.0969500	+	0.167922i
$951$		0			0
$952$	0.215163	+	0.424984i	0.00697347	+	0.0137738i
$953$			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
$956$	−14.3341	−	8.27578i	−0.463597	−	0.267658i
$957$		0			0
$958$	−24.4682	−	14.1267i	−0.790533	−	0.456414i
$959$	−12.6777	+	19.4123i	−0.409384	+	0.626855i
$960$		0			0
$961$	−63.1515			−2.03715
$962$	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	$0.844631\pi$
$968$	−0.798709	+	0.461135i	−0.0256715	+	0.0148214i
$969$		0			0
$970$	−2.19008	+	3.79334i	−0.0703193	+	0.121797i
$971$	4.76329	−	8.25026i	0.152861	−	0.264763i	−0.779417	−	0.626506i	$-0.784485\pi$
$971$	4.76329	−	8.25026i	0.152861	−	0.264763i	0.932278	+	0.361742i	$0.117818\pi$
$972$		0			0
$973$	−4.62245	+	7.07796i	−0.148189	+	0.226909i
$974$	6.42239	−	3.70797i	0.205787	−	0.118811i
$975$		0			0
$976$			2.89604i			0.0927001i
$977$		−	30.7329i		−	0.983231i	−0.870812	−	0.491616i	$-0.836407\pi$
$977$		−	30.7329i		−	0.983231i	0.870812	−	0.491616i	$-0.163593\pi$
$978$		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
$983$	−5.17474	+	8.96291i	−0.165049	+	0.285872i	−0.936673	−	0.350206i	$-0.886111\pi$
$983$	−5.17474	+	8.96291i	−0.165049	+	0.285872i	0.771624	+	0.636079i	$0.219445\pi$
$984$		0			0
$985$	11.5188	−	6.65040i	0.367021	−	0.211899i
$986$	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	0.850574	−	0.525856i	$-0.176255\pi$
$991$	−0.948097	−	1.64215i	−0.0301173	−	0.0521647i	−0.880691	+	0.473691i	$0.842921\pi$
$992$	−9.70317			−0.308076
$993$		0			0
$994$	−1.48013	+	26.9155i	−0.0469468	+	0.853706i
$995$	−16.1833	−	9.34343i	−0.513045	−	0.296207i
$996$		0			0
$997$	−24.8252	−	14.3329i	−0.786223	−	0.453926i	0.0524080	−	0.998626i	$-0.483310\pi$
$997$	−24.8252	−	14.3329i	−0.786223	−	0.453926i	−0.838631	+	0.544700i	$0.816644\pi$
$998$	−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.bk.b.341.4		28
3.2	odd	2		630.2.bk.b.131.1	yes	28
7.3	odd	6		1890.2.t.b.1151.2		28
9.2	odd	6		1890.2.t.b.1601.2		28
9.7	even	3		630.2.t.b.551.11	yes	28
21.17	even	6		630.2.t.b.311.11	✓	28
63.38	even	6	inner	1890.2.bk.b.521.4		28
63.52	odd	6		630.2.bk.b.101.8	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.11	✓	28	21.17	even	6
630.2.t.b.551.11	yes	28	9.7	even	3
630.2.bk.b.101.8	yes	28	63.52	odd	6
630.2.bk.b.131.1	yes	28	3.2	odd	2
1890.2.t.b.1151.2		28	7.3	odd	6
1890.2.t.b.1601.2		28	9.2	odd	6
1890.2.bk.b.341.4		28	1.1	even	1	trivial
1890.2.bk.b.521.4		28	63.38	even	6	inner

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.bk (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.145275 - 2.64176i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.145275 - 2.64176i) q^{7} -1.00000i q^{8} +(-0.866025 + 0.500000i) q^{10} +(2.74924 + 1.58727i) q^{11} +(1.82400 + 1.05309i) q^{13} +(2.64176 + 0.145275i) q^{14} +1.00000 q^{16} +(-0.0900212 - 0.155921i) q^{17} +(-5.17571 - 2.98820i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-1.58727 + 2.74924i) q^{22} +(0.683360 - 0.394538i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-1.05309 + 1.82400i) q^{26} +(-0.145275 + 2.64176i) q^{28} +(6.84694 - 3.95308i) q^{29} +9.70317i q^{31} +1.00000i q^{32} +(0.155921 - 0.0900212i) q^{34} +(2.36047 - 1.19507i) q^{35} +(4.27097 - 7.39754i) q^{37} +(2.98820 - 5.17571i) q^{38} +(0.866025 - 0.500000i) q^{40} +(5.85731 - 10.1452i) q^{41} +(-1.84922 - 3.20294i) q^{43} +(-2.74924 - 1.58727i) q^{44} +(0.394538 + 0.683360i) q^{46} +2.08361 q^{47} +(-6.95779 - 0.767563i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(-1.82400 - 1.05309i) q^{52} +(0.613086 - 0.353965i) q^{53} +3.17454i q^{55} +(-2.64176 - 0.145275i) q^{56} +(3.95308 + 6.84694i) q^{58} +11.7733 q^{59} +2.89604i q^{61} -9.70317 q^{62} -1.00000 q^{64} +2.10618i q^{65} +9.95697 q^{67} +(0.0900212 + 0.155921i) q^{68} +(1.19507 + 2.36047i) q^{70} +10.1885i q^{71} +(-5.09156 + 2.93961i) q^{73} +(7.39754 + 4.27097i) q^{74} +(5.17571 + 2.98820i) q^{76} +(4.59259 - 7.03223i) q^{77} +11.0054 q^{79} +(0.500000 + 0.866025i) q^{80} +(10.1452 + 5.85731i) q^{82} +(4.41475 + 7.64657i) q^{83} +(0.0900212 - 0.155921i) q^{85} +(3.20294 - 1.84922i) q^{86} +(1.58727 - 2.74924i) q^{88} +(2.91136 - 5.04262i) q^{89} +(3.04699 - 4.66559i) q^{91} +(-0.683360 + 0.394538i) q^{92} +2.08361i q^{94} -5.97640i q^{95} +(3.79334 - 2.19008i) q^{97} +(0.767563 - 6.95779i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{4} + 14 q^{5} + 8 q^{7}+O(q^{10}) \) 28 * q - 28 * q^4 + 14 * q^5 + 8 * q^7	\( 28 q - 28 q^{4} + 14 q^{5} + 8 q^{7} + 28 q^{16} - 6 q^{17} - 6 q^{19} - 14 q^{20} - 6 q^{22} - 30 q^{23} - 14 q^{25} + 12 q^{26} - 8 q^{28} + 4 q^{35} + 4 q^{37} + 6 q^{38} + 18 q^{41} + 28 q^{43} - 18 q^{46} - 60 q^{47} - 20 q^{49} - 42 q^{53} + 6 q^{58} + 48 q^{59} - 12 q^{62} - 28 q^{64} + 80 q^{67} + 6 q^{68} + 6 q^{70} + 6 q^{73} + 6 q^{76} + 18 q^{77} - 4 q^{79} + 14 q^{80} + 24 q^{82} - 18 q^{83} + 6 q^{85} + 96 q^{86} + 6 q^{88} + 6 q^{89} + 66 q^{91} + 30 q^{92} + 72 q^{97} - 24 q^{98}+O(q^{100}) \) 28 * q - 28 * q^4 + 14 * q^5 + 8 * q^7 + 28 * q^16 - 6 * q^17 - 6 * q^19 - 14 * q^20 - 6 * q^22 - 30 * q^23 - 14 * q^25 + 12 * q^26 - 8 * q^28 + 4 * q^35 + 4 * q^37 + 6 * q^38 + 18 * q^41 + 28 * q^43 - 18 * q^46 - 60 * q^47 - 20 * q^49 - 42 * q^53 + 6 * q^58 + 48 * q^59 - 12 * q^62 - 28 * q^64 + 80 * q^67 + 6 * q^68 + 6 * q^70 + 6 * q^73 + 6 * q^76 + 18 * q^77 - 4 * q^79 + 14 * q^80 + 24 * q^82 - 18 * q^83 + 6 * q^85 + 96 * q^86 + 6 * q^88 + 6 * q^89 + 66 * q^91 + 30 * q^92 + 72 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more