LMFDB - Embedded newform 1960.2.q.w.961.3

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			961.3
Root			$-0.391571i$ of defining polynomial
Character	$\chi$	$=$	1960.961
Dual form			1960.2.q.w.361.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.29211 + 2.23800i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.83911 + 3.18543i) q^{9} +O(q^{10})$	\(q+(1.29211 + 2.23800i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.83911 + 3.18543i) q^{9} +(-0.839111 - 1.45338i) q^{11} +4.84667 q^{13} +2.58423 q^{15} +(1.00000 + 1.73205i) q^{17} +(3.42334 - 5.92939i) q^{19} +(1.13122 - 1.95934i) q^{23} +(-0.500000 - 0.866025i) q^{25} -1.75268 q^{27} +3.32178 q^{29} +(4.58423 + 7.94011i) q^{31} +(2.16845 - 3.75587i) q^{33} +(1.42334 - 2.46529i) q^{37} +(6.26245 + 10.8469i) q^{39} -9.52489 q^{41} +6.58423 q^{43} +(1.83911 + 3.18543i) q^{45} +(-6.10156 + 10.5682i) q^{47} +(-2.58423 + 4.47601i) q^{51} +(-3.74511 - 6.48673i) q^{53} -1.67822 q^{55} +17.6933 q^{57} +(4.00000 + 6.92820i) q^{59} +(-3.24511 + 5.62070i) q^{61} +(2.42334 - 4.19734i) q^{65} +(2.87634 + 4.98196i) q^{67} +5.84667 q^{69} +(-5.84667 - 10.1267i) q^{73} +(1.29211 - 2.23800i) q^{75} +(-2.84667 + 4.93058i) q^{79} +(3.25268 + 5.63380i) q^{81} +12.5842 q^{83} +2.00000 q^{85} +(4.29211 + 7.43416i) q^{87} +(-2.92334 + 5.06337i) q^{89} +(-11.8467 + 20.5190i) q^{93} +(-3.42334 - 5.92939i) q^{95} +2.00000 q^{97} +6.17287 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.29211	+	2.23800i	0.746002	+	1.29211i	0.949725	+	0.313084i	$0.101362\pi$
$3$	1.29211	+	2.23800i	0.746002	+	1.29211i	−0.203724	+	0.979028i	$0.565304\pi$
$4$		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
$9$	−1.83911	+	3.18543i	−0.613037	+	1.06181i
$10$		0			0
$11$	−0.839111	−	1.45338i	−0.253001	−	0.438211i	0.711349	−	0.702839i	$-0.248084\pi$
$11$	−0.839111	−	1.45338i	−0.253001	−	0.438211i	−0.964351	+	0.264627i	$0.914751\pi$
$12$		0			0
$13$	4.84667			1.34422			0.672112	−	0.740449i	$-0.265387\pi$
$13$	4.84667			1.34422			0.672112	+	0.740449i	$0.265387\pi$
$14$		0			0
$15$	2.58423			0.667244
$16$		0			0
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$		0			0
$19$	3.42334	−	5.92939i	0.785367	−	1.36030i	−0.143412	−	0.989663i	$-0.545808\pi$
$19$	3.42334	−	5.92939i	0.785367	−	1.36030i	0.928779	−	0.370633i	$-0.120859\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.13122	−	1.95934i	0.235876	−	0.408550i	−0.723651	−	0.690166i	$-0.757537\pi$
$23$	1.13122	−	1.95934i	0.235876	−	0.408550i	0.959527	+	0.281617i	$0.0908706\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−1.75268			−0.337303
$28$		0			0
$29$	3.32178			0.616839			0.308419	−	0.951250i	$-0.400200\pi$
$29$	3.32178			0.616839			0.308419	+	0.951250i	$0.400200\pi$
$30$		0			0
$31$	4.58423	+	7.94011i	0.823351	+	1.42609i	0.903173	+	0.429277i	$0.141232\pi$
$31$	4.58423	+	7.94011i	0.823351	+	1.42609i	−0.0798217	+	0.996809i	$0.525435\pi$
$32$		0			0
$33$	2.16845	−	3.75587i	0.377479	−	0.653813i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.42334	−	2.46529i	0.233995	−	0.405291i	−0.724985	−	0.688765i	$-0.758153\pi$
$37$	1.42334	−	2.46529i	0.233995	−	0.405291i	0.958980	+	0.283473i	$0.0914867\pi$
$38$		0			0
$39$	6.26245	+	10.8469i	1.00279	+	1.73689i
$40$		0			0
$41$	−9.52489			−1.48754			−0.743769	−	0.668437i	$-0.766964\pi$
$41$	−9.52489			−1.48754			−0.743769	+	0.668437i	$0.766964\pi$
$42$		0			0
$43$	6.58423			1.00408			0.502042	−	0.864843i	$-0.332582\pi$
$43$	6.58423			1.00408			0.502042	+	0.864843i	$0.332582\pi$
$44$		0			0
$45$	1.83911	+	3.18543i	0.274158	+	0.474856i
$46$		0			0
$47$	−6.10156	+	10.5682i	−0.890004	+	1.54153i	−0.0501344	+	0.998742i	$0.515965\pi$
$47$	−6.10156	+	10.5682i	−0.890004	+	1.54153i	−0.839869	+	0.542789i	$0.817368\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−2.58423	+	4.47601i	−0.361864	+	0.626767i
$52$		0			0
$53$	−3.74511	−	6.48673i	−0.514431	−	0.891021i	−0.999860	−	0.0167445i	$-0.994670\pi$
$53$	−3.74511	−	6.48673i	−0.514431	−	0.891021i	0.485429	−	0.874276i	$-0.338664\pi$
$54$		0			0
$55$	−1.67822			−0.226291
$56$		0			0
$57$	17.6933			2.34354
$58$		0			0
$59$	4.00000	+	6.92820i	0.520756	+	0.901975i	0.999709	+	0.0241347i	$0.00768307\pi$
$59$	4.00000	+	6.92820i	0.520756	+	0.901975i	−0.478953	+	0.877841i	$0.658984\pi$
$60$		0			0
$61$	−3.24511	+	5.62070i	−0.415494	+	0.719657i	−0.995480	−	0.0949692i	$-0.969725\pi$
$61$	−3.24511	+	5.62070i	−0.415494	+	0.719657i	0.579986	+	0.814627i	$0.303058\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.42334	−	4.19734i	0.300578	−	0.520616i
$66$		0			0
$67$	2.87634	+	4.98196i	0.351401	+	0.608644i	0.986495	−	0.163791i	$-0.0523722\pi$
$67$	2.87634	+	4.98196i	0.351401	+	0.608644i	−0.635094	+	0.772434i	$0.719039\pi$
$68$		0			0
$69$	5.84667			0.703857
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−5.84667	−	10.1267i	−0.684301	−	1.18524i	−0.973656	−	0.228022i	$-0.926774\pi$
$73$	−5.84667	−	10.1267i	−0.684301	−	1.18524i	0.289355	−	0.957222i	$-0.406559\pi$
$74$		0			0
$75$	1.29211	−	2.23800i	0.149200	−	0.258423i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−2.84667	+	4.93058i	−0.320276	+	0.554734i	−0.980545	−	0.196295i	$-0.937109\pi$
$79$	−2.84667	+	4.93058i	−0.320276	+	0.554734i	0.660269	+	0.751029i	$0.270442\pi$
$80$		0			0
$81$	3.25268	+	5.63380i	0.361408	+	0.625978i
$82$		0			0
$83$	12.5842			1.38130			0.690649	−	0.723190i	$-0.257325\pi$
$83$	12.5842			1.38130			0.690649	+	0.723190i	$0.257325\pi$
$84$		0			0
$85$	2.00000			0.216930
$86$		0			0
$87$	4.29211	+	7.43416i	0.460163	+	0.797025i
$88$		0			0
$89$	−2.92334	+	5.06337i	−0.309873	+	0.536716i	−0.978334	−	0.207031i	$-0.933620\pi$
$89$	−2.92334	+	5.06337i	−0.309873	+	0.536716i	0.668461	+	0.743747i	$0.266953\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−11.8467	+	20.5190i	−1.22844	+	2.12773i
$94$		0			0
$95$	−3.42334	−	5.92939i	−0.351227	−	0.608343i
$96$		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
$99$	6.17287			0.620397
$100$		0			0
$101$	−8.50756	−	14.7355i	−0.846534	−	1.46624i	−0.884282	−	0.466953i	$-0.845352\pi$
$101$	−8.50756	−	14.7355i	−0.846534	−	1.46624i	0.0377483	−	0.999287i	$-0.487981\pi$
$102$		0			0
$103$	3.55456	−	6.15668i	0.350241	−	0.606635i	−0.636050	−	0.771648i	$-0.719433\pi$
$103$	3.55456	−	6.15668i	0.350241	−	0.606635i	0.986292	+	0.165012i	$0.0527663\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.876338	−	1.51786i	0.0847188	−	0.146737i	−0.820553	−	0.571571i	$-0.806334\pi$
$107$	0.876338	−	1.51786i	0.0847188	−	0.146737i	0.905271	+	0.424834i	$0.139667\pi$
$108$		0			0
$109$	−9.77001	−	16.9222i	−0.935797	−	1.62085i	−0.773206	−	0.634154i	$-0.781348\pi$
$109$	−9.77001	−	16.9222i	−0.935797	−	1.62085i	−0.162591	−	0.986694i	$-0.551985\pi$
$110$		0			0
$111$	7.35644			0.698243
$112$		0			0
$113$	10.3369			0.972414			0.486207	−	0.873844i	$-0.338380\pi$
$113$	10.3369			0.972414			0.486207	+	0.873844i	$0.338380\pi$
$114$		0			0
$115$	−1.13122	−	1.95934i	−0.105487	−	0.182709i
$116$		0			0
$117$	−8.91357	+	15.4387i	−0.824059	+	1.42731i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	4.09179	−	7.08718i	0.371981	−	0.644289i
$122$		0			0
$123$	−12.3072	−	21.3168i	−1.10971	−	1.92207i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−19.1836			−1.70227			−0.851133	−	0.524949i	$-0.824084\pi$
$127$	−19.1836			−1.70227			−0.851133	+	0.524949i	$0.824084\pi$
$128$		0			0
$129$	8.50756	+	14.7355i	0.749049	+	1.29739i
$130$		0			0
$131$	−8.91357	+	15.4387i	−0.778782	+	1.34889i	0.153862	+	0.988092i	$0.450829\pi$
$131$	−8.91357	+	15.4387i	−0.778782	+	1.34889i	−0.932644	+	0.360797i	$0.882505\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.876338	+	1.51786i	−0.0754232	+	0.130637i
$136$		0			0
$137$	−2.00000	−	3.46410i	−0.170872	−	0.295958i	0.767853	−	0.640626i	$-0.221325\pi$
$137$	−2.00000	−	3.46410i	−0.170872	−	0.295958i	−0.938725	+	0.344668i	$0.887992\pi$
$138$		0			0
$139$	5.16845			0.438382			0.219191	−	0.975682i	$-0.429658\pi$
$139$	5.16845			0.438382			0.219191	+	0.975682i	$0.429658\pi$
$140$		0			0
$141$	−31.5356			−2.65578
$142$		0			0
$143$	−4.06689	−	7.04407i	−0.340091	−	0.589054i
$144$		0			0
$145$	1.66089	−	2.87674i	0.137929	−	0.238901i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−0.398443	+	0.690123i	−0.0326417	+	0.0565371i	−0.881885	−	0.471465i	$-0.843725\pi$
$149$	−0.398443	+	0.690123i	−0.0326417	+	0.0565371i	0.849243	+	0.528002i	$0.177059\pi$
$150$		0			0
$151$	8.26245	+	14.3110i	0.672388	+	1.16461i	0.977225	+	0.212206i	$0.0680648\pi$
$151$	8.26245	+	14.3110i	0.672388	+	1.16461i	−0.304837	+	0.952405i	$0.598602\pi$
$152$		0			0
$153$	−7.35644			−0.594733
$154$		0			0
$155$	9.16845			0.736428
$156$		0			0
$157$	4.10156	+	7.10411i	0.327340	+	0.566969i	0.981983	−	0.188969i	$-0.0605145\pi$
$157$	4.10156	+	7.10411i	0.327340	+	0.566969i	−0.654643	+	0.755938i	$0.727181\pi$
$158$		0			0
$159$	9.67822	−	16.7632i	0.767533	−	1.32941i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−1.84667	+	3.19853i	−0.144643	+	0.250528i	−0.929240	−	0.369478i	$-0.879537\pi$
$163$	−1.84667	+	3.19853i	−0.144643	+	0.250528i	0.784597	+	0.620006i	$0.212870\pi$
$164$		0			0
$165$	−2.16845	−	3.75587i	−0.168814	−	0.292394i
$166$		0			0
$167$	0.262447			0.0203087			0.0101544	−	0.999948i	$-0.496768\pi$
$167$	0.262447			0.0203087			0.0101544	+	0.999948i	$0.496768\pi$
$168$		0			0
$169$	10.4902			0.806941
$170$		0			0
$171$	12.5918	+	21.8096i	0.962918	+	1.66782i
$172$		0			0
$173$	−9.42334	+	16.3217i	−0.716443	+	1.24092i	0.245957	+	0.969281i	$0.420898\pi$
$173$	−9.42334	+	16.3217i	−0.716443	+	1.24092i	−0.962400	+	0.271635i	$0.912436\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−10.3369	+	17.9040i	−0.776969	+	1.34575i
$178$		0			0
$179$	6.00756	+	10.4054i	0.449026	+	0.777736i	0.998323	−	0.0578912i	$-0.0184376\pi$
$179$	6.00756	+	10.4054i	0.449026	+	0.777736i	−0.549297	+	0.835627i	$0.685104\pi$
$180$		0			0
$181$	6.03466			0.448553			0.224276	−	0.974526i	$-0.427998\pi$
$181$	6.03466			0.448553			0.224276	+	0.974526i	$0.427998\pi$
$182$		0			0
$183$	−16.7722			−1.23984
$184$		0			0
$185$	−1.42334	−	2.46529i	−0.104646	−	0.181252i
$186$		0			0
$187$	1.67822	−	2.90676i	0.122724	−	0.212564i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.41577	+	2.45219i	−0.102442	+	0.177434i	−0.912690	−	0.408652i	$-0.865999\pi$
$191$	−1.41577	+	2.45219i	−0.102442	+	0.177434i	0.810248	+	0.586087i	$0.199332\pi$
$192$		0			0
$193$	−6.49023	−	11.2414i	−0.467177	−	0.809174i	0.532120	−	0.846669i	$-0.321396\pi$
$193$	−6.49023	−	11.2414i	−0.467177	−	0.809174i	−0.999297	+	0.0374948i	$0.988062\pi$
$194$		0			0
$195$	12.5249			0.896926
$196$		0			0
$197$	−4.84667			−0.345311			−0.172656	−	0.984982i	$-0.555235\pi$
$197$	−4.84667			−0.345311			−0.172656	+	0.984982i	$0.555235\pi$
$198$		0			0
$199$	−7.69334	−	13.3253i	−0.545367	−	0.944603i	−0.998584	−	0.0532026i	$-0.983057\pi$
$199$	−7.69334	−	13.3253i	−0.545367	−	0.944603i	0.453217	−	0.891400i	$-0.350276\pi$
$200$		0			0
$201$	−7.43311	+	12.8745i	−0.524291	+	0.908098i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−4.76245	+	8.24880i	−0.332624	+	0.576121i
$206$		0			0
$207$	4.16089	+	7.20687i	0.289202	+	0.500912i
$208$		0			0
$209$	−11.4902			−0.794796
$210$		0			0
$211$	9.18357			0.632223			0.316112	−	0.948722i	$-0.397623\pi$
$211$	9.18357			0.632223			0.316112	+	0.948722i	$0.397623\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	3.29211	−	5.70211i	0.224520	−	0.388880i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	15.1091	−	26.1698i	1.02098	−	1.76839i
$220$		0			0
$221$	4.84667	+	8.39468i	0.326022	+	0.564687i
$222$		0			0
$223$	12.9805			0.869236			0.434618	−	0.900615i	$-0.356883\pi$
$223$	12.9805			0.869236			0.434618	+	0.900615i	$0.356883\pi$
$224$		0			0
$225$	3.67822			0.245215
$226$		0			0
$227$	−11.0151	−	19.0788i	−0.731099	−	1.26630i	−0.956414	−	0.292015i	$-0.905674\pi$
$227$	−11.0151	−	19.0788i	−0.731099	−	1.26630i	0.225314	−	0.974286i	$-0.427659\pi$
$228$		0			0
$229$	2.15333	−	3.72967i	0.142296	−	0.246464i	−0.786065	−	0.618144i	$-0.787885\pi$
$229$	2.15333	−	3.72967i	0.142296	−	0.246464i	0.928361	+	0.371680i	$0.121218\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−9.00000	+	15.5885i	−0.589610	+	1.02123i	0.404674	+	0.914461i	$0.367385\pi$
$233$	−9.00000	+	15.5885i	−0.589610	+	1.02123i	−0.994283	+	0.106773i	$0.965948\pi$
$234$		0			0
$235$	6.10156	+	10.5682i	0.398022	+	0.689394i
$236$		0			0
$237$	−14.7129			−0.955705
$238$		0			0
$239$	10.8618			0.702591			0.351296	−	0.936265i	$-0.385741\pi$
$239$	10.8618			0.702591			0.351296	+	0.936265i	$0.385741\pi$
$240$		0			0
$241$	0.101557	+	0.175902i	0.00654187	+	0.0113309i	0.869278	−	0.494324i	$-0.164584\pi$
$241$	0.101557	+	0.175902i	0.00654187	+	0.0113309i	−0.862736	+	0.505655i	$0.831251\pi$
$242$		0			0
$243$	−11.0347	+	19.1126i	−0.707874	+	1.22607i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	16.5918	−	28.7378i	1.05571	−	1.82854i
$248$		0			0
$249$	16.2602	+	28.1636i	1.03045	+	1.78479i
$250$		0			0
$251$	−5.03466			−0.317785			−0.158893	−	0.987296i	$-0.550792\pi$
$251$	−5.03466			−0.317785			−0.158893	+	0.987296i	$0.550792\pi$
$252$		0			0
$253$	−3.79689			−0.238708
$254$		0			0
$255$	2.58423	+	4.47601i	0.161830	+	0.280299i
$256$		0			0
$257$	11.6933	−	20.2535i	0.729411	−	1.26338i	−0.227722	−	0.973726i	$-0.573128\pi$
$257$	11.6933	−	20.2535i	0.729411	−	1.26338i	0.957133	−	0.289650i	$-0.0935390\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−6.10912	+	10.5813i	−0.378145	+	0.654966i
$262$		0			0
$263$	−13.5546	−	23.4772i	−0.835810	−	1.44767i	−0.893369	−	0.449323i	$-0.851665\pi$
$263$	−13.5546	−	23.4772i	−0.835810	−	1.44767i	0.0575594	−	0.998342i	$-0.481668\pi$
$264$		0			0
$265$	−7.49023			−0.460121
$266$		0			0
$267$	−15.1091			−0.924663
$268$		0			0
$269$	3.24511	+	5.62070i	0.197858	+	0.342700i	0.947834	−	0.318765i	$-0.103268\pi$
$269$	3.24511	+	5.62070i	0.197858	+	0.342700i	−0.749976	+	0.661466i	$0.769935\pi$
$270$		0			0
$271$	−11.6933	+	20.2535i	−0.710320	+	1.23031i	0.254417	+	0.967095i	$0.418116\pi$
$271$	−11.6933	+	20.2535i	−0.710320	+	1.23031i	−0.964737	+	0.263216i	$0.915217\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.839111	+	1.45338i	−0.0506003	+	0.0876422i
$276$		0			0
$277$	−1.83155	−	3.17234i	−0.110047	−	0.190607i	0.805742	−	0.592267i	$-0.201767\pi$
$277$	−1.83155	−	3.17234i	−0.110047	−	0.190607i	−0.915789	+	0.401660i	$0.868434\pi$
$278$		0			0
$279$	−33.7236			−2.01898
$280$		0			0
$281$	13.8965			0.828993			0.414497	−	0.910051i	$-0.363958\pi$
$281$	13.8965			0.828993			0.414497	+	0.910051i	$0.363958\pi$
$282$		0			0
$283$	−10.1685	−	17.6123i	−0.604452	−	1.04694i	−0.992138	−	0.125150i	$-0.960059\pi$
$283$	−10.1685	−	17.6123i	−0.604452	−	1.04694i	0.387686	−	0.921791i	$-0.373274\pi$
$284$		0			0
$285$	8.84667	−	15.3229i	0.524032	−	0.907649i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$		0			0
$291$	2.58423	+	4.47601i	0.151490	+	0.262388i
$292$		0			0
$293$	−18.8467			−1.10103			−0.550517	−	0.834824i	$-0.685569\pi$
$293$	−18.8467			−1.10103			−0.550517	+	0.834824i	$0.685569\pi$
$294$		0			0
$295$	8.00000			0.465778
$296$		0			0
$297$	1.47069	+	2.54731i	0.0853380	+	0.147810i
$298$		0			0
$299$	5.48267	−	9.49626i	0.317071	−	0.549183i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	21.9855	−	38.0799i	1.26303	−	2.18763i
$304$		0			0
$305$	3.24511	+	5.62070i	0.185815	+	0.321841i
$306$		0			0
$307$	2.39623			0.136760			0.0683802	−	0.997659i	$-0.478217\pi$
$307$	2.39623			0.136760			0.0683802	+	0.997659i	$0.478217\pi$
$308$		0			0
$309$	18.3716			1.04512
$310$		0			0
$311$	−2.83155	−	4.90439i	−0.160562	−	0.278102i	0.774508	−	0.632564i	$-0.217997\pi$
$311$	−2.83155	−	4.90439i	−0.160562	−	0.278102i	−0.935071	+	0.354462i	$0.884664\pi$
$312$		0			0
$313$	14.8618	−	25.7414i	0.840038	−	1.45499i	−0.0498231	−	0.998758i	$-0.515866\pi$
$313$	14.8618	−	25.7414i	0.840038	−	1.45499i	0.889861	−	0.456231i	$-0.150801\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−9.52489	+	16.4976i	−0.534971	+	0.926597i	0.464193	+	0.885734i	$0.346344\pi$
$317$	−9.52489	+	16.4976i	−0.534971	+	0.926597i	−0.999165	+	0.0408636i	$0.986989\pi$
$318$		0			0
$319$	−2.78734	−	4.82781i	−0.156061	−	0.270306i
$320$		0			0
$321$	4.52931			0.252801
$322$		0			0
$323$	13.6933			0.761918
$324$		0			0
$325$	−2.42334	−	4.19734i	−0.134422	−	0.232827i
$326$		0			0
$327$	25.2479	−	43.7307i	1.39621	−	2.41831i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−1.16089	+	2.01072i	−0.0638083	+	0.110519i	−0.896165	−	0.443722i	$-0.853658\pi$
$331$	−1.16089	+	2.01072i	−0.0638083	+	0.110519i	0.832356	+	0.554241i	$0.186991\pi$
$332$		0			0
$333$	5.23534	+	9.06788i	0.286895	+	0.496917i
$334$		0			0
$335$	5.75268			0.314302
$336$		0			0
$337$	−16.4062			−0.893704			−0.446852	−	0.894608i	$-0.647455\pi$
$337$	−16.4062			−0.893704			−0.446852	+	0.894608i	$0.647455\pi$
$338$		0			0
$339$	13.3564	+	23.1340i	0.725422	+	1.25647i
$340$		0			0
$341$	7.69334	−	13.3253i	0.416618	−	0.721603i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	2.92334	−	5.06337i	0.157387	−	0.272602i
$346$		0			0
$347$	−2.29211	−	3.97006i	−0.123047	−	0.213124i	0.797921	−	0.602762i	$-0.205933\pi$
$347$	−2.29211	−	3.97006i	−0.123047	−	0.213124i	−0.920968	+	0.389639i	$0.872600\pi$
$348$		0			0
$349$	−12.3716			−0.662235			−0.331117	−	0.943590i	$-0.607426\pi$
$349$	−12.3716			−0.662235			−0.331117	+	0.943590i	$0.607426\pi$
$350$		0			0
$351$	−8.49465			−0.453411
$352$		0			0
$353$	9.69334	+	16.7894i	0.515925	+	0.893608i	0.999829	+	0.0184869i	$0.00588489\pi$
$353$	9.69334	+	16.7894i	0.515925	+	0.893608i	−0.483904	+	0.875121i	$0.660782\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	4.90600	−	8.49745i	0.258929	−	0.448478i	−0.707026	−	0.707187i	$-0.749964\pi$
$359$	4.90600	−	8.49745i	0.258929	−	0.448478i	0.965955	+	0.258709i	$0.0832971\pi$
$360$		0			0
$361$	−13.9385	−	24.1421i	−0.733603	−	1.27064i
$362$		0			0
$363$	21.1482			1.10999
$364$		0			0
$365$	−11.6933			−0.612058
$366$		0			0
$367$	−6.35901	−	11.0141i	−0.331937	−	0.574933i	0.650954	−	0.759117i	$-0.274369\pi$
$367$	−6.35901	−	11.0141i	−0.331937	−	0.574933i	−0.982892	+	0.184184i	$0.941036\pi$
$368$		0			0
$369$	17.5173	−	30.3409i	0.911916	−	1.57948i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	8.20311	−	14.2082i	0.424741	−	0.735673i	−0.571655	−	0.820494i	$-0.693698\pi$
$373$	8.20311	−	14.2082i	0.424741	−	0.735673i	0.996396	+	0.0848208i	$0.0270318\pi$
$374$		0			0
$375$	−1.29211	−	2.23800i	−0.0667244	−	0.115570i
$376$		0			0
$377$	16.0996			0.829170
$378$		0			0
$379$	14.4707			0.743309			0.371655	−	0.928371i	$-0.378791\pi$
$379$	14.4707			0.743309			0.371655	+	0.928371i	$0.378791\pi$
$380$		0			0
$381$	−24.7873	−	42.9329i	−1.26989	−	2.19952i
$382$		0			0
$383$	−1.77478	+	3.07401i	−0.0906871	+	0.157075i	−0.907800	−	0.419402i	$-0.862240\pi$
$383$	−1.77478	+	3.07401i	−0.0906871	+	0.157075i	0.817113	+	0.576477i	$0.195573\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−12.1091	+	20.9736i	−0.615541	+	1.06615i
$388$		0			0
$389$	−4.49023	−	7.77731i	−0.227664	−	0.394325i	0.729452	−	0.684032i	$-0.239775\pi$
$389$	−4.49023	−	7.77731i	−0.227664	−	0.394325i	−0.957115	+	0.289707i	$0.906442\pi$
$390$		0			0
$391$	4.52489			0.228834
$392$		0			0
$393$	−46.0693			−2.32389
$394$		0			0
$395$	2.84667	+	4.93058i	0.143232	+	0.248084i
$396$		0			0
$397$	−14.0498	+	24.3349i	−0.705139	+	1.22134i	0.261503	+	0.965203i	$0.415782\pi$
$397$	−14.0498	+	24.3349i	−0.705139	+	1.22134i	−0.966642	+	0.256133i	$0.917551\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	13.3467	−	23.1171i	0.666501	−	1.15441i	−0.312375	−	0.949959i	$-0.601125\pi$
$401$	13.3467	−	23.1171i	0.666501	−	1.15441i	0.978876	−	0.204455i	$-0.0655421\pi$
$402$		0			0
$403$	22.2182	+	38.4831i	1.10677	+	1.91698i
$404$		0			0
$405$	6.50535			0.323254
$406$		0			0
$407$	−4.77735			−0.236804
$408$		0			0
$409$	14.0325	+	24.3049i	0.693860	+	1.20180i	0.970563	+	0.240846i	$0.0774248\pi$
$409$	14.0325	+	24.3049i	0.693860	+	1.20180i	−0.276703	+	0.960955i	$0.589242\pi$
$410$		0			0
$411$	5.16845	−	8.95202i	0.254941	−	0.441571i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	6.29211	−	10.8983i	0.308868	−	0.534974i
$416$		0			0
$417$	6.67822	+	11.5670i	0.327034	+	0.566439i
$418$		0			0
$419$	18.8769			0.922198			0.461099	−	0.887349i	$-0.347455\pi$
$419$	18.8769			0.922198			0.461099	+	0.887349i	$0.347455\pi$
$420$		0			0
$421$	−28.1836			−1.37358			−0.686792	−	0.726854i	$-0.740982\pi$
$421$	−28.1836			−1.37358			−0.686792	+	0.726854i	$0.740982\pi$
$422$		0			0
$423$	−22.4429	−	38.8722i	−1.09121	−	1.89003i
$424$		0			0
$425$	1.00000	−	1.73205i	0.0485071	−	0.0840168i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	10.5098	−	18.2035i	0.507416	−	0.878871i
$430$		0			0
$431$	−1.41577	−	2.45219i	−0.0681955	−	0.118118i	0.829912	−	0.557895i	$-0.188391\pi$
$431$	−1.41577	−	2.45219i	−0.0681955	−	0.118118i	−0.898107	+	0.439777i	$0.855057\pi$
$432$		0			0
$433$	2.33690			0.112304			0.0561522	−	0.998422i	$-0.482117\pi$
$433$	2.33690			0.112304			0.0561522	+	0.998422i	$0.482117\pi$
$434$		0			0
$435$	8.58423			0.411582
$436$		0			0
$437$	−7.74511	−	13.4149i	−0.370499	−	0.641723i
$438$		0			0
$439$	−3.03466	+	5.25619i	−0.144837	+	0.250864i	−0.929312	−	0.369296i	$-0.879599\pi$
$439$	−3.03466	+	5.25619i	−0.144837	+	0.250864i	0.784475	+	0.620160i	$0.212932\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−5.80188	+	10.0492i	−0.275656	+	0.477450i	−0.970300	−	0.241903i	$-0.922228\pi$
$443$	−5.80188	+	10.0492i	−0.275656	+	0.477450i	0.694645	+	0.719353i	$0.255562\pi$
$444$		0			0
$445$	2.92334	+	5.06337i	0.138579	+	0.240027i
$446$		0			0
$447$	−2.05933			−0.0974031
$448$		0			0
$449$	4.13821			0.195294			0.0976470	−	0.995221i	$-0.468868\pi$
$449$	4.13821			0.195294			0.0976470	+	0.995221i	$0.468868\pi$
$450$		0			0
$451$	7.99244	+	13.8433i	0.376349	+	0.651856i
$452$		0			0
$453$	−21.3520	+	36.9828i	−1.00321	+	1.73760i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	6.32178	−	10.9496i	0.295720	−	0.512203i	−0.679432	−	0.733739i	$-0.737774\pi$
$457$	6.32178	−	10.9496i	0.295720	−	0.512203i	0.975152	+	0.221536i	$0.0711070\pi$
$458$		0			0
$459$	−1.75268	−	3.03572i	−0.0818079	−	0.141695i
$460$		0			0
$461$	−20.7129			−0.964695			−0.482348	−	0.875980i	$-0.660216\pi$
$461$	−20.7129			−0.964695			−0.482348	+	0.875980i	$0.660216\pi$
$462$		0			0
$463$	−16.3811			−0.761295			−0.380647	−	0.924720i	$-0.624299\pi$
$463$	−16.3811			−0.761295			−0.380647	+	0.924720i	$0.624299\pi$
$464$		0			0
$465$	11.8467	+	20.5190i	0.549376	+	0.951548i
$466$		0			0
$467$	−0.861215	+	1.49167i	−0.0398523	+	0.0690262i	−0.885264	−	0.465090i	$-0.846022\pi$
$467$	−0.861215	+	1.49167i	−0.0398523	+	0.0690262i	0.845411	+	0.534116i	$0.179355\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−10.5993	+	18.3586i	−0.488392	+	0.845920i
$472$		0			0
$473$	−5.52489	−	9.56940i	−0.254035	−	0.440001i
$474$		0			0
$475$	−6.84667			−0.314147
$476$		0			0
$477$	27.5507			1.26146
$478$		0			0
$479$	−0.890881	−	1.54305i	−0.0407054	−	0.0705038i	0.844955	−	0.534838i	$-0.179627\pi$
$479$	−0.890881	−	1.54305i	−0.0407054	−	0.0705038i	−0.885660	+	0.464334i	$0.846294\pi$
$480$		0			0
$481$	6.89844	−	11.9485i	0.314542	−	0.544803i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.00000	−	1.73205i	0.0454077	−	0.0786484i
$486$		0			0
$487$	5.50977	+	9.54320i	0.249672	+	0.432444i	0.963435	−	0.267943i	$-0.0863440\pi$
$487$	5.50977	+	9.54320i	0.249672	+	0.432444i	−0.713763	+	0.700387i	$0.753011\pi$
$488$		0			0
$489$	−9.54443			−0.431614
$490$		0			0
$491$	−20.9311			−0.944608			−0.472304	−	0.881436i	$-0.656578\pi$
$491$	−20.9311			−0.944608			−0.472304	+	0.881436i	$0.656578\pi$
$492$		0			0
$493$	3.32178	+	5.75349i	0.149605	+	0.259124i
$494$		0			0
$495$	3.08643	−	5.34586i	0.138725	−	0.240279i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	3.75268	−	6.49983i	0.167993	−	0.290972i	−0.769721	−	0.638380i	$-0.779605\pi$
$499$	3.75268	−	6.49983i	0.167993	−	0.290972i	0.937714	+	0.347408i	$0.112938\pi$
$500$		0			0
$501$	0.339111	+	0.587357i	0.0151503	+	0.0262412i
$502$		0			0
$503$	−20.5842			−0.917805			−0.458903	−	0.888487i	$-0.651757\pi$
$503$	−20.5842			−0.917805			−0.458903	+	0.888487i	$0.651757\pi$
$504$		0			0
$505$	−17.0151			−0.757163
$506$		0			0
$507$	13.5546	+	23.4772i	0.601979	+	1.04266i
$508$		0			0
$509$	6.82934	−	11.8288i	0.302705	−	0.524301i	−0.674043	−	0.738693i	$-0.735444\pi$
$509$	6.82934	−	11.8288i	0.302705	−	0.524301i	0.976748	+	0.214392i	$0.0687769\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−6.00000	+	10.3923i	−0.264906	+	0.458831i
$514$		0			0
$515$	−3.55456	−	6.15668i	−0.156633	−	0.271296i
$516$		0			0
$517$	20.4795			0.900688
$518$		0			0
$519$	−48.7040			−2.13787
$520$		0			0
$521$	−21.0820	−	36.5151i	−0.923620	−	1.59976i	−0.793766	−	0.608224i	$-0.791882\pi$
$521$	−21.0820	−	36.5151i	−0.923620	−	1.59976i	−0.129854	−	0.991533i	$-0.541451\pi$
$522$		0			0
$523$	−15.3218	+	26.5381i	−0.669975	+	1.16043i	0.307936	+	0.951407i	$0.400362\pi$
$523$	−15.3218	+	26.5381i	−0.669975	+	1.16043i	−0.977911	+	0.209023i	$0.932972\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−9.16845	+	15.8802i	−0.399384	+	0.691753i
$528$		0			0
$529$	8.94067	+	15.4857i	0.388725	+	0.673291i
$530$		0			0
$531$	−29.4258			−1.27697
$532$		0			0
$533$	−46.1640			−1.99959
$534$		0			0
$535$	−0.876338	−	1.51786i	−0.0378874	−	0.0656229i
$536$		0			0
$537$	−15.5249	+	26.8899i	−0.669949	+	1.16038i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	16.8445	−	29.1755i	0.724200	−	1.25435i	−0.235102	−	0.971971i	$-0.575543\pi$
$541$	16.8445	−	29.1755i	0.724200	−	1.25435i	0.959302	−	0.282381i	$-0.0911241\pi$
$542$		0			0
$543$	7.79747	+	13.5056i	0.334621	+	0.579581i
$544$		0			0
$545$	−19.5400			−0.837002
$546$		0			0
$547$	−3.03979			−0.129972			−0.0649861	−	0.997886i	$-0.520700\pi$
$547$	−3.03979			−0.129972			−0.0649861	+	0.997886i	$0.520700\pi$
$548$		0			0
$549$	−11.9363	−	20.6742i	−0.509427	−	0.882353i
$550$		0			0
$551$	11.3716	−	19.6961i	0.484445	−	0.839083i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	3.67822	−	6.37087i	0.156132	−	0.270428i
$556$		0			0
$557$	−9.08202	−	15.7305i	−0.384817	−	0.666523i	0.606926	−	0.794758i	$-0.292402\pi$
$557$	−9.08202	−	15.7305i	−0.384817	−	0.666523i	−0.991744	+	0.128235i	$0.959069\pi$
$558$		0			0
$559$	31.9116			1.34972
$560$		0			0
$561$	8.67380			0.366208
$562$		0			0
$563$	−18.4952	−	32.0347i	−0.779481	−	1.35010i	−0.932241	−	0.361837i	$-0.882150\pi$
$563$	−18.4952	−	32.0347i	−0.779481	−	1.35010i	0.152760	−	0.988263i	$-0.451184\pi$
$564$		0			0
$565$	5.16845	−	8.95202i	0.217438	−	0.376614i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−16.3047	+	28.2405i	−0.683527	+	1.18390i	0.290370	+	0.956915i	$0.406222\pi$
$569$	−16.3047	+	28.2405i	−0.683527	+	1.18390i	−0.973897	+	0.226990i	$0.927112\pi$
$570$		0			0
$571$	−20.2182	−	35.0190i	−0.846107	−	1.46550i	−0.884656	−	0.466243i	$-0.845607\pi$
$571$	−20.2182	−	35.0190i	−0.846107	−	1.46550i	0.0385496	−	0.999257i	$-0.487726\pi$
$572$		0			0
$573$	−7.31736			−0.305687
$574$		0			0
$575$	−2.26245			−0.0943505
$576$		0			0
$577$	−19.0151	−	32.9352i	−0.791610	−	1.37111i	−0.924970	−	0.380041i	$-0.875910\pi$
$577$	−19.0151	−	32.9352i	−0.791610	−	1.37111i	0.133360	−	0.991068i	$-0.457423\pi$
$578$		0			0
$579$	16.7722	−	29.0503i	0.697030	−	1.20729i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−6.28513	+	10.8862i	−0.260304	+	0.450859i
$584$		0			0
$585$	8.91357	+	15.4387i	0.368531	+	0.638314i
$586$		0			0
$587$	−34.0302			−1.40458			−0.702289	−	0.711892i	$-0.747839\pi$
$587$	−34.0302			−1.40458			−0.702289	+	0.711892i	$0.747839\pi$
$588$		0			0
$589$	62.7734			2.58653
$590$		0			0
$591$	−6.26245	−	10.8469i	−0.257603	−	0.446181i
$592$		0			0
$593$	−16.8618	+	29.2055i	−0.692431	+	1.19933i	0.278608	+	0.960405i	$0.410127\pi$
$593$	−16.8618	+	29.2055i	−0.692431	+	1.19933i	−0.971039	+	0.238921i	$0.923206\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	19.8813	−	34.4355i	0.813689	−	1.40935i
$598$		0			0
$599$	−3.15333	−	5.46172i	−0.128841	−	0.223160i	0.794387	−	0.607413i	$-0.207793\pi$
$599$	−3.15333	−	5.46172i	−0.128841	−	0.223160i	−0.923228	+	0.384253i	$0.874459\pi$
$600$		0			0
$601$	11.2871			0.460411			0.230206	−	0.973142i	$-0.426060\pi$
$601$	11.2871			0.460411			0.230206	+	0.973142i	$0.426060\pi$
$602$		0			0
$603$	−21.1596			−0.861686
$604$		0			0
$605$	−4.09179	−	7.08718i	−0.166355	−	0.288135i
$606$		0			0
$607$	−7.73057	+	13.3897i	−0.313774	+	0.543473i	−0.979176	−	0.203012i	$-0.934927\pi$
$607$	−7.73057	+	13.3897i	−0.313774	+	0.543473i	0.665402	+	0.746485i	$0.268260\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−29.5722	+	51.2206i	−1.19637	+	2.07217i
$612$		0			0
$613$	11.0820	+	19.1946i	0.447598	+	0.775263i	0.998229	−	0.0594857i	$-0.0189461\pi$
$613$	11.0820	+	19.1946i	0.447598	+	0.775263i	−0.550631	+	0.834749i	$0.685613\pi$
$614$		0			0
$615$	−24.6145			−0.992551
$616$		0			0
$617$	−14.9805			−0.603091			−0.301545	−	0.953452i	$-0.597502\pi$
$617$	−14.9805			−0.603091			−0.301545	+	0.953452i	$0.597502\pi$
$618$		0			0
$619$	11.8196	+	20.4721i	0.475069	+	0.822843i	0.999592	−	0.0285529i	$-0.00908990\pi$
$619$	11.8196	+	20.4721i	0.475069	+	0.822843i	−0.524524	+	0.851396i	$0.675757\pi$
$620$		0			0
$621$	−1.98267	+	3.43408i	−0.0795617	+	0.137805i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−14.8467	−	25.7152i	−0.592919	−	1.02697i
$628$		0			0
$629$	5.69334			0.227008
$630$		0			0
$631$	−13.7818			−0.548643			−0.274322	−	0.961638i	$-0.588453\pi$
$631$	−13.7818			−0.548643			−0.274322	+	0.961638i	$0.588453\pi$
$632$		0			0
$633$	11.8662	+	20.5529i	0.471640	+	0.816904i
$634$		0			0
$635$	−9.59179	+	16.6135i	−0.380638	+	0.659285i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−21.9309	−	37.9854i	−0.866218	−	1.50033i	−0.865832	−	0.500334i	$-0.833210\pi$
$641$	−21.9309	−	37.9854i	−0.866218	−	1.50033i	−0.000386062	−	1.00000i	$-0.500123\pi$
$642$		0			0
$643$	−7.04979			−0.278016			−0.139008	−	0.990291i	$-0.544391\pi$
$643$	−7.04979			−0.278016			−0.139008	+	0.990291i	$0.544391\pi$
$644$		0			0
$645$	17.0151			0.669970
$646$		0			0
$647$	−12.2403	−	21.2009i	−0.481217	−	0.833493i	0.518550	−	0.855047i	$-0.326472\pi$
$647$	−12.2403	−	21.2009i	−0.481217	−	0.833493i	−0.999768	+	0.0215540i	$0.993139\pi$
$648$		0			0
$649$	6.71288	−	11.6271i	0.263504	−	0.456402i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−0.408213	+	0.707046i	−0.0159746	+	0.0276688i	−0.873902	−	0.486102i	$-0.838418\pi$
$653$	−0.408213	+	0.707046i	−0.0159746	+	0.0276688i	0.857928	+	0.513771i	$0.171752\pi$
$654$		0			0
$655$	8.91357	+	15.4387i	0.348282	+	0.603242i
$656$		0			0
$657$	43.0107			1.67801
$658$		0			0
$659$	21.2871			0.829228			0.414614	−	0.909997i	$-0.363917\pi$
$659$	21.2871			0.829228			0.414614	+	0.909997i	$0.363917\pi$
$660$		0			0
$661$	12.9731	+	22.4701i	0.504596	+	0.873986i	0.999986	+	0.00531513i	$0.00169187\pi$
$661$	12.9731	+	22.4701i	0.504596	+	0.873986i	−0.495390	+	0.868671i	$0.664975\pi$
$662$		0			0
$663$	−12.5249	+	21.6938i	−0.486427	+	0.842515i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	3.75767	−	6.50848i	0.145498	−	0.252009i
$668$		0			0
$669$	16.7722	+	29.0503i	0.648451	+	1.12315i
$670$		0			0
$671$	10.8920			0.420483
$672$		0			0
$673$	22.0693			0.850710			0.425355	−	0.905027i	$-0.360149\pi$
$673$	22.0693			0.850710			0.425355	+	0.905027i	$0.360149\pi$
$674$		0			0
$675$	0.876338	+	1.51786i	0.0337303	+	0.0584225i
$676$		0			0
$677$	2.74511	−	4.75468i	0.105503	−	0.182737i	−0.808440	−	0.588578i	$-0.799688\pi$
$677$	2.74511	−	4.75468i	0.105503	−	0.182737i	0.913944	+	0.405841i	$0.133021\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	28.4656	−	49.3038i	1.09080	−	1.88933i
$682$		0			0
$683$	−9.61389	−	16.6517i	−0.367865	−	0.637161i	0.621366	−	0.783520i	$-0.286578\pi$
$683$	−9.61389	−	16.6517i	−0.367865	−	0.637161i	−0.989232	+	0.146359i	$0.953245\pi$
$684$		0			0
$685$	−4.00000			−0.152832
$686$		0			0
$687$	11.1294			0.424612
$688$		0			0
$689$	−18.1513	−	31.4390i	−0.691511	−	1.19773i
$690$		0			0
$691$	7.10912	−	12.3134i	0.270444	−	0.468422i	−0.698532	−	0.715579i	$-0.746163\pi$
$691$	7.10912	−	12.3134i	0.270444	−	0.468422i	0.968975	+	0.247157i	$0.0794963\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2.58423	−	4.47601i	0.0980253	−	0.169785i
$696$		0			0
$697$	−9.52489	−	16.4976i	−0.360781	−	0.624891i
$698$		0			0
$699$	−46.5161			−1.75940
$700$		0			0
$701$	14.1533			0.534564			0.267282	−	0.963618i	$-0.413875\pi$
$701$	14.1533			0.534564			0.267282	+	0.963618i	$0.413875\pi$
$702$		0			0
$703$	−9.74511	−	16.8790i	−0.367544	−	0.636605i
$704$		0			0
$705$	−15.7678	+	27.3106i	−0.593850	+	1.02858i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−8.52268	+	14.7617i	−0.320076	+	0.554388i	−0.980503	−	0.196502i	$-0.937042\pi$
$709$	−8.52268	+	14.7617i	−0.320076	+	0.554388i	0.660427	+	0.750890i	$0.270375\pi$
$710$		0			0
$711$	−10.4707	−	18.1358i	−0.392682	−	0.680144i
$712$		0			0
$713$	20.7431			0.776836
$714$		0			0
$715$	−8.13379			−0.304186
$716$		0			0
$717$	14.0347	+	24.3088i	0.524134	+	0.907827i
$718$		0			0
$719$	−5.75268	+	9.96393i	−0.214539	+	0.371592i	−0.953130	−	0.302562i	$-0.902158\pi$
$719$	−5.75268	+	9.96393i	−0.214539	+	0.371592i	0.738591	+	0.674154i	$0.235491\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−0.262447	+	0.454571i	−0.00976049	+	0.0169057i
$724$		0			0
$725$	−1.66089	−	2.87674i	−0.0616839	−	0.106840i
$726$		0			0
$727$	−16.4114			−0.608664			−0.304332	−	0.952566i	$-0.598433\pi$
$727$	−16.4114			−0.608664			−0.304332	+	0.952566i	$0.598433\pi$
$728$		0			0
$729$	−37.5161			−1.38948
$730$		0			0
$731$	6.58423	+	11.4042i	0.243526	+	0.421800i
$732$		0			0
$733$	−4.55712	+	7.89317i	−0.168321	+	0.291541i	−0.937830	−	0.347096i	$-0.887168\pi$
$733$	−4.55712	+	7.89317i	−0.168321	+	0.291541i	0.769509	+	0.638637i	$0.220501\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4.82713	−	8.36084i	0.177810	−	0.307975i
$738$		0			0
$739$	17.4978	+	30.3071i	0.643667	+	1.11486i	0.984608	+	0.174779i	$0.0559210\pi$
$739$	17.4978	+	30.3071i	0.643667	+	1.11486i	−0.340941	+	0.940085i	$0.610746\pi$
$740$		0			0
$741$	85.7538			3.15025
$742$		0			0
$743$	−43.5305			−1.59698			−0.798489	−	0.602009i	$-0.794367\pi$
$743$	−43.5305			−1.59698			−0.798489	+	0.602009i	$0.794367\pi$
$744$		0			0
$745$	0.398443	+	0.690123i	0.0145978	+	0.0252842i
$746$		0			0
$747$	−23.1438	+	40.0862i	−0.846787	+	1.46668i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−3.15333	+	5.46172i	−0.115067	+	0.199301i	−0.917806	−	0.397028i	$-0.870041\pi$
$751$	−3.15333	+	5.46172i	−0.115067	+	0.199301i	0.802740	+	0.596329i	$0.203375\pi$
$752$		0			0
$753$	−6.50535	−	11.2676i	−0.237068	−	0.410614i
$754$		0			0
$755$	16.5249			0.601402
$756$		0			0
$757$	24.3369			0.884540			0.442270	−	0.896882i	$-0.354173\pi$
$757$	24.3369			0.884540			0.442270	+	0.896882i	$0.354173\pi$
$758$		0			0
$759$	−4.90600	−	8.49745i	−0.178077	−	0.308438i
$760$		0			0
$761$	−14.1016	+	24.4246i	−0.511181	+	0.885392i	0.488735	+	0.872432i	$0.337459\pi$
$761$	−14.1016	+	24.4246i	−0.511181	+	0.885392i	−0.999916	+	0.0129592i	$0.995875\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−3.67822	+	6.37087i	−0.132986	+	0.230339i
$766$		0			0
$767$	19.3867	+	33.5787i	0.700013	+	1.21246i
$768$		0			0
$769$	41.8965			1.51082			0.755412	−	0.655250i	$-0.227437\pi$
$769$	41.8965			1.51082			0.755412	+	0.655250i	$0.227437\pi$
$770$		0			0
$771$	60.4365			2.17657
$772$		0			0
$773$	19.9287	+	34.5175i	0.716785	+	1.24151i	0.962267	+	0.272107i	$0.0877205\pi$
$773$	19.9287	+	34.5175i	0.716785	+	1.24151i	−0.245482	+	0.969401i	$0.578946\pi$
$774$		0			0
$775$	4.58423	−	7.94011i	0.164670	−	0.285217i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−32.6069	+	56.4768i	−1.16826	+	2.02349i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−5.82200			−0.208061
$784$		0			0
$785$	8.20311			0.292782
$786$		0			0
$787$	17.6637	+	30.5944i	0.629642	+	1.09057i	0.987623	+	0.156843i	$0.0501318\pi$
$787$	17.6637	+	30.5944i	0.629642	+	1.09057i	−0.357981	+	0.933729i	$0.616535\pi$
$788$		0			0
$789$	35.0280	−	60.6703i	1.24703	−	2.15992i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−15.7280	+	27.2417i	−0.558518	+	0.967381i
$794$		0			0
$795$	−9.67822	−	16.7632i	−0.343251	−	0.594528i
$796$		0			0
$797$	−29.6933			−1.05179			−0.525896	−	0.850549i	$-0.676270\pi$
$797$	−29.6933			−1.05179			−0.525896	+	0.850549i	$0.676270\pi$
$798$		0			0
$799$	−24.4062			−0.863430
$800$		0			0
$801$	−10.7527	−	18.6242i	−0.379927	−	0.658053i
$802$		0			0
$803$	−9.81201	+	16.9949i	−0.346258	+	0.599737i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−8.38611	+	14.5252i	−0.295205	+	0.511310i
$808$		0			0
$809$	9.82178	+	17.0118i	0.345315	+	0.598104i	0.985411	−	0.170191i	$-0.0544386\pi$
$809$	9.82178	+	17.0118i	0.345315	+	0.598104i	−0.640096	+	0.768295i	$0.721105\pi$
$810$		0			0
$811$	−0.252452			−0.00886479			−0.00443239	−	0.999990i	$-0.501411\pi$
$811$	−0.252452			−0.00886479			−0.00443239	+	0.999990i	$0.501411\pi$
$812$		0			0
$813$	−60.4365			−2.11960
$814$		0			0
$815$	1.84667	+	3.19853i	0.0646861	+	0.112040i
$816$		0			0
$817$	22.5400	−	39.0405i	0.788575	−	1.36585i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−22.3867	+	38.7749i	−0.781301	+	1.35325i	0.149883	+	0.988704i	$0.452110\pi$
$821$	−22.3867	+	38.7749i	−0.781301	+	1.35325i	−0.931184	+	0.364549i	$0.881223\pi$
$822$		0			0
$823$	−1.64856	−	2.85538i	−0.0574650	−	0.0995323i	0.835862	−	0.548940i	$-0.184968\pi$
$823$	−1.64856	−	2.85538i	−0.0574650	−	0.0995323i	−0.893327	+	0.449408i	$0.851635\pi$
$824$		0			0
$825$	−4.33690			−0.150992
$826$		0			0
$827$	9.41577			0.327419			0.163709	−	0.986509i	$-0.447654\pi$
$827$	9.41577			0.327419			0.163709	+	0.986509i	$0.447654\pi$
$828$		0			0
$829$	−2.35644	−	4.08148i	−0.0818426	−	0.141756i	0.822199	−	0.569200i	$-0.192747\pi$
$829$	−2.35644	−	4.08148i	−0.0818426	−	0.141756i	−0.904041	+	0.427445i	$0.859414\pi$
$830$		0			0
$831$	4.73314	−	8.19803i	0.164191	−	0.284387i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	0.131223	−	0.227285i	0.00454117	−	0.00786554i
$836$		0			0
$837$	−8.03466	−	13.9164i	−0.277719	−	0.481023i
$838$		0			0
$839$	−22.1880			−0.766015			−0.383007	−	0.923745i	$-0.625112\pi$
$839$	−22.1880			−0.766015			−0.383007	+	0.923745i	$0.625112\pi$
$840$		0			0
$841$	−17.9658			−0.619510
$842$		0			0
$843$	17.9558	+	31.1003i	0.618430	+	1.07115i
$844$		0			0
$845$	5.24511	−	9.08481i	0.180437	−	0.312527i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	26.2776	−	45.5141i	0.901844	−	1.56204i
$850$		0			0
$851$	−3.22022	−	5.57759i	−0.110388	−	0.191197i
$852$		0			0
$853$	−39.9267			−1.36706			−0.683532	−	0.729920i	$-0.739557\pi$
$853$	−39.9267			−1.36706			−0.683532	+	0.729920i	$0.739557\pi$
$854$		0			0
$855$	25.1836			0.861260
$856$		0			0
$857$	−0.812009	−	1.40644i	−0.0277377	−	0.0480431i	0.851823	−	0.523829i	$-0.175497\pi$
$857$	−0.812009	−	1.40644i	−0.0277377	−	0.0480431i	−0.879561	+	0.475786i	$0.842164\pi$
$858$		0			0
$859$	4.00000	−	6.92820i	0.136478	−	0.236387i	−0.789683	−	0.613515i	$-0.789755\pi$
$859$	4.00000	−	6.92820i	0.136478	−	0.236387i	0.926161	+	0.377128i	$0.123088\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−9.11168	+	15.7819i	−0.310165	+	0.537222i	−0.978398	−	0.206730i	$-0.933718\pi$
$863$	−9.11168	+	15.7819i	−0.310165	+	0.537222i	0.668233	+	0.743952i	$0.267051\pi$
$864$		0			0
$865$	9.42334	+	16.3217i	0.320403	+	0.554954i
$866$		0			0
$867$	33.5949			1.14094
$868$		0			0
$869$	9.55469			0.324121
$870$		0			0
$871$	13.9407	+	24.1459i	0.472362	+	0.818154i
$872$		0			0
$873$	−3.67822	+	6.37087i	−0.124489	+	0.215621i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	25.4385	−	44.0607i	0.858996	−	1.48782i	−0.0138922	−	0.999903i	$-0.504422\pi$
$877$	25.4385	−	44.0607i	0.858996	−	1.48782i	0.872888	−	0.487921i	$-0.162244\pi$
$878$		0			0
$879$	−24.3520	−	42.1789i	−0.821373	−	1.42266i
$880$		0			0
$881$	19.1187			0.644124			0.322062	−	0.946719i	$-0.395624\pi$
$881$	19.1187			0.644124			0.322062	+	0.946719i	$0.395624\pi$
$882$		0			0
$883$	39.3174			1.32313			0.661567	−	0.749886i	$-0.269892\pi$
$883$	39.3174			1.32313			0.661567	+	0.749886i	$0.269892\pi$
$884$		0			0
$885$	10.3369	+	17.9040i	0.347471	+	0.601838i
$886$		0			0
$887$	13.5199	−	23.4171i	0.453954	−	0.786271i	−0.544674	−	0.838648i	$-0.683346\pi$
$887$	13.5199	−	23.4171i	0.453954	−	0.786271i	0.998627	+	0.0523772i	$0.0166798\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	5.45871	−	9.45476i	0.182874	−	0.316746i
$892$		0			0
$893$	41.7754	+	72.3570i	1.39796	+	2.42134i
$894$		0			0
$895$	12.0151			0.401621
$896$		0			0
$897$	28.3369			0.946142
$898$		0			0
$899$	15.2278	+	26.3753i	0.507875	+	0.879665i
$900$		0			0
$901$	7.49023	−	12.9735i	0.249536	−	0.432209i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	3.01733	−	5.22617i	0.100299	−	0.173724i
$906$		0			0
$907$	−16.4012	−	28.4078i	−0.544594	−	0.943264i	−0.998632	−	0.0522823i	$-0.983350\pi$
$907$	−16.4012	−	28.4078i	−0.544594	−	0.943264i	0.454038	−	0.890982i	$-0.349983\pi$
$908$		0			0
$909$	62.5854			2.07583
$910$		0			0
$911$	6.18799			0.205017			0.102509	−	0.994732i	$-0.467313\pi$
$911$	6.18799			0.205017			0.102509	+	0.994732i	$0.467313\pi$
$912$		0			0
$913$	−10.5596	−	18.2897i	−0.349470	−	0.605300i
$914$		0			0
$915$	−8.38611	+	14.5252i	−0.277236	+	0.480187i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	23.8965	−	41.3899i	0.788271	−	1.36533i	−0.138754	−	0.990327i	$-0.544310\pi$
$919$	23.8965	−	41.3899i	0.788271	−	1.36533i	0.927025	−	0.374999i	$-0.122357\pi$
$920$		0			0
$921$	3.09620	+	5.36278i	0.102023	+	0.176710i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−2.84667			−0.0935980
$926$		0			0
$927$	13.0745	+	22.6456i	0.429421	+	0.743780i
$928$		0			0
$929$	−19.9309	+	34.5213i	−0.653912	+	1.13261i	0.328254	+	0.944590i	$0.393540\pi$
$929$	−19.9309	+	34.5213i	−0.653912	+	1.13261i	−0.982165	+	0.188018i	$0.939794\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	7.31736	−	12.6740i	0.239560	−	0.414929i
$934$		0			0
$935$	−1.67822	−	2.90676i	−0.0548837	−	0.0950614i
$936$		0			0
$937$	−0.406229			−0.0132709			−0.00663546	−	0.999978i	$-0.502112\pi$
$937$	−0.406229			−0.0132709			−0.00663546	+	0.999978i	$0.502112\pi$
$938$		0			0
$939$	76.8125			2.50668
$940$		0			0
$941$	16.8271	+	29.1454i	0.548549	+	0.950114i	0.998374	+	0.0569979i	$0.0181528\pi$
$941$	16.8271	+	29.1454i	0.548549	+	0.950114i	−0.449825	+	0.893116i	$0.648514\pi$
$942$		0			0
$943$	−10.7748	+	18.6625i	−0.350875	+	0.607734i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−2.92055	+	5.05854i	−0.0949050	+	0.164380i	−0.909569	−	0.415553i	$-0.863588\pi$
$947$	−2.92055	+	5.05854i	−0.0949050	+	0.164380i	0.814664	+	0.579933i	$0.196921\pi$
$948$		0			0
$949$	−28.3369	−	49.0810i	−0.919855	−	1.59324i
$950$		0			0
$951$	−49.2289			−1.59636
$952$		0			0
$953$	32.0605			1.03854			0.519271	−	0.854610i	$-0.326204\pi$
$953$	32.0605			1.03854			0.519271	+	0.854610i	$0.326204\pi$
$954$		0			0
$955$	1.41577	+	2.45219i	0.0458134	+	0.0793511i
$956$		0			0
$957$	7.20311	−	12.4762i	0.232844	−	0.403297i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−26.5302	+	45.9517i	−0.855814	+	1.48231i
$962$		0			0
$963$	3.22337	+	5.58303i	0.103872	+	0.179911i
$964$		0			0
$965$	−12.9805			−0.417856
$966$		0			0
$967$	24.0896			0.774669			0.387334	−	0.921939i	$-0.373396\pi$
$967$	24.0896			0.774669			0.387334	+	0.921939i	$0.373396\pi$
$968$		0			0
$969$	17.6933	+	30.6458i	0.568392	+	0.984484i
$970$		0			0
$971$	9.23534	−	15.9961i	0.296376	−	0.513339i	−0.678928	−	0.734205i	$-0.737555\pi$
$971$	9.23534	−	15.9961i	0.296376	−	0.513339i	0.975304	+	0.220866i	$0.0708884\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	6.26245	−	10.8469i	0.200559	−	0.347378i
$976$		0			0
$977$	−12.1685	−	21.0764i	−0.389303	−	0.674293i	0.603053	−	0.797701i	$-0.293951\pi$
$977$	−12.1685	−	21.0764i	−0.389303	−	0.674293i	−0.992356	+	0.123408i	$0.960618\pi$
$978$		0			0
$979$	9.81201			0.313593
$980$		0			0
$981$	71.8725			2.29471
$982$		0			0
$983$	4.33434	+	7.50729i	0.138244	+	0.239445i	0.926832	−	0.375476i	$-0.122521\pi$
$983$	4.33434	+	7.50729i	0.138244	+	0.239445i	−0.788588	+	0.614922i	$0.789188\pi$
$984$		0			0
$985$	−2.42334	+	4.19734i	−0.0772139	+	0.133738i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	7.44823	−	12.9007i	0.236840	−	0.410219i
$990$		0			0
$991$	27.7527	+	48.0690i	0.881593	+	1.52696i	0.849570	+	0.527476i	$0.176862\pi$
$991$	27.7527	+	48.0690i	0.881593	+	1.52696i	0.0320231	+	0.999487i	$0.489805\pi$
$992$		0			0
$993$	−6.00000			−0.190404
$994$		0			0
$995$	−15.3867			−0.487791
$996$		0			0
$997$	−17.5596	−	30.4140i	−0.556117	−	0.963222i	−0.997816	−	0.0660591i	$-0.978957\pi$
$997$	−17.5596	−	30.4140i	−0.556117	−	0.963222i	0.441699	−	0.897163i	$-0.354376\pi$
$998$		0			0
$999$	−2.49465	+	4.32086i	−0.0789271	+	0.136706i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1960.2.q.w.961.3		6
7.2	even	3		1960.2.a.v.1.1		3
7.3	odd	6		280.2.q.e.81.1	✓	6
7.4	even	3	inner	1960.2.q.w.361.3		6
7.5	odd	6		1960.2.a.w.1.3		3
7.6	odd	2		280.2.q.e.121.1	yes	6
21.17	even	6		2520.2.bi.q.361.1		6
21.20	even	2		2520.2.bi.q.1801.1		6
28.3	even	6		560.2.q.l.81.3		6
28.19	even	6		3920.2.a.cc.1.1		3
28.23	odd	6		3920.2.a.cb.1.3		3
28.27	even	2		560.2.q.l.401.3		6
35.3	even	12		1400.2.bh.i.249.2		12
35.9	even	6		9800.2.a.cf.1.3		3
35.13	even	4		1400.2.bh.i.849.5		12
35.17	even	12		1400.2.bh.i.249.5		12
35.19	odd	6		9800.2.a.ce.1.1		3
35.24	odd	6		1400.2.q.j.1201.3		6
35.27	even	4		1400.2.bh.i.849.2		12
35.34	odd	2		1400.2.q.j.401.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.q.e.81.1	✓	6	7.3	odd	6
280.2.q.e.121.1	yes	6	7.6	odd	2
560.2.q.l.81.3		6	28.3	even	6
560.2.q.l.401.3		6	28.27	even	2
1400.2.q.j.401.3		6	35.34	odd	2
1400.2.q.j.1201.3		6	35.24	odd	6
1400.2.bh.i.249.2		12	35.3	even	12
1400.2.bh.i.249.5		12	35.17	even	12
1400.2.bh.i.849.2		12	35.27	even	4
1400.2.bh.i.849.5		12	35.13	even	4
1960.2.a.v.1.1		3	7.2	even	3
1960.2.a.w.1.3		3	7.5	odd	6
1960.2.q.w.361.3		6	7.4	even	3	inner
1960.2.q.w.961.3		6	1.1	even	1	trivial
2520.2.bi.q.361.1		6	21.17	even	6
2520.2.bi.q.1801.1		6	21.20	even	2
3920.2.a.cb.1.3		3	28.23	odd	6
3920.2.a.cc.1.1		3	28.19	even	6
9800.2.a.ce.1.1		3	35.19	odd	6
9800.2.a.cf.1.3		3	35.9	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.29211 + 2.23800i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.83911 + 3.18543i) q^{9} +O(q^{10})\)	\(q+(1.29211 + 2.23800i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.83911 + 3.18543i) q^{9} +(-0.839111 - 1.45338i) q^{11} +4.84667 q^{13} +2.58423 q^{15} +(1.00000 + 1.73205i) q^{17} +(3.42334 - 5.92939i) q^{19} +(1.13122 - 1.95934i) q^{23} +(-0.500000 - 0.866025i) q^{25} -1.75268 q^{27} +3.32178 q^{29} +(4.58423 + 7.94011i) q^{31} +(2.16845 - 3.75587i) q^{33} +(1.42334 - 2.46529i) q^{37} +(6.26245 + 10.8469i) q^{39} -9.52489 q^{41} +6.58423 q^{43} +(1.83911 + 3.18543i) q^{45} +(-6.10156 + 10.5682i) q^{47} +(-2.58423 + 4.47601i) q^{51} +(-3.74511 - 6.48673i) q^{53} -1.67822 q^{55} +17.6933 q^{57} +(4.00000 + 6.92820i) q^{59} +(-3.24511 + 5.62070i) q^{61} +(2.42334 - 4.19734i) q^{65} +(2.87634 + 4.98196i) q^{67} +5.84667 q^{69} +(-5.84667 - 10.1267i) q^{73} +(1.29211 - 2.23800i) q^{75} +(-2.84667 + 4.93058i) q^{79} +(3.25268 + 5.63380i) q^{81} +12.5842 q^{83} +2.00000 q^{85} +(4.29211 + 7.43416i) q^{87} +(-2.92334 + 5.06337i) q^{89} +(-11.8467 + 20.5190i) q^{93} +(-3.42334 - 5.92939i) q^{95} +2.00000 q^{97} +6.17287 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} - 9 q^{9}+O(q^{10}) \) 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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