LMFDB - Embedded newform 1960.2.q.w.361.3

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			361.3
Root			$0.391571i$ of defining polynomial
Character	$\chi$	$=$	1960.361
Dual form			1960.2.q.w.961.3

$q$-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 $\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times$.

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

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
$3$	1.29211	−	2.23800i	0.746002	−	1.29211i	−0.203724	−	0.979028i	$-0.565304\pi$
$3$	1.29211	−	2.23800i	0.746002	−	1.29211i	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
$9$	−1.83911	−	3.18543i	−0.613037	−	1.06181i
$10$		0			0
$11$	−0.839111	+	1.45338i	−0.253001	+	0.438211i	−0.964351	−	0.264627i	$-0.914751\pi$
$11$	−0.839111	+	1.45338i	−0.253001	+	0.438211i	0.711349	+	0.702839i	$0.248084\pi$
$12$		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	−0.718900	−	0.695113i	$-0.755354\pi$
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	0.961436	+	0.275029i	$0.0886875\pi$
$18$		0			0
$19$	3.42334	+	5.92939i	0.785367	+	1.36030i	0.928779	+	0.370633i	$0.120859\pi$
$19$	3.42334	+	5.92939i	0.785367	+	1.36030i	−0.143412	+	0.989663i	$0.545808\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.13122	+	1.95934i	0.235876	+	0.408550i	0.959527	−	0.281617i	$-0.0908706\pi$
$23$	1.13122	+	1.95934i	0.235876	+	0.408550i	−0.723651	+	0.690166i	$0.757537\pi$
$24$		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	−0.0798217	−	0.996809i	$-0.525435\pi$
$31$	4.58423	−	7.94011i	0.823351	−	1.42609i	0.903173	−	0.429277i	$-0.141232\pi$
$32$		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	0.958980	−	0.283473i	$-0.0914867\pi$
$37$	1.42334	+	2.46529i	0.233995	+	0.405291i	−0.724985	+	0.688765i	$0.758153\pi$
$38$		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	−0.839869	−	0.542789i	$-0.817368\pi$
$47$	−6.10156	−	10.5682i	−0.890004	−	1.54153i	−0.0501344	−	0.998742i	$-0.515965\pi$
$48$		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	0.485429	+	0.874276i	$0.338664\pi$
$53$	−3.74511	+	6.48673i	−0.514431	+	0.891021i	−0.999860	+	0.0167445i	$0.994670\pi$
$54$		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	−0.478953	−	0.877841i	$-0.658984\pi$
$59$	4.00000	−	6.92820i	0.520756	−	0.901975i	0.999709	−	0.0241347i	$-0.00768307\pi$
$60$		0			0
$61$	−3.24511	−	5.62070i	−0.415494	−	0.719657i	0.579986	−	0.814627i	$-0.303058\pi$
$61$	−3.24511	−	5.62070i	−0.415494	−	0.719657i	−0.995480	+	0.0949692i	$0.969725\pi$
$62$		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	−0.635094	−	0.772434i	$-0.719039\pi$
$67$	2.87634	−	4.98196i	0.351401	−	0.608644i	0.986495	+	0.163791i	$0.0523722\pi$
$68$		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	0.289355	+	0.957222i	$0.406559\pi$
$73$	−5.84667	+	10.1267i	−0.684301	+	1.18524i	−0.973656	+	0.228022i	$0.926774\pi$
$74$		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	0.660269	−	0.751029i	$-0.270442\pi$
$79$	−2.84667	−	4.93058i	−0.320276	−	0.554734i	−0.980545	+	0.196295i	$0.937109\pi$
$80$		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	0.668461	−	0.743747i	$-0.266953\pi$
$89$	−2.92334	−	5.06337i	−0.309873	−	0.536716i	−0.978334	+	0.207031i	$0.933620\pi$
$90$		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	0.0377483	+	0.999287i	$0.487981\pi$
$101$	−8.50756	+	14.7355i	−0.846534	+	1.46624i	−0.884282	+	0.466953i	$0.845352\pi$
$102$		0			0
$103$	3.55456	+	6.15668i	0.350241	+	0.606635i	0.986292	−	0.165012i	$-0.0527663\pi$
$103$	3.55456	+	6.15668i	0.350241	+	0.606635i	−0.636050	+	0.771648i	$0.719433\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.876338	+	1.51786i	0.0847188	+	0.146737i	0.905271	−	0.424834i	$-0.139667\pi$
$107$	0.876338	+	1.51786i	0.0847188	+	0.146737i	−0.820553	+	0.571571i	$0.806334\pi$
$108$		0			0
$109$	−9.77001	+	16.9222i	−0.935797	+	1.62085i	−0.162591	+	0.986694i	$0.551985\pi$
$109$	−9.77001	+	16.9222i	−0.935797	+	1.62085i	−0.773206	+	0.634154i	$0.781348\pi$
$110$		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	−0.932644	−	0.360797i	$-0.882505\pi$
$131$	−8.91357	−	15.4387i	−0.778782	−	1.34889i	0.153862	−	0.988092i	$-0.450829\pi$
$132$		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	−0.938725	−	0.344668i	$-0.887992\pi$
$137$	−2.00000	+	3.46410i	−0.170872	+	0.295958i	0.767853	+	0.640626i	$0.221325\pi$
$138$		0			0
$139$	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	0.849243	−	0.528002i	$-0.177059\pi$
$149$	−0.398443	−	0.690123i	−0.0326417	−	0.0565371i	−0.881885	+	0.471465i	$0.843725\pi$
$150$		0			0
$151$	8.26245	−	14.3110i	0.672388	−	1.16461i	−0.304837	−	0.952405i	$-0.598602\pi$
$151$	8.26245	−	14.3110i	0.672388	−	1.16461i	0.977225	−	0.212206i	$-0.0680648\pi$
$152$		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	−0.654643	−	0.755938i	$-0.727181\pi$
$157$	4.10156	−	7.10411i	0.327340	−	0.566969i	0.981983	+	0.188969i	$0.0605145\pi$
$158$		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	0.784597	−	0.620006i	$-0.212870\pi$
$163$	−1.84667	−	3.19853i	−0.144643	−	0.250528i	−0.929240	+	0.369478i	$0.879537\pi$
$164$		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	−0.962400	−	0.271635i	$-0.912436\pi$
$173$	−9.42334	−	16.3217i	−0.716443	−	1.24092i	0.245957	−	0.969281i	$-0.420898\pi$
$174$		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	−0.549297	−	0.835627i	$-0.685104\pi$
$179$	6.00756	−	10.4054i	0.449026	−	0.777736i	0.998323	+	0.0578912i	$0.0184376\pi$
$180$		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	0.810248	−	0.586087i	$-0.199332\pi$
$191$	−1.41577	−	2.45219i	−0.102442	−	0.177434i	−0.912690	+	0.408652i	$0.865999\pi$
$192$		0			0
$193$	−6.49023	+	11.2414i	−0.467177	+	0.809174i	−0.999297	−	0.0374948i	$-0.988062\pi$
$193$	−6.49023	+	11.2414i	−0.467177	+	0.809174i	0.532120	+	0.846669i	$0.321396\pi$
$194$		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	0.453217	+	0.891400i	$0.350276\pi$
$199$	−7.69334	+	13.3253i	−0.545367	+	0.944603i	−0.998584	+	0.0532026i	$0.983057\pi$
$200$		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	0.225314	+	0.974286i	$0.427659\pi$
$227$	−11.0151	+	19.0788i	−0.731099	+	1.26630i	−0.956414	+	0.292015i	$0.905674\pi$
$228$		0			0
$229$	2.15333	+	3.72967i	0.142296	+	0.246464i	0.928361	−	0.371680i	$-0.121218\pi$
$229$	2.15333	+	3.72967i	0.142296	+	0.246464i	−0.786065	+	0.618144i	$0.787885\pi$
$230$		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
$235$	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	−0.862736	−	0.505655i	$-0.831251\pi$
$241$	0.101557	−	0.175902i	0.00654187	−	0.0113309i	0.869278	+	0.494324i	$0.164584\pi$
$242$		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	0.957133	+	0.289650i	$0.0935390\pi$
$257$	11.6933	+	20.2535i	0.729411	+	1.26338i	−0.227722	+	0.973726i	$0.573128\pi$
$258$		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	0.0575594	+	0.998342i	$0.481668\pi$
$263$	−13.5546	+	23.4772i	−0.835810	+	1.44767i	−0.893369	+	0.449323i	$0.851665\pi$
$264$		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	−0.749976	−	0.661466i	$-0.769935\pi$
$269$	3.24511	−	5.62070i	0.197858	−	0.342700i	0.947834	+	0.318765i	$0.103268\pi$
$270$		0			0
$271$	−11.6933	−	20.2535i	−0.710320	−	1.23031i	−0.964737	−	0.263216i	$-0.915217\pi$
$271$	−11.6933	−	20.2535i	−0.710320	−	1.23031i	0.254417	−	0.967095i	$-0.418116\pi$
$272$		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	−0.915789	−	0.401660i	$-0.868434\pi$
$277$	−1.83155	+	3.17234i	−0.110047	+	0.190607i	0.805742	+	0.592267i	$0.201767\pi$
$278$		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	0.387686	+	0.921791i	$0.373274\pi$
$283$	−10.1685	+	17.6123i	−0.604452	+	1.04694i	−0.992138	+	0.125150i	$0.960059\pi$
$284$		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	−0.935071	−	0.354462i	$-0.884664\pi$
$311$	−2.83155	+	4.90439i	−0.160562	+	0.278102i	0.774508	+	0.632564i	$0.217997\pi$
$312$		0			0
$313$	14.8618	+	25.7414i	0.840038	+	1.45499i	0.889861	+	0.456231i	$0.150801\pi$
$313$	14.8618	+	25.7414i	0.840038	+	1.45499i	−0.0498231	+	0.998758i	$0.515866\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−9.52489	−	16.4976i	−0.534971	−	0.926597i	−0.999165	−	0.0408636i	$-0.986989\pi$
$317$	−9.52489	−	16.4976i	−0.534971	−	0.926597i	0.464193	−	0.885734i	$-0.346344\pi$
$318$		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	0.832356	−	0.554241i	$-0.186991\pi$
$331$	−1.16089	−	2.01072i	−0.0638083	−	0.110519i	−0.896165	+	0.443722i	$0.853658\pi$
$332$		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	−0.920968	−	0.389639i	$-0.872600\pi$
$347$	−2.29211	+	3.97006i	−0.123047	+	0.213124i	0.797921	+	0.602762i	$0.205933\pi$
$348$		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	−0.483904	−	0.875121i	$-0.660782\pi$
$353$	9.69334	−	16.7894i	0.515925	−	0.893608i	0.999829	−	0.0184869i	$-0.00588489\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	4.90600	+	8.49745i	0.258929	+	0.448478i	0.965955	−	0.258709i	$-0.0832971\pi$
$359$	4.90600	+	8.49745i	0.258929	+	0.448478i	−0.707026	+	0.707187i	$0.749964\pi$
$360$		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	−0.982892	−	0.184184i	$-0.941036\pi$
$367$	−6.35901	+	11.0141i	−0.331937	+	0.574933i	0.650954	+	0.759117i	$0.274369\pi$
$368$		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	0.996396	−	0.0848208i	$-0.0270318\pi$
$373$	8.20311	+	14.2082i	0.424741	+	0.735673i	−0.571655	+	0.820494i	$0.693698\pi$
$374$		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	0.817113	−	0.576477i	$-0.195573\pi$
$383$	−1.77478	−	3.07401i	−0.0906871	−	0.157075i	−0.907800	+	0.419402i	$0.862240\pi$
$384$		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	−0.957115	−	0.289707i	$-0.906442\pi$
$389$	−4.49023	+	7.77731i	−0.227664	+	0.394325i	0.729452	+	0.684032i	$0.239775\pi$
$390$		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	−0.966642	−	0.256133i	$-0.917551\pi$
$397$	−14.0498	−	24.3349i	−0.705139	−	1.22134i	0.261503	−	0.965203i	$-0.415782\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	13.3467	+	23.1171i	0.666501	+	1.15441i	0.978876	+	0.204455i	$0.0655421\pi$
$401$	13.3467	+	23.1171i	0.666501	+	1.15441i	−0.312375	+	0.949959i	$0.601125\pi$
$402$		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	−0.276703	−	0.960955i	$-0.589242\pi$
$409$	14.0325	−	24.3049i	0.693860	−	1.20180i	0.970563	−	0.240846i	$-0.0774248\pi$
$410$		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	−0.898107	−	0.439777i	$-0.855057\pi$
$431$	−1.41577	+	2.45219i	−0.0681955	+	0.118118i	0.829912	+	0.557895i	$0.188391\pi$
$432$		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	0.784475	−	0.620160i	$-0.212932\pi$
$439$	−3.03466	−	5.25619i	−0.144837	−	0.250864i	−0.929312	+	0.369296i	$0.879599\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−5.80188	−	10.0492i	−0.275656	−	0.477450i	0.694645	−	0.719353i	$-0.255562\pi$
$443$	−5.80188	−	10.0492i	−0.275656	−	0.477450i	−0.970300	+	0.241903i	$0.922228\pi$
$444$		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	0.975152	−	0.221536i	$-0.0711070\pi$
$457$	6.32178	+	10.9496i	0.295720	+	0.512203i	−0.679432	+	0.733739i	$0.737774\pi$
$458$		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	0.845411	−	0.534116i	$-0.179355\pi$
$467$	−0.861215	−	1.49167i	−0.0398523	−	0.0690262i	−0.885264	+	0.465090i	$0.846022\pi$
$468$		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	−0.885660	−	0.464334i	$-0.846294\pi$
$479$	−0.890881	+	1.54305i	−0.0407054	+	0.0705038i	0.844955	+	0.534838i	$0.179627\pi$
$480$		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	−0.713763	−	0.700387i	$-0.753011\pi$
$487$	5.50977	−	9.54320i	0.249672	−	0.432444i	0.963435	+	0.267943i	$0.0863440\pi$
$488$		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	0.937714	−	0.347408i	$-0.112938\pi$
$499$	3.75268	+	6.49983i	0.167993	+	0.290972i	−0.769721	+	0.638380i	$0.779605\pi$
$500$		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	0.976748	−	0.214392i	$-0.0687769\pi$
$509$	6.82934	+	11.8288i	0.302705	+	0.524301i	−0.674043	+	0.738693i	$0.735444\pi$
$510$		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	−0.129854	+	0.991533i	$0.541451\pi$
$521$	−21.0820	+	36.5151i	−0.923620	+	1.59976i	−0.793766	+	0.608224i	$0.791882\pi$
$522$		0			0
$523$	−15.3218	−	26.5381i	−0.669975	−	1.16043i	−0.977911	−	0.209023i	$-0.932972\pi$
$523$	−15.3218	−	26.5381i	−0.669975	−	1.16043i	0.307936	−	0.951407i	$-0.400362\pi$
$524$		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	0.959302	+	0.282381i	$0.0911241\pi$
$541$	16.8445	+	29.1755i	0.724200	+	1.25435i	−0.235102	+	0.971971i	$0.575543\pi$
$542$		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	−0.991744	−	0.128235i	$-0.959069\pi$
$557$	−9.08202	+	15.7305i	−0.384817	+	0.666523i	0.606926	+	0.794758i	$0.292402\pi$
$558$		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	0.152760	+	0.988263i	$0.451184\pi$
$563$	−18.4952	+	32.0347i	−0.779481	+	1.35010i	−0.932241	+	0.361837i	$0.882150\pi$
$564$		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	−0.973897	−	0.226990i	$-0.927112\pi$
$569$	−16.3047	−	28.2405i	−0.683527	−	1.18390i	0.290370	−	0.956915i	$-0.406222\pi$
$570$		0			0
$571$	−20.2182	+	35.0190i	−0.846107	+	1.46550i	0.0385496	+	0.999257i	$0.487726\pi$
$571$	−20.2182	+	35.0190i	−0.846107	+	1.46550i	−0.884656	+	0.466243i	$0.845607\pi$
$572$		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	0.133360	+	0.991068i	$0.457423\pi$
$577$	−19.0151	+	32.9352i	−0.791610	+	1.37111i	−0.924970	+	0.380041i	$0.875910\pi$
$578$		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	−0.971039	−	0.238921i	$-0.923206\pi$
$593$	−16.8618	−	29.2055i	−0.692431	−	1.19933i	0.278608	−	0.960405i	$-0.410127\pi$
$594$		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	−0.923228	−	0.384253i	$-0.874459\pi$
$599$	−3.15333	+	5.46172i	−0.128841	+	0.223160i	0.794387	+	0.607413i	$0.207793\pi$
$600$		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	0.665402	−	0.746485i	$-0.268260\pi$
$607$	−7.73057	−	13.3897i	−0.313774	−	0.543473i	−0.979176	+	0.203012i	$0.934927\pi$
$608$		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	−0.550631	−	0.834749i	$-0.685613\pi$
$613$	11.0820	−	19.1946i	0.447598	−	0.775263i	0.998229	+	0.0594857i	$0.0189461\pi$
$614$		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	−0.524524	−	0.851396i	$-0.675757\pi$
$619$	11.8196	−	20.4721i	0.475069	−	0.822843i	0.999592	+	0.0285529i	$0.00908990\pi$
$620$		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	−0.000386062		1.00000i	$0.500123\pi$
$641$	−21.9309	+	37.9854i	−0.866218	+	1.50033i	−0.865832	+	0.500334i	$0.833210\pi$
$642$		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	−0.999768	−	0.0215540i	$-0.993139\pi$
$647$	−12.2403	+	21.2009i	−0.481217	+	0.833493i	0.518550	+	0.855047i	$0.326472\pi$
$648$		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	0.857928	−	0.513771i	$-0.171752\pi$
$653$	−0.408213	−	0.707046i	−0.0159746	−	0.0276688i	−0.873902	+	0.486102i	$0.838418\pi$
$654$		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	−0.495390	−	0.868671i	$-0.664975\pi$
$661$	12.9731	−	22.4701i	0.504596	−	0.873986i	0.999986	−	0.00531513i	$-0.00169187\pi$
$662$		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	0.913944	−	0.405841i	$-0.133021\pi$
$677$	2.74511	+	4.75468i	0.105503	+	0.182737i	−0.808440	+	0.588578i	$0.799688\pi$
$678$		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	−0.989232	−	0.146359i	$-0.953245\pi$
$683$	−9.61389	+	16.6517i	−0.367865	+	0.637161i	0.621366	+	0.783520i	$0.286578\pi$
$684$		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	0.968975	−	0.247157i	$-0.0794963\pi$
$691$	7.10912	+	12.3134i	0.270444	+	0.468422i	−0.698532	+	0.715579i	$0.746163\pi$
$692$		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	0.660427	−	0.750890i	$-0.270375\pi$
$709$	−8.52268	−	14.7617i	−0.320076	−	0.554388i	−0.980503	+	0.196502i	$0.937042\pi$
$710$		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	0.738591	−	0.674154i	$-0.235491\pi$
$719$	−5.75268	−	9.96393i	−0.214539	−	0.371592i	−0.953130	+	0.302562i	$0.902158\pi$
$720$		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	0.769509	−	0.638637i	$-0.220501\pi$
$733$	−4.55712	−	7.89317i	−0.168321	−	0.291541i	−0.937830	+	0.347096i	$0.887168\pi$
$734$		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	−0.340941	−	0.940085i	$-0.610746\pi$
$739$	17.4978	−	30.3071i	0.643667	−	1.11486i	0.984608	−	0.174779i	$-0.0559210\pi$
$740$		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	0.802740	−	0.596329i	$-0.203375\pi$
$751$	−3.15333	−	5.46172i	−0.115067	−	0.199301i	−0.917806	+	0.397028i	$0.870041\pi$
$752$		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	−0.999916	−	0.0129592i	$-0.995875\pi$
$761$	−14.1016	−	24.4246i	−0.511181	−	0.885392i	0.488735	−	0.872432i	$-0.337459\pi$
$762$		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	−0.245482	−	0.969401i	$-0.578946\pi$
$773$	19.9287	−	34.5175i	0.716785	−	1.24151i	0.962267	−	0.272107i	$-0.0877205\pi$
$774$		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	−0.357981	−	0.933729i	$-0.616535\pi$
$787$	17.6637	−	30.5944i	0.629642	−	1.09057i	0.987623	−	0.156843i	$-0.0501318\pi$
$788$		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	−0.640096	−	0.768295i	$-0.721105\pi$
$809$	9.82178	−	17.0118i	0.345315	−	0.598104i	0.985411	+	0.170191i	$0.0544386\pi$
$810$		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	−0.931184	−	0.364549i	$-0.881223\pi$
$821$	−22.3867	−	38.7749i	−0.781301	−	1.35325i	0.149883	−	0.988704i	$-0.452110\pi$
$822$		0			0
$823$	−1.64856	+	2.85538i	−0.0574650	+	0.0995323i	−0.893327	−	0.449408i	$-0.851635\pi$
$823$	−1.64856	+	2.85538i	−0.0574650	+	0.0995323i	0.835862	+	0.548940i	$0.184968\pi$
$824$		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	−0.904041	−	0.427445i	$-0.859414\pi$
$829$	−2.35644	+	4.08148i	−0.0818426	+	0.141756i	0.822199	+	0.569200i	$0.192747\pi$
$830$		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	−0.879561	−	0.475786i	$-0.842164\pi$
$857$	−0.812009	+	1.40644i	−0.0277377	+	0.0480431i	0.851823	+	0.523829i	$0.175497\pi$
$858$		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
$863$	−9.11168	−	15.7819i	−0.310165	−	0.537222i	0.668233	−	0.743952i	$-0.267051\pi$
$863$	−9.11168	−	15.7819i	−0.310165	−	0.537222i	−0.978398	+	0.206730i	$0.933718\pi$
$864$		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	0.872888	+	0.487921i	$0.162244\pi$
$877$	25.4385	+	44.0607i	0.858996	+	1.48782i	−0.0138922	+	0.999903i	$0.504422\pi$
$878$		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	0.998627	−	0.0523772i	$-0.0166798\pi$
$887$	13.5199	+	23.4171i	0.453954	+	0.786271i	−0.544674	+	0.838648i	$0.683346\pi$
$888$		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	0.454038	+	0.890982i	$0.349983\pi$
$907$	−16.4012	+	28.4078i	−0.544594	+	0.943264i	−0.998632	+	0.0522823i	$0.983350\pi$
$908$		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	0.927025	+	0.374999i	$0.122357\pi$
$919$	23.8965	+	41.3899i	0.788271	+	1.36533i	−0.138754	+	0.990327i	$0.544310\pi$
$920$		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	−0.982165	−	0.188018i	$-0.939794\pi$
$929$	−19.9309	−	34.5213i	−0.653912	−	1.13261i	0.328254	−	0.944590i	$-0.393540\pi$
$930$		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	−0.449825	−	0.893116i	$-0.648514\pi$
$941$	16.8271	−	29.1454i	0.548549	−	0.950114i	0.998374	−	0.0569979i	$-0.0181528\pi$
$942$		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	0.814664	−	0.579933i	$-0.196921\pi$
$947$	−2.92055	−	5.05854i	−0.0949050	−	0.164380i	−0.909569	+	0.415553i	$0.863588\pi$
$948$		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	0.975304	−	0.220866i	$-0.0708884\pi$
$971$	9.23534	+	15.9961i	0.296376	+	0.513339i	−0.678928	+	0.734205i	$0.737555\pi$
$972$		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	−0.992356	−	0.123408i	$-0.960618\pi$
$977$	−12.1685	+	21.0764i	−0.389303	+	0.674293i	0.603053	+	0.797701i	$0.293951\pi$
$978$		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	−0.788588	−	0.614922i	$-0.789188\pi$
$983$	4.33434	−	7.50729i	0.138244	−	0.239445i	0.926832	+	0.375476i	$0.122521\pi$
$984$		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	0.0320231	−	0.999487i	$-0.489805\pi$
$991$	27.7527	−	48.0690i	0.881593	−	1.52696i	0.849570	−	0.527476i	$-0.176862\pi$
$992$		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	0.441699	+	0.897163i	$0.354376\pi$
$997$	−17.5596	+	30.4140i	−0.556117	+	0.963222i	−0.997816	+	0.0660591i	$0.978957\pi$
$998$		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.361.3		6
7.2	even	3	inner	1960.2.q.w.961.3		6
7.3	odd	6		1960.2.a.w.1.3		3
7.4	even	3		1960.2.a.v.1.1		3
7.5	odd	6		280.2.q.e.121.1	yes	6
7.6	odd	2		280.2.q.e.81.1	✓	6
21.5	even	6		2520.2.bi.q.1801.1		6
21.20	even	2		2520.2.bi.q.361.1		6
28.3	even	6		3920.2.a.cc.1.1		3
28.11	odd	6		3920.2.a.cb.1.3		3
28.19	even	6		560.2.q.l.401.3		6
28.27	even	2		560.2.q.l.81.3		6
35.4	even	6		9800.2.a.cf.1.3		3
35.12	even	12		1400.2.bh.i.849.2		12
35.13	even	4		1400.2.bh.i.249.2		12
35.19	odd	6		1400.2.q.j.401.3		6
35.24	odd	6		9800.2.a.ce.1.1		3
35.27	even	4		1400.2.bh.i.249.5		12
35.33	even	12		1400.2.bh.i.849.5		12
35.34	odd	2		1400.2.q.j.1201.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.q.e.81.1	✓	6	7.6	odd	2
280.2.q.e.121.1	yes	6	7.5	odd	6
560.2.q.l.81.3		6	28.27	even	2
560.2.q.l.401.3		6	28.19	even	6
1400.2.q.j.401.3		6	35.19	odd	6
1400.2.q.j.1201.3		6	35.34	odd	2
1400.2.bh.i.249.2		12	35.13	even	4
1400.2.bh.i.249.5		12	35.27	even	4
1400.2.bh.i.849.2		12	35.12	even	12
1400.2.bh.i.849.5		12	35.33	even	12
1960.2.a.v.1.1		3	7.4	even	3
1960.2.a.w.1.3		3	7.3	odd	6
1960.2.q.w.361.3		6	1.1	even	1	trivial
1960.2.q.w.961.3		6	7.2	even	3	inner
2520.2.bi.q.361.1		6	21.20	even	2
2520.2.bi.q.1801.1		6	21.5	even	6
3920.2.a.cb.1.3		3	28.11	odd	6
3920.2.a.cc.1.1		3	28.3	even	6
9800.2.a.ce.1.1		3	35.24	odd	6
9800.2.a.cf.1.3		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)

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