LMFDB - Embedded newform 1890.2.bi.a.719.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1890,2,Mod(719,1890)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1890.719"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1890, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.bi (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,-48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			719.18
Character	$\chi$	$=$	1890.719
Dual form			1890.2.bi.a.899.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +1.00000 q^{4} +(1.55089 - 1.61082i) q^{5} +(-0.405354 - 2.61451i) q^{7} -1.00000 q^{8} +(-1.55089 + 1.61082i) q^{10} +(-0.922101 - 0.532375i) q^{11} +(2.83827 - 4.91604i) q^{13} +(0.405354 + 2.61451i) q^{14} +1.00000 q^{16} +(-1.18969 + 0.686867i) q^{17} +(-5.87638 - 3.39273i) q^{19} +(1.55089 - 1.61082i) q^{20} +(0.922101 + 0.532375i) q^{22} +(2.24743 + 3.89266i) q^{23} +(-0.189463 - 4.99641i) q^{25} +(-2.83827 + 4.91604i) q^{26} +(-0.405354 - 2.61451i) q^{28} +(-4.67691 + 2.70021i) q^{29} -7.52185i q^{31} -1.00000 q^{32} +(1.18969 - 0.686867i) q^{34} +(-4.84017 - 3.40188i) q^{35} +(7.42263 + 4.28546i) q^{37} +(5.87638 + 3.39273i) q^{38} +(-1.55089 + 1.61082i) q^{40} +(-1.21989 + 2.11292i) q^{41} +(-4.89080 + 2.82370i) q^{43} +(-0.922101 - 0.532375i) q^{44} +(-2.24743 - 3.89266i) q^{46} -8.75012i q^{47} +(-6.67138 + 2.11961i) q^{49} +(0.189463 + 4.99641i) q^{50} +(2.83827 - 4.91604i) q^{52} +(2.29752 + 3.97942i) q^{53} +(-2.28764 + 0.659679i) q^{55} +(0.405354 + 2.61451i) q^{56} +(4.67691 - 2.70021i) q^{58} -9.70296 q^{59} +9.92998i q^{61} +7.52185i q^{62} +1.00000 q^{64} +(-3.51697 - 12.1962i) q^{65} -0.0645415i q^{67} +(-1.18969 + 0.686867i) q^{68} +(4.84017 + 3.40188i) q^{70} +6.07978i q^{71} +(-4.78305 - 8.28448i) q^{73} +(-7.42263 - 4.28546i) q^{74} +(-5.87638 - 3.39273i) q^{76} +(-1.01813 + 2.62665i) q^{77} +7.34722 q^{79} +(1.55089 - 1.61082i) q^{80} +(1.21989 - 2.11292i) q^{82} +(7.57279 - 4.37215i) q^{83} +(-0.738663 + 2.98163i) q^{85} +(4.89080 - 2.82370i) q^{86} +(0.922101 + 0.532375i) q^{88} +(-5.74422 + 9.94928i) q^{89} +(-14.0036 - 5.42798i) q^{91} +(2.24743 + 3.89266i) q^{92} +8.75012i q^{94} +(-14.5787 + 4.20401i) q^{95} +(6.25791 + 10.8390i) q^{97} +(6.67138 - 2.11961i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{2} + 48 q^{4} + 3 q^{7} - 48 q^{8} - 6 q^{11} - 3 q^{14} + 48 q^{16} + 6 q^{22} - 3 q^{23} - 18 q^{25} + 3 q^{28} + 3 q^{29} - 48 q^{32} + 12 q^{35} + 3 q^{41} - 6 q^{44} + 3 q^{46} + 3 q^{49}+ \cdots - 3 q^{98}+O(q^{100}) $ 48 * q - 48 * q^2 + 48 * q^4 + 3 * q^7 - 48 * q^8 - 6 * q^11 - 3 * q^14 + 48 * q^16 + 6 * q^22 - 3 * q^23 - 18 * q^25 + 3 * q^28 + 3 * q^29 - 48 * q^32 + 12 * q^35 + 3 * q^41 - 6 * q^44 + 3 * q^46 + 3 * q^49 + 18 * q^50 - 42 * q^55 - 3 * q^56 - 3 * q^58 + 48 * q^64 - 12 * q^65 - 12 * q^70 - 18 * q^73 + 12 * q^77 - 3 * q^82 - 9 * q^83 - 33 * q^85 + 6 * q^88 + 33 * q^89 - 3 * q^92 - 24 * q^97 - 3 * q^98

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	1.55089	−	1.61082i	0.693580	−	0.720379i
$5$	1.55089	−	1.61082i	0.693580	−	0.720379i
$6$		0			0
$7$	−0.405354	−	2.61451i	−0.153209	−	0.988194i
$7$	−0.405354	−	2.61451i	−0.153209	−	0.988194i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−1.55089	+	1.61082i	−0.490435	+	0.509385i
$11$	−0.922101	−	0.532375i	−0.278024	−	0.160517i	0.354505	−	0.935054i	$-0.384650\pi$
$11$	−0.922101	−	0.532375i	−0.278024	−	0.160517i	−0.632528	+	0.774537i	$0.717983\pi$
$12$		0			0
$13$	2.83827	−	4.91604i	0.787196	−	1.36346i	−0.140483	−	0.990083i	$-0.544866\pi$
$13$	2.83827	−	4.91604i	0.787196	−	1.36346i	0.927679	−	0.373380i	$-0.121801\pi$
$14$	0.405354	+	2.61451i	0.108335	+	0.698759i
$15$		0			0
$16$	1.00000			0.250000
$17$	−1.18969	+	0.686867i	−0.288542	+	0.166590i	−0.637284	−	0.770629i	$-0.719942\pi$
$17$	−1.18969	+	0.686867i	−0.288542	+	0.166590i	0.348742	+	0.937219i	$0.386609\pi$
$18$		0			0
$19$	−5.87638	−	3.39273i	−1.34813	−	0.778345i	−0.360148	−	0.932895i	$-0.617274\pi$
$19$	−5.87638	−	3.39273i	−1.34813	−	0.778345i	−0.987985	+	0.154550i	$0.950607\pi$
$20$	1.55089	−	1.61082i	0.346790	−	0.360190i
$21$		0			0
$22$	0.922101	+	0.532375i	0.196593	+	0.113503i
$23$	2.24743	+	3.89266i	0.468621	+	0.811676i	0.999357	−	0.0358617i	$-0.0114176\pi$
$23$	2.24743	+	3.89266i	0.468621	+	0.811676i	−0.530736	+	0.847537i	$0.678084\pi$
$24$		0			0
$25$	−0.189463	−	4.99641i	−0.0378926	−	0.999282i
$26$	−2.83827	+	4.91604i	−0.556631	+	0.964114i
$27$		0			0
$28$	−0.405354	−	2.61451i	−0.0766046	−	0.494097i
$29$	−4.67691	+	2.70021i	−0.868480	+	0.501417i	−0.866843	−	0.498581i	$-0.833854\pi$
$29$	−4.67691	+	2.70021i	−0.868480	+	0.501417i	−0.00163724	+	0.999999i	$0.500521\pi$
$30$		0			0
$31$		−	7.52185i		−	1.35096i	−0.737376	−	0.675482i	$-0.763936\pi$
$31$		−	7.52185i		−	1.35096i	0.737376	−	0.675482i	$-0.236064\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	1.18969	−	0.686867i	0.204030	−	0.117797i
$35$	−4.84017	−	3.40188i	−0.818137	−	0.575023i
$36$		0			0
$37$	7.42263	+	4.28546i	1.22027	+	0.704525i	0.964976	−	0.262338i	$-0.0844934\pi$
$37$	7.42263	+	4.28546i	1.22027	+	0.704525i	0.255297	+	0.966863i	$0.417827\pi$
$38$	5.87638	+	3.39273i	0.953274	+	0.550373i
$39$		0			0
$40$	−1.55089	+	1.61082i	−0.245218	+	0.254693i
$41$	−1.21989	+	2.11292i	−0.190515	+	0.329982i	−0.945421	−	0.325851i	$-0.894349\pi$
$41$	−1.21989	+	2.11292i	−0.190515	+	0.329982i	0.754906	+	0.655833i	$0.227683\pi$
$42$		0			0
$43$	−4.89080	+	2.82370i	−0.745840	+	0.430611i	−0.824189	−	0.566315i	$-0.808368\pi$
$43$	−4.89080	+	2.82370i	−0.745840	+	0.430611i	0.0783491	+	0.996926i	$0.475035\pi$
$44$	−0.922101	−	0.532375i	−0.139012	−	0.0802586i
$45$		0			0
$46$	−2.24743	−	3.89266i	−0.331365	−	0.573941i
$47$		−	8.75012i		−	1.27634i	−0.769897	−	0.638168i	$-0.779692\pi$
$47$		−	8.75012i		−	1.27634i	0.769897	−	0.638168i	$-0.220308\pi$
$48$		0			0
$49$	−6.67138	+	2.11961i	−0.953054	+	0.302801i
$50$	0.189463	+	4.99641i	0.0267941	+	0.706599i
$51$		0			0
$52$	2.83827	−	4.91604i	0.393598	−	0.681731i
$53$	2.29752	+	3.97942i	0.315589	+	0.546615i	0.979562	−	0.201140i	$-0.0644647\pi$
$53$	2.29752	+	3.97942i	0.315589	+	0.546615i	−0.663974	+	0.747756i	$0.731131\pi$
$54$		0			0
$55$	−2.28764	+	0.659679i	−0.308465	+	0.0889511i
$56$	0.405354	+	2.61451i	0.0541676	+	0.349379i
$57$		0			0
$58$	4.67691	−	2.70021i	0.614108	−	0.354556i
$59$	−9.70296			−1.26322			−0.631609	−	0.775287i	$-0.717605\pi$
$59$	−9.70296			−1.26322			−0.631609	+	0.775287i	$0.717605\pi$
$60$		0			0
$61$			9.92998i			1.27140i	0.771935	+	0.635702i	$0.219289\pi$
$61$			9.92998i			1.27140i	−0.771935	+	0.635702i	$0.780711\pi$
$62$			7.52185i			0.955276i
$63$		0			0
$64$	1.00000			0.125000
$65$	−3.51697	−	12.1962i	−0.436227	−	1.51275i
$66$		0			0
$67$		−	0.0645415i		−	0.00788500i	−0.999992	−	0.00394250i	$-0.998745\pi$
$67$		−	0.0645415i		−	0.00788500i	0.999992	−	0.00394250i	$-0.00125494\pi$
$68$	−1.18969	+	0.686867i	−0.144271	+	0.0832949i
$69$		0			0
$70$	4.84017	+	3.40188i	0.578510	+	0.406603i
$71$			6.07978i			0.721537i	0.932655	+	0.360768i	$0.117486\pi$
$71$			6.07978i			0.721537i	−0.932655	+	0.360768i	$0.882514\pi$
$72$		0			0
$73$	−4.78305	−	8.28448i	−0.559813	−	0.969625i	−0.997512	−	0.0705034i	$-0.977539\pi$
$73$	−4.78305	−	8.28448i	−0.559813	−	0.969625i	0.437698	−	0.899122i	$-0.355794\pi$
$74$	−7.42263	−	4.28546i	−0.862863	−	0.498174i
$75$		0			0
$76$	−5.87638	−	3.39273i	−0.674067	−	0.389173i
$77$	−1.01813	+	2.62665i	−0.116026	+	0.299334i
$78$		0			0
$79$	7.34722			0.826627			0.413314	−	0.910589i	$-0.364371\pi$
$79$	7.34722			0.826627			0.413314	+	0.910589i	$0.364371\pi$
$80$	1.55089	−	1.61082i	0.173395	−	0.180095i
$81$		0			0
$82$	1.21989	−	2.11292i	0.134715	−	0.233332i
$83$	7.57279	−	4.37215i	0.831222	−	0.479906i	−0.0230489	−	0.999734i	$-0.507337\pi$
$83$	7.57279	−	4.37215i	0.831222	−	0.479906i	0.854271	+	0.519828i	$0.174004\pi$
$84$		0			0
$85$	−0.738663	+	2.98163i	−0.0801192	+	0.323403i
$86$	4.89080	−	2.82370i	0.527388	−	0.304488i
$87$		0			0
$88$	0.922101	+	0.532375i	0.0982963	+	0.0567514i
$89$	−5.74422	+	9.94928i	−0.608886	+	1.05462i	0.382538	+	0.923940i	$0.375050\pi$
$89$	−5.74422	+	9.94928i	−0.608886	+	1.05462i	−0.991424	+	0.130682i	$0.958283\pi$
$90$		0			0
$91$	−14.0036	−	5.42798i	−1.46797	−	0.569007i
$92$	2.24743	+	3.89266i	0.234311	+	0.405838i
$93$		0			0
$94$			8.75012i			0.902506i
$95$	−14.5787	+	4.20401i	−1.49574	+	0.431322i
$96$		0			0
$97$	6.25791	+	10.8390i	0.635394	+	1.10054i	0.986431	+	0.164174i	$0.0524957\pi$
$97$	6.25791	+	10.8390i	0.635394	+	1.10054i	−0.351037	+	0.936361i	$0.614171\pi$
$98$	6.67138	−	2.11961i	0.673911	−	0.214113i
$99$		0			0
$100$	−0.189463	−	4.99641i	−0.0189463	−	0.499641i
$101$	4.13794	−	7.16712i	0.411740	−	0.713155i	−0.583340	−	0.812228i	$-0.698254\pi$
$101$	4.13794	−	7.16712i	0.411740	−	0.713155i	0.995080	+	0.0990729i	$0.0315877\pi$
$102$		0			0
$103$	0.0267719	+	0.0463704i	0.00263792	+	0.00456901i	0.867341	−	0.497714i	$-0.165827\pi$
$103$	0.0267719	+	0.0463704i	0.00263792	+	0.00456901i	−0.864703	+	0.502283i	$0.832494\pi$
$104$	−2.83827	+	4.91604i	−0.278316	+	0.482057i
$105$		0			0
$106$	−2.29752	−	3.97942i	−0.223155	−	0.386515i
$107$	4.10444	−	7.10909i	0.396791	−	0.687262i	−0.596537	−	0.802586i	$-0.703457\pi$
$107$	4.10444	−	7.10909i	0.396791	−	0.687262i	0.993328	+	0.115323i	$0.0367904\pi$
$108$		0			0
$109$	6.86529	+	11.8910i	0.657575	+	1.13895i	0.981241	+	0.192783i	$0.0617512\pi$
$109$	6.86529	+	11.8910i	0.657575	+	1.13895i	−0.323666	+	0.946171i	$0.604915\pi$
$110$	2.28764	−	0.659679i	0.218118	−	0.0628979i
$111$		0			0
$112$	−0.405354	−	2.61451i	−0.0383023	−	0.247048i
$113$	−0.256031	+	0.443458i	−0.0240853	+	0.0417170i	−0.877817	−	0.478996i	$-0.841001\pi$
$113$	−0.256031	+	0.443458i	−0.0240853	+	0.0417170i	0.853732	+	0.520713i	$0.174334\pi$
$114$		0			0
$115$	9.75588	+	2.41690i	0.909741	+	0.225377i
$116$	−4.67691	+	2.70021i	−0.434240	+	0.250709i
$117$		0			0
$118$	9.70296			0.893230
$119$	2.27807	+	2.83204i	0.208830	+	0.259612i
$120$		0			0
$121$	−4.93315	−	8.54447i	−0.448468	−	0.776770i
$122$		−	9.92998i		−	0.899018i
$123$		0			0
$124$		−	7.52185i		−	0.675482i
$125$	−8.34214	−	7.44371i	−0.746143	−	0.665785i
$126$		0			0
$127$		−	4.60873i		−	0.408959i	−0.978871	−	0.204480i	$-0.934450\pi$
$127$		−	4.60873i		−	0.408959i	0.978871	−	0.204480i	$-0.0655502\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	3.51697	+	12.1962i	0.308459	+	1.06968i
$131$	−2.65642	−	4.60106i	−0.232093	−	0.401996i	0.726331	−	0.687345i	$-0.241224\pi$
$131$	−2.65642	−	4.60106i	−0.232093	−	0.401996i	−0.958424	+	0.285349i	$0.907891\pi$
$132$		0			0
$133$	−6.48833	+	16.7391i	−0.562609	+	1.45147i
$134$			0.0645415i			0.00557554i
$135$		0			0
$136$	1.18969	−	0.686867i	0.102015	−	0.0588984i
$137$	0.0371922	−	0.0644188i	0.00317754	−	0.00550367i	−0.864432	−	0.502749i	$-0.832322\pi$
$137$	0.0371922	−	0.0644188i	0.00317754	−	0.00550367i	0.867610	+	0.497246i	$0.165655\pi$
$138$		0			0
$139$	−14.6763	−	8.47337i	−1.24483	−	0.718702i	−0.274755	−	0.961514i	$-0.588597\pi$
$139$	−14.6763	−	8.47337i	−1.24483	−	0.718702i	−0.970073	+	0.242812i	$0.921930\pi$
$140$	−4.84017	−	3.40188i	−0.409069	−	0.287512i
$141$		0			0
$142$		−	6.07978i		−	0.510203i
$143$	−5.23435	+	3.02205i	−0.437718	+	0.252717i
$144$		0			0
$145$	−2.90383	+	11.7214i	−0.241150	+	0.973408i
$146$	4.78305	+	8.28448i	0.395848	+	0.685629i
$147$		0			0
$148$	7.42263	+	4.28546i	0.610137	+	0.352263i
$149$	14.4973	−	8.37004i	1.18767	−	0.685700i	0.229892	−	0.973216i	$-0.426163\pi$
$149$	14.4973	−	8.37004i	1.18767	−	0.685700i	0.957776	+	0.287516i	$0.0928295\pi$
$150$		0			0
$151$	3.00497	−	5.20476i	0.244541	−	0.423557i	−0.717462	−	0.696598i	$-0.754696\pi$
$151$	3.00497	−	5.20476i	0.244541	−	0.423557i	0.962002	+	0.273041i	$0.0880294\pi$
$152$	5.87638	+	3.39273i	0.476637	+	0.275187i
$153$		0			0
$154$	1.01813	−	2.62665i	0.0820429	−	0.211661i
$155$	−12.1163	−	11.6656i	−0.973207	−	0.937002i
$156$		0			0
$157$	−9.02952			−0.720634			−0.360317	−	0.932830i	$-0.617332\pi$
$157$	−9.02952			−0.720634			−0.360317	+	0.932830i	$0.617332\pi$
$158$	−7.34722			−0.584514
$159$		0			0
$160$	−1.55089	+	1.61082i	−0.122609	+	0.127346i
$161$	9.26641	−	7.45384i	0.730296	−	0.587445i
$162$		0			0
$163$	8.62716	+	4.98089i	0.675731	+	0.390134i	0.798245	−	0.602333i	$-0.205762\pi$
$163$	8.62716	+	4.98089i	0.675731	+	0.390134i	−0.122514	+	0.992467i	$0.539095\pi$
$164$	−1.21989	+	2.11292i	−0.0952576	+	0.164991i
$165$		0			0
$166$	−7.57279	+	4.37215i	−0.587763	+	0.339345i
$167$	−16.2295	−	9.37008i	−1.25587	−	0.725078i	−0.283603	−	0.958942i	$-0.591530\pi$
$167$	−16.2295	−	9.37008i	−1.25587	−	0.725078i	−0.972269	+	0.233863i	$0.924863\pi$
$168$		0			0
$169$	−9.61160	−	16.6478i	−0.739354	−	1.28060i
$170$	0.738663	−	2.98163i	0.0566528	−	0.228680i
$171$		0			0
$172$	−4.89080	+	2.82370i	−0.372920	+	0.215305i
$173$		−	22.1147i		−	1.68135i	−0.541538	−	0.840676i	$-0.682158\pi$
$173$		−	22.1147i		−	1.68135i	0.541538	−	0.840676i	$-0.317842\pi$
$174$		0			0
$175$	−12.9864	+	2.52067i	−0.981679	+	0.190544i
$176$	−0.922101	−	0.532375i	−0.0695060	−	0.0401293i
$177$		0			0
$178$	5.74422	−	9.94928i	0.430547	−	0.745730i
$179$	−9.16532	+	5.29160i	−0.685048	+	0.395513i	−0.801754	−	0.597654i	$-0.796100\pi$
$179$	−9.16532	+	5.29160i	−0.685048	+	0.395513i	0.116706	+	0.993166i	$0.462766\pi$
$180$		0			0
$181$		−	6.54895i		−	0.486780i	−0.969929	−	0.243390i	$-0.921741\pi$
$181$		−	6.54895i		−	0.486780i	0.969929	−	0.243390i	$-0.0782594\pi$
$182$	14.0036	+	5.42798i	1.03801	+	0.402349i
$183$		0			0
$184$	−2.24743	−	3.89266i	−0.165683	−	0.286971i
$185$	18.4148	−	5.31021i	1.35388	−	0.390415i
$186$		0			0
$187$	1.46268			0.106962
$188$		−	8.75012i		−	0.638168i
$189$		0			0
$190$	14.5787	−	4.20401i	1.05765	−	0.304991i
$191$			6.43820i			0.465852i	0.972495	+	0.232926i	$0.0748299\pi$
$191$			6.43820i			0.465852i	−0.972495	+	0.232926i	$0.925170\pi$
$192$		0			0
$193$		−	23.2031i		−	1.67019i	−0.550103	−	0.835097i	$-0.685411\pi$
$193$		−	23.2031i		−	1.67019i	0.550103	−	0.835097i	$-0.314589\pi$
$194$	−6.25791	−	10.8390i	−0.449292	−	0.778196i
$195$		0			0
$196$	−6.67138	+	2.11961i	−0.476527	+	0.151400i
$197$	2.32392			0.165572			0.0827861	−	0.996567i	$-0.473618\pi$
$197$	2.32392			0.165572			0.0827861	+	0.996567i	$0.473618\pi$
$198$		0			0
$199$	−10.1070	+	5.83527i	−0.716465	+	0.413651i	−0.813450	−	0.581635i	$-0.802413\pi$
$199$	−10.1070	+	5.83527i	−0.716465	+	0.413651i	0.0969854	+	0.995286i	$0.469080\pi$
$200$	0.189463	+	4.99641i	0.0133970	+	0.353299i
$201$		0			0
$202$	−4.13794	+	7.16712i	−0.291144	+	0.504277i
$203$	8.95555	+	11.1333i	0.628557	+	0.781405i
$204$		0			0
$205$	1.51160	+	5.24193i	0.105575	+	0.366112i
$206$	−0.0267719	−	0.0463704i	−0.00186529	−	0.00323078i
$207$		0			0
$208$	2.83827	−	4.91604i	0.196799	−	0.340866i
$209$	3.61241	+	6.25688i	0.249876	+	0.432797i
$210$		0			0
$211$	7.82600	−	13.5550i	0.538764	−	0.933167i	−0.460207	−	0.887812i	$-0.652225\pi$
$211$	7.82600	−	13.5550i	0.538764	−	0.933167i	0.998971	−	0.0453551i	$-0.0144419\pi$
$212$	2.29752	+	3.97942i	0.157794	+	0.273308i
$213$		0			0
$214$	−4.10444	+	7.10909i	−0.280574	+	0.485968i
$215$	−3.03663	+	12.2574i	−0.207097	+	0.835951i
$216$		0			0
$217$	−19.6660	+	3.04901i	−1.33501	+	0.206980i
$218$	−6.86529	−	11.8910i	−0.464976	−	0.805362i
$219$		0			0
$220$	−2.28764	+	0.659679i	−0.154233	+	0.0444755i
$221$			7.79807i			0.524555i
$222$		0			0
$223$	−6.52152	−	11.2956i	−0.436714	−	0.756410i	0.560720	−	0.828005i	$-0.310524\pi$
$223$	−6.52152	−	11.2956i	−0.436714	−	0.756410i	−0.997434	+	0.0715953i	$0.977191\pi$
$224$	0.405354	+	2.61451i	0.0270838	+	0.174690i
$225$		0			0
$226$	0.256031	−	0.443458i	0.0170309	−	0.0294984i
$227$	−24.8272	−	14.3340i	−1.64784	−	0.951380i	−0.977929	−	0.208936i	$-0.933000\pi$
$227$	−24.8272	−	14.3340i	−1.64784	−	0.951380i	−0.669909	−	0.742444i	$-0.733667\pi$
$228$		0			0
$229$	3.57358	−	2.06321i	0.236149	−	0.136341i	−0.377257	−	0.926109i	$-0.623133\pi$
$229$	3.57358	−	2.06321i	0.236149	−	0.136341i	0.613405	+	0.789768i	$0.289799\pi$
$230$	−9.75588	−	2.41690i	−0.643284	−	0.159366i
$231$		0			0
$232$	4.67691	−	2.70021i	0.307054	−	0.177278i
$233$	−0.859394	+	1.48851i	−0.0563008	+	0.0975158i	−0.892802	−	0.450449i	$-0.851264\pi$
$233$	−0.859394	+	1.48851i	−0.0563008	+	0.0975158i	0.836501	+	0.547965i	$0.184597\pi$
$234$		0			0
$235$	−14.0948	−	13.5705i	−0.919447	−	0.885242i
$236$	−9.70296			−0.631609
$237$		0			0
$238$	−2.27807	−	2.83204i	−0.147665	−	0.183574i
$239$	−7.92591	−	4.57603i	−0.512684	−	0.295999i	0.221252	−	0.975217i	$-0.428986\pi$
$239$	−7.92591	−	4.57603i	−0.512684	−	0.295999i	−0.733936	+	0.679218i	$0.762319\pi$
$240$		0			0
$241$	−0.696421	−	0.402079i	−0.0448605	−	0.0259002i	0.477402	−	0.878685i	$-0.341579\pi$
$241$	−0.696421	−	0.402079i	−0.0448605	−	0.0259002i	−0.522262	+	0.852785i	$0.674912\pi$
$242$	4.93315	+	8.54447i	0.317115	+	0.549259i
$243$		0			0
$244$			9.92998i			0.635702i
$245$	−6.93229	+	14.0336i	−0.442888	+	0.896577i
$246$		0			0
$247$	−33.3575	+	19.2590i	−2.12249	+	1.22542i
$248$			7.52185i			0.477638i
$249$		0			0
$250$	8.34214	+	7.44371i	0.527603	+	0.470781i
$251$	19.6454			1.24001			0.620004	−	0.784599i	$-0.287131\pi$
$251$	19.6454			1.24001			0.620004	+	0.784599i	$0.287131\pi$
$252$		0			0
$253$		−	4.78590i		−	0.300887i
$254$			4.60873i			0.289178i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−14.3279	+	8.27221i	−0.893749	+	0.516006i	−0.875167	−	0.483821i	$-0.839248\pi$
$257$	−14.3279	+	8.27221i	−0.893749	+	0.516006i	−0.0185820	+	0.999827i	$0.505915\pi$
$258$		0			0
$259$	8.19560	−	21.1437i	0.509250	−	1.31381i
$260$	−3.51697	−	12.1962i	−0.218113	−	0.756375i
$261$		0			0
$262$	2.65642	+	4.60106i	0.164114	+	0.284254i
$263$	−1.01677	+	1.76111i	−0.0626970	+	0.108594i	−0.895670	−	0.444719i	$-0.853304\pi$
$263$	−1.01677	+	1.76111i	−0.0626970	+	0.108594i	0.832973	+	0.553313i	$0.186637\pi$
$264$		0			0
$265$	9.97332	+	2.47077i	0.612656	+	0.151778i
$266$	6.48833	−	16.7391i	0.397825	−	1.02634i
$267$		0			0
$268$		−	0.0645415i		−	0.00394250i
$269$	−11.6388	−	20.1590i	−0.709631	−	1.22912i	−0.964994	−	0.262272i	$-0.915528\pi$
$269$	−11.6388	−	20.1590i	−0.709631	−	1.22912i	0.255363	−	0.966845i	$-0.417805\pi$
$270$		0			0
$271$	21.0788	+	12.1699i	1.28045	+	0.739266i	0.976930	−	0.213560i	$-0.0685059\pi$
$271$	21.0788	+	12.1699i	1.28045	+	0.739266i	0.303517	+	0.952826i	$0.401839\pi$
$272$	−1.18969	+	0.686867i	−0.0721355	+	0.0416474i
$273$		0			0
$274$	−0.0371922	+	0.0644188i	−0.00224686	+	0.00389168i
$275$	−2.48526	+	4.70806i	−0.149867	+	0.283907i
$276$		0			0
$277$	−7.08143	−	4.08846i	−0.425482	−	0.245652i	0.271938	−	0.962315i	$-0.412335\pi$
$277$	−7.08143	−	4.08846i	−0.425482	−	0.245652i	−0.697420	+	0.716663i	$0.745669\pi$
$278$	14.6763	+	8.47337i	0.880227	+	0.508199i
$279$		0			0
$280$	4.84017	+	3.40188i	0.289255	+	0.203301i
$281$	4.54162	−	2.62210i	0.270930	−	0.156422i	−0.358380	−	0.933576i	$-0.616671\pi$
$281$	4.54162	−	2.62210i	0.270930	−	0.156422i	0.629310	+	0.777154i	$0.283337\pi$
$282$		0			0
$283$	16.8827			1.00357			0.501785	−	0.864992i	$-0.332677\pi$
$283$	16.8827			1.00357			0.501785	+	0.864992i	$0.332677\pi$
$284$			6.07978i			0.360768i
$285$		0			0
$286$	5.23435	−	3.02205i	0.309514	−	0.178698i
$287$	6.01874	+	2.33295i	0.355275	+	0.137710i
$288$		0			0
$289$	−7.55643	+	13.0881i	−0.444496	+	0.769889i
$290$	2.90383	−	11.7214i	0.170519	−	0.688304i
$291$		0			0
$292$	−4.78305	−	8.28448i	−0.279907	−	0.484813i
$293$	25.5501	+	14.7514i	1.49265	+	0.861783i	0.999965	−	0.00842274i	$-0.00268107\pi$
$293$	25.5501	+	14.7514i	1.49265	+	0.861783i	0.492688	+	0.870206i	$0.336014\pi$
$294$		0			0
$295$	−15.0483	+	15.6297i	−0.876143	+	0.909996i
$296$	−7.42263	−	4.28546i	−0.431432	−	0.249087i
$297$		0			0
$298$	−14.4973	+	8.37004i	−0.839808	+	0.484863i
$299$	25.5153			1.47559
$300$		0			0
$301$	9.36512	+	11.6425i	0.539796	+	0.671061i
$302$	−3.00497	+	5.20476i	−0.172917	+	0.299500i
$303$		0			0
$304$	−5.87638	−	3.39273i	−0.337033	−	0.194586i
$305$	15.9954	+	15.4003i	0.915893	+	0.881821i
$306$		0			0
$307$	10.7900			0.615818			0.307909	−	0.951416i	$-0.400371\pi$
$307$	10.7900			0.615818			0.307909	+	0.951416i	$0.400371\pi$
$308$	−1.01813	+	2.62665i	−0.0580131	+	0.149667i
$309$		0			0
$310$	12.1163	+	11.6656i	0.688161	+	0.662561i
$311$	6.78533			0.384761			0.192380	−	0.981320i	$-0.438379\pi$
$311$	6.78533			0.384761			0.192380	+	0.981320i	$0.438379\pi$
$312$		0			0
$313$	22.5896			1.27684			0.638419	−	0.769689i	$-0.279589\pi$
$313$	22.5896			1.27684			0.638419	+	0.769689i	$0.279589\pi$
$314$	9.02952			0.509565
$315$		0			0
$316$	7.34722			0.413314
$317$	27.0432			1.51890			0.759449	−	0.650567i	$-0.225469\pi$
$317$	27.0432			1.51890			0.759449	+	0.650567i	$0.225469\pi$
$318$		0			0
$319$	5.75011			0.321944
$320$	1.55089	−	1.61082i	0.0866975	−	0.0900474i
$321$		0			0
$322$	−9.26641	+	7.45384i	−0.516397	+	0.415386i
$323$	9.32142			0.518657
$324$		0			0
$325$	−25.1003	−	13.2498i	−1.39231	−	0.734965i
$326$	−8.62716	−	4.98089i	−0.477814	−	0.275866i
$327$		0			0
$328$	1.21989	−	2.11292i	0.0673573	−	0.116666i
$329$	−22.8773	+	3.54689i	−1.26127	+	0.195547i
$330$		0			0
$331$	6.03337			0.331624			0.165812	−	0.986157i	$-0.446976\pi$
$331$	6.03337			0.331624			0.165812	+	0.986157i	$0.446976\pi$
$332$	7.57279	−	4.37215i	0.415611	−	0.239953i
$333$		0			0
$334$	16.2295	+	9.37008i	0.888036	+	0.512708i
$335$	−0.103965	−	0.100097i	−0.00568019	−	0.00546888i
$336$		0			0
$337$	14.4392	+	8.33650i	0.786555	+	0.454118i	0.838748	−	0.544519i	$-0.183288\pi$
$337$	14.4392	+	8.33650i	0.786555	+	0.454118i	−0.0521932	+	0.998637i	$0.516621\pi$
$338$	9.61160	+	16.6478i	0.522802	+	0.905520i
$339$		0			0
$340$	−0.738663	+	2.98163i	−0.0400596	+	0.161702i
$341$	−4.00445	+	6.93591i	−0.216853	+	0.375600i
$342$		0			0
$343$	8.24601	+	16.5832i	0.445243	+	0.895410i
$344$	4.89080	−	2.82370i	0.263694	−	0.152244i
$345$		0			0
$346$			22.1147i			1.18890i
$347$	−33.0004			−1.77156			−0.885778	−	0.464108i	$-0.846375\pi$
$347$	−33.0004			−1.77156			−0.885778	+	0.464108i	$0.846375\pi$
$348$		0			0
$349$	−9.69567	+	5.59780i	−0.518998	+	0.299643i	−0.736524	−	0.676411i	$-0.763534\pi$
$349$	−9.69567	+	5.59780i	−0.518998	+	0.299643i	0.217527	+	0.976054i	$0.430201\pi$
$350$	12.9864	−	2.52067i	0.694152	−	0.134735i
$351$		0			0
$352$	0.922101	+	0.532375i	0.0491481	+	0.0283757i
$353$	−12.5080	−	7.22147i	−0.665731	−	0.384360i	0.128726	−	0.991680i	$-0.458911\pi$
$353$	−12.5080	−	7.22147i	−0.665731	−	0.384360i	−0.794457	+	0.607320i	$0.792245\pi$
$354$		0			0
$355$	9.79341	+	9.42908i	0.519780	+	0.500444i
$356$	−5.74422	+	9.94928i	−0.304443	+	0.527311i
$357$		0			0
$358$	9.16532	−	5.29160i	0.484402	−	0.279670i
$359$	18.4344	+	10.6431i	0.972931	+	0.561722i	0.900129	−	0.435624i	$-0.143472\pi$
$359$	18.4344	+	10.6431i	0.972931	+	0.561722i	0.0728028	+	0.997346i	$0.476806\pi$
$360$		0			0
$361$	13.5212	+	23.4194i	0.711643	+	1.23260i
$362$			6.54895i			0.344205i
$363$		0			0
$364$	−14.0036	−	5.42798i	−0.733986	−	0.284503i
$365$	−20.7628	−	5.14373i	−1.08677	−	0.269235i
$366$		0			0
$367$	8.90707	−	15.4275i	0.464945	−	0.805309i	−0.534254	−	0.845324i	$-0.679407\pi$
$367$	8.90707	−	15.4275i	0.464945	−	0.805309i	0.999199	+	0.0400151i	$0.0127406\pi$
$368$	2.24743	+	3.89266i	0.117155	+	0.202919i
$369$		0			0
$370$	−18.4148	+	5.31021i	−0.957340	+	0.276065i
$371$	9.47295	−	7.61997i	0.491811	−	0.395609i
$372$		0			0
$373$	15.5268	−	8.96439i	0.803946	−	0.464159i	−0.0409028	−	0.999163i	$-0.513023\pi$
$373$	15.5268	−	8.96439i	0.803946	−	0.464159i	0.844849	+	0.535004i	$0.179690\pi$
$374$	−1.46268			−0.0756336
$375$		0			0
$376$			8.75012i			0.451253i
$377$			30.6558i			1.57885i
$378$		0			0
$379$	−0.162766			−0.00836075			−0.00418037	−	0.999991i	$-0.501331\pi$
$379$	−0.162766			−0.00836075			−0.00418037	+	0.999991i	$0.501331\pi$
$380$	−14.5787	+	4.20401i	−0.747871	+	0.215661i
$381$		0			0
$382$		−	6.43820i		−	0.329407i
$383$	8.64195	−	4.98943i	0.441583	−	0.254948i	−0.262686	−	0.964881i	$-0.584608\pi$
$383$	8.64195	−	4.98943i	0.441583	−	0.254948i	0.704269	+	0.709933i	$0.251275\pi$
$384$		0			0
$385$	2.65204	+	5.71366i	0.135161	+	0.291195i
$386$			23.2031i			1.18101i
$387$		0			0
$388$	6.25791	+	10.8390i	0.317697	+	0.550268i
$389$	−20.5762	−	11.8797i	−1.04326	−	0.602325i	−0.122503	−	0.992468i	$-0.539092\pi$
$389$	−20.5762	−	11.8797i	−1.04326	−	0.602325i	−0.920754	+	0.390144i	$0.872425\pi$
$390$		0			0
$391$	−5.34748	−	3.08737i	−0.270434	−	0.156135i
$392$	6.67138	−	2.11961i	0.336955	−	0.107056i
$393$		0			0
$394$	−2.32392			−0.117077
$395$	11.3948	−	11.8350i	0.573332	−	0.595485i
$396$		0			0
$397$	10.9098	−	18.8963i	0.547547	−	0.948379i	−0.450895	−	0.892577i	$-0.648895\pi$
$397$	10.9098	−	18.8963i	0.547547	−	0.948379i	0.998442	−	0.0558021i	$-0.0177716\pi$
$398$	10.1070	−	5.83527i	0.506617	−	0.292495i
$399$		0			0
$400$	−0.189463	−	4.99641i	−0.00947314	−	0.249820i
$401$	2.29120	−	1.32282i	0.114417	−	0.0660587i	−0.441699	−	0.897163i	$-0.645624\pi$
$401$	2.29120	−	1.32282i	0.114417	−	0.0660587i	0.556116	+	0.831104i	$0.312291\pi$
$402$		0			0
$403$	−36.9777	−	21.3491i	−1.84199	−	1.06347i
$404$	4.13794	−	7.16712i	0.205870	−	0.356578i
$405$		0			0
$406$	−8.95555	−	11.1333i	−0.444457	−	0.552537i
$407$	−4.56294	−	7.90325i	−0.226177	−	0.391750i
$408$		0			0
$409$		−	17.4968i		−	0.865163i	−0.901595	−	0.432582i	$-0.857603\pi$
$409$		−	17.4968i		−	0.865163i	0.901595	−	0.432582i	$-0.142397\pi$
$410$	−1.51160	−	5.24193i	−0.0746525	−	0.258880i
$411$		0			0
$412$	0.0267719	+	0.0463704i	0.00131896	+	0.00228450i
$413$	3.93313	+	25.3685i	0.193537	+	1.24830i
$414$		0			0
$415$	4.70185	−	18.9791i	0.230805	−	0.931649i
$416$	−2.83827	+	4.91604i	−0.139158	+	0.241028i
$417$		0			0
$418$	−3.61241	−	6.25688i	−0.176689	−	0.306034i
$419$	4.87854	−	8.44988i	0.238332	−	0.412804i	−0.721904	−	0.691994i	$-0.756733\pi$
$419$	4.87854	−	8.44988i	0.238332	−	0.412804i	0.960236	+	0.279190i	$0.0900659\pi$
$420$		0			0
$421$	15.0741	+	26.1091i	0.734667	+	1.27248i	0.954869	+	0.297027i	$0.0959951\pi$
$421$	15.0741	+	26.1091i	0.734667	+	1.27248i	−0.220202	+	0.975454i	$0.570672\pi$
$422$	−7.82600	+	13.5550i	−0.380964	+	0.659849i
$423$		0			0
$424$	−2.29752	−	3.97942i	−0.111577	−	0.193258i
$425$	3.65727	+	5.81404i	0.177404	+	0.282022i
$426$		0			0
$427$	25.9621	−	4.02515i	1.25639	−	0.194791i
$428$	4.10444	−	7.10909i	0.198395	−	0.343631i
$429$		0			0
$430$	3.03663	−	12.2574i	0.146439	−	0.591106i
$431$	30.1386	−	17.4005i	1.45172	−	0.838153i	0.453144	−	0.891437i	$-0.350302\pi$
$431$	30.1386	−	17.4005i	1.45172	−	0.838153i	0.998579	+	0.0532842i	$0.0169689\pi$
$432$		0			0
$433$	36.5774			1.75780			0.878899	−	0.477008i	$-0.158279\pi$
$433$	36.5774			1.75780			0.878899	+	0.477008i	$0.158279\pi$
$434$	19.6660	−	3.04901i	0.943998	−	0.146357i
$435$		0			0
$436$	6.86529	+	11.8910i	0.328788	+	0.569477i
$437$		−	30.4997i		−	1.45900i
$438$		0			0
$439$			1.51393i			0.0722559i	0.999347	+	0.0361280i	$0.0115024\pi$
$439$			1.51393i			0.0722559i	−0.999347	+	0.0361280i	$0.988498\pi$
$440$	2.28764	−	0.659679i	0.109059	−	0.0314490i
$441$		0			0
$442$		−	7.79807i		−	0.370916i
$443$	22.5770			1.07267			0.536333	−	0.844006i	$-0.319809\pi$
$443$	22.5770			1.07267			0.536333	+	0.844006i	$0.319809\pi$
$444$		0			0
$445$	7.11780	+	24.6831i	0.337416	+	1.17009i
$446$	6.52152	+	11.2956i	0.308803	+	0.534863i
$447$		0			0
$448$	−0.405354	−	2.61451i	−0.0191512	−	0.123524i
$449$			6.39415i			0.301758i	0.988552	+	0.150879i	$0.0482105\pi$
$449$			6.39415i			0.301758i	−0.988552	+	0.150879i	$0.951790\pi$
$450$		0			0
$451$	2.24973	−	1.29888i	0.105936	−	0.0611619i
$452$	−0.256031	+	0.443458i	−0.0120427	+	0.0208585i
$453$		0			0
$454$	24.8272	+	14.3340i	1.16520	+	0.672727i
$455$	−30.4615	+	14.1389i	−1.42806	+	0.662844i
$456$		0			0
$457$			1.55320i			0.0726557i	0.999340	+	0.0363278i	$0.0115661\pi$
$457$			1.55320i			0.0726557i	−0.999340	+	0.0363278i	$0.988434\pi$
$458$	−3.57358	+	2.06321i	−0.166982	+	0.0964073i
$459$		0			0
$460$	9.75588	+	2.41690i	0.454870	+	0.112689i
$461$	7.34634	+	12.7242i	0.342153	+	0.592626i	0.984832	−	0.173509i	$-0.0555105\pi$
$461$	7.34634	+	12.7242i	0.342153	+	0.592626i	−0.642679	+	0.766135i	$0.722177\pi$
$462$		0			0
$463$	1.02891	+	0.594041i	0.0478174	+	0.0276074i	0.523718	−	0.851892i	$-0.324545\pi$
$463$	1.02891	+	0.594041i	0.0478174	+	0.0276074i	−0.475901	+	0.879499i	$0.657878\pi$
$464$	−4.67691	+	2.70021i	−0.217120	+	0.125354i
$465$		0			0
$466$	0.859394	−	1.48851i	0.0398107	−	0.0689541i
$467$	−29.2203	−	16.8704i	−1.35216	−	0.780667i	−0.363604	−	0.931554i	$-0.618454\pi$
$467$	−29.2203	−	16.8704i	−1.35216	−	0.780667i	−0.988551	+	0.150886i	$0.951787\pi$
$468$		0			0
$469$	−0.168745	+	0.0261621i	−0.00779191	+	0.00120806i
$470$	14.0948	+	13.5705i	0.650147	+	0.625961i
$471$		0			0
$472$	9.70296			0.446615
$473$	6.01308			0.276482
$474$		0			0
$475$	−15.8381	+	30.0036i	−0.726702	+	1.37666i
$476$	2.27807	+	2.83204i	0.104415	+	0.129806i
$477$		0			0
$478$	7.92591	+	4.57603i	0.362523	+	0.209303i
$479$	−3.15505	+	5.46471i	−0.144158	+	0.249689i	−0.929058	−	0.369933i	$-0.879381\pi$
$479$	−3.15505	+	5.46471i	−0.144158	+	0.249689i	0.784901	+	0.619622i	$0.212714\pi$
$480$		0			0
$481$	42.1349	−	24.3266i	1.92119	−	1.10920i
$482$	0.696421	+	0.402079i	0.0317211	+	0.0183142i
$483$		0			0
$484$	−4.93315	−	8.54447i	−0.224234	−	0.388385i
$485$	27.1650	+	6.72980i	1.23350	+	0.305585i
$486$		0			0
$487$	−29.8197	+	17.2164i	−1.35126	+	0.780149i	−0.988426	−	0.151705i	$-0.951524\pi$
$487$	−29.8197	+	17.2164i	−1.35126	+	0.780149i	−0.362833	+	0.931854i	$0.618190\pi$
$488$		−	9.92998i		−	0.449509i
$489$		0			0
$490$	6.93229	−	14.0336i	0.313169	−	0.633976i
$491$	−0.145232	−	0.0838499i	−0.00655424	−	0.00378409i	0.496719	−	0.867911i	$-0.334538\pi$
$491$	−0.145232	−	0.0838499i	−0.00655424	−	0.00378409i	−0.503274	+	0.864127i	$0.667871\pi$
$492$		0			0
$493$	3.70938	−	6.42483i	0.167062	−	0.289360i
$494$	33.3575	−	19.2590i	1.50083	−	0.866503i
$495$		0			0
$496$		−	7.52185i		−	0.337741i
$497$	15.8957	−	2.46446i	0.713018	−	0.110546i
$498$		0			0
$499$	1.46377	+	2.53532i	0.0655272	+	0.113496i	0.896928	−	0.442177i	$-0.145794\pi$
$499$	1.46377	+	2.53532i	0.0655272	+	0.113496i	−0.831401	+	0.555674i	$0.812460\pi$
$500$	−8.34214	−	7.44371i	−0.373072	−	0.332893i
$501$		0			0
$502$	−19.6454			−0.876818
$503$		−	14.0715i		−	0.627418i	−0.949519	−	0.313709i	$-0.898428\pi$
$503$		−	14.0715i		−	0.627418i	0.949519	−	0.313709i	$-0.101572\pi$
$504$		0			0
$505$	−5.12742	−	17.7809i	−0.228167	−	0.791240i
$506$			4.78590i			0.212759i
$507$		0			0
$508$		−	4.60873i		−	0.204480i
$509$	13.8664	+	24.0173i	0.614616	+	1.06455i	0.990452	+	0.137860i	$0.0440224\pi$
$509$	13.8664	+	24.0173i	0.614616	+	1.06455i	−0.375836	+	0.926686i	$0.622644\pi$
$510$		0			0
$511$	−19.7211	+	15.8635i	−0.872409	+	0.701760i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	14.3279	−	8.27221i	0.631976	−	0.364871i
$515$	0.116215	+	0.0287908i	0.00512103	+	0.00126867i
$516$		0			0
$517$	−4.65835	+	8.06850i	−0.204874	+	0.354852i
$518$	−8.19560	+	21.1437i	−0.360094	+	0.929001i
$519$		0			0
$520$	3.51697	+	12.1962i	0.154230	+	0.534838i
$521$	−12.4542	−	21.5713i	−0.545627	−	0.945054i	−0.998567	−	0.0535127i	$-0.982958\pi$
$521$	−12.4542	−	21.5713i	−0.545627	−	0.945054i	0.452940	−	0.891541i	$-0.350375\pi$
$522$		0			0
$523$	−9.31147	+	16.1279i	−0.407162	+	0.705226i	−0.994570	−	0.104065i	$-0.966815\pi$
$523$	−9.31147	+	16.1279i	−0.407162	+	0.705226i	0.587408	+	0.809291i	$0.300148\pi$
$524$	−2.65642	−	4.60106i	−0.116046	−	0.200998i
$525$		0			0
$526$	1.01677	−	1.76111i	0.0443335	−	0.0767878i
$527$	5.16651	+	8.94866i	0.225057	+	0.389810i
$528$		0			0
$529$	1.39813	−	2.42164i	0.0607883	−	0.105289i
$530$	−9.97332	−	2.47077i	−0.433213	−	0.107323i
$531$		0			0
$532$	−6.48833	+	16.7391i	−0.281305	+	0.725733i
$533$	6.92478	+	11.9941i	0.299945	+	0.519521i
$534$		0			0
$535$	−5.08591	−	17.6369i	−0.219883	−	0.762512i
$536$			0.0645415i			0.00278777i
$537$		0			0
$538$	11.6388	+	20.1590i	0.501785	+	0.869117i
$539$	7.28011	+	1.59719i	0.313577	+	0.0687956i
$540$		0			0
$541$	−8.55300	+	14.8142i	−0.367722	+	0.636913i	−0.989209	−	0.146511i	$-0.953196\pi$
$541$	−8.55300	+	14.8142i	−0.367722	+	0.636913i	0.621487	+	0.783425i	$0.286529\pi$
$542$	−21.0788	−	12.1699i	−0.905412	−	0.522740i
$543$		0			0
$544$	1.18969	−	0.686867i	0.0510075	−	0.0294492i
$545$	29.8016	+	7.38299i	1.27656	+	0.316252i
$546$		0			0
$547$	−10.4426	+	6.02903i	−0.446493	+	0.257783i	−0.706348	−	0.707865i	$-0.749658\pi$
$547$	−10.4426	+	6.02903i	−0.446493	+	0.257783i	0.259855	+	0.965648i	$0.416325\pi$
$548$	0.0371922	−	0.0644188i	0.00158877	−	0.00275183i
$549$		0			0
$550$	2.48526	−	4.70806i	0.105972	−	0.200752i
$551$	36.6444			1.56110
$552$		0			0
$553$	−2.97822	−	19.2094i	−0.126647	−	0.816868i
$554$	7.08143	+	4.08846i	0.300861	+	0.173702i
$555$		0			0
$556$	−14.6763	−	8.47337i	−0.622414	−	0.359351i
$557$	5.85535	+	10.1418i	0.248099	+	0.429720i	0.962998	−	0.269507i	$-0.0868608\pi$
$557$	5.85535	+	10.1418i	0.248099	+	0.429720i	−0.714899	+	0.699227i	$0.753528\pi$
$558$		0			0
$559$			32.0578i			1.35590i
$560$	−4.84017	−	3.40188i	−0.204534	−	0.143756i
$561$		0			0
$562$	−4.54162	+	2.62210i	−0.191577	+	0.110607i
$563$			28.8230i			1.21474i	0.794417	+	0.607372i	$0.207776\pi$
$563$			28.8230i			1.21474i	−0.794417	+	0.607372i	$0.792224\pi$
$564$		0			0
$565$	0.317254	+	1.10017i	0.0133470	+	0.0462847i
$566$	−16.8827			−0.709632
$567$		0			0
$568$		−	6.07978i		−	0.255102i
$569$			44.5037i			1.86569i	0.360273	+	0.932847i	$0.382684\pi$
$569$			44.5037i			1.86569i	−0.360273	+	0.932847i	$0.617316\pi$
$570$		0			0
$571$	19.7658			0.827175			0.413587	−	0.910464i	$-0.364276\pi$
$571$	19.7658			0.827175			0.413587	+	0.910464i	$0.364276\pi$
$572$	−5.23435	+	3.02205i	−0.218859	+	0.126358i
$573$		0			0
$574$	−6.01874	−	2.33295i	−0.251217	−	0.0973754i
$575$	19.0235	−	11.9666i	0.793336	−	0.499041i
$576$		0			0
$577$	13.6853	+	23.7036i	0.569726	+	0.986795i	0.996593	+	0.0824802i	$0.0262841\pi$
$577$	13.6853	+	23.7036i	0.569726	+	0.986795i	−0.426866	+	0.904315i	$0.640383\pi$
$578$	7.55643	−	13.0881i	0.314306	−	0.544394i
$579$		0			0
$580$	−2.90383	+	11.7214i	−0.120575	+	0.486704i
$581$	−14.5007	−	18.0269i	−0.601591	−	0.747882i
$582$		0			0
$583$		−	4.89257i		−	0.202630i
$584$	4.78305	+	8.28448i	0.197924	+	0.342814i
$585$		0			0
$586$	−25.5501	−	14.7514i	−1.05546	−	0.609373i
$587$	22.8974	−	13.2198i	0.945077	−	0.545641i	0.0535291	−	0.998566i	$-0.482953\pi$
$587$	22.8974	−	13.2198i	0.945077	−	0.545641i	0.891548	+	0.452926i	$0.149620\pi$
$588$		0			0
$589$	−25.5196	+	44.2012i	−1.05152	+	1.82128i
$590$	15.0483	−	15.6297i	0.619527	−	0.643465i
$591$		0			0
$592$	7.42263	+	4.28546i	0.305068	+	0.176131i
$593$	−1.24355	−	0.717964i	−0.0510665	−	0.0294832i	0.474249	−	0.880391i	$-0.342720\pi$
$593$	−1.24355	−	0.717964i	−0.0510665	−	0.0294832i	−0.525316	+	0.850907i	$0.676053\pi$
$594$		0			0
$595$	8.09493	+	0.722631i	0.331860	+	0.0296250i
$596$	14.4973	−	8.37004i	0.593834	−	0.342850i
$597$		0			0
$598$	−25.5153			−1.04340
$599$		−	25.1094i		−	1.02594i	−0.858406	−	0.512972i	$-0.828545\pi$
$599$		−	25.1094i		−	1.02594i	0.858406	−	0.512972i	$-0.171455\pi$
$600$		0			0
$601$	18.4357	−	10.6439i	0.752009	−	0.434173i	−0.0744104	−	0.997228i	$-0.523707\pi$
$601$	18.4357	−	10.6439i	0.752009	−	0.434173i	0.826419	+	0.563055i	$0.190374\pi$
$602$	−9.36512	−	11.6425i	−0.381694	−	0.474511i
$603$		0			0
$604$	3.00497	−	5.20476i	0.122270	−	0.211779i
$605$	−21.4144	−	5.30515i	−0.870618	−	0.215685i
$606$		0			0
$607$	10.6016	+	18.3625i	0.430306	+	0.745311i	0.996899	−	0.0786859i	$-0.0250724\pi$
$607$	10.6016	+	18.3625i	0.430306	+	0.745311i	−0.566594	+	0.823997i	$0.691739\pi$
$608$	5.87638	+	3.39273i	0.238319	+	0.137593i
$609$		0			0
$610$	−15.9954	−	15.4003i	−0.647634	−	0.623542i
$611$	−43.0159	−	24.8353i	−1.74024	−	1.00473i
$612$		0			0
$613$	15.9028	−	9.18146i	0.642306	−	0.370836i	−0.143196	−	0.989694i	$-0.545738\pi$
$613$	15.9028	−	9.18146i	0.642306	−	0.370836i	0.785502	+	0.618859i	$0.212405\pi$
$614$	−10.7900			−0.435449
$615$		0			0
$616$	1.01813	−	2.62665i	0.0410215	−	0.105831i
$617$	4.58356	−	7.93896i	0.184527	−	0.319610i	−0.758890	−	0.651219i	$-0.774258\pi$
$617$	4.58356	−	7.93896i	0.184527	−	0.319610i	0.943417	+	0.331609i	$0.107591\pi$
$618$		0			0
$619$	28.7858	+	16.6195i	1.15700	+	0.667993i	0.950583	−	0.310472i	$-0.100487\pi$
$619$	28.7858	+	16.6195i	1.15700	+	0.667993i	0.206415	+	0.978465i	$0.433820\pi$
$620$	−12.1163	−	11.6656i	−0.486603	−	0.468501i
$621$		0			0
$622$	−6.78533			−0.272067
$623$	28.3410	+	10.9854i	1.13546	+	0.440120i
$624$		0			0
$625$	−24.9282	+	1.89327i	−0.997128	+	0.0757307i
$626$	−22.5896			−0.902860
$627$		0			0
$628$	−9.02952			−0.360317
$629$	−11.7742			−0.469467
$630$		0			0
$631$	−33.5594			−1.33598			−0.667989	−	0.744171i	$-0.732845\pi$
$631$	−33.5594			−1.33598			−0.667989	+	0.744171i	$0.732845\pi$
$632$	−7.34722			−0.292257
$633$		0			0
$634$	−27.0432			−1.07402
$635$	−7.42383	−	7.14765i	−0.294606	−	0.283646i
$636$		0			0
$637$	−8.51514	+	38.8127i	−0.337382	+	1.53782i
$638$	−5.75011			−0.227649
$639$		0			0
$640$	−1.55089	+	1.61082i	−0.0613044	+	0.0636731i
$641$	−24.6820	−	14.2502i	−0.974881	−	0.562848i	−0.0741605	−	0.997246i	$-0.523628\pi$
$641$	−24.6820	−	14.2502i	−0.974881	−	0.562848i	−0.900721	+	0.434398i	$0.856961\pi$
$642$		0			0
$643$	1.28905	−	2.23270i	0.0508352	−	0.0880491i	−0.839488	−	0.543378i	$-0.817145\pi$
$643$	1.28905	−	2.23270i	0.0508352	−	0.0880491i	0.890323	+	0.455329i	$0.150478\pi$
$644$	9.26641	−	7.45384i	0.365148	−	0.293722i
$645$		0			0
$646$	−9.32142			−0.366746
$647$	−6.52143	+	3.76515i	−0.256384	+	0.148023i	−0.622684	−	0.782473i	$-0.713958\pi$
$647$	−6.52143	+	3.76515i	−0.256384	+	0.148023i	0.366300	+	0.930497i	$0.380624\pi$
$648$		0			0
$649$	8.94711	+	5.16562i	0.351205	+	0.202768i
$650$	25.1003	+	13.2498i	0.984514	+	0.519699i
$651$		0			0
$652$	8.62716	+	4.98089i	0.337866	+	0.195067i
$653$	−16.9498	−	29.3579i	−0.663296	−	1.14886i	−0.979744	−	0.200252i	$-0.935824\pi$
$653$	−16.9498	−	29.3579i	−0.663296	−	1.14886i	0.316449	−	0.948610i	$-0.397509\pi$
$654$		0			0
$655$	−11.5313	−	2.85674i	−0.450565	−	0.111622i
$656$	−1.21989	+	2.11292i	−0.0476288	+	0.0824955i
$657$		0			0
$658$	22.8773	−	3.54689i	0.891851	−	0.138272i
$659$	−5.47266	+	3.15964i	−0.213185	+	0.123082i	−0.602791	−	0.797899i	$-0.705945\pi$
$659$	−5.47266	+	3.15964i	−0.213185	+	0.123082i	0.389606	+	0.920982i	$0.372611\pi$
$660$		0			0
$661$			22.2173i			0.864155i	0.901837	+	0.432077i	$0.142219\pi$
$661$			22.2173i			0.864155i	−0.901837	+	0.432077i	$0.857781\pi$
$662$	−6.03337			−0.234493
$663$		0			0
$664$	−7.57279	+	4.37215i	−0.293881	+	0.169672i
$665$	16.9010	+	36.4121i	0.655392	+	1.41200i
$666$		0			0
$667$	−21.0220	−	12.1371i	−0.813976	−	0.469949i
$668$	−16.2295	−	9.37008i	−0.627936	−	0.362539i
$669$		0			0
$670$	0.103965	+	0.100097i	0.00401650	+	0.00386708i
$671$	5.28648	−	9.15645i	0.204082	−	0.353481i
$672$		0			0
$673$	12.4379	−	7.18105i	0.479447	−	0.276809i	−0.240739	−	0.970590i	$-0.577390\pi$
$673$	12.4379	−	7.18105i	0.479447	−	0.276809i	0.720186	+	0.693781i	$0.244056\pi$
$674$	−14.4392	−	8.33650i	−0.556179	−	0.321110i
$675$		0			0
$676$	−9.61160	−	16.6478i	−0.369677	−	0.640299i
$677$			37.5022i			1.44132i	0.693286	+	0.720662i	$0.256162\pi$
$677$			37.5022i			1.44132i	−0.693286	+	0.720662i	$0.743838\pi$
$678$		0			0
$679$	25.8021	−	20.7550i	0.990194	−	0.796505i
$680$	0.738663	−	2.98163i	0.0283264	−	0.114340i
$681$		0			0
$682$	4.00445	−	6.93591i	0.153338	−	0.265590i
$683$	−2.22205	−	3.84871i	−0.0850245	−	0.147267i	0.820377	−	0.571823i	$-0.193764\pi$
$683$	−2.22205	−	3.84871i	−0.0850245	−	0.147267i	−0.905402	+	0.424556i	$0.860430\pi$
$684$		0			0
$685$	−0.0460858	−	0.159816i	−0.00176085	−	0.00610627i
$686$	−8.24601	−	16.5832i	−0.314834	−	0.633150i
$687$		0			0
$688$	−4.89080	+	2.82370i	−0.186460	+	0.107653i
$689$	26.0840			0.993720
$690$		0			0
$691$			41.5004i			1.57875i	0.613912	+	0.789374i	$0.289595\pi$
$691$			41.5004i			1.57875i	−0.613912	+	0.789374i	$0.710405\pi$
$692$		−	22.1147i		−	0.840676i
$693$		0			0
$694$	33.0004			1.25268
$695$	−36.4104	+	10.4996i	−1.38113	+	0.398271i
$696$		0			0
$697$		−	3.35162i		−	0.126952i
$698$	9.69567	−	5.59780i	0.366987	−	0.211880i
$699$		0			0
$700$	−12.9864	+	2.52067i	−0.490839	+	0.0952722i
$701$		−	26.9990i		−	1.01974i	−0.860252	−	0.509869i	$-0.829694\pi$
$701$		−	26.9990i		−	1.01974i	0.860252	−	0.509869i	$-0.170306\pi$
$702$		0			0
$703$	−29.0788	−	50.3659i	−1.09673	−	1.89959i
$704$	−0.922101	−	0.532375i	−0.0347530	−	0.0200646i
$705$		0			0
$706$	12.5080	+	7.22147i	0.470743	+	0.271784i
$707$	−20.4159	−	7.91349i	−0.767818	−	0.297617i
$708$		0			0
$709$	37.9992			1.42709			0.713545	−	0.700610i	$-0.247089\pi$
$709$	37.9992			1.42709			0.713545	+	0.700610i	$0.247089\pi$
$710$	−9.79341	−	9.42908i	−0.367540	−	0.353867i
$711$		0			0
$712$	5.74422	−	9.94928i	0.215274	−	0.372865i
$713$	29.2800	−	16.9048i	1.09654	−	0.633090i
$714$		0			0
$715$	−3.24994	+	13.1185i	−0.121541	+	0.490603i
$716$	−9.16532	+	5.29160i	−0.342524	+	0.197756i
$717$		0			0
$718$	−18.4344	−	10.6431i	−0.687966	−	0.397198i
$719$	−5.43173	+	9.40802i	−0.202569	+	0.350860i	−0.949356	−	0.314204i	$-0.898262\pi$
$719$	−5.43173	+	9.40802i	−0.202569	+	0.350860i	0.746786	+	0.665064i	$0.231596\pi$
$720$		0			0
$721$	0.110384	−	0.0887920i	0.00411091	−	0.00330679i
$722$	−13.5212	−	23.4194i	−0.503207	−	0.871581i
$723$		0			0
$724$		−	6.54895i		−	0.243390i
$725$	14.3775	+	22.8562i	0.533966	+	0.848856i
$726$		0			0
$727$	16.6696	+	28.8726i	0.618242	+	1.07083i	0.989806	+	0.142419i	$0.0454881\pi$
$727$	16.6696	+	28.8726i	0.618242	+	1.07083i	−0.371565	+	0.928407i	$0.621179\pi$
$728$	14.0036	+	5.42798i	0.519006	+	0.201174i
$729$		0			0
$730$	20.7628	+	5.14373i	0.768465	+	0.190378i
$731$	3.87902	−	6.71866i	0.143471	−	0.248499i
$732$		0			0
$733$	0.906200	+	1.56958i	0.0334713	+	0.0579739i	0.882276	−	0.470733i	$-0.156010\pi$
$733$	0.906200	+	1.56958i	0.0334713	+	0.0579739i	−0.848805	+	0.528707i	$0.822677\pi$
$734$	−8.90707	+	15.4275i	−0.328766	+	0.569440i
$735$		0			0
$736$	−2.24743	−	3.89266i	−0.0828413	−	0.143485i
$737$	−0.0343603	+	0.0595138i	−0.00126568	+	0.00219222i
$738$		0			0
$739$	−5.23342	−	9.06456i	−0.192515	−	0.333445i	0.753568	−	0.657370i	$-0.228331\pi$
$739$	−5.23342	−	9.06456i	−0.192515	−	0.333445i	−0.946083	+	0.323924i	$0.894998\pi$
$740$	18.4148	−	5.31021i	0.676941	−	0.195207i
$741$		0			0
$742$	−9.47295	+	7.61997i	−0.347763	+	0.279738i
$743$	8.55060	−	14.8101i	0.313691	−	0.543329i	−0.665467	−	0.746427i	$-0.731768\pi$
$743$	8.55060	−	14.8101i	0.313691	−	0.543329i	0.979158	+	0.203098i	$0.0651010\pi$
$744$		0			0
$745$	9.00121	−	36.3336i	0.329779	−	1.33116i
$746$	−15.5268	+	8.96439i	−0.568476	+	0.328210i
$747$		0			0
$748$	1.46268			0.0534810
$749$	−20.2506	−	7.84942i	−0.739940	−	0.286811i
$750$		0			0
$751$	−3.02573	−	5.24072i	−0.110410	−	0.191237i	0.805525	−	0.592561i	$-0.201883\pi$
$751$	−3.02573	−	5.24072i	−0.110410	−	0.191237i	−0.915936	+	0.401325i	$0.868550\pi$
$752$		−	8.75012i		−	0.319084i
$753$		0			0
$754$		−	30.6558i		−	1.11642i
$755$	−3.72353	−	12.9125i	−0.135513	−	0.469933i
$756$		0			0
$757$		−	29.0415i		−	1.05553i	−0.849390	−	0.527765i	$-0.823030\pi$
$757$		−	29.0415i		−	1.05553i	0.849390	−	0.527765i	$-0.176970\pi$
$758$	0.162766			0.00591194
$759$		0			0
$760$	14.5787	−	4.20401i	0.528825	−	0.152496i
$761$	−15.7946	−	27.3571i	−0.572555	−	0.991694i	−0.996303	−	0.0859137i	$-0.972619\pi$
$761$	−15.7946	−	27.3571i	−0.572555	−	0.991694i	0.423748	−	0.905780i	$-0.360714\pi$
$762$		0			0
$763$	28.3064	−	22.7695i	1.02476	−	0.824310i
$764$			6.43820i			0.232926i
$765$		0			0
$766$	−8.64195	+	4.98943i	−0.312246	+	0.180276i
$767$	−27.5397	+	47.7001i	−0.994400	+	1.72235i
$768$		0			0
$769$	−45.0333	−	26.0000i	−1.62394	−	0.937583i	−0.985851	−	0.167622i	$-0.946391\pi$
$769$	−45.0333	−	26.0000i	−1.62394	−	0.937583i	−0.638090	−	0.769961i	$-0.720275\pi$
$770$	−2.65204	−	5.71366i	−0.0955730	−	0.205906i
$771$		0			0
$772$		−	23.2031i		−	0.835097i
$773$	1.80797	−	1.04383i	0.0650283	−	0.0375441i	−0.467133	−	0.884187i	$-0.654713\pi$
$773$	1.80797	−	1.04383i	0.0650283	−	0.0375441i	0.532162	+	0.846643i	$0.321380\pi$
$774$		0			0
$775$	−37.5822	+	1.42511i	−1.34999	+	0.0511915i
$776$	−6.25791	−	10.8390i	−0.224646	−	0.389098i
$777$		0			0
$778$	20.5762	+	11.8797i	0.737694	+	0.425908i
$779$	14.3371	−	8.27753i	0.513680	−	0.296573i
$780$		0			0
$781$	3.23672	−	5.60617i	0.115819	−	0.200604i
$782$	5.34748	+	3.08737i	0.191226	+	0.110404i
$783$		0			0
$784$	−6.67138	+	2.11961i	−0.238263	+	0.0757002i
$785$	−14.0038	+	14.5449i	−0.499818	+	0.519130i
$786$		0			0
$787$	26.9597			0.961010			0.480505	−	0.876992i	$-0.340453\pi$
$787$	26.9597			0.961010			0.480505	+	0.876992i	$0.340453\pi$
$788$	2.32392			0.0827861
$789$		0			0
$790$	−11.3948	+	11.8350i	−0.405407	+	0.421072i
$791$	1.26321	+	0.489638i	0.0449146	+	0.0174095i
$792$		0			0
$793$	48.8161	+	28.1840i	1.73351	+	1.00084i
$794$	−10.9098	+	18.8963i	−0.387174	+	0.670605i
$795$		0			0
$796$	−10.1070	+	5.83527i	−0.358232	+	0.206826i
$797$	6.03754	+	3.48577i	0.213861	+	0.123472i	0.603104	−	0.797662i	$-0.293930\pi$
$797$	6.03754	+	3.48577i	0.213861	+	0.123472i	−0.389244	+	0.921135i	$0.627264\pi$
$798$		0			0
$799$	6.01017	+	10.4099i	0.212625	+	0.368277i
$800$	0.189463	+	4.99641i	0.00669852	+	0.176650i
$801$		0			0
$802$	−2.29120	+	1.32282i	−0.0809051	+	0.0467106i
$803$			10.1855i			0.359439i
$804$		0			0
$805$	2.36445	−	26.4866i	0.0833358	−	0.933530i
$806$	36.9777	+	21.3491i	1.30248	+	0.751989i
$807$		0			0
$808$	−4.13794	+	7.16712i	−0.145572	+	0.252138i
$809$	−9.53225	+	5.50345i	−0.335136	+	0.193491i	−0.658119	−	0.752914i	$-0.728648\pi$
$809$	−9.53225	+	5.50345i	−0.335136	+	0.193491i	0.322983	+	0.946405i	$0.395314\pi$
$810$		0			0
$811$		−	44.4197i		−	1.55979i	−0.625913	−	0.779893i	$-0.715273\pi$
$811$		−	44.4197i		−	1.55979i	0.625913	−	0.779893i	$-0.284727\pi$
$812$	8.95555	+	11.1333i	0.314278	+	0.390702i
$813$		0			0
$814$	4.56294	+	7.90325i	0.159931	+	0.277009i
$815$	21.4031	−	6.17194i	0.749718	−	0.216194i
$816$		0			0
$817$	38.3202			1.34066
$818$			17.4968i			0.611763i
$819$		0			0
$820$	1.51160	+	5.24193i	0.0527873	+	0.183056i
$821$			5.01695i			0.175093i	0.996160	+	0.0875464i	$0.0279026\pi$
$821$			5.01695i			0.175093i	−0.996160	+	0.0875464i	$0.972097\pi$
$822$		0			0
$823$		−	22.3769i		−	0.780008i	−0.920813	−	0.390004i	$-0.872474\pi$
$823$		−	22.3769i		−	0.780008i	0.920813	−	0.390004i	$-0.127526\pi$
$824$	−0.0267719	−	0.0463704i	−0.000932645	−	0.00161539i
$825$		0			0
$826$	−3.93313	−	25.3685i	−0.136851	−	0.882685i
$827$	−4.65264			−0.161788			−0.0808940	−	0.996723i	$-0.525778\pi$
$827$	−4.65264			−0.161788			−0.0808940	+	0.996723i	$0.525778\pi$
$828$		0			0
$829$	25.1125	−	14.4987i	0.872192	−	0.503561i	0.00411622	−	0.999992i	$-0.498690\pi$
$829$	25.1125	−	14.4987i	0.872192	−	0.503561i	0.868076	+	0.496431i	$0.165356\pi$
$830$	−4.70185	+	18.9791i	−0.163204	+	0.658775i
$831$		0			0
$832$	2.83827	−	4.91604i	0.0983995	−	0.170433i
$833$	6.48098	−	7.10402i	0.224553	−	0.246140i
$834$		0			0
$835$	−40.2636	+	11.6107i	−1.39338	+	0.401804i
$836$	3.61241	+	6.25688i	0.124938	+	0.216399i
$837$		0			0
$838$	−4.87854	+	8.44988i	−0.168526	+	0.291896i
$839$	−24.3540	−	42.1824i	−0.840793	−	1.45630i	−0.889225	−	0.457470i	$-0.848756\pi$
$839$	−24.3540	−	42.1824i	−0.840793	−	1.45630i	0.0484316	−	0.998827i	$-0.484578\pi$
$840$		0			0
$841$	0.0823151	−	0.142574i	0.00283845	−	0.00491634i
$842$	−15.0741	−	26.1091i	−0.519488	−	0.899780i
$843$		0			0
$844$	7.82600	−	13.5550i	0.269382	−	0.466583i
$845$	−41.7231	−	10.3364i	−1.43532	−	0.355583i
$846$		0			0
$847$	−20.3400	+	16.3613i	−0.698890	+	0.562182i
$848$	2.29752	+	3.97942i	0.0788971	+	0.136654i
$849$		0			0
$850$	−3.65727	−	5.81404i	−0.125443	−	0.199420i
$851$			38.5250i			1.32062i
$852$		0			0
$853$	6.96876	+	12.0702i	0.238606	+	0.413277i	0.960314	−	0.278920i	$-0.0899763\pi$
$853$	6.96876	+	12.0702i	0.238606	+	0.413277i	−0.721709	+	0.692197i	$0.756643\pi$
$854$	−25.9621	+	4.02515i	−0.888404	+	0.137738i
$855$		0			0
$856$	−4.10444	+	7.10909i	−0.140287	+	0.242984i
$857$	5.89936	+	3.40600i	0.201518	+	0.116347i	0.597363	−	0.801971i	$-0.296215\pi$
$857$	5.89936	+	3.40600i	0.201518	+	0.116347i	−0.395845	+	0.918317i	$0.629548\pi$
$858$		0			0
$859$	−21.8561	+	12.6186i	−0.745721	+	0.430542i	−0.824146	−	0.566378i	$-0.808344\pi$
$859$	−21.8561	+	12.6186i	−0.745721	+	0.430542i	0.0784245	+	0.996920i	$0.475011\pi$
$860$	−3.03663	+	12.2574i	−0.103548	+	0.417975i
$861$		0			0
$862$	−30.1386	+	17.4005i	−1.02652	+	0.592664i
$863$	−5.87923	+	10.1831i	−0.200131	+	0.346638i	−0.948571	−	0.316566i	$-0.897470\pi$
$863$	−5.87923	+	10.1831i	−0.200131	+	0.346638i	0.748439	+	0.663203i	$0.230804\pi$
$864$		0			0
$865$	−35.6228	−	34.2976i	−1.21121	−	1.16615i
$866$	−36.5774			−1.24295
$867$		0			0
$868$	−19.6660	+	3.04901i	−0.667507	+	0.103490i
$869$	−6.77488	−	3.91148i	−0.229822	−	0.132688i
$870$		0			0
$871$	−0.317288	−	0.183187i	−0.0107509	−	0.00620704i
$872$	−6.86529	−	11.8910i	−0.232488	−	0.402681i
$873$		0			0
$874$			30.4997i			1.03167i
$875$	−16.0802	+	24.8280i	−0.543609	+	0.839339i
$876$		0			0
$877$	−6.11879	+	3.53268i	−0.206617	+	0.119290i	−0.599738	−	0.800196i	$-0.704729\pi$
$877$	−6.11879	+	3.53268i	−0.206617	+	0.119290i	0.393121	+	0.919487i	$0.371395\pi$
$878$		−	1.51393i		−	0.0510927i
$879$		0			0
$880$	−2.28764	+	0.659679i	−0.0771163	+	0.0222378i
$881$	15.3713			0.517872			0.258936	−	0.965895i	$-0.416628\pi$
$881$	15.3713			0.517872			0.258936	+	0.965895i	$0.416628\pi$
$882$		0			0
$883$		−	29.3232i		−	0.986803i	−0.869802	−	0.493401i	$-0.835753\pi$
$883$		−	29.3232i		−	0.986803i	0.869802	−	0.493401i	$-0.164247\pi$
$884$			7.79807i			0.262278i
$885$		0			0
$886$	−22.5770			−0.758490
$887$	33.5481	−	19.3690i	1.12644	−	0.650348i	0.183400	−	0.983038i	$-0.441290\pi$
$887$	33.5481	−	19.3690i	1.12644	−	0.650348i	0.943036	+	0.332691i	$0.107956\pi$
$888$		0			0
$889$	−12.0496	+	1.86817i	−0.404131	+	0.0626563i
$890$	−7.11780	−	24.6831i	−0.238589	−	0.827381i
$891$		0			0
$892$	−6.52152	−	11.2956i	−0.218357	−	0.378205i
$893$	−29.6868	+	51.4190i	−0.993431	+	1.72067i
$894$		0			0
$895$	−5.69063	+	22.9704i	−0.190217	+	0.767814i
$896$	0.405354	+	2.61451i	0.0135419	+	0.0873448i
$897$		0			0
$898$		−	6.39415i		−	0.213375i
$899$	20.3106	+	35.1790i	0.677397	+	1.17329i
$900$		0			0
$901$	−5.46667	−	3.15618i	−0.182121	−	0.105148i
$902$	−2.24973	+	1.29888i	−0.0749077	+	0.0432480i
$903$		0			0
$904$	0.256031	−	0.443458i	0.00851545	−	0.0147492i
$905$	−10.5492	−	10.1567i	−0.350666	−	0.337621i
$906$		0			0
$907$	−34.3857	−	19.8526i	−1.14176	−	0.659194i	−0.194893	−	0.980825i	$-0.562436\pi$
$907$	−34.3857	−	19.8526i	−1.14176	−	0.659194i	−0.946865	+	0.321630i	$0.895769\pi$
$908$	−24.8272	−	14.3340i	−0.823919	−	0.475690i
$909$		0			0
$910$	30.4615	−	14.1389i	1.00979	−	0.468702i
$911$	−27.2064	+	15.7076i	−0.901388	+	0.520417i	−0.877650	−	0.479302i	$-0.840890\pi$
$911$	−27.2064	+	15.7076i	−0.901388	+	0.520417i	−0.0237377	+	0.999718i	$0.507557\pi$
$912$		0			0
$913$	−9.31051			−0.308133
$914$		−	1.55320i		−	0.0513753i
$915$		0			0
$916$	3.57358	−	2.06321i	0.118074	−	0.0681703i
$917$	−10.9527	+	8.81031i	−0.361691	+	0.290942i
$918$		0			0
$919$	15.2764	−	26.4595i	0.503921	−	0.872818i	−0.496068	−	0.868284i	$-0.665223\pi$
$919$	15.2764	−	26.4595i	0.503921	−	0.872818i	0.999990	−	0.00453405i	$-0.00144324\pi$
$920$	−9.75588	−	2.41690i	−0.321642	−	0.0796829i
$921$		0			0
$922$	−7.34634	−	12.7242i	−0.241939	−	0.419050i
$923$	29.8884	+	17.2561i	0.983788	+	0.567991i
$924$		0			0
$925$	20.0056	−	37.8984i	0.657780	−	1.24609i
$926$	−1.02891	−	0.594041i	−0.0338120	−	0.0195214i
$927$		0			0
$928$	4.67691	−	2.70021i	0.153527	−	0.0886389i
$929$	36.6852			1.20360			0.601801	−	0.798646i	$-0.294450\pi$
$929$	36.6852			1.20360			0.601801	+	0.798646i	$0.294450\pi$
$930$		0			0
$931$	46.3948	+	10.1786i	1.52053	+	0.333589i
$932$	−0.859394	+	1.48851i	−0.0281504	+	0.0487579i
$933$		0			0
$934$	29.2203	+	16.8704i	0.956118	+	0.552015i
$935$	2.26847	−	2.35612i	0.0741868	−	0.0770533i
$936$		0			0
$937$	−14.4145			−0.470900			−0.235450	−	0.971887i	$-0.575656\pi$
$937$	−14.4145			−0.470900			−0.235450	+	0.971887i	$0.575656\pi$
$938$	0.168745	−	0.0261621i	0.00550971	−	0.000854224i
$939$		0			0
$940$	−14.0948	−	13.5705i	−0.459723	−	0.442621i
$941$	−5.61702			−0.183110			−0.0915548	−	0.995800i	$-0.529184\pi$
$941$	−5.61702			−0.183110			−0.0915548	+	0.995800i	$0.529184\pi$
$942$		0			0
$943$	−10.9665			−0.357118
$944$	−9.70296			−0.315805
$945$		0			0
$946$	−6.01308			−0.195502
$947$	56.8287			1.84668			0.923342	−	0.383979i	$-0.125446\pi$
$947$	56.8287			1.84668			0.923342	+	0.383979i	$0.125446\pi$
$948$		0			0
$949$	−54.3024			−1.76273
$950$	15.8381	−	30.0036i	0.513856	−	0.973445i
$951$		0			0
$952$	−2.27807	−	2.83204i	−0.0738327	−	0.0917868i
$953$	17.2680			0.559366			0.279683	−	0.960092i	$-0.409771\pi$
$953$	17.2680			0.559366			0.279683	+	0.960092i	$0.409771\pi$
$954$		0			0
$955$	10.3708	+	9.98495i	0.335590	+	0.323105i
$956$	−7.92591	−	4.57603i	−0.256342	−	0.147999i
$957$		0			0
$958$	3.15505	−	5.46471i	0.101935	−	0.176557i
$959$	−0.183500	−	0.0711272i	−0.00592552	−	0.00229682i
$960$		0			0
$961$	−25.5782			−0.825104
$962$	−42.1349	+	24.3266i	−1.35848	+	0.784321i
$963$		0			0
$964$	−0.696421	−	0.402079i	−0.0224302	−	0.0129501i
$965$	−37.3759	−	35.9855i	−1.20317	−	1.15841i
$966$		0			0
$967$	−21.1215	−	12.1945i	−0.679222	−	0.392149i	0.120340	−	0.992733i	$-0.461602\pi$
$967$	−21.1215	−	12.1945i	−0.679222	−	0.392149i	−0.799562	+	0.600584i	$0.794935\pi$
$968$	4.93315	+	8.54447i	0.158558	+	0.274630i
$969$		0			0
$970$	−27.1650	−	6.72980i	−0.872216	−	0.216081i
$971$	−19.8177	+	34.3253i	−0.635980	+	1.10155i	0.350326	+	0.936628i	$0.386071\pi$
$971$	−19.8177	+	34.3253i	−0.635980	+	1.10155i	−0.986307	+	0.164923i	$0.947263\pi$
$972$		0			0
$973$	−16.2047	+	41.8062i	−0.519498	+	1.34024i
$974$	29.8197	−	17.2164i	0.955484	−	0.551649i
$975$		0			0
$976$			9.92998i			0.317851i
$977$	−4.03312			−0.129031			−0.0645155	−	0.997917i	$-0.520550\pi$
$977$	−4.03312			−0.129031			−0.0645155	+	0.997917i	$0.520550\pi$
$978$		0			0
$979$	10.5935	−	6.11616i	0.338570	−	0.195473i
$980$	−6.93229	+	14.0336i	−0.221444	+	0.448288i
$981$		0			0
$982$	0.145232	+	0.0838499i	0.00463455	+	0.00267576i
$983$	11.2271	+	6.48198i	0.358090	+	0.206743i	0.668242	−	0.743944i	$-0.267047\pi$
$983$	11.2271	+	6.48198i	0.358090	+	0.206743i	−0.310153	+	0.950687i	$0.600380\pi$
$984$		0			0
$985$	3.60415	−	3.74340i	0.114838	−	0.119275i
$986$	−3.70938	+	6.42483i	−0.118131	+	0.204608i
$987$		0			0
$988$	−33.3575	+	19.2590i	−1.06124	+	0.612710i
$989$	−21.9834	−	12.6921i	−0.699032	−	0.403587i
$990$		0			0
$991$	5.51935	+	9.55980i	0.175328	+	0.303677i	0.940275	−	0.340417i	$-0.110568\pi$
$991$	5.51935	+	9.55980i	0.175328	+	0.303677i	−0.764947	+	0.644094i	$0.777235\pi$
$992$			7.52185i			0.238819i
$993$		0			0
$994$	−15.8957	+	2.46446i	−0.504180	+	0.0781679i
$995$	−6.27529	+	25.3304i	−0.198940	+	0.803027i
$996$		0			0
$997$	12.2807	−	21.2708i	0.388934	−	0.673653i	−0.603373	−	0.797459i	$-0.706177\pi$
$997$	12.2807	−	21.2708i	0.388934	−	0.673653i	0.992306	+	0.123807i	$0.0395102\pi$
$998$	−1.46377	−	2.53532i	−0.0463347	−	0.0802540i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.bi.a.719.18		48
3.2	odd	2		630.2.bi.b.509.3	yes	48
5.4	even	2		1890.2.bi.b.719.2		48
7.3	odd	6		1890.2.r.b.1529.10		48
9.2	odd	6		1890.2.r.a.89.10		48
9.7	even	3		630.2.r.b.299.14	yes	48
15.14	odd	2		630.2.bi.a.509.22	yes	48
21.17	even	6		630.2.r.a.59.11	✓	48
35.24	odd	6		1890.2.r.a.1529.10		48
45.29	odd	6		1890.2.r.b.89.10		48
45.34	even	6		630.2.r.a.299.11	yes	48
63.38	even	6		1890.2.bi.b.899.2		48
63.52	odd	6		630.2.bi.a.479.22	yes	48
105.59	even	6		630.2.r.b.59.14	yes	48
315.164	even	6	inner	1890.2.bi.a.899.18		48
315.304	odd	6		630.2.bi.b.479.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.11	✓	48	21.17	even	6
630.2.r.a.299.11	yes	48	45.34	even	6
630.2.r.b.59.14	yes	48	105.59	even	6
630.2.r.b.299.14	yes	48	9.7	even	3
630.2.bi.a.479.22	yes	48	63.52	odd	6
630.2.bi.a.509.22	yes	48	15.14	odd	2
630.2.bi.b.479.3	yes	48	315.304	odd	6
630.2.bi.b.509.3	yes	48	3.2	odd	2
1890.2.r.a.89.10		48	9.2	odd	6
1890.2.r.a.1529.10		48	35.24	odd	6
1890.2.r.b.89.10		48	45.29	odd	6
1890.2.r.b.1529.10		48	7.3	odd	6
1890.2.bi.a.719.18		48	1.1	even	1	trivial
1890.2.bi.a.899.18		48	315.164	even	6	inner
1890.2.bi.b.719.2		48	5.4	even	2
1890.2.bi.b.899.2		48	63.38	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.bi (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(1.55089 - 1.61082i) q^{5} +(-0.405354 - 2.61451i) q^{7} -1.00000 q^{8} +(-1.55089 + 1.61082i) q^{10} +(-0.922101 - 0.532375i) q^{11} +(2.83827 - 4.91604i) q^{13} +(0.405354 + 2.61451i) q^{14} +1.00000 q^{16} +(-1.18969 + 0.686867i) q^{17} +(-5.87638 - 3.39273i) q^{19} +(1.55089 - 1.61082i) q^{20} +(0.922101 + 0.532375i) q^{22} +(2.24743 + 3.89266i) q^{23} +(-0.189463 - 4.99641i) q^{25} +(-2.83827 + 4.91604i) q^{26} +(-0.405354 - 2.61451i) q^{28} +(-4.67691 + 2.70021i) q^{29} -7.52185i q^{31} -1.00000 q^{32} +(1.18969 - 0.686867i) q^{34} +(-4.84017 - 3.40188i) q^{35} +(7.42263 + 4.28546i) q^{37} +(5.87638 + 3.39273i) q^{38} +(-1.55089 + 1.61082i) q^{40} +(-1.21989 + 2.11292i) q^{41} +(-4.89080 + 2.82370i) q^{43} +(-0.922101 - 0.532375i) q^{44} +(-2.24743 - 3.89266i) q^{46} -8.75012i q^{47} +(-6.67138 + 2.11961i) q^{49} +(0.189463 + 4.99641i) q^{50} +(2.83827 - 4.91604i) q^{52} +(2.29752 + 3.97942i) q^{53} +(-2.28764 + 0.659679i) q^{55} +(0.405354 + 2.61451i) q^{56} +(4.67691 - 2.70021i) q^{58} -9.70296 q^{59} +9.92998i q^{61} +7.52185i q^{62} +1.00000 q^{64} +(-3.51697 - 12.1962i) q^{65} -0.0645415i q^{67} +(-1.18969 + 0.686867i) q^{68} +(4.84017 + 3.40188i) q^{70} +6.07978i q^{71} +(-4.78305 - 8.28448i) q^{73} +(-7.42263 - 4.28546i) q^{74} +(-5.87638 - 3.39273i) q^{76} +(-1.01813 + 2.62665i) q^{77} +7.34722 q^{79} +(1.55089 - 1.61082i) q^{80} +(1.21989 - 2.11292i) q^{82} +(7.57279 - 4.37215i) q^{83} +(-0.738663 + 2.98163i) q^{85} +(4.89080 - 2.82370i) q^{86} +(0.922101 + 0.532375i) q^{88} +(-5.74422 + 9.94928i) q^{89} +(-14.0036 - 5.42798i) q^{91} +(2.24743 + 3.89266i) q^{92} +8.75012i q^{94} +(-14.5787 + 4.20401i) q^{95} +(6.25791 + 10.8390i) q^{97} +(6.67138 - 2.11961i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{2} + 48 q^{4} + 3 q^{7} - 48 q^{8} - 6 q^{11} - 3 q^{14} + 48 q^{16} + 6 q^{22} - 3 q^{23} - 18 q^{25} + 3 q^{28} + 3 q^{29} - 48 q^{32} + 12 q^{35} + 3 q^{41} - 6 q^{44} + 3 q^{46} + 3 q^{49}+ \cdots - 3 q^{98}+O(q^{100}) \) 48 * q - 48 * q^2 + 48 * q^4 + 3 * q^7 - 48 * q^8 - 6 * q^11 - 3 * q^14 + 48 * q^16 + 6 * q^22 - 3 * q^23 - 18 * q^25 + 3 * q^28 + 3 * q^29 - 48 * q^32 + 12 * q^35 + 3 * q^41 - 6 * q^44 + 3 * q^46 + 3 * q^49 + 18 * q^50 - 42 * q^55 - 3 * q^56 - 3 * q^58 + 48 * q^64 - 12 * q^65 - 12 * q^70 - 18 * q^73 + 12 * q^77 - 3 * q^82 - 9 * q^83 - 33 * q^85 + 6 * q^88 + 33 * q^89 - 3 * q^92 - 24 * q^97 - 3 * q^98

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