LMFDB - Embedded newform 945.2.k.a.856.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(361,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0, 4]))

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

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

chi := DirichletCharacter("945.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.k (of order $3$, 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{13})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 4x^{2} + 3x + 9 $ x^4 - x^3 + 4x^2 + 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			856.2
Root			$-0.651388 - 1.12824i$ of defining polynomial
Character	$\chi$	$=$	945.856
Dual form			945.2.k.a.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.651388 + 1.12824i) q^{2} +(0.151388 - 0.262211i) q^{4} +1.00000 q^{5} +(-2.00000 - 1.73205i) q^{7} +3.00000 q^{8} +O(q^{10})$	\(q+(0.651388 + 1.12824i) q^{2} +(0.151388 - 0.262211i) q^{4} +1.00000 q^{5} +(-2.00000 - 1.73205i) q^{7} +3.00000 q^{8} +(0.651388 + 1.12824i) q^{10} +(-0.802776 - 1.39045i) q^{13} +(0.651388 - 3.38471i) q^{14} +(1.65139 + 2.86029i) q^{16} +(2.80278 + 4.85455i) q^{17} +(1.80278 - 3.12250i) q^{19} +(0.151388 - 0.262211i) q^{20} +5.21110 q^{23} +1.00000 q^{25} +(1.04584 - 1.81144i) q^{26} +(-0.756939 + 0.262211i) q^{28} +(4.10555 - 7.11102i) q^{29} +(1.80278 - 3.12250i) q^{31} +(0.848612 - 1.46984i) q^{32} +(-3.65139 + 6.32439i) q^{34} +(-2.00000 - 1.73205i) q^{35} +(1.80278 - 3.12250i) q^{37} +4.69722 q^{38} +3.00000 q^{40} +(1.50000 + 2.59808i) q^{41} +(-2.10555 + 3.64692i) q^{43} +(3.39445 + 5.87936i) q^{46} +(-4.10555 - 7.11102i) q^{47} +(1.00000 + 6.92820i) q^{49} +(0.651388 + 1.12824i) q^{50} -0.486122 q^{52} +(0.197224 + 0.341603i) q^{53} +(-6.00000 - 5.19615i) q^{56} +10.6972 q^{58} +(-5.80278 + 10.0507i) q^{59} +(-2.10555 - 3.64692i) q^{61} +4.69722 q^{62} +8.81665 q^{64} +(-0.802776 - 1.39045i) q^{65} +(-2.10555 + 3.64692i) q^{67} +1.69722 q^{68} +(0.651388 - 3.38471i) q^{70} +(1.80278 + 3.12250i) q^{73} +4.69722 q^{74} +(-0.545837 - 0.945417i) q^{76} +(-6.40833 - 11.0995i) q^{79} +(1.65139 + 2.86029i) q^{80} +(-1.95416 + 3.38471i) q^{82} +(-7.10555 + 12.3072i) q^{83} +(2.80278 + 4.85455i) q^{85} -5.48612 q^{86} +(1.50000 - 2.59808i) q^{89} +(-0.802776 + 4.17134i) q^{91} +(0.788897 - 1.36641i) q^{92} +(5.34861 - 9.26407i) q^{94} +(1.80278 - 3.12250i) q^{95} +(-6.80278 + 11.7828i) q^{97} +(-7.16527 + 5.64118i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - 3 q^{4} + 4 q^{5} - 8 q^{7} + 12 q^{8}+O(q^{10}) $ 4 * q - q^2 - 3 * q^4 + 4 * q^5 - 8 * q^7 + 12 * q^8	$ 4 q - q^{2} - 3 q^{4} + 4 q^{5} - 8 q^{7} + 12 q^{8} - q^{10} + 4 q^{13} - q^{14} + 3 q^{16} + 4 q^{17} - 3 q^{20} - 8 q^{23} + 4 q^{25} + 15 q^{26} + 15 q^{28} + 2 q^{29} + 7 q^{32} - 11 q^{34} - 8 q^{35} + 26 q^{38} + 12 q^{40} + 6 q^{41} + 6 q^{43} + 28 q^{46} - 2 q^{47} + 4 q^{49} - q^{50} - 38 q^{52} + 8 q^{53} - 24 q^{56} + 50 q^{58} - 16 q^{59} + 6 q^{61} + 26 q^{62} - 8 q^{64} + 4 q^{65} + 6 q^{67} + 14 q^{68} - q^{70} + 26 q^{74} - 13 q^{76} - 4 q^{79} + 3 q^{80} + 3 q^{82} - 14 q^{83} + 4 q^{85} - 58 q^{86} + 6 q^{89} + 4 q^{91} + 32 q^{92} + 25 q^{94} - 20 q^{97} + 11 q^{98}+O(q^{100}) $ 4 * q - q^2 - 3 * q^4 + 4 * q^5 - 8 * q^7 + 12 * q^8 - q^10 + 4 * q^13 - q^14 + 3 * q^16 + 4 * q^17 - 3 * q^20 - 8 * q^23 + 4 * q^25 + 15 * q^26 + 15 * q^28 + 2 * q^29 + 7 * q^32 - 11 * q^34 - 8 * q^35 + 26 * q^38 + 12 * q^40 + 6 * q^41 + 6 * q^43 + 28 * q^46 - 2 * q^47 + 4 * q^49 - q^50 - 38 * q^52 + 8 * q^53 - 24 * q^56 + 50 * q^58 - 16 * q^59 + 6 * q^61 + 26 * q^62 - 8 * q^64 + 4 * q^65 + 6 * q^67 + 14 * q^68 - q^70 + 26 * q^74 - 13 * q^76 - 4 * q^79 + 3 * q^80 + 3 * q^82 - 14 * q^83 + 4 * q^85 - 58 * q^86 + 6 * q^89 + 4 * q^91 + 32 * q^92 + 25 * q^94 - 20 * q^97 + 11 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.651388	+	1.12824i	0.460601	+	0.797784i	0.998991	−	0.0449118i	$-0.0143007\pi$
$2$	0.651388	+	1.12824i	0.460601	+	0.797784i	−0.538390	+	0.842696i	$0.680967\pi$
$3$		0			0
$3$		0			0
$4$	0.151388	−	0.262211i	0.0756939	−	0.131106i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$8$	3.00000			1.06066
$9$		0			0
$10$	0.651388	+	1.12824i	0.205987	+	0.356780i
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$		0			0
$13$	−0.802776	−	1.39045i	−0.222650	−	0.385641i	0.732962	−	0.680270i	$-0.238137\pi$
$13$	−0.802776	−	1.39045i	−0.222650	−	0.385641i	−0.955612	+	0.294629i	$0.904804\pi$
$14$	0.651388	−	3.38471i	0.174091	−	0.904602i
$15$		0			0
$16$	1.65139	+	2.86029i	0.412847	+	0.715072i
$17$	2.80278	+	4.85455i	0.679773	+	1.17740i	0.975049	+	0.221989i	$0.0712550\pi$
$17$	2.80278	+	4.85455i	0.679773	+	1.17740i	−0.295276	+	0.955412i	$0.595412\pi$
$18$		0			0
$19$	1.80278	−	3.12250i	0.413585	−	0.716350i	−0.581694	−	0.813408i	$-0.697610\pi$
$19$	1.80278	−	3.12250i	0.413585	−	0.716350i	0.995279	+	0.0970575i	$0.0309431\pi$
$20$	0.151388	−	0.262211i	0.0338513	−	0.0586323i
$21$		0			0
$22$		0			0
$23$	5.21110			1.08659			0.543295	−	0.839542i	$-0.317177\pi$
$23$	5.21110			1.08659			0.543295	+	0.839542i	$0.317177\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	1.04584	−	1.81144i	0.205105	−	0.355253i
$27$		0			0
$28$	−0.756939	+	0.262211i	−0.143048	+	0.0495533i
$29$	4.10555	−	7.11102i	0.762382	−	1.32048i	−0.179238	−	0.983806i	$-0.557363\pi$
$29$	4.10555	−	7.11102i	0.762382	−	1.32048i	0.941620	−	0.336678i	$-0.109303\pi$
$30$		0			0
$31$	1.80278	−	3.12250i	0.323788	−	0.560817i	−0.657478	−	0.753474i	$-0.728377\pi$
$31$	1.80278	−	3.12250i	0.323788	−	0.560817i	0.981266	+	0.192656i	$0.0617102\pi$
$32$	0.848612	−	1.46984i	0.150015	−	0.259833i
$33$		0			0
$34$	−3.65139	+	6.32439i	−0.626208	+	1.08462i
$35$	−2.00000	−	1.73205i	−0.338062	−	0.292770i
$36$		0			0
$37$	1.80278	−	3.12250i	0.296374	−	0.513336i	−0.678929	−	0.734204i	$-0.737556\pi$
$37$	1.80278	−	3.12250i	0.296374	−	0.513336i	0.975304	+	0.220868i	$0.0708890\pi$
$38$	4.69722			0.761990
$39$		0			0
$40$	3.00000			0.474342
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	0.959058	−	0.283211i	$-0.0913998\pi$
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	−0.724797	+	0.688963i	$0.758066\pi$
$42$		0			0
$43$	−2.10555	+	3.64692i	−0.321094	+	0.556150i	−0.980714	−	0.195449i	$-0.937384\pi$
$43$	−2.10555	+	3.64692i	−0.321094	+	0.556150i	0.659620	+	0.751599i	$0.270717\pi$
$44$		0			0
$45$		0			0
$46$	3.39445	+	5.87936i	0.500484	+	0.866864i
$47$	−4.10555	−	7.11102i	−0.598856	−	1.03725i	−0.992990	−	0.118196i	$-0.962289\pi$
$47$	−4.10555	−	7.11102i	−0.598856	−	1.03725i	0.394134	−	0.919053i	$-0.371045\pi$
$48$		0			0
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$	0.651388	+	1.12824i	0.0921201	+	0.159557i
$51$		0			0
$52$	−0.486122			−0.0674130
$53$	0.197224	+	0.341603i	0.0270908	+	0.0469227i	0.879253	−	0.476355i	$-0.158042\pi$
$53$	0.197224	+	0.341603i	0.0270908	+	0.0469227i	−0.852162	+	0.523278i	$0.824709\pi$
$54$		0			0
$55$		0			0
$56$	−6.00000	−	5.19615i	−0.801784	−	0.694365i
$57$		0			0
$58$	10.6972			1.40461
$59$	−5.80278	+	10.0507i	−0.755457	+	1.30849i	0.189690	+	0.981844i	$0.439252\pi$
$59$	−5.80278	+	10.0507i	−0.755457	+	1.30849i	−0.945147	+	0.326646i	$0.894082\pi$
$60$		0			0
$61$	−2.10555	−	3.64692i	−0.269588	−	0.466940i	0.699167	−	0.714958i	$-0.253554\pi$
$61$	−2.10555	−	3.64692i	−0.269588	−	0.466940i	−0.968756	+	0.248018i	$0.920221\pi$
$62$	4.69722			0.596548
$63$		0			0
$64$	8.81665			1.10208
$65$	−0.802776	−	1.39045i	−0.0995721	−	0.172464i
$66$		0			0
$67$	−2.10555	+	3.64692i	−0.257234	+	0.445542i	−0.965500	−	0.260403i	$-0.916144\pi$
$67$	−2.10555	+	3.64692i	−0.257234	+	0.445542i	0.708266	+	0.705946i	$0.249478\pi$
$68$	1.69722			0.205819
$69$		0			0
$70$	0.651388	−	3.38471i	0.0778557	−	0.404550i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	1.80278	+	3.12250i	0.210999	+	0.365461i	0.952027	−	0.306013i	$-0.0989950\pi$
$73$	1.80278	+	3.12250i	0.210999	+	0.365461i	−0.741028	+	0.671474i	$0.765662\pi$
$74$	4.69722			0.546041
$75$		0			0
$76$	−0.545837	−	0.945417i	−0.0626117	−	0.108447i
$77$		0			0
$78$		0			0
$79$	−6.40833	−	11.0995i	−0.720993	−	1.24880i	−0.960602	−	0.277927i	$-0.910353\pi$
$79$	−6.40833	−	11.0995i	−0.720993	−	1.24880i	0.239609	−	0.970869i	$-0.422981\pi$
$80$	1.65139	+	2.86029i	0.184631	+	0.319790i
$81$		0			0
$82$	−1.95416	+	3.38471i	−0.215801	+	0.373779i
$83$	−7.10555	+	12.3072i	−0.779936	+	1.35089i	0.152043	+	0.988374i	$0.451415\pi$
$83$	−7.10555	+	12.3072i	−0.779936	+	1.35089i	−0.931978	+	0.362514i	$0.881918\pi$
$84$		0			0
$85$	2.80278	+	4.85455i	0.304004	+	0.526550i
$86$	−5.48612			−0.591584
$87$		0			0
$88$		0			0
$89$	1.50000	−	2.59808i	0.159000	−	0.275396i	−0.775509	−	0.631337i	$-0.782506\pi$
$89$	1.50000	−	2.59808i	0.159000	−	0.275396i	0.934508	+	0.355942i	$0.115840\pi$
$90$		0			0
$91$	−0.802776	+	4.17134i	−0.0841538	+	0.437276i
$92$	0.788897	−	1.36641i	0.0822482	−	0.142458i
$93$		0			0
$94$	5.34861	−	9.26407i	0.551667	−	0.955516i
$95$	1.80278	−	3.12250i	0.184961	−	0.320362i
$96$		0			0
$97$	−6.80278	+	11.7828i	−0.690717	+	1.19636i	0.280886	+	0.959741i	$0.409372\pi$
$97$	−6.80278	+	11.7828i	−0.690717	+	1.19636i	−0.971603	+	0.236616i	$0.923962\pi$
$98$	−7.16527	+	5.64118i	−0.723801	+	0.569846i
$99$		0			0
$100$	0.151388	−	0.262211i	0.0151388	−	0.0262211i
$101$	−16.4222			−1.63407			−0.817035	−	0.576588i	$-0.804384\pi$
$101$	−16.4222			−1.63407			−0.817035	+	0.576588i	$0.804384\pi$
$102$		0			0
$103$	8.00000			0.788263			0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000			0.788263			0.394132	+	0.919054i	$0.371045\pi$
$104$	−2.40833	−	4.17134i	−0.236156	−	0.409034i
$105$		0			0
$106$	−0.256939	+	0.445032i	−0.0249561	+	0.0432253i
$107$	−4.50000	+	7.79423i	−0.435031	+	0.753497i	−0.997298	−	0.0734594i	$-0.976596\pi$
$107$	−4.50000	+	7.79423i	−0.435031	+	0.753497i	0.562267	+	0.826956i	$0.309929\pi$
$108$		0			0
$109$	9.10555	+	15.7713i	0.872154	+	1.51061i	0.859764	+	0.510691i	$0.170610\pi$
$109$	9.10555	+	15.7713i	0.872154	+	1.51061i	0.0123894	+	0.999923i	$0.496056\pi$
$110$		0			0
$111$		0			0
$112$	1.65139	−	8.58086i	0.156041	−	0.810815i
$113$	5.40833	+	9.36750i	0.508773	+	0.881220i	0.999948	+	0.0101595i	$0.00323393\pi$
$113$	5.40833	+	9.36750i	0.508773	+	0.881220i	−0.491176	+	0.871060i	$0.663433\pi$
$114$		0			0
$115$	5.21110			0.485938
$116$	−1.24306	−	2.15304i	−0.115415	−	0.199905i
$117$		0			0
$118$	−15.1194			−1.39186
$119$	2.80278	−	14.5636i	0.256930	−	1.33505i
$120$		0			0
$121$	−11.0000			−1.00000
$122$	2.74306	−	4.75112i	0.248345	−	0.430146i
$123$		0			0
$124$	−0.545837	−	0.945417i	−0.0490176	−	0.0849009i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−4.00000			−0.354943			−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000			−0.354943			−0.177471	+	0.984126i	$0.556792\pi$
$128$	4.04584	+	7.00759i	0.357605	+	0.619390i
$129$		0			0
$130$	1.04584	−	1.81144i	0.0917259	−	0.158874i
$131$	−6.78890			−0.593149			−0.296574	−	0.955010i	$-0.595844\pi$
$131$	−6.78890			−0.593149			−0.296574	+	0.955010i	$0.595844\pi$
$132$		0			0
$133$	−9.01388	+	3.12250i	−0.781602	+	0.270755i
$134$	−5.48612			−0.473929
$135$		0			0
$136$	8.40833	+	14.5636i	0.721008	+	1.24882i
$137$	−0.788897			−0.0674001			−0.0337000	−	0.999432i	$-0.510729\pi$
$137$	−0.788897			−0.0674001			−0.0337000	+	0.999432i	$0.510729\pi$
$138$		0			0
$139$	−9.80278	−	16.9789i	−0.831461	−	1.44013i	−0.896880	−	0.442274i	$-0.854172\pi$
$139$	−9.80278	−	16.9789i	−0.831461	−	1.44013i	0.0654194	−	0.997858i	$-0.479161\pi$
$140$	−0.756939	+	0.262211i	−0.0639730	+	0.0221609i
$141$		0			0
$142$		0			0
$143$		0			0
$144$		0			0
$145$	4.10555	−	7.11102i	0.340947	−	0.590538i
$146$	−2.34861	+	4.06792i	−0.194373	+	0.336663i
$147$		0			0
$148$	−0.545837	−	0.945417i	−0.0448675	−	0.0777128i
$149$	23.2111			1.90153			0.950764	−	0.309916i	$-0.100301\pi$
$149$	23.2111			1.90153			0.950764	+	0.309916i	$0.100301\pi$
$150$		0			0
$151$	−16.0000			−1.30206			−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000			−1.30206			−0.651031	+	0.759051i	$0.725663\pi$
$152$	5.40833	−	9.36750i	0.438673	−	0.759804i
$153$		0			0
$154$		0			0
$155$	1.80278	−	3.12250i	0.144802	−	0.250805i
$156$		0			0
$157$	−12.0139	+	20.8086i	−0.958812	+	1.66071i	−0.233418	+	0.972376i	$0.574991\pi$
$157$	−12.0139	+	20.8086i	−0.958812	+	1.66071i	−0.725393	+	0.688334i	$0.758342\pi$
$158$	8.34861	−	14.4602i	0.664180	−	1.15039i
$159$		0			0
$160$	0.848612	−	1.46984i	0.0670887	−	0.116201i
$161$	−10.4222	−	9.02589i	−0.821385	−	0.711340i
$162$		0			0
$163$	9.10555	−	15.7713i	0.713202	−	1.23530i	−0.250447	−	0.968130i	$-0.580578\pi$
$163$	9.10555	−	15.7713i	0.713202	−	1.23530i	0.963649	−	0.267172i	$-0.0860890\pi$
$164$	0.908327			0.0709284
$165$		0			0
$166$	−18.5139			−1.43696
$167$	1.89445	+	3.28128i	0.146597	+	0.253913i	0.929968	−	0.367642i	$-0.119835\pi$
$167$	1.89445	+	3.28128i	0.146597	+	0.253913i	−0.783371	+	0.621555i	$0.786501\pi$
$168$		0			0
$169$	5.21110	−	9.02589i	0.400854	−	0.694300i
$170$	−3.65139	+	6.32439i	−0.280049	+	0.485059i
$171$		0			0
$172$	0.637510	+	1.10420i	0.0486097	+	0.0841944i
$173$	11.4083	+	19.7598i	0.867359	+	1.50231i	0.864686	+	0.502313i	$0.167518\pi$
$173$	11.4083	+	19.7598i	0.867359	+	1.50231i	0.00267345	+	0.999996i	$0.499149\pi$
$174$		0			0
$175$	−2.00000	−	1.73205i	−0.151186	−	0.130931i
$176$		0			0
$177$		0			0
$178$	3.90833			0.292941
$179$	0.591673	+	1.02481i	0.0442237	+	0.0765977i	0.887290	−	0.461212i	$-0.152585\pi$
$179$	0.591673	+	1.02481i	0.0442237	+	0.0765977i	−0.843066	+	0.537810i	$0.819252\pi$
$180$		0			0
$181$	−20.4222			−1.51797			−0.758985	−	0.651108i	$-0.774305\pi$
$181$	−20.4222			−1.51797			−0.758985	+	0.651108i	$0.774305\pi$
$182$	−5.22918	+	1.81144i	−0.387613	+	0.134273i
$183$		0			0
$184$	15.6333			1.15250
$185$	1.80278	−	3.12250i	0.132543	−	0.229571i
$186$		0			0
$187$		0			0
$188$	−2.48612			−0.181319
$189$		0			0
$190$	4.69722			0.340772
$191$	−2.80278	−	4.85455i	−0.202802	−	0.351263i	0.746628	−	0.665241i	$-0.231671\pi$
$191$	−2.80278	−	4.85455i	−0.202802	−	0.351263i	−0.949430	+	0.313978i	$0.898338\pi$
$192$		0			0
$193$	7.01388	−	12.1484i	0.504870	−	0.874460i	−0.495114	−	0.868828i	$-0.664874\pi$
$193$	7.01388	−	12.1484i	0.504870	−	0.874460i	0.999984	−	0.00563255i	$-0.00179291\pi$
$194$	−17.7250			−1.27258
$195$		0			0
$196$	1.96804	+	0.786634i	0.140574	+	0.0561882i
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$		0			0
$199$	1.40833	+	2.43929i	0.0998336	+	0.172917i	0.911616	−	0.411044i	$-0.134836\pi$
$199$	1.40833	+	2.43929i	0.0998336	+	0.172917i	−0.811782	+	0.583961i	$0.801502\pi$
$200$	3.00000			0.212132
$201$		0			0
$202$	−10.6972	−	18.5281i	−0.752654	−	1.30364i
$203$	−20.5278	+	7.11102i	−1.44077	+	0.499096i
$204$		0			0
$205$	1.50000	+	2.59808i	0.104765	+	0.181458i
$206$	5.21110	+	9.02589i	0.363075	+	0.628864i
$207$		0			0
$208$	2.65139	−	4.59234i	0.183841	−	0.318421i
$209$		0			0
$210$		0			0
$211$	−9.01388	−	15.6125i	−0.620541	−	1.07481i	−0.989385	−	0.145317i	$-0.953580\pi$
$211$	−9.01388	−	15.6125i	−0.620541	−	1.07481i	0.368844	−	0.929491i	$-0.379754\pi$
$212$	0.119429			0.00820245
$213$		0			0
$214$	−11.7250			−0.801503
$215$	−2.10555	+	3.64692i	−0.143597	+	0.248718i
$216$		0			0
$217$	−9.01388	+	3.12250i	−0.611902	+	0.211969i
$218$	−11.8625	+	20.5464i	−0.803429	+	1.39158i
$219$		0			0
$220$		0			0
$221$	4.50000	−	7.79423i	0.302703	−	0.524297i
$222$		0			0
$223$	−2.89445	+	5.01333i	−0.193827	+	0.335718i	−0.946515	−	0.322659i	$-0.895423\pi$
$223$	−2.89445	+	5.01333i	−0.193827	+	0.335718i	0.752689	+	0.658377i	$0.228757\pi$
$224$	−4.24306	+	1.46984i	−0.283501	+	0.0982078i
$225$		0			0
$226$	−7.04584	+	12.2037i	−0.468682	+	0.811781i
$227$	5.21110			0.345873			0.172937	−	0.984933i	$-0.444674\pi$
$227$	5.21110			0.345873			0.172937	+	0.984933i	$0.444674\pi$
$228$		0			0
$229$	−4.78890			−0.316459			−0.158230	−	0.987402i	$-0.550579\pi$
$229$	−4.78890			−0.316459			−0.158230	+	0.987402i	$0.550579\pi$
$230$	3.39445	+	5.87936i	0.223823	+	0.387673i
$231$		0			0
$232$	12.3167	−	21.3331i	0.808628	−	1.40058i
$233$	−8.40833	+	14.5636i	−0.550848	+	0.954096i	0.447366	+	0.894351i	$0.352362\pi$
$233$	−8.40833	+	14.5636i	−0.550848	+	0.954096i	−0.998214	+	0.0597453i	$0.980971\pi$
$234$		0			0
$235$	−4.10555	−	7.11102i	−0.267817	−	0.463872i
$236$	1.75694	+	3.04311i	0.114367	+	0.198089i
$237$		0			0
$238$	18.2569	−	6.32439i	1.18342	−	0.409949i
$239$	−0.197224	−	0.341603i	−0.0127574	−	0.0220964i	0.859576	−	0.511008i	$-0.170728\pi$
$239$	−0.197224	−	0.341603i	−0.0127574	−	0.0220964i	−0.872334	+	0.488911i	$0.837394\pi$
$240$		0			0
$241$	−3.21110			−0.206845			−0.103423	−	0.994637i	$-0.532979\pi$
$241$	−3.21110			−0.206845			−0.103423	+	0.994637i	$0.532979\pi$
$242$	−7.16527	−	12.4106i	−0.460601	−	0.797784i
$243$		0			0
$244$	−1.27502			−0.0816247
$245$	1.00000	+	6.92820i	0.0638877	+	0.442627i
$246$		0			0
$247$	−5.78890			−0.368339
$248$	5.40833	−	9.36750i	0.343429	−	0.594837i
$249$		0			0
$250$	0.651388	+	1.12824i	0.0411974	+	0.0713560i
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$		0			0
$254$	−2.60555	−	4.51295i	−0.163487	−	0.283167i
$255$		0			0
$256$	3.54584	−	6.14157i	0.221615	−	0.383848i
$257$	−18.0000			−1.12281			−0.561405	−	0.827541i	$-0.689739\pi$
$257$	−18.0000			−1.12281			−0.561405	+	0.827541i	$0.689739\pi$
$258$		0			0
$259$	−9.01388	+	3.12250i	−0.560095	+	0.194023i
$260$	−0.486122			−0.0301480
$261$		0			0
$262$	−4.42221	−	7.65948i	−0.273205	−	0.473204i
$263$	22.4222			1.38261			0.691306	−	0.722562i	$-0.257036\pi$
$263$	22.4222			1.38261			0.691306	+	0.722562i	$0.257036\pi$
$264$		0			0
$265$	0.197224	+	0.341603i	0.0121154	+	0.0209845i
$266$	−9.39445	−	8.13583i	−0.576011	−	0.498840i
$267$		0			0
$268$	0.637510	+	1.10420i	0.0389421	+	0.0674497i
$269$	0.711103	+	1.23167i	0.0433567	+	0.0750960i	0.886889	−	0.461982i	$-0.152861\pi$
$269$	0.711103	+	1.23167i	0.0433567	+	0.0750960i	−0.843533	+	0.537078i	$0.819528\pi$
$270$		0			0
$271$	13.0139	−	22.5407i	0.790537	−	1.36925i	−0.135098	−	0.990832i	$-0.543135\pi$
$271$	13.0139	−	22.5407i	0.790537	−	1.36925i	0.925635	−	0.378418i	$-0.123532\pi$
$272$	−9.25694	+	16.0335i	−0.561284	+	0.972173i
$273$		0			0
$274$	−0.513878	−	0.890063i	−0.0310445	−	0.0537707i
$275$		0			0
$276$		0			0
$277$	29.6333			1.78049			0.890246	−	0.455479i	$-0.150532\pi$
$277$	29.6333			1.78049			0.890246	+	0.455479i	$0.150532\pi$
$278$	12.7708	−	22.1197i	0.765943	−	1.32665i
$279$		0			0
$280$	−6.00000	−	5.19615i	−0.358569	−	0.310530i
$281$	9.31665	−	16.1369i	0.555785	−	0.962648i	−0.442057	−	0.896987i	$-0.645751\pi$
$281$	9.31665	−	16.1369i	0.555785	−	0.962648i	0.997842	−	0.0656609i	$-0.0209155\pi$
$282$		0			0
$283$	12.5000	−	21.6506i	0.743048	−	1.28700i	−0.208053	−	0.978117i	$-0.566713\pi$
$283$	12.5000	−	21.6506i	0.743048	−	1.28700i	0.951101	−	0.308879i	$-0.0999539\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.50000	−	7.79423i	0.0885422	−	0.460079i
$288$		0			0
$289$	−7.21110	+	12.4900i	−0.424183	+	0.734706i
$290$	10.6972			0.628163
$291$		0			0
$292$	1.09167			0.0638853
$293$	−11.0139	−	19.0766i	−0.643438	−	1.11447i	−0.984660	−	0.174484i	$-0.944174\pi$
$293$	−11.0139	−	19.0766i	−0.643438	−	1.11447i	0.341222	−	0.939983i	$-0.389159\pi$
$294$		0			0
$295$	−5.80278	+	10.0507i	−0.337851	+	0.585175i
$296$	5.40833	−	9.36750i	0.314353	−	0.544475i
$297$		0			0
$298$	15.1194	+	26.1876i	0.875845	+	1.51701i
$299$	−4.18335	−	7.24577i	−0.241929	−	0.419034i
$300$		0			0
$301$	10.5278	−	3.64692i	0.606810	−	0.210205i
$302$	−10.4222	−	18.0518i	−0.599731	−	1.03876i
$303$		0			0
$304$	11.9083			0.682989
$305$	−2.10555	−	3.64692i	−0.120564	−	0.208822i
$306$		0			0
$307$	−9.21110			−0.525705			−0.262853	−	0.964836i	$-0.584663\pi$
$307$	−9.21110			−0.525705			−0.262853	+	0.964836i	$0.584663\pi$
$308$		0			0
$309$		0			0
$310$	4.69722			0.266784
$311$	−8.40833	+	14.5636i	−0.476792	+	0.825829i	−0.999646	−	0.0265935i	$-0.991534\pi$
$311$	−8.40833	+	14.5636i	−0.476792	+	0.825829i	0.522854	+	0.852422i	$0.324867\pi$
$312$		0			0
$313$	4.40833	+	7.63545i	0.249173	+	0.431581i	0.963297	−	0.268439i	$-0.0865078\pi$
$313$	4.40833	+	7.63545i	0.249173	+	0.431581i	−0.714123	+	0.700020i	$0.753174\pi$
$314$	−31.3028			−1.76652
$315$		0			0
$316$	−3.88057			−0.218299
$317$	2.80278	+	4.85455i	0.157420	+	0.272659i	0.933937	−	0.357437i	$-0.116349\pi$
$317$	2.80278	+	4.85455i	0.157420	+	0.272659i	−0.776518	+	0.630095i	$0.783016\pi$
$318$		0			0
$319$		0			0
$320$	8.81665			0.492866
$321$		0			0
$322$	3.39445	−	17.6381i	0.189165	−	0.982931i
$323$	20.2111			1.12458
$324$		0			0
$325$	−0.802776	−	1.39045i	−0.0445300	−	0.0771282i
$326$	23.7250			1.31401
$327$		0			0
$328$	4.50000	+	7.79423i	0.248471	+	0.430364i
$329$	−4.10555	+	21.3331i	−0.226346	+	1.17613i
$330$		0			0
$331$	10.0139	+	17.3445i	0.550413	+	0.953342i	0.998245	+	0.0592248i	$0.0188629\pi$
$331$	10.0139	+	17.3445i	0.550413	+	0.953342i	−0.447832	+	0.894118i	$0.647804\pi$
$332$	2.15139	+	3.72631i	0.118073	+	0.204508i
$333$		0			0
$334$	−2.46804	+	4.27477i	−0.135045	+	0.233905i
$335$	−2.10555	+	3.64692i	−0.115039	+	0.199253i
$336$		0			0
$337$	13.8028	+	23.9071i	0.751885	+	1.30230i	0.946908	+	0.321505i	$0.104189\pi$
$337$	13.8028	+	23.9071i	0.751885	+	1.30230i	−0.195023	+	0.980799i	$0.562478\pi$
$338$	13.5778			0.738535
$339$		0			0
$340$	1.69722			0.0920449
$341$		0			0
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	−6.31665	+	10.9408i	−0.340571	+	0.589887i
$345$		0			0
$346$	−14.8625	+	25.7426i	−0.799012	+	1.38393i
$347$	−15.7111	+	27.2124i	−0.843416	+	1.46084i	0.0435734	+	0.999050i	$0.486126\pi$
$347$	−15.7111	+	27.2124i	−0.843416	+	1.46084i	−0.886990	+	0.461789i	$0.847208\pi$
$348$		0			0
$349$	−13.3167	+	23.0651i	−0.712824	+	1.23465i	0.250969	+	0.967995i	$0.419251\pi$
$349$	−13.3167	+	23.0651i	−0.712824	+	1.23465i	−0.963793	+	0.266652i	$0.914082\pi$
$350$	0.651388	−	3.38471i	0.0348181	−	0.180920i
$351$		0			0
$352$		0			0
$353$	−6.00000			−0.319348			−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000			−0.319348			−0.159674	+	0.987170i	$0.551044\pi$
$354$		0			0
$355$		0			0
$356$	−0.454163	−	0.786634i	−0.0240706	−	0.0416915i
$357$		0			0
$358$	−0.770817	+	1.33509i	−0.0407390	+	0.0705619i
$359$	3.59167	−	6.22096i	0.189561	−	0.328330i	−0.755543	−	0.655099i	$-0.772627\pi$
$359$	3.59167	−	6.22096i	0.189561	−	0.328330i	0.945104	+	0.326770i	$0.105960\pi$
$360$		0			0
$361$	3.00000	+	5.19615i	0.157895	+	0.273482i
$362$	−13.3028	−	23.0411i	−0.699178	−	1.21101i
$363$		0			0
$364$	0.972244	+	0.841988i	0.0509594	+	0.0441321i
$365$	1.80278	+	3.12250i	0.0943616	+	0.163439i
$366$		0			0
$367$	−14.4222			−0.752833			−0.376416	−	0.926451i	$-0.622844\pi$
$367$	−14.4222			−0.752833			−0.376416	+	0.926451i	$0.622844\pi$
$368$	8.60555	+	14.9053i	0.448595	+	0.776990i
$369$		0			0
$370$	4.69722			0.244197
$371$	0.197224	−	1.02481i	0.0102394	−	0.0532054i
$372$		0			0
$373$	−37.6333			−1.94858			−0.974289	−	0.225300i	$-0.927664\pi$
$373$	−37.6333			−1.94858			−0.974289	+	0.225300i	$0.927664\pi$
$374$		0			0
$375$		0			0
$376$	−12.3167	−	21.3331i	−0.635183	−	1.10017i
$377$	−13.1833			−0.678977
$378$		0			0
$379$	−4.00000			−0.205466			−0.102733	−	0.994709i	$-0.532759\pi$
$379$	−4.00000			−0.205466			−0.102733	+	0.994709i	$0.532759\pi$
$380$	−0.545837	−	0.945417i	−0.0280008	−	0.0484988i
$381$		0			0
$382$	3.65139	−	6.32439i	0.186821	−	0.323584i
$383$	−1.57779			−0.0806216			−0.0403108	−	0.999187i	$-0.512835\pi$
$383$	−1.57779			−0.0806216			−0.0403108	+	0.999187i	$0.512835\pi$
$384$		0			0
$385$		0			0
$386$	18.2750			0.930174
$387$		0			0
$388$	2.05971	+	3.56753i	0.104566	+	0.181114i
$389$	18.0000			0.912636			0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000			0.912636			0.456318	+	0.889817i	$0.349168\pi$
$390$		0			0
$391$	14.6056	+	25.2976i	0.738634	+	1.27935i
$392$	3.00000	+	20.7846i	0.151523	+	1.04978i
$393$		0			0
$394$	−3.90833	−	6.76942i	−0.196899	−	0.341038i
$395$	−6.40833	−	11.0995i	−0.322438	−	0.558479i
$396$		0			0
$397$	4.40833	−	7.63545i	0.221248	−	0.383212i	−0.733939	−	0.679215i	$-0.762320\pi$
$397$	4.40833	−	7.63545i	0.221248	−	0.383212i	0.955187	+	0.296003i	$0.0956538\pi$
$398$	−1.83473	+	3.17785i	−0.0919669	+	0.159291i
$399$		0			0
$400$	1.65139	+	2.86029i	0.0825694	+	0.143014i
$401$	−6.00000			−0.299626			−0.149813	−	0.988714i	$-0.547867\pi$
$401$	−6.00000			−0.299626			−0.149813	+	0.988714i	$0.547867\pi$
$402$		0			0
$403$	−5.78890			−0.288366
$404$	−2.48612	+	4.30609i	−0.123689	+	0.214236i
$405$		0			0
$406$	−21.3944	−	18.5281i	−1.06179	−	0.919536i
$407$		0			0
$408$		0			0
$409$	0.500000	−	0.866025i	0.0247234	−	0.0428222i	−0.853399	−	0.521258i	$-0.825463\pi$
$409$	0.500000	−	0.866025i	0.0247234	−	0.0428222i	0.878122	+	0.478436i	$0.158796\pi$
$410$	−1.95416	+	3.38471i	−0.0965093	+	0.167159i
$411$		0			0
$412$	1.21110	−	2.09769i	0.0596667	−	0.103346i
$413$	29.0139	−	10.0507i	1.42768	−	0.494563i
$414$		0			0
$415$	−7.10555	+	12.3072i	−0.348798	+	0.604136i
$416$	−2.72498			−0.133603
$417$		0			0
$418$		0			0
$419$	8.40833	+	14.5636i	0.410774	+	0.711481i	0.994975	−	0.100128i	$-0.0319253\pi$
$419$	8.40833	+	14.5636i	0.410774	+	0.711481i	−0.584201	+	0.811609i	$0.698592\pi$
$420$		0			0
$421$	11.7111	−	20.2842i	0.570764	−	0.988593i	−0.425723	−	0.904853i	$-0.639980\pi$
$421$	11.7111	−	20.2842i	0.570764	−	0.988593i	0.996488	−	0.0837393i	$-0.0266863\pi$
$422$	11.7431	−	20.3396i	0.571643	−	0.990115i
$423$		0			0
$424$	0.591673	+	1.02481i	0.0287342	+	0.0497691i
$425$	2.80278	+	4.85455i	0.135955	+	0.235480i
$426$		0			0
$427$	−2.10555	+	10.9408i	−0.101895	+	0.529461i
$428$	1.36249	+	2.35990i	0.0658585	+	0.114070i
$429$		0			0
$430$	−5.48612			−0.264564
$431$	3.19722	+	5.53776i	0.154005	+	0.266744i	0.932696	−	0.360663i	$-0.117450\pi$
$431$	3.19722	+	5.53776i	0.154005	+	0.266744i	−0.778691	+	0.627407i	$0.784116\pi$
$432$		0			0
$433$	22.8444			1.09783			0.548916	−	0.835877i	$-0.315041\pi$
$433$	22.8444			1.09783			0.548916	+	0.835877i	$0.315041\pi$
$434$	−9.39445	−	8.13583i	−0.450948	−	0.390532i
$435$		0			0
$436$	5.51388			0.264067
$437$	9.39445	−	16.2717i	0.449397	−	0.778379i
$438$		0			0
$439$	6.61943	+	11.4652i	0.315928	+	0.547204i	0.979634	−	0.200790i	$-0.0643508\pi$
$439$	6.61943	+	11.4652i	0.315928	+	0.547204i	−0.663706	+	0.747993i	$0.731017\pi$
$440$		0			0
$441$		0			0
$442$	11.7250			0.557700
$443$	−3.31665	−	5.74461i	−0.157579	−	0.272935i	0.776416	−	0.630221i	$-0.217036\pi$
$443$	−3.31665	−	5.74461i	−0.157579	−	0.272935i	−0.933995	+	0.357286i	$0.883702\pi$
$444$		0			0
$445$	1.50000	−	2.59808i	0.0711068	−	0.123161i
$446$	−7.54163			−0.357107
$447$		0			0
$448$	−17.6333	−	15.2709i	−0.833095	−	0.721482i
$449$	−21.6333			−1.02094			−0.510469	−	0.859896i	$-0.670528\pi$
$449$	−21.6333			−1.02094			−0.510469	+	0.859896i	$0.670528\pi$
$450$		0			0
$451$		0			0
$452$	3.27502			0.154044
$453$		0			0
$454$	3.39445	+	5.87936i	0.159309	+	0.275932i
$455$	−0.802776	+	4.17134i	−0.0376347	+	0.195556i
$456$		0			0
$457$	11.1972	+	19.3942i	0.523784	+	0.907221i	0.999617	+	0.0276848i	$0.00881346\pi$
$457$	11.1972	+	19.3942i	0.523784	+	0.907221i	−0.475833	+	0.879536i	$0.657853\pi$
$458$	−3.11943	−	5.40301i	−0.145761	−	0.252466i
$459$		0			0
$460$	0.788897	−	1.36641i	0.0367825	−	0.0637092i
$461$	−15.7111	+	27.2124i	−0.731739	+	1.26741i	0.224400	+	0.974497i	$0.427958\pi$
$461$	−15.7111	+	27.2124i	−0.731739	+	1.26741i	−0.956139	+	0.292912i	$0.905376\pi$
$462$		0			0
$463$	12.1056	+	20.9674i	0.562593	+	0.974439i	0.997269	+	0.0738524i	$0.0235294\pi$
$463$	12.1056	+	20.9674i	0.562593	+	0.974439i	−0.434677	+	0.900587i	$0.643137\pi$
$464$	27.1194			1.25899
$465$		0			0
$466$	−21.9083			−1.01488
$467$	−3.71110	+	6.42782i	−0.171729	+	0.297444i	−0.939025	−	0.343850i	$-0.888269\pi$
$467$	−3.71110	+	6.42782i	−0.171729	+	0.297444i	0.767295	+	0.641294i	$0.221602\pi$
$468$		0			0
$469$	10.5278	−	3.64692i	0.486127	−	0.168399i
$470$	5.34861	−	9.26407i	0.246713	−	0.427320i
$471$		0			0
$472$	−17.4083	+	30.1521i	−0.801283	+	1.38786i
$473$		0			0
$474$		0			0
$475$	1.80278	−	3.12250i	0.0827170	−	0.143270i
$476$	−3.39445	−	2.93968i	−0.155584	−	0.134740i
$477$		0			0
$478$	0.256939	−	0.445032i	0.0117521	−	0.0203553i
$479$	−22.4222			−1.02450			−0.512248	−	0.858837i	$-0.671187\pi$
$479$	−22.4222			−1.02450			−0.512248	+	0.858837i	$0.671187\pi$
$480$		0			0
$481$	−5.78890			−0.263951
$482$	−2.09167	−	3.62288i	−0.0952731	−	0.165018i
$483$		0			0
$484$	−1.66527	+	2.88433i	−0.0756939	+	0.131106i
$485$	−6.80278	+	11.7828i	−0.308898	+	0.535027i
$486$		0			0
$487$	11.3167	+	19.6010i	0.512807	+	0.888207i	0.999890	+	0.0148514i	$0.00472752\pi$
$487$	11.3167	+	19.6010i	0.512807	+	0.888207i	−0.487083	+	0.873356i	$0.661939\pi$
$488$	−6.31665	−	10.9408i	−0.285941	−	0.495265i
$489$		0			0
$490$	−7.16527	+	5.64118i	−0.323694	+	0.254843i
$491$	−19.2250	−	33.2986i	−0.867611	−	1.50275i	−0.864431	−	0.502752i	$-0.832321\pi$
$491$	−19.2250	−	33.2986i	−0.867611	−	1.50275i	−0.00318042	−	0.999995i	$-0.501012\pi$
$492$		0			0
$493$	46.0278			2.07299
$494$	−3.77082	−	6.53125i	−0.169657	−	0.293855i
$495$		0			0
$496$	11.9083			0.534700
$497$		0			0
$498$		0			0
$499$	−28.0000			−1.25345			−0.626726	−	0.779240i	$-0.715605\pi$
$499$	−28.0000			−1.25345			−0.626726	+	0.779240i	$0.715605\pi$
$500$	0.151388	−	0.262211i	0.00677027	−	0.0117265i
$501$		0			0
$502$	7.81665	+	13.5388i	0.348874	+	0.604268i
$503$	6.78890			0.302702			0.151351	−	0.988480i	$-0.451638\pi$
$503$	6.78890			0.302702			0.151351	+	0.988480i	$0.451638\pi$
$504$		0			0
$505$	−16.4222			−0.730779
$506$		0			0
$507$		0			0
$508$	−0.605551	+	1.04885i	−0.0268670	+	0.0465350i
$509$	24.7889			1.09875			0.549374	−	0.835576i	$-0.314866\pi$
$509$	24.7889			1.09875			0.549374	+	0.835576i	$0.314866\pi$
$510$		0			0
$511$	1.80278	−	9.36750i	0.0797501	−	0.414394i
$512$	25.4222			1.12351
$513$		0			0
$514$	−11.7250	−	20.3083i	−0.517167	−	0.895759i
$515$	8.00000			0.352522
$516$		0			0
$517$		0			0
$518$	−9.39445	−	8.13583i	−0.412768	−	0.357468i
$519$		0			0
$520$	−2.40833	−	4.17134i	−0.105612	−	0.182926i
$521$	10.1056	+	17.5033i	0.442732	+	0.766835i	0.997891	−	0.0649096i	$-0.0206759\pi$
$521$	10.1056	+	17.5033i	0.442732	+	0.766835i	−0.555159	+	0.831744i	$0.687343\pi$
$522$		0			0
$523$	12.5000	−	21.6506i	0.546587	−	0.946716i	−0.451918	−	0.892059i	$-0.649260\pi$
$523$	12.5000	−	21.6506i	0.546587	−	0.946716i	0.998505	−	0.0546569i	$-0.0174065\pi$
$524$	−1.02776	+	1.78013i	−0.0448977	+	0.0777652i
$525$		0			0
$526$	14.6056	+	25.2976i	0.636832	+	1.10303i
$527$	20.2111			0.880409
$528$		0			0
$529$	4.15559			0.180678
$530$	−0.256939	+	0.445032i	−0.0111607	+	0.0193309i
$531$		0			0
$532$	−0.545837	+	2.83625i	−0.0236650	+	0.122967i
$533$	2.40833	−	4.17134i	0.104316	−	0.180681i
$534$		0			0
$535$	−4.50000	+	7.79423i	−0.194552	+	0.336974i
$536$	−6.31665	+	10.9408i	−0.272838	+	0.472569i
$537$		0			0
$538$	−0.926407	+	1.60458i	−0.0399402	+	0.0691785i
$539$		0			0
$540$		0			0
$541$	−16.7111	+	28.9445i	−0.718466	+	1.24442i	0.243141	+	0.969991i	$0.421822\pi$
$541$	−16.7111	+	28.9445i	−0.718466	+	1.24442i	−0.961607	+	0.274429i	$0.911511\pi$
$542$	33.9083			1.45649
$543$		0			0
$544$	9.51388			0.407904
$545$	9.10555	+	15.7713i	0.390039	+	0.675567i
$546$		0			0
$547$	−2.89445	+	5.01333i	−0.123758	+	0.214355i	−0.921247	−	0.388979i	$-0.872828\pi$
$547$	−2.89445	+	5.01333i	−0.123758	+	0.214355i	0.797489	+	0.603334i	$0.206161\pi$
$548$	−0.119429	+	0.206858i	−0.00510177	+	0.00883653i
$549$		0			0
$550$		0			0
$551$	−14.8028	−	25.6392i	−0.630619	−	1.09226i
$552$		0			0
$553$	−6.40833	+	33.2986i	−0.272510	+	1.41600i
$554$	19.3028	+	33.4334i	0.820096	+	1.42045i
$555$		0			0
$556$	−5.93608			−0.251746
$557$	4.61943	+	8.00109i	0.195732	+	0.339017i	0.947140	−	0.320820i	$-0.103959\pi$
$557$	4.61943	+	8.00109i	0.195732	+	0.339017i	−0.751409	+	0.659837i	$0.770625\pi$
$558$		0			0
$559$	6.76114			0.285966
$560$	1.65139	−	8.58086i	0.0697839	−	0.362608i
$561$		0			0
$562$	24.2750			1.02398
$563$	17.9222	−	31.0422i	0.755331	−	1.30827i	−0.189879	−	0.981808i	$-0.560809\pi$
$563$	17.9222	−	31.0422i	0.755331	−	1.30827i	0.945210	−	0.326464i	$-0.105857\pi$
$564$		0			0
$565$	5.40833	+	9.36750i	0.227530	+	0.394094i
$566$	32.5694			1.36899
$567$		0			0
$568$		0			0
$569$	7.50000	+	12.9904i	0.314416	+	0.544585i	0.979313	−	0.202350i	$-0.0648579\pi$
$569$	7.50000	+	12.9904i	0.314416	+	0.544585i	−0.664897	+	0.746935i	$0.731525\pi$
$570$		0			0
$571$	7.01388	−	12.1484i	0.293522	−	0.508394i	−0.681118	−	0.732173i	$-0.738506\pi$
$571$	7.01388	−	12.1484i	0.293522	−	0.508394i	0.974640	+	0.223779i	$0.0718394\pi$
$572$		0			0
$573$		0			0
$574$	9.77082	−	3.38471i	0.407826	−	0.141275i
$575$	5.21110			0.217318
$576$		0			0
$577$	−16.1972	−	28.0544i	−0.674299	−	1.16792i	−0.976673	−	0.214731i	$-0.931112\pi$
$577$	−16.1972	−	28.0544i	−0.674299	−	1.16792i	0.302374	−	0.953189i	$-0.402221\pi$
$578$	−18.7889			−0.781515
$579$		0			0
$580$	−1.24306	−	2.15304i	−0.0516153	−	0.0894003i
$581$	35.5278	−	12.3072i	1.47394	−	0.510588i
$582$		0			0
$583$		0			0
$584$	5.40833	+	9.36750i	0.223798	+	0.387630i
$585$		0			0
$586$	14.3486	−	24.8525i	0.592736	−	1.02665i
$587$	−4.50000	+	7.79423i	−0.185735	+	0.321702i	−0.943824	−	0.330449i	$-0.892800\pi$
$587$	−4.50000	+	7.79423i	−0.185735	+	0.321702i	0.758089	+	0.652151i	$0.226133\pi$
$588$		0			0
$589$	−6.50000	−	11.2583i	−0.267828	−	0.463891i
$590$	−15.1194			−0.622457
$591$		0			0
$592$	11.9083			0.489429
$593$	−0.591673	+	1.02481i	−0.0242971	+	0.0420838i	−0.877918	−	0.478810i	$-0.841068\pi$
$593$	−0.591673	+	1.02481i	−0.0242971	+	0.0420838i	0.853621	+	0.520894i	$0.174401\pi$
$594$		0			0
$595$	2.80278	−	14.5636i	0.114903	−	0.597051i
$596$	3.51388	−	6.08622i	0.143934	−	0.249301i
$597$		0			0
$598$	5.44996	−	9.43961i	0.222865	−	0.386014i
$599$	−3.19722	+	5.53776i	−0.130635	+	0.226267i	−0.923922	−	0.382582i	$-0.875035\pi$
$599$	−3.19722	+	5.53776i	−0.130635	+	0.226267i	0.793286	+	0.608849i	$0.208368\pi$
$600$		0			0
$601$	15.1056	−	26.1636i	0.616168	−	1.06723i	−0.374010	−	0.927425i	$-0.622017\pi$
$601$	15.1056	−	26.1636i	0.616168	−	1.06723i	0.990178	−	0.139810i	$-0.0446492\pi$
$602$	10.9722	+	9.50224i	0.447195	+	0.387282i
$603$		0			0
$604$	−2.42221	+	4.19538i	−0.0985581	+	0.170708i
$605$	−11.0000			−0.447214
$606$		0			0
$607$	−4.00000			−0.162355			−0.0811775	−	0.996700i	$-0.525868\pi$
$607$	−4.00000			−0.162355			−0.0811775	+	0.996700i	$0.525868\pi$
$608$	−3.05971	−	5.29958i	−0.124088	−	0.214926i
$609$		0			0
$610$	2.74306	−	4.75112i	0.111063	−	0.192367i
$611$	−6.59167	+	11.4171i	−0.266671	+	0.461887i
$612$		0			0
$613$	−2.61943	−	4.53698i	−0.105798	−	0.183247i	0.808266	−	0.588817i	$-0.200406\pi$
$613$	−2.61943	−	4.53698i	−0.105798	−	0.183247i	−0.914064	+	0.405570i	$0.867073\pi$
$614$	−6.00000	−	10.3923i	−0.242140	−	0.419399i
$615$		0			0
$616$		0			0
$617$	−20.4083	−	35.3483i	−0.821608	−	1.42307i	−0.904484	−	0.426507i	$-0.859744\pi$
$617$	−20.4083	−	35.3483i	−0.821608	−	1.42307i	0.0828757	−	0.996560i	$-0.473590\pi$
$618$		0			0
$619$	14.7889			0.594416			0.297208	−	0.954813i	$-0.403945\pi$
$619$	14.7889			0.594416			0.297208	+	0.954813i	$0.403945\pi$
$620$	−0.545837	−	0.945417i	−0.0219213	−	0.0379688i
$621$		0			0
$622$	−21.9083			−0.878444
$623$	−7.50000	+	2.59808i	−0.300481	+	0.104090i
$624$		0			0
$625$	1.00000			0.0400000
$626$	−5.74306	+	9.94727i	−0.229539	+	0.397573i
$627$		0			0
$628$	3.63751	+	6.30035i	0.145152	+	0.251411i
$629$	20.2111			0.805869
$630$		0			0
$631$	26.7889			1.06645			0.533225	−	0.845974i	$-0.320980\pi$
$631$	26.7889			1.06645			0.533225	+	0.845974i	$0.320980\pi$
$632$	−19.2250	−	33.2986i	−0.764729	−	1.32455i
$633$		0			0
$634$	−3.65139	+	6.32439i	−0.145015	+	0.251174i
$635$	−4.00000			−0.158735
$636$		0			0
$637$	8.83053	−	6.95224i	0.349878	−	0.275458i
$638$		0			0
$639$		0			0
$640$	4.04584	+	7.00759i	0.159926	+	0.276999i
$641$	6.00000			0.236986			0.118493	−	0.992955i	$-0.462194\pi$
$641$	6.00000			0.236986			0.118493	+	0.992955i	$0.462194\pi$
$642$		0			0
$643$	−3.28890	−	5.69654i	−0.129701	−	0.224650i	0.793859	−	0.608101i	$-0.208069\pi$
$643$	−3.28890	−	5.69654i	−0.129701	−	0.224650i	−0.923561	+	0.383452i	$0.874735\pi$
$644$	−3.94449	+	1.36641i	−0.155435	+	0.0538441i
$645$		0			0
$646$	13.1653	+	22.8029i	0.517980	+	0.897168i
$647$	−13.5000	−	23.3827i	−0.530740	−	0.919268i	−0.999357	−	0.0358667i	$-0.988581\pi$
$647$	−13.5000	−	23.3827i	−0.530740	−	0.919268i	0.468617	−	0.883402i	$-0.344753\pi$
$648$		0			0
$649$		0			0
$650$	1.04584	−	1.81144i	0.0410211	−	0.0710506i
$651$		0			0
$652$	−2.75694	−	4.77516i	−0.107970	−	0.187010i
$653$	−16.4222			−0.642651			−0.321325	−	0.946969i	$-0.604128\pi$
$653$	−16.4222			−0.642651			−0.321325	+	0.946969i	$0.604128\pi$
$654$		0			0
$655$	−6.78890			−0.265264
$656$	−4.95416	+	8.58086i	−0.193428	+	0.335026i
$657$		0			0
$658$	−26.7431	+	9.26407i	−1.04255	+	0.361151i
$659$	19.2250	−	33.2986i	0.748899	−	1.29713i	−0.199452	−	0.979908i	$-0.563916\pi$
$659$	19.2250	−	33.2986i	0.748899	−	1.29713i	0.948351	−	0.317223i	$-0.102750\pi$
$660$		0			0
$661$	6.50000	−	11.2583i	0.252821	−	0.437898i	−0.711481	−	0.702706i	$-0.751975\pi$
$661$	6.50000	−	11.2583i	0.252821	−	0.437898i	0.964301	+	0.264807i	$0.0853084\pi$
$662$	−13.0458	+	22.5961i	−0.507041	+	0.878220i
$663$		0			0
$664$	−21.3167	+	36.9215i	−0.827247	+	1.43283i
$665$	−9.01388	+	3.12250i	−0.349543	+	0.121085i
$666$		0			0
$667$	21.3944	−	37.0563i	0.828396	−	1.43482i
$668$	1.14719			0.0443860
$669$		0			0
$670$	−5.48612			−0.211947
$671$		0			0
$672$		0			0
$673$	−11.2250	+	19.4422i	−0.432691	+	0.749443i	−0.997104	−	0.0760495i	$-0.975769\pi$
$673$	−11.2250	+	19.4422i	−0.432691	+	0.749443i	0.564413	+	0.825493i	$0.309103\pi$
$674$	−17.9819	+	31.1456i	−0.692638	+	1.19968i
$675$		0			0
$676$	−1.57779	−	2.73282i	−0.0606844	−	0.105108i
$677$	18.1972	+	31.5185i	0.699376	+	1.21136i	0.968683	+	0.248301i	$0.0798721\pi$
$677$	18.1972	+	31.5185i	0.699376	+	1.21136i	−0.269307	+	0.963054i	$0.586795\pi$
$678$		0			0
$679$	34.0139	−	11.7828i	1.30533	−	0.452181i
$680$	8.40833	+	14.5636i	0.322445	+	0.558490i
$681$		0			0
$682$		0			0
$683$	6.31665	+	10.9408i	0.241700	+	0.418637i	0.961199	−	0.275857i	$-0.0889617\pi$
$683$	6.31665	+	10.9408i	0.241700	+	0.418637i	−0.719499	+	0.694494i	$0.755628\pi$
$684$		0			0
$685$	−0.788897			−0.0301422
$686$	24.1013	+	1.12824i	0.920194	+	0.0430763i
$687$		0			0
$688$	−13.9083			−0.530250
$689$	0.316654	−	0.548461i	0.0120636	−	0.0208947i
$690$		0			0
$691$	20.1972	+	34.9826i	0.768339	+	1.33080i	0.938463	+	0.345379i	$0.112250\pi$
$691$	20.1972	+	34.9826i	0.768339	+	1.33080i	−0.170125	+	0.985423i	$0.554417\pi$
$692$	6.90833			0.262615
$693$		0			0
$694$	−40.9361			−1.55391
$695$	−9.80278	−	16.9789i	−0.371840	−	0.644047i
$696$		0			0
$697$	−8.40833	+	14.5636i	−0.318488	+	0.551638i
$698$	−34.6972			−1.31331
$699$		0			0
$700$	−0.756939	+	0.262211i	−0.0286096	+	0.00991066i
$701$	−38.8444			−1.46713			−0.733567	−	0.679618i	$-0.762146\pi$
$701$	−38.8444			−1.46713			−0.733567	+	0.679618i	$0.762146\pi$
$702$		0			0
$703$	−6.50000	−	11.2583i	−0.245152	−	0.424616i
$704$		0			0
$705$		0			0
$706$	−3.90833	−	6.76942i	−0.147092	−	0.254771i
$707$	32.8444	+	28.4441i	1.23524	+	1.06975i
$708$		0			0
$709$	−6.28890	−	10.8927i	−0.236185	−	0.409084i	0.723432	−	0.690396i	$-0.242564\pi$
$709$	−6.28890	−	10.8927i	−0.236185	−	0.409084i	−0.959616	+	0.281312i	$0.909230\pi$
$710$		0			0
$711$		0			0
$712$	4.50000	−	7.79423i	0.168645	−	0.292101i
$713$	9.39445	−	16.2717i	0.351825	−	0.609379i
$714$		0			0
$715$		0			0
$716$	0.358288			0.0133899
$717$		0			0
$718$	9.35829			0.349248
$719$	−11.0139	+	19.0766i	−0.410748	+	0.711437i	−0.994972	−	0.100156i	$-0.968066\pi$
$719$	−11.0139	+	19.0766i	−0.410748	+	0.711437i	0.584223	+	0.811593i	$0.301399\pi$
$720$		0			0
$721$	−16.0000	−	13.8564i	−0.595871	−	0.516040i
$722$	−3.90833	+	6.76942i	−0.145453	+	0.251932i
$723$		0			0
$724$	−3.09167	+	5.35493i	−0.114901	+	0.199015i
$725$	4.10555	−	7.11102i	0.152476	−	0.264097i
$726$		0			0
$727$	5.71110	−	9.89192i	0.211813	−	0.366871i	−0.740469	−	0.672091i	$-0.765397\pi$
$727$	5.71110	−	9.89192i	0.211813	−	0.366871i	0.952282	+	0.305220i	$0.0987299\pi$
$728$	−2.40833	+	12.5140i	−0.0892585	+	0.463801i
$729$		0			0
$730$	−2.34861	+	4.06792i	−0.0869260	+	0.150560i
$731$	−23.6056			−0.873083
$732$		0			0
$733$	−10.0000			−0.369358			−0.184679	−	0.982799i	$-0.559125\pi$
$733$	−10.0000			−0.369358			−0.184679	+	0.982799i	$0.559125\pi$
$734$	−9.39445	−	16.2717i	−0.346755	−	0.600598i
$735$		0			0
$736$	4.42221	−	7.65948i	0.163005	−	0.282332i
$737$		0			0
$738$		0			0
$739$	1.40833	+	2.43929i	0.0518061	+	0.0897309i	0.890766	−	0.454463i	$-0.150169\pi$
$739$	1.40833	+	2.43929i	0.0518061	+	0.0897309i	−0.838959	+	0.544194i	$0.816836\pi$
$740$	−0.545837	−	0.945417i	−0.0200654	−	0.0347542i
$741$		0			0
$742$	1.28470	−	0.445032i	0.0471627	−	0.0163376i
$743$	−13.5000	−	23.3827i	−0.495267	−	0.857828i	0.504718	−	0.863284i	$-0.331596\pi$
$743$	−13.5000	−	23.3827i	−0.495267	−	0.857828i	−0.999985	+	0.00545664i	$0.998263\pi$
$744$		0			0
$745$	23.2111			0.850389
$746$	−24.5139	−	42.4593i	−0.897517	−	1.55454i
$747$		0			0
$748$		0			0
$749$	22.5000	−	7.79423i	0.822132	−	0.284795i
$750$		0			0
$751$	−4.00000			−0.145962			−0.0729810	−	0.997333i	$-0.523251\pi$
$751$	−4.00000			−0.145962			−0.0729810	+	0.997333i	$0.523251\pi$
$752$	13.5597	−	23.4861i	0.494472	−	0.856450i
$753$		0			0
$754$	−8.58747	−	14.8739i	−0.312737	−	0.541677i
$755$	−16.0000			−0.582300
$756$		0			0
$757$	−37.6333			−1.36781			−0.683903	−	0.729573i	$-0.739719\pi$
$757$	−37.6333			−1.36781			−0.683903	+	0.729573i	$0.739719\pi$
$758$	−2.60555	−	4.51295i	−0.0946379	−	0.163918i
$759$		0			0
$760$	5.40833	−	9.36750i	0.196181	−	0.339795i
$761$	30.0000			1.08750			0.543750	−	0.839248i	$-0.317004\pi$
$761$	30.0000			1.08750			0.543750	+	0.839248i	$0.317004\pi$
$762$		0			0
$763$	9.10555	−	47.3138i	0.329643	−	1.71288i
$764$	−1.69722			−0.0614034
$765$		0			0
$766$	−1.02776	−	1.78013i	−0.0371343	−	0.0643186i
$767$	18.6333			0.672810
$768$		0			0
$769$	−1.31665	−	2.28051i	−0.0474798	−	0.0822373i	0.841309	−	0.540555i	$-0.181786\pi$
$769$	−1.31665	−	2.28051i	−0.0474798	−	0.0822373i	−0.888789	+	0.458317i	$0.848452\pi$
$770$		0			0
$771$		0			0
$772$	−2.12363	−	3.67824i	−0.0764312	−	0.132383i
$773$	−8.40833	−	14.5636i	−0.302426	−	0.523818i	0.674259	−	0.738495i	$-0.264463\pi$
$773$	−8.40833	−	14.5636i	−0.302426	−	0.523818i	−0.976685	+	0.214677i	$0.931130\pi$
$774$		0			0
$775$	1.80278	−	3.12250i	0.0647576	−	0.112163i
$776$	−20.4083	+	35.3483i	−0.732616	+	1.26893i
$777$		0			0
$778$	11.7250	+	20.3083i	0.420361	+	0.728086i
$779$	10.8167			0.387547
$780$		0			0
$781$		0			0
$782$	−19.0278	+	32.9570i	−0.680431	+	1.17854i
$783$		0			0
$784$	−18.1653	+	14.3014i	−0.648760	+	0.510766i
$785$	−12.0139	+	20.8086i	−0.428794	+	0.742692i
$786$		0			0
$787$	11.7111	−	20.2842i	0.417456	−	0.723055i	−0.578227	−	0.815876i	$-0.696255\pi$
$787$	11.7111	−	20.2842i	0.417456	−	0.723055i	0.995683	+	0.0928214i	$0.0295886\pi$
$788$	−0.908327	+	1.57327i	−0.0323578	+	0.0560454i
$789$		0			0
$790$	8.34861	−	14.4602i	0.297030	−	0.514472i
$791$	5.40833	−	28.1025i	0.192298	−	0.999210i
$792$		0			0
$793$	−3.38057	+	5.85532i	−0.120048	+	0.207929i
$794$	11.4861			0.407627
$795$		0			0
$796$	0.852814			0.0302272
$797$	−0.591673	−	1.02481i	−0.0209581	−	0.0363006i	0.855356	−	0.518040i	$-0.173338\pi$
$797$	−0.591673	−	1.02481i	−0.0209581	−	0.0363006i	−0.876314	+	0.481740i	$0.840005\pi$
$798$		0			0
$799$	23.0139	−	39.8612i	0.814172	−	1.41019i
$800$	0.848612	−	1.46984i	0.0300030	−	0.0519667i
$801$		0			0
$802$	−3.90833	−	6.76942i	−0.138008	−	0.239037i
$803$		0			0
$804$		0			0
$805$	−10.4222	−	9.02589i	−0.367334	−	0.318121i
$806$	−3.77082	−	6.53125i	−0.132821	−	0.230053i
$807$		0			0
$808$	−49.2666			−1.73319
$809$	−10.5000	−	18.1865i	−0.369160	−	0.639404i	0.620274	−	0.784385i	$-0.287021\pi$
$809$	−10.5000	−	18.1865i	−0.369160	−	0.639404i	−0.989434	+	0.144981i	$0.953688\pi$
$810$		0			0
$811$	42.4222			1.48965			0.744823	−	0.667263i	$-0.232534\pi$
$811$	42.4222			1.48965			0.744823	+	0.667263i	$0.232534\pi$
$812$	−1.24306	+	6.45913i	−0.0436229	+	0.226671i
$813$		0			0
$814$		0			0
$815$	9.10555	−	15.7713i	0.318954	−	0.552444i
$816$		0			0
$817$	7.59167	+	13.1492i	0.265599	+	0.460031i
$818$	1.30278			0.0455505
$819$		0			0
$820$	0.908327			0.0317202
$821$	7.50000	+	12.9904i	0.261752	+	0.453367i	0.966708	−	0.255884i	$-0.0823665\pi$
$821$	7.50000	+	12.9904i	0.261752	+	0.453367i	−0.704956	+	0.709251i	$0.749033\pi$
$822$		0			0
$823$	0.500000	−	0.866025i	0.0174289	−	0.0301877i	−0.857179	−	0.515018i	$-0.827785\pi$
$823$	0.500000	−	0.866025i	0.0174289	−	0.0301877i	0.874608	+	0.484830i	$0.161119\pi$
$824$	24.0000			0.836080
$825$		0			0
$826$	30.2389	+	26.1876i	1.05214	+	0.911184i
$827$	−48.0000			−1.66912			−0.834562	−	0.550914i	$-0.814279\pi$
$827$	−48.0000			−1.66912			−0.834562	+	0.550914i	$0.814279\pi$
$828$		0			0
$829$	−16.7111	−	28.9445i	−0.580401	−	1.00528i	−0.995432	−	0.0954761i	$-0.969563\pi$
$829$	−16.7111	−	28.9445i	−0.580401	−	1.00528i	0.415031	−	0.909807i	$-0.363771\pi$
$830$	−18.5139			−0.642626
$831$		0			0
$832$	−7.07779	−	12.2591i	−0.245378	−	0.425008i
$833$	−30.8305	+	24.2727i	−1.06821	+	0.841001i
$834$		0			0
$835$	1.89445	+	3.28128i	0.0655601	+	0.113553i
$836$		0			0
$837$		0			0
$838$	−10.9542	+	18.9732i	−0.378405	+	0.655417i
$839$	17.4083	−	30.1521i	0.601002	−	1.04097i	−0.391667	−	0.920107i	$-0.628102\pi$
$839$	17.4083	−	30.1521i	0.601002	−	1.04097i	0.992670	−	0.120859i	$-0.0385650\pi$
$840$		0			0
$841$	−19.2111	−	33.2746i	−0.662452	−	1.14740i
$842$	30.5139			1.05158
$843$		0			0
$844$	−5.45837			−0.187885
$845$	5.21110	−	9.02589i	0.179267	−	0.310500i
$846$		0			0
$847$	22.0000	+	19.0526i	0.755929	+	0.654654i
$848$	−0.651388	+	1.12824i	−0.0223687	+	0.0387438i
$849$		0			0
$850$	−3.65139	+	6.32439i	−0.125242	+	0.216925i
$851$	9.39445	−	16.2717i	0.322038	−	0.557785i
$852$		0			0
$853$	19.0139	−	32.9330i	0.651023	−	1.12760i	−0.331852	−	0.943331i	$-0.607674\pi$
$853$	19.0139	−	32.9330i	0.651023	−	1.12760i	0.982875	−	0.184273i	$-0.0589931\pi$
$854$	−13.7153	+	4.75112i	−0.469328	+	0.162580i
$855$		0			0
$856$	−13.5000	+	23.3827i	−0.461421	+	0.799204i
$857$	−9.63331			−0.329068			−0.164534	−	0.986371i	$-0.552612\pi$
$857$	−9.63331			−0.329068			−0.164534	+	0.986371i	$0.552612\pi$
$858$		0			0
$859$	−28.0000			−0.955348			−0.477674	−	0.878537i	$-0.658520\pi$
$859$	−28.0000			−0.955348			−0.477674	+	0.878537i	$0.658520\pi$
$860$	0.637510	+	1.10420i	0.0217389	+	0.0376529i
$861$		0			0
$862$	−4.16527	+	7.21445i	−0.141870	+	0.245725i
$863$	−0.316654	+	0.548461i	−0.0107790	+	0.0186698i	−0.871365	−	0.490636i	$-0.836764\pi$
$863$	−0.316654	+	0.548461i	−0.0107790	+	0.0186698i	0.860586	+	0.509306i	$0.170098\pi$
$864$		0			0
$865$	11.4083	+	19.7598i	0.387895	+	0.671853i
$866$	14.8806	+	25.7739i	0.505662	+	0.875833i
$867$		0			0
$868$	−0.545837	+	2.83625i	−0.0185269	+	0.0962686i
$869$		0			0
$870$		0			0
$871$	6.76114			0.229093
$872$	27.3167	+	47.3138i	0.925059	+	1.60225i
$873$		0			0
$874$	24.4777			0.827971
$875$	−2.00000	−	1.73205i	−0.0676123	−	0.0585540i
$876$		0			0
$877$	2.00000			0.0675352			0.0337676	−	0.999430i	$-0.489249\pi$
$877$	2.00000			0.0675352			0.0337676	+	0.999430i	$0.489249\pi$
$878$	−8.62363	+	14.9366i	−0.291033	+	0.504085i
$879$		0			0
$880$		0			0
$881$	45.6333			1.53743			0.768713	−	0.639594i	$-0.220898\pi$
$881$	45.6333			1.53743			0.768713	+	0.639594i	$0.220898\pi$
$882$		0			0
$883$	−38.4222			−1.29301			−0.646505	−	0.762910i	$-0.723770\pi$
$883$	−38.4222			−1.29301			−0.646505	+	0.762910i	$0.723770\pi$
$884$	−1.36249	−	2.35990i	−0.0458255	−	0.0793721i
$885$		0			0
$886$	4.32086	−	7.48394i	0.145162	−	0.251428i
$887$	−29.2111			−0.980813			−0.490406	−	0.871494i	$-0.663152\pi$
$887$	−29.2111			−0.980813			−0.490406	+	0.871494i	$0.663152\pi$
$888$		0			0
$889$	8.00000	+	6.92820i	0.268311	+	0.232364i
$890$	3.90833			0.131007
$891$		0			0
$892$	0.876369	+	1.51791i	0.0293430	+	0.0508235i
$893$	−29.6056			−0.990712
$894$		0			0
$895$	0.591673	+	1.02481i	0.0197775	+	0.0342555i
$896$	4.04584	−	21.0228i	0.135162	−	0.702322i
$897$		0			0
$898$	−14.0917	−	24.4075i	−0.470245	−	0.814489i
$899$	−14.8028	−	25.6392i	−0.493700	−	0.855114i
$900$		0			0
$901$	−1.10555	+	1.91487i	−0.0368313	+	0.0637936i
$902$		0			0
$903$		0			0
$904$	16.2250	+	28.1025i	0.539635	+	0.934675i
$905$	−20.4222			−0.678857
$906$		0			0
$907$	−42.0555			−1.39643			−0.698215	−	0.715888i	$-0.746022\pi$
$907$	−42.0555			−1.39643			−0.698215	+	0.715888i	$0.746022\pi$
$908$	0.788897	−	1.36641i	0.0261805	−	0.0453459i
$909$		0			0
$910$	−5.22918	+	1.81144i	−0.173346	+	0.0600487i
$911$	−28.2250	+	48.8871i	−0.935135	+	1.61970i	−0.160743	+	0.986996i	$0.551389\pi$
$911$	−28.2250	+	48.8871i	−0.935135	+	1.61970i	−0.774392	+	0.632706i	$0.781944\pi$
$912$		0			0
$913$		0			0
$914$	−14.5875	+	25.2662i	−0.482511	+	0.835733i
$915$		0			0
$916$	−0.724981	+	1.25570i	−0.0239540	+	0.0414896i
$917$	13.5778	+	11.7587i	0.448378	+	0.388307i
$918$		0			0
$919$	5.19722	−	9.00186i	0.171441	−	0.296944i	−0.767483	−	0.641069i	$-0.778491\pi$
$919$	5.19722	−	9.00186i	0.171441	−	0.296944i	0.938924	+	0.344125i	$0.111825\pi$
$920$	15.6333			0.515415
$921$		0			0
$922$	−40.9361			−1.34816
$923$		0			0
$924$		0			0
$925$	1.80278	−	3.12250i	0.0592749	−	0.102667i
$926$	−15.7708	+	27.3159i	−0.518261	+	0.897655i
$927$		0			0
$928$	−6.96804	−	12.0690i	−0.228737	−	0.396184i
$929$	4.10555	+	7.11102i	0.134699	+	0.233305i	0.925482	−	0.378791i	$-0.123660\pi$
$929$	4.10555	+	7.11102i	0.134699	+	0.233305i	−0.790784	+	0.612096i	$0.790327\pi$
$930$		0			0
$931$	23.4361	+	9.36750i	0.768087	+	0.307007i
$932$	2.54584	+	4.40952i	0.0833916	+	0.144439i
$933$		0			0
$934$	−9.66947			−0.316395
$935$		0			0
$936$		0			0
$937$	−16.7889			−0.548469			−0.274235	−	0.961663i	$-0.588425\pi$
$937$	−16.7889			−0.548469			−0.274235	+	0.961663i	$0.588425\pi$
$938$	10.9722	+	9.50224i	0.358256	+	0.310259i
$939$		0			0
$940$	−2.48612			−0.0810884
$941$	7.50000	−	12.9904i	0.244493	−	0.423474i	−0.717496	−	0.696563i	$-0.754712\pi$
$941$	7.50000	−	12.9904i	0.244493	−	0.423474i	0.961989	+	0.273088i	$0.0880451\pi$
$942$		0			0
$943$	7.81665	+	13.5388i	0.254545	+	0.440885i
$944$	−38.3305			−1.24755
$945$		0			0
$946$		0			0
$947$	7.89445	+	13.6736i	0.256535	+	0.444332i	0.965311	−	0.261102i	$-0.0840857\pi$
$947$	7.89445	+	13.6736i	0.256535	+	0.444332i	−0.708776	+	0.705433i	$0.750752\pi$
$948$		0			0
$949$	2.89445	−	5.01333i	0.0939578	−	0.162740i
$950$	4.69722			0.152398
$951$		0			0
$952$	8.40833	−	43.6909i	0.272515	−	1.41603i
$953$	56.0555			1.81582			0.907908	−	0.419169i	$-0.137679\pi$
$953$	56.0555			1.81582			0.907908	+	0.419169i	$0.137679\pi$
$954$		0			0
$955$	−2.80278	−	4.85455i	−0.0906957	−	0.157090i
$956$	−0.119429			−0.00386262
$957$		0			0
$958$	−14.6056	−	25.2976i	−0.471884	−	0.817327i
$959$	1.57779	+	1.36641i	0.0509497	+	0.0441237i
$960$		0			0
$961$	9.00000	+	15.5885i	0.290323	+	0.502853i
$962$	−3.77082	−	6.53125i	−0.121576	−	0.210576i
$963$		0			0
$964$	−0.486122	+	0.841988i	−0.0156569	+	0.0271186i
$965$	7.01388	−	12.1484i	0.225785	−	0.391071i
$966$		0			0
$967$	−12.9222	−	22.3819i	−0.415550	−	0.719754i	0.579936	−	0.814662i	$-0.303078\pi$
$967$	−12.9222	−	22.3819i	−0.415550	−	0.719754i	−0.995486	+	0.0949082i	$0.969744\pi$
$968$	−33.0000			−1.06066
$969$		0			0
$970$	−17.7250			−0.569115
$971$	2.80278	−	4.85455i	0.0899454	−	0.155790i	−0.817542	−	0.575868i	$-0.804664\pi$
$971$	2.80278	−	4.85455i	0.0899454	−	0.155790i	0.907488	+	0.420078i	$0.137997\pi$
$972$		0			0
$973$	−9.80278	+	50.9367i	−0.314263	+	1.63296i
$974$	−14.7431	+	25.5357i	−0.472398	+	0.818218i
$975$		0			0
$976$	6.95416	−	12.0450i	0.222597	−	0.385550i
$977$	10.6194	−	18.3934i	0.339746	−	0.588457i	−0.644639	−	0.764487i	$-0.722992\pi$
$977$	10.6194	−	18.3934i	0.339746	−	0.588457i	0.984385	+	0.176030i	$0.0563257\pi$
$978$		0			0
$979$		0			0
$980$	1.96804	+	0.786634i	0.0628668	+	0.0251281i
$981$		0			0
$982$	25.0458	−	43.3807i	0.799245	−	1.38433i
$983$	−26.0555			−0.831042			−0.415521	−	0.909584i	$-0.636401\pi$
$983$	−26.0555			−0.831042			−0.415521	+	0.909584i	$0.636401\pi$
$984$		0			0
$985$	−6.00000			−0.191176
$986$	29.9819	+	51.9302i	0.954819	+	1.65379i
$987$		0			0
$988$	−0.876369	+	1.51791i	−0.0278810	+	0.0482913i
$989$	−10.9722	+	19.0045i	−0.348897	+	0.604307i
$990$		0			0
$991$	−11.6194	−	20.1254i	−0.369103	−	0.639306i	0.620322	−	0.784347i	$-0.287002\pi$
$991$	−11.6194	−	20.1254i	−0.369103	−	0.639306i	−0.989426	+	0.145041i	$0.953668\pi$
$992$	−3.05971	−	5.29958i	−0.0971460	−	0.168262i
$993$		0			0
$994$		0			0
$995$	1.40833	+	2.43929i	0.0446470	+	0.0773308i
$996$		0			0
$997$	−53.2666			−1.68697			−0.843485	−	0.537152i	$-0.819500\pi$
$997$	−53.2666			−1.68697			−0.843485	+	0.537152i	$0.819500\pi$
$998$	−18.2389	−	31.5906i	−0.577341	−	0.999984i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.k.a.856.2		4
3.2	odd	2		315.2.k.a.16.1	✓	4
7.4	even	3		945.2.l.a.46.1		4
9.4	even	3		945.2.l.a.226.1		4
9.5	odd	6		315.2.l.a.121.2	yes	4
21.11	odd	6		315.2.l.a.151.2	yes	4
63.4	even	3	inner	945.2.k.a.361.2		4
63.32	odd	6		315.2.k.a.256.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.a.16.1	✓	4	3.2	odd	2
315.2.k.a.256.1	yes	4	63.32	odd	6
315.2.l.a.121.2	yes	4	9.5	odd	6
315.2.l.a.151.2	yes	4	21.11	odd	6
945.2.k.a.361.2		4	63.4	even	3	inner
945.2.k.a.856.2		4	1.1	even	1	trivial
945.2.l.a.46.1		4	7.4	even	3
945.2.l.a.226.1		4	9.4	even	3

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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.k (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.651388 + 1.12824i) q^{2} +(0.151388 - 0.262211i) q^{4} +1.00000 q^{5} +(-2.00000 - 1.73205i) q^{7} +3.00000 q^{8} +O(q^{10})\)	\(q+(0.651388 + 1.12824i) q^{2} +(0.151388 - 0.262211i) q^{4} +1.00000 q^{5} +(-2.00000 - 1.73205i) q^{7} +3.00000 q^{8} +(0.651388 + 1.12824i) q^{10} +(-0.802776 - 1.39045i) q^{13} +(0.651388 - 3.38471i) q^{14} +(1.65139 + 2.86029i) q^{16} +(2.80278 + 4.85455i) q^{17} +(1.80278 - 3.12250i) q^{19} +(0.151388 - 0.262211i) q^{20} +5.21110 q^{23} +1.00000 q^{25} +(1.04584 - 1.81144i) q^{26} +(-0.756939 + 0.262211i) q^{28} +(4.10555 - 7.11102i) q^{29} +(1.80278 - 3.12250i) q^{31} +(0.848612 - 1.46984i) q^{32} +(-3.65139 + 6.32439i) q^{34} +(-2.00000 - 1.73205i) q^{35} +(1.80278 - 3.12250i) q^{37} +4.69722 q^{38} +3.00000 q^{40} +(1.50000 + 2.59808i) q^{41} +(-2.10555 + 3.64692i) q^{43} +(3.39445 + 5.87936i) q^{46} +(-4.10555 - 7.11102i) q^{47} +(1.00000 + 6.92820i) q^{49} +(0.651388 + 1.12824i) q^{50} -0.486122 q^{52} +(0.197224 + 0.341603i) q^{53} +(-6.00000 - 5.19615i) q^{56} +10.6972 q^{58} +(-5.80278 + 10.0507i) q^{59} +(-2.10555 - 3.64692i) q^{61} +4.69722 q^{62} +8.81665 q^{64} +(-0.802776 - 1.39045i) q^{65} +(-2.10555 + 3.64692i) q^{67} +1.69722 q^{68} +(0.651388 - 3.38471i) q^{70} +(1.80278 + 3.12250i) q^{73} +4.69722 q^{74} +(-0.545837 - 0.945417i) q^{76} +(-6.40833 - 11.0995i) q^{79} +(1.65139 + 2.86029i) q^{80} +(-1.95416 + 3.38471i) q^{82} +(-7.10555 + 12.3072i) q^{83} +(2.80278 + 4.85455i) q^{85} -5.48612 q^{86} +(1.50000 - 2.59808i) q^{89} +(-0.802776 + 4.17134i) q^{91} +(0.788897 - 1.36641i) q^{92} +(5.34861 - 9.26407i) q^{94} +(1.80278 - 3.12250i) q^{95} +(-6.80278 + 11.7828i) q^{97} +(-7.16527 + 5.64118i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - 3 q^{4} + 4 q^{5} - 8 q^{7} + 12 q^{8}+O(q^{10}) \) 4 * q - q^2 - 3 * q^4 + 4 * q^5 - 8 * q^7 + 12 * q^8	\( 4 q - q^{2} - 3 q^{4} + 4 q^{5} - 8 q^{7} + 12 q^{8} - q^{10} + 4 q^{13} - q^{14} + 3 q^{16} + 4 q^{17} - 3 q^{20} - 8 q^{23} + 4 q^{25} + 15 q^{26} + 15 q^{28} + 2 q^{29} + 7 q^{32} - 11 q^{34} - 8 q^{35} + 26 q^{38} + 12 q^{40} + 6 q^{41} + 6 q^{43} + 28 q^{46} - 2 q^{47} + 4 q^{49} - q^{50} - 38 q^{52} + 8 q^{53} - 24 q^{56} + 50 q^{58} - 16 q^{59} + 6 q^{61} + 26 q^{62} - 8 q^{64} + 4 q^{65} + 6 q^{67} + 14 q^{68} - q^{70} + 26 q^{74} - 13 q^{76} - 4 q^{79} + 3 q^{80} + 3 q^{82} - 14 q^{83} + 4 q^{85} - 58 q^{86} + 6 q^{89} + 4 q^{91} + 32 q^{92} + 25 q^{94} - 20 q^{97} + 11 q^{98}+O(q^{100}) \) 4 * q - q^2 - 3 * q^4 + 4 * q^5 - 8 * q^7 + 12 * q^8 - q^10 + 4 * q^13 - q^14 + 3 * q^16 + 4 * q^17 - 3 * q^20 - 8 * q^23 + 4 * q^25 + 15 * q^26 + 15 * q^28 + 2 * q^29 + 7 * q^32 - 11 * q^34 - 8 * q^35 + 26 * q^38 + 12 * q^40 + 6 * q^41 + 6 * q^43 + 28 * q^46 - 2 * q^47 + 4 * q^49 - q^50 - 38 * q^52 + 8 * q^53 - 24 * q^56 + 50 * q^58 - 16 * q^59 + 6 * q^61 + 26 * q^62 - 8 * q^64 + 4 * q^65 + 6 * q^67 + 14 * q^68 - q^70 + 26 * q^74 - 13 * q^76 - 4 * q^79 + 3 * q^80 + 3 * q^82 - 14 * q^83 + 4 * q^85 - 58 * q^86 + 6 * q^89 + 4 * q^91 + 32 * q^92 + 25 * q^94 - 20 * q^97 + 11 * q^98

Introduction

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