LMFDB - Embedded newform 1960.2.q.l.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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
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.l.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(1.00000 - 1.73205i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(1.00000 - 1.73205i) q^{9} +(2.50000 + 4.33013i) q^{11} -7.00000 q^{13} -1.00000 q^{15} +(-1.50000 - 2.59808i) q^{17} +(-1.00000 + 1.73205i) q^{19} +(-4.00000 + 6.92820i) q^{23} +(-0.500000 - 0.866025i) q^{25} +5.00000 q^{27} -5.00000 q^{29} +(-5.00000 - 8.66025i) q^{31} +(-2.50000 + 4.33013i) q^{33} +(-2.00000 + 3.46410i) q^{37} +(-3.50000 - 6.06218i) q^{39} +6.00000 q^{41} +2.00000 q^{43} +(1.00000 + 1.73205i) q^{45} +(-3.50000 + 6.06218i) q^{47} +(1.50000 - 2.59808i) q^{51} +(5.00000 + 8.66025i) q^{53} -5.00000 q^{55} -2.00000 q^{57} +(-5.00000 - 8.66025i) q^{59} +(-6.00000 + 10.3923i) q^{61} +(3.50000 - 6.06218i) q^{65} +(1.00000 + 1.73205i) q^{67} -8.00000 q^{69} +(-1.00000 - 1.73205i) q^{73} +(0.500000 - 0.866025i) q^{75} +(3.50000 - 6.06218i) q^{79} +(-0.500000 - 0.866025i) q^{81} -4.00000 q^{83} +3.00000 q^{85} +(-2.50000 - 4.33013i) q^{87} +(-4.00000 + 6.92820i) q^{89} +(5.00000 - 8.66025i) q^{93} +(-1.00000 - 1.73205i) q^{95} -17.0000 q^{97} +10.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{3} - q^{5} + 2 q^{9}+O(q^{10}) $ 2 * q + q^3 - q^5 + 2 * q^9	$ 2 q + q^{3} - q^{5} + 2 q^{9} + 5 q^{11} - 14 q^{13} - 2 q^{15} - 3 q^{17} - 2 q^{19} - 8 q^{23} - q^{25} + 10 q^{27} - 10 q^{29} - 10 q^{31} - 5 q^{33} - 4 q^{37} - 7 q^{39} + 12 q^{41} + 4 q^{43} + 2 q^{45} - 7 q^{47} + 3 q^{51} + 10 q^{53} - 10 q^{55} - 4 q^{57} - 10 q^{59} - 12 q^{61} + 7 q^{65} + 2 q^{67} - 16 q^{69} - 2 q^{73} + q^{75} + 7 q^{79} - q^{81} - 8 q^{83} + 6 q^{85} - 5 q^{87} - 8 q^{89} + 10 q^{93} - 2 q^{95} - 34 q^{97} + 20 q^{99}+O(q^{100}) $ 2 * q + q^3 - q^5 + 2 * q^9 + 5 * q^11 - 14 * q^13 - 2 * q^15 - 3 * q^17 - 2 * q^19 - 8 * q^23 - q^25 + 10 * q^27 - 10 * q^29 - 10 * q^31 - 5 * q^33 - 4 * q^37 - 7 * q^39 + 12 * q^41 + 4 * q^43 + 2 * q^45 - 7 * q^47 + 3 * q^51 + 10 * q^53 - 10 * q^55 - 4 * q^57 - 10 * q^59 - 12 * q^61 + 7 * q^65 + 2 * q^67 - 16 * q^69 - 2 * q^73 + q^75 + 7 * q^79 - q^81 - 8 * q^83 + 6 * q^85 - 5 * q^87 - 8 * q^89 + 10 * q^93 - 2 * q^95 - 34 * q^97 + 20 * 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
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i	0.973494	−	0.228714i	$-0.0734519\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i	−0.684819	+	0.728714i	$0.740119\pi$
$4$		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
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$		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
$13$	−7.00000			−1.94145			−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−7.00000			−1.94145			−0.970725	+	0.240192i	$0.922790\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$		0			0
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$		0			0
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	0.728219	+	0.685344i	$0.240348\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.00000	+	6.92820i	−0.834058	+	1.44463i	0.0607377	+	0.998154i	$0.480655\pi$
$23$	−4.00000	+	6.92820i	−0.834058	+	1.44463i	−0.894795	+	0.446476i	$0.852679\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	5.00000			0.962250
$28$		0			0
$29$	−5.00000			−0.928477			−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000			−0.928477			−0.464238	+	0.885710i	$0.653672\pi$
$30$		0			0
$31$	−5.00000	−	8.66025i	−0.898027	−	1.55543i	−0.830014	−	0.557743i	$-0.811667\pi$
$31$	−5.00000	−	8.66025i	−0.898027	−	1.55543i	−0.0680129	−	0.997684i	$-0.521666\pi$
$32$		0			0
$33$	−2.50000	+	4.33013i	−0.435194	+	0.753778i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	−0.982274	−	0.187453i	$-0.939977\pi$
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	0.653476	+	0.756948i	$0.273310\pi$
$38$		0			0
$39$	−3.50000	−	6.06218i	−0.560449	−	0.970725i
$40$		0			0
$41$	6.00000			0.937043			0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$		0			0
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$		0			0
$45$	1.00000	+	1.73205i	0.149071	+	0.258199i
$46$		0			0
$47$	−3.50000	+	6.06218i	−0.510527	+	0.884260i	0.489398	+	0.872060i	$0.337217\pi$
$47$	−3.50000	+	6.06218i	−0.510527	+	0.884260i	−0.999926	+	0.0121990i	$0.996117\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	1.50000	−	2.59808i	0.210042	−	0.363803i
$52$		0			0
$53$	5.00000	+	8.66025i	0.686803	+	1.18958i	0.972867	+	0.231367i	$0.0743197\pi$
$53$	5.00000	+	8.66025i	0.686803	+	1.18958i	−0.286064	+	0.958211i	$0.592347\pi$
$54$		0			0
$55$	−5.00000			−0.674200
$56$		0			0
$57$	−2.00000			−0.264906
$58$		0			0
$59$	−5.00000	−	8.66025i	−0.650945	−	1.12747i	−0.982894	−	0.184172i	$-0.941040\pi$
$59$	−5.00000	−	8.66025i	−0.650945	−	1.12747i	0.331949	−	0.943297i	$-0.392294\pi$
$60$		0			0
$61$	−6.00000	+	10.3923i	−0.768221	+	1.33060i	0.170305	+	0.985391i	$0.445525\pi$
$61$	−6.00000	+	10.3923i	−0.768221	+	1.33060i	−0.938527	+	0.345207i	$0.887809\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.50000	−	6.06218i	0.434122	−	0.751921i
$66$		0			0
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	0.920623	−	0.390453i	$-0.127682\pi$
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	−0.798454	+	0.602056i	$0.794348\pi$
$68$		0			0
$69$	−8.00000			−0.963087
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	0.801553	−	0.597924i	$-0.204008\pi$
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	−0.918594	+	0.395203i	$0.870674\pi$
$74$		0			0
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	3.50000	−	6.06218i	0.393781	−	0.682048i	−0.599164	−	0.800626i	$-0.704500\pi$
$79$	3.50000	−	6.06218i	0.393781	−	0.682048i	0.992945	+	0.118578i	$0.0378336\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		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
$85$	3.00000			0.325396
$86$		0			0
$87$	−2.50000	−	4.33013i	−0.268028	−	0.464238i
$88$		0			0
$89$	−4.00000	+	6.92820i	−0.423999	+	0.734388i	−0.996326	−	0.0856373i	$-0.972707\pi$
$89$	−4.00000	+	6.92820i	−0.423999	+	0.734388i	0.572327	+	0.820025i	$0.306041\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	5.00000	−	8.66025i	0.518476	−	0.898027i
$94$		0			0
$95$	−1.00000	−	1.73205i	−0.102598	−	0.177705i
$96$		0			0
$97$	−17.0000			−1.72609			−0.863044	−	0.505128i	$-0.831445\pi$
$97$	−17.0000			−1.72609			−0.863044	+	0.505128i	$0.831445\pi$
$98$		0			0
$99$	10.0000			1.00504
$100$		0			0
$101$	5.00000	+	8.66025i	0.497519	+	0.861727i	0.999996	−	0.00286291i	$-0.000911295\pi$
$101$	5.00000	+	8.66025i	0.497519	+	0.861727i	−0.502477	+	0.864590i	$0.667578\pi$
$102$		0			0
$103$	0.500000	−	0.866025i	0.0492665	−	0.0853320i	−0.840341	−	0.542059i	$-0.817645\pi$
$103$	0.500000	−	0.866025i	0.0492665	−	0.0853320i	0.889607	+	0.456727i	$0.150978\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.00000	+	1.73205i	−0.0966736	+	0.167444i	−0.910306	−	0.413936i	$-0.864154\pi$
$107$	−1.00000	+	1.73205i	−0.0966736	+	0.167444i	0.813632	+	0.581380i	$0.197487\pi$
$108$		0			0
$109$	−6.50000	−	11.2583i	−0.622587	−	1.07835i	−0.989002	−	0.147901i	$-0.952748\pi$
$109$	−6.50000	−	11.2583i	−0.622587	−	1.07835i	0.366415	−	0.930451i	$-0.380585\pi$
$110$		0			0
$111$	−4.00000			−0.379663
$112$		0			0
$113$	−12.0000			−1.12887			−0.564433	−	0.825479i	$-0.690905\pi$
$113$	−12.0000			−1.12887			−0.564433	+	0.825479i	$0.690905\pi$
$114$		0			0
$115$	−4.00000	−	6.92820i	−0.373002	−	0.646058i
$116$		0			0
$117$	−7.00000	+	12.1244i	−0.647150	+	1.12090i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−7.00000	+	12.1244i	−0.636364	+	1.10221i
$122$		0			0
$123$	3.00000	+	5.19615i	0.270501	+	0.468521i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−6.00000			−0.532414			−0.266207	−	0.963916i	$-0.585770\pi$
$127$	−6.00000			−0.532414			−0.266207	+	0.963916i	$0.585770\pi$
$128$		0			0
$129$	1.00000	+	1.73205i	0.0880451	+	0.152499i
$130$		0			0
$131$	−4.00000	+	6.92820i	−0.349482	+	0.605320i	−0.986157	−	0.165812i	$-0.946976\pi$
$131$	−4.00000	+	6.92820i	−0.349482	+	0.605320i	0.636676	+	0.771132i	$0.280309\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−2.50000	+	4.33013i	−0.215166	+	0.372678i
$136$		0			0
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	−0.999893	−	0.0146279i	$-0.995344\pi$
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	0.487278	−	0.873247i	$-0.337990\pi$
$138$		0			0
$139$	16.0000			1.35710			0.678551	−	0.734553i	$-0.262608\pi$
$139$	16.0000			1.35710			0.678551	+	0.734553i	$0.262608\pi$
$140$		0			0
$141$	−7.00000			−0.589506
$142$		0			0
$143$	−17.5000	−	30.3109i	−1.46342	−	2.53472i
$144$		0			0
$145$	2.50000	−	4.33013i	0.207614	−	0.359597i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.00000	+	1.73205i	−0.0819232	+	0.141895i	−0.904076	−	0.427372i	$-0.859440\pi$
$149$	−1.00000	+	1.73205i	−0.0819232	+	0.141895i	0.822153	+	0.569267i	$0.192773\pi$
$150$		0			0
$151$	−0.500000	−	0.866025i	−0.0406894	−	0.0704761i	0.844963	−	0.534824i	$-0.179622\pi$
$151$	−0.500000	−	0.866025i	−0.0406894	−	0.0704761i	−0.885653	+	0.464348i	$0.846289\pi$
$152$		0			0
$153$	−6.00000			−0.485071
$154$		0			0
$155$	10.0000			0.803219
$156$		0			0
$157$	1.00000	+	1.73205i	0.0798087	+	0.138233i	0.903167	−	0.429289i	$-0.141236\pi$
$157$	1.00000	+	1.73205i	0.0798087	+	0.138233i	−0.823359	+	0.567521i	$0.807902\pi$
$158$		0			0
$159$	−5.00000	+	8.66025i	−0.396526	+	0.686803i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−4.00000	+	6.92820i	−0.313304	+	0.542659i	−0.979076	−	0.203497i	$-0.934769\pi$
$163$	−4.00000	+	6.92820i	−0.313304	+	0.542659i	0.665771	+	0.746156i	$0.268103\pi$
$164$		0			0
$165$	−2.50000	−	4.33013i	−0.194625	−	0.337100i
$166$		0			0
$167$	11.0000			0.851206			0.425603	−	0.904910i	$-0.360062\pi$
$167$	11.0000			0.851206			0.425603	+	0.904910i	$0.360062\pi$
$168$		0			0
$169$	36.0000			2.76923
$170$		0			0
$171$	2.00000	+	3.46410i	0.152944	+	0.264906i
$172$		0			0
$173$	4.50000	−	7.79423i	0.342129	−	0.592584i	−0.642699	−	0.766119i	$-0.722185\pi$
$173$	4.50000	−	7.79423i	0.342129	−	0.592584i	0.984828	+	0.173534i	$0.0555188\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	5.00000	−	8.66025i	0.375823	−	0.650945i
$178$		0			0
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	0.549825	−	0.835280i	$-0.314694\pi$
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	−0.998286	+	0.0585225i	$0.981361\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$		0			0
$183$	−12.0000			−0.887066
$184$		0			0
$185$	−2.00000	−	3.46410i	−0.147043	−	0.254686i
$186$		0			0
$187$	7.50000	−	12.9904i	0.548454	−	0.949951i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	8.50000	−	14.7224i	0.615038	−	1.06528i	−0.375339	−	0.926887i	$-0.622474\pi$
$191$	8.50000	−	14.7224i	0.615038	−	1.06528i	0.990378	−	0.138390i	$-0.0441928\pi$
$192$		0			0
$193$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$193$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$194$		0			0
$195$	7.00000			0.501280
$196$		0			0
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$	5.00000	+	8.66025i	0.354441	+	0.613909i	0.987022	−	0.160585i	$-0.0513380\pi$
$199$	5.00000	+	8.66025i	0.354441	+	0.613909i	−0.632581	+	0.774494i	$0.718005\pi$
$200$		0			0
$201$	−1.00000	+	1.73205i	−0.0705346	+	0.122169i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−3.00000	+	5.19615i	−0.209529	+	0.362915i
$206$		0			0
$207$	8.00000	+	13.8564i	0.556038	+	0.963087i
$208$		0			0
$209$	−10.0000			−0.691714
$210$		0			0
$211$	−19.0000			−1.30801			−0.654007	−	0.756489i	$-0.726913\pi$
$211$	−19.0000			−1.30801			−0.654007	+	0.756489i	$0.726913\pi$
$212$		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
$219$	1.00000	−	1.73205i	0.0675737	−	0.117041i
$220$		0			0
$221$	10.5000	+	18.1865i	0.706306	+	1.22336i
$222$		0			0
$223$	11.0000			0.736614			0.368307	−	0.929704i	$-0.379937\pi$
$223$	11.0000			0.736614			0.368307	+	0.929704i	$0.379937\pi$
$224$		0			0
$225$	−2.00000			−0.133333
$226$		0			0
$227$	0.500000	+	0.866025i	0.0331862	+	0.0574801i	0.882141	−	0.470985i	$-0.156101\pi$
$227$	0.500000	+	0.866025i	0.0331862	+	0.0574801i	−0.848955	+	0.528465i	$0.822768\pi$
$228$		0			0
$229$	−5.00000	+	8.66025i	−0.330409	+	0.572286i	−0.982592	−	0.185776i	$-0.940520\pi$
$229$	−5.00000	+	8.66025i	−0.330409	+	0.572286i	0.652183	+	0.758062i	$0.273853\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−4.00000	+	6.92820i	−0.262049	+	0.453882i	−0.966786	−	0.255586i	$-0.917731\pi$
$233$	−4.00000	+	6.92820i	−0.262049	+	0.453882i	0.704737	+	0.709468i	$0.251065\pi$
$234$		0			0
$235$	−3.50000	−	6.06218i	−0.228315	−	0.395453i
$236$		0			0
$237$	7.00000			0.454699
$238$		0			0
$239$	25.0000			1.61712			0.808558	−	0.588417i	$-0.200249\pi$
$239$	25.0000			1.61712			0.808558	+	0.588417i	$0.200249\pi$
$240$		0			0
$241$	10.0000	+	17.3205i	0.644157	+	1.11571i	0.984496	+	0.175409i	$0.0561248\pi$
$241$	10.0000	+	17.3205i	0.644157	+	1.11571i	−0.340339	+	0.940303i	$0.610542\pi$
$242$		0			0
$243$	8.00000	−	13.8564i	0.513200	−	0.888889i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	7.00000	−	12.1244i	0.445399	−	0.771454i
$248$		0			0
$249$	−2.00000	−	3.46410i	−0.126745	−	0.219529i
$250$		0			0
$251$	20.0000			1.26239			0.631194	−	0.775625i	$-0.282565\pi$
$251$	20.0000			1.26239			0.631194	+	0.775625i	$0.282565\pi$
$252$		0			0
$253$	−40.0000			−2.51478
$254$		0			0
$255$	1.50000	+	2.59808i	0.0939336	+	0.162698i
$256$		0			0
$257$	−7.00000	+	12.1244i	−0.436648	+	0.756297i	−0.997429	−	0.0716680i	$-0.977168\pi$
$257$	−7.00000	+	12.1244i	−0.436648	+	0.756297i	0.560781	+	0.827964i	$0.310501\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−5.00000	+	8.66025i	−0.309492	+	0.536056i
$262$		0			0
$263$	11.0000	+	19.0526i	0.678289	+	1.17483i	0.975496	+	0.220018i	$0.0706116\pi$
$263$	11.0000	+	19.0526i	0.678289	+	1.17483i	−0.297207	+	0.954813i	$0.596055\pi$
$264$		0			0
$265$	−10.0000			−0.614295
$266$		0			0
$267$	−8.00000			−0.489592
$268$		0			0
$269$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$269$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$270$		0			0
$271$	−10.0000	+	17.3205i	−0.607457	+	1.05215i	0.384201	+	0.923249i	$0.374477\pi$
$271$	−10.0000	+	17.3205i	−0.607457	+	1.05215i	−0.991658	+	0.128897i	$0.958856\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.50000	−	4.33013i	0.150756	−	0.261116i
$276$		0			0
$277$	14.0000	+	24.2487i	0.841178	+	1.45696i	0.888899	+	0.458103i	$0.151471\pi$
$277$	14.0000	+	24.2487i	0.841178	+	1.45696i	−0.0477206	+	0.998861i	$0.515196\pi$
$278$		0			0
$279$	−20.0000			−1.19737
$280$		0			0
$281$	11.0000			0.656205			0.328102	−	0.944642i	$-0.393591\pi$
$281$	11.0000			0.656205			0.328102	+	0.944642i	$0.393591\pi$
$282$		0			0
$283$	15.5000	+	26.8468i	0.921379	+	1.59588i	0.797283	+	0.603606i	$0.206270\pi$
$283$	15.5000	+	26.8468i	0.921379	+	1.59588i	0.124096	+	0.992270i	$0.460397\pi$
$284$		0			0
$285$	1.00000	−	1.73205i	0.0592349	−	0.102598i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$		0			0
$291$	−8.50000	−	14.7224i	−0.498279	−	0.863044i
$292$		0			0
$293$	−5.00000			−0.292103			−0.146052	−	0.989277i	$-0.546657\pi$
$293$	−5.00000			−0.292103			−0.146052	+	0.989277i	$0.546657\pi$
$294$		0			0
$295$	10.0000			0.582223
$296$		0			0
$297$	12.5000	+	21.6506i	0.725324	+	1.25630i
$298$		0			0
$299$	28.0000	−	48.4974i	1.61928	−	2.80468i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−5.00000	+	8.66025i	−0.287242	+	0.497519i
$304$		0			0
$305$	−6.00000	−	10.3923i	−0.343559	−	0.595062i
$306$		0			0
$307$	−7.00000			−0.399511			−0.199756	−	0.979846i	$-0.564015\pi$
$307$	−7.00000			−0.399511			−0.199756	+	0.979846i	$0.564015\pi$
$308$		0			0
$309$	1.00000			0.0568880
$310$		0			0
$311$	−15.0000	−	25.9808i	−0.850572	−	1.47323i	−0.880693	−	0.473688i	$-0.842923\pi$
$311$	−15.0000	−	25.9808i	−0.850572	−	1.47323i	0.0301210	−	0.999546i	$-0.490411\pi$
$312$		0			0
$313$	−2.50000	+	4.33013i	−0.141308	+	0.244753i	−0.927990	−	0.372606i	$-0.878464\pi$
$313$	−2.50000	+	4.33013i	−0.141308	+	0.244753i	0.786681	+	0.617359i	$0.211798\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−13.0000	+	22.5167i	−0.730153	+	1.26466i	0.226665	+	0.973973i	$0.427218\pi$
$317$	−13.0000	+	22.5167i	−0.730153	+	1.26466i	−0.956818	+	0.290689i	$0.906116\pi$
$318$		0			0
$319$	−12.5000	−	21.6506i	−0.699866	−	1.21220i
$320$		0			0
$321$	−2.00000			−0.111629
$322$		0			0
$323$	6.00000			0.333849
$324$		0			0
$325$	3.50000	+	6.06218i	0.194145	+	0.336269i
$326$		0			0
$327$	6.50000	−	11.2583i	0.359451	−	0.622587i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−14.0000	+	24.2487i	−0.769510	+	1.33283i	0.168320	+	0.985732i	$0.446166\pi$
$331$	−14.0000	+	24.2487i	−0.769510	+	1.33283i	−0.937829	+	0.347097i	$0.887167\pi$
$332$		0			0
$333$	4.00000	+	6.92820i	0.219199	+	0.379663i
$334$		0			0
$335$	−2.00000			−0.109272
$336$		0			0
$337$	−16.0000			−0.871576			−0.435788	−	0.900049i	$-0.643530\pi$
$337$	−16.0000			−0.871576			−0.435788	+	0.900049i	$0.643530\pi$
$338$		0			0
$339$	−6.00000	−	10.3923i	−0.325875	−	0.564433i
$340$		0			0
$341$	25.0000	−	43.3013i	1.35383	−	2.34490i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	4.00000	−	6.92820i	0.215353	−	0.373002i
$346$		0			0
$347$	−14.0000	−	24.2487i	−0.751559	−	1.30174i	−0.947067	−	0.321037i	$-0.895969\pi$
$347$	−14.0000	−	24.2487i	−0.751559	−	1.30174i	0.195507	−	0.980702i	$-0.437365\pi$
$348$		0			0
$349$	26.0000			1.39175			0.695874	−	0.718164i	$-0.255017\pi$
$349$	26.0000			1.39175			0.695874	+	0.718164i	$0.255017\pi$
$350$		0			0
$351$	−35.0000			−1.86816
$352$		0			0
$353$	10.5000	+	18.1865i	0.558859	+	0.967972i	0.997592	+	0.0693543i	$0.0220939\pi$
$353$	10.5000	+	18.1865i	0.558859	+	0.967972i	−0.438733	+	0.898617i	$0.644573\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	8.00000	−	13.8564i	0.422224	−	0.731313i	−0.573933	−	0.818902i	$-0.694583\pi$
$359$	8.00000	−	13.8564i	0.422224	−	0.731313i	0.996157	+	0.0875892i	$0.0279163\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$		0			0
$363$	−14.0000			−0.734809
$364$		0			0
$365$	2.00000			0.104685
$366$		0			0
$367$	−3.50000	−	6.06218i	−0.182699	−	0.316443i	0.760100	−	0.649806i	$-0.225150\pi$
$367$	−3.50000	−	6.06218i	−0.182699	−	0.316443i	−0.942799	+	0.333363i	$0.891817\pi$
$368$		0			0
$369$	6.00000	−	10.3923i	0.312348	−	0.541002i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$373$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$374$		0			0
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$		0			0
$377$	35.0000			1.80259
$378$		0			0
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$		0			0
$381$	−3.00000	−	5.19615i	−0.153695	−	0.266207i
$382$		0			0
$383$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$383$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.00000	−	3.46410i	0.101666	−	0.176090i
$388$		0			0
$389$	−16.5000	−	28.5788i	−0.836583	−	1.44900i	−0.892735	−	0.450582i	$-0.851216\pi$
$389$	−16.5000	−	28.5788i	−0.836583	−	1.44900i	0.0561516	−	0.998422i	$-0.482117\pi$
$390$		0			0
$391$	24.0000			1.21373
$392$		0			0
$393$	−8.00000			−0.403547
$394$		0			0
$395$	3.50000	+	6.06218i	0.176104	+	0.305021i
$396$		0			0
$397$	6.50000	−	11.2583i	0.326226	−	0.565039i	−0.655534	−	0.755166i	$-0.727556\pi$
$397$	6.50000	−	11.2583i	0.326226	−	0.565039i	0.981760	+	0.190126i	$0.0608897\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	−0.826139	−	0.563466i	$-0.809468\pi$
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	0.901046	+	0.433724i	$0.142801\pi$
$402$		0			0
$403$	35.0000	+	60.6218i	1.74347	+	3.01979i
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	−20.0000			−0.991363
$408$		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
$411$	6.00000	−	10.3923i	0.295958	−	0.512615i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	2.00000	−	3.46410i	0.0981761	−	0.170046i
$416$		0			0
$417$	8.00000	+	13.8564i	0.391762	+	0.678551i
$418$		0			0
$419$	26.0000			1.27018			0.635092	−	0.772437i	$-0.280962\pi$
$419$	26.0000			1.27018			0.635092	+	0.772437i	$0.280962\pi$
$420$		0			0
$421$	29.0000			1.41337			0.706687	−	0.707527i	$-0.250189\pi$
$421$	29.0000			1.41337			0.706687	+	0.707527i	$0.250189\pi$
$422$		0			0
$423$	7.00000	+	12.1244i	0.340352	+	0.589506i
$424$		0			0
$425$	−1.50000	+	2.59808i	−0.0727607	+	0.126025i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	17.5000	−	30.3109i	0.844908	−	1.46342i
$430$		0			0
$431$	10.5000	+	18.1865i	0.505767	+	0.876014i	0.999978	+	0.00667224i	$0.00212386\pi$
$431$	10.5000	+	18.1865i	0.505767	+	0.876014i	−0.494211	+	0.869342i	$0.664543\pi$
$432$		0			0
$433$	−2.00000			−0.0961139			−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000			−0.0961139			−0.0480569	+	0.998845i	$0.515303\pi$
$434$		0			0
$435$	5.00000			0.239732
$436$		0			0
$437$	−8.00000	−	13.8564i	−0.382692	−	0.662842i
$438$		0			0
$439$	−14.0000	+	24.2487i	−0.668184	+	1.15733i	0.310228	+	0.950662i	$0.399595\pi$
$439$	−14.0000	+	24.2487i	−0.668184	+	1.15733i	−0.978412	+	0.206666i	$0.933739\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−5.00000	+	8.66025i	−0.237557	+	0.411461i	−0.960013	−	0.279956i	$-0.909680\pi$
$443$	−5.00000	+	8.66025i	−0.237557	+	0.411461i	0.722456	+	0.691417i	$0.243013\pi$
$444$		0			0
$445$	−4.00000	−	6.92820i	−0.189618	−	0.328428i
$446$		0			0
$447$	−2.00000			−0.0945968
$448$		0			0
$449$	15.0000			0.707894			0.353947	−	0.935266i	$-0.384839\pi$
$449$	15.0000			0.707894			0.353947	+	0.935266i	$0.384839\pi$
$450$		0			0
$451$	15.0000	+	25.9808i	0.706322	+	1.22339i
$452$		0			0
$453$	0.500000	−	0.866025i	0.0234920	−	0.0406894i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	3.00000	−	5.19615i	0.140334	−	0.243066i	−0.787288	−	0.616585i	$-0.788516\pi$
$457$	3.00000	−	5.19615i	0.140334	−	0.243066i	0.927622	+	0.373519i	$0.121849\pi$
$458$		0			0
$459$	−7.50000	−	12.9904i	−0.350070	−	0.606339i
$460$		0			0
$461$	12.0000			0.558896			0.279448	−	0.960161i	$-0.409849\pi$
$461$	12.0000			0.558896			0.279448	+	0.960161i	$0.409849\pi$
$462$		0			0
$463$	32.0000			1.48717			0.743583	−	0.668644i	$-0.233125\pi$
$463$	32.0000			1.48717			0.743583	+	0.668644i	$0.233125\pi$
$464$		0			0
$465$	5.00000	+	8.66025i	0.231869	+	0.401610i
$466$		0			0
$467$	17.5000	−	30.3109i	0.809803	−	1.40262i	−0.103197	−	0.994661i	$-0.532907\pi$
$467$	17.5000	−	30.3109i	0.809803	−	1.40262i	0.913000	−	0.407960i	$-0.133760\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−1.00000	+	1.73205i	−0.0460776	+	0.0798087i
$472$		0			0
$473$	5.00000	+	8.66025i	0.229900	+	0.398199i
$474$		0			0
$475$	2.00000			0.0917663
$476$		0			0
$477$	20.0000			0.915737
$478$		0			0
$479$	6.00000	+	10.3923i	0.274147	+	0.474837i	0.969920	−	0.243426i	$-0.0782712\pi$
$479$	6.00000	+	10.3923i	0.274147	+	0.474837i	−0.695773	+	0.718262i	$0.744938\pi$
$480$		0			0
$481$	14.0000	−	24.2487i	0.638345	−	1.10565i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	8.50000	−	14.7224i	0.385965	−	0.668511i
$486$		0			0
$487$	−10.0000	−	17.3205i	−0.453143	−	0.784867i	0.545436	−	0.838152i	$-0.316364\pi$
$487$	−10.0000	−	17.3205i	−0.453143	−	0.784867i	−0.998579	+	0.0532853i	$0.983031\pi$
$488$		0			0
$489$	−8.00000			−0.361773
$490$		0			0
$491$	−27.0000			−1.21849			−0.609246	−	0.792981i	$-0.708528\pi$
$491$	−27.0000			−1.21849			−0.609246	+	0.792981i	$0.708528\pi$
$492$		0			0
$493$	7.50000	+	12.9904i	0.337783	+	0.585057i
$494$		0			0
$495$	−5.00000	+	8.66025i	−0.224733	+	0.389249i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	8.50000	−	14.7224i	0.380512	−	0.659067i	−0.610623	−	0.791921i	$-0.709081\pi$
$499$	8.50000	−	14.7224i	0.380512	−	0.659067i	0.991136	+	0.132855i	$0.0424144\pi$
$500$		0			0
$501$	5.50000	+	9.52628i	0.245722	+	0.425603i
$502$		0			0
$503$	9.00000			0.401290			0.200645	−	0.979664i	$-0.435696\pi$
$503$	9.00000			0.401290			0.200645	+	0.979664i	$0.435696\pi$
$504$		0			0
$505$	−10.0000			−0.444994
$506$		0			0
$507$	18.0000	+	31.1769i	0.799408	+	1.38462i
$508$		0			0
$509$	−4.00000	+	6.92820i	−0.177297	+	0.307087i	−0.940954	−	0.338535i	$-0.890069\pi$
$509$	−4.00000	+	6.92820i	−0.177297	+	0.307087i	0.763657	+	0.645622i	$0.223402\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−5.00000	+	8.66025i	−0.220755	+	0.382360i
$514$		0			0
$515$	0.500000	+	0.866025i	0.0220326	+	0.0381616i
$516$		0			0
$517$	−35.0000			−1.53930
$518$		0			0
$519$	9.00000			0.395056
$520$		0			0
$521$	−7.00000	−	12.1244i	−0.306676	−	0.531178i	0.670957	−	0.741496i	$-0.265883\pi$
$521$	−7.00000	−	12.1244i	−0.306676	−	0.531178i	−0.977633	+	0.210318i	$0.932550\pi$
$522$		0			0
$523$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$523$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−15.0000	+	25.9808i	−0.653410	+	1.13174i
$528$		0			0
$529$	−20.5000	−	35.5070i	−0.891304	−	1.54378i
$530$		0			0
$531$	−20.0000			−0.867926
$532$		0			0
$533$	−42.0000			−1.81922
$534$		0			0
$535$	−1.00000	−	1.73205i	−0.0432338	−	0.0748831i
$536$		0			0
$537$	6.00000	−	10.3923i	0.258919	−	0.448461i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−7.50000	+	12.9904i	−0.322450	+	0.558500i	−0.980993	−	0.194043i	$-0.937840\pi$
$541$	−7.50000	+	12.9904i	−0.322450	+	0.558500i	0.658543	+	0.752543i	$0.271173\pi$
$542$		0			0
$543$	−5.00000	−	8.66025i	−0.214571	−	0.371647i
$544$		0			0
$545$	13.0000			0.556859
$546$		0			0
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$		0			0
$549$	12.0000	+	20.7846i	0.512148	+	0.887066i
$550$		0			0
$551$	5.00000	−	8.66025i	0.213007	−	0.368939i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	2.00000	−	3.46410i	0.0848953	−	0.147043i
$556$		0			0
$557$	6.00000	+	10.3923i	0.254228	+	0.440336i	0.964686	−	0.263404i	$-0.0848453\pi$
$557$	6.00000	+	10.3923i	0.254228	+	0.440336i	−0.710457	+	0.703740i	$0.751512\pi$
$558$		0			0
$559$	−14.0000			−0.592137
$560$		0			0
$561$	15.0000			0.633300
$562$		0			0
$563$	2.00000	+	3.46410i	0.0842900	+	0.145994i	0.905088	−	0.425223i	$-0.139804\pi$
$563$	2.00000	+	3.46410i	0.0842900	+	0.145994i	−0.820798	+	0.571218i	$0.806471\pi$
$564$		0			0
$565$	6.00000	−	10.3923i	0.252422	−	0.437208i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	−0.990668	−	0.136295i	$-0.956481\pi$
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	0.613369	+	0.789797i	$0.289814\pi$
$570$		0			0
$571$	6.00000	+	10.3923i	0.251092	+	0.434904i	0.963827	−	0.266529i	$-0.0858769\pi$
$571$	6.00000	+	10.3923i	0.251092	+	0.434904i	−0.712735	+	0.701434i	$0.752544\pi$
$572$		0			0
$573$	17.0000			0.710185
$574$		0			0
$575$	8.00000			0.333623
$576$		0			0
$577$	−16.5000	−	28.5788i	−0.686904	−	1.18975i	−0.972834	−	0.231502i	$-0.925636\pi$
$577$	−16.5000	−	28.5788i	−0.686904	−	1.18975i	0.285930	−	0.958250i	$-0.407697\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−25.0000	+	43.3013i	−1.03539	+	1.79336i
$584$		0			0
$585$	−7.00000	−	12.1244i	−0.289414	−	0.501280i
$586$		0			0
$587$	12.0000			0.495293			0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000			0.495293			0.247647	+	0.968850i	$0.420343\pi$
$588$		0			0
$589$	20.0000			0.824086
$590$		0			0
$591$	9.00000	+	15.5885i	0.370211	+	0.641223i
$592$		0			0
$593$	5.50000	−	9.52628i	0.225858	−	0.391197i	−0.730719	−	0.682679i	$-0.760815\pi$
$593$	5.50000	−	9.52628i	0.225858	−	0.391197i	0.956576	+	0.291481i	$0.0941482\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−5.00000	+	8.66025i	−0.204636	+	0.354441i
$598$		0			0
$599$	−19.5000	−	33.7750i	−0.796748	−	1.38001i	−0.921723	−	0.387849i	$-0.873218\pi$
$599$	−19.5000	−	33.7750i	−0.796748	−	1.38001i	0.124975	−	0.992160i	$-0.460115\pi$
$600$		0			0
$601$	−10.0000			−0.407909			−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000			−0.407909			−0.203954	+	0.978980i	$0.565379\pi$
$602$		0			0
$603$	4.00000			0.162893
$604$		0			0
$605$	−7.00000	−	12.1244i	−0.284590	−	0.492925i
$606$		0			0
$607$	−14.5000	+	25.1147i	−0.588537	+	1.01938i	0.405887	+	0.913923i	$0.366962\pi$
$607$	−14.5000	+	25.1147i	−0.588537	+	1.01938i	−0.994424	+	0.105453i	$0.966371\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	24.5000	−	42.4352i	0.991164	−	1.71675i
$612$		0			0
$613$	−11.0000	−	19.0526i	−0.444286	−	0.769526i	0.553716	−	0.832705i	$-0.313209\pi$
$613$	−11.0000	−	19.0526i	−0.444286	−	0.769526i	−0.998002	+	0.0631797i	$0.979876\pi$
$614$		0			0
$615$	−6.00000			−0.241943
$616$		0			0
$617$	−12.0000			−0.483102			−0.241551	−	0.970388i	$-0.577656\pi$
$617$	−12.0000			−0.483102			−0.241551	+	0.970388i	$0.577656\pi$
$618$		0			0
$619$	18.0000	+	31.1769i	0.723481	+	1.25311i	0.959596	+	0.281381i	$0.0907924\pi$
$619$	18.0000	+	31.1769i	0.723481	+	1.25311i	−0.236115	+	0.971725i	$0.575874\pi$
$620$		0			0
$621$	−20.0000	+	34.6410i	−0.802572	+	1.39010i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−5.00000	−	8.66025i	−0.199681	−	0.345857i
$628$		0			0
$629$	12.0000			0.478471
$630$		0			0
$631$	19.0000			0.756378			0.378189	−	0.925728i	$-0.376547\pi$
$631$	19.0000			0.756378			0.378189	+	0.925728i	$0.376547\pi$
$632$		0			0
$633$	−9.50000	−	16.4545i	−0.377591	−	0.654007i
$634$		0			0
$635$	3.00000	−	5.19615i	0.119051	−	0.206203i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	13.0000	+	22.5167i	0.513469	+	0.889355i	0.999878	+	0.0156233i	$0.00497325\pi$
$641$	13.0000	+	22.5167i	0.513469	+	0.889355i	−0.486409	+	0.873731i	$0.661693\pi$
$642$		0			0
$643$	39.0000			1.53801			0.769005	−	0.639243i	$-0.220752\pi$
$643$	39.0000			1.53801			0.769005	+	0.639243i	$0.220752\pi$
$644$		0			0
$645$	−2.00000			−0.0787499
$646$		0			0
$647$	−6.00000	−	10.3923i	−0.235884	−	0.408564i	0.723645	−	0.690172i	$-0.242465\pi$
$647$	−6.00000	−	10.3923i	−0.235884	−	0.408564i	−0.959529	+	0.281609i	$0.909132\pi$
$648$		0			0
$649$	25.0000	−	43.3013i	0.981336	−	1.69972i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	3.00000	−	5.19615i	0.117399	−	0.203341i	−0.801337	−	0.598213i	$-0.795878\pi$
$653$	3.00000	−	5.19615i	0.117399	−	0.203341i	0.918736	+	0.394872i	$0.129211\pi$
$654$		0			0
$655$	−4.00000	−	6.92820i	−0.156293	−	0.270707i
$656$		0			0
$657$	−4.00000			−0.156055
$658$		0			0
$659$	23.0000			0.895953			0.447976	−	0.894045i	$-0.352145\pi$
$659$	23.0000			0.895953			0.447976	+	0.894045i	$0.352145\pi$
$660$		0			0
$661$	2.00000	+	3.46410i	0.0777910	+	0.134738i	0.902297	−	0.431116i	$-0.141880\pi$
$661$	2.00000	+	3.46410i	0.0777910	+	0.134738i	−0.824506	+	0.565854i	$0.808547\pi$
$662$		0			0
$663$	−10.5000	+	18.1865i	−0.407786	+	0.706306i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	20.0000	−	34.6410i	0.774403	−	1.34131i
$668$		0			0
$669$	5.50000	+	9.52628i	0.212642	+	0.368307i
$670$		0			0
$671$	−60.0000			−2.31627
$672$		0			0
$673$	−32.0000			−1.23351			−0.616755	−	0.787155i	$-0.711553\pi$
$673$	−32.0000			−1.23351			−0.616755	+	0.787155i	$0.711553\pi$
$674$		0			0
$675$	−2.50000	−	4.33013i	−0.0962250	−	0.166667i
$676$		0			0
$677$	5.50000	−	9.52628i	0.211382	−	0.366125i	−0.740765	−	0.671764i	$-0.765537\pi$
$677$	5.50000	−	9.52628i	0.211382	−	0.366125i	0.952147	+	0.305639i	$0.0988702\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−0.500000	+	0.866025i	−0.0191600	+	0.0331862i
$682$		0			0
$683$	6.00000	+	10.3923i	0.229584	+	0.397650i	0.957685	−	0.287819i	$-0.0929302\pi$
$683$	6.00000	+	10.3923i	0.229584	+	0.397650i	−0.728101	+	0.685470i	$0.759597\pi$
$684$		0			0
$685$	12.0000			0.458496
$686$		0			0
$687$	−10.0000			−0.381524
$688$		0			0
$689$	−35.0000	−	60.6218i	−1.33339	−	2.30951i
$690$		0			0
$691$	18.0000	−	31.1769i	0.684752	−	1.18603i	−0.288762	−	0.957401i	$-0.593244\pi$
$691$	18.0000	−	31.1769i	0.684752	−	1.18603i	0.973515	−	0.228625i	$-0.0734229\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−8.00000	+	13.8564i	−0.303457	+	0.525603i
$696$		0			0
$697$	−9.00000	−	15.5885i	−0.340899	−	0.590455i
$698$		0			0
$699$	−8.00000			−0.302588
$700$		0			0
$701$	−5.00000			−0.188847			−0.0944237	−	0.995532i	$-0.530101\pi$
$701$	−5.00000			−0.188847			−0.0944237	+	0.995532i	$0.530101\pi$
$702$		0			0
$703$	−4.00000	−	6.92820i	−0.150863	−	0.261302i
$704$		0			0
$705$	3.50000	−	6.06218i	0.131818	−	0.228315i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	10.5000	−	18.1865i	0.394336	−	0.683010i	−0.598680	−	0.800988i	$-0.704308\pi$
$709$	10.5000	−	18.1865i	0.394336	−	0.683010i	0.993016	+	0.117978i	$0.0376414\pi$
$710$		0			0
$711$	−7.00000	−	12.1244i	−0.262521	−	0.454699i
$712$		0			0
$713$	80.0000			2.99602
$714$		0			0
$715$	35.0000			1.30893
$716$		0			0
$717$	12.5000	+	21.6506i	0.466821	+	0.808558i
$718$		0			0
$719$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$719$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−10.0000	+	17.3205i	−0.371904	+	0.644157i
$724$		0			0
$725$	2.50000	+	4.33013i	0.0928477	+	0.160817i
$726$		0			0
$727$	−32.0000			−1.18681			−0.593407	−	0.804902i	$-0.702218\pi$
$727$	−32.0000			−1.18681			−0.593407	+	0.804902i	$0.702218\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	−3.00000	−	5.19615i	−0.110959	−	0.192187i
$732$		0			0
$733$	−2.50000	+	4.33013i	−0.0923396	+	0.159937i	−0.908495	−	0.417895i	$-0.862768\pi$
$733$	−2.50000	+	4.33013i	−0.0923396	+	0.159937i	0.816156	+	0.577832i	$0.196101\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−5.00000	+	8.66025i	−0.184177	+	0.319005i
$738$		0			0
$739$	12.5000	+	21.6506i	0.459820	+	0.796431i	0.998951	−	0.0457903i	$-0.0145806\pi$
$739$	12.5000	+	21.6506i	0.459820	+	0.796431i	−0.539131	+	0.842222i	$0.681247\pi$
$740$		0			0
$741$	14.0000			0.514303
$742$		0			0
$743$	6.00000			0.220119			0.110059	−	0.993925i	$-0.464896\pi$
$743$	6.00000			0.220119			0.110059	+	0.993925i	$0.464896\pi$
$744$		0			0
$745$	−1.00000	−	1.73205i	−0.0366372	−	0.0634574i
$746$		0			0
$747$	−4.00000	+	6.92820i	−0.146352	+	0.253490i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	11.5000	−	19.9186i	0.419641	−	0.726839i	−0.576262	−	0.817265i	$-0.695489\pi$
$751$	11.5000	−	19.9186i	0.419641	−	0.726839i	0.995903	+	0.0904254i	$0.0288227\pi$
$752$		0			0
$753$	10.0000	+	17.3205i	0.364420	+	0.631194i
$754$		0			0
$755$	1.00000			0.0363937
$756$		0			0
$757$	−24.0000			−0.872295			−0.436147	−	0.899875i	$-0.643657\pi$
$757$	−24.0000			−0.872295			−0.436147	+	0.899875i	$0.643657\pi$
$758$		0			0
$759$	−20.0000	−	34.6410i	−0.725954	−	1.25739i
$760$		0			0
$761$	−24.0000	+	41.5692i	−0.869999	+	1.50688i	−0.00800331	+	0.999968i	$0.502548\pi$
$761$	−24.0000	+	41.5692i	−0.869999	+	1.50688i	−0.861996	+	0.506915i	$0.830786\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	3.00000	−	5.19615i	0.108465	−	0.187867i
$766$		0			0
$767$	35.0000	+	60.6218i	1.26378	+	2.18893i
$768$		0			0
$769$	−34.0000			−1.22607			−0.613036	−	0.790055i	$-0.710052\pi$
$769$	−34.0000			−1.22607			−0.613036	+	0.790055i	$0.710052\pi$
$770$		0			0
$771$	−14.0000			−0.504198
$772$		0			0
$773$	−24.5000	−	42.4352i	−0.881204	−	1.52629i	−0.850004	−	0.526777i	$-0.823400\pi$
$773$	−24.5000	−	42.4352i	−0.881204	−	1.52629i	−0.0311999	−	0.999513i	$-0.509933\pi$
$774$		0			0
$775$	−5.00000	+	8.66025i	−0.179605	+	0.311086i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−6.00000	+	10.3923i	−0.214972	+	0.372343i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−25.0000			−0.893427
$784$		0			0
$785$	−2.00000			−0.0713831
$786$		0			0
$787$	22.5000	+	38.9711i	0.802038	+	1.38917i	0.918272	+	0.395949i	$0.129584\pi$
$787$	22.5000	+	38.9711i	0.802038	+	1.38917i	−0.116234	+	0.993222i	$0.537082\pi$
$788$		0			0
$789$	−11.0000	+	19.0526i	−0.391610	+	0.678289i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	42.0000	−	72.7461i	1.49146	−	2.58329i
$794$		0			0
$795$	−5.00000	−	8.66025i	−0.177332	−	0.307148i
$796$		0			0
$797$	−1.00000			−0.0354218			−0.0177109	−	0.999843i	$-0.505638\pi$
$797$	−1.00000			−0.0354218			−0.0177109	+	0.999843i	$0.505638\pi$
$798$		0			0
$799$	21.0000			0.742927
$800$		0			0
$801$	8.00000	+	13.8564i	0.282666	+	0.489592i
$802$		0			0
$803$	5.00000	−	8.66025i	0.176446	−	0.305614i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−6.50000	−	11.2583i	−0.228528	−	0.395822i	0.728844	−	0.684680i	$-0.240058\pi$
$809$	−6.50000	−	11.2583i	−0.228528	−	0.395822i	−0.957372	+	0.288858i	$0.906725\pi$
$810$		0			0
$811$	−40.0000			−1.40459			−0.702295	−	0.711886i	$-0.747841\pi$
$811$	−40.0000			−1.40459			−0.702295	+	0.711886i	$0.747841\pi$
$812$		0			0
$813$	−20.0000			−0.701431
$814$		0			0
$815$	−4.00000	−	6.92820i	−0.140114	−	0.242684i
$816$		0			0
$817$	−2.00000	+	3.46410i	−0.0699711	+	0.121194i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−18.5000	+	32.0429i	−0.645654	+	1.11831i	0.338495	+	0.940968i	$0.390082\pi$
$821$	−18.5000	+	32.0429i	−0.645654	+	1.11831i	−0.984150	+	0.177338i	$0.943251\pi$
$822$		0			0
$823$	7.00000	+	12.1244i	0.244005	+	0.422628i	0.961851	−	0.273573i	$-0.0882054\pi$
$823$	7.00000	+	12.1244i	0.244005	+	0.422628i	−0.717847	+	0.696201i	$0.754872\pi$
$824$		0			0
$825$	5.00000			0.174078
$826$		0			0
$827$	−24.0000			−0.834562			−0.417281	−	0.908778i	$-0.637017\pi$
$827$	−24.0000			−0.834562			−0.417281	+	0.908778i	$0.637017\pi$
$828$		0			0
$829$	1.00000	+	1.73205i	0.0347314	+	0.0601566i	0.882869	−	0.469620i	$-0.155609\pi$
$829$	1.00000	+	1.73205i	0.0347314	+	0.0601566i	−0.848137	+	0.529777i	$0.822276\pi$
$830$		0			0
$831$	−14.0000	+	24.2487i	−0.485655	+	0.841178i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−5.50000	+	9.52628i	−0.190335	+	0.329670i
$836$		0			0
$837$	−25.0000	−	43.3013i	−0.864126	−	1.49671i
$838$		0			0
$839$	4.00000			0.138095			0.0690477	−	0.997613i	$-0.478004\pi$
$839$	4.00000			0.138095			0.0690477	+	0.997613i	$0.478004\pi$
$840$		0			0
$841$	−4.00000			−0.137931
$842$		0			0
$843$	5.50000	+	9.52628i	0.189430	+	0.328102i
$844$		0			0
$845$	−18.0000	+	31.1769i	−0.619219	+	1.07252i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−15.5000	+	26.8468i	−0.531959	+	0.921379i
$850$		0			0
$851$	−16.0000	−	27.7128i	−0.548473	−	0.949983i
$852$		0			0
$853$	−38.0000			−1.30110			−0.650548	−	0.759465i	$-0.725461\pi$
$853$	−38.0000			−1.30110			−0.650548	+	0.759465i	$0.725461\pi$
$854$		0			0
$855$	−4.00000			−0.136797
$856$		0			0
$857$	−13.0000	−	22.5167i	−0.444072	−	0.769154i	0.553915	−	0.832573i	$-0.313133\pi$
$857$	−13.0000	−	22.5167i	−0.444072	−	0.769154i	−0.997987	+	0.0634184i	$0.979800\pi$
$858$		0			0
$859$	−22.0000	+	38.1051i	−0.750630	+	1.30013i	0.196887	+	0.980426i	$0.436917\pi$
$859$	−22.0000	+	38.1051i	−0.750630	+	1.30013i	−0.947518	+	0.319704i	$0.896417\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−3.00000	+	5.19615i	−0.102121	+	0.176879i	−0.912558	−	0.408946i	$-0.865896\pi$
$863$	−3.00000	+	5.19615i	−0.102121	+	0.176879i	0.810437	+	0.585826i	$0.199230\pi$
$864$		0			0
$865$	4.50000	+	7.79423i	0.153005	+	0.265012i
$866$		0			0
$867$	8.00000			0.271694
$868$		0			0
$869$	35.0000			1.18729
$870$		0			0
$871$	−7.00000	−	12.1244i	−0.237186	−	0.410818i
$872$		0			0
$873$	−17.0000	+	29.4449i	−0.575363	+	0.996558i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−3.00000	+	5.19615i	−0.101303	+	0.175462i	−0.912222	−	0.409697i	$-0.865634\pi$
$877$	−3.00000	+	5.19615i	−0.101303	+	0.175462i	0.810919	+	0.585159i	$0.198968\pi$
$878$		0			0
$879$	−2.50000	−	4.33013i	−0.0843229	−	0.146052i
$880$		0			0
$881$	32.0000			1.07811			0.539054	−	0.842271i	$-0.318782\pi$
$881$	32.0000			1.07811			0.539054	+	0.842271i	$0.318782\pi$
$882$		0			0
$883$	−36.0000			−1.21150			−0.605748	−	0.795656i	$-0.707126\pi$
$883$	−36.0000			−1.21150			−0.605748	+	0.795656i	$0.707126\pi$
$884$		0			0
$885$	5.00000	+	8.66025i	0.168073	+	0.291111i
$886$		0			0
$887$	−24.0000	+	41.5692i	−0.805841	+	1.39576i	0.109881	+	0.993945i	$0.464953\pi$
$887$	−24.0000	+	41.5692i	−0.805841	+	1.39576i	−0.915722	+	0.401813i	$0.868380\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	2.50000	−	4.33013i	0.0837532	−	0.145065i
$892$		0			0
$893$	−7.00000	−	12.1244i	−0.234246	−	0.405726i
$894$		0			0
$895$	12.0000			0.401116
$896$		0			0
$897$	56.0000			1.86979
$898$		0			0
$899$	25.0000	+	43.3013i	0.833797	+	1.44418i
$900$		0			0
$901$	15.0000	−	25.9808i	0.499722	−	0.865545i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	5.00000	−	8.66025i	0.166206	−	0.287877i
$906$		0			0
$907$	−14.0000	−	24.2487i	−0.464862	−	0.805165i	0.534333	−	0.845274i	$-0.320563\pi$
$907$	−14.0000	−	24.2487i	−0.464862	−	0.805165i	−0.999195	+	0.0401089i	$0.987230\pi$
$908$		0			0
$909$	20.0000			0.663358
$910$		0			0
$911$	−48.0000			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$912$		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
$919$	3.50000	−	6.06218i	0.115454	−	0.199973i	−0.802507	−	0.596643i	$-0.796501\pi$
$919$	3.50000	−	6.06218i	0.115454	−	0.199973i	0.917961	+	0.396670i	$0.129834\pi$
$920$		0			0
$921$	−3.50000	−	6.06218i	−0.115329	−	0.199756i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	4.00000			0.131519
$926$		0			0
$927$	−1.00000	−	1.73205i	−0.0328443	−	0.0568880i
$928$		0			0
$929$	−3.00000	+	5.19615i	−0.0984268	+	0.170480i	−0.911034	−	0.412332i	$-0.864714\pi$
$929$	−3.00000	+	5.19615i	−0.0984268	+	0.170480i	0.812607	+	0.582812i	$0.198048\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	15.0000	−	25.9808i	0.491078	−	0.850572i
$934$		0			0
$935$	7.50000	+	12.9904i	0.245276	+	0.424831i
$936$		0			0
$937$	3.00000			0.0980057			0.0490029	−	0.998799i	$-0.484396\pi$
$937$	3.00000			0.0980057			0.0490029	+	0.998799i	$0.484396\pi$
$938$		0			0
$939$	−5.00000			−0.163169
$940$		0			0
$941$	−22.0000	−	38.1051i	−0.717180	−	1.24219i	−0.962113	−	0.272651i	$-0.912099\pi$
$941$	−22.0000	−	38.1051i	−0.717180	−	1.24219i	0.244933	−	0.969540i	$-0.421234\pi$
$942$		0			0
$943$	−24.0000	+	41.5692i	−0.781548	+	1.35368i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.00000	−	1.73205i	0.0324956	−	0.0562841i	−0.849320	−	0.527878i	$-0.822988\pi$
$947$	1.00000	−	1.73205i	0.0324956	−	0.0562841i	0.881816	+	0.471594i	$0.156321\pi$
$948$		0			0
$949$	7.00000	+	12.1244i	0.227230	+	0.393573i
$950$		0			0
$951$	−26.0000			−0.843108
$952$		0			0
$953$	−42.0000			−1.36051			−0.680257	−	0.732974i	$-0.738132\pi$
$953$	−42.0000			−1.36051			−0.680257	+	0.732974i	$0.738132\pi$
$954$		0			0
$955$	8.50000	+	14.7224i	0.275054	+	0.476407i
$956$		0			0
$957$	12.5000	−	21.6506i	0.404068	−	0.699866i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−34.5000	+	59.7558i	−1.11290	+	1.92760i
$962$		0			0
$963$	2.00000	+	3.46410i	0.0644491	+	0.111629i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−50.0000			−1.60789			−0.803946	−	0.594703i	$-0.797270\pi$
$967$	−50.0000			−1.60789			−0.803946	+	0.594703i	$0.797270\pi$
$968$		0			0
$969$	3.00000	+	5.19615i	0.0963739	+	0.166924i
$970$		0			0
$971$	3.00000	−	5.19615i	0.0962746	−	0.166752i	−0.813865	−	0.581054i	$-0.802641\pi$
$971$	3.00000	−	5.19615i	0.0962746	−	0.166752i	0.910140	+	0.414301i	$0.135974\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−3.50000	+	6.06218i	−0.112090	+	0.194145i
$976$		0			0
$977$	21.0000	+	36.3731i	0.671850	+	1.16368i	0.977379	+	0.211495i	$0.0678332\pi$
$977$	21.0000	+	36.3731i	0.671850	+	1.16368i	−0.305530	+	0.952183i	$0.598833\pi$
$978$		0			0
$979$	−40.0000			−1.27841
$980$		0			0
$981$	−26.0000			−0.830116
$982$		0			0
$983$	1.50000	+	2.59808i	0.0478426	+	0.0828658i	0.888955	−	0.457995i	$-0.151432\pi$
$983$	1.50000	+	2.59808i	0.0478426	+	0.0828658i	−0.841112	+	0.540860i	$0.818099\pi$
$984$		0			0
$985$	−9.00000	+	15.5885i	−0.286764	+	0.496690i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−8.00000	+	13.8564i	−0.254385	+	0.440608i
$990$		0			0
$991$	6.00000	+	10.3923i	0.190596	+	0.330122i	0.945448	−	0.325773i	$-0.105625\pi$
$991$	6.00000	+	10.3923i	0.190596	+	0.330122i	−0.754852	+	0.655895i	$0.772291\pi$
$992$		0			0
$993$	−28.0000			−0.888553
$994$		0			0
$995$	−10.0000			−0.317021
$996$		0			0
$997$	−19.5000	−	33.7750i	−0.617571	−	1.06966i	−0.989928	−	0.141575i	$-0.954783\pi$
$997$	−19.5000	−	33.7750i	−0.617571	−	1.06966i	0.372356	−	0.928090i	$-0.378550\pi$
$998$		0			0
$999$	−10.0000	+	17.3205i	−0.316386	+	0.547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1960.2.q.l.961.1		2
7.2	even	3		1960.2.a.d.1.1	✓	1
7.3	odd	6		1960.2.q.g.361.1		2
7.4	even	3	inner	1960.2.q.l.361.1		2
7.5	odd	6		1960.2.a.h.1.1	yes	1
7.6	odd	2		1960.2.q.g.961.1		2
28.19	even	6		3920.2.a.o.1.1		1
28.23	odd	6		3920.2.a.bb.1.1		1
35.9	even	6		9800.2.a.y.1.1		1
35.19	odd	6		9800.2.a.m.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1960.2.a.d.1.1	✓	1	7.2	even	3
1960.2.a.h.1.1	yes	1	7.5	odd	6
1960.2.q.g.361.1		2	7.3	odd	6
1960.2.q.g.961.1		2	7.6	odd	2
1960.2.q.l.361.1		2	7.4	even	3	inner
1960.2.q.l.961.1		2	1.1	even	1	trivial
3920.2.a.o.1.1		1	28.19	even	6
3920.2.a.bb.1.1		1	28.23	odd	6
9800.2.a.m.1.1		1	35.19	odd	6
9800.2.a.y.1.1		1	35.9	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(1.00000 - 1.73205i) q^{9} +(2.50000 + 4.33013i) q^{11} -7.00000 q^{13} -1.00000 q^{15} +(-1.50000 - 2.59808i) q^{17} +(-1.00000 + 1.73205i) q^{19} +(-4.00000 + 6.92820i) q^{23} +(-0.500000 - 0.866025i) q^{25} +5.00000 q^{27} -5.00000 q^{29} +(-5.00000 - 8.66025i) q^{31} +(-2.50000 + 4.33013i) q^{33} +(-2.00000 + 3.46410i) q^{37} +(-3.50000 - 6.06218i) q^{39} +6.00000 q^{41} +2.00000 q^{43} +(1.00000 + 1.73205i) q^{45} +(-3.50000 + 6.06218i) q^{47} +(1.50000 - 2.59808i) q^{51} +(5.00000 + 8.66025i) q^{53} -5.00000 q^{55} -2.00000 q^{57} +(-5.00000 - 8.66025i) q^{59} +(-6.00000 + 10.3923i) q^{61} +(3.50000 - 6.06218i) q^{65} +(1.00000 + 1.73205i) q^{67} -8.00000 q^{69} +(-1.00000 - 1.73205i) q^{73} +(0.500000 - 0.866025i) q^{75} +(3.50000 - 6.06218i) q^{79} +(-0.500000 - 0.866025i) q^{81} -4.00000 q^{83} +3.00000 q^{85} +(-2.50000 - 4.33013i) q^{87} +(-4.00000 + 6.92820i) q^{89} +(5.00000 - 8.66025i) q^{93} +(-1.00000 - 1.73205i) q^{95} -17.0000 q^{97} +10.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{3} - q^{5} + 2 q^{9}+O(q^{10}) \) 2 * q + q^3 - q^5 + 2 * q^9	\( 2 q + q^{3} - q^{5} + 2 q^{9} + 5 q^{11} - 14 q^{13} - 2 q^{15} - 3 q^{17} - 2 q^{19} - 8 q^{23} - q^{25} + 10 q^{27} - 10 q^{29} - 10 q^{31} - 5 q^{33} - 4 q^{37} - 7 q^{39} + 12 q^{41} + 4 q^{43} + 2 q^{45} - 7 q^{47} + 3 q^{51} + 10 q^{53} - 10 q^{55} - 4 q^{57} - 10 q^{59} - 12 q^{61} + 7 q^{65} + 2 q^{67} - 16 q^{69} - 2 q^{73} + q^{75} + 7 q^{79} - q^{81} - 8 q^{83} + 6 q^{85} - 5 q^{87} - 8 q^{89} + 10 q^{93} - 2 q^{95} - 34 q^{97} + 20 q^{99}+O(q^{100}) \) 2 * q + q^3 - q^5 + 2 * q^9 + 5 * q^11 - 14 * q^13 - 2 * q^15 - 3 * q^17 - 2 * q^19 - 8 * q^23 - q^25 + 10 * q^27 - 10 * q^29 - 10 * q^31 - 5 * q^33 - 4 * q^37 - 7 * q^39 + 12 * q^41 + 4 * q^43 + 2 * q^45 - 7 * q^47 + 3 * q^51 + 10 * q^53 - 10 * q^55 - 4 * q^57 - 10 * q^59 - 12 * q^61 + 7 * q^65 + 2 * q^67 - 16 * q^69 - 2 * q^73 + q^75 + 7 * q^79 - q^81 - 8 * q^83 + 6 * q^85 - 5 * q^87 - 8 * q^89 + 10 * q^93 - 2 * q^95 - 34 * q^97 + 20 * q^99

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