LMFDB - Embedded newform 684.2.bo.a.613.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(73,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("684.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.bo (of order $9$, degree $6$, 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:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 228)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			613.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	684.613
Dual form			684.2.bo.a.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.93969 - 1.62760i) q^{5} +(1.61334 + 2.79439i) q^{7} +O(q^{10})$	$q+(-1.93969 - 1.62760i) q^{5} +(1.61334 + 2.79439i) q^{7} +(1.55303 - 2.68993i) q^{11} +(-1.05303 - 5.97205i) q^{13} +(-5.58512 + 2.03282i) q^{17} +(4.34002 + 0.405223i) q^{19} +(5.14543 - 4.31753i) q^{23} +(0.245100 + 1.39003i) q^{25} +(6.69846 + 2.43804i) q^{29} +(-3.81908 - 6.61484i) q^{31} +(1.41875 - 8.04612i) q^{35} +2.10607 q^{37} +(1.22281 - 6.93491i) q^{41} +(-7.17752 - 6.02265i) q^{43} +(-4.37211 - 1.59132i) q^{47} +(-1.70574 + 2.95442i) q^{49} +(4.86824 - 4.08494i) q^{53} +(-7.39053 + 2.68993i) q^{55} +(-0.252374 + 0.0918566i) q^{59} +(1.21688 - 1.02108i) q^{61} +(-7.67752 + 13.2979i) q^{65} +(1.22668 + 0.446476i) q^{67} +(6.34002 + 5.31991i) q^{71} +(0.159978 - 0.907278i) q^{73} +10.0223 q^{77} +(-2.09492 + 11.8809i) q^{79} +(0.0432332 + 0.0748822i) q^{83} +(14.1420 + 5.14728i) q^{85} +(1.22803 + 6.96448i) q^{89} +(14.9893 - 12.5775i) q^{91} +(-7.75877 - 7.84981i) q^{95} +(-3.12701 + 1.13814i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{5} + 3 q^{7}+O(q^{10}) $ 6 * q - 6 * q^5 + 3 * q^7	$ 6 q - 6 q^{5} + 3 q^{7} - 3 q^{11} + 6 q^{13} - 12 q^{17} + 6 q^{19} + 15 q^{23} + 12 q^{29} - 6 q^{31} + 6 q^{35} - 12 q^{37} + 18 q^{41} - 18 q^{43} + 3 q^{47} + 24 q^{53} - 27 q^{55} - 18 q^{59} - 9 q^{61} - 21 q^{65} - 6 q^{67} + 18 q^{71} + 21 q^{73} + 48 q^{77} + 6 q^{79} - 15 q^{83} + 27 q^{85} - 15 q^{89} + 30 q^{91} - 24 q^{95} + 9 q^{97}+O(q^{100}) $ 6 * q - 6 * q^5 + 3 * q^7 - 3 * q^11 + 6 * q^13 - 12 * q^17 + 6 * q^19 + 15 * q^23 + 12 * q^29 - 6 * q^31 + 6 * q^35 - 12 * q^37 + 18 * q^41 - 18 * q^43 + 3 * q^47 + 24 * q^53 - 27 * q^55 - 18 * q^59 - 9 * q^61 - 21 * q^65 - 6 * q^67 + 18 * q^71 + 21 * q^73 + 48 * q^77 + 6 * q^79 - 15 * q^83 + 27 * q^85 - 15 * q^89 + 30 * q^91 - 24 * q^95 + 9 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$	$1$

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			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.93969	−	1.62760i	−0.867457	−	0.727883i	0.0961041	−	0.995371i	$-0.469362\pi$
$5$	−1.93969	−	1.62760i	−0.867457	−	0.727883i	−0.963561	+	0.267489i	$0.913806\pi$
$6$		0			0
$7$	1.61334	+	2.79439i	0.609786	+	1.05618i	0.991275	+	0.131806i	$0.0420778\pi$
$7$	1.61334	+	2.79439i	0.609786	+	1.05618i	−0.381490	+	0.924373i	$0.624589\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.55303	−	2.68993i	0.468257	−	0.811045i	−0.531085	−	0.847319i	$-0.678215\pi$
$11$	1.55303	−	2.68993i	0.468257	−	0.811045i	0.999342	+	0.0362735i	$0.0115487\pi$
$12$		0			0
$13$	−1.05303	−	5.97205i	−0.292059	−	1.65635i	−0.678921	−	0.734211i	$-0.737552\pi$
$13$	−1.05303	−	5.97205i	−0.292059	−	1.65635i	0.386862	−	0.922137i	$-0.373559\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−5.58512	+	2.03282i	−1.35459	+	0.493031i	−0.914378	−	0.404862i	$-0.867319\pi$
$17$	−5.58512	+	2.03282i	−1.35459	+	0.493031i	−0.440213	+	0.897893i	$0.645097\pi$
$18$		0			0
$19$	4.34002	+	0.405223i	0.995669	+	0.0929645i
$19$	4.34002	+	0.405223i	0.995669	+	0.0929645i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	5.14543	−	4.31753i	1.07290	−	0.900267i	0.0775845	−	0.996986i	$-0.475279\pi$
$23$	5.14543	−	4.31753i	1.07290	−	0.900267i	0.995312	+	0.0967189i	$0.0308348\pi$
$24$		0			0
$25$	0.245100	+	1.39003i	0.0490200	+	0.278006i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	6.69846	+	2.43804i	1.24387	+	0.452733i	0.878327	−	0.478060i	$-0.158660\pi$
$29$	6.69846	+	2.43804i	1.24387	+	0.452733i	0.365546	+	0.930793i	$0.380882\pi$
$30$		0			0
$31$	−3.81908	−	6.61484i	−0.685927	−	1.18806i	−0.973145	−	0.230195i	$-0.926064\pi$
$31$	−3.81908	−	6.61484i	−0.685927	−	1.18806i	0.287218	−	0.957865i	$-0.407270\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.41875	−	8.04612i	0.239812	−	1.36004i
$36$		0			0
$37$	2.10607			0.346235			0.173118	−	0.984901i	$-0.444616\pi$
$37$	2.10607			0.346235			0.173118	+	0.984901i	$0.444616\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.22281	−	6.93491i	0.190971	−	1.08305i	−0.727069	−	0.686564i	$-0.759118\pi$
$41$	1.22281	−	6.93491i	0.190971	−	1.08305i	0.918041	−	0.396487i	$-0.129771\pi$
$42$		0			0
$43$	−7.17752	−	6.02265i	−1.09456	−	0.918446i	−0.0975139	−	0.995234i	$-0.531089\pi$
$43$	−7.17752	−	6.02265i	−1.09456	−	0.918446i	−0.997047	+	0.0767882i	$0.975533\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.37211	−	1.59132i	−0.637738	−	0.232118i	0.00285780	−	0.999996i	$-0.499090\pi$
$47$	−4.37211	−	1.59132i	−0.637738	−	0.232118i	−0.640596	+	0.767878i	$0.721313\pi$
$48$		0			0
$49$	−1.70574	+	2.95442i	−0.243677	+	0.422060i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.86824	−	4.08494i	0.668704	−	0.561110i	−0.243977	−	0.969781i	$-0.578452\pi$
$53$	4.86824	−	4.08494i	0.668704	−	0.561110i	0.912682	+	0.408671i	$0.134008\pi$
$54$		0			0
$55$	−7.39053	+	2.68993i	−0.996539	+	0.362710i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−0.252374	+	0.0918566i	−0.0328563	+	0.0119587i	−0.358396	−	0.933570i	$-0.616676\pi$
$59$	−0.252374	+	0.0918566i	−0.0328563	+	0.0119587i	0.325540	+	0.945528i	$0.394454\pi$
$60$		0			0
$61$	1.21688	−	1.02108i	0.155806	−	0.130737i	−0.561552	−	0.827441i	$-0.689796\pi$
$61$	1.21688	−	1.02108i	0.155806	−	0.130737i	0.717358	+	0.696705i	$0.245351\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−7.67752	+	13.2979i	−0.952279	+	1.64940i
$66$		0			0
$67$	1.22668	+	0.446476i	0.149863	+	0.0545457i	0.415863	−	0.909427i	$-0.363480\pi$
$67$	1.22668	+	0.446476i	0.149863	+	0.0545457i	−0.266000	+	0.963973i	$0.585702\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	6.34002	+	5.31991i	0.752422	+	0.631357i	0.936142	−	0.351621i	$-0.114370\pi$
$71$	6.34002	+	5.31991i	0.752422	+	0.631357i	−0.183720	+	0.982979i	$0.558814\pi$
$72$		0			0
$73$	0.159978	−	0.907278i	0.0187240	−	0.106189i	−0.974013	−	0.226490i	$-0.927275\pi$
$73$	0.159978	−	0.907278i	0.0187240	−	0.106189i	0.992737	+	0.120301i	$0.0383860\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	10.0223			1.14215
$78$		0			0
$79$	−2.09492	+	11.8809i	−0.235697	+	1.33671i	0.605443	+	0.795888i	$0.292996\pi$
$79$	−2.09492	+	11.8809i	−0.235697	+	1.33671i	−0.841140	+	0.540817i	$0.818115\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	0.0432332	+	0.0748822i	0.00474546	+	0.00821939i	0.868388	−	0.495885i	$-0.165156\pi$
$83$	0.0432332	+	0.0748822i	0.00474546	+	0.00821939i	−0.863643	+	0.504104i	$0.831823\pi$
$84$		0			0
$85$	14.1420	+	5.14728i	1.53392	+	0.558301i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.22803	+	6.96448i	0.130170	+	0.738233i	0.978102	+	0.208127i	$0.0667368\pi$
$89$	1.22803	+	6.96448i	0.130170	+	0.738233i	−0.847931	+	0.530106i	$0.822152\pi$
$90$		0			0
$91$	14.9893	−	12.5775i	1.57131	−	1.31848i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−7.75877	−	7.84981i	−0.796033	−	0.805373i
$96$		0			0
$97$	−3.12701	+	1.13814i	−0.317500	+	0.115561i	−0.495854	−	0.868406i	$-0.665145\pi$
$97$	−3.12701	+	1.13814i	−0.317500	+	0.115561i	0.178354	+	0.983966i	$0.442923\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.86824	+	10.5953i	0.185897	+	1.05427i	0.924798	+	0.380459i	$0.124234\pi$
$101$	1.86824	+	10.5953i	0.185897	+	1.05427i	−0.738901	+	0.673814i	$0.764655\pi$
$102$		0			0
$103$	−2.96451	+	5.13468i	−0.292102	+	0.505935i	−0.974306	−	0.225226i	$-0.927688\pi$
$103$	−2.96451	+	5.13468i	−0.292102	+	0.505935i	0.682205	+	0.731161i	$0.261021\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.29086	+	2.23583i	0.124792	+	0.216146i	0.921652	−	0.388018i	$-0.126840\pi$
$107$	1.29086	+	2.23583i	0.124792	+	0.216146i	−0.796860	+	0.604165i	$0.793507\pi$
$108$		0			0
$109$	3.66250	+	3.07321i	0.350804	+	0.294360i	0.801113	−	0.598513i	$-0.204242\pi$
$109$	3.66250	+	3.07321i	0.350804	+	0.294360i	−0.450309	+	0.892873i	$0.648686\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−16.6655			−1.56776			−0.783879	−	0.620914i	$-0.786762\pi$
$113$	−16.6655			−1.56776			−0.783879	+	0.620914i	$0.786762\pi$
$114$		0			0
$115$	−17.0077			−1.58598
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−14.6912	−	12.3274i	−1.34674	−	1.13005i
$120$		0			0
$121$	0.676174	+	1.17117i	0.0614704	+	0.106470i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−4.54323	+	7.86911i	−0.406359	+	0.703835i
$126$		0			0
$127$	0.906260	+	5.13965i	0.0804175	+	0.456070i	0.998252	+	0.0591064i	$0.0188251\pi$
$127$	0.906260	+	5.13965i	0.0804175	+	0.456070i	−0.917834	+	0.396964i	$0.870064\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−8.13563	+	2.96113i	−0.710813	+	0.258715i	−0.672021	−	0.740532i	$-0.734573\pi$
$131$	−8.13563	+	2.96113i	−0.710813	+	0.258715i	−0.0387926	+	0.999247i	$0.512351\pi$
$132$		0			0
$133$	5.86959	+	12.7815i	0.508958	+	1.10829i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	10.4684	−	8.78401i	0.894374	−	0.750469i	−0.0747087	−	0.997205i	$-0.523803\pi$
$137$	10.4684	−	8.78401i	0.894374	−	0.750469i	0.969083	+	0.246737i	$0.0793582\pi$
$138$		0			0
$139$	−2.37551	−	13.4722i	−0.201489	−	1.14270i	−0.902870	−	0.429913i	$-0.858544\pi$
$139$	−2.37551	−	13.4722i	−0.201489	−	1.14270i	0.701382	−	0.712786i	$-0.252567\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−17.6998	−	6.44220i	−1.48013	−	0.538724i
$144$		0			0
$145$	−9.02481	−	15.6314i	−0.749470	−	1.29812i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−4.12314	+	23.3835i	−0.337781	+	1.91565i	0.0600574	+	0.998195i	$0.480872\pi$
$149$	−4.12314	+	23.3835i	−0.337781	+	1.91565i	−0.397838	+	0.917456i	$0.630239\pi$
$150$		0			0
$151$	8.33544			0.678328			0.339164	−	0.940727i	$-0.389856\pi$
$151$	8.33544			0.678328			0.339164	+	0.940727i	$0.389856\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−3.35844	+	19.0467i	−0.269756	+	1.52986i
$156$		0			0
$157$	16.6197	+	13.9456i	1.32640	+	1.11298i	0.984905	+	0.173098i	$0.0553776\pi$
$157$	16.6197	+	13.9456i	1.32640	+	1.11298i	0.341495	+	0.939884i	$0.389067\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	20.3662	+	7.41268i	1.60508	+	0.584201i
$162$		0			0
$163$	11.4927	−	19.9060i	0.900180	−	1.55916i	0.0729198	−	0.997338i	$-0.476768\pi$
$163$	11.4927	−	19.9060i	0.900180	−	1.55916i	0.827260	−	0.561819i	$-0.189898\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	5.85710	−	4.91469i	0.453236	−	0.380310i	−0.387399	−	0.921912i	$-0.626626\pi$
$167$	5.85710	−	4.91469i	0.453236	−	0.380310i	0.840635	+	0.541602i	$0.182182\pi$
$168$		0			0
$169$	−22.3405	+	8.13127i	−1.71850	+	0.625483i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	11.0360	−	4.01676i	0.839048	−	0.305389i	0.113481	−	0.993540i	$-0.463800\pi$
$173$	11.0360	−	4.01676i	0.839048	−	0.305389i	0.725567	+	0.688151i	$0.241578\pi$
$174$		0			0
$175$	−3.48886	+	2.92750i	−0.263733	+	0.221298i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−2.09879	+	3.63522i	−0.156871	+	0.271709i	−0.933739	−	0.357955i	$-0.883474\pi$
$179$	−2.09879	+	3.63522i	−0.156871	+	0.271709i	0.776868	+	0.629664i	$0.216807\pi$
$180$		0			0
$181$	−11.5842	−	4.21632i	−0.861050	−	0.313397i	−0.126513	−	0.991965i	$-0.540379\pi$
$181$	−11.5842	−	4.21632i	−0.861050	−	0.313397i	−0.734537	+	0.678568i	$0.762601\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−4.08512	−	3.42782i	−0.300344	−	0.252019i
$186$		0			0
$187$	−3.20574	+	18.1806i	−0.234427	+	1.32950i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	10.2044			0.738364			0.369182	−	0.929357i	$-0.379638\pi$
$191$	10.2044			0.738364			0.369182	+	0.929357i	$0.379638\pi$
$192$		0			0
$193$	−3.76945	+	21.3776i	−0.271331	+	1.53879i	0.479050	+	0.877788i	$0.340981\pi$
$193$	−3.76945	+	21.3776i	−0.271331	+	1.53879i	−0.750381	+	0.661006i	$0.770130\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−8.34255	−	14.4497i	−0.594382	−	1.02950i	−0.993634	−	0.112658i	$-0.964063\pi$
$197$	−8.34255	−	14.4497i	−0.594382	−	1.02950i	0.399252	−	0.916841i	$-0.369270\pi$
$198$		0			0
$199$	2.31180	+	0.841428i	0.163879	+	0.0596472i	0.422657	−	0.906290i	$-0.361097\pi$
$199$	2.31180	+	0.841428i	0.163879	+	0.0596472i	−0.258778	+	0.965937i	$0.583320\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	3.99407	+	22.6515i	0.280329	+	1.58982i
$204$		0			0
$205$	−13.6591	+	11.4613i	−0.953993	+	0.800495i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	7.83022	−	11.0450i	0.541628	−	0.764002i
$210$		0			0
$211$	1.15745	−	0.421278i	0.0796822	−	0.0290020i	−0.301871	−	0.953349i	$-0.597611\pi$
$211$	1.15745	−	0.421278i	0.0796822	−	0.0290020i	0.381554	+	0.924347i	$0.375389\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	4.11974	+	23.3642i	0.280964	+	1.59342i
$216$		0			0
$217$	12.3229	−	21.3440i	0.836536	−	1.44892i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	18.0214	+	31.2140i	1.21225	+	2.09968i
$222$		0			0
$223$	5.03983	+	4.22892i	0.337492	+	0.283189i	0.795744	−	0.605633i	$-0.207080\pi$
$223$	5.03983	+	4.22892i	0.337492	+	0.283189i	−0.458252	+	0.888822i	$0.651524\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−9.72967			−0.645781			−0.322891	−	0.946436i	$-0.604655\pi$
$227$	−9.72967			−0.645781			−0.322891	+	0.946436i	$0.604655\pi$
$228$		0			0
$229$	−9.86753			−0.652064			−0.326032	−	0.945359i	$-0.605712\pi$
$229$	−9.86753			−0.652064			−0.326032	+	0.945359i	$0.605712\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−16.7121	−	14.0231i	−1.09485	−	0.918687i	−0.0977803	−	0.995208i	$-0.531174\pi$
$233$	−16.7121	−	14.0231i	−1.09485	−	0.918687i	−0.997068	+	0.0765212i	$0.975619\pi$
$234$		0			0
$235$	5.89053	+	10.2027i	0.384256	+	0.665551i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	10.6557	−	18.4562i	0.689260	−	1.19383i	−0.282818	−	0.959174i	$-0.591269\pi$
$239$	10.6557	−	18.4562i	0.689260	−	1.19383i	0.972078	−	0.234659i	$-0.0753974\pi$
$240$		0			0
$241$	2.71688	+	15.4082i	0.175010	+	0.992529i	0.938133	+	0.346276i	$0.112554\pi$
$241$	2.71688	+	15.4082i	0.175010	+	0.992529i	−0.763123	+	0.646253i	$0.776335\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	8.11721	−	2.95442i	0.518590	−	0.188751i
$246$		0			0
$247$	−2.15018	−	26.3455i	−0.136813	−	1.67633i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	7.75356	−	6.50601i	0.489400	−	0.410655i	−0.364411	−	0.931238i	$-0.618730\pi$
$251$	7.75356	−	6.50601i	0.489400	−	0.410655i	0.853811	+	0.520583i	$0.174285\pi$
$252$		0			0
$253$	−3.62284	−	20.5461i	−0.227766	−	1.29172i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.49020	−	1.63430i	−0.280091	−	0.101945i	0.198155	−	0.980171i	$-0.436505\pi$
$257$	−4.49020	−	1.63430i	−0.280091	−	0.101945i	−0.478246	+	0.878226i	$0.658727\pi$
$258$		0			0
$259$	3.39780	+	5.88517i	0.211129	+	0.365687i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	3.76651	−	21.3609i	0.232253	−	1.31717i	−0.616069	−	0.787692i	$-0.711276\pi$
$263$	3.76651	−	21.3609i	0.232253	−	1.31717i	0.848322	−	0.529480i	$-0.177613\pi$
$264$		0			0
$265$	−16.0915			−0.988494
$266$		0			0
$267$		0			0
$268$		0			0
$269$	0.561185	−	3.18264i	0.0342160	−	0.194049i	−0.962909	−	0.269828i	$-0.913033\pi$
$269$	0.561185	−	3.18264i	0.0342160	−	0.194049i	0.997125	+	0.0757790i	$0.0241443\pi$
$270$		0			0
$271$	−8.97952	−	7.53471i	−0.545467	−	0.457701i	0.327935	−	0.944700i	$-0.393647\pi$
$271$	−8.97952	−	7.53471i	−0.545467	−	0.457701i	−0.873403	+	0.486999i	$0.838092\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	4.11974	+	1.49946i	0.248430	+	0.0904209i
$276$		0			0
$277$	−4.38666	+	7.59792i	−0.263569	+	0.456515i	−0.967188	−	0.254063i	$-0.918233\pi$
$277$	−4.38666	+	7.59792i	−0.263569	+	0.456515i	0.703619	+	0.710578i	$0.251566\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−19.4702	+	16.3374i	−1.16149	+	0.974609i	−0.999925	−	0.0122521i	$-0.996100\pi$
$281$	−19.4702	+	16.3374i	−1.16149	+	0.974609i	−0.161569	+	0.986861i	$0.551655\pi$
$282$		0			0
$283$	2.51114	−	0.913982i	0.149272	−	0.0543306i	−0.266304	−	0.963889i	$-0.585802\pi$
$283$	2.51114	−	0.913982i	0.149272	−	0.0543306i	0.415576	+	0.909559i	$0.363580\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	21.3516	−	7.77136i	1.26035	−	0.458729i
$288$		0			0
$289$	14.0385	−	11.7797i	0.825793	−	0.692923i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	9.97683	−	17.2804i	0.582853	−	1.00953i	−0.412287	−	0.911054i	$-0.635270\pi$
$293$	9.97683	−	17.2804i	0.582853	−	1.00953i	0.995139	−	0.0984765i	$-0.0313969\pi$
$294$		0			0
$295$	0.639033	+	0.232589i	0.0372059	+	0.0135419i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−31.2028	−	26.1823i	−1.80450	−	1.51416i
$300$		0			0
$301$	5.24985	−	29.7734i	0.302596	−	1.71611i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−4.02229			−0.230316
$306$		0			0
$307$	−4.16431	+	23.6170i	−0.237670	+	1.34789i	0.599247	+	0.800564i	$0.295467\pi$
$307$	−4.16431	+	23.6170i	−0.237670	+	1.34789i	−0.836917	+	0.547330i	$0.815644\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−0.0812519	−	0.140732i	−0.00460737	−	0.00798020i	0.863713	−	0.503985i	$-0.168133\pi$
$311$	−0.0812519	−	0.140732i	−0.00460737	−	0.00798020i	−0.868320	+	0.496005i	$0.834800\pi$
$312$		0			0
$313$	−6.31655	−	2.29904i	−0.357033	−	0.129949i	0.157275	−	0.987555i	$-0.449729\pi$
$313$	−6.31655	−	2.29904i	−0.357033	−	0.129949i	−0.514308	+	0.857606i	$0.671951\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.48024	−	14.0661i	−0.139304	−	0.790032i	−0.971765	−	0.235949i	$-0.924180\pi$
$317$	−2.48024	−	14.0661i	−0.139304	−	0.790032i	0.832461	−	0.554083i	$-0.186931\pi$
$318$		0			0
$319$	16.9611	−	14.2321i	0.949640	−	0.796842i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−25.0633	+	6.55926i	−1.39456	+	0.364967i
$324$		0			0
$325$	8.04323	−	2.92750i	0.446158	−	0.162388i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−2.60694	−	14.7847i	−0.143725	−	0.815108i
$330$		0			0
$331$	16.6532	−	28.8441i	0.915341	−	1.58542i	0.108940	−	0.994048i	$-0.465254\pi$
$331$	16.6532	−	28.8441i	0.915341	−	1.58542i	0.806401	−	0.591369i	$-0.201412\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−1.65270	−	2.86257i	−0.0902968	−	0.156399i
$336$		0			0
$337$	−1.41669	−	1.18874i	−0.0771720	−	0.0647550i	0.603386	−	0.797450i	$-0.293818\pi$
$337$	−1.41669	−	1.18874i	−0.0771720	−	0.0647550i	−0.680558	+	0.732695i	$0.738262\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−23.7246			−1.28476
$342$		0			0
$343$	11.5790			0.625209
$344$		0			0
$345$		0			0
$346$		0			0
$347$	5.28493	+	4.43458i	0.283710	+	0.238061i	0.773525	−	0.633765i	$-0.218491\pi$
$347$	5.28493	+	4.43458i	0.283710	+	0.238061i	−0.489816	+	0.871826i	$0.662936\pi$
$348$		0			0
$349$	5.61081	+	9.71822i	0.300340	+	0.520204i	0.976213	−	0.216814i	$-0.0695665\pi$
$349$	5.61081	+	9.71822i	0.300340	+	0.520204i	−0.675873	+	0.737018i	$0.736233\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.954241	+	1.65279i	−0.0507891	+	0.0879693i	−0.890302	−	0.455370i	$-0.849507\pi$
$353$	−0.954241	+	1.65279i	−0.0507891	+	0.0879693i	0.839513	+	0.543339i	$0.182840\pi$
$354$		0			0
$355$	−3.63903	−	20.6380i	−0.193140	−	1.09535i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	8.95558	−	3.25957i	0.472658	−	0.172033i	−0.0946982	−	0.995506i	$-0.530189\pi$
$359$	8.95558	−	3.25957i	0.472658	−	0.172033i	0.567356	+	0.823473i	$0.307966\pi$
$360$		0			0
$361$	18.6716	+	3.51735i	0.982715	+	0.185124i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−1.78699	+	1.49946i	−0.0935353	+	0.0784854i
$366$		0			0
$367$	3.11216	+	17.6499i	0.162453	+	0.921319i	0.951651	+	0.307180i	$0.0993854\pi$
$367$	3.11216	+	17.6499i	0.162453	+	0.921319i	−0.789198	+	0.614139i	$0.789504\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	19.2690	+	7.01336i	1.00040	+	0.364115i
$372$		0			0
$373$	15.2344	+	26.3868i	0.788808	+	1.36626i	0.926697	+	0.375809i	$0.122635\pi$
$373$	15.2344	+	26.3868i	0.788808	+	1.36626i	−0.137889	+	0.990448i	$0.544032\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	7.50640	−	42.5709i	0.386599	−	2.19251i
$378$		0			0
$379$	6.57903			0.337942			0.168971	−	0.985621i	$-0.445956\pi$
$379$	6.57903			0.337942			0.168971	+	0.985621i	$0.445956\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−3.99525	+	22.6582i	−0.204148	+	1.15778i	0.694627	+	0.719370i	$0.255569\pi$
$383$	−3.99525	+	22.6582i	−0.204148	+	1.15778i	−0.898775	+	0.438410i	$0.855542\pi$
$384$		0			0
$385$	−19.4402	−	16.3122i	−0.990762	−	0.831348i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	25.6587	+	9.33900i	1.30095	+	0.473506i	0.897305	−	0.441411i	$-0.145522\pi$
$389$	25.6587	+	9.33900i	1.30095	+	0.473506i	0.403642	+	0.914917i	$0.367744\pi$
$390$		0			0
$391$	−19.9611	+	34.5736i	−1.00948	+	1.74846i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	23.4008	−	19.6356i	1.17742	−	0.987974i
$396$		0			0
$397$	5.52734	−	2.01179i	0.277409	−	0.100969i	−0.199569	−	0.979884i	$-0.563954\pi$
$397$	5.52734	−	2.01179i	0.277409	−	0.100969i	0.476978	+	0.878915i	$0.341732\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−4.02987	+	1.46675i	−0.201242	+	0.0732461i	−0.440675	−	0.897667i	$-0.645261\pi$
$401$	−4.02987	+	1.46675i	−0.201242	+	0.0732461i	0.239433	+	0.970913i	$0.423039\pi$
$402$		0			0
$403$	−35.4825	+	29.7734i	−1.76751	+	1.48312i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	3.27079	−	5.66518i	0.162127	−	0.280812i
$408$		0			0
$409$	30.4714	+	11.0907i	1.50671	+	0.548398i	0.957788	−	0.287474i	$-0.0928155\pi$
$409$	30.4714	+	11.0907i	1.50671	+	0.548398i	0.548924	+	0.835872i	$0.315038\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−0.663848	−	0.557035i	−0.0326658	−	0.0274099i
$414$		0			0
$415$	0.0380187	−	0.215615i	0.00186626	−	0.0105841i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−9.86577			−0.481974			−0.240987	−	0.970528i	$-0.577471\pi$
$419$	−9.86577			−0.481974			−0.240987	+	0.970528i	$0.577471\pi$
$420$		0			0
$421$	3.83884	−	21.7711i	0.187094	−	1.06106i	−0.736142	−	0.676827i	$-0.763355\pi$
$421$	3.83884	−	21.7711i	0.187094	−	1.06106i	0.923236	−	0.384234i	$-0.125534\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−4.19459	−	7.26525i	−0.203468	−	0.352416i
$426$		0			0
$427$	4.81655	+	1.75308i	0.233089	+	0.0848376i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	4.39693	+	24.9362i	0.211792	+	1.20113i	0.886387	+	0.462946i	$0.153208\pi$
$431$	4.39693	+	24.9362i	0.211792	+	1.20113i	−0.674594	+	0.738189i	$0.735681\pi$
$432$		0			0
$433$	9.81702	−	8.23746i	0.471776	−	0.395867i	−0.375666	−	0.926755i	$-0.622586\pi$
$433$	9.81702	−	8.23746i	0.471776	−	0.395867i	0.847442	+	0.530888i	$0.178142\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	24.0808	−	16.6531i	1.15194	−	0.796627i
$438$		0			0
$439$	4.90895	−	1.78671i	0.234291	−	0.0852751i	−0.222206	−	0.975000i	$-0.571326\pi$
$439$	4.90895	−	1.78671i	0.234291	−	0.0852751i	0.456498	+	0.889725i	$0.349104\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	3.02141	+	17.1353i	0.143552	+	0.814121i	0.968519	+	0.248941i	$0.0800825\pi$
$443$	3.02141	+	17.1353i	0.143552	+	0.814121i	−0.824967	+	0.565181i	$0.808806\pi$
$444$		0			0
$445$	8.95336	−	15.5077i	0.424430	−	0.735135i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	11.8255	+	20.4823i	0.558079	+	0.966621i	0.997657	+	0.0684163i	$0.0217946\pi$
$449$	11.8255	+	20.4823i	0.558079	+	0.966621i	−0.439578	+	0.898204i	$0.644872\pi$
$450$		0			0
$451$	−16.7554	−	14.0594i	−0.788979	−	0.662032i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−49.5458			−2.32274
$456$		0			0
$457$	−24.2695			−1.13528			−0.567640	−	0.823277i	$-0.692143\pi$
$457$	−24.2695			−1.13528			−0.567640	+	0.823277i	$0.692143\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−5.34318	−	4.48346i	−0.248857	−	0.208815i	0.509823	−	0.860279i	$-0.329711\pi$
$461$	−5.34318	−	4.48346i	−0.248857	−	0.208815i	−0.758680	+	0.651464i	$0.774155\pi$
$462$		0			0
$463$	−14.0385	−	24.3154i	−0.652424	−	1.13003i	−0.982533	−	0.186088i	$-0.940419\pi$
$463$	−14.0385	−	24.3154i	−0.652424	−	1.13003i	0.330109	−	0.943943i	$-0.392914\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.91147	−	3.31077i	0.0884525	−	0.153204i	−0.818405	−	0.574642i	$-0.805141\pi$
$467$	1.91147	−	3.31077i	0.0884525	−	0.153204i	0.906857	+	0.421438i	$0.138475\pi$
$468$		0			0
$469$	0.731429	+	4.14814i	0.0337743	+	0.191543i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−27.3475	+	9.95366i	−1.25744	+	0.457670i
$474$		0			0
$475$	0.500467	+	6.13208i	0.0229630	+	0.281359i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	23.7010	−	19.8875i	1.08293	−	0.908683i	0.0867654	−	0.996229i	$-0.472347\pi$
$479$	23.7010	−	19.8875i	1.08293	−	0.908683i	0.996160	+	0.0875461i	$0.0279025\pi$
$480$		0			0
$481$	−2.21776	−	12.5775i	−0.101121	−	0.573486i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	7.91787	+	2.88187i	0.359532	+	0.130859i
$486$		0			0
$487$	1.43242	+	2.48102i	0.0649091	+	0.112426i	0.896654	−	0.442733i	$-0.145991\pi$
$487$	1.43242	+	2.48102i	0.0649091	+	0.112426i	−0.831745	+	0.555159i	$0.812658\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	7.24985	−	41.1159i	0.327181	−	1.85554i	−0.166702	−	0.986007i	$-0.553312\pi$
$491$	7.24985	−	41.1159i	0.327181	−	1.85554i	0.493883	−	0.869529i	$-0.335577\pi$
$492$		0			0
$493$	−42.3678			−1.90815
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.63728	+	26.2993i	−0.208010	+	1.17969i
$498$		0			0
$499$	7.26991	+	6.10018i	0.325446	+	0.273082i	0.790841	−	0.612021i	$-0.209643\pi$
$499$	7.26991	+	6.10018i	0.325446	+	0.273082i	−0.465395	+	0.885103i	$0.654088\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−11.8785	−	4.32342i	−0.529636	−	0.192772i	0.0633395	−	0.997992i	$-0.479825\pi$
$503$	−11.8785	−	4.32342i	−0.529636	−	0.192772i	−0.592976	+	0.805220i	$0.702047\pi$
$504$		0			0
$505$	13.6211	−	23.5924i	0.606130	−	1.04985i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	14.9349	−	12.5319i	0.661980	−	0.555467i	−0.248700	−	0.968581i	$-0.580003\pi$
$509$	14.9349	−	12.5319i	0.661980	−	0.555467i	0.910679	+	0.413114i	$0.135559\pi$
$510$		0			0
$511$	2.79339	−	1.01671i	0.123572	−	0.0449766i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	14.1074	−	5.13468i	0.621647	−	0.226261i
$516$		0			0
$517$	−11.0706	+	9.28931i	−0.486883	+	0.408544i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	10.1416	−	17.5657i	0.444310	−	0.769567i	−0.553694	−	0.832720i	$-0.686782\pi$
$521$	10.1416	−	17.5657i	0.444310	−	0.769567i	0.998004	+	0.0631531i	$0.0201156\pi$
$522$		0			0
$523$	−14.3461	−	5.22156i	−0.627312	−	0.228323i	0.00874906	−	0.999962i	$-0.497215\pi$
$523$	−14.3461	−	5.22156i	−0.627312	−	0.228323i	−0.636061	+	0.771639i	$0.719437\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	34.7768	+	29.1812i	1.51490	+	1.27115i
$528$		0			0
$529$	3.84049	−	21.7805i	0.166978	−	0.946978i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−42.7033			−1.84968
$534$		0			0
$535$	1.13516	−	6.43783i	0.0490774	−	0.278332i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	5.29813	+	9.17664i	0.228207	+	0.395266i
$540$		0			0
$541$	19.3726	+	7.05104i	0.832892	+	0.303148i	0.723045	−	0.690801i	$-0.242742\pi$
$541$	19.3726	+	7.05104i	0.832892	+	0.303148i	0.109847	+	0.993949i	$0.464964\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−2.10220	−	11.9221i	−0.0900482	−	0.510689i
$546$		0			0
$547$	−21.7645	+	18.2625i	−0.930581	+	0.780850i	−0.975922	−	0.218122i	$-0.930007\pi$
$547$	−21.7645	+	18.2625i	−0.930581	+	0.780850i	0.0453408	+	0.998972i	$0.485563\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	28.0835	+	13.2955i	1.19640	+	0.566408i
$552$		0			0
$553$	−36.5797	+	13.3139i	−1.55553	+	0.566165i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	6.56717	+	37.2443i	0.278260	+	1.57809i	0.728412	+	0.685139i	$0.240259\pi$
$557$	6.56717	+	37.2443i	0.278260	+	1.57809i	−0.450152	+	0.892952i	$0.648630\pi$
$558$		0			0
$559$	−28.4094	+	49.2065i	−1.20159	+	2.08122i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	4.82042	+	8.34922i	0.203157	+	0.351877i	0.949544	−	0.313634i	$-0.101547\pi$
$563$	4.82042	+	8.34922i	0.203157	+	0.351877i	−0.746387	+	0.665512i	$0.768213\pi$
$564$		0			0
$565$	32.3259	+	27.1247i	1.35996	+	1.14114i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−21.1129			−0.885098			−0.442549	−	0.896744i	$-0.645926\pi$
$569$	−21.1129			−0.885098			−0.442549	+	0.896744i	$0.645926\pi$
$570$		0			0
$571$	−2.11112			−0.0883476			−0.0441738	−	0.999024i	$-0.514066\pi$
$571$	−2.11112			−0.0883476			−0.0441738	+	0.999024i	$0.514066\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	7.26264	+	6.09408i	0.302873	+	0.254141i
$576$		0			0
$577$	−11.5715	−	20.0423i	−0.481726	−	0.834374i	0.518054	−	0.855348i	$-0.326657\pi$
$577$	−11.5715	−	20.0423i	−0.481726	−	0.834374i	−0.999780	+	0.0209742i	$0.993323\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−0.139500	+	0.241621i	−0.00578743	+	0.0100241i
$582$		0			0
$583$	−3.42767	−	19.4393i	−0.141960	−	0.805093i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−18.0052	+	6.55336i	−0.743155	+	0.270486i	−0.685722	−	0.727863i	$-0.740514\pi$
$587$	−18.0052	+	6.55336i	−0.743155	+	0.270486i	−0.0574324	+	0.998349i	$0.518291\pi$
$588$		0			0
$589$	−13.8944	−	30.2561i	−0.572509	−	1.24668i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−28.4978	+	23.9125i	−1.17026	+	0.981968i	−0.999994	−	0.00342988i	$-0.998908\pi$
$593$	−28.4978	+	23.9125i	−1.17026	+	0.981968i	−0.170269	+	0.985398i	$0.554464\pi$
$594$		0			0
$595$	8.43242	+	47.8226i	0.345695	+	1.96054i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	29.0412	+	10.5701i	1.18659	+	0.431884i	0.858525	−	0.512772i	$-0.171381\pi$
$599$	29.0412	+	10.5701i	1.18659	+	0.431884i	0.328065	+	0.944655i	$0.393603\pi$
$600$		0			0
$601$	21.7802	+	37.7244i	0.888432	+	1.53881i	0.841729	+	0.539901i	$0.181538\pi$
$601$	21.7802	+	37.7244i	0.888432	+	1.53881i	0.0467035	+	0.998909i	$0.485128\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.594618	−	3.37225i	0.0241747	−	0.137101i
$606$		0			0
$607$	20.9659			0.850978			0.425489	−	0.904964i	$-0.360102\pi$
$607$	20.9659			0.850978			0.425489	+	0.904964i	$0.360102\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−4.89945	+	27.7862i	−0.198211	+	1.12411i
$612$		0			0
$613$	4.82951	+	4.05244i	0.195062	+	0.163676i	0.735088	−	0.677972i	$-0.237141\pi$
$613$	4.82951	+	4.05244i	0.195062	+	0.163676i	−0.540026	+	0.841649i	$0.681585\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−36.1241	−	13.1481i	−1.45430	−	0.529322i	−0.510512	−	0.859871i	$-0.670544\pi$
$617$	−36.1241	−	13.1481i	−1.45430	−	0.529322i	−0.943789	+	0.330549i	$0.892766\pi$
$618$		0			0
$619$	9.31908	−	16.1411i	0.374565	−	0.648766i	−0.615697	−	0.787983i	$-0.711125\pi$
$619$	9.31908	−	16.1411i	0.374565	−	0.648766i	0.990262	+	0.139217i	$0.0444586\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−17.4802	+	14.6677i	−0.700331	+	0.587647i
$624$		0			0
$625$	28.2520	−	10.2829i	1.13008	−	0.411315i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−11.7626	+	4.28125i	−0.469007	+	0.170705i
$630$		0			0
$631$	11.8407	−	9.93556i	0.471372	−	0.395528i	−0.375923	−	0.926651i	$-0.622674\pi$
$631$	11.8407	−	9.93556i	0.471372	−	0.395528i	0.847295	+	0.531123i	$0.178230\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	6.60741	−	11.4444i	0.262207	−	0.454156i
$636$		0			0
$637$	19.4402	+	7.07564i	0.770247	+	0.280347i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	19.1630	+	16.0796i	0.756892	+	0.635108i	0.937316	−	0.348481i	$-0.113303\pi$
$641$	19.1630	+	16.0796i	0.756892	+	0.635108i	−0.180424	+	0.983589i	$0.557747\pi$
$642$		0			0
$643$	3.96333	−	22.4771i	0.156298	−	0.886412i	−0.801291	−	0.598275i	$-0.795853\pi$
$643$	3.96333	−	22.4771i	0.156298	−	0.886412i	0.957589	−	0.288137i	$-0.0930358\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−46.1252			−1.81337			−0.906684	−	0.421811i	$-0.861395\pi$
$647$	−46.1252			−1.81337			−0.906684	+	0.421811i	$0.861395\pi$
$648$		0			0
$649$	−0.144857	+	0.821525i	−0.00568614	+	0.0322477i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−7.33868	−	12.7110i	−0.287185	−	0.497418i	0.685952	−	0.727647i	$-0.259386\pi$
$653$	−7.33868	−	12.7110i	−0.287185	−	0.497418i	−0.973137	+	0.230228i	$0.926053\pi$
$654$		0			0
$655$	20.6001	+	7.49784i	0.804914	+	0.292965i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	3.73648	+	21.1906i	0.145553	+	0.825470i	0.966922	+	0.255073i	$0.0820995\pi$
$659$	3.73648	+	21.1906i	0.145553	+	0.825470i	−0.821369	+	0.570397i	$0.806789\pi$
$660$		0			0
$661$	−24.0494	+	20.1798i	−0.935413	+	0.784904i	−0.976781	−	0.214240i	$-0.931273\pi$
$661$	−24.0494	+	20.1798i	−0.935413	+	0.784904i	0.0413686	+	0.999144i	$0.486828\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	9.41787	−	34.3454i	0.365209	−	1.33186i
$666$		0			0
$667$	44.9928	−	16.3760i	1.74213	−	0.634083i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−0.856792	−	4.85911i	−0.0330761	−	0.187584i
$672$		0			0
$673$	−5.83662	+	10.1093i	−0.224985	+	0.389686i	−0.956315	−	0.292338i	$-0.905567\pi$
$673$	−5.83662	+	10.1093i	−0.224985	+	0.389686i	0.731330	+	0.682024i	$0.238900\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	20.6866	+	35.8302i	0.795051	+	1.37707i	0.922807	+	0.385263i	$0.125889\pi$
$677$	20.6866	+	35.8302i	0.795051	+	1.37707i	−0.127756	+	0.991806i	$0.540777\pi$
$678$		0			0
$679$	−8.22534	−	6.90188i	−0.315659	−	0.264870i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	29.5117			1.12923			0.564616	−	0.825354i	$-0.309024\pi$
$683$	29.5117			1.12923			0.564616	+	0.825354i	$0.309024\pi$
$684$		0			0
$685$	−34.6023			−1.32208
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−29.5219	−	24.7718i	−1.12469	−	0.943730i
$690$		0			0
$691$	2.23917	+	3.87836i	0.0851820	+	0.147540i	0.905469	−	0.424413i	$-0.139519\pi$
$691$	2.23917	+	3.87836i	0.0851820	+	0.147540i	−0.820287	+	0.571953i	$0.806186\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−17.3195	+	29.9983i	−0.656968	+	1.13790i
$696$		0			0
$697$	7.26786	+	41.2181i	0.275290	+	1.56125i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	5.55690	−	2.02255i	0.209881	−	0.0763906i	−0.234940	−	0.972010i	$-0.575489\pi$
$701$	5.55690	−	2.02255i	0.209881	−	0.0763906i	0.444821	+	0.895619i	$0.353267\pi$
$702$		0			0
$703$	9.14038	+	0.853427i	0.344736	+	0.0321876i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−26.5933	+	22.3145i	−1.00015	+	0.839221i
$708$		0			0
$709$	5.19830	+	29.4810i	0.195226	+	1.10718i	0.912096	+	0.409976i	$0.134463\pi$
$709$	5.19830	+	29.4810i	0.195226	+	1.10718i	−0.716870	+	0.697207i	$0.754426\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−48.2105	−	17.5472i	−1.80550	−	0.657148i
$714$		0			0
$715$	23.8469	+	41.3040i	0.891823	+	1.54468i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−8.29709	+	47.0552i	−0.309429	+	1.75486i	0.292456	+	0.956279i	$0.405527\pi$
$719$	−8.29709	+	47.0552i	−0.309429	+	1.75486i	−0.601886	+	0.798582i	$0.705584\pi$
$720$		0			0
$721$	−19.1310			−0.712477
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1.74716	+	9.90863i	−0.0648879	+	0.367997i
$726$		0			0
$727$	−32.0933	−	26.9295i	−1.19028	−	0.998760i	−0.999855	−	0.0170574i	$-0.994570\pi$
$727$	−32.0933	−	26.9295i	−1.19028	−	0.998760i	−0.190421	−	0.981702i	$-0.560985\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	52.3303	+	19.0467i	1.93551	+	0.704466i
$732$		0			0
$733$	−10.8068	+	18.7178i	−0.399156	+	0.691359i	−0.993622	−	0.112762i	$-0.964030\pi$
$733$	−10.8068	+	18.7178i	−0.399156	+	0.691359i	0.594466	+	0.804121i	$0.297364\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	3.10607	−	2.60630i	0.114413	−	0.0960043i
$738$		0			0
$739$	−30.4688	+	11.0898i	−1.12081	+	0.407943i	−0.834949	−	0.550327i	$-0.814503\pi$
$739$	−30.4688	+	11.0898i	−1.12081	+	0.407943i	−0.285865	+	0.958270i	$0.592281\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−25.2754	+	9.19951i	−0.927266	+	0.337497i	−0.761125	−	0.648605i	$-0.775353\pi$
$743$	−25.2754	+	9.19951i	−0.927266	+	0.337497i	−0.166141	+	0.986102i	$0.553131\pi$
$744$		0			0
$745$	46.0565	−	38.6460i	1.68738	−	1.41588i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−4.16519	+	7.21432i	−0.152193	+	0.263606i
$750$		0			0
$751$	5.38103	+	1.95854i	0.196357	+	0.0714680i	0.438327	−	0.898816i	$-0.355571\pi$
$751$	5.38103	+	1.95854i	0.196357	+	0.0714680i	−0.241970	+	0.970284i	$0.577794\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−16.1682	−	13.5667i	−0.588421	−	0.493743i
$756$		0			0
$757$	1.50269	−	8.52217i	0.0546161	−	0.309744i	−0.945246	−	0.326359i	$-0.894178\pi$
$757$	1.50269	−	8.52217i	0.0546161	−	0.309744i	0.999862	+	0.0166157i	$0.00528920\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	37.7279			1.36764			0.683818	−	0.729653i	$-0.260318\pi$
$761$	37.7279			1.36764			0.683818	+	0.729653i	$0.260318\pi$
$762$		0			0
$763$	−2.67886	+	15.1926i	−0.0969813	+	0.550009i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.814330	+	1.41046i	0.0294038	+	0.0509288i
$768$		0			0
$769$	−34.5724	−	12.5833i	−1.24671	−	0.453766i	−0.367423	−	0.930054i	$-0.619760\pi$
$769$	−34.5724	−	12.5833i	−1.24671	−	0.453766i	−0.879289	+	0.476288i	$0.841982\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−3.46750	−	19.6652i	−0.124717	−	0.707307i	−0.981475	−	0.191588i	$-0.938636\pi$
$773$	−3.46750	−	19.6652i	−0.124717	−	0.707307i	0.856758	−	0.515719i	$-0.172475\pi$
$774$		0			0
$775$	8.25877	−	6.92993i	0.296664	−	0.248930i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	8.11721	−	29.6021i	0.290829	−	1.06061i
$780$		0			0
$781$	24.1565	−	8.79224i	0.864386	−	0.314611i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−9.53936	−	54.1004i	−0.340474	−	1.93093i
$786$		0			0
$787$	−4.18392	+	7.24675i	−0.149140	+	0.258319i	−0.930910	−	0.365249i	$-0.880984\pi$
$787$	−4.18392	+	7.24675i	−0.149140	+	0.258319i	0.781770	+	0.623567i	$0.214317\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−26.8871	−	46.5699i	−0.955996	−	1.65583i
$792$		0			0
$793$	−7.37939	−	6.19204i	−0.262050	−	0.219886i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	42.1729			1.49384			0.746921	−	0.664913i	$-0.231531\pi$
$797$	42.1729			1.49384			0.746921	+	0.664913i	$0.231531\pi$
$798$		0			0
$799$	27.6536			0.978315
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−2.19207	−	1.83936i	−0.0773563	−	0.0649097i
$804$		0			0
$805$	−27.4393	−	47.5262i	−0.967108	−	1.67508i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−3.03121	+	5.25021i	−0.106572	+	0.184588i	−0.914379	−	0.404859i	$-0.867321\pi$
$809$	−3.03121	+	5.25021i	−0.106572	+	0.184588i	0.807808	+	0.589446i	$0.200654\pi$
$810$		0			0
$811$	4.46168	+	25.3034i	0.156671	+	0.888523i	0.957243	+	0.289287i	$0.0934181\pi$
$811$	4.46168	+	25.3034i	0.156671	+	0.888523i	−0.800572	+	0.599237i	$0.795471\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−54.6912	+	19.9060i	−1.91575	+	0.697276i
$816$		0			0
$817$	−28.7101	−	29.0469i	−1.00444	−	1.01622i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.192533	−	0.161555i	0.00671946	−	0.00563830i	−0.639422	−	0.768856i	$-0.720826\pi$
$821$	0.192533	−	0.161555i	0.00671946	−	0.00563830i	0.646141	+	0.763218i	$0.276382\pi$
$822$		0			0
$823$	2.83497	+	16.0779i	0.0988208	+	0.560441i	0.993509	+	0.113750i	$0.0362864\pi$
$823$	2.83497	+	16.0779i	0.0988208	+	0.560441i	−0.894689	+	0.446691i	$0.852603\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	24.9008	+	9.06315i	0.865886	+	0.315157i	0.736500	−	0.676438i	$-0.236477\pi$
$827$	24.9008	+	9.06315i	0.865886	+	0.315157i	0.129386	+	0.991594i	$0.458699\pi$
$828$		0			0
$829$	−20.8148	−	36.0523i	−0.722928	−	1.25215i	−0.959821	−	0.280612i	$-0.909463\pi$
$829$	−20.8148	−	36.0523i	−0.722928	−	1.25215i	0.236894	−	0.971536i	$-0.423871\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	3.52094	−	19.9683i	0.121993	−	0.691860i
$834$		0			0
$835$	−19.3601			−0.669984
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−4.93289	+	27.9758i	−0.170302	+	0.965831i	0.773126	+	0.634253i	$0.218692\pi$
$839$	−4.93289	+	27.9758i	−0.170302	+	0.965831i	−0.943428	+	0.331578i	$0.892419\pi$
$840$		0			0
$841$	16.7101	+	14.0214i	0.576209	+	0.483497i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	56.5681	+	20.5891i	1.94600	+	0.708287i
$846$		0			0
$847$	−2.18180	+	3.77899i	−0.0749675	+	0.129848i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	10.8366	−	9.09300i	0.371475	−	0.311704i
$852$		0			0
$853$	25.5535	−	9.30071i	0.874935	−	0.318450i	0.134771	−	0.990877i	$-0.456970\pi$
$853$	25.5535	−	9.30071i	0.874935	−	0.318450i	0.740164	+	0.672426i	$0.234748\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	39.4381	−	14.3543i	1.34718	−	0.490333i	0.435113	−	0.900376i	$-0.356708\pi$
$857$	39.4381	−	14.3543i	1.34718	−	0.490333i	0.912066	+	0.410042i	$0.134486\pi$
$858$		0			0
$859$	27.0519	−	22.6992i	0.922999	−	0.774488i	−0.0515481	−	0.998671i	$-0.516416\pi$
$859$	27.0519	−	22.6992i	0.922999	−	0.774488i	0.974547	+	0.224182i	$0.0719711\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	6.00521	−	10.4013i	0.204420	−	0.354066i	−0.745528	−	0.666474i	$-0.767803\pi$
$863$	6.00521	−	10.4013i	0.204420	−	0.354066i	0.949948	+	0.312409i	$0.101136\pi$
$864$		0			0
$865$	−27.9440	−	10.1708i	−0.950126	−	0.345817i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	28.7053	+	24.0866i	0.973762	+	0.817083i
$870$		0			0
$871$	1.37464	−	7.79596i	0.0465778	−	0.264156i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−29.3191			−0.991168
$876$		0			0
$877$	−3.13145	+	17.7594i	−0.105742	+	0.599691i	0.885180	+	0.465249i	$0.154035\pi$
$877$	−3.13145	+	17.7594i	−0.105742	+	0.599691i	−0.990921	+	0.134442i	$0.957076\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	11.9101	+	20.6290i	0.401262	+	0.695007i	0.993879	−	0.110478i	$-0.0352382\pi$
$881$	11.9101	+	20.6290i	0.401262	+	0.695007i	−0.592616	+	0.805485i	$0.701905\pi$
$882$		0			0
$883$	−11.1197	−	4.04725i	−0.374209	−	0.136201i	0.148067	−	0.988977i	$-0.452695\pi$
$883$	−11.1197	−	4.04725i	−0.374209	−	0.136201i	−0.522276	+	0.852776i	$0.674917\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	6.37283	+	36.1421i	0.213979	+	1.21353i	0.882670	+	0.469993i	$0.155744\pi$
$887$	6.37283	+	36.1421i	0.213979	+	1.21353i	−0.668692	+	0.743540i	$0.733145\pi$
$888$		0			0
$889$	−12.9001	+	10.8245i	−0.432655	+	0.363041i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−18.3302	−	8.67804i	−0.613397	−	0.290399i
$894$		0			0
$895$	9.98767	−	3.63522i	0.333851	−	0.121512i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−9.45471	−	53.6203i	−0.315332	−	1.78834i
$900$		0			0
$901$	−18.8858	+	32.7111i	−0.629177	+	1.08977i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	15.6074	+	27.0328i	0.518808	+	0.898602i
$906$		0			0
$907$	−22.3746	−	18.7746i	−0.742938	−	0.623399i	0.190687	−	0.981651i	$-0.438928\pi$
$907$	−22.3746	−	18.7746i	−0.742938	−	0.623399i	−0.933625	+	0.358252i	$0.883373\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−3.12567			−0.103558			−0.0517790	−	0.998659i	$-0.516489\pi$
$911$	−3.12567			−0.103558			−0.0517790	+	0.998659i	$0.516489\pi$
$912$		0			0
$913$	0.268571			0.00888839
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−21.4001	−	17.9568i	−0.706693	−	0.592986i
$918$		0			0
$919$	4.39322	+	7.60928i	0.144919	+	0.251007i	0.929343	−	0.369218i	$-0.120375\pi$
$919$	4.39322	+	7.60928i	0.144919	+	0.251007i	−0.784424	+	0.620225i	$0.787041\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	25.0945	−	43.4650i	0.825996	−	1.43067i
$924$		0			0
$925$	0.516197	+	2.92750i	0.0169724	+	0.0962555i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	23.6377	−	8.60344i	0.775529	−	0.282270i	0.0762221	−	0.997091i	$-0.475714\pi$
$929$	23.6377	−	8.60344i	0.775529	−	0.282270i	0.699307	+	0.714821i	$0.253492\pi$
$930$		0			0
$931$	−8.60014	+	12.1311i	−0.281858	+	0.397579i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	35.8089	−	30.0472i	1.17108	−	0.982649i
$936$		0			0
$937$	−4.59698	−	26.0708i	−0.150177	−	0.851695i	−0.963064	−	0.269274i	$-0.913216\pi$
$937$	−4.59698	−	26.0708i	−0.150177	−	0.851695i	0.812887	−	0.582422i	$-0.197895\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	4.95171	+	1.80228i	0.161421	+	0.0587525i	0.421467	−	0.906844i	$-0.361515\pi$
$941$	4.95171	+	1.80228i	0.161421	+	0.0587525i	−0.260046	+	0.965596i	$0.583738\pi$
$942$		0			0
$943$	−23.6498	−	40.9626i	−0.770142	−	1.33393i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−4.23324	+	24.0079i	−0.137562	+	0.780152i	0.835480	+	0.549521i	$0.185190\pi$
$947$	−4.23324	+	24.0079i	−0.137562	+	0.780152i	−0.973041	+	0.230630i	$0.925921\pi$
$948$		0			0
$949$	−5.58677			−0.181354
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−8.61633	+	48.8657i	−0.279110	+	1.58291i	0.446484	+	0.894792i	$0.352676\pi$
$953$	−8.61633	+	48.8657i	−0.279110	+	1.58291i	−0.725595	+	0.688122i	$0.758435\pi$
$954$		0			0
$955$	−19.7934	−	16.6086i	−0.640499	−	0.537442i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	41.4350	+	15.0811i	1.33801	+	0.486994i
$960$		0			0
$961$	−13.6707	+	23.6784i	−0.440991	+	0.763818i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	42.1057	−	35.3308i	1.35543	−	1.13734i
$966$		0			0
$967$	24.3307	−	8.85565i	0.782422	−	0.284778i	0.0802399	−	0.996776i	$-0.474431\pi$
$967$	24.3307	−	8.85565i	0.782422	−	0.284778i	0.702182	+	0.711997i	$0.252209\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	11.8645	−	4.31834i	0.380751	−	0.138582i	−0.144552	−	0.989497i	$-0.546174\pi$
$971$	11.8645	−	4.31834i	0.380751	−	0.138582i	0.525303	+	0.850915i	$0.323952\pi$
$972$		0			0
$973$	33.8141	−	28.3734i	1.08403	−	0.909609i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.69072	−	2.92842i	0.0540910	−	0.0936884i	−0.837712	−	0.546112i	$-0.816107\pi$
$977$	1.69072	−	2.92842i	0.0540910	−	0.0936884i	0.891803	+	0.452424i	$0.149441\pi$
$978$		0			0
$979$	20.6411	+	7.51276i	0.659694	+	0.240109i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	0.170493	+	0.143061i	0.00543788	+	0.00456293i	0.645503	−	0.763758i	$-0.276648\pi$
$983$	0.170493	+	0.143061i	0.00543788	+	0.00456293i	−0.640065	+	0.768321i	$0.721092\pi$
$984$		0			0
$985$	−7.33631	+	41.6063i	−0.233754	+	1.32569i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−62.9344			−2.00120
$990$		0			0
$991$	−0.838536	+	4.75557i	−0.0266370	+	0.151066i	−0.995225	−	0.0976038i	$-0.968882\pi$
$991$	−0.838536	+	4.75557i	−0.0266370	+	0.151066i	0.968588	+	0.248670i	$0.0799933\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−3.11468	−	5.39479i	−0.0987422	−	0.171026i
$996$		0			0
$997$	11.8794	+	4.32374i	0.376224	+	0.136934i	0.523209	−	0.852204i	$-0.324735\pi$
$997$	11.8794	+	4.32374i	0.376224	+	0.136934i	−0.146985	+	0.989139i	$0.546957\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.bo.a.613.1		6
3.2	odd	2		228.2.q.a.157.1	yes	6
12.11	even	2		912.2.bo.e.385.1		6
19.4	even	9	inner	684.2.bo.a.289.1		6
57.2	even	18		4332.2.a.n.1.3		3
57.17	odd	18		4332.2.a.o.1.3		3
57.23	odd	18		228.2.q.a.61.1	✓	6
228.23	even	18		912.2.bo.e.289.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.q.a.61.1	✓	6	57.23	odd	18
228.2.q.a.157.1	yes	6	3.2	odd	2
684.2.bo.a.289.1		6	19.4	even	9	inner
684.2.bo.a.613.1		6	1.1	even	1	trivial
912.2.bo.e.289.1		6	228.23	even	18
912.2.bo.e.385.1		6	12.11	even	2
4332.2.a.n.1.3		3	57.2	even	18
4332.2.a.o.1.3		3	57.17	odd	18

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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.bo (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.93969 - 1.62760i) q^{5} +(1.61334 + 2.79439i) q^{7} +O(q^{10})\)	\(q+(-1.93969 - 1.62760i) q^{5} +(1.61334 + 2.79439i) q^{7} +(1.55303 - 2.68993i) q^{11} +(-1.05303 - 5.97205i) q^{13} +(-5.58512 + 2.03282i) q^{17} +(4.34002 + 0.405223i) q^{19} +(5.14543 - 4.31753i) q^{23} +(0.245100 + 1.39003i) q^{25} +(6.69846 + 2.43804i) q^{29} +(-3.81908 - 6.61484i) q^{31} +(1.41875 - 8.04612i) q^{35} +2.10607 q^{37} +(1.22281 - 6.93491i) q^{41} +(-7.17752 - 6.02265i) q^{43} +(-4.37211 - 1.59132i) q^{47} +(-1.70574 + 2.95442i) q^{49} +(4.86824 - 4.08494i) q^{53} +(-7.39053 + 2.68993i) q^{55} +(-0.252374 + 0.0918566i) q^{59} +(1.21688 - 1.02108i) q^{61} +(-7.67752 + 13.2979i) q^{65} +(1.22668 + 0.446476i) q^{67} +(6.34002 + 5.31991i) q^{71} +(0.159978 - 0.907278i) q^{73} +10.0223 q^{77} +(-2.09492 + 11.8809i) q^{79} +(0.0432332 + 0.0748822i) q^{83} +(14.1420 + 5.14728i) q^{85} +(1.22803 + 6.96448i) q^{89} +(14.9893 - 12.5775i) q^{91} +(-7.75877 - 7.84981i) q^{95} +(-3.12701 + 1.13814i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{5} + 3 q^{7}+O(q^{10}) \) 6 * q - 6 * q^5 + 3 * q^7	\( 6 q - 6 q^{5} + 3 q^{7} - 3 q^{11} + 6 q^{13} - 12 q^{17} + 6 q^{19} + 15 q^{23} + 12 q^{29} - 6 q^{31} + 6 q^{35} - 12 q^{37} + 18 q^{41} - 18 q^{43} + 3 q^{47} + 24 q^{53} - 27 q^{55} - 18 q^{59} - 9 q^{61} - 21 q^{65} - 6 q^{67} + 18 q^{71} + 21 q^{73} + 48 q^{77} + 6 q^{79} - 15 q^{83} + 27 q^{85} - 15 q^{89} + 30 q^{91} - 24 q^{95} + 9 q^{97}+O(q^{100}) \) 6 * q - 6 * q^5 + 3 * q^7 - 3 * q^11 + 6 * q^13 - 12 * q^17 + 6 * q^19 + 15 * q^23 + 12 * q^29 - 6 * q^31 + 6 * q^35 - 12 * q^37 + 18 * q^41 - 18 * q^43 + 3 * q^47 + 24 * q^53 - 27 * q^55 - 18 * q^59 - 9 * q^61 - 21 * q^65 - 6 * q^67 + 18 * q^71 + 21 * q^73 + 48 * q^77 + 6 * q^79 - 15 * q^83 + 27 * q^85 - 15 * q^89 + 30 * q^91 - 24 * q^95 + 9 * q^97

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