LMFDB - Embedded newform 2394.2.by.a.2357.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2394,2,Mod(647,2394)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2394, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 0]))

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

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

chi := DirichletCharacter("2394.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2394.by (of order $6$, degree $2$, 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:	$19.1161862439$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2357.12
Character	$\chi$	$=$	2394.2357
Dual form			2394.2.by.a.647.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.75570 - 3.04097i) q^{5} +(2.64573 + 0.00972055i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.75570 - 3.04097i) q^{5} +(2.64573 + 0.00972055i) q^{7} -1.00000i q^{8} +(-3.04097 + 1.75570i) q^{10} +(2.13849 - 1.23466i) q^{11} -0.595217i q^{13} +(-2.28641 - 1.33128i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.856393 - 1.48332i) q^{17} +(-0.866025 - 0.500000i) q^{19} +3.51141 q^{20} -2.46932 q^{22} +(-3.47984 - 2.00908i) q^{23} +(-3.66500 - 6.34796i) q^{25} +(-0.297608 + 0.515473i) q^{26} +(1.31445 + 2.29613i) q^{28} -8.62608i q^{29} +(-2.78011 + 1.60510i) q^{31} +(0.866025 - 0.500000i) q^{32} +1.71279i q^{34} +(4.67469 - 8.02853i) q^{35} +(-1.06702 + 1.84813i) q^{37} +(0.500000 + 0.866025i) q^{38} +(-3.04097 - 1.75570i) q^{40} +1.84541 q^{41} +0.168078 q^{43} +(2.13849 + 1.23466i) q^{44} +(2.00908 + 3.47984i) q^{46} +(2.33889 - 4.05108i) q^{47} +(6.99981 + 0.0514360i) q^{49} +7.32999i q^{50} +(0.515473 - 0.297608i) q^{52} +(0.675185 - 0.389819i) q^{53} -8.67078i q^{55} +(0.00972055 - 2.64573i) q^{56} +(-4.31304 + 7.47040i) q^{58} +(6.28968 + 10.8940i) q^{59} +(-10.7145 - 6.18602i) q^{61} +3.21019 q^{62} -1.00000 q^{64} +(-1.81004 - 1.04502i) q^{65} +(-1.56133 - 2.70431i) q^{67} +(0.856393 - 1.48332i) q^{68} +(-8.06266 + 4.61557i) q^{70} +8.22648i q^{71} +(1.84116 - 1.06300i) q^{73} +(1.84813 - 1.06702i) q^{74} -1.00000i q^{76} +(5.66988 - 3.24579i) q^{77} +(-2.36502 + 4.09633i) q^{79} +(1.75570 + 3.04097i) q^{80} +(-1.59817 - 0.922706i) q^{82} -3.01650 q^{83} -6.01429 q^{85} +(-0.145560 - 0.0840390i) q^{86} +(-1.23466 - 2.13849i) q^{88} +(1.73166 - 2.99933i) q^{89} +(0.00578583 - 1.57479i) q^{91} -4.01817i q^{92} +(-4.05108 + 2.33889i) q^{94} +(-3.04097 + 1.75570i) q^{95} +6.53619i q^{97} +(-6.03630 - 3.54445i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4} - 4 q^{7}+O(q^{10}) $ 48 * q + 24 * q^4 - 4 * q^7	$ 48 q + 24 q^{4} - 4 q^{7} - 12 q^{10} - 4 q^{14} - 24 q^{16} - 16 q^{17} + 8 q^{22} - 28 q^{25} + 4 q^{28} + 12 q^{31} - 24 q^{35} + 24 q^{38} - 12 q^{40} + 16 q^{41} + 8 q^{43} + 8 q^{46} - 32 q^{49} - 48 q^{53} + 4 q^{56} - 4 q^{58} + 16 q^{59} + 32 q^{62} - 48 q^{64} - 24 q^{67} + 16 q^{68} + 28 q^{70} + 12 q^{73} + 8 q^{77} - 20 q^{79} - 48 q^{82} + 128 q^{83} - 40 q^{85} + 4 q^{88} + 32 q^{89} + 40 q^{91} - 12 q^{95} - 16 q^{98}+O(q^{100}) $ 48 * q + 24 * q^4 - 4 * q^7 - 12 * q^10 - 4 * q^14 - 24 * q^16 - 16 * q^17 + 8 * q^22 - 28 * q^25 + 4 * q^28 + 12 * q^31 - 24 * q^35 + 24 * q^38 - 12 * q^40 + 16 * q^41 + 8 * q^43 + 8 * q^46 - 32 * q^49 - 48 * q^53 + 4 * q^56 - 4 * q^58 + 16 * q^59 + 32 * q^62 - 48 * q^64 - 24 * q^67 + 16 * q^68 + 28 * q^70 + 12 * q^73 + 8 * q^77 - 20 * q^79 - 48 * q^82 + 128 * q^83 - 40 * q^85 + 4 * q^88 + 32 * q^89 + 40 * q^91 - 12 * q^95 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times$.

$n$	$533$	$1009$	$1711$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.75570	−	3.04097i	0.785175	−	1.35996i	−0.143720	−	0.989618i	$-0.545906\pi$
$5$	1.75570	−	3.04097i	0.785175	−	1.35996i	0.928895	−	0.370344i	$-0.120760\pi$
$6$		0			0
$7$	2.64573	+	0.00972055i	0.999993	+	0.00367402i
$7$	2.64573	+	0.00972055i	0.999993	+	0.00367402i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−3.04097	+	1.75570i	−0.961639	+	0.555202i
$11$	2.13849	−	1.23466i	0.644779	−	0.372263i	−0.141674	−	0.989913i	$-0.545249\pi$
$11$	2.13849	−	1.23466i	0.644779	−	0.372263i	0.786453	+	0.617650i	$0.211915\pi$
$12$		0			0
$13$		−	0.595217i		−	0.165083i	−0.996588	−	0.0825417i	$-0.973696\pi$
$13$		−	0.595217i		−	0.165083i	0.996588	−	0.0825417i	$-0.0263038\pi$
$14$	−2.28641	−	1.33128i	−0.611069	−	0.355801i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.856393	−	1.48332i	−0.207706	−	0.359757i	0.743286	−	0.668974i	$-0.233266\pi$
$17$	−0.856393	−	1.48332i	−0.207706	−	0.359757i	−0.950991	+	0.309217i	$0.899933\pi$
$18$		0			0
$19$	−0.866025	−	0.500000i	−0.198680	−	0.114708i
$19$	−0.866025	−	0.500000i	−0.198680	−	0.114708i
$20$	3.51141			0.785175
$21$		0			0
$22$	−2.46932			−0.526460
$23$	−3.47984	−	2.00908i	−0.725596	−	0.418923i	0.0912129	−	0.995831i	$-0.470926\pi$
$23$	−3.47984	−	2.00908i	−0.725596	−	0.418923i	−0.816809	+	0.576908i	$0.804259\pi$
$24$		0			0
$25$	−3.66500	−	6.34796i	−0.732999	−	1.26959i
$26$	−0.297608	+	0.515473i	−0.0583658	+	0.101093i
$27$		0			0
$28$	1.31445	+	2.29613i	0.248407	+	0.433928i
$29$		−	8.62608i		−	1.60182i	−0.598783	−	0.800911i	$-0.704349\pi$
$29$		−	8.62608i		−	1.60182i	0.598783	−	0.800911i	$-0.295651\pi$
$30$		0			0
$31$	−2.78011	+	1.60510i	−0.499322	+	0.288284i	−0.728434	−	0.685116i	$-0.759751\pi$
$31$	−2.78011	+	1.60510i	−0.499322	+	0.288284i	0.229111	+	0.973400i	$0.426418\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$			1.71279i			0.293740i
$35$	4.67469	−	8.02853i	0.790166	−	1.35707i
$36$		0			0
$37$	−1.06702	+	1.84813i	−0.175416	+	0.303830i	−0.940305	−	0.340332i	$-0.889461\pi$
$37$	−1.06702	+	1.84813i	−0.175416	+	0.303830i	0.764889	+	0.644162i	$0.222794\pi$
$38$	0.500000	+	0.866025i	0.0811107	+	0.140488i
$39$		0			0
$40$	−3.04097	−	1.75570i	−0.480819	−	0.277601i
$41$	1.84541			0.288205			0.144102	−	0.989563i	$-0.453971\pi$
$41$	1.84541			0.288205			0.144102	+	0.989563i	$0.453971\pi$
$42$		0			0
$43$	0.168078			0.0256317			0.0128158	−	0.999918i	$-0.495920\pi$
$43$	0.168078			0.0256317			0.0128158	+	0.999918i	$0.495920\pi$
$44$	2.13849	+	1.23466i	0.322389	+	0.186132i
$45$		0			0
$46$	2.00908	+	3.47984i	0.296223	+	0.513074i
$47$	2.33889	−	4.05108i	0.341163	−	0.590911i	−0.643486	−	0.765458i	$-0.722513\pi$
$47$	2.33889	−	4.05108i	0.341163	−	0.590911i	0.984649	+	0.174546i	$0.0558459\pi$
$48$		0			0
$49$	6.99981	+	0.0514360i	0.999973	+	0.00734799i
$50$			7.32999i			1.03662i
$51$		0			0
$52$	0.515473	−	0.297608i	0.0714832	−	0.0412709i
$53$	0.675185	−	0.389819i	0.0927439	−	0.0535457i	−0.452911	−	0.891556i	$-0.649614\pi$
$53$	0.675185	−	0.389819i	0.0927439	−	0.0535457i	0.545655	+	0.838010i	$0.316281\pi$
$54$		0			0
$55$		−	8.67078i		−	1.16917i
$56$	0.00972055	−	2.64573i	0.00129896	−	0.353551i
$57$		0			0
$58$	−4.31304	+	7.47040i	−0.566330	+	0.980912i
$59$	6.28968	+	10.8940i	0.818846	+	1.41828i	0.906533	+	0.422135i	$0.138719\pi$
$59$	6.28968	+	10.8940i	0.818846	+	1.41828i	−0.0876865	+	0.996148i	$0.527947\pi$
$60$		0			0
$61$	−10.7145	−	6.18602i	−1.37185	−	0.792039i	−0.380690	−	0.924703i	$-0.624314\pi$
$61$	−10.7145	−	6.18602i	−1.37185	−	0.792039i	−0.991161	+	0.132664i	$0.957647\pi$
$62$	3.21019			0.407695
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−1.81004	−	1.04502i	−0.224507	−	0.129619i
$66$		0			0
$67$	−1.56133	−	2.70431i	−0.190747	−	0.330384i	0.754751	−	0.656012i	$-0.227758\pi$
$67$	−1.56133	−	2.70431i	−0.190747	−	0.330384i	−0.945498	+	0.325628i	$0.894424\pi$
$68$	0.856393	−	1.48332i	0.103853	−	0.179879i
$69$		0			0
$70$	−8.06266	+	4.61557i	−0.963672	+	0.551666i
$71$			8.22648i			0.976304i	0.872759	+	0.488152i	$0.162329\pi$
$71$			8.22648i			0.976304i	−0.872759	+	0.488152i	$0.837671\pi$
$72$		0			0
$73$	1.84116	−	1.06300i	0.215492	−	0.124414i	−0.388369	−	0.921504i	$-0.626961\pi$
$73$	1.84116	−	1.06300i	0.215492	−	0.124414i	0.603861	+	0.797090i	$0.293628\pi$
$74$	1.84813	−	1.06702i	0.214840	−	0.124038i
$75$		0			0
$76$		−	1.00000i		−	0.114708i
$77$	5.66988	−	3.24579i	0.646142	−	0.369892i
$78$		0			0
$79$	−2.36502	+	4.09633i	−0.266085	+	0.460873i	−0.967847	−	0.251538i	$-0.919064\pi$
$79$	−2.36502	+	4.09633i	−0.266085	+	0.460873i	0.701762	+	0.712411i	$0.252397\pi$
$80$	1.75570	+	3.04097i	0.196294	+	0.339991i
$81$		0			0
$82$	−1.59817	−	0.922706i	−0.176489	−	0.101896i
$83$	−3.01650			−0.331104			−0.165552	−	0.986201i	$-0.552941\pi$
$83$	−3.01650			−0.331104			−0.165552	+	0.986201i	$0.552941\pi$
$84$		0			0
$85$	−6.01429			−0.652342
$86$	−0.145560	−	0.0840390i	−0.0156961	−	0.00906216i
$87$		0			0
$88$	−1.23466	−	2.13849i	−0.131615	−	0.227964i
$89$	1.73166	−	2.99933i	0.183556	−	0.317928i	−0.759533	−	0.650469i	$-0.774573\pi$
$89$	1.73166	−	2.99933i	0.183556	−	0.317928i	0.943089	+	0.332541i	$0.107906\pi$
$90$		0			0
$91$	0.00578583	−	1.57479i	0.000606520	−	0.165082i
$92$		−	4.01817i		−	0.418923i
$93$		0			0
$94$	−4.05108	+	2.33889i	−0.417837	+	0.241239i
$95$	−3.04097	+	1.75570i	−0.311997	+	0.180131i
$96$		0			0
$97$			6.53619i			0.663650i	0.943341	+	0.331825i	$0.107664\pi$
$97$			6.53619i			0.663650i	−0.943341	+	0.331825i	$0.892336\pi$
$98$	−6.03630	−	3.54445i	−0.609758	−	0.358044i
$99$		0			0
$100$	3.66500	−	6.34796i	0.366500	−	0.634796i
$101$	2.38358	+	4.12849i	0.237176	+	0.410800i	0.959903	−	0.280333i	$-0.0904450\pi$
$101$	2.38358	+	4.12849i	0.237176	+	0.410800i	−0.722727	+	0.691133i	$0.757112\pi$
$102$		0			0
$103$	6.32073	+	3.64927i	0.622800	+	0.359574i	0.777958	−	0.628316i	$-0.216255\pi$
$103$	6.32073	+	3.64927i	0.622800	+	0.359574i	−0.155159	+	0.987890i	$0.549589\pi$
$104$	−0.595217			−0.0583658
$105$		0			0
$106$	−0.779637			−0.0757250
$107$	3.76674	+	2.17473i	0.364145	+	0.210239i	0.670897	−	0.741550i	$-0.265909\pi$
$107$	3.76674	+	2.17473i	0.364145	+	0.210239i	−0.306753	+	0.951789i	$0.599242\pi$
$108$		0			0
$109$	1.94523	+	3.36924i	0.186320	+	0.322715i	0.944020	−	0.329887i	$-0.107011\pi$
$109$	1.94523	+	3.36924i	0.186320	+	0.322715i	−0.757701	+	0.652602i	$0.773677\pi$
$110$	−4.33539	+	7.50911i	−0.413363	+	0.715966i
$111$		0			0
$112$	−1.33128	+	2.28641i	−0.125795	+	0.216046i
$113$		−	2.54003i		−	0.238946i	−0.992837	−	0.119473i	$-0.961880\pi$
$113$		−	2.54003i		−	0.238946i	0.992837	−	0.119473i	$-0.0381205\pi$
$114$		0			0
$115$	−12.2191	+	7.05472i	−1.13944	+	0.657856i
$116$	7.47040	−	4.31304i	0.693610	−	0.400456i
$117$		0			0
$118$		−	12.5794i		−	1.15802i
$119$	−2.25137	−	3.93278i	−0.206383	−	0.360518i
$120$		0			0
$121$	−2.45124	+	4.24567i	−0.222840	+	0.385970i
$122$	6.18602	+	10.7145i	0.560056	+	0.970046i
$123$		0			0
$124$	−2.78011	−	1.60510i	−0.249661	−	0.144142i
$125$	−8.18156			−0.731781
$126$		0			0
$127$	13.8932			1.23282			0.616410	−	0.787425i	$-0.288586\pi$
$127$	13.8932			1.23282			0.616410	+	0.787425i	$0.288586\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	1.04502	+	1.81004i	0.0916548	+	0.158751i
$131$	5.20576	−	9.01664i	0.454830	−	0.787788i	−0.543849	−	0.839183i	$-0.683034\pi$
$131$	5.20576	−	9.01664i	0.454830	−	0.787788i	0.998678	+	0.0513953i	$0.0163668\pi$
$132$		0			0
$133$	−2.28641	−	1.33128i	−0.198257	−	0.115437i
$134$			3.12267i			0.269758i
$135$		0			0
$136$	−1.48332	+	0.856393i	−0.127193	+	0.0734351i
$137$	5.54140	−	3.19933i	0.473433	−	0.273337i	−0.244242	−	0.969714i	$-0.578539\pi$
$137$	5.54140	−	3.19933i	0.473433	−	0.273337i	0.717676	+	0.696377i	$0.245206\pi$
$138$		0			0
$139$		−	17.6426i		−	1.49643i	−0.663457	−	0.748214i	$-0.730912\pi$
$139$		−	17.6426i		−	1.49643i	0.663457	−	0.748214i	$-0.269088\pi$
$140$	9.29025	+	0.0341328i	0.785170	+	0.00288475i
$141$		0			0
$142$	4.11324	−	7.12434i	0.345176	−	0.597862i
$143$	−0.734889	−	1.27287i	−0.0614545	−	0.106442i
$144$		0			0
$145$	−26.2316	−	15.1448i	−2.17842	−	1.25771i
$146$	−2.12599			−0.175948
$147$		0			0
$148$	−2.13403			−0.175416
$149$	−5.31374	−	3.06789i	−0.435318	−	0.251331i	0.266292	−	0.963893i	$-0.414202\pi$
$149$	−5.31374	−	3.06789i	−0.435318	−	0.251331i	−0.701610	+	0.712561i	$0.747535\pi$
$150$		0			0
$151$	9.87298	+	17.1005i	0.803451	+	1.39162i	0.917332	+	0.398124i	$0.130339\pi$
$151$	9.87298	+	17.1005i	0.803451	+	1.39162i	−0.113880	+	0.993494i	$0.536328\pi$
$152$	−0.500000	+	0.866025i	−0.0405554	+	0.0702439i
$153$		0			0
$154$	−6.53315	−	0.0240031i	−0.526456	−	0.00193422i
$155$			11.2723i			0.905413i
$156$		0			0
$157$	−19.0864	+	11.0195i	−1.52326	+	0.879456i	−0.523641	+	0.851939i	$0.675427\pi$
$157$	−19.0864	+	11.0195i	−1.52326	+	0.879456i	−0.999621	+	0.0275164i	$0.991240\pi$
$158$	4.09633	−	2.36502i	0.325886	−	0.188151i
$159$		0			0
$160$		−	3.51141i		−	0.277601i
$161$	−9.18719	−	5.34933i	−0.724052	−	0.421586i
$162$		0			0
$163$	5.39949	−	9.35218i	0.422920	−	0.732519i	−0.573303	−	0.819343i	$-0.694338\pi$
$163$	5.39949	−	9.35218i	0.422920	−	0.732519i	0.996224	+	0.0868237i	$0.0276717\pi$
$164$	0.922706	+	1.59817i	0.0720512	+	0.124796i
$165$		0			0
$166$	2.61237	+	1.50825i	0.202759	+	0.117063i
$167$	−16.7805			−1.29852			−0.649259	−	0.760568i	$-0.724921\pi$
$167$	−16.7805			−1.29852			−0.649259	+	0.760568i	$0.724921\pi$
$168$		0			0
$169$	12.6457			0.972747
$170$	5.20853	+	3.00715i	0.399476	+	0.230638i
$171$		0			0
$172$	0.0840390	+	0.145560i	0.00640791	+	0.0110988i
$173$	10.5495	−	18.2723i	0.802065	−	1.38922i	−0.116190	−	0.993227i	$-0.537068\pi$
$173$	10.5495	−	18.2723i	0.802065	−	1.38922i	0.918255	−	0.395990i	$-0.129598\pi$
$174$		0			0
$175$	−9.63490	−	16.8306i	−0.728330	−	1.27228i
$176$			2.46932i			0.186132i
$177$		0			0
$178$	−2.99933	+	1.73166i	−0.224809	+	0.129793i
$179$	−4.81969	+	2.78265i	−0.360241	+	0.207985i	−0.669186	−	0.743095i	$-0.733357\pi$
$179$	−4.81969	+	2.78265i	−0.360241	+	0.207985i	0.308946	+	0.951080i	$0.400024\pi$
$180$		0			0
$181$		−	18.6398i		−	1.38549i	−0.721184	−	0.692744i	$-0.756402\pi$
$181$		−	18.6398i		−	1.38549i	0.721184	−	0.692744i	$-0.243598\pi$
$182$	−0.792403	+	1.36091i	−0.0587368	+	0.100877i
$183$		0			0
$184$	−2.00908	+	3.47984i	−0.148112	+	0.256537i
$185$	3.74673	+	6.48953i	0.275465	+	0.477120i
$186$		0			0
$187$	−3.66278	−	2.11470i	−0.267849	−	0.154643i
$188$	4.67779			0.341163
$189$		0			0
$190$	3.51141			0.254744
$191$	−12.7116	−	7.33902i	−0.919776	−	0.531033i	−0.0362121	−	0.999344i	$-0.511529\pi$
$191$	−12.7116	−	7.33902i	−0.919776	−	0.531033i	−0.883563	+	0.468311i	$0.844863\pi$
$192$		0			0
$193$	3.74286	+	6.48283i	0.269417	+	0.466644i	0.968711	−	0.248190i	$-0.0798357\pi$
$193$	3.74286	+	6.48283i	0.269417	+	0.466644i	−0.699294	+	0.714834i	$0.746502\pi$
$194$	3.26810	−	5.66051i	0.234636	−	0.406401i
$195$		0			0
$196$	3.45536	+	6.08773i	0.246811	+	0.434838i
$197$		−	0.755615i		−	0.0538354i	−0.999638	−	0.0269177i	$-0.991431\pi$
$197$		−	0.755615i		−	0.0538354i	0.999638	−	0.0269177i	$-0.00856920\pi$
$198$		0			0
$199$	−2.97321	+	1.71658i	−0.210765	+	0.121685i	−0.601667	−	0.798747i	$-0.705497\pi$
$199$	−2.97321	+	1.71658i	−0.210765	+	0.121685i	0.390902	+	0.920432i	$0.372163\pi$
$200$	−6.34796	+	3.66500i	−0.448869	+	0.259154i
$201$		0			0
$202$		−	4.76717i		−	0.335417i
$203$	0.0838502	−	22.8223i	0.00588513	−	1.60181i
$204$		0			0
$205$	3.24000	−	5.61184i	0.226291	−	0.391948i
$206$	−3.64927	−	6.32073i	−0.254257	−	0.440386i
$207$		0			0
$208$	0.515473	+	0.297608i	0.0357416	+	0.0206354i
$209$	−2.46932			−0.170806
$210$		0			0
$211$	1.83114			0.126061			0.0630304	−	0.998012i	$-0.479923\pi$
$211$	1.83114			0.126061			0.0630304	+	0.998012i	$0.479923\pi$
$212$	0.675185	+	0.389819i	0.0463719	+	0.0267728i
$213$		0			0
$214$	−2.17473	−	3.76674i	−0.148662	−	0.257489i
$215$	0.295095	−	0.511120i	0.0201253	−	0.0348581i
$216$		0			0
$217$	−7.37103	+	4.21963i	−0.500378	+	0.286447i
$218$		−	3.89047i		−	0.263496i
$219$		0			0
$220$	7.50911	−	4.33539i	0.506264	−	0.292292i
$221$	−0.882895	+	0.509740i	−0.0593899	+	0.0342888i
$222$		0			0
$223$			13.7812i			0.922858i	0.887177	+	0.461429i	$0.152663\pi$
$223$			13.7812i			0.922858i	−0.887177	+	0.461429i	$0.847337\pi$
$224$	2.29613	−	1.31445i	0.153417	−	0.0878253i
$225$		0			0
$226$	−1.27001	+	2.19973i	−0.0844801	+	0.146324i
$227$	−6.32021	−	10.9469i	−0.419487	−	0.726572i	0.576401	−	0.817167i	$-0.304457\pi$
$227$	−6.32021	−	10.9469i	−0.419487	−	0.726572i	−0.995888	+	0.0905945i	$0.971123\pi$
$228$		0			0
$229$	−8.62930	−	4.98213i	−0.570240	−	0.329228i	0.187005	−	0.982359i	$-0.440122\pi$
$229$	−8.62930	−	4.98213i	−0.570240	−	0.329228i	−0.757245	+	0.653131i	$0.773455\pi$
$230$	14.1094			0.930348
$231$		0			0
$232$	−8.62608			−0.566330
$233$	−15.6790	−	9.05228i	−1.02717	−	0.593035i	−0.110995	−	0.993821i	$-0.535404\pi$
$233$	−15.6790	−	9.05228i	−1.02717	−	0.593035i	−0.916172	+	0.400786i	$0.868737\pi$
$234$		0			0
$235$	−8.21281	−	14.2250i	−0.535745	−	0.927937i
$236$	−6.28968	+	10.8940i	−0.409423	+	0.709142i
$237$		0			0
$238$	−0.0166492	+	4.53158i	−0.00107921	+	0.293738i
$239$		−	11.8112i		−	0.764001i	−0.924162	−	0.382001i	$-0.875235\pi$
$239$		−	11.8112i		−	0.764001i	0.924162	−	0.382001i	$-0.124765\pi$
$240$		0			0
$241$	8.48526	−	4.89897i	0.546583	−	0.315570i	−0.201159	−	0.979559i	$-0.564471\pi$
$241$	8.48526	−	4.89897i	0.546583	−	0.315570i	0.747743	+	0.663988i	$0.231138\pi$
$242$	4.24567	−	2.45124i	0.272922	−	0.157572i
$243$		0			0
$244$		−	12.3720i		−	0.792039i
$245$	12.4460	−	21.1959i	0.795147	−	1.35416i
$246$		0			0
$247$	−0.297608	+	0.515473i	−0.0189364	+	0.0327988i
$248$	1.60510	+	2.78011i	0.101924	+	0.176537i
$249$		0			0
$250$	7.08544	+	4.09078i	0.448122	+	0.258724i
$251$	9.52680			0.601326			0.300663	−	0.953730i	$-0.402792\pi$
$251$	9.52680			0.601326			0.300663	+	0.953730i	$0.402792\pi$
$252$		0			0
$253$	−9.92212			−0.623799
$254$	−12.0318	−	6.94659i	−0.754945	−	0.435868i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.27855	+	7.41067i	−0.266889	+	0.462265i	−0.968057	−	0.250731i	$-0.919329\pi$
$257$	−4.27855	+	7.41067i	−0.266889	+	0.462265i	0.701168	+	0.712996i	$0.252662\pi$
$258$		0			0
$259$	−2.84101	+	4.87928i	−0.176532	+	0.303184i
$260$		−	2.09005i		−	0.129619i
$261$		0			0
$262$	−9.01664	+	5.20576i	−0.557050	+	0.321613i
$263$	19.2672	−	11.1239i	1.18806	−	0.685929i	0.230198	−	0.973144i	$-0.426063\pi$
$263$	19.2672	−	11.1239i	1.18806	−	0.685929i	0.957866	+	0.287214i	$0.0927292\pi$
$264$		0			0
$265$		−	2.73762i		−	0.168171i
$266$	1.31445	+	2.29613i	0.0805940	+	0.140785i
$267$		0			0
$268$	1.56133	−	2.70431i	0.0953737	−	0.165192i
$269$	0.475904	+	0.824289i	0.0290164	+	0.0502578i	0.880169	−	0.474661i	$-0.157429\pi$
$269$	0.475904	+	0.824289i	0.0290164	+	0.0502578i	−0.851153	+	0.524918i	$0.824096\pi$
$270$		0			0
$271$	16.5345	+	9.54618i	1.00440	+	0.579889i	0.909546	−	0.415602i	$-0.136429\pi$
$271$	16.5345	+	9.54618i	1.00440	+	0.579889i	0.0948509	+	0.995491i	$0.469763\pi$
$272$	1.71279			0.103853
$273$		0			0
$274$	−6.39865			−0.386557
$275$	−15.6751	−	9.05003i	−0.945245	−	0.545737i
$276$		0			0
$277$	14.4005	+	24.9423i	0.865239	+	1.49864i	0.866809	+	0.498640i	$0.166167\pi$
$277$	14.4005	+	24.9423i	0.865239	+	1.49864i	−0.00156997	+	0.999999i	$0.500500\pi$
$278$	−8.82131	+	15.2790i	−0.529067	+	0.916371i
$279$		0			0
$280$	−8.02853	−	4.67469i	−0.479796	−	0.279366i
$281$			24.0917i			1.43719i	0.695427	+	0.718597i	$0.255215\pi$
$281$			24.0917i			1.43719i	−0.695427	+	0.718597i	$0.744785\pi$
$282$		0			0
$283$	19.3568	−	11.1756i	1.15064	−	0.664322i	0.201597	−	0.979469i	$-0.435387\pi$
$283$	19.3568	−	11.1756i	1.15064	−	0.664322i	0.949043	+	0.315146i	$0.102054\pi$
$284$	−7.12434	+	4.11324i	−0.422752	+	0.244076i
$285$		0			0
$286$			1.46978i			0.0869098i
$287$	4.88247	+	0.0179384i	0.288203	+	0.00105887i
$288$		0			0
$289$	7.03318	−	12.1818i	0.413717	−	0.716578i
$290$	15.1448	+	26.2316i	0.889336	+	1.54037i
$291$		0			0
$292$	1.84116	+	1.06300i	0.107746	+	0.0622071i
$293$	−28.6949			−1.67637			−0.838186	−	0.545384i	$-0.816384\pi$
$293$	−28.6949			−1.67637			−0.838186	+	0.545384i	$0.816384\pi$
$294$		0			0
$295$	44.1713			2.57175
$296$	1.84813	+	1.06702i	0.107420	+	0.0620191i
$297$		0			0
$298$	3.06789	+	5.31374i	0.177718	+	0.307816i
$299$	−1.19584	+	2.07126i	−0.0691573	+	0.119784i
$300$		0			0
$301$	0.444690	+	0.00163381i	0.0256315	+	9.41712e-5i
$302$		−	19.7460i		−	1.13625i
$303$		0			0
$304$	0.866025	−	0.500000i	0.0496700	−	0.0286770i
$305$	−37.6230	+	21.7217i	−2.15429	+	1.24378i
$306$		0			0
$307$		−	13.9150i		−	0.794171i	−0.917782	−	0.397085i	$-0.870022\pi$
$307$		−	13.9150i		−	0.794171i	0.917782	−	0.397085i	$-0.129978\pi$
$308$	5.64587	+	3.28736i	0.321703	+	0.187315i
$309$		0			0
$310$	5.63615	−	9.76210i	0.320112	−	0.554450i
$311$	−1.72103	−	2.98091i	−0.0975907	−	0.169032i	0.813096	−	0.582129i	$-0.197780\pi$
$311$	−1.72103	−	2.98091i	−0.0975907	−	0.169032i	−0.910687	+	0.413097i	$0.864447\pi$
$312$		0			0
$313$	3.17108	+	1.83082i	0.179240	+	0.103484i	0.586935	−	0.809634i	$-0.300334\pi$
$313$	3.17108	+	1.83082i	0.179240	+	0.103484i	−0.407696	+	0.913118i	$0.633668\pi$
$314$	22.0391			1.24374
$315$		0			0
$316$	−4.73003			−0.266085
$317$	−5.27797	−	3.04724i	−0.296440	−	0.171150i	0.344402	−	0.938822i	$-0.388082\pi$
$317$	−5.27797	−	3.04724i	−0.296440	−	0.171150i	−0.640843	+	0.767672i	$0.721415\pi$
$318$		0			0
$319$	−10.6503	−	18.4468i	−0.596300	−	1.03282i
$320$	−1.75570	+	3.04097i	−0.0981469	+	0.169995i
$321$		0			0
$322$	5.28168	+	9.22625i	0.294336	+	0.514159i
$323$			1.71279i			0.0953020i
$324$		0			0
$325$	−3.77841	+	2.18147i	−0.209589	+	0.121006i
$326$	−9.35218	+	5.39949i	−0.517969	+	0.299050i
$327$		0			0
$328$		−	1.84541i		−	0.101896i
$329$	6.22747	−	10.6954i	0.343331	−	0.589654i
$330$		0			0
$331$	−10.4336	+	18.0715i	−0.573480	+	0.993297i	0.422724	+	0.906258i	$0.361074\pi$
$331$	−10.4336	+	18.0715i	−0.573480	+	0.993297i	−0.996205	+	0.0870390i	$0.972260\pi$
$332$	−1.50825	−	2.61237i	−0.0827760	−	0.143372i
$333$		0			0
$334$	14.5324	+	8.39027i	0.795176	+	0.459095i
$335$	−10.9650			−0.599080
$336$		0			0
$337$	−9.40622			−0.512390			−0.256195	−	0.966625i	$-0.582469\pi$
$337$	−9.40622			−0.512390			−0.256195	+	0.966625i	$0.582469\pi$
$338$	−10.9515	−	6.32286i	−0.595684	−	0.343918i
$339$		0			0
$340$	−3.00715	−	5.20853i	−0.163085	−	0.282472i
$341$	−3.96349	+	6.86496i	−0.214635	+	0.371759i
$342$		0			0
$343$	18.5191	+	0.204128i	0.999939	+	0.0110219i
$344$		−	0.168078i		−	0.00906216i
$345$		0			0
$346$	−18.2723	+	10.5495i	−0.982325	+	0.567145i
$347$	−24.7087	+	14.2656i	−1.32643	+	0.765815i	−0.984746	−	0.173999i	$-0.944331\pi$
$347$	−24.7087	+	14.2656i	−1.32643	+	0.765815i	−0.341685	+	0.939814i	$0.610998\pi$
$348$		0			0
$349$			10.9001i			0.583471i	0.956499	+	0.291735i	$0.0942326\pi$
$349$			10.9001i			0.583471i	−0.956499	+	0.291735i	$0.905767\pi$
$350$	−0.0712515	+	19.3932i	−0.00380855	+	1.03661i
$351$		0			0
$352$	1.23466	−	2.13849i	0.0658075	−	0.113982i
$353$	−14.9806	−	25.9471i	−0.797334	−	1.38102i	−0.921346	−	0.388743i	$-0.872909\pi$
$353$	−14.9806	−	25.9471i	−0.797334	−	1.38102i	0.124012	−	0.992281i	$-0.460424\pi$
$354$		0			0
$355$	25.0165	+	14.4433i	1.32774	+	0.766569i
$356$	3.46332			0.183556
$357$		0			0
$358$	5.56530			0.294135
$359$	11.4065	+	6.58557i	0.602014	+	0.347573i	0.769833	−	0.638245i	$-0.220339\pi$
$359$	11.4065	+	6.58557i	0.602014	+	0.347573i	−0.167820	+	0.985818i	$0.553673\pi$
$360$		0			0
$361$	0.500000	+	0.866025i	0.0263158	+	0.0455803i
$362$	−9.31992	+	16.1426i	−0.489844	+	0.848435i
$363$		0			0
$364$	1.36670	−	0.782382i	0.0716344	−	0.0410080i
$365$		−	7.46523i		−	0.390748i
$366$		0			0
$367$	−13.3387	+	7.70112i	−0.696276	+	0.401995i	−0.805959	−	0.591972i	$-0.798350\pi$
$367$	−13.3387	+	7.70112i	−0.696276	+	0.401995i	0.109683	+	0.993967i	$0.465016\pi$
$368$	3.47984	−	2.00908i	0.181399	−	0.104731i
$369$		0			0
$370$		−	7.49346i		−	0.389567i
$371$	1.79015	−	1.02479i	0.0929400	−	0.0532046i
$372$		0			0
$373$	0.482656	−	0.835984i	0.0249910	−	0.0432856i	−0.853259	−	0.521487i	$-0.825378\pi$
$373$	0.482656	−	0.835984i	0.0249910	−	0.0432856i	0.878250	+	0.478201i	$0.158711\pi$
$374$	2.11470	+	3.66278i	0.109349	+	0.189398i
$375$		0			0
$376$	−4.05108	−	2.33889i	−0.208919	−	0.120619i
$377$	−5.13439			−0.264434
$378$		0			0
$379$	34.8827			1.79180			0.895902	−	0.444251i	$-0.146530\pi$
$379$	34.8827			1.79180			0.895902	+	0.444251i	$0.146530\pi$
$380$	−3.04097	−	1.75570i	−0.155998	−	0.0900657i
$381$		0			0
$382$	7.33902	+	12.7116i	0.375497	+	0.650380i
$383$	−7.87352	+	13.6373i	−0.402318	+	0.696836i	−0.994005	−	0.109332i	$-0.965129\pi$
$383$	−7.87352	+	13.6373i	−0.402318	+	0.696836i	0.591687	+	0.806168i	$0.298462\pi$
$384$		0			0
$385$	0.0842847	−	22.9406i	0.00429555	−	1.16916i
$386$		−	7.48572i		−	0.381013i
$387$		0			0
$388$	−5.66051	+	3.26810i	−0.287369	+	0.165912i
$389$	−1.05300	+	0.607951i	−0.0533893	+	0.0308244i	−0.526457	−	0.850202i	$-0.676480\pi$
$389$	−1.05300	+	0.607951i	−0.0533893	+	0.0308244i	0.473068	+	0.881026i	$0.343147\pi$
$390$		0			0
$391$			6.88226i			0.348051i
$392$	0.0514360	−	6.99981i	0.00259791	−	0.353544i
$393$		0			0
$394$	−0.377808	+	0.654382i	−0.0190337	+	0.0329673i
$395$	8.30454	+	14.3839i	0.417847	+	0.723732i
$396$		0			0
$397$	1.69826	+	0.980491i	0.0852332	+	0.0492094i	0.542011	−	0.840371i	$-0.317663\pi$
$397$	1.69826	+	0.980491i	0.0852332	+	0.0492094i	−0.456778	+	0.889581i	$0.650996\pi$
$398$	3.43317			0.172089
$399$		0			0
$400$	7.32999			0.366500
$401$	−29.5213	−	17.0441i	−1.47422	−	0.851143i	−0.474645	−	0.880177i	$-0.657424\pi$
$401$	−29.5213	−	17.0441i	−1.47422	−	0.851143i	−0.999578	+	0.0290337i	$0.990757\pi$
$402$		0			0
$403$	0.955380	+	1.65477i	0.0475909	+	0.0824298i
$404$	−2.38358	+	4.12849i	−0.118588	+	0.205400i
$405$		0			0
$406$	−11.4838	+	19.7228i	−0.569930	+	0.978825i
$407$			5.26960i			0.261204i
$408$		0			0
$409$	−32.6709	+	18.8625i	−1.61547	+	0.932692i	−0.627399	+	0.778698i	$0.715881\pi$
$409$	−32.6709	+	18.8625i	−1.61547	+	0.932692i	−0.988072	+	0.153995i	$0.950786\pi$
$410$	−5.61184	+	3.24000i	−0.277149	+	0.160012i
$411$		0			0
$412$			7.29855i			0.359574i
$413$	16.5349	+	28.8839i	0.813630	+	1.42128i
$414$		0			0
$415$	−5.29608	+	9.17308i	−0.259974	+	0.450289i
$416$	−0.297608	−	0.515473i	−0.0145915	−	0.0252731i
$417$		0			0
$418$	2.13849	+	1.23466i	0.104597	+	0.0603891i
$419$	14.1892			0.693189			0.346594	−	0.938015i	$-0.387338\pi$
$419$	14.1892			0.693189			0.346594	+	0.938015i	$0.387338\pi$
$420$		0			0
$421$	27.8221			1.35597			0.677984	−	0.735077i	$-0.262854\pi$
$421$	27.8221			1.35597			0.677984	+	0.735077i	$0.262854\pi$
$422$	−1.58581	−	0.915570i	−0.0771962	−	0.0445692i
$423$		0			0
$424$	−0.389819	−	0.675185i	−0.0189313	−	0.0327899i
$425$	−6.27735	+	10.8727i	−0.304496	+	0.527403i
$426$		0			0
$427$	−28.2876	−	16.4707i	−1.36893	−	0.797074i
$428$			4.34946i			0.210239i
$429$		0			0
$430$	−0.511120	+	0.295095i	−0.0246484	+	0.0142308i
$431$	−17.4360	+	10.0667i	−0.839862	+	0.484894i	−0.857217	−	0.514955i	$-0.827809\pi$
$431$	−17.4360	+	10.0667i	−0.839862	+	0.484894i	0.0173556	+	0.999849i	$0.494475\pi$
$432$		0			0
$433$		−	15.4757i		−	0.743715i	−0.928290	−	0.371858i	$-0.878721\pi$
$433$		−	15.4757i		−	0.743715i	0.928290	−	0.371858i	$-0.121279\pi$
$434$	8.49331	+	0.0312048i	0.407692	+	0.00149788i
$435$		0			0
$436$	−1.94523	+	3.36924i	−0.0931598	+	0.161358i
$437$	2.00908	+	3.47984i	0.0961075	+	0.166463i
$438$		0			0
$439$	25.0606	+	14.4687i	1.19608	+	0.690555i	0.959678	−	0.281101i	$-0.0906997\pi$
$439$	25.0606	+	14.4687i	1.19608	+	0.690555i	0.236398	+	0.971656i	$0.424033\pi$
$440$	−8.67078			−0.413363
$441$		0			0
$442$	1.01948			0.0484917
$443$	31.6887	+	18.2955i	1.50557	+	0.869244i	0.999979	+	0.00647350i	$0.00206059\pi$
$443$	31.6887	+	18.2955i	1.50557	+	0.869244i	0.505596	+	0.862771i	$0.331273\pi$
$444$		0			0
$445$	−6.08057	−	10.5319i	−0.288247	−	0.499258i
$446$	6.89060	−	11.9349i	0.326280	−	0.565133i
$447$		0			0
$448$	−2.64573	−	0.00972055i	−0.124999	−	0.000459253i
$449$			39.6301i			1.87026i	0.354302	+	0.935131i	$0.384719\pi$
$449$			39.6301i			1.87026i	−0.354302	+	0.935131i	$0.615281\pi$
$450$		0			0
$451$	3.94639	−	2.27845i	0.185828	−	0.107288i
$452$	2.19973	−	1.27001i	0.103467	−	0.0597365i
$453$		0			0
$454$			12.6404i			0.593244i
$455$	−4.77872	−	2.78245i	−0.224030	−	0.130443i
$456$		0			0
$457$	4.20628	−	7.28548i	0.196761	−	0.340800i	−0.750715	−	0.660626i	$-0.770291\pi$
$457$	4.20628	−	7.28548i	0.196761	−	0.340800i	0.947476	+	0.319825i	$0.103624\pi$
$458$	4.98213	+	8.62930i	0.232800	+	0.403221i
$459$		0			0
$460$	−12.2191	−	7.05472i	−0.569720	−	0.328928i
$461$	40.2269			1.87355			0.936776	−	0.349929i	$-0.113794\pi$
$461$	40.2269			1.87355			0.936776	+	0.349929i	$0.113794\pi$
$462$		0			0
$463$	23.8560			1.10868			0.554342	−	0.832289i	$-0.312970\pi$
$463$	23.8560			1.10868			0.554342	+	0.832289i	$0.312970\pi$
$464$	7.47040	+	4.31304i	0.346805	+	0.200228i
$465$		0			0
$466$	9.05228	+	15.6790i	0.419339	+	0.726316i
$467$	17.7826	−	30.8004i	0.822881	−	1.42527i	−0.0806471	−	0.996743i	$-0.525699\pi$
$467$	17.7826	−	30.8004i	0.822881	−	1.42527i	0.903528	−	0.428529i	$-0.140968\pi$
$468$		0			0
$469$	−4.10459	−	7.17006i	−0.189532	−	0.331083i
$470$			16.4256i			0.757658i
$471$		0			0
$472$	10.8940	−	6.28968i	0.501439	−	0.289506i
$473$	0.359433	−	0.207519i	0.0165267	−	0.00954172i
$474$		0			0
$475$			7.32999i			0.336323i
$476$	2.28021	−	3.91613i	0.104513	−	0.179496i
$477$		0			0
$478$	−5.90559	+	10.2288i	−0.270115	+	0.467853i
$479$	19.0260	+	32.9540i	0.869321	+	1.50571i	0.862692	+	0.505730i	$0.168777\pi$
$479$	19.0260	+	32.9540i	0.869321	+	1.50571i	0.00662907	+	0.999978i	$0.497890\pi$
$480$		0			0
$481$	1.10004	+	0.635106i	0.0501573	+	0.0289584i
$482$	−9.79793			−0.446283
$483$		0			0
$484$	−4.90248			−0.222840
$485$	19.8764	+	11.4756i	0.902539	+	0.521081i
$486$		0			0
$487$	−14.2268	−	24.6416i	−0.644680	−	1.11662i	−0.984375	−	0.176083i	$-0.943657\pi$
$487$	−14.2268	−	24.6416i	−0.644680	−	1.11662i	0.339695	−	0.940535i	$-0.389676\pi$
$488$	−6.18602	+	10.7145i	−0.280028	+	0.485023i
$489$		0			0
$490$	−21.3765	+	12.1332i	−0.965693	+	0.548121i
$491$		−	41.4753i		−	1.87175i	−0.352327	−	0.935877i	$-0.614609\pi$
$491$		−	41.4753i		−	1.87175i	0.352327	−	0.935877i	$-0.385391\pi$
$492$		0			0
$493$	−12.7952	+	7.38731i	−0.576267	+	0.332708i
$494$	0.515473	−	0.297608i	0.0231922	−	0.0133900i
$495$		0			0
$496$		−	3.21019i		−	0.144142i
$497$	−0.0799659	+	21.7651i	−0.00358696	+	0.976298i
$498$		0			0
$499$	−10.7711	+	18.6560i	−0.482179	+	0.835158i	−0.999791	−	0.0204573i	$-0.993488\pi$
$499$	−10.7711	+	18.6560i	−0.482179	+	0.835158i	0.517612	+	0.855616i	$0.326821\pi$
$500$	−4.09078	−	7.08544i	−0.182945	−	0.316870i
$501$		0			0
$502$	−8.25045	−	4.76340i	−0.368236	−	0.212601i
$503$	0.949169			0.0423214			0.0211607	−	0.999776i	$-0.493264\pi$
$503$	0.949169			0.0423214			0.0211607	+	0.999776i	$0.493264\pi$
$504$		0			0
$505$	16.7395			0.744897
$506$	8.59281	+	4.96106i	0.381997	+	0.220546i
$507$		0			0
$508$	6.94659	+	12.0318i	0.308205	+	0.533827i
$509$	−13.8688	+	24.0215i	−0.614724	+	1.06473i	0.375708	+	0.926738i	$0.377399\pi$
$509$	−13.8688	+	24.0215i	−0.614724	+	1.06473i	−0.990433	+	0.137996i	$0.955934\pi$
$510$		0			0
$511$	4.88156	−	2.79451i	0.215947	−	0.123622i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	7.41067	−	4.27855i	0.326870	−	0.188719i
$515$	22.1947	−	12.8141i	0.978013	−	0.564656i
$516$		0			0
$517$		−	11.5509i		−	0.508010i
$518$	4.90002	−	2.80508i	0.215295	−	0.123248i
$519$		0			0
$520$	−1.04502	+	1.81004i	−0.0458274	+	0.0793753i
$521$	7.62372	+	13.2047i	0.334001	+	0.578507i	0.983292	−	0.182033i	$-0.0582677\pi$
$521$	7.62372	+	13.2047i	0.334001	+	0.578507i	−0.649291	+	0.760540i	$0.724934\pi$
$522$		0			0
$523$	1.85055	+	1.06842i	0.0809190	+	0.0467186i	0.539914	−	0.841720i	$-0.318457\pi$
$523$	1.85055	+	1.06842i	0.0809190	+	0.0467186i	−0.458995	+	0.888439i	$0.651790\pi$
$524$	10.4115			0.454830
$525$		0			0
$526$	−22.2478			−0.970051
$527$	4.76173	+	2.74919i	0.207424	+	0.119756i
$528$		0			0
$529$	−3.42716	−	5.93602i	−0.149007	−	0.258088i
$530$	−1.36881	+	2.37085i	−0.0594574	+	0.102983i
$531$		0			0
$532$	0.00972055	−	2.64573i	0.000421439	−	0.114707i
$533$		−	1.09842i		−	0.0475779i
$534$		0			0
$535$	13.2266	−	7.63637i	0.571835	−	0.330149i
$536$	−2.70431	+	1.56133i	−0.116808	+	0.0674394i
$537$		0			0
$538$		−	0.951807i		−	0.0410353i
$539$	15.0325	−	8.53237i	0.647497	−	0.367515i
$540$		0			0
$541$	−9.26233	+	16.0428i	−0.398219	+	0.689735i	−0.993506	−	0.113778i	$-0.963705\pi$
$541$	−9.26233	+	16.0428i	−0.398219	+	0.689735i	0.595287	+	0.803513i	$0.297038\pi$
$542$	−9.54618	−	16.5345i	−0.410043	−	0.710216i
$543$		0			0
$544$	−1.48332	−	0.856393i	−0.0635967	−	0.0367176i
$545$	13.6610			0.585174
$546$		0			0
$547$	34.6461			1.48136			0.740680	−	0.671858i	$-0.234503\pi$
$547$	34.6461			1.48136			0.740680	+	0.671858i	$0.234503\pi$
$548$	5.54140	+	3.19933i	0.236717	+	0.136668i
$549$		0			0
$550$	9.05003	+	15.6751i	0.385895	+	0.668389i
$551$	−4.31304	+	7.47040i	−0.183742	+	0.318250i
$552$		0			0
$553$	−6.29702	+	10.8148i	−0.267777	+	0.459892i
$554$		−	28.8009i		−	1.22363i
$555$		0			0
$556$	15.2790	−	8.82131i	0.647972	−	0.374107i
$557$	−37.8710	+	21.8649i	−1.60465	+	0.926444i	−0.614107	+	0.789223i	$0.710484\pi$
$557$	−37.8710	+	21.8649i	−1.60465	+	0.926444i	−0.990540	+	0.137221i	$0.956183\pi$
$558$		0			0
$559$		−	0.100043i		−	0.00423136i
$560$	4.61557	+	8.06266i	0.195043	+	0.340710i
$561$		0			0
$562$	12.0459	−	20.8641i	0.508125	−	0.880098i
$563$	−21.2955	−	36.8848i	−0.897497	−	1.55451i	−0.830683	−	0.556745i	$-0.812050\pi$
$563$	−21.2955	−	36.8848i	−0.897497	−	1.55451i	−0.0668136	−	0.997765i	$-0.521283\pi$
$564$		0			0
$565$	−7.72415	−	4.45954i	−0.324958	−	0.187614i
$566$	−22.3513			−0.939494
$567$		0			0
$568$	8.22648			0.345176
$569$	37.1444	+	21.4454i	1.55718	+	0.899036i	0.997525	+	0.0703073i	$0.0223980\pi$
$569$	37.1444	+	21.4454i	1.55718	+	0.899036i	0.559651	+	0.828729i	$0.310935\pi$
$570$		0			0
$571$	13.8552	+	23.9980i	0.579824	+	1.00428i	0.995499	+	0.0947712i	$0.0302120\pi$
$571$	13.8552	+	23.9980i	0.579824	+	1.00428i	−0.415675	+	0.909513i	$0.636455\pi$
$572$	0.734889	−	1.27287i	0.0307273	−	0.0532212i
$573$		0			0
$574$	−4.21937	−	2.45677i	−0.176113	−	0.102544i
$575$			29.4531i			1.22828i
$576$		0			0
$577$	−12.3272	+	7.11713i	−0.513189	+	0.296290i	−0.734144	−	0.678994i	$-0.762416\pi$
$577$	−12.3272	+	7.11713i	−0.513189	+	0.296290i	0.220954	+	0.975284i	$0.429083\pi$
$578$	−12.1818	+	7.03318i	−0.506697	+	0.292542i
$579$		0			0
$580$		−	30.2897i		−	1.25771i
$581$	−7.98085	−	0.0293220i	−0.331102	−	0.00121648i
$582$		0			0
$583$	0.962585	−	1.66725i	0.0398662	−	0.0690503i
$584$	−1.06300	−	1.84116i	−0.0439871	−	0.0761879i
$585$		0			0
$586$	24.8505	+	14.3474i	1.02656	+	0.592687i
$587$	24.0614			0.993120			0.496560	−	0.868002i	$-0.334596\pi$
$587$	24.0614			0.993120			0.496560	+	0.868002i	$0.334596\pi$
$588$		0			0
$589$	3.21019			0.132274
$590$	−38.2534	−	22.0856i	−1.57487	−	0.909251i
$591$		0			0
$592$	−1.06702	−	1.84813i	−0.0438541	−	0.0759575i
$593$	12.0326	−	20.8410i	0.494119	−	0.855839i	−0.505858	−	0.862617i	$-0.668824\pi$
$593$	12.0326	−	20.8410i	0.494119	−	0.855839i	0.999977	+	0.00677788i	$0.00215748\pi$
$594$		0			0
$595$	−15.9122	−	0.0584622i	−0.652337	−	0.00239672i
$596$		−	6.13577i		−	0.251331i
$597$		0			0
$598$	2.07126	−	1.19584i	0.0847000	−	0.0489016i
$599$	1.13337	−	0.654351i	0.0463082	−	0.0267361i	−0.476667	−	0.879084i	$-0.658155\pi$
$599$	1.13337	−	0.654351i	0.0463082	−	0.0267361i	0.522975	+	0.852348i	$0.324822\pi$
$600$		0			0
$601$		−	8.10485i		−	0.330604i	−0.986243	−	0.165302i	$-0.947140\pi$
$601$		−	8.10485i		−	0.330604i	0.986243	−	0.165302i	$-0.0528598\pi$
$602$	−0.384296	−	0.223760i	−0.0156627	−	0.00911976i
$603$		0			0
$604$	−9.87298	+	17.1005i	−0.401726	+	0.695809i
$605$	8.60731	+	14.9083i	0.349937	+	0.606108i
$606$		0			0
$607$	14.0945	+	8.13749i	0.572080	+	0.330291i	0.757980	−	0.652278i	$-0.226187\pi$
$607$	14.0945	+	8.13749i	0.572080	+	0.330291i	−0.185900	+	0.982569i	$0.559520\pi$
$608$	−1.00000			−0.0405554
$609$		0			0
$610$	43.4433			1.75897
$611$	−2.41127	−	1.39215i	−0.0975497	−	0.0563203i
$612$		0			0
$613$	14.0546	+	24.3434i	0.567662	+	0.983219i	0.996797	+	0.0799787i	$0.0254852\pi$
$613$	14.0546	+	24.3434i	0.567662	+	0.983219i	−0.429135	+	0.903241i	$0.641181\pi$
$614$	−6.95750	+	12.0507i	−0.280782	+	0.486328i
$615$		0			0
$616$	−3.24579	−	5.66988i	−0.130777	−	0.228446i
$617$			7.61122i			0.306416i	0.988194	+	0.153208i	$0.0489605\pi$
$617$			7.61122i			0.306416i	−0.988194	+	0.153208i	$0.951040\pi$
$618$		0			0
$619$	2.51794	−	1.45373i	0.101204	−	0.0584304i	−0.448543	−	0.893761i	$-0.648057\pi$
$619$	2.51794	−	1.45373i	0.101204	−	0.0584304i	0.549748	+	0.835331i	$0.314724\pi$
$620$	−9.76210	+	5.63615i	−0.392055	+	0.226353i
$621$		0			0
$622$			3.44206i			0.138014i
$623$	4.61067	−	7.91858i	0.184723	−	0.317251i
$624$		0			0
$625$	3.96059	−	6.85994i	0.158423	−	0.274398i
$626$	−1.83082	−	3.17108i	−0.0731744	−	0.126742i
$627$		0			0
$628$	−19.0864	−	11.0195i	−0.761631	−	0.439728i
$629$	3.65514			0.145740
$630$		0			0
$631$	−1.84789			−0.0735633			−0.0367817	−	0.999323i	$-0.511711\pi$
$631$	−1.84789			−0.0735633			−0.0367817	+	0.999323i	$0.511711\pi$
$632$	4.09633	+	2.36502i	0.162943	+	0.0940753i
$633$		0			0
$634$	3.04724	+	5.27797i	0.121021	+	0.209615i
$635$	24.3923	−	42.2487i	0.967979	−	1.67659i
$636$		0			0
$637$	0.0306155	−	4.16641i	0.00121303	−	0.165079i
$638$			21.3005i			0.843295i
$639$		0			0
$640$	3.04097	−	1.75570i	0.120205	−	0.0694003i
$641$	−23.2092	+	13.3999i	−0.916710	+	0.529263i	−0.882584	−	0.470155i	$-0.844198\pi$
$641$	−23.2092	+	13.3999i	−0.916710	+	0.529263i	−0.0341261	+	0.999418i	$0.510865\pi$
$642$		0			0
$643$		−	13.3736i		−	0.527403i	−0.964604	−	0.263702i	$-0.915057\pi$
$643$		−	13.3736i		−	0.527403i	0.964604	−	0.263702i	$-0.0849434\pi$
$644$	0.0390588	−	10.6310i	0.00153913	−	0.418920i
$645$		0			0
$646$	0.856393	−	1.48332i	0.0336943	−	0.0583603i
$647$	−9.15663	−	15.8598i	−0.359984	−	0.623511i	0.627973	−	0.778235i	$-0.283885\pi$
$647$	−9.15663	−	15.8598i	−0.359984	−	0.623511i	−0.987958	+	0.154724i	$0.950551\pi$
$648$		0			0
$649$	26.9008	+	15.5312i	1.05595	+	0.609653i
$650$	4.36294			0.171128
$651$		0			0
$652$	10.7990			0.422920
$653$	32.0199	+	18.4867i	1.25304	+	0.723440i	0.971711	−	0.236172i	$-0.0758930\pi$
$653$	32.0199	+	18.4867i	1.25304	+	0.723440i	0.281324	+	0.959613i	$0.409226\pi$
$654$		0			0
$655$	−18.2796	−	31.6611i	−0.714241	−	1.23710i
$656$	−0.922706	+	1.59817i	−0.0360256	+	0.0623982i
$657$		0			0
$658$	−10.7408	+	6.14871i	−0.418721	+	0.239702i
$659$		−	5.54025i		−	0.215818i	−0.994161	−	0.107909i	$-0.965585\pi$
$659$		−	5.54025i		−	0.215818i	0.994161	−	0.107909i	$-0.0344155\pi$
$660$		0			0
$661$	31.8347	−	18.3798i	1.23822	−	0.714890i	0.269494	−	0.963002i	$-0.413144\pi$
$661$	31.8347	−	18.3798i	1.23822	−	0.714890i	0.968731	+	0.248113i	$0.0798103\pi$
$662$	18.0715	−	10.4336i	0.702367	−	0.405512i
$663$		0			0
$664$			3.01650i			0.117063i
$665$	−8.06266	+	4.61557i	−0.312657	+	0.178984i
$666$		0			0
$667$	−17.3305	+	30.0173i	−0.671040	+	1.16228i
$668$	−8.39027	−	14.5324i	−0.324629	−	0.562274i
$669$		0			0
$670$	9.49594	+	5.48248i	0.366860	+	0.211807i
$671$	−30.5505			−1.17939
$672$		0			0
$673$	39.9341			1.53935			0.769674	−	0.638437i	$-0.220419\pi$
$673$	39.9341			1.53935			0.769674	+	0.638437i	$0.220419\pi$
$674$	8.14603	+	4.70311i	0.313773	+	0.181157i
$675$		0			0
$676$	6.32286	+	10.9515i	0.243187	+	0.421212i
$677$	−13.1842	+	22.8357i	−0.506709	+	0.877645i	0.493261	+	0.869881i	$0.335805\pi$
$677$	−13.1842	+	22.8357i	−0.506709	+	0.877645i	−0.999970	+	0.00776410i	$0.997529\pi$
$678$		0			0
$679$	−0.0635354	+	17.2930i	−0.00243826	+	0.663645i
$680$			6.01429i			0.230638i
$681$		0			0
$682$	6.86496	−	3.96349i	0.262873	−	0.151770i
$683$	16.1103	−	9.30128i	0.616443	−	0.355904i	−0.159040	−	0.987272i	$-0.550840\pi$
$683$	16.1103	−	9.30128i	0.616443	−	0.355904i	0.775483	+	0.631369i	$0.217506\pi$
$684$		0			0
$685$		−	22.4683i		−	0.858469i
$686$	−15.9360	−	9.43635i	−0.608438	−	0.360281i
$687$		0			0
$688$	−0.0840390	+	0.145560i	−0.00320396	+	0.00554942i
$689$	−0.232027	−	0.401882i	−0.00883951	−	0.0153105i
$690$		0			0
$691$	24.9045	+	14.3786i	0.947413	+	0.546989i	0.892276	−	0.451490i	$-0.149107\pi$
$691$	24.9045	+	14.3786i	0.947413	+	0.546989i	0.0551367	+	0.998479i	$0.482441\pi$
$692$	21.0990			0.802065
$693$		0			0
$694$	28.5311			1.08303
$695$	−53.6507	−	30.9752i	−2.03509	−	1.17496i
$696$		0			0
$697$	−1.58040	−	2.73733i	−0.0598618	−	0.103684i
$698$	5.45007	−	9.43979i	0.206288	−	0.357301i
$699$		0			0
$700$	9.75831	−	16.7594i	0.368829	−	0.633445i
$701$			28.8513i			1.08970i	0.838535	+	0.544848i	$0.183413\pi$
$701$			28.8513i			1.08970i	−0.838535	+	0.544848i	$0.816587\pi$
$702$		0			0
$703$	1.84813	−	1.06702i	0.0697034	−	0.0402433i
$704$	−2.13849	+	1.23466i	−0.0805974	+	0.0465329i
$705$		0			0
$706$			29.9611i			1.12760i
$707$	6.26620	+	10.9461i	0.235665	+	0.411669i
$708$		0			0
$709$	−17.1282	+	29.6669i	−0.643263	+	1.11416i	0.341437	+	0.939905i	$0.389087\pi$
$709$	−17.1282	+	29.6669i	−0.643263	+	1.11416i	−0.984700	+	0.174260i	$0.944247\pi$
$710$	−14.4433	−	25.0165i	−0.542046	−	0.938852i
$711$		0			0
$712$	−2.99933	−	1.73166i	−0.112404	−	0.0648967i
$713$	12.8991			0.483075
$714$		0			0
$715$	−5.16099			−0.193010
$716$	−4.81969	−	2.78265i	−0.180120	−	0.103993i
$717$		0			0
$718$	−6.58557	−	11.4065i	−0.245771	−	0.425688i
$719$	13.3470	−	23.1178i	0.497761	−	0.862147i	−0.502236	−	0.864731i	$-0.667489\pi$
$719$	13.3470	−	23.1178i	0.497761	−	0.862147i	0.999997	+	0.00258353i	$0.000822364\pi$
$720$		0			0
$721$	16.6875	+	9.71645i	0.621474	+	0.361859i
$722$		−	1.00000i		−	0.0372161i
$723$		0			0
$724$	16.1426	−	9.31992i	0.599934	−	0.346372i
$725$	−54.7580	+	31.6145i	−2.03366	+	1.17413i
$726$		0			0
$727$			22.2729i			0.826056i	0.910718	+	0.413028i	$0.135529\pi$
$727$			22.2729i			0.826056i	−0.910718	+	0.413028i	$0.864471\pi$
$728$	−1.57479	−	0.00578583i	−0.0583654	−	0.000214437i
$729$		0			0
$730$	−3.73261	+	6.46508i	−0.138150	+	0.239283i
$731$	−0.143941	−	0.249313i	−0.00532384	−	0.00922117i
$732$		0			0
$733$	33.7349	+	19.4768i	1.24603	+	0.719393i	0.970314	−	0.241847i	$-0.0777533\pi$
$733$	33.7349	+	19.4768i	1.24603	+	0.719393i	0.275711	+	0.961241i	$0.411087\pi$
$734$	15.4022			0.568507
$735$		0			0
$736$	−4.01817			−0.148112
$737$	−6.67780	−	3.85543i	−0.245980	−	0.142016i
$738$		0			0
$739$	−11.5489	−	20.0033i	−0.424834	−	0.735834i	0.571571	−	0.820553i	$-0.306334\pi$
$739$	−11.5489	−	20.0033i	−0.424834	−	0.735834i	−0.996405	+	0.0847187i	$0.973001\pi$
$740$	−3.74673	+	6.48953i	−0.137733	+	0.238560i
$741$		0			0
$742$	−2.06271	−	0.00757850i	−0.0757245	−	0.000278215i
$743$			8.62955i			0.316587i	0.987392	+	0.158294i	$0.0505993\pi$
$743$			8.62955i			0.316587i	−0.987392	+	0.158294i	$0.949401\pi$
$744$		0			0
$745$	−18.6587	+	10.7726i	−0.683602	+	0.394678i
$746$	−0.835984	+	0.482656i	−0.0306076	+	0.0176713i
$747$		0			0
$748$		−	4.22941i		−	0.154643i
$749$	9.94466	+	5.79037i	0.363370	+	0.211576i
$750$		0			0
$751$	−9.46386	+	16.3919i	−0.345341	+	0.598148i	−0.985416	−	0.170164i	$-0.945570\pi$
$751$	−9.46386	+	16.3919i	−0.345341	+	0.598148i	0.640075	+	0.768313i	$0.278903\pi$
$752$	2.33889	+	4.05108i	0.0852907	+	0.147728i
$753$		0			0
$754$	4.44651	+	2.56719i	0.161932	+	0.0934917i
$755$	69.3361			2.52340
$756$		0			0
$757$	11.8603			0.431070			0.215535	−	0.976496i	$-0.430850\pi$
$757$	11.8603			0.431070			0.215535	+	0.976496i	$0.430850\pi$
$758$	−30.2093	−	17.4414i	−1.09725	−	0.633499i
$759$		0			0
$760$	1.75570	+	3.04097i	0.0636861	+	0.110308i
$761$	11.1902	−	19.3820i	0.405644	−	0.702596i	−0.588752	−	0.808314i	$-0.700381\pi$
$761$	11.1902	−	19.3820i	0.405644	−	0.702596i	0.994396	+	0.105718i	$0.0337140\pi$
$762$		0			0
$763$	5.11382	+	8.93303i	0.185133	+	0.323397i
$764$		−	14.6780i		−	0.531033i
$765$		0			0
$766$	13.6373	−	7.87352i	0.492737	−	0.284482i
$767$	6.48432	−	3.74372i	0.234135	−	0.135178i
$768$		0			0
$769$		−	40.7566i		−	1.46972i	−0.678218	−	0.734861i	$-0.737247\pi$
$769$		−	40.7566i		−	1.46972i	0.678218	−	0.734861i	$-0.262753\pi$
$770$	−11.5433	+	19.8250i	−0.415991	+	0.714442i
$771$		0			0
$772$	−3.74286	+	6.48283i	−0.134709	+	0.233322i
$773$	3.96252	+	6.86328i	0.142522	+	0.246855i	0.928446	−	0.371468i	$-0.121146\pi$
$773$	3.96252	+	6.86328i	0.142522	+	0.246855i	−0.785924	+	0.618323i	$0.787812\pi$
$774$		0			0
$775$	20.3782	+	11.7653i	0.732005	+	0.422624i
$776$	6.53619			0.234636
$777$		0			0
$778$	1.21590			0.0435922
$779$	−1.59817	−	0.922706i	−0.0572605	−	0.0330594i
$780$		0			0
$781$	10.1569	+	17.5923i	0.363442	+	0.629500i
$782$	3.44113	−	5.96021i	0.123055	−	0.213137i
$783$		0			0
$784$	−3.54445	+	6.03630i	−0.126588	+	0.215582i
$785$			77.3883i			2.76211i
$786$		0			0
$787$	36.7626	−	21.2249i	1.31045	−	0.756587i	0.328277	−	0.944582i	$-0.393532\pi$
$787$	36.7626	−	21.2249i	1.31045	−	0.756587i	0.982170	+	0.187995i	$0.0601988\pi$
$788$	0.654382	−	0.377808i	0.0233114	−	0.0134588i
$789$		0			0
$790$		−	16.6091i		−	0.590925i
$791$	0.0246905	−	6.72024i	0.000877892	−	0.238944i
$792$		0			0
$793$	−3.68202	+	6.37745i	−0.130753	+	0.226470i
$794$	−0.980491	−	1.69826i	−0.0347963	−	0.0602690i
$795$		0			0
$796$	−2.97321	−	1.71658i	−0.105383	−	0.0608427i
$797$	19.7757			0.700491			0.350245	−	0.936658i	$-0.386098\pi$
$797$	19.7757			0.700491			0.350245	+	0.936658i	$0.386098\pi$
$798$		0			0
$799$	−8.01205			−0.283446
$800$	−6.34796	−	3.66500i	−0.224434	−	0.129577i
$801$		0			0
$802$	17.0441	+	29.5213i	0.601849	+	1.04243i
$803$	2.62487	−	4.54641i	0.0926297	−	0.160439i
$804$		0			0
$805$	−32.3971	+	18.5461i	−1.14185	+	0.653665i
$806$		−	1.91076i		−	0.0673037i
$807$		0			0
$808$	4.12849	−	2.38358i	0.145240	−	0.0838542i
$809$	−48.6212	+	28.0714i	−1.70943	+	0.986939i	−0.774168	+	0.632980i	$0.781832\pi$
$809$	−48.6212	+	28.0714i	−1.70943	+	0.986939i	−0.935261	+	0.353960i	$0.884835\pi$
$810$		0			0
$811$			43.9345i			1.54275i	0.636381	+	0.771375i	$0.280431\pi$
$811$			43.9345i			1.54275i	−0.636381	+	0.771375i	$0.719569\pi$
$812$	19.8066	−	11.3385i	0.695076	−	0.397905i
$813$		0			0
$814$	2.63480	−	4.56361i	0.0923497	−	0.159954i
$815$	−18.9598	−	32.8393i	−0.664133	−	1.15031i
$816$		0			0
$817$	−0.145560	−	0.0840390i	−0.00509249	−	0.00294015i
$818$	37.7251			1.31903
$819$		0			0
$820$	6.48000			0.226291
$821$	25.3988	+	14.6640i	0.886424	+	0.511777i	0.872771	−	0.488129i	$-0.162321\pi$
$821$	25.3988	+	14.6640i	0.886424	+	0.511777i	0.0136531	+	0.999907i	$0.495654\pi$
$822$		0			0
$823$	10.5361	+	18.2491i	0.367267	+	0.636124i	0.989137	−	0.146996i	$-0.0469604\pi$
$823$	10.5361	+	18.2491i	0.367267	+	0.636124i	−0.621871	+	0.783120i	$0.713627\pi$
$824$	3.64927	−	6.32073i	0.127128	−	0.220193i
$825$		0			0
$826$	0.122278	−	33.2816i	0.00425460	−	1.15802i
$827$		−	47.6743i		−	1.65780i	−0.559397	−	0.828900i	$-0.688967\pi$
$827$		−	47.6743i		−	1.65780i	0.559397	−	0.828900i	$-0.311033\pi$
$828$		0			0
$829$	−13.6003	+	7.85212i	−0.472357	+	0.272715i	−0.717226	−	0.696841i	$-0.754588\pi$
$829$	−13.6003	+	7.85212i	−0.472357	+	0.272715i	0.244869	+	0.969556i	$0.421255\pi$
$830$	9.17308	−	5.29608i	0.318402	−	0.183830i
$831$		0			0
$832$			0.595217i			0.0206354i
$833$	−5.91829	−	10.4270i	−0.205057	−	0.361274i
$834$		0			0
$835$	−29.4617	+	51.0291i	−1.01956	+	1.76593i
$836$	−1.23466	−	2.13849i	−0.0427015	−	0.0739612i
$837$		0			0
$838$	−12.2882	−	7.09461i	−0.424490	−	0.245079i
$839$	−33.2819			−1.14902			−0.574509	−	0.818498i	$-0.694807\pi$
$839$	−33.2819			−1.14902			−0.574509	+	0.818498i	$0.694807\pi$
$840$		0			0
$841$	−45.4092			−1.56584
$842$	−24.0947	−	13.9111i	−0.830357	−	0.479407i
$843$		0			0
$844$	0.915570	+	1.58581i	0.0315152	+	0.0545860i
$845$	22.2021	−	38.4552i	0.763777	−	1.32290i
$846$		0			0
$847$	−6.52660	+	11.2091i	−0.224257	+	0.385149i
$848$			0.779637i			0.0267728i
$849$		0			0
$850$	10.8727	−	6.27735i	0.372930	−	0.215311i
$851$	7.42608	−	4.28745i	0.254563	−	0.146972i
$852$		0			0
$853$		−	23.7084i		−	0.811760i	−0.913926	−	0.405880i	$-0.866965\pi$
$853$		−	23.7084i		−	0.811760i	0.913926	−	0.405880i	$-0.133035\pi$
$854$	16.2624	+	28.4079i	0.556488	+	0.972097i
$855$		0			0
$856$	2.17473	−	3.76674i	0.0743308	−	0.128745i
$857$	5.33159	+	9.23459i	0.182124	+	0.315448i	0.942604	−	0.333914i	$-0.108370\pi$
$857$	5.33159	+	9.23459i	0.182124	+	0.315448i	−0.760480	+	0.649362i	$0.775036\pi$
$858$		0			0
$859$	−17.9964	−	10.3902i	−0.614028	−	0.354509i	0.160512	−	0.987034i	$-0.448685\pi$
$859$	−17.9964	−	10.3902i	−0.614028	−	0.354509i	−0.774540	+	0.632524i	$0.782019\pi$
$860$	0.590190			0.0201253
$861$		0			0
$862$	20.1333			0.685744
$863$	3.81749	+	2.20403i	0.129949	+	0.0750260i	0.563565	−	0.826072i	$-0.309429\pi$
$863$	3.81749	+	2.20403i	0.129949	+	0.0750260i	−0.433616	+	0.901098i	$0.642763\pi$
$864$		0			0
$865$	−37.0437	−	64.1615i	−1.25952	−	2.18156i
$866$	−7.73786	+	13.4024i	−0.262943	+	0.455431i
$867$		0			0
$868$	−7.33982	−	4.27368i	−0.249130	−	0.145058i
$869$			11.6799i			0.396215i
$870$		0			0
$871$	−1.60965	+	0.929333i	−0.0545410	+	0.0314892i
$872$	3.36924	−	1.94523i	0.114097	−	0.0658739i
$873$		0			0
$874$		−	4.01817i		−	0.135917i
$875$	−21.6462	−	0.0795292i	−0.731776	−	0.00268858i
$876$		0			0
$877$	−11.6203	+	20.1269i	−0.392388	+	0.679636i	−0.992764	−	0.120082i	$-0.961684\pi$
$877$	−11.6203	+	20.1269i	−0.392388	+	0.679636i	0.600376	+	0.799718i	$0.295018\pi$
$878$	−14.4687	−	25.0606i	−0.488296	−	0.845754i
$879$		0			0
$880$	7.50911	+	4.33539i	0.253132	+	0.146146i
$881$	39.9137			1.34473			0.672363	−	0.740222i	$-0.265280\pi$
$881$	39.9137			1.34473			0.672363	+	0.740222i	$0.265280\pi$
$882$		0			0
$883$	−35.7953			−1.20461			−0.602305	−	0.798266i	$-0.705751\pi$
$883$	−35.7953			−1.20461			−0.602305	+	0.798266i	$0.705751\pi$
$884$	−0.882895	−	0.509740i	−0.0296950	−	0.0171444i
$885$		0			0
$886$	−18.2955	−	31.6887i	−0.614648	−	1.06460i
$887$	−6.00830	+	10.4067i	−0.201739	+	0.349422i	−0.949089	−	0.315009i	$-0.897993\pi$
$887$	−6.00830	+	10.4067i	−0.201739	+	0.349422i	0.747350	+	0.664431i	$0.231326\pi$
$888$		0			0
$889$	36.7576	+	0.135049i	1.23281	+	0.00452941i
$890$			12.1611i			0.407642i
$891$		0			0
$892$	−11.9349	+	6.89060i	−0.399609	+	0.230714i
$893$	−4.05108	+	2.33889i	−0.135564	+	0.0782681i
$894$		0			0
$895$			19.5420i			0.653219i
$896$	2.28641	+	1.33128i	0.0763837	+	0.0444751i
$897$		0			0
$898$	19.8151	−	34.3207i	0.661238	−	1.14530i
$899$	13.8457	+	23.9814i	0.461779	+	0.799825i
$900$		0			0
$901$	−1.15645	−	0.667676i	−0.0385269	−	0.0222435i
$902$	−4.55690			−0.151728
$903$		0			0
$904$	−2.54003			−0.0844801
$905$	−56.6832	−	32.7260i	−1.88421	−	1.08785i
$906$		0			0
$907$	−20.9526	−	36.2910i	−0.695720	−	1.20502i	−0.969937	−	0.243355i	$-0.921752\pi$
$907$	−20.9526	−	36.2910i	−0.695720	−	1.20502i	0.274217	−	0.961668i	$-0.411581\pi$
$908$	6.32021	−	10.9469i	0.209743	−	0.363286i
$909$		0			0
$910$	2.74726	+	4.79903i	0.0910709	+	0.159086i
$911$		−	12.1167i		−	0.401445i	−0.979648	−	0.200723i	$-0.935671\pi$
$911$		−	12.1167i		−	0.401445i	0.979648	−	0.200723i	$-0.0643290\pi$
$912$		0			0
$913$	−6.45075	+	3.72434i	−0.213489	+	0.123258i
$914$	−7.28548	+	4.20628i	−0.240982	+	0.139131i
$915$		0			0
$916$		−	9.96426i		−	0.329228i
$917$	13.8607	−	23.8050i	0.457721	−	0.786112i
$918$		0			0
$919$	−15.6700	+	27.1412i	−0.516904	+	0.895304i	0.482903	+	0.875674i	$0.339582\pi$
$919$	−15.6700	+	27.1412i	−0.516904	+	0.895304i	−0.999807	+	0.0196305i	$0.993751\pi$
$920$	7.05472	+	12.2191i	0.232587	+	0.402853i
$921$		0			0
$922$	−34.8375	−	20.1134i	−1.14731	−	0.662401i
$923$	4.89654			0.161172
$924$		0			0
$925$	15.6424			0.514320
$926$	−20.6599	−	11.9280i	−0.678927	−	0.391979i
$927$		0			0
$928$	−4.31304	−	7.47040i	−0.141582	−	0.245228i
$929$	10.4378	−	18.0788i	0.342454	−	0.593148i	−0.642434	−	0.766341i	$-0.722075\pi$
$929$	10.4378	−	18.0788i	0.342454	−	0.593148i	0.984888	+	0.173194i	$0.0554086\pi$
$930$		0			0
$931$	−6.03630	−	3.54445i	−0.197832	−	0.116165i
$932$		−	18.1046i		−	0.593035i
$933$		0			0
$934$	−30.8004	+	17.7826i	−1.00782	+	0.581865i
$935$	−12.8615	+	7.42559i	−0.420616	+	0.242843i
$936$		0			0
$937$			3.69948i			0.120857i	0.998173	+	0.0604283i	$0.0192467\pi$
$937$			3.69948i			0.120857i	−0.998173	+	0.0604283i	$0.980753\pi$
$938$	−0.0303541	+	8.26175i	−0.000991095	+	0.269756i
$939$		0			0
$940$	8.21281	−	14.2250i	0.267872	−	0.463969i
$941$	−16.4609	−	28.5111i	−0.536610	−	0.929436i	−0.999084	−	0.0428029i	$-0.986371\pi$
$941$	−16.4609	−	28.5111i	−0.536610	−	0.929436i	0.462473	−	0.886633i	$-0.346962\pi$
$942$		0			0
$943$	−6.42173	−	3.70759i	−0.209120	−	0.120736i
$944$	−12.5794			−0.409423
$945$		0			0
$946$	−0.415038			−0.0134940
$947$	−23.7686	−	13.7228i	−0.772377	−	0.445932i	0.0613449	−	0.998117i	$-0.480461\pi$
$947$	−23.7686	−	13.7228i	−0.772377	−	0.445932i	−0.833722	+	0.552185i	$0.813794\pi$
$948$		0			0
$949$	−0.632713	−	1.09589i	−0.0205387	−	0.0355741i
$950$	3.66500	−	6.34796i	0.118908	−	0.205955i
$951$		0			0
$952$	−3.93278	+	2.25137i	−0.127462	+	0.0729673i
$953$			41.1355i			1.33251i	0.745725	+	0.666254i	$0.232103\pi$
$953$			41.1355i			1.33251i	−0.745725	+	0.666254i	$0.767897\pi$
$954$		0			0
$955$	−44.6355	+	25.7703i	−1.44437	+	0.833907i
$956$	10.2288	−	5.90559i	0.330822	−	0.191000i
$957$		0			0
$958$		−	38.0520i		−	1.22941i
$959$	14.6922	−	8.41070i	0.474434	−	0.271596i
$960$		0			0
$961$	−10.3473	+	17.9221i	−0.333785	+	0.578132i
$962$	−0.635106	−	1.10004i	−0.0204766	−	0.0354666i
$963$		0			0
$964$	8.48526	+	4.89897i	0.273292	+	0.157785i
$965$	26.2854			0.846158
$966$		0			0
$967$	−22.9162			−0.736934			−0.368467	−	0.929641i	$-0.620117\pi$
$967$	−22.9162			−0.736934			−0.368467	+	0.929641i	$0.620117\pi$
$968$	4.24567	+	2.45124i	0.136461	+	0.0787859i
$969$		0			0
$970$	−11.4756	−	19.8764i	−0.368460	−	0.638191i
$971$	−8.29489	+	14.3672i	−0.266196	+	0.461064i	−0.967876	−	0.251427i	$-0.919100\pi$
$971$	−8.29489	+	14.3672i	−0.266196	+	0.461064i	0.701680	+	0.712492i	$0.252433\pi$
$972$		0			0
$973$	0.171496	−	46.6777i	0.00549791	−	1.49642i
$974$			28.4537i			0.911715i
$975$		0			0
$976$	10.7145	−	6.18602i	0.342963	−	0.198010i
$977$	25.5981	−	14.7790i	0.818954	−	0.472824i	−0.0311013	−	0.999516i	$-0.509901\pi$
$977$	25.5981	−	14.7790i	0.818954	−	0.472824i	0.850056	+	0.526693i	$0.176568\pi$
$978$		0			0
$979$		−	8.55204i		−	0.273324i
$980$	24.5792	+	0.180613i	0.785154	+	0.00576946i
$981$		0			0
$982$	−20.7376	+	35.9187i	−0.661765	+	1.14621i
$983$	0.150054	+	0.259900i	0.00478596	+	0.00828953i	0.868408	−	0.495850i	$-0.165143\pi$
$983$	0.150054	+	0.259900i	0.00478596	+	0.00828953i	−0.863623	+	0.504139i	$0.831810\pi$
$984$		0			0
$985$	−2.29780	−	1.32664i	−0.0732141	−	0.0422702i
$986$	14.7746			0.470520
$987$		0			0
$988$	−0.595217			−0.0189364
$989$	−0.584884	−	0.337683i	−0.0185982	−	0.0107377i
$990$		0			0
$991$	4.57216	+	7.91922i	0.145240	+	0.251562i	0.929462	−	0.368917i	$-0.120271\pi$
$991$	4.57216	+	7.91922i	0.145240	+	0.251562i	−0.784223	+	0.620479i	$0.786938\pi$
$992$	−1.60510	+	2.78011i	−0.0509619	+	0.0882685i
$993$		0			0
$994$	10.9518	−	18.8091i	0.347370	−	0.596590i
$995$			12.0553i			0.382177i
$996$		0			0
$997$	−3.45887	+	1.99698i	−0.109544	+	0.0632450i	−0.553771	−	0.832669i	$-0.686812\pi$
$997$	−3.45887	+	1.99698i	−0.109544	+	0.0632450i	0.444227	+	0.895914i	$0.353478\pi$
$998$	18.6560	−	10.7711i	0.590546	−	0.340952i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2394.2.by.a.2357.12	yes	48
3.2	odd	2		2394.2.by.b.2357.13	yes	48
7.3	odd	6		2394.2.by.b.647.13	yes	48
21.17	even	6	inner	2394.2.by.a.647.12	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2394.2.by.a.647.12	✓	48	21.17	even	6	inner
2394.2.by.a.2357.12	yes	48	1.1	even	1	trivial
2394.2.by.b.647.13	yes	48	7.3	odd	6
2394.2.by.b.2357.13	yes	48	3.2	odd	2

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:	\( N \)	\(=\)	\( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2394.by (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.75570 - 3.04097i) q^{5} +(2.64573 + 0.00972055i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.75570 - 3.04097i) q^{5} +(2.64573 + 0.00972055i) q^{7} -1.00000i q^{8} +(-3.04097 + 1.75570i) q^{10} +(2.13849 - 1.23466i) q^{11} -0.595217i q^{13} +(-2.28641 - 1.33128i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.856393 - 1.48332i) q^{17} +(-0.866025 - 0.500000i) q^{19} +3.51141 q^{20} -2.46932 q^{22} +(-3.47984 - 2.00908i) q^{23} +(-3.66500 - 6.34796i) q^{25} +(-0.297608 + 0.515473i) q^{26} +(1.31445 + 2.29613i) q^{28} -8.62608i q^{29} +(-2.78011 + 1.60510i) q^{31} +(0.866025 - 0.500000i) q^{32} +1.71279i q^{34} +(4.67469 - 8.02853i) q^{35} +(-1.06702 + 1.84813i) q^{37} +(0.500000 + 0.866025i) q^{38} +(-3.04097 - 1.75570i) q^{40} +1.84541 q^{41} +0.168078 q^{43} +(2.13849 + 1.23466i) q^{44} +(2.00908 + 3.47984i) q^{46} +(2.33889 - 4.05108i) q^{47} +(6.99981 + 0.0514360i) q^{49} +7.32999i q^{50} +(0.515473 - 0.297608i) q^{52} +(0.675185 - 0.389819i) q^{53} -8.67078i q^{55} +(0.00972055 - 2.64573i) q^{56} +(-4.31304 + 7.47040i) q^{58} +(6.28968 + 10.8940i) q^{59} +(-10.7145 - 6.18602i) q^{61} +3.21019 q^{62} -1.00000 q^{64} +(-1.81004 - 1.04502i) q^{65} +(-1.56133 - 2.70431i) q^{67} +(0.856393 - 1.48332i) q^{68} +(-8.06266 + 4.61557i) q^{70} +8.22648i q^{71} +(1.84116 - 1.06300i) q^{73} +(1.84813 - 1.06702i) q^{74} -1.00000i q^{76} +(5.66988 - 3.24579i) q^{77} +(-2.36502 + 4.09633i) q^{79} +(1.75570 + 3.04097i) q^{80} +(-1.59817 - 0.922706i) q^{82} -3.01650 q^{83} -6.01429 q^{85} +(-0.145560 - 0.0840390i) q^{86} +(-1.23466 - 2.13849i) q^{88} +(1.73166 - 2.99933i) q^{89} +(0.00578583 - 1.57479i) q^{91} -4.01817i q^{92} +(-4.05108 + 2.33889i) q^{94} +(-3.04097 + 1.75570i) q^{95} +6.53619i q^{97} +(-6.03630 - 3.54445i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4} - 4 q^{7}+O(q^{10}) \) 48 * q + 24 * q^4 - 4 * q^7	\( 48 q + 24 q^{4} - 4 q^{7} - 12 q^{10} - 4 q^{14} - 24 q^{16} - 16 q^{17} + 8 q^{22} - 28 q^{25} + 4 q^{28} + 12 q^{31} - 24 q^{35} + 24 q^{38} - 12 q^{40} + 16 q^{41} + 8 q^{43} + 8 q^{46} - 32 q^{49} - 48 q^{53} + 4 q^{56} - 4 q^{58} + 16 q^{59} + 32 q^{62} - 48 q^{64} - 24 q^{67} + 16 q^{68} + 28 q^{70} + 12 q^{73} + 8 q^{77} - 20 q^{79} - 48 q^{82} + 128 q^{83} - 40 q^{85} + 4 q^{88} + 32 q^{89} + 40 q^{91} - 12 q^{95} - 16 q^{98}+O(q^{100}) \) 48 * q + 24 * q^4 - 4 * q^7 - 12 * q^10 - 4 * q^14 - 24 * q^16 - 16 * q^17 + 8 * q^22 - 28 * q^25 + 4 * q^28 + 12 * q^31 - 24 * q^35 + 24 * q^38 - 12 * q^40 + 16 * q^41 + 8 * q^43 + 8 * q^46 - 32 * q^49 - 48 * q^53 + 4 * q^56 - 4 * q^58 + 16 * q^59 + 32 * q^62 - 48 * q^64 - 24 * q^67 + 16 * q^68 + 28 * q^70 + 12 * q^73 + 8 * q^77 - 20 * q^79 - 48 * q^82 + 128 * q^83 - 40 * q^85 + 4 * q^88 + 32 * q^89 + 40 * q^91 - 12 * q^95 - 16 * q^98

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