LMFDB - Embedded newform 1350.2.j.f.199.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1350,2,Mod(199,1350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1350, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("1350.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1350 = 2 \cdot 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1350.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.7798042729$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.303595776.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 $ x^8 + 5x^6 + 16x^4 + 45*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.1
Root			$-0.396143 + 1.68614i$ of defining polynomial
Character	$\chi$	$=$	1350.199
Dual form			1350.2.j.f.1099.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.92048 + 1.68614i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.92048 + 1.68614i) q^{7} +1.00000i q^{8} +(-2.18614 - 3.78651i) q^{11} +(5.84096 + 3.37228i) q^{13} +(1.68614 - 2.92048i) q^{14} +(-0.500000 - 0.866025i) q^{16} -1.62772i q^{17} +2.37228 q^{19} +(3.78651 + 2.18614i) q^{22} +(1.18843 + 0.686141i) q^{23} -6.74456 q^{26} +3.37228i q^{28} +(-0.686141 - 1.18843i) q^{29} +(-2.37228 + 4.10891i) q^{31} +(0.866025 + 0.500000i) q^{32} +(0.813859 + 1.40965i) q^{34} +4.00000i q^{37} +(-2.05446 + 1.18614i) q^{38} +(-1.50000 + 2.59808i) q^{41} +(-4.87375 + 2.81386i) q^{43} -4.37228 q^{44} -1.37228 q^{46} +(-6.38458 + 3.68614i) q^{47} +(2.18614 - 3.78651i) q^{49} +(5.84096 - 3.37228i) q^{52} +11.4891i q^{53} +(-1.68614 - 2.92048i) q^{56} +(1.18843 + 0.686141i) q^{58} +(-2.18614 + 3.78651i) q^{59} +(4.05842 + 7.02939i) q^{61} -4.74456i q^{62} -1.00000 q^{64} +(-6.06218 - 3.50000i) q^{67} +(-1.40965 - 0.813859i) q^{68} +6.00000 q^{71} +3.11684i q^{73} +(-2.00000 - 3.46410i) q^{74} +(1.18614 - 2.05446i) q^{76} +(12.7692 + 7.37228i) q^{77} +(1.00000 + 1.73205i) q^{79} -3.00000i q^{82} +(-6.38458 + 3.68614i) q^{83} +(2.81386 - 4.87375i) q^{86} +(3.78651 - 2.18614i) q^{88} +16.1168 q^{89} -22.7446 q^{91} +(1.18843 - 0.686141i) q^{92} +(3.68614 - 6.38458i) q^{94} +(7.25061 - 4.18614i) q^{97} +4.37228i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4}+O(q^{10}) $ 8 * q + 4 * q^4	$ 8 q + 4 q^{4} - 6 q^{11} + 2 q^{14} - 4 q^{16} - 4 q^{19} - 8 q^{26} + 6 q^{29} + 4 q^{31} + 18 q^{34} - 12 q^{41} - 12 q^{44} + 12 q^{46} + 6 q^{49} - 2 q^{56} - 6 q^{59} - 2 q^{61} - 8 q^{64} + 48 q^{71} - 16 q^{74} - 2 q^{76} + 8 q^{79} + 34 q^{86} + 60 q^{89} - 136 q^{91} + 18 q^{94}+O(q^{100}) $ 8 * q + 4 * q^4 - 6 * q^11 + 2 * q^14 - 4 * q^16 - 4 * q^19 - 8 * q^26 + 6 * q^29 + 4 * q^31 + 18 * q^34 - 12 * q^41 - 12 * q^44 + 12 * q^46 + 6 * q^49 - 2 * q^56 - 6 * q^59 - 2 * q^61 - 8 * q^64 + 48 * q^71 - 16 * q^74 - 2 * q^76 + 8 * q^79 + 34 * q^86 + 60 * q^89 - 136 * q^91 + 18 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times$.

$n$	$1001$	$1027$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.92048	+	1.68614i	−1.10384	+	0.637301i	−0.937226	−	0.348721i	$-0.886616\pi$
$7$	−2.92048	+	1.68614i	−1.10384	+	0.637301i	−0.166612	+	0.986023i	$0.553283\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$		0			0
$11$	−2.18614	−	3.78651i	−0.659146	−	1.14167i	−0.980837	−	0.194830i	$-0.937584\pi$
$11$	−2.18614	−	3.78651i	−0.659146	−	1.14167i	0.321691	−	0.946845i	$-0.395749\pi$
$12$		0			0
$13$	5.84096	+	3.37228i	1.61999	+	0.935303i	0.986920	+	0.161209i	$0.0515393\pi$
$13$	5.84096	+	3.37228i	1.61999	+	0.935303i	0.633071	+	0.774094i	$0.281794\pi$
$14$	1.68614	−	2.92048i	0.450640	−	0.780531i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		−	1.62772i		−	0.394780i	−0.980325	−	0.197390i	$-0.936754\pi$
$17$		−	1.62772i		−	0.394780i	0.980325	−	0.197390i	$-0.0632465\pi$
$18$		0			0
$19$	2.37228			0.544239			0.272119	−	0.962264i	$-0.412275\pi$
$19$	2.37228			0.544239			0.272119	+	0.962264i	$0.412275\pi$
$20$		0			0
$21$		0			0
$22$	3.78651	+	2.18614i	0.807286	+	0.466087i
$23$	1.18843	+	0.686141i	0.247805	+	0.143070i	0.618759	−	0.785581i	$-0.287636\pi$
$23$	1.18843	+	0.686141i	0.247805	+	0.143070i	−0.370954	+	0.928651i	$0.620969\pi$
$24$		0			0
$25$		0			0
$26$	−6.74456			−1.32272
$27$		0			0
$28$			3.37228i			0.637301i
$29$	−0.686141	−	1.18843i	−0.127413	−	0.220686i	0.795261	−	0.606268i	$-0.207334\pi$
$29$	−0.686141	−	1.18843i	−0.127413	−	0.220686i	−0.922674	+	0.385582i	$0.874001\pi$
$30$		0			0
$31$	−2.37228	+	4.10891i	−0.426074	+	0.737982i	−0.996520	−	0.0833529i	$-0.973437\pi$
$31$	−2.37228	+	4.10891i	−0.426074	+	0.737982i	0.570446	+	0.821335i	$0.306770\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$	0.813859	+	1.40965i	0.139576	+	0.241752i
$35$		0			0
$36$		0			0
$37$			4.00000i			0.657596i	0.944400	+	0.328798i	$0.106644\pi$
$37$			4.00000i			0.657596i	−0.944400	+	0.328798i	$0.893356\pi$
$38$	−2.05446	+	1.18614i	−0.333277	+	0.192417i
$39$		0			0
$40$		0			0
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	−0.959058	−	0.283211i	$-0.908600\pi$
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	0.724797	+	0.688963i	$0.241934\pi$
$42$		0			0
$43$	−4.87375	+	2.81386i	−0.743240	+	0.429110i	−0.823246	−	0.567685i	$-0.807839\pi$
$43$	−4.87375	+	2.81386i	−0.743240	+	0.429110i	0.0800065	+	0.996794i	$0.474506\pi$
$44$	−4.37228			−0.659146
$45$		0			0
$46$	−1.37228			−0.202332
$47$	−6.38458	+	3.68614i	−0.931287	+	0.537679i	−0.887218	−	0.461350i	$-0.847365\pi$
$47$	−6.38458	+	3.68614i	−0.931287	+	0.537679i	−0.0440687	+	0.999029i	$0.514032\pi$
$48$		0			0
$49$	2.18614	−	3.78651i	0.312306	−	0.540930i
$50$		0			0
$51$		0			0
$52$	5.84096	−	3.37228i	0.809996	−	0.467651i
$53$			11.4891i			1.57815i	0.614295	+	0.789076i	$0.289440\pi$
$53$			11.4891i			1.57815i	−0.614295	+	0.789076i	$0.710560\pi$
$54$		0			0
$55$		0			0
$56$	−1.68614	−	2.92048i	−0.225320	−	0.390266i
$57$		0			0
$58$	1.18843	+	0.686141i	0.156049	+	0.0900947i
$59$	−2.18614	+	3.78651i	−0.284611	+	0.492961i	−0.972515	−	0.232841i	$-0.925198\pi$
$59$	−2.18614	+	3.78651i	−0.284611	+	0.492961i	0.687904	+	0.725802i	$0.258531\pi$
$60$		0			0
$61$	4.05842	+	7.02939i	0.519628	+	0.900022i	0.999740	+	0.0228144i	$0.00726267\pi$
$61$	4.05842	+	7.02939i	0.519628	+	0.900022i	−0.480112	+	0.877207i	$0.659404\pi$
$62$		−	4.74456i		−	0.602560i
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	−6.06218	−	3.50000i	−0.740613	−	0.427593i	0.0816792	−	0.996659i	$-0.473972\pi$
$67$	−6.06218	−	3.50000i	−0.740613	−	0.427593i	−0.822292	+	0.569066i	$0.807305\pi$
$68$	−1.40965	−	0.813859i	−0.170945	−	0.0986949i
$69$		0			0
$70$		0			0
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$			3.11684i			0.364799i	0.983225	+	0.182399i	$0.0583864\pi$
$73$			3.11684i			0.364799i	−0.983225	+	0.182399i	$0.941614\pi$
$74$	−2.00000	−	3.46410i	−0.232495	−	0.402694i
$75$		0			0
$76$	1.18614	−	2.05446i	0.136060	−	0.235662i
$77$	12.7692	+	7.37228i	1.45518	+	0.840149i
$78$		0			0
$79$	1.00000	+	1.73205i	0.112509	+	0.194871i	0.916781	−	0.399390i	$-0.130778\pi$
$79$	1.00000	+	1.73205i	0.112509	+	0.194871i	−0.804272	+	0.594261i	$0.797445\pi$
$80$		0			0
$81$		0			0
$82$		−	3.00000i		−	0.331295i
$83$	−6.38458	+	3.68614i	−0.700799	+	0.404607i	−0.807645	−	0.589669i	$-0.799258\pi$
$83$	−6.38458	+	3.68614i	−0.700799	+	0.404607i	0.106846	+	0.994276i	$0.465925\pi$
$84$		0			0
$85$		0			0
$86$	2.81386	−	4.87375i	0.303426	−	0.525550i
$87$		0			0
$88$	3.78651	−	2.18614i	0.403643	−	0.233043i
$89$	16.1168			1.70838			0.854191	−	0.519959i	$-0.174053\pi$
$89$	16.1168			1.70838			0.854191	+	0.519959i	$0.174053\pi$
$90$		0			0
$91$	−22.7446			−2.38428
$92$	1.18843	−	0.686141i	0.123902	−	0.0715351i
$93$		0			0
$94$	3.68614	−	6.38458i	0.380196	−	0.658519i
$95$		0			0
$96$		0			0
$97$	7.25061	−	4.18614i	0.736188	−	0.425038i	−0.0844938	−	0.996424i	$-0.526927\pi$
$97$	7.25061	−	4.18614i	0.736188	−	0.425038i	0.820682	+	0.571386i	$0.193594\pi$
$98$			4.37228i			0.441667i
$99$		0			0
$100$		0			0
$101$	1.37228	+	2.37686i	0.136547	+	0.236507i	0.926187	−	0.377064i	$-0.123066\pi$
$101$	1.37228	+	2.37686i	0.136547	+	0.236507i	−0.789640	+	0.613570i	$0.789733\pi$
$102$		0			0
$103$	13.8564	+	8.00000i	1.36531	+	0.788263i	0.990325	−	0.138767i	$-0.0443138\pi$
$103$	13.8564	+	8.00000i	1.36531	+	0.788263i	0.374987	+	0.927030i	$0.377647\pi$
$104$	−3.37228	+	5.84096i	−0.330679	+	0.572754i
$105$		0			0
$106$	−5.74456	−	9.94987i	−0.557961	−	0.966417i
$107$			8.48913i			0.820675i	0.911934	+	0.410337i	$0.134589\pi$
$107$			8.48913i			0.820675i	−0.911934	+	0.410337i	$0.865411\pi$
$108$		0			0
$109$	−15.3723			−1.47240			−0.736199	−	0.676765i	$-0.763381\pi$
$109$	−15.3723			−1.47240			−0.736199	+	0.676765i	$0.763381\pi$
$110$		0			0
$111$		0			0
$112$	2.92048	+	1.68614i	0.275960	+	0.159325i
$113$	2.81929	+	1.62772i	0.265217	+	0.153123i	0.626712	−	0.779251i	$-0.284400\pi$
$113$	2.81929	+	1.62772i	0.265217	+	0.153123i	−0.361495	+	0.932374i	$0.617734\pi$
$114$		0			0
$115$		0			0
$116$	−1.37228			−0.127413
$117$		0			0
$118$		−	4.37228i		−	0.402501i
$119$	2.74456	+	4.75372i	0.251594	+	0.435773i
$120$		0			0
$121$	−4.05842	+	7.02939i	−0.368947	+	0.639036i
$122$	−7.02939	−	4.05842i	−0.636411	−	0.367432i
$123$		0			0
$124$	2.37228	+	4.10891i	0.213037	+	0.368991i
$125$		0			0
$126$		0			0
$127$			8.11684i			0.720253i	0.932903	+	0.360127i	$0.117267\pi$
$127$			8.11684i			0.720253i	−0.932903	+	0.360127i	$0.882733\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$		0			0
$131$	−1.37228	+	2.37686i	−0.119897	+	0.207667i	−0.919727	−	0.392560i	$-0.871590\pi$
$131$	−1.37228	+	2.37686i	−0.119897	+	0.207667i	0.799830	+	0.600227i	$0.204923\pi$
$132$		0			0
$133$	−6.92820	+	4.00000i	−0.600751	+	0.346844i
$134$	7.00000			0.604708
$135$		0			0
$136$	1.62772			0.139576
$137$	−16.5557	+	9.55842i	−1.41445	+	0.816631i	−0.995803	−	0.0915197i	$-0.970828\pi$
$137$	−16.5557	+	9.55842i	−1.41445	+	0.816631i	−0.418643	+	0.908151i	$0.637494\pi$
$138$		0			0
$139$	0.441578	−	0.764836i	0.0374542	−	0.0648725i	−0.846691	−	0.532085i	$-0.821409\pi$
$139$	0.441578	−	0.764836i	0.0374542	−	0.0648725i	0.884145	+	0.467213i	$0.154742\pi$
$140$		0			0
$141$		0			0
$142$	−5.19615	+	3.00000i	−0.436051	+	0.251754i
$143$		−	29.4891i		−	2.46600i
$144$		0			0
$145$		0			0
$146$	−1.55842	−	2.69927i	−0.128976	−	0.223393i
$147$		0			0
$148$	3.46410	+	2.00000i	0.284747	+	0.164399i
$149$	−0.941578	+	1.63086i	−0.0771371	+	0.133605i	−0.902014	−	0.431708i	$-0.857911\pi$
$149$	−0.941578	+	1.63086i	−0.0771371	+	0.133605i	0.824877	+	0.565313i	$0.191245\pi$
$150$		0			0
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	0.994540	−	0.104357i	$-0.0332784\pi$
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	−0.587646	+	0.809118i	$0.699945\pi$
$152$			2.37228i			0.192417i
$153$		0			0
$154$	−14.7446			−1.18815
$155$		0			0
$156$		0			0
$157$	−5.84096	−	3.37228i	−0.466160	−	0.269137i	0.248471	−	0.968639i	$-0.420072\pi$
$157$	−5.84096	−	3.37228i	−0.466160	−	0.269137i	−0.714631	+	0.699502i	$0.753405\pi$
$158$	−1.73205	−	1.00000i	−0.137795	−	0.0795557i
$159$		0			0
$160$		0			0
$161$	−4.62772			−0.364715
$162$		0			0
$163$		−	21.4891i		−	1.68316i	−0.540134	−	0.841579i	$-0.681626\pi$
$163$		−	21.4891i		−	1.68316i	0.540134	−	0.841579i	$-0.318374\pi$
$164$	1.50000	+	2.59808i	0.117130	+	0.202876i
$165$		0			0
$166$	3.68614	−	6.38458i	0.286100	−	0.495540i
$167$	−11.5807	−	6.68614i	−0.896144	−	0.517389i	−0.0201970	−	0.999796i	$-0.506429\pi$
$167$	−11.5807	−	6.68614i	−0.896144	−	0.517389i	−0.875947	+	0.482407i	$0.839763\pi$
$168$		0			0
$169$	16.2446	+	28.1364i	1.24958	+	2.16434i
$170$		0			0
$171$		0			0
$172$			5.62772i			0.429110i
$173$	−17.9653	+	10.3723i	−1.36588	+	0.788590i	−0.990399	−	0.138241i	$-0.955855\pi$
$173$	−17.9653	+	10.3723i	−1.36588	+	0.788590i	−0.375479	+	0.926831i	$0.622522\pi$
$174$		0			0
$175$		0			0
$176$	−2.18614	+	3.78651i	−0.164787	+	0.285419i
$177$		0			0
$178$	−13.9576	+	8.05842i	−1.04617	+	0.604004i
$179$	−14.7446			−1.10206			−0.551030	−	0.834485i	$-0.685765\pi$
$179$	−14.7446			−1.10206			−0.551030	+	0.834485i	$0.685765\pi$
$180$		0			0
$181$	20.8614			1.55062			0.775308	−	0.631583i	$-0.217595\pi$
$181$	20.8614			1.55062			0.775308	+	0.631583i	$0.217595\pi$
$182$	19.6974	−	11.3723i	1.46007	−	0.842970i
$183$		0			0
$184$	−0.686141	+	1.18843i	−0.0505830	+	0.0876123i
$185$		0			0
$186$		0			0
$187$	−6.16337	+	3.55842i	−0.450710	+	0.260218i
$188$			7.37228i			0.537679i
$189$		0			0
$190$		0			0
$191$	8.74456	+	15.1460i	0.632734	+	1.09593i	0.986990	+	0.160780i	$0.0514008\pi$
$191$	8.74456	+	15.1460i	0.632734	+	1.09593i	−0.354256	+	0.935148i	$0.615266\pi$
$192$		0			0
$193$	−18.2877	−	10.5584i	−1.31638	−	0.760012i	−0.333235	−	0.942844i	$-0.608140\pi$
$193$	−18.2877	−	10.5584i	−1.31638	−	0.760012i	−0.983144	+	0.182832i	$0.941474\pi$
$194$	−4.18614	+	7.25061i	−0.300547	+	0.520563i
$195$		0			0
$196$	−2.18614	−	3.78651i	−0.156153	−	0.270465i
$197$		−	5.48913i		−	0.391084i	−0.980695	−	0.195542i	$-0.937353\pi$
$197$		−	5.48913i		−	0.391084i	0.980695	−	0.195542i	$-0.0626466\pi$
$198$		0			0
$199$	−13.4891			−0.956219			−0.478109	−	0.878300i	$-0.658678\pi$
$199$	−13.4891			−0.956219			−0.478109	+	0.878300i	$0.658678\pi$
$200$		0			0
$201$		0			0
$202$	−2.37686	−	1.37228i	−0.167235	−	0.0965534i
$203$	4.00772	+	2.31386i	0.281287	+	0.162401i
$204$		0			0
$205$		0			0
$206$	−16.0000			−1.11477
$207$		0			0
$208$		−	6.74456i		−	0.467651i
$209$	−5.18614	−	8.98266i	−0.358733	−	0.621344i
$210$		0			0
$211$	9.37228	−	16.2333i	0.645214	−	1.11754i	−0.339037	−	0.940773i	$-0.610101\pi$
$211$	9.37228	−	16.2333i	0.645214	−	1.11754i	0.984252	−	0.176771i	$-0.0565653\pi$
$212$	9.94987	+	5.74456i	0.683360	+	0.394538i
$213$		0			0
$214$	−4.24456	−	7.35180i	−0.290152	−	0.502559i
$215$		0			0
$216$		0			0
$217$		−	16.0000i		−	1.08615i
$218$	13.3128	−	7.68614i	0.901656	−	0.520571i
$219$		0			0
$220$		0			0
$221$	5.48913	−	9.50744i	0.369239	−	0.639540i
$222$		0			0
$223$	5.73977	−	3.31386i	0.384364	−	0.221912i	−0.295351	−	0.955389i	$-0.595437\pi$
$223$	5.73977	−	3.31386i	0.384364	−	0.221912i	0.679715	+	0.733476i	$0.262103\pi$
$224$	−3.37228			−0.225320
$225$		0			0
$226$	−3.25544			−0.216548
$227$	16.5557	−	9.55842i	1.09884	−	0.634415i	0.162923	−	0.986639i	$-0.447908\pi$
$227$	16.5557	−	9.55842i	1.09884	−	0.634415i	0.935916	+	0.352224i	$0.114574\pi$
$228$		0			0
$229$	6.31386	−	10.9359i	0.417232	−	0.722666i	−0.578428	−	0.815733i	$-0.696334\pi$
$229$	6.31386	−	10.9359i	0.417232	−	0.722666i	0.995660	+	0.0930670i	$0.0296671\pi$
$230$		0			0
$231$		0			0
$232$	1.18843	−	0.686141i	0.0780243	−	0.0450473i
$233$		−	7.11684i		−	0.466240i	−0.972448	−	0.233120i	$-0.925107\pi$
$233$		−	7.11684i		−	0.466240i	0.972448	−	0.233120i	$-0.0748935\pi$
$234$		0			0
$235$		0			0
$236$	2.18614	+	3.78651i	0.142306	+	0.246481i
$237$		0			0
$238$	−4.75372	−	2.74456i	−0.308138	−	0.177904i
$239$	1.62772	−	2.81929i	0.105288	−	0.182365i	−0.808568	−	0.588403i	$-0.799757\pi$
$239$	1.62772	−	2.81929i	0.105288	−	0.182365i	0.913856	+	0.406038i	$0.133090\pi$
$240$		0			0
$241$	6.24456	+	10.8159i	0.402248	+	0.696713i	0.993997	−	0.109409i	$-0.0348958\pi$
$241$	6.24456	+	10.8159i	0.402248	+	0.696713i	−0.591749	+	0.806122i	$0.701562\pi$
$242$		−	8.11684i		−	0.521770i
$243$		0			0
$244$	8.11684			0.519628
$245$		0			0
$246$		0			0
$247$	13.8564	+	8.00000i	0.881662	+	0.509028i
$248$	−4.10891	−	2.37228i	−0.260916	−	0.150640i
$249$		0			0
$250$		0			0
$251$	24.6060			1.55312			0.776558	−	0.630046i	$-0.216964\pi$
$251$	24.6060			1.55312			0.776558	+	0.630046i	$0.216964\pi$
$252$		0			0
$253$		−	6.00000i		−	0.377217i
$254$	−4.05842	−	7.02939i	−0.254648	−	0.441063i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.78651	−	2.18614i	−0.236196	−	0.136368i	0.377231	−	0.926119i	$-0.376876\pi$
$257$	−3.78651	−	2.18614i	−0.236196	−	0.136368i	−0.613427	+	0.789751i	$0.710210\pi$
$258$		0			0
$259$	−6.74456	−	11.6819i	−0.419087	−	0.725880i
$260$		0			0
$261$		0			0
$262$		−	2.74456i		−	0.169560i
$263$	15.1460	−	8.74456i	0.933944	−	0.539213i	0.0458872	−	0.998947i	$-0.485389\pi$
$263$	15.1460	−	8.74456i	0.933944	−	0.539213i	0.888057	+	0.459734i	$0.152055\pi$
$264$		0			0
$265$		0			0
$266$	4.00000	−	6.92820i	0.245256	−	0.424795i
$267$		0			0
$268$	−6.06218	+	3.50000i	−0.370306	+	0.213797i
$269$	−1.37228			−0.0836695			−0.0418347	−	0.999125i	$-0.513320\pi$
$269$	−1.37228			−0.0836695			−0.0418347	+	0.999125i	$0.513320\pi$
$270$		0			0
$271$	8.00000			0.485965			0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000			0.485965			0.242983	+	0.970031i	$0.421874\pi$
$272$	−1.40965	+	0.813859i	−0.0854723	+	0.0493475i
$273$		0			0
$274$	9.55842	−	16.5557i	0.577445	−	1.00016i
$275$		0			0
$276$		0			0
$277$	−14.5012	+	8.37228i	−0.871294	+	0.503042i	−0.867778	−	0.496952i	$-0.834452\pi$
$277$	−14.5012	+	8.37228i	−0.871294	+	0.503042i	−0.00351574	+	0.999994i	$0.501119\pi$
$278$			0.883156i			0.0529682i
$279$		0			0
$280$		0			0
$281$	−0.686141	−	1.18843i	−0.0409317	−	0.0708958i	0.844834	−	0.535029i	$-0.179699\pi$
$281$	−0.686141	−	1.18843i	−0.0409317	−	0.0708958i	−0.885765	+	0.464133i	$0.846366\pi$
$282$		0			0
$283$	2.71810	+	1.56930i	0.161574	+	0.0932850i	0.578607	−	0.815607i	$-0.303597\pi$
$283$	2.71810	+	1.56930i	0.161574	+	0.0932850i	−0.417033	+	0.908892i	$0.636930\pi$
$284$	3.00000	−	5.19615i	0.178017	−	0.308335i
$285$		0			0
$286$	14.7446	+	25.5383i	0.871864	+	1.51011i
$287$		−	10.1168i		−	0.597178i
$288$		0			0
$289$	14.3505			0.844149
$290$		0			0
$291$		0			0
$292$	2.69927	+	1.55842i	0.157963	+	0.0911997i
$293$	22.7190	+	13.1168i	1.32726	+	0.766294i	0.984875	−	0.173265i	$-0.0554318\pi$
$293$	22.7190	+	13.1168i	1.32726	+	0.766294i	0.342385	+	0.939560i	$0.388765\pi$
$294$		0			0
$295$		0			0
$296$	−4.00000			−0.232495
$297$		0			0
$298$		−	1.88316i		−	0.109088i
$299$	4.62772	+	8.01544i	0.267628	+	0.463545i
$300$		0			0
$301$	9.48913	−	16.4356i	0.546944	−	0.947335i
$302$	−8.66025	−	5.00000i	−0.498342	−	0.287718i
$303$		0			0
$304$	−1.18614	−	2.05446i	−0.0680298	−	0.117831i
$305$		0			0
$306$		0			0
$307$		−	1.23369i		−	0.0704103i	−0.999380	−	0.0352051i	$-0.988792\pi$
$307$		−	1.23369i		−	0.0704103i	0.999380	−	0.0352051i	$-0.0112085\pi$
$308$	12.7692	−	7.37228i	0.727591	−	0.420075i
$309$		0			0
$310$		0			0
$311$	−10.3723	+	17.9653i	−0.588158	+	1.01872i	0.406315	+	0.913733i	$0.366813\pi$
$311$	−10.3723	+	17.9653i	−0.588158	+	1.01872i	−0.994474	+	0.104987i	$0.966520\pi$
$312$		0			0
$313$	3.14170	−	1.81386i	0.177579	−	0.102525i	−0.408576	−	0.912724i	$-0.633974\pi$
$313$	3.14170	−	1.81386i	0.177579	−	0.102525i	0.586155	+	0.810199i	$0.300641\pi$
$314$	6.74456			0.380618
$315$		0			0
$316$	2.00000			0.112509
$317$	2.37686	−	1.37228i	0.133498	−	0.0770750i	−0.431764	−	0.901987i	$-0.642109\pi$
$317$	2.37686	−	1.37228i	0.133498	−	0.0770750i	0.565262	+	0.824912i	$0.308775\pi$
$318$		0			0
$319$	−3.00000	+	5.19615i	−0.167968	+	0.290929i
$320$		0			0
$321$		0			0
$322$	4.00772	−	2.31386i	0.223342	−	0.128946i
$323$		−	3.86141i		−	0.214854i
$324$		0			0
$325$		0			0
$326$	10.7446	+	18.6101i	0.595086	+	1.03072i
$327$		0			0
$328$	−2.59808	−	1.50000i	−0.143455	−	0.0828236i
$329$	12.4307	−	21.5306i	0.685327	−	1.18702i
$330$		0			0
$331$	−8.11684	−	14.0588i	−0.446142	−	0.772741i	0.551989	−	0.833851i	$-0.313869\pi$
$331$	−8.11684	−	14.0588i	−0.446142	−	0.772741i	−0.998131	+	0.0611107i	$0.980536\pi$
$332$			7.37228i			0.404607i
$333$		0			0
$334$	13.3723			0.731699
$335$		0			0
$336$		0			0
$337$	−2.05446	−	1.18614i	−0.111913	−	0.0646132i	0.442999	−	0.896522i	$-0.353915\pi$
$337$	−2.05446	−	1.18614i	−0.111913	−	0.0646132i	−0.554912	+	0.831909i	$0.687248\pi$
$338$	−28.1364	−	16.2446i	−1.53042	−	0.883588i
$339$		0			0
$340$		0			0
$341$	20.7446			1.12338
$342$		0			0
$343$		−	8.86141i		−	0.478471i
$344$	−2.81386	−	4.87375i	−0.151713	−	0.262775i
$345$		0			0
$346$	10.3723	−	17.9653i	0.557617	−	0.965821i
$347$	4.22894	+	2.44158i	0.227021	+	0.131071i	0.609197	−	0.793019i	$-0.291492\pi$
$347$	4.22894	+	2.44158i	0.227021	+	0.131071i	−0.382176	+	0.924090i	$0.624825\pi$
$348$		0			0
$349$	9.05842	+	15.6896i	0.484886	+	0.839848i	0.999849	−	0.0173648i	$-0.00552768\pi$
$349$	9.05842	+	15.6896i	0.484886	+	0.839848i	−0.514963	+	0.857212i	$0.672194\pi$
$350$		0			0
$351$		0			0
$352$		−	4.37228i		−	0.233043i
$353$	18.4901	−	10.6753i	0.984129	−	0.568187i	0.0806147	−	0.996745i	$-0.474312\pi$
$353$	18.4901	−	10.6753i	0.984129	−	0.568187i	0.903514	+	0.428558i	$0.140978\pi$
$354$		0			0
$355$		0			0
$356$	8.05842	−	13.9576i	0.427096	−	0.739751i
$357$		0			0
$358$	12.7692	−	7.37228i	0.674871	−	0.389637i
$359$	−17.4891			−0.923041			−0.461520	−	0.887130i	$-0.652696\pi$
$359$	−17.4891			−0.923041			−0.461520	+	0.887130i	$0.652696\pi$
$360$		0			0
$361$	−13.3723			−0.703804
$362$	−18.0665	+	10.4307i	−0.949555	+	0.548226i
$363$		0			0
$364$	−11.3723	+	19.6974i	−0.596070	+	1.03242i
$365$		0			0
$366$		0			0
$367$	13.8564	−	8.00000i	0.723299	−	0.417597i	−0.0926670	−	0.995697i	$-0.529539\pi$
$367$	13.8564	−	8.00000i	0.723299	−	0.417597i	0.815966	+	0.578101i	$0.196206\pi$
$368$		−	1.37228i		−	0.0715351i
$369$		0			0
$370$		0			0
$371$	−19.3723	−	33.5538i	−1.00576	−	1.74203i
$372$		0			0
$373$	13.4140	+	7.74456i	0.694549	+	0.400998i	0.805314	−	0.592848i	$-0.201997\pi$
$373$	13.4140	+	7.74456i	0.694549	+	0.400998i	−0.110765	+	0.993847i	$0.535330\pi$
$374$	3.55842	−	6.16337i	0.184002	−	0.318700i
$375$		0			0
$376$	−3.68614	−	6.38458i	−0.190098	−	0.329260i
$377$		−	9.25544i		−	0.476679i
$378$		0			0
$379$	−17.8614			−0.917479			−0.458739	−	0.888571i	$-0.651699\pi$
$379$	−17.8614			−0.917479			−0.458739	+	0.888571i	$0.651699\pi$
$380$		0			0
$381$		0			0
$382$	−15.1460	−	8.74456i	−0.774938	−	0.447411i
$383$	−19.8997	−	11.4891i	−1.01683	−	0.587067i	−0.103646	−	0.994614i	$-0.533051\pi$
$383$	−19.8997	−	11.4891i	−1.01683	−	0.587067i	−0.913184	+	0.407547i	$0.866384\pi$
$384$		0			0
$385$		0			0
$386$	21.1168			1.07482
$387$		0			0
$388$		−	8.37228i		−	0.425038i
$389$	2.31386	+	4.00772i	0.117317	+	0.203200i	0.918704	−	0.394947i	$-0.129237\pi$
$389$	2.31386	+	4.00772i	0.117317	+	0.203200i	−0.801386	+	0.598147i	$0.795904\pi$
$390$		0			0
$391$	1.11684	−	1.93443i	0.0564812	−	0.0978284i
$392$	3.78651	+	2.18614i	0.191247	+	0.110417i
$393$		0			0
$394$	2.74456	+	4.75372i	0.138269	+	0.239489i
$395$		0			0
$396$		0			0
$397$		−	22.7446i		−	1.14152i	−0.821118	−	0.570758i	$-0.806649\pi$
$397$		−	22.7446i		−	1.14152i	0.821118	−	0.570758i	$-0.193351\pi$
$398$	11.6819	−	6.74456i	0.585562	−	0.338074i
$399$		0			0
$400$		0			0
$401$	−0.558422	+	0.967215i	−0.0278863	+	0.0483004i	−0.879632	−	0.475655i	$-0.842211\pi$
$401$	−0.558422	+	0.967215i	−0.0278863	+	0.0483004i	0.851745	+	0.523956i	$0.175544\pi$
$402$		0			0
$403$	−27.7128	+	16.0000i	−1.38047	+	0.797017i
$404$	2.74456			0.136547
$405$		0			0
$406$	−4.62772			−0.229670
$407$	15.1460	−	8.74456i	0.750761	−	0.433452i
$408$		0			0
$409$	8.93070	−	15.4684i	0.441595	−	0.764865i	−0.556213	−	0.831040i	$-0.687746\pi$
$409$	8.93070	−	15.4684i	0.441595	−	0.764865i	0.997808	+	0.0661749i	$0.0210795\pi$
$410$		0			0
$411$		0			0
$412$	13.8564	−	8.00000i	0.682656	−	0.394132i
$413$		−	14.7446i		−	0.725532i
$414$		0			0
$415$		0			0
$416$	3.37228	+	5.84096i	0.165340	+	0.286377i
$417$		0			0
$418$	8.98266	+	5.18614i	0.439356	+	0.253662i
$419$	−12.8614	+	22.2766i	−0.628321	+	1.08828i	0.359568	+	0.933119i	$0.382924\pi$
$419$	−12.8614	+	22.2766i	−0.628321	+	1.08828i	−0.987889	+	0.155165i	$0.950409\pi$
$420$		0			0
$421$	−15.2337	−	26.3855i	−0.742445	−	1.28595i	−0.951379	−	0.308022i	$-0.900333\pi$
$421$	−15.2337	−	26.3855i	−0.742445	−	1.28595i	0.208935	−	0.977930i	$-0.433000\pi$
$422$			18.7446i			0.912471i
$423$		0			0
$424$	−11.4891			−0.557961
$425$		0			0
$426$		0			0
$427$	−23.7051	−	13.6861i	−1.14717	−	0.662319i
$428$	7.35180	+	4.24456i	0.355363	+	0.205169i
$429$		0			0
$430$		0			0
$431$	−8.23369			−0.396603			−0.198301	−	0.980141i	$-0.563542\pi$
$431$	−8.23369			−0.396603			−0.198301	+	0.980141i	$0.563542\pi$
$432$		0			0
$433$			6.37228i			0.306232i	0.988208	+	0.153116i	$0.0489309\pi$
$433$			6.37228i			0.306232i	−0.988208	+	0.153116i	$0.951069\pi$
$434$	8.00000	+	13.8564i	0.384012	+	0.665129i
$435$		0			0
$436$	−7.68614	+	13.3128i	−0.368099	+	0.637567i
$437$	2.81929	+	1.62772i	0.134865	+	0.0778643i
$438$		0			0
$439$	−9.11684	−	15.7908i	−0.435123	−	0.753656i	0.562182	−	0.827013i	$-0.309962\pi$
$439$	−9.11684	−	15.7908i	−0.435123	−	0.753656i	−0.997306	+	0.0733577i	$0.976629\pi$
$440$		0			0
$441$		0			0
$442$			10.9783i			0.522182i
$443$	3.04051	−	1.75544i	0.144459	−	0.0834033i	−0.426029	−	0.904710i	$-0.640088\pi$
$443$	3.04051	−	1.75544i	0.144459	−	0.0834033i	0.570487	+	0.821306i	$0.306754\pi$
$444$		0			0
$445$		0			0
$446$	−3.31386	+	5.73977i	−0.156916	+	0.271786i
$447$		0			0
$448$	2.92048	−	1.68614i	0.137980	−	0.0796627i
$449$	9.86141			0.465389			0.232694	−	0.972550i	$-0.425246\pi$
$449$	9.86141			0.465389			0.232694	+	0.972550i	$0.425246\pi$
$450$		0			0
$451$	13.1168			0.617648
$452$	2.81929	−	1.62772i	0.132608	−	0.0765614i
$453$		0			0
$454$	−9.55842	+	16.5557i	−0.448599	+	0.776996i
$455$		0			0
$456$		0			0
$457$	−11.1571	+	6.44158i	−0.521909	+	0.301324i	−0.737715	−	0.675112i	$-0.764095\pi$
$457$	−11.1571	+	6.44158i	−0.521909	+	0.301324i	0.215806	+	0.976436i	$0.430762\pi$
$458$			12.6277i			0.590055i
$459$		0			0
$460$		0			0
$461$	0.941578	+	1.63086i	0.0438537	+	0.0759568i	0.887119	−	0.461541i	$-0.152703\pi$
$461$	0.941578	+	1.63086i	0.0438537	+	0.0759568i	−0.843265	+	0.537497i	$0.819370\pi$
$462$		0			0
$463$	−17.3205	−	10.0000i	−0.804952	−	0.464739i	0.0402476	−	0.999190i	$-0.487185\pi$
$463$	−17.3205	−	10.0000i	−0.804952	−	0.464739i	−0.845200	+	0.534450i	$0.820519\pi$
$464$	−0.686141	+	1.18843i	−0.0318533	+	0.0551715i
$465$		0			0
$466$	3.55842	+	6.16337i	0.164841	+	0.285512i
$467$			43.1168i			1.99521i	0.0691713	+	0.997605i	$0.477964\pi$
$467$			43.1168i			1.99521i	−0.0691713	+	0.997605i	$0.522036\pi$
$468$		0			0
$469$	23.6060			1.09002
$470$		0			0
$471$		0			0
$472$	−3.78651	−	2.18614i	−0.174288	−	0.100625i
$473$	21.3094	+	12.3030i	0.979807	+	0.565692i
$474$		0			0
$475$		0			0
$476$	5.48913			0.251594
$477$		0			0
$478$			3.25544i			0.148900i
$479$	0.255437	+	0.442430i	0.0116712	+	0.0202152i	0.871802	−	0.489858i	$-0.162952\pi$
$479$	0.255437	+	0.442430i	0.0116712	+	0.0202152i	−0.860131	+	0.510074i	$0.829618\pi$
$480$		0			0
$481$	−13.4891	+	23.3639i	−0.615051	+	1.06530i
$482$	−10.8159	−	6.24456i	−0.492651	−	0.284432i
$483$		0			0
$484$	4.05842	+	7.02939i	0.184474	+	0.319518i
$485$		0			0
$486$		0			0
$487$			12.7446i			0.577511i	0.957403	+	0.288756i	$0.0932415\pi$
$487$			12.7446i			0.577511i	−0.957403	+	0.288756i	$0.906758\pi$
$488$	−7.02939	+	4.05842i	−0.318206	+	0.183716i
$489$		0			0
$490$		0			0
$491$	−18.3030	+	31.7017i	−0.826002	+	1.43068i	0.0751489	+	0.997172i	$0.476057\pi$
$491$	−18.3030	+	31.7017i	−0.826002	+	1.43068i	−0.901151	+	0.433505i	$0.857277\pi$
$492$		0			0
$493$	−1.93443	+	1.11684i	−0.0871224	+	0.0503001i
$494$	−16.0000			−0.719874
$495$		0			0
$496$	4.74456			0.213037
$497$	−17.5229	+	10.1168i	−0.786009	+	0.453802i
$498$		0			0
$499$	7.55842	−	13.0916i	0.338361	−	0.586059i	−0.645763	−	0.763538i	$-0.723461\pi$
$499$	7.55842	−	13.0916i	0.338361	−	0.586059i	0.984125	+	0.177479i	$0.0567940\pi$
$500$		0			0
$501$		0			0
$502$	−21.3094	+	12.3030i	−0.951085	+	0.549109i
$503$			6.86141i			0.305935i	0.988231	+	0.152967i	$0.0488830\pi$
$503$			6.86141i			0.305935i	−0.988231	+	0.152967i	$0.951117\pi$
$504$		0			0
$505$		0			0
$506$	3.00000	+	5.19615i	0.133366	+	0.230997i
$507$		0			0
$508$	7.02939	+	4.05842i	0.311879	+	0.180063i
$509$	21.1753	−	36.6766i	0.938577	−	1.62566i	0.170450	−	0.985366i	$-0.445478\pi$
$509$	21.1753	−	36.6766i	0.938577	−	1.62566i	0.768127	−	0.640297i	$-0.221189\pi$
$510$		0			0
$511$	−5.25544	−	9.10268i	−0.232487	−	0.402679i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	4.37228			0.192853
$515$		0			0
$516$		0			0
$517$	27.9152	+	16.1168i	1.22771	+	0.708818i
$518$	11.6819	+	6.74456i	0.513274	+	0.296339i
$519$		0			0
$520$		0			0
$521$	6.76631			0.296438			0.148219	−	0.988955i	$-0.452646\pi$
$521$	6.76631			0.296438			0.148219	+	0.988955i	$0.452646\pi$
$522$		0			0
$523$			6.11684i			0.267471i	0.991017	+	0.133735i	$0.0426972\pi$
$523$			6.11684i			0.267471i	−0.991017	+	0.133735i	$0.957303\pi$
$524$	1.37228	+	2.37686i	0.0599484	+	0.103834i
$525$		0			0
$526$	−8.74456	+	15.1460i	−0.381281	+	0.660398i
$527$	6.68815	+	3.86141i	0.291340	+	0.168206i
$528$		0			0
$529$	−10.5584	−	18.2877i	−0.459062	−	0.795118i
$530$		0			0
$531$		0			0
$532$			8.00000i			0.346844i
$533$	−17.5229	+	10.1168i	−0.759001	+	0.438209i
$534$		0			0
$535$		0			0
$536$	3.50000	−	6.06218i	0.151177	−	0.261846i
$537$		0			0
$538$	1.18843	−	0.686141i	0.0512369	−	0.0295816i
$539$	−19.1168			−0.823421
$540$		0			0
$541$	27.3723			1.17683			0.588413	−	0.808560i	$-0.299753\pi$
$541$	27.3723			1.17683			0.588413	+	0.808560i	$0.299753\pi$
$542$	−6.92820	+	4.00000i	−0.297592	+	0.171815i
$543$		0			0
$544$	0.813859	−	1.40965i	0.0348939	−	0.0604381i
$545$		0			0
$546$		0			0
$547$	25.5195	−	14.7337i	1.09113	−	0.629967i	0.157256	−	0.987558i	$-0.449735\pi$
$547$	25.5195	−	14.7337i	1.09113	−	0.629967i	0.933878	+	0.357591i	$0.116402\pi$
$548$			19.1168i			0.816631i
$549$		0			0
$550$		0			0
$551$	−1.62772	−	2.81929i	−0.0693431	−	0.120106i
$552$		0			0
$553$	−5.84096	−	3.37228i	−0.248383	−	0.143404i
$554$	8.37228	−	14.5012i	0.355704	−	0.616098i
$555$		0			0
$556$	−0.441578	−	0.764836i	−0.0187271	−	0.0324363i
$557$		−	44.2337i		−	1.87424i	−0.349005	−	0.937121i	$-0.613480\pi$
$557$		−	44.2337i		−	1.87424i	0.349005	−	0.937121i	$-0.386520\pi$
$558$		0			0
$559$	−37.9565			−1.60539
$560$		0			0
$561$		0			0
$562$	1.18843	+	0.686141i	0.0501309	+	0.0289431i
$563$	−35.2670	−	20.3614i	−1.48633	−	0.858131i	−0.486448	−	0.873710i	$-0.661708\pi$
$563$	−35.2670	−	20.3614i	−1.48633	−	0.858131i	−0.999879	+	0.0155787i	$0.995041\pi$
$564$		0			0
$565$		0			0
$566$	−3.13859			−0.131925
$567$		0			0
$568$			6.00000i			0.251754i
$569$	15.3030	+	26.5055i	0.641534	+	1.11117i	0.985090	+	0.172038i	$0.0550352\pi$
$569$	15.3030	+	26.5055i	0.641534	+	1.11117i	−0.343556	+	0.939132i	$0.611631\pi$
$570$		0			0
$571$	−4.30298	+	7.45299i	−0.180074	+	0.311898i	−0.941906	−	0.335878i	$-0.890967\pi$
$571$	−4.30298	+	7.45299i	−0.180074	+	0.311898i	0.761831	+	0.647775i	$0.224300\pi$
$572$	−25.5383	−	14.7446i	−1.06781	−	0.616501i
$573$		0			0
$574$	5.05842	+	8.76144i	0.211134	+	0.365696i
$575$		0			0
$576$		0			0
$577$			41.1168i			1.71172i	0.517210	+	0.855858i	$0.326970\pi$
$577$			41.1168i			1.71172i	−0.517210	+	0.855858i	$0.673030\pi$
$578$	−12.4279	+	7.17527i	−0.516934	+	0.298452i
$579$		0			0
$580$		0			0
$581$	12.4307	−	21.5306i	0.515712	−	0.893240i
$582$		0			0
$583$	43.5036	−	25.1168i	1.80174	−	1.04023i
$584$	−3.11684			−0.128976
$585$		0			0
$586$	−26.2337			−1.08370
$587$	23.3827	−	13.5000i	0.965107	−	0.557205i	0.0673658	−	0.997728i	$-0.478541\pi$
$587$	23.3827	−	13.5000i	0.965107	−	0.557205i	0.897741	+	0.440524i	$0.145207\pi$
$588$		0			0
$589$	−5.62772	+	9.74749i	−0.231886	+	0.401639i
$590$		0			0
$591$		0			0
$592$	3.46410	−	2.00000i	0.142374	−	0.0821995i
$593$			19.7228i			0.809919i	0.914335	+	0.404959i	$0.132714\pi$
$593$			19.7228i			0.809919i	−0.914335	+	0.404959i	$0.867286\pi$
$594$		0			0
$595$		0			0
$596$	0.941578	+	1.63086i	0.0385685	+	0.0668027i
$597$		0			0
$598$	−8.01544	−	4.62772i	−0.327776	−	0.189241i
$599$	1.88316	−	3.26172i	0.0769437	−	0.133270i	−0.824986	−	0.565153i	$-0.808817\pi$
$599$	1.88316	−	3.26172i	0.0769437	−	0.133270i	0.901930	+	0.431883i	$0.142151\pi$
$600$		0			0
$601$	0.930703	+	1.61203i	0.0379642	+	0.0657559i	0.884383	−	0.466762i	$-0.154579\pi$
$601$	0.930703	+	1.61203i	0.0379642	+	0.0657559i	−0.846419	+	0.532517i	$0.821246\pi$
$602$			18.9783i			0.773496i
$603$		0			0
$604$	10.0000			0.406894
$605$		0			0
$606$		0			0
$607$	15.6896	+	9.05842i	0.636823	+	0.367670i	0.783390	−	0.621531i	$-0.213489\pi$
$607$	15.6896	+	9.05842i	0.636823	+	0.367670i	−0.146567	+	0.989201i	$0.546822\pi$
$608$	2.05446	+	1.18614i	0.0833192	+	0.0481044i
$609$		0			0
$610$		0			0
$611$	−49.7228			−2.01157
$612$		0			0
$613$			34.2337i			1.38269i	0.722527	+	0.691343i	$0.242981\pi$
$613$			34.2337i			1.38269i	−0.722527	+	0.691343i	$0.757019\pi$
$614$	0.616844	+	1.06841i	0.0248938	+	0.0431173i
$615$		0			0
$616$	−7.37228	+	12.7692i	−0.297038	+	0.514484i
$617$	4.22894	+	2.44158i	0.170251	+	0.0982942i	0.582704	−	0.812684i	$-0.301995\pi$
$617$	4.22894	+	2.44158i	0.170251	+	0.0982942i	−0.412453	+	0.910979i	$0.635328\pi$
$618$		0			0
$619$	−10.4416	−	18.0853i	−0.419682	−	0.726911i	0.576225	−	0.817291i	$-0.304525\pi$
$619$	−10.4416	−	18.0853i	−0.419682	−	0.726911i	−0.995907	+	0.0903798i	$0.971192\pi$
$620$		0			0
$621$		0			0
$622$		−	20.7446i		−	0.831781i
$623$	−47.0689	+	27.1753i	−1.88578	+	1.08875i
$624$		0			0
$625$		0			0
$626$	−1.81386	+	3.14170i	−0.0724964	+	0.125567i
$627$		0			0
$628$	−5.84096	+	3.37228i	−0.233080	+	0.134569i
$629$	6.51087			0.259606
$630$		0			0
$631$	−23.7228			−0.944390			−0.472195	−	0.881494i	$-0.656538\pi$
$631$	−23.7228			−0.944390			−0.472195	+	0.881494i	$0.656538\pi$
$632$	−1.73205	+	1.00000i	−0.0688973	+	0.0397779i
$633$		0			0
$634$	−1.37228	+	2.37686i	−0.0545003	+	0.0943972i
$635$		0			0
$636$		0			0
$637$	25.5383	−	14.7446i	1.01187	−	0.584201i
$638$		−	6.00000i		−	0.237542i
$639$		0			0
$640$		0			0
$641$	−19.5000	−	33.7750i	−0.770204	−	1.33403i	−0.937451	−	0.348117i	$-0.886821\pi$
$641$	−19.5000	−	33.7750i	−0.770204	−	1.33403i	0.167247	−	0.985915i	$-0.446512\pi$
$642$		0			0
$643$	−9.52628	−	5.50000i	−0.375680	−	0.216899i	0.300257	−	0.953858i	$-0.402928\pi$
$643$	−9.52628	−	5.50000i	−0.375680	−	0.216899i	−0.675937	+	0.736959i	$0.736261\pi$
$644$	−2.31386	+	4.00772i	−0.0911788	+	0.157926i
$645$		0			0
$646$	1.93070	+	3.34408i	0.0759625	+	0.131571i
$647$		−	39.0951i		−	1.53699i	−0.639858	−	0.768493i	$-0.721007\pi$
$647$		−	39.0951i		−	1.53699i	0.639858	−	0.768493i	$-0.278993\pi$
$648$		0			0
$649$	19.1168			0.750402
$650$		0			0
$651$		0			0
$652$	−18.6101	−	10.7446i	−0.728829	−	0.420790i
$653$	17.0805	+	9.86141i	0.668410	+	0.385907i	0.795474	−	0.605988i	$-0.207222\pi$
$653$	17.0805	+	9.86141i	0.668410	+	0.385907i	−0.127064	+	0.991895i	$0.540555\pi$
$654$		0			0
$655$		0			0
$656$	3.00000			0.117130
$657$		0			0
$658$			24.8614i			0.969199i
$659$	−8.74456	−	15.1460i	−0.340640	−	0.590005i	0.643912	−	0.765100i	$-0.277310\pi$
$659$	−8.74456	−	15.1460i	−0.340640	−	0.590005i	−0.984552	+	0.175094i	$0.943977\pi$
$660$		0			0
$661$	6.11684	−	10.5947i	0.237918	−	0.412085i	−0.722199	−	0.691685i	$-0.756868\pi$
$661$	6.11684	−	10.5947i	0.237918	−	0.412085i	0.960117	+	0.279600i	$0.0902018\pi$
$662$	14.0588	+	8.11684i	0.546410	+	0.315470i
$663$		0			0
$664$	−3.68614	−	6.38458i	−0.143050	−	0.247770i
$665$		0			0
$666$		0			0
$667$		−	1.88316i		−	0.0729161i
$668$	−11.5807	+	6.68614i	−0.448072	+	0.258695i
$669$		0			0
$670$		0			0
$671$	17.7446	−	30.7345i	0.685021	−	1.18649i
$672$		0			0
$673$	−8.66025	+	5.00000i	−0.333828	+	0.192736i	−0.657539	−	0.753420i	$-0.728403\pi$
$673$	−8.66025	+	5.00000i	−0.333828	+	0.192736i	0.323711	+	0.946156i	$0.395069\pi$
$674$	2.37228			0.0913769
$675$		0			0
$676$	32.4891			1.24958
$677$	11.8843	−	6.86141i	0.456751	−	0.263705i	−0.253926	−	0.967224i	$-0.581722\pi$
$677$	11.8843	−	6.86141i	0.456751	−	0.263705i	0.710677	+	0.703518i	$0.248389\pi$
$678$		0			0
$679$	−14.1168	+	24.4511i	−0.541755	+	0.938347i
$680$		0			0
$681$		0			0
$682$	−17.9653	+	10.3723i	−0.687928	+	0.397175i
$683$			30.0951i			1.15156i	0.817606	+	0.575778i	$0.195301\pi$
$683$			30.0951i			1.15156i	−0.817606	+	0.575778i	$0.804699\pi$
$684$		0			0
$685$		0			0
$686$	4.43070	+	7.67420i	0.169165	+	0.293002i
$687$		0			0
$688$	4.87375	+	2.81386i	0.185810	+	0.107277i
$689$	−38.7446	+	67.1076i	−1.47605	+	2.55659i
$690$		0			0
$691$	18.1168	+	31.3793i	0.689197	+	1.19372i	0.972098	+	0.234575i	$0.0753700\pi$
$691$	18.1168	+	31.3793i	0.689197	+	1.19372i	−0.282901	+	0.959149i	$0.591297\pi$
$692$			20.7446i			0.788590i
$693$		0			0
$694$	−4.88316			−0.185362
$695$		0			0
$696$		0			0
$697$	4.22894	+	2.44158i	0.160182	+	0.0924814i
$698$	−15.6896	−	9.05842i	−0.593862	−	0.342866i
$699$		0			0
$700$		0			0
$701$	−42.8614			−1.61885			−0.809426	−	0.587221i	$-0.800222\pi$
$701$	−42.8614			−1.61885			−0.809426	+	0.587221i	$0.800222\pi$
$702$		0			0
$703$			9.48913i			0.357889i
$704$	2.18614	+	3.78651i	0.0823933	+	0.142709i
$705$		0			0
$706$	−10.6753	+	18.4901i	−0.401769	+	0.695884i
$707$	−8.01544	−	4.62772i	−0.301452	−	0.174043i
$708$		0			0
$709$	1.43070	+	2.47805i	0.0537312	+	0.0930652i	0.891640	−	0.452745i	$-0.149555\pi$
$709$	1.43070	+	2.47805i	0.0537312	+	0.0930652i	−0.837909	+	0.545810i	$0.816222\pi$
$710$		0			0
$711$		0			0
$712$			16.1168i			0.604004i
$713$	−5.63858	+	3.25544i	−0.211167	+	0.121917i
$714$		0			0
$715$		0			0
$716$	−7.37228	+	12.7692i	−0.275515	+	0.477206i
$717$		0			0
$718$	15.1460	−	8.74456i	0.565245	−	0.326344i
$719$	−3.76631			−0.140460			−0.0702299	−	0.997531i	$-0.522373\pi$
$719$	−3.76631			−0.140460			−0.0702299	+	0.997531i	$0.522373\pi$
$720$		0			0
$721$	−53.9565			−2.00945
$722$	11.5807	−	6.68614i	0.430990	−	0.248832i
$723$		0			0
$724$	10.4307	−	18.0665i	0.387654	−	0.671436i
$725$		0			0
$726$		0			0
$727$	−15.6896	+	9.05842i	−0.581897	+	0.335958i	−0.761887	−	0.647710i	$-0.775727\pi$
$727$	−15.6896	+	9.05842i	−0.581897	+	0.335958i	0.179990	+	0.983668i	$0.442393\pi$
$728$		−	22.7446i		−	0.842970i
$729$		0			0
$730$		0			0
$731$	4.58017	+	7.93309i	0.169404	+	0.293416i
$732$		0			0
$733$	0.202380	+	0.116844i	0.00747506	+	0.00431573i	0.503733	−	0.863859i	$-0.331960\pi$
$733$	0.202380	+	0.116844i	0.00747506	+	0.00431573i	−0.496258	+	0.868175i	$0.665293\pi$
$734$	−8.00000	+	13.8564i	−0.295285	+	0.511449i
$735$		0			0
$736$	0.686141	+	1.18843i	0.0252915	+	0.0438061i
$737$			30.6060i			1.12739i
$738$		0			0
$739$	41.1168			1.51251			0.756254	−	0.654278i	$-0.227028\pi$
$739$	41.1168			1.51251			0.756254	+	0.654278i	$0.227028\pi$
$740$		0			0
$741$		0			0
$742$	33.5538	+	19.3723i	1.23180	+	0.711179i
$743$	6.82701	+	3.94158i	0.250459	+	0.144602i	0.619974	−	0.784622i	$-0.287143\pi$
$743$	6.82701	+	3.94158i	0.250459	+	0.144602i	−0.369516	+	0.929225i	$0.620476\pi$
$744$		0			0
$745$		0			0
$746$	−15.4891			−0.567097
$747$		0			0
$748$			7.11684i			0.260218i
$749$	−14.3139	−	24.7923i	−0.523017	−	0.905892i
$750$		0			0
$751$	−8.11684	+	14.0588i	−0.296188	+	0.513012i	−0.975261	−	0.221059i	$-0.929049\pi$
$751$	−8.11684	+	14.0588i	−0.296188	+	0.513012i	0.679073	+	0.734071i	$0.262382\pi$
$752$	6.38458	+	3.68614i	0.232822	+	0.134420i
$753$		0			0
$754$	4.62772	+	8.01544i	0.168532	+	0.291905i
$755$		0			0
$756$		0			0
$757$			10.0000i			0.363456i	0.983349	+	0.181728i	$0.0581691\pi$
$757$			10.0000i			0.363456i	−0.983349	+	0.181728i	$0.941831\pi$
$758$	15.4684	−	8.93070i	0.561839	−	0.324378i
$759$		0			0
$760$		0			0
$761$	−25.5475	+	44.2496i	−0.926098	+	1.60405i	−0.136312	+	0.990666i	$0.543525\pi$
$761$	−25.5475	+	44.2496i	−0.926098	+	1.60405i	−0.789786	+	0.613383i	$0.789808\pi$
$762$		0			0
$763$	44.8945	−	25.9198i	1.62529	−	0.938361i
$764$	17.4891			0.632734
$765$		0			0
$766$	22.9783			0.830238
$767$	−25.5383	+	14.7446i	−0.922136	+	0.532395i
$768$		0			0
$769$	−23.4307	+	40.5832i	−0.844933	+	1.46347i	0.0407468	+	0.999170i	$0.487026\pi$
$769$	−23.4307	+	40.5832i	−0.844933	+	1.46347i	−0.885680	+	0.464297i	$0.846307\pi$
$770$		0			0
$771$		0			0
$772$	−18.2877	+	10.5584i	−0.658190	+	0.380006i
$773$		−	3.25544i		−	0.117090i	−0.998285	−	0.0585450i	$-0.981354\pi$
$773$		−	3.25544i		−	0.117090i	0.998285	−	0.0585450i	$-0.0186461\pi$
$774$		0			0
$775$		0			0
$776$	4.18614	+	7.25061i	0.150274	+	0.260282i
$777$		0			0
$778$	−4.00772	−	2.31386i	−0.143684	−	0.0829559i
$779$	−3.55842	+	6.16337i	−0.127494	+	0.220826i
$780$		0			0
$781$	−13.1168	−	22.7190i	−0.469358	−	0.812951i
$782$			2.23369i			0.0798765i
$783$		0			0
$784$	−4.37228			−0.156153
$785$		0			0
$786$		0			0
$787$	−24.2487	−	14.0000i	−0.864373	−	0.499046i	0.00110111	−	0.999999i	$-0.499650\pi$
$787$	−24.2487	−	14.0000i	−0.864373	−	0.499046i	−0.865474	+	0.500953i	$0.832983\pi$
$788$	−4.75372	−	2.74456i	−0.169344	−	0.0977710i
$789$		0			0
$790$		0			0
$791$	−10.9783			−0.390342
$792$		0			0
$793$			54.7446i			1.94404i
$794$	11.3723	+	19.6974i	0.403587	+	0.699033i
$795$		0			0
$796$	−6.74456	+	11.6819i	−0.239055	+	0.414055i
$797$	−12.7692	−	7.37228i	−0.452307	−	0.261140i	0.256497	−	0.966545i	$-0.417432\pi$
$797$	−12.7692	−	7.37228i	−0.452307	−	0.261140i	−0.708804	+	0.705405i	$0.750765\pi$
$798$		0			0
$799$	6.00000	+	10.3923i	0.212265	+	0.367653i
$800$		0			0
$801$		0			0
$802$		−	1.11684i		−	0.0394371i
$803$	11.8020	−	6.81386i	0.416482	−	0.240456i
$804$		0			0
$805$		0			0
$806$	16.0000	−	27.7128i	0.563576	−	0.976142i
$807$		0			0
$808$	−2.37686	+	1.37228i	−0.0836177	+	0.0482767i
$809$	39.3505			1.38349			0.691746	−	0.722141i	$-0.256842\pi$
$809$	39.3505			1.38349			0.691746	+	0.722141i	$0.256842\pi$
$810$		0			0
$811$	3.62772			0.127386			0.0636932	−	0.997970i	$-0.479712\pi$
$811$	3.62772			0.127386			0.0636932	+	0.997970i	$0.479712\pi$
$812$	4.00772	−	2.31386i	0.140643	−	0.0812005i
$813$		0			0
$814$	−8.74456	+	15.1460i	−0.306497	+	0.530868i
$815$		0			0
$816$		0			0
$817$	−11.5619	+	6.67527i	−0.404500	+	0.233538i
$818$			17.8614i			0.624509i
$819$		0			0
$820$		0			0
$821$	−11.9198	−	20.6457i	−0.416005	−	0.720542i	0.579528	−	0.814952i	$-0.303237\pi$
$821$	−11.9198	−	20.6457i	−0.416005	−	0.720542i	−0.995533	+	0.0944104i	$0.969903\pi$
$822$		0			0
$823$	21.7330	+	12.5475i	0.757564	+	0.437380i	0.828421	−	0.560107i	$-0.189240\pi$
$823$	21.7330	+	12.5475i	0.757564	+	0.437380i	−0.0708562	+	0.997487i	$0.522573\pi$
$824$	−8.00000	+	13.8564i	−0.278693	+	0.482711i
$825$		0			0
$826$	7.37228	+	12.7692i	0.256514	+	0.444296i
$827$			36.8614i			1.28180i	0.767626	+	0.640898i	$0.221438\pi$
$827$			36.8614i			1.28180i	−0.767626	+	0.640898i	$0.778562\pi$
$828$		0			0
$829$	50.1168			1.74063			0.870315	−	0.492496i	$-0.163915\pi$
$829$	50.1168			1.74063			0.870315	+	0.492496i	$0.163915\pi$
$830$		0			0
$831$		0			0
$832$	−5.84096	−	3.37228i	−0.202499	−	0.116913i
$833$	−6.16337	−	3.55842i	−0.213548	−	0.123292i
$834$		0			0
$835$		0			0
$836$	−10.3723			−0.358733
$837$		0			0
$838$		−	25.7228i		−	0.888580i
$839$	−4.88316	−	8.45787i	−0.168585	−	0.291998i	0.769337	−	0.638843i	$-0.220587\pi$
$839$	−4.88316	−	8.45787i	−0.168585	−	0.291998i	−0.937923	+	0.346844i	$0.887253\pi$
$840$		0			0
$841$	13.5584	−	23.4839i	0.467532	−	0.809789i
$842$	26.3855	+	15.2337i	0.909305	+	0.524988i
$843$		0			0
$844$	−9.37228	−	16.2333i	−0.322607	−	0.558772i
$845$		0			0
$846$		0			0
$847$		−	27.3723i		−	0.940523i
$848$	9.94987	−	5.74456i	0.341680	−	0.197269i
$849$		0			0
$850$		0			0
$851$	−2.74456	+	4.75372i	−0.0940824	+	0.162955i
$852$		0			0
$853$	−31.3793	+	18.1168i	−1.07441	+	0.620309i	−0.929382	−	0.369119i	$-0.879659\pi$
$853$	−31.3793	+	18.1168i	−1.07441	+	0.620309i	−0.145024	+	0.989428i	$0.546326\pi$
$854$	27.3723			0.936660
$855$		0			0
$856$	−8.48913			−0.290152
$857$	0.442430	−	0.255437i	0.0151131	−	0.00872557i	−0.492424	−	0.870355i	$-0.663889\pi$
$857$	0.442430	−	0.255437i	0.0151131	−	0.00872557i	0.507538	+	0.861630i	$0.330556\pi$
$858$		0			0
$859$	−8.55842	+	14.8236i	−0.292010	+	0.505775i	−0.974285	−	0.225320i	$-0.927657\pi$
$859$	−8.55842	+	14.8236i	−0.292010	+	0.505775i	0.682275	+	0.731095i	$0.260991\pi$
$860$		0			0
$861$		0			0
$862$	7.13058	−	4.11684i	0.242869	−	0.140220i
$863$			2.39403i			0.0814938i	0.999170	+	0.0407469i	$0.0129737\pi$
$863$			2.39403i			0.0814938i	−0.999170	+	0.0407469i	$0.987026\pi$
$864$		0			0
$865$		0			0
$866$	−3.18614	−	5.51856i	−0.108269	−	0.187528i
$867$		0			0
$868$	−13.8564	−	8.00000i	−0.470317	−	0.271538i
$869$	4.37228	−	7.57301i	0.148319	−	0.256897i
$870$		0			0
$871$	−23.6060	−	40.8867i	−0.799858	−	1.38539i
$872$		−	15.3723i		−	0.520571i
$873$		0			0
$874$	−3.25544			−0.110117
$875$		0			0
$876$		0			0
$877$	31.1392	+	17.9783i	1.05150	+	0.607082i	0.923068	−	0.384636i	$-0.125673\pi$
$877$	31.1392	+	17.9783i	1.05150	+	0.607082i	0.128429	+	0.991719i	$0.459006\pi$
$878$	15.7908	+	9.11684i	0.532915	+	0.307679i
$879$		0			0
$880$		0			0
$881$	24.3505			0.820390			0.410195	−	0.911998i	$-0.365461\pi$
$881$	24.3505			0.820390			0.410195	+	0.911998i	$0.365461\pi$
$882$		0			0
$883$		−	44.7228i		−	1.50504i	−0.658568	−	0.752521i	$-0.728837\pi$
$883$		−	44.7228i		−	1.50504i	0.658568	−	0.752521i	$-0.271163\pi$
$884$	−5.48913	−	9.50744i	−0.184619	−	0.319770i
$885$		0			0
$886$	−1.75544	+	3.04051i	−0.0589751	+	0.102148i
$887$	−17.0805	−	9.86141i	−0.573506	−	0.331114i	0.185043	−	0.982730i	$-0.440758\pi$
$887$	−17.0805	−	9.86141i	−0.573506	−	0.331114i	−0.758548	+	0.651617i	$0.774091\pi$
$888$		0			0
$889$	−13.6861	−	23.7051i	−0.459018	−	0.795043i
$890$		0			0
$891$		0			0
$892$		−	6.62772i		−	0.221912i
$893$	−15.1460	+	8.74456i	−0.506842	+	0.292626i
$894$		0			0
$895$		0			0
$896$	−1.68614	+	2.92048i	−0.0563300	+	0.0975664i
$897$		0			0
$898$	−8.54023	+	4.93070i	−0.284991	+	0.164540i
$899$	6.51087			0.217150
$900$		0			0
$901$	18.7011			0.623023
$902$	−11.3595	+	6.55842i	−0.378231	+	0.218372i
$903$		0			0
$904$	−1.62772	+	2.81929i	−0.0541371	+	0.0937682i
$905$		0			0
$906$		0			0
$907$	6.06218	−	3.50000i	0.201291	−	0.116216i	−0.395966	−	0.918265i	$-0.629590\pi$
$907$	6.06218	−	3.50000i	0.201291	−	0.116216i	0.597258	+	0.802049i	$0.296257\pi$
$908$		−	19.1168i		−	0.634415i
$909$		0			0
$910$		0			0
$911$	−21.0000	−	36.3731i	−0.695761	−	1.20509i	−0.969923	−	0.243410i	$-0.921734\pi$
$911$	−21.0000	−	36.3731i	−0.695761	−	1.20509i	0.274162	−	0.961683i	$-0.411599\pi$
$912$		0			0
$913$	27.9152	+	16.1168i	0.923858	+	0.533390i
$914$	6.44158	−	11.1571i	0.213068	−	0.369045i
$915$		0			0
$916$	−6.31386	−	10.9359i	−0.208616	−	0.361333i
$917$		−	9.25544i		−	0.305641i
$918$		0			0
$919$	26.4674			0.873078			0.436539	−	0.899685i	$-0.356204\pi$
$919$	26.4674			0.873078			0.436539	+	0.899685i	$0.356204\pi$
$920$		0			0
$921$		0			0
$922$	−1.63086	−	0.941578i	−0.0537095	−	0.0310092i
$923$	35.0458	+	20.2337i	1.15355	+	0.666000i
$924$		0			0
$925$		0			0
$926$	20.0000			0.657241
$927$		0			0
$928$		−	1.37228i		−	0.0450473i
$929$	−25.9783	−	44.9956i	−0.852319	−	1.47626i	−0.879110	−	0.476618i	$-0.841862\pi$
$929$	−25.9783	−	44.9956i	−0.852319	−	1.47626i	0.0267916	−	0.999641i	$-0.491471\pi$
$930$		0			0
$931$	5.18614	−	8.98266i	0.169969	−	0.294395i
$932$	−6.16337	−	3.55842i	−0.201888	−	0.116560i
$933$		0			0
$934$	−21.5584	−	37.3403i	−0.705413	−	1.22181i
$935$		0			0
$936$		0			0
$937$		−	39.7228i		−	1.29769i	−0.760922	−	0.648844i	$-0.775253\pi$
$937$		−	39.7228i		−	1.29769i	0.760922	−	0.648844i	$-0.224747\pi$
$938$	−20.4434	+	11.8030i	−0.667500	+	0.385381i
$939$		0			0
$940$		0			0
$941$	21.6861	−	37.5615i	0.706948	−	1.22447i	−0.259036	−	0.965868i	$-0.583405\pi$
$941$	21.6861	−	37.5615i	0.706948	−	1.22447i	0.965984	−	0.258602i	$-0.0832619\pi$
$942$		0			0
$943$	−3.56529	+	2.05842i	−0.116102	+	0.0670314i
$944$	4.37228			0.142306
$945$		0			0
$946$	−24.6060			−0.800009
$947$	−30.0708	+	17.3614i	−0.977171	+	0.564170i	−0.901415	−	0.432956i	$-0.857470\pi$
$947$	−30.0708	+	17.3614i	−0.977171	+	0.564170i	−0.0757561	+	0.997126i	$0.524137\pi$
$948$		0			0
$949$	−10.5109	+	18.2054i	−0.341197	+	0.590971i
$950$		0			0
$951$		0			0
$952$	−4.75372	+	2.74456i	−0.154069	+	0.0889518i
$953$		−	2.13859i		−	0.0692758i	−0.999400	−	0.0346379i	$-0.988972\pi$
$953$		−	2.13859i		−	0.0692758i	0.999400	−	0.0346379i	$-0.0110278\pi$
$954$		0			0
$955$		0			0
$956$	−1.62772	−	2.81929i	−0.0526442	−	0.0911824i
$957$		0			0
$958$	−0.442430	−	0.255437i	−0.0142943	−	0.00825281i
$959$	32.2337	−	55.8304i	1.04088	−	1.80286i
$960$		0			0
$961$	4.24456	+	7.35180i	0.136921	+	0.237155i
$962$		−	26.9783i		−	0.869814i
$963$		0			0
$964$	12.4891			0.402248
$965$		0			0
$966$		0			0
$967$	31.2781	+	18.0584i	1.00584	+	0.580720i	0.909970	−	0.414675i	$-0.136105\pi$
$967$	31.2781	+	18.0584i	1.00584	+	0.580720i	0.0958662	+	0.995394i	$0.469438\pi$
$968$	−7.02939	−	4.05842i	−0.225933	−	0.130443i
$969$		0			0
$970$		0			0
$971$	22.9783			0.737407			0.368704	−	0.929547i	$-0.379802\pi$
$971$	22.9783			0.737407			0.368704	+	0.929547i	$0.379802\pi$
$972$		0			0
$973$			2.97825i			0.0954783i
$974$	−6.37228	−	11.0371i	−0.204181	−	0.353652i
$975$		0			0
$976$	4.05842	−	7.02939i	0.129907	−	0.225005i
$977$	19.8174	+	11.4416i	0.634015	+	0.366049i	0.782305	−	0.622895i	$-0.214044\pi$
$977$	19.8174	+	11.4416i	0.634015	+	0.366049i	−0.148291	+	0.988944i	$0.547377\pi$
$978$		0			0
$979$	−35.2337	−	61.0265i	−1.12607	−	1.95042i
$980$		0			0
$981$		0			0
$982$		−	36.6060i		−	1.16814i
$983$	11.1383	−	6.43070i	0.355257	−	0.205108i	−0.311741	−	0.950167i	$-0.600912\pi$
$983$	11.1383	−	6.43070i	0.355257	−	0.205108i	0.666998	+	0.745059i	$0.267579\pi$
$984$		0			0
$985$		0			0
$986$	1.11684	−	1.93443i	0.0355676	−	0.0616048i
$987$		0			0
$988$	13.8564	−	8.00000i	0.440831	−	0.254514i
$989$	−7.72281			−0.245571
$990$		0			0
$991$	16.2337			0.515680			0.257840	−	0.966188i	$-0.416989\pi$
$991$	16.2337			0.515680			0.257840	+	0.966188i	$0.416989\pi$
$992$	−4.10891	+	2.37228i	−0.130458	+	0.0753200i
$993$		0			0
$994$	10.1168	−	17.5229i	0.320887	−	0.555792i
$995$		0			0
$996$		0			0
$997$	−12.1244	+	7.00000i	−0.383982	+	0.221692i	−0.679549	−	0.733630i	$-0.737825\pi$
$997$	−12.1244	+	7.00000i	−0.383982	+	0.221692i	0.295567	+	0.955322i	$0.404491\pi$
$998$			15.1168i			0.478515i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1350.2.j.f.199.1		8
3.2	odd	2		450.2.j.g.49.3		8
5.2	odd	4		270.2.e.c.91.1		4
5.3	odd	4		1350.2.e.l.901.2		4
5.4	even	2	inner	1350.2.j.f.199.4		8
9.2	odd	6		450.2.j.g.349.2		8
9.4	even	3		4050.2.c.ba.649.1		4
9.5	odd	6		4050.2.c.v.649.3		4
9.7	even	3	inner	1350.2.j.f.1099.4		8
15.2	even	4		90.2.e.c.31.2	✓	4
15.8	even	4		450.2.e.j.301.1		4
15.14	odd	2		450.2.j.g.49.2		8
20.7	even	4		2160.2.q.f.1441.2		4
45.2	even	12		90.2.e.c.61.1	yes	4
45.4	even	6		4050.2.c.ba.649.4		4
45.7	odd	12		270.2.e.c.181.1		4
45.13	odd	12		4050.2.a.bo.1.1		2
45.14	odd	6		4050.2.c.v.649.2		4
45.22	odd	12		810.2.a.k.1.2		2
45.23	even	12		4050.2.a.bw.1.1		2
45.29	odd	6		450.2.j.g.349.3		8
45.32	even	12		810.2.a.i.1.2		2
45.34	even	6	inner	1350.2.j.f.1099.1		8
45.38	even	12		450.2.e.j.151.2		4
45.43	odd	12		1350.2.e.l.451.2		4
60.47	odd	4		720.2.q.f.481.1		4
180.7	even	12		2160.2.q.f.721.2		4
180.47	odd	12		720.2.q.f.241.2		4
180.67	even	12		6480.2.a.bn.1.1		2
180.167	odd	12		6480.2.a.be.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.e.c.31.2	✓	4	15.2	even	4
90.2.e.c.61.1	yes	4	45.2	even	12
270.2.e.c.91.1		4	5.2	odd	4
270.2.e.c.181.1		4	45.7	odd	12
450.2.e.j.151.2		4	45.38	even	12
450.2.e.j.301.1		4	15.8	even	4
450.2.j.g.49.2		8	15.14	odd	2
450.2.j.g.49.3		8	3.2	odd	2
450.2.j.g.349.2		8	9.2	odd	6
450.2.j.g.349.3		8	45.29	odd	6
720.2.q.f.241.2		4	180.47	odd	12
720.2.q.f.481.1		4	60.47	odd	4
810.2.a.i.1.2		2	45.32	even	12
810.2.a.k.1.2		2	45.22	odd	12
1350.2.e.l.451.2		4	45.43	odd	12
1350.2.e.l.901.2		4	5.3	odd	4
1350.2.j.f.199.1		8	1.1	even	1	trivial
1350.2.j.f.199.4		8	5.4	even	2	inner
1350.2.j.f.1099.1		8	45.34	even	6	inner
1350.2.j.f.1099.4		8	9.7	even	3	inner
2160.2.q.f.721.2		4	180.7	even	12
2160.2.q.f.1441.2		4	20.7	even	4
4050.2.a.bo.1.1		2	45.13	odd	12
4050.2.a.bw.1.1		2	45.23	even	12
4050.2.c.v.649.2		4	45.14	odd	6
4050.2.c.v.649.3		4	9.5	odd	6
4050.2.c.ba.649.1		4	9.4	even	3
4050.2.c.ba.649.4		4	45.4	even	6
6480.2.a.be.1.1		2	180.167	odd	12
6480.2.a.bn.1.1		2	180.67	even	12

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:	\( N \)	\(=\)	\( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1350.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.92048 + 1.68614i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.92048 + 1.68614i) q^{7} +1.00000i q^{8} +(-2.18614 - 3.78651i) q^{11} +(5.84096 + 3.37228i) q^{13} +(1.68614 - 2.92048i) q^{14} +(-0.500000 - 0.866025i) q^{16} -1.62772i q^{17} +2.37228 q^{19} +(3.78651 + 2.18614i) q^{22} +(1.18843 + 0.686141i) q^{23} -6.74456 q^{26} +3.37228i q^{28} +(-0.686141 - 1.18843i) q^{29} +(-2.37228 + 4.10891i) q^{31} +(0.866025 + 0.500000i) q^{32} +(0.813859 + 1.40965i) q^{34} +4.00000i q^{37} +(-2.05446 + 1.18614i) q^{38} +(-1.50000 + 2.59808i) q^{41} +(-4.87375 + 2.81386i) q^{43} -4.37228 q^{44} -1.37228 q^{46} +(-6.38458 + 3.68614i) q^{47} +(2.18614 - 3.78651i) q^{49} +(5.84096 - 3.37228i) q^{52} +11.4891i q^{53} +(-1.68614 - 2.92048i) q^{56} +(1.18843 + 0.686141i) q^{58} +(-2.18614 + 3.78651i) q^{59} +(4.05842 + 7.02939i) q^{61} -4.74456i q^{62} -1.00000 q^{64} +(-6.06218 - 3.50000i) q^{67} +(-1.40965 - 0.813859i) q^{68} +6.00000 q^{71} +3.11684i q^{73} +(-2.00000 - 3.46410i) q^{74} +(1.18614 - 2.05446i) q^{76} +(12.7692 + 7.37228i) q^{77} +(1.00000 + 1.73205i) q^{79} -3.00000i q^{82} +(-6.38458 + 3.68614i) q^{83} +(2.81386 - 4.87375i) q^{86} +(3.78651 - 2.18614i) q^{88} +16.1168 q^{89} -22.7446 q^{91} +(1.18843 - 0.686141i) q^{92} +(3.68614 - 6.38458i) q^{94} +(7.25061 - 4.18614i) q^{97} +4.37228i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4}+O(q^{10}) \) 8 * q + 4 * q^4	\( 8 q + 4 q^{4} - 6 q^{11} + 2 q^{14} - 4 q^{16} - 4 q^{19} - 8 q^{26} + 6 q^{29} + 4 q^{31} + 18 q^{34} - 12 q^{41} - 12 q^{44} + 12 q^{46} + 6 q^{49} - 2 q^{56} - 6 q^{59} - 2 q^{61} - 8 q^{64} + 48 q^{71} - 16 q^{74} - 2 q^{76} + 8 q^{79} + 34 q^{86} + 60 q^{89} - 136 q^{91} + 18 q^{94}+O(q^{100}) \) 8 * q + 4 * q^4 - 6 * q^11 + 2 * q^14 - 4 * q^16 - 4 * q^19 - 8 * q^26 + 6 * q^29 + 4 * q^31 + 18 * q^34 - 12 * q^41 - 12 * q^44 + 12 * q^46 + 6 * q^49 - 2 * q^56 - 6 * q^59 - 2 * q^61 - 8 * q^64 + 48 * q^71 - 16 * q^74 - 2 * q^76 + 8 * q^79 + 34 * q^86 + 60 * q^89 - 136 * q^91 + 18 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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