LMFDB - Embedded newform 1960.2.q.o.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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1960.961
Dual form			1960.2.q.o.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})$	$q+(1.50000 + 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-3.00000 + 5.19615i) q^{9} +(2.50000 + 4.33013i) q^{11} -5.00000 q^{13} -3.00000 q^{15} +(3.50000 + 6.06218i) q^{17} +(1.00000 - 1.73205i) q^{19} +(1.00000 - 1.73205i) q^{23} +(-0.500000 - 0.866025i) q^{25} -9.00000 q^{27} +7.00000 q^{29} +(-2.00000 - 3.46410i) q^{31} +(-7.50000 + 12.9904i) q^{33} +(3.00000 - 5.19615i) q^{37} +(-7.50000 - 12.9904i) q^{39} -12.0000 q^{41} -2.00000 q^{43} +(-3.00000 - 5.19615i) q^{45} +(-0.500000 + 0.866025i) q^{47} +(-10.5000 + 18.1865i) q^{51} -5.00000 q^{55} +6.00000 q^{57} +(2.00000 + 3.46410i) q^{59} +(-2.00000 + 3.46410i) q^{61} +(2.50000 - 4.33013i) q^{65} +(-4.00000 - 6.92820i) q^{67} +6.00000 q^{69} +(-3.00000 - 5.19615i) q^{73} +(1.50000 - 2.59808i) q^{75} +(1.50000 - 2.59808i) q^{79} +(-4.50000 - 7.79423i) q^{81} -4.00000 q^{83} -7.00000 q^{85} +(10.5000 + 18.1865i) q^{87} +(6.00000 - 10.3923i) q^{93} +(1.00000 + 1.73205i) q^{95} +13.0000 q^{97} -30.0000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} - q^{5} - 6 q^{9}+O(q^{10}) $ 2 * q + 3 * q^3 - q^5 - 6 * q^9	$ 2 q + 3 q^{3} - q^{5} - 6 q^{9} + 5 q^{11} - 10 q^{13} - 6 q^{15} + 7 q^{17} + 2 q^{19} + 2 q^{23} - q^{25} - 18 q^{27} + 14 q^{29} - 4 q^{31} - 15 q^{33} + 6 q^{37} - 15 q^{39} - 24 q^{41} - 4 q^{43} - 6 q^{45} - q^{47} - 21 q^{51} - 10 q^{55} + 12 q^{57} + 4 q^{59} - 4 q^{61} + 5 q^{65} - 8 q^{67} + 12 q^{69} - 6 q^{73} + 3 q^{75} + 3 q^{79} - 9 q^{81} - 8 q^{83} - 14 q^{85} + 21 q^{87} + 12 q^{93} + 2 q^{95} + 26 q^{97} - 60 q^{99}+O(q^{100}) $ 2 * q + 3 * q^3 - q^5 - 6 * q^9 + 5 * q^11 - 10 * q^13 - 6 * q^15 + 7 * q^17 + 2 * q^19 + 2 * q^23 - q^25 - 18 * q^27 + 14 * q^29 - 4 * q^31 - 15 * q^33 + 6 * q^37 - 15 * q^39 - 24 * q^41 - 4 * q^43 - 6 * q^45 - q^47 - 21 * q^51 - 10 * q^55 + 12 * q^57 + 4 * q^59 - 4 * q^61 + 5 * q^65 - 8 * q^67 + 12 * q^69 - 6 * q^73 + 3 * q^75 + 3 * q^79 - 9 * q^81 - 8 * q^83 - 14 * q^85 + 21 * q^87 + 12 * q^93 + 2 * q^95 + 26 * q^97 - 60 * 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
$3$	1.50000	+	2.59808i	0.866025	+	1.50000i	0.866025	+	0.500000i	$0.166667\pi$
$3$	1.50000	+	2.59808i	0.866025	+	1.50000i			1.00000i	$0.5\pi$
$4$		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
$9$	−3.00000	+	5.19615i	−1.00000	+	1.73205i
$10$		0			0
$11$	2.50000	+	4.33013i	0.753778	+	1.30558i	0.945979	+	0.324227i	$0.105104\pi$
$11$	2.50000	+	4.33013i	0.753778	+	1.30558i	−0.192201	+	0.981356i	$0.561563\pi$
$12$		0			0
$13$	−5.00000			−1.38675			−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−5.00000			−1.38675			−0.693375	+	0.720577i	$0.743877\pi$
$14$		0			0
$15$	−3.00000			−0.774597
$16$		0			0
$17$	3.50000	+	6.06218i	0.848875	+	1.47029i	0.882213	+	0.470850i	$0.156053\pi$
$17$	3.50000	+	6.06218i	0.848875	+	1.47029i	−0.0333386	+	0.999444i	$0.510614\pi$
$18$		0			0
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	−0.728219	−	0.685344i	$-0.759652\pi$
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	0.957635	+	0.287984i	$0.0929851\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.00000	−	1.73205i	0.208514	−	0.361158i	−0.742732	−	0.669588i	$-0.766471\pi$
$23$	1.00000	−	1.73205i	0.208514	−	0.361158i	0.951247	+	0.308431i	$0.0998038\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−9.00000			−1.73205
$28$		0			0
$29$	7.00000			1.29987			0.649934	−	0.759991i	$-0.274797\pi$
$29$	7.00000			1.29987			0.649934	+	0.759991i	$0.274797\pi$
$30$		0			0
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$		0			0
$33$	−7.50000	+	12.9904i	−1.30558	+	2.26134i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.00000	−	5.19615i	0.493197	−	0.854242i	−0.506772	−	0.862080i	$-0.669162\pi$
$37$	3.00000	−	5.19615i	0.493197	−	0.854242i	0.999969	+	0.00783774i	$0.00249486\pi$
$38$		0			0
$39$	−7.50000	−	12.9904i	−1.20096	−	2.08013i
$40$		0			0
$41$	−12.0000			−1.87409			−0.937043	−	0.349215i	$-0.886448\pi$
$41$	−12.0000			−1.87409			−0.937043	+	0.349215i	$0.886448\pi$
$42$		0			0
$43$	−2.00000			−0.304997			−0.152499	−	0.988304i	$-0.548732\pi$
$43$	−2.00000			−0.304997			−0.152499	+	0.988304i	$0.548732\pi$
$44$		0			0
$45$	−3.00000	−	5.19615i	−0.447214	−	0.774597i
$46$		0			0
$47$	−0.500000	+	0.866025i	−0.0729325	+	0.126323i	−0.900185	−	0.435507i	$-0.856569\pi$
$47$	−0.500000	+	0.866025i	−0.0729325	+	0.126323i	0.827253	+	0.561830i	$0.189902\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−10.5000	+	18.1865i	−1.47029	+	2.54662i
$52$		0			0
$53$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$53$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$54$		0			0
$55$	−5.00000			−0.674200
$56$		0			0
$57$	6.00000			0.794719
$58$		0			0
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	0.966342	−	0.257260i	$-0.0828195\pi$
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	−0.705965	+	0.708247i	$0.749486\pi$
$60$		0			0
$61$	−2.00000	+	3.46410i	−0.256074	+	0.443533i	−0.965187	−	0.261562i	$-0.915762\pi$
$61$	−2.00000	+	3.46410i	−0.256074	+	0.443533i	0.709113	+	0.705095i	$0.249096\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.50000	−	4.33013i	0.310087	−	0.537086i
$66$		0			0
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	0.511237	−	0.859440i	$-0.329187\pi$
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	−0.999915	+	0.0130248i	$0.995854\pi$
$68$		0			0
$69$	6.00000			0.722315
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−3.00000	−	5.19615i	−0.351123	−	0.608164i	0.635323	−	0.772246i	$-0.280867\pi$
$73$	−3.00000	−	5.19615i	−0.351123	−	0.608164i	−0.986447	+	0.164083i	$0.947534\pi$
$74$		0			0
$75$	1.50000	−	2.59808i	0.173205	−	0.300000i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	1.50000	−	2.59808i	0.168763	−	0.292306i	−0.769222	−	0.638982i	$-0.779356\pi$
$79$	1.50000	−	2.59808i	0.168763	−	0.292306i	0.937985	+	0.346675i	$0.112689\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$		0			0
$83$	−4.00000			−0.439057			−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000			−0.439057			−0.219529	+	0.975606i	$0.570452\pi$
$84$		0			0
$85$	−7.00000			−0.759257
$86$		0			0
$87$	10.5000	+	18.1865i	1.12572	+	1.94980i
$88$		0			0
$89$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$89$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	6.00000	−	10.3923i	0.622171	−	1.07763i
$94$		0			0
$95$	1.00000	+	1.73205i	0.102598	+	0.177705i
$96$		0			0
$97$	13.0000			1.31995			0.659975	−	0.751288i	$-0.270567\pi$
$97$	13.0000			1.31995			0.659975	+	0.751288i	$0.270567\pi$
$98$		0			0
$99$	−30.0000			−3.01511
$100$		0			0
$101$	9.00000	+	15.5885i	0.895533	+	1.55111i	0.833143	+	0.553058i	$0.186539\pi$
$101$	9.00000	+	15.5885i	0.895533	+	1.55111i	0.0623905	+	0.998052i	$0.480128\pi$
$102$		0			0
$103$	−6.50000	+	11.2583i	−0.640464	+	1.10932i	0.344865	+	0.938652i	$0.387925\pi$
$103$	−6.50000	+	11.2583i	−0.640464	+	1.10932i	−0.985329	+	0.170664i	$0.945409\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.00000	+	15.5885i	−0.870063	+	1.50699i	−0.00813215	+	0.999967i	$0.502589\pi$
$107$	−9.00000	+	15.5885i	−0.870063	+	1.50699i	−0.861931	+	0.507026i	$0.830745\pi$
$108$		0			0
$109$	−2.50000	−	4.33013i	−0.239457	−	0.414751i	0.721102	−	0.692829i	$-0.243636\pi$
$109$	−2.50000	−	4.33013i	−0.239457	−	0.414751i	−0.960558	+	0.278078i	$0.910303\pi$
$110$		0			0
$111$	18.0000			1.70848
$112$		0			0
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$		0			0
$115$	1.00000	+	1.73205i	0.0932505	+	0.161515i
$116$		0			0
$117$	15.0000	−	25.9808i	1.38675	−	2.40192i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−7.00000	+	12.1244i	−0.636364	+	1.10221i
$122$		0			0
$123$	−18.0000	−	31.1769i	−1.62301	−	2.81113i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−12.0000			−1.06483			−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000			−1.06483			−0.532414	+	0.846484i	$0.678715\pi$
$128$		0			0
$129$	−3.00000	−	5.19615i	−0.264135	−	0.457496i
$130$		0			0
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	−0.704692	−	0.709514i	$-0.748915\pi$
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	0.966803	+	0.255524i	$0.0822479\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	4.50000	−	7.79423i	0.387298	−	0.670820i
$136$		0			0
$137$	4.00000	+	6.92820i	0.341743	+	0.591916i	0.984757	−	0.173939i	$-0.0556494\pi$
$137$	4.00000	+	6.92820i	0.341743	+	0.591916i	−0.643013	+	0.765855i	$0.722316\pi$
$138$		0			0
$139$	18.0000			1.52674			0.763370	−	0.645961i	$-0.223543\pi$
$139$	18.0000			1.52674			0.763370	+	0.645961i	$0.223543\pi$
$140$		0			0
$141$	−3.00000			−0.252646
$142$		0			0
$143$	−12.5000	−	21.6506i	−1.04530	−	1.81052i
$144$		0			0
$145$	−3.50000	+	6.06218i	−0.290659	+	0.503436i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	11.0000	−	19.0526i	0.901155	−	1.56085i	0.0751583	−	0.997172i	$-0.476054\pi$
$149$	11.0000	−	19.0526i	0.901155	−	1.56085i	0.825997	−	0.563675i	$-0.190613\pi$
$150$		0			0
$151$	9.50000	+	16.4545i	0.773099	+	1.33905i	0.935857	+	0.352381i	$0.114628\pi$
$151$	9.50000	+	16.4545i	0.773099	+	1.33905i	−0.162758	+	0.986666i	$0.552039\pi$
$152$		0			0
$153$	−42.0000			−3.39550
$154$		0			0
$155$	4.00000			0.321288
$156$		0			0
$157$	−5.00000	−	8.66025i	−0.399043	−	0.691164i	0.594565	−	0.804048i	$-0.297324\pi$
$157$	−5.00000	−	8.66025i	−0.399043	−	0.691164i	−0.993608	+	0.112884i	$0.963991\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	7.00000	−	12.1244i	0.548282	−	0.949653i	−0.450110	−	0.892973i	$-0.648615\pi$
$163$	7.00000	−	12.1244i	0.548282	−	0.949653i	0.998392	−	0.0566798i	$-0.0180514\pi$
$164$		0			0
$165$	−7.50000	−	12.9904i	−0.583874	−	1.01130i
$166$		0			0
$167$	−3.00000			−0.232147			−0.116073	−	0.993241i	$-0.537031\pi$
$167$	−3.00000			−0.232147			−0.116073	+	0.993241i	$0.537031\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$		0			0
$171$	6.00000	+	10.3923i	0.458831	+	0.794719i
$172$		0			0
$173$	3.50000	−	6.06218i	0.266100	−	0.460899i	−0.701751	−	0.712422i	$-0.747598\pi$
$173$	3.50000	−	6.06218i	0.266100	−	0.460899i	0.967851	+	0.251523i	$0.0809315\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−6.00000	+	10.3923i	−0.450988	+	0.781133i
$178$		0			0
$179$	2.00000	+	3.46410i	0.149487	+	0.258919i	0.931038	−	0.364922i	$-0.118904\pi$
$179$	2.00000	+	3.46410i	0.149487	+	0.258919i	−0.781551	+	0.623841i	$0.785571\pi$
$180$		0			0
$181$	8.00000			0.594635			0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000			0.594635			0.297318	+	0.954779i	$0.403908\pi$
$182$		0			0
$183$	−12.0000			−0.887066
$184$		0			0
$185$	3.00000	+	5.19615i	0.220564	+	0.382029i
$186$		0			0
$187$	−17.5000	+	30.3109i	−1.27973	+	2.21655i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	6.50000	−	11.2583i	0.470323	−	0.814624i	−0.529101	−	0.848559i	$-0.677471\pi$
$191$	6.50000	−	11.2583i	0.470323	−	0.814624i	0.999424	+	0.0339349i	$0.0108039\pi$
$192$		0			0
$193$	4.00000	+	6.92820i	0.287926	+	0.498703i	0.973315	−	0.229475i	$-0.0737008\pi$
$193$	4.00000	+	6.92820i	0.287926	+	0.498703i	−0.685388	+	0.728178i	$0.740368\pi$
$194$		0			0
$195$	15.0000			1.07417
$196$		0			0
$197$	−8.00000			−0.569976			−0.284988	−	0.958531i	$-0.591990\pi$
$197$	−8.00000			−0.569976			−0.284988	+	0.958531i	$0.591990\pi$
$198$		0			0
$199$	2.00000	+	3.46410i	0.141776	+	0.245564i	0.928166	−	0.372168i	$-0.121385\pi$
$199$	2.00000	+	3.46410i	0.141776	+	0.245564i	−0.786389	+	0.617731i	$0.788052\pi$
$200$		0			0
$201$	12.0000	−	20.7846i	0.846415	−	1.46603i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	6.00000	−	10.3923i	0.419058	−	0.725830i
$206$		0			0
$207$	6.00000	+	10.3923i	0.417029	+	0.722315i
$208$		0			0
$209$	10.0000			0.691714
$210$		0			0
$211$	5.00000			0.344214			0.172107	−	0.985078i	$-0.444942\pi$
$211$	5.00000			0.344214			0.172107	+	0.985078i	$0.444942\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.00000	−	1.73205i	0.0681994	−	0.118125i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	9.00000	−	15.5885i	0.608164	−	1.05337i
$220$		0			0
$221$	−17.5000	−	30.3109i	−1.17718	−	2.03893i
$222$		0			0
$223$	−19.0000			−1.27233			−0.636167	−	0.771551i	$-0.719481\pi$
$223$	−19.0000			−1.27233			−0.636167	+	0.771551i	$0.719481\pi$
$224$		0			0
$225$	6.00000			0.400000
$226$		0			0
$227$	−4.50000	−	7.79423i	−0.298675	−	0.517321i	0.677158	−	0.735838i	$-0.263211\pi$
$227$	−4.50000	−	7.79423i	−0.298675	−	0.517321i	−0.975833	+	0.218517i	$0.929878\pi$
$228$		0			0
$229$	−2.00000	+	3.46410i	−0.132164	+	0.228914i	−0.924510	−	0.381157i	$-0.875526\pi$
$229$	−2.00000	+	3.46410i	−0.132164	+	0.228914i	0.792347	+	0.610071i	$0.208859\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	12.0000	−	20.7846i	0.786146	−	1.36165i	−0.142166	−	0.989843i	$-0.545407\pi$
$233$	12.0000	−	20.7846i	0.786146	−	1.36165i	0.928312	−	0.371802i	$-0.121260\pi$
$234$		0			0
$235$	−0.500000	−	0.866025i	−0.0326164	−	0.0564933i
$236$		0			0
$237$	9.00000			0.584613
$238$		0			0
$239$	9.00000			0.582162			0.291081	−	0.956698i	$-0.405985\pi$
$239$	9.00000			0.582162			0.291081	+	0.956698i	$0.405985\pi$
$240$		0			0
$241$	11.0000	+	19.0526i	0.708572	+	1.22728i	0.965387	+	0.260822i	$0.0839937\pi$
$241$	11.0000	+	19.0526i	0.708572	+	1.22728i	−0.256814	+	0.966461i	$0.582673\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−5.00000	+	8.66025i	−0.318142	+	0.551039i
$248$		0			0
$249$	−6.00000	−	10.3923i	−0.380235	−	0.658586i
$250$		0			0
$251$	6.00000			0.378717			0.189358	−	0.981908i	$-0.439359\pi$
$251$	6.00000			0.378717			0.189358	+	0.981908i	$0.439359\pi$
$252$		0			0
$253$	10.0000			0.628695
$254$		0			0
$255$	−10.5000	−	18.1865i	−0.657536	−	1.13888i
$256$		0			0
$257$	−9.00000	+	15.5885i	−0.561405	+	0.972381i	0.435970	+	0.899961i	$0.356405\pi$
$257$	−9.00000	+	15.5885i	−0.561405	+	0.972381i	−0.997374	+	0.0724199i	$0.976928\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−21.0000	+	36.3731i	−1.29987	+	2.25144i
$262$		0			0
$263$	15.0000	+	25.9808i	0.924940	+	1.60204i	0.791658	+	0.610964i	$0.209218\pi$
$263$	15.0000	+	25.9808i	0.924940	+	1.60204i	0.133281	+	0.991078i	$0.457449\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−13.0000	−	22.5167i	−0.792624	−	1.37287i	−0.924337	−	0.381577i	$-0.875381\pi$
$269$	−13.0000	−	22.5167i	−0.792624	−	1.37287i	0.131713	−	0.991288i	$-0.457952\pi$
$270$		0			0
$271$	−6.00000	+	10.3923i	−0.364474	+	0.631288i	−0.988692	−	0.149963i	$-0.952085\pi$
$271$	−6.00000	+	10.3923i	−0.364474	+	0.631288i	0.624218	+	0.781251i	$0.285418\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.50000	−	4.33013i	0.150756	−	0.261116i
$276$		0			0
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	0.834419	−	0.551131i	$-0.185804\pi$
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	−0.894503	+	0.447062i	$0.852470\pi$
$278$		0			0
$279$	24.0000			1.43684
$280$		0			0
$281$	19.0000			1.13344			0.566722	−	0.823909i	$-0.308211\pi$
$281$	19.0000			1.13344			0.566722	+	0.823909i	$0.308211\pi$
$282$		0			0
$283$	12.5000	+	21.6506i	0.743048	+	1.28700i	0.951101	+	0.308879i	$0.0999539\pi$
$283$	12.5000	+	21.6506i	0.743048	+	1.28700i	−0.208053	+	0.978117i	$0.566713\pi$
$284$		0			0
$285$	−3.00000	+	5.19615i	−0.177705	+	0.307794i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−16.0000	+	27.7128i	−0.941176	+	1.63017i
$290$		0			0
$291$	19.5000	+	33.7750i	1.14311	+	1.97993i
$292$		0			0
$293$	13.0000			0.759468			0.379734	−	0.925096i	$-0.376015\pi$
$293$	13.0000			0.759468			0.379734	+	0.925096i	$0.376015\pi$
$294$		0			0
$295$	−4.00000			−0.232889
$296$		0			0
$297$	−22.5000	−	38.9711i	−1.30558	−	2.26134i
$298$		0			0
$299$	−5.00000	+	8.66025i	−0.289157	+	0.500835i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−27.0000	+	46.7654i	−1.55111	+	2.68660i
$304$		0			0
$305$	−2.00000	−	3.46410i	−0.114520	−	0.198354i
$306$		0			0
$307$	−17.0000			−0.970241			−0.485121	−	0.874447i	$-0.661224\pi$
$307$	−17.0000			−0.970241			−0.485121	+	0.874447i	$0.661224\pi$
$308$		0			0
$309$	−39.0000			−2.21863
$310$		0			0
$311$	17.0000	+	29.4449i	0.963982	+	1.66967i	0.712327	+	0.701848i	$0.247641\pi$
$311$	17.0000	+	29.4449i	0.963982	+	1.66967i	0.251655	+	0.967817i	$0.419025\pi$
$312$		0			0
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	−0.851549	−	0.524276i	$-0.824336\pi$
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	0.879810	+	0.475325i	$0.157669\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	−0.937892	−	0.346929i	$-0.887225\pi$
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	0.769395	+	0.638774i	$0.220558\pi$
$318$		0			0
$319$	17.5000	+	30.3109i	0.979812	+	1.69708i
$320$		0			0
$321$	−54.0000			−3.01399
$322$		0			0
$323$	14.0000			0.778981
$324$		0			0
$325$	2.50000	+	4.33013i	0.138675	+	0.240192i
$326$		0			0
$327$	7.50000	−	12.9904i	0.414751	−	0.718370i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	6.00000	−	10.3923i	0.329790	−	0.571213i	−0.652680	−	0.757634i	$-0.726355\pi$
$331$	6.00000	−	10.3923i	0.329790	−	0.571213i	0.982470	+	0.186421i	$0.0596888\pi$
$332$		0			0
$333$	18.0000	+	31.1769i	0.986394	+	1.70848i
$334$		0			0
$335$	8.00000			0.437087
$336$		0			0
$337$	34.0000			1.85210			0.926049	−	0.377403i	$-0.123183\pi$
$337$	34.0000			1.85210			0.926049	+	0.377403i	$0.123183\pi$
$338$		0			0
$339$	9.00000	+	15.5885i	0.488813	+	0.846649i
$340$		0			0
$341$	10.0000	−	17.3205i	0.541530	−	0.937958i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−3.00000	+	5.19615i	−0.161515	+	0.279751i
$346$		0			0
$347$	−13.0000	−	22.5167i	−0.697877	−	1.20876i	−0.969201	−	0.246270i	$-0.920795\pi$
$347$	−13.0000	−	22.5167i	−0.697877	−	1.20876i	0.271325	−	0.962488i	$-0.412538\pi$
$348$		0			0
$349$	18.0000			0.963518			0.481759	−	0.876304i	$-0.339998\pi$
$349$	18.0000			0.963518			0.481759	+	0.876304i	$0.339998\pi$
$350$		0			0
$351$	45.0000			2.40192
$352$		0			0
$353$	−2.50000	−	4.33013i	−0.133062	−	0.230469i	0.791794	−	0.610789i	$-0.209147\pi$
$353$	−2.50000	−	4.33013i	−0.133062	−	0.230469i	−0.924855	+	0.380319i	$0.875814\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$359$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$		0			0
$363$	−42.0000			−2.20443
$364$		0			0
$365$	6.00000			0.314054
$366$		0			0
$367$	3.50000	+	6.06218i	0.182699	+	0.316443i	0.942799	−	0.333363i	$-0.108183\pi$
$367$	3.50000	+	6.06218i	0.182699	+	0.316443i	−0.760100	+	0.649806i	$0.774850\pi$
$368$		0			0
$369$	36.0000	−	62.3538i	1.87409	−	3.24601i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−8.00000	+	13.8564i	−0.414224	+	0.717458i	−0.995347	−	0.0963587i	$-0.969280\pi$
$373$	−8.00000	+	13.8564i	−0.414224	+	0.717458i	0.581122	+	0.813816i	$0.302614\pi$
$374$		0			0
$375$	1.50000	+	2.59808i	0.0774597	+	0.134164i
$376$		0			0
$377$	−35.0000			−1.80259
$378$		0			0
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$		0			0
$381$	−18.0000	−	31.1769i	−0.922168	−	1.59724i
$382$		0			0
$383$	−6.00000	+	10.3923i	−0.306586	+	0.531022i	−0.977613	−	0.210411i	$-0.932520\pi$
$383$	−6.00000	+	10.3923i	−0.306586	+	0.531022i	0.671027	+	0.741433i	$0.265853\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	6.00000	−	10.3923i	0.304997	−	0.528271i
$388$		0			0
$389$	7.50000	+	12.9904i	0.380265	+	0.658638i	0.991100	−	0.133120i	$-0.0424994\pi$
$389$	7.50000	+	12.9904i	0.380265	+	0.658638i	−0.610835	+	0.791758i	$0.709166\pi$
$390$		0			0
$391$	14.0000			0.708010
$392$		0			0
$393$	18.0000			0.907980
$394$		0			0
$395$	1.50000	+	2.59808i	0.0754732	+	0.130723i
$396$		0			0
$397$	11.5000	−	19.9186i	0.577168	−	0.999685i	−0.418634	−	0.908155i	$-0.637491\pi$
$397$	11.5000	−	19.9186i	0.577168	−	0.999685i	0.995802	−	0.0915300i	$-0.0291757\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	7.50000	−	12.9904i	0.374532	−	0.648709i	−0.615725	−	0.787961i	$-0.711137\pi$
$401$	7.50000	−	12.9904i	0.374532	−	0.648709i	0.990257	+	0.139253i	$0.0444700\pi$
$402$		0			0
$403$	10.0000	+	17.3205i	0.498135	+	0.862796i
$404$		0			0
$405$	9.00000			0.447214
$406$		0			0
$407$	30.0000			1.48704
$408$		0			0
$409$	7.00000	+	12.1244i	0.346128	+	0.599511i	0.985558	−	0.169338i	$-0.0541630\pi$
$409$	7.00000	+	12.1244i	0.346128	+	0.599511i	−0.639430	+	0.768849i	$0.720830\pi$
$410$		0			0
$411$	−12.0000	+	20.7846i	−0.591916	+	1.02523i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	2.00000	−	3.46410i	0.0981761	−	0.170046i
$416$		0			0
$417$	27.0000	+	46.7654i	1.32220	+	2.29011i
$418$		0			0
$419$	−24.0000			−1.17248			−0.586238	−	0.810139i	$-0.699392\pi$
$419$	−24.0000			−1.17248			−0.586238	+	0.810139i	$0.699392\pi$
$420$		0			0
$421$	−3.00000			−0.146211			−0.0731055	−	0.997324i	$-0.523291\pi$
$421$	−3.00000			−0.146211			−0.0731055	+	0.997324i	$0.523291\pi$
$422$		0			0
$423$	−3.00000	−	5.19615i	−0.145865	−	0.252646i
$424$		0			0
$425$	3.50000	−	6.06218i	0.169775	−	0.294059i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	37.5000	−	64.9519i	1.81052	−	3.13591i
$430$		0			0
$431$	12.5000	+	21.6506i	0.602104	+	1.04287i	0.992502	+	0.122228i	$0.0390040\pi$
$431$	12.5000	+	21.6506i	0.602104	+	1.04287i	−0.390398	+	0.920646i	$0.627663\pi$
$432$		0			0
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$		0			0
$435$	−21.0000			−1.00687
$436$		0			0
$437$	−2.00000	−	3.46410i	−0.0956730	−	0.165710i
$438$		0			0
$439$	13.0000	−	22.5167i	0.620456	−	1.07466i	−0.368945	−	0.929451i	$-0.620281\pi$
$439$	13.0000	−	22.5167i	0.620456	−	1.07466i	0.989401	−	0.145210i	$-0.0463858\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−3.00000	+	5.19615i	−0.142534	+	0.246877i	−0.928450	−	0.371457i	$-0.878858\pi$
$443$	−3.00000	+	5.19615i	−0.142534	+	0.246877i	0.785916	+	0.618333i	$0.212192\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	66.0000			3.12169
$448$		0			0
$449$	−9.00000			−0.424736			−0.212368	−	0.977190i	$-0.568118\pi$
$449$	−9.00000			−0.424736			−0.212368	+	0.977190i	$0.568118\pi$
$450$		0			0
$451$	−30.0000	−	51.9615i	−1.41264	−	2.44677i
$452$		0			0
$453$	−28.5000	+	49.3634i	−1.33905	+	2.31930i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	4.00000	−	6.92820i	0.187112	−	0.324088i	−0.757174	−	0.653213i	$-0.773421\pi$
$457$	4.00000	−	6.92820i	0.187112	−	0.324088i	0.944286	+	0.329125i	$0.106754\pi$
$458$		0			0
$459$	−31.5000	−	54.5596i	−1.47029	−	2.54662i
$460$		0			0
$461$		0			0			−	1.00000i	$-0.5\pi$
$461$		0			0				1.00000i	$0.5\pi$
$462$		0			0
$463$	−36.0000			−1.67306			−0.836531	−	0.547920i	$-0.815420\pi$
$463$	−36.0000			−1.67306			−0.836531	+	0.547920i	$0.815420\pi$
$464$		0			0
$465$	6.00000	+	10.3923i	0.278243	+	0.481932i
$466$		0			0
$467$	−5.50000	+	9.52628i	−0.254510	+	0.440824i	−0.964762	−	0.263123i	$-0.915247\pi$
$467$	−5.50000	+	9.52628i	−0.254510	+	0.440824i	0.710253	+	0.703947i	$0.248581\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	15.0000	−	25.9808i	0.691164	−	1.19713i
$472$		0			0
$473$	−5.00000	−	8.66025i	−0.229900	−	0.398199i
$474$		0			0
$475$	−2.00000			−0.0917663
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−17.0000	−	29.4449i	−0.776750	−	1.34537i	−0.933806	−	0.357780i	$-0.883534\pi$
$479$	−17.0000	−	29.4449i	−0.776750	−	1.34537i	0.157056	−	0.987590i	$-0.449800\pi$
$480$		0			0
$481$	−15.0000	+	25.9808i	−0.683941	+	1.18462i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−6.50000	+	11.2583i	−0.295150	+	0.511214i
$486$		0			0
$487$	−11.0000	−	19.0526i	−0.498458	−	0.863354i	0.501541	−	0.865134i	$-0.332767\pi$
$487$	−11.0000	−	19.0526i	−0.498458	−	0.863354i	−0.999998	+	0.00178012i	$0.999433\pi$
$488$		0			0
$489$	42.0000			1.89931
$490$		0			0
$491$	9.00000			0.406164			0.203082	−	0.979162i	$-0.434904\pi$
$491$	9.00000			0.406164			0.203082	+	0.979162i	$0.434904\pi$
$492$		0			0
$493$	24.5000	+	42.4352i	1.10342	+	1.91119i
$494$		0			0
$495$	15.0000	−	25.9808i	0.674200	−	1.16775i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	0.500000	−	0.866025i	0.0223831	−	0.0387686i	−0.854617	−	0.519259i	$-0.826208\pi$
$499$	0.500000	−	0.866025i	0.0223831	−	0.0387686i	0.877000	+	0.480490i	$0.159541\pi$
$500$		0			0
$501$	−4.50000	−	7.79423i	−0.201045	−	0.348220i
$502$		0			0
$503$	3.00000			0.133763			0.0668817	−	0.997761i	$-0.478695\pi$
$503$	3.00000			0.133763			0.0668817	+	0.997761i	$0.478695\pi$
$504$		0			0
$505$	−18.0000			−0.800989
$506$		0			0
$507$	18.0000	+	31.1769i	0.799408	+	1.38462i
$508$		0			0
$509$	7.00000	−	12.1244i	0.310270	−	0.537403i	−0.668151	−	0.744026i	$-0.732914\pi$
$509$	7.00000	−	12.1244i	0.310270	−	0.537403i	0.978421	+	0.206623i	$0.0662474\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−9.00000	+	15.5885i	−0.397360	+	0.688247i
$514$		0			0
$515$	−6.50000	−	11.2583i	−0.286424	−	0.496101i
$516$		0			0
$517$	−5.00000			−0.219900
$518$		0			0
$519$	21.0000			0.921798
$520$		0			0
$521$	−11.0000	−	19.0526i	−0.481919	−	0.834708i	0.517866	−	0.855462i	$-0.326727\pi$
$521$	−11.0000	−	19.0526i	−0.481919	−	0.834708i	−0.999785	+	0.0207541i	$0.993393\pi$
$522$		0			0
$523$	22.0000	−	38.1051i	0.961993	−	1.66622i	0.244507	−	0.969648i	$-0.421374\pi$
$523$	22.0000	−	38.1051i	0.961993	−	1.66622i	0.717486	−	0.696573i	$-0.245293\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	14.0000	−	24.2487i	0.609850	−	1.05629i
$528$		0			0
$529$	9.50000	+	16.4545i	0.413043	+	0.715412i
$530$		0			0
$531$	−24.0000			−1.04151
$532$		0			0
$533$	60.0000			2.59889
$534$		0			0
$535$	−9.00000	−	15.5885i	−0.389104	−	0.673948i
$536$		0			0
$537$	−6.00000	+	10.3923i	−0.258919	+	0.448461i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−3.50000	+	6.06218i	−0.150477	+	0.260633i	−0.931403	−	0.363990i	$-0.881414\pi$
$541$	−3.50000	+	6.06218i	−0.150477	+	0.260633i	0.780926	+	0.624623i	$0.214748\pi$
$542$		0			0
$543$	12.0000	+	20.7846i	0.514969	+	0.891953i
$544$		0			0
$545$	5.00000			0.214176
$546$		0			0
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$		0			0
$549$	−12.0000	−	20.7846i	−0.512148	−	0.887066i
$550$		0			0
$551$	7.00000	−	12.1244i	0.298210	−	0.516515i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−9.00000	+	15.5885i	−0.382029	+	0.661693i
$556$		0			0
$557$	8.00000	+	13.8564i	0.338971	+	0.587115i	0.984239	−	0.176841i	$-0.0565879\pi$
$557$	8.00000	+	13.8564i	0.338971	+	0.587115i	−0.645269	+	0.763956i	$0.723255\pi$
$558$		0			0
$559$	10.0000			0.422955
$560$		0			0
$561$	−105.000			−4.43310
$562$		0			0
$563$	−2.00000	−	3.46410i	−0.0842900	−	0.145994i	0.820798	−	0.571218i	$-0.193529\pi$
$563$	−2.00000	−	3.46410i	−0.0842900	−	0.145994i	−0.905088	+	0.425223i	$0.860196\pi$
$564$		0			0
$565$	−3.00000	+	5.19615i	−0.126211	+	0.218604i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	11.0000	−	19.0526i	0.461144	−	0.798725i	−0.537874	−	0.843025i	$-0.680772\pi$
$569$	11.0000	−	19.0526i	0.461144	−	0.798725i	0.999018	+	0.0443003i	$0.0141058\pi$
$570$		0			0
$571$	−2.00000	−	3.46410i	−0.0836974	−	0.144968i	0.821138	−	0.570730i	$-0.193340\pi$
$571$	−2.00000	−	3.46410i	−0.0836974	−	0.144968i	−0.904835	+	0.425762i	$0.860006\pi$
$572$		0			0
$573$	39.0000			1.62925
$574$		0			0
$575$	−2.00000			−0.0834058
$576$		0			0
$577$	18.5000	+	32.0429i	0.770165	+	1.33397i	0.937472	+	0.348060i	$0.113160\pi$
$577$	18.5000	+	32.0429i	0.770165	+	1.33397i	−0.167307	+	0.985905i	$0.553507\pi$
$578$		0			0
$579$	−12.0000	+	20.7846i	−0.498703	+	0.863779i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	15.0000	+	25.9808i	0.620174	+	1.07417i
$586$		0			0
$587$		0			0			−	1.00000i	$-0.5\pi$
$587$		0			0				1.00000i	$0.5\pi$
$588$		0			0
$589$	−8.00000			−0.329634
$590$		0			0
$591$	−12.0000	−	20.7846i	−0.493614	−	0.854965i
$592$		0			0
$593$	−13.5000	+	23.3827i	−0.554379	+	0.960212i	0.443573	+	0.896238i	$0.353711\pi$
$593$	−13.5000	+	23.3827i	−0.554379	+	0.960212i	−0.997952	+	0.0639736i	$0.979623\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−6.00000	+	10.3923i	−0.245564	+	0.425329i
$598$		0			0
$599$	−7.50000	−	12.9904i	−0.306442	−	0.530773i	0.671140	−	0.741331i	$-0.265805\pi$
$599$	−7.50000	−	12.9904i	−0.306442	−	0.530773i	−0.977581	+	0.210558i	$0.932472\pi$
$600$		0			0
$601$	10.0000			0.407909			0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000			0.407909			0.203954	+	0.978980i	$0.434621\pi$
$602$		0			0
$603$	48.0000			1.95471
$604$		0			0
$605$	−7.00000	−	12.1244i	−0.284590	−	0.492925i
$606$		0			0
$607$	−1.50000	+	2.59808i	−0.0608831	+	0.105453i	−0.894860	−	0.446346i	$-0.852725\pi$
$607$	−1.50000	+	2.59808i	−0.0608831	+	0.105453i	0.833977	+	0.551799i	$0.186058\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	2.50000	−	4.33013i	0.101139	−	0.175178i
$612$		0			0
$613$	15.0000	+	25.9808i	0.605844	+	1.04935i	0.991917	+	0.126885i	$0.0404979\pi$
$613$	15.0000	+	25.9808i	0.605844	+	1.04935i	−0.386073	+	0.922468i	$0.626169\pi$
$614$		0			0
$615$	36.0000			1.45166
$616$		0			0
$617$	6.00000			0.241551			0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000			0.241551			0.120775	+	0.992680i	$0.461462\pi$
$618$		0			0
$619$	−13.0000	−	22.5167i	−0.522514	−	0.905021i	−0.999657	−	0.0261952i	$-0.991661\pi$
$619$	−13.0000	−	22.5167i	−0.522514	−	0.905021i	0.477143	−	0.878826i	$-0.341672\pi$
$620$		0			0
$621$	−9.00000	+	15.5885i	−0.361158	+	0.625543i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	15.0000	+	25.9808i	0.599042	+	1.03757i
$628$		0			0
$629$	42.0000			1.67465
$630$		0			0
$631$	7.00000			0.278666			0.139333	−	0.990246i	$-0.455504\pi$
$631$	7.00000			0.278666			0.139333	+	0.990246i	$0.455504\pi$
$632$		0			0
$633$	7.50000	+	12.9904i	0.298098	+	0.516321i
$634$		0			0
$635$	6.00000	−	10.3923i	0.238103	−	0.412406i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−9.00000	−	15.5885i	−0.355479	−	0.615707i	0.631721	−	0.775196i	$-0.282349\pi$
$641$	−9.00000	−	15.5885i	−0.355479	−	0.615707i	−0.987200	+	0.159489i	$0.949015\pi$
$642$		0			0
$643$	21.0000			0.828159			0.414080	−	0.910241i	$-0.364104\pi$
$643$	21.0000			0.828159			0.414080	+	0.910241i	$0.364104\pi$
$644$		0			0
$645$	6.00000			0.236250
$646$		0			0
$647$	−12.0000	−	20.7846i	−0.471769	−	0.817127i	0.527710	−	0.849425i	$-0.323051\pi$
$647$	−12.0000	−	20.7846i	−0.471769	−	0.817127i	−0.999478	+	0.0322975i	$0.989718\pi$
$648$		0			0
$649$	−10.0000	+	17.3205i	−0.392534	+	0.679889i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−19.0000	+	32.9090i	−0.743527	+	1.28783i	0.207352	+	0.978266i	$0.433515\pi$
$653$	−19.0000	+	32.9090i	−0.743527	+	1.28783i	−0.950880	+	0.309561i	$0.899818\pi$
$654$		0			0
$655$	3.00000	+	5.19615i	0.117220	+	0.203030i
$656$		0			0
$657$	36.0000			1.40449
$658$		0			0
$659$	15.0000			0.584317			0.292159	−	0.956370i	$-0.405627\pi$
$659$	15.0000			0.584317			0.292159	+	0.956370i	$0.405627\pi$
$660$		0			0
$661$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$661$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$662$		0			0
$663$	52.5000	−	90.9327i	2.03893	−	3.53153i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	7.00000	−	12.1244i	0.271041	−	0.469457i
$668$		0			0
$669$	−28.5000	−	49.3634i	−1.10187	−	1.90850i
$670$		0			0
$671$	−20.0000			−0.772091
$672$		0			0
$673$		0			0			−	1.00000i	$-0.5\pi$
$673$		0			0				1.00000i	$0.5\pi$
$674$		0			0
$675$	4.50000	+	7.79423i	0.173205	+	0.300000i
$676$		0			0
$677$	14.5000	−	25.1147i	0.557280	−	0.965238i	−0.440442	−	0.897781i	$-0.645178\pi$
$677$	14.5000	−	25.1147i	0.557280	−	0.965238i	0.997722	−	0.0674566i	$-0.0214884\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	13.5000	−	23.3827i	0.517321	−	0.896026i
$682$		0			0
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	0.728101	−	0.685470i	$-0.240403\pi$
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	−0.957685	+	0.287819i	$0.907070\pi$
$684$		0			0
$685$	−8.00000			−0.305664
$686$		0			0
$687$	−12.0000			−0.457829
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−22.0000	+	38.1051i	−0.836919	+	1.44959i	0.0555386	+	0.998457i	$0.482312\pi$
$691$	−22.0000	+	38.1051i	−0.836919	+	1.44959i	−0.892458	+	0.451130i	$0.851021\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−9.00000	+	15.5885i	−0.341389	+	0.591304i
$696$		0			0
$697$	−42.0000	−	72.7461i	−1.59086	−	2.75546i
$698$		0			0
$699$	72.0000			2.72329
$700$		0			0
$701$	35.0000			1.32193			0.660966	−	0.750416i	$-0.270147\pi$
$701$	35.0000			1.32193			0.660966	+	0.750416i	$0.270147\pi$
$702$		0			0
$703$	−6.00000	−	10.3923i	−0.226294	−	0.391953i
$704$		0			0
$705$	1.50000	−	2.59808i	0.0564933	−	0.0978492i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	12.5000	−	21.6506i	0.469447	−	0.813107i	−0.529943	−	0.848034i	$-0.677787\pi$
$709$	12.5000	−	21.6506i	0.469447	−	0.813107i	0.999390	+	0.0349269i	$0.0111198\pi$
$710$		0			0
$711$	9.00000	+	15.5885i	0.337526	+	0.584613i
$712$		0			0
$713$	−8.00000			−0.299602
$714$		0			0
$715$	25.0000			0.934947
$716$		0			0
$717$	13.5000	+	23.3827i	0.504167	+	0.873242i
$718$		0			0
$719$	7.00000	−	12.1244i	0.261056	−	0.452162i	−0.705467	−	0.708743i	$-0.749263\pi$
$719$	7.00000	−	12.1244i	0.261056	−	0.452162i	0.966523	+	0.256581i	$0.0825960\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−33.0000	+	57.1577i	−1.22728	+	2.12572i
$724$		0			0
$725$	−3.50000	−	6.06218i	−0.129987	−	0.225144i
$726$		0			0
$727$	−40.0000			−1.48352			−0.741759	−	0.670667i	$-0.766008\pi$
$727$	−40.0000			−1.48352			−0.741759	+	0.670667i	$0.766008\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−7.00000	−	12.1244i	−0.258904	−	0.448435i
$732$		0			0
$733$	16.5000	−	28.5788i	0.609441	−	1.05558i	−0.381891	−	0.924207i	$-0.624727\pi$
$733$	16.5000	−	28.5788i	0.609441	−	1.05558i	0.991333	−	0.131376i	$-0.0419396\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	20.0000	−	34.6410i	0.736709	−	1.27602i
$738$		0			0
$739$	−25.5000	−	44.1673i	−0.938033	−	1.62472i	−0.769135	−	0.639087i	$-0.779313\pi$
$739$	−25.5000	−	44.1673i	−0.938033	−	1.62472i	−0.168898	−	0.985634i	$-0.554021\pi$
$740$		0			0
$741$	−30.0000			−1.10208
$742$		0			0
$743$	24.0000			0.880475			0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000			0.880475			0.440237	+	0.897881i	$0.354894\pi$
$744$		0			0
$745$	11.0000	+	19.0526i	0.403009	+	0.698032i
$746$		0			0
$747$	12.0000	−	20.7846i	0.439057	−	0.760469i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	1.50000	−	2.59808i	0.0547358	−	0.0948051i	−0.837359	−	0.546653i	$-0.815902\pi$
$751$	1.50000	−	2.59808i	0.0547358	−	0.0948051i	0.892095	+	0.451848i	$0.149235\pi$
$752$		0			0
$753$	9.00000	+	15.5885i	0.327978	+	0.568075i
$754$		0			0
$755$	−19.0000			−0.691481
$756$		0			0
$757$	−40.0000			−1.45382			−0.726912	−	0.686730i	$-0.759045\pi$
$757$	−40.0000			−1.45382			−0.726912	+	0.686730i	$0.759045\pi$
$758$		0			0
$759$	15.0000	+	25.9808i	0.544466	+	0.943042i
$760$		0			0
$761$	−9.00000	+	15.5885i	−0.326250	+	0.565081i	−0.981764	−	0.190101i	$-0.939118\pi$
$761$	−9.00000	+	15.5885i	−0.326250	+	0.565081i	0.655515	+	0.755182i	$0.272452\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	21.0000	−	36.3731i	0.759257	−	1.31507i
$766$		0			0
$767$	−10.0000	−	17.3205i	−0.361079	−	0.625407i
$768$		0			0
$769$	34.0000			1.22607			0.613036	−	0.790055i	$-0.289948\pi$
$769$	34.0000			1.22607			0.613036	+	0.790055i	$0.289948\pi$
$770$		0			0
$771$	−54.0000			−1.94476
$772$		0			0
$773$	10.5000	+	18.1865i	0.377659	+	0.654124i	0.990721	−	0.135910i	$-0.0433959\pi$
$773$	10.5000	+	18.1865i	0.377659	+	0.654124i	−0.613062	+	0.790034i	$0.710063\pi$
$774$		0			0
$775$	−2.00000	+	3.46410i	−0.0718421	+	0.124434i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−12.0000	+	20.7846i	−0.429945	+	0.744686i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−63.0000			−2.25144
$784$		0			0
$785$	10.0000			0.356915
$786$		0			0
$787$	−8.50000	−	14.7224i	−0.302992	−	0.524798i	0.673820	−	0.738896i	$-0.264652\pi$
$787$	−8.50000	−	14.7224i	−0.302992	−	0.524798i	−0.976812	+	0.214097i	$0.931319\pi$
$788$		0			0
$789$	−45.0000	+	77.9423i	−1.60204	+	2.77482i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	10.0000	−	17.3205i	0.355110	−	0.615069i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−39.0000			−1.38145			−0.690725	−	0.723117i	$-0.742709\pi$
$797$	−39.0000			−1.38145			−0.690725	+	0.723117i	$0.742709\pi$
$798$		0			0
$799$	−7.00000			−0.247642
$800$		0			0
$801$		0			0
$802$		0			0
$803$	15.0000	−	25.9808i	0.529339	−	0.916841i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	39.0000	−	67.5500i	1.37287	−	2.37787i
$808$		0			0
$809$	19.5000	+	33.7750i	0.685583	+	1.18747i	0.973253	+	0.229736i	$0.0737862\pi$
$809$	19.5000	+	33.7750i	0.685583	+	1.18747i	−0.287670	+	0.957730i	$0.592880\pi$
$810$		0			0
$811$	−10.0000			−0.351147			−0.175574	−	0.984466i	$-0.556178\pi$
$811$	−10.0000			−0.351147			−0.175574	+	0.984466i	$0.556178\pi$
$812$		0			0
$813$	−36.0000			−1.26258
$814$		0			0
$815$	7.00000	+	12.1244i	0.245199	+	0.424698i
$816$		0			0
$817$	−2.00000	+	3.46410i	−0.0699711	+	0.121194i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.500000	+	0.866025i	−0.0174501	+	0.0302245i	−0.874619	−	0.484812i	$-0.838888\pi$
$821$	−0.500000	+	0.866025i	−0.0174501	+	0.0302245i	0.857168	+	0.515036i	$0.172221\pi$
$822$		0			0
$823$	−14.0000	−	24.2487i	−0.488009	−	0.845257i	0.511896	−	0.859048i	$-0.328943\pi$
$823$	−14.0000	−	24.2487i	−0.488009	−	0.845257i	−0.999905	+	0.0137907i	$0.995610\pi$
$824$		0			0
$825$	15.0000			0.522233
$826$		0			0
$827$	6.00000			0.208640			0.104320	−	0.994544i	$-0.466733\pi$
$827$	6.00000			0.208640			0.104320	+	0.994544i	$0.466733\pi$
$828$		0			0
$829$	10.0000	+	17.3205i	0.347314	+	0.601566i	0.985771	−	0.168091i	$-0.0537604\pi$
$829$	10.0000	+	17.3205i	0.347314	+	0.601566i	−0.638457	+	0.769657i	$0.720427\pi$
$830$		0			0
$831$	3.00000	−	5.19615i	0.104069	−	0.180253i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	1.50000	−	2.59808i	0.0519096	−	0.0899101i
$836$		0			0
$837$	18.0000	+	31.1769i	0.622171	+	1.07763i
$838$		0			0
$839$	−34.0000			−1.17381			−0.586905	−	0.809656i	$-0.699654\pi$
$839$	−34.0000			−1.17381			−0.586905	+	0.809656i	$0.699654\pi$
$840$		0			0
$841$	20.0000			0.689655
$842$		0			0
$843$	28.5000	+	49.3634i	0.981592	+	1.70017i
$844$		0			0
$845$	−6.00000	+	10.3923i	−0.206406	+	0.357506i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−37.5000	+	64.9519i	−1.28700	+	2.22914i
$850$		0			0
$851$	−6.00000	−	10.3923i	−0.205677	−	0.356244i
$852$		0			0
$853$	−22.0000			−0.753266			−0.376633	−	0.926363i	$-0.622918\pi$
$853$	−22.0000			−0.753266			−0.376633	+	0.926363i	$0.622918\pi$
$854$		0			0
$855$	−12.0000			−0.410391
$856$		0			0
$857$	−3.00000	−	5.19615i	−0.102478	−	0.177497i	0.810227	−	0.586116i	$-0.199344\pi$
$857$	−3.00000	−	5.19615i	−0.102478	−	0.177497i	−0.912705	+	0.408619i	$0.866010\pi$
$858$		0			0
$859$	2.00000	−	3.46410i	0.0682391	−	0.118194i	−0.829887	−	0.557931i	$-0.811595\pi$
$859$	2.00000	−	3.46410i	0.0682391	−	0.118194i	0.898126	+	0.439738i	$0.144929\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−24.0000	+	41.5692i	−0.816970	+	1.41503i	0.0909355	+	0.995857i	$0.471014\pi$
$863$	−24.0000	+	41.5692i	−0.816970	+	1.41503i	−0.907905	+	0.419176i	$0.862319\pi$
$864$		0			0
$865$	3.50000	+	6.06218i	0.119004	+	0.206120i
$866$		0			0
$867$	−96.0000			−3.26033
$868$		0			0
$869$	15.0000			0.508840
$870$		0			0
$871$	20.0000	+	34.6410i	0.677674	+	1.17377i
$872$		0			0
$873$	−39.0000	+	67.5500i	−1.31995	+	2.28622i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−11.0000	+	19.0526i	−0.371444	+	0.643359i	−0.989788	−	0.142548i	$-0.954470\pi$
$877$	−11.0000	+	19.0526i	−0.371444	+	0.643359i	0.618344	+	0.785907i	$0.287804\pi$
$878$		0			0
$879$	19.5000	+	33.7750i	0.657719	+	1.13920i
$880$		0			0
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$		0			0
$883$	−40.0000			−1.34611			−0.673054	−	0.739594i	$-0.735018\pi$
$883$	−40.0000			−1.34611			−0.673054	+	0.739594i	$0.735018\pi$
$884$		0			0
$885$	−6.00000	−	10.3923i	−0.201688	−	0.349334i
$886$		0			0
$887$	−8.00000	+	13.8564i	−0.268614	+	0.465253i	−0.968504	−	0.248998i	$-0.919899\pi$
$887$	−8.00000	+	13.8564i	−0.268614	+	0.465253i	0.699890	+	0.714250i	$0.253232\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	22.5000	−	38.9711i	0.753778	−	1.30558i
$892$		0			0
$893$	1.00000	+	1.73205i	0.0334637	+	0.0579609i
$894$		0			0
$895$	−4.00000			−0.133705
$896$		0			0
$897$	−30.0000			−1.00167
$898$		0			0
$899$	−14.0000	−	24.2487i	−0.466926	−	0.808740i
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−4.00000	+	6.92820i	−0.132964	+	0.230301i
$906$		0			0
$907$	9.00000	+	15.5885i	0.298840	+	0.517606i	0.975871	−	0.218348i	$-0.0700669\pi$
$907$	9.00000	+	15.5885i	0.298840	+	0.517606i	−0.677031	+	0.735955i	$0.736734\pi$
$908$		0			0
$909$	−108.000			−3.58213
$910$		0			0
$911$	−8.00000			−0.265052			−0.132526	−	0.991180i	$-0.542309\pi$
$911$	−8.00000			−0.265052			−0.132526	+	0.991180i	$0.542309\pi$
$912$		0			0
$913$	−10.0000	−	17.3205i	−0.330952	−	0.573225i
$914$		0			0
$915$	6.00000	−	10.3923i	0.198354	−	0.343559i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	27.5000	−	47.6314i	0.907141	−	1.57121i	0.0891245	−	0.996020i	$-0.471593\pi$
$919$	27.5000	−	47.6314i	0.907141	−	1.57121i	0.818017	−	0.575194i	$-0.195074\pi$
$920$		0			0
$921$	−25.5000	−	44.1673i	−0.840254	−	1.45536i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−6.00000			−0.197279
$926$		0			0
$927$	−39.0000	−	67.5500i	−1.28093	−	2.21863i
$928$		0			0
$929$	16.0000	−	27.7128i	0.524943	−	0.909228i	−0.474635	−	0.880183i	$-0.657420\pi$
$929$	16.0000	−	27.7128i	0.524943	−	0.909228i	0.999578	−	0.0290452i	$-0.00924669\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−51.0000	+	88.3346i	−1.66967	+	2.89194i
$934$		0			0
$935$	−17.5000	−	30.3109i	−0.572311	−	0.991272i
$936$		0			0
$937$	13.0000			0.424691			0.212346	−	0.977195i	$-0.431890\pi$
$937$	13.0000			0.424691			0.212346	+	0.977195i	$0.431890\pi$
$938$		0			0
$939$	3.00000			0.0979013
$940$		0			0
$941$	−14.0000	−	24.2487i	−0.456387	−	0.790485i	0.542380	−	0.840133i	$-0.317523\pi$
$941$	−14.0000	−	24.2487i	−0.456387	−	0.790485i	−0.998767	+	0.0496480i	$0.984190\pi$
$942$		0			0
$943$	−12.0000	+	20.7846i	−0.390774	+	0.676840i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−20.0000	+	34.6410i	−0.649913	+	1.12568i	0.333231	+	0.942845i	$0.391861\pi$
$947$	−20.0000	+	34.6410i	−0.649913	+	1.12568i	−0.983143	+	0.182836i	$0.941472\pi$
$948$		0			0
$949$	15.0000	+	25.9808i	0.486921	+	0.843371i
$950$		0			0
$951$	−18.0000			−0.583690
$952$		0			0
$953$		0			0			−	1.00000i	$-0.5\pi$
$953$		0			0				1.00000i	$0.5\pi$
$954$		0			0
$955$	6.50000	+	11.2583i	0.210335	+	0.364311i
$956$		0			0
$957$	−52.5000	+	90.9327i	−1.69708	+	2.93944i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$		0			0
$963$	−54.0000	−	93.5307i	−1.74013	−	3.01399i
$964$		0			0
$965$	−8.00000			−0.257529
$966$		0			0
$967$	6.00000			0.192947			0.0964735	−	0.995336i	$-0.469244\pi$
$967$	6.00000			0.192947			0.0964735	+	0.995336i	$0.469244\pi$
$968$		0			0
$969$	21.0000	+	36.3731i	0.674617	+	1.16847i
$970$		0			0
$971$	8.00000	−	13.8564i	0.256732	−	0.444673i	−0.708632	−	0.705578i	$-0.750687\pi$
$971$	8.00000	−	13.8564i	0.256732	−	0.444673i	0.965365	+	0.260905i	$0.0840208\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−7.50000	+	12.9904i	−0.240192	+	0.416025i
$976$		0			0
$977$	−13.0000	−	22.5167i	−0.415907	−	0.720372i	0.579616	−	0.814890i	$-0.303202\pi$
$977$	−13.0000	−	22.5167i	−0.415907	−	0.720372i	−0.995523	+	0.0945177i	$0.969869\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	30.0000			0.957826
$982$		0			0
$983$	−1.50000	−	2.59808i	−0.0478426	−	0.0828658i	0.841112	−	0.540860i	$-0.181901\pi$
$983$	−1.50000	−	2.59808i	−0.0478426	−	0.0828658i	−0.888955	+	0.457995i	$0.848568\pi$
$984$		0			0
$985$	4.00000	−	6.92820i	0.127451	−	0.220751i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2.00000	+	3.46410i	−0.0635963	+	0.110152i
$990$		0			0
$991$	−16.0000	−	27.7128i	−0.508257	−	0.880327i	−0.999954	−	0.00956046i	$-0.996957\pi$
$991$	−16.0000	−	27.7128i	−0.508257	−	0.880327i	0.491698	−	0.870766i	$-0.336377\pi$
$992$		0			0
$993$	36.0000			1.14243
$994$		0			0
$995$	−4.00000			−0.126809
$996$		0			0
$997$	1.50000	+	2.59808i	0.0475055	+	0.0822819i	0.888800	−	0.458295i	$-0.151540\pi$
$997$	1.50000	+	2.59808i	0.0475055	+	0.0822819i	−0.841295	+	0.540576i	$0.818206\pi$
$998$		0			0
$999$	−27.0000	+	46.7654i	−0.854242	+	1.47959i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1960.2.q.o.961.1		2
7.2	even	3		280.2.a.a.1.1	✓	1
7.3	odd	6		1960.2.q.a.361.1		2
7.4	even	3	inner	1960.2.q.o.361.1		2
7.5	odd	6		1960.2.a.o.1.1		1
7.6	odd	2		1960.2.q.a.961.1		2
21.2	odd	6		2520.2.a.i.1.1		1
28.19	even	6		3920.2.a.c.1.1		1
28.23	odd	6		560.2.a.f.1.1		1
35.2	odd	12		1400.2.g.a.449.2		2
35.9	even	6		1400.2.a.n.1.1		1
35.19	odd	6		9800.2.a.a.1.1		1
35.23	odd	12		1400.2.g.a.449.1		2
56.37	even	6		2240.2.a.z.1.1		1
56.51	odd	6		2240.2.a.a.1.1		1
84.23	even	6		5040.2.a.a.1.1		1
140.23	even	12		2800.2.g.b.449.2		2
140.79	odd	6		2800.2.a.c.1.1		1
140.107	even	12		2800.2.g.b.449.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.a.a.1.1	✓	1	7.2	even	3
560.2.a.f.1.1		1	28.23	odd	6
1400.2.a.n.1.1		1	35.9	even	6
1400.2.g.a.449.1		2	35.23	odd	12
1400.2.g.a.449.2		2	35.2	odd	12
1960.2.a.o.1.1		1	7.5	odd	6
1960.2.q.a.361.1		2	7.3	odd	6
1960.2.q.a.961.1		2	7.6	odd	2
1960.2.q.o.361.1		2	7.4	even	3	inner
1960.2.q.o.961.1		2	1.1	even	1	trivial
2240.2.a.a.1.1		1	56.51	odd	6
2240.2.a.z.1.1		1	56.37	even	6
2520.2.a.i.1.1		1	21.2	odd	6
2800.2.a.c.1.1		1	140.79	odd	6
2800.2.g.b.449.1		2	140.107	even	12
2800.2.g.b.449.2		2	140.23	even	12
3920.2.a.c.1.1		1	28.19	even	6
5040.2.a.a.1.1		1	84.23	even	6
9800.2.a.a.1.1		1	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)

\(f(q)\)	\(=\)	\(q+(1.50000 + 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})\)	\(q+(1.50000 + 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-3.00000 + 5.19615i) q^{9} +(2.50000 + 4.33013i) q^{11} -5.00000 q^{13} -3.00000 q^{15} +(3.50000 + 6.06218i) q^{17} +(1.00000 - 1.73205i) q^{19} +(1.00000 - 1.73205i) q^{23} +(-0.500000 - 0.866025i) q^{25} -9.00000 q^{27} +7.00000 q^{29} +(-2.00000 - 3.46410i) q^{31} +(-7.50000 + 12.9904i) q^{33} +(3.00000 - 5.19615i) q^{37} +(-7.50000 - 12.9904i) q^{39} -12.0000 q^{41} -2.00000 q^{43} +(-3.00000 - 5.19615i) q^{45} +(-0.500000 + 0.866025i) q^{47} +(-10.5000 + 18.1865i) q^{51} -5.00000 q^{55} +6.00000 q^{57} +(2.00000 + 3.46410i) q^{59} +(-2.00000 + 3.46410i) q^{61} +(2.50000 - 4.33013i) q^{65} +(-4.00000 - 6.92820i) q^{67} +6.00000 q^{69} +(-3.00000 - 5.19615i) q^{73} +(1.50000 - 2.59808i) q^{75} +(1.50000 - 2.59808i) q^{79} +(-4.50000 - 7.79423i) q^{81} -4.00000 q^{83} -7.00000 q^{85} +(10.5000 + 18.1865i) q^{87} +(6.00000 - 10.3923i) q^{93} +(1.00000 + 1.73205i) q^{95} +13.0000 q^{97} -30.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} - q^{5} - 6 q^{9}+O(q^{10}) \) 2 * q + 3 * q^3 - q^5 - 6 * q^9	\( 2 q + 3 q^{3} - q^{5} - 6 q^{9} + 5 q^{11} - 10 q^{13} - 6 q^{15} + 7 q^{17} + 2 q^{19} + 2 q^{23} - q^{25} - 18 q^{27} + 14 q^{29} - 4 q^{31} - 15 q^{33} + 6 q^{37} - 15 q^{39} - 24 q^{41} - 4 q^{43} - 6 q^{45} - q^{47} - 21 q^{51} - 10 q^{55} + 12 q^{57} + 4 q^{59} - 4 q^{61} + 5 q^{65} - 8 q^{67} + 12 q^{69} - 6 q^{73} + 3 q^{75} + 3 q^{79} - 9 q^{81} - 8 q^{83} - 14 q^{85} + 21 q^{87} + 12 q^{93} + 2 q^{95} + 26 q^{97} - 60 q^{99}+O(q^{100}) \) 2 * q + 3 * q^3 - q^5 - 6 * q^9 + 5 * q^11 - 10 * q^13 - 6 * q^15 + 7 * q^17 + 2 * q^19 + 2 * q^23 - q^25 - 18 * q^27 + 14 * q^29 - 4 * q^31 - 15 * q^33 + 6 * q^37 - 15 * q^39 - 24 * q^41 - 4 * q^43 - 6 * q^45 - q^47 - 21 * q^51 - 10 * q^55 + 12 * q^57 + 4 * q^59 - 4 * q^61 + 5 * q^65 - 8 * q^67 + 12 * q^69 - 6 * q^73 + 3 * q^75 + 3 * q^79 - 9 * q^81 - 8 * q^83 - 14 * q^85 + 21 * q^87 + 12 * q^93 + 2 * q^95 + 26 * q^97 - 60 * q^99

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