LMFDB - Embedded newform 1960.2.q.y.961.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1960,2,Mod(361,1960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1960, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 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("1960.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1960 = 2^{3} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1960.q (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:	$15.6506787962$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.21913473024.16
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 11x^{6} - 2x^{5} + 51x^{4} + 162x^{2} + 112x + 196 $ x^8 - 2x^7 + 11x^6 - 2x^5 + 51x^4 + 162x^2 + 112x + 196
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.4
Root			$1.43998 + 2.49412i$ of defining polynomial
Character	$\chi$	$=$	1960.961
Dual form			1960.2.q.y.361.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.43998 + 2.49412i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-2.64709 + 4.58489i) q^{9} +O(q^{10})$	\(q+(1.43998 + 2.49412i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-2.64709 + 4.58489i) q^{9} +(-0.732874 - 1.26937i) q^{11} -2.22129 q^{13} +2.87996 q^{15} +(3.63290 + 6.29237i) q^{17} +(-2.74355 + 4.75196i) q^{19} +(-1.25773 + 2.17846i) q^{23} +(-0.500000 - 0.866025i) q^{25} -6.60713 q^{27} -7.12260 q^{29} +(-3.25773 - 5.64256i) q^{31} +(2.11065 - 3.65575i) q^{33} +(-3.45065 + 5.97671i) q^{37} +(-3.19862 - 5.54017i) q^{39} +11.3199 q^{41} +3.31733 q^{43} +(2.64709 + 4.58489i) q^{45} +(-4.18353 + 7.24608i) q^{47} +(-10.4626 + 18.1218i) q^{51} +(3.50219 + 6.06597i) q^{53} -1.46575 q^{55} -15.8026 q^{57} +(4.53553 + 7.85578i) q^{59} +(5.60713 - 9.71184i) q^{61} +(-1.11065 + 1.92370i) q^{65} +(3.20620 + 5.55330i) q^{67} -7.24445 q^{69} -10.5316 q^{71} +(5.26083 + 9.11202i) q^{73} +(1.43998 - 2.49412i) q^{75} +(-5.09555 + 8.82576i) q^{79} +(-1.57288 - 2.72431i) q^{81} -16.4186 q^{83} +7.26580 q^{85} +(-10.2564 - 17.7646i) q^{87} +(4.91512 - 8.51324i) q^{89} +(9.38215 - 16.2504i) q^{93} +(2.74355 + 4.75196i) q^{95} +2.09423 q^{97} +7.75992 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} + 4 q^{5} - 6 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 + 4 * q^5 - 6 * q^9	$ 8 q + 2 q^{3} + 4 q^{5} - 6 q^{9} - 2 q^{11} - 20 q^{13} + 4 q^{15} + 6 q^{17} + 4 q^{23} - 4 q^{25} - 28 q^{27} - 4 q^{29} - 12 q^{31} + 18 q^{33} - 14 q^{39} - 24 q^{41} - 16 q^{43} + 6 q^{45} - 2 q^{47} - 2 q^{51} + 4 q^{53} - 4 q^{55} - 16 q^{57} + 8 q^{59} + 20 q^{61} - 10 q^{65} + 8 q^{67} - 48 q^{69} + 8 q^{71} + 16 q^{73} + 2 q^{75} - 22 q^{79} + 20 q^{81} - 72 q^{83} + 12 q^{85} - 18 q^{87} + 40 q^{89} + 32 q^{93} - 52 q^{97} + 24 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 + 4 * q^5 - 6 * q^9 - 2 * q^11 - 20 * q^13 + 4 * q^15 + 6 * q^17 + 4 * q^23 - 4 * q^25 - 28 * q^27 - 4 * q^29 - 12 * q^31 + 18 * q^33 - 14 * q^39 - 24 * q^41 - 16 * q^43 + 6 * q^45 - 2 * q^47 - 2 * q^51 + 4 * q^53 - 4 * q^55 - 16 * q^57 + 8 * q^59 + 20 * q^61 - 10 * q^65 + 8 * q^67 - 48 * q^69 + 8 * q^71 + 16 * q^73 + 2 * q^75 - 22 * q^79 + 20 * q^81 - 72 * q^83 + 12 * q^85 - 18 * q^87 + 40 * q^89 + 32 * q^93 - 52 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times$.

$n$	$981$	$1081$	$1177$	$1471$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	1.43998	+	2.49412i	0.831373	+	1.43998i	0.896950	+	0.442133i	$0.145778\pi$
$3$	1.43998	+	2.49412i	0.831373	+	1.43998i	−0.0655765	+	0.997848i	$0.520889\pi$
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−2.64709	+	4.58489i	−0.882362	+	1.52830i
$10$		0			0
$11$	−0.732874	−	1.26937i	−0.220970	−	0.382731i	0.734133	−	0.679006i	$-0.237589\pi$
$11$	−0.732874	−	1.26937i	−0.220970	−	0.382731i	−0.955103	+	0.296275i	$0.904256\pi$
$12$		0			0
$13$	−2.22129			−0.616076			−0.308038	−	0.951374i	$-0.599672\pi$
$13$	−2.22129			−0.616076			−0.308038	+	0.951374i	$0.599672\pi$
$14$		0			0
$15$	2.87996			0.743603
$16$		0			0
$17$	3.63290	+	6.29237i	0.881107	+	1.52612i	0.850111	+	0.526603i	$0.176535\pi$
$17$	3.63290	+	6.29237i	0.881107	+	1.52612i	0.0309964	+	0.999519i	$0.490132\pi$
$18$		0			0
$19$	−2.74355	+	4.75196i	−0.629413	+	1.09017i	0.358257	+	0.933623i	$0.383371\pi$
$19$	−2.74355	+	4.75196i	−0.629413	+	1.09017i	−0.987670	+	0.156552i	$0.949962\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.25773	+	2.17846i	−0.262256	+	0.454240i	−0.966841	−	0.255379i	$-0.917800\pi$
$23$	−1.25773	+	2.17846i	−0.262256	+	0.454240i	0.704585	+	0.709619i	$0.251133\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−6.60713			−1.27154
$28$		0			0
$29$	−7.12260			−1.32263			−0.661317	−	0.750107i	$-0.730002\pi$
$29$	−7.12260			−1.32263			−0.661317	+	0.750107i	$0.730002\pi$
$30$		0			0
$31$	−3.25773	−	5.64256i	−0.585106	−	1.01343i	−0.994862	−	0.101239i	$-0.967719\pi$
$31$	−3.25773	−	5.64256i	−0.585106	−	1.01343i	0.409756	−	0.912195i	$-0.365614\pi$
$32$		0			0
$33$	2.11065	−	3.65575i	0.367417	−	0.636384i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.45065	+	5.97671i	−0.567284	+	0.982565i	0.429549	+	0.903043i	$0.358672\pi$
$37$	−3.45065	+	5.97671i	−0.567284	+	0.982565i	−0.996833	+	0.0795211i	$0.974661\pi$
$38$		0			0
$39$	−3.19862	−	5.54017i	−0.512189	−	0.887138i
$40$		0			0
$41$	11.3199			1.76787			0.883935	−	0.467609i	$-0.154885\pi$
$41$	11.3199			1.76787			0.883935	+	0.467609i	$0.154885\pi$
$42$		0			0
$43$	3.31733			0.505888			0.252944	−	0.967481i	$-0.418601\pi$
$43$	3.31733			0.505888			0.252944	+	0.967481i	$0.418601\pi$
$44$		0			0
$45$	2.64709	+	4.58489i	0.394604	+	0.683475i
$46$		0			0
$47$	−4.18353	+	7.24608i	−0.610230	+	1.05695i	0.380971	+	0.924587i	$0.375590\pi$
$47$	−4.18353	+	7.24608i	−0.610230	+	1.05695i	−0.991201	+	0.132363i	$0.957744\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−10.4626	+	18.1218i	−1.46506	+	2.53756i
$52$		0			0
$53$	3.50219	+	6.06597i	0.481062	+	0.833225i	0.999764	−	0.0217309i	$-0.00691771\pi$
$53$	3.50219	+	6.06597i	0.481062	+	0.833225i	−0.518701	+	0.854955i	$0.673584\pi$
$54$		0			0
$55$	−1.46575			−0.197641
$56$		0			0
$57$	−15.8026			−2.09311
$58$		0			0
$59$	4.53553	+	7.85578i	0.590476	+	1.02273i	0.994168	+	0.107840i	$0.0343934\pi$
$59$	4.53553	+	7.85578i	0.590476	+	1.02273i	−0.403692	+	0.914895i	$0.632273\pi$
$60$		0			0
$61$	5.60713	−	9.71184i	0.717920	−	1.24347i	−0.243903	−	0.969800i	$-0.578428\pi$
$61$	5.60713	−	9.71184i	0.717920	−	1.24347i	0.961823	−	0.273674i	$-0.0882389\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.11065	+	1.92370i	−0.137759	+	0.238605i
$66$		0			0
$67$	3.20620	+	5.55330i	0.391700	+	0.678444i	0.992674	−	0.120825i	$-0.0385539\pi$
$67$	3.20620	+	5.55330i	0.391700	+	0.678444i	−0.600974	+	0.799268i	$0.705221\pi$
$68$		0			0
$69$	−7.24445			−0.872130
$70$		0			0
$71$	−10.5316			−1.24987			−0.624935	−	0.780677i	$-0.714875\pi$
$71$	−10.5316			−1.24987			−0.624935	+	0.780677i	$0.714875\pi$
$72$		0			0
$73$	5.26083	+	9.11202i	0.615733	+	1.06648i	0.990255	+	0.139263i	$0.0444735\pi$
$73$	5.26083	+	9.11202i	0.615733	+	1.06648i	−0.374522	+	0.927218i	$0.622193\pi$
$74$		0			0
$75$	1.43998	−	2.49412i	0.166275	−	0.287996i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−5.09555	+	8.82576i	−0.573295	+	0.992975i	0.422930	+	0.906162i	$0.361002\pi$
$79$	−5.09555	+	8.82576i	−0.573295	+	0.992975i	−0.996225	+	0.0868130i	$0.972332\pi$
$80$		0			0
$81$	−1.57288	−	2.72431i	−0.174764	−	0.302701i
$82$		0			0
$83$	−16.4186			−1.80217			−0.901087	−	0.433638i	$-0.857230\pi$
$83$	−16.4186			−1.80217			−0.901087	+	0.433638i	$0.857230\pi$
$84$		0			0
$85$	7.26580			0.788086
$86$		0			0
$87$	−10.2564	−	17.7646i	−1.09960	−	1.90457i
$88$		0			0
$89$	4.91512	−	8.51324i	0.521002	−	0.902401i	−0.478700	−	0.877978i	$-0.658892\pi$
$89$	4.91512	−	8.51324i	0.521002	−	0.902401i	0.999702	−	0.0244228i	$-0.00777479\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	9.38215	−	16.2504i	0.972883	−	1.68508i
$94$		0			0
$95$	2.74355	+	4.75196i	0.281482	+	0.487541i
$96$		0			0
$97$	2.09423			0.212636			0.106318	−	0.994332i	$-0.466094\pi$
$97$	2.09423			0.212636			0.106318	+	0.994332i	$0.466094\pi$
$98$		0			0
$99$	7.75992			0.779901
$100$		0			0
$101$	−6.83280	−	11.8348i	−0.679889	−	1.17760i	−0.975014	−	0.222144i	$-0.928695\pi$
$101$	−6.83280	−	11.8348i	−0.679889	−	1.17760i	0.295125	−	0.955459i	$-0.404639\pi$
$102$		0			0
$103$	5.01195	−	8.68096i	0.493843	−	0.855360i	−0.506132	−	0.862456i	$-0.668925\pi$
$103$	5.01195	−	8.68096i	0.493843	−	0.855360i	0.999975	+	0.00709551i	$0.00225859\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.71020	−	8.15831i	0.455352	−	0.788693i	−0.543356	−	0.839502i	$-0.682847\pi$
$107$	4.71020	−	8.15831i	0.455352	−	0.788693i	0.998708	+	0.0508091i	$0.0161800\pi$
$108$		0			0
$109$	4.49280	+	7.78175i	0.430332	+	0.745356i	0.996902	−	0.0786572i	$-0.0250632\pi$
$109$	4.49280	+	7.78175i	0.430332	+	0.745356i	−0.566570	+	0.824014i	$0.691730\pi$
$110$		0			0
$111$	−19.8755			−1.88650
$112$		0			0
$113$	10.9476			1.02987			0.514933	−	0.857231i	$-0.327817\pi$
$113$	10.9476			1.02987			0.514933	+	0.857231i	$0.327817\pi$
$114$		0			0
$115$	1.25773	+	2.17846i	0.117284	+	0.203142i
$116$		0			0
$117$	5.87996	−	10.1844i	0.543603	−	0.941547i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	4.42579	−	7.66570i	0.402345	−	0.696882i
$122$		0			0
$123$	16.3004	+	28.2332i	1.46976	+	2.54570i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−5.44696			−0.483340			−0.241670	−	0.970359i	$-0.577695\pi$
$127$	−5.44696			−0.483340			−0.241670	+	0.970359i	$0.577695\pi$
$128$		0			0
$129$	4.77689	+	8.27382i	0.420582	+	0.728469i
$130$		0			0
$131$	4.58707	−	7.94503i	0.400774	−	0.694161i	−0.593046	−	0.805169i	$-0.702075\pi$
$131$	4.58707	−	7.94503i	0.400774	−	0.694161i	0.993820	+	0.111008i	$0.0354079\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−3.30357	+	5.72194i	−0.284326	+	0.492467i
$136$		0			0
$137$	−5.65685	−	9.79796i	−0.483298	−	0.837096i	0.516518	−	0.856276i	$-0.327228\pi$
$137$	−5.65685	−	9.79796i	−0.483298	−	0.837096i	−0.999816	+	0.0191800i	$0.993894\pi$
$138$		0			0
$139$	6.83099			0.579397			0.289698	−	0.957118i	$-0.406445\pi$
$139$	6.83099			0.579397			0.289698	+	0.957118i	$0.406445\pi$
$140$		0			0
$141$	−24.0968			−2.02932
$142$		0			0
$143$	1.62793	+	2.81965i	0.136134	+	0.235791i
$144$		0			0
$145$	−3.56130	+	6.16835i	−0.295750	+	0.512254i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	0.981216	−	1.69952i	0.0803844	−	0.139230i	−0.823031	−	0.567997i	$-0.807719\pi$
$149$	0.981216	−	1.69952i	0.0803844	−	0.139230i	0.903415	+	0.428767i	$0.141052\pi$
$150$		0			0
$151$	3.66256	+	6.34373i	0.298055	+	0.516246i	0.975691	−	0.219152i	$-0.0703289\pi$
$151$	3.66256	+	6.34373i	0.298055	+	0.516246i	−0.677636	+	0.735397i	$0.736996\pi$
$152$		0			0
$153$	−38.4664			−3.10982
$154$		0			0
$155$	−6.51547			−0.523335
$156$		0			0
$157$	−3.73155	−	6.46323i	−0.297810	−	0.515822i	0.677825	−	0.735223i	$-0.262923\pi$
$157$	−3.73155	−	6.46323i	−0.297810	−	0.515822i	−0.975635	+	0.219402i	$0.929589\pi$
$158$		0			0
$159$	−10.0862	+	17.4697i	−0.799885	+	1.38544i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	6.13951	−	10.6339i	0.480883	−	0.832914i	−0.518876	−	0.854849i	$-0.673649\pi$
$163$	6.13951	−	10.6339i	0.480883	−	0.832914i	0.999759	+	0.0219351i	$0.00698273\pi$
$164$		0			0
$165$	−2.11065	−	3.65575i	−0.164314	−	0.284600i
$166$		0			0
$167$	18.2300			1.41068			0.705342	−	0.708868i	$-0.250794\pi$
$167$	18.2300			1.41068			0.705342	+	0.708868i	$0.250794\pi$
$168$		0			0
$169$	−8.06585			−0.620450
$170$		0			0
$171$	−14.5248	−	25.1577i	−1.11074	−	1.92386i
$172$		0			0
$173$	8.96223	−	15.5230i	0.681386	−	1.18020i	−0.293172	−	0.956060i	$-0.594711\pi$
$173$	8.96223	−	15.5230i	0.681386	−	1.18020i	0.974558	−	0.224135i	$-0.0719558\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−13.0622	+	22.6243i	−0.981812	+	1.70055i
$178$		0			0
$179$	−0.0187836	−	0.0325342i	−0.00140395	−	0.00243172i	0.865323	−	0.501215i	$-0.167114\pi$
$179$	−0.0187836	−	0.0325342i	−0.00140395	−	0.00243172i	−0.866727	+	0.498784i	$0.833780\pi$
$180$		0			0
$181$	6.82105			0.507004			0.253502	−	0.967335i	$-0.418417\pi$
$181$	6.82105			0.507004			0.253502	+	0.967335i	$0.418417\pi$
$182$		0			0
$183$	32.2966			2.38744
$184$		0			0
$185$	3.45065	+	5.97671i	0.253697	+	0.439416i
$186$		0			0
$187$	5.32491	−	9.22302i	0.389396	−	0.674454i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	2.93101	−	5.07666i	0.212080	−	0.367334i	−0.740285	−	0.672293i	$-0.765309\pi$
$191$	2.93101	−	5.07666i	0.212080	−	0.367334i	0.952365	+	0.304959i	$0.0986428\pi$
$192$		0			0
$193$	2.38584	+	4.13239i	0.171736	+	0.297456i	0.939027	−	0.343843i	$-0.111729\pi$
$193$	2.38584	+	4.13239i	0.171736	+	0.297456i	−0.767291	+	0.641300i	$0.778396\pi$
$194$		0			0
$195$	−6.39724			−0.458116
$196$		0			0
$197$	−9.28714			−0.661682			−0.330841	−	0.943687i	$-0.607332\pi$
$197$	−9.28714			−0.661682			−0.330841	+	0.943687i	$0.607332\pi$
$198$		0			0
$199$	−1.60088	−	2.77281i	−0.113483	−	0.196559i	0.803689	−	0.595049i	$-0.202868\pi$
$199$	−1.60088	−	2.77281i	−0.113483	−	0.196559i	−0.917172	+	0.398490i	$0.869534\pi$
$200$		0			0
$201$	−9.23373	+	15.9933i	−0.651297	+	1.12808i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	5.65995	−	9.80332i	0.395308	−	0.684693i
$206$		0			0
$207$	−6.65867	−	11.5331i	−0.462809	−	0.801609i
$208$		0			0
$209$	8.04269			0.556325
$210$		0			0
$211$	−26.1055			−1.79718			−0.898590	−	0.438790i	$-0.855407\pi$
$211$	−26.1055			−1.79718			−0.898590	+	0.438790i	$0.855407\pi$
$212$		0			0
$213$	−15.1653	−	26.2671i	−1.03911	−	1.79979i
$214$		0			0
$215$	1.65867	−	2.87289i	0.113120	−	0.195930i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−15.1510	+	26.2423i	−1.02381	+	1.77329i
$220$		0			0
$221$	−8.06974	−	13.9772i	−0.542829	−	0.940208i
$222$		0			0
$223$	23.8214			1.59520			0.797599	−	0.603188i	$-0.206103\pi$
$223$	23.8214			1.59520			0.797599	+	0.603188i	$0.206103\pi$
$224$		0			0
$225$	5.29417			0.352945
$226$		0			0
$227$	−4.71100	−	8.15969i	−0.312680	−	0.541577i	0.666262	−	0.745718i	$-0.267893\pi$
$227$	−4.71100	−	8.15969i	−0.312680	−	0.541577i	−0.978942	+	0.204141i	$0.934560\pi$
$228$		0			0
$229$	4.96793	−	8.60471i	0.328290	−	0.568616i	−0.653882	−	0.756596i	$-0.726861\pi$
$229$	4.96793	−	8.60471i	0.328290	−	0.568616i	0.982173	+	0.187981i	$0.0601942\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.618537	+	1.07134i	−0.0405217	+	0.0701856i	−0.885575	−	0.464497i	$-0.846235\pi$
$233$	−0.618537	+	1.07134i	−0.0405217	+	0.0701856i	0.845053	+	0.534682i	$0.179569\pi$
$234$		0			0
$235$	4.18353	+	7.24608i	0.272903	+	0.472682i
$236$		0			0
$237$	−29.3500			−1.90649
$238$		0			0
$239$	1.05710			0.0683782			0.0341891	−	0.999415i	$-0.489115\pi$
$239$	1.05710			0.0683782			0.0341891	+	0.999415i	$0.489115\pi$
$240$		0			0
$241$	2.26452	+	3.92226i	0.145870	+	0.252655i	0.929697	−	0.368324i	$-0.120068\pi$
$241$	2.26452	+	3.92226i	0.145870	+	0.252655i	−0.783827	+	0.620979i	$0.786735\pi$
$242$		0			0
$243$	−5.38087	+	9.31993i	−0.345183	+	0.597874i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	6.09423	−	10.5555i	0.387766	−	0.671631i
$248$		0			0
$249$	−23.6424	−	40.9499i	−1.49828	−	2.59510i
$250$		0			0
$251$	−4.74198			−0.299311			−0.149656	−	0.988738i	$-0.547816\pi$
$251$	−4.74198			−0.299311			−0.149656	+	0.988738i	$0.547816\pi$
$252$		0			0
$253$	3.68704			0.231802
$254$		0			0
$255$	10.4626	+	18.1218i	0.655194	+	1.13483i
$256$		0			0
$257$	7.96484	−	13.7955i	0.496833	−	0.860540i	−0.503160	−	0.864193i	$-0.667829\pi$
$257$	7.96484	−	13.7955i	0.496833	−	0.860540i	0.999993	+	0.00365291i	$0.00116276\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	18.8541	−	32.6563i	1.16704	−	2.02138i
$262$		0			0
$263$	6.63732	+	11.4962i	0.409275	+	0.708885i	0.994809	−	0.101763i	$-0.0324484\pi$
$263$	6.63732	+	11.4962i	0.409275	+	0.708885i	−0.585534	+	0.810648i	$0.699115\pi$
$264$		0			0
$265$	7.00437			0.430275
$266$		0			0
$267$	28.3107			1.73259
$268$		0			0
$269$	12.4301	+	21.5295i	0.757874	+	1.31268i	0.943933	+	0.330138i	$0.107095\pi$
$269$	12.4301	+	21.5295i	0.757874	+	1.31268i	−0.186059	+	0.982539i	$0.559571\pi$
$270$		0			0
$271$	−15.2143	+	26.3519i	−0.924201	+	1.60076i	−0.131359	+	0.991335i	$0.541934\pi$
$271$	−15.2143	+	26.3519i	−0.924201	+	1.60076i	−0.792842	+	0.609428i	$0.791399\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.732874	+	1.26937i	−0.0441939	+	0.0765462i
$276$		0			0
$277$	10.8649	+	18.8185i	0.652807	+	1.13069i	0.982439	+	0.186585i	$0.0597419\pi$
$277$	10.8649	+	18.8185i	0.652807	+	1.13069i	−0.329632	+	0.944109i	$0.606925\pi$
$278$		0			0
$279$	34.4940			2.06510
$280$		0			0
$281$	−0.285426			−0.0170271			−0.00851354	−	0.999964i	$-0.502710\pi$
$281$	−0.285426			−0.0170271			−0.00851354	+	0.999964i	$0.502710\pi$
$282$		0			0
$283$	2.75731	+	4.77581i	0.163905	+	0.283892i	0.936266	−	0.351292i	$-0.114258\pi$
$283$	2.75731	+	4.77581i	0.163905	+	0.283892i	−0.772361	+	0.635184i	$0.780924\pi$
$284$		0			0
$285$	−7.90131	+	13.6855i	−0.468033	+	0.810657i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−17.8959	+	30.9966i	−1.05270	+	1.82333i
$290$		0			0
$291$	3.01564	+	5.22325i	0.176780	+	0.306192i
$292$		0			0
$293$	−17.5777			−1.02690			−0.513450	−	0.858120i	$-0.671633\pi$
$293$	−17.5777			−1.02690			−0.513450	+	0.858120i	$0.671633\pi$
$294$		0			0
$295$	9.07107			0.528138
$296$		0			0
$297$	4.84219	+	8.38692i	0.280973	+	0.486659i
$298$		0			0
$299$	2.79380	−	4.83900i	0.161570	−	0.279847i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	19.6782	−	34.0836i	1.13048	−	1.95805i
$304$		0			0
$305$	−5.60713	−	9.71184i	−0.321063	−	0.556098i
$306$		0			0
$307$	25.4771			1.45405			0.727026	−	0.686610i	$-0.240902\pi$
$307$	25.4771			1.45405			0.727026	+	0.686610i	$0.240902\pi$
$308$		0			0
$309$	28.8685			1.64227
$310$		0			0
$311$	10.7831	+	18.6768i	0.611452	+	1.05907i	0.990996	+	0.133893i	$0.0427477\pi$
$311$	10.7831	+	18.6768i	0.611452	+	1.05907i	−0.379544	+	0.925174i	$0.623919\pi$
$312$		0			0
$313$	1.48970	−	2.58024i	0.0842030	−	0.145844i	−0.820848	−	0.571146i	$-0.806499\pi$
$313$	1.48970	−	2.58024i	0.0842030	−	0.145844i	0.905051	+	0.425302i	$0.139832\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.99819	−	6.92507i	0.224561	−	0.388950i	−0.731627	−	0.681705i	$-0.761239\pi$
$317$	3.99819	−	6.92507i	0.224561	−	0.388950i	0.956188	+	0.292755i	$0.0945720\pi$
$318$		0			0
$319$	5.21997	+	9.04125i	0.292262	+	0.506213i
$320$		0			0
$321$	27.1304			1.51427
$322$		0			0
$323$	−39.8681			−2.21832
$324$		0			0
$325$	1.11065	+	1.92370i	0.0616076	+	0.106708i
$326$		0			0
$327$	−12.9391	+	22.4111i	−0.715532	+	1.23934i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−17.1483	+	29.7018i	−0.942557	+	1.63256i	−0.181987	+	0.983301i	$0.558253\pi$
$331$	−17.1483	+	29.7018i	−0.942557	+	1.63256i	−0.760570	+	0.649256i	$0.775081\pi$
$332$		0			0
$333$	−18.2684	−	31.6417i	−1.00110	−	1.73396i
$334$		0			0
$335$	6.41240			0.350347
$336$		0			0
$337$	23.8719			1.30038			0.650192	−	0.759770i	$-0.274689\pi$
$337$	23.8719			1.30038			0.650192	+	0.759770i	$0.274689\pi$
$338$		0			0
$339$	15.7644	+	27.3047i	0.856203	+	1.48299i
$340$		0			0
$341$	−4.77502	+	8.27057i	−0.258582	+	0.447876i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−3.62223	+	6.27388i	−0.195014	+	0.337774i
$346$		0			0
$347$	−3.17782	−	5.50415i	−0.170595	−	0.295478i	0.768033	−	0.640410i	$-0.221236\pi$
$347$	−3.17782	−	5.50415i	−0.170595	−	0.295478i	−0.938628	+	0.344931i	$0.887902\pi$
$348$		0			0
$349$	9.24821			0.495045			0.247523	−	0.968882i	$-0.420384\pi$
$349$	9.24821			0.495045			0.247523	+	0.968882i	$0.420384\pi$
$350$		0			0
$351$	14.6764			0.783368
$352$		0			0
$353$	8.98042	+	15.5545i	0.477979	+	0.827885i	0.999681	−	0.0252431i	$-0.00803599\pi$
$353$	8.98042	+	15.5545i	0.477979	+	0.827885i	−0.521702	+	0.853128i	$0.674703\pi$
$354$		0			0
$355$	−5.26580	+	9.12063i	−0.279480	+	0.484073i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	10.1421	−	17.5667i	0.535281	−	0.927135i	−0.463868	−	0.885904i	$-0.653539\pi$
$359$	10.1421	−	17.5667i	0.535281	−	0.927135i	0.999150	−	0.0412304i	$-0.0131278\pi$
$360$		0			0
$361$	−5.55410	−	9.61998i	−0.292321	−	0.506315i
$362$		0			0
$363$	25.4922			1.33799
$364$		0			0
$365$	10.5217			0.550729
$366$		0			0
$367$	12.5719	+	21.7752i	0.656249	+	1.13666i	0.981579	+	0.191056i	$0.0611913\pi$
$367$	12.5719	+	21.7752i	0.656249	+	1.13666i	−0.325330	+	0.945601i	$0.605475\pi$
$368$		0			0
$369$	−29.9647	+	51.9005i	−1.55990	+	2.70183i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−0.368866	+	0.638895i	−0.0190992	+	0.0330807i	−0.875417	−	0.483368i	$-0.839413\pi$
$373$	−0.368866	+	0.638895i	−0.0190992	+	0.0330807i	0.856318	+	0.516449i	$0.172746\pi$
$374$		0			0
$375$	−1.43998	−	2.49412i	−0.0743603	−	0.128796i
$376$		0			0
$377$	15.8214			0.814843
$378$		0			0
$379$	−7.11120			−0.365278			−0.182639	−	0.983180i	$-0.558464\pi$
$379$	−7.11120			−0.365278			−0.182639	+	0.983180i	$0.558464\pi$
$380$		0			0
$381$	−7.84352	−	13.5854i	−0.401836	−	0.696000i
$382$		0			0
$383$	14.3421	−	24.8412i	0.732846	−	1.26933i	−0.222816	−	0.974861i	$-0.571525\pi$
$383$	14.3421	−	24.8412i	0.732846	−	1.26933i	0.955662	−	0.294466i	$-0.0951419\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−8.78127	+	15.2096i	−0.446377	+	0.773148i
$388$		0			0
$389$	−6.75944	−	11.7077i	−0.342717	−	0.593603i	0.642219	−	0.766521i	$-0.278014\pi$
$389$	−6.75944	−	11.7077i	−0.342717	−	0.593603i	−0.984936	+	0.172918i	$0.944681\pi$
$390$		0			0
$391$	−18.2769			−0.924302
$392$		0			0
$393$	26.4212			1.33277
$394$		0			0
$395$	5.09555	+	8.82576i	0.256385	+	0.444072i
$396$		0			0
$397$	2.01195	−	3.48481i	0.100977	−	0.174897i	−0.811110	−	0.584893i	$-0.801136\pi$
$397$	2.01195	−	3.48481i	0.100977	−	0.174897i	0.912087	+	0.409996i	$0.134470\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	12.1898	−	21.1133i	0.608729	−	1.05435i	−0.382722	−	0.923864i	$-0.625013\pi$
$401$	12.1898	−	21.1133i	0.608729	−	1.05435i	0.991450	−	0.130485i	$-0.0416535\pi$
$402$		0			0
$403$	7.23639	+	12.5338i	0.360470	+	0.624353i
$404$		0			0
$405$	−3.14576			−0.156314
$406$		0			0
$407$	10.1156			0.501410
$408$		0			0
$409$	4.24761	+	7.35708i	0.210031	+	0.363784i	0.951724	−	0.306955i	$-0.0993102\pi$
$409$	4.24761	+	7.35708i	0.210031	+	0.363784i	−0.741693	+	0.670739i	$0.765977\pi$
$410$		0			0
$411$	16.2915	−	28.2177i	0.803601	−	1.39188i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−8.20929	+	14.2189i	−0.402978	+	0.697979i
$416$		0			0
$417$	9.83649	+	17.0373i	0.481695	+	0.834320i
$418$		0			0
$419$	−3.07469			−0.150209			−0.0751043	−	0.997176i	$-0.523929\pi$
$419$	−3.07469			−0.150209			−0.0751043	+	0.997176i	$0.523929\pi$
$420$		0			0
$421$	22.4790			1.09556			0.547780	−	0.836623i	$-0.315473\pi$
$421$	22.4790			1.09556			0.547780	+	0.836623i	$0.315473\pi$
$422$		0			0
$423$	−22.1483	−	38.3620i	−1.07689	−	1.86523i
$424$		0			0
$425$	3.63290	−	6.29237i	0.176221	−	0.305225i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−4.68837	+	8.12049i	−0.226357	+	0.392061i
$430$		0			0
$431$	2.58627	+	4.47955i	0.124576	+	0.215772i	0.921567	−	0.388219i	$-0.126910\pi$
$431$	2.58627	+	4.47955i	0.124576	+	0.215772i	−0.796991	+	0.603991i	$0.793576\pi$
$432$		0			0
$433$	−1.78030			−0.0855557			−0.0427779	−	0.999085i	$-0.513621\pi$
$433$	−1.78030			−0.0855557			−0.0427779	+	0.999085i	$0.513621\pi$
$434$		0			0
$435$	−20.5128			−0.983514
$436$		0			0
$437$	−6.90131	−	11.9534i	−0.330134	−	0.571809i
$438$		0			0
$439$	−12.8932	+	22.3318i	−0.615361	+	1.06584i	0.374960	+	0.927041i	$0.377656\pi$
$439$	−12.8932	+	22.3318i	−0.615361	+	1.06584i	−0.990321	+	0.138795i	$0.955677\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	6.22129	−	10.7756i	0.295583	−	0.511964i	−0.679538	−	0.733641i	$-0.737820\pi$
$443$	6.22129	−	10.7756i	0.295583	−	0.511964i	0.975120	+	0.221677i	$0.0711529\pi$
$444$		0			0
$445$	−4.91512	−	8.51324i	−0.232999	−	0.403566i
$446$		0			0
$447$	5.65173			0.267318
$448$		0			0
$449$	−25.3574			−1.19669			−0.598344	−	0.801239i	$-0.704174\pi$
$449$	−25.3574			−1.19669			−0.598344	+	0.801239i	$0.704174\pi$
$450$		0			0
$451$	−8.29605	−	14.3692i	−0.390646	−	0.676618i
$452$		0			0
$453$	−10.5480	+	18.2697i	−0.495589	+	0.858386i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	17.3520	−	30.0545i	0.811690	−	1.40589i	−0.0999897	−	0.994988i	$-0.531881\pi$
$457$	17.3520	−	30.0545i	0.811690	−	1.40589i	0.911680	−	0.410901i	$-0.134786\pi$
$458$		0			0
$459$	−24.0030	−	41.5745i	−1.12037	−	1.94053i
$460$		0			0
$461$	40.8762			1.90380			0.951898	−	0.306414i	$-0.0991293\pi$
$461$	40.8762			1.90380			0.951898	+	0.306414i	$0.0991293\pi$
$462$		0			0
$463$	−25.1236			−1.16759			−0.583796	−	0.811901i	$-0.698433\pi$
$463$	−25.1236			−1.16759			−0.583796	+	0.811901i	$0.698433\pi$
$464$		0			0
$465$	−9.38215	−	16.2504i	−0.435087	−	0.753592i
$466$		0			0
$467$	−13.5883	+	23.5356i	−0.628792	+	1.08910i	0.359003	+	0.933336i	$0.383117\pi$
$467$	−13.5883	+	23.5356i	−0.628792	+	1.08910i	−0.987795	+	0.155763i	$0.950217\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	10.7467	−	18.6138i	0.495182	−	0.857680i
$472$		0			0
$473$	−2.43119	−	4.21094i	−0.111786	−	0.193619i
$474$		0			0
$475$	5.48709			0.251765
$476$		0			0
$477$	−37.0824			−1.69789
$478$		0			0
$479$	−1.03644	−	1.79517i	−0.0473561	−	0.0820232i	0.841376	−	0.540451i	$-0.181746\pi$
$479$	−1.03644	−	1.79517i	−0.0473561	−	0.0820232i	−0.888732	+	0.458427i	$0.848413\pi$
$480$		0			0
$481$	7.66492	−	13.2760i	0.349490	−	0.605335i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.04711	−	1.81365i	0.0475469	−	0.0823537i
$486$		0			0
$487$	−16.6745	−	28.8811i	−0.755594	−	1.30873i	−0.945078	−	0.326844i	$-0.894015\pi$
$487$	−16.6745	−	28.8811i	−0.755594	−	1.30873i	0.189484	−	0.981884i	$-0.439318\pi$
$488$		0			0
$489$	35.3631			1.59917
$490$		0			0
$491$	36.4487			1.64491			0.822453	−	0.568833i	$-0.192605\pi$
$491$	36.4487			1.64491			0.822453	+	0.568833i	$0.192605\pi$
$492$		0			0
$493$	−25.8757	−	44.8180i	−1.16538	−	2.01850i
$494$		0			0
$495$	3.87996	−	6.72029i	0.174391	−	0.302055i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	3.74684	−	6.48972i	0.167732	−	0.290520i	−0.769890	−	0.638176i	$-0.779689\pi$
$499$	3.74684	−	6.48972i	0.167732	−	0.290520i	0.937622	+	0.347657i	$0.113022\pi$
$500$		0			0
$501$	26.2509	+	45.4679i	1.17280	+	2.03136i
$502$		0			0
$503$	15.6381			0.697267			0.348634	−	0.937259i	$-0.386646\pi$
$503$	15.6381			0.697267			0.348634	+	0.937259i	$0.386646\pi$
$504$		0			0
$505$	−13.6656			−0.608111
$506$		0			0
$507$	−11.6147	−	20.1172i	−0.515825	−	0.893436i
$508$		0			0
$509$	3.60525	−	6.24448i	0.159800	−	0.276782i	−0.774996	−	0.631966i	$-0.782248\pi$
$509$	3.60525	−	6.24448i	0.159800	−	0.276782i	0.934797	+	0.355184i	$0.115582\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	18.1270	−	31.3968i	0.800326	−	1.38620i
$514$		0			0
$515$	−5.01195	−	8.68096i	−0.220853	−	0.382529i
$516$		0			0
$517$	12.2640			0.539370
$518$		0			0
$519$	51.6218			2.26594
$520$		0			0
$521$	7.41181	+	12.8376i	0.324717	+	0.562426i	0.981455	−	0.191692i	$-0.0613976\pi$
$521$	7.41181	+	12.8376i	0.324717	+	0.562426i	−0.656738	+	0.754119i	$0.728064\pi$
$522$		0			0
$523$	−2.13641	+	3.70038i	−0.0934189	+	0.161806i	−0.908948	−	0.416910i	$-0.863113\pi$
$523$	−2.13641	+	3.70038i	−0.0934189	+	0.161806i	0.815529	+	0.578717i	$0.196446\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	23.6700	−	40.9977i	1.03108	−	1.78589i
$528$		0			0
$529$	8.33621	+	14.4387i	0.362444	+	0.627771i
$530$		0			0
$531$	−48.0238			−2.08406
$532$		0			0
$533$	−25.1448			−1.08914
$534$		0			0
$535$	−4.71020	−	8.15831i	−0.203640	−	0.352714i
$536$		0			0
$537$	0.0540961	−	0.0936971i	0.00233442	−	0.00404333i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	0.471449	−	0.816574i	0.0202692	−	0.0351073i	−0.855713	−	0.517451i	$-0.826881\pi$
$541$	0.471449	−	0.816574i	0.0202692	−	0.0351073i	0.875982	+	0.482344i	$0.160214\pi$
$542$		0			0
$543$	9.82218	+	17.0125i	0.421510	+	0.730077i
$544$		0			0
$545$	8.98559			0.384900
$546$		0			0
$547$	−11.1871			−0.478327			−0.239164	−	0.970979i	$-0.576873\pi$
$547$	−11.1871			−0.478327			−0.239164	+	0.970979i	$0.576873\pi$
$548$		0			0
$549$	29.6851	+	51.4162i	1.26693	+	2.19439i
$550$		0			0
$551$	19.5412	−	33.8463i	0.832483	−	1.44190i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−9.93775	+	17.2127i	−0.421834	+	0.730638i
$556$		0			0
$557$	−14.3652	−	24.8813i	−0.608675	−	1.05426i	−0.991459	−	0.130418i	$-0.958368\pi$
$557$	−14.3652	−	24.8813i	−0.608675	−	1.05426i	0.382784	−	0.923838i	$-0.374965\pi$
$558$		0			0
$559$	−7.36877			−0.311666
$560$		0			0
$561$	30.6711			1.29493
$562$		0			0
$563$	1.22370	+	2.11952i	0.0515729	+	0.0893270i	0.890659	−	0.454671i	$-0.150243\pi$
$563$	1.22370	+	2.11952i	0.0515729	+	0.0893270i	−0.839086	+	0.543998i	$0.816910\pi$
$564$		0			0
$565$	5.47381	−	9.48092i	0.230285	−	0.398865i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−17.7529	+	30.7489i	−0.744240	+	1.28906i	0.206309	+	0.978487i	$0.433855\pi$
$569$	−17.7529	+	30.7489i	−0.744240	+	1.28906i	−0.950549	+	0.310575i	$0.899479\pi$
$570$		0			0
$571$	−2.89437	−	5.01320i	−0.121126	−	0.209796i	0.799086	−	0.601216i	$-0.205317\pi$
$571$	−2.89437	−	5.01320i	−0.121126	−	0.209796i	−0.920212	+	0.391421i	$0.871984\pi$
$572$		0			0
$573$	16.8824			0.705272
$574$		0			0
$575$	2.51547			0.104902
$576$		0			0
$577$	1.10386	+	1.91195i	0.0459545	+	0.0795955i	0.888088	−	0.459674i	$-0.152034\pi$
$577$	1.10386	+	1.91195i	0.0459545	+	0.0795955i	−0.842133	+	0.539270i	$0.818700\pi$
$578$		0			0
$579$	−6.87112	+	11.9011i	−0.285554	+	0.494594i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	5.13332	−	8.89117i	0.212600	−	0.368235i
$584$		0			0
$585$	−5.87996	−	10.1844i	−0.243106	−	0.421073i
$586$		0			0
$587$	−39.6719			−1.63744			−0.818718	−	0.574196i	$-0.805315\pi$
$587$	−39.6719			−1.63744			−0.818718	+	0.574196i	$0.805315\pi$
$588$		0			0
$589$	35.7510			1.47309
$590$		0			0
$591$	−13.3733	−	23.1632i	−0.550104	−	0.952809i
$592$		0			0
$593$	−4.46654	+	7.73628i	−0.183419	+	0.317691i	−0.943043	−	0.332672i	$-0.892050\pi$
$593$	−4.46654	+	7.73628i	−0.183419	+	0.317691i	0.759624	+	0.650363i	$0.225383\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	4.61047	−	7.98557i	0.188694	−	0.326828i
$598$		0			0
$599$	−9.19500	−	15.9262i	−0.375697	−	0.650727i	0.614734	−	0.788735i	$-0.289263\pi$
$599$	−9.19500	−	15.9262i	−0.375697	−	0.650727i	−0.990431	+	0.138008i	$0.955930\pi$
$600$		0			0
$601$	−17.5063			−0.714096			−0.357048	−	0.934086i	$-0.616217\pi$
$601$	−17.5063			−0.714096			−0.357048	+	0.934086i	$0.616217\pi$
$602$		0			0
$603$	−33.9484			−1.38248
$604$		0			0
$605$	−4.42579	−	7.66570i	−0.179934	−	0.311655i
$606$		0			0
$607$	−22.5719	+	39.0957i	−0.916166	+	1.58685i	−0.110981	+	0.993822i	$0.535399\pi$
$607$	−22.5719	+	39.0957i	−0.916166	+	1.58685i	−0.805185	+	0.593024i	$0.797934\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	9.29285	−	16.0957i	0.375948	−	0.651162i
$612$		0			0
$613$	5.92787	+	10.2674i	0.239424	+	0.414695i	0.960549	−	0.278110i	$-0.0897079\pi$
$613$	5.92787	+	10.2674i	0.239424	+	0.414695i	−0.721125	+	0.692805i	$0.756375\pi$
$614$		0			0
$615$	32.6009			1.31459
$616$		0			0
$617$	−20.8174			−0.838078			−0.419039	−	0.907968i	$-0.637633\pi$
$617$	−20.8174			−0.838078			−0.419039	+	0.907968i	$0.637633\pi$
$618$		0			0
$619$	−4.39074	−	7.60499i	−0.176479	−	0.305670i	0.764193	−	0.644987i	$-0.223137\pi$
$619$	−4.39074	−	7.60499i	−0.176479	−	0.305670i	−0.940672	+	0.339317i	$0.889804\pi$
$620$		0			0
$621$	8.31002	−	14.3934i	0.333470	−	0.577586i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	11.5813	+	20.0594i	0.462513	+	0.801097i
$628$		0			0
$629$	−50.1435			−1.99935
$630$		0			0
$631$	22.1004			0.879803			0.439902	−	0.898046i	$-0.355013\pi$
$631$	22.1004			0.879803			0.439902	+	0.898046i	$0.355013\pi$
$632$		0			0
$633$	−37.5915	−	65.1103i	−1.49413	−	2.58790i
$634$		0			0
$635$	−2.72348	+	4.71721i	−0.108078	+	0.187197i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	27.8781	−	48.2862i	1.10284	−	1.91017i
$640$		0			0
$641$	21.9288	+	37.9819i	0.866137	+	1.50019i	0.865914	+	0.500193i	$0.166738\pi$
$641$	21.9288	+	37.9819i	0.866137	+	1.50019i	0.000223352		1.00000i	$0.499929\pi$
$642$		0			0
$643$	−37.9895			−1.49816			−0.749079	−	0.662480i	$-0.769504\pi$
$643$	−37.9895			−1.49816			−0.749079	+	0.662480i	$0.769504\pi$
$644$		0			0
$645$	9.55379			0.376180
$646$		0			0
$647$	16.6852	+	28.8997i	0.655964	+	1.13616i	0.981651	+	0.190686i	$0.0610711\pi$
$647$	16.6852	+	28.8997i	0.655964	+	1.13616i	−0.325687	+	0.945478i	$0.605596\pi$
$648$		0			0
$649$	6.64795	−	11.5146i	0.260955	−	0.451987i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−7.53160	+	13.0451i	−0.294734	+	0.510495i	−0.974923	−	0.222542i	$-0.928564\pi$
$653$	−7.53160	+	13.0451i	−0.294734	+	0.510495i	0.680189	+	0.733037i	$0.261898\pi$
$654$		0			0
$655$	−4.58707	−	7.94503i	−0.179232	−	0.310438i
$656$		0			0
$657$	−55.7035			−2.17320
$658$		0			0
$659$	−0.153540			−0.00598106			−0.00299053	−	0.999996i	$-0.500952\pi$
$659$	−0.153540			−0.00598106			−0.00299053	+	0.999996i	$0.500952\pi$
$660$		0			0
$661$	6.15279	+	10.6569i	0.239316	+	0.414507i	0.960518	−	0.278217i	$-0.0897436\pi$
$661$	6.15279	+	10.6569i	0.239316	+	0.414507i	−0.721202	+	0.692724i	$0.756410\pi$
$662$		0			0
$663$	23.2405	−	40.2538i	0.902588	−	1.56333i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	8.95834	−	15.5163i	0.346868	−	0.600794i
$668$		0			0
$669$	34.3023	+	59.4134i	1.32621	+	2.29705i
$670$		0			0
$671$	−16.4373			−0.634554
$672$		0			0
$673$	4.82480			0.185983			0.0929913	−	0.995667i	$-0.470357\pi$
$673$	4.82480			0.185983			0.0929913	+	0.995667i	$0.470357\pi$
$674$		0			0
$675$	3.30357	+	5.72194i	0.127154	+	0.220238i
$676$		0			0
$677$	8.25203	−	14.2929i	0.317151	−	0.549322i	−0.662741	−	0.748849i	$-0.730607\pi$
$677$	8.25203	−	14.2929i	0.317151	−	0.549322i	0.979892	+	0.199526i	$0.0639403\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	13.5675	−	23.4996i	0.519907	−	0.900506i
$682$		0			0
$683$	−16.1811	−	28.0264i	−0.619152	−	1.07240i	−0.989641	−	0.143565i	$-0.954143\pi$
$683$	−16.1811	−	28.0264i	−0.619152	−	1.07240i	0.370489	−	0.928837i	$-0.379190\pi$
$684$		0			0
$685$	−11.3137			−0.432275
$686$		0			0
$687$	28.6149			1.09173
$688$		0			0
$689$	−7.77939	−	13.4743i	−0.296371	−	0.513330i
$690$		0			0
$691$	1.16223	−	2.01304i	0.0442132	−	0.0765796i	−0.843072	−	0.537801i	$-0.819255\pi$
$691$	1.16223	−	2.01304i	0.0442132	−	0.0765796i	0.887285	+	0.461221i	$0.152589\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	3.41549	−	5.91581i	0.129557	−	0.224399i
$696$		0			0
$697$	41.1240	+	71.2289i	1.55768	+	2.69799i
$698$		0			0
$699$	−3.56272			−0.134755
$700$		0			0
$701$	−6.77071			−0.255726			−0.127863	−	0.991792i	$-0.540812\pi$
$701$	−6.77071			−0.255726			−0.127863	+	0.991792i	$0.540812\pi$
$702$		0			0
$703$	−18.9341	−	32.7947i	−0.714111	−	1.23688i
$704$		0			0
$705$	−12.0484	+	20.8684i	−0.453769	+	0.785951i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	3.11871	−	5.40177i	0.117126	−	0.202868i	−0.801502	−	0.597992i	$-0.795965\pi$
$709$	3.11871	−	5.40177i	0.117126	−	0.202868i	0.918627	+	0.395125i	$0.129299\pi$
$710$		0			0
$711$	−26.9767	−	46.7251i	−1.01171	−	1.75233i
$712$		0			0
$713$	16.3895			0.613790
$714$		0			0
$715$	3.25586			0.121762
$716$		0			0
$717$	1.52221	+	2.63654i	0.0568478	+	0.0984633i
$718$		0			0
$719$	2.47466	−	4.28623i	0.0922891	−	0.159849i	−0.816185	−	0.577791i	$-0.803915\pi$
$719$	2.47466	−	4.28623i	0.0922891	−	0.159849i	0.908474	+	0.417941i	$0.137248\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−6.52172	+	11.2960i	−0.242545	+	0.420101i
$724$		0			0
$725$	3.56130	+	6.16835i	0.132263	+	0.229087i
$726$		0			0
$727$	18.5847			0.689269			0.344635	−	0.938737i	$-0.388003\pi$
$727$	18.5847			0.689269			0.344635	+	0.938737i	$0.388003\pi$
$728$		0			0
$729$	−40.4306			−1.49743
$730$		0			0
$731$	12.0515	+	20.8739i	0.445742	+	0.772048i
$732$		0			0
$733$	−12.2848	+	21.2779i	−0.453749	+	0.785916i	−0.998615	−	0.0526068i	$-0.983247\pi$
$733$	−12.2848	+	21.2779i	−0.453749	+	0.785916i	0.544867	+	0.838523i	$0.316580\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4.69948	−	8.13974i	0.173108	−	0.299831i
$738$		0			0
$739$	4.21475	+	7.30016i	0.155042	+	0.268541i	0.933074	−	0.359684i	$-0.117115\pi$
$739$	4.21475	+	7.30016i	0.155042	+	0.268541i	−0.778032	+	0.628224i	$0.783782\pi$
$740$		0			0
$741$	35.1023			1.28951
$742$		0			0
$743$	−11.4705			−0.420811			−0.210405	−	0.977614i	$-0.567478\pi$
$743$	−11.4705			−0.420811			−0.210405	+	0.977614i	$0.567478\pi$
$744$		0			0
$745$	−0.981216	−	1.69952i	−0.0359490	−	0.0622655i
$746$		0			0
$747$	43.4614	−	75.2774i	1.59017	−	2.75426i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	8.15146	−	14.1187i	0.297451	−	0.515200i	−0.678101	−	0.734969i	$-0.737197\pi$
$751$	8.15146	−	14.1187i	0.297451	−	0.515200i	0.975552	+	0.219768i	$0.0705302\pi$
$752$		0			0
$753$	−6.82836	−	11.8271i	−0.248839	−	0.431002i
$754$		0			0
$755$	7.32511			0.266588
$756$		0			0
$757$	25.0875			0.911821			0.455910	−	0.890026i	$-0.349314\pi$
$757$	25.0875			0.911821			0.455910	+	0.890026i	$0.349314\pi$
$758$		0			0
$759$	5.30927	+	9.19592i	0.192714	+	0.333791i
$760$		0			0
$761$	24.5425	−	42.5088i	0.889664	−	1.54094i	0.0493908	−	0.998780i	$-0.484272\pi$
$761$	24.5425	−	42.5088i	0.889664	−	1.54094i	0.840273	−	0.542163i	$-0.182395\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−19.2332	+	33.3129i	−0.695378	+	1.20443i
$766$		0			0
$767$	−10.0748	−	17.4500i	−0.363778	−	0.630083i
$768$		0			0
$769$	27.0548			0.975619			0.487810	−	0.872950i	$-0.337796\pi$
$769$	27.0548			0.975619			0.487810	+	0.872950i	$0.337796\pi$
$770$		0			0
$771$	45.8769			1.65221
$772$		0			0
$773$	−20.5414	−	35.5787i	−0.738822	−	1.27968i	−0.953026	−	0.302889i	$-0.902049\pi$
$773$	−20.5414	−	35.5787i	−0.738822	−	1.27968i	0.214203	−	0.976789i	$-0.431284\pi$
$774$		0			0
$775$	−3.25773	+	5.64256i	−0.117021	+	0.202687i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−31.0567	+	53.7917i	−1.11272	+	1.92729i
$780$		0			0
$781$	7.71833	+	13.3685i	0.276184	+	0.478364i
$782$		0			0
$783$	47.0600			1.68179
$784$		0			0
$785$	−7.46309			−0.266369
$786$		0			0
$787$	−9.87373	−	17.1018i	−0.351960	−	0.609613i	0.634632	−	0.772814i	$-0.281151\pi$
$787$	−9.87373	−	17.1018i	−0.351960	−	0.609613i	−0.986593	+	0.163201i	$0.947818\pi$
$788$		0			0
$789$	−19.1152	+	33.1085i	−0.680520	+	1.17870i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−12.4551	+	21.5729i	−0.442293	+	0.766075i
$794$		0			0
$795$	10.0862	+	17.4697i	0.357719	+	0.619588i
$796$		0			0
$797$	35.9488			1.27337			0.636685	−	0.771124i	$-0.280305\pi$
$797$	35.9488			1.27337			0.636685	+	0.771124i	$0.280305\pi$
$798$		0			0
$799$	−60.7933			−2.15071
$800$		0			0
$801$	26.0215	+	45.0706i	0.919424	+	1.59249i
$802$		0			0
$803$	7.71104	−	13.3559i	0.272117	−	0.471320i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−35.7981	+	62.0041i	−1.26015	+	2.18265i
$808$		0			0
$809$	−19.5568	−	33.8734i	−0.687582	−	1.19093i	−0.972618	−	0.232410i	$-0.925339\pi$
$809$	−19.5568	−	33.8734i	−0.687582	−	1.19093i	0.285036	−	0.958517i	$-0.407994\pi$
$810$		0			0
$811$	−43.4017			−1.52404			−0.762019	−	0.647555i	$-0.775792\pi$
$811$	−43.4017			−1.52404			−0.762019	+	0.647555i	$0.775792\pi$
$812$		0			0
$813$	−87.6330			−3.07342
$814$		0			0
$815$	−6.13951	−	10.6339i	−0.215058	−	0.372491i
$816$		0			0
$817$	−9.10126	+	15.7638i	−0.318413	+	0.551507i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−6.50676	+	11.2700i	−0.227088	+	0.393327i	−0.956944	−	0.290274i	$-0.906254\pi$
$821$	−6.50676	+	11.2700i	−0.227088	+	0.393327i	0.729856	+	0.683601i	$0.239587\pi$
$822$		0			0
$823$	0.0295033	+	0.0511012i	0.00102842	+	0.00178127i	0.866539	−	0.499109i	$-0.166339\pi$
$823$	0.0295033	+	0.0511012i	0.00102842	+	0.00178127i	−0.865511	+	0.500890i	$0.833006\pi$
$824$		0			0
$825$	−4.22129			−0.146967
$826$		0			0
$827$	0.519093			0.0180506			0.00902531	−	0.999959i	$-0.497127\pi$
$827$	0.519093			0.0180506			0.00902531	+	0.999959i	$0.497127\pi$
$828$		0			0
$829$	25.0787	+	43.4376i	0.871019	+	1.50865i	0.860944	+	0.508700i	$0.169874\pi$
$829$	25.0787	+	43.4376i	0.871019	+	1.50865i	0.0100748	+	0.999949i	$0.496793\pi$
$830$		0			0
$831$	−31.2904	+	54.1965i	−1.08545	+	1.88006i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	9.11502	−	15.7877i	0.315438	−	0.546355i
$836$		0			0
$837$	21.5243	+	37.2812i	0.743988	+	1.28863i
$838$		0			0
$839$	−9.44696			−0.326145			−0.163073	−	0.986614i	$-0.552141\pi$
$839$	−9.44696			−0.326145			−0.163073	+	0.986614i	$0.552141\pi$
$840$		0			0
$841$	21.7315			0.749360
$842$		0			0
$843$	−0.411008	−	0.711886i	−0.0141559	−	0.0245187i
$844$		0			0
$845$	−4.03292	+	6.98523i	−0.138737	+	0.240299i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−7.94095	+	13.7541i	−0.272533	+	0.472041i
$850$		0			0
$851$	−8.68001	−	15.0342i	−0.297547	−	0.515366i
$852$		0			0
$853$	−21.2482			−0.727525			−0.363762	−	0.931492i	$-0.618508\pi$
$853$	−21.2482			−0.727525			−0.363762	+	0.931492i	$0.618508\pi$
$854$		0			0
$855$	−29.0496			−0.993476
$856$		0			0
$857$	3.28217	+	5.68489i	0.112117	+	0.194192i	0.916624	−	0.399751i	$-0.130904\pi$
$857$	3.28217	+	5.68489i	0.112117	+	0.194192i	−0.804507	+	0.593944i	$0.797570\pi$
$858$		0			0
$859$	10.6253	−	18.4036i	0.362531	−	0.627922i	−0.625845	−	0.779947i	$-0.715246\pi$
$859$	10.6253	−	18.4036i	0.362531	−	0.627922i	0.988377	+	0.152025i	$0.0485793\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	0.717296	−	1.24239i	0.0244170	−	0.0422915i	−0.853559	−	0.520997i	$-0.825560\pi$
$863$	0.717296	−	1.24239i	0.0244170	−	0.0422915i	0.877976	+	0.478705i	$0.158894\pi$
$864$		0			0
$865$	−8.96223	−	15.5230i	−0.304725	−	0.527799i
$866$		0			0
$867$	−103.079			−3.50075
$868$		0			0
$869$	14.9376			0.506723
$870$		0			0
$871$	−7.12192	−	12.3355i	−0.241317	−	0.417973i
$872$		0			0
$873$	−5.54360	+	9.60179i	−0.187622	+	0.324971i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−11.3020	+	19.5756i	−0.381640	+	0.661020i	−0.991297	−	0.131646i	$-0.957974\pi$
$877$	−11.3020	+	19.5756i	−0.381640	+	0.661020i	0.609657	+	0.792665i	$0.291307\pi$
$878$		0			0
$879$	−25.3115	−	43.8409i	−0.853737	−	1.47872i
$880$		0			0
$881$	−25.2167			−0.849572			−0.424786	−	0.905294i	$-0.639651\pi$
$881$	−25.2167			−0.849572			−0.424786	+	0.905294i	$0.639651\pi$
$882$		0			0
$883$	−42.0869			−1.41634			−0.708168	−	0.706044i	$-0.750478\pi$
$883$	−42.0869			−1.41634			−0.708168	+	0.706044i	$0.750478\pi$
$884$		0			0
$885$	13.0622	+	22.6243i	0.439080	+	0.760508i
$886$		0			0
$887$	11.5361	−	19.9810i	0.387343	−	0.670898i	−0.604748	−	0.796417i	$-0.706726\pi$
$887$	11.5361	−	19.9810i	0.387343	−	0.670898i	0.992091	+	0.125519i	$0.0400595\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−2.30544	+	3.99315i	−0.0772353	+	0.133775i
$892$		0			0
$893$	−22.9554	−	39.7599i	−0.768173	−	1.33052i
$894$		0			0
$895$	−0.0375672			−0.00125573
$896$		0			0
$897$	16.0921			0.537298
$898$		0			0
$899$	23.2035	+	40.1897i	0.773882	+	1.34040i
$900$		0			0
$901$	−25.4462	+	44.0741i	−0.847735	+	1.46832i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	3.41052	−	5.90720i	0.113370	−	0.196362i
$906$		0			0
$907$	−11.1962	−	19.3923i	−0.371763	−	0.643912i	0.618074	−	0.786120i	$-0.287913\pi$
$907$	−11.1962	−	19.3923i	−0.371763	−	0.643912i	−0.989837	+	0.142208i	$0.954580\pi$
$908$		0			0
$909$	72.3481			2.39963
$910$		0			0
$911$	−54.7584			−1.81423			−0.907114	−	0.420886i	$-0.861719\pi$
$911$	−54.7584			−1.81423			−0.907114	+	0.420886i	$0.861719\pi$
$912$		0			0
$913$	12.0328	+	20.8413i	0.398226	+	0.689748i
$914$		0			0
$915$	16.1483	−	27.9697i	0.533847	−	0.924650i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−28.0295	+	48.5485i	−0.924608	+	1.60147i	−0.132419	+	0.991194i	$0.542274\pi$
$919$	−28.0295	+	48.5485i	−0.924608	+	1.60147i	−0.792190	+	0.610275i	$0.791059\pi$
$920$		0			0
$921$	36.6865	+	63.5428i	1.20886	+	2.09381i
$922$		0			0
$923$	23.3938			0.770016
$924$		0			0
$925$	6.90131			0.226914
$926$		0			0
$927$	26.5342	+	45.9585i	0.871496	+	1.50948i
$928$		0			0
$929$	18.7940	−	32.5521i	0.616610	−	1.06800i	−0.373490	−	0.927634i	$-0.621839\pi$
$929$	18.7940	−	32.5521i	0.616610	−	1.06800i	0.990100	−	0.140365i	$-0.0448276\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−31.0548	+	53.7886i	−1.01669	+	1.76096i
$934$		0			0
$935$	−5.32491	−	9.22302i	−0.174143	−	0.301625i
$936$		0			0
$937$	55.4322			1.81089			0.905446	−	0.424461i	$-0.139536\pi$
$937$	55.4322			1.81089			0.905446	+	0.424461i	$0.139536\pi$
$938$		0			0
$939$	8.58057			0.280016
$940$		0			0
$941$	7.57694	+	13.1237i	0.247001	+	0.427819i	0.962692	−	0.270598i	$-0.0872215\pi$
$941$	7.57694	+	13.1237i	0.247001	+	0.427819i	−0.715691	+	0.698417i	$0.753888\pi$
$942$		0			0
$943$	−14.2374	+	24.6599i	−0.463634	+	0.803038i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	9.84533	−	17.0526i	0.319930	−	0.554136i	−0.660543	−	0.750788i	$-0.729674\pi$
$947$	9.84533	−	17.0526i	0.319930	−	0.554136i	0.980473	+	0.196653i	$0.0630072\pi$
$948$		0			0
$949$	−11.6858	−	20.2405i	−0.379339	−	0.657034i
$950$		0			0
$951$	23.0293			0.746775
$952$		0			0
$953$	44.8194			1.45184			0.725921	−	0.687778i	$-0.241414\pi$
$953$	44.8194			1.45184			0.725921	+	0.687778i	$0.241414\pi$
$954$		0			0
$955$	−2.93101	−	5.07666i	−0.0948453	−	0.164277i
$956$		0			0
$957$	−15.0333	+	26.0384i	−0.485958	+	0.841703i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−5.72567	+	9.91715i	−0.184699	+	0.319908i
$962$		0			0
$963$	24.9366	+	43.1915i	0.803571	+	1.39183i
$964$		0			0
$965$	4.77168			0.153606
$966$		0			0
$967$	32.3195			1.03932			0.519662	−	0.854372i	$-0.326058\pi$
$967$	32.3195			1.03932			0.519662	+	0.854372i	$0.326058\pi$
$968$		0			0
$969$	−57.4093	−	99.4358i	−1.84425	−	3.19434i
$970$		0			0
$971$	6.29033	−	10.8952i	0.201866	−	0.349643i	−0.747263	−	0.664528i	$-0.768633\pi$
$971$	6.29033	−	10.8952i	0.201866	−	0.349643i	0.949130	+	0.314885i	$0.101966\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−3.19862	+	5.54017i	−0.102438	+	0.177428i
$976$		0			0
$977$	−21.0585	−	36.4743i	−0.673720	−	1.16692i	−0.976841	−	0.213965i	$-0.931362\pi$
$977$	−21.0585	−	36.4743i	−0.673720	−	1.16692i	0.303121	−	0.952952i	$-0.401971\pi$
$978$		0			0
$979$	−14.4086			−0.460502
$980$		0			0
$981$	−47.5713			−1.51883
$982$		0			0
$983$	13.3551	+	23.1317i	0.425962	+	0.737787i	0.996510	−	0.0834771i	$-0.0266026\pi$
$983$	13.3551	+	23.1317i	0.425962	+	0.737787i	−0.570548	+	0.821264i	$0.693269\pi$
$984$		0			0
$985$	−4.64357	+	8.04290i	−0.147957	+	0.256268i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−4.17232	+	7.22668i	−0.132672	+	0.229795i
$990$		0			0
$991$	3.72452	+	6.45105i	0.118313	+	0.204924i	0.919099	−	0.394026i	$-0.128918\pi$
$991$	3.72452	+	6.45105i	0.118313	+	0.204924i	−0.800786	+	0.598950i	$0.795585\pi$
$992$		0			0
$993$	−98.7730			−3.13447
$994$		0			0
$995$	−3.20176			−0.101503
$996$		0			0
$997$	26.9534	+	46.6846i	0.853622	+	1.47852i	0.877917	+	0.478813i	$0.158933\pi$
$997$	26.9534	+	46.6846i	0.853622	+	1.47852i	−0.0242947	+	0.999705i	$0.507734\pi$
$998$		0			0
$999$	22.7989	−	39.4889i	0.721326	−	1.24937i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1960.2.q.y.961.4		8
7.2	even	3		1960.2.a.x.1.1	✓	4
7.3	odd	6		1960.2.q.x.361.1		8
7.4	even	3	inner	1960.2.q.y.361.4		8
7.5	odd	6		1960.2.a.y.1.4	yes	4
7.6	odd	2		1960.2.q.x.961.1		8
28.19	even	6		3920.2.a.cd.1.1		4
28.23	odd	6		3920.2.a.ce.1.4		4
35.9	even	6		9800.2.a.cs.1.4		4
35.19	odd	6		9800.2.a.cl.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1960.2.a.x.1.1	✓	4	7.2	even	3
1960.2.a.y.1.4	yes	4	7.5	odd	6
1960.2.q.x.361.1		8	7.3	odd	6
1960.2.q.x.961.1		8	7.6	odd	2
1960.2.q.y.361.4		8	7.4	even	3	inner
1960.2.q.y.961.4		8	1.1	even	1	trivial
3920.2.a.cd.1.1		4	28.19	even	6
3920.2.a.ce.1.4		4	28.23	odd	6
9800.2.a.cl.1.1		4	35.19	odd	6
9800.2.a.cs.1.4		4	35.9	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1960.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.43998 + 2.49412i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-2.64709 + 4.58489i) q^{9} +O(q^{10})\)	\(q+(1.43998 + 2.49412i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-2.64709 + 4.58489i) q^{9} +(-0.732874 - 1.26937i) q^{11} -2.22129 q^{13} +2.87996 q^{15} +(3.63290 + 6.29237i) q^{17} +(-2.74355 + 4.75196i) q^{19} +(-1.25773 + 2.17846i) q^{23} +(-0.500000 - 0.866025i) q^{25} -6.60713 q^{27} -7.12260 q^{29} +(-3.25773 - 5.64256i) q^{31} +(2.11065 - 3.65575i) q^{33} +(-3.45065 + 5.97671i) q^{37} +(-3.19862 - 5.54017i) q^{39} +11.3199 q^{41} +3.31733 q^{43} +(2.64709 + 4.58489i) q^{45} +(-4.18353 + 7.24608i) q^{47} +(-10.4626 + 18.1218i) q^{51} +(3.50219 + 6.06597i) q^{53} -1.46575 q^{55} -15.8026 q^{57} +(4.53553 + 7.85578i) q^{59} +(5.60713 - 9.71184i) q^{61} +(-1.11065 + 1.92370i) q^{65} +(3.20620 + 5.55330i) q^{67} -7.24445 q^{69} -10.5316 q^{71} +(5.26083 + 9.11202i) q^{73} +(1.43998 - 2.49412i) q^{75} +(-5.09555 + 8.82576i) q^{79} +(-1.57288 - 2.72431i) q^{81} -16.4186 q^{83} +7.26580 q^{85} +(-10.2564 - 17.7646i) q^{87} +(4.91512 - 8.51324i) q^{89} +(9.38215 - 16.2504i) q^{93} +(2.74355 + 4.75196i) q^{95} +2.09423 q^{97} +7.75992 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 4 q^{5} - 6 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 + 4 * q^5 - 6 * q^9	\( 8 q + 2 q^{3} + 4 q^{5} - 6 q^{9} - 2 q^{11} - 20 q^{13} + 4 q^{15} + 6 q^{17} + 4 q^{23} - 4 q^{25} - 28 q^{27} - 4 q^{29} - 12 q^{31} + 18 q^{33} - 14 q^{39} - 24 q^{41} - 16 q^{43} + 6 q^{45} - 2 q^{47} - 2 q^{51} + 4 q^{53} - 4 q^{55} - 16 q^{57} + 8 q^{59} + 20 q^{61} - 10 q^{65} + 8 q^{67} - 48 q^{69} + 8 q^{71} + 16 q^{73} + 2 q^{75} - 22 q^{79} + 20 q^{81} - 72 q^{83} + 12 q^{85} - 18 q^{87} + 40 q^{89} + 32 q^{93} - 52 q^{97} + 24 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 + 4 * q^5 - 6 * q^9 - 2 * q^11 - 20 * q^13 + 4 * q^15 + 6 * q^17 + 4 * q^23 - 4 * q^25 - 28 * q^27 - 4 * q^29 - 12 * q^31 + 18 * q^33 - 14 * q^39 - 24 * q^41 - 16 * q^43 + 6 * q^45 - 2 * q^47 - 2 * q^51 + 4 * q^53 - 4 * q^55 - 16 * q^57 + 8 * q^59 + 20 * q^61 - 10 * q^65 + 8 * q^67 - 48 * q^69 + 8 * q^71 + 16 * q^73 + 2 * q^75 - 22 * q^79 + 20 * q^81 - 72 * q^83 + 12 * q^85 - 18 * q^87 + 40 * q^89 + 32 * q^93 - 52 * q^97 + 24 * q^99

Introduction

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