LMFDB - Embedded newform 378.2.t.a.89.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(17,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 1]))

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

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

chi := DirichletCharacter("378.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.6
Root			$-1.70672 - 0.295146i$ of defining polynomial
Character	$\chi$	$=$	378.89
Dual form			378.2.t.a.17.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -0.967324 q^{5} +(2.40137 + 1.11060i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -0.967324 q^{5} +(2.40137 + 1.11060i) q^{7} -1.00000i q^{8} +(-0.837727 + 0.483662i) q^{10} -5.57361i q^{11} +(3.76893 - 2.17600i) q^{13} +(2.63495 - 0.238876i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.97267 + 3.41677i) q^{17} +(3.86796 + 2.23317i) q^{19} +(-0.483662 + 0.837727i) q^{20} +(-2.78681 - 4.82689i) q^{22} +2.65334i q^{23} -4.06428 q^{25} +(2.17600 - 3.76893i) q^{26} +(2.16249 - 1.52435i) q^{28} +(-4.61157 - 2.66249i) q^{29} +(-5.34038 - 3.08327i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(3.41677 + 1.97267i) q^{34} +(-2.32290 - 1.07431i) q^{35} +(0.243608 - 0.421942i) q^{37} +4.46634 q^{38} +0.967324i q^{40} +(0.0818856 + 0.141830i) q^{41} +(-4.35045 + 7.53520i) q^{43} +(-4.82689 - 2.78681i) q^{44} +(1.32667 + 2.29786i) q^{46} +(4.74500 + 8.21859i) q^{47} +(4.53314 + 5.33392i) q^{49} +(-3.51977 + 2.03214i) q^{50} -4.35199i q^{52} +(-1.74520 + 1.00759i) q^{53} +5.39149i q^{55} +(1.11060 - 2.40137i) q^{56} -5.32498 q^{58} +(-0.836931 + 1.44961i) q^{59} +(-4.47927 + 2.58611i) q^{61} -6.16655 q^{62} -1.00000 q^{64} +(-3.64578 + 2.10489i) q^{65} +(2.72126 - 4.71336i) q^{67} +3.94535 q^{68} +(-2.54885 + 0.231071i) q^{70} +3.64006i q^{71} +(-2.15468 + 1.24401i) q^{73} -0.487217i q^{74} +(3.86796 - 2.23317i) q^{76} +(6.19005 - 13.3843i) q^{77} +(-2.30121 - 3.98581i) q^{79} +(0.483662 + 0.837727i) q^{80} +(0.141830 + 0.0818856i) q^{82} +(-4.20979 + 7.29158i) q^{83} +(-1.90821 - 3.30512i) q^{85} +8.70089i q^{86} -5.57361 q^{88} +(-2.05811 + 3.56475i) q^{89} +(11.4673 - 1.03959i) q^{91} +(2.29786 + 1.32667i) q^{92} +(8.21859 + 4.74500i) q^{94} +(-3.74157 - 2.16020i) q^{95} +(-10.2669 - 5.92762i) q^{97} +(6.59277 + 2.35274i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 2 q^{7}+O(q^{10}) $ 16 * q + 8 * q^4 + 2 * q^7	$ 16 q + 8 q^{4} + 2 q^{7} - 6 q^{13} + 6 q^{14} - 8 q^{16} - 18 q^{17} + 16 q^{25} + 12 q^{26} - 2 q^{28} - 6 q^{29} + 6 q^{31} + 30 q^{35} - 2 q^{37} - 6 q^{41} - 2 q^{43} - 12 q^{44} + 6 q^{46} + 18 q^{47} + 10 q^{49} + 12 q^{50} - 36 q^{53} - 12 q^{58} - 30 q^{59} - 60 q^{61} + 36 q^{62} - 16 q^{64} - 42 q^{65} + 14 q^{67} - 36 q^{68} + 18 q^{77} - 16 q^{79} - 12 q^{85} - 24 q^{89} - 12 q^{91} - 6 q^{92} + 66 q^{95} - 6 q^{97} - 24 q^{98}+O(q^{100}) $ 16 * q + 8 * q^4 + 2 * q^7 - 6 * q^13 + 6 * q^14 - 8 * q^16 - 18 * q^17 + 16 * q^25 + 12 * q^26 - 2 * q^28 - 6 * q^29 + 6 * q^31 + 30 * q^35 - 2 * q^37 - 6 * q^41 - 2 * q^43 - 12 * q^44 + 6 * q^46 + 18 * q^47 + 10 * q^49 + 12 * q^50 - 36 * q^53 - 12 * q^58 - 30 * q^59 - 60 * q^61 + 36 * q^62 - 16 * q^64 - 42 * q^65 + 14 * q^67 - 36 * q^68 + 18 * q^77 - 16 * q^79 - 12 * q^85 - 24 * q^89 - 12 * q^91 - 6 * q^92 + 66 * q^95 - 6 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.967324			−0.432600			−0.216300	−	0.976327i	$-0.569399\pi$
$5$	−0.967324			−0.432600			−0.216300	+	0.976327i	$0.569399\pi$
$6$		0			0
$7$	2.40137	+	1.11060i	0.907632	+	0.419767i
$7$	2.40137	+	1.11060i	0.907632	+	0.419767i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−0.837727	+	0.483662i	−0.264913	+	0.152947i
$11$		−	5.57361i		−	1.68051i	−0.542193	−	0.840254i	$-0.682406\pi$
$11$		−	5.57361i		−	1.68051i	0.542193	−	0.840254i	$-0.317594\pi$
$12$		0			0
$13$	3.76893	−	2.17600i	1.04531	−	0.603512i	0.123980	−	0.992285i	$-0.460434\pi$
$13$	3.76893	−	2.17600i	1.04531	−	0.603512i	0.921334	+	0.388772i	$0.127101\pi$
$14$	2.63495	−	0.238876i	0.704219	−	0.0638424i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.97267	+	3.41677i	0.478443	+	0.828688i	0.999695	−	0.0247150i	$-0.00786784\pi$
$17$	1.97267	+	3.41677i	0.478443	+	0.828688i	−0.521251	+	0.853403i	$0.674535\pi$
$18$		0			0
$19$	3.86796	+	2.23317i	0.887371	+	0.512324i	0.873082	−	0.487574i	$-0.162118\pi$
$19$	3.86796	+	2.23317i	0.887371	+	0.512324i	0.0142896	+	0.999898i	$0.495451\pi$
$20$	−0.483662	+	0.837727i	−0.108150	+	0.187322i
$21$		0			0
$22$	−2.78681	−	4.82689i	−0.594149	−	1.02910i
$23$			2.65334i			0.553260i	0.960976	+	0.276630i	$0.0892177\pi$
$23$			2.65334i			0.553260i	−0.960976	+	0.276630i	$0.910782\pi$
$24$		0			0
$25$	−4.06428			−0.812857
$26$	2.17600	−	3.76893i	0.426748	−	0.739149i
$27$		0			0
$28$	2.16249	−	1.52435i	0.408673	−	0.288074i
$29$	−4.61157	−	2.66249i	−0.856347	−	0.494412i	0.00644015	−	0.999979i	$-0.497950\pi$
$29$	−4.61157	−	2.66249i	−0.856347	−	0.494412i	−0.862787	+	0.505567i	$0.831283\pi$
$30$		0			0
$31$	−5.34038	−	3.08327i	−0.959161	−	0.553772i	−0.0632466	−	0.997998i	$-0.520145\pi$
$31$	−5.34038	−	3.08327i	−0.959161	−	0.553772i	−0.895915	+	0.444226i	$0.853479\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$	3.41677	+	1.97267i	0.585971	+	0.338311i
$35$	−2.32290	−	1.07431i	−0.392642	−	0.181592i
$36$		0			0
$37$	0.243608	−	0.421942i	0.0400490	−	0.0693669i	−0.845306	−	0.534282i	$-0.820582\pi$
$37$	0.243608	−	0.421942i	0.0400490	−	0.0693669i	0.885355	+	0.464915i	$0.153915\pi$
$38$	4.46634			0.724536
$39$		0			0
$40$			0.967324i			0.152947i
$41$	0.0818856	+	0.141830i	0.0127884	+	0.0221501i	0.872349	−	0.488884i	$-0.162596\pi$
$41$	0.0818856	+	0.141830i	0.0127884	+	0.0221501i	−0.859560	+	0.511034i	$0.829263\pi$
$42$		0			0
$43$	−4.35045	+	7.53520i	−0.663437	+	1.14911i	0.316270	+	0.948669i	$0.397570\pi$
$43$	−4.35045	+	7.53520i	−0.663437	+	1.14911i	−0.979707	+	0.200437i	$0.935764\pi$
$44$	−4.82689	−	2.78681i	−0.727681	−	0.420127i
$45$		0			0
$46$	1.32667	+	2.29786i	0.195607	+	0.338801i
$47$	4.74500	+	8.21859i	0.692130	+	1.19880i	0.971139	+	0.238516i	$0.0766609\pi$
$47$	4.74500	+	8.21859i	0.692130	+	1.19880i	−0.279009	+	0.960289i	$0.590006\pi$
$48$		0			0
$49$	4.53314	+	5.33392i	0.647591	+	0.761988i
$50$	−3.51977	+	2.03214i	−0.497771	+	0.287388i
$51$		0			0
$52$		−	4.35199i		−	0.603512i
$53$	−1.74520	+	1.00759i	−0.239722	+	0.138403i	−0.615049	−	0.788489i	$-0.710864\pi$
$53$	−1.74520	+	1.00759i	−0.239722	+	0.138403i	0.375327	+	0.926892i	$0.377530\pi$
$54$		0			0
$55$			5.39149i			0.726988i
$56$	1.11060	−	2.40137i	0.148410	−	0.320896i
$57$		0			0
$58$	−5.32498			−0.699205
$59$	−0.836931	+	1.44961i	−0.108959	+	0.188723i	−0.915349	−	0.402662i	$-0.868085\pi$
$59$	−0.836931	+	1.44961i	−0.108959	+	0.188723i	0.806390	+	0.591384i	$0.201418\pi$
$60$		0			0
$61$	−4.47927	+	2.58611i	−0.573512	+	0.331117i	−0.758551	−	0.651614i	$-0.774092\pi$
$61$	−4.47927	+	2.58611i	−0.573512	+	0.331117i	0.185039	+	0.982731i	$0.440759\pi$
$62$	−6.16655			−0.783152
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−3.64578	+	2.10489i	−0.452203	+	0.261080i
$66$		0			0
$67$	2.72126	−	4.71336i	0.332455	−	0.575828i	−0.650538	−	0.759474i	$-0.725456\pi$
$67$	2.72126	−	4.71336i	0.332455	−	0.575828i	0.982993	+	0.183645i	$0.0587898\pi$
$68$	3.94535			0.478443
$69$		0			0
$70$	−2.54885	+	0.231071i	−0.304645	+	0.0276182i
$71$			3.64006i			0.431996i	0.976394	+	0.215998i	$0.0693005\pi$
$71$			3.64006i			0.431996i	−0.976394	+	0.215998i	$0.930700\pi$
$72$		0			0
$73$	−2.15468	+	1.24401i	−0.252186	+	0.145600i	−0.620765	−	0.783997i	$-0.713178\pi$
$73$	−2.15468	+	1.24401i	−0.252186	+	0.145600i	0.368579	+	0.929597i	$0.379845\pi$
$74$		−	0.487217i		−	0.0566378i
$75$		0			0
$76$	3.86796	−	2.23317i	0.443686	−	0.256162i
$77$	6.19005	−	13.3843i	0.705422	−	1.52528i
$78$		0			0
$79$	−2.30121	−	3.98581i	−0.258906	−	0.448438i	0.707043	−	0.707170i	$-0.250029\pi$
$79$	−2.30121	−	3.98581i	−0.258906	−	0.448438i	−0.965949	+	0.258732i	$0.916695\pi$
$80$	0.483662	+	0.837727i	0.0540751	+	0.0936608i
$81$		0			0
$82$	0.141830	+	0.0818856i	0.0156625	+	0.00904275i
$83$	−4.20979	+	7.29158i	−0.462085	+	0.800355i	−0.999065	−	0.0432405i	$-0.986232\pi$
$83$	−4.20979	+	7.29158i	−0.462085	+	0.800355i	0.536980	+	0.843595i	$0.319565\pi$
$84$		0			0
$85$	−1.90821	−	3.30512i	−0.206975	−	0.358491i
$86$			8.70089i			0.938242i
$87$		0			0
$88$	−5.57361			−0.594149
$89$	−2.05811	+	3.56475i	−0.218159	+	0.377863i	−0.954245	−	0.299025i	$-0.903338\pi$
$89$	−2.05811	+	3.56475i	−0.218159	+	0.377863i	0.736086	+	0.676888i	$0.236672\pi$
$90$		0			0
$91$	11.4673	−	1.03959i	1.20210	−	0.108978i
$92$	2.29786	+	1.32667i	0.239569	+	0.138315i
$93$		0			0
$94$	8.21859	+	4.74500i	0.847683	+	0.489410i
$95$	−3.74157	−	2.16020i	−0.383877	−	0.221632i
$96$		0			0
$97$	−10.2669	−	5.92762i	−1.04245	−	0.601859i	−0.121924	−	0.992539i	$-0.538906\pi$
$97$	−10.2669	−	5.92762i	−1.04245	−	0.601859i	−0.920526	+	0.390681i	$0.872240\pi$
$98$	6.59277	+	2.35274i	0.665970	+	0.237663i
$99$		0			0
$100$	−2.03214	+	3.51977i	−0.203214	+	0.351977i
$101$	−5.31626			−0.528988			−0.264494	−	0.964387i	$-0.585205\pi$
$101$	−5.31626			−0.528988			−0.264494	+	0.964387i	$0.585205\pi$
$102$		0			0
$103$			8.94450i			0.881327i	0.897672	+	0.440664i	$0.145257\pi$
$103$			8.94450i			0.881327i	−0.897672	+	0.440664i	$0.854743\pi$
$104$	−2.17600	−	3.76893i	−0.213374	−	0.369574i
$105$		0			0
$106$	−1.00759	+	1.74520i	−0.0978659	+	0.169509i
$107$	16.5898	+	9.57813i	1.60380	+	0.925953i	0.990718	+	0.135931i	$0.0434026\pi$
$107$	16.5898	+	9.57813i	1.60380	+	0.925953i	0.613079	+	0.790022i	$0.289931\pi$
$108$		0			0
$109$	−9.62168	−	16.6652i	−0.921590	−	1.59624i	−0.796955	−	0.604038i	$-0.793557\pi$
$109$	−9.62168	−	16.6652i	−0.921590	−	1.59624i	−0.124635	−	0.992203i	$-0.539776\pi$
$110$	2.69574	+	4.66917i	0.257029	+	0.445188i
$111$		0			0
$112$	−0.238876	−	2.63495i	−0.0225717	−	0.248979i
$113$	−7.31199	+	4.22158i	−0.687854	+	0.397133i	−0.802808	−	0.596238i	$-0.796661\pi$
$113$	−7.31199	+	4.22158i	−0.687854	+	0.397133i	0.114953	+	0.993371i	$0.463328\pi$
$114$		0			0
$115$		−	2.56664i		−	0.239341i
$116$	−4.61157	+	2.66249i	−0.428174	+	0.247206i
$117$		0			0
$118$			1.67386i			0.154091i
$119$	0.942449	+	10.3958i	0.0863942	+	0.952979i
$120$		0			0
$121$	−20.0652			−1.82411
$122$	−2.58611	+	4.47927i	−0.234135	+	0.405534i
$123$		0			0
$124$	−5.34038	+	3.08327i	−0.479581	+	0.276886i
$125$	8.76810			0.784243
$126$		0			0
$127$	3.31883			0.294498			0.147249	−	0.989099i	$-0.452958\pi$
$127$	3.31883			0.294498			0.147249	+	0.989099i	$0.452958\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−2.10489	+	3.64578i	−0.184611	+	0.319756i
$131$	18.7467			1.63791			0.818954	−	0.573859i	$-0.194554\pi$
$131$	18.7467			1.63791			0.818954	+	0.573859i	$0.194554\pi$
$132$		0			0
$133$	6.80824	+	9.65842i	0.590350	+	0.837491i
$134$		−	5.44252i		−	0.470162i
$135$		0			0
$136$	3.41677	−	1.97267i	0.292986	−	0.169155i
$137$		−	16.9343i		−	1.44680i	−0.690430	−	0.723399i	$-0.742579\pi$
$137$		−	16.9343i		−	1.44680i	0.690430	−	0.723399i	$-0.257421\pi$
$138$		0			0
$139$	10.5033	−	6.06406i	0.890875	−	0.514347i	0.0166466	−	0.999861i	$-0.494701\pi$
$139$	10.5033	−	6.06406i	0.890875	−	0.514347i	0.874229	+	0.485514i	$0.161368\pi$
$140$	−2.09183	+	1.47454i	−0.176792	+	0.124621i
$141$		0			0
$142$	1.82003	+	3.15239i	0.152734	+	0.264543i
$143$	−12.1282	−	21.0066i	−1.01421	−	1.75666i
$144$		0			0
$145$	4.46088	+	2.57549i	0.370456	+	0.213883i
$146$	−1.24401	+	2.15468i	−0.102955	+	0.178323i
$147$		0			0
$148$	−0.243608	−	0.421942i	−0.0200245	−	0.0346834i
$149$		−	8.74051i		−	0.716051i	−0.933712	−	0.358025i	$-0.883450\pi$
$149$		−	8.74051i		−	0.716051i	0.933712	−	0.358025i	$-0.116550\pi$
$150$		0			0
$151$	22.0941			1.79799			0.898997	−	0.437954i	$-0.144297\pi$
$151$	22.0941			1.79799			0.898997	+	0.437954i	$0.144297\pi$
$152$	2.23317	−	3.86796i	0.181134	−	0.313733i
$153$		0			0
$154$	−1.33140	−	14.6862i	−0.107288	−	1.18345i
$155$	5.16588	+	2.98252i	0.414934	+	0.239562i
$156$		0			0
$157$	1.23372	+	0.712287i	0.0984614	+	0.0568467i	0.548422	−	0.836202i	$-0.315229\pi$
$157$	1.23372	+	0.712287i	0.0984614	+	0.0568467i	−0.449961	+	0.893048i	$0.648562\pi$
$158$	−3.98581	−	2.30121i	−0.317094	−	0.183074i
$159$		0			0
$160$	0.837727	+	0.483662i	0.0662282	+	0.0382368i
$161$	−2.94680	+	6.37165i	−0.232241	+	0.502157i
$162$		0			0
$163$	−3.72148	+	6.44579i	−0.291489	+	0.504873i	−0.974162	−	0.225851i	$-0.927484\pi$
$163$	−3.72148	+	6.44579i	−0.291489	+	0.504873i	0.682673	+	0.730724i	$0.260817\pi$
$164$	0.163771			0.0127884
$165$		0			0
$166$			8.41959i			0.653487i
$167$	−3.24855	−	5.62665i	−0.251380	−	0.435404i	0.712526	−	0.701646i	$-0.247551\pi$
$167$	−3.24855	−	5.62665i	−0.251380	−	0.435404i	−0.963906	+	0.266242i	$0.914218\pi$
$168$		0			0
$169$	2.96991	−	5.14404i	0.228455	−	0.395695i
$170$	−3.30512	−	1.90821i	−0.253491	−	0.146353i
$171$		0			0
$172$	4.35045	+	7.53520i	0.331718	+	0.574553i
$173$	−5.90938	−	10.2354i	−0.449282	−	0.778179i	0.549057	−	0.835785i	$-0.314987\pi$
$173$	−5.90938	−	10.2354i	−0.449282	−	0.778179i	−0.998339	+	0.0576053i	$0.981654\pi$
$174$		0			0
$175$	−9.75984	−	4.51379i	−0.737775	−	0.341211i
$176$	−4.82689	+	2.78681i	−0.363841	+	0.210063i
$177$		0			0
$178$			4.11622i			0.308523i
$179$	−2.10764	+	1.21685i	−0.157533	+	0.0909515i	−0.576694	−	0.816960i	$-0.695657\pi$
$179$	−2.10764	+	1.21685i	−0.157533	+	0.0909515i	0.419161	+	0.907912i	$0.362324\pi$
$180$		0			0
$181$			11.5342i			0.857327i	0.903464	+	0.428663i	$0.141015\pi$
$181$			11.5342i			0.857327i	−0.903464	+	0.428663i	$0.858985\pi$
$182$	9.41114	−	6.63394i	0.697600	−	0.491740i
$183$		0			0
$184$	2.65334			0.195607
$185$	−0.235648	+	0.408155i	−0.0173252	+	0.0300081i
$186$		0			0
$187$	19.0438	−	10.9949i	1.39262	−	0.804028i
$188$	9.49001			0.692130
$189$		0			0
$190$	−4.32040			−0.313435
$191$	−19.1122	+	11.0345i	−1.38291	+	0.798425i	−0.992503	−	0.122216i	$-0.961000\pi$
$191$	−19.1122	+	11.0345i	−1.38291	+	0.798425i	−0.390409	+	0.920641i	$0.627666\pi$
$192$		0			0
$193$	9.96979	−	17.2682i	0.717641	−	1.24299i	−0.244291	−	0.969702i	$-0.578555\pi$
$193$	9.96979	−	17.2682i	0.717641	−	1.24299i	0.961932	−	0.273289i	$-0.0881116\pi$
$194$	−11.8552			−0.851157
$195$		0			0
$196$	6.88588	−	1.25885i	0.491848	−	0.0899180i
$197$		−	4.62560i		−	0.329560i	−0.986330	−	0.164780i	$-0.947309\pi$
$197$		−	4.62560i		−	0.329560i	0.986330	−	0.164780i	$-0.0526914\pi$
$198$		0			0
$199$	−18.1024	+	10.4514i	−1.28324	+	0.740882i	−0.977440	−	0.211212i	$-0.932259\pi$
$199$	−18.1024	+	10.4514i	−1.28324	+	0.740882i	−0.305805	+	0.952094i	$0.598925\pi$
$200$			4.06428i			0.287388i
$201$		0			0
$202$	−4.60402	+	2.65813i	−0.323938	+	0.187025i
$203$	−8.11712	−	11.5152i	−0.569710	−	0.808211i
$204$		0			0
$205$	−0.0792099	−	0.137196i	−0.00553226	−	0.00958215i
$206$	4.47225	+	7.74616i	0.311596	+	0.539701i
$207$		0			0
$208$	−3.76893	−	2.17600i	−0.261329	−	0.150878i
$209$	12.4468	−	21.5585i	0.860965	−	1.49123i
$210$		0			0
$211$	−3.34310	−	5.79042i	−0.230148	−	0.398629i	0.727703	−	0.685892i	$-0.240588\pi$
$211$	−3.34310	−	5.79042i	−0.230148	−	0.398629i	−0.957852	+	0.287263i	$0.907254\pi$
$212$			2.01518i			0.138403i
$213$		0			0
$214$	19.1563			1.30949
$215$	4.20829	−	7.28898i	0.287003	−	0.497104i
$216$		0			0
$217$	−9.39995	−	13.3351i	−0.638110	−	0.905246i
$218$	−16.6652	−	9.62168i	−1.12871	−	0.651663i
$219$		0			0
$220$	4.66917	+	2.69574i	0.314795	+	0.181747i
$221$	14.8697	+	8.58505i	1.00025	+	0.577493i
$222$		0			0
$223$	−7.08622	−	4.09123i	−0.474528	−	0.273969i	0.243605	−	0.969875i	$-0.421670\pi$
$223$	−7.08622	−	4.09123i	−0.474528	−	0.273969i	−0.718133	+	0.695905i	$0.755003\pi$
$224$	−1.52435	−	2.16249i	−0.101850	−	0.144488i
$225$		0			0
$226$	−4.22158	+	7.31199i	−0.280815	+	0.486386i
$227$	10.6938			0.709769			0.354885	−	0.934910i	$-0.384520\pi$
$227$	10.6938			0.709769			0.354885	+	0.934910i	$0.384520\pi$
$228$		0			0
$229$			29.2072i			1.93007i	0.262125	+	0.965034i	$0.415577\pi$
$229$			29.2072i			1.93007i	−0.262125	+	0.965034i	$0.584423\pi$
$230$	−1.28332	−	2.22278i	−0.0846197	−	0.146566i
$231$		0			0
$232$	−2.66249	+	4.61157i	−0.174801	+	0.302764i
$233$	5.57664	+	3.21967i	0.365338	+	0.210928i	0.671420	−	0.741077i	$-0.265685\pi$
$233$	5.57664	+	3.21967i	0.365338	+	0.210928i	−0.306082	+	0.952005i	$0.599018\pi$
$234$		0			0
$235$	−4.58996	−	7.95004i	−0.299416	−	0.518603i
$236$	0.836931	+	1.44961i	0.0544796	+	0.0943614i
$237$		0			0
$238$	6.01407	+	8.53178i	0.389834	+	0.553033i
$239$	4.01452	−	2.31778i	0.259678	−	0.149925i	−0.364510	−	0.931200i	$-0.618763\pi$
$239$	4.01452	−	2.31778i	0.259678	−	0.149925i	0.624187	+	0.781275i	$0.285430\pi$
$240$		0			0
$241$		−	10.4944i		−	0.676007i	−0.941145	−	0.338003i	$-0.890248\pi$
$241$		−	10.4944i		−	0.676007i	0.941145	−	0.338003i	$-0.109752\pi$
$242$	−17.3769	+	10.0326i	−1.11703	+	0.644919i
$243$		0			0
$244$			5.17221i			0.331117i
$245$	−4.38501	−	5.15963i	−0.280148	−	0.329636i
$246$		0			0
$247$	19.4375			1.23678
$248$	−3.08327	+	5.34038i	−0.195788	+	0.339115i
$249$		0			0
$250$	7.59340	−	4.38405i	0.480249	−	0.277272i
$251$	7.85271			0.495659			0.247829	−	0.968804i	$-0.420283\pi$
$251$	7.85271			0.495659			0.247829	+	0.968804i	$0.420283\pi$
$252$		0			0
$253$	14.7887			0.929758
$254$	2.87419	−	1.65941i	0.180343	−	0.104121i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.43136			0.214042			0.107021	−	0.994257i	$-0.465869\pi$
$257$	3.43136			0.214042			0.107021	+	0.994257i	$0.465869\pi$
$258$		0			0
$259$	1.05360	−	0.742687i	0.0654677	−	0.0461483i
$260$			4.20979i			0.261080i
$261$		0			0
$262$	16.2351	−	9.37335i	1.00301	−	0.579088i
$263$			3.66132i			0.225767i	0.993608	+	0.112883i	$0.0360087\pi$
$263$			3.66132i			0.225767i	−0.993608	+	0.112883i	$0.963991\pi$
$264$		0			0
$265$	1.68817	−	0.974668i	0.103704	−	0.0598734i
$266$	10.7253	+	4.96031i	0.657612	+	0.304136i
$267$		0			0
$268$	−2.72126	−	4.71336i	−0.166227	−	0.287914i
$269$	−6.34303	−	10.9865i	−0.386741	−	0.669856i	0.605268	−	0.796022i	$-0.293066\pi$
$269$	−6.34303	−	10.9865i	−0.386741	−	0.669856i	−0.992009	+	0.126166i	$0.959733\pi$
$270$		0			0
$271$	−17.2136	−	9.93828i	−1.04565	−	0.603708i	−0.124223	−	0.992254i	$-0.539644\pi$
$271$	−17.2136	−	9.93828i	−1.04565	−	0.603708i	−0.921429	+	0.388547i	$0.872977\pi$
$272$	1.97267	−	3.41677i	0.119611	−	0.207172i
$273$		0			0
$274$	−8.46717	−	14.6656i	−0.511520	−	0.885979i
$275$			22.6527i			1.36601i
$276$		0			0
$277$	−7.46605			−0.448591			−0.224296	−	0.974521i	$-0.572008\pi$
$277$	−7.46605			−0.448591			−0.224296	+	0.974521i	$0.572008\pi$
$278$	6.06406	−	10.5033i	0.363698	−	0.629944i
$279$		0			0
$280$	−1.07431	+	2.32290i	−0.0642023	+	0.138820i
$281$	19.2746	+	11.1282i	1.14983	+	0.663854i	0.948845	−	0.315741i	$-0.102253\pi$
$281$	19.2746	+	11.1282i	1.14983	+	0.663854i	0.200983	+	0.979595i	$0.435586\pi$
$282$		0			0
$283$	14.0125	+	8.09012i	0.832957	+	0.480908i	0.854864	−	0.518852i	$-0.173641\pi$
$283$	14.0125	+	8.09012i	0.832957	+	0.480908i	−0.0219073	+	0.999760i	$0.506974\pi$
$284$	3.15239	+	1.82003i	0.187060	+	0.107999i
$285$		0			0
$286$	−21.0066	−	12.1282i	−1.24215	−	0.717153i
$287$	0.0391210	+	0.431528i	0.00230924	+	0.0254723i
$288$		0			0
$289$	0.717124	−	1.24210i	0.0421838	−	0.0730644i
$290$	5.15098			0.302476
$291$		0			0
$292$			2.48801i			0.145600i
$293$	−4.43406	−	7.68002i	−0.259041	−	0.448672i	0.706944	−	0.707269i	$-0.250073\pi$
$293$	−4.43406	−	7.68002i	−0.259041	−	0.448672i	−0.965985	+	0.258597i	$0.916740\pi$
$294$		0			0
$295$	0.809584	−	1.40224i	0.0471358	−	0.0816416i
$296$	−0.421942	−	0.243608i	−0.0245249	−	0.0141595i
$297$		0			0
$298$	−4.37026	−	7.56951i	−0.253162	−	0.438490i
$299$	5.77366	+	10.0003i	0.333899	+	0.578331i
$300$		0			0
$301$	−18.8156	+	13.2632i	−1.08451	+	0.764476i
$302$	19.1341	−	11.0471i	1.10104	−	0.635687i
$303$		0			0
$304$		−	4.46634i		−	0.256162i
$305$	4.33290	−	2.50160i	0.248101	−	0.143241i
$306$		0			0
$307$		−	27.1427i		−	1.54912i	−0.632501	−	0.774559i	$-0.717972\pi$
$307$		−	27.1427i		−	1.54912i	0.632501	−	0.774559i	$-0.282028\pi$
$308$	−8.49611	−	12.0529i	−0.484111	−	0.686777i
$309$		0			0
$310$	5.96505			0.338792
$311$	−8.44774	+	14.6319i	−0.479028	+	0.829700i	−0.999711	−	0.0240499i	$-0.992344\pi$
$311$	−8.44774	+	14.6319i	−0.479028	+	0.829700i	0.520683	+	0.853750i	$0.325677\pi$
$312$		0			0
$313$	3.70433	−	2.13870i	0.209381	−	0.120886i	−0.391643	−	0.920117i	$-0.628093\pi$
$313$	3.70433	−	2.13870i	0.209381	−	0.120886i	0.601024	+	0.799231i	$0.294760\pi$
$314$	1.42457			0.0803934
$315$		0			0
$316$	−4.60242			−0.258906
$317$	5.74123	−	3.31470i	0.322460	−	0.186172i	−0.330029	−	0.943971i	$-0.607058\pi$
$317$	5.74123	−	3.31470i	0.322460	−	0.186172i	0.652488	+	0.757799i	$0.273725\pi$
$318$		0			0
$319$	−14.8397	+	25.7031i	−0.830864	+	1.43910i
$320$	0.967324			0.0540751
$321$		0			0
$322$	0.633821	+	6.99141i	0.0353214	+	0.389616i
$323$			17.6212i			0.980472i
$324$		0			0
$325$	−15.3180	+	8.84386i	−0.849691	+	0.490569i
$326$			7.44296i			0.412227i
$327$		0			0
$328$	0.141830	−	0.0818856i	0.00783125	−	0.00452137i
$329$	2.26694	+	25.0057i	0.124980	+	1.37861i
$330$		0			0
$331$	0.378896	+	0.656267i	0.0208260	+	0.0360717i	0.876251	−	0.481856i	$-0.160037\pi$
$331$	0.378896	+	0.656267i	0.0208260	+	0.0360717i	−0.855425	+	0.517927i	$0.826704\pi$
$332$	4.20979	+	7.29158i	0.231042	+	0.400177i
$333$		0			0
$334$	−5.62665	−	3.24855i	−0.307877	−	0.177753i
$335$	−2.63234	+	4.55935i	−0.143820	+	0.249104i
$336$		0			0
$337$	1.01088	+	1.75089i	0.0550660	+	0.0953772i	0.892244	−	0.451553i	$-0.149130\pi$
$337$	1.01088	+	1.75089i	0.0550660	+	0.0953772i	−0.837178	+	0.546930i	$0.815796\pi$
$338$		−	5.93982i		−	0.323084i
$339$		0			0
$340$	−3.81643			−0.206975
$341$	−17.1850	+	29.7652i	−0.930618	+	1.61188i
$342$		0			0
$343$	4.96188	+	17.8432i	0.267916	+	0.963442i
$344$	7.53520	+	4.35045i	0.406271	+	0.234560i
$345$		0			0
$346$	−10.2354	−	5.90938i	−0.550256	−	0.317690i
$347$	−18.1572	−	10.4831i	−0.974730	−	0.562761i	−0.0740550	−	0.997254i	$-0.523594\pi$
$347$	−18.1572	−	10.4831i	−0.974730	−	0.562761i	−0.900675	+	0.434494i	$0.856927\pi$
$348$		0			0
$349$	5.36406	+	3.09694i	0.287132	+	0.165776i	0.636648	−	0.771155i	$-0.280321\pi$
$349$	5.36406	+	3.09694i	0.287132	+	0.165776i	−0.349516	+	0.936930i	$0.613654\pi$
$350$	−10.7092	+	0.970861i	−0.572429	+	0.0518947i
$351$		0			0
$352$	−2.78681	+	4.82689i	−0.148537	+	0.257274i
$353$	−18.8378			−1.00263			−0.501317	−	0.865264i	$-0.667151\pi$
$353$	−18.8378			−1.00263			−0.501317	+	0.865264i	$0.667151\pi$
$354$		0			0
$355$		−	3.52112i		−	0.186882i
$356$	2.05811	+	3.56475i	0.109080	+	0.188931i
$357$		0			0
$358$	−1.21685	+	2.10764i	−0.0643124	+	0.111392i
$359$	−24.0735	−	13.8988i	−1.27055	−	0.733553i	−0.295459	−	0.955355i	$-0.595473\pi$
$359$	−24.0735	−	13.8988i	−1.27055	−	0.733553i	−0.975092	+	0.221803i	$0.928806\pi$
$360$		0			0
$361$	0.474089	+	0.821146i	0.0249520	+	0.0432182i
$362$	5.76708	+	9.98887i	0.303111	+	0.525003i
$363$		0			0
$364$	4.83332	−	10.4507i	0.253335	−	0.547767i
$365$	2.08428	−	1.20336i	0.109096	−	0.0629866i
$366$		0			0
$367$			21.7534i			1.13552i	0.823195	+	0.567759i	$0.192190\pi$
$367$			21.7534i			1.13552i	−0.823195	+	0.567759i	$0.807810\pi$
$368$	2.29786	−	1.32667i	0.119784	−	0.0691575i
$369$		0			0
$370$			0.471297i			0.0245016i
$371$	−5.30990	+	0.481379i	−0.275676	+	0.0249920i
$372$		0			0
$373$	11.7312			0.607419			0.303709	−	0.952765i	$-0.401775\pi$
$373$	11.7312			0.607419			0.303709	+	0.952765i	$0.401775\pi$
$374$	10.9949	−	19.0438i	0.568533	−	0.984729i
$375$		0			0
$376$	8.21859	−	4.74500i	0.423841	−	0.244705i
$377$	−23.1743			−1.19354
$378$		0			0
$379$	34.8881			1.79208			0.896041	−	0.443971i	$-0.146431\pi$
$379$	34.8881			1.79208			0.896041	+	0.443971i	$0.146431\pi$
$380$	−3.74157	+	2.16020i	−0.191939	+	0.110816i
$381$		0			0
$382$	−11.0345	+	19.1122i	−0.564572	+	0.977867i
$383$	−11.8482			−0.605416			−0.302708	−	0.953083i	$-0.597891\pi$
$383$	−11.8482			−0.605416			−0.302708	+	0.953083i	$0.597891\pi$
$384$		0			0
$385$	−5.98779	+	12.9470i	−0.305166	+	0.659838i
$386$		−	19.9396i		−	1.01490i
$387$		0			0
$388$	−10.2669	+	5.92762i	−0.521225	+	0.300929i
$389$			6.35344i			0.322132i	0.986944	+	0.161066i	$0.0514933\pi$
$389$			6.35344i			0.322132i	−0.986944	+	0.161066i	$0.948507\pi$
$390$		0			0
$391$	−9.06586	+	5.23418i	−0.458480	+	0.264704i
$392$	5.33392	−	4.53314i	0.269404	−	0.228958i
$393$		0			0
$394$	−2.31280	−	4.00588i	−0.116517	−	0.201814i
$395$	2.22601	+	3.85557i	0.112003	+	0.193995i
$396$		0			0
$397$	−7.42647	−	4.28768i	−0.372724	−	0.215192i	0.301924	−	0.953332i	$-0.402371\pi$
$397$	−7.42647	−	4.28768i	−0.372724	−	0.215192i	−0.674648	+	0.738140i	$0.735704\pi$
$398$	−10.4514	+	18.1024i	−0.523883	+	0.907391i
$399$		0			0
$400$	2.03214	+	3.51977i	0.101607	+	0.175989i
$401$		−	23.1190i		−	1.15451i	−0.816565	−	0.577254i	$-0.804124\pi$
$401$		−	23.1190i		−	1.15451i	0.816565	−	0.577254i	$-0.195876\pi$
$402$		0			0
$403$	−26.8367			−1.33683
$404$	−2.65813	+	4.60402i	−0.132247	+	0.229058i
$405$		0			0
$406$	−12.7872	−	5.91393i	−0.634620	−	0.293503i
$407$	−2.35174	−	1.35778i	−0.116572	−	0.0673026i
$408$		0			0
$409$	−1.35091	−	0.779947i	−0.0667981	−	0.0385659i	0.466229	−	0.884664i	$-0.345612\pi$
$409$	−1.35091	−	0.779947i	−0.0667981	−	0.0385659i	−0.533027	+	0.846098i	$0.678946\pi$
$410$	−0.137196	−	0.0792099i	−0.00677561	−	0.00391190i
$411$		0			0
$412$	7.74616	+	4.47225i	0.381626	+	0.220332i
$413$	−3.61971	+	2.55154i	−0.178114	+	0.125553i
$414$		0			0
$415$	4.07224	−	7.05332i	0.199898	−	0.346234i
$416$	−4.35199			−0.213374
$417$		0			0
$418$		−	24.8936i		−	1.21759i
$419$	3.40822	+	5.90321i	0.166502	+	0.288391i	0.937188	−	0.348825i	$-0.113419\pi$
$419$	3.40822	+	5.90321i	0.166502	+	0.288391i	−0.770685	+	0.637216i	$0.780086\pi$
$420$		0			0
$421$	−6.75727	+	11.7039i	−0.329329	+	0.570415i	−0.982379	−	0.186900i	$-0.940156\pi$
$421$	−6.75727	+	11.7039i	−0.329329	+	0.570415i	0.653050	+	0.757315i	$0.273489\pi$
$422$	−5.79042	−	3.34310i	−0.281873	−	0.162740i
$423$		0			0
$424$	1.00759	+	1.74520i	0.0489330	+	0.0847544i
$425$	−8.01750	−	13.8867i	−0.388906	−	0.673605i
$426$		0			0
$427$	−13.6285	+	1.23552i	−0.659529	+	0.0597910i
$428$	16.5898	−	9.57813i	0.801899	−	0.462976i
$429$		0			0
$430$		−	8.41658i		−	0.405884i
$431$	12.2628	−	7.07990i	0.590676	−	0.341027i	−0.174689	−	0.984624i	$-0.555892\pi$
$431$	12.2628	−	7.07990i	0.590676	−	0.341027i	0.765365	+	0.643597i	$0.222559\pi$
$432$		0			0
$433$			23.4830i			1.12852i	0.825597	+	0.564260i	$0.190839\pi$
$433$			23.4830i			1.12852i	−0.825597	+	0.564260i	$0.809161\pi$
$434$	−14.8081	−	6.84856i	−0.710814	−	0.328742i
$435$		0			0
$436$	−19.2434			−0.921590
$437$	−5.92536	+	10.2630i	−0.283449	+	0.490947i
$438$		0			0
$439$	3.66398	−	2.11540i	0.174872	−	0.100963i	−0.410009	−	0.912081i	$-0.634474\pi$
$439$	3.66398	−	2.11540i	0.174872	−	0.100963i	0.584881	+	0.811119i	$0.301141\pi$
$440$	5.39149			0.257029
$441$		0			0
$442$	17.1701			0.816699
$443$	25.8161	−	14.9049i	1.22656	−	0.708154i	0.260250	−	0.965541i	$-0.416195\pi$
$443$	25.8161	−	14.9049i	1.22656	−	0.708154i	0.966308	+	0.257388i	$0.0828618\pi$
$444$		0			0
$445$	1.99086	−	3.44827i	0.0943757	−	0.163464i
$446$	−8.18246			−0.387451
$447$		0			0
$448$	−2.40137	−	1.11060i	−0.113454	−	0.0524709i
$449$			8.41716i			0.397230i	0.980078	+	0.198615i	$0.0636444\pi$
$449$			8.41716i			0.397230i	−0.980078	+	0.198615i	$0.936356\pi$
$450$		0			0
$451$	0.790505	−	0.456399i	0.0372234	−	0.0214910i
$452$			8.44316i			0.397133i
$453$		0			0
$454$	9.26106	−	5.34688i	0.434643	−	0.250941i
$455$	−11.0926	+	1.00562i	−0.520027	+	0.0471441i
$456$		0			0
$457$	1.94109	+	3.36207i	0.0908006	+	0.157271i	0.907848	−	0.419299i	$-0.137724\pi$
$457$	1.94109	+	3.36207i	0.0908006	+	0.157271i	−0.817048	+	0.576570i	$0.804391\pi$
$458$	14.6036	+	25.2942i	0.682382	+	1.18192i
$459$		0			0
$460$	−2.22278	−	1.28332i	−0.103638	−	0.0598352i
$461$	−17.0423	+	29.5181i	−0.793739	+	1.37480i	0.129898	+	0.991527i	$0.458535\pi$
$461$	−17.0423	+	29.5181i	−0.793739	+	1.37480i	−0.923637	+	0.383269i	$0.874798\pi$
$462$		0			0
$463$	−6.10962	−	10.5822i	−0.283938	−	0.491796i	0.688413	−	0.725319i	$-0.258308\pi$
$463$	−6.10962	−	10.5822i	−0.283938	−	0.491796i	−0.972351	+	0.233523i	$0.924974\pi$
$464$			5.32498i			0.247206i
$465$		0			0
$466$	6.43935			0.298297
$467$	15.4057	−	26.6835i	0.712893	−	1.23477i	−0.250874	−	0.968020i	$-0.580718\pi$
$467$	15.4057	−	26.6835i	0.712893	−	1.23477i	0.963767	−	0.266747i	$-0.0859488\pi$
$468$		0			0
$469$	11.7694	−	8.29628i	0.543460	−	0.383087i
$470$	−7.95004	−	4.58996i	−0.366708	−	0.211719i
$471$		0			0
$472$	1.44961	+	0.836931i	0.0667236	+	0.0385229i
$473$	41.9983	+	24.2477i	1.93108	+	1.11491i
$474$		0			0
$475$	−15.7205	−	9.07623i	−0.721306	−	0.416446i
$476$	9.47423	+	4.38170i	0.434250	+	0.200835i
$477$		0			0
$478$	2.31778	−	4.01452i	0.106013	−	0.183620i
$479$	41.7493			1.90758			0.953788	−	0.300481i	$-0.0971472\pi$
$479$	41.7493			1.90758			0.953788	+	0.300481i	$0.0971472\pi$
$480$		0			0
$481$		−	2.12036i		−	0.0966803i
$482$	−5.24722	−	9.08846i	−0.239004	−	0.413968i
$483$		0			0
$484$	−10.0326	+	17.3769i	−0.456026	+	0.789861i
$485$	9.93146	+	5.73393i	0.450964	+	0.260364i
$486$		0			0
$487$	10.5832	+	18.3306i	0.479568	+	0.830637i	0.999725	−	0.0234338i	$-0.00745988\pi$
$487$	10.5832	+	18.3306i	0.479568	+	0.830637i	−0.520157	+	0.854071i	$0.674127\pi$
$488$	2.58611	+	4.47927i	0.117068	+	0.202767i
$489$		0			0
$490$	−6.37734	−	2.27586i	−0.288099	−	0.102813i
$491$	−32.3428	+	18.6731i	−1.45961	+	0.842707i	−0.998992	−	0.0448915i	$-0.985706\pi$
$491$	−32.3428	+	18.6731i	−1.45961	+	0.842707i	−0.460619	+	0.887598i	$0.652372\pi$
$492$		0			0
$493$		−	21.0089i		−	0.946193i
$494$	16.8333	−	9.71873i	0.757368	−	0.437266i
$495$		0			0
$496$			6.16655i			0.276886i
$497$	−4.04266	+	8.74113i	−0.181338	+	0.392093i
$498$		0			0
$499$	27.4197			1.22748			0.613738	−	0.789510i	$-0.289665\pi$
$499$	27.4197			1.22748			0.613738	+	0.789510i	$0.289665\pi$
$500$	4.38405	−	7.59340i	0.196061	−	0.339587i
$501$		0			0
$502$	6.80065	−	3.92635i	0.303528	−	0.175242i
$503$	−11.2791			−0.502909			−0.251454	−	0.967869i	$-0.580909\pi$
$503$	−11.2791			−0.502909			−0.251454	+	0.967869i	$0.580909\pi$
$504$		0			0
$505$	5.14255			0.228840
$506$	12.8074	−	7.39435i	0.569358	−	0.328719i
$507$		0			0
$508$	1.65941	−	2.87419i	0.0736246	−	0.127522i
$509$	−18.6333			−0.825909			−0.412954	−	0.910752i	$-0.635503\pi$
$509$	−18.6333			−0.825909			−0.412954	+	0.910752i	$0.635503\pi$
$510$		0			0
$511$	−6.55578	+	0.594327i	−0.290010	+	0.0262915i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	2.97164	−	1.71568i	0.131074	−	0.0756753i
$515$		−	8.65223i		−	0.381263i
$516$		0			0
$517$	45.8072	−	26.4468i	2.01460	−	1.16313i
$518$	0.541103	−	1.16999i	0.0237747	−	0.0514063i
$519$		0			0
$520$	2.10489	+	3.64578i	0.0923056	+	0.159878i
$521$	−7.64255	−	13.2373i	−0.334826	−	0.579936i	0.648625	−	0.761108i	$-0.275344\pi$
$521$	−7.64255	−	13.2373i	−0.334826	−	0.579936i	−0.983451	+	0.181172i	$0.942011\pi$
$522$		0			0
$523$	−31.5991	−	18.2437i	−1.38173	−	0.797743i	−0.389368	−	0.921082i	$-0.627306\pi$
$523$	−31.5991	−	18.2437i	−1.38173	−	0.797743i	−0.992365	+	0.123339i	$0.960640\pi$
$524$	9.37335	−	16.2351i	0.409477	−	0.709235i
$525$		0			0
$526$	1.83066	+	3.17080i	0.0798207	+	0.138253i
$527$		−	24.3292i		−	1.05979i
$528$		0			0
$529$	15.9598			0.693903
$530$	0.974668	−	1.68817i	0.0423369	−	0.0733296i
$531$		0			0
$532$	11.7686	−	1.06690i	0.510232	−	0.0462561i
$533$	0.617243	+	0.356365i	0.0267358	+	0.0154359i
$534$		0			0
$535$	−16.0477	−	9.26516i	−0.693803	−	0.400568i
$536$	−4.71336	−	2.72126i	−0.203586	−	0.117540i
$537$		0			0
$538$	−10.9865	−	6.34303i	−0.473660	−	0.273467i
$539$	29.7292	−	25.2659i	1.28053	−	1.08828i
$540$		0			0
$541$	2.63647	−	4.56649i	0.113351	−	0.196329i	−0.803769	−	0.594942i	$-0.797175\pi$
$541$	2.63647	−	4.56649i	0.113351	−	0.196329i	0.917119	+	0.398613i	$0.130508\pi$
$542$	−19.8766			−0.853771
$543$		0			0
$544$		−	3.94535i		−	0.169155i
$545$	9.30729	+	16.1207i	0.398680	+	0.690535i
$546$		0			0
$547$	−9.29831	+	16.1051i	−0.397567	+	0.688606i	−0.993425	−	0.114484i	$-0.963479\pi$
$547$	−9.29831	+	16.1051i	−0.397567	+	0.688606i	0.595858	+	0.803090i	$0.296812\pi$
$548$	−14.6656	−	8.46717i	−0.626482	−	0.361700i
$549$		0			0
$550$	11.3264	+	19.6179i	0.482958	+	0.836508i
$551$	−11.8916	−	20.5968i	−0.506599	−	0.877455i
$552$		0			0
$553$	−1.09941	−	12.1271i	−0.0467516	−	0.515697i
$554$	−6.46579	+	3.73302i	−0.274705	+	0.158601i
$555$		0			0
$556$		−	12.1281i		−	0.514347i
$557$	23.8694	−	13.7810i	1.01138	−	0.583920i	0.0997845	−	0.995009i	$-0.468185\pi$
$557$	23.8694	−	13.7810i	1.01138	−	0.583920i	0.911595	+	0.411089i	$0.134851\pi$
$558$		0			0
$559$			37.8662i			1.60157i
$560$	0.231071	+	2.54885i	0.00976452	+	0.107708i
$561$		0			0
$562$	22.2564			0.938831
$563$	9.42577	−	16.3259i	0.397249	−	0.688055i	−0.596137	−	0.802883i	$-0.703298\pi$
$563$	9.42577	−	16.3259i	0.397249	−	0.688055i	0.993385	+	0.114828i	$0.0366317\pi$
$564$		0			0
$565$	7.07306	−	4.08364i	0.297566	−	0.171800i
$566$	16.1802			0.680106
$567$		0			0
$568$	3.64006			0.152734
$569$	−3.87103	+	2.23494i	−0.162282	+	0.0936936i	−0.578942	−	0.815369i	$-0.696534\pi$
$569$	−3.87103	+	2.23494i	−0.162282	+	0.0936936i	0.416659	+	0.909063i	$0.363201\pi$
$570$		0			0
$571$	−9.31245	+	16.1296i	−0.389714	+	0.675004i	−0.992411	−	0.122966i	$-0.960759\pi$
$571$	−9.31245	+	16.1296i	−0.389714	+	0.675004i	0.602697	+	0.797970i	$0.294093\pi$
$572$	−24.2563			−1.01421
$573$		0			0
$574$	0.249644	+	0.354154i	0.0104199	+	0.0147821i
$575$		−	10.7839i		−	0.449721i
$576$		0			0
$577$	31.9418	−	18.4416i	1.32976	−	0.767735i	0.344495	−	0.938788i	$-0.388050\pi$
$577$	31.9418	−	18.4416i	1.32976	−	0.767735i	0.985262	+	0.171053i	$0.0547170\pi$
$578$		−	1.43425i		−	0.0596569i
$579$		0			0
$580$	4.46088	−	2.57549i	0.185228	−	0.106941i
$581$	−18.2073	+	12.8344i	−0.755366	+	0.532459i
$582$		0			0
$583$	5.61593	+	9.72707i	0.232588	+	0.402854i
$584$	1.24401	+	2.15468i	0.0514773	+	0.0891614i
$585$		0			0
$586$	−7.68002	−	4.43406i	−0.317259	−	0.183170i
$587$	13.2295	−	22.9141i	0.546039	−	0.945766i	−0.452502	−	0.891763i	$-0.649469\pi$
$587$	13.2295	−	22.9141i	0.546039	−	0.945766i	0.998541	−	0.0540032i	$-0.0171981\pi$
$588$		0			0
$589$	−13.7709	−	23.8520i	−0.567422	−	0.982803i
$590$		−	1.61917i		−	0.0666601i
$591$		0			0
$592$	−0.487217			−0.0200245
$593$	−17.3351	+	30.0254i	−0.711869	+	1.23299i	0.252285	+	0.967653i	$0.418818\pi$
$593$	−17.3351	+	30.0254i	−0.711869	+	1.23299i	−0.964155	+	0.265341i	$0.914516\pi$
$594$		0			0
$595$	−0.911654	−	10.0561i	−0.0373742	−	0.412259i
$596$	−7.56951	−	4.37026i	−0.310059	−	0.179013i
$597$		0			0
$598$	10.0003	+	5.77366i	0.408942	+	0.236103i
$599$	−21.2079	−	12.2444i	−0.866530	−	0.500291i	−0.000336253	−	1.00000i	$-0.500107\pi$
$599$	−21.2079	−	12.2444i	−0.866530	−	0.500291i	−0.866193	+	0.499709i	$0.833440\pi$
$600$		0			0
$601$	19.3812	+	11.1898i	0.790577	+	0.456440i	0.840166	−	0.542330i	$-0.182458\pi$
$601$	19.3812	+	11.1898i	0.790577	+	0.456440i	−0.0495885	+	0.998770i	$0.515791\pi$
$602$	−9.66321	+	20.8940i	−0.393843	+	0.851578i
$603$		0			0
$604$	11.0471	−	19.1341i	0.449499	−	0.778555i
$605$	19.4095			0.789109
$606$		0			0
$607$		−	32.5834i		−	1.32252i	−0.750158	−	0.661259i	$-0.770022\pi$
$607$		−	32.5834i		−	1.32252i	0.750158	−	0.661259i	$-0.229978\pi$
$608$	−2.23317	−	3.86796i	−0.0905670	−	0.156867i
$609$		0			0
$610$	2.50160	−	4.33290i	0.101287	−	0.175434i
$611$	35.7672	+	20.6502i	1.44699	+	0.835418i
$612$		0			0
$613$	5.86931	+	10.1659i	0.237059	+	0.410598i	0.959869	−	0.280449i	$-0.0904832\pi$
$613$	5.86931	+	10.1659i	0.237059	+	0.410598i	−0.722810	+	0.691047i	$0.757150\pi$
$614$	−13.5714	−	23.5063i	−0.547696	−	0.948637i
$615$		0			0
$616$	−13.3843	−	6.19005i	−0.539269	−	0.249404i
$617$	38.1947	−	22.0517i	1.53766	−	0.887770i	0.538687	−	0.842506i	$-0.318920\pi$
$617$	38.1947	−	22.0517i	1.53766	−	0.887770i	0.998975	−	0.0452639i	$-0.0144129\pi$
$618$		0			0
$619$			4.94644i			0.198814i	0.995047	+	0.0994070i	$0.0316946\pi$
$619$			4.94644i			0.198814i	−0.995047	+	0.0994070i	$0.968305\pi$
$620$	5.16588	−	2.98252i	0.207467	−	0.119781i
$621$		0			0
$622$			16.8955i			0.677447i
$623$	−8.90128	+	6.27454i	−0.356622	+	0.251384i
$624$		0			0
$625$	11.8398			0.473593
$626$	2.13870	−	3.70433i	0.0854795	−	0.148055i
$627$		0			0
$628$	1.23372	−	0.712287i	0.0492307	−	0.0284233i
$629$	1.92224			0.0766447
$630$		0			0
$631$	−9.08478			−0.361659			−0.180830	−	0.983514i	$-0.557878\pi$
$631$	−9.08478			−0.361659			−0.180830	+	0.983514i	$0.557878\pi$
$632$	−3.98581	+	2.30121i	−0.158547	+	0.0915371i
$633$		0			0
$634$	3.31470	−	5.74123i	0.131644	−	0.228013i
$635$	−3.21038			−0.127400
$636$		0			0
$637$	28.6917	+	10.2391i	1.13681	+	0.405688i
$638$			29.6794i			1.17502i
$639$		0			0
$640$	0.837727	−	0.483662i	0.0331141	−	0.0191184i
$641$			14.0821i			0.556209i	0.960551	+	0.278105i	$0.0897062\pi$
$641$			14.0821i			0.556209i	−0.960551	+	0.278105i	$0.910294\pi$
$642$		0			0
$643$	−7.33157	+	4.23288i	−0.289129	+	0.166929i	−0.637549	−	0.770410i	$-0.720052\pi$
$643$	−7.33157	+	4.23288i	−0.289129	+	0.166929i	0.348420	+	0.937339i	$0.386718\pi$
$644$	4.04461	+	5.73783i	0.159380	+	0.226102i
$645$		0			0
$646$	8.81062	+	15.2604i	0.346649	+	0.600414i
$647$	−12.1662	−	21.0725i	−0.478304	−	0.828446i	0.521387	−	0.853320i	$-0.325415\pi$
$647$	−12.1662	−	21.0725i	−0.478304	−	0.828446i	−0.999691	+	0.0248742i	$0.992081\pi$
$648$		0			0
$649$	8.07955	+	4.66473i	0.317150	+	0.183107i
$650$	−8.84386	+	15.3180i	−0.346885	+	0.600822i
$651$		0			0
$652$	3.72148	+	6.44579i	0.145744	+	0.252437i
$653$		−	41.6446i		−	1.62968i	−0.579686	−	0.814840i	$-0.696825\pi$
$653$		−	41.6446i		−	1.62968i	0.579686	−	0.814840i	$-0.303175\pi$
$654$		0			0
$655$	−18.1341			−0.708560
$656$	0.0818856	−	0.141830i	0.00319709	−	0.00553753i
$657$		0			0
$658$	14.4661	+	20.5221i	0.563946	+	0.800033i
$659$	9.09866	+	5.25312i	0.354434	+	0.204632i	0.666636	−	0.745383i	$-0.267733\pi$
$659$	9.09866	+	5.25312i	0.354434	+	0.204632i	−0.312203	+	0.950016i	$0.601067\pi$
$660$		0			0
$661$	−16.8988	−	9.75655i	−0.657289	−	0.379486i	0.133954	−	0.990987i	$-0.457232\pi$
$661$	−16.8988	−	9.75655i	−0.657289	−	0.379486i	−0.791243	+	0.611502i	$0.790566\pi$
$662$	0.656267	+	0.378896i	0.0255065	+	0.0147262i
$663$		0			0
$664$	7.29158	+	4.20979i	0.282968	+	0.163372i
$665$	−6.58578	−	9.34282i	−0.255386	−	0.362299i
$666$		0			0
$667$	7.06450	−	12.2361i	0.273539	−	0.473783i
$668$	−6.49710			−0.251380
$669$		0			0
$670$			5.26468i			0.203392i
$671$	14.4140	+	24.9657i	0.556445	+	0.963790i
$672$		0			0
$673$	−3.10277	+	5.37415i	−0.119603	+	0.207158i	−0.919610	−	0.392832i	$-0.871495\pi$
$673$	−3.10277	+	5.37415i	−0.119603	+	0.207158i	0.800007	+	0.599990i	$0.204829\pi$
$674$	1.75089	+	1.01088i	0.0674419	+	0.0389376i
$675$		0			0
$676$	−2.96991	−	5.14404i	−0.114227	−	0.197848i
$677$	−12.3765	−	21.4368i	−0.475669	−	0.823883i	0.523942	−	0.851754i	$-0.324461\pi$
$677$	−12.3765	−	21.4368i	−0.475669	−	0.823883i	−0.999612	+	0.0278703i	$0.991127\pi$
$678$		0			0
$679$	−18.0715	−	25.6369i	−0.693520	−	0.983852i
$680$	−3.30512	+	1.90821i	−0.126746	+	0.0731767i
$681$		0			0
$682$			34.3699i			1.31609i
$683$	−18.3119	+	10.5724i	−0.700687	+	0.404542i	−0.807603	−	0.589726i	$-0.799236\pi$
$683$	−18.3119	+	10.5724i	−0.700687	+	0.404542i	0.106916	+	0.994268i	$0.465902\pi$
$684$		0			0
$685$			16.3810i			0.625886i
$686$	13.2187	+	12.9717i	0.504693	+	0.495263i
$687$		0			0
$688$	8.70089			0.331718
$689$	−4.38503	+	7.59509i	−0.167056	+	0.289350i
$690$		0			0
$691$	5.58127	−	3.22235i	0.212322	−	0.122584i	−0.390068	−	0.920786i	$-0.627549\pi$
$691$	5.58127	−	3.22235i	0.212322	−	0.122584i	0.602390	+	0.798202i	$0.294215\pi$
$692$	−11.8188			−0.449282
$693$		0			0
$694$	−20.9661			−0.795864
$695$	−10.1601	+	5.86591i	−0.385393	+	0.222507i
$696$		0			0
$697$	−0.323067	+	0.559568i	−0.0122370	+	0.0211952i
$698$	6.19389			0.234442
$699$		0			0
$700$	−8.78898	+	6.19537i	−0.332192	+	0.234163i
$701$		−	24.5717i		−	0.928061i	−0.885819	−	0.464031i	$-0.846403\pi$
$701$		−	24.5717i		−	0.928061i	0.885819	−	0.464031i	$-0.153597\pi$
$702$		0			0
$703$	1.88454	−	1.08804i	0.0710767	−	0.0410361i
$704$			5.57361i			0.210063i
$705$		0			0
$706$	−16.3140	+	9.41889i	−0.613985	+	0.354484i
$707$	−12.7663	−	5.90424i	−0.480126	−	0.222052i
$708$		0			0
$709$	−22.1370	−	38.3424i	−0.831373	−	1.43998i	−0.896950	−	0.442133i	$-0.854222\pi$
$709$	−22.1370	−	38.3424i	−0.831373	−	1.43998i	0.0655765	−	0.997848i	$-0.479111\pi$
$710$	−1.76056	−	3.04938i	−0.0660727	−	0.114441i
$711$		0			0
$712$	3.56475	+	2.05811i	0.133595	+	0.0771309i
$713$	8.18098	−	14.1699i	0.306380	−	0.530666i
$714$		0			0
$715$	11.7319	+	20.3202i	0.438747	+	0.759931i
$716$			2.43370i			0.0909515i
$717$		0			0
$718$	−27.7977			−1.03740
$719$	2.22433	−	3.85266i	0.0829537	−	0.143680i	−0.821564	−	0.570117i	$-0.806898\pi$
$719$	2.22433	−	3.85266i	0.0829537	−	0.143680i	0.904517	+	0.426437i	$0.140231\pi$
$720$		0			0
$721$	−9.93376	+	21.4790i	−0.369952	+	0.799921i
$722$	0.821146	+	0.474089i	0.0305599	+	0.0176438i
$723$		0			0
$724$	9.98887	+	5.76708i	0.371233	+	0.214332i
$725$	18.7427	+	10.8211i	0.696088	+	0.401886i
$726$		0			0
$727$	−30.4270	−	17.5670i	−1.12848	−	0.651525i	−0.184924	−	0.982753i	$-0.559204\pi$
$727$	−30.4270	−	17.5670i	−1.12848	−	0.651525i	−0.943551	+	0.331227i	$0.892537\pi$
$728$	−1.03959	−	11.4673i	−0.0385297	−	0.425005i
$729$		0			0
$730$	1.20336	−	2.08428i	0.0445382	−	0.0771425i
$731$	−34.3280			−1.26967
$732$		0			0
$733$		−	5.81725i		−	0.214865i	−0.994212	−	0.107433i	$-0.965737\pi$
$733$		−	5.81725i		−	0.214865i	0.994212	−	0.107433i	$-0.0342630\pi$
$734$	10.8767	+	18.8390i	0.401467	+	0.695360i
$735$		0			0
$736$	1.32667	−	2.29786i	0.0489018	−	0.0847003i
$737$	−26.2704	−	15.1672i	−0.967684	−	0.558693i
$738$		0			0
$739$	−5.51675	−	9.55529i	−0.202937	−	0.351497i	0.746537	−	0.665344i	$-0.231715\pi$
$739$	−5.51675	−	9.55529i	−0.202937	−	0.351497i	−0.949473	+	0.313847i	$0.898382\pi$
$740$	0.235648	+	0.408155i	0.00866261	+	0.0150041i
$741$		0			0
$742$	−4.35782	+	3.07184i	−0.159980	+	0.112771i
$743$	0.543196	−	0.313615i	0.0199279	−	0.0115054i	−0.490003	−	0.871721i	$-0.663004\pi$
$743$	0.543196	−	0.313615i	0.0199279	−	0.0115054i	0.509931	+	0.860215i	$0.329671\pi$
$744$		0			0
$745$			8.45491i			0.309764i
$746$	10.1595	−	5.86560i	0.371966	−	0.214755i
$747$		0			0
$748$		−	21.9898i		−	0.804028i
$749$	29.2008	+	41.4253i	1.06697	+	1.51365i
$750$		0			0
$751$	4.47058			0.163134			0.0815668	−	0.996668i	$-0.474008\pi$
$751$	4.47058			0.163134			0.0815668	+	0.996668i	$0.474008\pi$
$752$	4.74500	−	8.21859i	0.173033	−	0.299701i
$753$		0			0
$754$	−20.0695	+	11.5871i	−0.730889	+	0.421979i
$755$	−21.3722			−0.777813
$756$		0			0
$757$	5.75624			0.209214			0.104607	−	0.994514i	$-0.466642\pi$
$757$	5.75624			0.209214			0.104607	+	0.994514i	$0.466642\pi$
$758$	30.2140	−	17.4441i	1.09742	−	0.633597i
$759$		0			0
$760$	−2.16020	+	3.74157i	−0.0783586	+	0.135721i
$761$	20.9940			0.761032			0.380516	−	0.924774i	$-0.375746\pi$
$761$	20.9940			0.761032			0.380516	+	0.924774i	$0.375746\pi$
$762$		0			0
$763$	−4.59678	−	50.7052i	−0.166415	−	1.83565i
$764$			22.0689i			0.798425i
$765$		0			0
$766$	−10.2609	+	5.92412i	−0.370740	+	0.214047i
$767$			7.28463i			0.263033i
$768$		0			0
$769$	−34.1729	+	19.7298i	−1.23231	+	0.711473i	−0.967511	−	0.252831i	$-0.918638\pi$
$769$	−34.1729	+	19.7298i	−1.23231	+	0.711473i	−0.264797	+	0.964304i	$0.585305\pi$
$770$	1.28790	+	14.2063i	0.0464127	+	0.511959i
$771$		0			0
$772$	−9.96979	−	17.2682i	−0.358821	−	0.621496i
$773$	17.3164	+	29.9929i	0.622829	+	1.07877i	0.988956	+	0.148206i	$0.0473499\pi$
$773$	17.3164	+	29.9929i	0.622829	+	1.07877i	−0.366128	+	0.930565i	$0.619317\pi$
$774$		0			0
$775$	21.7048	+	12.5313i	0.779661	+	0.450137i
$776$	−5.92762	+	10.2669i	−0.212789	+	0.368562i
$777$		0			0
$778$	3.17672	+	5.50224i	0.113891	+	0.197265i
$779$			0.731457i			0.0262072i
$780$		0			0
$781$	20.2883			0.725973
$782$	−5.23418	+	9.06586i	−0.187174	+	0.324195i
$783$		0			0
$784$	2.35274	−	6.59277i	0.0840264	−	0.235456i
$785$	−1.19340	−	0.689012i	−0.0425944	−	0.0245919i
$786$		0			0
$787$	30.5793	+	17.6550i	1.09003	+	0.629332i	0.933586	−	0.358355i	$-0.116662\pi$
$787$	30.5793	+	17.6550i	1.09003	+	0.629332i	0.156449	+	0.987686i	$0.449995\pi$
$788$	−4.00588	−	2.31280i	−0.142704	−	0.0823900i
$789$		0			0
$790$	3.85557	+	2.22601i	0.137175	+	0.0791980i
$791$	−22.2473	+	2.01687i	−0.791022	+	0.0717116i
$792$		0			0
$793$	−11.2547	+	19.4937i	−0.399667	+	0.692243i
$794$	−8.57535			−0.304328
$795$		0			0
$796$			20.9028i			0.740882i
$797$	9.60992	+	16.6449i	0.340401	+	0.589591i	0.984507	−	0.175344i	$-0.0561039\pi$
$797$	9.60992	+	16.6449i	0.340401	+	0.589591i	−0.644106	+	0.764936i	$0.722771\pi$
$798$		0			0
$799$	−18.7207	+	32.4252i	−0.662290	+	1.14712i
$800$	3.51977	+	2.03214i	0.124443	+	0.0718471i
$801$		0			0
$802$	−11.5595	−	20.0216i	−0.408180	−	0.706989i
$803$	6.93361	+	12.0094i	0.244682	+	0.423801i
$804$		0			0
$805$	2.85051	−	6.16345i	0.100467	−	0.217233i
$806$	−23.2413	+	13.4184i	−0.818640	+	0.472642i
$807$		0			0
$808$			5.31626i			0.187025i
$809$	−34.0157	+	19.6390i	−1.19593	+	0.690469i	−0.959645	−	0.281215i	$-0.909263\pi$
$809$	−34.0157	+	19.6390i	−1.19593	+	0.690469i	−0.236283	+	0.971684i	$0.575929\pi$
$810$		0			0
$811$		−	9.68436i		−	0.340064i	−0.985439	−	0.170032i	$-0.945613\pi$
$811$		−	9.68436i		−	0.340064i	0.985439	−	0.170032i	$-0.0543871\pi$
$812$	−14.0310	+	1.27201i	−0.492393	+	0.0446389i
$813$		0			0
$814$	−2.71556			−0.0951803
$815$	3.59987	−	6.23517i	0.126098	−	0.218408i
$816$		0			0
$817$	−33.6547	+	19.4306i	−1.17743	+	0.679790i
$818$	−1.55989			−0.0545404
$819$		0			0
$820$	−0.158420			−0.00553226
$821$	−10.9919	+	6.34620i	−0.383621	+	0.221484i	−0.679393	−	0.733775i	$-0.737757\pi$
$821$	−10.9919	+	6.34620i	−0.383621	+	0.221484i	0.295771	+	0.955259i	$0.404423\pi$
$822$		0			0
$823$	−8.73837	+	15.1353i	−0.304600	+	0.527583i	−0.977172	−	0.212448i	$-0.931856\pi$
$823$	−8.73837	+	15.1353i	−0.304600	+	0.527583i	0.672572	+	0.740032i	$0.265190\pi$
$824$	8.94450			0.311596
$825$		0			0
$826$	−1.85899	+	4.01956i	−0.0646826	+	0.139858i
$827$		−	46.9482i		−	1.63255i	−0.577665	−	0.816274i	$-0.696036\pi$
$827$		−	46.9482i		−	1.63255i	0.577665	−	0.816274i	$-0.303964\pi$
$828$		0			0
$829$	−1.99797	+	1.15353i	−0.0693924	+	0.0400637i	−0.534295	−	0.845298i	$-0.679423\pi$
$829$	−1.99797	+	1.15353i	−0.0693924	+	0.0400637i	0.464902	+	0.885362i	$0.346089\pi$
$830$		−	8.14447i		−	0.282699i
$831$		0			0
$832$	−3.76893	+	2.17600i	−0.130664	+	0.0754391i
$833$	−9.28237	+	26.0108i	−0.321615	+	0.901219i
$834$		0			0
$835$	3.14240	+	5.44280i	0.108747	+	0.188356i
$836$	−12.4468	−	21.5585i	−0.430482	−	0.745617i
$837$		0			0
$838$	5.90321	+	3.40822i	0.203923	+	0.117735i
$839$	8.51664	−	14.7513i	0.294027	−	0.509270i	−0.680731	−	0.732533i	$-0.738338\pi$
$839$	8.51664	−	14.7513i	0.294027	−	0.509270i	0.974758	+	0.223264i	$0.0716711\pi$
$840$		0			0
$841$	−0.322276	−	0.558199i	−0.0111130	−	0.0192482i
$842$			13.5145i			0.465742i
$843$		0			0
$844$	−6.68620			−0.230148
$845$	−2.87287	+	4.97595i	−0.0988296	+	0.171178i
$846$		0			0
$847$	−48.1838	−	22.2844i	−1.65562	−	0.765700i
$848$	1.74520	+	1.00759i	0.0599304	+	0.0346008i
$849$		0			0
$850$	−13.8867	−	8.01750i	−0.476311	−	0.274998i
$851$	1.11956	+	0.646377i	0.0383779	+	0.0221575i
$852$		0			0
$853$	−2.87158	−	1.65791i	−0.0983209	−	0.0567656i	0.450033	−	0.893012i	$-0.351412\pi$
$853$	−2.87158	−	1.65791i	−0.0983209	−	0.0567656i	−0.548354	+	0.836246i	$0.684745\pi$
$854$	−11.1849	+	7.88424i	−0.382738	+	0.269793i
$855$		0			0
$856$	9.57813	−	16.5898i	0.327374	−	0.567028i
$857$	9.49024			0.324180			0.162090	−	0.986776i	$-0.448176\pi$
$857$	9.49024			0.324180			0.162090	+	0.986776i	$0.448176\pi$
$858$		0			0
$859$		−	29.4569i		−	1.00506i	−0.864561	−	0.502528i	$-0.832403\pi$
$859$		−	29.4569i		−	1.00506i	0.864561	−	0.502528i	$-0.167597\pi$
$860$	−4.20829	−	7.28898i	−0.143502	−	0.248552i
$861$		0			0
$862$	7.07990	−	12.2628i	0.241143	−	0.417671i
$863$	13.4610	+	7.77172i	0.458218	+	0.264553i	0.711295	−	0.702894i	$-0.248109\pi$
$863$	13.4610	+	7.77172i	0.458218	+	0.264553i	−0.253076	+	0.967446i	$0.581442\pi$
$864$		0			0
$865$	5.71629	+	9.90090i	0.194360	+	0.336641i
$866$	11.7415	+	20.3369i	0.398992	+	0.691075i
$867$		0			0
$868$	−16.2485	+	1.47304i	−0.551510	+	0.0499983i
$869$	−22.2154	+	12.8260i	−0.753604	+	0.435094i
$870$		0			0
$871$		−	23.6858i		−	0.802562i
$872$	−16.6652	+	9.62168i	−0.564356	+	0.325831i
$873$		0			0
$874$			11.8507i			0.400857i
$875$	21.0554	+	9.73785i	0.711804	+	0.329199i
$876$		0			0
$877$	−45.4497			−1.53473			−0.767364	−	0.641212i	$-0.778432\pi$
$877$	−45.4497			−1.53473			−0.767364	+	0.641212i	$0.778432\pi$
$878$	2.11540	−	3.66398i	0.0713913	−	0.123653i
$879$		0			0
$880$	4.66917	−	2.69574i	0.157398	−	0.0908735i
$881$	15.6912			0.528651			0.264326	−	0.964433i	$-0.414851\pi$
$881$	15.6912			0.528651			0.264326	+	0.964433i	$0.414851\pi$
$882$		0			0
$883$	−10.5344			−0.354510			−0.177255	−	0.984165i	$-0.556722\pi$
$883$	−10.5344			−0.354510			−0.177255	+	0.984165i	$0.556722\pi$
$884$	14.8697	−	8.58505i	0.500124	−	0.288747i
$885$		0			0
$886$	14.9049	−	25.8161i	0.500740	−	0.867307i
$887$	−0.0605481			−0.00203301			−0.00101650	−	0.999999i	$-0.500324\pi$
$887$	−0.0605481			−0.00203301			−0.00101650	+	0.999999i	$0.500324\pi$
$888$		0			0
$889$	7.96973	+	3.68589i	0.267296	+	0.123621i
$890$		−	3.98172i		−	0.133467i
$891$		0			0
$892$	−7.08622	+	4.09123i	−0.237264	+	0.136985i
$893$			42.3856i			1.41838i
$894$		0			0
$895$	2.03877	−	1.17709i	0.0681487	−	0.0393456i
$896$	−2.63495	+	0.238876i	−0.0880274	+	0.00798029i
$897$		0			0
$898$	4.20858	+	7.28948i	0.140442	+	0.243253i
$899$	16.4184	+	28.4375i	0.547583	+	0.948442i
$900$		0			0
$901$	−6.88542	−	3.97530i	−0.229386	−	0.132436i
$902$	0.456399	−	0.790505i	0.0151964	−	0.0263210i
$903$		0			0
$904$	4.22158	+	7.31199i	0.140408	+	0.243193i
$905$		−	11.1573i		−	0.370880i
$906$		0			0
$907$	24.0980			0.800162			0.400081	−	0.916480i	$-0.368982\pi$
$907$	24.0980			0.800162			0.400081	+	0.916480i	$0.368982\pi$
$908$	5.34688	−	9.26106i	0.177442	−	0.307339i
$909$		0			0
$910$	−9.10363	+	6.41717i	−0.301782	+	0.212727i
$911$	−22.0494	−	12.7302i	−0.730528	−	0.421771i	0.0880873	−	0.996113i	$-0.471925\pi$
$911$	−22.0494	−	12.7302i	−0.730528	−	0.421771i	−0.818615	+	0.574342i	$0.805258\pi$
$912$		0			0
$913$	40.6404	+	23.4638i	1.34500	+	0.776537i
$914$	3.36207	+	1.94109i	0.111208	+	0.0642057i
$915$		0			0
$916$	25.2942	+	14.6036i	0.835744	+	0.482517i
$917$	45.0177	+	20.8201i	1.48662	+	0.687540i
$918$		0			0
$919$	11.4534	−	19.8378i	0.377812	−	0.654389i	−0.612932	−	0.790136i	$-0.710010\pi$
$919$	11.4534	−	19.8378i	0.377812	−	0.654389i	0.990744	+	0.135747i	$0.0433433\pi$
$920$	−2.56664			−0.0846197
$921$		0			0
$922$			34.0846i			1.12252i
$923$	7.92076	+	13.7192i	0.260715	+	0.451572i
$924$		0			0
$925$	−0.990094	+	1.71489i	−0.0325541	+	0.0563853i
$926$	−10.5822	−	6.10962i	−0.347752	−	0.200775i
$927$		0			0
$928$	2.66249	+	4.61157i	0.0874006	+	0.151382i
$929$	−14.3986	−	24.9392i	−0.472404	−	0.818228i	0.527097	−	0.849805i	$-0.323280\pi$
$929$	−14.3986	−	24.9392i	−0.472404	−	0.818228i	−0.999501	+	0.0315768i	$0.989947\pi$
$930$		0			0
$931$	5.62246	+	30.7547i	0.184269	+	1.00794i
$932$	5.57664	−	3.21967i	0.182669	−	0.105464i
$933$		0			0
$934$		−	30.8115i		−	1.00818i
$935$	−18.4215	+	10.6356i	−0.602447	+	0.347823i
$936$		0			0
$937$		−	53.6825i		−	1.75373i	−0.480736	−	0.876865i	$-0.659631\pi$
$937$		−	53.6825i		−	1.75373i	0.480736	−	0.876865i	$-0.340369\pi$
$938$	6.04446	−	13.0695i	0.197359	−	0.426734i
$939$		0			0
$940$	−9.17991			−0.299416
$941$	22.9511	−	39.7524i	0.748184	−	1.29589i	−0.200509	−	0.979692i	$-0.564260\pi$
$941$	22.9511	−	39.7524i	0.748184	−	1.29589i	0.948693	−	0.316200i	$-0.102407\pi$
$942$		0			0
$943$	−0.376324	+	0.217271i	−0.0122548	+	0.00707530i
$944$	1.67386			0.0544796
$945$		0			0
$946$	48.4954			1.57672
$947$	25.0440	−	14.4591i	0.813820	−	0.469859i	−0.0344607	−	0.999406i	$-0.510971\pi$
$947$	25.0440	−	14.4591i	0.813820	−	0.469859i	0.848281	+	0.529547i	$0.177638\pi$
$948$		0			0
$949$	−5.41390	+	9.37715i	−0.175743	+	0.304395i
$950$	−18.1525			−0.588944
$951$		0			0
$952$	10.3958	−	0.942449i	0.336929	−	0.0305450i
$953$		−	12.8715i		−	0.416949i	−0.978028	−	0.208475i	$-0.933150\pi$
$953$		−	12.8715i		−	0.416949i	0.978028	−	0.208475i	$-0.0668498\pi$
$954$		0			0
$955$	18.4877	−	10.6739i	0.598249	−	0.345399i
$956$		−	4.63557i		−	0.149925i
$957$		0			0
$958$	36.1560	−	20.8747i	1.16815	−	0.674430i
$959$	18.8073	−	40.6656i	0.607319	−	1.31316i
$960$		0			0
$961$	3.51314	+	6.08494i	0.113327	+	0.196288i
$962$	−1.06018	−	1.83629i	−0.0341816	−	0.0592043i
$963$		0			0
$964$	−9.08846	−	5.24722i	−0.292719	−	0.169002i
$965$	−9.64402	+	16.7039i	−0.310452	+	0.537719i
$966$		0			0
$967$	3.11725	+	5.39923i	0.100244	+	0.173627i	0.911785	−	0.410668i	$-0.134704\pi$
$967$	3.11725	+	5.39923i	0.100244	+	0.173627i	−0.811541	+	0.584295i	$0.801371\pi$
$968$			20.0652i			0.644919i
$969$		0			0
$970$	11.4679			0.368211
$971$	−19.6863	+	34.0977i	−0.631764	+	1.09425i	0.355426	+	0.934704i	$0.384336\pi$
$971$	−19.6863	+	34.0977i	−0.631764	+	1.09425i	−0.987191	+	0.159544i	$0.948998\pi$
$972$		0			0
$973$	31.9570	−	2.89712i	1.02449	−	0.0928774i
$974$	18.3306	+	10.5832i	0.587349	+	0.339106i
$975$		0			0
$976$	4.47927	+	2.58611i	0.143378	+	0.0827793i
$977$	−23.2474	−	13.4219i	−0.743751	−	0.429405i	0.0796807	−	0.996820i	$-0.474610\pi$
$977$	−23.2474	−	13.4219i	−0.743751	−	0.429405i	−0.823431	+	0.567416i	$0.807943\pi$
$978$		0			0
$979$	19.8685	+	11.4711i	0.635001	+	0.366618i
$980$	−6.66087	+	1.21772i	−0.212774	+	0.0388986i
$981$		0			0
$982$	−18.6731	+	32.3428i	−0.595884	+	1.03210i
$983$	−11.9691			−0.381756			−0.190878	−	0.981614i	$-0.561134\pi$
$983$	−11.9691			−0.381756			−0.190878	+	0.981614i	$0.561134\pi$
$984$		0			0
$985$			4.47445i			0.142568i
$986$	−10.5044	−	18.1942i	−0.334530	−	0.579423i
$987$		0			0
$988$	9.71873	−	16.8333i	0.309194	−	0.535540i
$989$	−19.9935	−	11.5432i	−0.635755	−	0.367053i
$990$		0			0
$991$	−5.40420	−	9.36036i	−0.171670	−	0.297342i	0.767334	−	0.641248i	$-0.221583\pi$
$991$	−5.40420	−	9.36036i	−0.171670	−	0.297342i	−0.939004	+	0.343906i	$0.888250\pi$
$992$	3.08327	+	5.34038i	0.0978940	+	0.169557i
$993$		0			0
$994$	0.869525	+	9.59137i	0.0275797	+	0.304220i
$995$	17.5109	−	10.1099i	0.555132	−	0.320506i
$996$		0			0
$997$			13.4700i			0.426598i	0.976987	+	0.213299i	$0.0684208\pi$
$997$			13.4700i			0.426598i	−0.976987	+	0.213299i	$0.931579\pi$
$998$	23.7462	−	13.7099i	0.751672	−	0.433978i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.t.a.89.6		16
3.2	odd	2		126.2.t.a.47.1	yes	16
4.3	odd	2		3024.2.df.c.1601.4		16
7.2	even	3		2646.2.m.a.1763.3		16
7.3	odd	6		378.2.l.a.143.6		16
7.4	even	3		2646.2.l.a.521.7		16
7.5	odd	6		2646.2.m.b.1763.2		16
7.6	odd	2		2646.2.t.b.1979.7		16
9.2	odd	6		1134.2.k.b.971.6		16
9.4	even	3		126.2.l.a.5.7	✓	16
9.5	odd	6		378.2.l.a.341.2		16
9.7	even	3		1134.2.k.a.971.3		16
12.11	even	2		1008.2.df.c.929.7		16
21.2	odd	6		882.2.m.a.587.7		16
21.5	even	6		882.2.m.b.587.6		16
21.11	odd	6		882.2.l.b.227.2		16
21.17	even	6		126.2.l.a.101.3	yes	16
21.20	even	2		882.2.t.a.803.4		16
28.3	even	6		3024.2.ca.c.2033.4		16
36.23	even	6		3024.2.ca.c.2609.4		16
36.31	odd	6		1008.2.ca.c.257.5		16
63.4	even	3		882.2.t.a.815.4		16
63.5	even	6		2646.2.m.a.881.3		16
63.13	odd	6		882.2.l.b.509.6		16
63.23	odd	6		2646.2.m.b.881.2		16
63.31	odd	6		126.2.t.a.59.1	yes	16
63.32	odd	6		2646.2.t.b.2285.7		16
63.38	even	6		1134.2.k.a.647.3		16
63.40	odd	6		882.2.m.a.293.7		16
63.41	even	6		2646.2.l.a.1097.3		16
63.52	odd	6		1134.2.k.b.647.6		16
63.58	even	3		882.2.m.b.293.6		16
63.59	even	6	inner	378.2.t.a.17.6		16
84.59	odd	6		1008.2.ca.c.353.5		16
252.31	even	6		1008.2.df.c.689.7		16
252.59	odd	6		3024.2.df.c.17.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.7	✓	16	9.4	even	3
126.2.l.a.101.3	yes	16	21.17	even	6
126.2.t.a.47.1	yes	16	3.2	odd	2
126.2.t.a.59.1	yes	16	63.31	odd	6
378.2.l.a.143.6		16	7.3	odd	6
378.2.l.a.341.2		16	9.5	odd	6
378.2.t.a.17.6		16	63.59	even	6	inner
378.2.t.a.89.6		16	1.1	even	1	trivial
882.2.l.b.227.2		16	21.11	odd	6
882.2.l.b.509.6		16	63.13	odd	6
882.2.m.a.293.7		16	63.40	odd	6
882.2.m.a.587.7		16	21.2	odd	6
882.2.m.b.293.6		16	63.58	even	3
882.2.m.b.587.6		16	21.5	even	6
882.2.t.a.803.4		16	21.20	even	2
882.2.t.a.815.4		16	63.4	even	3
1008.2.ca.c.257.5		16	36.31	odd	6
1008.2.ca.c.353.5		16	84.59	odd	6
1008.2.df.c.689.7		16	252.31	even	6
1008.2.df.c.929.7		16	12.11	even	2
1134.2.k.a.647.3		16	63.38	even	6
1134.2.k.a.971.3		16	9.7	even	3
1134.2.k.b.647.6		16	63.52	odd	6
1134.2.k.b.971.6		16	9.2	odd	6
2646.2.l.a.521.7		16	7.4	even	3
2646.2.l.a.1097.3		16	63.41	even	6
2646.2.m.a.881.3		16	63.5	even	6
2646.2.m.a.1763.3		16	7.2	even	3
2646.2.m.b.881.2		16	63.23	odd	6
2646.2.m.b.1763.2		16	7.5	odd	6
2646.2.t.b.1979.7		16	7.6	odd	2
2646.2.t.b.2285.7		16	63.32	odd	6
3024.2.ca.c.2033.4		16	28.3	even	6
3024.2.ca.c.2609.4		16	36.23	even	6
3024.2.df.c.17.4		16	252.59	odd	6
3024.2.df.c.1601.4		16	4.3	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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -0.967324 q^{5} +(2.40137 + 1.11060i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -0.967324 q^{5} +(2.40137 + 1.11060i) q^{7} -1.00000i q^{8} +(-0.837727 + 0.483662i) q^{10} -5.57361i q^{11} +(3.76893 - 2.17600i) q^{13} +(2.63495 - 0.238876i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.97267 + 3.41677i) q^{17} +(3.86796 + 2.23317i) q^{19} +(-0.483662 + 0.837727i) q^{20} +(-2.78681 - 4.82689i) q^{22} +2.65334i q^{23} -4.06428 q^{25} +(2.17600 - 3.76893i) q^{26} +(2.16249 - 1.52435i) q^{28} +(-4.61157 - 2.66249i) q^{29} +(-5.34038 - 3.08327i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(3.41677 + 1.97267i) q^{34} +(-2.32290 - 1.07431i) q^{35} +(0.243608 - 0.421942i) q^{37} +4.46634 q^{38} +0.967324i q^{40} +(0.0818856 + 0.141830i) q^{41} +(-4.35045 + 7.53520i) q^{43} +(-4.82689 - 2.78681i) q^{44} +(1.32667 + 2.29786i) q^{46} +(4.74500 + 8.21859i) q^{47} +(4.53314 + 5.33392i) q^{49} +(-3.51977 + 2.03214i) q^{50} -4.35199i q^{52} +(-1.74520 + 1.00759i) q^{53} +5.39149i q^{55} +(1.11060 - 2.40137i) q^{56} -5.32498 q^{58} +(-0.836931 + 1.44961i) q^{59} +(-4.47927 + 2.58611i) q^{61} -6.16655 q^{62} -1.00000 q^{64} +(-3.64578 + 2.10489i) q^{65} +(2.72126 - 4.71336i) q^{67} +3.94535 q^{68} +(-2.54885 + 0.231071i) q^{70} +3.64006i q^{71} +(-2.15468 + 1.24401i) q^{73} -0.487217i q^{74} +(3.86796 - 2.23317i) q^{76} +(6.19005 - 13.3843i) q^{77} +(-2.30121 - 3.98581i) q^{79} +(0.483662 + 0.837727i) q^{80} +(0.141830 + 0.0818856i) q^{82} +(-4.20979 + 7.29158i) q^{83} +(-1.90821 - 3.30512i) q^{85} +8.70089i q^{86} -5.57361 q^{88} +(-2.05811 + 3.56475i) q^{89} +(11.4673 - 1.03959i) q^{91} +(2.29786 + 1.32667i) q^{92} +(8.21859 + 4.74500i) q^{94} +(-3.74157 - 2.16020i) q^{95} +(-10.2669 - 5.92762i) q^{97} +(6.59277 + 2.35274i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 2 q^{7}+O(q^{10}) \) 16 * q + 8 * q^4 + 2 * q^7	\( 16 q + 8 q^{4} + 2 q^{7} - 6 q^{13} + 6 q^{14} - 8 q^{16} - 18 q^{17} + 16 q^{25} + 12 q^{26} - 2 q^{28} - 6 q^{29} + 6 q^{31} + 30 q^{35} - 2 q^{37} - 6 q^{41} - 2 q^{43} - 12 q^{44} + 6 q^{46} + 18 q^{47} + 10 q^{49} + 12 q^{50} - 36 q^{53} - 12 q^{58} - 30 q^{59} - 60 q^{61} + 36 q^{62} - 16 q^{64} - 42 q^{65} + 14 q^{67} - 36 q^{68} + 18 q^{77} - 16 q^{79} - 12 q^{85} - 24 q^{89} - 12 q^{91} - 6 q^{92} + 66 q^{95} - 6 q^{97} - 24 q^{98}+O(q^{100}) \) 16 * q + 8 * q^4 + 2 * q^7 - 6 * q^13 + 6 * q^14 - 8 * q^16 - 18 * q^17 + 16 * q^25 + 12 * q^26 - 2 * q^28 - 6 * q^29 + 6 * q^31 + 30 * q^35 - 2 * q^37 - 6 * q^41 - 2 * q^43 - 12 * q^44 + 6 * q^46 + 18 * q^47 + 10 * q^49 + 12 * q^50 - 36 * q^53 - 12 * q^58 - 30 * q^59 - 60 * q^61 + 36 * q^62 - 16 * q^64 - 42 * q^65 + 14 * q^67 - 36 * q^68 + 18 * q^77 - 16 * q^79 - 12 * q^85 - 24 * q^89 - 12 * q^91 - 6 * q^92 + 66 * q^95 - 6 * q^97 - 24 * q^98

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