LMFDB - Embedded newform 819.2.j.i.352.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [819,2,Mod(235,819)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("819.235"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(819, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.j (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 8x^{10} + 47x^{8} + 122x^{6} + 233x^{4} + 119x^{2} + 49 $ x^12 + 8x^10 + 47x^8 + 122x^6 + 233x^4 + 119*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			352.3
Root			$0.367252 + 0.636099i$ of defining polynomial
Character	$\chi$	$=$	819.352
Dual form			819.2.j.i.235.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.367252 + 0.636099i) q^{2} +(0.730252 + 1.26483i) q^{4} +(1.27088 - 2.20122i) q^{5} +(-2.25729 + 1.38008i) q^{7} -2.54175 q^{8} +(0.933463 + 1.61680i) q^{10} +(1.85612 + 3.21490i) q^{11} -1.00000 q^{13} +(-0.0488718 - 1.94270i) q^{14} +(-0.527042 + 0.912864i) q^{16} +(-1.05288 - 1.82365i) q^{17} +(-2.96050 + 5.12774i) q^{19} +3.71224 q^{20} -2.72665 q^{22} +(-3.12700 + 5.41612i) q^{23} +(-0.730252 - 1.26483i) q^{25} +(0.367252 - 0.636099i) q^{26} +(-3.39397 - 1.84730i) q^{28} +8.83547 q^{29} +(2.85087 + 4.93786i) q^{31} +(-2.92887 - 5.07295i) q^{32} +1.54669 q^{34} +(0.169121 + 6.72272i) q^{35} +(-3.28434 + 5.68864i) q^{37} +(-2.17450 - 3.76635i) q^{38} +(-3.23025 + 5.59496i) q^{40} +10.3045 q^{41} -10.6477 q^{43} +(-2.71087 + 4.69537i) q^{44} +(-2.29679 - 3.97816i) q^{46} +(0.734503 - 1.27220i) q^{47} +(3.19076 - 6.23049i) q^{49} +1.07275 q^{50} +(-0.730252 - 1.26483i) q^{52} +(3.22738 + 5.58999i) q^{53} +9.43560 q^{55} +(5.73748 - 3.50782i) q^{56} +(-3.24484 + 5.62023i) q^{58} +(-5.71762 - 9.90321i) q^{59} +(4.55768 - 7.89414i) q^{61} -4.18795 q^{62} +2.19436 q^{64} +(-1.27088 + 2.20122i) q^{65} +(7.02704 + 12.1712i) q^{67} +(1.53774 - 2.66345i) q^{68} +(-4.33842 - 2.36135i) q^{70} -14.4527 q^{71} +(3.07014 + 5.31763i) q^{73} +(-2.41236 - 4.17832i) q^{74} -8.64766 q^{76} +(-8.62663 - 4.69537i) q^{77} +(3.98395 - 6.90040i) q^{79} +(1.33961 + 2.32027i) q^{80} +(-3.78434 + 6.55466i) q^{82} -12.1515 q^{83} -5.35234 q^{85} +(3.91037 - 6.77296i) q^{86} +(-4.71780 - 8.17147i) q^{88} +(-5.90660 + 10.2305i) q^{89} +(2.25729 - 1.38008i) q^{91} -9.13399 q^{92} +(0.539495 + 0.934433i) q^{94} +(7.52487 + 13.0335i) q^{95} +7.10097 q^{97} +(2.79140 + 4.31780i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{4} + 4 q^{7} + 4 q^{10} - 12 q^{13} + 12 q^{16} - 10 q^{19} - 36 q^{22} + 4 q^{25} - 8 q^{28} - 8 q^{31} + 12 q^{34} + 10 q^{37} - 26 q^{40} - 80 q^{43} - 22 q^{46} + 4 q^{52} + 36 q^{58} + 2 q^{61}+ \cdots + 44 q^{97}+O(q^{100}) $ 12 * q - 4 * q^4 + 4 * q^7 + 4 * q^10 - 12 * q^13 + 12 * q^16 - 10 * q^19 - 36 * q^22 + 4 * q^25 - 8 * q^28 - 8 * q^31 + 12 * q^34 + 10 * q^37 - 26 * q^40 - 80 * q^43 - 22 * q^46 + 4 * q^52 + 36 * q^58 + 2 * q^61 - 28 * q^64 + 66 * q^67 + 34 * q^70 + 28 * q^73 - 56 * q^76 + 20 * q^79 + 4 * q^82 - 112 * q^85 - 4 * q^91 + 32 * q^94 + 44 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.367252	+	0.636099i	−0.259686	+	0.449790i	−0.966158	−	0.257952i	$-0.916952\pi$
$2$	−0.367252	+	0.636099i	−0.259686	+	0.449790i	0.706472	+	0.707741i	$0.250286\pi$
$3$		0			0
$3$		0			0
$4$	0.730252	+	1.26483i	0.365126	+	0.632417i
$5$	1.27088	−	2.20122i	0.568353	−	0.984416i	−0.428376	−	0.903601i	$-0.640914\pi$
$5$	1.27088	−	2.20122i	0.568353	−	0.984416i	0.996729	−	0.0808158i	$-0.0257526\pi$
$6$		0			0
$7$	−2.25729	+	1.38008i	−0.853177	+	0.521621i
$7$	−2.25729	+	1.38008i	−0.853177	+	0.521621i
$8$	−2.54175			−0.898645
$9$		0			0
$10$	0.933463	+	1.61680i	0.295187	+	0.511279i
$11$	1.85612	+	3.21490i	0.559641	+	0.969327i	0.997526	+	0.0702963i	$0.0223945\pi$
$11$	1.85612	+	3.21490i	0.559641	+	0.969327i	−0.437885	+	0.899031i	$0.644272\pi$
$12$		0			0
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	−0.0488718	−	1.94270i	−0.0130615	−	0.519208i
$15$		0			0
$16$	−0.527042	+	0.912864i	−0.131761	+	0.228216i
$17$	−1.05288	−	1.82365i	−0.255362	−	0.442299i	0.709632	−	0.704572i	$-0.248861\pi$
$17$	−1.05288	−	1.82365i	−0.255362	−	0.442299i	−0.964994	+	0.262273i	$0.915528\pi$
$18$		0			0
$19$	−2.96050	+	5.12774i	−0.679186	+	1.17639i	0.296040	+	0.955176i	$0.404334\pi$
$19$	−2.96050	+	5.12774i	−0.679186	+	1.17639i	−0.975226	+	0.221210i	$0.928999\pi$
$20$	3.71224			0.830082
$21$		0			0
$22$	−2.72665			−0.581325
$23$	−3.12700	+	5.41612i	−0.652024	+	1.12934i	0.330607	+	0.943768i	$0.392747\pi$
$23$	−3.12700	+	5.41612i	−0.652024	+	1.12934i	−0.982631	+	0.185570i	$0.940587\pi$
$24$		0			0
$25$	−0.730252	−	1.26483i	−0.146050	−	0.252967i
$26$	0.367252	−	0.636099i	0.0720240	−	0.124749i
$27$		0			0
$28$	−3.39397	−	1.84730i	−0.641400	−	0.349106i
$29$	8.83547			1.64071			0.820353	−	0.571858i	$-0.193777\pi$
$29$	8.83547			1.64071			0.820353	+	0.571858i	$0.193777\pi$
$30$		0			0
$31$	2.85087	+	4.93786i	0.512032	+	0.886866i	0.999903	+	0.0139496i	$0.00444044\pi$
$31$	2.85087	+	4.93786i	0.512032	+	0.886866i	−0.487871	+	0.872916i	$0.662226\pi$
$32$	−2.92887	−	5.07295i	−0.517755	−	0.896779i
$33$		0			0
$34$	1.54669			0.265256
$35$	0.169121	+	6.72272i	0.0285867	+	1.13635i
$36$		0			0
$37$	−3.28434	+	5.68864i	−0.539942	+	0.935206i	0.458965	+	0.888454i	$0.348220\pi$
$37$	−3.28434	+	5.68864i	−0.539942	+	0.935206i	−0.998907	+	0.0467519i	$0.985113\pi$
$38$	−2.17450	−	3.76635i	−0.352751	−	0.610982i
$39$		0			0
$40$	−3.23025	+	5.59496i	−0.510748	+	0.884641i
$41$	10.3045			1.60929			0.804645	−	0.593757i	$-0.202356\pi$
$41$	10.3045			1.60929			0.804645	+	0.593757i	$0.202356\pi$
$42$		0			0
$43$	−10.6477			−1.62375			−0.811877	−	0.583829i	$-0.801554\pi$
$43$	−10.6477			−1.62375			−0.811877	+	0.583829i	$0.801554\pi$
$44$	−2.71087	+	4.69537i	−0.408680	+	0.707854i
$45$		0			0
$46$	−2.29679	−	3.97816i	−0.338643	−	0.586547i
$47$	0.734503	−	1.27220i	0.107138	−	0.185569i	−0.807472	−	0.589907i	$-0.799165\pi$
$47$	0.734503	−	1.27220i	0.107138	−	0.185569i	0.914610	+	0.404338i	$0.132498\pi$
$48$		0			0
$49$	3.19076	−	6.23049i	0.455822	−	0.890071i
$50$	1.07275			0.151709
$51$		0			0
$52$	−0.730252	−	1.26483i	−0.101268	−	0.175401i
$53$	3.22738	+	5.58999i	0.443315	+	0.767845i	0.997933	−	0.0642606i	$-0.0204689\pi$
$53$	3.22738	+	5.58999i	0.443315	+	0.767845i	−0.554618	+	0.832105i	$0.687136\pi$
$54$		0			0
$55$	9.43560			1.27230
$56$	5.73748	−	3.50782i	0.766704	−	0.468752i
$57$		0			0
$58$	−3.24484	+	5.62023i	−0.426069	+	0.737972i
$59$	−5.71762	−	9.90321i	−0.744371	−	1.28929i	−0.950488	−	0.310761i	$-0.899416\pi$
$59$	−5.71762	−	9.90321i	−0.744371	−	1.28929i	0.206117	−	0.978527i	$-0.433917\pi$
$60$		0			0
$61$	4.55768	−	7.89414i	0.583551	−	1.01074i	−0.411503	−	0.911408i	$-0.634996\pi$
$61$	4.55768	−	7.89414i	0.583551	−	1.01074i	0.995054	−	0.0993323i	$-0.0316707\pi$
$62$	−4.18795			−0.531871
$63$		0			0
$64$	2.19436			0.274294
$65$	−1.27088	+	2.20122i	−0.157633	+	0.273028i
$66$		0			0
$67$	7.02704	+	12.1712i	0.858490	+	1.48695i	0.873369	+	0.487059i	$0.161930\pi$
$67$	7.02704	+	12.1712i	0.858490	+	1.48695i	−0.0148794	+	0.999889i	$0.504736\pi$
$68$	1.53774	−	2.66345i	0.186478	−	0.322990i
$69$		0			0
$70$	−4.33842	−	2.36135i	−0.518540	−	0.282235i
$71$	−14.4527			−1.71522			−0.857610	−	0.514300i	$-0.828052\pi$
$71$	−14.4527			−1.71522			−0.857610	+	0.514300i	$0.828052\pi$
$72$		0			0
$73$	3.07014	+	5.31763i	0.359332	+	0.622382i	0.987849	−	0.155414i	$-0.0496712\pi$
$73$	3.07014	+	5.31763i	0.359332	+	0.622382i	−0.628517	+	0.777796i	$0.716338\pi$
$74$	−2.41236	−	4.17832i	−0.280431	−	0.485720i
$75$		0			0
$76$	−8.64766			−0.991955
$77$	−8.62663	−	4.69537i	−0.983095	−	0.535087i
$78$		0			0
$79$	3.98395	−	6.90040i	0.448229	−	0.776356i	−0.550042	−	0.835137i	$-0.685388\pi$
$79$	3.98395	−	6.90040i	0.448229	−	0.776356i	0.998271	+	0.0587814i	$0.0187215\pi$
$80$	1.33961	+	2.32027i	0.149773	+	0.259414i
$81$		0			0
$82$	−3.78434	+	6.55466i	−0.417910	+	0.723841i
$83$	−12.1515			−1.33380			−0.666898	−	0.745149i	$-0.732378\pi$
$83$	−12.1515			−1.33380			−0.666898	+	0.745149i	$0.732378\pi$
$84$		0			0
$85$	−5.35234			−0.580542
$86$	3.91037	−	6.77296i	0.421666	−	0.730347i
$87$		0			0
$88$	−4.71780	−	8.17147i	−0.502919	−	0.871081i
$89$	−5.90660	+	10.2305i	−0.626099	+	1.08444i	0.362228	+	0.932089i	$0.382016\pi$
$89$	−5.90660	+	10.2305i	−0.626099	+	1.08444i	−0.988327	+	0.152346i	$0.951317\pi$
$90$		0			0
$91$	2.25729	−	1.38008i	0.236629	−	0.144672i
$92$	−9.13399			−0.952284
$93$		0			0
$94$	0.539495	+	0.934433i	0.0556447	+	0.0963794i
$95$	7.52487	+	13.0335i	0.772035	+	1.33720i
$96$		0			0
$97$	7.10097			0.720994			0.360497	−	0.932760i	$-0.382607\pi$
$97$	7.10097			0.720994			0.360497	+	0.932760i	$0.382607\pi$
$98$	2.79140	+	4.31780i	0.281974	+	0.436163i
$99$		0			0
$100$	1.06654	−	1.84730i	0.106654	−	0.184730i
$101$	−4.24861	−	7.35882i	−0.422753	−	0.732230i	0.573455	−	0.819237i	$-0.305603\pi$
$101$	−4.24861	−	7.35882i	−0.422753	−	0.732230i	−0.996208	+	0.0870077i	$0.972270\pi$
$102$		0			0
$103$	−1.09358	+	1.89413i	−0.107754	+	0.186635i	−0.914860	−	0.403771i	$-0.867699\pi$
$103$	−1.09358	+	1.89413i	−0.107754	+	0.186635i	0.807106	+	0.590406i	$0.201032\pi$
$104$	2.54175			0.249239
$105$		0			0
$106$	−4.74105			−0.460491
$107$	3.76376	−	6.51902i	0.363856	−	0.630217i	−0.624736	−	0.780836i	$-0.714793\pi$
$107$	3.76376	−	6.51902i	0.363856	−	0.630217i	0.988592	+	0.150619i	$0.0481267\pi$
$108$		0			0
$109$	−0.0270421	−	0.0468383i	−0.00259016	−	0.00448630i	0.864727	−	0.502241i	$-0.167491\pi$
$109$	−0.0270421	−	0.0468383i	−0.00259016	−	0.00448630i	−0.867318	+	0.497755i	$0.834158\pi$
$110$	−3.46524	+	6.00197i	−0.330398	+	0.572265i
$111$		0			0
$112$	−0.0701359	−	2.78796i	−0.00662722	−	0.263438i
$113$	−6.25399			−0.588326			−0.294163	−	0.955755i	$-0.595041\pi$
$113$	−6.25399			−0.588326			−0.294163	+	0.955755i	$0.595041\pi$
$114$		0			0
$115$	7.94805	+	13.7664i	0.741160	+	1.28373i
$116$	6.45212	+	11.1754i	0.599065	+	1.03761i
$117$		0			0
$118$	8.39922			0.773211
$119$	4.89345	+	2.66345i	0.448582	+	0.244158i
$120$		0			0
$121$	−1.39037	+	2.40819i	−0.126397	+	0.218926i
$122$	3.34763	+	5.79827i	0.303080	+	0.524951i
$123$		0			0
$124$	−4.16372	+	7.21177i	−0.373913	+	0.647636i
$125$	8.99652			0.804673
$126$		0			0
$127$	−2.49261			−0.221183			−0.110592	−	0.993866i	$-0.535275\pi$
$127$	−2.49261			−0.221183			−0.110592	+	0.993866i	$0.535275\pi$
$128$	5.05185	−	8.75006i	0.446525	−	0.773404i
$129$		0			0
$130$	−0.933463	−	1.61680i	−0.0818701	−	0.141803i
$131$	4.42688	−	7.66759i	0.386779	−	0.669920i	−0.605236	−	0.796046i	$-0.706921\pi$
$131$	4.42688	−	7.66759i	0.386779	−	0.669920i	0.992014	+	0.126126i	$0.0402545\pi$
$132$		0			0
$133$	−0.393968	−	15.6606i	−0.0341613	−	1.35794i
$134$	−10.3228			−0.891752
$135$		0			0
$136$	2.67617	+	4.63526i	0.229480	+	0.397470i
$137$	−1.35947	−	2.35468i	−0.116148	−	0.201174i	0.802090	−	0.597203i	$-0.203721\pi$
$137$	−1.35947	−	2.35468i	−0.116148	−	0.201174i	−0.918238	+	0.396029i	$0.870388\pi$
$138$		0			0
$139$	13.1694			1.11702			0.558509	−	0.829498i	$-0.311374\pi$
$139$	13.1694			1.11702			0.558509	+	0.829498i	$0.311374\pi$
$140$	−8.37962	+	5.12319i	−0.708207	+	0.432989i
$141$		0			0
$142$	5.30778	−	9.19334i	0.445419	−	0.771488i
$143$	−1.85612	−	3.21490i	−0.155217	−	0.268843i
$144$		0			0
$145$	11.2288	−	19.4488i	0.932500	−	1.61514i
$146$	−4.51005			−0.373254
$147$		0			0
$148$	−9.59358			−0.788587
$149$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$149$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$150$		0			0
$151$	3.64766	+	6.31794i	0.296843	+	0.514147i	0.975412	−	0.220390i	$-0.0707330\pi$
$151$	3.64766	+	6.31794i	0.296843	+	0.514147i	−0.678569	+	0.734536i	$0.737400\pi$
$152$	7.52487	−	13.0335i	0.610348	−	1.05715i
$153$		0			0
$154$	6.15486	−	3.76300i	0.495973	−	0.303231i
$155$	14.4924			1.16406
$156$		0			0
$157$	2.83628	+	4.91259i	0.226360	+	0.392067i	0.956727	−	0.290988i	$-0.0939840\pi$
$157$	2.83628	+	4.91259i	0.226360	+	0.392067i	−0.730366	+	0.683055i	$0.760651\pi$
$158$	2.92622	+	5.06837i	0.232798	+	0.403218i
$159$		0			0
$160$	−14.8889			−1.17707
$161$	−0.416123	−	16.5413i	−0.0327951	−	1.30364i
$162$		0			0
$163$	10.3581	−	17.9407i	0.811307	−	1.40522i	−0.100643	−	0.994923i	$-0.532090\pi$
$163$	10.3581	−	17.9407i	0.811307	−	1.40522i	0.911950	−	0.410302i	$-0.134577\pi$
$164$	7.52487	+	13.0335i	0.587594	+	1.01774i
$165$		0			0
$166$	4.46264	−	7.72952i	0.346368	−	0.599927i
$167$	14.3152			1.10775			0.553873	−	0.832601i	$-0.313149\pi$
$167$	14.3152			1.10775			0.553873	+	0.832601i	$0.313149\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	1.96565	−	3.40461i	0.150759	−	0.261122i
$171$		0			0
$172$	−7.77548	−	13.4675i	−0.592875	−	1.02689i
$173$	11.2081	−	19.4130i	0.852136	−	1.47594i	−0.0271403	−	0.999632i	$-0.508640\pi$
$173$	11.2081	−	19.4130i	0.852136	−	1.47594i	0.879277	−	0.476312i	$-0.158027\pi$
$174$		0			0
$175$	3.39397	+	1.84730i	0.256560	+	0.139643i
$176$	−3.91302			−0.294955
$177$		0			0
$178$	−4.33842	−	7.51437i	−0.325178	−	0.563225i
$179$	−4.13101	−	7.15512i	−0.308766	−	0.534799i	0.669327	−	0.742968i	$-0.266583\pi$
$179$	−4.13101	−	7.15512i	−0.308766	−	0.534799i	−0.978093	+	0.208170i	$0.933249\pi$
$180$		0			0
$181$	−0.787935			−0.0585668			−0.0292834	−	0.999571i	$-0.509323\pi$
$181$	−0.787935			−0.0585668			−0.0292834	+	0.999571i	$0.509323\pi$
$182$	0.0488718	+	1.94270i	0.00362262	+	0.144002i
$183$		0			0
$184$	7.94805	−	13.7664i	0.585938	−	1.01487i
$185$	8.34797	+	14.4591i	0.613755	+	1.06305i
$186$		0			0
$187$	3.90856	−	6.76982i	0.285822	−	0.495058i
$188$	2.14549			0.156476
$189$		0			0
$190$	−11.0541			−0.801948
$191$	−0.198130	+	0.343172i	−0.0143362	+	0.0248311i	−0.873105	−	0.487533i	$-0.837897\pi$
$191$	−0.198130	+	0.343172i	−0.0143362	+	0.0248311i	0.858768	+	0.512364i	$0.171230\pi$
$192$		0			0
$193$	−1.89397	−	3.28045i	−0.136331	−	0.236132i	0.789774	−	0.613398i	$-0.210198\pi$
$193$	−1.89397	−	3.28045i	−0.136331	−	0.236132i	−0.926105	+	0.377266i	$0.876864\pi$
$194$	−2.60784	+	4.51692i	−0.187232	+	0.324296i
$195$		0			0
$196$	10.2106	−	0.514055i	0.729329	−	0.0367182i
$197$	12.0484			0.858415			0.429207	−	0.903206i	$-0.358793\pi$
$197$	12.0484			0.858415			0.429207	+	0.903206i	$0.358793\pi$
$198$		0			0
$199$	2.58113	+	4.47064i	0.182971	+	0.316915i	0.942891	−	0.333101i	$-0.108095\pi$
$199$	2.58113	+	4.47064i	0.182971	+	0.316915i	−0.759920	+	0.650017i	$0.774762\pi$
$200$	1.85612	+	3.21490i	0.131248	+	0.227327i
$201$		0			0
$202$	6.24124			0.439132
$203$	−19.9443	+	12.1937i	−1.39981	+	0.855827i
$204$		0			0
$205$	13.0957	−	22.6824i	0.914644	−	1.58421i
$206$	−0.803238	−	1.39125i	−0.0559642	−	0.0969329i
$207$		0			0
$208$	0.527042	−	0.912864i	0.0365438	−	0.0632957i
$209$	−21.9802			−1.52040
$210$		0			0
$211$	17.9794			1.23775			0.618875	−	0.785489i	$-0.287589\pi$
$211$	17.9794			1.23775			0.618875	+	0.785489i	$0.287589\pi$
$212$	−4.71361	+	8.16421i	−0.323732	+	0.560720i
$213$		0			0
$214$	2.76449	+	4.78824i	0.188977	+	0.327317i
$215$	−13.5319	+	23.4379i	−0.922865	+	1.59845i
$216$		0			0
$217$	−13.2499	−	7.21177i	−0.899462	−	0.489567i
$218$	0.0397250			0.00269052
$219$		0			0
$220$	6.89037	+	11.9345i	0.464549	+	0.804622i
$221$	1.05288	+	1.82365i	0.0708246	+	0.122672i
$222$		0			0
$223$	1.96790			0.131780			0.0658901	−	0.997827i	$-0.479011\pi$
$223$	1.96790			0.131780			0.0658901	+	0.997827i	$0.479011\pi$
$224$	13.6124	+	7.40906i	0.909516	+	0.495039i
$225$		0			0
$226$	2.29679	−	3.97816i	0.152780	−	0.264623i
$227$	6.21427	+	10.7634i	0.412456	+	0.714394i	0.995158	−	0.0982919i	$-0.0313379\pi$
$227$	6.21427	+	10.7634i	0.412456	+	0.714394i	−0.582702	+	0.812686i	$0.698005\pi$
$228$		0			0
$229$	−10.5292	+	18.2371i	−0.695788	+	1.20514i	0.274127	+	0.961694i	$0.411611\pi$
$229$	−10.5292	+	18.2371i	−0.695788	+	1.20514i	−0.969914	+	0.243446i	$0.921722\pi$
$230$	−11.6757			−0.769876
$231$		0			0
$232$	−22.4576			−1.47441
$233$	3.63436	−	6.29490i	0.238095	−	0.412392i	−0.722073	−	0.691817i	$-0.756810\pi$
$233$	3.63436	−	6.29490i	0.238095	−	0.412392i	0.960168	+	0.279425i	$0.0901437\pi$
$234$		0			0
$235$	−1.86693	−	3.23361i	−0.121785	−	0.210937i
$236$	8.35061	−	14.4637i	0.543579	−	0.941506i
$237$		0			0
$238$	−3.49134	+	2.13456i	−0.226310	+	0.138363i
$239$	12.8698			0.832479			0.416239	−	0.909255i	$-0.363348\pi$
$239$	12.8698			0.832479			0.416239	+	0.909255i	$0.363348\pi$
$240$		0			0
$241$	−6.59931	−	11.4303i	−0.425099	−	0.736293i	0.571331	−	0.820720i	$-0.306427\pi$
$241$	−6.59931	−	11.4303i	−0.425099	−	0.736293i	−0.996430	+	0.0844267i	$0.973094\pi$
$242$	−1.02123	−	1.76882i	−0.0656472	−	0.113704i
$243$		0			0
$244$	13.3130			0.852280
$245$	−9.65965	−	14.9418i	−0.617132	−	0.954594i
$246$		0			0
$247$	2.96050	−	5.12774i	0.188372	−	0.326271i
$248$	−7.24622	−	12.5508i	−0.460135	−	0.796977i
$249$		0			0
$250$	−3.30399	+	5.72267i	−0.208962	+	0.361934i
$251$	10.1617			0.641402			0.320701	−	0.947180i	$-0.396081\pi$
$251$	10.1617			0.641402			0.320701	+	0.947180i	$0.396081\pi$
$252$		0			0
$253$	−23.2163			−1.45960
$254$	0.915414	−	1.58554i	0.0574382	−	0.0994859i
$255$		0			0
$256$	5.90496	+	10.2277i	0.369060	+	0.639230i
$257$	−0.120249	+	0.208278i	−0.00750095	+	0.0129920i	−0.869752	−	0.493490i	$-0.835721\pi$
$257$	−0.120249	+	0.208278i	−0.00750095	+	0.0129920i	0.862251	+	0.506482i	$0.169054\pi$
$258$		0			0
$259$	−0.437061	−	17.3736i	−0.0271577	−	1.07954i
$260$	−3.71224			−0.230223
$261$		0			0
$262$	3.25156	+	5.63187i	0.200882	+	0.347938i
$263$	−8.37962	−	14.5139i	−0.516710	−	0.894967i	−0.999812	−	0.0194034i	$-0.993823\pi$
$263$	−8.37962	−	14.5139i	−0.516710	−	0.894967i	0.483102	−	0.875564i	$-0.339510\pi$
$264$		0			0
$265$	16.4064			1.00784
$266$	10.1063	+	5.50077i	0.619660	+	0.337274i
$267$		0			0
$268$	−10.2630	+	17.7761i	−0.626914	+	1.08585i
$269$	7.41534	+	12.8437i	0.452121	+	0.783097i	0.998518	−	0.0544300i	$-0.0173342\pi$
$269$	7.41534	+	12.8437i	0.452121	+	0.783097i	−0.546397	+	0.837527i	$0.684001\pi$
$270$		0			0
$271$	−13.6352	+	23.6169i	−0.828280	+	1.43462i	0.0711064	+	0.997469i	$0.477347\pi$
$271$	−13.6352	+	23.6169i	−0.828280	+	1.43462i	−0.899386	+	0.437154i	$0.855986\pi$
$272$	2.21966			0.134586
$273$		0			0
$274$	1.99707			0.120648
$275$	2.71087	−	4.69537i	0.163472	−	0.283142i
$276$		0			0
$277$	13.8456	+	23.9813i	0.831903	+	1.44090i	0.896528	+	0.442988i	$0.146082\pi$
$277$	13.8456	+	23.9813i	0.831903	+	1.44090i	−0.0646250	+	0.997910i	$0.520585\pi$
$278$	−4.83650	+	8.37707i	−0.290074	+	0.502423i
$279$		0			0
$280$	−0.429864	−	17.0875i	−0.0256893	−	1.02117i
$281$	−16.6959			−0.995996			−0.497998	−	0.867178i	$-0.665931\pi$
$281$	−16.6959			−0.995996			−0.497998	+	0.867178i	$0.665931\pi$
$282$		0			0
$283$	0.160117	+	0.277330i	0.00951794	+	0.0164856i	0.870745	−	0.491735i	$-0.163637\pi$
$283$	0.160117	+	0.277330i	0.00951794	+	0.0164856i	−0.861227	+	0.508220i	$0.830304\pi$
$284$	−10.5541	−	18.2803i	−0.626272	−	1.08473i
$285$		0			0
$286$	2.72665			0.161230
$287$	−23.2602	+	14.2210i	−1.37301	+	0.839439i
$288$		0			0
$289$	6.28287	−	10.8823i	0.369581	−	0.640133i
$290$	8.24758	+	14.2852i	0.484315	+	0.838858i
$291$		0			0
$292$	−4.48395	+	7.76643i	−0.262403	+	0.454496i
$293$	8.07954			0.472012			0.236006	−	0.971752i	$-0.424162\pi$
$293$	8.07954			0.472012			0.236006	+	0.971752i	$0.424162\pi$
$294$		0			0
$295$	−29.0656			−1.69226
$296$	8.34797	−	14.4591i	0.485216	−	0.840419i
$297$		0			0
$298$		0			0
$299$	3.12700	−	5.41612i	0.180839	−	0.313222i
$300$		0			0
$301$	24.0349	−	14.6946i	1.38535	−	0.846984i
$302$	−5.35844			−0.308344
$303$		0			0
$304$	−3.12062	−	5.40507i	−0.178980	−	0.310002i
$305$	−11.5845	−	20.0649i	−0.663327	−	1.14892i
$306$		0			0
$307$	−4.94299			−0.282111			−0.141056	−	0.990002i	$-0.545050\pi$
$307$	−4.94299			−0.282111			−0.141056	+	0.990002i	$0.545050\pi$
$308$	−0.360748	−	14.3401i	−0.0205555	−	0.817101i
$309$		0			0
$310$	−5.32237	+	9.21861i	−0.302290	+	0.523582i
$311$	2.02524	+	3.50782i	0.114841	+	0.198910i	0.917716	−	0.397237i	$-0.130031\pi$
$311$	2.02524	+	3.50782i	0.114841	+	0.198910i	−0.802875	+	0.596147i	$0.796697\pi$
$312$		0			0
$313$	5.18356	−	8.97819i	0.292992	−	0.507477i	−0.681524	−	0.731796i	$-0.738682\pi$
$313$	5.18356	−	8.97819i	0.292992	−	0.507477i	0.974516	+	0.224319i	$0.0720157\pi$
$314$	−4.16652			−0.235130
$315$		0			0
$316$	11.6372			0.654641
$317$	−6.03864	+	10.4592i	−0.339164	+	0.587449i	−0.984276	−	0.176639i	$-0.943478\pi$
$317$	−6.03864	+	10.4592i	−0.339164	+	0.587449i	0.645112	+	0.764088i	$0.276811\pi$
$318$		0			0
$319$	16.3997	+	28.4051i	0.918207	+	1.59038i
$320$	2.78875	−	4.83026i	0.155896	−	0.270020i
$321$		0			0
$322$	10.6747	+	5.81012i	0.594878	+	0.323785i
$323$	12.4683			0.693753
$324$		0			0
$325$	0.730252	+	1.26483i	0.0405071	+	0.0701604i
$326$	7.60804	+	13.1775i	0.421370	+	0.729835i
$327$		0			0
$328$	−26.1914			−1.44618
$329$	0.0977436	+	3.88540i	0.00538878	+	0.214209i
$330$		0			0
$331$	11.0883	−	19.2055i	0.609469	−	1.05563i	−0.381859	−	0.924221i	$-0.624716\pi$
$331$	11.0883	−	19.2055i	0.609469	−	1.05563i	0.991328	−	0.131411i	$-0.0419508\pi$
$332$	−8.87363	−	15.3696i	−0.487004	−	0.843515i
$333$		0			0
$334$	−5.25729	+	9.10590i	−0.287666	+	0.498253i
$335$	35.7220			1.95170
$336$		0			0
$337$	−5.95311			−0.324287			−0.162143	−	0.986767i	$-0.551841\pi$
$337$	−5.95311			−0.324287			−0.162143	+	0.986767i	$0.551841\pi$
$338$	−0.367252	+	0.636099i	−0.0199759	+	0.0345992i
$339$		0			0
$340$	−3.90856	−	6.76982i	−0.211971	−	0.367145i
$341$	−10.5831	+	18.3305i	−0.573109	+	0.992654i
$342$		0			0
$343$	1.39610	+	18.4676i	0.0753825	+	0.997155i
$344$	27.0637			1.45918
$345$		0			0
$346$	8.23239	+	14.2589i	0.442576	+	0.766564i
$347$	9.52110	+	16.4910i	0.511120	+	0.885285i	0.999917	+	0.0128877i	$0.00410241\pi$
$347$	9.52110	+	16.4910i	0.511120	+	0.885285i	−0.488797	+	0.872397i	$0.662564\pi$
$348$		0			0
$349$	−3.61556			−0.193537			−0.0967683	−	0.995307i	$-0.530851\pi$
$349$	−3.61556			−0.193537			−0.0967683	+	0.995307i	$0.530851\pi$
$350$	−2.42150	+	1.48048i	−0.129435	+	0.0791347i
$351$		0			0
$352$	10.8727	−	18.8320i	0.579515	−	1.00375i
$353$	−2.98845	−	5.17615i	−0.159059	−	0.275499i	0.775470	−	0.631384i	$-0.217513\pi$
$353$	−2.98845	−	5.17615i	−0.159059	−	0.275499i	−0.934530	+	0.355885i	$0.884179\pi$
$354$		0			0
$355$	−18.3676	+	31.8136i	−0.974851	+	1.68849i
$356$	−17.2533			−0.914420
$357$		0			0
$358$	6.06848			0.320729
$359$	7.57639	−	13.1227i	0.399866	−	0.692589i	−0.593843	−	0.804581i	$-0.702390\pi$
$359$	7.57639	−	13.1227i	0.399866	−	0.692589i	0.993709	+	0.111992i	$0.0357232\pi$
$360$		0			0
$361$	−8.02918	−	13.9069i	−0.422588	−	0.731944i
$362$	0.289371	−	0.501204i	0.0152090	−	0.0263427i
$363$		0			0
$364$	3.39397	+	1.84730i	0.177892	+	0.0968247i
$365$	15.6070			0.816910
$366$		0			0
$367$	3.37578	+	5.84702i	0.176214	+	0.305212i	0.940581	−	0.339570i	$-0.110282\pi$
$367$	3.37578	+	5.84702i	0.176214	+	0.305212i	−0.764367	+	0.644782i	$0.776948\pi$
$368$	−3.29612	−	5.70904i	−0.171822	−	0.297604i
$369$		0			0
$370$	−12.2632			−0.637535
$371$	−14.9998	−	8.16421i	−0.778751	−	0.423865i
$372$		0			0
$373$	−3.15486	+	5.46438i	−0.163352	+	0.282935i	−0.936069	−	0.351816i	$-0.885564\pi$
$373$	−3.15486	+	5.46438i	−0.163352	+	0.282935i	0.772716	+	0.634751i	$0.218897\pi$
$374$	2.87085	+	4.97245i	0.148448	+	0.257119i
$375$		0			0
$376$	−1.86693	+	3.23361i	−0.0962793	+	0.166761i
$377$	−8.83547			−0.455050
$378$		0			0
$379$	0.0861875			0.00442715			0.00221358	−	0.999998i	$-0.499295\pi$
$379$	0.0861875			0.00442715			0.00221358	+	0.999998i	$0.499295\pi$
$380$	−10.9901	+	19.0354i	−0.563781	+	0.976497i
$381$		0			0
$382$	−0.145527	−	0.252061i	−0.00744583	−	0.0128966i
$383$	10.6889	−	18.5138i	0.546180	−	0.946011i	−0.452352	−	0.891840i	$-0.649415\pi$
$383$	10.6889	−	18.5138i	0.546180	−	0.946011i	0.998532	−	0.0541716i	$-0.0172518\pi$
$384$		0			0
$385$	−21.2989	+	13.0219i	−1.08549	+	0.663657i
$386$	2.78225			0.141613
$387$		0			0
$388$	5.18550	+	8.98155i	0.263254	+	0.455969i
$389$	16.0420	+	27.7855i	0.813360	+	1.40878i	0.910500	+	0.413510i	$0.135697\pi$
$389$	16.0420	+	27.7855i	0.813360	+	1.40878i	−0.0971400	+	0.995271i	$0.530969\pi$
$390$		0			0
$391$	13.1694			0.666008
$392$	−8.11011	+	15.8364i	−0.409623	+	0.799858i
$393$		0			0
$394$	−4.42480	+	7.66398i	−0.222918	+	0.386106i
$395$	−10.1262	−	17.5391i	−0.509505	−	0.882488i
$396$		0			0
$397$	−6.05982	+	10.4959i	−0.304134	+	0.526775i	−0.977068	−	0.212927i	$-0.931700\pi$
$397$	−6.05982	+	10.4959i	−0.304134	+	0.526775i	0.672934	+	0.739702i	$0.265034\pi$
$398$	−3.79169			−0.190060
$399$		0			0
$400$	1.53950			0.0769748
$401$	−13.3139	+	23.0603i	−0.664863	+	1.15158i	0.314460	+	0.949271i	$0.398177\pi$
$401$	−13.3139	+	23.0603i	−0.664863	+	1.15158i	−0.979322	+	0.202305i	$0.935157\pi$
$402$		0			0
$403$	−2.85087	−	4.93786i	−0.142012	−	0.245972i
$404$	6.20512	−	10.7476i	0.308716	−	0.534712i
$405$		0			0
$406$	−0.431806	−	17.1647i	−0.0214302	−	0.851868i
$407$	−24.3845			−1.20869
$408$		0			0
$409$	3.24484	+	5.62023i	0.160447	+	0.277903i	0.935029	−	0.354571i	$-0.115373\pi$
$409$	3.24484	+	5.62023i	0.160447	+	0.277903i	−0.774582	+	0.632473i	$0.782040\pi$
$410$	9.61885	+	16.6603i	0.475041	+	0.822795i
$411$		0			0
$412$	−3.19436			−0.157375
$413$	26.5736	+	14.4637i	1.30760	+	0.711712i
$414$		0			0
$415$	−15.4430	+	26.7480i	−0.758067	+	1.31301i
$416$	2.92887	+	5.07295i	0.143599	+	0.248722i
$417$		0			0
$418$	8.07227	−	13.9816i	0.394828	−	0.683862i
$419$	−31.3097			−1.52958			−0.764789	−	0.644280i	$-0.777157\pi$
$419$	−31.3097			−1.52958			−0.764789	+	0.644280i	$0.777157\pi$
$420$		0			0
$421$	−24.3097			−1.18478			−0.592392	−	0.805650i	$-0.701816\pi$
$421$	−24.3097			−1.18478			−0.592392	+	0.805650i	$0.701816\pi$
$422$	−6.60295	+	11.4366i	−0.321427	+	0.556727i
$423$		0			0
$424$	−8.20321	−	14.2084i	−0.398383	−	0.690020i
$425$	−1.53774	+	2.66345i	−0.0745914	+	0.129196i
$426$		0			0
$427$	0.606511	+	24.1094i	0.0293511	+	1.16673i
$428$	10.9940			0.531414
$429$		0			0
$430$	−9.93920	−	17.2152i	−0.479311	−	0.830190i
$431$	−9.89750	−	17.1430i	−0.476746	−	0.825748i	0.522899	−	0.852395i	$-0.324850\pi$
$431$	−9.89750	−	17.1430i	−0.476746	−	0.825748i	−0.999645	+	0.0266466i	$0.991517\pi$
$432$		0			0
$433$	−31.8932			−1.53269			−0.766344	−	0.642430i	$-0.777926\pi$
$433$	−31.8932			−1.53269			−0.766344	+	0.642430i	$0.777926\pi$
$434$	9.45344	−	5.77971i	0.453780	−	0.277435i
$435$		0			0
$436$	0.0394951	−	0.0684076i	0.00189147	−	0.00327613i
$437$	−18.5150	−	32.0689i	−0.885692	−	1.53406i
$438$		0			0
$439$	14.4231	−	24.9816i	0.688379	−	1.19231i	−0.283983	−	0.958829i	$-0.591656\pi$
$439$	14.4231	−	24.9816i	0.688379	−	1.19231i	0.972362	−	0.233478i	$-0.0750108\pi$
$440$	−23.9830			−1.14334
$441$		0			0
$442$	−1.54669			−0.0735687
$443$	−1.62898	+	2.82148i	−0.0773952	+	0.134052i	−0.902125	−	0.431474i	$-0.857994\pi$
$443$	−1.62898	+	2.82148i	−0.0773952	+	0.134052i	0.824730	+	0.565526i	$0.191327\pi$
$444$		0			0
$445$	15.0131	+	26.0035i	0.711690	+	1.23268i
$446$	−0.722713	+	1.25178i	−0.0342215	+	0.0592733i
$447$		0			0
$448$	−4.95331	+	3.02839i	−0.234022	+	0.143078i
$449$	1.03302			0.0487513			0.0243756	−	0.999703i	$-0.492240\pi$
$449$	1.03302			0.0487513			0.0243756	+	0.999703i	$0.492240\pi$
$450$		0			0
$451$	19.1264	+	33.1278i	0.900625	+	1.55993i
$452$	−4.56699	−	7.91027i	−0.214813	−	0.372068i
$453$		0			0
$454$	−9.12880			−0.428436
$455$	−0.169121	−	6.72272i	−0.00792852	−	0.315166i
$456$		0			0
$457$	8.73239	−	15.1249i	0.408484	−	0.707515i	−0.586236	−	0.810140i	$-0.699391\pi$
$457$	8.73239	−	15.1249i	0.408484	−	0.707515i	0.994720	+	0.102625i	$0.0327243\pi$
$458$	−7.73372	−	13.3952i	−0.361373	−	0.625916i
$459$		0			0
$460$	−11.6082	+	20.1059i	−0.541234	+	0.937444i
$461$	−32.4060			−1.50930			−0.754649	−	0.656128i	$-0.772193\pi$
$461$	−32.4060			−1.50930			−0.754649	+	0.656128i	$0.772193\pi$
$462$		0			0
$463$	−34.8788			−1.62095			−0.810477	−	0.585770i	$-0.800792\pi$
$463$	−34.8788			−1.62095			−0.810477	+	0.585770i	$0.800792\pi$
$464$	−4.65667	+	8.06558i	−0.216180	+	0.374435i
$465$		0			0
$466$	2.66945	+	4.62362i	0.123660	+	0.214185i
$467$	16.2626	−	28.1676i	0.752543	−	1.30344i	−0.194043	−	0.980993i	$-0.562160\pi$
$467$	16.2626	−	28.1676i	0.752543	−	1.30344i	0.946586	−	0.322450i	$-0.104506\pi$
$468$		0			0
$469$	−32.6593	−	17.7761i	−1.50807	−	0.820823i
$470$	2.74253			0.126503
$471$		0			0
$472$	14.5328	+	25.1715i	0.668925	+	1.15861i
$473$	−19.7634	−	34.2311i	−0.908720	−	1.57395i
$474$		0			0
$475$	8.64766			0.396782
$476$	0.204634	+	8.13439i	0.00937939	+	0.372839i
$477$		0			0
$478$	−4.72646	+	8.18647i	−0.216183	+	0.374440i
$479$	2.52189	+	4.36804i	0.115228	+	0.199581i	0.917871	−	0.396879i	$-0.129907\pi$
$479$	2.52189	+	4.36804i	0.115228	+	0.199581i	−0.802643	+	0.596460i	$0.796573\pi$
$480$		0			0
$481$	3.28434	−	5.68864i	0.149753	−	0.259380i
$482$	9.69444			0.441569
$483$		0			0
$484$	−4.06128			−0.184604
$485$	9.02446	−	15.6308i	0.409779	−	0.709759i
$486$		0			0
$487$	5.60097	+	9.70117i	0.253804	+	0.439602i	0.964570	−	0.263827i	$-0.0849848\pi$
$487$	5.60097	+	9.70117i	0.253804	+	0.439602i	−0.710766	+	0.703429i	$0.751651\pi$
$488$	−11.5845	+	20.0649i	−0.524406	+	0.908297i
$489$		0			0
$490$	13.0519	−	0.657103i	0.589627	−	0.0296849i
$491$	−21.6420			−0.976689			−0.488344	−	0.872651i	$-0.662399\pi$
$491$	−21.6420			−0.976689			−0.488344	+	0.872651i	$0.662399\pi$
$492$		0			0
$493$	−9.30272	−	16.1128i	−0.418973	−	0.725683i
$494$	2.17450	+	3.76635i	0.0978354	+	0.169456i
$495$		0			0
$496$	−6.01012			−0.269862
$497$	32.6240	−	19.9459i	1.46339	−	0.894696i
$498$		0			0
$499$	6.40642	−	11.0962i	0.286791	−	0.496736i	−0.686251	−	0.727365i	$-0.740745\pi$
$499$	6.40642	−	11.0962i	0.286791	−	0.496736i	0.973042	+	0.230629i	$0.0740782\pi$
$500$	6.56973	+	11.3791i	0.293807	+	0.508889i
$501$		0			0
$502$	−3.73191	+	6.46386i	−0.166563	+	0.288496i
$503$	24.9763			1.11364			0.556818	−	0.830635i	$-0.312022\pi$
$503$	24.9763			1.11364			0.556818	+	0.830635i	$0.312022\pi$
$504$		0			0
$505$	−21.5979			−0.961092
$506$	8.52624	−	14.7679i	0.379038	−	0.656512i
$507$		0			0
$508$	−1.82023	−	3.15274i	−0.0807598	−	0.139880i
$509$	−17.8003	+	30.8311i	−0.788986	+	1.36656i	0.137602	+	0.990488i	$0.456060\pi$
$509$	−17.8003	+	30.8311i	−0.788986	+	1.36656i	−0.926589	+	0.376077i	$0.877273\pi$
$510$		0			0
$511$	−14.2690	−	7.76643i	−0.631222	−	0.343566i
$512$	11.5330			0.509691
$513$		0			0
$514$	−0.0883236	−	0.152981i	−0.00389578	−	0.00674770i
$515$	2.77961	+	4.81442i	0.122484	+	0.212149i
$516$		0			0
$517$	5.45331			0.239836
$518$	11.2118	+	6.10246i	0.492619	+	0.268127i
$519$		0			0
$520$	3.23025	−	5.59496i	0.141656	−	0.245355i
$521$	18.4039	+	31.8765i	0.806288	+	1.39653i	0.915418	+	0.402505i	$0.131860\pi$
$521$	18.4039	+	31.8765i	0.806288	+	1.39653i	−0.109129	+	0.994028i	$0.534806\pi$
$522$		0			0
$523$	7.75876	−	13.4386i	0.339267	−	0.587627i	−0.645028	−	0.764159i	$-0.723154\pi$
$523$	7.75876	−	13.4386i	0.339267	−	0.587627i	0.984295	+	0.176531i	$0.0564877\pi$
$524$	12.9310			0.564892
$525$		0			0
$526$	12.3097			0.536729
$527$	6.00327	−	10.3980i	0.261507	−	0.452943i
$528$		0			0
$529$	−8.05622	−	13.9538i	−0.350270	−	0.606686i
$530$	−6.02529	+	10.4361i	−0.261722	+	0.453315i
$531$		0			0
$532$	19.5203	−	11.9345i	0.846313	−	0.517425i
$533$	−10.3045			−0.446336
$534$		0			0
$535$	−9.56654	−	16.5697i	−0.413597	−	0.716372i
$536$	−17.8610	−	30.9362i	−0.771478	−	1.33624i
$537$		0			0
$538$	−10.8932			−0.469638
$539$	25.9528	−	1.30660i	1.11787	−	0.0562792i
$540$		0			0
$541$	−11.2630	+	19.5081i	−0.484235	+	0.838720i	−0.999836	−	0.0181087i	$-0.994236\pi$
$541$	−11.2630	+	19.5081i	−0.484235	+	0.838720i	0.515601	+	0.856829i	$0.327569\pi$
$542$	−10.0151	−	17.3467i	−0.430186	−	0.745103i
$543$		0			0
$544$	−6.16751	+	10.6824i	−0.264430	+	0.458006i
$545$	−0.137469			−0.00588851
$546$		0			0
$547$	1.73812			0.0743168			0.0371584	−	0.999309i	$-0.488169\pi$
$547$	1.73812			0.0743168			0.0371584	+	0.999309i	$0.488169\pi$
$548$	1.98552	−	3.43902i	0.0848171	−	0.146907i
$549$		0			0
$550$	1.99115	+	3.44877i	0.0849027	+	0.147056i
$551$	−26.1575	+	45.3060i	−1.11435	+	1.93010i
$552$		0			0
$553$	0.530162	+	21.0744i	0.0225448	+	0.896175i
$554$	−20.3393			−0.864134
$555$		0			0
$556$	9.61702	+	16.6572i	0.407853	+	0.706421i
$557$	13.1528	+	22.7814i	0.557303	+	0.965277i	0.997720	+	0.0674838i	$0.0214971\pi$
$557$	13.1528	+	22.7814i	0.557303	+	0.965277i	−0.440417	+	0.897793i	$0.645170\pi$
$558$		0			0
$559$	10.6477			0.450348
$560$	−6.22606	−	3.38877i	−0.263099	−	0.143202i
$561$		0			0
$562$	6.13161	−	10.6203i	0.258646	−	0.447989i
$563$	−6.86825	−	11.8962i	−0.289462	−	0.501363i	0.684219	−	0.729276i	$-0.260143\pi$
$563$	−6.86825	−	11.8962i	−0.289462	−	0.501363i	−0.973681	+	0.227913i	$0.926810\pi$
$564$		0			0
$565$	−7.94805	+	13.7664i	−0.334377	+	0.579158i
$566$	−0.235212			−0.00988671
$567$		0			0
$568$	36.7352			1.54137
$569$	−9.82612	+	17.0193i	−0.411933	+	0.713488i	−0.995101	−	0.0988631i	$-0.968479\pi$
$569$	−9.82612	+	17.0193i	−0.411933	+	0.713488i	0.583169	+	0.812351i	$0.301813\pi$
$570$		0			0
$571$	8.37578	+	14.5073i	0.350515	+	0.607111i	0.986340	−	0.164723i	$-0.0526731\pi$
$571$	8.37578	+	14.5073i	0.350515	+	0.607111i	−0.635824	+	0.771834i	$0.719340\pi$
$572$	2.71087	−	4.69537i	0.113347	−	0.196323i
$573$		0			0
$574$	−0.503599	−	20.0185i	−0.0210198	−	0.835556i
$575$	9.13399			0.380914
$576$		0			0
$577$	11.6965	+	20.2589i	0.486931	+	0.843390i	0.999887	−	0.0150252i	$-0.00478286\pi$
$577$	11.6965	+	20.2589i	0.486931	+	0.843390i	−0.512956	+	0.858415i	$0.671450\pi$
$578$	4.61479	+	7.99305i	0.191950	+	0.332467i
$579$		0			0
$580$	32.7994			1.36192
$581$	27.4294	−	16.7700i	1.13796	−	0.695736i
$582$		0			0
$583$	−11.9808	+	20.7514i	−0.496195	+	0.859435i
$584$	−7.80352	−	13.5161i	−0.322912	−	0.559300i
$585$		0			0
$586$	−2.96722	+	5.13938i	−0.122575	+	0.212306i
$587$	6.05322			0.249843			0.124922	−	0.992167i	$-0.460132\pi$
$587$	6.05322			0.249843			0.124922	+	0.992167i	$0.460132\pi$
$588$		0			0
$589$	−33.7601			−1.39106
$590$	10.6744	−	18.4886i	0.439457	−	0.761162i
$591$		0			0
$592$	−3.46197	−	5.99630i	−0.142286	−	0.246447i
$593$	−3.27361	+	5.67006i	−0.134431	+	0.232842i	−0.925380	−	0.379041i	$-0.876254\pi$
$593$	−3.27361	+	5.67006i	−0.134431	+	0.232842i	0.790949	+	0.611882i	$0.209587\pi$
$594$		0			0
$595$	12.0818	−	7.38665i	0.495306	−	0.302823i
$596$		0			0
$597$		0			0
$598$	2.29679	+	3.97816i	0.0939227	+	0.162679i
$599$	1.18121	+	2.04591i	0.0482627	+	0.0835935i	0.889148	−	0.457621i	$-0.151298\pi$
$599$	1.18121	+	2.04591i	0.0482627	+	0.0835935i	−0.840885	+	0.541214i	$0.817965\pi$
$600$		0			0
$601$	40.5408			1.65370			0.826848	−	0.562426i	$-0.190132\pi$
$601$	40.5408			1.65370			0.826848	+	0.562426i	$0.190132\pi$
$602$	0.520371	+	20.6852i	0.0212087	+	0.843066i
$603$		0			0
$604$	−5.32743	+	9.22738i	−0.216770	+	0.375457i
$605$	3.53397	+	6.12102i	0.143676	+	0.248855i
$606$		0			0
$607$	5.72306	−	9.91262i	0.232292	−	0.402341i	−0.726190	−	0.687494i	$-0.758711\pi$
$607$	5.72306	−	9.91262i	0.232292	−	0.402341i	0.958482	+	0.285153i	$0.0920443\pi$
$608$	34.6837			1.40661
$609$		0			0
$610$	17.0177			0.689027
$611$	−0.734503	+	1.27220i	−0.0297148	+	0.0514676i
$612$		0			0
$613$	−6.35301	−	11.0037i	−0.256596	−	0.444437i	0.708732	−	0.705478i	$-0.249268\pi$
$613$	−6.35301	−	11.0037i	−0.256596	−	0.444437i	−0.965328	+	0.261041i	$0.915934\pi$
$614$	1.81532	−	3.14423i	0.0732604	−	0.126891i
$615$		0			0
$616$	21.9267	+	11.9345i	0.883454	+	0.480853i
$617$	30.9500			1.24600			0.623000	−	0.782221i	$-0.285913\pi$
$617$	30.9500			1.24600			0.623000	+	0.782221i	$0.285913\pi$
$618$		0			0
$619$	−2.28220	−	3.95289i	−0.0917294	−	0.158880i	0.816510	−	0.577332i	$-0.195906\pi$
$619$	−2.28220	−	3.95289i	−0.0917294	−	0.158880i	−0.908239	+	0.418452i	$0.862573\pi$
$620$	10.5831	+	18.3305i	0.425029	+	0.736172i
$621$		0			0
$622$	−2.97509			−0.119290
$623$	−0.786018	−	31.2449i	−0.0314912	−	1.25180i
$624$		0			0
$625$	15.0847	−	26.1275i	0.603389	−	1.04510i
$626$	3.80734	+	6.59451i	0.152172	+	0.263570i
$627$		0			0
$628$	−4.14241	+	7.17486i	−0.165300	+	0.286308i
$629$	13.8321			0.551522
$630$		0			0
$631$	15.0803			0.600339			0.300169	−	0.953886i	$-0.402957\pi$
$631$	15.0803			0.600339			0.300169	+	0.953886i	$0.402957\pi$
$632$	−10.1262	+	17.5391i	−0.402799	+	0.697668i
$633$		0			0
$634$	−4.43540	−	7.68235i	−0.176152	−	0.305105i
$635$	−3.16780	+	5.48678i	−0.125710	+	0.217736i
$636$		0			0
$637$	−3.19076	+	6.23049i	−0.126422	+	0.246861i
$638$	−24.0913			−0.953783
$639$		0			0
$640$	−12.8406	−	22.2405i	−0.507568	−	0.879133i
$641$	3.02118	+	5.23284i	0.119329	+	0.206685i	0.919502	−	0.393085i	$-0.128592\pi$
$641$	3.02118	+	5.23284i	0.119329	+	0.206685i	−0.800173	+	0.599770i	$0.795259\pi$
$642$		0			0
$643$	−16.2881			−0.642341			−0.321171	−	0.947021i	$-0.604076\pi$
$643$	−16.2881			−0.642341			−0.321171	+	0.947021i	$0.604076\pi$
$644$	20.6181	−	12.6056i	0.812467	−	0.496732i
$645$		0			0
$646$	−4.57899	+	7.93104i	−0.180158	+	0.312043i
$647$	3.58020	+	6.20109i	0.140752	+	0.243790i	0.927780	−	0.373127i	$-0.121715\pi$
$647$	3.58020	+	6.20109i	0.140752	+	0.243790i	−0.787028	+	0.616917i	$0.788381\pi$
$648$		0			0
$649$	21.2252	−	36.7631i	0.833162	−	1.44308i
$650$	−1.07275			−0.0420765
$651$		0			0
$652$	30.2560			1.18492
$653$	−11.7628	+	20.3737i	−0.460313	+	0.797285i	−0.998976	−	0.0452359i	$-0.985596\pi$
$653$	−11.7628	+	20.3737i	−0.460313	+	0.797285i	0.538664	+	0.842521i	$0.318929\pi$
$654$		0			0
$655$	−11.2520	−	19.4891i	−0.439654	−	0.761502i
$656$	−5.43089	+	9.40658i	−0.212041	+	0.367265i
$657$		0			0
$658$	−2.50739	−	1.36474i	−0.0977483	−	0.0532033i
$659$	−8.73459			−0.340251			−0.170126	−	0.985422i	$-0.554417\pi$
$659$	−8.73459			−0.340251			−0.170126	+	0.985422i	$0.554417\pi$
$660$		0			0
$661$	−5.60078	−	9.70083i	−0.217845	−	0.377319i	0.736304	−	0.676651i	$-0.236569\pi$
$661$	−5.60078	−	9.70083i	−0.217845	−	0.377319i	−0.954149	+	0.299332i	$0.903236\pi$
$662$	8.14441	+	14.1065i	0.316542	+	0.548266i
$663$		0			0
$664$	30.8860			1.19861
$665$	−34.9731	−	19.0354i	−1.35620	−	0.738162i
$666$		0			0
$667$	−27.6285	+	47.8540i	−1.06978	+	1.85291i
$668$	10.4537	+	18.1064i	0.404467	+	0.700558i
$669$		0			0
$670$	−13.1190	+	22.7227i	−0.506830	+	0.877855i
$671$	33.8384			1.30632
$672$		0			0
$673$	−11.0728			−0.426823			−0.213412	−	0.976962i	$-0.568458\pi$
$673$	−11.0728			−0.426823			−0.213412	+	0.976962i	$0.568458\pi$
$674$	2.18629	−	3.78677i	0.0842128	−	0.145861i
$675$		0			0
$676$	0.730252	+	1.26483i	0.0280866	+	0.0486475i
$677$	18.0419	−	31.2495i	0.693407	−	1.20102i	−0.277308	−	0.960781i	$-0.589442\pi$
$677$	18.0419	−	31.2495i	0.693407	−	1.20102i	0.970715	−	0.240235i	$-0.0772245\pi$
$678$		0			0
$679$	−16.0290	+	9.79991i	−0.615136	+	0.376086i
$680$	13.6043			0.521702
$681$		0			0
$682$	−7.77335	−	13.4638i	−0.297657	−	0.515557i
$683$	−24.4624	−	42.3701i	−0.936027	−	1.62125i	−0.772792	−	0.634659i	$-0.781140\pi$
$683$	−24.4624	−	42.3701i	−0.936027	−	1.62125i	−0.163235	−	0.986587i	$-0.552193\pi$
$684$		0			0
$685$	−6.91089			−0.264051
$686$	−12.2599	−	5.89418i	−0.468086	−	0.225041i
$687$		0			0
$688$	5.61177	−	9.71987i	0.213947	−	0.370566i
$689$	−3.22738	−	5.58999i	−0.122954	−	0.212962i
$690$		0			0
$691$	18.8353	−	32.6237i	0.716529	−	1.24106i	−0.245838	−	0.969311i	$-0.579063\pi$
$691$	18.8353	−	32.6237i	0.716529	−	1.24106i	0.962367	−	0.271753i	$-0.0876034\pi$
$692$	32.7390			1.24455
$693$		0			0
$694$	−13.9866			−0.530923
$695$	16.7367	−	28.9889i	0.634861	−	1.09961i
$696$		0			0
$697$	−10.8494	−	18.7917i	−0.410951	−	0.711788i
$698$	1.32782	−	2.29985i	0.0502587	−	0.0870507i
$699$		0			0
$700$	0.141929	+	5.64180i	0.00536441	+	0.213240i
$701$	−19.9325			−0.752839			−0.376420	−	0.926449i	$-0.622845\pi$
$701$	−19.9325			−0.752839			−0.376420	+	0.926449i	$0.622845\pi$
$702$		0			0
$703$	−19.4466	−	33.6825i	−0.733442	−	1.27036i
$704$	4.07299	+	7.05463i	0.153507	+	0.265881i
$705$		0			0
$706$	4.39006			0.165222
$707$	19.7461	+	10.7476i	0.742630	+	0.404205i
$708$		0			0
$709$	2.03803	−	3.52998i	0.0765399	−	0.132571i	−0.825215	−	0.564819i	$-0.808946\pi$
$709$	2.03803	−	3.52998i	0.0765399	−	0.132571i	0.901755	+	0.432248i	$0.142279\pi$
$710$	−13.4911	−	23.3672i	−0.506311	−	0.876956i
$711$		0			0
$712$	15.0131	−	26.0035i	0.562641	−	0.974522i
$713$	−35.6587			−1.33543
$714$		0			0
$715$	−9.43560			−0.352871
$716$	6.03336	−	10.4501i	0.225477	−	0.390538i
$717$		0			0
$718$	5.56488	+	9.63865i	0.207679	+	0.359711i
$719$	2.06232	−	3.57205i	0.0769117	−	0.133215i	−0.825004	−	0.565126i	$-0.808827\pi$
$719$	2.06232	−	3.57205i	0.0769117	−	0.133215i	0.901916	+	0.431911i	$0.142161\pi$
$720$		0			0
$721$	−0.145527	−	5.78485i	−0.00541973	−	0.215439i
$722$	11.7949			0.438961
$723$		0			0
$724$	−0.575392	−	0.996608i	−0.0213843	−	0.0370386i
$725$	−6.45212	−	11.1754i	−0.239626	−	0.415044i
$726$		0			0
$727$	−7.39203			−0.274155			−0.137078	−	0.990560i	$-0.543771\pi$
$727$	−7.39203			−0.274155			−0.137078	+	0.990560i	$0.543771\pi$
$728$	−5.73748	+	3.50782i	−0.212645	+	0.130009i
$729$		0			0
$730$	−5.73171	+	9.92762i	−0.212140	+	0.367438i
$731$	11.2107	+	19.4176i	0.414644	+	0.718185i
$732$		0			0
$733$	3.52918	−	6.11272i	0.130353	−	0.225778i	−0.793460	−	0.608623i	$-0.791722\pi$
$733$	3.52918	−	6.11272i	0.130353	−	0.225778i	0.923813	+	0.382845i	$0.125056\pi$
$734$	−4.95904			−0.183042
$735$		0			0
$736$	36.6342			1.35036
$737$	−26.0861	+	45.1824i	−0.960893	+	1.66432i
$738$		0			0
$739$	16.9517	+	29.3611i	0.623577	+	1.08007i	0.988814	+	0.149152i	$0.0476544\pi$
$739$	16.9517	+	29.3611i	0.623577	+	1.08007i	−0.365238	+	0.930914i	$0.619012\pi$
$740$	−12.1923	+	21.1176i	−0.448196	+	0.776298i
$741$		0			0
$742$	10.7019	−	6.54303i	0.392881	−	0.240202i
$743$	−16.3211			−0.598763			−0.299382	−	0.954133i	$-0.596780\pi$
$743$	−16.3211			−0.598763			−0.299382	+	0.954133i	$0.596780\pi$
$744$		0			0
$745$		0			0
$746$	−2.31726	−	4.01360i	−0.0848408	−	0.146949i
$747$		0			0
$748$	11.4169			0.417444
$749$	0.500860	+	19.9096i	0.0183010	+	0.727482i
$750$		0			0
$751$	11.7733	−	20.3920i	0.429616	−	0.744116i	−0.567224	−	0.823564i	$-0.691982\pi$
$751$	11.7733	−	20.3920i	0.429616	−	0.744116i	0.996839	+	0.0794480i	$0.0253158\pi$
$752$	0.774228	+	1.34100i	0.0282332	+	0.0489013i
$753$		0			0
$754$	3.24484	−	5.62023i	0.118170	−	0.204677i
$755$	18.5429			0.674846
$756$		0			0
$757$	35.1019			1.27580			0.637901	−	0.770119i	$-0.279803\pi$
$757$	35.1019			1.27580			0.637901	+	0.770119i	$0.279803\pi$
$758$	−0.0316525	+	0.0548237i	−0.00114967	+	0.00199129i
$759$		0			0
$760$	−19.1264	−	33.1278i	−0.693786	−	1.20167i
$761$	22.7346	−	39.3775i	0.824128	−	1.42743i	−0.0784558	−	0.996918i	$-0.524999\pi$
$761$	22.7346	−	39.3775i	0.824128	−	1.42743i	0.902584	−	0.430514i	$-0.141668\pi$
$762$		0			0
$763$	0.125683	+	0.0684076i	0.00455002	+	0.00247652i
$764$	−0.578741			−0.0209381
$765$		0			0
$766$	7.85107	+	13.5984i	0.283671	+	0.491332i
$767$	5.71762	+	9.90321i	0.206451	+	0.357584i
$768$		0			0
$769$	−42.4543			−1.53094			−0.765470	−	0.643472i	$-0.777493\pi$
$769$	−42.4543			−1.53094			−0.765470	+	0.643472i	$0.777493\pi$
$770$	−0.461135	−	18.3305i	−0.0166181	−	0.660586i
$771$		0			0
$772$	2.76615	−	4.79111i	0.0995559	−	0.172436i
$773$	23.3010	+	40.3586i	0.838080	+	1.45160i	0.891498	+	0.453025i	$0.149655\pi$
$773$	23.3010	+	40.3586i	0.838080	+	1.45160i	−0.0534175	+	0.998572i	$0.517011\pi$
$774$		0			0
$775$	4.16372	−	7.21177i	0.149565	−	0.259054i
$776$	−18.0489			−0.647918
$777$		0			0
$778$	−23.5657			−0.844873
$779$	−30.5065	+	52.8387i	−1.09301	+	1.89314i
$780$		0			0
$781$	−26.8260	−	46.4639i	−0.959909	−	1.66261i
$782$	−4.83650	+	8.37707i	−0.172953	+	0.299563i
$783$		0			0
$784$	4.00593	+	6.19646i	0.143069	+	0.221302i
$785$	14.4183			0.514610
$786$		0			0
$787$	−13.1908	−	22.8471i	−0.470200	−	0.814410i	0.529220	−	0.848485i	$-0.322485\pi$
$787$	−13.1908	−	22.8471i	−0.470200	−	0.814410i	−0.999419	+	0.0340751i	$0.989151\pi$
$788$	8.79839	+	15.2393i	0.313430	+	0.542876i
$789$		0			0
$790$	14.8755			0.529245
$791$	14.1171	−	8.63101i	0.501947	−	0.306884i
$792$		0			0
$793$	−4.55768	+	7.89414i	−0.161848	+	0.280329i
$794$	−4.45096	−	7.70928i	−0.157959	−	0.273592i
$795$		0			0
$796$	−3.76975	+	6.52939i	−0.133615	+	0.231428i
$797$	−17.6474			−0.625102			−0.312551	−	0.949901i	$-0.601183\pi$
$797$	−17.6474			−0.625102			−0.312551	+	0.949901i	$0.601183\pi$
$798$		0			0
$799$	−3.09338			−0.109436
$800$	−4.27762	+	7.40906i	−0.151237	+	0.261950i
$801$		0			0
$802$	−9.77908	−	16.9379i	−0.345311	−	0.598097i
$803$	−11.3971	+	19.7403i	−0.402194	+	0.696621i
$804$		0			0
$805$	−36.9399	−	20.1059i	−1.30196	−	0.708641i
$806$	4.18795			0.147514
$807$		0			0
$808$	10.7989	+	18.7043i	0.379905	+	0.658015i
$809$	−8.98580	−	15.5639i	−0.315924	−	0.547197i	0.663709	−	0.747990i	$-0.268981\pi$
$809$	−8.98580	−	15.5639i	−0.315924	−	0.547197i	−0.979633	+	0.200794i	$0.935648\pi$
$810$		0			0
$811$	43.5159			1.52805			0.764026	−	0.645186i	$-0.223220\pi$
$811$	43.5159			1.52805			0.764026	+	0.645186i	$0.223220\pi$
$812$	−29.9873	−	16.3217i	−1.05235	−	0.572781i
$813$		0			0
$814$	8.95525	−	15.5109i	0.313881	−	0.543658i
$815$	−26.3277	−	45.6008i	−0.922217	−	1.59733i
$816$		0			0
$817$	31.5225	−	54.5985i	1.10283	−	1.91016i
$818$	−4.76669			−0.166664
$819$		0			0
$820$	38.2527			1.33584
$821$	18.3642	−	31.8076i	0.640913	−	1.11009i	−0.344316	−	0.938854i	$-0.611889\pi$
$821$	18.3642	−	31.8076i	0.640913	−	1.11009i	0.985229	−	0.171241i	$-0.0547775\pi$
$822$		0			0
$823$	20.6118	+	35.7006i	0.718481	+	1.24445i	0.961601	+	0.274450i	$0.0884956\pi$
$823$	20.6118	+	35.7006i	0.718481	+	1.24445i	−0.243120	+	0.969996i	$0.578171\pi$
$824$	2.77961	−	4.81442i	0.0968322	−	0.167718i
$825$		0			0
$826$	−18.9595	+	11.5916i	−0.659686	+	0.403323i
$827$	10.0060			0.347941			0.173971	−	0.984751i	$-0.444340\pi$
$827$	10.0060			0.347941			0.173971	+	0.984751i	$0.444340\pi$
$828$		0			0
$829$	−7.48035	−	12.9563i	−0.259803	−	0.449992i	0.706386	−	0.707827i	$-0.250324\pi$
$829$	−7.48035	−	12.9563i	−0.259803	−	0.449992i	−0.966189	+	0.257835i	$0.916991\pi$
$830$	−11.3429	−	19.6465i	−0.393719	−	0.681941i
$831$		0			0
$832$	−2.19436			−0.0760756
$833$	−14.7217	+	0.741168i	−0.510077	+	0.0256799i
$834$		0			0
$835$	18.1929	−	31.5110i	0.629591	−	1.09048i
$836$	−16.0511	−	27.8013i	−0.555139	−	0.961529i
$837$		0			0
$838$	11.4985	−	19.9161i	0.397210	−	0.687989i
$839$	27.0026			0.932232			0.466116	−	0.884724i	$-0.345653\pi$
$839$	27.0026			0.932232			0.466116	+	0.884724i	$0.345653\pi$
$840$		0			0
$841$	49.0656			1.69192
$842$	8.92779	−	15.4634i	0.307672	−	0.532903i
$843$		0			0
$844$	13.1295	+	22.7409i	0.451935	+	0.782775i
$845$	1.27088	−	2.20122i	0.0437195	−	0.0757243i
$846$		0			0
$847$	−0.185023	−	7.35481i	−0.00635745	−	0.252714i
$848$	−6.80387			−0.233646
$849$		0			0
$850$	−1.12948	−	1.95631i	−0.0387407	−	0.0671009i
$851$	−20.5402	−	35.5767i	−0.704110	−	1.21955i
$852$		0			0
$853$	−10.5438			−0.361012			−0.180506	−	0.983574i	$-0.557773\pi$
$853$	−10.5438			−0.361012			−0.180506	+	0.983574i	$0.557773\pi$
$854$	−15.5587	−	8.46840i	−0.532407	−	0.289783i
$855$		0			0
$856$	−9.56654	+	16.5697i	−0.326978	+	0.566342i
$857$	−3.74018	−	6.47818i	−0.127762	−	0.221290i	0.795047	−	0.606548i	$-0.207446\pi$
$857$	−3.74018	−	6.47818i	−0.127762	−	0.221290i	−0.922809	+	0.385257i	$0.874113\pi$
$858$		0			0
$859$	−21.6862	+	37.5616i	−0.739923	+	1.28158i	0.212607	+	0.977138i	$0.431805\pi$
$859$	−21.6862	+	37.5616i	−0.739923	+	1.28158i	−0.952530	+	0.304446i	$0.901529\pi$
$860$	−39.5267			−1.34785
$861$		0			0
$862$	14.5395			0.495217
$863$	−16.0114	+	27.7325i	−0.545034	+	0.944026i	0.453571	+	0.891220i	$0.350150\pi$
$863$	−16.0114	+	27.7325i	−0.545034	+	0.944026i	−0.998605	+	0.0528061i	$0.983183\pi$
$864$		0			0
$865$	−28.4882	−	49.3430i	−0.968629	−	1.67771i
$866$	11.7128	−	20.2872i	0.398018	−	0.689387i
$867$		0			0
$868$	−0.554084	−	22.0253i	−0.0188068	−	0.747589i
$869$	29.5788			1.00339
$870$		0			0
$871$	−7.02704	−	12.1712i	−0.238102	−	0.412405i
$872$	0.0687343	+	0.119051i	0.00232764	+	0.00403159i
$873$		0			0
$874$	27.1986			0.920007
$875$	−20.3078	+	12.4159i	−0.686529	+	0.419735i
$876$		0			0
$877$	−16.3078	+	28.2459i	−0.550675	+	0.953796i	0.447551	+	0.894258i	$0.352296\pi$
$877$	−16.3078	+	28.2459i	−0.550675	+	0.953796i	−0.998226	+	0.0595382i	$0.981037\pi$
$878$	10.5938	+	18.3491i	0.357525	+	0.619252i
$879$		0			0
$880$	−4.97296	+	8.61342i	−0.167638	+	0.290358i
$881$	−34.6890			−1.16870			−0.584351	−	0.811501i	$-0.698651\pi$
$881$	−34.6890			−1.16870			−0.584351	+	0.811501i	$0.698651\pi$
$882$		0			0
$883$	7.36381			0.247812			0.123906	−	0.992294i	$-0.460458\pi$
$883$	7.36381			0.247812			0.123906	+	0.992294i	$0.460458\pi$
$884$	−1.53774	+	2.66345i	−0.0517198	+	0.0895814i
$885$		0			0
$886$	−1.19649	−	2.07238i	−0.0401969	−	0.0696231i
$887$	−15.6258	+	27.0647i	−0.524664	+	0.908745i	0.474923	+	0.880027i	$0.342476\pi$
$887$	−15.6258	+	27.0647i	−0.524664	+	0.908745i	−0.999588	+	0.0287180i	$0.990858\pi$
$888$		0			0
$889$	5.62655	−	3.44000i	0.188708	−	0.115374i
$890$	−22.0544			−0.739265
$891$		0			0
$892$	1.43706	+	2.48906i	0.0481164	+	0.0833400i
$893$	4.34900	+	7.53269i	0.145534	+	0.252072i
$894$		0			0
$895$	−21.0000			−0.701953
$896$	0.672273	+	26.7234i	0.0224591	+	0.892767i
$897$		0			0
$898$	−0.379379	+	0.657103i	−0.0126600	+	0.0219278i
$899$	25.1888	+	43.6283i	0.840094	+	1.45509i
$900$		0			0
$901$	6.79612	−	11.7712i	0.226411	−	0.392156i
$902$	−28.0967			−0.935519
$903$		0			0
$904$	15.8961			0.528697
$905$	−1.00137	+	1.73442i	−0.0332866	+	0.0576541i
$906$		0			0
$907$	28.3602	+	49.1213i	0.941685	+	1.63105i	0.762256	+	0.647276i	$0.224092\pi$
$907$	28.3602	+	49.1213i	0.941685	+	1.63105i	0.179429	+	0.983771i	$0.442575\pi$
$908$	−9.07597	+	15.7200i	−0.301197	+	0.521688i
$909$		0			0
$910$	4.33842	+	2.36135i	0.143817	+	0.0782780i
$911$	−22.4742			−0.744604			−0.372302	−	0.928112i	$-0.621431\pi$
$911$	−22.4742			−0.744604			−0.372302	+	0.928112i	$0.621431\pi$
$912$		0			0
$913$	−22.5546	−	39.0656i	−0.746447	−	1.29288i
$914$	6.41397	+	11.1093i	0.212155	+	0.367464i
$915$		0			0
$916$	−30.7558			−1.01620
$917$	0.589105	+	23.4175i	0.0194540	+	0.773312i
$918$		0			0
$919$	−1.24271	+	2.15243i	−0.0409931	+	0.0710021i	−0.885794	−	0.464079i	$-0.846385\pi$
$919$	−1.24271	+	2.15243i	−0.0409931	+	0.0710021i	0.844801	+	0.535081i	$0.179719\pi$
$920$	−20.2020	−	34.9909i	−0.666040	−	1.15361i
$921$		0			0
$922$	11.9012	−	20.6134i	0.391944	−	0.678867i
$923$	14.4527			0.475717
$924$		0			0
$925$	9.59358			0.315435
$926$	12.8093	−	22.1863i	0.420939	−	0.729088i
$927$		0			0
$928$	−25.8779	−	44.8219i	−0.849484	−	1.47135i
$929$	−17.5996	+	30.4833i	−0.577423	+	1.00013i	0.418351	+	0.908286i	$0.362608\pi$
$929$	−17.5996	+	30.4833i	−0.577423	+	1.00013i	−0.995774	+	0.0918404i	$0.970725\pi$
$930$		0			0
$931$	22.5021	+	34.8068i	0.737478	+	1.14075i
$932$	10.6160			0.347739
$933$		0			0
$934$	11.9449	+	20.6892i	0.390850	+	0.676972i
$935$	−9.93458	−	17.2072i	−0.324896	−	0.562736i
$936$		0			0
$937$	40.0613			1.30875			0.654373	−	0.756172i	$-0.272933\pi$
$937$	40.0613			1.30875			0.654373	+	0.756172i	$0.272933\pi$
$938$	23.3015	−	14.2463i	0.760822	−	0.465157i
$939$		0			0
$940$	2.72665	−	4.72270i	0.0889336	−	0.154038i
$941$	16.0038	+	27.7194i	0.521709	+	0.903627i	0.999681	+	0.0252517i	$0.00803871\pi$
$941$	16.0038	+	27.7194i	0.521709	+	0.903627i	−0.477972	+	0.878375i	$0.658628\pi$
$942$		0			0
$943$	−32.2221	+	55.8103i	−1.04930	+	1.81743i
$944$	12.0537			0.392315
$945$		0			0
$946$	29.0325			0.943928
$947$	11.3692	−	19.6919i	0.369448	−	0.639902i	−0.620032	−	0.784577i	$-0.712880\pi$
$947$	11.3692	−	19.6919i	0.369448	−	0.639902i	0.989479	+	0.144675i	$0.0462135\pi$
$948$		0			0
$949$	−3.07014	−	5.31763i	−0.0996608	−	0.172618i
$950$	−3.17587	+	5.50077i	−0.103039	+	0.178468i
$951$		0			0
$952$	−12.4379	−	6.76982i	−0.403116	−	0.219411i
$953$	16.7884			0.543830			0.271915	−	0.962321i	$-0.412343\pi$
$953$	16.7884			0.543830			0.271915	+	0.962321i	$0.412343\pi$
$954$		0			0
$955$	0.503599	+	0.872258i	0.0162961	+	0.0282256i
$956$	9.39821	+	16.2782i	0.303960	+	0.526474i
$957$		0			0
$958$	−3.70467			−0.119693
$959$	6.31837	+	3.43902i	0.204031	+	0.111052i
$960$		0			0
$961$	−0.754964	+	1.30764i	−0.0243537	+	0.0421818i
$962$	2.41236	+	4.17832i	0.0777775	+	0.134715i
$963$		0			0
$964$	9.63833	−	16.6941i	0.310430	−	0.537680i
$965$	−9.62799			−0.309936
$966$		0			0
$967$	44.3533			1.42631			0.713153	−	0.701009i	$-0.247267\pi$
$967$	44.3533			1.42631			0.713153	+	0.701009i	$0.247267\pi$
$968$	3.53397	−	6.12102i	0.113586	−	0.196737i
$969$		0			0
$970$	6.62849	+	11.4809i	0.212828	+	0.368629i
$971$	2.03968	−	3.53282i	0.0654563	−	0.113374i	−0.831440	−	0.555615i	$-0.812483\pi$
$971$	2.03968	−	3.53282i	0.0654563	−	0.113374i	0.896896	+	0.442241i	$0.145816\pi$
$972$		0			0
$973$	−29.7273	+	18.1749i	−0.953014	+	0.582660i
$974$	−8.22786			−0.263638
$975$		0			0
$976$	4.80418	+	8.32109i	0.153778	+	0.266351i
$977$	−4.88009	−	8.45256i	−0.156128	−	0.270421i	0.777341	−	0.629079i	$-0.216568\pi$
$977$	−4.88009	−	8.45256i	−0.156128	−	0.270421i	−0.933469	+	0.358658i	$0.883235\pi$
$978$		0			0
$979$	−43.8535			−1.40156
$980$	11.8449	−	23.1291i	0.378370	−	0.738832i
$981$		0			0
$982$	7.94805	−	13.7664i	0.253633	−	0.439304i
$983$	25.6582	+	44.4412i	0.818368	+	1.41746i	0.906884	+	0.421381i	$0.138454\pi$
$983$	25.6582	+	44.4412i	0.818368	+	1.41746i	−0.0885154	+	0.996075i	$0.528212\pi$
$984$		0			0
$985$	15.3121	−	26.5213i	0.487883	−	0.845037i
$986$	13.6658			0.435206
$987$		0			0
$988$	8.64766			0.275119
$989$	33.2952	−	57.6690i	1.05873	−	1.83377i
$990$		0			0
$991$	0.352336	+	0.610265i	0.0111923	+	0.0193857i	0.871567	−	0.490276i	$-0.163104\pi$
$991$	0.352336	+	0.610265i	0.0111923	+	0.0193857i	−0.860375	+	0.509662i	$0.829771\pi$
$992$	16.6997	−	28.9247i	0.530215	−	0.918359i
$993$		0			0
$994$	0.706330	+	28.0772i	0.0224034	+	0.890556i
$995$	13.1212			0.415969
$996$		0			0
$997$	−17.0129	−	29.4673i	−0.538805	−	0.933238i	−0.998969	−	0.0454035i	$-0.985543\pi$
$997$	−17.0129	−	29.4673i	−0.538805	−	0.933238i	0.460164	−	0.887834i	$-0.347791\pi$
$998$	4.70554	+	8.15023i	0.148951	+	0.257991i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.j.i.352.3	yes	12
3.2	odd	2	inner	819.2.j.i.352.4	yes	12
7.2	even	3		5733.2.a.bs.1.4		6
7.4	even	3	inner	819.2.j.i.235.3	✓	12
7.5	odd	6		5733.2.a.bt.1.4		6
21.2	odd	6		5733.2.a.bs.1.3		6
21.5	even	6		5733.2.a.bt.1.3		6
21.11	odd	6	inner	819.2.j.i.235.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.j.i.235.3	✓	12	7.4	even	3	inner
819.2.j.i.235.4	yes	12	21.11	odd	6	inner
819.2.j.i.352.3	yes	12	1.1	even	1	trivial
819.2.j.i.352.4	yes	12	3.2	odd	2	inner
5733.2.a.bs.1.3		6	21.2	odd	6
5733.2.a.bs.1.4		6	7.2	even	3
5733.2.a.bt.1.3		6	21.5	even	6
5733.2.a.bt.1.4		6	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.367252 + 0.636099i) q^{2} +(0.730252 + 1.26483i) q^{4} +(1.27088 - 2.20122i) q^{5} +(-2.25729 + 1.38008i) q^{7} -2.54175 q^{8} +(0.933463 + 1.61680i) q^{10} +(1.85612 + 3.21490i) q^{11} -1.00000 q^{13} +(-0.0488718 - 1.94270i) q^{14} +(-0.527042 + 0.912864i) q^{16} +(-1.05288 - 1.82365i) q^{17} +(-2.96050 + 5.12774i) q^{19} +3.71224 q^{20} -2.72665 q^{22} +(-3.12700 + 5.41612i) q^{23} +(-0.730252 - 1.26483i) q^{25} +(0.367252 - 0.636099i) q^{26} +(-3.39397 - 1.84730i) q^{28} +8.83547 q^{29} +(2.85087 + 4.93786i) q^{31} +(-2.92887 - 5.07295i) q^{32} +1.54669 q^{34} +(0.169121 + 6.72272i) q^{35} +(-3.28434 + 5.68864i) q^{37} +(-2.17450 - 3.76635i) q^{38} +(-3.23025 + 5.59496i) q^{40} +10.3045 q^{41} -10.6477 q^{43} +(-2.71087 + 4.69537i) q^{44} +(-2.29679 - 3.97816i) q^{46} +(0.734503 - 1.27220i) q^{47} +(3.19076 - 6.23049i) q^{49} +1.07275 q^{50} +(-0.730252 - 1.26483i) q^{52} +(3.22738 + 5.58999i) q^{53} +9.43560 q^{55} +(5.73748 - 3.50782i) q^{56} +(-3.24484 + 5.62023i) q^{58} +(-5.71762 - 9.90321i) q^{59} +(4.55768 - 7.89414i) q^{61} -4.18795 q^{62} +2.19436 q^{64} +(-1.27088 + 2.20122i) q^{65} +(7.02704 + 12.1712i) q^{67} +(1.53774 - 2.66345i) q^{68} +(-4.33842 - 2.36135i) q^{70} -14.4527 q^{71} +(3.07014 + 5.31763i) q^{73} +(-2.41236 - 4.17832i) q^{74} -8.64766 q^{76} +(-8.62663 - 4.69537i) q^{77} +(3.98395 - 6.90040i) q^{79} +(1.33961 + 2.32027i) q^{80} +(-3.78434 + 6.55466i) q^{82} -12.1515 q^{83} -5.35234 q^{85} +(3.91037 - 6.77296i) q^{86} +(-4.71780 - 8.17147i) q^{88} +(-5.90660 + 10.2305i) q^{89} +(2.25729 - 1.38008i) q^{91} -9.13399 q^{92} +(0.539495 + 0.934433i) q^{94} +(7.52487 + 13.0335i) q^{95} +7.10097 q^{97} +(2.79140 + 4.31780i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{4} + 4 q^{7} + 4 q^{10} - 12 q^{13} + 12 q^{16} - 10 q^{19} - 36 q^{22} + 4 q^{25} - 8 q^{28} - 8 q^{31} + 12 q^{34} + 10 q^{37} - 26 q^{40} - 80 q^{43} - 22 q^{46} + 4 q^{52} + 36 q^{58} + 2 q^{61}+ \cdots + 44 q^{97}+O(q^{100}) \) 12 * q - 4 * q^4 + 4 * q^7 + 4 * q^10 - 12 * q^13 + 12 * q^16 - 10 * q^19 - 36 * q^22 + 4 * q^25 - 8 * q^28 - 8 * q^31 + 12 * q^34 + 10 * q^37 - 26 * q^40 - 80 * q^43 - 22 * q^46 + 4 * q^52 + 36 * q^58 + 2 * q^61 - 28 * q^64 + 66 * q^67 + 34 * q^70 + 28 * q^73 - 56 * q^76 + 20 * q^79 + 4 * q^82 - 112 * q^85 - 4 * q^91 + 32 * q^94 + 44 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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