LMFDB - Embedded newform 819.2.j.i.235.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(235,819)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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			235.4
Root			$-0.367252 + 0.636099i$ of defining polynomial
Character	$\chi$	$=$	819.235
Dual form			819.2.j.i.352.4

$q$-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 $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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	$-0.0830476\pi$
$2$	0.367252	+	0.636099i	0.259686	+	0.449790i	−0.706472	+	0.707741i	$0.749714\pi$
$3$		0			0
$3$		0			0
$4$	0.730252	−	1.26483i	0.365126	−	0.632417i
$5$	−1.27088	−	2.20122i	−0.568353	−	0.984416i	−0.996729	−	0.0808158i	$-0.974247\pi$
$5$	−1.27088	−	2.20122i	−0.568353	−	0.984416i	0.428376	−	0.903601i	$-0.359086\pi$
$6$		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	0.437885	+	0.899031i	$0.355728\pi$
$11$	−1.85612	+	3.21490i	−0.559641	+	0.969327i	−0.997526	+	0.0702963i	$0.977606\pi$
$12$		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	$-0.751139\pi$
$17$	1.05288	−	1.82365i	0.255362	−	0.442299i	0.964994	+	0.262273i	$0.0844721\pi$
$18$		0			0
$19$	−2.96050	−	5.12774i	−0.679186	−	1.17639i	−0.975226	−	0.221210i	$-0.928999\pi$
$19$	−2.96050	−	5.12774i	−0.679186	−	1.17639i	0.296040	−	0.955176i	$-0.404334\pi$
$20$	−3.71224			−0.830082
$21$		0			0
$22$	−2.72665			−0.581325
$23$	3.12700	+	5.41612i	0.652024	+	1.12934i	0.982631	+	0.185570i	$0.0594132\pi$
$23$	3.12700	+	5.41612i	0.652024	+	1.12934i	−0.330607	+	0.943768i	$0.607253\pi$
$24$		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	$-0.806223\pi$
$29$	−8.83547			−1.64071			−0.820353	+	0.571858i	$0.806223\pi$
$30$		0			0
$31$	2.85087	−	4.93786i	0.512032	−	0.886866i	−0.487871	−	0.872916i	$-0.662226\pi$
$31$	2.85087	−	4.93786i	0.512032	−	0.886866i	0.999903	−	0.0139496i	$-0.00444044\pi$
$32$	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	−0.998907	−	0.0467519i	$-0.985113\pi$
$37$	−3.28434	−	5.68864i	−0.539942	−	0.935206i	0.458965	−	0.888454i	$-0.348220\pi$
$38$	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	$-0.797644\pi$
$41$	−10.3045			−1.60929			−0.804645	+	0.593757i	$0.797644\pi$
$42$		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	$-0.200835\pi$
$47$	−0.734503	−	1.27220i	−0.107138	−	0.185569i	−0.914610	+	0.404338i	$0.867502\pi$
$48$		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	$-0.979531\pi$
$53$	−3.22738	+	5.58999i	−0.443315	+	0.767845i	0.554618	+	0.832105i	$0.312864\pi$
$54$		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	−0.206117	−	0.978527i	$-0.566083\pi$
$59$	5.71762	−	9.90321i	0.744371	−	1.28929i	0.950488	−	0.310761i	$-0.100584\pi$
$60$		0			0
$61$	4.55768	+	7.89414i	0.583551	+	1.01074i	0.995054	+	0.0993323i	$0.0316707\pi$
$61$	4.55768	+	7.89414i	0.583551	+	1.01074i	−0.411503	+	0.911408i	$0.634996\pi$
$62$	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	−0.0148794	−	0.999889i	$-0.504736\pi$
$67$	7.02704	−	12.1712i	0.858490	−	1.48695i	0.873369	−	0.487059i	$-0.161930\pi$
$68$	−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	$-0.171948\pi$
$71$	14.4527			1.71522			0.857610	+	0.514300i	$0.171948\pi$
$72$		0			0
$73$	3.07014	−	5.31763i	0.359332	−	0.622382i	−0.628517	−	0.777796i	$-0.716338\pi$
$73$	3.07014	−	5.31763i	0.359332	−	0.622382i	0.987849	+	0.155414i	$0.0496712\pi$
$74$	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	0.998271	−	0.0587814i	$-0.0187215\pi$
$79$	3.98395	+	6.90040i	0.448229	+	0.776356i	−0.550042	+	0.835137i	$0.685388\pi$
$80$	−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	$-0.267622\pi$
$83$	12.1515			1.33380			0.666898	+	0.745149i	$0.267622\pi$
$84$		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	0.988327	+	0.152346i	$0.0486827\pi$
$89$	5.90660	+	10.2305i	0.626099	+	1.08444i	−0.362228	+	0.932089i	$0.617984\pi$
$90$		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	$-0.694397\pi$
$101$	4.24861	−	7.35882i	0.422753	−	0.732230i	0.996208	+	0.0870077i	$0.0277305\pi$
$102$		0			0
$103$	−1.09358	−	1.89413i	−0.107754	−	0.186635i	0.807106	−	0.590406i	$-0.201032\pi$
$103$	−1.09358	−	1.89413i	−0.107754	−	0.186635i	−0.914860	+	0.403771i	$0.867699\pi$
$104$	−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	$-0.285207\pi$
$107$	−3.76376	−	6.51902i	−0.363856	−	0.630217i	−0.988592	+	0.150619i	$0.951873\pi$
$108$		0			0
$109$	−0.0270421	+	0.0468383i	−0.00259016	+	0.00448630i	−0.867318	−	0.497755i	$-0.834158\pi$
$109$	−0.0270421	+	0.0468383i	−0.00259016	+	0.00448630i	0.864727	+	0.502241i	$0.167491\pi$
$110$	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	$-0.404959\pi$
$113$	6.25399			0.588326			0.294163	+	0.955755i	$0.404959\pi$
$114$		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	$-0.293079\pi$
$131$	−4.42688	−	7.66759i	−0.386779	−	0.669920i	−0.992014	+	0.126126i	$0.959746\pi$
$132$		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	$-0.796279\pi$
$137$	1.35947	−	2.35468i	0.116148	−	0.201174i	0.918238	+	0.396029i	$0.129612\pi$
$138$		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	$-0.166667\pi$
$149$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$150$		0			0
$151$	3.64766	−	6.31794i	0.296843	−	0.514147i	−0.678569	−	0.734536i	$-0.737400\pi$
$151$	3.64766	−	6.31794i	0.296843	−	0.514147i	0.975412	+	0.220390i	$0.0707330\pi$
$152$	−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	−0.730366	−	0.683055i	$-0.760651\pi$
$157$	2.83628	−	4.91259i	0.226360	−	0.392067i	0.956727	+	0.290988i	$0.0939840\pi$
$158$	−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	0.911950	+	0.410302i	$0.134577\pi$
$163$	10.3581	+	17.9407i	0.811307	+	1.40522i	−0.100643	+	0.994923i	$0.532090\pi$
$164$	−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	$-0.686851\pi$
$167$	−14.3152			−1.10775			−0.553873	+	0.832601i	$0.686851\pi$
$168$		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	−0.879277	−	0.476312i	$-0.841973\pi$
$173$	−11.2081	−	19.4130i	−0.852136	−	1.47594i	0.0271403	−	0.999632i	$-0.491360\pi$
$174$		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	$-0.733417\pi$
$179$	4.13101	−	7.15512i	0.308766	−	0.534799i	0.978093	+	0.208170i	$0.0667506\pi$
$180$		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	$-0.162103\pi$
$191$	0.198130	+	0.343172i	0.0143362	+	0.0248311i	−0.858768	+	0.512364i	$0.828770\pi$
$192$		0			0
$193$	−1.89397	+	3.28045i	−0.136331	+	0.236132i	−0.926105	−	0.377266i	$-0.876864\pi$
$193$	−1.89397	+	3.28045i	−0.136331	+	0.236132i	0.789774	+	0.613398i	$0.210198\pi$
$194$	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	$-0.641207\pi$
$197$	−12.0484			−0.858415			−0.429207	+	0.903206i	$0.641207\pi$
$198$		0			0
$199$	2.58113	−	4.47064i	0.182971	−	0.316915i	−0.759920	−	0.650017i	$-0.774762\pi$
$199$	2.58113	−	4.47064i	0.182971	−	0.316915i	0.942891	+	0.333101i	$0.108095\pi$
$200$	−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	$-0.968662\pi$
$227$	−6.21427	+	10.7634i	−0.412456	+	0.714394i	0.582702	+	0.812686i	$0.301995\pi$
$228$		0			0
$229$	−10.5292	−	18.2371i	−0.695788	−	1.20514i	−0.969914	−	0.243446i	$-0.921722\pi$
$229$	−10.5292	−	18.2371i	−0.695788	−	1.20514i	0.274127	−	0.961694i	$-0.411611\pi$
$230$	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	$-0.243190\pi$
$233$	−3.63436	−	6.29490i	−0.238095	−	0.412392i	−0.960168	+	0.279425i	$0.909856\pi$
$234$		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	$-0.636652\pi$
$239$	−12.8698			−0.832479			−0.416239	+	0.909255i	$0.636652\pi$
$240$		0			0
$241$	−6.59931	+	11.4303i	−0.425099	+	0.736293i	−0.996430	−	0.0844267i	$-0.973094\pi$
$241$	−6.59931	+	11.4303i	−0.425099	+	0.736293i	0.571331	+	0.820720i	$0.306427\pi$
$242$	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	$-0.603919\pi$
$251$	−10.1617			−0.641402			−0.320701	+	0.947180i	$0.603919\pi$
$252$		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	$-0.164279\pi$
$257$	0.120249	+	0.208278i	0.00750095	+	0.0129920i	−0.862251	+	0.506482i	$0.830946\pi$
$258$		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	−0.483102	−	0.875564i	$-0.660490\pi$
$263$	8.37962	−	14.5139i	0.516710	−	0.894967i	0.999812	−	0.0194034i	$-0.00617667\pi$
$264$		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	$-0.982666\pi$
$269$	−7.41534	+	12.8437i	−0.452121	+	0.783097i	0.546397	+	0.837527i	$0.315999\pi$
$270$		0			0
$271$	−13.6352	−	23.6169i	−0.828280	−	1.43462i	−0.899386	−	0.437154i	$-0.855986\pi$
$271$	−13.6352	−	23.6169i	−0.828280	−	1.43462i	0.0711064	−	0.997469i	$-0.477347\pi$
$272$	−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	−0.0646250	−	0.997910i	$-0.520585\pi$
$277$	13.8456	−	23.9813i	0.831903	−	1.44090i	0.896528	−	0.442988i	$-0.146082\pi$
$278$	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	$-0.334069\pi$
$281$	16.6959			0.995996			0.497998	+	0.867178i	$0.334069\pi$
$282$		0			0
$283$	0.160117	−	0.277330i	0.00951794	−	0.0164856i	−0.861227	−	0.508220i	$-0.830304\pi$
$283$	0.160117	−	0.277330i	0.00951794	−	0.0164856i	0.870745	+	0.491735i	$0.163637\pi$
$284$	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	$-0.575838\pi$
$293$	−8.07954			−0.472012			−0.236006	+	0.971752i	$0.575838\pi$
$294$		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	$-0.869969\pi$
$311$	−2.02524	+	3.50782i	−0.114841	+	0.198910i	0.802875	+	0.596147i	$0.203303\pi$
$312$		0			0
$313$	5.18356	+	8.97819i	0.292992	+	0.507477i	0.974516	−	0.224319i	$-0.0720157\pi$
$313$	5.18356	+	8.97819i	0.292992	+	0.507477i	−0.681524	+	0.731796i	$0.738682\pi$
$314$	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	$-0.0565225\pi$
$317$	6.03864	+	10.4592i	0.339164	+	0.587449i	−0.645112	+	0.764088i	$0.723189\pi$
$318$		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	0.991328	+	0.131411i	$0.0419508\pi$
$331$	11.0883	+	19.2055i	0.609469	+	1.05563i	−0.381859	+	0.924221i	$0.624716\pi$
$332$	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	0.488797	+	0.872397i	$0.337436\pi$
$347$	−9.52110	+	16.4910i	−0.511120	+	0.885285i	−0.999917	+	0.0128877i	$0.995898\pi$
$348$		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	$-0.782487\pi$
$353$	2.98845	−	5.17615i	0.159059	−	0.275499i	0.934530	+	0.355885i	$0.115821\pi$
$354$		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	$-0.297610\pi$
$359$	−7.57639	−	13.1227i	−0.399866	−	0.692589i	−0.993709	+	0.111992i	$0.964277\pi$
$360$		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	−0.764367	−	0.644782i	$-0.776948\pi$
$367$	3.37578	−	5.84702i	0.176214	−	0.305212i	0.940581	+	0.339570i	$0.110282\pi$
$368$	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	0.772716	−	0.634751i	$-0.218897\pi$
$373$	−3.15486	−	5.46438i	−0.163352	−	0.282935i	−0.936069	+	0.351816i	$0.885564\pi$
$374$	−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	−0.998532	−	0.0541716i	$-0.982748\pi$
$383$	−10.6889	−	18.5138i	−0.546180	−	0.946011i	0.452352	−	0.891840i	$-0.350585\pi$
$384$		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	0.0971400	+	0.995271i	$0.469031\pi$
$389$	−16.0420	+	27.7855i	−0.813360	+	1.40878i	−0.910500	+	0.413510i	$0.864303\pi$
$390$		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	0.672934	−	0.739702i	$-0.265034\pi$
$397$	−6.05982	−	10.4959i	−0.304134	−	0.526775i	−0.977068	+	0.212927i	$0.931700\pi$
$398$	3.79169			0.190060
$399$		0			0
$400$	1.53950			0.0769748
$401$	13.3139	+	23.0603i	0.664863	+	1.15158i	0.979322	+	0.202305i	$0.0648434\pi$
$401$	13.3139	+	23.0603i	0.664863	+	1.15158i	−0.314460	+	0.949271i	$0.601823\pi$
$402$		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	−0.774582	−	0.632473i	$-0.782040\pi$
$409$	3.24484	−	5.62023i	0.160447	−	0.277903i	0.935029	+	0.354571i	$0.115373\pi$
$410$	−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	$-0.222843\pi$
$419$	31.3097			1.52958			0.764789	+	0.644280i	$0.222843\pi$
$420$		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	$-0.675150\pi$
$431$	9.89750	−	17.1430i	0.476746	−	0.825748i	0.999645	+	0.0266466i	$0.00848287\pi$
$432$		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	0.972362	+	0.233478i	$0.0750108\pi$
$439$	14.4231	+	24.9816i	0.688379	+	1.19231i	−0.283983	+	0.958829i	$0.591656\pi$
$440$	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	$-0.142006\pi$
$443$	1.62898	+	2.82148i	0.0773952	+	0.134052i	−0.824730	+	0.565526i	$0.808673\pi$
$444$		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	$-0.507760\pi$
$449$	−1.03302			−0.0487513			−0.0243756	+	0.999703i	$0.507760\pi$
$450$		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	0.994720	−	0.102625i	$-0.0327243\pi$
$457$	8.73239	+	15.1249i	0.408484	+	0.707515i	−0.586236	+	0.810140i	$0.699391\pi$
$458$	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	$-0.227807\pi$
$461$	32.4060			1.50930			0.754649	+	0.656128i	$0.227807\pi$
$462$		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	−0.946586	−	0.322450i	$-0.895494\pi$
$467$	−16.2626	−	28.1676i	−0.752543	−	1.30344i	0.194043	−	0.980993i	$-0.437840\pi$
$468$		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	$-0.870093\pi$
$479$	−2.52189	+	4.36804i	−0.115228	+	0.199581i	0.802643	+	0.596460i	$0.203427\pi$
$480$		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	−0.710766	−	0.703429i	$-0.751651\pi$
$487$	5.60097	−	9.70117i	0.253804	−	0.439602i	0.964570	+	0.263827i	$0.0849848\pi$
$488$	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	$-0.337601\pi$
$491$	21.6420			0.976689			0.488344	+	0.872651i	$0.337601\pi$
$492$		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	0.973042	−	0.230629i	$-0.0740782\pi$
$499$	6.40642	+	11.0962i	0.286791	+	0.496736i	−0.686251	+	0.727365i	$0.740745\pi$
$500$	−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	$-0.687978\pi$
$503$	−24.9763			−1.11364			−0.556818	+	0.830635i	$0.687978\pi$
$504$		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	0.926589	+	0.376077i	$0.122727\pi$
$509$	17.8003	+	30.8311i	0.788986	+	1.36656i	−0.137602	+	0.990488i	$0.543940\pi$
$510$		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	0.109129	+	0.994028i	$0.465194\pi$
$521$	−18.4039	+	31.8765i	−0.806288	+	1.39653i	−0.915418	+	0.402505i	$0.868140\pi$
$522$		0			0
$523$	7.75876	+	13.4386i	0.339267	+	0.587627i	0.984295	−	0.176531i	$-0.0564877\pi$
$523$	7.75876	+	13.4386i	0.339267	+	0.587627i	−0.645028	+	0.764159i	$0.723154\pi$
$524$	−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	0.515601	−	0.856829i	$-0.327569\pi$
$541$	−11.2630	−	19.5081i	−0.484235	−	0.838720i	−0.999836	+	0.0181087i	$0.994236\pi$
$542$	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	0.440417	+	0.897793i	$0.354830\pi$
$557$	−13.1528	+	22.7814i	−0.557303	+	0.965277i	−0.997720	+	0.0674838i	$0.978503\pi$
$558$		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	$-0.739857\pi$
$563$	6.86825	−	11.8962i	0.289462	−	0.501363i	0.973681	+	0.227913i	$0.0731902\pi$
$564$		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	$-0.0315206\pi$
$569$	9.82612	+	17.0193i	0.411933	+	0.713488i	−0.583169	+	0.812351i	$0.698187\pi$
$570$		0			0
$571$	8.37578	−	14.5073i	0.350515	−	0.607111i	−0.635824	−	0.771834i	$-0.719340\pi$
$571$	8.37578	−	14.5073i	0.350515	−	0.607111i	0.986340	+	0.164723i	$0.0526731\pi$
$572$	−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	−0.512956	−	0.858415i	$-0.671450\pi$
$577$	11.6965	−	20.2589i	0.486931	−	0.843390i	0.999887	+	0.0150252i	$0.00478286\pi$
$578$	−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	$-0.539868\pi$
$587$	−6.05322			−0.249843			−0.124922	+	0.992167i	$0.539868\pi$
$588$		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	$-0.123746\pi$
$593$	3.27361	+	5.67006i	0.134431	+	0.232842i	−0.790949	+	0.611882i	$0.790413\pi$
$594$		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	$-0.848702\pi$
$599$	−1.18121	+	2.04591i	−0.0482627	+	0.0835935i	0.840885	+	0.541214i	$0.182035\pi$
$600$		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	0.958482	−	0.285153i	$-0.0920443\pi$
$607$	5.72306	+	9.91262i	0.232292	+	0.402341i	−0.726190	+	0.687494i	$0.758711\pi$
$608$	−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	−0.965328	−	0.261041i	$-0.915934\pi$
$613$	−6.35301	+	11.0037i	−0.256596	+	0.444437i	0.708732	+	0.705478i	$0.249268\pi$
$614$	−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	$-0.714087\pi$
$617$	−30.9500			−1.24600			−0.623000	+	0.782221i	$0.714087\pi$
$618$		0			0
$619$	−2.28220	+	3.95289i	−0.0917294	+	0.158880i	−0.908239	−	0.418452i	$-0.862573\pi$
$619$	−2.28220	+	3.95289i	−0.0917294	+	0.158880i	0.816510	+	0.577332i	$0.195906\pi$
$620$	−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	$-0.871408\pi$
$641$	−3.02118	+	5.23284i	−0.119329	+	0.206685i	0.800173	+	0.599770i	$0.204741\pi$
$642$		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	$-0.878285\pi$
$647$	−3.58020	+	6.20109i	−0.140752	+	0.243790i	0.787028	+	0.616917i	$0.211619\pi$
$648$		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	$-0.0144040\pi$
$653$	11.7628	+	20.3737i	0.460313	+	0.797285i	−0.538664	+	0.842521i	$0.681071\pi$
$654$		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	$-0.445583\pi$
$659$	8.73459			0.340251			0.170126	+	0.985422i	$0.445583\pi$
$660$		0			0
$661$	−5.60078	+	9.70083i	−0.217845	+	0.377319i	−0.954149	−	0.299332i	$-0.903236\pi$
$661$	−5.60078	+	9.70083i	−0.217845	+	0.377319i	0.736304	+	0.676651i	$0.236569\pi$
$662$	−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	−0.970715	−	0.240235i	$-0.922775\pi$
$677$	−18.0419	−	31.2495i	−0.693407	−	1.20102i	0.277308	−	0.960781i	$-0.410558\pi$
$678$		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	0.163235	−	0.986587i	$-0.447807\pi$
$683$	24.4624	−	42.3701i	0.936027	−	1.62125i	0.772792	−	0.634659i	$-0.218860\pi$
$684$		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	0.962367	+	0.271753i	$0.0876034\pi$
$691$	18.8353	+	32.6237i	0.716529	+	1.24106i	−0.245838	+	0.969311i	$0.579063\pi$
$692$	−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	$-0.377155\pi$
$701$	19.9325			0.752839			0.376420	+	0.926449i	$0.377155\pi$
$702$		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	0.901755	−	0.432248i	$-0.142279\pi$
$709$	2.03803	+	3.52998i	0.0765399	+	0.132571i	−0.825215	+	0.564819i	$0.808946\pi$
$710$	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	$-0.191173\pi$
$719$	−2.06232	−	3.57205i	−0.0769117	−	0.133215i	−0.901916	+	0.431911i	$0.857839\pi$
$720$		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	0.923813	−	0.382845i	$-0.125056\pi$
$733$	3.52918	+	6.11272i	0.130353	+	0.225778i	−0.793460	+	0.608623i	$0.791722\pi$
$734$	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	−0.365238	−	0.930914i	$-0.619012\pi$
$739$	16.9517	−	29.3611i	0.623577	−	1.08007i	0.988814	−	0.149152i	$-0.0476544\pi$
$740$	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	$-0.403220\pi$
$743$	16.3211			0.598763			0.299382	+	0.954133i	$0.403220\pi$
$744$		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	0.996839	−	0.0794480i	$-0.0253158\pi$
$751$	11.7733	+	20.3920i	0.429616	+	0.744116i	−0.567224	+	0.823564i	$0.691982\pi$
$752$	−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	−0.902584	−	0.430514i	$-0.858332\pi$
$761$	−22.7346	−	39.3775i	−0.824128	−	1.42743i	0.0784558	−	0.996918i	$-0.475001\pi$
$762$		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	0.0534175	+	0.998572i	$0.482989\pi$
$773$	−23.3010	+	40.3586i	−0.838080	+	1.45160i	−0.891498	+	0.453025i	$0.850345\pi$
$774$		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	−0.999419	−	0.0340751i	$-0.989151\pi$
$787$	−13.1908	+	22.8471i	−0.470200	+	0.814410i	0.529220	+	0.848485i	$0.322485\pi$
$788$	−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	$-0.398817\pi$
$797$	17.6474			0.625102			0.312551	+	0.949901i	$0.398817\pi$
$798$		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	$-0.731019\pi$
$809$	8.98580	−	15.5639i	0.315924	−	0.547197i	0.979633	+	0.200794i	$0.0643522\pi$
$810$		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	−0.985229	−	0.171241i	$-0.945222\pi$
$821$	−18.3642	−	31.8076i	−0.640913	−	1.11009i	0.344316	−	0.938854i	$-0.388111\pi$
$822$		0			0
$823$	20.6118	−	35.7006i	0.718481	−	1.24445i	−0.243120	−	0.969996i	$-0.578171\pi$
$823$	20.6118	−	35.7006i	0.718481	−	1.24445i	0.961601	−	0.274450i	$-0.0884956\pi$
$824$	−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	$-0.555660\pi$
$827$	−10.0060			−0.347941			−0.173971	+	0.984751i	$0.555660\pi$
$828$		0			0
$829$	−7.48035	+	12.9563i	−0.259803	+	0.449992i	−0.966189	−	0.257835i	$-0.916991\pi$
$829$	−7.48035	+	12.9563i	−0.259803	+	0.449992i	0.706386	+	0.707827i	$0.250324\pi$
$830$	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	$-0.654347\pi$
$839$	−27.0026			−0.932232			−0.466116	+	0.884724i	$0.654347\pi$
$840$		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	$-0.792554\pi$
$857$	3.74018	−	6.47818i	0.127762	−	0.221290i	0.922809	+	0.385257i	$0.125887\pi$
$858$		0			0
$859$	−21.6862	−	37.5616i	−0.739923	−	1.28158i	−0.952530	−	0.304446i	$-0.901529\pi$
$859$	−21.6862	−	37.5616i	−0.739923	−	1.28158i	0.212607	−	0.977138i	$-0.431805\pi$
$860$	39.5267			1.34785
$861$		0			0
$862$	14.5395			0.495217
$863$	16.0114	+	27.7325i	0.545034	+	0.944026i	0.998605	+	0.0528061i	$0.0168165\pi$
$863$	16.0114	+	27.7325i	0.545034	+	0.944026i	−0.453571	+	0.891220i	$0.649850\pi$
$864$		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	−0.998226	−	0.0595382i	$-0.981037\pi$
$877$	−16.3078	−	28.2459i	−0.550675	−	0.953796i	0.447551	−	0.894258i	$-0.352296\pi$
$878$	−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	$-0.301349\pi$
$881$	34.6890			1.16870			0.584351	+	0.811501i	$0.301349\pi$
$882$		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	0.999588	+	0.0287180i	$0.00914248\pi$
$887$	15.6258	+	27.0647i	0.524664	+	0.908745i	−0.474923	+	0.880027i	$0.657524\pi$
$888$		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	0.179429	−	0.983771i	$-0.442575\pi$
$907$	28.3602	−	49.1213i	0.941685	−	1.63105i	0.762256	−	0.647276i	$-0.224092\pi$
$908$	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	$-0.378569\pi$
$911$	22.4742			0.744604			0.372302	+	0.928112i	$0.378569\pi$
$912$		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	0.844801	−	0.535081i	$-0.179719\pi$
$919$	−1.24271	−	2.15243i	−0.0409931	−	0.0710021i	−0.885794	+	0.464079i	$0.846385\pi$
$920$	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	0.995774	+	0.0918404i	$0.0292750\pi$
$929$	17.5996	+	30.4833i	0.577423	+	1.00013i	−0.418351	+	0.908286i	$0.637392\pi$
$930$		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	0.477972	+	0.878375i	$0.341372\pi$
$941$	−16.0038	+	27.7194i	−0.521709	+	0.903627i	−0.999681	+	0.0252517i	$0.991961\pi$
$942$		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	$-0.287120\pi$
$947$	−11.3692	−	19.6919i	−0.369448	−	0.639902i	−0.989479	+	0.144675i	$0.953786\pi$
$948$		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	$-0.587657\pi$
$953$	−16.7884			−0.543830			−0.271915	+	0.962321i	$0.587657\pi$
$954$		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	$-0.187517\pi$
$971$	−2.03968	−	3.53282i	−0.0654563	−	0.113374i	−0.896896	+	0.442241i	$0.854184\pi$
$972$		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	$-0.783432\pi$
$977$	4.88009	−	8.45256i	0.156128	−	0.270421i	0.933469	+	0.358658i	$0.116765\pi$
$978$		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	0.0885154	+	0.996075i	$0.471788\pi$
$983$	−25.6582	+	44.4412i	−0.818368	+	1.41746i	−0.906884	+	0.421381i	$0.861546\pi$
$984$		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	−0.860375	−	0.509662i	$-0.829771\pi$
$991$	0.352336	−	0.610265i	0.0111923	−	0.0193857i	0.871567	+	0.490276i	$0.163104\pi$
$992$	−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	0.460164	+	0.887834i	$0.347791\pi$
$997$	−17.0129	+	29.4673i	−0.538805	+	0.933238i	−0.998969	+	0.0454035i	$0.985543\pi$
$998$	−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.235.4	yes	12
3.2	odd	2	inner	819.2.j.i.235.3	✓	12
7.2	even	3	inner	819.2.j.i.352.4	yes	12
7.3	odd	6		5733.2.a.bt.1.3		6
7.4	even	3		5733.2.a.bs.1.3		6
21.2	odd	6	inner	819.2.j.i.352.3	yes	12
21.11	odd	6		5733.2.a.bs.1.4		6
21.17	even	6		5733.2.a.bt.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.j.i.235.3	✓	12	3.2	odd	2	inner
819.2.j.i.235.4	yes	12	1.1	even	1	trivial
819.2.j.i.352.3	yes	12	21.2	odd	6	inner
819.2.j.i.352.4	yes	12	7.2	even	3	inner
5733.2.a.bs.1.3		6	7.4	even	3
5733.2.a.bs.1.4		6	21.11	odd	6
5733.2.a.bt.1.3		6	7.3	odd	6
5733.2.a.bt.1.4		6	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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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