LMFDB - Embedded newform 1960.2.q.x.961.1

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			961.1
Root			$1.43998 + 2.49412i$ of defining polynomial
Character	$\chi$	$=$	1960.961
Dual form			1960.2.q.x.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.43998 - 2.49412i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-2.64709 + 4.58489i) q^{9} +O(q^{10})$	\(q+(-1.43998 - 2.49412i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-2.64709 + 4.58489i) q^{9} +(-0.732874 - 1.26937i) q^{11} +2.22129 q^{13} +2.87996 q^{15} +(-3.63290 - 6.29237i) q^{17} +(2.74355 - 4.75196i) q^{19} +(-1.25773 + 2.17846i) q^{23} +(-0.500000 - 0.866025i) q^{25} +6.60713 q^{27} -7.12260 q^{29} +(3.25773 + 5.64256i) q^{31} +(-2.11065 + 3.65575i) q^{33} +(-3.45065 + 5.97671i) q^{37} +(-3.19862 - 5.54017i) q^{39} -11.3199 q^{41} +3.31733 q^{43} +(-2.64709 - 4.58489i) q^{45} +(4.18353 - 7.24608i) q^{47} +(-10.4626 + 18.1218i) q^{51} +(3.50219 + 6.06597i) q^{53} +1.46575 q^{55} -15.8026 q^{57} +(-4.53553 - 7.85578i) q^{59} +(-5.60713 + 9.71184i) q^{61} +(-1.11065 + 1.92370i) q^{65} +(3.20620 + 5.55330i) q^{67} +7.24445 q^{69} -10.5316 q^{71} +(-5.26083 - 9.11202i) q^{73} +(-1.43998 + 2.49412i) q^{75} +(-5.09555 + 8.82576i) q^{79} +(-1.57288 - 2.72431i) q^{81} +16.4186 q^{83} +7.26580 q^{85} +(10.2564 + 17.7646i) q^{87} +(-4.91512 + 8.51324i) q^{89} +(9.38215 - 16.2504i) q^{93} +(2.74355 + 4.75196i) q^{95} -2.09423 q^{97} +7.75992 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.854222\pi$
$3$	−1.43998	−	2.49412i	−0.831373	−	1.43998i	0.0655765	−	0.997848i	$-0.479111\pi$
$4$		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	$-0.400328\pi$
$13$	2.22129			0.616076			0.308038	+	0.951374i	$0.400328\pi$
$14$		0			0
$15$	2.87996			0.743603
$16$		0			0
$17$	−3.63290	−	6.29237i	−0.881107	−	1.52612i	−0.850111	−	0.526603i	$-0.823465\pi$
$17$	−3.63290	−	6.29237i	−0.881107	−	1.52612i	−0.0309964	−	0.999519i	$-0.509868\pi$
$18$		0			0
$19$	2.74355	−	4.75196i	0.629413	−	1.09017i	−0.358257	−	0.933623i	$-0.616629\pi$
$19$	2.74355	−	4.75196i	0.629413	−	1.09017i	0.987670	−	0.156552i	$-0.0500378\pi$
$20$		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	$0.0322806\pi$
$31$	3.25773	+	5.64256i	0.585106	+	1.01343i	−0.409756	+	0.912195i	$0.634386\pi$
$32$		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	$-0.845115\pi$
$41$	−11.3199			−1.76787			−0.883935	+	0.467609i	$0.845115\pi$
$42$		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	$-0.624410\pi$
$47$	4.18353	−	7.24608i	0.610230	−	1.05695i	0.991201	−	0.132363i	$-0.0422564\pi$
$48$		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	$-0.965607\pi$
$59$	−4.53553	−	7.85578i	−0.590476	−	1.02273i	0.403692	−	0.914895i	$-0.367727\pi$
$60$		0			0
$61$	−5.60713	+	9.71184i	−0.717920	+	1.24347i	0.243903	+	0.969800i	$0.421572\pi$
$61$	−5.60713	+	9.71184i	−0.717920	+	1.24347i	−0.961823	+	0.273674i	$0.911761\pi$
$62$		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	$-0.955527\pi$
$73$	−5.26083	−	9.11202i	−0.615733	−	1.06648i	0.374522	−	0.927218i	$-0.377807\pi$
$74$		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	$-0.142770\pi$
$83$	16.4186			1.80217			0.901087	+	0.433638i	$0.142770\pi$
$84$		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	$0.341108\pi$
$89$	−4.91512	+	8.51324i	−0.521002	+	0.902401i	−0.999702	+	0.0244228i	$0.992225\pi$
$90$		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	$-0.533906\pi$
$97$	−2.09423			−0.212636			−0.106318	+	0.994332i	$0.533906\pi$
$98$		0			0
$99$	7.75992			0.779901
$100$		0			0
$101$	6.83280	+	11.8348i	0.679889	+	1.17760i	0.975014	+	0.222144i	$0.0713054\pi$
$101$	6.83280	+	11.8348i	0.679889	+	1.17760i	−0.295125	+	0.955459i	$0.595361\pi$
$102$		0			0
$103$	−5.01195	+	8.68096i	−0.493843	+	0.855360i	−0.999975	−	0.00709551i	$-0.997741\pi$
$103$	−5.01195	+	8.68096i	−0.493843	+	0.855360i	0.506132	+	0.862456i	$0.331075\pi$
$104$		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	−0.993820	−	0.111008i	$-0.964592\pi$
$131$	−4.58707	+	7.94503i	−0.400774	+	0.694161i	0.593046	+	0.805169i	$0.297925\pi$
$132$		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	$-0.593555\pi$
$139$	−6.83099			−0.579397			−0.289698	+	0.957118i	$0.593555\pi$
$140$		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	0.975635	−	0.219402i	$-0.0704106\pi$
$157$	3.73155	+	6.46323i	0.297810	+	0.515822i	−0.677825	+	0.735223i	$0.737077\pi$
$158$		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	$-0.749206\pi$
$167$	−18.2300			−1.41068			−0.705342	+	0.708868i	$0.749206\pi$
$168$		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	$0.405289\pi$
$173$	−8.96223	+	15.5230i	−0.681386	+	1.18020i	−0.974558	+	0.224135i	$0.928044\pi$
$174$		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	$-0.581583\pi$
$181$	−6.82105			−0.507004			−0.253502	+	0.967335i	$0.581583\pi$
$182$		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	0.917172	−	0.398490i	$-0.130466\pi$
$199$	1.60088	+	2.77281i	0.113483	+	0.196559i	−0.803689	+	0.595049i	$0.797132\pi$
$200$		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	$-0.793897\pi$
$223$	−23.8214			−1.59520			−0.797599	+	0.603188i	$0.793897\pi$
$224$		0			0
$225$	5.29417			0.352945
$226$		0			0
$227$	4.71100	+	8.15969i	0.312680	+	0.541577i	0.978942	−	0.204141i	$-0.0654400\pi$
$227$	4.71100	+	8.15969i	0.312680	+	0.541577i	−0.666262	+	0.745718i	$0.732107\pi$
$228$		0			0
$229$	−4.96793	+	8.60471i	−0.328290	+	0.568616i	−0.982173	−	0.187981i	$-0.939806\pi$
$229$	−4.96793	+	8.60471i	−0.328290	+	0.568616i	0.653882	+	0.756596i	$0.273139\pi$
$230$		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	0.783827	−	0.620979i	$-0.213265\pi$
$241$	−2.26452	−	3.92226i	−0.145870	−	0.252655i	−0.929697	+	0.368324i	$0.879932\pi$
$242$		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	$-0.452184\pi$
$251$	4.74198			0.299311			0.149656	+	0.988738i	$0.452184\pi$
$252$		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	−0.999993	−	0.00365291i	$-0.998837\pi$
$257$	−7.96484	+	13.7955i	−0.496833	+	0.860540i	0.503160	+	0.864193i	$0.332171\pi$
$258$		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	$-0.892905\pi$
$269$	−12.4301	−	21.5295i	−0.757874	−	1.31268i	0.186059	−	0.982539i	$-0.440429\pi$
$270$		0			0
$271$	15.2143	−	26.3519i	0.924201	−	1.60076i	0.131359	−	0.991335i	$-0.458066\pi$
$271$	15.2143	−	26.3519i	0.924201	−	1.60076i	0.792842	−	0.609428i	$-0.208601\pi$
$272$		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	0.772361	−	0.635184i	$-0.219076\pi$
$283$	−2.75731	−	4.77581i	−0.163905	−	0.283892i	−0.936266	+	0.351292i	$0.885742\pi$
$284$		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	$-0.328367\pi$
$293$	17.5777			1.02690			0.513450	+	0.858120i	$0.328367\pi$
$294$		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	$-0.759098\pi$
$307$	−25.4771			−1.45405			−0.727026	+	0.686610i	$0.759098\pi$
$308$		0			0
$309$	28.8685			1.64227
$310$		0			0
$311$	−10.7831	−	18.6768i	−0.611452	−	1.05907i	−0.990996	−	0.133893i	$-0.957252\pi$
$311$	−10.7831	−	18.6768i	−0.611452	−	1.05907i	0.379544	−	0.925174i	$-0.376081\pi$
$312$		0			0
$313$	−1.48970	+	2.58024i	−0.0842030	+	0.145844i	−0.905051	−	0.425302i	$-0.860168\pi$
$313$	−1.48970	+	2.58024i	−0.0842030	+	0.145844i	0.820848	+	0.571146i	$0.193501\pi$
$314$		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	$-0.579616\pi$
$349$	−9.24821			−0.495045			−0.247523	+	0.968882i	$0.579616\pi$
$350$		0			0
$351$	14.6764			0.783368
$352$		0			0
$353$	−8.98042	−	15.5545i	−0.477979	−	0.827885i	0.521702	−	0.853128i	$-0.325297\pi$
$353$	−8.98042	−	15.5545i	−0.477979	−	0.827885i	−0.999681	+	0.0252431i	$0.991964\pi$
$354$		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	$-0.938809\pi$
$367$	−12.5719	−	21.7752i	−0.656249	−	1.13666i	0.325330	−	0.945601i	$-0.394525\pi$
$368$		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	$0.428475\pi$
$383$	−14.3421	+	24.8412i	−0.732846	+	1.26933i	−0.955662	+	0.294466i	$0.904858\pi$
$384$		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	−0.912087	−	0.409996i	$-0.865530\pi$
$397$	−2.01195	+	3.48481i	−0.100977	+	0.174897i	0.811110	+	0.584893i	$0.198864\pi$
$398$		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	0.741693	−	0.670739i	$-0.234023\pi$
$409$	−4.24761	−	7.35708i	−0.210031	−	0.363784i	−0.951724	+	0.306955i	$0.900690\pi$
$410$		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	$-0.476071\pi$
$419$	3.07469			0.150209			0.0751043	+	0.997176i	$0.476071\pi$
$420$		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	$-0.486379\pi$
$433$	1.78030			0.0855557			0.0427779	+	0.999085i	$0.486379\pi$
$434$		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	$-0.622344\pi$
$439$	12.8932	−	22.3318i	0.615361	−	1.06584i	0.990321	−	0.138795i	$-0.0443231\pi$
$440$		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	$-0.900871\pi$
$461$	−40.8762			−1.90380			−0.951898	+	0.306414i	$0.900871\pi$
$462$		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	$-0.616883\pi$
$467$	13.5883	−	23.5356i	0.628792	−	1.08910i	0.987795	−	0.155763i	$-0.0497835\pi$
$468$		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	0.888732	−	0.458427i	$-0.151587\pi$
$479$	1.03644	+	1.79517i	0.0473561	+	0.0820232i	−0.841376	+	0.540451i	$0.818254\pi$
$480$		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	$-0.613354\pi$
$503$	−15.6381			−0.697267			−0.348634	+	0.937259i	$0.613354\pi$
$504$		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	−0.934797	−	0.355184i	$-0.884418\pi$
$509$	−3.60525	+	6.24448i	−0.159800	+	0.276782i	0.774996	+	0.631966i	$0.217752\pi$
$510$		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	0.656738	−	0.754119i	$-0.271936\pi$
$521$	−7.41181	−	12.8376i	−0.324717	−	0.562426i	−0.981455	+	0.191692i	$0.938602\pi$
$522$		0			0
$523$	2.13641	−	3.70038i	0.0934189	−	0.161806i	−0.815529	−	0.578717i	$-0.803554\pi$
$523$	2.13641	−	3.70038i	0.0934189	−	0.161806i	0.908948	+	0.416910i	$0.136887\pi$
$524$		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	0.839086	−	0.543998i	$-0.183090\pi$
$563$	−1.22370	−	2.11952i	−0.0515729	−	0.0893270i	−0.890659	+	0.454671i	$0.849757\pi$
$564$		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	0.842133	−	0.539270i	$-0.181300\pi$
$577$	−1.10386	−	1.91195i	−0.0459545	−	0.0795955i	−0.888088	+	0.459674i	$0.847966\pi$
$578$		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	$-0.194685\pi$
$587$	39.6719			1.63744			0.818718	+	0.574196i	$0.194685\pi$
$588$		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	−0.759624	−	0.650363i	$-0.774617\pi$
$593$	4.46654	−	7.73628i	0.183419	−	0.317691i	0.943043	+	0.332672i	$0.107950\pi$
$594$		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	$-0.383783\pi$
$601$	17.5063			0.714096			0.357048	+	0.934086i	$0.383783\pi$
$602$		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	$-0.464601\pi$
$607$	22.5719	−	39.0957i	0.916166	−	1.58685i	0.805185	−	0.593024i	$-0.202066\pi$
$608$		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	0.940672	−	0.339317i	$-0.110196\pi$
$619$	4.39074	+	7.60499i	0.176479	+	0.305670i	−0.764193	+	0.644987i	$0.776863\pi$
$620$		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	$-0.230496\pi$
$643$	37.9895			1.49816			0.749079	+	0.662480i	$0.230496\pi$
$644$		0			0
$645$	9.55379			0.376180
$646$		0			0
$647$	−16.6852	−	28.8997i	−0.655964	−	1.13616i	−0.981651	−	0.190686i	$-0.938929\pi$
$647$	−16.6852	−	28.8997i	−0.655964	−	1.13616i	0.325687	−	0.945478i	$-0.394404\pi$
$648$		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	0.721202	−	0.692724i	$-0.243590\pi$
$661$	−6.15279	−	10.6569i	−0.239316	−	0.414507i	−0.960518	+	0.278217i	$0.910256\pi$
$662$		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	−0.979892	−	0.199526i	$-0.936060\pi$
$677$	−8.25203	+	14.2929i	−0.317151	+	0.549322i	0.662741	+	0.748849i	$0.269393\pi$
$678$		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	−0.887285	−	0.461221i	$-0.847411\pi$
$691$	−1.16223	+	2.01304i	−0.0442132	+	0.0765796i	0.843072	+	0.537801i	$0.180745\pi$
$692$		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	−0.908474	−	0.417941i	$-0.862752\pi$
$719$	−2.47466	+	4.28623i	−0.0922891	+	0.159849i	0.816185	+	0.577791i	$0.196085\pi$
$720$		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	$-0.611997\pi$
$727$	−18.5847			−0.689269			−0.344635	+	0.938737i	$0.611997\pi$
$728$		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	−0.544867	−	0.838523i	$-0.683420\pi$
$733$	12.2848	−	21.2779i	0.453749	−	0.785916i	0.998615	+	0.0526068i	$0.0167530\pi$
$734$		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	$0.515728\pi$
$761$	−24.5425	+	42.5088i	−0.889664	+	1.54094i	−0.840273	+	0.542163i	$0.817605\pi$
$762$		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	$-0.662204\pi$
$769$	−27.0548			−0.975619			−0.487810	+	0.872950i	$0.662204\pi$
$770$		0			0
$771$	45.8769			1.65221
$772$		0			0
$773$	20.5414	+	35.5787i	0.738822	+	1.27968i	0.953026	+	0.302889i	$0.0979511\pi$
$773$	20.5414	+	35.5787i	0.738822	+	1.27968i	−0.214203	+	0.976789i	$0.568716\pi$
$774$		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	0.986593	−	0.163201i	$-0.0521818\pi$
$787$	9.87373	+	17.1018i	0.351960	+	0.609613i	−0.634632	+	0.772814i	$0.718849\pi$
$788$		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	$-0.719695\pi$
$797$	−35.9488			−1.27337			−0.636685	+	0.771124i	$0.719695\pi$
$798$		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	$-0.224208\pi$
$811$	43.4017			1.52404			0.762019	+	0.647555i	$0.224208\pi$
$812$		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	$-0.830126\pi$
$829$	−25.0787	−	43.4376i	−0.871019	−	1.50865i	−0.0100748	−	0.999949i	$-0.503207\pi$
$830$		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	$-0.447859\pi$
$839$	9.44696			0.326145			0.163073	+	0.986614i	$0.447859\pi$
$840$		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	$-0.381492\pi$
$853$	21.2482			0.727525			0.363762	+	0.931492i	$0.381492\pi$
$854$		0			0
$855$	−29.0496			−0.993476
$856$		0			0
$857$	−3.28217	−	5.68489i	−0.112117	−	0.194192i	0.804507	−	0.593944i	$-0.202430\pi$
$857$	−3.28217	−	5.68489i	−0.112117	−	0.194192i	−0.916624	+	0.399751i	$0.869096\pi$
$858$		0			0
$859$	−10.6253	+	18.4036i	−0.362531	+	0.627922i	−0.988377	−	0.152025i	$-0.951421\pi$
$859$	−10.6253	+	18.4036i	−0.362531	+	0.627922i	0.625845	+	0.779947i	$0.284754\pi$
$860$		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	$-0.360349\pi$
$881$	25.2167			0.849572			0.424786	+	0.905294i	$0.360349\pi$
$882$		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	−0.992091	−	0.125519i	$-0.959940\pi$
$887$	−11.5361	+	19.9810i	−0.387343	+	0.670898i	0.604748	+	0.796417i	$0.293274\pi$
$888$		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	$0.378161\pi$
$929$	−18.7940	+	32.5521i	−0.616610	+	1.06800i	−0.990100	+	0.140365i	$0.955172\pi$
$930$		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	$-0.860464\pi$
$937$	−55.4322			−1.81089			−0.905446	+	0.424461i	$0.860464\pi$
$938$		0			0
$939$	8.58057			0.280016
$940$		0			0
$941$	−7.57694	−	13.1237i	−0.247001	−	0.427819i	0.715691	−	0.698417i	$-0.246112\pi$
$941$	−7.57694	−	13.1237i	−0.247001	−	0.427819i	−0.962692	+	0.270598i	$0.912779\pi$
$942$		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	−0.949130	−	0.314885i	$-0.898034\pi$
$971$	−6.29033	+	10.8952i	−0.201866	+	0.349643i	0.747263	+	0.664528i	$0.231367\pi$
$972$		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	0.570548	−	0.821264i	$-0.306731\pi$
$983$	−13.3551	−	23.1317i	−0.425962	−	0.737787i	−0.996510	+	0.0834771i	$0.973397\pi$
$984$		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	$-0.841067\pi$
$997$	−26.9534	−	46.6846i	−0.853622	−	1.47852i	0.0242947	−	0.999705i	$-0.492266\pi$
$998$		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.x.961.1		8
7.2	even	3		1960.2.a.y.1.4	yes	4
7.3	odd	6		1960.2.q.y.361.4		8
7.4	even	3	inner	1960.2.q.x.361.1		8
7.5	odd	6		1960.2.a.x.1.1	✓	4
7.6	odd	2		1960.2.q.y.961.4		8
28.19	even	6		3920.2.a.ce.1.4		4
28.23	odd	6		3920.2.a.cd.1.1		4
35.9	even	6		9800.2.a.cl.1.1		4
35.19	odd	6		9800.2.a.cs.1.4		4

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

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