LMFDB - Embedded newform 1960.2.q.w.361.2

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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.11337408.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 18x^{4} + 81x^{2} + 12 $ x^6 + 18x^4 + 81x^2 + 12
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.2
Root			$-3.17656i$ of defining polynomial
Character	$\chi$	$=$	1960.361
Dual form			1960.2.q.w.961.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.352860 - 0.611171i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.25098 + 2.16676i) q^{9} +O(q^{10})$	\(q+(0.352860 - 0.611171i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.25098 + 2.16676i) q^{9} +(2.25098 - 3.89881i) q^{11} -5.09052 q^{13} +0.705720 q^{15} +(1.00000 - 1.73205i) q^{17} +(-1.54526 - 2.67647i) q^{19} +(-2.89812 - 5.01969i) q^{23} +(-0.500000 + 0.866025i) q^{25} +3.88284 q^{27} +9.50196 q^{29} +(2.70572 - 4.68644i) q^{31} +(-1.58856 - 2.75147i) q^{33} +(-3.54526 - 6.14057i) q^{37} +(-1.79624 + 3.11118i) q^{39} +6.59248 q^{41} +4.70572 q^{43} +(-1.25098 + 2.16676i) q^{45} +(5.04722 + 8.74204i) q^{47} +(-0.705720 - 1.22234i) q^{51} +(-4.95670 + 8.58526i) q^{53} +4.50196 q^{55} -2.18104 q^{57} +(4.00000 - 6.92820i) q^{59} +(-4.45670 - 7.71923i) q^{61} +(-2.54526 - 4.40852i) q^{65} +(0.0585795 - 0.101463i) q^{67} -4.09052 q^{69} +(4.09052 - 7.08499i) q^{73} +(0.352860 + 0.611171i) q^{75} +(7.09052 + 12.2811i) q^{79} +(-2.38284 + 4.12720i) q^{81} +10.7057 q^{83} +2.00000 q^{85} +(3.35286 - 5.80732i) q^{87} +(2.04526 + 3.54249i) q^{89} +(-1.90948 - 3.30732i) q^{93} +(1.54526 - 2.67647i) q^{95} +2.00000 q^{97} +11.2637 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{5} - 9 q^{9}+O(q^{10}) $ 6 * q + 3 * q^5 - 9 * q^9	$ 6 q + 3 q^{5} - 9 q^{9} - 3 q^{11} - 6 q^{13} + 6 q^{17} + 3 q^{19} - 3 q^{23} - 3 q^{25} + 36 q^{27} + 24 q^{29} + 12 q^{31} - 18 q^{33} - 9 q^{37} + 18 q^{39} - 18 q^{41} + 24 q^{43} + 9 q^{45} - 15 q^{47} - 9 q^{53} - 6 q^{55} + 36 q^{57} + 24 q^{59} - 6 q^{61} - 3 q^{65} - 6 q^{67} + 18 q^{79} - 27 q^{81} + 60 q^{83} + 12 q^{85} + 18 q^{87} - 36 q^{93} - 3 q^{95} + 12 q^{97} + 126 q^{99}+O(q^{100}) $ 6 * q + 3 * q^5 - 9 * q^9 - 3 * q^11 - 6 * q^13 + 6 * q^17 + 3 * q^19 - 3 * q^23 - 3 * q^25 + 36 * q^27 + 24 * q^29 + 12 * q^31 - 18 * q^33 - 9 * q^37 + 18 * q^39 - 18 * q^41 + 24 * q^43 + 9 * q^45 - 15 * q^47 - 9 * q^53 - 6 * q^55 + 36 * q^57 + 24 * q^59 - 6 * q^61 - 3 * q^65 - 6 * q^67 + 18 * q^79 - 27 * q^81 + 60 * q^83 + 12 * q^85 + 18 * q^87 - 36 * q^93 - 3 * q^95 + 12 * q^97 + 126 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$981$	$1081$	$1177$	$1471$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	0.352860	−	0.611171i	0.203724	−	0.352860i	−0.746002	−	0.665944i	$-0.768029\pi$
$3$	0.352860	−	0.611171i	0.203724	−	0.352860i	0.949725	+	0.313084i	$0.101362\pi$
$4$		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
$9$	1.25098	+	2.16676i	0.416993	+	0.722254i
$10$		0			0
$11$	2.25098	−	3.89881i	0.678696	−	1.17554i	−0.296678	−	0.954978i	$-0.595879\pi$
$11$	2.25098	−	3.89881i	0.678696	−	1.17554i	0.975374	−	0.220558i	$-0.0707879\pi$
$12$		0			0
$13$	−5.09052			−1.41186			−0.705928	−	0.708283i	$-0.749470\pi$
$13$	−5.09052			−1.41186			−0.705928	+	0.708283i	$0.749470\pi$
$14$		0			0
$15$	0.705720			0.182216
$16$		0			0
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	−0.718900	−	0.695113i	$-0.755354\pi$
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	0.961436	+	0.275029i	$0.0886875\pi$
$18$		0			0
$19$	−1.54526	−	2.67647i	−0.354507	−	0.614024i	0.632526	−	0.774539i	$-0.282018\pi$
$19$	−1.54526	−	2.67647i	−0.354507	−	0.614024i	−0.987033	+	0.160515i	$0.948685\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.89812	−	5.01969i	−0.604300	−	1.04668i	−0.992162	−	0.124960i	$-0.960120\pi$
$23$	−2.89812	−	5.01969i	−0.604300	−	1.04668i	0.387862	−	0.921717i	$-0.373214\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	3.88284			0.747253
$28$		0			0
$29$	9.50196			1.76447			0.882235	−	0.470810i	$-0.156038\pi$
$29$	9.50196			1.76447			0.882235	+	0.470810i	$0.156038\pi$
$30$		0			0
$31$	2.70572	−	4.68644i	0.485962	−	0.841710i	−0.513908	−	0.857845i	$-0.671803\pi$
$31$	2.70572	−	4.68644i	0.485962	−	0.841710i	0.999870	+	0.0161350i	$0.00513615\pi$
$32$		0			0
$33$	−1.58856	−	2.75147i	−0.276533	−	0.478969i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.54526	−	6.14057i	−0.582837	−	1.00950i	−0.995141	−	0.0984573i	$-0.968609\pi$
$37$	−3.54526	−	6.14057i	−0.582837	−	1.00950i	0.412304	−	0.911046i	$-0.364724\pi$
$38$		0			0
$39$	−1.79624	+	3.11118i	−0.287629	+	0.498187i
$40$		0			0
$41$	6.59248			1.02957			0.514786	−	0.857319i	$-0.327871\pi$
$41$	6.59248			1.02957			0.514786	+	0.857319i	$0.327871\pi$
$42$		0			0
$43$	4.70572			0.717616			0.358808	−	0.933411i	$-0.383183\pi$
$43$	4.70572			0.717616			0.358808	+	0.933411i	$0.383183\pi$
$44$		0			0
$45$	−1.25098	+	2.16676i	−0.186485	+	0.323002i
$46$		0			0
$47$	5.04722	+	8.74204i	0.736213	+	1.27516i	0.954189	+	0.299204i	$0.0967210\pi$
$47$	5.04722	+	8.74204i	0.736213	+	1.27516i	−0.217977	+	0.975954i	$0.569946\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−0.705720	−	1.22234i	−0.0988205	−	0.171162i
$52$		0			0
$53$	−4.95670	+	8.58526i	−0.680855	+	1.17928i	0.293865	+	0.955847i	$0.405058\pi$
$53$	−4.95670	+	8.58526i	−0.680855	+	1.17928i	−0.974720	+	0.223429i	$0.928275\pi$
$54$		0			0
$55$	4.50196			0.607044
$56$		0			0
$57$	−2.18104			−0.288886
$58$		0			0
$59$	4.00000	−	6.92820i	0.520756	−	0.901975i	−0.478953	−	0.877841i	$-0.658984\pi$
$59$	4.00000	−	6.92820i	0.520756	−	0.901975i	0.999709	−	0.0241347i	$-0.00768307\pi$
$60$		0			0
$61$	−4.45670	−	7.71923i	−0.570622	−	0.988346i	−0.996502	−	0.0835666i	$-0.973369\pi$
$61$	−4.45670	−	7.71923i	−0.570622	−	0.988346i	0.425880	−	0.904780i	$-0.359964\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.54526	−	4.40852i	−0.315701	−	0.546810i
$66$		0			0
$67$	0.0585795	−	0.101463i	0.00715662	−	0.0123956i	−0.862425	−	0.506185i	$-0.831055\pi$
$67$	0.0585795	−	0.101463i	0.00715662	−	0.0123956i	0.869582	+	0.493789i	$0.164389\pi$
$68$		0			0
$69$	−4.09052			−0.492441
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	4.09052	−	7.08499i	0.478759	−	0.829235i	−0.520944	−	0.853591i	$-0.674420\pi$
$73$	4.09052	−	7.08499i	0.478759	−	0.829235i	0.999703	+	0.0243555i	$0.00775336\pi$
$74$		0			0
$75$	0.352860	+	0.611171i	0.0407447	+	0.0705720i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	7.09052	+	12.2811i	0.797746	+	1.38174i	0.921081	+	0.389371i	$0.127308\pi$
$79$	7.09052	+	12.2811i	0.797746	+	1.38174i	−0.123335	+	0.992365i	$0.539359\pi$
$80$		0			0
$81$	−2.38284	+	4.12720i	−0.264760	+	0.458578i
$82$		0			0
$83$	10.7057			1.17511			0.587553	−	0.809186i	$-0.300091\pi$
$83$	10.7057			1.17511			0.587553	+	0.809186i	$0.300091\pi$
$84$		0			0
$85$	2.00000			0.216930
$86$		0			0
$87$	3.35286	−	5.80732i	0.359464	−	0.622610i
$88$		0			0
$89$	2.04526	+	3.54249i	0.216797	+	0.375504i	0.953827	−	0.300356i	$-0.0971056\pi$
$89$	2.04526	+	3.54249i	0.216797	+	0.375504i	−0.737030	+	0.675860i	$0.763772\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−1.90948	−	3.30732i	−0.198004	−	0.342953i
$94$		0			0
$95$	1.54526	−	2.67647i	0.158540	−	0.274600i
$96$		0			0
$97$	2.00000			0.203069			0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$		0			0
$99$	11.2637			1.13205
$100$		0			0
$101$	−1.66046	+	2.87600i	−0.165222	+	0.286173i	−0.936734	−	0.350042i	$-0.886167\pi$
$101$	−1.66046	+	2.87600i	−0.165222	+	0.286173i	0.771512	+	0.636215i	$0.219501\pi$
$102$		0			0
$103$	−5.44338	−	9.42821i	−0.536352	−	0.928989i	−0.999097	−	0.0424975i	$-0.986469\pi$
$103$	−5.44338	−	9.42821i	−0.536352	−	0.928989i	0.462744	−	0.886492i	$-0.346865\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.94142	−	3.36264i	−0.187684	−	0.325079i	0.756794	−	0.653654i	$-0.226765\pi$
$107$	−1.94142	−	3.36264i	−0.187684	−	0.325079i	−0.944478	+	0.328575i	$0.893431\pi$
$108$		0			0
$109$	5.13578	−	8.89543i	0.491919	−	0.852028i	−0.508038	−	0.861335i	$-0.669629\pi$
$109$	5.13578	−	8.89543i	0.491919	−	0.852028i	0.999957	+	0.00930661i	$0.00296243\pi$
$110$		0			0
$111$	−5.00392			−0.474951
$112$		0			0
$113$	2.82288			0.265554			0.132777	−	0.991146i	$-0.457611\pi$
$113$	2.82288			0.265554			0.132777	+	0.991146i	$0.457611\pi$
$114$		0			0
$115$	2.89812	−	5.01969i	0.270251	−	0.468089i
$116$		0			0
$117$	−6.36814	−	11.0299i	−0.588735	−	1.01972i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−4.63382	−	8.02601i	−0.421256	−	0.729638i
$122$		0			0
$123$	2.32622	−	4.02913i	0.209748	−	0.363295i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−1.73236			−0.153722			−0.0768610	−	0.997042i	$-0.524490\pi$
$127$	−1.73236			−0.153722			−0.0768610	+	0.997042i	$0.524490\pi$
$128$		0			0
$129$	1.66046	−	2.87600i	0.146195	−	0.253218i
$130$		0			0
$131$	−6.36814	−	11.0299i	−0.556387	−	0.963690i	−0.997794	−	0.0663835i	$-0.978854\pi$
$131$	−6.36814	−	11.0299i	−0.556387	−	0.963690i	0.441407	−	0.897307i	$-0.354479\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	1.94142	+	3.36264i	0.167091	+	0.289410i
$136$		0			0
$137$	−2.00000	+	3.46410i	−0.170872	+	0.295958i	−0.938725	−	0.344668i	$-0.887992\pi$
$137$	−2.00000	+	3.46410i	−0.170872	+	0.295958i	0.767853	+	0.640626i	$0.221325\pi$
$138$		0			0
$139$	1.41144			0.119717			0.0598584	−	0.998207i	$-0.480935\pi$
$139$	1.41144			0.119717			0.0598584	+	0.998207i	$0.480935\pi$
$140$		0			0
$141$	7.12384			0.599936
$142$		0			0
$143$	−11.4587	+	19.8470i	−0.958221	+	1.65969i
$144$		0			0
$145$	4.75098	+	8.22894i	0.394547	+	0.683376i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−11.5472	−	20.0004i	−0.945985	−	1.63849i	−0.753767	−	0.657142i	$-0.771765\pi$
$149$	−11.5472	−	20.0004i	−0.945985	−	1.63849i	−0.192218	−	0.981352i	$-0.561568\pi$
$150$		0			0
$151$	0.203760	−	0.352922i	0.0165817	−	0.0287204i	−0.857615	−	0.514291i	$-0.828055\pi$
$151$	0.203760	−	0.352922i	0.0165817	−	0.0287204i	0.874197	+	0.485571i	$0.161388\pi$
$152$		0			0
$153$	5.00392			0.404543
$154$		0			0
$155$	5.41144			0.434657
$156$		0			0
$157$	−7.04722	+	12.2061i	−0.562429	+	0.974156i	0.434854	+	0.900501i	$0.356800\pi$
$157$	−7.04722	+	12.2061i	−0.562429	+	0.974156i	−0.997284	+	0.0736555i	$0.976533\pi$
$158$		0			0
$159$	3.49804	+	6.05878i	0.277413	+	0.480493i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	8.09052	+	14.0132i	0.633698	+	1.09760i	0.986789	+	0.162009i	$0.0517973\pi$
$163$	8.09052	+	14.0132i	0.633698	+	1.09760i	−0.353091	+	0.935589i	$0.614869\pi$
$164$		0			0
$165$	1.58856	−	2.75147i	0.123669	−	0.214201i
$166$		0			0
$167$	−7.79624			−0.603291			−0.301646	−	0.953420i	$-0.597536\pi$
$167$	−7.79624			−0.603291			−0.301646	+	0.953420i	$0.597536\pi$
$168$		0			0
$169$	12.9134			0.993338
$170$		0			0
$171$	3.86618	−	6.69642i	0.295654	−	0.512088i
$172$		0			0
$173$	−4.45474	−	7.71584i	−0.338688	−	0.586624i	0.645499	−	0.763762i	$-0.276650\pi$
$173$	−4.45474	−	7.71584i	−0.338688	−	0.586624i	−0.984186	+	0.177137i	$0.943316\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−2.82288	−	4.88937i	−0.212181	−	0.367507i
$178$		0			0
$179$	−0.839541	+	1.45413i	−0.0627502	+	0.108687i	−0.895694	−	0.444671i	$-0.853320\pi$
$179$	−0.839541	+	1.45413i	−0.0627502	+	0.108687i	0.832944	+	0.553358i	$0.186654\pi$
$180$		0			0
$181$	−12.5059			−0.929555			−0.464777	−	0.885428i	$-0.653866\pi$
$181$	−12.5059			−0.929555			−0.464777	+	0.885428i	$0.653866\pi$
$182$		0			0
$183$	−6.29036			−0.464997
$184$		0			0
$185$	3.54526	−	6.14057i	0.260653	−	0.451464i
$186$		0			0
$187$	−4.50196	−	7.79762i	−0.329216	−	0.570219i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−3.29428	−	5.70586i	−0.238366	−	0.412862i	0.721880	−	0.692019i	$-0.243278\pi$
$191$	−3.29428	−	5.70586i	−0.238366	−	0.412862i	−0.960245	+	0.279157i	$0.909945\pi$
$192$		0			0
$193$	−8.91340	+	15.4385i	−0.641601	+	1.11128i	0.343475	+	0.939162i	$0.388396\pi$
$193$	−8.91340	+	15.4385i	−0.641601	+	1.11128i	−0.985075	+	0.172123i	$0.944937\pi$
$194$		0			0
$195$	−3.59248			−0.257263
$196$		0			0
$197$	5.09052			0.362685			0.181342	−	0.983420i	$-0.441956\pi$
$197$	5.09052			0.362685			0.181342	+	0.983420i	$0.441956\pi$
$198$		0			0
$199$	12.1810	−	21.0982i	0.863491	−	1.49561i	−0.00504654	−	0.999987i	$-0.501606\pi$
$199$	12.1810	−	21.0982i	0.863491	−	1.49561i	0.868538	−	0.495623i	$-0.165060\pi$
$200$		0			0
$201$	−0.0413407	−	0.0716041i	−0.00291595	−	0.00505057i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	3.29624	+	5.70926i	0.230219	+	0.398752i
$206$		0			0
$207$	7.25098	−	12.5591i	0.503978	−	0.872915i
$208$		0			0
$209$	−13.9134			−0.962410
$210$		0			0
$211$	−8.26764			−0.569168			−0.284584	−	0.958651i	$-0.591855\pi$
$211$	−8.26764			−0.569168			−0.284584	+	0.958651i	$0.591855\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	2.35286	+	4.07527i	0.160464	+	0.277931i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−2.88676	−	5.00002i	−0.195069	−	0.337870i
$220$		0			0
$221$	−5.09052	+	8.81704i	−0.342425	+	0.593098i
$222$		0			0
$223$	17.8268			1.19377			0.596885	−	0.802327i	$-0.296405\pi$
$223$	17.8268			1.19377			0.596885	+	0.802327i	$0.296405\pi$
$224$		0			0
$225$	−2.50196			−0.166797
$226$		0			0
$227$	2.67908	−	4.64030i	0.177817	−	0.307988i	−0.763316	−	0.646026i	$-0.776430\pi$
$227$	2.67908	−	4.64030i	0.177817	−	0.307988i	0.941133	+	0.338038i	$0.109763\pi$
$228$		0			0
$229$	12.0905	+	20.9414i	0.798964	+	1.38385i	0.920291	+	0.391234i	$0.127952\pi$
$229$	12.0905	+	20.9414i	0.798964	+	1.38385i	−0.121327	+	0.992613i	$0.538715\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−9.00000	−	15.5885i	−0.589610	−	1.02123i	−0.994283	−	0.106773i	$-0.965948\pi$
$233$	−9.00000	−	15.5885i	−0.589610	−	1.02123i	0.404674	−	0.914461i	$-0.367385\pi$
$234$		0			0
$235$	−5.04722	+	8.74204i	−0.329244	+	0.570268i
$236$		0			0
$237$	10.0078			0.650079
$238$		0			0
$239$	−12.7696			−0.825997			−0.412998	−	0.910732i	$-0.635519\pi$
$239$	−12.7696			−0.825997			−0.412998	+	0.910732i	$0.635519\pi$
$240$		0			0
$241$	−11.0472	+	19.1343i	−0.711614	+	1.23255i	0.252637	+	0.967561i	$0.418702\pi$
$241$	−11.0472	+	19.1343i	−0.711614	+	1.23255i	−0.964251	+	0.264990i	$0.914631\pi$
$242$		0			0
$243$	7.50588	+	13.0006i	0.481502	+	0.833987i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	7.86618	+	13.6246i	0.500513	+	0.866914i
$248$		0			0
$249$	3.77762	−	6.54303i	0.239397	−	0.414647i
$250$		0			0
$251$	13.5059			0.852484			0.426242	−	0.904609i	$-0.359837\pi$
$251$	13.5059			0.852484			0.426242	+	0.904609i	$0.359837\pi$
$252$		0			0
$253$	−26.0944			−1.64054
$254$		0			0
$255$	0.705720	−	1.22234i	0.0441939	−	0.0765460i
$256$		0			0
$257$	−8.18104	−	14.1700i	−0.510319	−	0.883899i	−0.999929	−	0.0119570i	$-0.996194\pi$
$257$	−8.18104	−	14.1700i	−0.510319	−	0.883899i	0.489609	−	0.871942i	$-0.337139\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	11.8868	+	20.5885i	0.735772	+	1.27439i
$262$		0			0
$263$	−4.55662	+	7.89230i	−0.280973	+	0.486660i	−0.971625	−	0.236528i	$-0.923991\pi$
$263$	−4.55662	+	7.89230i	−0.280973	+	0.486660i	0.690651	+	0.723188i	$0.257324\pi$
$264$		0			0
$265$	−9.91340			−0.608975
$266$		0			0
$267$	2.88676			0.176667
$268$		0			0
$269$	4.45670	−	7.71923i	0.271730	−	0.470650i	−0.697575	−	0.716512i	$-0.745738\pi$
$269$	4.45670	−	7.71923i	0.271730	−	0.470650i	0.969305	+	0.245862i	$0.0790710\pi$
$270$		0			0
$271$	8.18104	+	14.1700i	0.496963	+	0.860765i	0.999994	−	0.00350346i	$-0.00111519\pi$
$271$	8.18104	+	14.1700i	0.496963	+	0.860765i	−0.503031	+	0.864268i	$0.667782\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.25098	+	3.89881i	0.135739	+	0.235107i
$276$		0			0
$277$	−5.58856	+	9.67967i	−0.335784	+	0.581595i	−0.983635	−	0.180172i	$-0.942335\pi$
$277$	−5.58856	+	9.67967i	−0.335784	+	0.581595i	0.647851	+	0.761767i	$0.275668\pi$
$278$		0			0
$279$	13.5392			0.810571
$280$		0			0
$281$	−28.2755			−1.68677			−0.843387	−	0.537307i	$-0.819442\pi$
$281$	−28.2755			−1.68677			−0.843387	+	0.537307i	$0.819442\pi$
$282$		0			0
$283$	−6.41144	+	11.1049i	−0.381121	+	0.660120i	−0.991223	−	0.132203i	$-0.957795\pi$
$283$	−6.41144	+	11.1049i	−0.381121	+	0.660120i	0.610102	+	0.792323i	$0.291128\pi$
$284$		0			0
$285$	−1.09052	−	1.88884i	−0.0645969	−	0.111885i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$		0			0
$291$	0.705720	−	1.22234i	0.0413700	−	0.0716550i
$292$		0			0
$293$	−8.90948			−0.520497			−0.260249	−	0.965542i	$-0.583805\pi$
$293$	−8.90948			−0.520497			−0.260249	+	0.965542i	$0.583805\pi$
$294$		0			0
$295$	8.00000			0.465778
$296$		0			0
$297$	8.74020	−	15.1385i	0.507158	−	0.878423i
$298$		0			0
$299$	14.7529	+	25.5528i	0.853185	+	1.47776i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	1.17182	+	2.02965i	0.0673192	+	0.116600i
$304$		0			0
$305$	4.45670	−	7.71923i	0.255190	−	0.442002i
$306$		0			0
$307$	9.12108			0.520567			0.260284	−	0.965532i	$-0.416184\pi$
$307$	9.12108			0.520567			0.260284	+	0.965532i	$0.416184\pi$
$308$		0			0
$309$	−7.68300			−0.437071
$310$		0			0
$311$	−6.58856	+	11.4117i	−0.373603	+	0.647099i	−0.990117	−	0.140245i	$-0.955211\pi$
$311$	−6.58856	+	11.4117i	−0.373603	+	0.647099i	0.616514	+	0.787344i	$0.288544\pi$
$312$		0			0
$313$	−8.76960	−	15.1894i	−0.495687	−	0.858555i	0.504300	−	0.863528i	$-0.331750\pi$
$313$	−8.76960	−	15.1894i	−0.495687	−	0.858555i	−0.999988	+	0.00497286i	$0.998417\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.59248	+	11.4185i	0.370271	+	0.641327i	0.989607	−	0.143798i	$-0.0459316\pi$
$317$	6.59248	+	11.4185i	0.370271	+	0.641327i	−0.619336	+	0.785126i	$0.712598\pi$
$318$		0			0
$319$	21.3887	−	37.0464i	1.19754	−	2.07420i
$320$		0			0
$321$	−2.74020			−0.152943
$322$		0			0
$323$	−6.18104			−0.343922
$324$		0			0
$325$	2.54526	−	4.40852i	0.141186	−	0.244541i
$326$		0			0
$327$	−3.62442	−	6.27768i	−0.200431	−	0.347157i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−4.25098	−	7.36291i	−0.233655	−	0.404702i	0.725226	−	0.688511i	$-0.241735\pi$
$331$	−4.25098	−	7.36291i	−0.233655	−	0.404702i	−0.958881	+	0.283809i	$0.908402\pi$
$332$		0			0
$333$	8.87010	−	15.3635i	0.486078	−	0.841913i
$334$		0			0
$335$	0.117159			0.00640108
$336$		0			0
$337$	28.1889			1.53555			0.767773	−	0.640722i	$-0.221365\pi$
$337$	28.1889			1.53555			0.767773	+	0.640722i	$0.221365\pi$
$338$		0			0
$339$	0.996080	−	1.72526i	0.0540997	−	0.0937034i
$340$		0			0
$341$	−12.1810	−	21.0982i	−0.659640	−	1.14253i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−2.04526	−	3.54249i	−0.110113	−	0.190722i
$346$		0			0
$347$	−1.35286	+	2.34322i	−0.0726253	+	0.125791i	−0.900051	−	0.435784i	$-0.856471\pi$
$347$	−1.35286	+	2.34322i	−0.0726253	+	0.125791i	0.827426	+	0.561575i	$0.189804\pi$
$348$		0			0
$349$	13.6830			0.732434			0.366217	−	0.930529i	$-0.380653\pi$
$349$	13.6830			0.732434			0.366217	+	0.930529i	$0.380653\pi$
$350$		0			0
$351$	−19.7657			−1.05501
$352$		0			0
$353$	−10.1810	+	17.6341i	−0.541882	+	0.938567i	0.456914	+	0.889511i	$0.348955\pi$
$353$	−10.1810	+	17.6341i	−0.541882	+	0.938567i	−0.998796	+	0.0490565i	$0.984379\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	9.20768	+	15.9482i	0.485963	+	0.841712i	0.999870	−	0.0161337i	$-0.00513574\pi$
$359$	9.20768	+	15.9482i	0.485963	+	0.841712i	−0.513907	+	0.857846i	$0.671802\pi$
$360$		0			0
$361$	4.72434	−	8.18280i	0.248650	−	0.430674i
$362$		0			0
$363$	−6.54036			−0.343280
$364$		0			0
$365$	8.18104			0.428215
$366$		0			0
$367$	−12.8115	+	22.1902i	−0.668756	+	1.15832i	0.309496	+	0.950901i	$0.399840\pi$
$367$	−12.8115	+	22.1902i	−0.668756	+	1.15832i	−0.978252	+	0.207419i	$0.933494\pi$
$368$		0			0
$369$	8.24706	+	14.2843i	0.429325	+	0.743612i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−14.0944	−	24.4123i	−0.729782	−	1.26402i	−0.956975	−	0.290170i	$-0.906288\pi$
$373$	−14.0944	−	24.4123i	−0.729782	−	1.26402i	0.227193	−	0.973850i	$-0.427045\pi$
$374$		0			0
$375$	−0.352860	+	0.611171i	−0.0182216	+	0.0315607i
$376$		0			0
$377$	−48.3699			−2.49118
$378$		0			0
$379$	21.7402			1.11672			0.558359	−	0.829599i	$-0.311431\pi$
$379$	21.7402			1.11672			0.558359	+	0.829599i	$0.311431\pi$
$380$		0			0
$381$	−0.611280	+	1.05877i	−0.0313168	+	0.0542423i
$382$		0			0
$383$	−10.1058	−	17.5038i	−0.516382	−	0.894400i	−0.999819	−	0.0190210i	$-0.993945\pi$
$383$	−10.1058	−	17.5038i	−0.516382	−	0.894400i	0.483437	−	0.875379i	$-0.339388\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	5.88676	+	10.1962i	0.299241	+	0.518300i
$388$		0			0
$389$	−6.91340	+	11.9744i	−0.350523	+	0.607124i	−0.986341	−	0.164715i	$-0.947330\pi$
$389$	−6.91340	+	11.9744i	−0.350523	+	0.607124i	0.635818	+	0.771839i	$0.280663\pi$
$390$		0			0
$391$	−11.5925			−0.586257
$392$		0			0
$393$	−8.98824			−0.453397
$394$		0			0
$395$	−7.09052	+	12.2811i	−0.356763	+	0.617931i
$396$		0			0
$397$	18.1850	+	31.4973i	0.912677	+	1.58080i	0.810267	+	0.586061i	$0.199322\pi$
$397$	18.1850	+	31.4973i	0.912677	+	1.58080i	0.102410	+	0.994742i	$0.467345\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	3.40948	+	5.90539i	0.170261	+	0.294901i	0.938511	−	0.345249i	$-0.112205\pi$
$401$	3.40948	+	5.90539i	0.170261	+	0.294901i	−0.768250	+	0.640150i	$0.778872\pi$
$402$		0			0
$403$	−13.7735	+	23.8564i	−0.686108	+	1.18837i
$404$		0			0
$405$	−4.76568			−0.236809
$406$		0			0
$407$	−31.9212			−1.58228
$408$		0			0
$409$	−8.93202	+	15.4707i	−0.441660	+	0.764978i	−0.997813	−	0.0661025i	$-0.978944\pi$
$409$	−8.93202	+	15.4707i	−0.441660	+	0.764978i	0.556153	+	0.831080i	$0.312277\pi$
$410$		0			0
$411$	1.41144	+	2.44468i	0.0696212	+	0.120587i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	5.35286	+	9.27143i	0.262762	+	0.455116i
$416$		0			0
$417$	0.498040	−	0.862631i	0.0243891	−	0.0422432i
$418$		0			0
$419$	−18.4487			−0.901277			−0.450639	−	0.892706i	$-0.648804\pi$
$419$	−18.4487			−0.901277			−0.450639	+	0.892706i	$0.648804\pi$
$420$		0			0
$421$	−10.7324			−0.523063			−0.261532	−	0.965195i	$-0.584228\pi$
$421$	−10.7324			−0.523063			−0.261532	+	0.965195i	$0.584228\pi$
$422$		0			0
$423$	−12.6279	+	21.8722i	−0.613992	+	1.06346i
$424$		0			0
$425$	1.00000	+	1.73205i	0.0485071	+	0.0840168i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	8.08660	+	14.0064i	0.390425	+	0.676236i
$430$		0			0
$431$	−3.29428	+	5.70586i	−0.158680	+	0.274842i	−0.934393	−	0.356244i	$-0.884057\pi$
$431$	−3.29428	+	5.70586i	−0.158680	+	0.274842i	0.775713	+	0.631086i	$0.217390\pi$
$432$		0			0
$433$	−5.17712			−0.248797			−0.124398	−	0.992232i	$-0.539700\pi$
$433$	−5.17712			−0.248797			−0.124398	+	0.992232i	$0.539700\pi$
$434$		0			0
$435$	6.70572			0.321515
$436$		0			0
$437$	−8.95670	+	15.5135i	−0.428457	+	0.742109i
$438$		0			0
$439$	15.5059	+	26.8570i	0.740055	+	1.28181i	0.952470	+	0.304634i	$0.0985340\pi$
$439$	15.5059	+	26.8570i	0.740055	+	1.28181i	−0.212414	+	0.977180i	$0.568133\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.43946	−	4.22527i	−0.115902	−	0.200749i	0.802238	−	0.597005i	$-0.203643\pi$
$443$	−2.43946	−	4.22527i	−0.115902	−	0.200749i	−0.918140	+	0.396256i	$0.870309\pi$
$444$		0			0
$445$	−2.04526	+	3.54249i	−0.0969546	+	0.167930i
$446$		0			0
$447$	−16.2982			−0.770878
$448$		0			0
$449$	27.7696			1.31053			0.655264	−	0.755400i	$-0.272557\pi$
$449$	27.7696			1.31053			0.655264	+	0.755400i	$0.272557\pi$
$450$		0			0
$451$	14.8395	−	25.7028i	0.698767	−	1.21030i
$452$		0			0
$453$	−0.143797	−	0.249064i	−0.00675619	−	0.0117021i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	12.5020	+	21.6540i	0.584817	+	1.01293i	0.994898	+	0.100884i	$0.0321670\pi$
$457$	12.5020	+	21.6540i	0.584817	+	1.01293i	−0.410081	+	0.912049i	$0.634500\pi$
$458$		0			0
$459$	3.88284	−	6.72528i	0.181236	−	0.313909i
$460$		0			0
$461$	4.00784			0.186664			0.0933318	−	0.995635i	$-0.470248\pi$
$461$	4.00784			0.186664			0.0933318	+	0.995635i	$0.470248\pi$
$462$		0			0
$463$	−36.8002			−1.71025			−0.855124	−	0.518423i	$-0.826519\pi$
$463$	−36.8002			−1.71025			−0.855124	+	0.518423i	$0.826519\pi$
$464$		0			0
$465$	1.90948	−	3.30732i	0.0885500	−	0.153373i
$466$		0			0
$467$	−11.7377	−	20.3302i	−0.543154	−	0.940771i	−0.998721	−	0.0505688i	$-0.983897\pi$
$467$	−11.7377	−	20.3302i	−0.543154	−	0.940771i	0.455566	−	0.890202i	$-0.349437\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	4.97336	+	8.61411i	0.229160	+	0.396917i
$472$		0			0
$473$	10.5925	−	18.3467i	0.487043	−	0.843583i
$474$		0			0
$475$	3.09052			0.141803
$476$		0			0
$477$	−24.8029			−1.13565
$478$		0			0
$479$	−18.8868	+	32.7128i	−0.862958	+	1.49469i	0.00610232	+	0.999981i	$0.498058\pi$
$479$	−18.8868	+	32.7128i	−0.862958	+	1.49469i	−0.869060	+	0.494706i	$0.835276\pi$
$480$		0			0
$481$	18.0472	+	31.2587i	0.822882	+	1.42527i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.00000	+	1.73205i	0.0454077	+	0.0786484i
$486$		0			0
$487$	3.08660	−	5.34615i	0.139867	−	0.242257i	−0.787579	−	0.616214i	$-0.788666\pi$
$487$	3.08660	−	5.34615i	0.139867	−	0.242257i	0.927446	+	0.373957i	$0.121999\pi$
$488$		0			0
$489$	11.4193			0.516398
$490$		0			0
$491$	39.7814			1.79531			0.897654	−	0.440701i	$-0.145270\pi$
$491$	39.7814			1.79531			0.897654	+	0.440701i	$0.145270\pi$
$492$		0			0
$493$	9.50196	−	16.4579i	0.427947	−	0.741226i
$494$		0			0
$495$	5.63186	+	9.75467i	0.253133	+	0.438440i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−1.88284	−	3.26118i	−0.0842875	−	0.145990i	0.820800	−	0.571216i	$-0.193528\pi$
$499$	−1.88284	−	3.26118i	−0.0842875	−	0.145990i	−0.905087	+	0.425226i	$0.860195\pi$
$500$		0			0
$501$	−2.75098	+	4.76484i	−0.122905	+	0.212877i
$502$		0			0
$503$	−18.7057			−0.834047			−0.417023	−	0.908896i	$-0.636927\pi$
$503$	−18.7057			−0.834047			−0.417023	+	0.908896i	$0.636927\pi$
$504$		0			0
$505$	−3.32092			−0.147779
$506$		0			0
$507$	4.55662	−	7.89230i	0.202367	−	0.350509i
$508$		0			0
$509$	6.16242	+	10.6736i	0.273144	+	0.473100i	0.969665	−	0.244437i	$-0.0786030\pi$
$509$	6.16242	+	10.6736i	0.273144	+	0.473100i	−0.696521	+	0.717537i	$0.745270\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−6.00000	−	10.3923i	−0.264906	−	0.458831i
$514$		0			0
$515$	5.44338	−	9.42821i	0.239864	−	0.415457i
$516$		0			0
$517$	45.4448			1.99866
$518$		0			0
$519$	−6.28759			−0.275995
$520$		0			0
$521$	−14.7796	+	25.5990i	−0.647505	+	1.12151i	0.336212	+	0.941786i	$0.390854\pi$
$521$	−14.7796	+	25.5990i	−0.647505	+	1.12151i	−0.983717	+	0.179725i	$0.942479\pi$
$522$		0			0
$523$	−21.5020	−	37.2425i	−0.940215	−	1.62850i	−0.765060	−	0.643959i	$-0.777291\pi$
$523$	−21.5020	−	37.2425i	−0.940215	−	1.62850i	−0.175155	−	0.984541i	$-0.556043\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−5.41144	−	9.37289i	−0.235726	−	0.408289i
$528$		0			0
$529$	−5.29820	+	9.17675i	−0.230357	+	0.398989i
$530$		0			0
$531$	20.0157			0.868606
$532$		0			0
$533$	−33.5592			−1.45361
$534$		0			0
$535$	1.94142	−	3.36264i	0.0839349	−	0.145380i
$536$		0			0
$537$	0.592480	+	1.02621i	0.0255674	+	0.0442841i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	2.48334	+	4.30127i	0.106767	+	0.184926i	0.914459	−	0.404679i	$-0.132617\pi$
$541$	2.48334	+	4.30127i	0.106767	+	0.184926i	−0.807692	+	0.589605i	$0.799283\pi$
$542$		0			0
$543$	−4.41282	+	7.64323i	−0.189372	+	0.328003i
$544$		0			0
$545$	10.2716			0.439985
$546$		0			0
$547$	−22.1250			−0.945997			−0.472998	−	0.881063i	$-0.656828\pi$
$547$	−22.1250			−0.945997			−0.472998	+	0.881063i	$0.656828\pi$
$548$		0			0
$549$	11.1505	−	19.3132i	0.475891	−	0.824267i
$550$		0			0
$551$	−14.6830	−	25.4317i	−0.625517	−	1.08343i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−2.50196	−	4.33352i	−0.106202	−	0.183948i
$556$		0			0
$557$	−2.77958	+	4.81437i	−0.117775	+	0.203991i	−0.918885	−	0.394524i	$-0.870909\pi$
$557$	−2.77958	+	4.81437i	−0.117775	+	0.203991i	0.801111	+	0.598516i	$0.204243\pi$
$558$		0			0
$559$	−23.9546			−1.01317
$560$		0			0
$561$	−6.35424			−0.268276
$562$		0			0
$563$	4.74158	−	8.21266i	0.199834	−	0.346122i	−0.748641	−	0.662976i	$-0.769293\pi$
$563$	4.74158	−	8.21266i	0.199834	−	0.346122i	0.948474	+	0.316854i	$0.102626\pi$
$564$		0			0
$565$	1.41144	+	2.44468i	0.0593797	+	0.102849i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	17.1417	+	29.6902i	0.718616	+	1.24468i	0.961548	+	0.274636i	$0.0885573\pi$
$569$	17.1417	+	29.6902i	0.718616	+	1.24468i	−0.242933	+	0.970043i	$0.578109\pi$
$570$		0			0
$571$	15.7735	−	27.3205i	0.660101	−	1.14333i	−0.320487	−	0.947253i	$-0.603847\pi$
$571$	15.7735	−	27.3205i	0.660101	−	1.14333i	0.980589	−	0.196076i	$-0.0628200\pi$
$572$		0			0
$573$	−4.64968			−0.194243
$574$		0			0
$575$	5.79624			0.241720
$576$		0			0
$577$	−5.32092	+	9.21610i	−0.221513	+	0.383671i	−0.955268	−	0.295743i	$-0.904433\pi$
$577$	−5.32092	+	9.21610i	−0.221513	+	0.383671i	0.733755	+	0.679414i	$0.237766\pi$
$578$		0			0
$579$	6.29036	+	10.8952i	0.261418	+	0.452790i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	22.3149	+	38.6505i	0.924187	+	1.60074i
$584$		0			0
$585$	6.36814	−	11.0299i	0.263290	−	0.456032i
$586$		0			0
$587$	−6.64184			−0.274138			−0.137069	−	0.990562i	$-0.543768\pi$
$587$	−6.64184			−0.274138			−0.137069	+	0.990562i	$0.543768\pi$
$588$		0			0
$589$	−16.7242			−0.689107
$590$		0			0
$591$	1.79624	−	3.11118i	0.0738874	−	0.127977i
$592$		0			0
$593$	6.76960	+	11.7253i	0.277994	+	0.481500i	0.970886	−	0.239541i	$-0.0769971\pi$
$593$	6.76960	+	11.7253i	0.277994	+	0.481500i	−0.692892	+	0.721041i	$0.743664\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−8.59640	−	14.8894i	−0.351827	−	0.609383i
$598$		0			0
$599$	−13.0905	+	22.6734i	−0.534864	+	0.926412i	0.464306	+	0.885675i	$0.346304\pi$
$599$	−13.0905	+	22.6734i	−0.534864	+	0.926412i	−0.999170	+	0.0407369i	$0.987029\pi$
$600$		0			0
$601$	36.0078			1.46879			0.734395	−	0.678722i	$-0.237466\pi$
$601$	36.0078			1.46879			0.734395	+	0.678722i	$0.237466\pi$
$602$		0			0
$603$	0.293127			0.0119371
$604$		0			0
$605$	4.63382	−	8.02601i	0.188392	−	0.326304i
$606$		0			0
$607$	11.8715	+	20.5620i	0.481849	+	0.834586i	0.999783	−	0.0208341i	$-0.00663219\pi$
$607$	11.8715	+	20.5620i	0.481849	+	0.834586i	−0.517934	+	0.855420i	$0.673299\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−25.6930	−	44.5015i	−1.03943	−	1.80034i
$612$		0			0
$613$	4.77958	−	8.27847i	0.193045	−	0.334364i	−0.753213	−	0.657777i	$-0.771497\pi$
$613$	4.77958	−	8.27847i	0.193045	−	0.334364i	0.946258	+	0.323413i	$0.104830\pi$
$614$		0			0
$615$	4.65244			0.187605
$616$		0			0
$617$	−19.8268			−0.798197			−0.399098	−	0.916908i	$-0.630677\pi$
$617$	−19.8268			−0.798197			−0.399098	+	0.916908i	$0.630677\pi$
$618$		0			0
$619$	13.5758	−	23.5140i	0.545658	−	0.945108i	−0.452907	−	0.891558i	$-0.649613\pi$
$619$	13.5758	−	23.5140i	0.545658	−	0.945108i	0.998565	−	0.0535500i	$-0.0170536\pi$
$620$		0			0
$621$	−11.2529	−	19.4907i	−0.451565	−	0.782133i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−4.90948	+	8.50347i	−0.196066	+	0.339596i
$628$		0			0
$629$	−14.1810			−0.565435
$630$		0			0
$631$	−49.7735			−1.98145			−0.990726	−	0.135873i	$-0.956616\pi$
$631$	−49.7735			−1.98145			−0.990726	+	0.135873i	$0.956616\pi$
$632$		0			0
$633$	−2.91732	+	5.05294i	−0.115953	+	0.200836i
$634$		0			0
$635$	−0.866179	−	1.50027i	−0.0343733	−	0.0595362i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−10.1152	+	17.5200i	−0.399526	+	0.692000i	−0.993667	−	0.112361i	$-0.964159\pi$
$641$	−10.1152	+	17.5200i	−0.399526	+	0.692000i	0.594141	+	0.804361i	$0.297492\pi$
$642$		0			0
$643$	25.1850			0.993198			0.496599	−	0.867980i	$-0.334582\pi$
$643$	25.1850			0.993198			0.496599	+	0.867980i	$0.334582\pi$
$644$		0			0
$645$	3.32092			0.130761
$646$		0			0
$647$	9.78488	−	16.9479i	0.384683	−	0.666291i	−0.607042	−	0.794670i	$-0.707644\pi$
$647$	9.78488	−	16.9479i	0.384683	−	0.666291i	0.991725	+	0.128379i	$0.0409773\pi$
$648$		0			0
$649$	−18.0078	−	31.1905i	−0.706870	−	1.22433i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−9.13382	−	15.8202i	−0.357434	−	0.619094i	0.630097	−	0.776516i	$-0.283015\pi$
$653$	−9.13382	−	15.8202i	−0.357434	−	0.619094i	−0.987531	+	0.157422i	$0.949682\pi$
$654$		0			0
$655$	6.36814	−	11.0299i	0.248824	−	0.430975i
$656$		0			0
$657$	20.4686			0.798558
$658$		0			0
$659$	46.0078			1.79221			0.896105	−	0.443841i	$-0.146385\pi$
$659$	46.0078			1.79221			0.896105	+	0.443841i	$0.146385\pi$
$660$		0			0
$661$	−24.2302	+	41.9680i	−0.942446	+	1.63236i	−0.181661	+	0.983361i	$0.558147\pi$
$661$	−24.2302	+	41.9680i	−0.942446	+	1.63236i	−0.760785	+	0.649004i	$0.775186\pi$
$662$		0			0
$663$	3.59248	+	6.22236i	0.139520	+	0.241656i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−27.5378	−	47.6969i	−1.06627	−	1.84683i
$668$		0			0
$669$	6.29036	−	10.8952i	0.243199	−	0.421234i
$670$		0			0
$671$	−40.1278			−1.54912
$672$		0			0
$673$	−15.0118			−0.578661			−0.289330	−	0.957229i	$-0.593433\pi$
$673$	−15.0118			−0.578661			−0.289330	+	0.957229i	$0.593433\pi$
$674$		0			0
$675$	−1.94142	+	3.36264i	−0.0747253	+	0.129428i
$676$		0			0
$677$	3.95670	+	6.85320i	0.152068	+	0.263390i	0.931988	−	0.362490i	$-0.118073\pi$
$677$	3.95670	+	6.85320i	0.152068	+	0.263390i	−0.779919	+	0.625880i	$0.784740\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−1.89068	−	3.27475i	−0.0724510	−	0.125489i
$682$		0			0
$683$	−14.8548	+	25.7293i	−0.568404	+	0.984504i	0.428320	+	0.903627i	$0.359106\pi$
$683$	−14.8548	+	25.7293i	−0.568404	+	0.984504i	−0.996724	+	0.0808774i	$0.974228\pi$
$684$		0			0
$685$	−4.00000			−0.152832
$686$		0			0
$687$	17.0650			0.651072
$688$		0			0
$689$	25.2322	−	43.7034i	0.961270	−	1.66497i
$690$		0			0
$691$	−10.8868	−	18.8564i	−0.414152	−	0.717332i	0.581187	−	0.813770i	$-0.302588\pi$
$691$	−10.8868	−	18.8564i	−0.414152	−	0.717332i	−0.995339	+	0.0964378i	$0.969255\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.705720	+	1.22234i	0.0267695	+	0.0463661i
$696$		0			0
$697$	6.59248	−	11.4185i	0.249708	−	0.432507i
$698$		0			0
$699$	−12.7030			−0.480470
$700$		0			0
$701$	24.0905			0.909886			0.454943	−	0.890520i	$-0.349660\pi$
$701$	24.0905			0.909886			0.454943	+	0.890520i	$0.349660\pi$
$702$		0			0
$703$	−10.9567	+	18.9776i	−0.413240	+	0.715752i
$704$		0			0
$705$	3.56192	+	6.16943i	0.134150	+	0.232354i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	12.0186	+	20.8169i	0.451369	+	0.781794i	0.998471	−	0.0552719i	$-0.0176026\pi$
$709$	12.0186	+	20.8169i	0.451369	+	0.781794i	−0.547103	+	0.837066i	$0.684269\pi$
$710$		0			0
$711$	−17.7402	+	30.7269i	−0.665309	+	1.15235i
$712$		0			0
$713$	−31.3660			−1.17467
$714$		0			0
$715$	−22.9173			−0.857059
$716$		0			0
$717$	−4.50588	+	7.80441i	−0.168275	+	0.291461i
$718$		0			0
$719$	−0.117159	−	0.202925i	−0.00436929	−	0.00756783i	0.863832	−	0.503779i	$-0.168057\pi$
$719$	−0.117159	−	0.202925i	−0.00436929	−	0.00756783i	−0.868202	+	0.496211i	$0.834724\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	7.79624	+	13.5035i	0.289945	+	0.502200i
$724$		0			0
$725$	−4.75098	+	8.22894i	−0.176447	+	0.305615i
$726$		0			0
$727$	−9.44200			−0.350184			−0.175092	−	0.984552i	$-0.556022\pi$
$727$	−9.44200			−0.350184			−0.175092	+	0.984552i	$0.556022\pi$
$728$		0			0
$729$	−3.70295			−0.137146
$730$		0			0
$731$	4.70572	−	8.15055i	0.174047	−	0.301459i
$732$		0			0
$733$	−14.3721	−	24.8931i	−0.530844	−	0.919449i	−0.999352	−	0.0359897i	$-0.988542\pi$
$733$	−14.3721	−	24.8931i	−0.530844	−	0.919449i	0.468508	−	0.883459i	$-0.344792\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.263722	−	0.456781i	−0.00971434	−	0.0168257i
$738$		0			0
$739$	13.0739	−	22.6446i	0.480930	−	0.832995i	−0.518831	−	0.854877i	$-0.673633\pi$
$739$	13.0739	−	22.6446i	0.480930	−	0.832995i	0.999761	+	0.0218823i	$0.00696591\pi$
$740$		0			0
$741$	11.1026			0.407865
$742$		0			0
$743$	32.7547			1.20165			0.600827	−	0.799379i	$-0.294838\pi$
$743$	32.7547			1.20165			0.600827	+	0.799379i	$0.294838\pi$
$744$		0			0
$745$	11.5472	−	20.0004i	0.423057	−	0.732757i
$746$		0			0
$747$	13.3926	+	23.1967i	0.490011	+	0.848724i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−13.0905	−	22.6734i	−0.477680	−	0.827366i	0.521993	−	0.852950i	$-0.325189\pi$
$751$	−13.0905	−	22.6734i	−0.477680	−	0.827366i	−0.999673	+	0.0255841i	$0.991855\pi$
$752$		0			0
$753$	4.76568	−	8.25440i	0.173671	−	0.300807i
$754$		0			0
$755$	0.407520			0.0148312
$756$		0			0
$757$	16.8229			0.611438			0.305719	−	0.952122i	$-0.401103\pi$
$757$	16.8229			0.611438			0.305719	+	0.952122i	$0.401103\pi$
$758$		0			0
$759$	−9.20768	+	15.9482i	−0.334218	+	0.578882i
$760$		0			0
$761$	−2.95278	−	5.11436i	−0.107038	−	0.185396i	0.807531	−	0.589825i	$-0.200803\pi$
$761$	−2.95278	−	5.11436i	−0.107038	−	0.185396i	−0.914569	+	0.404430i	$0.867470\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	2.50196	+	4.33352i	0.0904585	+	0.156679i
$766$		0			0
$767$	−20.3621	+	35.2682i	−0.735232	+	1.27346i
$768$		0			0
$769$	−0.275481			−0.00993410			−0.00496705	−	0.999988i	$-0.501581\pi$
$769$	−0.275481			−0.00993410			−0.00496705	+	0.999988i	$0.501581\pi$
$770$		0			0
$771$	−11.5470			−0.415857
$772$		0			0
$773$	3.68906	−	6.38964i	0.132686	−	0.229819i	−0.792025	−	0.610489i	$-0.790973\pi$
$773$	3.68906	−	6.38964i	0.132686	−	0.229819i	0.924711	+	0.380669i	$0.124306\pi$
$774$		0			0
$775$	2.70572	+	4.68644i	0.0971923	+	0.168342i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−10.1871	−	17.6446i	−0.364991	−	0.632182i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	36.8946			1.31851
$784$		0			0
$785$	−14.0944			−0.503052
$786$		0			0
$787$	−9.33014	+	16.1603i	−0.332584	+	0.576052i	−0.983018	−	0.183511i	$-0.941254\pi$
$787$	−9.33014	+	16.1603i	−0.332584	+	0.576052i	0.650434	+	0.759563i	$0.274587\pi$
$788$		0			0
$789$	3.21570	+	5.56975i	0.114482	+	0.198288i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	22.6869	+	39.2949i	0.805636	+	1.39540i
$794$		0			0
$795$	−3.49804	+	6.05878i	−0.124063	+	0.214883i
$796$		0			0
$797$	−9.81896			−0.347805			−0.173903	−	0.984763i	$-0.555638\pi$
$797$	−9.81896			−0.347805			−0.173903	+	0.984763i	$0.555638\pi$
$798$		0			0
$799$	20.1889			0.714231
$800$		0			0
$801$	−5.11716	+	8.86318i	−0.180806	+	0.313165i
$802$		0			0
$803$	−18.4154	−	31.8963i	−0.649864	−	1.12560i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−3.14518	−	5.44761i	−0.110716	−	0.191765i
$808$		0			0
$809$	16.0020	−	27.7162i	0.562599	−	0.974450i	−0.434670	−	0.900590i	$-0.643135\pi$
$809$	16.0020	−	27.7162i	0.562599	−	0.974450i	0.997269	−	0.0738600i	$-0.0235318\pi$
$810$		0			0
$811$	−43.5137			−1.52797			−0.763987	−	0.645232i	$-0.776761\pi$
$811$	−43.5137			−1.52797			−0.763987	+	0.645232i	$0.776761\pi$
$812$		0			0
$813$	11.5470			0.404972
$814$		0			0
$815$	−8.09052	+	14.0132i	−0.283399	+	0.490861i
$816$		0			0
$817$	−7.27156	−	12.5947i	−0.254400	−	0.440633i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	17.3621	+	30.0720i	0.605941	+	1.04952i	0.991902	+	0.127005i	$0.0405365\pi$
$821$	17.3621	+	30.0720i	0.605941	+	1.04952i	−0.385961	+	0.922515i	$0.626130\pi$
$822$		0			0
$823$	11.6511	−	20.1802i	0.406130	−	0.703439i	−0.588322	−	0.808627i	$-0.700211\pi$
$823$	11.6511	−	20.1802i	0.406130	−	0.703439i	0.994452	+	0.105188i	$0.0335445\pi$
$824$		0			0
$825$	3.17712			0.110613
$826$		0			0
$827$	11.2943			0.392741			0.196370	−	0.980530i	$-0.437085\pi$
$827$	11.2943			0.392741			0.196370	+	0.980530i	$0.437085\pi$
$828$		0			0
$829$	10.0039	−	17.3273i	0.347450	−	0.601802i	−0.638345	−	0.769750i	$-0.720381\pi$
$829$	10.0039	−	17.3273i	0.347450	−	0.601802i	0.985796	+	0.167948i	$0.0537141\pi$
$830$		0			0
$831$	3.94396	+	6.83113i	0.136814	+	0.236969i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−3.89812	−	6.75174i	−0.134900	−	0.233654i
$836$		0			0
$837$	10.5059	−	18.1967i	0.363136	−	0.628971i
$838$		0			0
$839$	−13.5846			−0.468994			−0.234497	−	0.972117i	$-0.575344\pi$
$839$	−13.5846			−0.468994			−0.234497	+	0.972117i	$0.575344\pi$
$840$		0			0
$841$	61.2872			2.11335
$842$		0			0
$843$	−9.97728	+	17.2812i	−0.343636	+	0.595195i
$844$		0			0
$845$	6.45670	+	11.1833i	0.222117	+	0.384718i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	4.52468	+	7.83697i	0.155287	+	0.268964i
$850$		0			0
$851$	−20.5492	+	35.5922i	−0.704417	+	1.22009i
$852$		0			0
$853$	29.6336			1.01464			0.507318	−	0.861759i	$-0.330637\pi$
$853$	29.6336			1.01464			0.507318	+	0.861759i	$0.330637\pi$
$854$		0			0
$855$	7.73236			0.264441
$856$		0			0
$857$	−9.41536	+	16.3079i	−0.321623	+	0.557067i	−0.980823	−	0.194901i	$-0.937562\pi$
$857$	−9.41536	+	16.3079i	−0.321623	+	0.557067i	0.659200	+	0.751967i	$0.270895\pi$
$858$		0			0
$859$	4.00000	+	6.92820i	0.136478	+	0.236387i	0.926161	−	0.377128i	$-0.123088\pi$
$859$	4.00000	+	6.92820i	0.136478	+	0.236387i	−0.789683	+	0.613515i	$0.789755\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−9.92868	−	17.1970i	−0.337976	−	0.585392i	0.646076	−	0.763273i	$-0.276409\pi$
$863$	−9.92868	−	17.1970i	−0.337976	−	0.585392i	−0.984052	+	0.177881i	$0.943076\pi$
$864$		0			0
$865$	4.45474	−	7.71584i	0.151466	−	0.262346i
$866$		0			0
$867$	9.17436			0.311577
$868$		0			0
$869$	63.8425			2.16571
$870$		0			0
$871$	−0.298200	+	0.516497i	−0.0101041	+	0.0175008i
$872$		0			0
$873$	2.50196	+	4.33352i	0.0846785	+	0.146667i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	6.77566	+	11.7358i	0.228798	+	0.396289i	0.957452	−	0.288592i	$-0.0931872\pi$
$877$	6.77566	+	11.7358i	0.228798	+	0.396289i	−0.728654	+	0.684882i	$0.759854\pi$
$878$		0			0
$879$	−3.14380	+	5.44522i	−0.106038	+	0.183663i
$880$		0			0
$881$	47.5964			1.60356			0.801782	−	0.597617i	$-0.203886\pi$
$881$	47.5964			1.60356			0.801782	+	0.597617i	$0.203886\pi$
$882$		0			0
$883$	36.6497			1.23336			0.616680	−	0.787214i	$-0.288477\pi$
$883$	36.6497			1.23336			0.616680	+	0.787214i	$0.288477\pi$
$884$		0			0
$885$	2.82288	−	4.88937i	0.0948900	−	0.164354i
$886$		0			0
$887$	23.0625	+	39.9454i	0.774363	+	1.34124i	0.935152	+	0.354247i	$0.115263\pi$
$887$	23.0625	+	39.9454i	0.774363	+	1.34124i	−0.160789	+	0.986989i	$0.551404\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	10.7275	+	18.5805i	0.359383	+	0.622470i
$892$		0			0
$893$	15.5985	−	27.0175i	0.521985	−	0.904105i
$894$		0			0
$895$	−1.67908			−0.0561255
$896$		0			0
$897$	20.8229			0.695256
$898$		0			0
$899$	25.7096	−	44.5304i	0.857464	−	1.48517i
$900$		0			0
$901$	9.91340	+	17.1705i	0.330263	+	0.572033i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−6.25294	−	10.8304i	−0.207855	−	0.360015i
$906$		0			0
$907$	2.53390	−	4.38884i	0.0841368	−	0.145729i	−0.820886	−	0.571092i	$-0.806520\pi$
$907$	2.53390	−	4.38884i	0.0841368	−	0.145729i	0.905023	+	0.425363i	$0.139853\pi$
$908$		0			0
$909$	−8.30881			−0.275586
$910$		0			0
$911$	−2.41536			−0.0800244			−0.0400122	−	0.999199i	$-0.512740\pi$
$911$	−2.41536			−0.0800244			−0.0400122	+	0.999199i	$0.512740\pi$
$912$		0			0
$913$	24.0984	−	41.7396i	0.797539	−	1.38138i
$914$		0			0
$915$	−3.14518	−	5.44761i	−0.103976	−	0.180093i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−18.2755	−	31.6541i	−0.602852	−	1.04417i	−0.992387	−	0.123159i	$-0.960697\pi$
$919$	−18.2755	−	31.6541i	−0.602852	−	1.04417i	0.389534	−	0.921012i	$-0.372636\pi$
$920$		0			0
$921$	3.21846	−	5.57454i	0.106052	−	0.183687i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	7.09052			0.233135
$926$		0			0
$927$	13.6191	−	23.5890i	0.447311	−	0.774765i
$928$		0			0
$929$	−8.11520	−	14.0559i	−0.266251	−	0.461160i	0.701640	−	0.712532i	$-0.252452\pi$
$929$	−8.11520	−	14.0559i	−0.266251	−	0.461160i	−0.967891	+	0.251372i	$0.919118\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	4.64968	+	8.05348i	0.152224	+	0.263659i
$934$		0			0
$935$	4.50196	−	7.79762i	0.147230	−	0.255010i
$936$		0			0
$937$	44.1889			1.44359			0.721794	−	0.692108i	$-0.243318\pi$
$937$	44.1889			1.44359			0.721794	+	0.692108i	$0.243318\pi$
$938$		0			0
$939$	−12.3778			−0.403933
$940$		0			0
$941$	11.7363	−	20.3278i	0.382592	−	0.662668i	−0.608840	−	0.793293i	$-0.708365\pi$
$941$	11.7363	−	20.3278i	0.382592	−	0.662668i	0.991432	+	0.130625i	$0.0416983\pi$
$942$		0			0
$943$	−19.1058	−	33.0922i	−0.622170	−	1.07763i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−28.0359	−	48.5595i	−0.911043	−	1.57797i	−0.812594	−	0.582831i	$-0.801945\pi$
$947$	−28.0359	−	48.5595i	−0.911043	−	1.57797i	−0.0984495	−	0.995142i	$-0.531388\pi$
$948$		0			0
$949$	−20.8229	+	36.0663i	−0.675939	+	1.17076i
$950$		0			0
$951$	9.30489			0.301732
$952$		0			0
$953$	−22.7163			−0.735854			−0.367927	−	0.929855i	$-0.619932\pi$
$953$	−22.7163			−0.735854			−0.367927	+	0.929855i	$0.619932\pi$
$954$		0			0
$955$	3.29428	−	5.70586i	0.106600	−	0.184637i
$956$		0			0
$957$	−15.0944	−	26.1443i	−0.487934	−	0.845126i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.858162	+	1.48638i	0.0276827	+	0.0479478i
$962$		0			0
$963$	4.85736	−	8.41319i	0.156526	−	0.271111i
$964$		0			0
$965$	−17.8268			−0.573865
$966$		0			0
$967$	10.9400			0.351808			0.175904	−	0.984407i	$-0.443715\pi$
$967$	10.9400			0.351808			0.175904	+	0.984407i	$0.443715\pi$
$968$		0			0
$969$	−2.18104	+	3.77767i	−0.0700651	+	0.121356i
$970$		0			0
$971$	12.8701	+	22.2917i	0.413021	+	0.715374i	0.995218	−	0.0976739i	$-0.0311402\pi$
$971$	12.8701	+	22.2917i	0.413021	+	0.715374i	−0.582197	+	0.813048i	$0.697807\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−1.79624	−	3.11118i	−0.0575257	−	0.0996375i
$976$		0			0
$977$	−8.41144	+	14.5690i	−0.269106	+	0.466105i	−0.968631	−	0.248503i	$-0.920061\pi$
$977$	−8.41144	+	14.5690i	−0.269106	+	0.466105i	0.699525	+	0.714608i	$0.253395\pi$
$978$		0			0
$979$	18.4154			0.588557
$980$		0			0
$981$	25.6990			0.820507
$982$		0			0
$983$	−21.9926	+	38.0922i	−0.701454	+	1.21495i	0.266502	+	0.963834i	$0.414132\pi$
$983$	−21.9926	+	38.0922i	−0.701454	+	1.21495i	−0.967956	+	0.251119i	$0.919201\pi$
$984$		0			0
$985$	2.54526	+	4.40852i	0.0810987	+	0.140467i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−13.6377	−	23.6213i	−0.433655	−	0.751112i
$990$		0			0
$991$	22.1172	−	38.3080i	0.702575	−	1.21690i	−0.264985	−	0.964253i	$-0.585367\pi$
$991$	22.1172	−	38.3080i	0.702575	−	1.21690i	0.967560	−	0.252643i	$-0.0812997\pi$
$992$		0			0
$993$	−6.00000			−0.190404
$994$		0			0
$995$	24.3621			0.772330
$996$		0			0
$997$	17.0984	−	29.6152i	0.541510	−	0.937924i	−0.457307	−	0.889309i	$-0.651186\pi$
$997$	17.0984	−	29.6152i	0.541510	−	0.937924i	0.998818	−	0.0486148i	$-0.0154807\pi$
$998$		0			0
$999$	−13.7657	−	23.8429i	−0.435527	−	0.754355i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1960.2.q.w.361.2		6
7.2	even	3	inner	1960.2.q.w.961.2		6
7.3	odd	6		1960.2.a.w.1.2		3
7.4	even	3		1960.2.a.v.1.2		3
7.5	odd	6		280.2.q.e.121.2	yes	6
7.6	odd	2		280.2.q.e.81.2	✓	6
21.5	even	6		2520.2.bi.q.1801.2		6
21.20	even	2		2520.2.bi.q.361.2		6
28.3	even	6		3920.2.a.cc.1.2		3
28.11	odd	6		3920.2.a.cb.1.2		3
28.19	even	6		560.2.q.l.401.2		6
28.27	even	2		560.2.q.l.81.2		6
35.4	even	6		9800.2.a.cf.1.2		3
35.12	even	12		1400.2.bh.i.849.3		12
35.13	even	4		1400.2.bh.i.249.3		12
35.19	odd	6		1400.2.q.j.401.2		6
35.24	odd	6		9800.2.a.ce.1.2		3
35.27	even	4		1400.2.bh.i.249.4		12
35.33	even	12		1400.2.bh.i.849.4		12
35.34	odd	2		1400.2.q.j.1201.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.q.e.81.2	✓	6	7.6	odd	2
280.2.q.e.121.2	yes	6	7.5	odd	6
560.2.q.l.81.2		6	28.27	even	2
560.2.q.l.401.2		6	28.19	even	6
1400.2.q.j.401.2		6	35.19	odd	6
1400.2.q.j.1201.2		6	35.34	odd	2
1400.2.bh.i.249.3		12	35.13	even	4
1400.2.bh.i.249.4		12	35.27	even	4
1400.2.bh.i.849.3		12	35.12	even	12
1400.2.bh.i.849.4		12	35.33	even	12
1960.2.a.v.1.2		3	7.4	even	3
1960.2.a.w.1.2		3	7.3	odd	6
1960.2.q.w.361.2		6	1.1	even	1	trivial
1960.2.q.w.961.2		6	7.2	even	3	inner
2520.2.bi.q.361.2		6	21.20	even	2
2520.2.bi.q.1801.2		6	21.5	even	6
3920.2.a.cb.1.2		3	28.11	odd	6
3920.2.a.cc.1.2		3	28.3	even	6
9800.2.a.ce.1.2		3	35.24	odd	6
9800.2.a.cf.1.2		3	35.4	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)

\(f(q)\)	\(=\)	\(q+(0.352860 - 0.611171i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.25098 + 2.16676i) q^{9} +O(q^{10})\)	\(q+(0.352860 - 0.611171i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.25098 + 2.16676i) q^{9} +(2.25098 - 3.89881i) q^{11} -5.09052 q^{13} +0.705720 q^{15} +(1.00000 - 1.73205i) q^{17} +(-1.54526 - 2.67647i) q^{19} +(-2.89812 - 5.01969i) q^{23} +(-0.500000 + 0.866025i) q^{25} +3.88284 q^{27} +9.50196 q^{29} +(2.70572 - 4.68644i) q^{31} +(-1.58856 - 2.75147i) q^{33} +(-3.54526 - 6.14057i) q^{37} +(-1.79624 + 3.11118i) q^{39} +6.59248 q^{41} +4.70572 q^{43} +(-1.25098 + 2.16676i) q^{45} +(5.04722 + 8.74204i) q^{47} +(-0.705720 - 1.22234i) q^{51} +(-4.95670 + 8.58526i) q^{53} +4.50196 q^{55} -2.18104 q^{57} +(4.00000 - 6.92820i) q^{59} +(-4.45670 - 7.71923i) q^{61} +(-2.54526 - 4.40852i) q^{65} +(0.0585795 - 0.101463i) q^{67} -4.09052 q^{69} +(4.09052 - 7.08499i) q^{73} +(0.352860 + 0.611171i) q^{75} +(7.09052 + 12.2811i) q^{79} +(-2.38284 + 4.12720i) q^{81} +10.7057 q^{83} +2.00000 q^{85} +(3.35286 - 5.80732i) q^{87} +(2.04526 + 3.54249i) q^{89} +(-1.90948 - 3.30732i) q^{93} +(1.54526 - 2.67647i) q^{95} +2.00000 q^{97} +11.2637 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} - 9 q^{9}+O(q^{10}) \) 6 * q + 3 * q^5 - 9 * q^9	\( 6 q + 3 q^{5} - 9 q^{9} - 3 q^{11} - 6 q^{13} + 6 q^{17} + 3 q^{19} - 3 q^{23} - 3 q^{25} + 36 q^{27} + 24 q^{29} + 12 q^{31} - 18 q^{33} - 9 q^{37} + 18 q^{39} - 18 q^{41} + 24 q^{43} + 9 q^{45} - 15 q^{47} - 9 q^{53} - 6 q^{55} + 36 q^{57} + 24 q^{59} - 6 q^{61} - 3 q^{65} - 6 q^{67} + 18 q^{79} - 27 q^{81} + 60 q^{83} + 12 q^{85} + 18 q^{87} - 36 q^{93} - 3 q^{95} + 12 q^{97} + 126 q^{99}+O(q^{100}) \) 6 * q + 3 * q^5 - 9 * q^9 - 3 * q^11 - 6 * q^13 + 6 * q^17 + 3 * q^19 - 3 * q^23 - 3 * q^25 + 36 * q^27 + 24 * q^29 + 12 * q^31 - 18 * q^33 - 9 * q^37 + 18 * q^39 - 18 * q^41 + 24 * q^43 + 9 * q^45 - 15 * q^47 - 9 * q^53 - 6 * q^55 + 36 * q^57 + 24 * q^59 - 6 * q^61 - 3 * q^65 - 6 * q^67 + 18 * q^79 - 27 * q^81 + 60 * q^83 + 12 * q^85 + 18 * q^87 - 36 * q^93 - 3 * q^95 + 12 * q^97 + 126 * q^99

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