LMFDB - Embedded newform 945.2.l.a.226.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(46,945)]

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([4, 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("945.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.l (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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.1
Root			$1.15139 - 1.99426i$ of defining polynomial
Character	$\chi$	$=$	945.226
Dual form			945.2.l.a.46.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.30278 q^{2} -0.302776 q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.50000 - 0.866025i) q^{7} +3.00000 q^{8} +O(q^{10})$	\(q-1.30278 q^{2} -0.302776 q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.50000 - 0.866025i) q^{7} +3.00000 q^{8} +(0.651388 + 1.12824i) q^{10} +(-0.802776 + 1.39045i) q^{13} +(-3.25694 + 1.12824i) q^{14} -3.30278 q^{16} +(2.80278 + 4.85455i) q^{17} +(1.80278 - 3.12250i) q^{19} +(0.151388 + 0.262211i) q^{20} +(-2.60555 - 4.51295i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(1.04584 - 1.81144i) q^{26} +(-0.756939 + 0.262211i) q^{28} +(4.10555 + 7.11102i) q^{29} -3.60555 q^{31} -1.69722 q^{32} +(-3.65139 - 6.32439i) q^{34} +(-2.00000 - 1.73205i) q^{35} +(1.80278 - 3.12250i) q^{37} +(-2.34861 + 4.06792i) q^{38} +(-1.50000 - 2.59808i) q^{40} +(1.50000 - 2.59808i) q^{41} +(-2.10555 - 3.64692i) q^{43} +(3.39445 + 5.87936i) q^{46} +8.21110 q^{47} +(5.50000 - 4.33013i) q^{49} +(0.651388 - 1.12824i) q^{50} +(0.243061 - 0.420994i) q^{52} +(0.197224 + 0.341603i) q^{53} +(7.50000 - 2.59808i) q^{56} +(-5.34861 - 9.26407i) q^{58} +11.6056 q^{59} +4.21110 q^{61} +4.69722 q^{62} +8.81665 q^{64} +1.60555 q^{65} +4.21110 q^{67} +(-0.848612 - 1.46984i) q^{68} +(2.60555 + 2.25647i) q^{70} +(1.80278 + 3.12250i) q^{73} +(-2.34861 + 4.06792i) q^{74} +(-0.545837 + 0.945417i) q^{76} +12.8167 q^{79} +(1.65139 + 2.86029i) q^{80} +(-1.95416 + 3.38471i) q^{82} +(-7.10555 - 12.3072i) q^{83} +(2.80278 - 4.85455i) q^{85} +(2.74306 + 4.75112i) q^{86} +(1.50000 - 2.59808i) q^{89} +(-0.802776 + 4.17134i) q^{91} +(0.788897 + 1.36641i) q^{92} -10.6972 q^{94} -3.60555 q^{95} +(-6.80278 - 11.7828i) q^{97} +(-7.16527 + 5.64118i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 10 q^{7} + 12 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 + 6 * q^4 - 2 * q^5 + 10 * q^7 + 12 * q^8	$ 4 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 10 q^{7} + 12 q^{8} - q^{10} + 4 q^{13} + 5 q^{14} - 6 q^{16} + 4 q^{17} - 3 q^{20} + 4 q^{23} - 2 q^{25} + 15 q^{26} + 15 q^{28} + 2 q^{29} - 14 q^{32} - 11 q^{34} - 8 q^{35} - 13 q^{38} - 6 q^{40} + 6 q^{41} + 6 q^{43} + 28 q^{46} + 4 q^{47} + 22 q^{49} - q^{50} + 19 q^{52} + 8 q^{53} + 30 q^{56} - 25 q^{58} + 32 q^{59} - 12 q^{61} + 26 q^{62} - 8 q^{64} - 8 q^{65} - 12 q^{67} - 7 q^{68} - 4 q^{70} - 13 q^{74} - 13 q^{76} + 8 q^{79} + 3 q^{80} + 3 q^{82} - 14 q^{83} + 4 q^{85} + 29 q^{86} + 6 q^{89} + 4 q^{91} + 32 q^{92} - 50 q^{94} - 20 q^{97} + 11 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 + 6 * q^4 - 2 * q^5 + 10 * q^7 + 12 * q^8 - q^10 + 4 * q^13 + 5 * q^14 - 6 * q^16 + 4 * q^17 - 3 * q^20 + 4 * q^23 - 2 * q^25 + 15 * q^26 + 15 * q^28 + 2 * q^29 - 14 * q^32 - 11 * q^34 - 8 * q^35 - 13 * q^38 - 6 * q^40 + 6 * q^41 + 6 * q^43 + 28 * q^46 + 4 * q^47 + 22 * q^49 - q^50 + 19 * q^52 + 8 * q^53 + 30 * q^56 - 25 * q^58 + 32 * q^59 - 12 * q^61 + 26 * q^62 - 8 * q^64 - 8 * q^65 - 12 * q^67 - 7 * q^68 - 4 * q^70 - 13 * q^74 - 13 * q^76 + 8 * q^79 + 3 * q^80 + 3 * q^82 - 14 * q^83 + 4 * q^85 + 29 * q^86 + 6 * q^89 + 4 * q^91 + 32 * q^92 - 50 * q^94 - 20 * q^97 + 11 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.30278			−0.921201			−0.460601	−	0.887607i	$-0.652366\pi$
$2$	−1.30278			−0.921201			−0.460601	+	0.887607i	$0.652366\pi$
$3$		0			0
$3$		0			0
$4$	−0.302776			−0.151388
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$8$	3.00000			1.06066
$9$		0			0
$10$	0.651388	+	1.12824i	0.205987	+	0.356780i
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$		0			0
$13$	−0.802776	+	1.39045i	−0.222650	+	0.385641i	−0.955612	−	0.294629i	$-0.904804\pi$
$13$	−0.802776	+	1.39045i	−0.222650	+	0.385641i	0.732962	+	0.680270i	$0.238137\pi$
$14$	−3.25694	+	1.12824i	−0.870454	+	0.301534i
$15$		0			0
$16$	−3.30278			−0.825694
$17$	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
$23$	−2.60555	−	4.51295i	−0.543295	−	0.941015i	−0.998712	−	0.0507363i	$-0.983843\pi$
$23$	−2.60555	−	4.51295i	−0.543295	−	0.941015i	0.455417	−	0.890278i	$-0.349490\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	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	0.941620	+	0.336678i	$0.109303\pi$
$29$	4.10555	+	7.11102i	0.762382	+	1.32048i	−0.179238	+	0.983806i	$0.557363\pi$
$30$		0			0
$31$	−3.60555			−0.647576			−0.323788	−	0.946130i	$-0.604956\pi$
$31$	−3.60555			−0.647576			−0.323788	+	0.946130i	$0.604956\pi$
$32$	−1.69722			−0.300030
$33$		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	$0.0708890\pi$
$38$	−2.34861	+	4.06792i	−0.380995	+	0.659903i
$39$		0			0
$40$	−1.50000	−	2.59808i	−0.237171	−	0.410792i
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	−0.724797	−	0.688963i	$-0.758066\pi$
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	0.959058	+	0.283211i	$0.0913998\pi$
$42$		0			0
$43$	−2.10555	−	3.64692i	−0.321094	−	0.556150i	0.659620	−	0.751599i	$-0.270717\pi$
$43$	−2.10555	−	3.64692i	−0.321094	−	0.556150i	−0.980714	+	0.195449i	$0.937384\pi$
$44$		0			0
$45$		0			0
$46$	3.39445	+	5.87936i	0.500484	+	0.866864i
$47$	8.21110			1.19771			0.598856	−	0.800857i	$-0.295622\pi$
$47$	8.21110			1.19771			0.598856	+	0.800857i	$0.295622\pi$
$48$		0			0
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	0.651388	−	1.12824i	0.0921201	−	0.159557i
$51$		0			0
$52$	0.243061	−	0.420994i	0.0337065	−	0.0583813i
$53$	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
$56$	7.50000	−	2.59808i	1.00223	−	0.347183i
$57$		0			0
$58$	−5.34861	−	9.26407i	−0.702307	−	1.21643i
$59$	11.6056			1.51091			0.755457	−	0.655198i	$-0.227415\pi$
$59$	11.6056			1.51091			0.755457	+	0.655198i	$0.227415\pi$
$60$		0			0
$61$	4.21110			0.539176			0.269588	−	0.962976i	$-0.413112\pi$
$61$	4.21110			0.539176			0.269588	+	0.962976i	$0.413112\pi$
$62$	4.69722			0.596548
$63$		0			0
$64$	8.81665			1.10208
$65$	1.60555			0.199144
$66$		0			0
$67$	4.21110			0.514468			0.257234	−	0.966349i	$-0.417189\pi$
$67$	4.21110			0.514468			0.257234	+	0.966349i	$0.417189\pi$
$68$	−0.848612	−	1.46984i	−0.102909	−	0.178244i
$69$		0			0
$70$	2.60555	+	2.25647i	0.311423	+	0.269700i
$71$		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	$0.765662\pi$
$74$	−2.34861	+	4.06792i	−0.273021	+	0.472886i
$75$		0			0
$76$	−0.545837	+	0.945417i	−0.0626117	+	0.108447i
$77$		0			0
$78$		0			0
$79$	12.8167			1.44199			0.720993	−	0.692942i	$-0.243686\pi$
$79$	12.8167			1.44199			0.720993	+	0.692942i	$0.243686\pi$
$80$	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	−0.931978	−	0.362514i	$-0.881918\pi$
$83$	−7.10555	−	12.3072i	−0.779936	−	1.35089i	0.152043	−	0.988374i	$-0.451415\pi$
$84$		0			0
$85$	2.80278	−	4.85455i	0.304004	−	0.526550i
$86$	2.74306	+	4.75112i	0.295792	+	0.512327i
$87$		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
$94$	−10.6972			−1.10333
$95$	−3.60555			−0.369922
$96$		0			0
$97$	−6.80278	−	11.7828i	−0.690717	−	1.19636i	−0.971603	−	0.236616i	$-0.923962\pi$
$97$	−6.80278	−	11.7828i	−0.690717	−	1.19636i	0.280886	−	0.959741i	$-0.409372\pi$
$98$	−7.16527	+	5.64118i	−0.723801	+	0.569846i
$99$		0			0
$100$	0.151388	−	0.262211i	0.0151388	−	0.0262211i
$101$	8.21110	−	14.2220i	0.817035	−	1.41515i	−0.0908220	−	0.995867i	$-0.528949\pi$
$101$	8.21110	−	14.2220i	0.817035	−	1.41515i	0.907857	−	0.419279i	$-0.137717\pi$
$102$		0			0
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	0.598858	−	0.800855i	$-0.295621\pi$
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	−0.992990	+	0.118199i	$0.962288\pi$
$104$	−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
$112$	−8.25694	+	2.86029i	−0.780207	+	0.270272i
$113$	5.40833	−	9.36750i	0.508773	−	0.881220i	−0.491176	−	0.871060i	$-0.663433\pi$
$113$	5.40833	−	9.36750i	0.508773	−	0.881220i	0.999948	−	0.0101595i	$-0.00323393\pi$
$114$		0			0
$115$	−2.60555	+	4.51295i	−0.242969	+	0.420834i
$116$	−1.24306	−	2.15304i	−0.115415	−	0.199905i
$117$		0			0
$118$	−15.1194			−1.39186
$119$	11.2111	+	9.70910i	1.02772	+	0.890032i
$120$		0			0
$121$	5.50000	+	9.52628i	0.500000	+	0.866025i
$122$	−5.48612			−0.496690
$123$		0			0
$124$	1.09167			0.0980351
$125$	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	$0.556792\pi$
$128$	−8.09167			−0.715210
$129$		0			0
$130$	−2.09167			−0.183452
$131$	3.39445	+	5.87936i	0.296574	+	0.513682i	0.975350	−	0.220664i	$-0.0708224\pi$
$131$	3.39445	+	5.87936i	0.296574	+	0.513682i	−0.678776	+	0.734346i	$0.737489\pi$
$132$		0			0
$133$	1.80278	−	9.36750i	0.156320	−	0.812265i
$134$	−5.48612			−0.473929
$135$		0			0
$136$	8.40833	+	14.5636i	0.721008	+	1.24882i
$137$	0.394449	−	0.683205i	0.0337000	−	0.0583702i	−0.848683	−	0.528901i	$-0.822604\pi$
$137$	0.394449	−	0.683205i	0.0337000	−	0.0583702i	0.882384	+	0.470531i	$0.155938\pi$
$138$		0			0
$139$	−9.80278	+	16.9789i	−0.831461	+	1.44013i	0.0654194	+	0.997858i	$0.479161\pi$
$139$	−9.80278	+	16.9789i	−0.831461	+	1.44013i	−0.896880	+	0.442274i	$0.854172\pi$
$140$	0.605551	+	0.524423i	0.0511784	+	0.0443218i
$141$		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
$149$	−11.6056	−	20.1014i	−0.950764	−	1.64677i	−0.743777	−	0.668427i	$-0.766968\pi$
$149$	−11.6056	−	20.1014i	−0.950764	−	1.64677i	−0.206986	−	0.978344i	$-0.566366\pi$
$150$		0			0
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	−0.331842	−	0.943335i	$-0.607670\pi$
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	0.982873	−	0.184284i	$-0.0589965\pi$
$152$	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
$157$	24.0278			1.91762			0.958812	−	0.284042i	$-0.0916755\pi$
$157$	24.0278			1.91762			0.958812	+	0.284042i	$0.0916755\pi$
$158$	−16.6972			−1.32836
$159$		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	$-0.0860890\pi$
$164$	−0.454163	+	0.786634i	−0.0354642	+	0.0614258i
$165$		0			0
$166$	9.25694	+	16.0335i	0.718478	+	1.24444i
$167$	1.89445	−	3.28128i	0.146597	−	0.253913i	−0.783371	−	0.621555i	$-0.786501\pi$
$167$	1.89445	−	3.28128i	0.146597	−	0.253913i	0.929968	+	0.367642i	$0.119835\pi$
$168$		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
$173$	−22.8167			−1.73472			−0.867359	−	0.497683i	$-0.834184\pi$
$173$	−22.8167			−1.73472			−0.867359	+	0.497683i	$0.834184\pi$
$174$		0			0
$175$	−0.500000	+	2.59808i	−0.0377964	+	0.196396i
$176$		0			0
$177$		0			0
$178$	−1.95416	+	3.38471i	−0.146471	+	0.253695i
$179$	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	$0.774305\pi$
$182$	1.04584	−	5.43433i	0.0775226	−	0.402819i
$183$		0			0
$184$	−7.81665	−	13.5388i	−0.576251	−	0.998097i
$185$	−3.60555			−0.265085
$186$		0			0
$187$		0			0
$188$	−2.48612			−0.181319
$189$		0			0
$190$	4.69722			0.340772
$191$	5.60555			0.405603			0.202802	−	0.979220i	$-0.434995\pi$
$191$	5.60555			0.405603			0.202802	+	0.979220i	$0.434995\pi$
$192$		0			0
$193$	−14.0278			−1.00974			−0.504870	−	0.863195i	$-0.668460\pi$
$193$	−14.0278			−1.00974			−0.504870	+	0.863195i	$0.668460\pi$
$194$	8.86249	+	15.3503i	0.636290	+	1.10209i
$195$		0			0
$196$	−1.66527	+	1.31106i	−0.118948	+	0.0936469i
$197$	−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	$0.801502\pi$
$200$	−1.50000	+	2.59808i	−0.106066	+	0.183712i
$201$		0			0
$202$	−10.6972	+	18.5281i	−0.752654	+	1.30364i
$203$	16.4222	+	14.2220i	1.15261	+	0.998192i
$204$		0			0
$205$	−3.00000			−0.209529
$206$	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	0.368844	+	0.929491i	$0.379754\pi$
$211$	−9.01388	+	15.6125i	−0.620541	+	1.07481i	−0.989385	+	0.145317i	$0.953580\pi$
$212$	−0.0597147	−	0.103429i	−0.00410122	−	0.00710353i
$213$		0			0
$214$	5.86249	−	10.1541i	0.400752	−	0.694122i
$215$	−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
$221$	−9.00000			−0.605406
$222$		0			0
$223$	−2.89445	−	5.01333i	−0.193827	−	0.335718i	0.752689	−	0.658377i	$-0.228757\pi$
$223$	−2.89445	−	5.01333i	−0.193827	−	0.335718i	−0.946515	+	0.322659i	$0.895423\pi$
$224$	−4.24306	+	1.46984i	−0.283501	+	0.0982078i
$225$		0			0
$226$	−7.04584	+	12.2037i	−0.468682	+	0.811781i
$227$	−2.60555	+	4.51295i	−0.172937	+	0.299535i	−0.939445	−	0.342699i	$-0.888659\pi$
$227$	−2.60555	+	4.51295i	−0.172937	+	0.299535i	0.766509	+	0.642234i	$0.221992\pi$
$228$		0			0
$229$	2.39445	+	4.14731i	0.158230	+	0.274062i	0.934230	−	0.356670i	$-0.116088\pi$
$229$	2.39445	+	4.14731i	0.158230	+	0.274062i	−0.776001	+	0.630732i	$0.782755\pi$
$230$	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
$236$	−3.51388			−0.228734
$237$		0			0
$238$	−14.6056	−	12.6488i	−0.946737	−	0.819899i
$239$	−0.197224	+	0.341603i	−0.0127574	+	0.0220964i	−0.872334	−	0.488911i	$-0.837394\pi$
$239$	−0.197224	+	0.341603i	−0.0127574	+	0.0220964i	0.859576	+	0.511008i	$0.170728\pi$
$240$		0			0
$241$	1.60555	−	2.78090i	0.103423	−	0.179133i	−0.809670	−	0.586885i	$-0.800354\pi$
$241$	1.60555	−	2.78090i	0.103423	−	0.179133i	0.913093	+	0.407752i	$0.133687\pi$
$242$	−7.16527	−	12.4106i	−0.460601	−	0.797784i
$243$		0			0
$244$	−1.27502			−0.0816247
$245$	−6.50000	−	2.59808i	−0.415270	−	0.165985i
$246$		0			0
$247$	2.89445	+	5.01333i	0.184169	+	0.318991i
$248$	−10.8167			−0.686858
$249$		0			0
$250$	−1.30278			−0.0823948
$251$	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
$254$	5.21110			0.326974
$255$		0			0
$256$	−7.09167			−0.443230
$257$	9.00000	+	15.5885i	0.561405	+	0.972381i	0.997374	+	0.0724199i	$0.0230722\pi$
$257$	9.00000	+	15.5885i	0.561405	+	0.972381i	−0.435970	+	0.899961i	$0.643595\pi$
$258$		0			0
$259$	1.80278	−	9.36750i	0.112019	−	0.582068i
$260$	−0.486122			−0.0301480
$261$		0			0
$262$	−4.42221	−	7.65948i	−0.273205	−	0.473204i
$263$	−11.2111	+	19.4182i	−0.691306	+	1.19738i	0.280104	+	0.959970i	$0.409631\pi$
$263$	−11.2111	+	19.4182i	−0.691306	+	1.19738i	−0.971410	+	0.237408i	$0.923702\pi$
$264$		0			0
$265$	0.197224	−	0.341603i	0.0121154	−	0.0209845i
$266$	−2.34861	+	12.2037i	−0.144003	+	0.748260i
$267$		0			0
$268$	−1.27502			−0.0778842
$269$	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
$277$	−14.8167	+	25.6632i	−0.890246	+	1.54195i	−0.0506667	+	0.998716i	$0.516135\pi$
$277$	−14.8167	+	25.6632i	−0.890246	+	1.54195i	−0.839580	+	0.543236i	$0.817199\pi$
$278$	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	0.997842	+	0.0656609i	$0.0209155\pi$
$281$	9.31665	+	16.1369i	0.555785	+	0.962648i	−0.442057	+	0.896987i	$0.645751\pi$
$282$		0			0
$283$	−25.0000			−1.48610			−0.743048	−	0.669238i	$-0.766621\pi$
$283$	−25.0000			−1.48610			−0.743048	+	0.669238i	$0.766621\pi$
$284$		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
$290$	−5.34861	+	9.26407i	−0.314081	+	0.544005i
$291$		0			0
$292$	−0.545837	−	0.945417i	−0.0319427	−	0.0553263i
$293$	−11.0139	+	19.0766i	−0.643438	+	1.11447i	0.341222	+	0.939983i	$0.389159\pi$
$293$	−11.0139	+	19.0766i	−0.643438	+	1.11447i	−0.984660	+	0.174484i	$0.944174\pi$
$294$		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
$299$	8.36669			0.483858
$300$		0			0
$301$	−8.42221	−	7.29384i	−0.485448	−	0.420410i
$302$	−10.4222	+	18.0518i	−0.599731	+	1.03876i
$303$		0			0
$304$	−5.95416	+	10.3129i	−0.341495	+	0.591486i
$305$	−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
$310$	−2.34861	−	4.06792i	−0.133392	−	0.231042i
$311$	16.8167			0.953585			0.476792	−	0.879016i	$-0.341799\pi$
$311$	16.8167			0.953585			0.476792	+	0.879016i	$0.341799\pi$
$312$		0			0
$313$	−8.81665			−0.498347			−0.249173	−	0.968459i	$-0.580159\pi$
$313$	−8.81665			−0.498347			−0.249173	+	0.968459i	$0.580159\pi$
$314$	−31.3028			−1.76652
$315$		0			0
$316$	−3.88057			−0.218299
$317$	−5.60555			−0.314839			−0.157420	−	0.987532i	$-0.550318\pi$
$317$	−5.60555			−0.314839			−0.157420	+	0.987532i	$0.550318\pi$
$318$		0			0
$319$		0			0
$320$	−4.40833	−	7.63545i	−0.246433	−	0.426834i
$321$		0			0
$322$	13.5778	+	11.7587i	0.756661	+	0.655288i
$323$	20.2111			1.12458
$324$		0			0
$325$	−0.802776	−	1.39045i	−0.0445300	−	0.0771282i
$326$	−11.8625	+	20.5464i	−0.657003	+	1.13796i
$327$		0			0
$328$	4.50000	−	7.79423i	0.248471	−	0.430364i
$329$	20.5278	−	7.11102i	1.13173	−	0.392043i
$330$		0			0
$331$	−20.0278			−1.10083			−0.550413	−	0.834893i	$-0.685530\pi$
$331$	−20.0278			−1.10083			−0.550413	+	0.834893i	$0.685530\pi$
$332$	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	−0.195023	−	0.980799i	$-0.562478\pi$
$337$	13.8028	−	23.9071i	0.751885	−	1.30230i	0.946908	−	0.321505i	$-0.104189\pi$
$338$	−6.78890	−	11.7587i	−0.369267	−	0.639590i
$339$		0			0
$340$	−0.848612	+	1.46984i	−0.0460225	+	0.0797132i
$341$		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
$346$	29.7250			1.59802
$347$	31.4222			1.68683			0.843416	−	0.537261i	$-0.180541\pi$
$347$	31.4222			1.68683			0.843416	+	0.537261i	$0.180541\pi$
$348$		0			0
$349$	−13.3167	−	23.0651i	−0.712824	−	1.23465i	−0.963793	−	0.266652i	$-0.914082\pi$
$349$	−13.3167	−	23.0651i	−0.712824	−	1.23465i	0.250969	−	0.967995i	$-0.419251\pi$
$350$	0.651388	−	3.38471i	0.0348181	−	0.180920i
$351$		0			0
$352$		0			0
$353$	3.00000	−	5.19615i	0.159674	−	0.276563i	−0.775077	−	0.631867i	$-0.782289\pi$
$353$	3.00000	−	5.19615i	0.159674	−	0.276563i	0.934751	+	0.355303i	$0.115622\pi$
$354$		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
$362$	26.6056			1.39836
$363$		0			0
$364$	0.243061	−	1.26298i	0.0127399	−	0.0661982i
$365$	1.80278	−	3.12250i	0.0943616	−	0.163439i
$366$		0			0
$367$	7.21110	−	12.4900i	0.376416	−	0.651972i	−0.614121	−	0.789212i	$-0.710490\pi$
$367$	7.21110	−	12.4900i	0.376416	−	0.651972i	0.990538	+	0.137239i	$0.0438228\pi$
$368$	8.60555	+	14.9053i	0.448595	+	0.776990i
$369$		0			0
$370$	4.69722			0.244197
$371$	0.788897	+	0.683205i	0.0409575	+	0.0354702i
$372$		0			0
$373$	18.8167	+	32.5914i	0.974289	+	1.68752i	0.682260	+	0.731109i	$0.260997\pi$
$373$	18.8167	+	32.5914i	0.974289	+	1.68752i	0.292029	+	0.956409i	$0.405670\pi$
$374$		0			0
$375$		0			0
$376$	24.6333			1.27037
$377$	−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	$0.532759\pi$
$380$	1.09167			0.0560016
$381$		0			0
$382$	−7.30278			−0.373643
$383$	0.788897	+	1.36641i	0.0403108	+	0.0698203i	0.885477	−	0.464683i	$-0.153832\pi$
$383$	0.788897	+	1.36641i	0.0403108	+	0.0698203i	−0.845166	+	0.534504i	$0.820499\pi$
$384$		0			0
$385$		0			0
$386$	18.2750			0.930174
$387$		0			0
$388$	2.05971	+	3.56753i	0.104566	+	0.181114i
$389$	−9.00000	+	15.5885i	−0.456318	+	0.790366i	−0.998763	−	0.0497253i	$-0.984165\pi$
$389$	−9.00000	+	15.5885i	−0.456318	+	0.790366i	0.542445	+	0.840091i	$0.317499\pi$
$390$		0			0
$391$	14.6056	−	25.2976i	0.738634	−	1.27935i
$392$	16.5000	−	12.9904i	0.833376	−	0.656113i
$393$		0			0
$394$	7.81665			0.393797
$395$	−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
$401$	3.00000	+	5.19615i	0.149813	+	0.259483i	0.931158	−	0.364615i	$-0.118800\pi$
$401$	3.00000	+	5.19615i	0.149813	+	0.259483i	−0.781345	+	0.624099i	$0.785466\pi$
$402$		0			0
$403$	2.89445	−	5.01333i	0.144183	−	0.249732i
$404$	−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
$409$	−1.00000			−0.0494468			−0.0247234	−	0.999694i	$-0.507871\pi$
$409$	−1.00000			−0.0494468			−0.0247234	+	0.999694i	$0.507871\pi$
$410$	3.90833			0.193019
$411$		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
$416$	1.36249	−	2.35990i	0.0668016	−	0.115704i
$417$		0			0
$418$		0			0
$419$	8.40833	−	14.5636i	0.410774	−	0.711481i	−0.584201	−	0.811609i	$-0.698592\pi$
$419$	8.40833	−	14.5636i	0.410774	−	0.711481i	0.994975	+	0.100128i	$0.0319253\pi$
$420$		0			0
$421$	11.7111	+	20.2842i	0.570764	+	0.988593i	0.996488	+	0.0837393i	$0.0266863\pi$
$421$	11.7111	+	20.2842i	0.570764	+	0.988593i	−0.425723	+	0.904853i	$0.639980\pi$
$422$	11.7431	−	20.3396i	0.571643	−	0.990115i
$423$		0			0
$424$	0.591673	+	1.02481i	0.0287342	+	0.0497691i
$425$	−5.60555			−0.271909
$426$		0			0
$427$	10.5278	−	3.64692i	0.509474	−	0.176487i
$428$	1.36249	−	2.35990i	0.0658585	−	0.114070i
$429$		0			0
$430$	2.74306	−	4.75112i	0.132282	−	0.229119i
$431$	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	$0.315041\pi$
$434$	11.7431	−	4.06792i	0.563685	−	0.195266i
$435$		0			0
$436$	−2.75694	−	4.77516i	−0.132033	−	0.228689i
$437$	−18.7889			−0.898795
$438$		0			0
$439$	−13.2389			−0.631856			−0.315928	−	0.948783i	$-0.602316\pi$
$439$	−13.2389			−0.631856			−0.315928	+	0.948783i	$0.602316\pi$
$440$		0			0
$441$		0			0
$442$	11.7250			0.557700
$443$	6.63331			0.315158			0.157579	−	0.987506i	$-0.449631\pi$
$443$	6.63331			0.315158			0.157579	+	0.987506i	$0.449631\pi$
$444$		0			0
$445$	−3.00000			−0.142214
$446$	3.77082	+	6.53125i	0.178553	+	0.309264i
$447$		0			0
$448$	22.0416	−	7.63545i	1.04137	−	0.360741i
$449$	−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
$452$	−1.63751	+	2.83625i	−0.0770220	+	0.133406i
$453$		0			0
$454$	3.39445	−	5.87936i	0.159309	−	0.275932i
$455$	4.01388	−	1.39045i	0.188174	−	0.0651852i
$456$		0			0
$457$	−22.3944			−1.04757			−0.523784	−	0.851851i	$-0.675480\pi$
$457$	−22.3944			−1.04757			−0.523784	+	0.851851i	$0.675480\pi$
$458$	−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	−0.956139	−	0.292912i	$-0.905376\pi$
$461$	−15.7111	−	27.2124i	−0.731739	−	1.26741i	0.224400	−	0.974497i	$-0.427958\pi$
$462$		0			0
$463$	12.1056	−	20.9674i	0.562593	−	0.974439i	−0.434677	−	0.900587i	$-0.643137\pi$
$463$	12.1056	−	20.9674i	0.562593	−	0.974439i	0.997269	−	0.0738524i	$-0.0235294\pi$
$464$	−13.5597	−	23.4861i	−0.629494	−	1.09032i
$465$		0			0
$466$	10.9542	−	18.9732i	0.507442	−	0.878915i
$467$	−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
$472$	34.8167			1.60257
$473$		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
$479$	11.2111	−	19.4182i	0.512248	−	0.887240i	−0.487651	−	0.873039i	$-0.662146\pi$
$479$	11.2111	−	19.4182i	0.512248	−	0.887240i	0.999899	−	0.0142014i	$-0.00452060\pi$
$480$		0			0
$481$	2.89445	+	5.01333i	0.131976	+	0.228588i
$482$	−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	$0.661939\pi$
$488$	12.6333			0.571883
$489$		0			0
$490$	8.46804	+	3.38471i	0.382547	+	0.152906i
$491$	−19.2250	+	33.2986i	−0.867611	+	1.50275i	−0.00318042	+	0.999995i	$0.501012\pi$
$491$	−19.2250	+	33.2986i	−0.867611	+	1.50275i	−0.864431	+	0.502752i	$0.832321\pi$
$492$		0			0
$493$	−23.0139	+	39.8612i	−1.03649	+	1.79526i
$494$	−3.77082	−	6.53125i	−0.169657	−	0.293855i
$495$		0			0
$496$	11.9083			0.534700
$497$		0			0
$498$		0			0
$499$	14.0000	+	24.2487i	0.626726	+	1.08552i	0.988204	+	0.153141i	$0.0489388\pi$
$499$	14.0000	+	24.2487i	0.626726	+	1.08552i	−0.361478	+	0.932381i	$0.617728\pi$
$500$	−0.302776			−0.0135405
$501$		0			0
$502$	−15.6333			−0.697749
$503$	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
$508$	1.21110			0.0537340
$509$	−12.3944	−	21.4678i	−0.549374	−	0.951544i	−0.998318	−	0.0579839i	$-0.981533\pi$
$509$	−12.3944	−	21.4678i	−0.549374	−	0.951544i	0.448943	−	0.893560i	$-0.351801\pi$
$510$		0			0
$511$	7.21110	+	6.24500i	0.319000	+	0.276262i
$512$	25.4222			1.12351
$513$		0			0
$514$	−11.7250	−	20.3083i	−0.517167	−	0.895759i
$515$	−4.00000	+	6.92820i	−0.176261	+	0.305293i
$516$		0			0
$517$		0			0
$518$	−2.34861	+	12.2037i	−0.103192	+	0.536202i
$519$		0			0
$520$	4.81665			0.211224
$521$	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
$527$	−10.1056	−	17.5033i	−0.440205	−	0.762457i
$528$		0			0
$529$	−2.07779	+	3.59885i	−0.0903389	+	0.156472i
$530$	−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
$535$	9.00000			0.389104
$536$	12.6333			0.545676
$537$		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	$0.911511\pi$
$542$	−16.9542	+	29.3655i	−0.728244	+	1.26136i
$543$		0			0
$544$	−4.75694	−	8.23926i	−0.203952	−	0.353255i
$545$	9.10555	−	15.7713i	0.390039	−	0.675567i
$546$		0			0
$547$	−2.89445	−	5.01333i	−0.123758	−	0.214355i	0.797489	−	0.603334i	$-0.206161\pi$
$547$	−2.89445	−	5.01333i	−0.123758	−	0.214355i	−0.921247	+	0.388979i	$0.872828\pi$
$548$	−0.119429	+	0.206858i	−0.00510177	+	0.00883653i
$549$		0			0
$550$		0			0
$551$	29.6056			1.26124
$552$		0			0
$553$	32.0416	−	11.0995i	1.36255	−	0.472001i
$554$	19.3028	−	33.4334i	0.820096	−	1.42045i
$555$		0			0
$556$	2.96804	−	5.14080i	0.125873	−	0.218018i
$557$	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
$560$	6.60555	+	5.72058i	0.279135	+	0.241738i
$561$		0			0
$562$	−12.1375	−	21.0228i	−0.511990	−	0.886793i
$563$	−35.8444			−1.51066			−0.755331	−	0.655344i	$-0.772524\pi$
$563$	−35.8444			−1.51066			−0.755331	+	0.655344i	$0.772524\pi$
$564$		0			0
$565$	−10.8167			−0.455060
$566$	32.5694			1.36899
$567$		0			0
$568$		0			0
$569$	−15.0000			−0.628833			−0.314416	−	0.949285i	$-0.601809\pi$
$569$	−15.0000			−0.628833			−0.314416	+	0.949285i	$0.601809\pi$
$570$		0			0
$571$	−14.0278			−0.587043			−0.293522	−	0.955952i	$-0.594827\pi$
$571$	−14.0278			−0.587043			−0.293522	+	0.955952i	$0.594827\pi$
$572$		0			0
$573$		0			0
$574$	−1.95416	+	10.1541i	−0.0815652	+	0.423825i
$575$	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	$-0.402221\pi$
$578$	9.39445	−	16.2717i	0.390758	−	0.676812i
$579$		0			0
$580$	−1.24306	+	2.15304i	−0.0516153	+	0.0894003i
$581$	−28.4222	−	24.6144i	−1.17915	−	1.02118i
$582$		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	0.758089	−	0.652151i	$-0.226133\pi$
$587$	−4.50000	−	7.79423i	−0.185735	−	0.321702i	−0.943824	+	0.330449i	$0.892800\pi$
$588$		0			0
$589$	−6.50000	+	11.2583i	−0.267828	+	0.463891i
$590$	7.55971	+	13.0938i	0.311229	+	0.539064i
$591$		0			0
$592$	−5.95416	+	10.3129i	−0.244715	+	0.423858i
$593$	−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
$598$	−10.8999			−0.445731
$599$	6.39445			0.261270			0.130635	−	0.991431i	$-0.458298\pi$
$599$	6.39445			0.261270			0.130635	+	0.991431i	$0.458298\pi$
$600$		0			0
$601$	15.1056	+	26.1636i	0.616168	+	1.06723i	0.990178	+	0.139810i	$0.0446492\pi$
$601$	15.1056	+	26.1636i	0.616168	+	1.06723i	−0.374010	+	0.927425i	$0.622017\pi$
$602$	10.9722	+	9.50224i	0.447195	+	0.387282i
$603$		0			0
$604$	−2.42221	+	4.19538i	−0.0985581	+	0.170708i
$605$	5.50000	−	9.52628i	0.223607	−	0.387298i
$606$		0			0
$607$	2.00000	+	3.46410i	0.0811775	+	0.140604i	0.903756	−	0.428048i	$-0.140799\pi$
$607$	2.00000	+	3.46410i	0.0811775	+	0.140604i	−0.822578	+	0.568652i	$0.807465\pi$
$608$	−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	$0.867073\pi$
$614$	12.0000			0.484281
$615$		0			0
$616$		0			0
$617$	−20.4083	+	35.3483i	−0.821608	+	1.42307i	0.0828757	+	0.996560i	$0.473590\pi$
$617$	−20.4083	+	35.3483i	−0.821608	+	1.42307i	−0.904484	+	0.426507i	$0.859744\pi$
$618$		0			0
$619$	−7.39445	+	12.8076i	−0.297208	+	0.514779i	−0.975496	−	0.220017i	$-0.929389\pi$
$619$	−7.39445	+	12.8076i	−0.297208	+	0.514779i	0.678288	+	0.734796i	$0.262722\pi$
$620$	−0.545837	−	0.945417i	−0.0219213	−	0.0379688i
$621$		0			0
$622$	−21.9083			−0.878444
$623$	1.50000	−	7.79423i	0.0600962	−	0.312269i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	11.4861			0.459078
$627$		0			0
$628$	−7.27502			−0.290305
$629$	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	$0.320980\pi$
$632$	38.4500			1.52946
$633$		0			0
$634$	7.30278			0.290030
$635$	2.00000	+	3.46410i	0.0793676	+	0.137469i
$636$		0			0
$637$	1.60555	+	11.1236i	0.0636143	+	0.440733i
$638$		0			0
$639$		0			0
$640$	4.04584	+	7.00759i	0.159926	+	0.276999i
$641$	−3.00000	+	5.19615i	−0.118493	+	0.205236i	−0.919171	−	0.393860i	$-0.871140\pi$
$641$	−3.00000	+	5.19615i	−0.118493	+	0.205236i	0.800678	+	0.599095i	$0.204473\pi$
$642$		0			0
$643$	−3.28890	+	5.69654i	−0.129701	+	0.224650i	−0.923561	−	0.383452i	$-0.874735\pi$
$643$	−3.28890	+	5.69654i	−0.129701	+	0.224650i	0.793859	+	0.608101i	$0.208069\pi$
$644$	3.15559	+	2.73282i	0.124348	+	0.107688i
$645$		0			0
$646$	−26.3305			−1.03596
$647$	−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
$653$	8.21110	+	14.2220i	0.321325	+	0.556552i	0.980762	−	0.195209i	$-0.0625384\pi$
$653$	8.21110	+	14.2220i	0.321325	+	0.556552i	−0.659436	+	0.751760i	$0.729205\pi$
$654$		0			0
$655$	3.39445	−	5.87936i	0.132632	−	0.229726i
$656$	−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	0.948351	+	0.317223i	$0.102750\pi$
$659$	19.2250	+	33.2986i	0.748899	+	1.29713i	−0.199452	+	0.979908i	$0.563916\pi$
$660$		0			0
$661$	−13.0000			−0.505641			−0.252821	−	0.967513i	$-0.581358\pi$
$661$	−13.0000			−0.505641			−0.252821	+	0.967513i	$0.581358\pi$
$662$	26.0917			1.01408
$663$		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
$668$	−0.573593	+	0.993492i	−0.0221930	+	0.0384394i
$669$		0			0
$670$	2.74306	+	4.75112i	0.105974	+	0.183552i
$671$		0			0
$672$		0			0
$673$	−11.2250	−	19.4422i	−0.432691	−	0.749443i	0.564413	−	0.825493i	$-0.309103\pi$
$673$	−11.2250	−	19.4422i	−0.432691	−	0.749443i	−0.997104	+	0.0760495i	$0.975769\pi$
$674$	−17.9819	+	31.1456i	−0.692638	+	1.19968i
$675$		0			0
$676$	−1.57779	−	2.73282i	−0.0606844	−	0.105108i
$677$	−36.3944			−1.39875			−0.699376	−	0.714754i	$-0.746539\pi$
$677$	−36.3944			−1.39875			−0.699376	+	0.714754i	$0.746539\pi$
$678$		0			0
$679$	−27.2111	−	23.5655i	−1.04427	−	0.904361i
$680$	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
$686$	−13.0278	+	20.3083i	−0.497402	+	0.775373i
$687$		0			0
$688$	6.95416	+	12.0450i	0.265125	+	0.459210i
$689$	−0.633308			−0.0241271
$690$		0			0
$691$	−40.3944			−1.53668			−0.768339	−	0.640044i	$-0.778916\pi$
$691$	−40.3944			−1.53668			−0.768339	+	0.640044i	$0.778916\pi$
$692$	6.90833			0.262615
$693$		0			0
$694$	−40.9361			−1.55391
$695$	19.6056			0.743681
$696$		0			0
$697$	16.8167			0.636976
$698$	17.3486	+	30.0487i	0.656655	+	1.13736i
$699$		0			0
$700$	0.151388	−	0.786634i	0.00572192	−	0.0297320i
$701$	−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
$707$	8.21110	−	42.6661i	0.308810	−	1.60463i
$708$		0			0
$709$	12.5778			0.472369			0.236185	−	0.971708i	$-0.424103\pi$
$709$	12.5778			0.472369			0.236185	+	0.971708i	$0.424103\pi$
$710$		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
$716$	−0.179144	−	0.310287i	−0.00669493	−	0.0115960i
$717$		0			0
$718$	−4.67914	+	8.10452i	−0.174624	+	0.302458i
$719$	−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
$724$	6.18335			0.229802
$725$	−8.21110			−0.304953
$726$		0			0
$727$	5.71110	+	9.89192i	0.211813	+	0.366871i	0.952282	−	0.305220i	$-0.0987299\pi$
$727$	5.71110	+	9.89192i	0.211813	+	0.366871i	−0.740469	+	0.672091i	$0.765397\pi$
$728$	−2.40833	+	12.5140i	−0.0892585	+	0.463801i
$729$		0			0
$730$	−2.34861	+	4.06792i	−0.0869260	+	0.150560i
$731$	11.8028	−	20.4430i	0.436541	−	0.756112i
$732$		0			0
$733$	5.00000	+	8.66025i	0.184679	+	0.319874i	0.943468	−	0.331463i	$-0.107542\pi$
$733$	5.00000	+	8.66025i	0.184679	+	0.319874i	−0.758789	+	0.651336i	$0.774209\pi$
$734$	−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	$0.816836\pi$
$740$	1.09167			0.0401307
$741$		0			0
$742$	−1.02776	−	0.890063i	−0.0377301	−	0.0326752i
$743$	−13.5000	+	23.3827i	−0.495267	+	0.857828i	−0.999985	−	0.00545664i	$-0.998263\pi$
$743$	−13.5000	+	23.3827i	−0.495267	+	0.857828i	0.504718	+	0.863284i	$0.331596\pi$
$744$		0			0
$745$	−11.6056	+	20.1014i	−0.425195	+	0.736458i
$746$	−24.5139	−	42.4593i	−0.897517	−	1.55454i
$747$		0			0
$748$		0			0
$749$	−4.50000	+	23.3827i	−0.164426	+	0.854385i
$750$		0			0
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	0.900207	−	0.435463i	$-0.143415\pi$
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	−0.827225	+	0.561870i	$0.810082\pi$
$752$	−27.1194			−0.988944
$753$		0			0
$754$	17.1749			0.625475
$755$	−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	$0.739719\pi$
$758$	5.21110			0.189276
$759$		0			0
$760$	−10.8167			−0.392361
$761$	−15.0000	−	25.9808i	−0.543750	−	0.941802i	−0.998684	−	0.0512772i	$-0.983671\pi$
$761$	−15.0000	−	25.9808i	−0.543750	−	0.941802i	0.454935	−	0.890525i	$-0.349663\pi$
$762$		0			0
$763$	36.4222	+	31.5426i	1.31857	+	1.14192i
$764$	−1.69722			−0.0614034
$765$		0			0
$766$	−1.02776	−	1.78013i	−0.0371343	−	0.0643186i
$767$	−9.31665	+	16.1369i	−0.336405	+	0.582670i
$768$		0			0
$769$	−1.31665	+	2.28051i	−0.0474798	+	0.0822373i	−0.888789	−	0.458317i	$-0.848452\pi$
$769$	−1.31665	+	2.28051i	−0.0474798	+	0.0822373i	0.841309	+	0.540555i	$0.181786\pi$
$770$		0			0
$771$		0			0
$772$	4.24726			0.152862
$773$	−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
$779$	−5.40833	−	9.36750i	−0.193773	−	0.335625i
$780$		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
$787$	−23.4222			−0.834911			−0.417456	−	0.908697i	$-0.637078\pi$
$787$	−23.4222			−0.834911			−0.417456	+	0.908697i	$0.637078\pi$
$788$	1.81665			0.0647156
$789$		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
$794$	−5.74306	+	9.94727i	−0.203814	+	0.353016i
$795$		0			0
$796$	−0.426407	−	0.738559i	−0.0151136	−	0.0261775i
$797$	−0.591673	+	1.02481i	−0.0209581	+	0.0363006i	−0.876314	−	0.481740i	$-0.840005\pi$
$797$	−0.591673	+	1.02481i	−0.0209581	+	0.0363006i	0.855356	+	0.518040i	$0.173338\pi$
$798$		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
$805$	−2.60555	+	13.5388i	−0.0918336	+	0.477181i
$806$	−3.77082	+	6.53125i	−0.132821	+	0.230053i
$807$		0			0
$808$	24.6333	−	42.6661i	0.866597	−	1.50099i
$809$	−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	$0.232534\pi$
$812$	−4.97224	−	4.30609i	−0.174492	−	0.151114i
$813$		0			0
$814$		0			0
$815$	−18.2111			−0.637907
$816$		0			0
$817$	−15.1833			−0.531198
$818$	1.30278			0.0455505
$819$		0			0
$820$	0.908327			0.0317202
$821$	−15.0000			−0.523504			−0.261752	−	0.965135i	$-0.584300\pi$
$821$	−15.0000			−0.523504			−0.261752	+	0.965135i	$0.584300\pi$
$822$		0			0
$823$	−1.00000			−0.0348578			−0.0174289	−	0.999848i	$-0.505548\pi$
$823$	−1.00000			−0.0348578			−0.0174289	+	0.999848i	$0.505548\pi$
$824$	−12.0000	−	20.7846i	−0.418040	−	0.724066i
$825$		0			0
$826$	−37.7986	+	13.0938i	−1.31518	+	0.455592i
$827$	−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	$-0.363771\pi$
$830$	9.25694	−	16.0335i	0.321313	−	0.556531i
$831$		0			0
$832$	−7.07779	+	12.2591i	−0.245378	+	0.425008i
$833$	36.4361	+	14.5636i	1.26244	+	0.504601i
$834$		0			0
$835$	−3.78890			−0.131120
$836$		0			0
$837$		0			0
$838$	−10.9542	+	18.9732i	−0.378405	+	0.655417i
$839$	17.4083	+	30.1521i	0.601002	+	1.04097i	0.992670	+	0.120859i	$0.0385650\pi$
$839$	17.4083	+	30.1521i	0.601002	+	1.04097i	−0.391667	+	0.920107i	$0.628102\pi$
$840$		0			0
$841$	−19.2111	+	33.2746i	−0.662452	+	1.14740i
$842$	−15.2569	−	26.4258i	−0.525789	−	0.910693i
$843$		0			0
$844$	2.72918	−	4.72708i	0.0939423	−	0.162713i
$845$	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
$850$	7.30278			0.250483
$851$	−18.7889			−0.644075
$852$		0			0
$853$	19.0139	+	32.9330i	0.651023	+	1.12760i	0.982875	+	0.184273i	$0.0589931\pi$
$853$	19.0139	+	32.9330i	0.651023	+	1.12760i	−0.331852	+	0.943331i	$0.607674\pi$
$854$	−13.7153	+	4.75112i	−0.469328	+	0.162580i
$855$		0			0
$856$	−13.5000	+	23.3827i	−0.461421	+	0.799204i
$857$	4.81665	−	8.34269i	0.164534	−	0.284981i	−0.771956	−	0.635676i	$-0.780721\pi$
$857$	4.81665	−	8.34269i	0.164534	−	0.284981i	0.936490	+	0.350695i	$0.114055\pi$
$858$		0			0
$859$	14.0000	+	24.2487i	0.477674	+	0.827355i	0.999672	−	0.0255910i	$-0.00814674\pi$
$859$	14.0000	+	24.2487i	0.477674	+	0.827355i	−0.521999	+	0.852946i	$0.674813\pi$
$860$	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
$866$	−29.7611			−1.01132
$867$		0			0
$868$	2.72918	−	0.945417i	0.0926345	−	0.0320895i
$869$		0			0
$870$		0			0
$871$	−3.38057	+	5.85532i	−0.114546	+	0.198400i
$872$	27.3167	+	47.3138i	0.925059	+	1.60225i
$873$		0			0
$874$	24.4777			0.827971
$875$	2.50000	−	0.866025i	0.0845154	−	0.0292770i
$876$		0			0
$877$	−1.00000	−	1.73205i	−0.0337676	−	0.0584872i	0.848648	−	0.528958i	$-0.177417\pi$
$877$	−1.00000	−	1.73205i	−0.0337676	−	0.0584872i	−0.882415	+	0.470471i	$0.844084\pi$
$878$	17.2473			0.582067
$879$		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	$0.723770\pi$
$884$	2.72498			0.0916510
$885$		0			0
$886$	−8.64171			−0.290324
$887$	14.6056	+	25.2976i	0.490406	+	0.849409i	0.999939	−	0.0110425i	$-0.00351501\pi$
$887$	14.6056	+	25.2976i	0.490406	+	0.849409i	−0.509533	+	0.860451i	$0.670182\pi$
$888$		0			0
$889$	−10.0000	+	3.46410i	−0.335389	+	0.116182i
$890$	3.90833			0.131007
$891$		0			0
$892$	0.876369	+	1.51791i	0.0293430	+	0.0508235i
$893$	14.8028	−	25.6392i	0.495356	−	0.857982i
$894$		0			0
$895$	0.591673	−	1.02481i	0.0197775	−	0.0342555i
$896$	−20.2292	+	7.00759i	−0.675810	+	0.234107i
$897$		0			0
$898$	28.1833			0.940490
$899$	−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
$905$	10.2111	+	17.6861i	0.339429	+	0.587907i
$906$		0			0
$907$	21.0278	−	36.4211i	0.698215	−	1.20934i	−0.270870	−	0.962616i	$-0.587311\pi$
$907$	21.0278	−	36.4211i	0.698215	−	1.20934i	0.969085	−	0.246728i	$-0.0793555\pi$
$908$	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	−0.774392	−	0.632706i	$-0.781944\pi$
$911$	−28.2250	−	48.8871i	−0.935135	−	1.61970i	−0.160743	−	0.986996i	$-0.551389\pi$
$912$		0			0
$913$		0			0
$914$	29.1749			0.965021
$915$		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	$0.111825\pi$
$920$	−7.81665	+	13.5388i	−0.257707	+	0.446362i
$921$		0			0
$922$	20.4680	+	35.4517i	0.674079	+	1.16754i
$923$		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
$929$	−8.21110			−0.269398			−0.134699	−	0.990887i	$-0.543007\pi$
$929$	−8.21110			−0.269398			−0.134699	+	0.990887i	$0.543007\pi$
$930$		0			0
$931$	−3.60555	−	24.9800i	−0.118167	−	0.818686i
$932$	2.54584	−	4.40952i	0.0833916	−	0.144439i
$933$		0			0
$934$	4.83473	−	8.37400i	0.158197	−	0.274006i
$935$		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	$0.588425\pi$
$938$	−13.7153	+	4.75112i	−0.447821	+	0.155130i
$939$		0			0
$940$	1.24306	+	2.15304i	0.0405442	+	0.0702246i
$941$	−15.0000			−0.488986			−0.244493	−	0.969651i	$-0.578622\pi$
$941$	−15.0000			−0.488986			−0.244493	+	0.969651i	$0.578622\pi$
$942$		0			0
$943$	−15.6333			−0.509091
$944$	−38.3305			−1.24755
$945$		0			0
$946$		0			0
$947$	−15.7889			−0.513070			−0.256535	−	0.966535i	$-0.582581\pi$
$947$	−15.7889			−0.513070			−0.256535	+	0.966535i	$0.582581\pi$
$948$		0			0
$949$	−5.78890			−0.187916
$950$	−2.34861	−	4.06792i	−0.0761990	−	0.131981i
$951$		0			0
$952$	33.6333	+	29.1273i	1.09006	+	0.944021i
$953$	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
$956$	0.0597147	−	0.103429i	0.00193131	−	0.00334513i
$957$		0			0
$958$	−14.6056	+	25.2976i	−0.471884	+	0.817327i
$959$	0.394449	−	2.04962i	0.0127374	−	0.0661855i
$960$		0			0
$961$	−18.0000			−0.580645
$962$	−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	−0.995486	−	0.0949082i	$-0.969744\pi$
$967$	−12.9222	+	22.3819i	−0.415550	+	0.719754i	0.579936	+	0.814662i	$0.303078\pi$
$968$	16.5000	+	28.5788i	0.530330	+	0.918559i
$969$		0			0
$970$	8.86249	−	15.3503i	0.284557	−	0.492868i
$971$	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
$976$	−13.9083			−0.445195
$977$	−21.2389			−0.679491			−0.339746	−	0.940517i	$-0.610341\pi$
$977$	−21.2389			−0.679491			−0.339746	+	0.940517i	$0.610341\pi$
$978$		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
$983$	13.0278	−	22.5647i	0.415521	−	0.719703i	−0.579962	−	0.814643i	$-0.696933\pi$
$983$	13.0278	−	22.5647i	0.415521	−	0.719703i	0.995483	+	0.0949402i	$0.0302660\pi$
$984$		0			0
$985$	3.00000	+	5.19615i	0.0955879	+	0.165563i
$986$	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	$0.953668\pi$
$992$	6.11943			0.194292
$993$		0			0
$994$		0			0
$995$	1.40833	−	2.43929i	0.0446470	−	0.0773308i
$996$		0			0
$997$	26.6333	−	46.1302i	0.843485	−	1.46096i	−0.0434448	−	0.999056i	$-0.513833\pi$
$997$	26.6333	−	46.1302i	0.843485	−	1.46096i	0.886930	−	0.461904i	$-0.152833\pi$
$998$	−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.l.a.226.1		4
3.2	odd	2		315.2.l.a.121.2	yes	4
7.4	even	3		945.2.k.a.361.2		4
9.2	odd	6		315.2.k.a.16.1	✓	4
9.7	even	3		945.2.k.a.856.2		4
21.11	odd	6		315.2.k.a.256.1	yes	4
63.11	odd	6		315.2.l.a.151.2	yes	4
63.25	even	3	inner	945.2.l.a.46.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.a.16.1	✓	4	9.2	odd	6
315.2.k.a.256.1	yes	4	21.11	odd	6
315.2.l.a.121.2	yes	4	3.2	odd	2
315.2.l.a.151.2	yes	4	63.11	odd	6
945.2.k.a.361.2		4	7.4	even	3
945.2.k.a.856.2		4	9.7	even	3
945.2.l.a.46.1		4	63.25	even	3	inner
945.2.l.a.226.1		4	1.1	even	1	trivial

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.l (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.30278 q^{2} -0.302776 q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.50000 - 0.866025i) q^{7} +3.00000 q^{8} +O(q^{10})\)	\(q-1.30278 q^{2} -0.302776 q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.50000 - 0.866025i) q^{7} +3.00000 q^{8} +(0.651388 + 1.12824i) q^{10} +(-0.802776 + 1.39045i) q^{13} +(-3.25694 + 1.12824i) q^{14} -3.30278 q^{16} +(2.80278 + 4.85455i) q^{17} +(1.80278 - 3.12250i) q^{19} +(0.151388 + 0.262211i) q^{20} +(-2.60555 - 4.51295i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(1.04584 - 1.81144i) q^{26} +(-0.756939 + 0.262211i) q^{28} +(4.10555 + 7.11102i) q^{29} -3.60555 q^{31} -1.69722 q^{32} +(-3.65139 - 6.32439i) q^{34} +(-2.00000 - 1.73205i) q^{35} +(1.80278 - 3.12250i) q^{37} +(-2.34861 + 4.06792i) q^{38} +(-1.50000 - 2.59808i) q^{40} +(1.50000 - 2.59808i) q^{41} +(-2.10555 - 3.64692i) q^{43} +(3.39445 + 5.87936i) q^{46} +8.21110 q^{47} +(5.50000 - 4.33013i) q^{49} +(0.651388 - 1.12824i) q^{50} +(0.243061 - 0.420994i) q^{52} +(0.197224 + 0.341603i) q^{53} +(7.50000 - 2.59808i) q^{56} +(-5.34861 - 9.26407i) q^{58} +11.6056 q^{59} +4.21110 q^{61} +4.69722 q^{62} +8.81665 q^{64} +1.60555 q^{65} +4.21110 q^{67} +(-0.848612 - 1.46984i) q^{68} +(2.60555 + 2.25647i) q^{70} +(1.80278 + 3.12250i) q^{73} +(-2.34861 + 4.06792i) q^{74} +(-0.545837 + 0.945417i) q^{76} +12.8167 q^{79} +(1.65139 + 2.86029i) q^{80} +(-1.95416 + 3.38471i) q^{82} +(-7.10555 - 12.3072i) q^{83} +(2.80278 - 4.85455i) q^{85} +(2.74306 + 4.75112i) q^{86} +(1.50000 - 2.59808i) q^{89} +(-0.802776 + 4.17134i) q^{91} +(0.788897 + 1.36641i) q^{92} -10.6972 q^{94} -3.60555 q^{95} +(-6.80278 - 11.7828i) q^{97} +(-7.16527 + 5.64118i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 10 q^{7} + 12 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 + 6 * q^4 - 2 * q^5 + 10 * q^7 + 12 * q^8	\( 4 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 10 q^{7} + 12 q^{8} - q^{10} + 4 q^{13} + 5 q^{14} - 6 q^{16} + 4 q^{17} - 3 q^{20} + 4 q^{23} - 2 q^{25} + 15 q^{26} + 15 q^{28} + 2 q^{29} - 14 q^{32} - 11 q^{34} - 8 q^{35} - 13 q^{38} - 6 q^{40} + 6 q^{41} + 6 q^{43} + 28 q^{46} + 4 q^{47} + 22 q^{49} - q^{50} + 19 q^{52} + 8 q^{53} + 30 q^{56} - 25 q^{58} + 32 q^{59} - 12 q^{61} + 26 q^{62} - 8 q^{64} - 8 q^{65} - 12 q^{67} - 7 q^{68} - 4 q^{70} - 13 q^{74} - 13 q^{76} + 8 q^{79} + 3 q^{80} + 3 q^{82} - 14 q^{83} + 4 q^{85} + 29 q^{86} + 6 q^{89} + 4 q^{91} + 32 q^{92} - 50 q^{94} - 20 q^{97} + 11 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 + 6 * q^4 - 2 * q^5 + 10 * q^7 + 12 * q^8 - q^10 + 4 * q^13 + 5 * q^14 - 6 * q^16 + 4 * q^17 - 3 * q^20 + 4 * q^23 - 2 * q^25 + 15 * q^26 + 15 * q^28 + 2 * q^29 - 14 * q^32 - 11 * q^34 - 8 * q^35 - 13 * q^38 - 6 * q^40 + 6 * q^41 + 6 * q^43 + 28 * q^46 + 4 * q^47 + 22 * q^49 - q^50 + 19 * q^52 + 8 * q^53 + 30 * q^56 - 25 * q^58 + 32 * q^59 - 12 * q^61 + 26 * q^62 - 8 * q^64 - 8 * q^65 - 12 * q^67 - 7 * q^68 - 4 * q^70 - 13 * q^74 - 13 * q^76 + 8 * q^79 + 3 * q^80 + 3 * q^82 - 14 * q^83 + 4 * q^85 + 29 * q^86 + 6 * q^89 + 4 * q^91 + 32 * q^92 - 50 * q^94 - 20 * q^97 + 11 * q^98

Introduction

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